Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(76,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.i (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.6 | ||
Root | \(-1.26217 - 1.18614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.76 |
Dual form | 1155.2.i.a.76.3 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.792287i | 0.560232i | 0.959966 | + | 0.280116i | \(0.0903729\pi\) | ||||
−0.959966 | + | 0.280116i | \(0.909627\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.37228 | 0.686141 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −0.792287 | −0.323450 | ||||||||
\(7\) | −0.792287 | − | 2.52434i | −0.299456 | − | 0.954110i | ||||
\(8\) | 2.67181i | 0.944629i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.792287 | 0.250543 | ||||||||
\(11\) | − | 3.31662i | − | 1.00000i | ||||||
\(12\) | 1.37228i | 0.396143i | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 2.00000 | − | 0.627719i | 0.534522 | − | 0.167765i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0.627719 | 0.156930 | ||||||||
\(17\) | 4.10891 | 0.996557 | 0.498279 | − | 0.867017i | \(-0.333966\pi\) | ||||
0.498279 | + | 0.867017i | \(0.333966\pi\) | |||||||
\(18\) | − | 0.792287i | − | 0.186744i | ||||||
\(19\) | −4.40387 | −1.01032 | −0.505158 | − | 0.863027i | \(-0.668566\pi\) | ||||
−0.505158 | + | 0.863027i | \(0.668566\pi\) | |||||||
\(20\) | − | 1.37228i | − | 0.306851i | ||||||
\(21\) | 2.52434 | − | 0.792287i | 0.550856 | − | 0.172891i | ||||
\(22\) | 2.62772 | 0.560232 | ||||||||
\(23\) | 9.11684 | 1.90099 | 0.950497 | − | 0.310735i | \(-0.100575\pi\) | ||||
0.950497 | + | 0.310735i | \(0.100575\pi\) | |||||||
\(24\) | −2.67181 | −0.545382 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.08724 | − | 3.46410i | −0.205469 | − | 0.654654i | ||||
\(29\) | − | 5.98844i | − | 1.11203i | −0.831174 | − | 0.556013i | \(-0.812331\pi\) | ||
0.831174 | − | 0.556013i | \(-0.187669\pi\) | |||||||
\(30\) | 0.792287i | 0.144651i | ||||||||
\(31\) | 6.74456i | 1.21136i | 0.795709 | + | 0.605680i | \(0.207099\pi\) | ||||
−0.795709 | + | 0.605680i | \(0.792901\pi\) | |||||||
\(32\) | 5.84096i | 1.03255i | ||||||||
\(33\) | 3.31662 | 0.577350 | ||||||||
\(34\) | 3.25544i | 0.558303i | ||||||||
\(35\) | −2.52434 | + | 0.792287i | −0.426691 | + | 0.133921i | ||||
\(36\) | −1.37228 | −0.228714 | ||||||||
\(37\) | 10.7446 | 1.76640 | 0.883198 | − | 0.469001i | \(-0.155386\pi\) | ||||
0.883198 | + | 0.469001i | \(0.155386\pi\) | |||||||
\(38\) | − | 3.48913i | − | 0.566011i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.67181 | 0.422451 | ||||||||
\(41\) | 11.6819 | 1.82441 | 0.912205 | − | 0.409734i | \(-0.134378\pi\) | ||||
0.912205 | + | 0.409734i | \(0.134378\pi\) | |||||||
\(42\) | 0.627719 | + | 2.00000i | 0.0968591 | + | 0.308607i | ||||
\(43\) | − | 4.10891i | − | 0.626603i | −0.949654 | − | 0.313302i | \(-0.898565\pi\) | ||
0.949654 | − | 0.313302i | \(-0.101435\pi\) | |||||||
\(44\) | − | 4.55134i | − | 0.686141i | ||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 7.22316i | 1.06500i | ||||||||
\(47\) | − | 12.7446i | − | 1.85899i | −0.368840 | − | 0.929493i | \(-0.620245\pi\) | ||
0.368840 | − | 0.929493i | \(-0.379755\pi\) | |||||||
\(48\) | 0.627719i | 0.0906034i | ||||||||
\(49\) | −5.74456 | + | 4.00000i | −0.820652 | + | 0.571429i | ||||
\(50\) | − | 0.792287i | − | 0.112046i | ||||||
\(51\) | 4.10891i | 0.575363i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.62772 | −0.223584 | −0.111792 | − | 0.993732i | \(-0.535659\pi\) | ||||
−0.111792 | + | 0.993732i | \(0.535659\pi\) | |||||||
\(54\) | 0.792287 | 0.107817 | ||||||||
\(55\) | −3.31662 | −0.447214 | ||||||||
\(56\) | 6.74456 | − | 2.11684i | 0.901280 | − | 0.282875i | ||||
\(57\) | − | 4.40387i | − | 0.583306i | ||||||
\(58\) | 4.74456 | 0.622992 | ||||||||
\(59\) | − | 1.62772i | − | 0.211911i | −0.994371 | − | 0.105955i | \(-0.966210\pi\) | ||
0.994371 | − | 0.105955i | \(-0.0337901\pi\) | |||||||
\(60\) | 1.37228 | 0.177161 | ||||||||
\(61\) | −11.0371 | −1.41316 | −0.706579 | − | 0.707634i | \(-0.749762\pi\) | ||||
−0.706579 | + | 0.707634i | \(0.749762\pi\) | |||||||
\(62\) | −5.34363 | −0.678642 | ||||||||
\(63\) | 0.792287 | + | 2.52434i | 0.0998188 | + | 0.318037i | ||||
\(64\) | −3.37228 | −0.421535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.62772i | 0.323450i | ||||||||
\(67\) | −4.74456 | −0.579641 | −0.289820 | − | 0.957081i | \(-0.593596\pi\) | ||||
−0.289820 | + | 0.957081i | \(0.593596\pi\) | |||||||
\(68\) | 5.63858 | 0.683779 | ||||||||
\(69\) | 9.11684i | 1.09754i | ||||||||
\(70\) | −0.627719 | − | 2.00000i | −0.0750267 | − | 0.239046i | ||||
\(71\) | 3.25544 | 0.386349 | 0.193175 | − | 0.981164i | \(-0.438122\pi\) | ||||
0.193175 | + | 0.981164i | \(0.438122\pi\) | |||||||
\(72\) | − | 2.67181i | − | 0.314876i | ||||||
\(73\) | 6.92820 | 0.810885 | 0.405442 | − | 0.914121i | \(-0.367117\pi\) | ||||
0.405442 | + | 0.914121i | \(0.367117\pi\) | |||||||
\(74\) | 8.51278i | 0.989590i | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | −6.04334 | −0.693219 | ||||||||
\(77\) | −8.37228 | + | 2.62772i | −0.954110 | + | 0.299456i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.294954i | 0.0331849i | 0.999862 | + | 0.0165924i | \(0.00528178\pi\) | ||||
−0.999862 | + | 0.0165924i | \(0.994718\pi\) | |||||||
\(80\) | − | 0.627719i | − | 0.0701811i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.25544i | 1.02209i | ||||||||
\(83\) | −9.45254 | −1.03755 | −0.518776 | − | 0.854910i | \(-0.673612\pi\) | ||||
−0.518776 | + | 0.854910i | \(0.673612\pi\) | |||||||
\(84\) | 3.46410 | − | 1.08724i | 0.377964 | − | 0.118628i | ||||
\(85\) | − | 4.10891i | − | 0.445674i | ||||||
\(86\) | 3.25544 | 0.351043 | ||||||||
\(87\) | 5.98844 | 0.642028 | ||||||||
\(88\) | 8.86141 | 0.944629 | ||||||||
\(89\) | 8.37228i | 0.887460i | 0.896161 | + | 0.443730i | \(0.146345\pi\) | ||||
−0.896161 | + | 0.443730i | \(0.853655\pi\) | |||||||
\(90\) | −0.792287 | −0.0835144 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.5109 | 1.30435 | ||||||||
\(93\) | −6.74456 | −0.699379 | ||||||||
\(94\) | 10.0974 | 1.04146 | ||||||||
\(95\) | 4.40387i | 0.451827i | ||||||||
\(96\) | −5.84096 | −0.596141 | ||||||||
\(97\) | − | 8.37228i | − | 0.850076i | −0.905175 | − | 0.425038i | \(-0.860261\pi\) | ||
0.905175 | − | 0.425038i | \(-0.139739\pi\) | |||||||
\(98\) | −3.16915 | − | 4.55134i | −0.320132 | − | 0.459755i | ||||
\(99\) | 3.31662i | 0.333333i | ||||||||
\(100\) | −1.37228 | −0.137228 | ||||||||
\(101\) | −10.3923 | −1.03407 | −0.517036 | − | 0.855963i | \(-0.672965\pi\) | ||||
−0.517036 | + | 0.855963i | \(0.672965\pi\) | |||||||
\(102\) | −3.25544 | −0.322336 | ||||||||
\(103\) | 11.1168i | 1.09538i | 0.836683 | + | 0.547688i | \(0.184492\pi\) | ||||
−0.836683 | + | 0.547688i | \(0.815508\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.792287 | − | 2.52434i | −0.0773193 | − | 0.246350i | ||||
\(106\) | − | 1.28962i | − | 0.125259i | ||||||
\(107\) | 4.75372i | 0.459560i | 0.973243 | + | 0.229780i | \(0.0738006\pi\) | ||||
−0.973243 | + | 0.229780i | \(0.926199\pi\) | |||||||
\(108\) | − | 1.37228i | − | 0.132048i | ||||||
\(109\) | 1.87953i | 0.180026i | 0.995941 | + | 0.0900130i | \(0.0286909\pi\) | ||||
−0.995941 | + | 0.0900130i | \(0.971309\pi\) | |||||||
\(110\) | − | 2.62772i | − | 0.250543i | ||||||
\(111\) | 10.7446i | 1.01983i | ||||||||
\(112\) | −0.497333 | − | 1.58457i | −0.0469936 | − | 0.149728i | ||||
\(113\) | −1.62772 | −0.153123 | −0.0765614 | − | 0.997065i | \(-0.524394\pi\) | ||||
−0.0765614 | + | 0.997065i | \(0.524394\pi\) | |||||||
\(114\) | 3.48913 | 0.326787 | ||||||||
\(115\) | − | 9.11684i | − | 0.850150i | ||||||
