Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(113,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 113.4 | ||
Root | \(-2.80721i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.113 |
Dual form | 210.2.j.a.197.4 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.799269 | + | 1.53661i | −0.461458 | + | 0.887162i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.91438 | + | 1.15549i | −0.856135 | + | 0.516753i | ||||
\(6\) | −1.65172 | + | 0.521378i | −0.674310 | + | 0.212852i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −1.72234 | − | 2.45633i | −0.574113 | − | 0.818776i | ||||
\(10\) | −2.17073 | − | 0.536610i | −0.686444 | − | 0.169691i | ||||
\(11\) | − | 1.70489i | − | 0.514045i | −0.966405 | − | 0.257022i | \(-0.917259\pi\) | ||
0.966405 | − | 0.257022i | \(-0.0827414\pi\) | |||||||
\(12\) | −1.53661 | − | 0.799269i | −0.443581 | − | 0.230729i | ||||
\(13\) | 0.921665 | + | 0.921665i | 0.255624 | + | 0.255624i | 0.823272 | − | 0.567648i | \(-0.192146\pi\) |
−0.567648 | + | 0.823272i | \(0.692146\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.245443 | − | 3.86520i | −0.0633732 | − | 0.997990i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.76445 | + | 4.76445i | 1.15555 | + | 1.15555i | 0.985422 | + | 0.170128i | \(0.0544180\pi\) |
0.170128 | + | 0.985422i | \(0.445582\pi\) | |||||||
\(18\) | 0.519010 | − | 2.95476i | 0.122332 | − | 0.696444i | ||||
\(19\) | 5.94473i | 1.36381i | 0.731439 | + | 0.681907i | \(0.238849\pi\) | ||||
−0.731439 | + | 0.681907i | \(0.761151\pi\) | |||||||
\(20\) | −1.15549 | − | 1.91438i | −0.258376 | − | 0.428067i | ||||
\(21\) | −0.521378 | − | 1.65172i | −0.113774 | − | 0.360434i | ||||
\(22\) | 1.20554 | − | 1.20554i | 0.257022 | − | 0.257022i | ||||
\(23\) | −2.49622 | + | 2.49622i | −0.520498 | + | 0.520498i | −0.917722 | − | 0.397224i | \(-0.869974\pi\) |
0.397224 | + | 0.917722i | \(0.369974\pi\) | |||||||
\(24\) | −0.521378 | − | 1.65172i | −0.106426 | − | 0.337155i | ||||
\(25\) | 2.32966 | − | 4.42410i | 0.465933 | − | 0.884820i | ||||
\(26\) | 1.30343i | 0.255624i | ||||||||
\(27\) | 5.15103 | − | 0.683293i | 0.991316 | − | 0.131500i | ||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | 5.19708 | 0.965073 | 0.482536 | − | 0.875876i | \(-0.339716\pi\) | ||||
0.482536 | + | 0.875876i | \(0.339716\pi\) | |||||||
\(30\) | 2.55955 | − | 2.90666i | 0.467308 | − | 0.530682i | ||||
\(31\) | −3.40667 | −0.611856 | −0.305928 | − | 0.952055i | \(-0.598967\pi\) | ||||
−0.305928 | + | 0.952055i | \(0.598967\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 2.61976 | + | 1.36267i | 0.456041 | + | 0.237210i | ||||
\(34\) | 6.73795i | 1.15555i | ||||||||
\(35\) | 0.536610 | − | 2.17073i | 0.0907036 | − | 0.366920i | ||||
\(36\) | 2.45633 | − | 1.72234i | 0.409388 | − | 0.287056i | ||||
\(37\) | −1.02910 | + | 1.02910i | −0.169183 | + | 0.169183i | −0.786620 | − | 0.617437i | \(-0.788171\pi\) |
0.617437 | + | 0.786620i | \(0.288171\pi\) | |||||||
\(38\) | −4.20356 | + | 4.20356i | −0.681907 | + | 0.681907i | ||||
\(39\) | −2.15290 | + | 0.679581i | −0.344740 | + | 0.108820i | ||||
\(40\) | 0.536610 | − | 2.17073i | 0.0848454 | − | 0.343222i | ||||
\(41\) | − | 10.9749i | − | 1.71399i | −0.515328 | − | 0.856993i | \(-0.672330\pi\) | ||
0.515328 | − | 0.856993i | \(-0.327670\pi\) | |||||||
\(42\) | 0.799269 | − | 1.53661i | 0.123330 | − | 0.237104i | ||||
\(43\) | 8.17020 | + | 8.17020i | 1.24594 | + | 1.24594i | 0.957495 | + | 0.288449i | \(0.0931395\pi\) |
0.288449 | + | 0.957495i | \(0.406861\pi\) | |||||||
\(44\) | 1.70489 | 0.257022 | ||||||||
\(45\) | 6.13548 | + | 2.71218i | 0.914623 | + | 0.404308i | ||||
\(46\) | −3.53019 | −0.520498 | ||||||||
\(47\) | 0.436661 | + | 0.436661i | 0.0636935 | + | 0.0636935i | 0.738236 | − | 0.674542i | \(-0.235659\pi\) |
−0.674542 | + | 0.738236i | \(0.735659\pi\) | |||||||
\(48\) | 0.799269 | − | 1.53661i | 0.115365 | − | 0.221790i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 4.77563 | − | 1.48099i | 0.675376 | − | 0.209444i | ||||
\(51\) | −11.1292 | + | 3.51302i | −1.55840 | + | 0.491922i | ||||
\(52\) | −0.921665 | + | 0.921665i | −0.127812 | + | 0.127812i | ||||
\(53\) | 6.87196 | − | 6.87196i | 0.943937 | − | 0.943937i | −0.0545729 | − | 0.998510i | \(-0.517380\pi\) |
0.998510 | + | 0.0545729i | \(0.0173797\pi\) | |||||||
\(54\) | 4.12549 | + | 3.15917i | 0.561408 | + | 0.429908i | ||||
\(55\) | 1.96999 | + | 3.26380i | 0.265634 | + | 0.440091i | ||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | −9.13472 | − | 4.75144i | −1.20992 | − | 0.629343i | ||||
\(58\) | 3.67489 | + | 3.67489i | 0.482536 | + | 0.482536i | ||||
\(59\) | −0.686337 | −0.0893535 | −0.0446767 | − | 0.999001i | \(-0.514226\pi\) | ||||
−0.0446767 | + | 0.999001i | \(0.514226\pi\) | |||||||
\(60\) | 3.86520 | − | 0.245443i | 0.498995 | − | 0.0316866i | ||||
\(61\) | −1.74994 | −0.224056 | −0.112028 | − | 0.993705i | \(-0.535735\pi\) | ||||
−0.112028 | + | 0.993705i | \(0.535735\pi\) | |||||||
\(62\) | −2.40888 | − | 2.40888i | −0.305928 | − | 0.305928i | ||||
\(63\) | 2.95476 | + | 0.519010i | 0.372265 | + | 0.0653891i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −2.82939 | − | 0.699434i | −0.350943 | − | 0.0867541i | ||||
\(66\) | 0.888895 | + | 2.81600i | 0.109415 | + | 0.346625i | ||||
\(67\) | 1.03802 | − | 1.03802i | 0.126814 | − | 0.126814i | −0.640851 | − | 0.767665i | \(-0.721418\pi\) |
0.767665 | + | 0.640851i | \(0.221418\pi\) | |||||||
\(68\) | −4.76445 | + | 4.76445i | −0.577775 | + | 0.577775i | ||||
\(69\) | −1.84056 | − | 5.83087i | −0.221578 | − | 0.701954i | ||||
\(70\) | 1.91438 | − | 1.15549i | 0.228812 | − | 0.138108i | ||||
\(71\) | − | 12.2611i | − | 1.45513i | −0.686040 | − | 0.727564i | \(-0.740652\pi\) | ||
0.686040 | − | 0.727564i | \(-0.259348\pi\) | |||||||
\(72\) | 2.95476 | + | 0.519010i | 0.348222 | + | 0.0611659i | ||||
\(73\) | −4.59693 | − | 4.59693i | −0.538030 | − | 0.538030i | 0.384920 | − | 0.922950i | \(-0.374229\pi\) |
−0.922950 | + | 0.384920i | \(0.874229\pi\) | |||||||
\(74\) | −1.45536 | −0.169183 | ||||||||
\(75\) | 4.93609 | + | 7.11583i | 0.569970 | + | 0.821665i | ||||
\(76\) | −5.94473 | −0.681907 | ||||||||
\(77\) | 1.20554 | + | 1.20554i | 0.137384 | + | 0.137384i | ||||
\(78\) | −2.00286 | − | 1.04179i | −0.226780 | − | 0.117960i | ||||
\(79\) | 7.19515i | 0.809517i | 0.914424 | + | 0.404759i | \(0.132644\pi\) | ||||
−0.914424 | + | 0.404759i | \(0.867356\pi\) | |||||||
\(80\) | 1.91438 | − | 1.15549i | 0.214034 | − | 0.129188i | ||||
\(81\) | −3.06710 | + | 8.46126i | −0.340789 | + | 0.940140i | ||||
\(82\) | 7.76040 | − | 7.76040i | 0.856993 | − | 0.856993i | ||||
\(83\) | −6.64687 | + | 6.64687i | −0.729589 | + | 0.729589i | −0.970538 | − | 0.240949i | \(-0.922541\pi\) |
0.240949 | + | 0.970538i | \(0.422541\pi\) | |||||||
\(84\) | 1.65172 | − | 0.521378i | 0.180217 | − | 0.0568871i | ||||
\(85\) | −14.6263 | − | 3.61565i | −1.58644 | − | 0.392172i | ||||
\(86\) | 11.5544i | 1.24594i | ||||||||
\(87\) | −4.15386 | + | 7.98588i | −0.445341 | + | 0.856176i | ||||
\(88\) | 1.20554 | + | 1.20554i | 0.128511 | + | 0.128511i | ||||
\(89\) | 2.25517 | 0.239048 | 0.119524 | − | 0.992831i | \(-0.461863\pi\) | ||||
0.119524 | + | 0.992831i | \(0.461863\pi\) | |||||||
\(90\) | 2.42063 | + | 6.25624i | 0.255157 | + | 0.659466i | ||||
\(91\) | −1.30343 | −0.136637 | ||||||||
\(92\) | −2.49622 | − | 2.49622i | −0.260249 | − | 0.260249i | ||||
\(93\) | 2.72285 | − | 5.23472i | 0.282346 | − | 0.542815i | ||||
\(94\) | 0.617532i | 0.0636935i | ||||||||
\(95\) | −6.86910 | − | 11.3804i | −0.704755 | − | 1.16761i | ||||
\(96\) | 1.65172 | − | 0.521378i | 0.168578 | − | 0.0532130i | ||||
\(97\) | 13.2182 | − | 13.2182i | 1.34210 | − | 1.34210i | 0.448133 | − | 0.893967i | \(-0.352089\pi\) |
0.893967 | − | 0.448133i | \(-0.147911\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | −4.18778 | + | 2.93640i | −0.420888 | + | 0.295120i | ||||
\(100\) | 4.42410 | + | 2.32966i | 0.442410 | + | 0.232966i | ||||
\(101\) | 17.8429i | 1.77544i | 0.460385 | + | 0.887719i | \(0.347711\pi\) | ||||
−0.460385 | + | 0.887719i | \(0.652289\pi\) | |||||||
\(102\) | −10.3536 | − | 5.38544i | −1.02516 | − | 0.533238i | ||||
\(103\) | −11.9006 | − | 11.9006i | −1.17260 | − | 1.17260i | −0.981587 | − | 0.191013i | \(-0.938823\pi\) |
−0.191013 | − | 0.981587i | \(-0.561177\pi\) | |||||||
\(104\) | −1.30343 | −0.127812 | ||||||||
\(105\) | 2.90666 | + | 2.55955i | 0.283661 | + | 0.249787i | ||||
\(106\) | 9.71842 | 0.943937 | ||||||||
\(107\) | 3.96954 | + | 3.96954i | 0.383750 | + | 0.383750i | 0.872451 | − | 0.488701i | \(-0.162529\pi\) |
−0.488701 | + | 0.872451i | \(0.662529\pi\) | |||||||
\(108\) | 0.683293 | + | 5.15103i | 0.0657499 | + | 0.495658i | ||||
\(109\) | − | 6.66506i | − | 0.638397i | −0.947688 | − | 0.319198i | \(-0.896586\pi\) | ||
0.947688 | − | 0.319198i | \(-0.103414\pi\) | |||||||
\(110\) | −0.914862 | + | 3.70086i | −0.0872287 | + | 0.352863i | ||||
\(111\) | −0.758796 | − | 2.40385i | −0.0720217 | − | 0.228163i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | −4.33754 | + | 4.33754i | −0.408042 | + | 0.408042i | −0.881055 | − | 0.473014i | \(-0.843166\pi\) |
0.473014 | + | 0.881055i | \(0.343166\pi\) | |||||||
\(114\) | −3.09945 | − | 9.81900i | −0.290290 | − | 0.919633i | ||||
\(115\) | 1.89433 | − | 7.66307i | 0.176648 | − | 0.714585i | ||||
\(116\) | 5.19708i | 0.482536i | ||||||||
\(117\) | 0.676494 | − | 3.85133i | 0.0625419 | − | 0.356056i | ||||
\(118\) | −0.485314 | − | 0.485314i | −0.0446767 | − | 0.0446767i | ||||
\(119\) | −6.73795 | −0.617667 | ||||||||
\(120\) | 2.90666 | + | 2.55955i | 0.265341 | + | 0.233654i | ||||
\(121\) | 8.09334 | 0.735758 | ||||||||
