Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (of order \(5\), 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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} - 350 x^{3} + 510 x^{2} - 175 x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 71.3 | ||
Root | \(0.885530 + 2.72538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.71 |
Dual form | 770.2.n.j.141.3 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | ||||
\(3\) | 2.31835 | + | 1.68438i | 1.33850 | + | 0.972476i | 0.999498 | + | 0.0316901i | \(0.0100890\pi\) |
0.339001 | + | 0.940786i | \(0.389911\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 0.309017 | − | 0.951057i | 0.138197 | − | 0.425325i | ||||
\(6\) | 0.885530 | − | 2.72538i | 0.361516 | − | 1.11263i | ||||
\(7\) | −0.809017 | + | 0.587785i | −0.305780 | + | 0.222162i | ||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | 1.61056 | + | 4.95678i | 0.536852 | + | 1.65226i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.27905 | + | 0.497839i | 0.988670 | + | 0.150104i | ||||
\(12\) | −2.86564 | −0.827238 | ||||||||
\(13\) | −1.74183 | − | 5.36082i | −0.483098 | − | 1.48682i | −0.834717 | − | 0.550680i | \(-0.814369\pi\) |
0.351619 | − | 0.936143i | \(-0.385631\pi\) | |||||||
\(14\) | 0.809017 | + | 0.587785i | 0.216219 | + | 0.157092i | ||||
\(15\) | 2.31835 | − | 1.68438i | 0.598595 | − | 0.434905i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −0.719966 | + | 2.21583i | −0.174617 | + | 0.537417i | −0.999616 | − | 0.0277181i | \(-0.991176\pi\) |
0.824998 | + | 0.565135i | \(0.191176\pi\) | |||||||
\(18\) | 4.21649 | − | 3.06346i | 0.993836 | − | 0.722064i | ||||
\(19\) | 6.32242 | + | 4.59351i | 1.45046 | + | 1.05382i | 0.985723 | + | 0.168376i | \(0.0538522\pi\) |
0.464740 | + | 0.885447i | \(0.346148\pi\) | |||||||
\(20\) | 0.309017 | + | 0.951057i | 0.0690983 | + | 0.212663i | ||||
\(21\) | −2.86564 | −0.625333 | ||||||||
\(22\) | −0.539809 | − | 3.27240i | −0.115088 | − | 0.697678i | ||||
\(23\) | 7.98434 | 1.66485 | 0.832425 | − | 0.554138i | \(-0.186952\pi\) | ||||
0.832425 | + | 0.554138i | \(0.186952\pi\) | |||||||
\(24\) | 0.885530 | + | 2.72538i | 0.180758 | + | 0.556316i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | −4.56018 | + | 3.31317i | −0.894325 | + | 0.649765i | ||||
\(27\) | −1.95867 | + | 6.02818i | −0.376947 | + | 1.16012i | ||||
\(28\) | 0.309017 | − | 0.951057i | 0.0583987 | − | 0.179733i | ||||
\(29\) | −2.42257 | + | 1.76010i | −0.449860 | + | 0.326842i | −0.789540 | − | 0.613699i | \(-0.789681\pi\) |
0.339681 | + | 0.940541i | \(0.389681\pi\) | |||||||
\(30\) | −2.31835 | − | 1.68438i | −0.423270 | − | 0.307524i | ||||
\(31\) | 1.57145 | + | 4.83644i | 0.282241 | + | 0.868650i | 0.987212 | + | 0.159413i | \(0.0509602\pi\) |
−0.704971 | + | 0.709237i | \(0.749040\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.76342 | + | 6.67732i | 1.17736 | + | 1.16237i | ||||
\(34\) | 2.32986 | 0.399567 | ||||||||
\(35\) | 0.309017 | + | 0.951057i | 0.0522334 | + | 0.160758i | ||||
\(36\) | −4.21649 | − | 3.06346i | −0.702748 | − | 0.510576i | ||||
\(37\) | 1.12195 | − | 0.815144i | 0.184447 | − | 0.134009i | −0.491730 | − | 0.870748i | \(-0.663635\pi\) |
0.676177 | + | 0.736739i | \(0.263635\pi\) | |||||||
\(38\) | 2.41495 | − | 7.43245i | 0.391757 | − | 1.20570i | ||||
\(39\) | 4.99146 | − | 15.3621i | 0.799274 | − | 2.45991i | ||||
\(40\) | 0.809017 | − | 0.587785i | 0.127917 | − | 0.0929370i | ||||
\(41\) | −5.58347 | − | 4.05663i | −0.871991 | − | 0.633538i | 0.0591296 | − | 0.998250i | \(-0.481167\pi\) |
−0.931120 | + | 0.364712i | \(0.881167\pi\) | |||||||
\(42\) | 0.885530 | + | 2.72538i | 0.136640 | + | 0.420535i | ||||
\(43\) | −11.5492 | −1.76124 | −0.880622 | − | 0.473820i | \(-0.842875\pi\) | ||||
−0.880622 | + | 0.473820i | \(0.842875\pi\) | |||||||
\(44\) | −2.94543 | + | 1.52462i | −0.444040 | + | 0.229845i | ||||
\(45\) | 5.21187 | 0.776939 | ||||||||
\(46\) | −2.46730 | − | 7.59356i | −0.363783 | − | 1.11961i | ||||
\(47\) | 4.16255 | + | 3.02427i | 0.607170 | + | 0.441135i | 0.848417 | − | 0.529329i | \(-0.177556\pi\) |
−0.241246 | + | 0.970464i | \(0.577556\pi\) | |||||||
\(48\) | 2.31835 | − | 1.68438i | 0.334625 | − | 0.243119i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | −0.309017 | + | 0.951057i | −0.0437016 | + | 0.134500i | ||||
\(51\) | −5.40142 | + | 3.92436i | −0.756350 | + | 0.549521i | ||||
\(52\) | 4.56018 | + | 3.31317i | 0.632384 | + | 0.459454i | ||||
\(53\) | 0.180063 | + | 0.554176i | 0.0247335 | + | 0.0761219i | 0.962661 | − | 0.270709i | \(-0.0872580\pi\) |
−0.937928 | + | 0.346830i | \(0.887258\pi\) | |||||||
\(54\) | 6.33840 | 0.862547 | ||||||||
\(55\) | 1.48675 | − | 2.96472i | 0.200474 | − | 0.399763i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 6.92037 | + | 21.2987i | 0.916625 | + | 2.82108i | ||||
\(58\) | 2.42257 | + | 1.76010i | 0.318099 | + | 0.231112i | ||||
\(59\) | −11.1881 | + | 8.12860i | −1.45656 | + | 1.05825i | −0.472319 | + | 0.881428i | \(0.656583\pi\) |
−0.984242 | + | 0.176826i | \(0.943417\pi\) | |||||||
\(60\) | −0.885530 | + | 2.72538i | −0.114321 | + | 0.351845i | ||||
\(61\) | 2.41788 | − | 7.44148i | 0.309578 | − | 0.952783i | −0.668351 | − | 0.743846i | \(-0.733000\pi\) |
0.977929 | − | 0.208937i | \(-0.0670005\pi\) | |||||||
\(62\) | 4.11412 | − | 2.98908i | 0.522494 | − | 0.379614i | ||||
\(63\) | −4.21649 | − | 3.06346i | −0.531228 | − | 0.385959i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | −5.63670 | −0.699146 | ||||||||
\(66\) | 4.26050 | − | 8.49580i | 0.524431 | − | 1.04576i | ||||
\(67\) | −0.0485769 | −0.00593462 | −0.00296731 | − | 0.999996i | \(-0.500945\pi\) | ||||
−0.00296731 | + | 0.999996i | \(0.500945\pi\) | |||||||
\(68\) | −0.719966 | − | 2.21583i | −0.0873087 | − | 0.268708i | ||||
\(69\) | 18.5105 | + | 13.4486i | 2.22840 | + | 1.61903i | ||||
\(70\) | 0.809017 | − | 0.587785i | 0.0966960 | − | 0.0702538i | ||||
\(71\) | 1.37624 | − | 4.23563i | 0.163330 | − | 0.502677i | −0.835580 | − | 0.549369i | \(-0.814868\pi\) |
0.998909 | + | 0.0466921i | \(0.0148680\pi\) | |||||||
\(72\) | −1.61056 | + | 4.95678i | −0.189806 | + | 0.584162i | ||||
\(73\) | 0.272488 | − | 0.197974i | 0.0318923 | − | 0.0231711i | −0.571725 | − | 0.820445i | \(-0.693726\pi\) |
0.603617 | + | 0.797274i | \(0.293726\pi\) | |||||||
\(74\) | −1.12195 | − | 0.815144i | −0.130424 | − | 0.0947585i | ||||
\(75\) | −0.885530 | − | 2.72538i | −0.102252 | − | 0.314700i | ||||
\(76\) | −7.81494 | −0.896435 | ||||||||
\(77\) | −2.94543 | + | 1.52462i | −0.335663 | + | 0.173746i | ||||
\(78\) | −16.1527 | −1.82893 | ||||||||
\(79\) | 0.325367 | + | 1.00138i | 0.0366067 | + | 0.112664i | 0.967690 | − | 0.252143i | \(-0.0811352\pi\) |
−0.931083 | + | 0.364806i | \(0.881135\pi\) | |||||||
\(80\) | −0.809017 | − | 0.587785i | −0.0904508 | − | 0.0657164i | ||||
\(81\) | −2.04515 | + | 1.48589i | −0.227239 | + | 0.165099i | ||||
\(82\) | −2.13269 | + | 6.56376i | −0.235517 | + | 0.724846i | ||||
\(83\) | 3.34711 | − | 10.3014i | 0.367393 | − | 1.13072i | −0.581075 | − | 0.813850i | \(-0.697368\pi\) |
0.948469 | − | 0.316871i | \(-0.102632\pi\) | |||||||
\(84\) | 2.31835 | − | 1.68438i | 0.252952 | − | 0.183781i | ||||
\(85\) | 1.88489 | + | 1.36946i | 0.204446 | + | 0.148538i | ||||
\(86\) | 3.56891 | + | 10.9840i | 0.384846 | + | 1.18443i | ||||
\(87\) | −8.58103 | −0.919983 | ||||||||
\(88\) | 2.36018 | + | 2.33014i | 0.251596 | + | 0.248393i | ||||
\(89\) | −18.5268 | −1.96384 | −0.981921 | − | 0.189291i | \(-0.939381\pi\) | ||||
−0.981921 | + | 0.189291i | \(0.939381\pi\) | |||||||
\(90\) | −1.61056 | − | 4.95678i | −0.169767 | − | 0.522490i | ||||
\(91\) | 4.56018 | + | 3.31317i | 0.478037 | + | 0.347314i | ||||
\(92\) | −6.45947 | + | 4.69308i | −0.673446 | + | 0.489287i | ||||
\(93\) | −4.50321 | + | 13.8595i | −0.466961 | + | 1.43716i | ||||
\(94\) | 1.58995 | − | 4.89337i | 0.163991 | − | 0.504713i | ||||
\(95\) | 6.32242 | − | 4.59351i | 0.648667 | − | 0.471284i | ||||
\(96\) | −2.31835 | − | 1.68438i | −0.236615 | − | 0.171911i | ||||
\(97\) | −1.64762 | − | 5.07084i | −0.167290 | − | 0.514866i | 0.831908 | − | 0.554914i | \(-0.187249\pi\) |
−0.999198 | + | 0.0400482i | \(0.987249\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 2.81341 | + | 17.0553i | 0.282758 | + | 1.71412i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.64578 | − | 17.3759i | −0.561776 | − | 1.72897i | −0.677340 | − | 0.735670i | \(-0.736867\pi\) |
0.115564 | − | 0.993300i | \(-0.463133\pi\) | |||||||
\(102\) | 5.40142 | + | 3.92436i | 0.534820 | + | 0.388570i | ||||
\(103\) | 9.08908 | − | 6.60361i | 0.895574 | − | 0.650673i | −0.0417513 | − | 0.999128i | \(-0.513294\pi\) |
0.937325 | + | 0.348455i | \(0.113294\pi\) | |||||||
\(104\) | 1.74183 | − | 5.36082i | 0.170801 | − | 0.525671i | ||||
\(105\) | −0.885530 | + | 2.72538i | −0.0864189 | + | 0.265970i | ||||
\(106\) | 0.471410 | − | 0.342499i | 0.0457874 | − | 0.0332665i | ||||
\(107\) | −3.95736 | − | 2.87519i | −0.382573 | − | 0.277955i | 0.379833 | − | 0.925055i | \(-0.375982\pi\) |
−0.762405 | + | 0.647100i | \(0.775982\pi\) | |||||||
\(108\) | −1.95867 | − | 6.02818i | −0.188473 | − | 0.580062i | ||||
\(109\) | 6.26442 | 0.600023 | 0.300011 | − | 0.953936i | \(-0.403009\pi\) | ||||
0.300011 | + | 0.953936i | \(0.403009\pi\) | |||||||
\(110\) | −3.27905 | − | 0.497839i | −0.312645 | − | 0.0474671i | ||||
\(111\) | 3.97408 | 0.377203 | ||||||||
\(112\) | 0.309017 | + | 0.951057i | 0.0291994 | + | 0.0898664i | ||||
\(113\) | −8.22373 | − | 5.97489i | −0.773624 | − | 0.562071i | 0.129435 | − | 0.991588i | \(-0.458684\pi\) |
−0.903059 | + | 0.429517i | \(0.858684\pi\) | |||||||
\(114\) | 18.1178 | − | 13.1633i | 1.69688 | − | 1.23286i | ||||
\(115\) | 2.46730 | − | 7.59356i | 0.230077 | − | 0.708103i | ||||
\(116\) | 0.925339 | − | 2.84790i | 0.0859155 | − | 0.264421i | ||||
\(117\) | 23.7671 | − | 17.2678i | 2.19727 | − | 1.59641i | ||||
