Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [62,2,Mod(33,62)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(62, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("62.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 62 = 2 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 62.d (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: | \(0.495072492532\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.511890625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 7x^{6} - 5x^{5} + 16x^{4} + 15x^{3} + 63x^{2} + 81x + 81 \) |
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 | 33.1 | ||
Root | \(-0.448193 + 1.37940i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 62.33 |
Dual form | 62.2.d.a.47.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/62\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 0.587785i | −0.572061 | − | 0.415627i | ||||
\(3\) | −2.48240 | + | 1.80357i | −1.43322 | + | 1.04129i | −0.443809 | + | 0.896121i | \(0.646373\pi\) |
−0.989407 | + | 0.145171i | \(0.953627\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | −3.34677 | −1.49672 | −0.748361 | − | 0.663292i | \(-0.769159\pi\) | ||||
−0.748361 | + | 0.663292i | \(0.769159\pi\) | |||||||
\(6\) | 3.06842 | 1.25268 | ||||||||
\(7\) | 0.778353 | + | 2.39552i | 0.294190 | + | 0.905423i | 0.983492 | + | 0.180949i | \(0.0579170\pi\) |
−0.689303 | + | 0.724473i | \(0.742083\pi\) | |||||||
\(8\) | 0.309017 | − | 0.951057i | 0.109254 | − | 0.336249i | ||||
\(9\) | 1.98240 | − | 6.10121i | 0.660801 | − | 2.03374i | ||||
\(10\) | 2.70759 | + | 1.96718i | 0.856216 | + | 0.622078i | ||||
\(11\) | 0.532018 | + | 1.63738i | 0.160410 | + | 0.493690i | 0.998669 | − | 0.0515821i | \(-0.0164264\pi\) |
−0.838259 | + | 0.545272i | \(0.816426\pi\) | |||||||
\(12\) | −2.48240 | − | 1.80357i | −0.716608 | − | 0.520646i | ||||
\(13\) | −1.89284 | + | 1.37523i | −0.524980 | + | 0.381420i | −0.818477 | − | 0.574540i | \(-0.805181\pi\) |
0.293497 | + | 0.955960i | \(0.405181\pi\) | |||||||
\(14\) | 0.778353 | − | 2.39552i | 0.208023 | − | 0.640230i | ||||
\(15\) | 8.30803 | − | 6.03614i | 2.14512 | − | 1.55852i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −0.244144 | + | 0.751397i | −0.0592135 | + | 0.182240i | −0.976288 | − | 0.216475i | \(-0.930544\pi\) |
0.917075 | + | 0.398716i | \(0.130544\pi\) | |||||||
\(18\) | −5.19000 | + | 3.77075i | −1.22329 | + | 0.888775i | ||||
\(19\) | −0.326615 | − | 0.237300i | −0.0749306 | − | 0.0544402i | 0.549689 | − | 0.835369i | \(-0.314746\pi\) |
−0.624620 | + | 0.780929i | \(0.714746\pi\) | |||||||
\(20\) | −1.03421 | − | 3.18297i | −0.231256 | − | 0.711733i | ||||
\(21\) | −6.25268 | − | 4.54284i | −1.36445 | − | 0.991328i | ||||
\(22\) | 0.532018 | − | 1.63738i | 0.113427 | − | 0.349091i | ||||
\(23\) | −1.56623 | + | 4.82035i | −0.326581 | + | 1.00511i | 0.644141 | + | 0.764907i | \(0.277215\pi\) |
−0.970722 | + | 0.240206i | \(0.922785\pi\) | |||||||
\(24\) | 0.948193 | + | 2.91824i | 0.193549 | + | 0.595683i | ||||
\(25\) | 6.20087 | 1.24017 | ||||||||
\(26\) | 2.33968 | 0.458849 | ||||||||
\(27\) | 3.23826 | + | 9.96634i | 0.623203 | + | 1.91802i | ||||
\(28\) | −2.03775 | + | 1.48051i | −0.385099 | + | 0.279791i | ||||
\(29\) | 4.20759 | + | 3.05700i | 0.781331 | + | 0.567670i | 0.905378 | − | 0.424606i | \(-0.139588\pi\) |
−0.124047 | + | 0.992276i | \(0.539588\pi\) | |||||||
\(30\) | −10.2693 | −1.87491 | ||||||||
\(31\) | −2.94366 | + | 4.72598i | −0.528697 | + | 0.848810i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.27382 | − | 3.10511i | −0.743977 | − | 0.540531i | ||||
\(34\) | 0.639176 | − | 0.464389i | 0.109618 | − | 0.0796420i | ||||
\(35\) | −2.60497 | − | 8.01727i | −0.440320 | − | 1.35517i | ||||
\(36\) | 6.41519 | 1.06920 | ||||||||
\(37\) | 5.88930 | 0.968195 | 0.484097 | − | 0.875014i | \(-0.339148\pi\) | ||||
0.484097 | + | 0.875014i | \(0.339148\pi\) | |||||||
\(38\) | 0.124756 | + | 0.383959i | 0.0202381 | + | 0.0622863i | ||||
\(39\) | 2.21847 | − | 6.82775i | 0.355240 | − | 1.09331i | ||||
\(40\) | −1.03421 | + | 3.18297i | −0.163523 | + | 0.503271i | ||||
\(41\) | −6.27601 | − | 4.55979i | −0.980148 | − | 0.712120i | −0.0224066 | − | 0.999749i | \(-0.507133\pi\) |
−0.957742 | + | 0.287629i | \(0.907133\pi\) | |||||||
\(42\) | 2.38831 | + | 7.35047i | 0.368524 | + | 1.13420i | ||||
\(43\) | −6.18645 | − | 4.49472i | −0.943425 | − | 0.685438i | 0.00581761 | − | 0.999983i | \(-0.498148\pi\) |
−0.949243 | + | 0.314545i | \(0.898148\pi\) | |||||||
\(44\) | −1.39284 | + | 1.01196i | −0.209979 | + | 0.152559i | ||||
\(45\) | −6.63465 | + | 20.4193i | −0.989035 | + | 3.04394i | ||||
\(46\) | 4.10044 | − | 2.97914i | 0.604576 | − | 0.439250i | ||||
\(47\) | 3.91519 | − | 2.84455i | 0.571089 | − | 0.414920i | −0.264412 | − | 0.964410i | \(-0.585178\pi\) |
0.835501 | + | 0.549490i | \(0.185178\pi\) | |||||||
\(48\) | 0.948193 | − | 2.91824i | 0.136860 | − | 0.421211i | ||||
\(49\) | 0.530422 | − | 0.385374i | 0.0757746 | − | 0.0550534i | ||||
\(50\) | −5.01661 | − | 3.64478i | −0.709456 | − | 0.515450i | ||||
\(51\) | −0.749135 | − | 2.30560i | −0.104900 | − | 0.322848i | ||||
\(52\) | −1.89284 | − | 1.37523i | −0.262490 | − | 0.190710i | ||||
\(53\) | −0.812562 | + | 2.50081i | −0.111614 | + | 0.343512i | −0.991226 | − | 0.132180i | \(-0.957802\pi\) |
0.879612 | + | 0.475692i | \(0.157802\pi\) | |||||||
\(54\) | 3.23826 | − | 9.96634i | 0.440671 | − | 1.35625i | ||||
\(55\) | −1.78054 | − | 5.47995i | −0.240088 | − | 0.738916i | ||||
\(56\) | 2.51880 | 0.336589 | ||||||||
\(57\) | 1.23878 | 0.164080 | ||||||||
\(58\) | −1.60716 | − | 4.94632i | −0.211030 | − | 0.649484i | ||||
\(59\) | 3.53202 | − | 2.56616i | 0.459830 | − | 0.334086i | −0.333635 | − | 0.942702i | \(-0.608275\pi\) |
0.793464 | + | 0.608617i | \(0.208275\pi\) | |||||||
\(60\) | 8.30803 | + | 6.03614i | 1.07256 | + | 0.779262i | ||||