\(122\) | −1.23739 | − | 1.23739i | −0.112028 | − | 0.112028i | ||||
\(123\) | 16.8641 | + | 8.77187i | 1.52058 | + | 0.790933i | ||||
\(124\) | − | 3.40667i | − | 0.305928i | ||||||
\(125\) | 0.652173 | + | 11.1613i | 0.0583321 | + | 0.998297i | ||||
\(126\) | 1.72234 | + | 2.45633i | 0.153438 | + | 0.218827i | ||||
\(127\) | −11.2191 | + | 11.2191i | −0.995531 | + | 0.995531i | −0.999990 | − | 0.00445951i | \(-0.998580\pi\) |
0.00445951 | + | 0.999990i | \(0.498580\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −19.0846 | + | 6.02422i | −1.68031 | + | 0.530403i | ||||
\(130\) | −1.50611 | − | 2.49526i | −0.132094 | − | 0.218848i | ||||
\(131\) | − | 4.60740i | − | 0.402550i | −0.979535 | − | 0.201275i | \(-0.935491\pi\) | ||
0.979535 | − | 0.201275i | \(-0.0645085\pi\) | |||||||
\(132\) | −1.36267 | + | 2.61976i | −0.118605 | + | 0.228020i | ||||
\(133\) | −4.20356 | − | 4.20356i | −0.364495 | − | 0.364495i | ||||
\(134\) | 1.46798 | 0.126814 | ||||||||
\(135\) | −9.07146 | + | 7.26007i | −0.780747 | + | 0.624847i | ||||
\(136\) | −6.73795 | −0.577775 | ||||||||
\(137\) | 2.21669 | + | 2.21669i | 0.189384 | + | 0.189384i | 0.795430 | − | 0.606046i | \(-0.207245\pi\) |
−0.606046 | + | 0.795430i | \(0.707245\pi\) | |||||||
\(138\) | 2.82157 | − | 5.42452i | 0.240188 | − | 0.461766i | ||||
\(139\) | − | 0.322961i | − | 0.0273932i | −0.999906 | − | 0.0136966i | \(-0.995640\pi\) | ||
0.999906 | − | 0.0136966i | \(-0.00435990\pi\) | |||||||
\(140\) | 2.17073 | + | 0.536610i | 0.183460 | + | 0.0453518i | ||||
\(141\) | −1.01999 | + | 0.321968i | −0.0858984 | + | 0.0271146i | ||||
\(142\) | 8.66993 | − | 8.66993i | 0.727564 | − | 0.727564i | ||||
\(143\) | 1.57134 | − | 1.57134i | 0.131402 | − | 0.131402i | ||||
\(144\) | 1.72234 | + | 2.45633i | 0.143528 | + | 0.204694i | ||||
\(145\) | −9.94915 | + | 6.00519i | −0.826232 | + | 0.498704i | ||||
\(146\) | − | 6.50104i | − | 0.538030i | ||||||
\(147\) | 1.53661 | + | 0.799269i | 0.126737 | + | 0.0659226i | ||||
\(148\) | −1.02910 | − | 1.02910i | −0.0845913 | − | 0.0845913i | ||||
\(149\) | −3.82532 | −0.313382 | −0.156691 | − | 0.987648i | \(-0.550083\pi\) | ||||
−0.156691 | + | 0.987648i | \(0.550083\pi\) | |||||||
\(150\) | −1.54131 | + | 8.52199i | −0.125848 | + | 0.695818i | ||||
\(151\) | 4.75057 | 0.386596 | 0.193298 | − | 0.981140i | \(-0.438082\pi\) | ||||
0.193298 | + | 0.981140i | \(0.438082\pi\) | |||||||
\(152\) | −4.20356 | − | 4.20356i | −0.340953 | − | 0.340953i | ||||
\(153\) | 3.49707 | − | 19.9091i | 0.282721 | − | 1.60955i | ||||
\(154\) | 1.70489i | 0.137384i | ||||||||
\(155\) | 6.52164 | − | 3.93639i | 0.523831 | − | 0.316178i | ||||
\(156\) | −0.679581 | − | 2.15290i | −0.0544100 | − | 0.172370i | ||||
\(157\) | −10.3066 | + | 10.3066i | −0.822559 | + | 0.822559i | −0.986474 | − | 0.163915i | \(-0.947588\pi\) |
0.163915 | + | 0.986474i | \(0.447588\pi\) | |||||||
\(158\) | −5.08774 | + | 5.08774i | −0.404759 | + | 0.404759i | ||||
\(159\) | 5.06698 | + | 16.0521i | 0.401837 | + | 1.27301i | ||||
\(160\) | 2.17073 | + | 0.536610i | 0.171611 | + | 0.0424227i | ||||
\(161\) | − | 3.53019i | − | 0.278218i | ||||||
\(162\) | −8.15178 | + | 3.81424i | −0.640465 | + | 0.299675i | ||||
\(163\) | 4.45269 | + | 4.45269i | 0.348762 | + | 0.348762i | 0.859648 | − | 0.510887i | \(-0.170683\pi\) |
−0.510887 | + | 0.859648i | \(0.670683\pi\) | |||||||
\(164\) | 10.9749 | 0.856993 | ||||||||
\(165\) | −6.58975 | + | 0.418454i | −0.513011 | + | 0.0325766i | ||||
\(166\) | −9.40009 | −0.729589 | ||||||||
\(167\) | 8.92259 | + | 8.92259i | 0.690451 | + | 0.690451i | 0.962331 | − | 0.271880i | \(-0.0876455\pi\) |
−0.271880 | + | 0.962331i | \(0.587646\pi\) | |||||||
\(168\) | 1.53661 | + | 0.799269i | 0.118552 | + | 0.0616649i | ||||
\(169\) | − | 11.3011i | − | 0.869313i | ||||||
\(170\) | −7.78567 | − | 12.8990i | −0.597134 | − | 0.989306i | ||||
\(171\) | 14.6022 | − | 10.2388i | 1.11666 | − | 0.782983i | ||||
\(172\) | −8.17020 | + | 8.17020i | −0.622972 | + | 0.622972i | ||||
\(173\) | 4.45093 | − | 4.45093i | 0.338398 | − | 0.338398i | −0.517366 | − | 0.855764i | \(-0.673087\pi\) |
0.855764 | + | 0.517366i | \(0.173087\pi\) | |||||||
\(174\) | −8.58409 | + | 2.70964i | −0.650758 | + | 0.205418i | ||||
\(175\) | 1.48099 | + | 4.77563i | 0.111952 | + | 0.361004i | ||||
\(176\) | 1.70489i | 0.128511i | ||||||||
\(177\) | 0.548568 | − | 1.05463i | 0.0412329 | − | 0.0792710i | ||||
\(178\) | 1.59465 | + | 1.59465i | 0.119524 | + | 0.119524i | ||||
\(179\) | 10.6798 | 0.798243 | 0.399121 | − | 0.916898i | \(-0.369315\pi\) | ||||
0.399121 | + | 0.916898i | \(0.369315\pi\) | |||||||
\(180\) | −2.71218 | + | 6.13548i | −0.202154 | + | 0.457311i | ||||
\(181\) | 12.8215 | 0.953012 | 0.476506 | − | 0.879171i | \(-0.341903\pi\) | ||||
0.476506 | + | 0.879171i | \(0.341903\pi\) | |||||||
\(182\) | −0.921665 | − | 0.921665i | −0.0683184 | − | 0.0683184i | ||||
\(183\) | 1.39867 | − | 2.68897i | 0.103393 | − | 0.198774i | ||||
\(184\) | − | 3.53019i | − | 0.260249i | ||||||
\(185\) | 0.780962 | − | 3.15920i | 0.0574175 | − | 0.232269i | ||||
\(186\) | 5.62685 | − | 1.77616i | 0.412581 | − | 0.130235i | ||||
\(187\) | 8.12288 | − | 8.12288i | 0.594004 | − | 0.594004i | ||||
\(188\) | −0.436661 | + | 0.436661i | −0.0318468 | + | 0.0318468i | ||||
\(189\) | −3.15917 | + | 4.12549i | −0.229796 | + | 0.300085i | ||||
\(190\) | 3.19000 | − | 12.9044i | 0.231427 | − | 0.936181i | ||||
\(191\) | − | 8.28637i | − | 0.599580i | −0.954005 | − | 0.299790i | \(-0.903083\pi\) | ||
0.954005 | − | 0.299790i | \(-0.0969167\pi\) | |||||||
\(192\) | 1.53661 | + | 0.799269i | 0.110895 | + | 0.0576823i | ||||
\(193\) | −3.59731 | − | 3.59731i | −0.258940 | − | 0.258940i | 0.565683 | − | 0.824623i | \(-0.308613\pi\) |
−0.824623 | + | 0.565683i | \(0.808613\pi\) | |||||||
\(194\) | 18.6933 | 1.34210 | ||||||||
\(195\) | 3.33620 | − | 3.78863i | 0.238910 | − | 0.271310i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 5.50386 | + | 5.50386i | 0.392134 | + | 0.392134i | 0.875447 | − | 0.483314i | \(-0.160567\pi\) |
−0.483314 | + | 0.875447i | \(0.660567\pi\) | |||||||
\(198\) | −5.03756 | − | 0.884857i | −0.358004 | − | 0.0628840i | ||||
\(199\) | − | 20.7662i | − | 1.47208i | −0.676940 | − | 0.736038i | \(-0.736694\pi\) | ||
0.676940 | − | 0.736038i | \(-0.263306\pi\) | |||||||
\(200\) | 1.48099 | + | 4.77563i | 0.104722 | + | 0.337688i | ||||
\(201\) | 0.765374 | + | 2.42469i | 0.0539853 | + | 0.171024i | ||||
\(202\) | −12.6169 | + | 12.6169i | −0.887719 | + | 0.887719i | ||||
\(203\) | −3.67489 | + | 3.67489i | −0.257927 | + | 0.257927i | ||||
\(204\) | −3.51302 | − | 11.1292i | −0.245961 | − | 0.779199i | ||||
\(205\) | 12.6814 | + | 21.0100i | 0.885707 | + | 1.46740i | ||||
\(206\) | − | 16.8300i | − | 1.17260i | ||||||
\(207\) | 10.4309 | + | 1.83220i | 0.724996 | + | 0.127347i | ||||
\(208\) | −0.921665 | − | 0.921665i | −0.0639060 | − | 0.0639060i | ||||
\(209\) | 10.1351 | 0.701061 | ||||||||
\(210\) | 0.245443 | + | 3.86520i | 0.0169372 | + | 0.266724i | ||||
\(211\) | 26.0519 | 1.79349 | 0.896743 | − | 0.442551i | \(-0.145927\pi\) | ||||
0.896743 | + | 0.442551i | \(0.145927\pi\) | |||||||
\(212\) | 6.87196 | + | 6.87196i | 0.471968 | + | 0.471968i | ||||
\(213\) | 18.8406 | + | 9.79994i | 1.29093 | + | 0.671481i | ||||
\(214\) | 5.61377i | 0.383750i | ||||||||
\(215\) | −25.0815 | − | 6.20021i | −1.71054 | − | 0.422851i | ||||
\(216\) | −3.15917 | + | 4.12549i | −0.214954 | + | 0.280704i | ||||
\(217\) | 2.40888 | − | 2.40888i | 0.163525 | − | 0.163525i | ||||
\(218\) | 4.71291 | − | 4.71291i | 0.319198 | − | 0.319198i | ||||
\(219\) | 10.7379 | − | 3.38950i | 0.725598 | − | 0.229041i | ||||
\(220\) | −3.26380 | + | 1.96999i | −0.220046 | + | 0.132817i | ||||
\(221\) | 8.78246i | 0.590772i | ||||||||
\(222\) | 1.16323 | − | 2.23633i | 0.0780707 | − | 0.150092i | ||||
\(223\) | −1.49400 | − | 1.49400i | −0.100045 | − | 0.100045i | 0.655312 | − | 0.755358i | \(-0.272537\pi\) |
−0.755358 | + | 0.655312i | \(0.772537\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −14.8795 | + | 1.89737i | −0.991968 | + | 0.126492i | ||||
\(226\) | −6.13421 | −0.408042 | ||||||||
\(227\) | −7.38425 | − | 7.38425i | −0.490110 | − | 0.490110i | 0.418231 | − | 0.908341i | \(-0.362650\pi\) |
−0.908341 | + | 0.418231i | \(0.862650\pi\) | |||||||
\(228\) | 4.75144 | − | 9.13472i | 0.314672 | − | 0.604962i | ||||
\(229\) | − | 13.4219i | − | 0.886944i | −0.896288 | − | 0.443472i | \(-0.853746\pi\) | ||
0.896288 | − | 0.443472i | \(-0.146254\pi\) | |||||||
\(230\) | 6.75811 | − | 4.07912i | 0.445616 | − | 0.268969i | ||||
\(231\) | −2.81600 | + | 0.888895i | −0.185279 | + | 0.0584850i | ||||
\(232\) | −3.67489 | + | 3.67489i | −0.241268 | + | 0.241268i | ||||
\(233\) | 8.32952 | − | 8.32952i | 0.545685 | − | 0.545685i | −0.379505 | − | 0.925190i | \(-0.623906\pi\) |
0.925190 | + | 0.379505i | \(0.123906\pi\) | |||||||
\(234\) | 3.20166 | − | 2.24495i | 0.209299 | − | 0.146757i | ||||
\(235\) | −1.34049 | − | 0.331373i | −0.0874440 | − | 0.0216164i | ||||
\(236\) | − | 0.686337i | − | 0.0446767i | ||||||
\(237\) | −11.0561 | − | 5.75086i | −0.718173 | − | 0.373558i | ||||
\(238\) | −4.76445 | − | 4.76445i | −0.308834 | − | 0.308834i | ||||
\(239\) | 0.372694 | 0.0241076 | 0.0120538 | − | 0.999927i | \(-0.496163\pi\) | ||||
0.0120538 | + | 0.999927i | \(0.496163\pi\) | |||||||
\(240\) | 0.245443 | + | 3.86520i | 0.0158433 | + | 0.249497i | ||||
\(241\) | 29.4165 | 1.89489 | 0.947443 | − | 0.319924i | \(-0.103657\pi\) | ||||
0.947443 | + | 0.319924i | \(0.103657\pi\) | |||||||
\(242\) | 5.72286 | + | 5.72286i | 0.367879 | + | 0.367879i | ||||
\(243\) | −10.5502 | − | 11.4758i | −0.676796 | − | 0.736171i | ||||
\(244\) | − | 1.74994i | − | 0.112028i | ||||||