\(118\) | 11.1881 | + | 8.12860i | 1.02994 | + | 0.748298i | ||||
\(119\) | −0.719966 | − | 2.21583i | −0.0659991 | − | 0.203124i | ||||
\(120\) | 2.86564 | 0.261596 | ||||||||
\(121\) | 10.5043 | + | 3.26487i | 0.954938 | + | 0.296807i | ||||
\(122\) | −7.82443 | −0.708391 | ||||||||
\(123\) | −6.11152 | − | 18.8093i | −0.551058 | − | 1.69598i | ||||
\(124\) | −4.11412 | − | 2.98908i | −0.369459 | − | 0.268428i | ||||
\(125\) | −0.809017 | + | 0.587785i | −0.0723607 | + | 0.0525731i | ||||
\(126\) | −1.61056 | + | 4.95678i | −0.143480 | + | 0.441585i | ||||
\(127\) | 2.03558 | − | 6.26487i | 0.180628 | − | 0.555917i | −0.819217 | − | 0.573483i | \(-0.805592\pi\) |
0.999846 | + | 0.0175661i | \(0.00559175\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | −26.7752 | − | 19.4533i | −2.35742 | − | 1.71277i | ||||
\(130\) | 1.74183 | + | 5.36082i | 0.152769 | + | 0.470175i | ||||
\(131\) | 1.20821 | 0.105562 | 0.0527808 | − | 0.998606i | \(-0.483192\pi\) | ||||
0.0527808 | + | 0.998606i | \(0.483192\pi\) | |||||||
\(132\) | −9.39656 | − | 1.42662i | −0.817865 | − | 0.124172i | ||||
\(133\) | −7.81494 | −0.677641 | ||||||||
\(134\) | 0.0150111 | + | 0.0461994i | 0.00129676 | + | 0.00399102i | ||||
\(135\) | 5.12787 | + | 3.72562i | 0.441337 | + | 0.320650i | ||||
\(136\) | −1.88489 | + | 1.36946i | −0.161628 | + | 0.117430i | ||||
\(137\) | 4.35184 | − | 13.3936i | 0.371803 | − | 1.14429i | −0.573807 | − | 0.818991i | \(-0.694534\pi\) |
0.945610 | − | 0.325302i | \(-0.105466\pi\) | |||||||
\(138\) | 7.07037 | − | 21.7604i | 0.601870 | − | 1.85237i | ||||
\(139\) | −2.21905 | + | 1.61224i | −0.188218 | + | 0.136748i | −0.677904 | − | 0.735151i | \(-0.737111\pi\) |
0.489686 | + | 0.871899i | \(0.337111\pi\) | |||||||
\(140\) | −0.809017 | − | 0.587785i | −0.0683744 | − | 0.0496769i | ||||
\(141\) | 4.55623 | + | 14.0226i | 0.383703 | + | 1.18092i | ||||
\(142\) | −4.45361 | −0.373739 | ||||||||
\(143\) | −3.04274 | − | 18.4455i | −0.254446 | − | 1.54249i | ||||
\(144\) | 5.21187 | 0.434322 | ||||||||
\(145\) | 0.925339 | + | 2.84790i | 0.0768452 | + | 0.236505i | ||||
\(146\) | −0.272488 | − | 0.197974i | −0.0225513 | − | 0.0163844i | ||||
\(147\) | 2.31835 | − | 1.68438i | 0.191214 | − | 0.138925i | ||||
\(148\) | −0.428546 | + | 1.31893i | −0.0352263 | + | 0.108415i | ||||
\(149\) | −5.30404 | + | 16.3242i | −0.434524 | + | 1.33733i | 0.459049 | + | 0.888411i | \(0.348190\pi\) |
−0.893573 | + | 0.448917i | \(0.851810\pi\) | |||||||
\(150\) | −2.31835 | + | 1.68438i | −0.189292 | + | 0.137529i | ||||
\(151\) | −4.80802 | − | 3.49323i | −0.391271 | − | 0.284275i | 0.374705 | − | 0.927144i | \(-0.377744\pi\) |
−0.765976 | + | 0.642869i | \(0.777744\pi\) | |||||||
\(152\) | 2.41495 | + | 7.43245i | 0.195878 | + | 0.602851i | ||||
\(153\) | −12.1429 | −0.981696 | ||||||||
\(154\) | 2.36018 | + | 2.33014i | 0.190189 | + | 0.187768i | ||||
\(155\) | 5.08533 | 0.408464 | ||||||||
\(156\) | 4.99146 | + | 15.3621i | 0.399637 | + | 1.22996i | ||||
\(157\) | 13.5872 | + | 9.87170i | 1.08438 | + | 0.787847i | 0.978441 | − | 0.206526i | \(-0.0662157\pi\) |
0.105937 | + | 0.994373i | \(0.466216\pi\) | |||||||
\(158\) | 0.851822 | − | 0.618885i | 0.0677673 | − | 0.0492358i | ||||
\(159\) | −0.515994 | + | 1.58807i | −0.0409210 | + | 0.125942i | ||||
\(160\) | −0.309017 | + | 0.951057i | −0.0244299 | + | 0.0751876i | ||||
\(161\) | −6.45947 | + | 4.69308i | −0.509077 | + | 0.369866i | ||||
\(162\) | 2.04515 | + | 1.48589i | 0.160682 | + | 0.116743i | ||||
\(163\) | 0.751037 | + | 2.31146i | 0.0588258 | + | 0.181047i | 0.976151 | − | 0.217090i | \(-0.0696567\pi\) |
−0.917326 | + | 0.398138i | \(0.869657\pi\) | |||||||
\(164\) | 6.90154 | 0.538920 | ||||||||
\(165\) | 8.44052 | − | 4.36899i | 0.657094 | − | 0.340126i | ||||
\(166\) | −10.8315 | −0.840686 | ||||||||
\(167\) | −3.40864 | − | 10.4907i | −0.263768 | − | 0.811795i | −0.991975 | − | 0.126437i | \(-0.959646\pi\) |
0.728206 | − | 0.685358i | \(-0.240354\pi\) | |||||||
\(168\) | −2.31835 | − | 1.68438i | −0.178864 | − | 0.129953i | ||||
\(169\) | −15.1871 | + | 11.0341i | −1.16824 | + | 0.848777i | ||||
\(170\) | 0.719966 | − | 2.21583i | 0.0552189 | − | 0.169946i | ||||
\(171\) | −12.5864 | + | 38.7369i | −0.962506 | + | 2.96229i | ||||
\(172\) | 9.34354 | − | 6.78848i | 0.712438 | − | 0.517617i | ||||
\(173\) | −11.8882 | − | 8.63730i | −0.903845 | − | 0.656682i | 0.0356057 | − | 0.999366i | \(-0.488664\pi\) |
−0.939451 | + | 0.342684i | \(0.888664\pi\) | |||||||
\(174\) | 2.65168 | + | 8.16104i | 0.201024 | + | 0.618687i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 1.48675 | − | 2.96472i | 0.112068 | − | 0.223474i | ||||
\(177\) | −39.6294 | −2.97873 | ||||||||
\(178\) | 5.72511 | + | 17.6201i | 0.429115 | + | 1.32068i | ||||
\(179\) | −3.65184 | − | 2.65322i | −0.272951 | − | 0.198311i | 0.442886 | − | 0.896578i | \(-0.353955\pi\) |
−0.715837 | + | 0.698267i | \(0.753955\pi\) | |||||||
\(180\) | −4.21649 | + | 3.06346i | −0.314278 | + | 0.228337i | ||||
\(181\) | −3.14487 | + | 9.67891i | −0.233756 | + | 0.719427i | 0.763528 | + | 0.645775i | \(0.223466\pi\) |
−0.997284 | + | 0.0736525i | \(0.976534\pi\) | |||||||
\(182\) | 1.74183 | − | 5.36082i | 0.129113 | − | 0.397370i | ||||
\(183\) | 18.1398 | − | 13.1793i | 1.34093 | − | 0.974242i | ||||
\(184\) | 6.45947 | + | 4.69308i | 0.476198 | + | 0.345978i | ||||
\(185\) | −0.428546 | − | 1.31893i | −0.0315074 | − | 0.0969697i | ||||
\(186\) | 14.5727 | 1.06852 | ||||||||
\(187\) | −3.46393 | + | 6.90738i | −0.253307 | + | 0.505117i | ||||
\(188\) | −5.14520 | −0.375252 | ||||||||
\(189\) | −1.95867 | − | 6.02818i | −0.142473 | − | 0.438485i | ||||
\(190\) | −6.32242 | − | 4.59351i | −0.458677 | − | 0.333248i | ||||
\(191\) | −9.70127 | + | 7.04838i | −0.701959 | + | 0.510003i | −0.880570 | − | 0.473917i | \(-0.842840\pi\) |
0.178611 | + | 0.983920i | \(0.442840\pi\) | |||||||
\(192\) | −0.885530 | + | 2.72538i | −0.0639076 | + | 0.196687i | ||||
\(193\) | −5.52363 | + | 17.0000i | −0.397600 | + | 1.22369i | 0.529319 | + | 0.848423i | \(0.322448\pi\) |
−0.926918 | + | 0.375263i | \(0.877552\pi\) | |||||||
\(194\) | −4.31351 | + | 3.13395i | −0.309692 | + | 0.225005i | ||||
\(195\) | −13.0678 | − | 9.49433i | −0.935806 | − | 0.679903i | ||||
\(196\) | 0.309017 | + | 0.951057i | 0.0220726 | + | 0.0679326i | ||||
\(197\) | −11.7871 | −0.839795 | −0.419897 | − | 0.907572i | \(-0.637934\pi\) | ||||
−0.419897 | + | 0.907572i | \(0.637934\pi\) | |||||||
\(198\) | 15.3512 | − | 7.94609i | 1.09096 | − | 0.564704i | ||||
\(199\) | −13.9342 | −0.987767 | −0.493884 | − | 0.869528i | \(-0.664423\pi\) | ||||
−0.493884 | + | 0.869528i | \(0.664423\pi\) | |||||||
\(200\) | −0.309017 | − | 0.951057i | −0.0218508 | − | 0.0672499i | ||||
\(201\) | −0.112618 | − | 0.0818219i | −0.00794348 | − | 0.00577127i | ||||
\(202\) | −14.7809 | + | 10.7389i | −1.03998 | + | 0.755588i | ||||
\(203\) | 0.925339 | − | 2.84790i | 0.0649460 | − | 0.199883i | ||||
\(204\) | 2.06316 | − | 6.34975i | 0.144450 | − | 0.444572i | ||||
\(205\) | −5.58347 | + | 4.05663i | −0.389966 | + | 0.283327i | ||||
\(206\) | −9.08908 | − | 6.60361i | −0.633266 | − | 0.460095i | ||||
\(207\) | 12.8592 | + | 39.5766i | 0.893778 | + | 2.75076i | ||||
\(208\) | −5.63670 | −0.390835 | ||||||||
\(209\) | 18.4447 | + | 18.2099i | 1.27585 | + | 1.25960i | ||||
\(210\) | 2.86564 | 0.197748 | ||||||||
\(211\) | 8.17339 | + | 25.1551i | 0.562680 | + | 1.73175i | 0.674747 | + | 0.738049i | \(0.264253\pi\) |
−0.112067 | + | 0.993701i | \(0.535747\pi\) | |||||||
\(212\) | −0.471410 | − | 0.342499i | −0.0323766 | − | 0.0235230i | ||||
\(213\) | 10.3250 | − | 7.50156i | 0.707458 | − | 0.513999i | ||||
\(214\) | −1.51158 | + | 4.65216i | −0.103329 | + | 0.318015i | ||||
\(215\) | −3.56891 | + | 10.9840i | −0.243398 | + | 0.749102i | ||||
\(216\) | −5.12787 | + | 3.72562i | −0.348908 | + | 0.253496i | ||||
\(217\) | −4.11412 | − | 2.98908i | −0.279285 | − | 0.202912i | ||||
\(218\) | −1.93581 | − | 5.95782i | −0.131110 | − | 0.403515i | ||||
\(219\) | 0.965185 | 0.0652211 | ||||||||
\(220\) | 0.539809 | + | 3.27240i | 0.0363939 | + | 0.220625i | ||||
\(221\) | 13.1327 | 0.883401 | ||||||||
\(222\) | −1.22806 | − | 3.77957i | −0.0824218 | − | 0.253668i | ||||
\(223\) | −19.8932 | − | 14.4532i | −1.33215 | − | 0.967860i | −0.999694 | − | 0.0247396i | \(-0.992124\pi\) |
−0.332451 | − | 0.943120i | \(-0.607876\pi\) | |||||||
\(224\) | 0.809017 | − | 0.587785i | 0.0540547 | − | 0.0392731i | ||||
\(225\) | 1.61056 | − | 4.95678i | 0.107370 | − | 0.330452i | ||||
\(226\) | −3.14119 | + | 9.66758i | −0.208949 | + | 0.643078i | ||||
\(227\) | 4.52437 | − | 3.28714i | 0.300293 | − | 0.218175i | −0.427427 | − | 0.904050i | \(-0.640580\pi\) |
0.727720 | + | 0.685874i | \(0.240580\pi\) | |||||||
\(228\) | −18.1178 | − | 13.1633i | −1.19988 | − | 0.871762i | ||||
\(229\) | −2.50409 | − | 7.70679i | −0.165475 | − | 0.509279i | 0.833596 | − | 0.552374i | \(-0.186278\pi\) |
−0.999071 | + | 0.0430954i | \(0.986278\pi\) | |||||||
\(230\) | −7.98434 | −0.526472 | ||||||||
\(231\) | −9.39656 | − | 1.42662i | −0.618248 | − | 0.0938650i | ||||
\(232\) | −2.99446 | −0.196596 | ||||||||
\(233\) | 3.70224 | + | 11.3943i | 0.242542 | + | 0.746467i | 0.996031 | + | 0.0890066i | \(0.0283692\pi\) |
−0.753489 | + | 0.657460i | \(0.771631\pi\) | |||||||
\(234\) | −23.7671 | − | 17.2678i | −1.55370 | − | 1.12883i | ||||
\(235\) | 4.16255 | − | 3.02427i | 0.271535 | − | 0.197282i | ||||
\(236\) | 4.27346 | − | 13.1523i | 0.278178 | − | 0.856145i | ||||
\(237\) | −0.932383 | + | 2.86958i | −0.0605648 | + | 0.186399i | ||||
\(238\) | −1.88489 | + | 1.36946i | −0.122180 | + | 0.0887687i | ||||
\(239\) | 5.23120 | + | 3.80069i | 0.338378 | + | 0.245846i | 0.743977 | − | 0.668205i | \(-0.232937\pi\) |
−0.405599 | + | 0.914051i | \(0.632937\pi\) | |||||||
\(240\) | −0.885530 | − | 2.72538i | −0.0571607 | − | 0.175923i | ||||
