Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(13,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.x (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.61 |
Dual form | 144.2.x.d.85.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.965926 | + | 0.258819i | ||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | 0.500000 | + | 0.133975i | 0.223607 | + | 0.0599153i | 0.368883 | − | 0.929476i | \(-0.379740\pi\) |
−0.145276 | + | 0.989391i | \(0.546407\pi\) | |||||||
\(6\) | 0.633975 | − | 2.36603i | 0.258819 | − | 0.965926i | ||||
\(7\) | −2.13397 | − | 1.23205i | −0.806567 | − | 0.465671i | 0.0391956 | − | 0.999232i | \(-0.487520\pi\) |
−0.845762 | + | 0.533560i | \(0.820854\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0.633975 | + | 0.366025i | 0.200480 | + | 0.115747i | ||||
\(11\) | 0.133975 | + | 0.500000i | 0.0403949 | + | 0.150756i | 0.983178 | − | 0.182652i | \(-0.0584681\pi\) |
−0.942783 | + | 0.333408i | \(0.891801\pi\) | |||||||
\(12\) | 1.73205 | − | 3.00000i | 0.500000 | − | 0.866025i | ||||
\(13\) | −1.23205 | + | 4.59808i | −0.341709 | + | 1.27528i | 0.554700 | + | 0.832050i | \(0.312833\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | −2.46410 | − | 2.46410i | −0.658559 | − | 0.658559i | ||||
\(15\) | 0.232051 | − | 0.866025i | 0.0599153 | − | 0.223607i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | −4.09808 | − | 1.09808i | −0.965926 | − | 0.258819i | ||||
\(19\) | −3.00000 | − | 3.00000i | −0.688247 | − | 0.688247i | 0.273597 | − | 0.961844i | \(-0.411786\pi\) |
−0.961844 | + | 0.273597i | \(0.911786\pi\) | |||||||
\(20\) | 0.732051 | + | 0.732051i | 0.163692 | + | 0.163692i | ||||
\(21\) | −2.13397 | + | 3.69615i | −0.465671 | + | 0.806567i | ||||
\(22\) | 0.732051i | 0.156074i | ||||||||
\(23\) | 0.401924 | − | 0.232051i | 0.0838069 | − | 0.0483859i | −0.457511 | − | 0.889204i | \(-0.651259\pi\) |
0.541318 | + | 0.840818i | \(0.317926\pi\) | |||||||
\(24\) | 3.46410 | − | 3.46410i | 0.707107 | − | 0.707107i | ||||
\(25\) | −4.09808 | − | 2.36603i | −0.819615 | − | 0.473205i | ||||
\(26\) | −3.36603 | + | 5.83013i | −0.660132 | + | 1.14338i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −2.46410 | − | 4.26795i | −0.465671 | − | 0.806567i | ||||
\(29\) | −3.23205 | + | 0.866025i | −0.600177 | + | 0.160817i | −0.546100 | − | 0.837720i | \(-0.683888\pi\) |
−0.0540766 | + | 0.998537i | \(0.517222\pi\) | |||||||
\(30\) | 0.633975 | − | 1.09808i | 0.115747 | − | 0.200480i | ||||
\(31\) | 0.598076 | + | 1.03590i | 0.107418 | + | 0.186053i | 0.914723 | − | 0.404081i | \(-0.132408\pi\) |
−0.807306 | + | 0.590133i | \(0.799075\pi\) | |||||||
\(32\) | 1.46410 | + | 5.46410i | 0.258819 | + | 0.965926i | ||||
\(33\) | 0.866025 | − | 0.232051i | 0.150756 | − | 0.0403949i | ||||
\(34\) | 5.46410 | + | 1.46410i | 0.937086 | + | 0.251091i | ||||
\(35\) | −0.901924 | − | 0.901924i | −0.152453 | − | 0.152453i | ||||
\(36\) | −5.19615 | − | 3.00000i | −0.866025 | − | 0.500000i | ||||
\(37\) | −7.73205 | + | 7.73205i | −1.27114 | + | 1.27114i | −0.325651 | + | 0.945490i | \(0.605584\pi\) |
−0.945490 | + | 0.325651i | \(0.894416\pi\) | |||||||
\(38\) | −3.00000 | − | 5.19615i | −0.486664 | − | 0.842927i | ||||
\(39\) | 7.96410 | + | 2.13397i | 1.27528 | + | 0.341709i | ||||
\(40\) | 0.732051 | + | 1.26795i | 0.115747 | + | 0.200480i | ||||
\(41\) | 9.69615 | − | 5.59808i | 1.51428 | − | 0.874273i | 0.514425 | − | 0.857536i | \(-0.328006\pi\) |
0.999860 | − | 0.0167371i | \(-0.00532782\pi\) | |||||||
\(42\) | −4.26795 | + | 4.26795i | −0.658559 | + | 0.658559i | ||||
\(43\) | −2.33013 | − | 8.69615i | −0.355341 | − | 1.32615i | −0.880055 | − | 0.474872i | \(-0.842494\pi\) |
0.524714 | − | 0.851279i | \(-0.324172\pi\) | |||||||
\(44\) | −0.267949 | + | 1.00000i | −0.0403949 | + | 0.150756i | ||||
\(45\) | −1.50000 | − | 0.401924i | −0.223607 | − | 0.0599153i | ||||
\(46\) | 0.633975 | − | 0.169873i | 0.0934745 | − | 0.0250464i | ||||
\(47\) | 4.59808 | − | 7.96410i | 0.670698 | − | 1.16168i | −0.307008 | − | 0.951707i | \(-0.599328\pi\) |
0.977706 | − | 0.209977i | \(-0.0673388\pi\) | |||||||
\(48\) | 6.00000 | − | 3.46410i | 0.866025 | − | 0.500000i | ||||
\(49\) | −0.464102 | − | 0.803848i | −0.0663002 | − | 0.114835i | ||||
\(50\) | −4.73205 | − | 4.73205i | −0.669213 | − | 0.669213i | ||||
\(51\) | − | 6.92820i | − | 0.970143i | ||||||
\(52\) | −6.73205 | + | 6.73205i | −0.933567 | + | 0.933567i | ||||
\(53\) | 2.26795 | − | 2.26795i | 0.311527 | − | 0.311527i | −0.533974 | − | 0.845501i | \(-0.679302\pi\) |
0.845501 | + | 0.533974i | \(0.179302\pi\) | |||||||
\(54\) | −1.90192 | + | 7.09808i | −0.258819 | + | 0.965926i | ||||
\(55\) | 0.267949i | 0.0361303i | ||||||||
\(56\) | −1.80385 | − | 6.73205i | −0.241049 | − | 0.899608i | ||||
\(57\) | −5.19615 | + | 5.19615i | −0.688247 | + | 0.688247i | ||||
\(58\) | −4.73205 | −0.621349 | ||||||||
\(59\) | 5.59808 | + | 1.50000i | 0.728807 | + | 0.195283i | 0.604098 | − | 0.796910i | \(-0.293533\pi\) |
0.124709 | + | 0.992193i | \(0.460200\pi\) | |||||||
\(60\) | 1.26795 | − | 1.26795i | 0.163692 | − | 0.163692i | ||||
\(61\) | 14.4282 | − | 3.86603i | 1.84734 | − | 0.494994i | 0.847957 | − | 0.530065i | \(-0.177832\pi\) |
0.999385 | + | 0.0350707i | \(0.0111656\pi\) | |||||||
\(62\) | 0.437822 | + | 1.63397i | 0.0556035 | + | 0.207515i | ||||
\(63\) | 6.40192 | + | 3.69615i | 0.806567 | + | 0.465671i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −1.23205 | + | 2.13397i | −0.152817 | + | 0.264687i | ||||
\(66\) | 1.26795 | 0.156074 | ||||||||
\(67\) | −0.330127 | + | 1.23205i | −0.0403314 | + | 0.150519i | −0.983155 | − | 0.182773i | \(-0.941493\pi\) |
0.942824 | + | 0.333292i | \(0.108159\pi\) | |||||||
\(68\) | 6.92820 | + | 4.00000i | 0.840168 | + | 0.485071i | ||||
\(69\) | −0.401924 | − | 0.696152i | −0.0483859 | − | 0.0838069i | ||||
\(70\) | −0.901924 | − | 1.56218i | −0.107801 | − | 0.186716i | ||||
\(71\) | 10.9282i | 1.29694i | 0.761241 | + | 0.648470i | \(0.224591\pi\) | ||||
−0.761241 | + | 0.648470i | \(0.775409\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.707107 | − | 0.707107i | ||||
\(73\) | 0.535898i | 0.0627222i | 0.999508 | + | 0.0313611i | \(0.00998418\pi\) | ||||
−0.999508 | + | 0.0313611i | \(0.990016\pi\) | |||||||
\(74\) | −13.3923 | + | 7.73205i | −1.55682 | + | 0.898833i | ||||
\(75\) | −4.09808 | + | 7.09808i | −0.473205 | + | 0.819615i | ||||
\(76\) | −2.19615 | − | 8.19615i | −0.251916 | − | 0.940163i | ||||
\(77\) | 0.330127 | − | 1.23205i | 0.0376215 | − | 0.140405i | ||||
\(78\) | 10.0981 | + | 5.83013i | 1.14338 | + | 0.660132i | ||||
\(79\) | 0.866025 | − | 1.50000i | 0.0974355 | − | 0.168763i | −0.813187 | − | 0.582003i | \(-0.802269\pi\) |
0.910622 | + | 0.413239i | \(0.135603\pi\) | |||||||
\(80\) | 0.535898 | + | 2.00000i | 0.0599153 | + | 0.223607i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 15.2942 | − | 4.09808i | 1.68897 | − | 0.452557i | ||||
\(83\) | −11.7942 | + | 3.16025i | −1.29458 | + | 0.346883i | −0.839400 | − | 0.543514i | \(-0.817093\pi\) |
−0.455185 | + | 0.890397i | \(0.650427\pi\) | |||||||
\(84\) | −7.39230 | + | 4.26795i | −0.806567 | + | 0.465671i | ||||
\(85\) | 2.00000 | + | 0.535898i | 0.216930 | + | 0.0581263i | ||||
\(86\) | − | 12.7321i | − | 1.37293i | ||||||
\(87\) | 1.50000 | + | 5.59808i | 0.160817 | + | 0.600177i | ||||
\(88\) | −0.732051 | + | 1.26795i | −0.0780369 | + | 0.135164i | ||||
\(89\) | − | 11.8564i | − | 1.25678i | −0.777900 | − | 0.628388i | \(-0.783715\pi\) | ||
0.777900 | − | 0.628388i | \(-0.216285\pi\) | |||||||
\(90\) | −1.90192 | − | 1.09808i | −0.200480 | − | 0.115747i | ||||
\(91\) | 8.29423 | − | 8.29423i | 0.869471 | − | 0.869471i | ||||
\(92\) | 0.928203 | 0.0967719 | ||||||||
\(93\) | 1.79423 | − | 1.03590i | 0.186053 | − | 0.107418i | ||||
\(94\) | 9.19615 | − | 9.19615i | 0.948511 | − | 0.948511i | ||||
\(95\) | −1.09808 | − | 1.90192i | −0.112660 | − | 0.195133i | ||||
\(96\) | 9.46410 | − | 2.53590i | 0.965926 | − | 0.258819i | ||||
\(97\) | −0.500000 | + | 0.866025i | −0.0507673 | + | 0.0879316i | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | −0.339746 | − | 1.26795i | −0.0343195 | − | 0.128082i | ||||
\(99\) | −0.401924 | − | 1.50000i | −0.0403949 | − | 0.150756i | ||||
\(100\) | −4.73205 | − | 8.19615i | −0.473205 | − | 0.819615i | ||||
\(101\) | 0.500000 | + | 1.86603i | 0.0497519 | + | 0.185676i | 0.986330 | − | 0.164783i | \(-0.0526922\pi\) |
−0.936578 | + | 0.350459i | \(0.886026\pi\) | |||||||
\(102\) | 2.53590 | − | 9.46410i | 0.251091 | − | 0.937086i | ||||
\(103\) | 1.79423 | − | 1.03590i | 0.176791 | − | 0.102070i | −0.408993 | − | 0.912537i | \(-0.634120\pi\) |
0.585784 | + | 0.810467i | \(0.300787\pi\) | |||||||
\(104\) | −11.6603 | + | 6.73205i | −1.14338 | + | 0.660132i | ||||
\(105\) | −1.56218 | + | 1.56218i | −0.152453 | + | 0.152453i | ||||
\(106\) | 3.92820 | − | 2.26795i | 0.381541 | − | 0.220283i | ||||
\(107\) | −11.3923 | + | 11.3923i | −1.10134 | + | 1.10134i | −0.107086 | + | 0.994250i | \(0.534152\pi\) |
−0.994250 | + | 0.107086i | \(0.965848\pi\) | |||||||
\(108\) | −5.19615 | + | 9.00000i | −0.500000 | + | 0.866025i | ||||
\(109\) | 1.73205 | + | 1.73205i | 0.165900 | + | 0.165900i | 0.785175 | − | 0.619274i | \(-0.212573\pi\) |
−0.619274 | + | 0.785175i | \(0.712573\pi\) | |||||||
\(110\) | −0.0980762 | + | 0.366025i | −0.00935120 | + | 0.0348992i | ||||
\(111\) | 13.3923 | + | 13.3923i | 1.27114 | + | 1.27114i | ||||
\(112\) | − | 9.85641i | − | 0.931343i | ||||||
\(113\) | −2.76795 | − | 4.79423i | −0.260387 | − | 0.451003i | 0.705958 | − | 0.708254i | \(-0.250517\pi\) |
−0.966345 | + | 0.257251i | \(0.917183\pi\) | |||||||
\(114\) | −9.00000 | + | 5.19615i | −0.842927 | + | 0.486664i | ||||
\(115\) | 0.232051 | − | 0.0621778i | 0.0216388 | − | 0.00579811i | ||||
\(116\) | −6.46410 | − | 1.73205i | −0.600177 | − | 0.160817i | ||||
\(117\) | 3.69615 | − | 13.7942i | 0.341709 | − | 1.27528i | ||||
\(118\) | 7.09808 | + | 4.09808i | 0.653431 | + | 0.377258i | ||||
\(119\) | −8.53590 | − | 4.92820i | −0.782485 | − | 0.451768i | ||||
\(120\) | 2.19615 | − | 1.26795i | 0.200480 | − | 0.115747i | ||||