\(116\) | − | 8.21782i | − | 0.763006i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.28962 | 0.118719 | ||||||||
\(119\) | −3.25544 | − | 10.3723i | −0.298425 | − | 0.950825i | ||||
\(120\) | 2.67181i | 0.243902i | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 8.74456i | − | 0.791696i | ||||||
\(123\) | 11.6819i | 1.05332i | ||||||||
\(124\) | 9.25544i | 0.831163i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −2.00000 | + | 0.627719i | −0.178174 | + | 0.0559216i | ||||
\(127\) | 9.74749i | 0.864950i | 0.901646 | + | 0.432475i | \(0.142360\pi\) | ||||
−0.901646 | + | 0.432475i | \(0.857640\pi\) | |||||||
\(128\) | 9.01011i | 0.796389i | ||||||||
\(129\) | 4.10891 | 0.361770 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.28962 | −0.112675 | −0.0563373 | − | 0.998412i | \(-0.517942\pi\) | ||||
−0.0563373 | + | 0.998412i | \(0.517942\pi\) | |||||||
\(132\) | 4.55134 | 0.396143 | ||||||||
\(133\) | 3.48913 | + | 11.1168i | 0.302546 | + | 0.963953i | ||||
\(134\) | − | 3.75906i | − | 0.324733i | ||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 10.9783i | 0.941377i | ||||||||
\(137\) | 12.7446 | 1.08884 | 0.544421 | − | 0.838812i | \(-0.316750\pi\) | ||||
0.544421 | + | 0.838812i | \(0.316750\pi\) | |||||||
\(138\) | −7.22316 | −0.614876 | ||||||||
\(139\) | 3.46410 | 0.293821 | 0.146911 | − | 0.989150i | \(-0.453067\pi\) | ||||
0.146911 | + | 0.989150i | \(0.453067\pi\) | |||||||
\(140\) | −3.46410 | + | 1.08724i | −0.292770 | + | 0.0918886i | ||||
\(141\) | 12.7446 | 1.07329 | ||||||||
\(142\) | 2.57924i | 0.216445i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.627719 | −0.0523099 | ||||||||
\(145\) | −5.98844 | −0.497313 | ||||||||
\(146\) | 5.48913i | 0.454283i | ||||||||
\(147\) | −4.00000 | − | 5.74456i | −0.329914 | − | 0.473804i | ||||
\(148\) | 14.7446 | 1.21200 | ||||||||
\(149\) | 13.8564i | 1.13516i | 0.823318 | + | 0.567581i | \(0.192120\pi\) | ||||
−0.823318 | + | 0.567581i | \(0.807880\pi\) | |||||||
\(150\) | 0.792287 | 0.0646900 | ||||||||
\(151\) | 8.51278i | 0.692760i | 0.938094 | + | 0.346380i | \(0.112589\pi\) | ||||
−0.938094 | + | 0.346380i | \(0.887411\pi\) | |||||||
\(152\) | − | 11.7663i | − | 0.954374i | ||||||
\(153\) | −4.10891 | −0.332186 | ||||||||
\(154\) | −2.08191 | − | 6.63325i | −0.167765 | − | 0.534522i | ||||
\(155\) | 6.74456 | 0.541736 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.88316i | − | 0.230101i | −0.993360 | − | 0.115050i | \(-0.963297\pi\) | ||
0.993360 | − | 0.115050i | \(-0.0367030\pi\) | |||||||
\(158\) | −0.233688 | −0.0185912 | ||||||||
\(159\) | − | 1.62772i | − | 0.129086i | ||||||
\(160\) | 5.84096 | 0.461769 | ||||||||
\(161\) | −7.22316 | − | 23.0140i | −0.569265 | − | 1.81376i | ||||
\(162\) | 0.792287i | 0.0622479i | ||||||||
\(163\) | −18.2337 | −1.42817 | −0.714086 | − | 0.700058i | \(-0.753158\pi\) | ||||
−0.714086 | + | 0.700058i | \(0.753158\pi\) | |||||||
\(164\) | 16.0309 | 1.25180 | ||||||||
\(165\) | − | 3.31662i | − | 0.258199i | ||||||
\(166\) | − | 7.48913i | − | 0.581269i | ||||||
\(167\) | 2.87419 | 0.222412 | 0.111206 | − | 0.993797i | \(-0.464529\pi\) | ||||
0.111206 | + | 0.993797i | \(0.464529\pi\) | |||||||
\(168\) | 2.11684 | + | 6.74456i | 0.163318 | + | 0.520354i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 3.25544 | 0.249681 | ||||||||
\(171\) | 4.40387 | 0.336772 | ||||||||
\(172\) | − | 5.63858i | − | 0.429938i | ||||||
\(173\) | 6.92820 | 0.526742 | 0.263371 | − | 0.964695i | \(-0.415166\pi\) | ||||
0.263371 | + | 0.964695i | \(0.415166\pi\) | |||||||
\(174\) | 4.74456i | 0.359684i | ||||||||
\(175\) | 0.792287 | + | 2.52434i | 0.0598913 | + | 0.190822i | ||||
\(176\) | − | 2.08191i | − | 0.156930i | ||||||
\(177\) | 1.62772 | 0.122347 | ||||||||
\(178\) | −6.63325 | −0.497183 | ||||||||
\(179\) | −21.4891 | −1.60617 | −0.803086 | − | 0.595863i | \(-0.796810\pi\) | ||||
−0.803086 | + | 0.595863i | \(0.796810\pi\) | |||||||
\(180\) | 1.37228i | 0.102284i | ||||||||
\(181\) | − | 16.7446i | − | 1.24461i | −0.782773 | − | 0.622307i | \(-0.786196\pi\) | ||
0.782773 | − | 0.622307i | \(-0.213804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.0371i | − | 0.815887i | ||||||
\(184\) | 24.3585i | 1.79573i | ||||||||
\(185\) | − | 10.7446i | − | 0.789956i | ||||||
\(186\) | − | 5.34363i | − | 0.391814i | ||||||
\(187\) | − | 13.6277i | − | 0.996557i | ||||||
\(188\) | − | 17.4891i | − | 1.27553i | ||||||
\(189\) | −2.52434 | + | 0.792287i | −0.183619 | + | 0.0576304i | ||||
\(190\) | −3.48913 | −0.253128 | ||||||||
\(191\) | −8.74456 | −0.632734 | −0.316367 | − | 0.948637i | \(-0.602463\pi\) | ||||
−0.316367 | + | 0.948637i | \(0.602463\pi\) | |||||||
\(192\) | − | 3.37228i | − | 0.243373i | ||||||
\(193\) | 4.75372i | 0.342180i | 0.985255 | + | 0.171090i | \(0.0547290\pi\) | ||||
−0.985255 | + | 0.171090i | \(0.945271\pi\) | |||||||
\(194\) | 6.63325 | 0.476240 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.88316 | + | 5.48913i | −0.563083 | + | 0.392080i | ||||
\(197\) | 3.16915i | 0.225792i | 0.993607 | + | 0.112896i | \(0.0360128\pi\) | ||||
−0.993607 | + | 0.112896i | \(0.963987\pi\) | |||||||
\(198\) | −2.62772 | −0.186744 | ||||||||
\(199\) | 6.74456i | 0.478109i | 0.971006 | + | 0.239055i | \(0.0768375\pi\) | ||||
−0.971006 | + | 0.239055i | \(0.923162\pi\) | |||||||
\(200\) | − | 2.67181i | − | 0.188926i | ||||||
\(201\) | − | 4.74456i | − | 0.334656i | ||||||
\(202\) | − | 8.23369i | − | 0.579320i | ||||||
\(203\) | −15.1168 | + | 4.74456i | −1.06099 | + | 0.333003i | ||||
\(204\) | 5.63858i | 0.394780i | ||||||||
\(205\) | − | 11.6819i | − | 0.815901i | ||||||
\(206\) | −8.80773 | −0.613664 | ||||||||
\(207\) | −9.11684 | −0.633664 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.6060i | 1.01032i | ||||||||
\(210\) | 2.00000 | − | 0.627719i | 0.138013 | − | 0.0433167i | ||||
\(211\) | − | 3.46410i | − | 0.238479i | −0.992866 | − | 0.119239i | \(-0.961954\pi\) | ||
0.992866 | − | 0.119239i | \(-0.0380456\pi\) | |||||||
\(212\) | −2.23369 | −0.153410 | ||||||||
\(213\) | 3.25544i | 0.223059i | ||||||||
\(214\) | −3.76631 | −0.257460 | ||||||||
\(215\) | −4.10891 | −0.280225 | ||||||||
\(216\) | 2.67181 | 0.181794 | ||||||||
\(217\) | 17.0256 | − | 5.34363i | 1.15577 | − | 0.362749i | ||||
\(218\) | −1.48913 | −0.100856 | ||||||||
\(219\) | 6.92820i | 0.468165i | ||||||||
\(220\) | −4.55134 | −0.306851 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.51278 | −0.571340 | ||||||||
\(223\) | − | 14.3723i | − | 0.962439i | −0.876600 | − | 0.481220i | \(-0.840194\pi\) | ||
0.876600 | − | 0.481220i | \(-0.159806\pi\) | |||||||
\(224\) | 14.7446 | − | 4.62772i | 0.985163 | − | 0.309202i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | − | 1.28962i | − | 0.0857843i | ||||||
\(227\) | 24.5986 | 1.63266 | 0.816332 | − | 0.577583i | \(-0.196004\pi\) | ||||
0.816332 | + | 0.577583i | \(0.196004\pi\) | |||||||
\(228\) | − | 6.04334i | − | 0.400230i | ||||||
\(229\) | 11.2554i | 0.743780i | 0.928277 | + | 0.371890i | \(0.121290\pi\) | ||||
−0.928277 | + | 0.371890i | \(0.878710\pi\) | |||||||
\(230\) | 7.22316 | 0.476281 | ||||||||
\(231\) | −2.62772 | − | 8.37228i | −0.172891 | − | 0.550856i | ||||
\(232\) | 16.0000 | 1.05045 | ||||||||
\(233\) | 16.4356i | 1.07674i | 0.842710 | + | 0.538368i | \(0.180959\pi\) | ||||
−0.842710 | + | 0.538368i | \(0.819041\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.7446 | −0.831364 | ||||||||
\(236\) | − | 2.23369i | − | 0.145401i | ||||||
\(237\) | −0.294954 | −0.0191593 | ||||||||
\(238\) | 8.21782 | − | 2.57924i | 0.532682 | − | 0.167187i | ||||
\(239\) | − | 20.8395i | − | 1.34800i | −0.738733 | − | 0.673998i | \(-0.764576\pi\) | ||