\(241\) | 20.3441 | 1.31048 | 0.655238 | − | 0.755423i | \(-0.272568\pi\) | ||||
0.655238 | + | 0.755423i | \(0.272568\pi\) | |||||||
\(242\) | −0.140931 | − | 10.9991i | −0.00905938 | − | 0.707049i | ||||
\(243\) | 11.7710 | 0.755112 | ||||||||
\(244\) | 2.41788 | + | 7.44148i | 0.154789 | + | 0.476392i | ||||
\(245\) | −0.809017 | − | 0.587785i | −0.0516862 | − | 0.0375522i | ||||
\(246\) | −16.0002 | + | 11.6248i | −1.02013 | + | 0.741171i | ||||
\(247\) | 13.6123 | − | 41.8945i | 0.866132 | − | 2.66568i | ||||
\(248\) | −1.57145 | + | 4.83644i | −0.0997874 | + | 0.307114i | ||||
\(249\) | 25.1112 | − | 18.2443i | 1.59135 | − | 1.15619i | ||||
\(250\) | 0.809017 | + | 0.587785i | 0.0511667 | + | 0.0371748i | ||||
\(251\) | 3.88875 | + | 11.9683i | 0.245456 | + | 0.755434i | 0.995561 | + | 0.0941164i | \(0.0300026\pi\) |
−0.750106 | + | 0.661318i | \(0.769997\pi\) | |||||||
\(252\) | 5.21187 | 0.328317 | ||||||||
\(253\) | 26.1810 | + | 3.97491i | 1.64599 | + | 0.249901i | ||||
\(254\) | −6.58727 | −0.413322 | ||||||||
\(255\) | 2.06316 | + | 6.34975i | 0.129200 | + | 0.397637i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −2.79916 | + | 2.03371i | −0.174607 | + | 0.126859i | −0.671656 | − | 0.740863i | \(-0.734417\pi\) |
0.497050 | + | 0.867722i | \(0.334417\pi\) | |||||||
\(258\) | −10.2272 | + | 31.4761i | −0.636718 | + | 1.95962i | ||||
\(259\) | −0.428546 | + | 1.31893i | −0.0266286 | + | 0.0819543i | ||||
\(260\) | 4.56018 | − | 3.31317i | 0.282811 | − | 0.205474i | ||||
\(261\) | −12.6261 | − | 9.17340i | −0.781536 | − | 0.567819i | ||||
\(262\) | −0.373357 | − | 1.14907i | −0.0230661 | − | 0.0709900i | ||||
\(263\) | −8.01789 | −0.494404 | −0.247202 | − | 0.968964i | \(-0.579511\pi\) | ||||
−0.247202 | + | 0.968964i | \(0.579511\pi\) | |||||||
\(264\) | 1.54690 | + | 9.37751i | 0.0952048 | + | 0.577146i | ||||
\(265\) | 0.582695 | 0.0357946 | ||||||||
\(266\) | 2.41495 | + | 7.43245i | 0.148070 | + | 0.455713i | ||||
\(267\) | −42.9517 | − | 31.2062i | −2.62860 | − | 1.90979i | ||||
\(268\) | 0.0392996 | − | 0.0285528i | 0.00240060 | − | 0.00174414i | ||||
\(269\) | −5.73690 | + | 17.6563i | −0.349785 | + | 1.07653i | 0.609187 | + | 0.793026i | \(0.291496\pi\) |
−0.958972 | + | 0.283500i | \(0.908504\pi\) | |||||||
\(270\) | 1.95867 | − | 6.02818i | 0.119201 | − | 0.366863i | ||||
\(271\) | −20.3914 | + | 14.8152i | −1.23869 | + | 0.899960i | −0.997510 | − | 0.0705210i | \(-0.977534\pi\) |
−0.241178 | + | 0.970481i | \(0.577534\pi\) | |||||||
\(272\) | 1.88489 | + | 1.36946i | 0.114289 | + | 0.0830355i | ||||
\(273\) | 4.99146 | + | 15.3621i | 0.302097 | + | 0.929759i | ||||
\(274\) | −14.0829 | −0.850777 | ||||||||
\(275\) | −2.36018 | − | 2.33014i | −0.142324 | − | 0.140512i | ||||
\(276\) | −22.8802 | −1.37723 | ||||||||
\(277\) | −3.77868 | − | 11.6296i | −0.227039 | − | 0.698754i | −0.998078 | − | 0.0619665i | \(-0.980263\pi\) |
0.771039 | − | 0.636788i | \(-0.219737\pi\) | |||||||
\(278\) | 2.21905 | + | 1.61224i | 0.133090 | + | 0.0966956i | ||||
\(279\) | −21.4422 | + | 15.5787i | −1.28371 | + | 0.932672i | ||||
\(280\) | −0.309017 | + | 0.951057i | −0.0184673 | + | 0.0568365i | ||||
\(281\) | 8.21782 | − | 25.2919i | 0.490234 | − | 1.50879i | −0.334020 | − | 0.942566i | \(-0.608405\pi\) |
0.824254 | − | 0.566220i | \(-0.191595\pi\) | |||||||
\(282\) | 11.9284 | − | 8.66646i | 0.710323 | − | 0.516080i | ||||
\(283\) | 11.1013 | + | 8.06560i | 0.659906 | + | 0.479450i | 0.866631 | − | 0.498949i | \(-0.166281\pi\) |
−0.206725 | + | 0.978399i | \(0.566281\pi\) | |||||||
\(284\) | 1.37624 | + | 4.23563i | 0.0816649 | + | 0.251339i | ||||
\(285\) | 22.3948 | 1.32655 | ||||||||
\(286\) | −16.6025 | + | 8.59380i | −0.981725 | + | 0.508162i | ||||
\(287\) | 6.90154 | 0.407385 | ||||||||
\(288\) | −1.61056 | − | 4.95678i | −0.0949029 | − | 0.292081i | ||||
\(289\) | 9.36175 | + | 6.80171i | 0.550691 | + | 0.400101i | ||||
\(290\) | 2.42257 | − | 1.76010i | 0.142258 | − | 0.103357i | ||||
\(291\) | 4.72147 | − | 14.5312i | 0.276777 | − | 0.851833i | ||||
\(292\) | −0.104081 | + | 0.320329i | −0.00609089 | + | 0.0187458i | ||||
\(293\) | −0.578013 | + | 0.419951i | −0.0337679 | + | 0.0245338i | −0.604541 | − | 0.796574i | \(-0.706644\pi\) |
0.570773 | + | 0.821108i | \(0.306644\pi\) | |||||||
\(294\) | −2.31835 | − | 1.68438i | −0.135209 | − | 0.0982349i | ||||
\(295\) | 4.27346 | + | 13.1523i | 0.248810 | + | 0.765759i | ||||
\(296\) | 1.38681 | 0.0806064 | ||||||||
\(297\) | −9.42365 | + | 18.7916i | −0.546815 | + | 1.09040i | ||||
\(298\) | 17.1642 | 0.994298 | ||||||||
\(299\) | −13.9074 | − | 42.8026i | −0.804286 | − | 2.47534i | ||||
\(300\) | 2.31835 | + | 1.68438i | 0.133850 | + | 0.0972476i | ||||
\(301\) | 9.34354 | − | 6.78848i | 0.538553 | − | 0.391281i | ||||
\(302\) | −1.83650 | + | 5.65216i | −0.105679 | + | 0.325245i | ||||
\(303\) | 16.1788 | − | 49.7931i | 0.929445 | − | 2.86054i | ||||
\(304\) | 6.32242 | − | 4.59351i | 0.362616 | − | 0.263456i | ||||
\(305\) | −6.33010 | − | 4.59909i | −0.362460 | − | 0.263343i | ||||
\(306\) | 3.75236 | + | 11.5486i | 0.214508 | + | 0.660189i | ||||
\(307\) | −19.3442 | −1.10403 | −0.552015 | − | 0.833834i | \(-0.686141\pi\) | ||||
−0.552015 | + | 0.833834i | \(0.686141\pi\) | |||||||
\(308\) | 1.48675 | − | 2.96472i | 0.0847157 | − | 0.168931i | ||||
\(309\) | 32.1946 | 1.83149 | ||||||||
\(310\) | −1.57145 | − | 4.83644i | −0.0892526 | − | 0.274691i | ||||
\(311\) | −1.47831 | − | 1.07405i | −0.0838271 | − | 0.0609039i | 0.545082 | − | 0.838382i | \(-0.316498\pi\) |
−0.628909 | + | 0.777479i | \(0.716498\pi\) | |||||||
\(312\) | 13.0678 | − | 9.49433i | 0.739820 | − | 0.537510i | ||||
\(313\) | −3.03797 | + | 9.34991i | −0.171716 | + | 0.528488i | −0.999468 | − | 0.0326057i | \(-0.989619\pi\) |
0.827752 | + | 0.561094i | \(0.189619\pi\) | |||||||
\(314\) | 5.18986 | − | 15.9727i | 0.292881 | − | 0.901394i | ||||
\(315\) | −4.21649 | + | 3.06346i | −0.237572 | + | 0.172606i | ||||
\(316\) | −0.851822 | − | 0.618885i | −0.0479187 | − | 0.0348150i | ||||
\(317\) | −4.28127 | − | 13.1764i | −0.240460 | − | 0.740060i | −0.996350 | − | 0.0853616i | \(-0.972795\pi\) |
0.755890 | − | 0.654699i | \(-0.227205\pi\) | |||||||
\(318\) | 1.66979 | 0.0936372 | ||||||||
\(319\) | −8.81996 | + | 4.56540i | −0.493823 | + | 0.255613i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −4.33163 | − | 13.3314i | −0.241768 | − | 0.744086i | ||||
\(322\) | 6.45947 | + | 4.69308i | 0.359972 | + | 0.261535i | ||||
\(323\) | −14.7303 | + | 10.7022i | −0.819618 | + | 0.595487i | ||||
\(324\) | 0.781179 | − | 2.40422i | 0.0433988 | − | 0.133568i | ||||
\(325\) | −1.74183 | + | 5.36082i | −0.0966196 | + | 0.297365i | ||||
\(326\) | 1.96624 | − | 1.42856i | 0.108900 | − | 0.0791205i | ||||
\(327\) | 14.5231 | + | 10.5517i | 0.803130 | + | 0.583508i | ||||
\(328\) | −2.13269 | − | 6.56376i | −0.117758 | − | 0.362423i | ||||
\(329\) | −5.14520 | −0.283664 | ||||||||
\(330\) | −6.76342 | − | 6.67732i | −0.372314 | − | 0.367574i | ||||
\(331\) | 8.02084 | 0.440865 | 0.220433 | − | 0.975402i | \(-0.429253\pi\) | ||||
0.220433 | + | 0.975402i | \(0.429253\pi\) | |||||||
\(332\) | 3.34711 | + | 10.3014i | 0.183697 | + | 0.565360i | ||||
\(333\) | 5.84745 | + | 4.24842i | 0.320438 | + | 0.232812i | ||||
\(334\) | −8.92393 | + | 6.48361i | −0.488296 | + | 0.354768i | ||||
\(335\) | −0.0150111 | + | 0.0461994i | −0.000820144 | + | 0.00252414i | ||||
\(336\) | −0.885530 | + | 2.72538i | −0.0483096 | + | 0.148682i | ||||
\(337\) | 9.38943 | − | 6.82182i | 0.511475 | − | 0.371608i | −0.301908 | − | 0.953337i | \(-0.597624\pi\) |
0.813383 | + | 0.581729i | \(0.197624\pi\) | |||||||
\(338\) | 15.1871 | + | 11.0341i | 0.826071 | + | 0.600176i | ||||
\(339\) | −9.00149 | − | 27.7038i | −0.488894 | − | 1.50466i | ||||
\(340\) | −2.32986 | −0.126354 | ||||||||
\(341\) | 2.74511 | + | 16.6412i | 0.148656 | + | 0.901174i | ||||
\(342\) | 40.7304 | 2.20245 | ||||||||
\(343\) | 0.309017 | + | 0.951057i | 0.0166853 | + | 0.0513522i | ||||
\(344\) | −9.34354 | − | 6.78848i | −0.503770 | − | 0.366010i | ||||
\(345\) | 18.5105 | − | 13.4486i | 0.996571 | − | 0.724051i | ||||
\(346\) | −4.54090 | + | 13.9754i | −0.244120 | + | 0.751325i | ||||
\(347\) | −8.16734 | + | 25.1365i | −0.438446 | + | 1.34940i | 0.451069 | + | 0.892489i | \(0.351043\pi\) |
−0.889514 | + | 0.456907i | \(0.848957\pi\) | |||||||
\(348\) | 6.94220 | − | 5.04380i | 0.372141 | − | 0.270376i | ||||
\(349\) | −22.1490 | − | 16.0922i | −1.18561 | − | 0.861396i | −0.192816 | − | 0.981235i | \(-0.561762\pi\) |
−0.992793 | + | 0.119839i | \(0.961762\pi\) | |||||||
\(350\) | −0.309017 | − | 0.951057i | −0.0165177 | − | 0.0508361i | ||||
\(351\) | 35.7276 | 1.90700 | ||||||||
\(352\) | −3.27905 | − | 0.497839i | −0.174774 | − | 0.0265349i | ||||
\(353\) | 21.3772 | 1.13779 | 0.568897 | − | 0.822409i | \(-0.307370\pi\) | ||||
0.568897 | + | 0.822409i | \(0.307370\pi\) | |||||||
\(354\) | 12.2462 | + | 37.6898i | 0.650877 | + | 2.00319i | ||||
\(355\) | −3.60305 | − | 2.61777i | −0.191230 | − | 0.138937i | ||||
\(356\) | 14.9885 | − | 10.8898i | 0.794391 | − | 0.577159i | ||||
\(357\) | 2.06316 | − | 6.34975i | 0.109194 | − | 0.336064i | ||||
\(358\) | −1.39488 | + | 4.29300i | −0.0737217 | + | 0.226892i | ||||
\(359\) | 8.81053 | − | 6.40123i | 0.465002 | − | 0.337844i | −0.330488 | − | 0.943810i | \(-0.607213\pi\) |
0.795490 | + | 0.605966i | \(0.207213\pi\) | |||||||
\(360\) | 4.21649 | + | 3.06346i | 0.222228 | + | 0.161458i | ||||
\(361\) | 13.0014 | + | 40.0141i | 0.684283 | + | 2.10601i | ||||
\(362\) | 10.1770 | 0.534891 | ||||||||
\(363\) | 18.8534 | + | 25.2624i | 0.989545 | + | 1.32593i | ||||
\(364\) | −5.63670 | −0.295443 | ||||||||
\(365\) | −0.104081 | − | 0.320329i | −0.00544785 | − | 0.0167668i | ||||
\(366\) | −18.1398 | − | 13.1793i | −0.948180 | − | 0.688893i | ||||
\(367\) | −9.15059 | + | 6.64829i | −0.477657 | + | 0.347038i | −0.800418 | − | 0.599442i | \(-0.795389\pi\) |