\(245\) | 1.15549 | + | 1.91438i | 0.0738218 | + | 0.122305i | ||||
\(246\) | 5.72206 | + | 18.1274i | 0.364825 | + | 1.15576i | ||||
\(247\) | −5.47905 | + | 5.47905i | −0.348623 | + | 0.348623i | ||||
\(248\) | 2.40888 | − | 2.40888i | 0.152964 | − | 0.152964i | ||||
\(249\) | −4.90100 | − | 15.5263i | −0.310589 | − | 0.983938i | ||||
\(250\) | −7.43108 | + | 8.35339i | −0.469983 | + | 0.528315i | ||||
\(251\) | 2.86106i | 0.180589i | 0.995915 | + | 0.0902943i | \(0.0287808\pi\) | ||||
−0.995915 | + | 0.0902943i | \(0.971219\pi\) | |||||||
\(252\) | −0.519010 | + | 2.95476i | −0.0326946 | + | 0.186133i | ||||
\(253\) | 4.25579 | + | 4.25579i | 0.267559 | + | 0.267559i | ||||
\(254\) | −15.8661 | −0.995531 | ||||||||
\(255\) | 17.2462 | − | 19.5850i | 1.08000 | − | 1.22646i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.93961 | − | 2.93961i | −0.183368 | − | 0.183368i | 0.609454 | − | 0.792822i | \(-0.291389\pi\) |
−0.792822 | + | 0.609454i | \(0.791389\pi\) | |||||||
\(258\) | −17.7546 | − | 9.23508i | −1.10535 | − | 0.574951i | ||||
\(259\) | − | 1.45536i | − | 0.0904319i | ||||||
\(260\) | 0.699434 | − | 2.82939i | 0.0433770 | − | 0.175471i | ||||
\(261\) | −8.95112 | − | 12.7657i | −0.554061 | − | 0.790179i | ||||
\(262\) | 3.25792 | − | 3.25792i | 0.201275 | − | 0.201275i | ||||
\(263\) | −16.7008 | + | 16.7008i | −1.02982 | + | 1.02982i | −0.0302760 | + | 0.999542i | \(0.509639\pi\) |
−0.999542 | + | 0.0302760i | \(0.990361\pi\) | |||||||
\(264\) | −2.81600 | + | 0.888895i | −0.173313 | + | 0.0547077i | ||||
\(265\) | −5.21500 | + | 21.0960i | −0.320355 | + | 1.29592i | ||||
\(266\) | − | 5.94473i | − | 0.364495i | ||||||
\(267\) | −1.80249 | + | 3.46532i | −0.110311 | + | 0.212074i | ||||
\(268\) | 1.03802 | + | 1.03802i | 0.0634072 | + | 0.0634072i | ||||
\(269\) | −1.10509 | −0.0673783 | −0.0336891 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336891 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(270\) | −11.5481 | − | 1.28085i | −0.702797 | − | 0.0779501i | ||||
\(271\) | −23.9149 | −1.45272 | −0.726362 | − | 0.687312i | \(-0.758790\pi\) | ||||
−0.726362 | + | 0.687312i | \(0.758790\pi\) | |||||||
\(272\) | −4.76445 | − | 4.76445i | −0.288887 | − | 0.288887i | ||||
\(273\) | 1.04179 | − | 2.00286i | 0.0630521 | − | 0.121219i | ||||
\(274\) | 3.13487i | 0.189384i | ||||||||
\(275\) | −7.54262 | − | 3.97183i | −0.454837 | − | 0.239510i | ||||
\(276\) | 5.83087 | − | 1.84056i | 0.350977 | − | 0.110789i | ||||
\(277\) | −10.5902 | + | 10.5902i | −0.636304 | + | 0.636304i | −0.949642 | − | 0.313338i | \(-0.898553\pi\) |
0.313338 | + | 0.949642i | \(0.398553\pi\) | |||||||
\(278\) | 0.228368 | − | 0.228368i | 0.0136966 | − | 0.0136966i | ||||
\(279\) | 5.86744 | + | 8.36790i | 0.351274 | + | 0.500973i | ||||
\(280\) | 1.15549 | + | 1.91438i | 0.0690540 | + | 0.114406i | ||||
\(281\) | 19.4466i | 1.16009i | 0.814585 | + | 0.580044i | \(0.196964\pi\) | ||||
−0.814585 | + | 0.580044i | \(0.803036\pi\) | |||||||
\(282\) | −0.948905 | − | 0.493574i | −0.0565065 | − | 0.0293919i | ||||
\(283\) | −17.2984 | − | 17.2984i | −1.02829 | − | 1.02829i | −0.999588 | − | 0.0286974i | \(-0.990864\pi\) |
−0.0286974 | − | 0.999588i | \(-0.509136\pi\) | |||||||
\(284\) | 12.2611 | 0.727564 | ||||||||
\(285\) | 22.9775 | − | 1.45909i | 1.36107 | − | 0.0864292i | ||||
\(286\) | 2.22221 | 0.131402 | ||||||||
\(287\) | 7.76040 | + | 7.76040i | 0.458082 | + | 0.458082i | ||||
\(288\) | −0.519010 | + | 2.95476i | −0.0305830 | + | 0.174111i | ||||
\(289\) | 28.4000i | 1.67059i | ||||||||
\(290\) | −11.2814 | − | 2.78880i | −0.662468 | − | 0.163764i | ||||
\(291\) | 9.74628 | + | 30.8760i | 0.571337 | + | 1.80998i | ||||
\(292\) | 4.59693 | − | 4.59693i | 0.269015 | − | 0.269015i | ||||
\(293\) | −17.8992 | + | 17.8992i | −1.04568 | + | 1.04568i | −0.0467777 | + | 0.998905i | \(0.514895\pi\) |
−0.998905 | + | 0.0467777i | \(0.985105\pi\) | |||||||
\(294\) | 0.521378 | + | 1.65172i | 0.0304074 | + | 0.0963300i | ||||
\(295\) | 1.31391 | − | 0.793059i | 0.0764986 | − | 0.0461737i | ||||
\(296\) | − | 1.45536i | − | 0.0845913i | ||||||
\(297\) | −1.16494 | − | 8.78196i | −0.0675968 | − | 0.509581i | ||||
\(298\) | −2.70491 | − | 2.70491i | −0.156691 | − | 0.156691i | ||||
\(299\) | −4.60136 | −0.266103 | ||||||||
\(300\) | −7.11583 | + | 4.93609i | −0.410833 | + | 0.284985i | ||||
\(301\) | −11.5544 | −0.665985 | ||||||||
\(302\) | 3.35916 | + | 3.35916i | 0.193298 | + | 0.193298i | ||||
\(303\) | −27.4176 | − | 14.2613i | −1.57510 | − | 0.819291i | ||||
\(304\) | − | 5.94473i | − | 0.340953i | ||||||
\(305\) | 3.35003 | − | 2.02204i | 0.191822 | − | 0.115782i | ||||
\(306\) | 16.5506 | − | 11.6050i | 0.946137 | − | 0.663416i | ||||
\(307\) | 7.54591 | − | 7.54591i | 0.430668 | − | 0.430668i | −0.458187 | − | 0.888856i | \(-0.651501\pi\) |
0.888856 | + | 0.458187i | \(0.151501\pi\) | |||||||
\(308\) | −1.20554 | + | 1.20554i | −0.0686921 | + | 0.0686921i | ||||
\(309\) | 27.7984 | − | 8.77479i | 1.58139 | − | 0.499181i | ||||
\(310\) | 7.39494 | + | 1.82805i | 0.420005 | + | 0.103826i | ||||
\(311\) | − | 7.09388i | − | 0.402257i | −0.979565 | − | 0.201129i | \(-0.935539\pi\) | ||
0.979565 | − | 0.201129i | \(-0.0644609\pi\) | |||||||
\(312\) | 1.04179 | − | 2.00286i | 0.0589799 | − | 0.113390i | ||||
\(313\) | 13.7044 | + | 13.7044i | 0.774616 | + | 0.774616i | 0.978910 | − | 0.204293i | \(-0.0654897\pi\) |
−0.204293 | + | 0.978910i | \(0.565490\pi\) | |||||||
\(314\) | −14.5758 | −0.822559 | ||||||||
\(315\) | −6.25624 | + | 2.42063i | −0.352499 | + | 0.136387i | ||||
\(316\) | −7.19515 | −0.404759 | ||||||||
\(317\) | −20.1184 | − | 20.1184i | −1.12996 | − | 1.12996i | −0.990183 | − | 0.139778i | \(-0.955361\pi\) |
−0.139778 | − | 0.990183i | \(-0.544639\pi\) | |||||||
\(318\) | −7.76764 | + | 14.9334i | −0.435587 | + | 0.837425i | ||||
\(319\) | − | 8.86046i | − | 0.496090i | ||||||
\(320\) | 1.15549 | + | 1.91438i | 0.0645941 | + | 0.107017i | ||||
\(321\) | −9.27236 | + | 2.92690i | −0.517533 | + | 0.163364i | ||||
\(322\) | 2.49622 | − | 2.49622i | 0.139109 | − | 0.139109i | ||||
\(323\) | −28.3234 | + | 28.3234i | −1.57595 | + | 1.57595i | ||||
\(324\) | −8.46126 | − | 3.06710i | −0.470070 | − | 0.170395i | ||||
\(325\) | 6.22471 | − | 1.93037i | 0.345285 | − | 0.107078i | ||||
\(326\) | 6.29706i | 0.348762i | ||||||||
\(327\) | 10.2416 | + | 5.32718i | 0.566361 | + | 0.294593i | ||||
\(328\) | 7.76040 | + | 7.76040i | 0.428497 | + | 0.428497i | ||||
\(329\) | −0.617532 | −0.0340456 | ||||||||
\(330\) | −4.95555 | − | 4.36376i | −0.272794 | − | 0.240217i | ||||
\(331\) | 7.35408 | 0.404217 | 0.202108 | − | 0.979363i | \(-0.435221\pi\) | ||||
0.202108 | + | 0.979363i | \(0.435221\pi\) | |||||||
\(332\) | −6.64687 | − | 6.64687i | −0.364794 | − | 0.364794i | ||||
\(333\) | 4.30026 | + | 0.755349i | 0.235653 | + | 0.0413929i | ||||
\(334\) | 12.6184i | 0.690451i | ||||||||
\(335\) | −0.787733 | + | 3.18659i | −0.0430385 | + | 0.174102i | ||||
\(336\) | 0.521378 | + | 1.65172i | 0.0284435 | + | 0.0901085i | ||||
\(337\) | −22.3830 | + | 22.3830i | −1.21928 | + | 1.21928i | −0.251397 | + | 0.967884i | \(0.580890\pi\) |
−0.967884 | + | 0.251397i | \(0.919110\pi\) | |||||||
\(338\) | 7.99106 | − | 7.99106i | 0.434656 | − | 0.434656i | ||||
\(339\) | −3.19824 | − | 10.1320i | −0.173705 | − | 0.550293i | ||||
\(340\) | 3.61565 | − | 14.6263i | 0.196086 | − | 0.793220i | ||||
\(341\) | 5.80801i | 0.314521i | ||||||||
\(342\) | 17.5653 | + | 3.08537i | 0.949821 | + | 0.166838i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −11.5544 | −0.622972 | ||||||||
\(345\) | 10.2611 | + | 9.03571i | 0.552437 | + | 0.486466i | ||||
\(346\) | 6.29457 | 0.338398 | ||||||||
\(347\) | −13.9437 | − | 13.9437i | −0.748536 | − | 0.748536i | 0.225668 | − | 0.974204i | \(-0.427543\pi\) |
−0.974204 | + | 0.225668i | \(0.927543\pi\) | |||||||
\(348\) | −7.98588 | − | 4.15386i | −0.428088 | − | 0.222670i | ||||
\(349\) | 4.36703i | 0.233762i | 0.993146 | + | 0.116881i | \(0.0372896\pi\) | ||||
−0.993146 | + | 0.116881i | \(0.962710\pi\) | |||||||
\(350\) | −2.32966 | + | 4.42410i | −0.124526 | + | 0.236478i | ||||
\(351\) | 5.37729 | + | 4.11776i | 0.287019 | + | 0.219790i | ||||
\(352\) | −1.20554 | + | 1.20554i | −0.0642556 | + | 0.0642556i | ||||
\(353\) | 9.91003 | − | 9.91003i | 0.527458 | − | 0.527458i | −0.392356 | − | 0.919814i | \(-0.628340\pi\) |
0.919814 | + | 0.392356i | \(0.128340\pi\) | |||||||
\(354\) | 1.13363 | − | 0.357841i | 0.0602520 | − | 0.0190191i | ||||
\(355\) | 14.1677 | + | 23.4724i | 0.751942 | + | 1.24579i | ||||
\(356\) | 2.25517i | 0.119524i | ||||||||
\(357\) | 5.38544 | − | 10.3536i | 0.285028 | − | 0.547971i | ||||
\(358\) | 7.55173 | + | 7.55173i | 0.399121 | + | 0.399121i | ||||
\(359\) | 31.8147 | 1.67912 | 0.839559 | − | 0.543269i | \(-0.182814\pi\) | ||||
0.839559 | + | 0.543269i | \(0.182814\pi\) | |||||||
\(360\) | −6.25624 | + | 2.42063i | −0.329733 | + | 0.127579i | ||||
\(361\) | −16.3398 | −0.859988 | ||||||||
\(362\) | 9.06614 | + | 9.06614i | 0.476506 | + | 0.476506i | ||||
\(363\) | −6.46876 | + | 12.4363i | −0.339522 | + | 0.652737i | ||||
\(364\) | − | 1.30343i | − | 0.0683184i | ||||||
\(365\) | 14.1120 | + | 3.48852i | 0.738655 | + | 0.182598i | ||||
\(366\) | 2.89040 | − | 0.912379i | 0.151083 | − | 0.0476908i | ||||
\(367\) | −14.4435 | + | 14.4435i | −0.753945 | + | 0.753945i | −0.975213 | − | 0.221268i | \(-0.928980\pi\) |
0.221268 | + | 0.975213i | \(0.428980\pi\) | |||||||
\(368\) | 2.49622 | − | 2.49622i | 0.130125 | − | 0.130125i | ||||
\(369\) | −26.9579 | + | 18.9024i | −1.40337 | + | 0.984021i | ||||
\(370\) | 2.78611 | − | 1.68167i | 0.144843 | − | 0.0874256i | ||||
\(371\) | 9.71842i | 0.504555i | ||||||||