\(121\) | 9.29423 | − | 5.36603i | 0.844930 | − | 0.487820i | ||||
\(122\) | 21.1244 | 1.91251 | ||||||||
\(123\) | −9.69615 | − | 16.7942i | −0.874273 | − | 1.51428i | ||||
\(124\) | 2.39230i | 0.214835i | ||||||||
\(125\) | −3.56218 | − | 3.56218i | −0.318611 | − | 0.318611i | ||||
\(126\) | 7.39230 | + | 7.39230i | 0.658559 | + | 0.658559i | ||||
\(127\) | −20.3923 | −1.80952 | −0.904762 | − | 0.425917i | \(-0.859952\pi\) | ||||
−0.904762 | + | 0.425917i | \(0.859952\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.258819 | + | 0.965926i | ||||
\(129\) | −15.0622 | + | 4.03590i | −1.32615 | + | 0.355341i | ||||
\(130\) | −2.46410 | + | 2.46410i | −0.216116 | + | 0.216116i | ||||
\(131\) | −3.13397 | + | 11.6962i | −0.273817 | + | 1.02190i | 0.682814 | + | 0.730593i | \(0.260756\pi\) |
−0.956630 | + | 0.291305i | \(0.905911\pi\) | |||||||
\(132\) | 1.73205 | + | 0.464102i | 0.150756 | + | 0.0403949i | ||||
\(133\) | 2.70577 | + | 10.0981i | 0.234620 | + | 0.875614i | ||||
\(134\) | −0.901924 | + | 1.56218i | −0.0779143 | + | 0.134952i | ||||
\(135\) | −0.696152 | + | 2.59808i | −0.0599153 | + | 0.223607i | ||||
\(136\) | 8.00000 | + | 8.00000i | 0.685994 | + | 0.685994i | ||||
\(137\) | 14.4282 | + | 8.33013i | 1.23268 | + | 0.711691i | 0.967589 | − | 0.252531i | \(-0.0812631\pi\) |
0.265096 | + | 0.964222i | \(0.414596\pi\) | |||||||
\(138\) | −0.294229 | − | 1.09808i | −0.0250464 | − | 0.0934745i | ||||
\(139\) | 4.33013 | + | 1.16025i | 0.367277 | + | 0.0984115i | 0.437737 | − | 0.899103i | \(-0.355780\pi\) |
−0.0704603 | + | 0.997515i | \(0.522447\pi\) | |||||||
\(140\) | −0.660254 | − | 2.46410i | −0.0558017 | − | 0.208255i | ||||
\(141\) | −13.7942 | − | 7.96410i | −1.16168 | − | 0.670698i | ||||
\(142\) | −4.00000 | + | 14.9282i | −0.335673 | + | 1.25275i | ||||
\(143\) | −2.46410 | −0.206059 | ||||||||
\(144\) | −6.00000 | − | 10.3923i | −0.500000 | − | 0.866025i | ||||
\(145\) | −1.73205 | −0.143839 | ||||||||
\(146\) | −0.196152 | + | 0.732051i | −0.0162337 | + | 0.0605850i | ||||
\(147\) | −1.39230 | + | 0.803848i | −0.114835 | + | 0.0663002i | ||||
\(148\) | −21.1244 | + | 5.66025i | −1.73641 | + | 0.465270i | ||||
\(149\) | −14.6962 | − | 3.93782i | −1.20396 | − | 0.322599i | −0.399568 | − | 0.916704i | \(-0.630840\pi\) |
−0.804388 | + | 0.594105i | \(0.797507\pi\) | |||||||
\(150\) | −8.19615 | + | 8.19615i | −0.669213 | + | 0.669213i | ||||
\(151\) | −6.06218 | − | 3.50000i | −0.493333 | − | 0.284826i | 0.232623 | − | 0.972567i | \(-0.425269\pi\) |
−0.725956 | + | 0.687741i | \(0.758602\pi\) | |||||||
\(152\) | − | 12.0000i | − | 0.973329i | ||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0.901924 | − | 1.56218i | 0.0726791 | − | 0.125884i | ||||
\(155\) | 0.160254 | + | 0.598076i | 0.0128719 | + | 0.0480386i | ||||
\(156\) | 11.6603 | + | 11.6603i | 0.933567 | + | 0.933567i | ||||
\(157\) | −0.232051 | + | 0.866025i | −0.0185197 | + | 0.0691164i | −0.974567 | − | 0.224095i | \(-0.928057\pi\) |
0.956048 | + | 0.293212i | \(0.0947240\pi\) | |||||||
\(158\) | 1.73205 | − | 1.73205i | 0.137795 | − | 0.137795i | ||||
\(159\) | −3.92820 | − | 3.92820i | −0.311527 | − | 0.311527i | ||||
\(160\) | 2.92820i | 0.231495i | ||||||||
\(161\) | −1.14359 | −0.0901278 | ||||||||
\(162\) | 12.2942 | + | 3.29423i | 0.965926 | + | 0.258819i | ||||
\(163\) | 11.9282 | + | 11.9282i | 0.934289 | + | 0.934289i | 0.997970 | − | 0.0636813i | \(-0.0202841\pi\) |
−0.0636813 | + | 0.997970i | \(0.520284\pi\) | |||||||
\(164\) | 22.3923 | 1.74855 | ||||||||
\(165\) | 0.464102 | 0.0361303 | ||||||||
\(166\) | −17.2679 | −1.34025 | ||||||||
\(167\) | −8.25833 | + | 4.76795i | −0.639049 | + | 0.368955i | −0.784248 | − | 0.620447i | \(-0.786951\pi\) |
0.145199 | + | 0.989402i | \(0.453618\pi\) | |||||||
\(168\) | −11.6603 | + | 3.12436i | −0.899608 | + | 0.241049i | ||||
\(169\) | −8.36603 | − | 4.83013i | −0.643540 | − | 0.371548i | ||||
\(170\) | 2.53590 | + | 1.46410i | 0.194495 | + | 0.112291i | ||||
\(171\) | 9.00000 | + | 9.00000i | 0.688247 | + | 0.688247i | ||||
\(172\) | 4.66025 | − | 17.3923i | 0.355341 | − | 1.32615i | ||||
\(173\) | −8.96410 | + | 2.40192i | −0.681528 | + | 0.182615i | −0.582942 | − | 0.812514i | \(-0.698099\pi\) |
−0.0985859 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(174\) | 8.19615i | 0.621349i | ||||||||
\(175\) | 5.83013 | + | 10.0981i | 0.440716 | + | 0.763343i | ||||
\(176\) | −1.46410 | + | 1.46410i | −0.110361 | + | 0.110361i | ||||
\(177\) | 2.59808 | − | 9.69615i | 0.195283 | − | 0.728807i | ||||
\(178\) | 4.33975 | − | 16.1962i | 0.325278 | − | 1.21395i | ||||
\(179\) | 7.92820 | + | 7.92820i | 0.592582 | + | 0.592582i | 0.938328 | − | 0.345746i | \(-0.112374\pi\) |
−0.345746 | + | 0.938328i | \(0.612374\pi\) | |||||||
\(180\) | −2.19615 | − | 2.19615i | −0.163692 | − | 0.163692i | ||||
\(181\) | −4.26795 | + | 4.26795i | −0.317234 | + | 0.317234i | −0.847704 | − | 0.530470i | \(-0.822016\pi\) |
0.530470 | + | 0.847704i | \(0.322016\pi\) | |||||||
\(182\) | 14.3660 | − | 8.29423i | 1.06488 | − | 0.614809i | ||||
\(183\) | −6.69615 | − | 24.9904i | −0.494994 | − | 1.84734i | ||||
\(184\) | 1.26795 | + | 0.339746i | 0.0934745 | + | 0.0250464i | ||||
\(185\) | −4.90192 | + | 2.83013i | −0.360397 | + | 0.208075i | ||||
\(186\) | 2.83013 | − | 0.758330i | 0.207515 | − | 0.0556035i | ||||
\(187\) | 0.535898 | + | 2.00000i | 0.0391888 | + | 0.146254i | ||||
\(188\) | 15.9282 | − | 9.19615i | 1.16168 | − | 0.670698i | ||||
\(189\) | 6.40192 | − | 11.0885i | 0.465671 | − | 0.806567i | ||||
\(190\) | −0.803848 | − | 3.00000i | −0.0583172 | − | 0.217643i | ||||
\(191\) | 6.59808 | − | 11.4282i | 0.477420 | − | 0.826916i | −0.522245 | − | 0.852795i | \(-0.674905\pi\) |
0.999665 | + | 0.0258797i | \(0.00823869\pi\) | |||||||
\(192\) | 13.8564 | 1.00000 | ||||||||
\(193\) | −1.23205 | − | 2.13397i | −0.0886850 | − | 0.153607i | 0.818271 | − | 0.574833i | \(-0.194933\pi\) |
−0.906956 | + | 0.421226i | \(0.861600\pi\) | |||||||
\(194\) | −1.00000 | + | 1.00000i | −0.0717958 | + | 0.0717958i | ||||
\(195\) | 3.69615 | + | 2.13397i | 0.264687 | + | 0.152817i | ||||
\(196\) | − | 1.85641i | − | 0.132600i | ||||||
\(197\) | 10.4641 | − | 10.4641i | 0.745536 | − | 0.745536i | −0.228101 | − | 0.973637i | \(-0.573252\pi\) |
0.973637 | + | 0.228101i | \(0.0732517\pi\) | |||||||
\(198\) | − | 2.19615i | − | 0.156074i | ||||||
\(199\) | 5.85641i | 0.415150i | 0.978219 | + | 0.207575i | \(0.0665570\pi\) | ||||
−0.978219 | + | 0.207575i | \(0.933443\pi\) | |||||||
\(200\) | −3.46410 | − | 12.9282i | −0.244949 | − | 0.914162i | ||||
\(201\) | 2.13397 | + | 0.571797i | 0.150519 | + | 0.0403314i | ||||
\(202\) | 2.73205i | 0.192226i | ||||||||
\(203\) | 7.96410 | + | 2.13397i | 0.558970 | + | 0.149776i | ||||
\(204\) | 6.92820 | − | 12.0000i | 0.485071 | − | 0.840168i | ||||
\(205\) | 5.59808 | − | 1.50000i | 0.390987 | − | 0.104765i | ||||
\(206\) | 2.83013 | − | 0.758330i | 0.197184 | − | 0.0528354i | ||||
\(207\) | −1.20577 | + | 0.696152i | −0.0838069 | + | 0.0483859i | ||||
\(208\) | −18.3923 | + | 4.92820i | −1.27528 | + | 0.341709i | ||||
\(209\) | 1.09808 | − | 1.90192i | 0.0759555 | − | 0.131559i | ||||
\(210\) | −2.70577 | + | 1.56218i | −0.186716 | + | 0.107801i | ||||
\(211\) | −0.526279 | + | 1.96410i | −0.0362306 | + | 0.135214i | −0.981672 | − | 0.190577i | \(-0.938964\pi\) |
0.945442 | + | 0.325791i | \(0.105631\pi\) | |||||||
\(212\) | 6.19615 | − | 1.66025i | 0.425553 | − | 0.114027i | ||||
\(213\) | 18.9282 | 1.29694 | ||||||||
\(214\) | −19.7321 | + | 11.3923i | −1.34886 | + | 0.778762i | ||||
\(215\) | − | 4.66025i | − | 0.317827i | ||||||
\(216\) | −10.3923 | + | 10.3923i | −0.707107 | + | 0.707107i | ||||
\(217\) | − | 2.94744i | − | 0.200085i | ||||||
\(218\) | 1.73205 | + | 3.00000i | 0.117309 | + | 0.203186i | ||||
\(219\) | 0.928203 | 0.0627222 | ||||||||
\(220\) | −0.267949 | + | 0.464102i | −0.0180651 | + | 0.0312897i | ||||
\(221\) | −4.92820 | + | 18.3923i | −0.331507 | + | 1.23720i | ||||
\(222\) | 13.3923 | + | 23.1962i | 0.898833 | + | 1.55682i | ||||
\(223\) | −7.79423 | + | 13.5000i | −0.521940 | + | 0.904027i | 0.477734 | + | 0.878504i | \(0.341458\pi\) |
−0.999674 | + | 0.0255224i | \(0.991875\pi\) | |||||||
\(224\) | 3.60770 | − | 13.4641i | 0.241049 | − | 0.899608i | ||||
\(225\) | 12.2942 | + | 7.09808i | 0.819615 | + | 0.473205i | ||||
\(226\) | −2.02628 | − | 7.56218i | −0.134786 | − | 0.503029i | ||||
\(227\) | 17.2583 | − | 4.62436i | 1.14548 | − | 0.306929i | 0.364325 | − | 0.931272i | \(-0.381300\pi\) |
0.781151 | + | 0.624343i | \(0.214633\pi\) | |||||||
\(228\) | −14.1962 | + | 3.80385i | −0.940163 | + | 0.251916i | ||||
\(229\) | 9.42820 | + | 2.52628i | 0.623033 | + | 0.166941i | 0.556506 | − | 0.830843i | \(-0.312142\pi\) |
0.0665269 | + | 0.997785i | \(0.478808\pi\) | |||||||
\(230\) | 0.339746 | 0.0224022 | ||||||||
\(231\) | −2.13397 | − | 0.571797i | −0.140405 | − | 0.0376215i | ||||
\(232\) | −8.19615 | − | 4.73205i | −0.538104 | − | 0.310674i | ||||
\(233\) | 22.9282i | 1.50208i | 0.660259 | + | 0.751038i | \(0.270447\pi\) | ||||
−0.660259 | + | 0.751038i | \(0.729553\pi\) | |||||||
\(234\) | 10.0981 | − | 17.4904i | 0.660132 | − | 1.14338i | ||||
\(235\) | 3.36603 | − | 3.36603i | 0.219575 | − | 0.219575i | ||||
\(236\) | 8.19615 | + | 8.19615i | 0.533524 | + | 0.533524i | ||||
\(237\) | −2.59808 | − | 1.50000i | −0.168763 | − | 0.0974355i | ||||
\(238\) | −9.85641 | − | 9.85641i | −0.638896 | − | 0.638896i | ||||
\(239\) | −5.59808 | − | 9.69615i | −0.362109 | − | 0.627192i | 0.626198 | − | 0.779664i | \(-0.284610\pi\) |
−0.988308 | + | 0.152472i | \(0.951277\pi\) | |||||||
\(240\) | 3.46410 | − | 0.928203i | 0.223607 | − | 0.0599153i | ||||
\(241\) | −6.23205 | + | 10.7942i | −0.401442 | + | 0.695317i | −0.993900 | − | 0.110284i | \(-0.964824\pi\) |
0.592458 | + | 0.805601i | \(0.298157\pi\) | |||||||
\(242\) | 14.6603 | − | 3.92820i | 0.942397 | − | 0.252514i | ||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 28.8564 | + | 7.73205i | 1.84734 | + | 0.494994i | ||||
\(245\) | −0.124356 | − | 0.464102i | −0.00794479 | − | 0.0296504i | ||||
\(246\) | −7.09808 | − | 26.4904i | −0.452557 | − | 1.68897i | ||||