0.322761 | + | 0.946481i | \(0.395389\pi\) | |||||||
\(368\) | 2.46730 | − | 7.59356i | 0.128617 | − | 0.395842i | ||||
\(369\) | 11.1153 | − | 34.2094i | 0.578640 | − | 1.78087i | ||||
\(370\) | −1.12195 | + | 0.815144i | −0.0583273 | + | 0.0423773i | ||||
\(371\) | −0.471410 | − | 0.342499i | −0.0244744 | − | 0.0177817i | ||||
\(372\) | −4.50321 | − | 13.8595i | −0.233481 | − | 0.718580i | ||||
\(373\) | 11.6658 | 0.604034 | 0.302017 | − | 0.953303i | \(-0.402340\pi\) | ||||
0.302017 | + | 0.953303i | \(0.402340\pi\) | |||||||
\(374\) | 7.63972 | + | 1.15989i | 0.395040 | + | 0.0599767i | ||||
\(375\) | −2.86564 | −0.147981 | ||||||||
\(376\) | 1.58995 | + | 4.89337i | 0.0819956 | + | 0.252356i | ||||
\(377\) | 13.6553 | + | 9.92114i | 0.703283 | + | 0.510965i | ||||
\(378\) | −5.12787 | + | 3.72562i | −0.263749 | + | 0.191625i | ||||
\(379\) | 0.190691 | − | 0.586886i | 0.00979512 | − | 0.0301463i | −0.946040 | − | 0.324051i | \(-0.894955\pi\) |
0.955835 | + | 0.293905i | \(0.0949549\pi\) | |||||||
\(380\) | −2.41495 | + | 7.43245i | −0.123884 | + | 0.381277i | ||||
\(381\) | 15.2716 | − | 11.0955i | 0.782387 | − | 0.568438i | ||||
\(382\) | 9.70127 | + | 7.04838i | 0.496360 | + | 0.360627i | ||||
\(383\) | −8.17261 | − | 25.1527i | −0.417601 | − | 1.28524i | −0.909904 | − | 0.414819i | \(-0.863845\pi\) |
0.492303 | − | 0.870424i | \(-0.336155\pi\) | |||||||
\(384\) | 2.86564 | 0.146236 | ||||||||
\(385\) | 0.539809 | + | 3.27240i | 0.0275112 | + | 0.166777i | ||||
\(386\) | 17.8748 | 0.909806 | ||||||||
\(387\) | −18.6007 | − | 57.2471i | −0.945527 | − | 2.91003i | ||||
\(388\) | 4.31351 | + | 3.13395i | 0.218986 | + | 0.159102i | ||||
\(389\) | −1.29803 | + | 0.943076i | −0.0658129 | + | 0.0478158i | −0.620205 | − | 0.784440i | \(-0.712951\pi\) |
0.554392 | + | 0.832255i | \(0.312951\pi\) | |||||||
\(390\) | −4.99146 | + | 15.3621i | −0.252753 | + | 0.777892i | ||||
\(391\) | −5.74845 | + | 17.6919i | −0.290712 | + | 0.894719i | ||||
\(392\) | 0.809017 | − | 0.587785i | 0.0408615 | − | 0.0296876i | ||||
\(393\) | 2.80105 | + | 2.03508i | 0.141294 | + | 0.102656i | ||||
\(394\) | 3.64241 | + | 11.2102i | 0.183502 | + | 0.564761i | ||||
\(395\) | 1.05291 | 0.0529776 | ||||||||
\(396\) | −12.3010 | − | 12.1444i | −0.618146 | − | 0.610277i | ||||
\(397\) | 5.28819 | 0.265407 | 0.132703 | − | 0.991156i | \(-0.457634\pi\) | ||||
0.132703 | + | 0.991156i | \(0.457634\pi\) | |||||||
\(398\) | 4.30590 | + | 13.2522i | 0.215835 | + | 0.664272i | ||||
\(399\) | −18.1178 | − | 13.1633i | −0.907022 | − | 0.658990i | ||||
\(400\) | −0.809017 | + | 0.587785i | −0.0404508 | + | 0.0293893i | ||||
\(401\) | −4.20445 | + | 12.9400i | −0.209960 | + | 0.646192i | 0.789513 | + | 0.613734i | \(0.210333\pi\) |
−0.999473 | + | 0.0324575i | \(0.989667\pi\) | |||||||
\(402\) | −0.0430163 | + | 0.132391i | −0.00214546 | + | 0.00660304i | ||||
\(403\) | 23.1900 | − | 16.8485i | 1.15518 | − | 0.839286i | ||||
\(404\) | 14.7809 | + | 10.7389i | 0.735375 | + | 0.534281i | ||||
\(405\) | 0.781179 | + | 2.40422i | 0.0388171 | + | 0.119467i | ||||
\(406\) | −2.99446 | −0.148613 | ||||||||
\(407\) | 4.08473 | − | 2.11435i | 0.202473 | − | 0.104804i | ||||
\(408\) | −6.67652 | −0.330537 | ||||||||
\(409\) | −1.05137 | − | 3.23578i | −0.0519868 | − | 0.159999i | 0.921693 | − | 0.387921i | \(-0.126807\pi\) |
−0.973679 | + | 0.227922i | \(0.926807\pi\) | |||||||
\(410\) | 5.58347 | + | 4.05663i | 0.275748 | + | 0.200342i | ||||
\(411\) | 32.6490 | − | 23.7209i | 1.61046 | − | 1.17006i | ||||
\(412\) | −3.47172 | + | 10.6849i | −0.171039 | + | 0.526405i | ||||
\(413\) | 4.27346 | − | 13.1523i | 0.210283 | − | 0.647185i | ||||
\(414\) | 33.6659 | − | 24.4597i | 1.65459 | − | 1.20213i | ||||
\(415\) | −8.76286 | − | 6.36659i | −0.430152 | − | 0.312524i | ||||
\(416\) | 1.74183 | + | 5.36082i | 0.0854005 | + | 0.262836i | ||||
\(417\) | −7.86016 | −0.384914 | ||||||||
\(418\) | 11.6189 | − | 23.1691i | 0.568299 | − | 1.13324i | ||||
\(419\) | −39.5263 | −1.93099 | −0.965493 | − | 0.260428i | \(-0.916136\pi\) | ||||
−0.965493 | + | 0.260428i | \(0.916136\pi\) | |||||||
\(420\) | −0.885530 | − | 2.72538i | −0.0432094 | − | 0.132985i | ||||
\(421\) | 12.6706 | + | 9.20571i | 0.617526 | + | 0.448659i | 0.852057 | − | 0.523450i | \(-0.175355\pi\) |
−0.234530 | + | 0.972109i | \(0.575355\pi\) | |||||||
\(422\) | 21.3982 | − | 15.5467i | 1.04165 | − | 0.756802i | ||||
\(423\) | −8.28662 | + | 25.5036i | −0.402909 | + | 1.24003i | ||||
\(424\) | −0.180063 | + | 0.554176i | −0.00874461 | + | 0.0269131i | ||||
\(425\) | 1.88489 | − | 1.36946i | 0.0914308 | − | 0.0664284i | ||||
\(426\) | −10.3250 | − | 7.50156i | −0.500249 | − | 0.363452i | ||||
\(427\) | 2.41788 | + | 7.44148i | 0.117010 | + | 0.360118i | ||||
\(428\) | 4.89157 | 0.236443 | ||||||||
\(429\) | 24.0151 | − | 47.8883i | 1.15946 | − | 2.31207i | ||||
\(430\) | 11.5492 | 0.556954 | ||||||||
\(431\) | 1.74023 | + | 5.35587i | 0.0838239 | + | 0.257983i | 0.984180 | − | 0.177170i | \(-0.0566942\pi\) |
−0.900356 | + | 0.435153i | \(0.856694\pi\) | |||||||
\(432\) | 5.12787 | + | 3.72562i | 0.246715 | + | 0.179249i | ||||
\(433\) | 27.9291 | − | 20.2917i | 1.34219 | − | 0.975156i | 0.342827 | − | 0.939399i | \(-0.388616\pi\) |
0.999360 | − | 0.0357576i | \(-0.0113844\pi\) | |||||||
\(434\) | −1.57145 | + | 4.83644i | −0.0754322 | + | 0.232156i | ||||
\(435\) | −2.65168 | + | 8.16104i | −0.127138 | + | 0.391292i | ||||
\(436\) | −5.06802 | + | 3.68214i | −0.242714 | + | 0.176342i | ||||
\(437\) | 50.4804 | + | 36.6761i | 2.41480 | + | 1.75446i | ||||
\(438\) | −0.298258 | − | 0.917945i | −0.0142513 | − | 0.0438611i | ||||
\(439\) | 30.0533 | 1.43437 | 0.717184 | − | 0.696884i | \(-0.245431\pi\) | ||||
0.717184 | + | 0.696884i | \(0.245431\pi\) | |||||||
\(440\) | 2.94543 | − | 1.52462i | 0.140418 | − | 0.0726832i | ||||
\(441\) | 5.21187 | 0.248184 | ||||||||
\(442\) | −4.05823 | − | 12.4899i | −0.193030 | − | 0.594086i | ||||
\(443\) | 25.9412 | + | 18.8474i | 1.23251 | + | 0.895468i | 0.997075 | − | 0.0764234i | \(-0.0243501\pi\) |
0.235430 | + | 0.971891i | \(0.424350\pi\) | |||||||
\(444\) | −3.21510 | + | 2.33590i | −0.152582 | + | 0.110857i | ||||
\(445\) | −5.72511 | + | 17.6201i | −0.271396 | + | 0.835272i | ||||
\(446\) | −7.59851 | + | 23.3858i | −0.359800 | + | 1.10735i | ||||
\(447\) | −39.7927 | + | 28.9111i | −1.88213 | + | 1.36745i | ||||
\(448\) | −0.809017 | − | 0.587785i | −0.0382225 | − | 0.0277702i | ||||
\(449\) | −2.86677 | − | 8.82300i | −0.135291 | − | 0.416383i | 0.860344 | − | 0.509714i | \(-0.170249\pi\) |
−0.995635 | + | 0.0933305i | \(0.970249\pi\) | |||||||
\(450\) | −5.21187 | −0.245690 | ||||||||
\(451\) | −16.2889 | − | 16.0815i | −0.767015 | − | 0.757250i | ||||
\(452\) | 10.1651 | 0.478126 | ||||||||
\(453\) | −5.26274 | − | 16.1970i | −0.247265 | − | 0.761003i | ||||
\(454\) | −4.52437 | − | 3.28714i | −0.212339 | − | 0.154273i | ||||
\(455\) | 4.56018 | − | 3.31317i | 0.213785 | − | 0.155324i | ||||
\(456\) | −6.92037 | + | 21.2987i | −0.324076 | + | 0.997403i | ||||
\(457\) | −6.20449 | + | 19.0955i | −0.290234 | + | 0.893248i | 0.694547 | + | 0.719448i | \(0.255605\pi\) |
−0.984781 | + | 0.173801i | \(0.944395\pi\) | |||||||
\(458\) | −6.55579 | + | 4.76306i | −0.306332 | + | 0.222563i | ||||
\(459\) | −11.9472 | − | 8.68016i | −0.557648 | − | 0.405155i | ||||
\(460\) | 2.46730 | + | 7.59356i | 0.115038 | + | 0.354052i | ||||
\(461\) | 14.6490 | 0.682272 | 0.341136 | − | 0.940014i | \(-0.389188\pi\) | ||||
0.341136 | + | 0.940014i | \(0.389188\pi\) | |||||||
\(462\) | 1.54690 | + | 9.37751i | 0.0719681 | + | 0.436281i | ||||
\(463\) | 11.0973 | 0.515737 | 0.257869 | − | 0.966180i | \(-0.416980\pi\) | ||||
0.257869 | + | 0.966180i | \(0.416980\pi\) | |||||||
\(464\) | 0.925339 | + | 2.84790i | 0.0429578 | + | 0.132210i | ||||
\(465\) | 11.7896 | + | 8.56562i | 0.546728 | + | 0.397221i | ||||
\(466\) | 9.69259 | − | 7.04208i | 0.449001 | − | 0.326218i | ||||
\(467\) | 7.63033 | − | 23.4838i | 0.353090 | − | 1.08670i | −0.604019 | − | 0.796970i | \(-0.706435\pi\) |
0.957109 | − | 0.289729i | \(-0.0935650\pi\) | |||||||
\(468\) | −9.07821 | + | 27.9399i | −0.419640 | + | 1.29152i | ||||
\(469\) | 0.0392996 | − | 0.0285528i | 0.00181469 | − | 0.00131845i | ||||
\(470\) | −4.16255 | − | 3.02427i | −0.192004 | − | 0.139499i | ||||
\(471\) | 14.8722 | + | 45.7720i | 0.685277 | + | 2.10906i | ||||
\(472\) | −13.8292 | −0.636540 | ||||||||
\(473\) | −37.8705 | − | 5.74966i | −1.74129 | − | 0.264370i | ||||
\(474\) | 3.01726 | 0.138587 | ||||||||
\(475\) | −2.41495 | − | 7.43245i | −0.110805 | − | 0.341024i | ||||
\(476\) | 1.88489 | + | 1.36946i | 0.0863940 | + | 0.0627689i | ||||
\(477\) | −2.45693 | + | 1.78506i | −0.112495 | + | 0.0817323i | ||||
\(478\) | 1.99814 | − | 6.14964i | 0.0913928 | − | 0.281278i | ||||
\(479\) | −9.64485 | + | 29.6838i | −0.440684 | + | 1.35629i | 0.446464 | + | 0.894802i | \(0.352683\pi\) |
−0.887148 | + | 0.461485i | \(0.847317\pi\) | |||||||
\(480\) | −2.31835 | + | 1.68438i | −0.105818 | + | 0.0768810i | ||||
\(481\) | −6.32408 | − | 4.59472i | −0.288353 | − | 0.209501i | ||||
\(482\) | −6.28666 | − | 19.3483i | −0.286349 | − | 0.881293i | ||||
\(483\) | −22.8802 | −1.04109 | ||||||||
\(484\) | −10.4172 | + | 3.53294i | −0.473510 | + | 0.160588i | ||||
\(485\) | −5.33180 | −0.242104 | ||||||||
\(486\) | −3.63745 | − | 11.1949i | −0.164998 | − | 0.507811i | ||||
\(487\) | −2.44952 | − | 1.77968i | −0.110998 | − | 0.0806449i | 0.530901 | − | 0.847434i | \(-0.321853\pi\) |
−0.641900 | + | 0.766789i | \(0.721853\pi\) | |||||||
\(488\) | 6.33010 | − | 4.59909i | 0.286550 | − | 0.208191i | ||||
\(489\) | −2.15220 | + | 6.62379i | −0.0973258 | + | 0.299538i | ||||
\(490\) | −0.309017 | + | 0.951057i | −0.0139600 | + | 0.0429644i | ||||
\(491\) | 11.9791 | − | 8.70331i | 0.540608 | − | 0.392775i | −0.283703 | − | 0.958912i | \(-0.591563\pi\) |
0.824311 | + | 0.566138i | \(0.191563\pi\) | |||||||