\(61\) | 9.60897 | 1.23030 | 0.615151 | − | 0.788409i | \(-0.289095\pi\) | ||||
0.615151 | + | 0.788409i | \(0.289095\pi\) | |||||||
\(62\) | 5.15933 | − | 2.09315i | 0.655236 | − | 0.265831i | ||||
\(63\) | 16.1586 | 2.03579 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 6.33491 | − | 4.60258i | 0.785749 | − | 0.570880i | ||||
\(66\) | 1.63245 | + | 5.02418i | 0.200941 | + | 0.618434i | ||||
\(67\) | −8.86119 | −1.08257 | −0.541283 | − | 0.840840i | \(-0.682061\pi\) | ||||
−0.541283 | + | 0.840840i | \(0.682061\pi\) | |||||||
\(68\) | −0.790065 | −0.0958095 | ||||||||
\(69\) | −4.80584 | − | 14.7909i | −0.578555 | − | 1.78061i | ||||
\(70\) | −2.60497 | + | 8.01727i | −0.311353 | + | 0.958246i | ||||
\(71\) | −3.67558 | + | 11.3123i | −0.436211 | + | 1.34252i | 0.455630 | + | 0.890169i | \(0.349414\pi\) |
−0.891841 | + | 0.452349i | \(0.850586\pi\) | |||||||
\(72\) | −5.19000 | − | 3.77075i | −0.611647 | − | 0.444388i | ||||
\(73\) | 2.42471 | + | 7.46249i | 0.283791 | + | 0.873419i | 0.986758 | + | 0.162197i | \(0.0518579\pi\) |
−0.702968 | + | 0.711222i | \(0.748142\pi\) | |||||||
\(74\) | −4.76454 | − | 3.46164i | −0.553867 | − | 0.402408i | ||||
\(75\) | −15.3931 | + | 11.1837i | −1.77744 | + | 1.29138i | ||||
\(76\) | 0.124756 | − | 0.383959i | 0.0143105 | − | 0.0440431i | ||||
\(77\) | −3.50829 | + | 2.54892i | −0.399807 | + | 0.290477i | ||||
\(78\) | −5.80803 | + | 4.21978i | −0.657630 | + | 0.477796i | ||||
\(79\) | −0.647345 | + | 1.99232i | −0.0728320 | + | 0.224154i | −0.980846 | − | 0.194787i | \(-0.937598\pi\) |
0.908014 | + | 0.418941i | \(0.137598\pi\) | |||||||
\(80\) | 2.70759 | − | 1.96718i | 0.302718 | − | 0.219938i | ||||
\(81\) | −10.4437 | − | 7.58776i | −1.16041 | − | 0.843085i | ||||
\(82\) | 2.39722 | + | 7.37789i | 0.264729 | + | 0.814752i | ||||
\(83\) | 9.91519 | + | 7.20381i | 1.08833 | + | 0.790720i | 0.979117 | − | 0.203298i | \(-0.0651659\pi\) |
0.109216 | + | 0.994018i | \(0.465166\pi\) | |||||||
\(84\) | 2.38831 | − | 7.35047i | 0.260586 | − | 0.802002i | ||||
\(85\) | 0.817093 | − | 2.51475i | 0.0886261 | − | 0.272763i | ||||
\(86\) | 2.36301 | + | 7.27261i | 0.254810 | + | 0.784226i | ||||
\(87\) | −15.9584 | −1.71093 | ||||||||
\(88\) | 1.72165 | 0.183528 | ||||||||
\(89\) | 4.52530 | + | 13.9274i | 0.479680 | + | 1.47630i | 0.839540 | + | 0.543298i | \(0.182825\pi\) |
−0.359859 | + | 0.933007i | \(0.617175\pi\) | |||||||
\(90\) | 17.3697 | − | 12.6198i | 1.83093 | − | 1.33025i | ||||
\(91\) | −4.76769 | − | 3.46393i | −0.499790 | − | 0.363119i | ||||
\(92\) | −5.06842 | −0.528419 | ||||||||
\(93\) | −1.21628 | − | 17.0409i | −0.126122 | − | 1.76706i | ||||
\(94\) | −4.83944 | −0.499150 | ||||||||
\(95\) | 1.09310 | + | 0.794187i | 0.112150 | + | 0.0814819i | ||||
\(96\) | −2.48240 | + | 1.80357i | −0.253359 | + | 0.184076i | ||||
\(97\) | −5.80449 | − | 17.8644i | −0.589356 | − | 1.81385i | −0.581024 | − | 0.813887i | \(-0.697348\pi\) |
−0.00833268 | − | 0.999965i | \(-0.502652\pi\) | |||||||
\(98\) | −0.655638 | −0.0662294 | ||||||||
\(99\) | 11.0447 | 1.11003 | ||||||||
\(100\) | 1.91617 | + | 5.89738i | 0.191617 | + | 0.589738i | ||||
\(101\) | −2.92191 | + | 8.99271i | −0.290741 | + | 0.894809i | 0.693878 | + | 0.720093i | \(0.255901\pi\) |
−0.984619 | + | 0.174716i | \(0.944099\pi\) | |||||||
\(102\) | −0.749135 | + | 2.30560i | −0.0741754 | + | 0.228288i | ||||
\(103\) | 1.05754 | + | 0.768349i | 0.104203 | + | 0.0757077i | 0.638666 | − | 0.769484i | \(-0.279486\pi\) |
−0.534464 | + | 0.845191i | \(0.679486\pi\) | |||||||
\(104\) | 0.723001 | + | 2.22517i | 0.0708961 | + | 0.218196i | ||||
\(105\) | 20.9263 | + | 15.2038i | 2.04220 | + | 1.48374i | ||||
\(106\) | 2.12731 | − | 1.54558i | 0.206623 | − | 0.150120i | ||||
\(107\) | 4.63903 | − | 14.2775i | 0.448472 | − | 1.38025i | −0.430160 | − | 0.902753i | \(-0.641543\pi\) |
0.878631 | − | 0.477501i | \(-0.158457\pi\) | |||||||
\(108\) | −8.47787 | + | 6.15953i | −0.815784 | + | 0.592701i | ||||
\(109\) | −5.71333 | + | 4.15098i | −0.547238 | + | 0.397591i | −0.826766 | − | 0.562546i | \(-0.809822\pi\) |
0.279528 | + | 0.960137i | \(0.409822\pi\) | |||||||
\(110\) | −1.78054 | + | 5.47995i | −0.169768 | + | 0.522493i | ||||
\(111\) | −14.6196 | + | 10.6218i | −1.38763 | + | 1.00817i | ||||
\(112\) | −2.03775 | − | 1.48051i | −0.192550 | − | 0.139895i | ||||
\(113\) | 1.67792 | + | 5.16410i | 0.157845 | + | 0.485797i | 0.998438 | − | 0.0558701i | \(-0.0177933\pi\) |
−0.840593 | + | 0.541667i | \(0.817793\pi\) | |||||||
\(114\) | −1.00219 | − | 0.728134i | −0.0938638 | − | 0.0681960i | ||||
\(115\) | 5.24180 | − | 16.1326i | 0.488801 | − | 1.50437i | ||||
\(116\) | −1.60716 | + | 4.94632i | −0.149221 | + | 0.459255i | ||||
\(117\) | 4.63819 | + | 14.2749i | 0.428801 | + | 1.31971i | ||||
\(118\) | −4.36581 | −0.401906 | ||||||||
\(119\) | −1.99002 | −0.182425 | ||||||||
\(120\) | −3.17339 | − | 9.76668i | −0.289689 | − | 0.891571i | ||||
\(121\) | 6.50120 | − | 4.72340i | 0.591019 | − | 0.429400i | ||||
\(122\) | −7.77382 | − | 5.64801i | −0.703809 | − | 0.511347i | ||||
\(123\) | 23.8035 | 2.14629 | ||||||||
\(124\) | −5.40431 | − | 1.33918i | −0.485322 | − | 0.120262i | ||||
\(125\) | −4.01904 | −0.359474 | ||||||||
\(126\) | −13.0726 | − | 9.49778i | −1.16460 | − | 0.846129i | ||||
\(127\) | −3.38098 | + | 2.45643i | −0.300013 | + | 0.217972i | −0.727600 | − | 0.686002i | \(-0.759364\pi\) |
0.427586 | + | 0.903975i | \(0.359364\pi\) | |||||||
\(128\) | 0.309017 | + | 0.951057i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | 23.4638 | 2.06587 | ||||||||
\(130\) | −7.83038 | −0.686769 | ||||||||
\(131\) | 2.13918 | + | 6.58371i | 0.186901 | + | 0.575221i | 0.999976 | − | 0.00693742i | \(-0.00220827\pi\) |
−0.813075 | + | 0.582159i | \(0.802208\pi\) | |||||||
\(132\) | 1.63245 | − | 5.02418i | 0.142087 | − | 0.437299i | ||||