\(247\) | 17.4904 | − | 10.0981i | 1.11289 | − | 0.642525i | ||||
\(248\) | −0.875644 | + | 3.26795i | −0.0556035 | + | 0.207515i | ||||
\(249\) | 5.47372 | + | 20.4282i | 0.346883 | + | 1.29458i | ||||
\(250\) | −3.56218 | − | 6.16987i | −0.225292 | − | 0.390217i | ||||
\(251\) | 7.39230 | − | 7.39230i | 0.466598 | − | 0.466598i | −0.434212 | − | 0.900811i | \(-0.642973\pi\) |
0.900811 | + | 0.434212i | \(0.142973\pi\) | |||||||
\(252\) | 7.39230 | + | 12.8038i | 0.465671 | + | 0.806567i | ||||
\(253\) | 0.169873 | + | 0.169873i | 0.0106798 | + | 0.0106798i | ||||
\(254\) | −27.8564 | − | 7.46410i | −1.74787 | − | 0.468339i | ||||
\(255\) | 0.928203 | − | 3.46410i | 0.0581263 | − | 0.216930i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −5.16025 | − | 8.93782i | −0.321888 | − | 0.557526i | 0.658990 | − | 0.752152i | \(-0.270984\pi\) |
−0.980878 | + | 0.194626i | \(0.937651\pi\) | |||||||
\(258\) | −22.0526 | −1.37293 | ||||||||
\(259\) | 26.0263 | − | 6.97372i | 1.61719 | − | 0.433326i | ||||
\(260\) | −4.26795 | + | 2.46410i | −0.264687 | + | 0.152817i | ||||
\(261\) | 9.69615 | − | 2.59808i | 0.600177 | − | 0.160817i | ||||
\(262\) | −8.56218 | + | 14.8301i | −0.528973 | + | 0.916208i | ||||
\(263\) | 3.40192 | + | 1.96410i | 0.209772 | + | 0.121112i | 0.601205 | − | 0.799095i | \(-0.294687\pi\) |
−0.391434 | + | 0.920206i | \(0.628021\pi\) | |||||||
\(264\) | 2.19615 | + | 1.26795i | 0.135164 | + | 0.0780369i | ||||
\(265\) | 1.43782 | − | 0.830127i | 0.0883247 | − | 0.0509943i | ||||
\(266\) | 14.7846i | 0.906503i | ||||||||
\(267\) | −20.5359 | −1.25678 | ||||||||
\(268\) | −1.80385 | + | 1.80385i | −0.110188 | + | 0.110188i | ||||
\(269\) | 7.73205 | + | 7.73205i | 0.471431 | + | 0.471431i | 0.902378 | − | 0.430946i | \(-0.141820\pi\) |
−0.430946 | + | 0.902378i | \(0.641820\pi\) | |||||||
\(270\) | −1.90192 | + | 3.29423i | −0.115747 | + | 0.200480i | ||||
\(271\) | −14.9282 | −0.906824 | −0.453412 | − | 0.891301i | \(-0.649793\pi\) | ||||
−0.453412 | + | 0.891301i | \(0.649793\pi\) | |||||||
\(272\) | 8.00000 | + | 13.8564i | 0.485071 | + | 0.840168i | ||||
\(273\) | −14.3660 | − | 14.3660i | −0.869471 | − | 0.869471i | ||||
\(274\) | 16.6603 | + | 16.6603i | 1.00648 | + | 1.00648i | ||||
\(275\) | 0.633975 | − | 2.36603i | 0.0382301 | − | 0.142677i | ||||
\(276\) | − | 1.60770i | − | 0.0967719i | ||||||
\(277\) | −3.69615 | − | 13.7942i | −0.222080 | − | 0.828815i | −0.983553 | − | 0.180618i | \(-0.942190\pi\) |
0.761473 | − | 0.648197i | \(-0.224477\pi\) | |||||||
\(278\) | 5.49038 | + | 3.16987i | 0.329291 | + | 0.190116i | ||||
\(279\) | −1.79423 | − | 3.10770i | −0.107418 | − | 0.186053i | ||||
\(280\) | − | 3.60770i | − | 0.215601i | ||||||
\(281\) | 16.9641 | + | 9.79423i | 1.01199 | + | 0.584275i | 0.911775 | − | 0.410691i | \(-0.134712\pi\) |
0.100219 | + | 0.994965i | \(0.468046\pi\) | |||||||
\(282\) | −15.9282 | − | 15.9282i | −0.948511 | − | 0.948511i | ||||
\(283\) | −15.5263 | − | 4.16025i | −0.922942 | − | 0.247301i | −0.234099 | − | 0.972213i | \(-0.575214\pi\) |
−0.688842 | + | 0.724911i | \(0.741881\pi\) | |||||||
\(284\) | −10.9282 | + | 18.9282i | −0.648470 | + | 1.12318i | ||||
\(285\) | −3.29423 | + | 1.90192i | −0.195133 | + | 0.112660i | ||||
\(286\) | −3.36603 | − | 0.901924i | −0.199037 | − | 0.0533319i | ||||
\(287\) | −27.5885 | −1.62850 | ||||||||
\(288\) | −4.39230 | − | 16.3923i | −0.258819 | − | 0.965926i | ||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −2.36603 | − | 0.633975i | −0.138938 | − | 0.0372283i | ||||
\(291\) | 1.50000 | + | 0.866025i | 0.0879316 | + | 0.0507673i | ||||
\(292\) | −0.535898 | + | 0.928203i | −0.0313611 | + | 0.0543190i | ||||
\(293\) | −14.4282 | − | 3.86603i | −0.842905 | − | 0.225856i | −0.188569 | − | 0.982060i | \(-0.560385\pi\) |
−0.654336 | + | 0.756204i | \(0.727052\pi\) | |||||||
\(294\) | −2.19615 | + | 0.588457i | −0.128082 | + | 0.0343195i | ||||
\(295\) | 2.59808 | + | 1.50000i | 0.151266 | + | 0.0873334i | ||||
\(296\) | −30.9282 | −1.79767 | ||||||||
\(297\) | −2.59808 | + | 0.696152i | −0.150756 | + | 0.0403949i | ||||
\(298\) | −18.6340 | − | 10.7583i | −1.07944 | − | 0.623213i | ||||
\(299\) | 0.571797 | + | 2.13397i | 0.0330679 | + | 0.123411i | ||||
\(300\) | −14.1962 | + | 8.19615i | −0.819615 | + | 0.473205i | ||||
\(301\) | −5.74167 | + | 21.4282i | −0.330944 | + | 1.23510i | ||||
\(302\) | −7.00000 | − | 7.00000i | −0.402805 | − | 0.402805i | ||||
\(303\) | 3.23205 | − | 0.866025i | 0.185676 | − | 0.0497519i | ||||
\(304\) | 4.39230 | − | 16.3923i | 0.251916 | − | 0.940163i | ||||
\(305\) | 7.73205 | 0.442736 | ||||||||
\(306\) | −16.3923 | − | 4.39230i | −0.937086 | − | 0.251091i | ||||
\(307\) | −5.92820 | − | 5.92820i | −0.338340 | − | 0.338340i | 0.517402 | − | 0.855742i | \(-0.326899\pi\) |
−0.855742 | + | 0.517402i | \(0.826899\pi\) | |||||||
\(308\) | 1.80385 | − | 1.80385i | 0.102784 | − | 0.102784i | ||||
\(309\) | −1.79423 | − | 3.10770i | −0.102070 | − | 0.176791i | ||||
\(310\) | 0.875644i | 0.0497333i | ||||||||
\(311\) | 27.1865 | − | 15.6962i | 1.54161 | − | 0.890047i | 0.542869 | − | 0.839817i | \(-0.317338\pi\) |
0.998738 | − | 0.0502299i | \(-0.0159954\pi\) | |||||||
\(312\) | 11.6603 | + | 20.1962i | 0.660132 | + | 1.14338i | ||||
\(313\) | −7.83975 | − | 4.52628i | −0.443129 | − | 0.255840i | 0.261795 | − | 0.965123i | \(-0.415686\pi\) |
−0.704924 | + | 0.709283i | \(0.749019\pi\) | |||||||
\(314\) | −0.633975 | + | 1.09808i | −0.0357773 | + | 0.0619680i | ||||
\(315\) | 2.70577 | + | 2.70577i | 0.152453 | + | 0.152453i | ||||
\(316\) | 3.00000 | − | 1.73205i | 0.168763 | − | 0.0974355i | ||||
\(317\) | 2.03590 | − | 0.545517i | 0.114347 | − | 0.0306393i | −0.201192 | − | 0.979552i | \(-0.564481\pi\) |
0.315539 | + | 0.948913i | \(0.397815\pi\) | |||||||
\(318\) | −3.92820 | − | 6.80385i | −0.220283 | − | 0.381541i | ||||
\(319\) | −0.866025 | − | 1.50000i | −0.0484881 | − | 0.0839839i | ||||
\(320\) | −1.07180 | + | 4.00000i | −0.0599153 | + | 0.223607i | ||||
\(321\) | 19.7321 | + | 19.7321i | 1.10134 | + | 1.10134i | ||||
\(322\) | −1.56218 | − | 0.418584i | −0.0870568 | − | 0.0233268i | ||||
\(323\) | −12.0000 | − | 12.0000i | −0.667698 | − | 0.667698i | ||||
\(324\) | 15.5885 | + | 9.00000i | 0.866025 | + | 0.500000i | ||||
\(325\) | 15.9282 | − | 15.9282i | 0.883538 | − | 0.883538i | ||||
\(326\) | 11.9282 | + | 20.6603i | 0.660642 | + | 1.14427i | ||||
\(327\) | 3.00000 | − | 3.00000i | 0.165900 | − | 0.165900i | ||||
\(328\) | 30.5885 | + | 8.19615i | 1.68897 | + | 0.452557i | ||||
\(329\) | −19.6244 | + | 11.3301i | −1.08193 | + | 0.624650i | ||||
\(330\) | 0.633975 | + | 0.169873i | 0.0348992 | + | 0.00935120i | ||||
\(331\) | 7.06218 | + | 26.3564i | 0.388172 | + | 1.44868i | 0.833105 | + | 0.553115i | \(0.186561\pi\) |
−0.444933 | + | 0.895564i | \(0.646772\pi\) | |||||||
\(332\) | −23.5885 | − | 6.32051i | −1.29458 | − | 0.346883i | ||||
\(333\) | 23.1962 | − | 23.1962i | 1.27114 | − | 1.27114i | ||||
\(334\) | −13.0263 | + | 3.49038i | −0.712766 | + | 0.190985i | ||||
\(335\) | −0.330127 | + | 0.571797i | −0.0180368 | + | 0.0312406i | ||||
\(336\) | −17.0718 | −0.931343 | ||||||||
\(337\) | 0.696152 | + | 1.20577i | 0.0379218 | + | 0.0656826i | 0.884363 | − | 0.466799i | \(-0.154593\pi\) |
−0.846442 | + | 0.532482i | \(0.821260\pi\) | |||||||
\(338\) | −9.66025 | − | 9.66025i | −0.525449 | − | 0.525449i | ||||
\(339\) | −8.30385 | + | 4.79423i | −0.451003 | + | 0.260387i | ||||
\(340\) | 2.92820 | + | 2.92820i | 0.158804 | + | 0.158804i | ||||
\(341\) | −0.437822 | + | 0.437822i | −0.0237094 | + | 0.0237094i | ||||
\(342\) | 9.00000 | + | 15.5885i | 0.486664 | + | 0.842927i | ||||
\(343\) | 19.5359i | 1.05484i | ||||||||
\(344\) | 12.7321 | − | 22.0526i | 0.686466 | − | 1.18899i | ||||
\(345\) | −0.107695 | − | 0.401924i | −0.00579811 | − | 0.0216388i | ||||
\(346\) | −13.1244 | −0.705570 | ||||||||
\(347\) | 19.5263 | + | 5.23205i | 1.04823 | + | 0.280871i | 0.741518 | − | 0.670933i | \(-0.234106\pi\) |
0.306707 | + | 0.951804i | \(0.400773\pi\) | |||||||
\(348\) | −3.00000 | + | 11.1962i | −0.160817 | + | 0.600177i | ||||
\(349\) | 7.96410 | − | 2.13397i | 0.426309 | − | 0.114229i | −0.0392843 | − | 0.999228i | \(-0.512508\pi\) |
0.465593 | + | 0.884999i | \(0.345841\pi\) | |||||||
\(350\) | 4.26795 | + | 15.9282i | 0.228131 | + | 0.851398i | ||||
\(351\) | −23.8923 | − | 6.40192i | −1.27528 | − | 0.341709i | ||||
\(352\) | −2.53590 | + | 1.46410i | −0.135164 | + | 0.0780369i | ||||
\(353\) | −15.2321 | + | 26.3827i | −0.810720 | + | 1.40421i | 0.101640 | + | 0.994821i | \(0.467591\pi\) |
−0.912361 | + | 0.409387i | \(0.865742\pi\) | |||||||
\(354\) | 7.09808 | − | 12.2942i | 0.377258 | − | 0.653431i | ||||
\(355\) | −1.46410 | + | 5.46410i | −0.0777064 | + | 0.290004i | ||||
\(356\) | 11.8564 | − | 20.5359i | 0.628388 | − | 1.08840i | ||||
\(357\) | −8.53590 | + | 14.7846i | −0.451768 | + | 0.782485i | ||||
\(358\) | 7.92820 | + | 13.7321i | 0.419019 | + | 0.725761i | ||||
\(359\) | − | 15.0718i | − | 0.795459i | −0.917503 | − | 0.397730i | \(-0.869798\pi\) | ||
0.917503 | − | 0.397730i | \(-0.130202\pi\) | |||||||
\(360\) | −2.19615 | − | 3.80385i | −0.115747 | − | 0.200480i | ||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | −7.39230 | + | 4.26795i | −0.388531 | + | 0.224318i | ||||
\(363\) | −9.29423 | − | 16.0981i | −0.487820 | − | 0.844930i | ||||
\(364\) | 22.6603 | − | 6.07180i | 1.18772 | − | 0.318249i | ||||
\(365\) | −0.0717968 | + | 0.267949i | −0.00375801 | + | 0.0140251i | ||||
\(366\) | − | 36.5885i | − | 1.91251i | ||||||
\(367\) | 15.4545 | − | 26.7679i | 0.806717 | − | 1.39728i | −0.108408 | − | 0.994106i | \(-0.534575\pi\) |
0.915125 | − | 0.403169i | \(-0.132091\pi\) | |||||||
\(368\) | 1.60770 | + | 0.928203i | 0.0838069 | + | 0.0483859i | ||||
\(369\) | −29.0885 | + | 16.7942i | −1.51428 | + | 0.874273i | ||||
\(370\) | −7.73205 | + | 2.07180i | −0.401970 | + | 0.107708i | ||||
\(371\) | −7.63397 | + | 2.04552i | −0.396336 | + | 0.106198i | ||||
\(372\) | 4.14359 | 0.214835 | ||||||||
\(373\) | −13.4282 | − | 3.59808i | −0.695286 | − | 0.186301i | −0.106168 | − | 0.994348i | \(-0.533858\pi\) |