\(492\) | 16.0002 | + | 11.6248i | 0.721344 | + | 0.524087i | ||||
\(493\) | −2.15591 | − | 6.63520i | −0.0970972 | − | 0.298834i | ||||
\(494\) | −44.0504 | −1.98192 | ||||||||
\(495\) | 17.0900 | + | 2.59467i | 0.768137 | + | 0.116622i | ||||
\(496\) | 5.08533 | 0.228338 | ||||||||
\(497\) | 1.37624 | + | 4.23563i | 0.0617328 | + | 0.189994i | ||||
\(498\) | −25.1112 | − | 18.2443i | −1.12526 | − | 0.817548i | ||||
\(499\) | 5.65863 | − | 4.11124i | 0.253315 | − | 0.184044i | −0.453880 | − | 0.891063i | \(-0.649960\pi\) |
0.707195 | + | 0.707019i | \(0.249960\pi\) | |||||||
\(500\) | 0.309017 | − | 0.951057i | 0.0138197 | − | 0.0425325i | ||||
\(501\) | 9.76791 | − | 30.0625i | 0.436398 | − | 1.34310i | ||||
\(502\) | 10.1809 | − | 7.39684i | 0.454395 | − | 0.330137i | ||||
\(503\) | 1.56788 | + | 1.13913i | 0.0699081 | + | 0.0507912i | 0.622190 | − | 0.782866i | \(-0.286243\pi\) |
−0.552282 | + | 0.833657i | \(0.686243\pi\) | |||||||
\(504\) | −1.61056 | − | 4.95678i | −0.0717398 | − | 0.220792i | ||||
\(505\) | −18.2701 | −0.813011 | ||||||||
\(506\) | −4.31002 | − | 26.1280i | −0.191604 | − | 1.16153i | ||||
\(507\) | −53.7947 | −2.38910 | ||||||||
\(508\) | 2.03558 | + | 6.26487i | 0.0903142 | + | 0.277959i | ||||
\(509\) | −10.4783 | − | 7.61290i | −0.464441 | − | 0.337436i | 0.330830 | − | 0.943690i | \(-0.392671\pi\) |
−0.795271 | + | 0.606254i | \(0.792671\pi\) | |||||||
\(510\) | 5.40142 | − | 3.92436i | 0.239179 | − | 0.173774i | ||||
\(511\) | −0.104081 | + | 0.320329i | −0.00460428 | + | 0.0141705i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | −40.0740 | + | 29.1155i | −1.76931 | + | 1.28548i | ||||
\(514\) | 2.79916 | + | 2.03371i | 0.123465 | + | 0.0897029i | ||||
\(515\) | −3.47172 | − | 10.6849i | −0.152982 | − | 0.470831i | ||||
\(516\) | 33.0959 | 1.45697 | ||||||||
\(517\) | 12.1436 | + | 11.9890i | 0.534075 | + | 0.527276i | ||||
\(518\) | 1.38681 | 0.0609327 | ||||||||
\(519\) | −13.0126 | − | 40.0485i | −0.571188 | − | 1.75794i | ||||
\(520\) | −4.56018 | − | 3.31317i | −0.199977 | − | 0.145292i | ||||
\(521\) | 4.77691 | − | 3.47063i | 0.209280 | − | 0.152051i | −0.478208 | − | 0.878247i | \(-0.658713\pi\) |
0.687488 | + | 0.726196i | \(0.258713\pi\) | |||||||
\(522\) | −4.82274 | + | 14.8429i | −0.211086 | + | 0.649655i | ||||
\(523\) | −5.62239 | + | 17.3039i | −0.245850 | + | 0.756649i | 0.749645 | + | 0.661840i | \(0.230224\pi\) |
−0.995495 | + | 0.0948089i | \(0.969776\pi\) | |||||||
\(524\) | −0.977461 | + | 0.710167i | −0.0427006 | + | 0.0310238i | ||||
\(525\) | 2.31835 | + | 1.68438i | 0.101181 | + | 0.0735123i | ||||
\(526\) | 2.47766 | + | 7.62546i | 0.108031 | + | 0.332486i | ||||
\(527\) | −11.8481 | −0.516111 | ||||||||
\(528\) | 8.44052 | − | 4.36899i | 0.367327 | − | 0.190136i | ||||
\(529\) | 40.7497 | 1.77173 | ||||||||
\(530\) | −0.180063 | − | 0.554176i | −0.00782142 | − | 0.0240718i | ||||
\(531\) | −58.3106 | − | 42.3652i | −2.53047 | − | 1.83849i | ||||
\(532\) | 6.32242 | − | 4.59351i | 0.274112 | − | 0.199154i | ||||
\(533\) | −12.0213 | + | 36.9979i | −0.520702 | + | 1.60256i | ||||
\(534\) | −16.4061 | + | 50.4927i | −0.709961 | + | 2.18503i | ||||
\(535\) | −3.95736 | + | 2.87519i | −0.171092 | + | 0.124305i | ||||
\(536\) | −0.0392996 | − | 0.0285528i | −0.00169748 | − | 0.00123329i | ||||
\(537\) | −3.99722 | − | 12.3022i | −0.172493 | − | 0.530878i | ||||
\(538\) | 18.5650 | 0.800393 | ||||||||
\(539\) | 1.48675 | − | 2.96472i | 0.0640390 | − | 0.127700i | ||||
\(540\) | −6.33840 | −0.272761 | ||||||||
\(541\) | −4.68238 | − | 14.4109i | −0.201311 | − | 0.619573i | −0.999845 | − | 0.0176221i | \(-0.994390\pi\) |
0.798533 | − | 0.601951i | \(-0.205610\pi\) | |||||||
\(542\) | 20.3914 | + | 14.8152i | 0.875885 | + | 0.636368i | ||||
\(543\) | −23.5938 | + | 17.1419i | −1.01251 | + | 0.735630i | ||||
\(544\) | 0.719966 | − | 2.21583i | 0.0308683 | − | 0.0950028i | ||||
\(545\) | 1.93581 | − | 5.95782i | 0.0829211 | − | 0.255205i | ||||
\(546\) | 13.0678 | − | 9.49433i | 0.559251 | − | 0.406320i | ||||
\(547\) | 8.36275 | + | 6.07590i | 0.357566 | + | 0.259787i | 0.752036 | − | 0.659122i | \(-0.229072\pi\) |
−0.394470 | + | 0.918909i | \(0.629072\pi\) | |||||||
\(548\) | 4.35184 | + | 13.3936i | 0.185902 | + | 0.572146i | ||||
\(549\) | 40.7799 | 1.74044 | ||||||||
\(550\) | −1.48675 | + | 2.96472i | −0.0633954 | + | 0.126416i | ||||
\(551\) | −23.4015 | −0.996938 | ||||||||
\(552\) | 7.07037 | + | 21.7604i | 0.300935 | + | 0.926183i | ||||
\(553\) | −0.851822 | − | 0.618885i | −0.0362232 | − | 0.0263177i | ||||
\(554\) | −9.89272 | + | 7.18748i | −0.420301 | + | 0.305367i | ||||
\(555\) | 1.22806 | − | 3.77957i | 0.0521281 | − | 0.160434i | ||||
\(556\) | 0.847603 | − | 2.60865i | 0.0359464 | − | 0.110632i | ||||
\(557\) | 5.18625 | − | 3.76803i | 0.219749 | − | 0.159657i | −0.472465 | − | 0.881350i | \(-0.656636\pi\) |
0.692214 | + | 0.721693i | \(0.256636\pi\) | |||||||
\(558\) | 21.4422 | + | 15.5787i | 0.907722 | + | 0.659499i | ||||
\(559\) | 20.1169 | + | 61.9134i | 0.850853 | + | 2.61866i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −19.6652 | + | 10.1791i | −0.830266 | + | 0.429763i | ||||
\(562\) | −26.5934 | −1.12178 | ||||||||
\(563\) | −11.2328 | − | 34.5710i | −0.473405 | − | 1.45699i | −0.848096 | − | 0.529842i | \(-0.822251\pi\) |
0.374691 | − | 0.927150i | \(-0.377749\pi\) | |||||||
\(564\) | −11.9284 | − | 8.66646i | −0.502274 | − | 0.364924i | ||||
\(565\) | −8.22373 | + | 5.97489i | −0.345975 | + | 0.251366i | ||||
\(566\) | 4.24034 | − | 13.0504i | 0.178235 | − | 0.548550i | ||||
\(567\) | 0.781179 | − | 2.40422i | 0.0328064 | − | 0.100968i | ||||
\(568\) | 3.60305 | − | 2.61777i | 0.151180 | − | 0.109839i | ||||
\(569\) | 36.5596 | + | 26.5621i | 1.53266 | + | 1.11354i | 0.954739 | + | 0.297445i | \(0.0961344\pi\) |
0.577917 | + | 0.816095i | \(0.303866\pi\) | |||||||
\(570\) | −6.92037 | − | 21.2987i | −0.289862 | − | 0.892104i | ||||
\(571\) | 24.7479 | 1.03567 | 0.517834 | − | 0.855481i | \(-0.326738\pi\) | ||||
0.517834 | + | 0.855481i | \(0.326738\pi\) | |||||||
\(572\) | 13.3036 | + | 13.1343i | 0.556253 | + | 0.549171i | ||||
\(573\) | −34.3630 | −1.43554 | ||||||||
\(574\) | −2.13269 | − | 6.56376i | −0.0890169 | − | 0.273966i | ||||
\(575\) | −6.45947 | − | 4.69308i | −0.269378 | − | 0.195715i | ||||
\(576\) | −4.21649 | + | 3.06346i | −0.175687 | + | 0.127644i | ||||
\(577\) | −0.811773 | + | 2.49838i | −0.0337946 | + | 0.104009i | −0.966531 | − | 0.256550i | \(-0.917414\pi\) |
0.932736 | + | 0.360559i | \(0.117414\pi\) | |||||||
\(578\) | 3.57587 | − | 11.0054i | 0.148737 | − | 0.457764i | ||||
\(579\) | −41.4401 | + | 30.1080i | −1.72219 | + | 1.25125i | ||||
\(580\) | −2.42257 | − | 1.76010i | −0.100592 | − | 0.0730841i | ||||
\(581\) | 3.34711 | + | 10.3014i | 0.138862 | + | 0.427372i | ||||
\(582\) | −15.2790 | −0.633334 | ||||||||
\(583\) | 0.314544 | + | 1.90681i | 0.0130271 | + | 0.0789720i | ||||
\(584\) | 0.336814 | 0.0139374 | ||||||||
\(585\) | −9.07821 | − | 27.9399i | −0.375338 | − | 1.15517i | ||||
\(586\) | 0.578013 | + | 0.419951i | 0.0238775 | + | 0.0173480i | ||||
\(587\) | −10.4339 | + | 7.58071i | −0.430655 | + | 0.312889i | −0.781911 | − | 0.623390i | \(-0.785755\pi\) |
0.351256 | + | 0.936280i | \(0.385755\pi\) | |||||||
\(588\) | −0.885530 | + | 2.72538i | −0.0365186 | + | 0.112393i | ||||
\(589\) | −12.2808 | + | 37.7965i | −0.506022 | + | 1.55738i | ||||
\(590\) | 11.1881 | − | 8.12860i | 0.460605 | − | 0.334649i | ||||
\(591\) | −27.3266 | − | 19.8539i | −1.12406 | − | 0.816680i | ||||
\(592\) | −0.428546 | − | 1.31893i | −0.0176131 | − | 0.0542077i | ||||
\(593\) | −33.4157 | −1.37222 | −0.686110 | − | 0.727498i | \(-0.740683\pi\) | ||||
−0.686110 | + | 0.727498i | \(0.740683\pi\) | |||||||
\(594\) | 20.7839 | + | 3.15550i | 0.852775 | + | 0.129472i | ||||
\(595\) | −2.32986 | −0.0955149 | ||||||||
\(596\) | −5.30404 | − | 16.3242i | −0.217262 | − | 0.668664i | ||||
\(597\) | −32.3043 | − | 23.4704i | −1.32213 | − | 0.960580i | ||||
\(598\) | −36.4100 | + | 26.4534i | −1.48892 | + | 1.08176i | ||||
\(599\) | 10.6556 | − | 32.7946i | 0.435377 | − | 1.33995i | −0.457323 | − | 0.889301i | \(-0.651192\pi\) |
0.892700 | − | 0.450652i | \(-0.148808\pi\) | |||||||
\(600\) | 0.885530 | − | 2.72538i | 0.0361516 | − | 0.111263i | ||||
\(601\) | 26.4921 | − | 19.2476i | 1.08063 | − | 0.785127i | 0.102841 | − | 0.994698i | \(-0.467207\pi\) |
0.977794 | + | 0.209571i | \(0.0672066\pi\) | |||||||
\(602\) | −9.34354 | − | 6.78848i | −0.380814 | − | 0.276678i | ||||
\(603\) | −0.0782358 | − | 0.240785i | −0.00318601 | − | 0.00980553i | ||||
\(604\) | 5.94304 | 0.241819 | ||||||||
\(605\) | 6.35109 | − | 8.98129i | 0.258209 | − | 0.365142i | ||||
\(606\) | −52.3556 | −2.12680 | ||||||||
\(607\) | −1.79094 | − | 5.51193i | −0.0726918 | − | 0.223722i | 0.908109 | − | 0.418733i | \(-0.137526\pi\) |
−0.980801 | + | 0.195011i | \(0.937526\pi\) | |||||||
\(608\) | −6.32242 | − | 4.59351i | −0.256408 | − | 0.186291i | ||||
\(609\) | 6.94220 | − | 5.04380i | 0.281312 | − | 0.204385i | ||||
\(610\) | −2.41788 | + | 7.44148i | −0.0978972 | + | 0.301297i | ||||
\(611\) | 8.96208 | − | 27.5824i | 0.362567 | − | 1.11587i | ||||
\(612\) | 9.82382 | − | 7.13742i | 0.397104 | − | 0.288513i | ||||
\(613\) | 31.8434 | + | 23.1356i | 1.28614 | + | 0.934437i | 0.999720 | − | 0.0236667i | \(-0.00753406\pi\) |
0.286422 | + | 0.958104i | \(0.407534\pi\) | |||||||
\(614\) | 5.97768 | + | 18.3974i | 0.241239 | + | 0.742459i | ||||
\(615\) | −19.7773 | −0.797498 | ||||||||
\(616\) | −3.27905 | − | 0.497839i | −0.132117 | − | 0.0200585i | ||||
\(617\) | −16.3175 | −0.656918 | −0.328459 | − | 0.944518i | \(-0.606529\pi\) | ||||
−0.328459 | + | 0.944518i | \(0.606529\pi\) | |||||||
\(618\) | −9.94869 | − | 30.6189i | −0.400195 | − | 1.23167i | ||||
\(619\) | 36.1810 | + | 26.2870i | 1.45424 | + | 1.05656i | 0.984819 | + | 0.173587i | \(0.0555358\pi\) |