\(133\) | 0.314235 | − | 0.967116i | 0.0272476 | − | 0.0838596i | ||||
\(134\) | 7.16885 | + | 5.20848i | 0.619295 | + | 0.449944i | ||||
\(135\) | −10.8377 | − | 33.3550i | −0.932761 | − | 2.87074i | ||||
\(136\) | 0.639176 | + | 0.464389i | 0.0548089 | + | 0.0398210i | ||||
\(137\) | 2.87365 | − | 2.08783i | 0.245512 | − | 0.178375i | −0.458223 | − | 0.888837i | \(-0.651514\pi\) |
0.703736 | + | 0.710462i | \(0.251514\pi\) | |||||||
\(138\) | −4.80584 | + | 14.7909i | −0.409100 | + | 1.25908i | ||||
\(139\) | 1.99646 | − | 1.45051i | 0.169337 | − | 0.123031i | −0.499889 | − | 0.866090i | \(-0.666626\pi\) |
0.669226 | + | 0.743059i | \(0.266626\pi\) | |||||||
\(140\) | 6.81989 | − | 4.95494i | 0.576386 | − | 0.418769i | ||||
\(141\) | −4.58872 | + | 14.1226i | −0.386440 | + | 1.18934i | ||||
\(142\) | 9.62278 | − | 6.99136i | 0.807526 | − | 0.586702i | ||||
\(143\) | −3.25881 | − | 2.36766i | −0.272515 | − | 0.197994i | ||||
\(144\) | 1.98240 | + | 6.10121i | 0.165200 | + | 0.508434i | ||||
\(145\) | −14.0819 | − | 10.2311i | −1.16943 | − | 0.849644i | ||||
\(146\) | 2.42471 | − | 7.46249i | 0.200670 | − | 0.617600i | ||||
\(147\) | −0.621671 | + | 1.91331i | −0.0512746 | + | 0.157807i | ||||
\(148\) | 1.81989 | + | 5.60105i | 0.149594 | + | 0.460404i | ||||
\(149\) | −14.2287 | −1.16566 | −0.582829 | − | 0.812595i | \(-0.698054\pi\) | ||||
−0.582829 | + | 0.812595i | \(0.698054\pi\) | |||||||
\(150\) | 19.0269 | 1.55354 | ||||||||
\(151\) | −1.46345 | − | 4.50404i | −0.119094 | − | 0.366533i | 0.873685 | − | 0.486492i | \(-0.161724\pi\) |
−0.992779 | + | 0.119959i | \(0.961724\pi\) | |||||||
\(152\) | −0.326615 | + | 0.237300i | −0.0264920 | + | 0.0192475i | ||||
\(153\) | 4.10044 | + | 2.97914i | 0.331501 | + | 0.240849i | ||||
\(154\) | 4.33649 | 0.349444 | ||||||||
\(155\) | 9.85176 | − | 15.8168i | 0.791313 | − | 1.27043i | ||||
\(156\) | 7.17912 | 0.574790 | ||||||||
\(157\) | 14.8602 | + | 10.7966i | 1.18597 | + | 0.861660i | 0.992833 | − | 0.119511i | \(-0.0381327\pi\) |
0.193141 | + | 0.981171i | \(0.438133\pi\) | |||||||
\(158\) | 1.69477 | − | 1.23132i | 0.134829 | − | 0.0979588i | ||||
\(159\) | −2.49328 | − | 7.67352i | −0.197730 | − | 0.608550i | ||||
\(160\) | −3.34677 | −0.264585 | ||||||||
\(161\) | −12.7663 | −1.00613 | ||||||||
\(162\) | 3.98912 | + | 12.2773i | 0.313415 | + | 0.964593i | ||||
\(163\) | −3.91753 | + | 12.0569i | −0.306845 | + | 0.944370i | 0.672138 | + | 0.740426i | \(0.265376\pi\) |
−0.978982 | + | 0.203944i | \(0.934624\pi\) | |||||||
\(164\) | 2.39722 | − | 7.37789i | 0.187192 | − | 0.576117i | ||||
\(165\) | 14.3035 | + | 10.3921i | 1.11353 | + | 0.809024i | ||||
\(166\) | −3.78726 | − | 11.6560i | −0.293949 | − | 0.904681i | ||||
\(167\) | −18.6653 | − | 13.5611i | −1.44436 | − | 1.04939i | −0.987108 | − | 0.160056i | \(-0.948833\pi\) |
−0.457255 | − | 0.889336i | \(-0.651167\pi\) | |||||||
\(168\) | −6.25268 | + | 4.54284i | −0.482405 | + | 0.350488i | ||||
\(169\) | −2.32563 | + | 7.15755i | −0.178894 | + | 0.550581i | ||||
\(170\) | −2.13918 | + | 1.55420i | −0.164067 | + | 0.119202i | ||||
\(171\) | −2.09530 | + | 1.52232i | −0.160231 | + | 0.116415i | ||||
\(172\) | 2.36301 | − | 7.27261i | 0.180178 | − | 0.554531i | ||||
\(173\) | 16.3838 | − | 11.9035i | 1.24564 | − | 0.905007i | 0.247675 | − | 0.968843i | \(-0.420333\pi\) |
0.997960 | + | 0.0638358i | \(0.0203334\pi\) | |||||||
\(174\) | 12.9107 | + | 9.38014i | 0.978754 | + | 0.711107i | ||||
\(175\) | 4.82646 | + | 14.8543i | 0.364846 | + | 1.12288i | ||||
\(176\) | −1.39284 | − | 1.01196i | −0.104989 | − | 0.0762793i | ||||
\(177\) | −4.13964 | + | 12.7405i | −0.311154 | + | 0.957634i | ||||
\(178\) | 4.52530 | − | 13.9274i | 0.339185 | − | 1.04391i | ||||
\(179\) | −2.45235 | − | 7.54755i | −0.183297 | − | 0.564130i | 0.816618 | − | 0.577179i | \(-0.195846\pi\) |
−0.999915 | + | 0.0130484i | \(0.995846\pi\) | |||||||
\(180\) | −21.4702 | −1.60029 | ||||||||
\(181\) | −24.2847 | −1.80507 | −0.902533 | − | 0.430620i | \(-0.858295\pi\) | ||||
−0.902533 | + | 0.430620i | \(0.858295\pi\) | |||||||
\(182\) | 1.82110 | + | 5.60476i | 0.134989 | + | 0.415452i | ||||
\(183\) | −23.8533 | + | 17.3305i | −1.76329 | + | 1.28110i | ||||
\(184\) | 4.10044 | + | 2.97914i | 0.302288 | + | 0.219625i | ||||
\(185\) | −19.7101 | −1.44912 | ||||||||
\(186\) | −9.03239 | + | 14.5013i | −0.662287 | + | 1.06328i | ||||
\(187\) | −1.36021 | −0.0994687 | ||||||||
\(188\) | 3.91519 | + | 2.84455i | 0.285544 | + | 0.207460i | ||||
\(189\) | −21.3541 | + | 15.5146i | −1.55328 | + | 1.12852i | ||||
\(190\) | −0.417529 | − | 1.28502i | −0.0302907 | − | 0.0932253i | ||||
\(191\) | 11.3915 | 0.824257 | 0.412129 | − | 0.911126i | \(-0.364785\pi\) | ||||
0.412129 | + | 0.911126i | \(0.364785\pi\) | |||||||
\(192\) | 3.06842 | 0.221444 | ||||||||
\(193\) | −3.13502 | − | 9.64861i | −0.225664 | − | 0.694522i | −0.998224 | − | 0.0595797i | \(-0.981024\pi\) |
0.772560 | − | 0.634942i | \(-0.218976\pi\) | |||||||
\(194\) | −5.80449 | + | 17.8644i | −0.416738 | + | 1.28259i | ||||
\(195\) | −7.42471 | + | 22.8509i | −0.531695 | + | 1.63639i | ||||
\(196\) | 0.530422 | + | 0.385374i | 0.0378873 | + | 0.0275267i | ||||
\(197\) | −0.723369 | − | 2.22630i | −0.0515379 | − | 0.158617i | 0.921975 | − | 0.387249i | \(-0.126575\pi\) |
−0.973513 | + | 0.228632i | \(0.926575\pi\) | |||||||
\(198\) | −8.93534 | − | 6.49191i | −0.635007 | − | 0.461360i | ||||
\(199\) | 9.63624 | − | 7.00114i | 0.683095 | − | 0.496298i | −0.191288 | − | 0.981534i | \(-0.561266\pi\) |
0.874383 | + | 0.485236i | \(0.161266\pi\) | |||||||
\(200\) | 1.91617 | − | 5.89738i | 0.135494 | − | 0.417008i | ||||
\(201\) | 21.9970 | − | 15.9818i | 1.55155 | − | 1.12727i | ||||
\(202\) | 7.64966 | − | 5.55780i | 0.538228 | − | 0.391046i | ||||
\(203\) | −4.04811 | + | 12.4588i | −0.284122 | + | 0.874437i | ||||
\(204\) | 1.96126 | − | 1.42494i | 0.137316 | − | 0.0997657i | ||||