0.738733 | − | 0.673998i | \(-0.235424\pi\) | |||||||
\(240\) | 0.627719 | 0.0405191 | ||||||||
\(241\) | −13.8564 | −0.892570 | −0.446285 | − | 0.894891i | \(-0.647253\pi\) | ||||
−0.446285 | + | 0.894891i | \(0.647253\pi\) | |||||||
\(242\) | − | 8.71516i | − | 0.560232i | ||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −15.1460 | −0.969625 | ||||||||
\(245\) | 4.00000 | + | 5.74456i | 0.255551 | + | 0.367007i | ||||
\(246\) | −9.25544 | −0.590105 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −18.0202 | −1.14429 | ||||||||
\(249\) | − | 9.45254i | − | 0.599030i | ||||||
\(250\) | −0.792287 | −0.0501086 | ||||||||
\(251\) | − | 17.4891i | − | 1.10390i | −0.833876 | − | 0.551952i | \(-0.813883\pi\) | ||
0.833876 | − | 0.551952i | \(-0.186117\pi\) | |||||||
\(252\) | 1.08724 | + | 3.46410i | 0.0684897 | + | 0.218218i | ||||
\(253\) | − | 30.2372i | − | 1.90099i | ||||||
\(254\) | −7.72281 | −0.484572 | ||||||||
\(255\) | 4.10891 | 0.257310 | ||||||||
\(256\) | −13.8832 | −0.867697 | ||||||||
\(257\) | − | 24.2337i | − | 1.51166i | −0.654770 | − | 0.755828i | \(-0.727235\pi\) | ||
0.654770 | − | 0.755828i | \(-0.272765\pi\) | |||||||
\(258\) | 3.25544i | 0.202675i | ||||||||
\(259\) | −8.51278 | − | 27.1229i | −0.528958 | − | 1.68534i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.98844i | 0.370675i | ||||||||
\(262\) | − | 1.02175i | − | 0.0631239i | ||||||
\(263\) | 16.7306i | 1.03165i | 0.856693 | + | 0.515827i | \(0.172515\pi\) | ||||
−0.856693 | + | 0.515827i | \(0.827485\pi\) | |||||||
\(264\) | 8.86141i | 0.545382i | ||||||||
\(265\) | 1.62772i | 0.0999900i | ||||||||
\(266\) | −8.80773 | + | 2.76439i | −0.540037 | + | 0.169496i | ||||
\(267\) | −8.37228 | −0.512375 | ||||||||
\(268\) | −6.51087 | −0.397715 | ||||||||
\(269\) | 19.6277i | 1.19672i | 0.801226 | + | 0.598362i | \(0.204181\pi\) | ||||
−0.801226 | + | 0.598362i | \(0.795819\pi\) | |||||||
\(270\) | − | 0.792287i | − | 0.0482171i | ||||||
\(271\) | −2.52434 | −0.153343 | −0.0766713 | − | 0.997056i | \(-0.524429\pi\) | ||||
−0.0766713 | + | 0.997056i | \(0.524429\pi\) | |||||||
\(272\) | 2.57924 | 0.156389 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0974i | 0.610003i | ||||||||
\(275\) | 3.31662i | 0.200000i | ||||||||
\(276\) | 12.5109i | 0.753066i | ||||||||
\(277\) | 22.3692i | 1.34403i | 0.740536 | + | 0.672017i | \(0.234572\pi\) | ||||
−0.740536 | + | 0.672017i | \(0.765428\pi\) | |||||||
\(278\) | 2.74456i | 0.164608i | ||||||||
\(279\) | − | 6.74456i | − | 0.403786i | ||||||
\(280\) | −2.11684 | − | 6.74456i | −0.126506 | − | 0.403065i | ||||
\(281\) | 0.589907i | 0.0351909i | 0.999845 | + | 0.0175955i | \(0.00560110\pi\) | ||||
−0.999845 | + | 0.0175955i | \(0.994399\pi\) | |||||||
\(282\) | 10.0974i | 0.601289i | ||||||||
\(283\) | −2.17448 | −0.129259 | −0.0646297 | − | 0.997909i | \(-0.520587\pi\) | ||||
−0.0646297 | + | 0.997909i | \(0.520587\pi\) | |||||||
\(284\) | 4.46738 | 0.265090 | ||||||||
\(285\) | −4.40387 | −0.260862 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.25544 | − | 29.4891i | −0.546331 | − | 1.74069i | ||||
\(288\) | − | 5.84096i | − | 0.344182i | ||||||
\(289\) | −0.116844 | −0.00687317 | ||||||||
\(290\) | − | 4.74456i | − | 0.278610i | ||||||
\(291\) | 8.37228 | 0.490792 | ||||||||
\(292\) | 9.50744 | 0.556381 | ||||||||
\(293\) | 21.7244 | 1.26915 | 0.634576 | − | 0.772861i | \(-0.281175\pi\) | ||||
0.634576 | + | 0.772861i | \(0.281175\pi\) | |||||||
\(294\) | 4.55134 | − | 3.16915i | 0.265440 | − | 0.184828i | ||||
\(295\) | −1.62772 | −0.0947694 | ||||||||
\(296\) | 28.7075i | 1.66859i | ||||||||
\(297\) | −3.31662 | −0.192450 | ||||||||
\(298\) | −10.9783 | −0.635953 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | − | 1.37228i | − | 0.0792287i | ||||||
\(301\) | −10.3723 | + | 3.25544i | −0.597848 | + | 0.187640i | ||||
\(302\) | −6.74456 | −0.388106 | ||||||||
\(303\) | − | 10.3923i | − | 0.597022i | ||||||
\(304\) | −2.76439 | −0.158549 | ||||||||
\(305\) | 11.0371i | 0.631983i | ||||||||
\(306\) | − | 3.25544i | − | 0.186101i | ||||||
\(307\) | −15.4410 | −0.881263 | −0.440632 | − | 0.897688i | \(-0.645245\pi\) | ||||
−0.440632 | + | 0.897688i | \(0.645245\pi\) | |||||||
\(308\) | −11.4891 | + | 3.60597i | −0.654654 | + | 0.205469i | ||||
\(309\) | −11.1168 | −0.632415 | ||||||||
\(310\) | 5.34363i | 0.303498i | ||||||||
\(311\) | − | 16.0000i | − | 0.907277i | −0.891186 | − | 0.453638i | \(-0.850126\pi\) | ||
0.891186 | − | 0.453638i | \(-0.149874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.8614i | 1.23568i | 0.786304 | + | 0.617840i | \(0.211992\pi\) | ||||
−0.786304 | + | 0.617840i | \(0.788008\pi\) | |||||||
\(314\) | 2.28429 | 0.128910 | ||||||||
\(315\) | 2.52434 | − | 0.792287i | 0.142230 | − | 0.0446403i | ||||
\(316\) | 0.404759i | 0.0227695i | ||||||||
\(317\) | −24.7446 | −1.38979 | −0.694897 | − | 0.719110i | \(-0.744550\pi\) | ||||
−0.694897 | + | 0.719110i | \(0.744550\pi\) | |||||||
\(318\) | 1.28962 | 0.0723183 | ||||||||
\(319\) | −19.8614 | −1.11203 | ||||||||
\(320\) | 3.37228i | 0.188516i | ||||||||
\(321\) | −4.75372 | −0.265327 | ||||||||
\(322\) | 18.2337 | − | 5.72281i | 1.01612 | − | 0.318920i | ||||
\(323\) | −18.0951 | −1.00684 | ||||||||
\(324\) | 1.37228 | 0.0762379 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 14.4463i | − | 0.800107i | ||||||
\(327\) | −1.87953 | −0.103938 | ||||||||
\(328\) | 31.2119i | 1.72339i | ||||||||
\(329\) | −32.1716 | + | 10.0974i | −1.77368 | + | 0.556685i | ||||
\(330\) | 2.62772 | 0.144651 | ||||||||
\(331\) | −9.62772 | −0.529187 | −0.264594 | − | 0.964360i | \(-0.585238\pi\) | ||||
−0.264594 | + | 0.964360i | \(0.585238\pi\) | |||||||
\(332\) | −12.9715 | −0.711906 | ||||||||
\(333\) | −10.7446 | −0.588798 | ||||||||
\(334\) | 2.27719i | 0.124602i | ||||||||
\(335\) | 4.74456i | 0.259223i | ||||||||
\(336\) | 1.58457 | − | 0.497333i | 0.0864456 | − | 0.0271318i | ||||
\(337\) | − | 13.9113i | − | 0.757797i | −0.925438 | − | 0.378899i | \(-0.876303\pi\) | ||
0.925438 | − | 0.378899i | \(-0.123697\pi\) | |||||||
\(338\) | − | 10.2997i | − | 0.560232i | ||||||
\(339\) | − | 1.62772i | − | 0.0884055i | ||||||
\(340\) | − | 5.63858i | − | 0.305795i | ||||||
\(341\) | 22.3692 | 1.21136 | ||||||||
\(342\) | 3.48913i | 0.188670i | ||||||||
\(343\) | 14.6487 | + | 11.3321i | 0.790955 | + | 0.611874i | ||||
\(344\) | 10.9783 | 0.591908 | ||||||||
\(345\) | 9.11684 | 0.490834 | ||||||||
\(346\) | 5.48913i | 0.295097i | ||||||||
\(347\) | − | 24.2487i | − | 1.30174i | −0.759190 | − | 0.650870i | \(-0.774404\pi\) | ||
0.759190 | − | 0.650870i | \(-0.225596\pi\) | |||||||
\(348\) | 8.21782 | 0.440522 | ||||||||
\(349\) | 12.3267 | 0.659835 | 0.329918 | − | 0.944010i | \(-0.392979\pi\) | ||||
0.329918 | + | 0.944010i | \(0.392979\pi\) | |||||||
\(350\) | −2.00000 | + | 0.627719i | −0.106904 | + | 0.0335530i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.3723 | 1.03255 | ||||||||
\(353\) | 17.2554i | 0.918414i | 0.888329 | + | 0.459207i | \(0.151866\pi\) | ||||
−0.888329 | + | 0.459207i | \(0.848134\pi\) | |||||||
\(354\) | 1.28962i | 0.0685425i | ||||||||
\(355\) | − | 3.25544i | − | 0.172781i | ||||||
\(356\) | 11.4891i | 0.608922i | ||||||||
\(357\) | 10.3723 | − | 3.25544i | 0.548959 | − | 0.172296i | ||||
\(358\) | − | 17.0256i | − | 0.899829i | ||||||
\(359\) | − | 13.9113i | − | 0.734211i | −0.930179 | − | 0.367105i | \(-0.880349\pi\) | ||
0.930179 | − | 0.367105i | \(-0.119651\pi\) | |||||||
\(360\) | −2.67181 | −0.140817 | ||||||||
\(361\) | 0.394031 | 0.0207385 | ||||||||
\(362\) | 13.2665 | 0.697272 | ||||||||
\(363\) | − | 11.0000i | − | 0.577350i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6.92820i | − | 0.362639i | ||||||