−0.589118 | + | 0.808047i | \(0.700525\pi\) | |||||||
\(374\) | 2.92820i | 0.151414i | ||||||||
\(375\) | −6.16987 | + | 6.16987i | −0.318611 | + | 0.318611i | ||||
\(376\) | 25.1244 | − | 6.73205i | 1.29569 | − | 0.347179i | ||||
\(377\) | − | 15.9282i | − | 0.820344i | ||||||
\(378\) | 12.8038 | − | 12.8038i | 0.658559 | − | 0.658559i | ||||
\(379\) | 15.5885 | − | 15.5885i | 0.800725 | − | 0.800725i | −0.182484 | − | 0.983209i | \(-0.558414\pi\) |
0.983209 | + | 0.182484i | \(0.0584137\pi\) | |||||||
\(380\) | − | 4.39230i | − | 0.225320i | ||||||
\(381\) | 35.3205i | 1.80952i | ||||||||
\(382\) | 13.1962 | − | 13.1962i | 0.675174 | − | 0.675174i | ||||
\(383\) | 12.3301 | + | 21.3564i | 0.630040 | + | 1.09126i | 0.987543 | + | 0.157349i | \(0.0502949\pi\) |
−0.357503 | + | 0.933912i | \(0.616372\pi\) | |||||||
\(384\) | 18.9282 | + | 5.07180i | 0.965926 | + | 0.258819i | ||||
\(385\) | 0.330127 | − | 0.571797i | 0.0168248 | − | 0.0291415i | ||||
\(386\) | −0.901924 | − | 3.36603i | −0.0459067 | − | 0.171326i | ||||
\(387\) | 6.99038 | + | 26.0885i | 0.355341 | + | 1.32615i | ||||
\(388\) | −1.73205 | + | 1.00000i | −0.0879316 | + | 0.0507673i | ||||
\(389\) | −2.03590 | − | 7.59808i | −0.103224 | − | 0.385238i | 0.894914 | − | 0.446240i | \(-0.147237\pi\) |
−0.998138 | + | 0.0610019i | \(0.980570\pi\) | |||||||
\(390\) | 4.26795 | + | 4.26795i | 0.216116 | + | 0.216116i | ||||
\(391\) | 1.60770 | − | 0.928203i | 0.0813046 | − | 0.0469413i | ||||
\(392\) | 0.679492 | − | 2.53590i | 0.0343195 | − | 0.128082i | ||||
\(393\) | 20.2583 | + | 5.42820i | 1.02190 | + | 0.273817i | ||||
\(394\) | 18.1244 | − | 10.4641i | 0.913092 | − | 0.527174i | ||||
\(395\) | 0.633975 | − | 0.633975i | 0.0318987 | − | 0.0318987i | ||||
\(396\) | 0.803848 | − | 3.00000i | 0.0403949 | − | 0.150756i | ||||
\(397\) | −21.0526 | − | 21.0526i | −1.05660 | − | 1.05660i | −0.998299 | − | 0.0582984i | \(-0.981433\pi\) |
−0.0582984 | − | 0.998299i | \(-0.518567\pi\) | |||||||
\(398\) | −2.14359 | + | 8.00000i | −0.107449 | + | 0.401004i | ||||
\(399\) | 17.4904 | − | 4.68653i | 0.875614 | − | 0.234620i | ||||
\(400\) | − | 18.9282i | − | 0.946410i | ||||||
\(401\) | 1.16025 | + | 2.00962i | 0.0579403 | + | 0.100356i | 0.893541 | − | 0.448982i | \(-0.148213\pi\) |
−0.835600 | + | 0.549338i | \(0.814880\pi\) | |||||||
\(402\) | 2.70577 | + | 1.56218i | 0.134952 | + | 0.0779143i | ||||
\(403\) | −5.50000 | + | 1.47372i | −0.273975 | + | 0.0734112i | ||||
\(404\) | −1.00000 | + | 3.73205i | −0.0497519 | + | 0.185676i | ||||
\(405\) | 4.50000 | + | 1.20577i | 0.223607 | + | 0.0599153i | ||||
\(406\) | 10.0981 | + | 5.83013i | 0.501159 | + | 0.289344i | ||||
\(407\) | −4.90192 | − | 2.83013i | −0.242979 | − | 0.140284i | ||||
\(408\) | 13.8564 | − | 13.8564i | 0.685994 | − | 0.685994i | ||||
\(409\) | −4.62436 | + | 2.66987i | −0.228660 | + | 0.132017i | −0.609954 | − | 0.792437i | \(-0.708812\pi\) |
0.381294 | + | 0.924454i | \(0.375479\pi\) | |||||||
\(410\) | 8.19615 | 0.404779 | ||||||||
\(411\) | 14.4282 | − | 24.9904i | 0.711691 | − | 1.23268i | ||||
\(412\) | 4.14359 | 0.204140 | ||||||||
\(413\) | −10.0981 | − | 10.0981i | −0.496894 | − | 0.496894i | ||||
\(414\) | −1.90192 | + | 0.509619i | −0.0934745 | + | 0.0250464i | ||||
\(415\) | −6.32051 | −0.310262 | ||||||||
\(416\) | −26.9282 | −1.32026 | ||||||||
\(417\) | 2.00962 | − | 7.50000i | 0.0984115 | − | 0.367277i | ||||
\(418\) | 2.19615 | − | 2.19615i | 0.107417 | − | 0.107417i | ||||
\(419\) | −0.526279 | + | 1.96410i | −0.0257104 | + | 0.0959526i | −0.977589 | − | 0.210523i | \(-0.932483\pi\) |
0.951878 | + | 0.306476i | \(0.0991499\pi\) | |||||||
\(420\) | −4.26795 | + | 1.14359i | −0.208255 | + | 0.0558017i | ||||
\(421\) | −2.89230 | − | 10.7942i | −0.140962 | − | 0.526079i | −0.999902 | − | 0.0140017i | \(-0.995543\pi\) |
0.858940 | − | 0.512077i | \(-0.171124\pi\) | |||||||
\(422\) | −1.43782 | + | 2.49038i | −0.0699921 | + | 0.121230i | ||||
\(423\) | −13.7942 | + | 23.8923i | −0.670698 | + | 1.16168i | ||||
\(424\) | 9.07180 | 0.440565 | ||||||||
\(425\) | −16.3923 | − | 9.46410i | −0.795144 | − | 0.459076i | ||||
\(426\) | 25.8564 | + | 6.92820i | 1.25275 | + | 0.335673i | ||||
\(427\) | −35.5526 | − | 9.52628i | −1.72051 | − | 0.461009i | ||||
\(428\) | −31.1244 | + | 8.33975i | −1.50445 | + | 0.403117i | ||||
\(429\) | 4.26795i | 0.206059i | ||||||||
\(430\) | 1.70577 | − | 6.36603i | 0.0822596 | − | 0.306997i | ||||
\(431\) | 31.3205 | 1.50866 | 0.754328 | − | 0.656498i | \(-0.227963\pi\) | ||||
0.754328 | + | 0.656498i | \(0.227963\pi\) | |||||||
\(432\) | −18.0000 | + | 10.3923i | −0.866025 | + | 0.500000i | ||||
\(433\) | 24.3923 | 1.17222 | 0.586110 | − | 0.810232i | \(-0.300659\pi\) | ||||
0.586110 | + | 0.810232i | \(0.300659\pi\) | |||||||
\(434\) | 1.07884 | − | 4.02628i | 0.0517859 | − | 0.193268i | ||||
\(435\) | 3.00000i | 0.143839i | ||||||||
\(436\) | 1.26795 | + | 4.73205i | 0.0607238 | + | 0.226624i | ||||
\(437\) | −1.90192 | − | 0.509619i | −0.0909814 | − | 0.0243784i | ||||
\(438\) | 1.26795 | + | 0.339746i | 0.0605850 | + | 0.0162337i | ||||
\(439\) | −18.0622 | − | 10.4282i | −0.862061 | − | 0.497711i | 0.00264111 | − | 0.999997i | \(-0.499159\pi\) |
−0.864702 | + | 0.502286i | \(0.832493\pi\) | |||||||
\(440\) | −0.535898 | + | 0.535898i | −0.0255480 | + | 0.0255480i | ||||
\(441\) | 1.39230 | + | 2.41154i | 0.0663002 | + | 0.114835i | ||||
\(442\) | −13.4641 | + | 23.3205i | −0.640422 | + | 1.10924i | ||||
\(443\) | −4.33013 | − | 16.1603i | −0.205731 | − | 0.767797i | −0.989226 | − | 0.146399i | \(-0.953232\pi\) |
0.783495 | − | 0.621398i | \(-0.213435\pi\) | |||||||
\(444\) | 9.80385 | + | 36.5885i | 0.465270 | + | 1.73641i | ||||
\(445\) | 1.58846 | − | 5.92820i | 0.0753001 | − | 0.281024i | ||||
\(446\) | −15.5885 | + | 15.5885i | −0.738135 | + | 0.738135i | ||||
\(447\) | −6.82051 | + | 25.4545i | −0.322599 | + | 1.20396i | ||||
\(448\) | 9.85641 | − | 17.0718i | 0.465671 | − | 0.806567i | ||||
\(449\) | 0.679492 | 0.0320672 | 0.0160336 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160336 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(450\) | 14.1962 | + | 14.1962i | 0.669213 | + | 0.669213i | ||||
\(451\) | 4.09808 | + | 4.09808i | 0.192971 | + | 0.192971i | ||||
\(452\) | − | 11.0718i | − | 0.520774i | ||||||
\(453\) | −6.06218 | + | 10.5000i | −0.284826 | + | 0.493333i | ||||
\(454\) | 25.2679 | 1.18588 | ||||||||
\(455\) | 5.25833 | − | 3.03590i | 0.246514 | − | 0.142325i | ||||
\(456\) | −20.7846 | −0.973329 | ||||||||
\(457\) | −19.0359 | − | 10.9904i | −0.890462 | − | 0.514108i | −0.0163683 | − | 0.999866i | \(-0.505210\pi\) |
−0.874094 | + | 0.485758i | \(0.838544\pi\) | |||||||
\(458\) | 11.9545 | + | 6.90192i | 0.558596 | + | 0.322506i | ||||
\(459\) | 20.7846i | 0.970143i | ||||||||
\(460\) | 0.464102 | + | 0.124356i | 0.0216388 | + | 0.00579811i | ||||
\(461\) | 2.23205 | − | 0.598076i | 0.103957 | − | 0.0278552i | −0.206466 | − | 0.978454i | \(-0.566196\pi\) |
0.310423 | + | 0.950599i | \(0.399529\pi\) | |||||||
\(462\) | −2.70577 | − | 1.56218i | −0.125884 | − | 0.0726791i | ||||
\(463\) | 3.33013 | + | 5.76795i | 0.154764 | + | 0.268059i | 0.932973 | − | 0.359946i | \(-0.117205\pi\) |
−0.778209 | + | 0.628005i | \(0.783872\pi\) | |||||||
\(464\) | −9.46410 | − | 9.46410i | −0.439360 | − | 0.439360i | ||||
\(465\) | 1.03590 | − | 0.277568i | 0.0480386 | − | 0.0128719i | ||||
\(466\) | −8.39230 | + | 31.3205i | −0.388766 | + | 1.45089i | ||||
\(467\) | −19.7846 | − | 19.7846i | −0.915523 | − | 0.915523i | 0.0811771 | − | 0.996700i | \(-0.474132\pi\) |
−0.996700 | + | 0.0811771i | \(0.974132\pi\) | |||||||
\(468\) | 20.1962 | − | 20.1962i | 0.933567 | − | 0.933567i | ||||
\(469\) | 2.22243 | − | 2.22243i | 0.102622 | − | 0.102622i | ||||
\(470\) | 5.83013 | − | 3.36603i | 0.268924 | − | 0.155263i | ||||
\(471\) | 1.50000 | + | 0.401924i | 0.0691164 | + | 0.0185197i | ||||
\(472\) | 8.19615 | + | 14.1962i | 0.377258 | + | 0.653431i | ||||
\(473\) | 4.03590 | − | 2.33013i | 0.185571 | − | 0.107139i | ||||
\(474\) | −3.00000 | − | 3.00000i | −0.137795 | − | 0.137795i | ||||
\(475\) | 5.19615 | + | 19.3923i | 0.238416 | + | 0.889780i | ||||
\(476\) | −9.85641 | − | 17.0718i | −0.451768 | − | 0.782485i | ||||
\(477\) | −6.80385 | + | 6.80385i | −0.311527 | + | 0.311527i | ||||
\(478\) | −4.09808 | − | 15.2942i | −0.187442 | − | 0.699542i | ||||
\(479\) | 0.669873 | − | 1.16025i | 0.0306073 | − | 0.0530134i | −0.850316 | − | 0.526272i | \(-0.823589\pi\) |
0.880923 | + | 0.473259i | \(0.156923\pi\) | |||||||
\(480\) | 5.07180 | 0.231495 | ||||||||
\(481\) | −26.0263 | − | 45.0788i | −1.18670 | − | 2.05542i | ||||
\(482\) | −12.4641 | + | 12.4641i | −0.567724 | + | 0.567724i | ||||
\(483\) | 1.98076i | 0.0901278i | ||||||||
\(484\) | 21.4641 | 0.975641 | ||||||||
\(485\) | −0.366025 | + | 0.366025i | −0.0166204 | + | 0.0166204i | ||||
\(486\) | 5.70577 | − | 21.2942i | 0.258819 | − | 0.965926i | ||||
\(487\) | 34.7846i | 1.57624i | 0.615521 | + | 0.788121i | \(0.288946\pi\) | ||||
−0.615521 | + | 0.788121i | \(0.711054\pi\) | |||||||
\(488\) | 36.5885 | + | 21.1244i | 1.65628 | + | 0.956255i | ||||
\(489\) | 20.6603 | − | 20.6603i | 0.934289 | − | 0.934289i | ||||
\(490\) | − | 0.679492i | − | 0.0306963i | ||||||
\(491\) | −1.86603 | − | 0.500000i | −0.0842125 | − | 0.0225647i | 0.216467 | − | 0.976290i | \(-0.430547\pi\) |
−0.300679 | + | 0.953725i | \(0.597213\pi\) | |||||||
\(492\) | − | 38.7846i | − | 1.74855i | ||||||
\(493\) | −12.9282 | + | 3.46410i | −0.582257 | + | 0.156015i | ||||
\(494\) | 27.5885 | − | 7.39230i | 1.24126 | − | 0.332596i | ||||
\(495\) | − | 0.803848i | − | 0.0361303i | ||||||
\(496\) | −2.39230 | + | 4.14359i | −0.107418 | + | 0.186053i | ||||
\(497\) | 13.4641 | − | 23.3205i | 0.603947 | − | 1.04607i | ||||
\(498\) | 29.9090i | 1.34025i | ||||||||
\(499\) | 0.669873 | − | 2.50000i | 0.0299876 | − | 0.111915i | −0.949310 | − | 0.314342i | \(-0.898216\pi\) |
0.979297 | + | 0.202427i | \(0.0648828\pi\) | |||||||
\(500\) | −2.60770 | − | 9.73205i | −0.116620 | − | 0.435231i | ||||
\(501\) | 8.25833 | + | 14.3038i | 0.368955 | + | 0.639049i | ||||