\(205\) | 21.0044 | + | 15.2606i | 1.46701 | + | 1.06584i | ||||
\(206\) | −0.403945 | − | 1.24322i | −0.0281442 | − | 0.0866189i | ||||
\(207\) | 26.3051 | + | 19.1118i | 1.82833 | + | 1.32836i | ||||
\(208\) | 0.723001 | − | 2.22517i | 0.0501311 | − | 0.154288i | ||||
\(209\) | 0.214785 | − | 0.661042i | 0.0148570 | − | 0.0457252i | ||||
\(210\) | −7.99313 | − | 24.6003i | −0.551578 | − | 1.69758i | ||||
\(211\) | 20.5097 | 1.41195 | 0.705974 | − | 0.708237i | \(-0.250509\pi\) | ||||
0.705974 | + | 0.708237i | \(0.250509\pi\) | |||||||
\(212\) | −2.62950 | −0.180595 | ||||||||
\(213\) | −11.2782 | − | 34.7107i | −0.772770 | − | 2.37834i | ||||
\(214\) | −12.1451 | + | 8.82395i | −0.830224 | + | 0.603193i | ||||
\(215\) | 20.7046 | + | 15.0428i | 1.41204 | + | 1.02591i | ||||
\(216\) | 10.4792 | 0.713021 | ||||||||
\(217\) | −13.6124 | − | 3.37313i | −0.924069 | − | 0.228983i | ||||
\(218\) | 7.06206 | 0.478303 | ||||||||
\(219\) | −19.4782 | − | 14.1518i | −1.31622 | − | 0.956288i | ||||
\(220\) | 4.66152 | − | 3.38679i | 0.314280 | − | 0.228338i | ||||
\(221\) | −0.571218 | − | 1.75803i | −0.0384243 | − | 0.118258i | ||||
\(222\) | 18.0708 | 1.21283 | ||||||||
\(223\) | −3.53346 | −0.236618 | −0.118309 | − | 0.992977i | \(-0.537747\pi\) | ||||
−0.118309 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(224\) | 0.778353 | + | 2.39552i | 0.0520059 | + | 0.160058i | ||||
\(225\) | 12.2926 | − | 37.8328i | 0.819508 | − | 2.52219i | ||||
\(226\) | 1.67792 | − | 5.16410i | 0.111613 | − | 0.343511i | ||||
\(227\) | −0.453928 | − | 0.329798i | −0.0301283 | − | 0.0218895i | 0.572619 | − | 0.819821i | \(-0.305927\pi\) |
−0.602747 | + | 0.797932i | \(0.705927\pi\) | |||||||
\(228\) | 0.382803 | + | 1.17815i | 0.0253517 | + | 0.0780246i | ||||
\(229\) | −4.02016 | − | 2.92081i | −0.265659 | − | 0.193013i | 0.446979 | − | 0.894544i | \(-0.352500\pi\) |
−0.712638 | + | 0.701532i | \(0.752500\pi\) | |||||||
\(230\) | −13.7232 | + | 9.97050i | −0.904882 | + | 0.657435i | ||||
\(231\) | 4.11183 | − | 12.6549i | 0.270539 | − | 0.832632i | ||||
\(232\) | 4.20759 | − | 3.05700i | 0.276242 | − | 0.200702i | ||||
\(233\) | 7.68606 | − | 5.58425i | 0.503530 | − | 0.365836i | −0.306833 | − | 0.951763i | \(-0.599269\pi\) |
0.810364 | + | 0.585927i | \(0.199269\pi\) | |||||||
\(234\) | 4.63819 | − | 14.2749i | 0.303208 | − | 0.933178i | ||||
\(235\) | −13.1032 | + | 9.52006i | −0.854761 | + | 0.621020i | ||||
\(236\) | 3.53202 | + | 2.56616i | 0.229915 | + | 0.167043i | ||||
\(237\) | −1.98632 | − | 6.11328i | −0.129026 | − | 0.397100i | ||||
\(238\) | 1.60996 | + | 1.16970i | 0.104358 | + | 0.0758206i | ||||
\(239\) | −3.81989 | + | 11.7564i | −0.247088 | + | 0.760460i | 0.748198 | + | 0.663476i | \(0.230919\pi\) |
−0.995286 | + | 0.0969838i | \(0.969081\pi\) | |||||||
\(240\) | −3.17339 | + | 9.76668i | −0.204841 | + | 0.630436i | ||||
\(241\) | 6.15504 | + | 18.9433i | 0.396481 | + | 1.22024i | 0.927802 | + | 0.373073i | \(0.121696\pi\) |
−0.531321 | + | 0.847171i | \(0.678304\pi\) | |||||||
\(242\) | −8.03593 | −0.516569 | ||||||||
\(243\) | 8.17277 | 0.524283 | ||||||||
\(244\) | 2.96934 | + | 9.13868i | 0.190092 | + | 0.585044i | ||||
\(245\) | −1.77520 | + | 1.28976i | −0.113413 | + | 0.0823997i | ||||
\(246\) | −19.2574 | − | 13.9913i | −1.22781 | − | 0.892055i | ||||
\(247\) | 0.944572 | 0.0601017 | ||||||||
\(248\) | 3.58503 | + | 4.26000i | 0.227650 | + | 0.270510i | ||||
\(249\) | −37.6061 | −2.38319 | ||||||||
\(250\) | 3.25148 | + | 2.36233i | 0.205641 | + | 0.149407i | ||||
\(251\) | 19.9146 | − | 14.4688i | 1.25700 | − | 0.913261i | 0.258390 | − | 0.966041i | \(-0.416808\pi\) |
0.998606 | + | 0.0527792i | \(0.0168080\pi\) | |||||||
\(252\) | 4.99328 | + | 15.3677i | 0.314547 | + | 0.968076i | ||||
\(253\) | −8.72603 | −0.548601 | ||||||||
\(254\) | 4.17912 | 0.262221 | ||||||||
\(255\) | 2.50718 | + | 7.71631i | 0.157006 | + | 0.483214i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 6.33567 | − | 19.4992i | 0.395208 | − | 1.21633i | −0.533591 | − | 0.845742i | \(-0.679158\pi\) |
0.928799 | − | 0.370583i | \(-0.120842\pi\) | |||||||
\(258\) | −18.9826 | − | 13.7917i | −1.18181 | − | 0.858633i | ||||
\(259\) | 4.58395 | + | 14.1079i | 0.284833 | + | 0.876625i | ||||
\(260\) | 6.33491 | + | 4.60258i | 0.392874 | + | 0.285440i | ||||
\(261\) | 26.9925 | − | 19.6112i | 1.67079 | − | 1.21390i | ||||
\(262\) | 2.13918 | − | 6.58371i | 0.132159 | − | 0.406743i | ||||
\(263\) | −4.10167 | + | 2.98003i | −0.252920 | + | 0.183757i | −0.707020 | − | 0.707194i | \(-0.749961\pi\) |
0.454100 | + | 0.890951i | \(0.349961\pi\) | |||||||
\(264\) | −4.27382 | + | 3.10511i | −0.263036 | + | 0.191106i | ||||
\(265\) | 2.71946 | − | 8.36963i | 0.167055 | − | 0.514142i | ||||
\(266\) | −0.822678 | + | 0.597710i | −0.0504416 | + | 0.0366480i | ||||
\(267\) | −36.3527 | − | 26.4118i | −2.22475 | − | 1.61638i | ||||
\(268\) | −2.73826 | − | 8.42749i | −0.167266 | − | 0.514791i | ||||
\(269\) | 4.28568 | + | 3.11373i | 0.261303 | + | 0.189848i | 0.710721 | − | 0.703474i | \(-0.248369\pi\) |
−0.449418 | + | 0.893321i | \(0.648369\pi\) | |||||||
\(270\) | −10.8377 | + | 33.3550i | −0.659562 | + | 2.02992i | ||||
\(271\) | −2.41473 | + | 7.43177i | −0.146684 | + | 0.451448i | −0.997224 | − | 0.0744634i | \(-0.976276\pi\) |
0.850539 | + | 0.525911i | \(0.176276\pi\) | |||||||
\(272\) | −0.244144 | − | 0.751397i | −0.0148034 | − | 0.0455601i | ||||
\(273\) | 18.0828 | 1.09442 | ||||||||
\(274\) | −3.55202 | −0.214586 | ||||||||
\(275\) | 3.29898 | + | 10.1532i | 0.198936 | + | 0.612262i | ||||
\(276\) | 12.5819 | − | 9.14125i | 0.757338 | − | 0.550239i | ||||
\(277\) | 0.833554 | + | 0.605612i | 0.0500834 | + | 0.0363877i | 0.612545 | − | 0.790435i | \(-0.290146\pi\) |
−0.562462 | + | 0.826823i | \(0.690146\pi\) | |||||||
\(278\) | −2.46775 | −0.148006 | ||||||||