\(366\) | 8.74456 | 0.457086 | ||||||||
\(367\) | − | 11.1168i | − | 0.580295i | −0.956982 | − | 0.290147i | \(-0.906296\pi\) | ||
0.956982 | − | 0.290147i | \(-0.0937043\pi\) | |||||||
\(368\) | 5.72281 | 0.298322 | ||||||||
\(369\) | −11.6819 | −0.608137 | ||||||||
\(370\) | 8.51278 | 0.442558 | ||||||||
\(371\) | 1.28962 | + | 4.10891i | 0.0669538 | + | 0.213324i | ||||
\(372\) | −9.25544 | −0.479872 | ||||||||
\(373\) | 28.3576i | 1.46830i | 0.678986 | + | 0.734151i | \(0.262420\pi\) | ||||
−0.678986 | + | 0.734151i | \(0.737580\pi\) | |||||||
\(374\) | 10.7971 | 0.558303 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 34.0511 | 1.75605 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.627719 | − | 2.00000i | −0.0322864 | − | 0.102869i | ||||
\(379\) | 30.3723 | 1.56012 | 0.780060 | − | 0.625705i | \(-0.215189\pi\) | ||||
0.780060 | + | 0.625705i | \(0.215189\pi\) | |||||||
\(380\) | 6.04334i | 0.310017i | ||||||||
\(381\) | −9.74749 | −0.499379 | ||||||||
\(382\) | − | 6.92820i | − | 0.354478i | ||||||
\(383\) | 30.2337i | 1.54487i | 0.635094 | + | 0.772435i | \(0.280961\pi\) | ||||
−0.635094 | + | 0.772435i | \(0.719039\pi\) | |||||||
\(384\) | −9.01011 | −0.459795 | ||||||||
\(385\) | 2.62772 | + | 8.37228i | 0.133921 | + | 0.426691i | ||||
\(386\) | −3.76631 | −0.191700 | ||||||||
\(387\) | 4.10891i | 0.208868i | ||||||||
\(388\) | − | 11.4891i | − | 0.583272i | ||||||
\(389\) | −2.00000 | −0.101404 | −0.0507020 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507020 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.4603 | 1.89445 | ||||||||
\(392\) | −10.6873 | − | 15.3484i | −0.539788 | − | 0.775212i | ||||
\(393\) | − | 1.28962i | − | 0.0650527i | ||||||
\(394\) | −2.51087 | −0.126496 | ||||||||
\(395\) | 0.294954 | 0.0148407 | ||||||||
\(396\) | 4.55134i | 0.228714i | ||||||||
\(397\) | − | 27.4891i | − | 1.37964i | −0.723981 | − | 0.689820i | \(-0.757690\pi\) | ||
0.723981 | − | 0.689820i | \(-0.242310\pi\) | |||||||
\(398\) | −5.34363 | −0.267852 | ||||||||
\(399\) | −11.1168 | + | 3.48913i | −0.556538 | + | 0.174675i | ||||
\(400\) | −0.627719 | −0.0313859 | ||||||||
\(401\) | 29.7228 | 1.48429 | 0.742143 | − | 0.670241i | \(-0.233809\pi\) | ||||
0.742143 | + | 0.670241i | \(0.233809\pi\) | |||||||
\(402\) | 3.75906 | 0.187485 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.2612 | −0.709520 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | −3.75906 | − | 11.9769i | −0.186559 | − | 0.594403i | ||||
\(407\) | − | 35.6357i | − | 1.76640i | ||||||
\(408\) | −10.9783 | −0.543504 | ||||||||
\(409\) | 34.6410 | 1.71289 | 0.856444 | − | 0.516240i | \(-0.172669\pi\) | ||||
0.856444 | + | 0.516240i | \(0.172669\pi\) | |||||||
\(410\) | 9.25544 | 0.457093 | ||||||||
\(411\) | 12.7446i | 0.628643i | ||||||||
\(412\) | 15.2554i | 0.751581i | ||||||||
\(413\) | −4.10891 | + | 1.28962i | −0.202186 | + | 0.0634581i | ||||
\(414\) | − | 7.22316i | − | 0.354999i | ||||||
\(415\) | 9.45254i | 0.464007i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.46410i | 0.169638i | ||||||||
\(418\) | −11.5721 | −0.566011 | ||||||||
\(419\) | − | 10.3723i | − | 0.506719i | −0.967372 | − | 0.253360i | \(-0.918464\pi\) | ||
0.967372 | − | 0.253360i | \(-0.0815356\pi\) | |||||||
\(420\) | −1.08724 | − | 3.46410i | −0.0530519 | − | 0.169031i | ||||
\(421\) | −9.86141 | −0.480616 | −0.240308 | − | 0.970697i | \(-0.577248\pi\) | ||||
−0.240308 | + | 0.970697i | \(0.577248\pi\) | |||||||
\(422\) | 2.74456 | 0.133603 | ||||||||
\(423\) | 12.7446i | 0.619662i | ||||||||
\(424\) | − | 4.34896i | − | 0.211204i | ||||||
\(425\) | −4.10891 | −0.199311 | ||||||||
\(426\) | −2.57924 | −0.124965 | ||||||||
\(427\) | 8.74456 | + | 27.8614i | 0.423179 | + | 1.34831i | ||||
\(428\) | 6.52344i | 0.315323i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 3.25544i | − | 0.156991i | ||||||
\(431\) | 12.9715i | 0.624817i | 0.949948 | + | 0.312409i | \(0.101136\pi\) | ||||
−0.949948 | + | 0.312409i | \(0.898864\pi\) | |||||||
\(432\) | − | 0.627719i | − | 0.0302011i | ||||||
\(433\) | 12.9783i | 0.623695i | 0.950132 | + | 0.311847i | \(0.100948\pi\) | ||||
−0.950132 | + | 0.311847i | \(0.899052\pi\) | |||||||
\(434\) | 4.23369 | + | 13.4891i | 0.203224 | + | 0.647499i | ||||
\(435\) | − | 5.98844i | − | 0.287124i | ||||||
\(436\) | 2.57924i | 0.123523i | ||||||||
\(437\) | −40.1494 | −1.92060 | ||||||||
\(438\) | −5.48913 | −0.262281 | ||||||||
\(439\) | −30.9369 | −1.47654 | −0.738268 | − | 0.674508i | \(-0.764356\pi\) | ||||
−0.738268 | + | 0.674508i | \(0.764356\pi\) | |||||||
\(440\) | − | 8.86141i | − | 0.422451i | ||||||
\(441\) | 5.74456 | − | 4.00000i | 0.273551 | − | 0.190476i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.233688 | 0.0111028 | 0.00555142 | − | 0.999985i | \(-0.498233\pi\) | ||||
0.00555142 | + | 0.999985i | \(0.498233\pi\) | |||||||
\(444\) | 14.7446i | 0.699746i | ||||||||
\(445\) | 8.37228 | 0.396884 | ||||||||
\(446\) | 11.3870 | 0.539189 | ||||||||
\(447\) | −13.8564 | −0.655386 | ||||||||
\(448\) | 2.67181 | + | 8.51278i | 0.126231 | + | 0.402191i | ||||
\(449\) | 25.7228 | 1.21393 | 0.606967 | − | 0.794727i | \(-0.292386\pi\) | ||||
0.606967 | + | 0.794727i | \(0.292386\pi\) | |||||||
\(450\) | 0.792287i | 0.0373488i | ||||||||
\(451\) | − | 38.7446i | − | 1.82441i | ||||||
\(452\) | −2.23369 | −0.105064 | ||||||||
\(453\) | −8.51278 | −0.399965 | ||||||||
\(454\) | 19.4891i | 0.914670i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.7663 | 0.551008 | ||||||||
\(457\) | 31.5268i | 1.47476i | 0.675478 | + | 0.737380i | \(0.263937\pi\) | ||||
−0.675478 | + | 0.737380i | \(0.736063\pi\) | |||||||
\(458\) | −8.91754 | −0.416689 | ||||||||
\(459\) | − | 4.10891i | − | 0.191788i | ||||||
\(460\) | − | 12.5109i | − | 0.583323i | ||||||
\(461\) | 16.7306 | 0.779222 | 0.389611 | − | 0.920980i | \(-0.372610\pi\) | ||||
0.389611 | + | 0.920980i | \(0.372610\pi\) | |||||||
\(462\) | 6.63325 | − | 2.08191i | 0.308607 | − | 0.0968591i | ||||
\(463\) | −2.51087 | −0.116690 | −0.0583451 | − | 0.998296i | \(-0.518582\pi\) | ||||
−0.0583451 | + | 0.998296i | \(0.518582\pi\) | |||||||
\(464\) | − | 3.75906i | − | 0.174510i | ||||||
\(465\) | 6.74456i | 0.312772i | ||||||||
\(466\) | −13.0217 | −0.603221 | ||||||||
\(467\) | 6.97825i | 0.322915i | 0.986880 | + | 0.161457i | \(0.0516195\pi\) | ||||
−0.986880 | + | 0.161457i | \(0.948381\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.75906 | + | 11.9769i | 0.173577 | + | 0.553041i | ||||
\(470\) | − | 10.0974i | − | 0.465756i | ||||||
\(471\) | 2.88316 | 0.132849 | ||||||||
\(472\) | 4.34896 | 0.200177 | ||||||||
\(473\) | −13.6277 | −0.626603 | ||||||||
\(474\) | − | 0.233688i | − | 0.0107336i | ||||||
\(475\) | 4.40387 | 0.202063 | ||||||||
\(476\) | −4.46738 | − | 14.2337i | −0.204762 | − | 0.652400i | ||||
\(477\) | 1.62772 | 0.0745281 | ||||||||
\(478\) | 16.5109 | 0.755190 | ||||||||
\(479\) | −34.0511 | −1.55583 | −0.777917 | − | 0.628367i | \(-0.783724\pi\) | ||||
−0.777917 | + | 0.628367i | \(0.783724\pi\) | |||||||
\(480\) | 5.84096i | 0.266602i | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 10.9783i | − | 0.500046i | ||||||
\(483\) | 23.0140 | − | 7.22316i | 1.04717 | − | 0.328665i | ||||
\(484\) | −15.0951 | −0.686141 | ||||||||
\(485\) | −8.37228 | −0.380166 | ||||||||
\(486\) | −0.792287 | −0.0359389 | ||||||||
\(487\) | 30.9783 | 1.40376 | 0.701879 | − | 0.712296i | \(-0.252345\pi\) | ||||
0.701879 | + | 0.712296i | \(0.252345\pi\) | |||||||
\(488\) | − | 29.4891i | − | 1.33491i | ||||||
\(489\) | − | 18.2337i | − | 0.824556i | ||||||
\(490\) | −4.55134 | + | 3.16915i | −0.205609 | + | 0.143168i | ||||