\(372\) | 5.23472 | + | 2.72285i | 0.271408 | + | 0.141173i | ||||
\(373\) | −13.5553 | − | 13.5553i | −0.701867 | − | 0.701867i | 0.262944 | − | 0.964811i | \(-0.415307\pi\) |
−0.964811 | + | 0.262944i | \(0.915307\pi\) | |||||||
\(374\) | 11.4875 | 0.594004 | ||||||||
\(375\) | −17.6718 | − | 7.91875i | −0.912569 | − | 0.408922i | ||||
\(376\) | −0.617532 | −0.0318468 | ||||||||
\(377\) | 4.78996 | + | 4.78996i | 0.246696 | + | 0.246696i | ||||
\(378\) | −5.15103 | + | 0.683293i | −0.264940 | + | 0.0351448i | ||||
\(379\) | − | 15.1496i | − | 0.778182i | −0.921199 | − | 0.389091i | \(-0.872789\pi\) | ||
0.921199 | − | 0.389091i | \(-0.127211\pi\) | |||||||
\(380\) | 11.3804 | − | 6.86910i | 0.583804 | − | 0.352377i | ||||
\(381\) | −8.27227 | − | 26.2064i | −0.423801 | − | 1.34259i | ||||
\(382\) | 5.85935 | − | 5.85935i | 0.299790 | − | 0.299790i | ||||
\(383\) | 16.7428 | − | 16.7428i | 0.855519 | − | 0.855519i | −0.135287 | − | 0.990806i | \(-0.543196\pi\) |
0.990806 | + | 0.135287i | \(0.0431957\pi\) | |||||||
\(384\) | 0.521378 | + | 1.65172i | 0.0266065 | + | 0.0842888i | ||||
\(385\) | −3.70086 | − | 0.914862i | −0.188613 | − | 0.0466257i | ||||
\(386\) | − | 5.08736i | − | 0.258940i | ||||||
\(387\) | 5.99686 | − | 34.1406i | 0.304837 | − | 1.73546i | ||||
\(388\) | 13.2182 | + | 13.2182i | 0.671050 | + | 0.671050i | ||||
\(389\) | −10.3633 | −0.525439 | −0.262719 | − | 0.964872i | \(-0.584619\pi\) | ||||
−0.262719 | + | 0.964872i | \(0.584619\pi\) | |||||||
\(390\) | 5.03802 | − | 0.319918i | 0.255110 | − | 0.0161997i | ||||
\(391\) | −23.7863 | −1.20292 | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 7.07977 | + | 3.68255i | 0.357127 | + | 0.185760i | ||||
\(394\) | 7.78363i | 0.392134i | ||||||||
\(395\) | −8.31395 | − | 13.7742i | −0.418320 | − | 0.693056i | ||||
\(396\) | −2.93640 | − | 4.18778i | −0.147560 | − | 0.210444i | ||||
\(397\) | 10.6075 | − | 10.6075i | 0.532373 | − | 0.532373i | −0.388905 | − | 0.921278i | \(-0.627147\pi\) |
0.921278 | + | 0.388905i | \(0.127147\pi\) | |||||||
\(398\) | 14.6839 | − | 14.6839i | 0.736038 | − | 0.736038i | ||||
\(399\) | 9.81900 | − | 3.09945i | 0.491565 | − | 0.155167i | ||||
\(400\) | −2.32966 | + | 4.42410i | −0.116483 | + | 0.221205i | ||||
\(401\) | 9.37124i | 0.467977i | 0.972239 | + | 0.233989i | \(0.0751779\pi\) | ||||
−0.972239 | + | 0.233989i | \(0.924822\pi\) | |||||||
\(402\) | −1.17331 | + | 2.25572i | −0.0585195 | + | 0.112505i | ||||
\(403\) | −3.13981 | − | 3.13981i | −0.156405 | − | 0.156405i | ||||
\(404\) | −17.8429 | −0.887719 | ||||||||
\(405\) | −3.90535 | − | 19.7420i | −0.194058 | − | 0.980990i | ||||
\(406\) | −5.19708 | −0.257927 | ||||||||
\(407\) | 1.75450 | + | 1.75450i | 0.0869674 | + | 0.0869674i | ||||
\(408\) | 5.38544 | − | 10.3536i | 0.266619 | − | 0.512580i | ||||
\(409\) | 23.1943i | 1.14689i | 0.819245 | + | 0.573443i | \(0.194393\pi\) | ||||
−0.819245 | + | 0.573443i | \(0.805607\pi\) | |||||||
\(410\) | −5.88922 | + | 23.8234i | −0.290848 | + | 1.17655i | ||||
\(411\) | −5.17791 | + | 1.63445i | −0.255408 | + | 0.0806216i | ||||
\(412\) | 11.9006 | − | 11.9006i | 0.586300 | − | 0.586300i | ||||
\(413\) | 0.485314 | − | 0.485314i | 0.0238807 | − | 0.0238807i | ||||
\(414\) | 6.08018 | + | 8.67131i | 0.298825 | + | 0.426171i | ||||
\(415\) | 5.04418 | − | 20.4050i | 0.247609 | − | 1.00164i | ||||
\(416\) | − | 1.30343i | − | 0.0639060i | ||||||
\(417\) | 0.496265 | + | 0.258133i | 0.0243022 | + | 0.0126408i | ||||
\(418\) | 7.16661 | + | 7.16661i | 0.350531 | + | 0.350531i | ||||
\(419\) | 1.64096 | 0.0801662 | 0.0400831 | − | 0.999196i | \(-0.487238\pi\) | ||||
0.0400831 | + | 0.999196i | \(0.487238\pi\) | |||||||
\(420\) | −2.55955 | + | 2.90666i | −0.124893 | + | 0.141831i | ||||
\(421\) | 3.92047 | 0.191072 | 0.0955359 | − | 0.995426i | \(-0.469544\pi\) | ||||
0.0955359 | + | 0.995426i | \(0.469544\pi\) | |||||||
\(422\) | 18.4215 | + | 18.4215i | 0.896743 | + | 0.896743i | ||||
\(423\) | 0.320505 | − | 1.82466i | 0.0155835 | − | 0.0887180i | ||||
\(424\) | 9.71842i | 0.471968i | ||||||||
\(425\) | 32.1780 | − | 9.97884i | 1.56086 | − | 0.484045i | ||||
\(426\) | 6.39269 | + | 20.2519i | 0.309727 | + | 0.981208i | ||||
\(427\) | 1.23739 | − | 1.23739i | 0.0598815 | − | 0.0598815i | ||||
\(428\) | −3.96954 | + | 3.96954i | −0.191875 | + | 0.191875i | ||||
\(429\) | 1.15861 | + | 3.67046i | 0.0559384 | + | 0.177212i | ||||
\(430\) | −13.3511 | − | 22.1195i | −0.643845 | − | 1.06670i | ||||
\(431\) | − | 28.0498i | − | 1.35111i | −0.737308 | − | 0.675557i | \(-0.763903\pi\) | ||
0.737308 | − | 0.675557i | \(-0.236097\pi\) | |||||||
\(432\) | −5.15103 | + | 0.683293i | −0.247829 | + | 0.0328750i | ||||
\(433\) | −7.42460 | − | 7.42460i | −0.356804 | − | 0.356804i | 0.505830 | − | 0.862633i | \(-0.331186\pi\) |
−0.862633 | + | 0.505830i | \(0.831186\pi\) | |||||||
\(434\) | 3.40667 | 0.163525 | ||||||||
\(435\) | −1.27559 | − | 20.0877i | −0.0611597 | − | 0.963133i | ||||
\(436\) | 6.66506 | 0.319198 | ||||||||
\(437\) | −14.8394 | − | 14.8394i | −0.709862 | − | 0.709862i | ||||
\(438\) | 9.98957 | + | 5.19608i | 0.477320 | + | 0.248278i | ||||
\(439\) | − | 23.4410i | − | 1.11878i | −0.828905 | − | 0.559389i | \(-0.811036\pi\) | ||
0.828905 | − | 0.559389i | \(-0.188964\pi\) | |||||||
\(440\) | −3.70086 | − | 0.914862i | −0.176431 | − | 0.0436143i | ||||
\(441\) | −2.45633 | + | 1.72234i | −0.116968 | + | 0.0820161i | ||||
\(442\) | −6.21014 | + | 6.21014i | −0.295386 | + | 0.295386i | ||||
\(443\) | 10.0545 | − | 10.0545i | 0.477706 | − | 0.477706i | −0.426692 | − | 0.904397i | \(-0.640321\pi\) |
0.904397 | + | 0.426692i | \(0.140321\pi\) | |||||||
\(444\) | 2.40385 | − | 0.758796i | 0.114082 | − | 0.0360108i | ||||
\(445\) | −4.31724 | + | 2.60584i | −0.204657 | + | 0.123529i | ||||
\(446\) | − | 2.11283i | − | 0.100045i | ||||||
\(447\) | 3.05746 | − | 5.87802i | 0.144613 | − | 0.278021i | ||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | −29.2933 | −1.38244 | −0.691218 | − | 0.722646i | \(-0.742926\pi\) | ||||
−0.691218 | + | 0.722646i | \(0.742926\pi\) | |||||||
\(450\) | −11.8631 | − | 9.17976i | −0.559230 | − | 0.432738i | ||||
\(451\) | −18.7110 | −0.881065 | ||||||||
\(452\) | −4.33754 | − | 4.33754i | −0.204021 | − | 0.204021i | ||||
\(453\) | −3.79699 | + | 7.29977i | −0.178398 | + | 0.342973i | ||||
\(454\) | − | 10.4429i | − | 0.490110i | ||||||
\(455\) | 2.49526 | − | 1.50611i | 0.116979 | − | 0.0706074i | ||||
\(456\) | 9.81900 | − | 3.09945i | 0.459817 | − | 0.145145i | ||||
\(457\) | 21.3134 | − | 21.3134i | 0.996997 | − | 0.996997i | −0.00299860 | − | 0.999996i | \(-0.500954\pi\) |
0.999996 | + | 0.00299860i | \(0.000954486\pi\) | |||||||
\(458\) | 9.49072 | − | 9.49072i | 0.443472 | − | 0.443472i | ||||
\(459\) | 27.7974 | + | 21.2863i | 1.29747 | + | 0.993561i | ||||
\(460\) | 7.66307 | + | 1.89433i | 0.357293 | + | 0.0883238i | ||||
\(461\) | − | 9.53108i | − | 0.443907i | −0.975057 | − | 0.221953i | \(-0.928757\pi\) | ||
0.975057 | − | 0.221953i | \(-0.0712433\pi\) | |||||||
\(462\) | −2.61976 | − | 1.36267i | −0.121882 | − | 0.0633971i | ||||
\(463\) | 19.8492 | + | 19.8492i | 0.922471 | + | 0.922471i | 0.997204 | − | 0.0747323i | \(-0.0238102\pi\) |
−0.0747323 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(464\) | −5.19708 | −0.241268 | ||||||||
\(465\) | 0.836144 | + | 13.1675i | 0.0387752 | + | 0.610626i | ||||
\(466\) | 11.7797 | 0.545685 | ||||||||
\(467\) | 16.9197 | + | 16.9197i | 0.782949 | + | 0.782949i | 0.980327 | − | 0.197379i | \(-0.0632429\pi\) |
−0.197379 | + | 0.980327i | \(0.563243\pi\) | |||||||
\(468\) | 3.85133 | + | 0.676494i | 0.178028 | + | 0.0312709i | ||||
\(469\) | 1.46798i | 0.0677851i | ||||||||
\(470\) | −0.713554 | − | 1.18219i | −0.0329138 | − | 0.0545302i | ||||
\(471\) | −7.59950 | − | 24.0751i | −0.350167 | − | 1.10932i | ||||
\(472\) | 0.485314 | − | 0.485314i | 0.0223384 | − | 0.0223384i | ||||
\(473\) | 13.9293 | − | 13.9293i | 0.640471 | − | 0.640471i | ||||
\(474\) | −3.75139 | − | 11.8843i | −0.172307 | − | 0.545866i | ||||
\(475\) | 26.3001 | + | 13.8492i | 1.20673 | + | 0.635446i | ||||
\(476\) | − | 6.73795i | − | 0.308834i | ||||||
\(477\) | −28.7156 | − | 5.04396i | −1.31480 | − | 0.230947i | ||||
\(478\) | 0.263534 | + | 0.263534i | 0.0120538 | + | 0.0120538i | ||||
\(479\) | 5.16727 | 0.236099 | 0.118049 | − | 0.993008i | \(-0.462336\pi\) | ||||
0.118049 | + | 0.993008i | \(0.462336\pi\) | |||||||
\(480\) | −2.55955 | + | 2.90666i | −0.116827 | + | 0.132670i | ||||
\(481\) | −1.89697 | −0.0864943 | ||||||||
\(482\) | 20.8006 | + | 20.8006i | 0.947443 | + | 0.947443i | ||||
\(483\) | 5.42452 | + | 2.82157i | 0.246824 | + | 0.128386i | ||||
\(484\) | 8.09334i | 0.367879i | ||||||||
\(485\) | −10.0310 | + | 40.5780i | −0.455484 | + | 1.84255i | ||||
\(486\) | 0.654467 | − | 15.5747i | 0.0296872 | − | 0.706483i | ||||
\(487\) | −16.2445 | + | 16.2445i | −0.736107 | + | 0.736107i | −0.971822 | − | 0.235715i | \(-0.924257\pi\) |
0.235715 | + | 0.971822i | \(0.424257\pi\) | |||||||
\(488\) | 1.23739 | − | 1.23739i | 0.0560141 | − | 0.0560141i | ||||
\(489\) | −10.4009 | + | 3.28315i | −0.470347 | + | 0.148469i | ||||
\(490\) | −0.536610 | + | 2.17073i | −0.0242415 | + | 0.0980634i | ||||
\(491\) | − | 9.61274i | − | 0.433817i | −0.976192 | − | 0.216908i | \(-0.930403\pi\) | ||
0.976192 | − | 0.216908i | \(-0.0695973\pi\) | |||||||
\(492\) | −8.77187 | + | 16.8641i | −0.395466 | + | 0.760292i | ||||
\(493\) | 24.7612 | + | 24.7612i | 1.11519 | + | 1.11519i | ||||
\(494\) | −7.74854 | −0.348623 | ||||||||
\(495\) | 4.62398 | − | 10.4603i | 0.207833 | − | 0.470157i | ||||
\(496\) | 3.40667 | 0.152964 | ||||||||
\(497\) | 8.66993 | + | 8.66993i | 0.388899 | + | 0.388899i | ||||