\(502\) | 12.8038 | − | 7.39230i | 0.571464 | − | 0.329935i | ||||
\(503\) | − | 13.8564i | − | 0.617827i | −0.951090 | − | 0.308913i | \(-0.900035\pi\) | ||
0.951090 | − | 0.308913i | \(-0.0999653\pi\) | |||||||
\(504\) | 5.41154 | + | 20.1962i | 0.241049 | + | 0.899608i | ||||
\(505\) | 1.00000i | 0.0444994i | ||||||||
\(506\) | 0.169873 | + | 0.294229i | 0.00755178 | + | 0.0130801i | ||||
\(507\) | −8.36603 | + | 14.4904i | −0.371548 | + | 0.643540i | ||||
\(508\) | −35.3205 | − | 20.3923i | −1.56709 | − | 0.904762i | ||||
\(509\) | 5.69615 | − | 21.2583i | 0.252478 | − | 0.942259i | −0.716999 | − | 0.697074i | \(-0.754485\pi\) |
0.969476 | − | 0.245185i | \(-0.0788486\pi\) | |||||||
\(510\) | 2.53590 | − | 4.39230i | 0.112291 | − | 0.194495i | ||||
\(511\) | 0.660254 | − | 1.14359i | 0.0292079 | − | 0.0505896i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 15.5885 | − | 15.5885i | 0.688247 | − | 0.688247i | ||||
\(514\) | −3.77757 | − | 14.0981i | −0.166621 | − | 0.621839i | ||||
\(515\) | 1.03590 | − | 0.277568i | 0.0456471 | − | 0.0122311i | ||||
\(516\) | −30.1244 | − | 8.07180i | −1.32615 | − | 0.355341i | ||||
\(517\) | 4.59808 | + | 1.23205i | 0.202223 | + | 0.0541855i | ||||
\(518\) | 38.1051 | 1.67424 | ||||||||
\(519\) | 4.16025 | + | 15.5263i | 0.182615 | + | 0.681528i | ||||
\(520\) | −6.73205 | + | 1.80385i | −0.295220 | + | 0.0791039i | ||||
\(521\) | − | 14.1436i | − | 0.619642i | −0.950795 | − | 0.309821i | \(-0.899731\pi\) | ||
0.950795 | − | 0.309821i | \(-0.100269\pi\) | |||||||
\(522\) | 14.1962 | 0.621349 | ||||||||
\(523\) | −2.12436 | + | 2.12436i | −0.0928916 | + | 0.0928916i | −0.752026 | − | 0.659134i | \(-0.770923\pi\) |
0.659134 | + | 0.752026i | \(0.270923\pi\) | |||||||
\(524\) | −17.1244 | + | 17.1244i | −0.748081 | + | 0.748081i | ||||
\(525\) | 17.4904 | − | 10.0981i | 0.763343 | − | 0.440716i | ||||
\(526\) | 3.92820 | + | 3.92820i | 0.171278 | + | 0.171278i | ||||
\(527\) | 2.39230 | + | 4.14359i | 0.104210 | + | 0.180498i | ||||
\(528\) | 2.53590 | + | 2.53590i | 0.110361 | + | 0.110361i | ||||
\(529\) | −11.3923 | + | 19.7321i | −0.495318 | + | 0.857915i | ||||
\(530\) | 2.26795 | − | 0.607695i | 0.0985134 | − | 0.0263966i | ||||
\(531\) | −16.7942 | − | 4.50000i | −0.728807 | − | 0.195283i | ||||
\(532\) | −5.41154 | + | 20.1962i | −0.234620 | + | 0.875614i | ||||
\(533\) | 13.7942 | + | 51.4808i | 0.597494 | + | 2.22988i | ||||
\(534\) | −28.0526 | − | 7.51666i | −1.21395 | − | 0.325278i | ||||
\(535\) | −7.22243 | + | 4.16987i | −0.312253 | + | 0.180279i | ||||
\(536\) | −3.12436 | + | 1.80385i | −0.134952 | + | 0.0779143i | ||||
\(537\) | 13.7321 | − | 13.7321i | 0.592582 | − | 0.592582i | ||||
\(538\) | 7.73205 | + | 13.3923i | 0.333352 | + | 0.577383i | ||||
\(539\) | 0.339746 | − | 0.339746i | 0.0146339 | − | 0.0146339i | ||||
\(540\) | −3.80385 | + | 3.80385i | −0.163692 | + | 0.163692i | ||||
\(541\) | −15.0000 | − | 15.0000i | −0.644900 | − | 0.644900i | 0.306856 | − | 0.951756i | \(-0.400723\pi\) |
−0.951756 | + | 0.306856i | \(0.900723\pi\) | |||||||
\(542\) | −20.3923 | − | 5.46410i | −0.875924 | − | 0.234703i | ||||
\(543\) | 7.39230 | + | 7.39230i | 0.317234 | + | 0.317234i | ||||
\(544\) | 5.85641 | + | 21.8564i | 0.251091 | + | 0.937086i | ||||
\(545\) | 0.633975 | + | 1.09808i | 0.0271565 | + | 0.0470364i | ||||
\(546\) | −14.3660 | − | 24.8827i | −0.614809 | − | 1.06488i | ||||
\(547\) | −28.2583 | + | 7.57180i | −1.20824 | + | 0.323747i | −0.806071 | − | 0.591819i | \(-0.798410\pi\) |
−0.402168 | + | 0.915566i | \(0.631743\pi\) | |||||||
\(548\) | 16.6603 | + | 28.8564i | 0.711691 | + | 1.23268i | ||||
\(549\) | −43.2846 | + | 11.5981i | −1.84734 | + | 0.494994i | ||||
\(550\) | 1.73205 | − | 3.00000i | 0.0738549 | − | 0.127920i | ||||
\(551\) | 12.2942 | + | 7.09808i | 0.523752 | + | 0.302388i | ||||
\(552\) | 0.588457 | − | 2.19615i | 0.0250464 | − | 0.0934745i | ||||
\(553\) | −3.69615 | + | 2.13397i | −0.157176 | + | 0.0907458i | ||||
\(554\) | − | 20.1962i | − | 0.858052i | ||||||
\(555\) | 4.90192 | + | 8.49038i | 0.208075 | + | 0.360397i | ||||
\(556\) | 6.33975 | + | 6.33975i | 0.268865 | + | 0.268865i | ||||
\(557\) | 27.9808 | + | 27.9808i | 1.18558 | + | 1.18558i | 0.978276 | + | 0.207307i | \(0.0664699\pi\) |
0.207307 | + | 0.978276i | \(0.433530\pi\) | |||||||
\(558\) | −1.31347 | − | 4.90192i | −0.0556035 | − | 0.207515i | ||||
\(559\) | 42.8564 | 1.81263 | ||||||||
\(560\) | 1.32051 | − | 4.92820i | 0.0558017 | − | 0.208255i | ||||
\(561\) | 3.46410 | − | 0.928203i | 0.146254 | − | 0.0391888i | ||||
\(562\) | 19.5885 | + | 19.5885i | 0.826289 | + | 0.826289i | ||||
\(563\) | 7.86603 | − | 29.3564i | 0.331513 | − | 1.23723i | −0.576086 | − | 0.817389i | \(-0.695421\pi\) |
0.907600 | − | 0.419836i | \(-0.137912\pi\) | |||||||
\(564\) | −15.9282 | − | 27.5885i | −0.670698 | − | 1.16168i | ||||
\(565\) | −0.741670 | − | 2.76795i | −0.0312023 | − | 0.116448i | ||||
\(566\) | −19.6865 | − | 11.3660i | −0.827487 | − | 0.477750i | ||||
\(567\) | −19.2058 | − | 11.0885i | −0.806567 | − | 0.465671i | ||||
\(568\) | −21.8564 | + | 21.8564i | −0.917074 | + | 0.917074i | ||||
\(569\) | −24.4808 | − | 14.1340i | −1.02629 | − | 0.592527i | −0.110368 | − | 0.993891i | \(-0.535203\pi\) |
−0.915919 | + | 0.401364i | \(0.868536\pi\) | |||||||
\(570\) | −5.19615 | + | 1.39230i | −0.217643 | + | 0.0583172i | ||||
\(571\) | −5.40192 | − | 1.44744i | −0.226063 | − | 0.0605735i | 0.144009 | − | 0.989576i | \(-0.454001\pi\) |
−0.370073 | + | 0.929003i | \(0.620667\pi\) | |||||||
\(572\) | −4.26795 | − | 2.46410i | −0.178452 | − | 0.103029i | ||||
\(573\) | −19.7942 | − | 11.4282i | −0.826916 | − | 0.477420i | ||||
\(574\) | −37.6865 | − | 10.0981i | −1.57301 | − | 0.421486i | ||||
\(575\) | −2.19615 | −0.0915859 | ||||||||
\(576\) | − | 24.0000i | − | 1.00000i | ||||||
\(577\) | 37.1769 | 1.54770 | 0.773848 | − | 0.633372i | \(-0.218330\pi\) | ||||
0.773848 | + | 0.633372i | \(0.218330\pi\) | |||||||
\(578\) | −1.36603 | − | 0.366025i | −0.0568192 | − | 0.0152246i | ||||
\(579\) | −3.69615 | + | 2.13397i | −0.153607 | + | 0.0886850i | ||||
\(580\) | −3.00000 | − | 1.73205i | −0.124568 | − | 0.0719195i | ||||
\(581\) | 29.0622 | + | 7.78719i | 1.20570 | + | 0.323067i | ||||
\(582\) | 1.73205 | + | 1.73205i | 0.0717958 | + | 0.0717958i | ||||
\(583\) | 1.43782 | + | 0.830127i | 0.0595485 | + | 0.0343803i | ||||
\(584\) | −1.07180 | + | 1.07180i | −0.0443513 | + | 0.0443513i | ||||
\(585\) | 3.69615 | − | 6.40192i | 0.152817 | − | 0.264687i | ||||
\(586\) | −18.2942 | − | 10.5622i | −0.755728 | − | 0.436320i | ||||
\(587\) | 0.794229 | + | 2.96410i | 0.0327813 | + | 0.122342i | 0.980378 | − | 0.197129i | \(-0.0631617\pi\) |
−0.947596 | + | 0.319470i | \(0.896495\pi\) | |||||||
\(588\) | −3.21539 | −0.132600 | ||||||||
\(589\) | 1.31347 | − | 4.90192i | 0.0541204 | − | 0.201980i | ||||
\(590\) | 3.00000 | + | 3.00000i | 0.123508 | + | 0.123508i | ||||
\(591\) | −18.1244 | − | 18.1244i | −0.745536 | − | 0.745536i | ||||
\(592\) | −42.2487 | − | 11.3205i | −1.73641 | − | 0.465270i | ||||
\(593\) | 1.46410 | 0.0601234 | 0.0300617 | − | 0.999548i | \(-0.490430\pi\) | ||||
0.0300617 | + | 0.999548i | \(0.490430\pi\) | |||||||
\(594\) | −3.80385 | −0.156074 | ||||||||
\(595\) | −3.60770 | − | 3.60770i | −0.147901 | − | 0.147901i | ||||
\(596\) | −21.5167 | − | 21.5167i | −0.881357 | − | 0.881357i | ||||
\(597\) | 10.1436 | 0.415150 | ||||||||
\(598\) | 3.12436i | 0.127764i | ||||||||
\(599\) | −30.3109 | + | 17.5000i | −1.23847 | + | 0.715031i | −0.968781 | − | 0.247917i | \(-0.920254\pi\) |
−0.269688 | + | 0.962948i | \(0.586921\pi\) | |||||||
\(600\) | −22.3923 | + | 6.00000i | −0.914162 | + | 0.244949i | ||||
\(601\) | 30.2321 | + | 17.4545i | 1.23319 | + | 0.711983i | 0.967694 | − | 0.252128i | \(-0.0811305\pi\) |
0.265497 | + | 0.964112i | \(0.414464\pi\) | |||||||
\(602\) | −15.6865 | + | 27.1699i | −0.639335 | + | 1.10736i | ||||
\(603\) | 0.990381 | − | 3.69615i | 0.0403314 | − | 0.150519i | ||||
\(604\) | −7.00000 | − | 12.1244i | −0.284826 | − | 0.493333i | ||||
\(605\) | 5.36603 | − | 1.43782i | 0.218160 | − | 0.0584558i | ||||
\(606\) | 4.73205 | 0.192226 | ||||||||
\(607\) | −4.59808 | − | 7.96410i | −0.186630 | − | 0.323253i | 0.757494 | − | 0.652842i | \(-0.226423\pi\) |
−0.944125 | + | 0.329589i | \(0.893090\pi\) | |||||||
\(608\) | 12.0000 | − | 20.7846i | 0.486664 | − | 0.842927i | ||||
\(609\) | 3.69615 | − | 13.7942i | 0.149776 | − | 0.558970i | ||||
\(610\) | 10.5622 | + | 2.83013i | 0.427650 | + | 0.114588i | ||||
\(611\) | 30.9545 | + | 30.9545i | 1.25228 | + | 1.25228i | ||||
\(612\) | −20.7846 | − | 12.0000i | −0.840168 | − | 0.485071i | ||||
\(613\) | −7.58846 | + | 7.58846i | −0.306495 | + | 0.306495i | −0.843548 | − | 0.537053i | \(-0.819537\pi\) |
0.537053 | + | 0.843548i | \(0.319537\pi\) | |||||||
\(614\) | −5.92820 | − | 10.2679i | −0.239243 | − | 0.414381i | ||||
\(615\) | −2.59808 | − | 9.69615i | −0.104765 | − | 0.390987i | ||||
\(616\) | 3.12436 | − | 1.80385i | 0.125884 | − | 0.0726791i | ||||
\(617\) | 8.08846 | − | 4.66987i | 0.325629 | − | 0.188002i | −0.328270 | − | 0.944584i | \(-0.606466\pi\) |
0.653899 | + | 0.756582i | \(0.273132\pi\) | |||||||
\(618\) | −1.31347 | − | 4.90192i | −0.0528354 | − | 0.197184i | ||||
\(619\) | 8.86603 | + | 33.0885i | 0.356356 | + | 1.32994i | 0.878770 | + | 0.477246i | \(0.158365\pi\) |
−0.522414 | + | 0.852692i | \(0.674969\pi\) | |||||||
\(620\) | −0.320508 | + | 1.19615i | −0.0128719 | + | 0.0480386i | ||||
\(621\) | 1.20577 | + | 2.08846i | 0.0483859 | + | 0.0838069i | ||||
\(622\) | 42.8827 | − | 11.4904i | 1.71944 | − | 0.460722i | ||||
\(623\) | −14.6077 | + | 25.3013i | −0.585245 | + | 1.01367i | ||||
\(624\) | 8.53590 | + | 31.8564i | 0.341709 | + | 1.27528i | ||||
\(625\) | 10.5263 | + | 18.2321i | 0.421051 | + | 0.729282i | ||||
\(626\) | −9.05256 | − | 9.05256i | −0.361813 | − | 0.361813i | ||||
\(627\) | −3.29423 | − | 1.90192i | −0.131559 | − | 0.0759555i | ||||
\(628\) | −1.26795 | + | 1.26795i | −0.0505967 | + | 0.0505967i | ||||
\(629\) | −30.9282 | + | 30.9282i | −1.23319 | + | 1.23319i | ||||
\(630\) | 2.70577 | + | 4.68653i | 0.107801 | + | 0.186716i | ||||