\(491\) | 3.81396i | 0.172122i | 0.996290 | + | 0.0860608i | \(0.0274279\pi\) | ||||
−0.996290 | + | 0.0860608i | \(0.972572\pi\) | |||||||
\(492\) | 16.0309i | 0.722728i | ||||||||
\(493\) | − | 24.6060i | − | 1.10820i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.31662 | 0.149071 | ||||||||
\(496\) | 4.23369i | 0.190098i | ||||||||
\(497\) | −2.57924 | − | 8.21782i | −0.115695 | − | 0.368620i | ||||
\(498\) | 7.48913 | 0.335596 | ||||||||
\(499\) | 17.3505 | 0.776716 | 0.388358 | − | 0.921508i | \(-0.373042\pi\) | ||||
0.388358 | + | 0.921508i | \(0.373042\pi\) | |||||||
\(500\) | 1.37228i | 0.0613703i | ||||||||
\(501\) | 2.87419i | 0.128410i | ||||||||
\(502\) | 13.8564 | 0.618442 | ||||||||
\(503\) | 5.69349 | 0.253860 | 0.126930 | − | 0.991912i | \(-0.459488\pi\) | ||||
0.126930 | + | 0.991912i | \(0.459488\pi\) | |||||||
\(504\) | −6.74456 | + | 2.11684i | −0.300427 | + | 0.0942917i | ||||
\(505\) | 10.3923i | 0.462451i | ||||||||
\(506\) | 23.9565 | 1.06500 | ||||||||
\(507\) | − | 13.0000i | − | 0.577350i | ||||||
\(508\) | 13.3763i | 0.593478i | ||||||||
\(509\) | 16.3723i | 0.725689i | 0.931850 | + | 0.362844i | \(0.118194\pi\) | ||||
−0.931850 | + | 0.362844i | \(0.881806\pi\) | |||||||
\(510\) | 3.25544i | 0.144153i | ||||||||
\(511\) | −5.48913 | − | 17.4891i | −0.242825 | − | 0.773673i | ||||
\(512\) | 7.02078i | 0.310277i | ||||||||
\(513\) | 4.40387i | 0.194435i | ||||||||
\(514\) | 19.2000 | 0.846877 | ||||||||
\(515\) | 11.1168 | 0.489867 | ||||||||
\(516\) | 5.63858 | 0.248225 | ||||||||
\(517\) | −42.2689 | −1.85899 | ||||||||
\(518\) | 21.4891 | − | 6.74456i | 0.944178 | − | 0.296339i | ||||
\(519\) | 6.92820i | 0.304114i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.3723i | 1.24301i | 0.783409 | + | 0.621506i | \(0.213479\pi\) | ||||
−0.783409 | + | 0.621506i | \(0.786521\pi\) | |||||||
\(522\) | −4.74456 | −0.207664 | ||||||||
\(523\) | 10.3923 | 0.454424 | 0.227212 | − | 0.973845i | \(-0.427039\pi\) | ||||
0.227212 | + | 0.973845i | \(0.427039\pi\) | |||||||
\(524\) | −1.76972 | −0.0773107 | ||||||||
\(525\) | −2.52434 | + | 0.792287i | −0.110171 | + | 0.0345782i | ||||
\(526\) | −13.2554 | −0.577965 | ||||||||
\(527\) | 27.7128i | 1.20719i | ||||||||
\(528\) | 2.08191 | 0.0906034 | ||||||||
\(529\) | 60.1168 | 2.61378 | ||||||||
\(530\) | −1.28962 | −0.0560175 | ||||||||
\(531\) | 1.62772i | 0.0706370i | ||||||||
\(532\) | 4.78806 | + | 15.2554i | 0.207589 | + | 0.661407i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | − | 6.63325i | − | 0.287049i | ||||||
\(535\) | 4.75372 | 0.205521 | ||||||||
\(536\) | − | 12.6766i | − | 0.547545i | ||||||
\(537\) | − | 21.4891i | − | 0.927324i | ||||||
\(538\) | −15.5508 | −0.670442 | ||||||||
\(539\) | 13.2665 | + | 19.0526i | 0.571429 | + | 0.820652i | ||||
\(540\) | −1.37228 | −0.0590536 | ||||||||
\(541\) | 30.2921i | 1.30236i | 0.758925 | + | 0.651179i | \(0.225725\pi\) | ||||
−0.758925 | + | 0.651179i | \(0.774275\pi\) | |||||||
\(542\) | − | 2.00000i | − | 0.0859074i | ||||||
\(543\) | 16.7446 | 0.718578 | ||||||||
\(544\) | 24.0000i | 1.02899i | ||||||||
\(545\) | 1.87953 | 0.0805101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.39853i | 0.230825i | 0.993318 | + | 0.115412i | \(0.0368189\pi\) | ||||
−0.993318 | + | 0.115412i | \(0.963181\pi\) | |||||||
\(548\) | 17.4891 | 0.747098 | ||||||||
\(549\) | 11.0371 | 0.471053 | ||||||||
\(550\) | −2.62772 | −0.112046 | ||||||||
\(551\) | 26.3723i | 1.12350i | ||||||||
\(552\) | −24.3585 | −1.03677 | ||||||||
\(553\) | 0.744563 | − | 0.233688i | 0.0316620 | − | 0.00993742i | ||||
\(554\) | −17.7228 | −0.752970 | ||||||||
\(555\) | 10.7446 | 0.456081 | ||||||||
\(556\) | 4.75372 | 0.201603 | ||||||||
\(557\) | 19.6048i | 0.830682i | 0.909666 | + | 0.415341i | \(0.136338\pi\) | ||||
−0.909666 | + | 0.415341i | \(0.863662\pi\) | |||||||
\(558\) | 5.34363 | 0.226214 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.58457 | + | 0.497333i | −0.0669605 | + | 0.0210162i | ||||
\(561\) | 13.6277 | 0.575363 | ||||||||
\(562\) | −0.467376 | −0.0197151 | ||||||||
\(563\) | −44.4434 | −1.87307 | −0.936533 | − | 0.350579i | \(-0.885985\pi\) | ||||
−0.936533 | + | 0.350579i | \(0.885985\pi\) | |||||||
\(564\) | 17.4891 | 0.736425 | ||||||||
\(565\) | 1.62772i | 0.0684786i | ||||||||
\(566\) | − | 1.72281i | − | 0.0724152i | ||||||
\(567\) | −0.792287 | − | 2.52434i | −0.0332729 | − | 0.106012i | ||||
\(568\) | 8.69793i | 0.364957i | ||||||||
\(569\) | 31.2318i | 1.30931i | 0.755930 | + | 0.654653i | \(0.227185\pi\) | ||||
−0.755930 | + | 0.654653i | \(0.772815\pi\) | |||||||
\(570\) | − | 3.48913i | − | 0.146143i | ||||||
\(571\) | − | 10.3923i | − | 0.434904i | −0.976071 | − | 0.217452i | \(-0.930225\pi\) | ||
0.976071 | − | 0.217452i | \(-0.0697746\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 8.74456i | − | 0.365309i | ||||||
\(574\) | 23.3639 | − | 7.33296i | 0.975188 | − | 0.306072i | ||||
\(575\) | −9.11684 | −0.380199 | ||||||||
\(576\) | 3.37228 | 0.140512 | ||||||||
\(577\) | − | 26.4674i | − | 1.10185i | −0.834554 | − | 0.550926i | \(-0.814275\pi\) | ||
0.834554 | − | 0.550926i | \(-0.185725\pi\) | |||||||
\(578\) | − | 0.0925740i | − | 0.00385057i | ||||||
\(579\) | −4.75372 | −0.197558 | ||||||||
\(580\) | −8.21782 | −0.341227 | ||||||||
\(581\) | 7.48913 | + | 23.8614i | 0.310701 | + | 0.989938i | ||||
\(582\) | 6.63325i | 0.274957i | ||||||||
\(583\) | 5.39853i | 0.223584i | ||||||||
\(584\) | 18.5109i | 0.765985i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.2119i | 0.711019i | ||||||||
\(587\) | − | 4.00000i | − | 0.165098i | −0.996587 | − | 0.0825488i | \(-0.973694\pi\) | ||
0.996587 | − | 0.0825488i | \(-0.0263060\pi\) | |||||||
\(588\) | −5.48913 | − | 7.88316i | −0.226368 | − | 0.325096i | ||||
\(589\) | − | 29.7021i | − | 1.22386i | ||||||
\(590\) | − | 1.28962i | − | 0.0530928i | ||||||
\(591\) | −3.16915 | −0.130361 | ||||||||
\(592\) | 6.74456 | 0.277200 | ||||||||
\(593\) | 12.6766 | 0.520565 | 0.260283 | − | 0.965532i | \(-0.416184\pi\) | ||||
0.260283 | + | 0.965532i | \(0.416184\pi\) | |||||||
\(594\) | − | 2.62772i | − | 0.107817i | ||||||
\(595\) | −10.3723 | + | 3.25544i | −0.425222 | + | 0.133460i | ||||
\(596\) | 19.0149i | 0.778880i | ||||||||
\(597\) | −6.74456 | −0.276037 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.7228 | −1.78647 | −0.893233 | − | 0.449594i | \(-0.851569\pi\) | ||||
−0.893233 | + | 0.449594i | \(0.851569\pi\) | |||||||
\(600\) | 2.67181 | 0.109076 | ||||||||
\(601\) | −19.8448 | −0.809488 | −0.404744 | − | 0.914430i | \(-0.632639\pi\) | ||||
−0.404744 | + | 0.914430i | \(0.632639\pi\) | |||||||
\(602\) | −2.57924 | − | 8.21782i | −0.105122 | − | 0.334933i | ||||
\(603\) | 4.74456 | 0.193214 | ||||||||
\(604\) | 11.6819i | 0.475331i | ||||||||
\(605\) | 11.0000i | 0.447214i | ||||||||
\(606\) | 8.23369 | 0.334471 | ||||||||
\(607\) | −33.7562 | −1.37012 | −0.685060 | − | 0.728487i | \(-0.740224\pi\) | ||||
−0.685060 | + | 0.728487i | \(0.740224\pi\) | |||||||
\(608\) | − | 25.7228i | − | 1.04320i | ||||||
\(609\) | −4.74456 | − | 15.1168i | −0.192259 | − | 0.612565i | ||||
\(610\) | −8.74456 | −0.354057 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.63858 | −0.227926 | ||||||||
\(613\) | − | 25.5383i | − | 1.03148i | −0.856744 | − | 0.515742i | \(-0.827516\pi\) | ||
0.856744 | − | 0.515742i | \(-0.172484\pi\) | |||||||
\(614\) | − | 12.2337i | − | 0.493711i | ||||||
\(615\) | 11.6819 | 0.471061 | ||||||||
\(616\) | −7.02078 | − | 22.3692i | −0.282875 | − | 0.901280i | ||||
\(617\) | 3.25544 | 0.131059 | 0.0655295 | − | 0.997851i | \(-0.479126\pi\) | ||||
0.0655295 | + | 0.997851i | \(0.479126\pi\) | |||||||