\(498\) | 7.51320 | − | 14.4443i | 0.336675 | − | 0.647263i | ||||
\(499\) | − | 6.60885i | − | 0.295853i | −0.988998 | − | 0.147926i | \(-0.952740\pi\) | ||
0.988998 | − | 0.147926i | \(-0.0472599\pi\) | |||||||
\(500\) | −11.1613 | + | 0.652173i | −0.499149 | + | 0.0291660i | ||||
\(501\) | −20.8421 | + | 6.57899i | −0.931156 | + | 0.293927i | ||||
\(502\) | −2.02308 | + | 2.02308i | −0.0902943 | + | 0.0902943i | ||||
\(503\) | 14.3231 | − | 14.3231i | 0.638634 | − | 0.638634i | −0.311584 | − | 0.950219i | \(-0.600860\pi\) |
0.950219 | + | 0.311584i | \(0.100860\pi\) | |||||||
\(504\) | −2.45633 | + | 1.72234i | −0.109414 | + | 0.0767190i | ||||
\(505\) | −20.6174 | − | 34.1581i | −0.917463 | − | 1.52001i | ||||
\(506\) | 6.01860i | 0.267559i | ||||||||
\(507\) | 17.3653 | + | 9.03259i | 0.771221 | + | 0.401152i | ||||
\(508\) | −11.2191 | − | 11.2191i | −0.497765 | − | 0.497765i | ||||
\(509\) | −21.9532 | −0.973058 | −0.486529 | − | 0.873664i | \(-0.661737\pi\) | ||||
−0.486529 | + | 0.873664i | \(0.661737\pi\) | |||||||
\(510\) | 26.0435 | − | 1.65379i | 1.15323 | − | 0.0732308i | ||||
\(511\) | 6.50104 | 0.287589 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.06199 | + | 30.6215i | 0.179341 | + | 1.35197i | ||||
\(514\) | − | 4.15724i | − | 0.183368i | ||||||
\(515\) | 36.5333 | + | 9.03113i | 1.60985 | + | 0.397959i | ||||
\(516\) | −6.02422 | − | 19.0846i | −0.265202 | − | 0.840153i | ||||
\(517\) | 0.744460 | − | 0.744460i | 0.0327413 | − | 0.0327413i | ||||
\(518\) | 1.02910 | − | 1.02910i | 0.0452160 | − | 0.0452160i | ||||
\(519\) | 3.28185 | + | 10.3968i | 0.144057 | + | 0.456371i | ||||
\(520\) | 2.49526 | − | 1.50611i | 0.109424 | − | 0.0660472i | ||||
\(521\) | 33.6715i | 1.47518i | 0.675251 | + | 0.737588i | \(0.264035\pi\) | ||||
−0.675251 | + | 0.737588i | \(0.735965\pi\) | |||||||
\(522\) | 2.69734 | − | 15.3561i | 0.118059 | − | 0.672120i | ||||
\(523\) | 6.88874 | + | 6.88874i | 0.301223 | + | 0.301223i | 0.841492 | − | 0.540269i | \(-0.181677\pi\) |
−0.540269 | + | 0.841492i | \(0.681677\pi\) | |||||||
\(524\) | 4.60740 | 0.201275 | ||||||||
\(525\) | −8.52199 | − | 1.54131i | −0.371930 | − | 0.0672684i | ||||
\(526\) | −23.6185 | −1.02982 | ||||||||
\(527\) | −16.2309 | − | 16.2309i | −0.707030 | − | 0.707030i | ||||
\(528\) | −2.61976 | − | 1.36267i | −0.114010 | − | 0.0593025i | ||||
\(529\) | 10.5378i | 0.458164i | ||||||||
\(530\) | −18.6047 | + | 11.2296i | −0.808137 | + | 0.487782i | ||||
\(531\) | 1.18210 | + | 1.68587i | 0.0512990 | + | 0.0731605i | ||||
\(532\) | 4.20356 | − | 4.20356i | 0.182247 | − | 0.182247i | ||||
\(533\) | 10.1152 | − | 10.1152i | 0.438136 | − | 0.438136i | ||||
\(534\) | −3.72490 | + | 1.17580i | −0.161192 | + | 0.0508817i | ||||
\(535\) | −12.1860 | − | 3.01240i | −0.526845 | − | 0.130238i | ||||
\(536\) | 1.46798i | 0.0634072i | ||||||||
\(537\) | −8.53600 | + | 16.4106i | −0.368356 | + | 0.708170i | ||||
\(538\) | −0.781414 | − | 0.781414i | −0.0336891 | − | 0.0336891i | ||||
\(539\) | −1.70489 | −0.0734349 | ||||||||
\(540\) | −7.26007 | − | 9.07146i | −0.312424 | − | 0.390374i | ||||
\(541\) | 1.57604 | 0.0677593 | 0.0338797 | − | 0.999426i | \(-0.489214\pi\) | ||||
0.0338797 | + | 0.999426i | \(0.489214\pi\) | |||||||
\(542\) | −16.9104 | − | 16.9104i | −0.726362 | − | 0.726362i | ||||
\(543\) | −10.2478 | + | 19.7016i | −0.439775 | + | 0.845476i | ||||
\(544\) | − | 6.73795i | − | 0.288887i | ||||||
\(545\) | 7.70144 | + | 12.7594i | 0.329893 | + | 0.546554i | ||||
\(546\) | 2.15290 | − | 0.679581i | 0.0921355 | − | 0.0290834i | ||||
\(547\) | 5.30755 | − | 5.30755i | 0.226934 | − | 0.226934i | −0.584476 | − | 0.811411i | \(-0.698700\pi\) |
0.811411 | + | 0.584476i | \(0.198700\pi\) | |||||||
\(548\) | −2.21669 | + | 2.21669i | −0.0946922 | + | 0.0946922i | ||||
\(549\) | 3.01398 | + | 4.29842i | 0.128634 | + | 0.183452i | ||||
\(550\) | −2.52493 | − | 8.14194i | −0.107663 | − | 0.347174i | ||||
\(551\) | 30.8952i | 1.31618i | ||||||||
\(552\) | 5.42452 | + | 2.82157i | 0.230883 | + | 0.120094i | ||||
\(553\) | −5.08774 | − | 5.08774i | −0.216353 | − | 0.216353i | ||||
\(554\) | −14.9768 | −0.636304 | ||||||||
\(555\) | 4.23025 | + | 3.72508i | 0.179564 | + | 0.158121i | ||||
\(556\) | 0.322961 | 0.0136966 | ||||||||
\(557\) | 5.78892 | + | 5.78892i | 0.245284 | + | 0.245284i | 0.819032 | − | 0.573748i | \(-0.194511\pi\) |
−0.573748 | + | 0.819032i | \(0.694511\pi\) | |||||||
\(558\) | −1.76810 | + | 10.0659i | −0.0748495 | + | 0.426124i | ||||
\(559\) | 15.0604i | 0.636986i | ||||||||
\(560\) | −0.536610 | + | 2.17073i | −0.0226759 | + | 0.0917299i | ||||
\(561\) | 5.98933 | + | 18.9741i | 0.252870 | + | 0.801086i | ||||
\(562\) | −13.7508 | + | 13.7508i | −0.580044 | + | 0.580044i | ||||
\(563\) | −1.00705 | + | 1.00705i | −0.0424423 | + | 0.0424423i | −0.728009 | − | 0.685567i | \(-0.759554\pi\) |
0.685567 | + | 0.728009i | \(0.259554\pi\) | |||||||
\(564\) | −0.321968 | − | 1.01999i | −0.0135573 | − | 0.0429492i | ||||
\(565\) | 3.29168 | − | 13.3157i | 0.138482 | − | 0.560195i | ||||
\(566\) | − | 24.4637i | − | 1.02829i | ||||||
\(567\) | −3.81424 | − | 8.15178i | −0.160183 | − | 0.342343i | ||||
\(568\) | 8.66993 | + | 8.66993i | 0.363782 | + | 0.363782i | ||||
\(569\) | 13.9047 | 0.582917 | 0.291459 | − | 0.956583i | \(-0.405859\pi\) | ||||
0.291459 | + | 0.956583i | \(0.405859\pi\) | |||||||
\(570\) | 17.2793 | + | 15.2158i | 0.723751 | + | 0.637322i | ||||
\(571\) | 34.8923 | 1.46020 | 0.730098 | − | 0.683343i | \(-0.239475\pi\) | ||||
0.730098 | + | 0.683343i | \(0.239475\pi\) | |||||||
\(572\) | 1.57134 | + | 1.57134i | 0.0657010 | + | 0.0657010i | ||||
\(573\) | 12.7329 | + | 6.62304i | 0.531925 | + | 0.276681i | ||||
\(574\) | 10.9749i | 0.458082i | ||||||||
\(575\) | 5.22818 | + | 16.8589i | 0.218030 | + | 0.703064i | ||||
\(576\) | −2.45633 | + | 1.72234i | −0.102347 | + | 0.0717641i | ||||
\(577\) | 11.6857 | − | 11.6857i | 0.486482 | − | 0.486482i | −0.420712 | − | 0.907194i | \(-0.638220\pi\) |
0.907194 | + | 0.420712i | \(0.138220\pi\) | |||||||
\(578\) | −20.0819 | + | 20.0819i | −0.835295 | + | 0.835295i | ||||
\(579\) | 8.40287 | − | 2.65244i | 0.349212 | − | 0.110232i | ||||
\(580\) | −6.00519 | − | 9.94915i | −0.249352 | − | 0.413116i | ||||
\(581\) | − | 9.40009i | − | 0.389981i | ||||||
\(582\) | −14.9410 | + | 28.7243i | −0.619323 | + | 1.19066i | ||||
\(583\) | −11.7160 | − | 11.7160i | −0.485226 | − | 0.485226i | ||||
\(584\) | 6.50104 | 0.269015 | ||||||||
\(585\) | 3.15513 | + | 8.15458i | 0.130449 | + | 0.337150i | ||||
\(586\) | −25.3133 | −1.04568 | ||||||||
\(587\) | −19.5496 | − | 19.5496i | −0.806898 | − | 0.806898i | 0.177265 | − | 0.984163i | \(-0.443275\pi\) |
−0.984163 | + | 0.177265i | \(0.943275\pi\) | |||||||
\(588\) | −0.799269 | + | 1.53661i | −0.0329613 | + | 0.0633687i | ||||
\(589\) | − | 20.2517i | − | 0.834457i | ||||||
\(590\) | 1.48985 | + | 0.368295i | 0.0613361 | + | 0.0151625i | ||||
\(591\) | −12.8563 | + | 4.05822i | −0.528840 | + | 0.166933i | ||||
\(592\) | 1.02910 | − | 1.02910i | 0.0422957 | − | 0.0422957i | ||||
\(593\) | 11.8939 | − | 11.8939i | 0.488424 | − | 0.488424i | −0.419385 | − | 0.907809i | \(-0.637754\pi\) |
0.907809 | + | 0.419385i | \(0.137754\pi\) | |||||||
\(594\) | 5.38604 | − | 7.03352i | 0.220992 | − | 0.288589i | ||||
\(595\) | 12.8990 | − | 7.78567i | 0.528806 | − | 0.319181i | ||||
\(596\) | − | 3.82532i | − | 0.156691i | ||||||
\(597\) | 31.9095 | + | 16.5978i | 1.30597 | + | 0.679302i | ||||
\(598\) | −3.25365 | − | 3.25365i | −0.133052 | − | 0.133052i | ||||
\(599\) | −33.0557 | −1.35062 | −0.675309 | − | 0.737535i | \(-0.735990\pi\) | ||||
−0.675309 | + | 0.737535i | \(0.735990\pi\) | |||||||
\(600\) | −8.52199 | − | 1.54131i | −0.347909 | − | 0.0629238i | ||||
\(601\) | −39.7500 | −1.62144 | −0.810718 | − | 0.585436i | \(-0.800923\pi\) | ||||
−0.810718 | + | 0.585436i | \(0.800923\pi\) | |||||||
\(602\) | −8.17020 | − | 8.17020i | −0.332993 | − | 0.332993i | ||||
\(603\) | −4.33754 | − | 0.761898i | −0.176638 | − | 0.0310269i | ||||
\(604\) | 4.75057i | 0.193298i | ||||||||
\(605\) | −15.4937 | + | 9.35181i | −0.629908 | + | 0.380205i | ||||
\(606\) | −9.30292 | − | 29.4715i | −0.377905 | − | 1.19720i | ||||
\(607\) | 22.5491 | − | 22.5491i | 0.915238 | − | 0.915238i | −0.0814398 | − | 0.996678i | \(-0.525952\pi\) |
0.996678 | + | 0.0814398i | \(0.0259518\pi\) | |||||||
\(608\) | 4.20356 | − | 4.20356i | 0.170477 | − | 0.170477i | ||||
\(609\) | −2.70964 | − | 8.58409i | −0.109800 | − | 0.347845i | ||||
\(610\) | 3.79863 | + | 0.939032i | 0.153802 | + | 0.0380203i | ||||
\(611\) | 0.804910i | 0.0325632i | ||||||||
\(612\) | 19.9091 | + | 3.49707i | 0.804776 | + | 0.141361i | ||||
\(613\) | −0.341141 | − | 0.341141i | −0.0137786 | − | 0.0137786i | 0.700184 | − | 0.713962i | \(-0.253101\pi\) |
−0.713962 | + | 0.700184i | \(0.753101\pi\) | |||||||
\(614\) | 10.6715 | 0.430668 | ||||||||
\(615\) | −42.4200 | + | 2.69371i | −1.71054 | + | 0.108621i | ||||
\(616\) | −1.70489 | −0.0686921 | ||||||||
\(617\) | −24.0144 | − | 24.0144i | −0.966784 | − | 0.966784i | 0.0326817 | − | 0.999466i | \(-0.489595\pi\) |
−0.999466 | + | 0.0326817i | \(0.989595\pi\) | |||||||
\(618\) | 25.8611 | + | 13.4517i | 1.04029 | + | 0.541106i | ||||
\(619\) | − | 15.8572i | − | 0.637355i | −0.947863 | − | 0.318677i | \(-0.896761\pi\) | ||
0.947863 | − | 0.318677i | \(-0.103239\pi\) | |||||||
\(620\) | 3.93639 | + | 6.52164i | 0.158089 | + | 0.261915i | ||||
\(621\) | −11.1525 | + | 14.5638i | −0.447533 | + | 0.584424i | ||||
\(622\) | 5.01613 | − | 5.01613i | 0.201129 | − | 0.201129i | ||||
\(623\) | −1.59465 | + | 1.59465i | −0.0638882 | + | 0.0638882i | ||||