0.469417 | + | 0.882977i | \(0.344464\pi\) | |||||||
\(620\) | −4.11412 | + | 2.98908i | −0.165227 | + | 0.120044i | ||||
\(621\) | −15.6387 | + | 48.1310i | −0.627560 | + | 1.93143i | ||||
\(622\) | −0.564663 | + | 1.73785i | −0.0226409 | + | 0.0696816i | ||||
\(623\) | 14.9885 | − | 10.8898i | 0.600503 | − | 0.436291i | ||||
\(624\) | −13.0678 | − | 9.49433i | −0.523131 | − | 0.380077i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | 9.83108 | 0.392929 | ||||||||
\(627\) | 12.0889 | + | 73.2847i | 0.482784 | + | 2.92671i | ||||
\(628\) | −16.7947 | −0.670183 | ||||||||
\(629\) | 0.998452 | + | 3.07292i | 0.0398109 | + | 0.122525i | ||||
\(630\) | 4.21649 | + | 3.06346i | 0.167989 | + | 0.122051i | ||||
\(631\) | 24.3599 | − | 17.6985i | 0.969752 | − | 0.704566i | 0.0143573 | − | 0.999897i | \(-0.495430\pi\) |
0.955395 | + | 0.295331i | \(0.0954298\pi\) | |||||||
\(632\) | −0.325367 | + | 1.00138i | −0.0129424 | + | 0.0398326i | ||||
\(633\) | −23.4220 | + | 72.0854i | −0.930940 | + | 2.86514i | ||||
\(634\) | −11.2085 | + | 8.14346i | −0.445147 | + | 0.323418i | ||||
\(635\) | −5.32922 | − | 3.87190i | −0.211483 | − | 0.153652i | ||||
\(636\) | −0.515994 | − | 1.58807i | −0.0204605 | − | 0.0629709i | ||||
\(637\) | −5.63670 | −0.223334 | ||||||||
\(638\) | 7.06747 | + | 6.97750i | 0.279804 | + | 0.276242i | ||||
\(639\) | 23.2116 | 0.918237 | ||||||||
\(640\) | −0.309017 | − | 0.951057i | −0.0122150 | − | 0.0375938i | ||||
\(641\) | 0.758680 | + | 0.551214i | 0.0299661 | + | 0.0217716i | 0.602667 | − | 0.797992i | \(-0.294105\pi\) |
−0.572701 | + | 0.819764i | \(0.694105\pi\) | |||||||
\(642\) | −11.3404 | + | 8.23925i | −0.447568 | + | 0.325177i | ||||
\(643\) | 13.9028 | − | 42.7885i | 0.548273 | − | 1.68741i | −0.164804 | − | 0.986326i | \(-0.552699\pi\) |
0.713077 | − | 0.701085i | \(-0.247301\pi\) | |||||||
\(644\) | 2.46730 | − | 7.59356i | 0.0972251 | − | 0.299228i | ||||
\(645\) | −26.7752 | + | 19.4533i | −1.05427 | + | 0.765973i | ||||
\(646\) | 14.7303 | + | 10.7022i | 0.579558 | + | 0.421073i | ||||
\(647\) | −10.1716 | − | 31.3050i | −0.399888 | − | 1.23073i | −0.925089 | − | 0.379750i | \(-0.876010\pi\) |
0.525202 | − | 0.850978i | \(-0.323990\pi\) | |||||||
\(648\) | −2.52795 | −0.0993072 | ||||||||
\(649\) | −40.7329 | + | 21.0842i | −1.59891 | + | 0.827628i | ||||
\(650\) | 5.63670 | 0.221089 | ||||||||
\(651\) | −4.50321 | − | 13.8595i | −0.176495 | − | 0.543195i | ||||
\(652\) | −1.96624 | − | 1.42856i | −0.0770040 | − | 0.0559466i | ||||
\(653\) | 2.68675 | − | 1.95203i | 0.105140 | − | 0.0763890i | −0.533973 | − | 0.845502i | \(-0.679302\pi\) |
0.639113 | + | 0.769113i | \(0.279302\pi\) | |||||||
\(654\) | 5.54733 | − | 17.0729i | 0.216918 | − | 0.667605i | ||||
\(655\) | 0.373357 | − | 1.14907i | 0.0145883 | − | 0.0448980i | ||||
\(656\) | −5.58347 | + | 4.05663i | −0.217998 | + | 0.158385i | ||||
\(657\) | 1.42017 | + | 1.03181i | 0.0554061 | + | 0.0402549i | ||||
\(658\) | 1.58995 | + | 4.89337i | 0.0619828 | + | 0.190764i | ||||
\(659\) | −20.5642 | −0.801069 | −0.400535 | − | 0.916282i | \(-0.631176\pi\) | ||||
−0.400535 | + | 0.916282i | \(0.631176\pi\) | |||||||
\(660\) | −4.26050 | + | 8.49580i | −0.165840 | + | 0.330699i | ||||
\(661\) | −43.9387 | −1.70902 | −0.854508 | − | 0.519438i | \(-0.826141\pi\) | ||||
−0.854508 | + | 0.519438i | \(0.826141\pi\) | |||||||
\(662\) | −2.47858 | − | 7.62827i | −0.0963326 | − | 0.296481i | ||||
\(663\) | 30.4462 | + | 22.1204i | 1.18243 | + | 0.859086i | ||||
\(664\) | 8.76286 | − | 6.36659i | 0.340065 | − | 0.247072i | ||||
\(665\) | −2.41495 | + | 7.43245i | −0.0936477 | + | 0.288218i | ||||
\(666\) | 2.23353 | − | 6.87409i | 0.0865474 | − | 0.266365i | ||||
\(667\) | −19.3426 | + | 14.0532i | −0.748949 | + | 0.544143i | ||||
\(668\) | 8.92393 | + | 6.48361i | 0.345277 | + | 0.250859i | ||||
\(669\) | −21.7746 | − | 67.0152i | −0.841854 | − | 2.59096i | ||||
\(670\) | 0.0485769 | 0.00187669 | ||||||||
\(671\) | 11.6330 | − | 23.1972i | 0.449087 | − | 0.895520i | ||||
\(672\) | 2.86564 | 0.110544 | ||||||||
\(673\) | −0.192636 | − | 0.592874i | −0.00742559 | − | 0.0228536i | 0.947275 | − | 0.320421i | \(-0.103825\pi\) |
−0.954701 | + | 0.297568i | \(0.903825\pi\) | |||||||
\(674\) | −9.38943 | − | 6.82182i | −0.361667 | − | 0.262767i | ||||
\(675\) | 5.12787 | − | 3.72562i | 0.197372 | − | 0.143399i | ||||
\(676\) | 5.80097 | − | 17.8536i | 0.223114 | − | 0.686675i | ||||
\(677\) | −9.47479 | + | 29.1604i | −0.364146 | + | 1.12073i | 0.586369 | + | 0.810044i | \(0.300557\pi\) |
−0.950514 | + | 0.310681i | \(0.899443\pi\) | |||||||
\(678\) | −23.5662 | + | 17.1219i | −0.905055 | + | 0.657561i | ||||
\(679\) | 4.31351 | + | 3.13395i | 0.165537 | + | 0.120270i | ||||
\(680\) | 0.719966 | + | 2.21583i | 0.0276094 | + | 0.0849731i | ||||
\(681\) | 16.0258 | 0.614112 | ||||||||
\(682\) | 14.9785 | − | 7.75318i | 0.573555 | − | 0.296884i | ||||
\(683\) | −4.08570 | −0.156335 | −0.0781676 | − | 0.996940i | \(-0.524907\pi\) | ||||
−0.0781676 | + | 0.996940i | \(0.524907\pi\) | |||||||
\(684\) | −12.5864 | − | 38.7369i | −0.481253 | − | 1.48114i | ||||
\(685\) | −11.3933 | − | 8.27770i | −0.435315 | − | 0.316275i | ||||
\(686\) | 0.809017 | − | 0.587785i | 0.0308884 | − | 0.0224417i | ||||
\(687\) | 7.17580 | − | 22.0848i | 0.273774 | − | 0.842589i | ||||
\(688\) | −3.56891 | + | 10.9840i | −0.136064 | + | 0.418761i | ||||
\(689\) | 2.65719 | − | 1.93056i | 0.101231 | − | 0.0735486i | ||||
\(690\) | −18.5105 | − | 13.4486i | −0.704682 | − | 0.511981i | ||||
\(691\) | −3.01411 | − | 9.27646i | −0.114662 | − | 0.352893i | 0.877214 | − | 0.480099i | \(-0.159399\pi\) |
−0.991876 | + | 0.127206i | \(0.959399\pi\) | |||||||
\(692\) | 14.6947 | 0.558607 | ||||||||
\(693\) | −12.3010 | − | 12.1444i | −0.467275 | − | 0.461326i | ||||
\(694\) | 26.4301 | 1.00327 | ||||||||
\(695\) | 0.847603 | + | 2.60865i | 0.0321514 | + | 0.0989519i | ||||
\(696\) | −6.94220 | − | 5.04380i | −0.263143 | − | 0.191185i | ||||
\(697\) | 13.0087 | − | 9.45136i | 0.492739 | − | 0.357996i | ||||
\(698\) | −8.46017 | + | 26.0377i | −0.320222 | + | 0.985542i | ||||
\(699\) | −10.6093 | + | 32.6520i | −0.401279 | + | 1.23501i | ||||
\(700\) | −0.809017 | + | 0.587785i | −0.0305780 | + | 0.0222162i | ||||
\(701\) | 6.75471 | + | 4.90758i | 0.255122 | + | 0.185357i | 0.707994 | − | 0.706219i | \(-0.249600\pi\) |
−0.452872 | + | 0.891576i | \(0.649600\pi\) | |||||||
\(702\) | −11.0404 | − | 33.9790i | −0.416695 | − | 1.28245i | ||||
\(703\) | 10.8378 | 0.408755 | ||||||||
\(704\) | 0.539809 | + | 3.27240i | 0.0203448 | + | 0.123333i | ||||
\(705\) | 14.7443 | 0.555301 | ||||||||
\(706\) | −6.60592 | − | 20.3309i | −0.248617 | − | 0.765164i | ||||
\(707\) | 14.7809 | + | 10.7389i | 0.555891 | + | 0.403879i | ||||
\(708\) | 32.0609 | − | 23.2936i | 1.20492 | − | 0.875427i | ||||
\(709\) | 12.8706 | − | 39.6117i | 0.483366 | − | 1.48765i | −0.350967 | − | 0.936388i | \(-0.614147\pi\) |
0.834333 | − | 0.551261i | \(-0.185853\pi\) | |||||||
\(710\) | −1.37624 | + | 4.23563i | −0.0516494 | + | 0.158961i | ||||
\(711\) | −4.43958 | + | 3.22555i | −0.166497 | + | 0.120967i | ||||
\(712\) | −14.9885 | − | 10.8898i | −0.561719 | − | 0.408113i | ||||
\(713\) | 12.5470 | + | 38.6158i | 0.469890 | + | 1.44617i | ||||
\(714\) | −6.67652 | −0.249863 | ||||||||
\(715\) | −18.4830 | − | 2.80617i | −0.691225 | − | 0.104945i | ||||
\(716\) | 4.51392 | 0.168693 | ||||||||
\(717\) | 5.72594 | + | 17.6226i | 0.213839 | + | 0.658129i | ||||
\(718\) | −8.81053 | − | 6.40123i | −0.328806 | − | 0.238892i | ||||
\(719\) | −21.9996 | + | 15.9836i | −0.820446 | + | 0.596089i | −0.916840 | − | 0.399254i | \(-0.869269\pi\) |
0.0963940 | + | 0.995343i | \(0.469269\pi\) | |||||||
\(720\) | 1.61056 | − | 4.95678i | 0.0600218 | − | 0.184728i | ||||
\(721\) | −3.47172 | + | 10.6849i | −0.129294 | + | 0.397925i | ||||
\(722\) | 34.0380 | − | 24.7301i | 1.26676 | − | 0.920358i | ||||
\(723\) | 47.1646 | + | 34.2671i | 1.75407 | + | 1.27441i | ||||
\(724\) | −3.14487 | − | 9.67891i | −0.116878 | − | 0.359714i | ||||
\(725\) | 2.99446 | 0.111211 | ||||||||
\(726\) | 18.1999 | − | 25.7371i | 0.675462 | − | 0.955194i | ||||
\(727\) | 26.4443 | 0.980766 | 0.490383 | − | 0.871507i | \(-0.336857\pi\) | ||||
0.490383 | + | 0.871507i | \(0.336857\pi\) | |||||||
\(728\) | 1.74183 | + | 5.36082i | 0.0645567 | + | 0.198685i | ||||
\(729\) | 33.4248 | + | 24.2845i | 1.23796 | + | 0.899427i | ||||
\(730\) | −0.272488 | + | 0.197974i | −0.0100852 | + | 0.00732735i | ||||
\(731\) | 8.31506 | − | 25.5911i | 0.307544 | − | 0.946522i | ||||
\(732\) | −6.92877 | + | 21.3246i | −0.256095 | + | 0.788178i | ||||
\(733\) | −20.3844 | + | 14.8101i | −0.752914 | + | 0.547024i | −0.896729 | − | 0.442581i | \(-0.854063\pi\) |
0.143815 | + | 0.989605i | \(0.454063\pi\) | |||||||
\(734\) | 9.15059 | + | 6.64829i | 0.337754 | + | 0.245393i | ||||
\(735\) | −0.885530 | − | 2.72538i | −0.0326633 | − | 0.100527i | ||||
\(736\) | −7.98434 | −0.294307 | ||||||||
\(737\) | −0.159286 | − | 0.0241835i | −0.00586738 | − | 0.000890810i | ||||
\(738\) | −35.9699 | −1.32407 | ||||||||
\(739\) | 1.82531 | + | 5.61772i | 0.0671450 | + | 0.206651i | 0.979000 | − | 0.203862i | \(-0.0653495\pi\) |
−0.911855 | + | 0.410513i | \(0.865349\pi\) | |||||||
\(740\) | 1.12195 | + | 0.815144i | 0.0412437 | + | 0.0299653i | ||||
\(741\) | 102.124 | − | 74.1976i | 3.75163 | − | 2.72572i | ||||
\(742\) | −0.180063 | + | 0.554176i | −0.00661030 | + | 0.0203444i | ||||
\(743\) | 6.05499 | − | 18.6353i | 0.222136 | − | 0.683664i | −0.776434 | − | 0.630199i | \(-0.782973\pi\) |
0.998570 | − | 0.0534654i | \(-0.0170267\pi\) | |||||||
\(744\) | −11.7896 | + | 8.56562i | −0.432226 | + | 0.314031i | ||||
\(745\) | 13.8862 | + | 10.0889i | 0.508750 | + | 0.369628i | ||||
\(746\) | −3.60494 | − | 11.0949i | −0.131986 | − | 0.406212i | ||||
\(747\) | 56.4523 | 2.06548 | ||||||||
\(748\) | −1.25768 | − | 7.62423i | −0.0459853 | − | 0.278769i | ||||