\(631\) | − | 32.2487i | − | 1.28380i | −0.766788 | − | 0.641900i | \(-0.778146\pi\) | ||
0.766788 | − | 0.641900i | \(-0.221854\pi\) | |||||||
\(632\) | 4.73205 | − | 1.26795i | 0.188231 | − | 0.0504363i | ||||
\(633\) | 3.40192 | + | 0.911543i | 0.135214 | + | 0.0362306i | ||||
\(634\) | 2.98076 | 0.118381 | ||||||||
\(635\) | −10.1962 | − | 2.73205i | −0.404622 | − | 0.108418i | ||||
\(636\) | −2.87564 | − | 10.7321i | −0.114027 | − | 0.425553i | ||||
\(637\) | 4.26795 | − | 1.14359i | 0.169102 | − | 0.0453108i | ||||
\(638\) | −0.633975 | − | 2.36603i | −0.0250993 | − | 0.0936718i | ||||
\(639\) | − | 32.7846i | − | 1.29694i | ||||||
\(640\) | −2.92820 | + | 5.07180i | −0.115747 | + | 0.200480i | ||||
\(641\) | 5.76795 | − | 9.99038i | 0.227820 | − | 0.394596i | −0.729342 | − | 0.684150i | \(-0.760173\pi\) |
0.957162 | + | 0.289553i | \(0.0935068\pi\) | |||||||
\(642\) | 19.7321 | + | 34.1769i | 0.778762 | + | 1.34886i | ||||
\(643\) | −0.277568 | + | 1.03590i | −0.0109462 | + | 0.0408518i | −0.971183 | − | 0.238335i | \(-0.923398\pi\) |
0.960237 | + | 0.279187i | \(0.0900650\pi\) | |||||||
\(644\) | −1.98076 | − | 1.14359i | −0.0780530 | − | 0.0450639i | ||||
\(645\) | −8.07180 | −0.317827 | ||||||||
\(646\) | −12.0000 | − | 20.7846i | −0.472134 | − | 0.817760i | ||||
\(647\) | 46.3923i | 1.82387i | 0.410335 | + | 0.911935i | \(0.365412\pi\) | ||||
−0.410335 | + | 0.911935i | \(0.634588\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.707107 | + | 0.707107i | ||||
\(649\) | 3.00000i | 0.117760i | ||||||||
\(650\) | 27.5885 | − | 15.9282i | 1.08211 | − | 0.624756i | ||||
\(651\) | −5.10512 | −0.200085 | ||||||||
\(652\) | 8.73205 | + | 32.5885i | 0.341974 | + | 1.27626i | ||||
\(653\) | 5.71539 | − | 21.3301i | 0.223661 | − | 0.834712i | −0.759276 | − | 0.650768i | \(-0.774447\pi\) |
0.982937 | − | 0.183944i | \(-0.0588865\pi\) | |||||||
\(654\) | 5.19615 | − | 3.00000i | 0.203186 | − | 0.117309i | ||||
\(655\) | −3.13397 | + | 5.42820i | −0.122455 | + | 0.212097i | ||||
\(656\) | 38.7846 | + | 22.3923i | 1.51428 | + | 0.874273i | ||||
\(657\) | − | 1.60770i | − | 0.0627222i | ||||||
\(658\) | −30.9545 | + | 8.29423i | −1.20673 | + | 0.323343i | ||||
\(659\) | 8.33013 | − | 2.23205i | 0.324496 | − | 0.0869484i | −0.0928939 | − | 0.995676i | \(-0.529612\pi\) |
0.417390 | + | 0.908728i | \(0.362945\pi\) | |||||||
\(660\) | 0.803848 | + | 0.464102i | 0.0312897 | + | 0.0180651i | ||||
\(661\) | −15.6962 | − | 4.20577i | −0.610510 | − | 0.163586i | −0.0596998 | − | 0.998216i | \(-0.519014\pi\) |
−0.550810 | + | 0.834631i | \(0.685681\pi\) | |||||||
\(662\) | 38.5885i | 1.49978i | ||||||||
\(663\) | 31.8564 | + | 8.53590i | 1.23720 | + | 0.331507i | ||||
\(664\) | −29.9090 | − | 17.2679i | −1.16069 | − | 0.670126i | ||||
\(665\) | 5.41154i | 0.209851i | ||||||||
\(666\) | 40.1769 | − | 23.1962i | 1.55682 | − | 0.898833i | ||||
\(667\) | −1.09808 | + | 1.09808i | −0.0425177 | + | 0.0425177i | ||||
\(668\) | −19.0718 | −0.737910 | ||||||||
\(669\) | 23.3827 | + | 13.5000i | 0.904027 | + | 0.521940i | ||||
\(670\) | −0.660254 | + | 0.660254i | −0.0255078 | + | 0.0255078i | ||||
\(671\) | 3.86603 | + | 6.69615i | 0.149246 | + | 0.258502i | ||||
\(672\) | −23.3205 | − | 6.24871i | −0.899608 | − | 0.241049i | ||||
\(673\) | 3.83975 | − | 6.65064i | 0.148011 | − | 0.256363i | −0.782481 | − | 0.622674i | \(-0.786046\pi\) |
0.930492 | + | 0.366311i | \(0.119379\pi\) | |||||||
\(674\) | 0.509619 | + | 1.90192i | 0.0196298 | + | 0.0732594i | ||||
\(675\) | 12.2942 | − | 21.2942i | 0.473205 | − | 0.819615i | ||||
\(676\) | −9.66025 | − | 16.7321i | −0.371548 | − | 0.643540i | ||||
\(677\) | −12.2321 | − | 45.6506i | −0.470116 | − | 1.75450i | −0.639345 | − | 0.768920i | \(-0.720795\pi\) |
0.169229 | − | 0.985577i | \(-0.445872\pi\) | |||||||
\(678\) | −13.0981 | + | 3.50962i | −0.503029 | + | 0.134786i | ||||
\(679\) | 2.13397 | − | 1.23205i | 0.0818944 | − | 0.0472818i | ||||
\(680\) | 2.92820 | + | 5.07180i | 0.112291 | + | 0.194495i | ||||
\(681\) | −8.00962 | − | 29.8923i | −0.306929 | − | 1.14548i | ||||
\(682\) | −0.758330 | + | 0.437822i | −0.0290380 | + | 0.0167651i | ||||
\(683\) | −5.39230 | + | 5.39230i | −0.206331 | + | 0.206331i | −0.802706 | − | 0.596375i | \(-0.796607\pi\) |
0.596375 | + | 0.802706i | \(0.296607\pi\) | |||||||
\(684\) | 6.58846 | + | 24.5885i | 0.251916 | + | 0.940163i | ||||
\(685\) | 6.09808 | + | 6.09808i | 0.232996 | + | 0.232996i | ||||
\(686\) | −7.15064 | + | 26.6865i | −0.273013 | + | 1.01890i | ||||
\(687\) | 4.37564 | − | 16.3301i | 0.166941 | − | 0.623033i | ||||
\(688\) | 25.4641 | − | 25.4641i | 0.970810 | − | 0.970810i | ||||
\(689\) | 7.63397 | + | 13.2224i | 0.290831 | + | 0.503735i | ||||
\(690\) | − | 0.588457i | − | 0.0224022i | ||||||
\(691\) | −18.5263 | + | 4.96410i | −0.704773 | + | 0.188843i | −0.593367 | − | 0.804932i | \(-0.702202\pi\) |
−0.111405 | + | 0.993775i | \(0.535535\pi\) | |||||||
\(692\) | −17.9282 | − | 4.80385i | −0.681528 | − | 0.182615i | ||||
\(693\) | −0.990381 | + | 3.69615i | −0.0376215 | + | 0.140405i | ||||
\(694\) | 24.7583 | + | 14.2942i | 0.939813 | + | 0.542601i | ||||
\(695\) | 2.00962 | + | 1.16025i | 0.0762292 | + | 0.0440109i | ||||
\(696\) | −8.19615 | + | 14.1962i | −0.310674 | + | 0.538104i | ||||
\(697\) | 38.7846 | − | 22.3923i | 1.46907 | − | 0.848169i | ||||
\(698\) | 11.6603 | 0.441347 | ||||||||
\(699\) | 39.7128 | 1.50208 | ||||||||
\(700\) | 23.3205i | 0.881432i | ||||||||
\(701\) | −21.0526 | − | 21.0526i | −0.795144 | − | 0.795144i | 0.187181 | − | 0.982325i | \(-0.440065\pi\) |
−0.982325 | + | 0.187181i | \(0.940065\pi\) | |||||||
\(702\) | −30.2942 | − | 17.4904i | −1.14338 | − | 0.660132i | ||||
\(703\) | 46.3923 | 1.74972 | ||||||||
\(704\) | −4.00000 | + | 1.07180i | −0.150756 | + | 0.0403949i | ||||
\(705\) | −5.83013 | − | 5.83013i | −0.219575 | − | 0.219575i | ||||
\(706\) | −30.4641 | + | 30.4641i | −1.14653 | + | 1.14653i | ||||
\(707\) | 1.23205 | − | 4.59808i | 0.0463360 | − | 0.172928i | ||||
\(708\) | 14.1962 | − | 14.1962i | 0.533524 | − | 0.533524i | ||||
\(709\) | 10.7487 | + | 40.1147i | 0.403676 | + | 1.50654i | 0.806484 | + | 0.591256i | \(0.201368\pi\) |
−0.402808 | + | 0.915285i | \(0.631966\pi\) | |||||||
\(710\) | −4.00000 | + | 6.92820i | −0.150117 | + | 0.260011i | ||||
\(711\) | −2.59808 | + | 4.50000i | −0.0974355 | + | 0.168763i | ||||
\(712\) | 23.7128 | − | 23.7128i | 0.888675 | − | 0.888675i | ||||
\(713\) | 0.480762 | + | 0.277568i | 0.0180047 | + | 0.0103950i | ||||
\(714\) | −17.0718 | + | 17.0718i | −0.638896 | + | 0.638896i | ||||
\(715\) | −1.23205 | − | 0.330127i | −0.0460761 | − | 0.0123461i | ||||
\(716\) | 5.80385 | + | 21.6603i | 0.216900 | + | 0.809482i | ||||
\(717\) | −16.7942 | + | 9.69615i | −0.627192 | + | 0.362109i | ||||
\(718\) | 5.51666 | − | 20.5885i | 0.205880 | − | 0.768354i | ||||
\(719\) | 23.3205 | 0.869708 | 0.434854 | − | 0.900501i | \(-0.356800\pi\) | ||||
0.434854 | + | 0.900501i | \(0.356800\pi\) | |||||||
\(720\) | −1.60770 | − | 6.00000i | −0.0599153 | − | 0.223607i | ||||
\(721\) | −5.10512 | −0.190125 | ||||||||
\(722\) | 0.366025 | − | 1.36603i | 0.0136221 | − | 0.0508382i | ||||
\(723\) | 18.6962 | + | 10.7942i | 0.695317 | + | 0.401442i | ||||
\(724\) | −11.6603 | + | 3.12436i | −0.433350 | + | 0.116116i | ||||
\(725\) | 15.2942 | + | 4.09808i | 0.568013 | + | 0.152199i | ||||
\(726\) | −6.80385 | − | 25.3923i | −0.252514 | − | 0.942397i | ||||
\(727\) | 9.06218 | + | 5.23205i | 0.336098 | + | 0.194046i | 0.658545 | − | 0.752541i | \(-0.271172\pi\) |
−0.322447 | + | 0.946587i | \(0.604506\pi\) | |||||||
\(728\) | 33.1769 | 1.22962 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −0.196152 | + | 0.339746i | −0.00725993 | + | 0.0125746i | ||||
\(731\) | −9.32051 | − | 34.7846i | −0.344731 | − | 1.28656i | ||||
\(732\) | 13.3923 | − | 49.9808i | 0.494994 | − | 1.84734i | ||||
\(733\) | −7.37564 | + | 27.5263i | −0.272426 | + | 1.01671i | 0.685121 | + | 0.728429i | \(0.259749\pi\) |
−0.957547 | + | 0.288277i | \(0.906917\pi\) | |||||||
\(734\) | 30.9090 | − | 30.9090i | 1.14087 | − | 1.14087i | ||||
\(735\) | −0.803848 | + | 0.215390i | −0.0296504 | + | 0.00794479i | ||||
\(736\) | 1.85641 | + | 1.85641i | 0.0684280 | + | 0.0684280i | ||||
\(737\) | −0.660254 | −0.0243208 | ||||||||
\(738\) | −45.8827 | + | 12.2942i | −1.68897 | + | 0.452557i | ||||
\(739\) | −29.7321 | − | 29.7321i | −1.09371 | − | 1.09371i | −0.995129 | − | 0.0985823i | \(-0.968569\pi\) |
−0.0985823 | − | 0.995129i | \(-0.531431\pi\) | |||||||
\(740\) | −11.3205 | −0.416150 | ||||||||
\(741\) | −17.4904 | − | 30.2942i | −0.642525 | − | 1.11289i | ||||
\(742\) | −11.1769 | −0.410317 | ||||||||
\(743\) | 25.1147 | − | 14.5000i | 0.921370 | − | 0.531953i | 0.0372984 | − | 0.999304i | \(-0.488125\pi\) |
0.884072 | + | 0.467351i | \(0.154791\pi\) | |||||||
\(744\) | 5.66025 | + | 1.51666i | 0.207515 | + | 0.0556035i | ||||
\(745\) | −6.82051 | − | 3.93782i | −0.249884 | − | 0.144271i | ||||
\(746\) | −17.0263 | − | 9.83013i | −0.623376 | − | 0.359907i | ||||
\(747\) | 35.3827 | − | 9.48076i | 1.29458 | − | 0.346883i | ||||
\(748\) | −1.07180 | + | 4.00000i | −0.0391888 | + | 0.146254i | ||||
\(749\) | 38.3468 | − | 10.2750i | 1.40116 | − | 0.375440i | ||||
\(750\) | −10.6865 | + | 6.16987i | −0.390217 | + | 0.225292i | ||||
\(751\) | 4.72243 | + | 8.17949i | 0.172324 | + | 0.298474i | 0.939232 | − | 0.343283i | \(-0.111539\pi\) |
−0.766908 | + | 0.641757i | \(0.778206\pi\) | |||||||
\(752\) | 36.7846 | 1.34140 | ||||||||
\(753\) | −12.8038 | − | 12.8038i | −0.466598 | − | 0.466598i | ||||
\(754\) | 5.83013 | − | 21.7583i | 0.212321 | − | 0.792392i | ||||
\(755\) | −2.56218 | − | 2.56218i | −0.0932472 | − | 0.0932472i | ||||
\(756\) | 22.1769 | − | 12.8038i | 0.806567 | − | 0.465671i | ||||
\(757\) | 8.46410 | − | 8.46410i | 0.307633 | − | 0.307633i | −0.536358 | − | 0.843991i | \(-0.680200\pi\) |
0.843991 | + | 0.536358i | \(0.180200\pi\) | |||||||
\(758\) | 27.0000 | − | 15.5885i | 0.980684 | − | 0.566198i | ||||
\(759\) | 0.294229 | − | 0.294229i | 0.0106798 | − | 0.0106798i | ||||