\(624\) | 2.15290 | − | 0.679581i | 0.0861849 | − | 0.0272050i | ||||
\(625\) | −14.1453 | − | 20.6133i | −0.565813 | − | 0.824534i | ||||
\(626\) | 19.3809i | 0.774616i | ||||||||
\(627\) | −8.10069 | + | 15.5737i | −0.323510 | + | 0.621955i | ||||
\(628\) | −10.3066 | − | 10.3066i | −0.411280 | − | 0.411280i | ||||
\(629\) | −9.80618 | −0.390998 | ||||||||
\(630\) | −6.13548 | − | 2.71218i | −0.244443 | − | 0.108056i | ||||
\(631\) | 9.22404 | 0.367203 | 0.183602 | − | 0.983001i | \(-0.441224\pi\) | ||||
0.183602 | + | 0.983001i | \(0.441224\pi\) | |||||||
\(632\) | −5.08774 | − | 5.08774i | −0.202379 | − | 0.202379i | ||||
\(633\) | −20.8225 | + | 40.0316i | −0.827619 | + | 1.59111i | ||||
\(634\) | − | 28.4517i | − | 1.12996i | ||||||
\(635\) | 8.51393 | − | 34.4411i | 0.337865 | − | 1.36675i | ||||
\(636\) | −16.0521 | + | 5.06698i | −0.636506 | + | 0.200919i | ||||
\(637\) | 0.921665 | − | 0.921665i | 0.0365177 | − | 0.0365177i | ||||
\(638\) | 6.26529 | − | 6.26529i | 0.248045 | − | 0.248045i | ||||
\(639\) | −30.1174 | + | 21.1178i | −1.19142 | + | 0.835408i | ||||
\(640\) | −0.536610 | + | 2.17073i | −0.0212114 | + | 0.0858055i | ||||
\(641\) | − | 46.8024i | − | 1.84858i | −0.381688 | − | 0.924291i | \(-0.624657\pi\) | ||
0.381688 | − | 0.924291i | \(-0.375343\pi\) | |||||||
\(642\) | −8.62618 | − | 4.48692i | −0.340448 | − | 0.177084i | ||||
\(643\) | −15.5179 | − | 15.5179i | −0.611968 | − | 0.611968i | 0.331491 | − | 0.943458i | \(-0.392448\pi\) |
−0.943458 | + | 0.331491i | \(0.892448\pi\) | |||||||
\(644\) | 3.53019 | 0.139109 | ||||||||
\(645\) | 29.5741 | − | 33.5848i | 1.16448 | − | 1.32240i | ||||
\(646\) | −40.0553 | −1.57595 | ||||||||
\(647\) | 13.4045 | + | 13.4045i | 0.526986 | + | 0.526986i | 0.919672 | − | 0.392687i | \(-0.128454\pi\) |
−0.392687 | + | 0.919672i | \(0.628454\pi\) | |||||||
\(648\) | −3.81424 | − | 8.15178i | −0.149838 | − | 0.320232i | ||||
\(649\) | 1.17013i | 0.0459317i | ||||||||
\(650\) | 5.76651 | + | 3.03656i | 0.226181 | + | 0.119104i | ||||
\(651\) | 1.77616 | + | 5.62685i | 0.0696134 | + | 0.220534i | ||||
\(652\) | −4.45269 | + | 4.45269i | −0.174381 | + | 0.174381i | ||||
\(653\) | −22.3383 | + | 22.3383i | −0.874165 | + | 0.874165i | −0.992923 | − | 0.118758i | \(-0.962109\pi\) |
0.118758 | + | 0.992923i | \(0.462109\pi\) | |||||||
\(654\) | 3.47502 | + | 11.0088i | 0.135884 | + | 0.430477i | ||||
\(655\) | 5.32382 | + | 8.82029i | 0.208019 | + | 0.344637i | ||||
\(656\) | 10.9749i | 0.428497i | ||||||||
\(657\) | −3.37411 | + | 19.2090i | −0.131636 | + | 0.749416i | ||||
\(658\) | −0.436661 | − | 0.436661i | −0.0170228 | − | 0.0170228i | ||||
\(659\) | 9.99021 | 0.389163 | 0.194582 | − | 0.980886i | \(-0.437665\pi\) | ||||
0.194582 | + | 0.980886i | \(0.437665\pi\) | |||||||
\(660\) | −0.418454 | − | 6.58975i | −0.0162883 | − | 0.256506i | ||||
\(661\) | −0.298368 | −0.0116052 | −0.00580259 | − | 0.999983i | \(-0.501847\pi\) | ||||
−0.00580259 | + | 0.999983i | \(0.501847\pi\) | |||||||
\(662\) | 5.20012 | + | 5.20012i | 0.202108 | + | 0.202108i | ||||
\(663\) | −13.4952 | − | 7.01955i | −0.524111 | − | 0.272617i | ||||
\(664\) | − | 9.40009i | − | 0.364794i | ||||||
\(665\) | 12.9044 | + | 3.19000i | 0.500410 | + | 0.123703i | ||||
\(666\) | 2.50663 | + | 3.57485i | 0.0971299 | + | 0.138523i | ||||
\(667\) | −12.9731 | + | 12.9731i | −0.502319 | + | 0.502319i | ||||
\(668\) | −8.92259 | + | 8.92259i | −0.345225 | + | 0.345225i | ||||
\(669\) | 3.48980 | − | 1.10158i | 0.134923 | − | 0.0425897i | ||||
\(670\) | −2.81027 | + | 1.69625i | −0.108570 | + | 0.0655317i | ||||
\(671\) | 2.98345i | 0.115175i | ||||||||
\(672\) | −0.799269 | + | 1.53661i | −0.0308325 | + | 0.0592760i | ||||
\(673\) | 3.14231 | + | 3.14231i | 0.121127 | + | 0.121127i | 0.765072 | − | 0.643945i | \(-0.222703\pi\) |
−0.643945 | + | 0.765072i | \(0.722703\pi\) | |||||||
\(674\) | −31.6544 | −1.21928 | ||||||||
\(675\) | 8.97721 | − | 24.3805i | 0.345533 | − | 0.938407i | ||||
\(676\) | 11.3011 | 0.434656 | ||||||||
\(677\) | 4.61132 | + | 4.61132i | 0.177227 | + | 0.177227i | 0.790146 | − | 0.612919i | \(-0.210005\pi\) |
−0.612919 | + | 0.790146i | \(0.710005\pi\) | |||||||
\(678\) | 4.90288 | − | 9.42588i | 0.188294 | − | 0.361999i | ||||
\(679\) | 18.6933i | 0.717383i | ||||||||
\(680\) | 12.8990 | − | 7.78567i | 0.494653 | − | 0.298567i | ||||
\(681\) | 17.2487 | − | 5.44471i | 0.660972 | − | 0.208642i | ||||
\(682\) | −4.10688 | + | 4.10688i | −0.157261 | + | 0.157261i | ||||
\(683\) | −8.26190 | + | 8.26190i | −0.316133 | + | 0.316133i | −0.847280 | − | 0.531147i | \(-0.821761\pi\) |
0.531147 | + | 0.847280i | \(0.321761\pi\) | |||||||
\(684\) | 10.2388 | + | 14.6022i | 0.391491 | + | 0.558329i | ||||
\(685\) | −6.80494 | − | 1.68220i | −0.260003 | − | 0.0642736i | ||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 20.6242 | + | 10.7277i | 0.786863 | + | 0.409288i | ||||
\(688\) | −8.17020 | − | 8.17020i | −0.311486 | − | 0.311486i | ||||
\(689\) | 12.6673 | 0.482586 | ||||||||
\(690\) | 0.866461 | + | 13.6449i | 0.0329856 | + | 0.519452i | ||||
\(691\) | −21.6167 | −0.822338 | −0.411169 | − | 0.911559i | \(-0.634879\pi\) | ||||
−0.411169 | + | 0.911559i | \(0.634879\pi\) | |||||||
\(692\) | 4.45093 | + | 4.45093i | 0.169199 | + | 0.169199i | ||||
\(693\) | 0.884857 | − | 5.03756i | 0.0336129 | − | 0.191361i | ||||
\(694\) | − | 19.7193i | − | 0.748536i | ||||||
\(695\) | 0.373179 | + | 0.618268i | 0.0141555 | + | 0.0234522i | ||||
\(696\) | −2.70964 | − | 8.58409i | −0.102709 | − | 0.325379i | ||||
\(697\) | 52.2892 | − | 52.2892i | 1.98060 | − | 1.98060i | ||||
\(698\) | −3.08796 | + | 3.08796i | −0.116881 | + | 0.116881i | ||||
\(699\) | 6.14169 | + | 19.4567i | 0.232300 | + | 0.735922i | ||||
\(700\) | −4.77563 | + | 1.48099i | −0.180502 | + | 0.0559762i | ||||
\(701\) | 1.45001i | 0.0547660i | 0.999625 | + | 0.0273830i | \(0.00871737\pi\) | ||||
−0.999625 | + | 0.0273830i | \(0.991283\pi\) | |||||||
\(702\) | 0.890626 | + | 6.71401i | 0.0336145 | + | 0.253404i | ||||
\(703\) | −6.11771 | − | 6.11771i | −0.230734 | − | 0.230734i | ||||
\(704\) | −1.70489 | −0.0642556 | ||||||||
\(705\) | 1.58061 | − | 1.79496i | 0.0595290 | − | 0.0676019i | ||||
\(706\) | 14.0149 | 0.527458 | ||||||||
\(707\) | −12.6169 | − | 12.6169i | −0.474506 | − | 0.474506i | ||||
\(708\) | 1.05463 | + | 0.548568i | 0.0396355 | + | 0.0206165i | ||||
\(709\) | 0.737376i | 0.0276927i | 0.999904 | + | 0.0138464i | \(0.00440758\pi\) | ||||
−0.999904 | + | 0.0138464i | \(0.995592\pi\) | |||||||
\(710\) | −6.57944 | + | 26.6156i | −0.246922 | + | 0.998864i | ||||
\(711\) | 17.6736 | − | 12.3925i | 0.662814 | − | 0.464754i | ||||
\(712\) | −1.59465 | + | 1.59465i | −0.0597619 | + | 0.0597619i | ||||
\(713\) | 8.50380 | − | 8.50380i | 0.318470 | − | 0.318470i | ||||
\(714\) | 11.1292 | − | 3.51302i | 0.416499 | − | 0.131472i | ||||
\(715\) | −1.19246 | + | 4.82381i | −0.0445955 | + | 0.180400i | ||||
\(716\) | 10.6798i | 0.399121i | ||||||||
\(717\) | −0.297883 | + | 0.572685i | −0.0111246 | + | 0.0213873i | ||||
\(718\) | 22.4964 | + | 22.4964i | 0.839559 | + | 0.839559i | ||||
\(719\) | −24.2873 | −0.905762 | −0.452881 | − | 0.891571i | \(-0.649604\pi\) | ||||
−0.452881 | + | 0.891571i | \(0.649604\pi\) | |||||||
\(720\) | −6.13548 | − | 2.71218i | −0.228656 | − | 0.101077i | ||||
\(721\) | 16.8300 | 0.626781 | ||||||||
\(722\) | −11.5540 | − | 11.5540i | −0.429994 | − | 0.429994i | ||||
\(723\) | −23.5117 | + | 45.2017i | −0.874411 | + | 1.68107i | ||||
\(724\) | 12.8215i | 0.476506i | ||||||||
\(725\) | 12.1074 | − | 22.9924i | 0.449659 | − | 0.853916i | ||||
\(726\) | −13.3679 | + | 4.21969i | −0.496129 | + | 0.156607i | ||||
\(727\) | 0.423061 | − | 0.423061i | 0.0156905 | − | 0.0156905i | −0.699218 | − | 0.714908i | \(-0.746468\pi\) |
0.714908 | + | 0.699218i | \(0.246468\pi\) | |||||||
\(728\) | 0.921665 | − | 0.921665i | 0.0341592 | − | 0.0341592i | ||||
\(729\) | 26.0662 | − | 7.03933i | 0.965416 | − | 0.260716i | ||||
\(730\) | 7.51192 | + | 12.4454i | 0.278029 | + | 0.460626i | ||||
\(731\) | 77.8531i | 2.87950i | ||||||||
\(732\) | 2.68897 | + | 1.39867i | 0.0993871 | + | 0.0516963i | ||||
\(733\) | −0.238162 | − | 0.238162i | −0.00879670 | − | 0.00879670i | 0.702695 | − | 0.711491i | \(-0.251980\pi\) |
−0.711491 | + | 0.702695i | \(0.751980\pi\) | |||||||
\(734\) | −20.4262 | −0.753945 | ||||||||
\(735\) | −3.86520 | + | 0.245443i | −0.142570 | + | 0.00905331i | ||||
\(736\) | 3.53019 | 0.130125 | ||||||||
\(737\) | −1.76971 | − | 1.76971i | −0.0651882 | − | 0.0651882i | ||||
\(738\) | −32.4281 | − | 5.69607i | −1.19370 | − | 0.209675i | ||||
\(739\) | 41.6831i | 1.53334i | 0.642042 | + | 0.766669i | \(0.278087\pi\) | ||||
−0.642042 | + | 0.766669i | \(0.721913\pi\) | |||||||
\(740\) | 3.15920 | + | 0.780962i | 0.116134 | + | 0.0287088i | ||||
\(741\) | −4.03992 | − | 12.7984i | −0.148410 | − | 0.470161i | ||||
\(742\) | −6.87196 | + | 6.87196i | −0.252278 | + | 0.252278i | ||||
\(743\) | 1.84534 | − | 1.84534i | 0.0676990 | − | 0.0676990i | −0.672447 | − | 0.740146i | \(-0.734757\pi\) |
0.740146 | + | 0.672447i | \(0.234757\pi\) | |||||||
\(744\) | 1.77616 | + | 5.62685i | 0.0651173 | + | 0.206290i | ||||
\(745\) | 7.32309 | − | 4.42013i | 0.268297 | − | 0.161941i | ||||
\(746\) | − | 19.1701i | − | 0.701867i | ||||||
\(747\) | 27.7750 | + | 4.87874i | 1.01624 | + | 0.178504i | ||||
\(748\) | 8.12288 | + | 8.12288i | 0.297002 | + | 0.297002i | ||||
\(749\) | −5.61377 | −0.205123 | ||||||||
\(750\) | −6.89647 | − | 18.0953i | −0.251823 | − | 0.660746i | ||||
\(751\) | 27.4131 | 1.00032 | 0.500160 | − | 0.865933i | \(-0.333275\pi\) | ||||
0.500160 | + | 0.865933i | \(0.333275\pi\) | |||||||
\(752\) | −0.436661 | − | 0.436661i | −0.0159234 | − | 0.0159234i | ||||