\(279\) | 22.9986 | + | 27.3287i | 1.37689 | + | 1.63613i | ||||
\(280\) | −8.42985 | −0.503780 | ||||||||
\(281\) | −5.71370 | − | 4.15124i | −0.340851 | − | 0.247642i | 0.404170 | − | 0.914684i | \(-0.367560\pi\) |
−0.745021 | + | 0.667041i | \(0.767560\pi\) | |||||||
\(282\) | 12.0134 | − | 8.72827i | 0.715390 | − | 0.519761i | ||||
\(283\) | 6.70026 | + | 20.6213i | 0.398289 | + | 1.22581i | 0.926370 | + | 0.376614i | \(0.122912\pi\) |
−0.528081 | + | 0.849194i | \(0.677088\pi\) | |||||||
\(284\) | −11.8944 | −0.705804 | ||||||||
\(285\) | −4.14590 | −0.245582 | ||||||||
\(286\) | 1.24475 | + | 3.83096i | 0.0736038 | + | 0.226529i | ||||
\(287\) | 6.03813 | − | 18.5835i | 0.356420 | − | 1.09695i | ||||
\(288\) | 1.98240 | − | 6.10121i | 0.116814 | − | 0.359517i | ||||
\(289\) | 13.2483 | + | 9.62545i | 0.779312 | + | 0.566203i | ||||
\(290\) | 5.37879 | + | 16.5542i | 0.315853 | + | 0.972097i | ||||
\(291\) | 46.6287 | + | 33.8778i | 2.73342 | + | 1.98595i | ||||
\(292\) | −6.34797 | + | 4.61207i | −0.371487 | + | 0.269901i | ||||
\(293\) | −2.77555 | + | 8.54227i | −0.162149 | + | 0.499045i | −0.998815 | − | 0.0486695i | \(-0.984502\pi\) |
0.836665 | + | 0.547714i | \(0.184502\pi\) | |||||||
\(294\) | 1.62756 | − | 1.18249i | 0.0949210 | − | 0.0689641i | ||||
\(295\) | −11.8209 | + | 8.58835i | −0.688237 | + | 0.500033i | ||||
\(296\) | 1.81989 | − | 5.60105i | 0.105779 | − | 0.325555i | ||||
\(297\) | −14.5959 | + | 10.6045i | −0.846940 | + | 0.615338i | ||||
\(298\) | 11.5112 | + | 8.36341i | 0.666828 | + | 0.484479i | ||||
\(299\) | −3.66447 | − | 11.2781i | −0.211922 | − | 0.652229i | ||||
\(300\) | −15.3931 | − | 11.1837i | −0.888719 | − | 0.645692i | ||||
\(301\) | 5.95196 | − | 18.3183i | 0.343066 | − | 1.05585i | ||||
\(302\) | −1.46345 | + | 4.50404i | −0.0842121 | + | 0.259178i | ||||
\(303\) | −8.96564 | − | 27.5934i | −0.515063 | − | 1.58520i | ||||
\(304\) | 0.403718 | 0.0231548 | ||||||||
\(305\) | −32.1590 | −1.84142 | ||||||||
\(306\) | −1.56623 | − | 4.82035i | −0.0895353 | − | 0.275561i | ||||
\(307\) | 11.7641 | − | 8.54715i | 0.671415 | − | 0.487812i | −0.199083 | − | 0.979983i | \(-0.563796\pi\) |
0.870499 | + | 0.492171i | \(0.163796\pi\) | |||||||
\(308\) | −3.50829 | − | 2.54892i | −0.199904 | − | 0.145238i | ||||
\(309\) | −4.01102 | −0.228179 | ||||||||
\(310\) | −17.2671 | + | 7.00531i | −0.980705 | + | 0.397875i | ||||
\(311\) | −10.6398 | −0.603327 | −0.301663 | − | 0.953414i | \(-0.597542\pi\) | ||||
−0.301663 | + | 0.953414i | \(0.597542\pi\) | |||||||
\(312\) | −5.80803 | − | 4.21978i | −0.328815 | − | 0.238898i | ||||
\(313\) | −2.73252 | + | 1.98529i | −0.154451 | + | 0.112215i | −0.662327 | − | 0.749215i | \(-0.730431\pi\) |
0.507876 | + | 0.861430i | \(0.330431\pi\) | |||||||
\(314\) | −5.67609 | − | 17.4692i | −0.320320 | − | 0.985845i | ||||
\(315\) | −54.0791 | −3.04701 | ||||||||
\(316\) | −2.09485 | −0.117845 | ||||||||
\(317\) | 2.02016 | + | 6.21740i | 0.113463 | + | 0.349204i | 0.991623 | − | 0.129163i | \(-0.0412290\pi\) |
−0.878160 | + | 0.478367i | \(0.841229\pi\) | |||||||
\(318\) | −2.49328 | + | 7.67352i | −0.139816 | + | 0.430310i | ||||
\(319\) | −2.76696 | + | 8.51583i | −0.154920 | + | 0.476795i | ||||
\(320\) | 2.70759 | + | 1.96718i | 0.151359 | + | 0.109969i | ||||
\(321\) | 14.2345 | + | 43.8092i | 0.794491 | + | 2.44519i | ||||
\(322\) | 10.3282 | + | 7.50387i | 0.575567 | + | 0.418174i | ||||
\(323\) | 0.258047 | − | 0.187482i | 0.0143581 | − | 0.0104318i | ||||
\(324\) | 3.98912 | − | 12.2773i | 0.221618 | − | 0.682070i | ||||
\(325\) | −11.7373 | + | 8.52763i | −0.651067 | + | 0.473028i | ||||
\(326\) | 10.2562 | − | 7.45158i | 0.568040 | − | 0.412705i | ||||
\(327\) | 6.69620 | − | 20.6088i | 0.370301 | − | 1.13967i | ||||
\(328\) | −6.27601 | + | 4.55979i | −0.346535 | + | 0.251772i | ||||
\(329\) | 9.86158 | + | 7.16486i | 0.543687 | + | 0.395012i | ||||
\(330\) | −5.46345 | − | 16.8148i | −0.300753 | − | 0.925623i | ||||
\(331\) | −22.6560 | − | 16.4606i | −1.24529 | − | 0.904754i | −0.247348 | − | 0.968927i | \(-0.579559\pi\) |
−0.997939 | + | 0.0641730i | \(0.979559\pi\) | |||||||
\(332\) | −3.78726 | + | 11.6560i | −0.207853 | + | 0.639706i | ||||
\(333\) | 11.6750 | − | 35.9318i | 0.639784 | − | 1.96905i | ||||
\(334\) | 7.12950 | + | 21.9424i | 0.390109 | + | 1.20063i | ||||
\(335\) | 29.6564 | 1.62030 | ||||||||
\(336\) | 7.72874 | 0.421637 | ||||||||
\(337\) | 9.18116 | + | 28.2567i | 0.500130 | + | 1.53924i | 0.808807 | + | 0.588074i | \(0.200114\pi\) |
−0.308677 | + | 0.951167i | \(0.599886\pi\) | |||||||
\(338\) | 6.08857 | − | 4.42361i | 0.331175 | − | 0.240613i | ||||
\(339\) | −13.4791 | − | 9.79312i | −0.732083 | − | 0.531889i | ||||
\(340\) | 2.64417 | 0.143400 | ||||||||
\(341\) | −9.30432 | − | 2.30560i | −0.503857 | − | 0.124855i | ||||
\(342\) | 2.58993 | 0.140047 | ||||||||
\(343\) | 15.6003 | + | 11.3343i | 0.842337 | + | 0.611994i | ||||
\(344\) | −6.18645 | + | 4.49472i | −0.333551 | + | 0.242339i | ||||
\(345\) | 16.0840 | + | 49.5016i | 0.865936 | + | 2.66508i | ||||
\(346\) | −20.2515 | −1.08873 | ||||||||
\(347\) | −9.82039 | −0.527186 | −0.263593 | − | 0.964634i | \(-0.584908\pi\) | ||||
−0.263593 | + | 0.964634i | \(0.584908\pi\) | |||||||
\(348\) | −4.93143 | − | 15.1774i | −0.264353 | − | 0.813593i | ||||
\(349\) | 0.317093 | − | 0.975911i | 0.0169736 | − | 0.0522393i | −0.942211 | − | 0.335020i | \(-0.891257\pi\) |
0.959185 | + | 0.282781i | \(0.0912569\pi\) | |||||||
\(350\) | 4.82646 | − | 14.8543i | 0.257985 | − | 0.793997i | ||||
\(351\) | −19.8355 | − | 14.4113i | −1.05874 | − | 0.769221i | ||||
\(352\) | 0.532018 | + | 1.63738i | 0.0283567 | + | 0.0872729i | ||||
\(353\) | −16.9992 | − | 12.3507i | −0.904778 | − | 0.657360i | 0.0349109 | − | 0.999390i | \(-0.488885\pi\) |
−0.939689 | + | 0.342031i | \(0.888885\pi\) | |||||||