\(760\) | 1.60770 | − | 6.00000i | 0.0583172 | − | 0.217643i | ||||
\(761\) | −25.2846 | + | 14.5981i | −0.916566 | + | 0.529180i | −0.882538 | − | 0.470241i | \(-0.844167\pi\) |
−0.0340283 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(762\) | −12.9282 | + | 48.2487i | −0.468339 | + | 1.74787i | ||||
\(763\) | −1.56218 | − | 5.83013i | −0.0565546 | − | 0.211065i | ||||
\(764\) | 22.8564 | − | 13.1962i | 0.826916 | − | 0.477420i | ||||
\(765\) | −6.00000 | − | 1.60770i | −0.216930 | − | 0.0581263i | ||||
\(766\) | 9.02628 | + | 33.6865i | 0.326133 | + | 1.21714i | ||||
\(767\) | −13.7942 | + | 23.8923i | −0.498081 | + | 0.862701i | ||||
\(768\) | 24.0000 | + | 13.8564i | 0.866025 | + | 0.500000i | ||||
\(769\) | −3.50000 | − | 6.06218i | −0.126213 | − | 0.218608i | 0.795993 | − | 0.605305i | \(-0.206949\pi\) |
−0.922207 | + | 0.386698i | \(0.873616\pi\) | |||||||
\(770\) | 0.660254 | − | 0.660254i | 0.0237939 | − | 0.0237939i | ||||
\(771\) | −15.4808 | + | 8.93782i | −0.557526 | + | 0.321888i | ||||
\(772\) | − | 4.92820i | − | 0.177370i | ||||||
\(773\) | 7.58846 | − | 7.58846i | 0.272938 | − | 0.272938i | −0.557344 | − | 0.830282i | \(-0.688179\pi\) |
0.830282 | + | 0.557344i | \(0.188179\pi\) | |||||||
\(774\) | 38.1962i | 1.37293i | ||||||||
\(775\) | − | 5.66025i | − | 0.203322i | ||||||
\(776\) | −2.73205 | + | 0.732051i | −0.0980749 | + | 0.0262791i | ||||
\(777\) | −12.0788 | − | 45.0788i | −0.433326 | − | 1.61719i | ||||
\(778\) | − | 11.1244i | − | 0.398827i | ||||||
\(779\) | −45.8827 | − | 12.2942i | −1.64392 | − | 0.440486i | ||||
\(780\) | 4.26795 | + | 7.39230i | 0.152817 | + | 0.264687i | ||||
\(781\) | −5.46410 | + | 1.46410i | −0.195521 | + | 0.0523897i | ||||
\(782\) | 2.53590 | − | 0.679492i | 0.0906835 | − | 0.0242986i | ||||
\(783\) | −4.50000 | − | 16.7942i | −0.160817 | − | 0.600177i | ||||
\(784\) | 1.85641 | − | 3.21539i | 0.0663002 | − | 0.114835i | ||||
\(785\) | −0.232051 | + | 0.401924i | −0.00828225 | + | 0.0143453i | ||||
\(786\) | 25.6865 | + | 14.8301i | 0.916208 | + | 0.528973i | ||||
\(787\) | 9.06218 | − | 33.8205i | 0.323032 | − | 1.20557i | −0.593244 | − | 0.805023i | \(-0.702153\pi\) |
0.916276 | − | 0.400548i | \(-0.131180\pi\) | |||||||
\(788\) | 28.5885 | − | 7.66025i | 1.01842 | − | 0.272885i | ||||
\(789\) | 3.40192 | − | 5.89230i | 0.121112 | − | 0.209772i | ||||
\(790\) | 1.09808 | − | 0.633975i | 0.0390678 | − | 0.0225558i | ||||
\(791\) | 13.6410i | 0.485019i | ||||||||
\(792\) | 2.19615 | − | 3.80385i | 0.0780369 | − | 0.135164i | ||||
\(793\) | 71.1051i | 2.52502i | ||||||||
\(794\) | −21.0526 | − | 36.4641i | −0.747127 | − | 1.29406i | ||||
\(795\) | −1.43782 | − | 2.49038i | −0.0509943 | − | 0.0883247i | ||||
\(796\) | −5.85641 | + | 10.1436i | −0.207575 | + | 0.359530i | ||||
\(797\) | 0.284610 | − | 1.06218i | 0.0100814 | − | 0.0376243i | −0.960702 | − | 0.277582i | \(-0.910467\pi\) |
0.970783 | + | 0.239958i | \(0.0771336\pi\) | |||||||
\(798\) | 25.6077 | 0.906503 | ||||||||
\(799\) | 18.3923 | − | 31.8564i | 0.650673 | − | 1.12700i | ||||
\(800\) | 6.92820 | − | 25.8564i | 0.244949 | − | 0.914162i | ||||
\(801\) | 35.5692i | 1.25678i | ||||||||
\(802\) | 0.849365 | + | 3.16987i | 0.0299921 | + | 0.111932i | ||||
\(803\) | −0.267949 | + | 0.0717968i | −0.00945572 | + | 0.00253365i | ||||
\(804\) | 3.12436 | + | 3.12436i | 0.110188 | + | 0.110188i | ||||
\(805\) | −0.571797 | − | 0.153212i | −0.0201532 | − | 0.00540003i | ||||
\(806\) | −8.05256 | −0.283639 | ||||||||
\(807\) | 13.3923 | − | 13.3923i | 0.471431 | − | 0.471431i | ||||
\(808\) | −2.73205 | + | 4.73205i | −0.0961132 | + | 0.166473i | ||||
\(809\) | 32.6410i | 1.14760i | 0.818997 | + | 0.573799i | \(0.194531\pi\) | ||||
−0.818997 | + | 0.573799i | \(0.805469\pi\) | |||||||
\(810\) | 5.70577 | + | 3.29423i | 0.200480 | + | 0.115747i | ||||
\(811\) | −11.5359 | + | 11.5359i | −0.405080 | + | 0.405080i | −0.880019 | − | 0.474939i | \(-0.842470\pi\) |
0.474939 | + | 0.880019i | \(0.342470\pi\) | |||||||
\(812\) | 11.6603 | + | 11.6603i | 0.409195 | + | 0.409195i | ||||
\(813\) | 25.8564i | 0.906824i | ||||||||
\(814\) | −5.66025 | − | 5.66025i | −0.198392 | − | 0.198392i | ||||
\(815\) | 4.36603 | + | 7.56218i | 0.152935 | + | 0.264892i | ||||
\(816\) | 24.0000 | − | 13.8564i | 0.840168 | − | 0.485071i | ||||
\(817\) | −19.0981 | + | 33.0788i | −0.668157 | + | 1.15728i | ||||
\(818\) | −7.29423 | + | 1.95448i | −0.255037 | + | 0.0683369i | ||||
\(819\) | −24.8827 | + | 24.8827i | −0.869471 | + | 0.869471i | ||||
\(820\) | 11.1962 | + | 3.00000i | 0.390987 | + | 0.104765i | ||||
\(821\) | 5.01666 | + | 18.7224i | 0.175083 | + | 0.653417i | 0.996538 | + | 0.0831439i | \(0.0264961\pi\) |
−0.821455 | + | 0.570273i | \(0.806837\pi\) | |||||||
\(822\) | 28.8564 | − | 28.8564i | 1.00648 | − | 1.00648i | ||||
\(823\) | 6.65064 | − | 3.83975i | 0.231827 | − | 0.133845i | −0.379588 | − | 0.925156i | \(-0.623934\pi\) |
0.611414 | + | 0.791311i | \(0.290601\pi\) | |||||||
\(824\) | 5.66025 | + | 1.51666i | 0.197184 | + | 0.0528354i | ||||
\(825\) | −4.09808 | − | 1.09808i | −0.142677 | − | 0.0382301i | ||||
\(826\) | −10.0981 | − | 17.4904i | −0.351357 | − | 0.608568i | ||||
\(827\) | −10.6077 | + | 10.6077i | −0.368866 | + | 0.368866i | −0.867063 | − | 0.498198i | \(-0.833995\pi\) |
0.498198 | + | 0.867063i | \(0.333995\pi\) | |||||||
\(828\) | −2.78461 | −0.0967719 | ||||||||
\(829\) | −17.7321 | − | 17.7321i | −0.615860 | − | 0.615860i | 0.328607 | − | 0.944467i | \(-0.393421\pi\) |
−0.944467 | + | 0.328607i | \(0.893421\pi\) | |||||||
\(830\) | −8.63397 | − | 2.31347i | −0.299690 | − | 0.0803016i | ||||
\(831\) | −23.8923 | + | 6.40192i | −0.828815 | + | 0.222080i | ||||
\(832\) | −36.7846 | − | 9.85641i | −1.27528 | − | 0.341709i | ||||
\(833\) | −1.85641 | − | 3.21539i | −0.0643207 | − | 0.111407i | ||||
\(834\) | 5.49038 | − | 9.50962i | 0.190116 | − | 0.329291i | ||||
\(835\) | −4.76795 | + | 1.27757i | −0.165002 | + | 0.0442121i | ||||
\(836\) | 3.80385 | − | 2.19615i | 0.131559 | − | 0.0759555i | ||||
\(837\) | −5.38269 | + | 3.10770i | −0.186053 | + | 0.107418i | ||||
\(838\) | −1.43782 | + | 2.49038i | −0.0496687 | + | 0.0860288i | ||||
\(839\) | −29.2583 | − | 16.8923i | −1.01011 | − | 0.583187i | −0.0988859 | − | 0.995099i | \(-0.531528\pi\) |
−0.911224 | + | 0.411912i | \(0.864861\pi\) | |||||||
\(840\) | −6.24871 | −0.215601 | ||||||||
\(841\) | −15.4186 | + | 8.90192i | −0.531675 | + | 0.306963i | ||||
\(842\) | − | 15.8038i | − | 0.544637i | ||||||
\(843\) | 16.9641 | − | 29.3827i | 0.584275 | − | 1.01199i | ||||
\(844\) | −2.87564 | + | 2.87564i | −0.0989838 | + | 0.0989838i | ||||
\(845\) | −3.53590 | − | 3.53590i | −0.121639 | − | 0.121639i | ||||
\(846\) | −27.5885 | + | 27.5885i | −0.948511 | + | 0.948511i | ||||
\(847\) | −26.4449 | −0.908656 | ||||||||
\(848\) | 12.3923 | + | 3.32051i | 0.425553 | + | 0.114027i | ||||
\(849\) | −7.20577 | + | 26.8923i | −0.247301 | + | 0.922942i | ||||
\(850\) | −18.9282 | − | 18.9282i | −0.649232 | − | 0.649232i | ||||
\(851\) | −1.31347 | + | 4.90192i | −0.0450251 | + | 0.168036i | ||||
\(852\) | 32.7846 | + | 18.9282i | 1.12318 | + | 0.648470i | ||||
\(853\) | −2.69615 | − | 10.0622i | −0.0923145 | − | 0.344522i | 0.904284 | − | 0.426931i | \(-0.140405\pi\) |
−0.996599 | + | 0.0824088i | \(0.973739\pi\) | |||||||
\(854\) | −45.0788 | − | 26.0263i | −1.54257 | − | 0.890601i | ||||
\(855\) | 3.29423 | + | 5.70577i | 0.112660 | + | 0.195133i | ||||
\(856\) | −45.5692 | −1.55752 | ||||||||
\(857\) | −42.3564 | − | 24.4545i | −1.44687 | − | 0.835349i | −0.448574 | − | 0.893746i | \(-0.648068\pi\) |
−0.998293 | + | 0.0583966i | \(0.981401\pi\) | |||||||
\(858\) | −1.56218 | + | 5.83013i | −0.0533319 | + | 0.199037i | ||||
\(859\) | 16.7942 | + | 4.50000i | 0.573012 | + | 0.153538i | 0.533677 | − | 0.845688i | \(-0.320810\pi\) |
0.0393342 | + | 0.999226i | \(0.487476\pi\) | |||||||
\(860\) | 4.66025 | − | 8.07180i | 0.158913 | − | 0.275246i | ||||
\(861\) | 47.7846i | 1.62850i | ||||||||
\(862\) | 42.7846 | + | 11.4641i | 1.45725 | + | 0.390469i | ||||
\(863\) | −33.4641 | −1.13913 | −0.569566 | − | 0.821946i | \(-0.692889\pi\) | ||||
−0.569566 | + | 0.821946i | \(0.692889\pi\) | |||||||
\(864\) | −28.3923 | + | 7.60770i | −0.965926 | + | 0.258819i | ||||
\(865\) | −4.80385 | −0.163336 | ||||||||
\(866\) | 33.3205 | + | 8.92820i | 1.13228 | + | 0.303393i | ||||
\(867\) | 1.73205i | 0.0588235i | ||||||||
\(868\) | 2.94744 | − | 5.10512i | 0.100043 | − | 0.173279i | ||||
\(869\) | 0.866025 | + | 0.232051i | 0.0293779 | + | 0.00787178i | ||||
\(870\) | −1.09808 | + | 4.09808i | −0.0372283 | + | 0.138938i | ||||
\(871\) | −5.25833 | − | 3.03590i | −0.178172 | − | 0.102867i | ||||
\(872\) | 6.92820i | 0.234619i | ||||||||
\(873\) | 1.50000 | − | 2.59808i | 0.0507673 | − | 0.0879316i | ||||
\(874\) | −2.41154 | − | 1.39230i | −0.0815716 | − | 0.0470954i | ||||
\(875\) | 3.21281 | + | 11.9904i | 0.108613 | + | 0.405349i | ||||
\(876\) | 1.60770 | + | 0.928203i | 0.0543190 | + | 0.0313611i | ||||
\(877\) | −8.94486 | + | 33.3827i | −0.302047 | + | 1.12725i | 0.633411 | + | 0.773815i | \(0.281654\pi\) |
−0.935458 | + | 0.353438i | \(0.885013\pi\) | |||||||
\(878\) | −20.8564 | − | 20.8564i | −0.703870 | − | 0.703870i | ||||
\(879\) | −6.69615 | + | 24.9904i | −0.225856 | + | 0.842905i | ||||
\(880\) | −0.928203 | + | 0.535898i | −0.0312897 | + | 0.0180651i | ||||
\(881\) | −3.32051 | −0.111871 | −0.0559354 | − | 0.998434i | \(-0.517814\pi\) | ||||
−0.0559354 | + | 0.998434i | \(0.517814\pi\) | |||||||
\(882\) | 1.01924 | + | 3.80385i | 0.0343195 | + | 0.128082i | ||||
\(883\) | −3.00000 | − | 3.00000i | −0.100958 | − | 0.100958i | 0.654824 | − | 0.755782i | \(-0.272743\pi\) |
−0.755782 | + | 0.654824i | \(0.772743\pi\) | |||||||
\(884\) | −26.9282 | + | 26.9282i | −0.905693 | + | 0.905693i | ||||
\(885\) | 2.59808 | − | 4.50000i | 0.0873334 | − | 0.151266i | ||||
\(886\) | − | 23.6603i | − | 0.794882i | ||||||
\(887\) | −21.0622 | + | 12.1603i | −0.707199 | + | 0.408301i | −0.810023 | − | 0.586398i | \(-0.800545\pi\) |
0.102824 | + | 0.994700i | \(0.467212\pi\) | |||||||
\(888\) | 53.5692i | 1.79767i | ||||||||