\(749\) | 4.89157 | 0.178734 | ||||||||
\(750\) | 0.885530 | + | 2.72538i | 0.0323350 | + | 0.0995168i | ||||
\(751\) | −0.376424 | − | 0.273488i | −0.0137359 | − | 0.00997972i | 0.580896 | − | 0.813978i | \(-0.302702\pi\) |
−0.594632 | + | 0.803998i | \(0.702702\pi\) | |||||||
\(752\) | 4.16255 | − | 3.02427i | 0.151793 | − | 0.110284i | ||||
\(753\) | −11.1437 | + | 34.2969i | −0.406100 | + | 1.24985i | ||||
\(754\) | 5.21585 | − | 16.0527i | 0.189950 | − | 0.584606i | ||||
\(755\) | −4.80802 | + | 3.49323i | −0.174982 | + | 0.127132i | ||||
\(756\) | 5.12787 | + | 3.72562i | 0.186499 | + | 0.135499i | ||||
\(757\) | −2.11887 | − | 6.52121i | −0.0770116 | − | 0.237017i | 0.905138 | − | 0.425117i | \(-0.139767\pi\) |
−0.982150 | + | 0.188100i | \(0.939767\pi\) | |||||||
\(758\) | −0.617088 | −0.0224136 | ||||||||
\(759\) | 54.0015 | + | 53.3140i | 1.96013 | + | 1.93518i | ||||
\(760\) | 7.81494 | 0.283478 | ||||||||
\(761\) | 12.8279 | + | 39.4802i | 0.465011 | + | 1.43116i | 0.858969 | + | 0.512027i | \(0.171105\pi\) |
−0.393959 | + | 0.919128i | \(0.628895\pi\) | |||||||
\(762\) | −15.2716 | − | 11.0955i | −0.553231 | − | 0.401946i | ||||
\(763\) | −5.06802 | + | 3.68214i | −0.183475 | + | 0.133302i | ||||
\(764\) | 3.70555 | − | 11.4045i | 0.134062 | − | 0.412601i | ||||
\(765\) | −3.75236 | + | 11.5486i | −0.135667 | + | 0.417540i | ||||
\(766\) | −21.3962 | + | 15.5452i | −0.773075 | + | 0.561672i | ||||
\(767\) | 63.0637 | + | 45.8184i | 2.27710 | + | 1.65441i | ||||
\(768\) | −0.885530 | − | 2.72538i | −0.0319538 | − | 0.0983437i | ||||
\(769\) | −17.8632 | −0.644164 | −0.322082 | − | 0.946712i | \(-0.604383\pi\) | ||||
−0.322082 | + | 0.946712i | \(0.604383\pi\) | |||||||
\(770\) | 2.94543 | − | 1.52462i | 0.106146 | − | 0.0549433i | ||||
\(771\) | −9.91495 | −0.357078 | ||||||||
\(772\) | −5.52363 | − | 17.0000i | −0.198800 | − | 0.611843i | ||||
\(773\) | −8.02110 | − | 5.82767i | −0.288499 | − | 0.209607i | 0.434117 | − | 0.900857i | \(-0.357060\pi\) |
−0.722616 | + | 0.691250i | \(0.757060\pi\) | |||||||
\(774\) | −48.6973 | + | 35.3806i | −1.75039 | + | 1.27173i | ||||
\(775\) | 1.57145 | − | 4.83644i | 0.0564483 | − | 0.173730i | ||||
\(776\) | 1.64762 | − | 5.07084i | 0.0591460 | − | 0.182033i | ||||
\(777\) | −3.21510 | + | 2.33590i | −0.115341 | + | 0.0838001i | ||||
\(778\) | 1.29803 | + | 0.943076i | 0.0465367 | + | 0.0338109i | ||||
\(779\) | −16.6669 | − | 51.2954i | −0.597153 | − | 1.83785i | ||||
\(780\) | 16.1527 | 0.578360 | ||||||||
\(781\) | 6.62142 | − | 13.2037i | 0.236933 | − | 0.472466i | ||||
\(782\) | 18.6024 | 0.665220 | ||||||||
\(783\) | −5.86517 | − | 18.0511i | −0.209604 | − | 0.645095i | ||||
\(784\) | −0.809017 | − | 0.587785i | −0.0288935 | − | 0.0209923i | ||||
\(785\) | 13.5872 | − | 9.87170i | 0.484949 | − | 0.352336i | ||||
\(786\) | 1.06990 | − | 3.29283i | 0.0381622 | − | 0.117451i | ||||
\(787\) | −0.251113 | + | 0.772846i | −0.00895120 | + | 0.0275490i | −0.955432 | − | 0.295210i | \(-0.904610\pi\) |
0.946481 | + | 0.322759i | \(0.104610\pi\) | |||||||
\(788\) | 9.53595 | − | 6.92827i | 0.339704 | − | 0.246810i | ||||
\(789\) | −18.5883 | − | 13.5052i | −0.661759 | − | 0.480796i | ||||
\(790\) | −0.325367 | − | 1.00138i | −0.0115760 | − | 0.0356274i | ||||
\(791\) | 10.1651 | 0.361429 | ||||||||
\(792\) | −7.74876 | + | 15.4517i | −0.275340 | + | 0.549053i | ||||
\(793\) | −44.1039 | −1.56618 | ||||||||
\(794\) | −1.63414 | − | 5.02937i | −0.0579935 | − | 0.178486i | ||||
\(795\) | 1.35089 | + | 0.981478i | 0.0479111 | + | 0.0348094i | ||||
\(796\) | 11.2730 | − | 8.19030i | 0.399560 | − | 0.290297i | ||||
\(797\) | 9.99149 | − | 30.7507i | 0.353917 | − | 1.08924i | −0.602718 | − | 0.797954i | \(-0.705916\pi\) |
0.956635 | − | 0.291290i | \(-0.0940844\pi\) | |||||||
\(798\) | −6.92037 | + | 21.2987i | −0.244978 | + | 0.753966i | ||||
\(799\) | −9.69815 | + | 7.04612i | −0.343096 | + | 0.249274i | ||||
\(800\) | 0.809017 | + | 0.587785i | 0.0286031 | + | 0.0207813i | ||||
\(801\) | −29.8385 | − | 91.8335i | −1.05429 | − | 3.24478i | ||||
\(802\) | 13.6059 | 0.480441 | ||||||||
\(803\) | 0.992060 | − | 0.513511i | 0.0350090 | − | 0.0181214i | ||||
\(804\) | 0.139204 | 0.00490934 | ||||||||
\(805\) | 2.46730 | + | 7.59356i | 0.0869608 | + | 0.267638i | ||||
\(806\) | −23.1900 | − | 16.8485i | −0.816834 | − | 0.593465i | ||||
\(807\) | −43.0401 | + | 31.2705i | −1.51508 | + | 1.10077i | ||||
\(808\) | 5.64578 | − | 17.3759i | 0.198618 | − | 0.611283i | ||||
\(809\) | −7.58639 | + | 23.3485i | −0.266723 | + | 0.820890i | 0.724568 | + | 0.689203i | \(0.242039\pi\) |
−0.991291 | + | 0.131687i | \(0.957961\pi\) | |||||||
\(810\) | 2.04515 | − | 1.48589i | 0.0718593 | − | 0.0522089i | ||||
\(811\) | −33.4443 | − | 24.2987i | −1.17439 | − | 0.853243i | −0.182861 | − | 0.983139i | \(-0.558536\pi\) |
−0.991528 | + | 0.129896i | \(0.958536\pi\) | |||||||
\(812\) | 0.925339 | + | 2.84790i | 0.0324730 | + | 0.0999417i | ||||
\(813\) | −72.2287 | −2.53317 | ||||||||
\(814\) | −3.27311 | − | 3.23144i | −0.114723 | − | 0.113262i | ||||
\(815\) | 2.43041 | 0.0851335 | ||||||||
\(816\) | 2.06316 | + | 6.34975i | 0.0722250 | + | 0.222286i | ||||
\(817\) | −73.0192 | − | 53.0516i | −2.55462 | − | 1.85604i | ||||
\(818\) | −2.75252 | + | 1.99982i | −0.0962395 | + | 0.0699221i | ||||
\(819\) | −9.07821 | + | 27.9399i | −0.317218 | + | 0.976297i | ||||
\(820\) | 2.13269 | − | 6.56376i | 0.0744769 | − | 0.229216i | ||||
\(821\) | −12.9602 | + | 9.41613i | −0.452314 | + | 0.328625i | −0.790509 | − | 0.612451i | \(-0.790184\pi\) |
0.338195 | + | 0.941076i | \(0.390184\pi\) | |||||||
\(822\) | −32.6490 | − | 23.7209i | −1.13876 | − | 0.827360i | ||||
\(823\) | 5.98204 | + | 18.4108i | 0.208521 | + | 0.641761i | 0.999550 | + | 0.0299831i | \(0.00954534\pi\) |
−0.791030 | + | 0.611778i | \(0.790455\pi\) | |||||||
\(824\) | 11.2347 | 0.391380 | ||||||||
\(825\) | −1.54690 | − | 9.37751i | −0.0538560 | − | 0.326483i | ||||
\(826\) | −13.8292 | −0.481179 | ||||||||
\(827\) | 13.3420 | + | 41.0625i | 0.463947 | + | 1.42788i | 0.860302 | + | 0.509785i | \(0.170275\pi\) |
−0.396354 | + | 0.918098i | \(0.629725\pi\) | |||||||
\(828\) | −33.6659 | − | 24.4597i | −1.16997 | − | 0.850033i | ||||
\(829\) | 31.2150 | − | 22.6791i | 1.08414 | − | 0.787676i | 0.105742 | − | 0.994394i | \(-0.466278\pi\) |
0.978401 | + | 0.206717i | \(0.0662781\pi\) | |||||||
\(830\) | −3.34711 | + | 10.3014i | −0.116180 | + | 0.357565i | ||||
\(831\) | 10.8283 | − | 33.3262i | 0.375630 | − | 1.15607i | ||||
\(832\) | 4.56018 | − | 3.31317i | 0.158096 | − | 0.114863i | ||||
\(833\) | 1.88489 | + | 1.36946i | 0.0653077 | + | 0.0474488i | ||||
\(834\) | 2.42892 | + | 7.47545i | 0.0841067 | + | 0.258854i | ||||
\(835\) | −11.0306 | −0.381729 | ||||||||
\(836\) | −25.6256 | − | 3.89058i | −0.886279 | − | 0.134559i | ||||
\(837\) | −32.2329 | −1.11413 | ||||||||
\(838\) | 12.2143 | + | 37.5918i | 0.421936 | + | 1.29859i | ||||
\(839\) | −7.53991 | − | 5.47806i | −0.260306 | − | 0.189124i | 0.449976 | − | 0.893041i | \(-0.351433\pi\) |
−0.710282 | + | 0.703917i | \(0.751433\pi\) | |||||||
\(840\) | −2.31835 | + | 1.68438i | −0.0799906 | + | 0.0581166i | ||||
\(841\) | −6.19060 | + | 19.0527i | −0.213469 | + | 0.656990i | ||||
\(842\) | 4.83973 | − | 14.8952i | 0.166788 | − | 0.513321i | ||||
\(843\) | 61.6528 | − | 44.7934i | 2.12344 | − | 1.54277i | ||||
\(844\) | −21.3982 | − | 15.5467i | −0.736557 | − | 0.535140i | ||||
\(845\) | 5.80097 | + | 17.8536i | 0.199559 | + | 0.614181i | ||||
\(846\) | 26.8161 | 0.921956 | ||||||||
\(847\) | −10.4172 | + | 3.53294i | −0.357940 | + | 0.121393i | ||||
\(848\) | 0.582695 | 0.0200098 | ||||||||
\(849\) | 12.1513 | + | 37.3977i | 0.417030 | + | 1.28349i | ||||
\(850\) | −1.88489 | − | 1.36946i | −0.0646514 | − | 0.0469720i | ||||
\(851\) | 8.95802 | − | 6.50838i | 0.307077 | − | 0.223105i | ||||
\(852\) | −3.94381 | + | 12.1378i | −0.135113 | + | 0.415834i | ||||
\(853\) | 2.98414 | − | 9.18424i | 0.102175 | − | 0.314462i | −0.886882 | − | 0.461996i | \(-0.847133\pi\) |
0.989057 | + | 0.147534i | \(0.0471334\pi\) | |||||||
\(854\) | 6.33010 | − | 4.59909i | 0.216611 | − | 0.157377i | ||||
\(855\) | 32.9516 | + | 23.9407i | 1.12692 | + | 0.818756i | ||||
\(856\) | −1.51158 | − | 4.65216i | −0.0516647 | − | 0.159007i | ||||
\(857\) | 7.88344 | 0.269293 | 0.134647 | − | 0.990894i | \(-0.457010\pi\) | ||||
0.134647 | + | 0.990894i | \(0.457010\pi\) | |||||||
\(858\) | −52.9655 | − | 8.04145i | −1.80821 | − | 0.274530i | ||||
\(859\) | 9.00176 | 0.307136 | 0.153568 | − | 0.988138i | \(-0.450924\pi\) | ||||
0.153568 | + | 0.988138i | \(0.450924\pi\) | |||||||
\(860\) | −3.56891 | − | 10.9840i | −0.121699 | − | 0.374551i | ||||
\(861\) | 16.0002 | + | 11.6248i | 0.545285 | + | 0.396172i | ||||
\(862\) | 4.55598 | − | 3.31011i | 0.155177 | − | 0.112743i | ||||
\(863\) | −4.50825 | + | 13.8750i | −0.153463 | + | 0.472310i | −0.998002 | − | 0.0631841i | \(-0.979874\pi\) |
0.844539 | + | 0.535494i | \(0.179874\pi\) | |||||||
\(864\) | 1.95867 | − | 6.02818i | 0.0666354 | − | 0.205083i | ||||
\(865\) | −11.8882 | + | 8.63730i | −0.404212 | + | 0.293677i | ||||
\(866\) | −27.9291 | − | 20.2917i | −0.949070 | − | 0.689540i | ||||
\(867\) | 10.2471 | + | 31.5375i | 0.348011 | + | 1.07107i | ||||
\(868\) | 5.08533 | 0.172607 | ||||||||
\(869\) | 0.568370 | + | 3.44554i | 0.0192806 | + | 0.116882i | ||||
\(870\) | 8.58103 | 0.290924 | ||||||||
\(871\) | 0.0846130 | + | 0.260412i | 0.00286700 | + | 0.00882372i | ||||
\(872\) | 5.06802 | + | 3.68214i | 0.171625 | + | 0.124693i | ||||
\(873\) | 22.4815 | − | 16.3337i | 0.760882 | − | 0.552813i | ||||
\(874\) | 19.2818 | − | 59.3432i | 0.652216 | − | 2.00731i | ||||
\(875\) | 0.309017 | − | 0.951057i | 0.0104467 | − | 0.0321516i | ||||
\(876\) | −0.780851 | + | 0.567321i | −0.0263825 | + | 0.0191680i | ||||
\(877\) | −13.8190 | − | 10.0401i | −0.466634 | − | 0.339029i | 0.329494 | − | 0.944158i | \(-0.393122\pi\) |