\(354\) | 10.8377 | − | 7.87406i | 0.576018 | − | 0.418501i | ||||
\(355\) | 12.3013 | − | 37.8595i | 0.652886 | − | 2.00938i | ||||
\(356\) | −11.8474 | + | 8.60763i | −0.627910 | + | 0.456203i | ||||
\(357\) | 4.94003 | − | 3.58914i | 0.261454 | − | 0.189957i | ||||
\(358\) | −2.45235 | + | 7.54755i | −0.129611 | + | 0.398900i | ||||
\(359\) | 24.6099 | − | 17.8802i | 1.29886 | − | 0.943680i | 0.298920 | − | 0.954278i | \(-0.403374\pi\) |
0.999944 | + | 0.0105988i | \(0.00337376\pi\) | |||||||
\(360\) | 17.3697 | + | 12.6198i | 0.915465 | + | 0.665124i | ||||
\(361\) | −5.82096 | − | 17.9151i | −0.306366 | − | 0.942898i | ||||
\(362\) | 19.6467 | + | 14.2742i | 1.03261 | + | 0.750234i | ||||
\(363\) | −7.61961 | + | 23.4508i | −0.399926 | + | 1.23085i | ||||
\(364\) | 1.82110 | − | 5.60476i | 0.0954514 | − | 0.293769i | ||||
\(365\) | −8.11495 | − | 24.9752i | −0.424756 | − | 1.30726i | ||||
\(366\) | 29.4843 | 1.54117 | ||||||||
\(367\) | 25.8054 | 1.34703 | 0.673516 | − | 0.739172i | \(-0.264783\pi\) | ||||
0.673516 | + | 0.739172i | \(0.264783\pi\) | |||||||
\(368\) | −1.56623 | − | 4.82035i | −0.0816452 | − | 0.251278i | ||||
\(369\) | −40.2618 | + | 29.2519i | −2.09595 | + | 1.52279i | ||||
\(370\) | 15.9458 | + | 11.5853i | 0.828984 | + | 0.602292i | ||||
\(371\) | −6.62320 | −0.343859 | ||||||||
\(372\) | 15.8310 | − | 6.42267i | 0.820798 | − | 0.333000i | ||||
\(373\) | 12.4846 | 0.646430 | 0.323215 | − | 0.946326i | \(-0.395236\pi\) | ||||
0.323215 | + | 0.946326i | \(0.395236\pi\) | |||||||
\(374\) | 1.10044 | + | 0.799514i | 0.0569022 | + | 0.0413419i | ||||
\(375\) | 9.97688 | − | 7.24863i | 0.515204 | − | 0.374318i | ||||
\(376\) | −1.49547 | − | 4.60258i | −0.0771229 | − | 0.237360i | ||||
\(377\) | −12.1684 | −0.626704 | ||||||||
\(378\) | 26.3951 | 1.35762 | ||||||||
\(379\) | 0.582244 | + | 1.79196i | 0.0299079 | + | 0.0920470i | 0.964896 | − | 0.262631i | \(-0.0845903\pi\) |
−0.934988 | + | 0.354678i | \(0.884590\pi\) | |||||||
\(380\) | −0.417529 | + | 1.28502i | −0.0214188 | + | 0.0659202i | ||||
\(381\) | 3.96261 | − | 12.1957i | 0.203011 | − | 0.624803i | ||||
\(382\) | −9.21589 | − | 6.69573i | −0.471526 | − | 0.342584i | ||||
\(383\) | 4.02861 | + | 12.3988i | 0.205852 | + | 0.633548i | 0.999677 | + | 0.0254019i | \(0.00808656\pi\) |
−0.793825 | + | 0.608146i | \(0.791913\pi\) | |||||||
\(384\) | −2.48240 | − | 1.80357i | −0.126680 | − | 0.0920381i | ||||
\(385\) | 11.7415 | − | 8.53066i | 0.598400 | − | 0.434763i | ||||
\(386\) | −3.13502 | + | 9.64861i | −0.159568 | + | 0.491101i | ||||
\(387\) | −39.6873 | + | 28.8345i | −2.01742 | + | 1.46574i | ||||
\(388\) | 15.1963 | − | 11.0408i | 0.771477 | − | 0.560511i | ||||
\(389\) | 3.18962 | − | 9.81664i | 0.161720 | − | 0.497723i | −0.837060 | − | 0.547112i | \(-0.815727\pi\) |
0.998780 | + | 0.0493885i | \(0.0157272\pi\) | |||||||
\(390\) | 19.4381 | − | 14.1226i | 0.984289 | − | 0.715128i | ||||
\(391\) | −3.23961 | − | 2.35372i | −0.163834 | − | 0.119033i | ||||
\(392\) | −0.202603 | − | 0.623548i | −0.0102330 | − | 0.0314939i | ||||
\(393\) | −17.1845 | − | 12.4853i | −0.866842 | − | 0.629798i | ||||
\(394\) | −0.723369 | + | 2.22630i | −0.0364428 | + | 0.112159i | ||||
\(395\) | 2.16651 | − | 6.66784i | 0.109009 | − | 0.335496i | ||||
\(396\) | 3.41300 | + | 10.5041i | 0.171510 | + | 0.527852i | ||||
\(397\) | 14.8604 | 0.745824 | 0.372912 | − | 0.927867i | \(-0.378359\pi\) | ||||
0.372912 | + | 0.927867i | \(0.378359\pi\) | |||||||
\(398\) | −11.9110 | −0.597047 | ||||||||
\(399\) | 0.964204 | + | 2.96752i | 0.0482706 | + | 0.148562i | ||||
\(400\) | −5.01661 | + | 3.64478i | −0.250831 | + | 0.182239i | ||||
\(401\) | −9.88612 | − | 7.18269i | −0.493689 | − | 0.358686i | 0.312912 | − | 0.949782i | \(-0.398695\pi\) |
−0.806601 | + | 0.591096i | \(0.798695\pi\) | |||||||
\(402\) | −27.1898 | −1.35611 | ||||||||
\(403\) | −0.927418 | − | 12.9937i | −0.0461980 | − | 0.647264i | ||||
\(404\) | −9.45550 | −0.470429 | ||||||||
\(405\) | 34.9525 | + | 25.3945i | 1.73681 | + | 1.26186i | ||||
\(406\) | 10.5981 | − | 7.69997i | 0.525975 | − | 0.382143i | ||||
\(407\) | 3.13321 | + | 9.64304i | 0.155308 | + | 0.477988i | ||||
\(408\) | −2.42425 | −0.120018 | ||||||||
\(409\) | 14.9660 | 0.740021 | 0.370010 | − | 0.929028i | \(-0.379354\pi\) | ||||
0.370010 | + | 0.929028i | \(0.379354\pi\) | |||||||
\(410\) | −8.02296 | − | 24.6921i | −0.396226 | − | 1.21946i | ||||
\(411\) | −3.36801 | + | 10.3657i | −0.166131 | + | 0.511300i | ||||
\(412\) | −0.403945 | + | 1.24322i | −0.0199009 | + | 0.0612488i | ||||
\(413\) | 8.89645 | + | 6.46365i | 0.437766 | + | 0.318056i | ||||
\(414\) | −10.0476 | − | 30.9235i | −0.493815 | − | 1.51981i | ||||
\(415\) | −33.1839 | − | 24.1095i | −1.62893 | − | 1.18349i | ||||
\(416\) | −1.89284 | + | 1.37523i | −0.0928042 | + | 0.0674262i | ||||
\(417\) | −2.33991 | + | 7.20150i | −0.114586 | + | 0.352659i | ||||
\(418\) | −0.562315 | + | 0.408546i | −0.0275037 | + | 0.0199826i | ||||
\(419\) | −12.3701 | + | 8.98739i | −0.604318 | + | 0.439063i | −0.847409 | − | 0.530941i | \(-0.821839\pi\) |
0.243091 | + | 0.970003i | \(0.421839\pi\) | |||||||
\(420\) | −7.99313 | + | 24.6003i | −0.390025 | + | 1.20037i | ||||
\(421\) | −17.3497 | + | 12.6053i | −0.845572 | + | 0.614344i | −0.923922 | − | 0.382582i | \(-0.875035\pi\) |
0.0783493 | + | 0.996926i | \(0.475035\pi\) | |||||||
\(422\) | −16.5927 | − | 12.0553i | −0.807721 | − | 0.586844i | ||||
\(423\) | −9.59371 | − | 29.5264i | −0.466462 | − | 1.43562i | ||||
\(424\) | 2.12731 | + | 1.54558i | 0.103311 | + | 0.0750602i | ||||
\(425\) | −1.51390 | + | 4.65932i | −0.0734351 | + | 0.226010i | ||||
\(426\) | −11.2782 | + | 34.7107i | −0.546431 | + | 1.68174i | ||||
\(427\) | 7.47917 | + | 23.0185i | 0.361942 | + | 1.11394i | ||||
\(428\) | 15.0122 | 0.725642 | ||||||||
\(429\) | 12.3599 | 0.596742 | ||||||||