\(618\) | − | 8.80773i | − | 0.354299i | ||||||
\(619\) | 3.48913i | 0.140240i | 0.997539 | + | 0.0701199i | \(0.0223382\pi\) | ||||
−0.997539 | + | 0.0701199i | \(0.977662\pi\) | |||||||
\(620\) | 9.25544 | 0.371707 | ||||||||
\(621\) | − | 9.11684i | − | 0.365846i | ||||||
\(622\) | 12.6766 | 0.508285 | ||||||||
\(623\) | 21.1345 | − | 6.63325i | 0.846735 | − | 0.265756i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −17.3205 | −0.692267 | ||||||||
\(627\) | −14.6060 | −0.583306 | ||||||||
\(628\) | − | 3.95650i | − | 0.157882i | ||||||
\(629\) | 44.1485 | 1.76031 | ||||||||
\(630\) | 0.627719 | + | 2.00000i | 0.0250089 | + | 0.0796819i | ||||
\(631\) | −16.6060 | −0.661073 | −0.330537 | − | 0.943793i | \(-0.607230\pi\) | ||||
−0.330537 | + | 0.943793i | \(0.607230\pi\) | |||||||
\(632\) | −0.788061 | −0.0313474 | ||||||||
\(633\) | 3.46410 | 0.137686 | ||||||||
\(634\) | − | 19.6048i | − | 0.778606i | ||||||
\(635\) | 9.74749 | 0.386818 | ||||||||
\(636\) | − | 2.23369i | − | 0.0885715i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 15.7359i | − | 0.622992i | ||||||
\(639\) | −3.25544 | −0.128783 | ||||||||
\(640\) | 9.01011 | 0.356156 | ||||||||
\(641\) | 33.2554 | 1.31351 | 0.656755 | − | 0.754104i | \(-0.271928\pi\) | ||||
0.656755 | + | 0.754104i | \(0.271928\pi\) | |||||||
\(642\) | − | 3.76631i | − | 0.148644i | ||||||
\(643\) | − | 6.37228i | − | 0.251298i | −0.992075 | − | 0.125649i | \(-0.959899\pi\) | ||
0.992075 | − | 0.125649i | \(-0.0401014\pi\) | |||||||
\(644\) | −9.91220 | − | 31.5817i | −0.390596 | − | 1.24449i | ||||
\(645\) | − | 4.10891i | − | 0.161788i | ||||||
\(646\) | − | 14.3365i | − | 0.564062i | ||||||
\(647\) | 38.2337i | 1.50312i | 0.659664 | + | 0.751561i | \(0.270699\pi\) | ||||
−0.659664 | + | 0.751561i | \(0.729301\pi\) | |||||||
\(648\) | 2.67181i | 0.104959i | ||||||||
\(649\) | −5.39853 | −0.211911 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.34363 | + | 17.0256i | 0.209433 | + | 0.667284i | ||||
\(652\) | −25.0217 | −0.979927 | ||||||||
\(653\) | 13.3505 | 0.522447 | 0.261223 | − | 0.965278i | \(-0.415874\pi\) | ||||
0.261223 | + | 0.965278i | \(0.415874\pi\) | |||||||
\(654\) | − | 1.48913i | − | 0.0582294i | ||||||
\(655\) | 1.28962i | 0.0503896i | ||||||||
\(656\) | 7.33296 | 0.286304 | ||||||||
\(657\) | −6.92820 | −0.270295 | ||||||||
\(658\) | −8.00000 | − | 25.4891i | −0.311872 | − | 0.993670i | ||||
\(659\) | 23.3089i | 0.907988i | 0.891005 | + | 0.453994i | \(0.150001\pi\) | ||||
−0.891005 | + | 0.453994i | \(0.849999\pi\) | |||||||
\(660\) | − | 4.55134i | − | 0.177161i | ||||||
\(661\) | 14.2337i | 0.553626i | 0.960924 | + | 0.276813i | \(0.0892783\pi\) | ||||
−0.960924 | + | 0.276813i | \(0.910722\pi\) | |||||||
\(662\) | − | 7.62792i | − | 0.296467i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 25.2554i | − | 0.980101i | ||||||
\(665\) | 11.1168 | − | 3.48913i | 0.431093 | − | 0.135302i | ||||
\(666\) | − | 8.51278i | − | 0.329863i | ||||||
\(667\) | − | 54.5957i | − | 2.11395i | ||||||
\(668\) | 3.94420 | 0.152606 | ||||||||
\(669\) | 14.3723 | 0.555664 | ||||||||
\(670\) | −3.75906 | −0.145225 | ||||||||
\(671\) | 36.6060i | 1.41316i | ||||||||
\(672\) | 4.62772 | + | 14.7446i | 0.178518 | + | 0.568784i | ||||
\(673\) | − | 8.16292i | − | 0.314657i | −0.987546 | − | 0.157329i | \(-0.949712\pi\) | ||
0.987546 | − | 0.157329i | \(-0.0502882\pi\) | |||||||
\(674\) | 11.0217 | 0.424542 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | −17.8397 | −0.686141 | ||||||||
\(677\) | 48.8473 | 1.87735 | 0.938677 | − | 0.344799i | \(-0.112053\pi\) | ||||
0.938677 | + | 0.344799i | \(0.112053\pi\) | |||||||
\(678\) | 1.28962 | 0.0495276 | ||||||||
\(679\) | −21.1345 | + | 6.63325i | −0.811066 | + | 0.254561i | ||||
\(680\) | 10.9783 | 0.420997 | ||||||||
\(681\) | 24.5986i | 0.942619i | ||||||||
\(682\) | 17.7228i | 0.678642i | ||||||||
\(683\) | 2.74456 | 0.105018 | 0.0525089 | − | 0.998620i | \(-0.483278\pi\) | ||||
0.0525089 | + | 0.998620i | \(0.483278\pi\) | |||||||
\(684\) | 6.04334 | 0.231073 | ||||||||
\(685\) | − | 12.7446i | − | 0.486945i | ||||||
\(686\) | −8.97825 | + | 11.6060i | −0.342791 | + | 0.443118i | ||||
\(687\) | −11.2554 | −0.429422 | ||||||||
\(688\) | − | 2.57924i | − | 0.0983326i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 7.22316i | 0.274981i | ||||||||
\(691\) | − | 42.4674i | − | 1.61554i | −0.589501 | − | 0.807768i | \(-0.700676\pi\) | ||
0.589501 | − | 0.807768i | \(-0.299324\pi\) | |||||||
\(692\) | 9.50744 | 0.361419 | ||||||||
\(693\) | 8.37228 | − | 2.62772i | 0.318037 | − | 0.0998188i | ||||
\(694\) | 19.2119 | 0.729275 | ||||||||
\(695\) | − | 3.46410i | − | 0.131401i | ||||||
\(696\) | 16.0000i | 0.606478i | ||||||||
\(697\) | 48.0000 | 1.81813 | ||||||||
\(698\) | 9.76631i | 0.369660i | ||||||||
\(699\) | −16.4356 | −0.621653 | ||||||||
\(700\) | 1.08724 | + | 3.46410i | 0.0410938 | + | 0.130931i | ||||
\(701\) | − | 41.9191i | − | 1.58326i | −0.611000 | − | 0.791631i | \(-0.709232\pi\) | ||
0.611000 | − | 0.791631i | \(-0.290768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −47.3176 | −1.78462 | ||||||||
\(704\) | 11.1846i | 0.421535i | ||||||||
\(705\) | − | 12.7446i | − | 0.479988i | ||||||
\(706\) | −13.6713 | −0.514525 | ||||||||
\(707\) | 8.23369 | + | 26.2337i | 0.309660 | + | 0.986619i | ||||
\(708\) | 2.23369 | 0.0839471 | ||||||||
\(709\) | 20.0951 | 0.754687 | 0.377344 | − | 0.926073i | \(-0.376838\pi\) | ||||
0.377344 | + | 0.926073i | \(0.376838\pi\) | |||||||
\(710\) | 2.57924 | 0.0967972 | ||||||||
\(711\) | − | 0.294954i | − | 0.0110616i | ||||||
\(712\) | −22.3692 | −0.838321 | ||||||||
\(713\) | 61.4891i | 2.30279i | ||||||||
\(714\) | 2.57924 | + | 8.21782i | 0.0965257 | + | 0.307544i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −29.4891 | −1.10206 | ||||||||
\(717\) | 20.8395 | 0.778266 | ||||||||
\(718\) | 11.0217 | 0.411328 | ||||||||
\(719\) | − | 5.62772i | − | 0.209878i | −0.994479 | − | 0.104939i | \(-0.966535\pi\) | ||
0.994479 | − | 0.104939i | \(-0.0334648\pi\) | |||||||
\(720\) | 0.627719i | 0.0233937i | ||||||||
\(721\) | 28.0627 | − | 8.80773i | 1.04511 | − | 0.328017i | ||||
\(722\) | 0.312185i | 0.0116183i | ||||||||
\(723\) | − | 13.8564i | − | 0.515325i | ||||||
\(724\) | − | 22.9783i | − | 0.853980i | ||||||
\(725\) | 5.98844i | 0.222405i | ||||||||
\(726\) | 8.71516 | 0.323450 | ||||||||
\(727\) | 24.8832i | 0.922865i | 0.887175 | + | 0.461433i | \(0.152664\pi\) | ||||
−0.887175 | + | 0.461433i | \(0.847336\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 5.48913 | 0.203162 | ||||||||
\(731\) | − | 16.8832i | − | 0.624446i | ||||||
\(732\) | − | 15.1460i | − | 0.559813i | ||||||
\(733\) | 0.699713 | 0.0258445 | 0.0129222 | − | 0.999917i | \(-0.495887\pi\) | ||||
0.0129222 | + | 0.999917i | \(0.495887\pi\) | |||||||
\(734\) | 8.80773 | 0.325099 | ||||||||
\(735\) | −5.74456 | + | 4.00000i | −0.211891 | + | 0.147542i | ||||
\(736\) | 53.2511i | 1.96286i | ||||||||
\(737\) | 15.7359i | 0.579641i | ||||||||
\(738\) | − | 9.25544i | − | 0.340697i | ||||||
\(739\) | 49.4921i | 1.82060i | 0.413954 | + | 0.910298i | \(0.364148\pi\) | ||||
−0.413954 | + | 0.910298i | \(0.635852\pi\) | |||||||
\(740\) | − | 14.7446i | − | 0.542021i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.25544 | + | 1.02175i | −0.119511 | + | 0.0375096i | ||||
\(743\) | − | 2.17448i | − | 0.0797740i | −0.999204 | − | 0.0398870i | \(-0.987300\pi\) | ||
0.999204 | − | 0.0398870i | \(-0.0126998\pi\) | |||||||
\(744\) | − | 18.0202i | − | 0.660653i | ||||||
\(745\) | 13.8564 | 0.507659 | ||||||||
\(746\) | −22.4674 | −0.822589 | ||||||||
\(747\) | 9.45254 | 0.345850 | ||||||||
\(748\) | − | 18.7011i | − | 0.683779i | ||||||