\(889\) | 43.5167 | + | 25.1244i | 1.45950 | + | 0.842644i | ||||
\(890\) | 4.33975 | − | 7.51666i | 0.145469 | − | 0.251959i | ||||
\(891\) | 1.20577 | + | 4.50000i | 0.0403949 | + | 0.150756i | ||||
\(892\) | −27.0000 | + | 15.5885i | −0.904027 | + | 0.521940i | ||||
\(893\) | −37.6865 | + | 10.0981i | −1.26113 | + | 0.337919i | ||||
\(894\) | −18.6340 | + | 32.2750i | −0.623213 | + | 1.07944i | ||||
\(895\) | 2.90192 | + | 5.02628i | 0.0970006 | + | 0.168010i | ||||
\(896\) | 19.7128 | − | 19.7128i | 0.658559 | − | 0.658559i | ||||
\(897\) | 3.69615 | − | 0.990381i | 0.123411 | − | 0.0330679i | ||||
\(898\) | 0.928203 | + | 0.248711i | 0.0309745 | + | 0.00829960i | ||||
\(899\) | −2.83013 | − | 2.83013i | −0.0943900 | − | 0.0943900i | ||||
\(900\) | 14.1962 | + | 24.5885i | 0.473205 | + | 0.819615i | ||||
\(901\) | 9.07180 | − | 9.07180i | 0.302225 | − | 0.302225i | ||||
\(902\) | 4.09808 | + | 7.09808i | 0.136451 | + | 0.236340i | ||||
\(903\) | 37.1147 | + | 9.94486i | 1.23510 | + | 0.330944i | ||||
\(904\) | 4.05256 | − | 15.1244i | 0.134786 | − | 0.503029i | ||||
\(905\) | −2.70577 | + | 1.56218i | −0.0899429 | + | 0.0519285i | ||||
\(906\) | −12.1244 | + | 12.1244i | −0.402805 | + | 0.402805i | ||||
\(907\) | −3.06218 | − | 11.4282i | −0.101678 | − | 0.379467i | 0.896269 | − | 0.443510i | \(-0.146267\pi\) |
−0.997947 | + | 0.0640432i | \(0.979600\pi\) | |||||||
\(908\) | 34.5167 | + | 9.24871i | 1.14548 | + | 0.306929i | ||||
\(909\) | −1.50000 | − | 5.59808i | −0.0497519 | − | 0.185676i | ||||
\(910\) | 8.29423 | − | 2.22243i | 0.274951 | − | 0.0736729i | ||||
\(911\) | −5.86603 | + | 10.1603i | −0.194350 | + | 0.336624i | −0.946687 | − | 0.322154i | \(-0.895593\pi\) |
0.752337 | + | 0.658778i | \(0.228926\pi\) | |||||||
\(912\) | −28.3923 | − | 7.60770i | −0.940163 | − | 0.251916i | ||||
\(913\) | −3.16025 | − | 5.47372i | −0.104589 | − | 0.181154i | ||||
\(914\) | −21.9808 | − | 21.9808i | −0.727059 | − | 0.727059i | ||||
\(915\) | − | 13.3923i | − | 0.442736i | ||||||
\(916\) | 13.8038 | + | 13.8038i | 0.456092 | + | 0.456092i | ||||
\(917\) | 21.0981 | − | 21.0981i | 0.696720 | − | 0.696720i | ||||
\(918\) | −7.60770 | + | 28.3923i | −0.251091 | + | 0.937086i | ||||
\(919\) | − | 43.4641i | − | 1.43375i | −0.697203 | − | 0.716874i | \(-0.745572\pi\) | ||
0.697203 | − | 0.716874i | \(-0.254428\pi\) | |||||||
\(920\) | 0.588457 | + | 0.339746i | 0.0194009 | + | 0.0112011i | ||||
\(921\) | −10.2679 | + | 10.2679i | −0.338340 | + | 0.338340i | ||||
\(922\) | 3.26795 | 0.107624 | ||||||||
\(923\) | −50.2487 | − | 13.4641i | −1.65396 | − | 0.443176i | ||||
\(924\) | −3.12436 | − | 3.12436i | −0.102784 | − | 0.102784i | ||||
\(925\) | 49.9808 | − | 13.3923i | 1.64336 | − | 0.440336i | ||||
\(926\) | 2.43782 | + | 9.09808i | 0.0801118 | + | 0.298981i | ||||
\(927\) | −5.38269 | + | 3.10770i | −0.176791 | + | 0.102070i | ||||
\(928\) | −9.46410 | − | 16.3923i | −0.310674 | − | 0.538104i | ||||
\(929\) | −18.3564 | + | 31.7942i | −0.602254 | + | 1.04313i | 0.390225 | + | 0.920720i | \(0.372397\pi\) |
−0.992479 | + | 0.122415i | \(0.960936\pi\) | |||||||
\(930\) | 1.51666 | 0.0497333 | ||||||||
\(931\) | −1.01924 | + | 3.80385i | −0.0334042 | + | 0.124666i | ||||
\(932\) | −22.9282 | + | 39.7128i | −0.751038 | + | 1.30084i | ||||
\(933\) | −27.1865 | − | 47.0885i | −0.890047 | − | 1.54161i | ||||
\(934\) | −19.7846 | − | 34.2679i | −0.647372 | − | 1.12128i | ||||
\(935\) | 1.07180i | 0.0350515i | ||||||||
\(936\) | 34.9808 | − | 20.1962i | 1.14338 | − | 0.660132i | ||||
\(937\) | 32.9282i | 1.07572i | 0.843035 | + | 0.537859i | \(0.180767\pi\) | ||||
−0.843035 | + | 0.537859i | \(0.819233\pi\) | |||||||
\(938\) | 3.84936 | − | 2.22243i | 0.125686 | − | 0.0725650i | ||||
\(939\) | −7.83975 | + | 13.5788i | −0.255840 | + | 0.443129i | ||||
\(940\) | 9.19615 | − | 2.46410i | 0.299945 | − | 0.0803701i | ||||
\(941\) | −2.91154 | + | 10.8660i | −0.0949136 | + | 0.354222i | −0.997006 | − | 0.0773199i | \(-0.975364\pi\) |
0.902093 | + | 0.431542i | \(0.142030\pi\) | |||||||
\(942\) | 1.90192 | + | 1.09808i | 0.0619680 | + | 0.0357773i | ||||
\(943\) | 2.59808 | − | 4.50000i | 0.0846050 | − | 0.146540i | ||||
\(944\) | 6.00000 | + | 22.3923i | 0.195283 | + | 0.728807i | ||||
\(945\) | 4.68653 | − | 4.68653i | 0.152453 | − | 0.152453i | ||||
\(946\) | 6.36603 | − | 1.70577i | 0.206977 | − | 0.0554594i | ||||
\(947\) | −14.9904 | + | 4.01666i | −0.487122 | + | 0.130524i | −0.494017 | − | 0.869452i | \(-0.664472\pi\) |
0.00689497 | + | 0.999976i | \(0.497805\pi\) | |||||||
\(948\) | −3.00000 | − | 5.19615i | −0.0974355 | − | 0.168763i | ||||
\(949\) | −2.46410 | − | 0.660254i | −0.0799881 | − | 0.0214328i | ||||
\(950\) | 28.3923i | 0.921168i | ||||||||
\(951\) | −0.944864 | − | 3.52628i | −0.0306393 | − | 0.114347i | ||||
\(952\) | −7.21539 | − | 26.9282i | −0.233852 | − | 0.872748i | ||||
\(953\) | − | 39.4641i | − | 1.27837i | −0.769054 | − | 0.639184i | \(-0.779272\pi\) | ||
0.769054 | − | 0.639184i | \(-0.220728\pi\) | |||||||
\(954\) | −11.7846 | + | 6.80385i | −0.381541 | + | 0.220283i | ||||
\(955\) | 4.83013 | − | 4.83013i | 0.156299 | − | 0.156299i | ||||
\(956\) | − | 22.3923i | − | 0.724219i | ||||||
\(957\) | −2.59808 | + | 1.50000i | −0.0839839 | + | 0.0484881i | ||||
\(958\) | 1.33975 | − | 1.33975i | 0.0432852 | − | 0.0432852i | ||||
\(959\) | −20.5263 | − | 35.5526i | −0.662828 | − | 1.14805i | ||||
\(960\) | 6.92820 | + | 1.85641i | 0.223607 | + | 0.0599153i | ||||
\(961\) | 14.7846 | − | 25.6077i | 0.476923 | − | 0.826055i | ||||
\(962\) | −19.0526 | − | 71.1051i | −0.614279 | − | 2.29252i | ||||
\(963\) | 34.1769 | − | 34.1769i | 1.10134 | − | 1.10134i | ||||
\(964\) | −21.5885 | + | 12.4641i | −0.695317 | + | 0.401442i | ||||
\(965\) | −0.330127 | − | 1.23205i | −0.0106272 | − | 0.0396611i | ||||
\(966\) | −0.725009 | + | 2.70577i | −0.0233268 | + | 0.0870568i | ||||
\(967\) | 14.9378 | − | 8.62436i | 0.480368 | − | 0.277341i | −0.240202 | − | 0.970723i | \(-0.577214\pi\) |
0.720570 | + | 0.693382i | \(0.243880\pi\) | |||||||
\(968\) | 29.3205 | + | 7.85641i | 0.942397 | + | 0.252514i | ||||
\(969\) | −20.7846 | + | 20.7846i | −0.667698 | + | 0.667698i | ||||
\(970\) | −0.633975 | + | 0.366025i | −0.0203557 | + | 0.0117524i | ||||
\(971\) | 27.9808 | − | 27.9808i | 0.897945 | − | 0.897945i | −0.0973088 | − | 0.995254i | \(-0.531023\pi\) |
0.995254 | + | 0.0973088i | \(0.0310235\pi\) | |||||||
\(972\) | 15.5885 | − | 27.0000i | 0.500000 | − | 0.866025i | ||||
\(973\) | −7.81089 | − | 7.81089i | −0.250406 | − | 0.250406i | ||||
\(974\) | −12.7321 | + | 47.5167i | −0.407961 | + | 1.52253i | ||||
\(975\) | −27.5885 | − | 27.5885i | −0.883538 | − | 0.883538i | ||||
\(976\) | 42.2487 | + | 42.2487i | 1.35235 | + | 1.35235i | ||||
\(977\) | 17.2846 | + | 29.9378i | 0.552984 | + | 0.957796i | 0.998057 | + | 0.0623018i | \(0.0198441\pi\) |
−0.445074 | + | 0.895494i | \(0.646823\pi\) | |||||||
\(978\) | 35.7846 | − | 20.6603i | 1.14427 | − | 0.660642i | ||||
\(979\) | 5.92820 | − | 1.58846i | 0.189466 | − | 0.0507673i | ||||
\(980\) | 0.248711 | − | 0.928203i | 0.00794479 | − | 0.0296504i | ||||
\(981\) | −5.19615 | − | 5.19615i | −0.165900 | − | 0.165900i | ||||
\(982\) | −2.36603 | − | 1.36603i | −0.0755029 | − | 0.0435916i | ||||
\(983\) | 40.9186 | + | 23.6244i | 1.30510 | + | 0.753500i | 0.981274 | − | 0.192617i | \(-0.0616974\pi\) |
0.323826 | + | 0.946117i | \(0.395031\pi\) | |||||||
\(984\) | 14.1962 | − | 52.9808i | 0.452557 | − | 1.68897i | ||||
\(985\) | 6.63397 | − | 3.83013i | 0.211376 | − | 0.122038i | ||||
\(986\) | −18.9282 | −0.602797 | ||||||||
\(987\) | 19.6244 | + | 33.9904i | 0.624650 | + | 1.08193i | ||||
\(988\) | 40.3923 | 1.28505 | ||||||||
\(989\) | −2.95448 | − | 2.95448i | −0.0939471 | − | 0.0939471i | ||||
\(990\) | 0.294229 | − | 1.09808i | 0.00935120 | − | 0.0348992i | ||||
\(991\) | −23.6077 | −0.749923 | −0.374962 | − | 0.927040i | \(-0.622344\pi\) | ||||
−0.374962 | + | 0.927040i | \(0.622344\pi\) | |||||||
\(992\) | −4.78461 | + | 4.78461i | −0.151912 | + | 0.151912i | ||||
\(993\) | 45.6506 | − | 12.2321i | 1.44868 | − | 0.388172i | ||||
\(994\) | 26.9282 | − | 26.9282i | 0.854111 | − | 0.854111i | ||||
\(995\) | −0.784610 | + | 2.92820i | −0.0248738 | + | 0.0928303i | ||||
\(996\) | −10.9474 | + | 40.8564i | −0.346883 | + | 1.29458i | ||||
\(997\) | −2.96410 | − | 11.0622i | −0.0938740 | − | 0.350343i | 0.902972 | − | 0.429699i | \(-0.141380\pi\) |
−0.996846 | + | 0.0793561i | \(0.974714\pi\) | |||||||
\(998\) | 1.83013 | − | 3.16987i | 0.0579317 | − | 0.100341i | ||||
\(999\) | −40.1769 | − | 40.1769i | −1.27114 | − | 1.27114i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.2.x.d.61.1 | yes | 4 | |
3.2 | odd | 2 | 432.2.y.a.397.1 | 4 | |||
4.3 | odd | 2 | 576.2.bb.b.529.1 | 4 | |||
9.4 | even | 3 | 144.2.x.a.13.1 | ✓ | 4 | ||
9.5 | odd | 6 | 432.2.y.d.253.1 | 4 | |||
12.11 | even | 2 | 1728.2.bc.b.721.1 | 4 | |||
16.5 | even | 4 | 144.2.x.a.133.1 | yes | 4 | ||
16.11 | odd | 4 | 576.2.bb.a.241.1 | 4 | |||
36.23 | even | 6 | 1728.2.bc.c.145.1 | 4 | |||
36.31 | odd | 6 | 576.2.bb.a.337.1 | 4 | |||
48.5 | odd | 4 | 432.2.y.d.181.1 | 4 | |||
48.11 | even | 4 | 1728.2.bc.c.1585.1 | 4 | |||
144.5 | odd | 12 | 432.2.y.a.37.1 | 4 | |||
144.59 | even | 12 | 1728.2.bc.b.1009.1 | 4 | |||
144.85 | even | 12 | inner | 144.2.x.d.85.1 | yes | 4 | |
144.139 | odd | 12 | 576.2.bb.b.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.a.13.1 | ✓ | 4 | 9.4 | even | 3 | ||
144.2.x.a.133.1 | yes | 4 | 16.5 | even | 4 | ||
144.2.x.d.61.1 | yes | 4 | 1.1 | even | 1 | trivial | |
144.2.x.d.85.1 | yes | 4 | 144.85 | even | 12 | inner | |
432.2.y.a.37.1 | 4 | 144.5 | odd | 12 | |||
432.2.y.a.397.1 | 4 | 3.2 | odd | 2 | |||
432.2.y.d.181.1 | 4 | 48.5 | odd | 4 | |||
432.2.y.d.253.1 | 4 | 9.5 | odd | 6 | |||
576.2.bb.a.241.1 | 4 | 16.11 | odd | 4 | |||
576.2.bb.a.337.1 | 4 | 36.31 | odd | 6 | |||
576.2.bb.b.49.1 | 4 | 144.139 | odd | 12 | |||
576.2.bb.b.529.1 | 4 | 4.3 | odd | 2 | |||
1728.2.bc.b.721.1 | 4 | 12.11 | even | 2 | |||
1728.2.bc.b.1009.1 | 4 | 144.59 | even | 12 | |||
1728.2.bc.c.145.1 | 4 | 36.23 | even | 6 | |||
1728.2.bc.c.1585.1 | 4 | 48.11 | even | 4 |