\(430\) | −7.90847 | − | 24.3398i | −0.381380 | − | 1.17377i | ||||
\(431\) | −7.24276 | + | 5.26218i | −0.348872 | + | 0.253470i | −0.748396 | − | 0.663253i | \(-0.769175\pi\) |
0.399524 | + | 0.916723i | \(0.369175\pi\) | |||||||
\(432\) | −8.47787 | − | 6.15953i | −0.407892 | − | 0.296351i | ||||
\(433\) | 5.18109 | 0.248987 | 0.124494 | − | 0.992220i | \(-0.460269\pi\) | ||||
0.124494 | + | 0.992220i | \(0.460269\pi\) | |||||||
\(434\) | 9.02998 | + | 10.7301i | 0.433453 | + | 0.515061i | ||||
\(435\) | 53.4093 | 2.56078 | ||||||||
\(436\) | −5.71333 | − | 4.15098i | −0.273619 | − | 0.198796i | ||||
\(437\) | 1.65542 | − | 1.20273i | 0.0791895 | − | 0.0575345i | ||||
\(438\) | 7.44003 | + | 22.8980i | 0.355498 | + | 1.09411i | ||||
\(439\) | −2.26810 | −0.108251 | −0.0541253 | − | 0.998534i | \(-0.517237\pi\) | ||||
−0.0541253 | + | 0.998534i | \(0.517237\pi\) | |||||||
\(440\) | −5.76196 | −0.274691 | ||||||||
\(441\) | −1.29974 | − | 4.00018i | −0.0618923 | − | 0.190485i | ||||
\(442\) | −0.571218 | + | 1.75803i | −0.0271701 | + | 0.0836209i | ||||
\(443\) | −6.83506 | + | 21.0361i | −0.324743 | + | 0.999457i | 0.646813 | + | 0.762649i | \(0.276101\pi\) |
−0.971556 | + | 0.236809i | \(0.923899\pi\) | |||||||
\(444\) | −14.6196 | − | 10.6218i | −0.693816 | − | 0.504087i | ||||
\(445\) | −15.1451 | − | 46.6119i | −0.717948 | − | 2.20962i | ||||
\(446\) | 2.85863 | + | 2.07692i | 0.135360 | + | 0.0983449i | ||||
\(447\) | 35.3213 | − | 25.6624i | 1.67064 | − | 1.21379i | ||||
\(448\) | 0.778353 | − | 2.39552i | 0.0367737 | − | 0.113178i | ||||
\(449\) | 13.4381 | − | 9.76338i | 0.634185 | − | 0.460763i | −0.223662 | − | 0.974667i | \(-0.571801\pi\) |
0.857848 | + | 0.513904i | \(0.171801\pi\) | |||||||
\(450\) | −32.1825 | + | 23.3820i | −1.51710 | + | 1.10224i | ||||
\(451\) | 4.12717 | − | 12.7021i | 0.194341 | − | 0.598120i | ||||
\(452\) | −4.39284 | + | 3.19159i | −0.206622 | + | 0.150120i | ||||
\(453\) | 11.7562 | + | 8.54140i | 0.552356 | + | 0.401310i | ||||
\(454\) | 0.173385 | + | 0.533625i | 0.00813737 | + | 0.0250443i | ||||
\(455\) | 15.9564 | + | 11.5930i | 0.748046 | + | 0.543488i | ||||
\(456\) | 0.382803 | − | 1.17815i | 0.0179264 | − | 0.0551717i | ||||
\(457\) | −11.2417 | + | 34.5984i | −0.525865 | + | 1.61845i | 0.236734 | + | 0.971575i | \(0.423923\pi\) |
−0.762599 | + | 0.646872i | \(0.776077\pi\) | |||||||
\(458\) | 1.53556 | + | 4.72598i | 0.0717521 | + | 0.220830i | ||||
\(459\) | −8.27927 | −0.386443 | ||||||||
\(460\) | 16.9628 | 0.790896 | ||||||||
\(461\) | 1.07920 | + | 3.32144i | 0.0502634 | + | 0.154695i | 0.973038 | − | 0.230646i | \(-0.0740839\pi\) |
−0.922774 | + | 0.385341i | \(0.874084\pi\) | |||||||
\(462\) | −10.7649 | + | 7.82116i | −0.500829 | + | 0.363873i | ||||
\(463\) | −4.90751 | − | 3.56551i | −0.228071 | − | 0.165703i | 0.467881 | − | 0.883791i | \(-0.345018\pi\) |
−0.695952 | + | 0.718088i | \(0.745018\pi\) | |||||||
\(464\) | −5.20087 | −0.241444 | ||||||||
\(465\) | 4.07061 | + | 57.0319i | 0.188770 | + | 2.64479i | ||||
\(466\) | −9.50049 | −0.440102 | ||||||||
\(467\) | −2.48066 | − | 1.80230i | −0.114791 | − | 0.0834006i | 0.528909 | − | 0.848679i | \(-0.322601\pi\) |
−0.643700 | + | 0.765278i | \(0.722601\pi\) | |||||||
\(468\) | −12.1429 | + | 8.82236i | −0.561308 | + | 0.407814i | ||||
\(469\) | −6.89713 | − | 21.2272i | −0.318480 | − | 0.980180i | ||||
\(470\) | 16.1965 | 0.747088 | ||||||||
\(471\) | −56.3614 | −2.59700 | ||||||||
\(472\) | −1.34911 | − | 4.15214i | −0.0620979 | − | 0.191118i | ||||
\(473\) | 4.06828 | − | 12.5209i | 0.187060 | − | 0.575710i | ||||
\(474\) | −1.98632 | + | 6.11328i | −0.0912349 | + | 0.280792i | ||||
\(475\) | −2.02530 | − | 1.47146i | −0.0929270 | − | 0.0675154i | ||||
\(476\) | −0.614949 | − | 1.89262i | −0.0281862 | − | 0.0867481i | ||||
\(477\) | 13.6471 | + | 9.91521i | 0.624859 | + | 0.453986i | ||||
\(478\) | 10.0006 | − | 7.26587i | 0.457417 | − | 0.332333i | ||||
\(479\) | 1.62355 | − | 4.99678i | 0.0741820 | − | 0.228309i | −0.907090 | − | 0.420937i | \(-0.861701\pi\) |
0.981272 | + | 0.192629i | \(0.0617013\pi\) | |||||||
\(480\) | 8.30803 | − | 6.03614i | 0.379208 | − | 0.275511i | ||||
\(481\) | −11.1475 | + | 8.09914i | −0.508283 | + | 0.369289i | ||||
\(482\) | 6.15504 | − | 18.9433i | 0.280355 | − | 0.862843i | ||||
\(483\) | 31.6912 | − | 23.0250i | 1.44200 | − | 1.04767i | ||||
\(484\) | 6.50120 | + | 4.72340i | 0.295509 | + | 0.214700i | ||||
\(485\) | 19.4263 | + | 59.7879i | 0.882102 | + | 2.71483i | ||||
\(486\) | −6.61191 | − | 4.80383i | −0.299922 | − | 0.217906i | ||||
\(487\) | −2.09983 | + | 6.46260i | −0.0951522 | + | 0.292848i | −0.987293 | − | 0.158908i | \(-0.949203\pi\) |
0.892141 | + | 0.451757i | \(0.149203\pi\) | |||||||
\(488\) | 2.96934 | − | 9.13868i | 0.134416 | − | 0.413688i | ||||
\(489\) | −12.0206 | − | 36.9957i | −0.543591 | − | 1.67300i | ||||
\(490\) | 2.19427 | 0.0991269 | ||||||||
\(491\) | 23.1009 | 1.04253 | 0.521264 | − | 0.853395i | \(-0.325461\pi\) | ||||
0.521264 | + | 0.853395i | \(0.325461\pi\) | |||||||
\(492\) | 7.35568 | + | 22.6385i | 0.331620 | + | 1.02062i | ||||
\(493\) | −3.32427 | + | 2.41523i | −0.149718 | + | 0.108776i | ||||
\(494\) | −0.764175 | − | 0.555205i | −0.0343818 | − | 0.0249799i | ||||
\(495\) | −36.9641 | −1.66141 | ||||||||
\(496\) | −0.396387 | − | 5.55364i | −0.0177983 | − | 0.249366i | ||||
\(497\) | −29.9597 | −1.34387 | ||||||||
\(498\) | 30.4239 | + | 22.1043i | 1.36333 | + | 0.990517i | ||||
\(499\) | −20.3630 | + | 14.7946i | −0.911573 | + | 0.662297i | −0.941412 | − | 0.337258i | \(-0.890501\pi\) |
0.0298390 | + | 0.999555i | \(0.490501\pi\) | |||||||
\(500\) | −1.24195 | − | 3.82234i | −0.0555418 | − | 0.170940i | ||||
\(501\) | 70.7932 | 3.16281 | ||||||||
\(502\) | −24.6158 | −1.09866 | ||||||||
\(503\) | −2.30850 | − | 7.10483i | −0.102931 | − | 0.316789i | 0.886308 | − | 0.463096i | \(-0.153261\pi\) |