\(749\) | 12.0000 | − | 3.76631i | 0.438470 | − | 0.137618i | ||||
\(750\) | − | 0.792287i | − | 0.0289302i | ||||||
\(751\) | −27.8614 | −1.01668 | −0.508339 | − | 0.861157i | \(-0.669740\pi\) | ||||
−0.508339 | + | 0.861157i | \(0.669740\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | 17.4891 | 0.637339 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.51278 | 0.309812 | ||||||||
\(756\) | −3.46410 | + | 1.08724i | −0.125988 | + | 0.0395426i | ||||
\(757\) | 44.9783 | 1.63476 | 0.817381 | − | 0.576097i | \(-0.195425\pi\) | ||||
0.817381 | + | 0.576097i | \(0.195425\pi\) | |||||||
\(758\) | 24.0636i | 0.874028i | ||||||||
\(759\) | 30.2372 | 1.09754 | ||||||||
\(760\) | −11.7663 | −0.426809 | ||||||||
\(761\) | 8.51278 | 0.308588 | 0.154294 | − | 0.988025i | \(-0.450690\pi\) | ||||
0.154294 | + | 0.988025i | \(0.450690\pi\) | |||||||
\(762\) | − | 7.72281i | − | 0.279768i | ||||||
\(763\) | 4.74456 | − | 1.48913i | 0.171765 | − | 0.0539100i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 4.10891i | 0.148558i | ||||||||
\(766\) | −23.9538 | −0.865484 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 13.8832i | − | 0.500965i | ||||||
\(769\) | −45.0882 | −1.62592 | −0.812961 | − | 0.582317i | \(-0.802146\pi\) | ||||
−0.812961 | + | 0.582317i | \(0.802146\pi\) | |||||||
\(770\) | −6.63325 | + | 2.08191i | −0.239046 | + | 0.0750267i | ||||
\(771\) | 24.2337 | 0.872755 | ||||||||
\(772\) | 6.52344i | 0.234784i | ||||||||
\(773\) | 34.4674i | 1.23971i | 0.784718 | + | 0.619853i | \(0.212808\pi\) | ||||
−0.784718 | + | 0.619853i | \(0.787192\pi\) | |||||||
\(774\) | −3.25544 | −0.117014 | ||||||||
\(775\) | − | 6.74456i | − | 0.242272i | ||||||
\(776\) | 22.3692 | 0.803007 | ||||||||
\(777\) | 27.1229 | − | 8.51278i | 0.973029 | − | 0.305394i | ||||
\(778\) | − | 1.58457i | − | 0.0568097i | ||||||
\(779\) | −51.4456 | −1.84323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 10.7971i | − | 0.386349i | ||||||
\(782\) | 29.6793i | 1.06133i | ||||||||
\(783\) | −5.98844 | −0.214009 | ||||||||
\(784\) | −3.60597 | + | 2.51087i | −0.128785 | + | 0.0896741i | ||||
\(785\) | −2.88316 | −0.102904 | ||||||||
\(786\) | 1.02175 | 0.0364446 | ||||||||
\(787\) | 48.2025 | 1.71823 | 0.859116 | − | 0.511781i | \(-0.171014\pi\) | ||||
0.859116 | + | 0.511781i | \(0.171014\pi\) | |||||||
\(788\) | 4.34896i | 0.154925i | ||||||||
\(789\) | −16.7306 | −0.595625 | ||||||||
\(790\) | 0.233688i | 0.00831424i | ||||||||
\(791\) | 1.28962 | + | 4.10891i | 0.0458536 | + | 0.146096i | ||||
\(792\) | −8.86141 | −0.314876 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 21.7793 | 0.772918 | ||||||||
\(795\) | −1.62772 | −0.0577292 | ||||||||
\(796\) | 9.25544i | 0.328050i | ||||||||
\(797\) | 46.0000i | 1.62940i | 0.579880 | + | 0.814702i | \(0.303099\pi\) | ||||
−0.579880 | + | 0.814702i | \(0.696901\pi\) | |||||||
\(798\) | −2.76439 | − | 8.80773i | −0.0978583 | − | 0.311790i | ||||
\(799\) | − | 52.3663i | − | 1.85259i | ||||||
\(800\) | − | 5.84096i | − | 0.206509i | ||||||
\(801\) | − | 8.37228i | − | 0.295820i | ||||||
\(802\) | 23.5490i | 0.831544i | ||||||||
\(803\) | − | 22.9783i | − | 0.810885i | ||||||
\(804\) | − | 6.51087i | − | 0.229621i | ||||||
\(805\) | −23.0140 | + | 7.22316i | −0.811137 | + | 0.254583i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.6277 | −0.690928 | ||||||||
\(808\) | − | 27.7663i | − | 0.976815i | ||||||
\(809\) | − | 13.2665i | − | 0.466425i | −0.972426 | − | 0.233213i | \(-0.925076\pi\) | ||
0.972426 | − | 0.233213i | \(-0.0749238\pi\) | |||||||
\(810\) | 0.792287 | 0.0278381 | ||||||||
\(811\) | 6.63325 | 0.232925 | 0.116462 | − | 0.993195i | \(-0.462845\pi\) | ||||
0.116462 | + | 0.993195i | \(0.462845\pi\) | |||||||
\(812\) | −20.7446 | + | 6.51087i | −0.727991 | + | 0.228487i | ||||
\(813\) | − | 2.52434i | − | 0.0885324i | ||||||
\(814\) | 28.2337 | 0.989590 | ||||||||
\(815\) | 18.2337i | 0.638698i | ||||||||
\(816\) | 2.57924i | 0.0902915i | ||||||||
\(817\) | 18.0951i | 0.633067i | ||||||||
\(818\) | 27.4456i | 0.959614i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 16.0309i | − | 0.559823i | ||||||
\(821\) | − | 19.8448i | − | 0.692590i | −0.938126 | − | 0.346295i | \(-0.887440\pi\) | ||
0.938126 | − | 0.346295i | \(-0.112560\pi\) | |||||||
\(822\) | −10.0974 | −0.352186 | ||||||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | −29.7021 | −1.03472 | ||||||||
\(825\) | −3.31662 | −0.115470 | ||||||||
\(826\) | −1.02175 | − | 3.25544i | −0.0355512 | − | 0.113271i | ||||
\(827\) | 5.34363i | 0.185816i | 0.995675 | + | 0.0929081i | \(0.0296163\pi\) | ||||
−0.995675 | + | 0.0929081i | \(0.970384\pi\) | |||||||
\(828\) | −12.5109 | −0.434783 | ||||||||
\(829\) | 1.48913i | 0.0517195i | 0.999666 | + | 0.0258597i | \(0.00823233\pi\) | ||||
−0.999666 | + | 0.0258597i | \(0.991768\pi\) | |||||||
\(830\) | −7.48913 | −0.259951 | ||||||||
\(831\) | −22.3692 | −0.775978 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.6039 | + | 16.4356i | −0.817827 | + | 0.569461i | ||||
\(834\) | −2.74456 | −0.0950364 | ||||||||
\(835\) | − | 2.87419i | − | 0.0994656i | ||||||
\(836\) | 20.0435i | 0.693219i | ||||||||
\(837\) | 6.74456 | 0.233126 | ||||||||
\(838\) | 8.21782 | 0.283880 | ||||||||
\(839\) | − | 11.1168i | − | 0.383796i | −0.981415 | − | 0.191898i | \(-0.938536\pi\) | ||
0.981415 | − | 0.191898i | \(-0.0614643\pi\) | |||||||
\(840\) | 6.74456 | − | 2.11684i | 0.232710 | − | 0.0730381i | ||||
\(841\) | −6.86141 | −0.236600 | ||||||||
\(842\) | − | 7.81306i | − | 0.269256i | ||||||
\(843\) | −0.589907 | −0.0203175 | ||||||||
\(844\) | − | 4.75372i | − | 0.163630i | ||||||
\(845\) | 13.0000i | 0.447214i | ||||||||
\(846\) | −10.0974 | −0.347154 | ||||||||
\(847\) | 8.71516 | + | 27.7677i | 0.299456 | + | 0.954110i | ||||
\(848\) | −1.02175 | −0.0350870 | ||||||||
\(849\) | − | 2.17448i | − | 0.0746280i | ||||||
\(850\) | − | 3.25544i | − | 0.111661i | ||||||
\(851\) | 97.9565 | 3.35791 | ||||||||
\(852\) | 4.46738i | 0.153050i | ||||||||
\(853\) | −51.6666 | −1.76903 | −0.884515 | − | 0.466512i | \(-0.845510\pi\) | ||||
−0.884515 | + | 0.466512i | \(0.845510\pi\) | |||||||
\(854\) | −22.0742 | + | 6.92820i | −0.755365 | + | 0.237078i | ||||
\(855\) | − | 4.40387i | − | 0.150609i | ||||||
\(856\) | −12.7011 | −0.434113 | ||||||||
\(857\) | −20.7846 | −0.709989 | −0.354994 | − | 0.934868i | \(-0.615517\pi\) | ||||
−0.354994 | + | 0.934868i | \(0.615517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.72281i | 0.331738i | 0.986148 | + | 0.165869i | \(0.0530429\pi\) | ||||
−0.986148 | + | 0.165869i | \(0.946957\pi\) | |||||||
\(860\) | −5.63858 | −0.192274 | ||||||||
\(861\) | 29.4891 | − | 9.25544i | 1.00499 | − | 0.315424i | ||||
\(862\) | −10.2772 | −0.350042 | ||||||||
\(863\) | −26.8832 | −0.915113 | −0.457557 | − | 0.889180i | \(-0.651275\pi\) | ||||
−0.457557 | + | 0.889180i | \(0.651275\pi\) | |||||||
\(864\) | 5.84096 | 0.198714 | ||||||||
\(865\) | − | 6.92820i | − | 0.235566i | ||||||
\(866\) | −10.2825 | −0.349414 | ||||||||
\(867\) | − | 0.116844i | − | 0.00396823i | ||||||
\(868\) | 23.3639 | − | 7.33296i | 0.793021 | − | 0.248897i | ||||
\(869\) | 0.978251 | 0.0331849 | ||||||||
\(870\) | 4.74456 | 0.160856 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −5.02175 | −0.170058 | ||||||||
\(873\) | 8.37228i | 0.283359i | ||||||||
\(874\) | − | 31.8098i | − | 1.07598i | ||||||
\(875\) | 2.52434 | − | 0.792287i | 0.0853382 | − | 0.0267842i | ||||
\(876\) | 9.50744i | 0.321227i | ||||||||
\(877\) | − | 43.5036i | − | 1.46901i | −0.678601 | − | 0.734507i | \(-0.737414\pi\) | ||
0.678601 | − | 0.734507i | \(-0.262586\pi\) | |||||||
\(878\) | − | 24.5109i | − | 0.827202i | ||||||