−0.796128 | + | 0.605128i | \(0.793122\pi\) | |||||||
\(878\) | −9.28699 | − | 28.5824i | −0.313421 | − | 0.964610i | ||||
\(879\) | −2.04739 | −0.0690568 | ||||||||
\(880\) | −2.36018 | − | 2.33014i | −0.0795618 | − | 0.0785489i | ||||
\(881\) | −30.9541 | −1.04287 | −0.521435 | − | 0.853291i | \(-0.674603\pi\) | ||||
−0.521435 | + | 0.853291i | \(0.674603\pi\) | |||||||
\(882\) | −1.61056 | − | 4.95678i | −0.0542302 | − | 0.166903i | ||||
\(883\) | 10.9999 | + | 7.99186i | 0.370175 | + | 0.268948i | 0.757283 | − | 0.653086i | \(-0.226526\pi\) |
−0.387109 | + | 0.922034i | \(0.626526\pi\) | |||||||
\(884\) | −10.6246 | + | 7.71921i | −0.357343 | + | 0.259625i | ||||
\(885\) | −12.2462 | + | 37.6898i | −0.411650 | + | 1.26693i | ||||
\(886\) | 9.90867 | − | 30.4958i | 0.332888 | − | 1.02453i | ||||
\(887\) | −13.9071 | + | 10.1041i | −0.466955 | + | 0.339263i | −0.796253 | − | 0.604963i | \(-0.793188\pi\) |
0.329298 | + | 0.944226i | \(0.393188\pi\) | |||||||
\(888\) | 3.21510 | + | 2.33590i | 0.107892 | + | 0.0783878i | ||||
\(889\) | 2.03558 | + | 6.26487i | 0.0682711 | + | 0.210117i | ||||
\(890\) | 18.5268 | 0.621021 | ||||||||
\(891\) | −7.44589 | + | 3.85415i | −0.249447 | + | 0.129119i | ||||
\(892\) | 24.5893 | 0.823311 | ||||||||
\(893\) | 12.4254 | + | 38.2414i | 0.415800 | + | 1.27970i | ||||
\(894\) | 39.7927 | + | 28.9111i | 1.33087 | + | 0.966931i | ||||
\(895\) | −3.65184 | + | 2.65322i | −0.122068 | + | 0.0886873i | ||||
\(896\) | −0.309017 | + | 0.951057i | −0.0103235 | + | 0.0317726i | ||||
\(897\) | 39.8535 | − | 122.657i | 1.33067 | − | 4.09538i | ||||
\(898\) | −7.50530 | + | 5.45292i | −0.250455 | + | 0.181966i | ||||
\(899\) | −12.3196 | − | 8.95069i | −0.410880 | − | 0.298522i | ||||
\(900\) | 1.61056 | + | 4.95678i | 0.0536852 | + | 0.165226i | ||||
\(901\) | −1.35760 | −0.0452281 | ||||||||
\(902\) | −10.2609 | + | 20.4611i | −0.341651 | + | 0.681281i | ||||
\(903\) | 33.0959 | 1.10136 | ||||||||
\(904\) | −3.14119 | − | 9.66758i | −0.104474 | − | 0.321539i | ||||
\(905\) | 8.23337 | + | 5.98189i | 0.273686 | + | 0.198845i | ||||
\(906\) | −13.7780 | + | 10.0103i | −0.457744 | + | 0.332571i | ||||
\(907\) | −7.29036 | + | 22.4374i | −0.242073 | + | 0.745023i | 0.754032 | + | 0.656838i | \(0.228107\pi\) |
−0.996104 | + | 0.0881845i | \(0.971893\pi\) | |||||||
\(908\) | −1.72815 | + | 5.31871i | −0.0573508 | + | 0.176508i | ||||
\(909\) | 77.0358 | − | 55.9698i | 2.55512 | − | 1.85640i | ||||
\(910\) | −4.56018 | − | 3.31317i | −0.151169 | − | 0.109830i | ||||
\(911\) | 15.4724 | + | 47.6191i | 0.512623 | + | 1.57769i | 0.787566 | + | 0.616230i | \(0.211341\pi\) |
−0.274944 | + | 0.961460i | \(0.588659\pi\) | |||||||
\(912\) | 22.3948 | 0.741565 | ||||||||
\(913\) | 16.1038 | − | 32.1123i | 0.532957 | − | 1.06276i | ||||
\(914\) | 20.0782 | 0.664127 | ||||||||
\(915\) | −6.92877 | − | 21.3246i | −0.229058 | − | 0.704968i | ||||
\(916\) | 6.55579 | + | 4.76306i | 0.216609 | + | 0.157376i | ||||
\(917\) | −0.977461 | + | 0.710167i | −0.0322786 | + | 0.0234518i | ||||
\(918\) | −4.56343 | + | 14.0448i | −0.150616 | + | 0.463547i | ||||
\(919\) | −4.06752 | + | 12.5185i | −0.134175 | + | 0.412949i | −0.995461 | − | 0.0951725i | \(-0.969660\pi\) |
0.861286 | + | 0.508121i | \(0.169660\pi\) | |||||||
\(920\) | 6.45947 | − | 4.69308i | 0.212962 | − | 0.154726i | ||||
\(921\) | −44.8465 | − | 32.5829i | −1.47774 | − | 1.07364i | ||||
\(922\) | −4.52679 | − | 13.9320i | −0.149082 | − | 0.458827i | ||||
\(923\) | −25.1036 | −0.826296 | ||||||||
\(924\) | 8.44052 | − | 4.36899i | 0.277673 | − | 0.143729i | ||||
\(925\) | −1.38681 | −0.0455979 | ||||||||
\(926\) | −3.42927 | − | 10.5542i | −0.112693 | − | 0.346833i | ||||
\(927\) | 47.3711 | + | 34.4171i | 1.55587 | + | 1.13041i | ||||
\(928\) | 2.42257 | − | 1.76010i | 0.0795247 | − | 0.0577781i | ||||
\(929\) | −3.05081 | + | 9.38942i | −0.100094 | + | 0.308057i | −0.988548 | − | 0.150909i | \(-0.951780\pi\) |
0.888454 | + | 0.458966i | \(0.151780\pi\) | |||||||
\(930\) | 4.50321 | − | 13.8595i | 0.147666 | − | 0.454470i | ||||
\(931\) | 6.32242 | − | 4.59351i | 0.207209 | − | 0.150546i | ||||
\(932\) | −9.69259 | − | 7.04208i | −0.317491 | − | 0.230671i | ||||
\(933\) | −1.61812 | − | 4.98005i | −0.0529748 | − | 0.163040i | ||||
\(934\) | −24.6923 | −0.807956 | ||||||||
\(935\) | 5.49889 | + | 5.42889i | 0.179833 | + | 0.177544i | ||||
\(936\) | 29.3777 | 0.960240 | ||||||||
\(937\) | 1.48941 | + | 4.58393i | 0.0486569 | + | 0.149751i | 0.972433 | − | 0.233183i | \(-0.0749140\pi\) |
−0.923776 | + | 0.382933i | \(0.874914\pi\) | |||||||
\(938\) | −0.0392996 | − | 0.0285528i | −0.00128318 | − | 0.000932282i | ||||
\(939\) | −22.7919 | + | 16.5593i | −0.743784 | + | 0.540391i | ||||
\(940\) | −1.58995 | + | 4.89337i | −0.0518586 | + | 0.159604i | ||||
\(941\) | −17.7346 | + | 54.5815i | −0.578132 | + | 1.77931i | 0.0471262 | + | 0.998889i | \(0.484994\pi\) |
−0.625258 | + | 0.780418i | \(0.715006\pi\) | |||||||
\(942\) | 38.9360 | − | 28.2887i | 1.26860 | − | 0.921695i | ||||
\(943\) | −44.5803 | − | 32.3895i | −1.45173 | − | 1.05475i | ||||
\(944\) | 4.27346 | + | 13.1523i | 0.139089 | + | 0.428072i | ||||
\(945\) | −6.33840 | −0.206188 | ||||||||
\(946\) | 6.23439 | + | 37.7938i | 0.202697 | + | 1.22878i | ||||
\(947\) | −4.22221 | −0.137203 | −0.0686017 | − | 0.997644i | \(-0.521854\pi\) | ||||
−0.0686017 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(948\) | −0.932383 | − | 2.86958i | −0.0302824 | − | 0.0931997i | ||||
\(949\) | −1.53593 | − | 1.11592i | −0.0498584 | − | 0.0362243i | ||||
\(950\) | −6.32242 | + | 4.59351i | −0.205126 | + | 0.149033i | ||||
\(951\) | 12.2686 | − | 37.7588i | 0.397835 | − | 1.22441i | ||||
\(952\) | 0.719966 | − | 2.21583i | 0.0233342 | − | 0.0718154i | ||||
\(953\) | 4.13003 | − | 3.00064i | 0.133785 | − | 0.0972004i | −0.518880 | − | 0.854847i | \(-0.673651\pi\) |
0.652665 | + | 0.757647i | \(0.273651\pi\) | |||||||
\(954\) | 2.45693 | + | 1.78506i | 0.0795459 | + | 0.0577935i | ||||
\(955\) | 3.70555 | + | 11.4045i | 0.119909 | + | 0.369042i | ||||
\(956\) | −6.46612 | −0.209129 | ||||||||
\(957\) | −28.1376 | − | 4.27197i | −0.909560 | − | 0.138093i | ||||
\(958\) | 31.2114 | 1.00839 | ||||||||
\(959\) | 4.35184 | + | 13.3936i | 0.140528 | + | 0.432502i | ||||
\(960\) | 2.31835 | + | 1.68438i | 0.0748243 | + | 0.0543631i | ||||
\(961\) | 4.15787 | − | 3.02087i | 0.134125 | − | 0.0974474i | ||||
\(962\) | −2.41559 | + | 7.43441i | −0.0778816 | + | 0.239695i | ||||
\(963\) | 7.87814 | − | 24.2464i | 0.253870 | − | 0.781330i | ||||
\(964\) | −16.4587 | + | 11.9579i | −0.530099 | + | 0.385139i | ||||
\(965\) | 14.4611 | + | 10.5066i | 0.465518 | + | 0.338218i | ||||
\(966\) | 7.07037 | + | 21.7604i | 0.227486 | + | 0.700128i | ||||
\(967\) | 61.6521 | 1.98260 | 0.991298 | − | 0.131633i | \(-0.0420221\pi\) | ||||
0.991298 | + | 0.131633i | \(0.0420221\pi\) | |||||||
\(968\) | 6.57912 | + | 8.81562i | 0.211461 | + | 0.283345i | ||||
\(969\) | −52.1766 | −1.67616 | ||||||||
\(970\) | 1.64762 | + | 5.07084i | 0.0529018 | + | 0.162815i | ||||
\(971\) | 21.0918 | + | 15.3241i | 0.676869 | + | 0.491774i | 0.872317 | − | 0.488940i | \(-0.162616\pi\) |
−0.195449 | + | 0.980714i | \(0.562616\pi\) | |||||||
\(972\) | −9.52296 | + | 6.91884i | −0.305449 | + | 0.221922i | ||||
\(973\) | 0.847603 | − | 2.60865i | 0.0271729 | − | 0.0836296i | ||||
\(974\) | −0.935632 | + | 2.87958i | −0.0299796 | + | 0.0922677i | ||||
\(975\) | −13.0678 | + | 9.49433i | −0.418505 | + | 0.304062i | ||||
\(976\) | −6.33010 | − | 4.59909i | −0.202621 | − | 0.147213i | ||||
\(977\) | 5.88482 | + | 18.1116i | 0.188272 | + | 0.579442i | 0.999989 | − | 0.00460870i | \(-0.00146700\pi\) |
−0.811717 | + | 0.584050i | \(0.801467\pi\) | |||||||
\(978\) | 6.96466 | 0.222705 | ||||||||
\(979\) | −60.7504 | − | 9.22338i | −1.94159 | − | 0.294781i | ||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 10.0892 | + | 31.0514i | 0.322123 | + | 0.991394i | ||||
\(982\) | −11.9791 | − | 8.70331i | −0.382268 | − | 0.277734i | ||||
\(983\) | 15.6421 | − | 11.3646i | 0.498905 | − | 0.362476i | −0.309693 | − | 0.950836i | \(-0.600226\pi\) |
0.808599 | + | 0.588361i | \(0.200226\pi\) | |||||||
\(984\) | 6.11152 | − | 18.8093i | 0.194828 | − | 0.599620i | ||||
\(985\) | −3.64241 | + | 11.2102i | −0.116057 | + | 0.357186i | ||||
\(986\) | −5.64424 | + | 4.10078i | −0.179749 | + | 0.130595i | ||||
\(987\) | −11.9284 | − | 8.66646i | −0.379684 | − | 0.275856i | ||||
\(988\) | 13.6123 | + | 41.8945i | 0.433066 | + | 1.33284i | ||||
\(989\) | −92.2131 | −2.93221 | ||||||||
\(990\) | −2.81341 | − | 17.0553i | −0.0894161 | − | 0.542053i | ||||
\(991\) | −28.4567 | −0.903958 | −0.451979 | − | 0.892029i | \(-0.649282\pi\) | ||||
−0.451979 | + | 0.892029i | \(0.649282\pi\) | |||||||
\(992\) | −1.57145 | − | 4.83644i | −0.0498937 | − | 0.153557i | ||||
\(993\) | 18.5951 | + | 13.5101i | 0.590098 | + | 0.428731i | ||||
\(994\) | 3.60305 | − | 2.61777i | 0.114282 | − | 0.0830305i | ||||
\(995\) | −4.30590 | + | 13.2522i | −0.136506 | + | 0.420122i | ||||
\(996\) | −9.59161 | + | 29.5199i | −0.303922 | + | 0.935375i | ||||
\(997\) | −11.4188 | + | 8.29624i | −0.361637 | + | 0.262744i | −0.753734 | − | 0.657179i | \(-0.771750\pi\) |
0.392098 | + | 0.919924i | \(0.371750\pi\) | |||||||
\(998\) | −5.65863 | − | 4.11124i | −0.179121 | − | 0.130139i | ||||
\(999\) | 2.71630 | + | 8.35991i | 0.0859399 | + | 0.264496i |
(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 | 770.2.n.j.71.3 | ✓ | 12 | |
11.3 | even | 5 | 8470.2.a.cw.1.1 | 6 | |||
11.8 | odd | 10 | 8470.2.a.dc.1.1 | 6 | |||
11.9 | even | 5 | inner | 770.2.n.j.141.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.j.71.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
770.2.n.j.141.3 | yes | 12 | 11.9 | even | 5 | inner | |
8470.2.a.cw.1.1 | 6 | 11.3 | even | 5 | |||
8470.2.a.dc.1.1 | 6 | 11.8 | odd | 10 |