\(753\) | −4.39633 | − | 2.28676i | −0.160211 | − | 0.0833341i | ||||
\(754\) | 6.77403i | 0.246696i | ||||||||
\(755\) | −9.09438 | + | 5.48926i | −0.330978 | + | 0.199775i | ||||
\(756\) | −4.12549 | − | 3.15917i | −0.150043 | − | 0.114898i | ||||
\(757\) | 28.1863 | − | 28.1863i | 1.02445 | − | 1.02445i | 0.0247547 | − | 0.999694i | \(-0.492120\pi\) |
0.999694 | − | 0.0247547i | \(-0.00788046\pi\) | |||||||
\(758\) | 10.7124 | − | 10.7124i | 0.389091 | − | 0.389091i | ||||
\(759\) | −9.94101 | + | 3.13797i | −0.360836 | + | 0.113901i | ||||
\(760\) | 12.9044 | + | 3.19000i | 0.468091 | + | 0.115713i | ||||
\(761\) | − | 17.7595i | − | 0.643782i | −0.946777 | − | 0.321891i | \(-0.895682\pi\) | ||
0.946777 | − | 0.321891i | \(-0.104318\pi\) | |||||||
\(762\) | 12.6813 | − | 24.3801i | 0.459396 | − | 0.883197i | ||||
\(763\) | 4.71291 | + | 4.71291i | 0.170619 | + | 0.170619i | ||||
\(764\) | 8.28637 | 0.299790 | ||||||||
\(765\) | 16.3101 | + | 42.1543i | 0.589694 | + | 1.52409i | ||||
\(766\) | 23.6779 | 0.855519 | ||||||||
\(767\) | −0.632573 | − | 0.632573i | −0.0228409 | − | 0.0228409i | ||||
\(768\) | −0.799269 | + | 1.53661i | −0.0288411 | + | 0.0554476i | ||||
\(769\) | 31.6783i | 1.14235i | 0.820828 | + | 0.571175i | \(0.193512\pi\) | ||||
−0.820828 | + | 0.571175i | \(0.806488\pi\) | |||||||
\(770\) | −1.96999 | − | 3.26380i | −0.0709937 | − | 0.117619i | ||||
\(771\) | 6.86658 | − | 2.16750i | 0.247294 | − | 0.0780605i | ||||
\(772\) | 3.59731 | − | 3.59731i | 0.129470 | − | 0.129470i | ||||
\(773\) | 24.0703 | − | 24.0703i | 0.865748 | − | 0.865748i | −0.126250 | − | 0.991998i | \(-0.540294\pi\) |
0.991998 | + | 0.126250i | \(0.0402942\pi\) | |||||||
\(774\) | 28.3814 | − | 19.9006i | 1.02015 | − | 0.715312i | ||||
\(775\) | −7.93640 | + | 15.0714i | −0.285084 | + | 0.541382i | ||||
\(776\) | 18.6933i | 0.671050i | ||||||||
\(777\) | 2.23633 | + | 1.16323i | 0.0802278 | + | 0.0417306i | ||||
\(778\) | −7.32794 | − | 7.32794i | −0.262719 | − | 0.262719i | ||||
\(779\) | 65.2426 | 2.33756 | ||||||||
\(780\) | 3.78863 | + | 3.33620i | 0.135655 | + | 0.119455i | ||||
\(781\) | −20.9039 | −0.748001 | ||||||||
\(782\) | −16.8194 | − | 16.8194i | −0.601461 | − | 0.601461i | ||||
\(783\) | 26.7703 | − | 3.55113i | 0.956692 | − | 0.126907i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 7.82151 | − | 31.6400i | 0.279162 | − | 1.12928i | ||||
\(786\) | 2.40220 | + | 7.61011i | 0.0856836 | + | 0.271444i | ||||
\(787\) | −19.3092 | + | 19.3092i | −0.688297 | + | 0.688297i | −0.961855 | − | 0.273558i | \(-0.911799\pi\) |
0.273558 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(788\) | −5.50386 | + | 5.50386i | −0.196067 | + | 0.196067i | ||||
\(789\) | −12.3142 | − | 39.0111i | −0.438397 | − | 1.38883i | ||||
\(790\) | 3.86098 | − | 15.6187i | 0.137368 | − | 0.555688i | ||||
\(791\) | − | 6.13421i | − | 0.218107i | ||||||
\(792\) | 0.884857 | − | 5.03756i | 0.0314420 | − | 0.179002i | ||||
\(793\) | −1.61285 | − | 1.61285i | −0.0572741 | − | 0.0572741i | ||||
\(794\) | 15.0012 | 0.532373 | ||||||||
\(795\) | −28.2482 | − | 24.8748i | −1.00186 | − | 0.882219i | ||||
\(796\) | 20.7662 | 0.736038 | ||||||||
\(797\) | −16.7052 | − | 16.7052i | −0.591727 | − | 0.591727i | 0.346371 | − | 0.938098i | \(-0.387414\pi\) |
−0.938098 | + | 0.346371i | \(0.887414\pi\) | |||||||
\(798\) | 9.13472 | + | 4.75144i | 0.323366 | + | 0.168199i | ||||
\(799\) | 4.16090i | 0.147202i | ||||||||
\(800\) | −4.77563 | + | 1.48099i | −0.168844 | + | 0.0523609i | ||||
\(801\) | −3.88417 | − | 5.53944i | −0.137240 | − | 0.195727i | ||||
\(802\) | −6.62647 | + | 6.62647i | −0.233989 | + | 0.233989i | ||||
\(803\) | −7.83728 | + | 7.83728i | −0.276572 | + | 0.276572i | ||||
\(804\) | −2.42469 | + | 0.765374i | −0.0855122 | + | 0.0269927i | ||||
\(805\) | 4.07912 | + | 6.75811i | 0.143770 | + | 0.238192i | ||||
\(806\) | − | 4.44036i | − | 0.156405i | ||||||
\(807\) | 0.883261 | − | 1.69809i | 0.0310923 | − | 0.0597754i | ||||
\(808\) | −12.6169 | − | 12.6169i | −0.443860 | − | 0.443860i | ||||
\(809\) | −12.8721 | −0.452560 | −0.226280 | − | 0.974062i | \(-0.572657\pi\) | ||||
−0.226280 | + | 0.974062i | \(0.572657\pi\) | |||||||
\(810\) | 11.1982 | − | 16.7212i | 0.393466 | − | 0.587524i | ||||
\(811\) | −1.25946 | −0.0442256 | −0.0221128 | − | 0.999755i | \(-0.507039\pi\) | ||||
−0.0221128 | + | 0.999755i | \(0.507039\pi\) | |||||||
\(812\) | −3.67489 | − | 3.67489i | −0.128963 | − | 0.128963i | ||||
\(813\) | 19.1144 | − | 36.7478i | 0.670372 | − | 1.28880i | ||||
\(814\) | 2.48124i | 0.0869674i | ||||||||
\(815\) | −13.6692 | − | 3.37906i | −0.478811 | − | 0.118363i | ||||
\(816\) | 11.1292 | − | 3.51302i | 0.389599 | − | 0.122980i | ||||
\(817\) | −48.5696 | + | 48.5696i | −1.69924 | + | 1.69924i | ||||
\(818\) | −16.4009 | + | 16.4009i | −0.573443 | + | 0.573443i | ||||
\(819\) | 2.24495 | + | 3.20166i | 0.0784449 | + | 0.111875i | ||||
\(820\) | −21.0100 | + | 12.6814i | −0.733701 | + | 0.442854i | ||||
\(821\) | − | 26.4873i | − | 0.924415i | −0.886772 | − | 0.462207i | \(-0.847058\pi\) | ||
0.886772 | − | 0.462207i | \(-0.152942\pi\) | |||||||
\(822\) | −4.81707 | − | 2.50560i | −0.168015 | − | 0.0873930i | ||||
\(823\) | 2.53245 | + | 2.53245i | 0.0882758 | + | 0.0882758i | 0.749866 | − | 0.661590i | \(-0.230118\pi\) |
−0.661590 | + | 0.749866i | \(0.730118\pi\) | |||||||
\(824\) | 16.8300 | 0.586300 | ||||||||
\(825\) | 12.1317 | − | 8.41550i | 0.422373 | − | 0.292990i | ||||
\(826\) | 0.686337 | 0.0238807 | ||||||||
\(827\) | 9.56258 | + | 9.56258i | 0.332524 | + | 0.332524i | 0.853544 | − | 0.521021i | \(-0.174449\pi\) |
−0.521021 | + | 0.853544i | \(0.674449\pi\) | |||||||
\(828\) | −1.83220 | + | 10.4309i | −0.0636735 | + | 0.362498i | ||||
\(829\) | 38.5455i | 1.33874i | 0.742928 | + | 0.669371i | \(0.233436\pi\) | ||||
−0.742928 | + | 0.669371i | \(0.766564\pi\) | |||||||
\(830\) | 17.9953 | − | 10.8618i | 0.624626 | − | 0.377017i | ||||
\(831\) | −7.80859 | − | 24.7374i | −0.270877 | − | 0.858132i | ||||
\(832\) | 0.921665 | − | 0.921665i | 0.0319530 | − | 0.0319530i | ||||
\(833\) | 4.76445 | − | 4.76445i | 0.165079 | − | 0.165079i | ||||
\(834\) | 0.168385 | + | 0.533439i | 0.00583069 | + | 0.0184715i | ||||
\(835\) | −27.3912 | − | 6.77118i | −0.947911 | − | 0.234326i | ||||
\(836\) | 10.1351i | 0.350531i | ||||||||
\(837\) | −17.5479 | + | 2.32775i | −0.606543 | + | 0.0804589i | ||||
\(838\) | 1.16034 | + | 1.16034i | 0.0400831 | + | 0.0400831i | ||||
\(839\) | 18.9721 | 0.654989 | 0.327495 | − | 0.944853i | \(-0.393796\pi\) | ||||
0.327495 | + | 0.944853i | \(0.393796\pi\) | |||||||
\(840\) | −3.86520 | + | 0.245443i | −0.133362 | + | 0.00846860i | ||||
\(841\) | −1.99040 | −0.0686344 | ||||||||
\(842\) | 2.77219 | + | 2.77219i | 0.0955359 | + | 0.0955359i | ||||
\(843\) | −29.8818 | − | 15.5431i | −1.02919 | − | 0.535332i | ||||
\(844\) | 26.0519i | 0.896743i | ||||||||
\(845\) | 13.0583 | + | 21.6345i | 0.449220 | + | 0.744249i | ||||
\(846\) | 1.51686 | − | 1.06360i | 0.0521507 | − | 0.0365673i | ||||
\(847\) | −5.72286 | + | 5.72286i | −0.196640 | + | 0.196640i | ||||
\(848\) | −6.87196 | + | 6.87196i | −0.235984 | + | 0.235984i | ||||
\(849\) | 40.4071 | − | 12.7548i | 1.38677 | − | 0.437745i | ||||
\(850\) | 29.8094 | + | 15.6972i | 1.02245 | + | 0.538409i | ||||
\(851\) | − | 5.13771i | − | 0.176119i | ||||||
\(852\) | −9.79994 | + | 18.8406i | −0.335741 | + | 0.645467i | ||||
\(853\) | −25.7974 | − | 25.7974i | −0.883284 | − | 0.883284i | 0.110582 | − | 0.993867i | \(-0.464728\pi\) |
−0.993867 | + | 0.110582i | \(0.964728\pi\) | |||||||
\(854\) | 1.74994 | 0.0598815 | ||||||||
\(855\) | −16.1232 | + | 36.4737i | −0.551401 | + | 1.24738i | ||||
\(856\) | −5.61377 | −0.191875 | ||||||||
\(857\) | 13.3333 | + | 13.3333i | 0.455458 | + | 0.455458i | 0.897161 | − | 0.441703i | \(-0.145626\pi\) |
−0.441703 | + | 0.897161i | \(0.645626\pi\) | |||||||
\(858\) | −1.77614 | + | 3.41467i | −0.0606366 | + | 0.116575i | ||||
\(859\) | − | 7.46319i | − | 0.254641i | −0.991862 | − | 0.127320i | \(-0.959362\pi\) | ||
0.991862 | − | 0.127320i | \(-0.0406377\pi\) | |||||||
\(860\) | 6.20021 | − | 25.0815i | 0.211425 | − | 0.855271i | ||||
\(861\) | −18.1274 | + | 5.72206i | −0.617779 | + | 0.195007i | ||||
\(862\) | 19.8342 | − | 19.8342i | 0.675557 | − | 0.675557i | ||||
\(863\) | 14.6455 | − | 14.6455i | 0.498539 | − | 0.498539i | −0.412444 | − | 0.910983i | \(-0.635325\pi\) |
0.910983 | + | 0.412444i | \(0.135325\pi\) | |||||||
\(864\) | −4.12549 | − | 3.15917i | −0.140352 | − | 0.107477i | ||||
\(865\) | −3.37773 | + | 13.6638i | −0.114846 | + | 0.464583i | ||||
\(866\) | − | 10.5000i | − | 0.356804i | ||||||
\(867\) | −43.6398 | − | 22.6993i | −1.48208 | − | 0.770908i | ||||
\(868\) | 2.40888 | + | 2.40888i | 0.0817627 | + | 0.0817627i | ||||
\(869\) | 12.2670 | 0.416128 | ||||||||
\(870\) | 13.3022 | − | 15.1061i | 0.450987 | − | 0.512146i | ||||
\(871\) | 1.91341 | 0.0648336 | ||||||||
\(872\) | 4.71291 | + | 4.71291i | 0.159599 | + | 0.159599i | ||||
\(873\) | −55.2343 | − | 9.70201i | −1.86940 | − | 0.328363i | ||||
\(874\) | − | 20.9860i | − | 0.709862i | ||||||
\(875\) | −8.35339 | − | 7.43108i | −0.282396 | − | 0.251216i | ||||
\(876\) | 3.38950 | + | 10.7379i | 0.114521 | + | 0.362799i | ||||
\(877\) | 3.06648 | − | 3.06648i | 0.103548 | − | 0.103548i | −0.653435 | − | 0.756983i | \(-0.726673\pi\) |
0.756983 | + | 0.653435i | \(0.226673\pi\) | |||||||
\(878\) | 16.5753 | − | 16.5753i | 0.559389 | − | 0.559389i | ||||
\(879\) | −13.1978 | − | 41.8104i | −0.445151 | − | 1.41023i | ||||
\(880\) | −1.96999 | − | 3.26380i | −0.0664085 | − | 0.110023i | ||||
\(881\) | 4.11283i | 0.138565i | 0.997597 | + | 0.0692824i | \(0.0220710\pi\) | ||||