\(879\) | 21.7244i | 0.732745i | ||||||||
\(880\) | −2.08191 | −0.0701811 | ||||||||
\(881\) | − | 4.37228i | − | 0.147306i | −0.997284 | − | 0.0736530i | \(-0.976534\pi\) | ||
0.997284 | − | 0.0736530i | \(-0.0234657\pi\) | |||||||
\(882\) | 3.16915 | + | 4.55134i | 0.106711 | + | 0.153252i | ||||
\(883\) | 7.72281 | 0.259893 | 0.129947 | − | 0.991521i | \(-0.458519\pi\) | ||||
0.129947 | + | 0.991521i | \(0.458519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 1.62772i | − | 0.0547152i | ||||||
\(886\) | 0.185148i | 0.00622017i | ||||||||
\(887\) | −44.0936 | −1.48052 | −0.740258 | − | 0.672322i | \(-0.765297\pi\) | ||||
−0.740258 | + | 0.672322i | \(0.765297\pi\) | |||||||
\(888\) | −28.7075 | −0.963360 | ||||||||
\(889\) | 24.6060 | − | 7.72281i | 0.825258 | − | 0.259015i | ||||
\(890\) | 6.63325i | 0.222347i | ||||||||
\(891\) | − | 3.31662i | − | 0.111111i | ||||||
\(892\) | − | 19.7228i | − | 0.660369i | ||||||
\(893\) | 56.1253i | 1.87816i | ||||||||
\(894\) | − | 10.9783i | − | 0.367168i | ||||||
\(895\) | 21.4891i | 0.718302i | ||||||||
\(896\) | 22.7446 | − | 7.13859i | 0.759843 | − | 0.238484i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.3799i | 0.680084i | ||||||||
\(899\) | 40.3894 | 1.34706 | ||||||||
\(900\) | 1.37228 | 0.0457427 | ||||||||
\(901\) | −6.68815 | −0.222815 | ||||||||
\(902\) | 30.6968 | 1.02209 | ||||||||
\(903\) | −3.25544 | − | 10.3723i | −0.108334 | − | 0.345168i | ||||
\(904\) | − | 4.34896i | − | 0.144644i | ||||||
\(905\) | −16.7446 | −0.556608 | ||||||||
\(906\) | − | 6.74456i | − | 0.224073i | ||||||
\(907\) | −44.4674 | −1.47651 | −0.738257 | − | 0.674519i | \(-0.764351\pi\) | ||||
−0.738257 | + | 0.674519i | \(0.764351\pi\) | |||||||
\(908\) | 33.7562 | 1.12024 | ||||||||
\(909\) | 10.3923 | 0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7446 | −0.819824 | −0.409912 | − | 0.912125i | \(-0.634441\pi\) | ||||
−0.409912 | + | 0.912125i | \(0.634441\pi\) | |||||||
\(912\) | − | 2.76439i | − | 0.0915381i | ||||||
\(913\) | 31.3505i | 1.03755i | ||||||||
\(914\) | −24.9783 | −0.826207 | ||||||||
\(915\) | −11.0371 | −0.364876 | ||||||||
\(916\) | 15.4456i | 0.510338i | ||||||||
\(917\) | 1.02175 | + | 3.25544i | 0.0337411 | + | 0.107504i | ||||
\(918\) | 3.25544 | 0.107445 | ||||||||
\(919\) | 23.0689i | 0.760973i | 0.924787 | + | 0.380486i | \(0.124243\pi\) | ||||
−0.924787 | + | 0.380486i | \(0.875757\pi\) | |||||||
\(920\) | 24.3585 | 0.803077 | ||||||||
\(921\) | − | 15.4410i | − | 0.508798i | ||||||
\(922\) | 13.2554i | 0.436545i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.60597 | − | 11.4891i | −0.118628 | − | 0.377964i | ||||
\(925\) | −10.7446 | −0.353279 | ||||||||
\(926\) | − | 1.98933i | − | 0.0653736i | ||||||
\(927\) | − | 11.1168i | − | 0.365125i | ||||||
\(928\) | 34.9783 | 1.14822 | ||||||||
\(929\) | 36.5109i | 1.19788i | 0.800793 | + | 0.598941i | \(0.204412\pi\) | ||||
−0.800793 | + | 0.598941i | \(0.795588\pi\) | |||||||
\(930\) | −5.34363 | −0.175225 | ||||||||
\(931\) | 25.2983 | − | 17.6155i | 0.829118 | − | 0.577323i | ||||
\(932\) | 22.5543i | 0.738792i | ||||||||
\(933\) | 16.0000 | 0.523816 | ||||||||
\(934\) | −5.52878 | −0.180907 | ||||||||
\(935\) | −13.6277 | −0.445674 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.2434 | 0.824665 | 0.412333 | − | 0.911033i | \(-0.364714\pi\) | ||||
0.412333 | + | 0.911033i | \(0.364714\pi\) | |||||||
\(938\) | −9.48913 | + | 2.97825i | −0.309831 | + | 0.0972433i | ||||
\(939\) | −21.8614 | −0.713420 | ||||||||
\(940\) | −17.4891 | −0.570432 | ||||||||
\(941\) | −46.3229 | −1.51008 | −0.755042 | − | 0.655676i | \(-0.772384\pi\) | ||||
−0.755042 | + | 0.655676i | \(0.772384\pi\) | |||||||
\(942\) | 2.28429i | 0.0744261i | ||||||||
\(943\) | 106.502 | 3.46819 | ||||||||
\(944\) | − | 1.02175i | − | 0.0332551i | ||||||
\(945\) | 0.792287 | + | 2.52434i | 0.0257731 | + | 0.0821167i | ||||
\(946\) | − | 10.7971i | − | 0.351043i | ||||||
\(947\) | −3.35053 | −0.108878 | −0.0544388 | − | 0.998517i | \(-0.517337\pi\) | ||||
−0.0544388 | + | 0.998517i | \(0.517337\pi\) | |||||||
\(948\) | −0.404759 | −0.0131460 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.48913i | 0.113202i | ||||||||
\(951\) | − | 24.7446i | − | 0.802397i | ||||||
\(952\) | 27.7128 | − | 8.69793i | 0.898177 | − | 0.281901i | ||||
\(953\) | − | 44.8482i | − | 1.45277i | −0.687285 | − | 0.726387i | \(-0.741198\pi\) | ||
0.687285 | − | 0.726387i | \(-0.258802\pi\) | |||||||
\(954\) | 1.28962i | 0.0417530i | ||||||||
\(955\) | 8.74456i | 0.282967i | ||||||||
\(956\) | − | 28.5977i | − | 0.924915i | ||||||
\(957\) | − | 19.8614i | − | 0.642028i | ||||||
\(958\) | − | 26.9783i | − | 0.871628i | ||||||
\(959\) | −10.0974 | − | 32.1716i | −0.326060 | − | 1.03887i | ||||
\(960\) | −3.37228 | −0.108840 | ||||||||
\(961\) | −14.4891 | −0.467391 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 4.75372i | − | 0.153187i | ||||||
\(964\) | −19.0149 | −0.612428 | ||||||||
\(965\) | 4.75372 | 0.153028 | ||||||||
\(966\) | 5.72281 | + | 18.2337i | 0.184128 | + | 0.586659i | ||||
\(967\) | 17.9653i | 0.577726i | 0.957370 | + | 0.288863i | \(0.0932772\pi\) | ||||
−0.957370 | + | 0.288863i | \(0.906723\pi\) | |||||||
\(968\) | − | 29.3900i | − | 0.944629i | ||||||
\(969\) | − | 18.0951i | − | 0.581298i | ||||||
\(970\) | − | 6.63325i | − | 0.212981i | ||||||
\(971\) | − | 1.62772i | − | 0.0522360i | −0.999659 | − | 0.0261180i | \(-0.991685\pi\) | ||
0.999659 | − | 0.0261180i | \(-0.00831456\pi\) | |||||||
\(972\) | 1.37228i | 0.0440159i | ||||||||
\(973\) | −2.74456 | − | 8.74456i | −0.0879866 | − | 0.280338i | ||||
\(974\) | 24.5437i | 0.786430i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.92820 | −0.221766 | ||||||||
\(977\) | −30.0951 | −0.962827 | −0.481414 | − | 0.876494i | \(-0.659877\pi\) | ||||
−0.481414 | + | 0.876494i | \(0.659877\pi\) | |||||||
\(978\) | 14.4463 | 0.461942 | ||||||||
\(979\) | 27.7677 | 0.887460 | ||||||||
\(980\) | 5.48913 | + | 7.88316i | 0.175344 | + | 0.251818i | ||||
\(981\) | − | 1.87953i | − | 0.0600087i | ||||||
\(982\) | −3.02175 | −0.0964279 | ||||||||
\(983\) | − | 28.4674i | − | 0.907968i | −0.891010 | − | 0.453984i | \(-0.850002\pi\) | ||
0.891010 | − | 0.453984i | \(-0.149998\pi\) | |||||||
\(984\) | −31.2119 | −0.995000 | ||||||||
\(985\) | 3.16915 | 0.100977 | ||||||||
\(986\) | 19.4950 | 0.620847 | ||||||||
\(987\) | −10.0974 | − | 32.1716i | −0.321402 | − | 1.02403i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 37.4603i | − | 1.19117i | ||||||
\(990\) | 2.62772i | 0.0835144i | ||||||||
\(991\) | −50.3723 | −1.60013 | −0.800064 | − | 0.599914i | \(-0.795201\pi\) | ||||
−0.800064 | + | 0.599914i | \(0.795201\pi\) | |||||||
\(992\) | −39.3947 | −1.25078 | ||||||||
\(993\) | − | 9.62772i | − | 0.305526i | ||||||
\(994\) | 6.51087 | − | 2.04350i | 0.206512 | − | 0.0648158i | ||||
\(995\) | 6.74456 | 0.213817 | ||||||||
\(996\) | − | 12.9715i | − | 0.411019i | ||||||
\(997\) | −19.4950 | −0.617413 | −0.308706 | − | 0.951157i | \(-0.599896\pi\) | ||||
−0.308706 | + | 0.951157i | \(0.599896\pi\) | |||||||
\(998\) | 13.7466i | 0.435141i | ||||||||
\(999\) | − | 10.7446i | − | 0.339943i |
(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 | 1155.2.i.a.76.6 | yes | 8 | |
7.6 | odd | 2 | inner | 1155.2.i.a.76.5 | yes | 8 | |
11.10 | odd | 2 | inner | 1155.2.i.a.76.4 | yes | 8 | |
77.76 | even | 2 | inner | 1155.2.i.a.76.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.i.a.76.3 | ✓ | 8 | 77.76 | even | 2 | inner | |
1155.2.i.a.76.4 | yes | 8 | 11.10 | odd | 2 | inner | |
1155.2.i.a.76.5 | yes | 8 | 7.6 | odd | 2 | inner | |
1155.2.i.a.76.6 | yes | 8 | 1.1 | even | 1 | trivial |