−0.997597 | + | 0.0692824i | \(0.977929\pi\) | |||||||
\(882\) | −2.95476 | − | 0.519010i | −0.0994921 | − | 0.0174760i | ||||
\(883\) | −8.74068 | − | 8.74068i | −0.294147 | − | 0.294147i | 0.544569 | − | 0.838716i | \(-0.316693\pi\) |
−0.838716 | + | 0.544569i | \(0.816693\pi\) | |||||||
\(884\) | −8.78246 | −0.295386 | ||||||||
\(885\) | 0.168457 | + | 2.65283i | 0.00566261 | + | 0.0891739i | ||||
\(886\) | 14.2193 | 0.477706 | ||||||||
\(887\) | −2.49148 | − | 2.49148i | −0.0836558 | − | 0.0836558i | 0.664041 | − | 0.747696i | \(-0.268840\pi\) |
−0.747696 | + | 0.664041i | \(0.768840\pi\) | |||||||
\(888\) | 2.23633 | + | 1.16323i | 0.0750462 | + | 0.0390354i | ||||
\(889\) | − | 15.8661i | − | 0.532133i | ||||||
\(890\) | −4.89536 | − | 1.21015i | −0.164093 | − | 0.0405642i | ||||
\(891\) | 14.4255 | + | 5.22909i | 0.483274 | + | 0.175181i | ||||
\(892\) | 1.49400 | − | 1.49400i | 0.0500227 | − | 0.0500227i | ||||
\(893\) | −2.59583 | + | 2.59583i | −0.0868661 | + | 0.0868661i | ||||
\(894\) | 6.31833 | − | 1.99444i | 0.211317 | − | 0.0667040i | ||||
\(895\) | −20.4451 | + | 12.3404i | −0.683403 | + | 0.412494i | ||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 3.67772 | − | 7.07049i | 0.122796 | − | 0.236077i | ||||
\(898\) | −20.7135 | − | 20.7135i | −0.691218 | − | 0.691218i | ||||
\(899\) | −17.7047 | −0.590485 | ||||||||
\(900\) | −1.89737 | − | 14.8795i | −0.0632458 | − | 0.495984i | ||||
\(901\) | 65.4823 | 2.18153 | ||||||||
\(902\) | −13.2307 | − | 13.2307i | −0.440533 | − | 0.440533i | ||||
\(903\) | 9.23508 | − | 17.7546i | 0.307324 | − | 0.590837i | ||||
\(904\) | − | 6.13421i | − | 0.204021i | ||||||
\(905\) | −24.5451 | + | 14.8151i | −0.815906 | + | 0.492472i | ||||
\(906\) | −7.84659 | + | 2.47685i | −0.260686 | + | 0.0822877i | ||||
\(907\) | −28.0384 | + | 28.0384i | −0.931001 | + | 0.931001i | −0.997769 | − | 0.0667678i | \(-0.978731\pi\) |
0.0667678 | + | 0.997769i | \(0.478731\pi\) | |||||||
\(908\) | 7.38425 | − | 7.38425i | 0.245055 | − | 0.245055i | ||||
\(909\) | 43.8281 | − | 30.7316i | 1.45369 | − | 1.01930i | ||||
\(910\) | 2.82939 | + | 0.699434i | 0.0937934 | + | 0.0231860i | ||||
\(911\) | − | 35.7595i | − | 1.18476i | −0.805657 | − | 0.592382i | \(-0.798188\pi\) | ||
0.805657 | − | 0.592382i | \(-0.201812\pi\) | |||||||
\(912\) | 9.13472 | + | 4.75144i | 0.302481 | + | 0.157336i | ||||
\(913\) | 11.3322 | + | 11.3322i | 0.375041 | + | 0.375041i | ||||
\(914\) | 30.1416 | 0.996997 | ||||||||
\(915\) | 0.429510 | + | 6.76385i | 0.0141992 | + | 0.223606i | ||||
\(916\) | 13.4219 | 0.443472 | ||||||||
\(917\) | 3.25792 | + | 3.25792i | 0.107586 | + | 0.107586i | ||||
\(918\) | 4.60400 | + | 34.7074i | 0.151955 | + | 1.14552i | ||||
\(919\) | − | 55.1175i | − | 1.81816i | −0.416623 | − | 0.909079i | \(-0.636786\pi\) | ||
0.416623 | − | 0.909079i | \(-0.363214\pi\) | |||||||
\(920\) | 4.07912 | + | 6.75811i | 0.134484 | + | 0.222808i | ||||
\(921\) | 5.56391 | + | 17.6263i | 0.183337 | + | 0.580808i | ||||
\(922\) | 6.73949 | − | 6.73949i | 0.221953 | − | 0.221953i | ||||
\(923\) | 11.3007 | − | 11.3007i | 0.371966 | − | 0.371966i | ||||
\(924\) | −0.888895 | − | 2.81600i | −0.0292425 | − | 0.0926396i | ||||
\(925\) | 2.15538 | + | 6.95029i | 0.0708685 | + | 0.228524i | ||||
\(926\) | 28.0710i | 0.922471i | ||||||||
\(927\) | −8.73493 | + | 49.7286i | −0.286893 | + | 1.63330i | ||||
\(928\) | −3.67489 | − | 3.67489i | −0.120634 | − | 0.120634i | ||||
\(929\) | 6.70076 | 0.219845 | 0.109922 | − | 0.993940i | \(-0.464940\pi\) | ||||
0.109922 | + | 0.993940i | \(0.464940\pi\) | |||||||
\(930\) | −8.71955 | + | 9.90204i | −0.285925 | + | 0.324701i | ||||
\(931\) | 5.94473 | 0.194831 | ||||||||
\(932\) | 8.32952 | + | 8.32952i | 0.272842 | + | 0.272842i | ||||
\(933\) | 10.9005 | + | 5.66992i | 0.356867 | + | 0.185625i | ||||
\(934\) | 23.9280i | 0.782949i | ||||||||
\(935\) | −6.16430 | + | 24.9362i | −0.201594 | + | 0.815501i | ||||
\(936\) | 2.24495 | + | 3.20166i | 0.0733785 | + | 0.104649i | ||||
\(937\) | 9.53939 | − | 9.53939i | 0.311638 | − | 0.311638i | −0.533906 | − | 0.845544i | \(-0.679276\pi\) |
0.845544 | + | 0.533906i | \(0.179276\pi\) | |||||||
\(938\) | −1.03802 | + | 1.03802i | −0.0338926 | + | 0.0338926i | ||||
\(939\) | −32.0117 | + | 10.1048i | −1.04466 | + | 0.329757i | ||||
\(940\) | 0.331373 | − | 1.34049i | 0.0108082 | − | 0.0437220i | ||||
\(941\) | 44.9315i | 1.46472i | 0.680915 | + | 0.732362i | \(0.261582\pi\) | ||||
−0.680915 | + | 0.732362i | \(0.738418\pi\) | |||||||
\(942\) | 11.6500 | − | 22.3973i | 0.379577 | − | 0.729743i | ||||
\(943\) | 27.3957 | + | 27.3957i | 0.892126 | + | 0.892126i | ||||
\(944\) | 0.686337 | 0.0223384 | ||||||||
\(945\) | 1.28085 | − | 11.5481i | 0.0416661 | − | 0.375661i | ||||
\(946\) | 19.6990 | 0.640471 | ||||||||
\(947\) | 1.70096 | + | 1.70096i | 0.0552738 | + | 0.0552738i | 0.734203 | − | 0.678930i | \(-0.237556\pi\) |
−0.678930 | + | 0.734203i | \(0.737556\pi\) | |||||||
\(948\) | 5.75086 | − | 11.0561i | 0.186779 | − | 0.359086i | ||||
\(949\) | − | 8.47366i | − | 0.275067i | ||||||
\(950\) | 8.80408 | + | 28.3898i | 0.285642 | + | 0.921088i | ||||
\(951\) | 46.9941 | − | 14.8341i | 1.52389 | − | 0.481029i | ||||
\(952\) | 4.76445 | − | 4.76445i | 0.154417 | − | 0.154417i | ||||
\(953\) | 31.9131 | − | 31.9131i | 1.03377 | − | 1.03377i | 0.0343567 | − | 0.999410i | \(-0.489062\pi\) |
0.999410 | − | 0.0343567i | \(-0.0109382\pi\) | |||||||
\(954\) | −16.7384 | − | 23.8716i | −0.541926 | − | 0.772873i | ||||
\(955\) | 9.57485 | + | 15.8632i | 0.309835 | + | 0.513322i | ||||
\(956\) | 0.372694i | 0.0120538i | ||||||||
\(957\) | 13.6151 | + | 7.08189i | 0.440113 | + | 0.228925i | ||||
\(958\) | 3.65381 | + | 3.65381i | 0.118049 | + | 0.118049i | ||||
\(959\) | −3.13487 | −0.101230 | ||||||||
\(960\) | −3.86520 | + | 0.245443i | −0.124749 | + | 0.00792165i | ||||
\(961\) | −19.3946 | −0.625632 | ||||||||
\(962\) | −1.34136 | − | 1.34136i | −0.0432471 | − | 0.0432471i | ||||
\(963\) | 2.91361 | − | 16.5874i | 0.0938896 | − | 0.534521i | ||||
\(964\) | 29.4165i | 0.947443i | ||||||||
\(965\) | 11.0433 | + | 2.72993i | 0.355495 | + | 0.0878795i | ||||
\(966\) | 1.84056 | + | 5.83087i | 0.0592192 | + | 0.187605i | ||||
\(967\) | −24.6132 | + | 24.6132i | −0.791508 | + | 0.791508i | −0.981739 | − | 0.190232i | \(-0.939076\pi\) |
0.190232 | + | 0.981739i | \(0.439076\pi\) | |||||||
\(968\) | −5.72286 | + | 5.72286i | −0.183940 | + | 0.183940i | ||||
\(969\) | −20.8840 | − | 66.1600i | −0.670890 | − | 2.12536i | ||||
\(970\) | −35.7860 | + | 21.6000i | −1.14902 | + | 0.693534i | ||||
\(971\) | − | 17.9560i | − | 0.576235i | −0.957595 | − | 0.288117i | \(-0.906971\pi\) | ||
0.957595 | − | 0.288117i | \(-0.0930293\pi\) | |||||||
\(972\) | 11.4758 | − | 10.5502i | 0.368085 | − | 0.338398i | ||||
\(973\) | 0.228368 | + | 0.228368i | 0.00732113 | + | 0.00732113i | ||||
\(974\) | −22.9731 | −0.736107 | ||||||||
\(975\) | −2.00899 | + | 11.1078i | −0.0643393 | + | 0.355735i | ||||
\(976\) | 1.74994 | 0.0560141 | ||||||||
\(977\) | 14.6134 | + | 14.6134i | 0.467526 | + | 0.467526i | 0.901112 | − | 0.433586i | \(-0.142752\pi\) |
−0.433586 | + | 0.901112i | \(0.642752\pi\) | |||||||
\(978\) | −9.67612 | − | 5.03304i | −0.309408 | − | 0.160939i | ||||
\(979\) | − | 3.84483i | − | 0.122881i | ||||||
\(980\) | −1.91438 | + | 1.15549i | −0.0611525 | + | 0.0369109i | ||||
\(981\) | −16.3716 | + | 11.4795i | −0.522704 | + | 0.366512i | ||||
\(982\) | 6.79723 | − | 6.79723i | 0.216908 | − | 0.216908i | ||||
\(983\) | 1.53415 | − | 1.53415i | 0.0489318 | − | 0.0489318i | −0.682217 | − | 0.731149i | \(-0.738984\pi\) |
0.731149 | + | 0.682217i | \(0.238984\pi\) | |||||||
\(984\) | −18.1274 | + | 5.72206i | −0.577879 | + | 0.182413i | ||||
\(985\) | −16.8961 | − | 4.17677i | −0.538356 | − | 0.133083i | ||||
\(986\) | 35.0177i | 1.11519i | ||||||||
\(987\) | 0.493574 | − | 0.948905i | 0.0157106 | − | 0.0302040i | ||||
\(988\) | −5.47905 | − | 5.47905i | −0.174312 | − | 0.174312i | ||||
\(989\) | −40.7893 | −1.29702 | ||||||||
\(990\) | 10.6662 | − | 4.12692i | 0.338995 | − | 0.131162i | ||||
\(991\) | −6.06527 | −0.192670 | −0.0963348 | − | 0.995349i | \(-0.530712\pi\) | ||||
−0.0963348 | + | 0.995349i | \(0.530712\pi\) | |||||||
\(992\) | 2.40888 | + | 2.40888i | 0.0764820 | + | 0.0764820i | ||||
\(993\) | −5.87789 | + | 11.3003i | −0.186529 | + | 0.358606i | ||||
\(994\) | 12.2611i | 0.388899i | ||||||||
\(995\) | 23.9952 | + | 39.7543i | 0.760700 | + | 1.26030i | ||||
\(996\) | 15.5263 | − | 4.90100i | 0.491969 | − | 0.155294i | ||||
\(997\) | 12.6897 | − | 12.6897i | 0.401887 | − | 0.401887i | −0.477011 | − | 0.878897i | \(-0.658280\pi\) |
0.878897 | + | 0.477011i | \(0.158280\pi\) | |||||||
\(998\) | 4.67316 | − | 4.67316i | 0.147926 | − | 0.147926i | ||||
\(999\) | −4.59774 | + | 6.00409i | −0.145466 | + | 0.189961i |
(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 | 210.2.j.a.113.4 | ✓ | 12 | |
3.2 | odd | 2 | 210.2.j.b.113.3 | yes | 12 | ||
5.2 | odd | 4 | 210.2.j.b.197.3 | yes | 12 | ||
5.3 | odd | 4 | 1050.2.j.d.407.4 | 12 | |||
5.4 | even | 2 | 1050.2.j.c.743.3 | 12 | |||
15.2 | even | 4 | inner | 210.2.j.a.197.4 | yes | 12 | |
15.8 | even | 4 | 1050.2.j.c.407.3 | 12 | |||
15.14 | odd | 2 | 1050.2.j.d.743.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.j.a.113.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
210.2.j.a.197.4 | yes | 12 | 15.2 | even | 4 | inner | |
210.2.j.b.113.3 | yes | 12 | 3.2 | odd | 2 | ||
210.2.j.b.197.3 | yes | 12 | 5.2 | odd | 4 | ||
1050.2.j.c.407.3 | 12 | 15.8 | even | 4 | |||
1050.2.j.c.743.3 | 12 | 5.4 | even | 2 | |||
1050.2.j.d.407.4 | 12 | 5.3 | odd | 4 | |||
1050.2.j.d.743.4 | 12 | 15.14 | odd | 2 |