−0.989239 | + | 0.146307i | \(0.953261\pi\) | |||||||
\(504\) | 4.99328 | − | 15.3677i | 0.222418 | − | 0.684533i | ||||
\(505\) | 9.77896 | − | 30.0966i | 0.435158 | − | 1.33928i | ||||
\(506\) | 7.05951 | + | 5.12903i | 0.313833 | + | 0.228013i | ||||
\(507\) | −7.13600 | − | 21.9623i | −0.316921 | − | 0.975382i | ||||
\(508\) | −3.38098 | − | 2.45643i | −0.150007 | − | 0.108986i | ||||
\(509\) | −27.6648 | + | 20.0996i | −1.22622 | + | 0.890901i | −0.996601 | − | 0.0823797i | \(-0.973748\pi\) |
−0.229619 | + | 0.973281i | \(0.573748\pi\) | |||||||
\(510\) | 2.50718 | − | 7.71631i | 0.111020 | − | 0.341684i | ||||
\(511\) | −15.9893 | + | 11.6169i | −0.707325 | + | 0.513901i | ||||
\(512\) | −0.809017 | + | 0.587785i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | 1.30734 | − | 4.02359i | 0.0577206 | − | 0.177646i | ||||
\(514\) | −16.5870 | + | 12.0512i | −0.731621 | + | 0.531554i | ||||
\(515\) | −3.53935 | − | 2.57149i | −0.155962 | − | 0.113313i | ||||
\(516\) | 7.25072 | + | 22.3154i | 0.319195 | + | 0.982381i | ||||
\(517\) | 6.74057 | + | 4.89731i | 0.296450 | + | 0.215384i | ||||
\(518\) | 4.58395 | − | 14.1079i | 0.201407 | − | 0.619868i | ||||
\(519\) | −19.2023 | + | 59.0986i | −0.842888 | + | 2.59414i | ||||
\(520\) | −2.41972 | − | 7.44713i | −0.106112 | − | 0.326578i | ||||
\(521\) | −6.22092 | −0.272543 | −0.136272 | − | 0.990671i | \(-0.543512\pi\) | ||||
−0.136272 | + | 0.990671i | \(0.543512\pi\) | |||||||
\(522\) | −33.3646 | −1.46033 | ||||||||
\(523\) | −5.94426 | − | 18.2945i | −0.259924 | − | 0.799964i | −0.992819 | − | 0.119623i | \(-0.961831\pi\) |
0.732895 | − | 0.680342i | \(-0.238169\pi\) | |||||||
\(524\) | −5.60044 | + | 4.06896i | −0.244656 | + | 0.177753i | ||||
\(525\) | −38.7721 | − | 28.1696i | −1.69215 | − | 1.22942i | ||||
\(526\) | 5.06994 | 0.221060 | ||||||||
\(527\) | −2.83241 | − | 3.36568i | −0.123382 | − | 0.146611i | ||||
\(528\) | 5.28273 | 0.229901 | ||||||||
\(529\) | −2.17533 | − | 1.58047i | −0.0945797 | − | 0.0687162i | ||||
\(530\) | −7.11963 | + | 5.17271i | −0.309257 | + | 0.224688i | ||||
\(531\) | −8.65480 | − | 26.6367i | −0.375586 | − | 1.15594i | ||||
\(532\) | 1.01689 | 0.0440876 | ||||||||
\(533\) | 18.1503 | 0.786175 | ||||||||
\(534\) | 13.8855 | + | 42.7352i | 0.600884 | + | 1.84933i | ||||
\(535\) | −15.5258 | + | 47.7834i | −0.671237 | + | 2.06586i | ||||
\(536\) | −2.73826 | + | 8.42749i | −0.118275 | + | 0.364012i | ||||
\(537\) | 19.7003 | + | 14.3131i | 0.850129 | + | 0.617655i | ||||
\(538\) | −1.63699 | − | 5.03812i | −0.0705755 | − | 0.217209i | ||||
\(539\) | 0.913200 | + | 0.663478i | 0.0393343 | + | 0.0285780i | ||||
\(540\) | 28.3735 | − | 20.6145i | 1.22100 | − | 0.887109i | ||||
\(541\) | 7.03792 | − | 21.6605i | 0.302584 | − | 0.931258i | −0.677984 | − | 0.735077i | \(-0.737146\pi\) |
0.980568 | − | 0.196181i | \(-0.0628539\pi\) | |||||||
\(542\) | 6.32184 | − | 4.59309i | 0.271546 | − | 0.197290i | ||||
\(543\) | 60.2844 | − | 43.7992i | 2.58705 | − | 1.87960i | ||||
\(544\) | −0.244144 | + | 0.751397i | −0.0104676 | + | 0.0322159i | ||||
\(545\) | 19.1212 | − | 13.8924i | 0.819062 | − | 0.595084i | ||||
\(546\) | −14.6293 | − | 10.6288i | −0.626075 | − | 0.454870i | ||||
\(547\) | 0.683801 | + | 2.10452i | 0.0292372 | + | 0.0899830i | 0.964610 | − | 0.263680i | \(-0.0849361\pi\) |
−0.935373 | + | 0.353662i | \(0.884936\pi\) | |||||||
\(548\) | 2.87365 | + | 2.08783i | 0.122756 | + | 0.0891876i | ||||
\(549\) | 19.0488 | − | 58.6263i | 0.812985 | − | 2.50211i | ||||
\(550\) | 3.29898 | − | 10.1532i | 0.140669 | − | 0.432934i | ||||
\(551\) | −0.648839 | − | 1.99692i | −0.0276415 | − | 0.0850717i | ||||
\(552\) | −15.5520 | −0.661938 | ||||||||
\(553\) | −5.27651 | −0.224380 | ||||||||
\(554\) | −0.318389 | − | 0.979901i | −0.0135271 | − | 0.0416320i | ||||
\(555\) | 48.9285 | − | 35.5486i | 2.07690 | − | 1.50895i | ||||
\(556\) | 1.99646 | + | 1.45051i | 0.0846686 | + | 0.0615153i | ||||
\(557\) | 30.0188 | 1.27194 | 0.635969 | − | 0.771715i | \(-0.280601\pi\) | ||||
0.635969 | + | 0.771715i | \(0.280601\pi\) | |||||||
\(558\) | −2.54289 | − | 35.6276i | −0.107649 | − | 1.50824i | ||||
\(559\) | 17.8913 | 0.756719 | ||||||||
\(560\) | 6.81989 | + | 4.95494i | 0.288193 | + | 0.209385i | ||||
\(561\) | 3.37660 | − | 2.45324i | 0.142560 | − | 0.103576i | ||||
\(562\) | 2.18244 | + | 6.71685i | 0.0920606 | + | 0.283333i | ||||
\(563\) | −4.60946 | −0.194265 | −0.0971327 | − | 0.995271i | \(-0.530967\pi\) | ||||
−0.0971327 | + | 0.995271i | \(0.530967\pi\) | |||||||
\(564\) | −14.8494 | −0.625273 | ||||||||
\(565\) | −5.61560 | − | 17.2830i | −0.236250 | − | 0.727103i | ||||
\(566\) | 6.70026 | − | 20.6213i | 0.281633 | − | 0.866777i | ||||
\(567\) | 10.0478 | − | 30.9240i | 0.421968 | − | 1.29869i | ||||
\(568\) | 9.62278 | + | 6.99136i | 0.403763 | + | 0.293351i | ||||
\(569\) | 4.81521 | + | 14.8197i | 0.201864 | + | 0.621274i | 0.999828 | + | 0.0185682i | \(0.00591078\pi\) |
−0.797963 | + | 0.602706i | \(0.794089\pi\) | |||||||
\(570\) | 3.35410 | + | 2.43690i | 0.140488 | + | 0.102070i | ||||
\(571\) | −1.51012 | + | 1.09716i | −0.0631964 | + | 0.0459149i | −0.618935 | − | 0.785442i | \(-0.712436\pi\) |
0.555739 | + | 0.831357i | \(0.312436\pi\) | |||||||
\(572\) | 1.24475 | − | 3.83096i | 0.0520458 | − | 0.160180i | ||||
\(573\) | −28.2782 | + | 20.5453i | −1.18134 | + | 0.858293i | ||||
\(574\) | −15.8080 | + | 11.4852i | −0.659814 | + | 0.479383i | ||||
\(575\) | −9.71198 | + | 29.8904i | −0.405017 | + | 1.24652i | ||||
\(576\) | −5.19000 | + | 3.77075i | −0.216250 | + | 0.157115i | ||||
\(577\) | 24.4672 | + | 17.7765i | 1.01858 | + | 0.740045i | 0.965992 | − | 0.258571i | \(-0.0832518\pi\) |
0.0525919 | + | 0.998616i | \(0.483252\pi\) | |||||||
\(578\) | −5.06040 | − | 15.5743i | −0.210485 | − | 0.647806i | ||||
\(579\) | 25.1843 | + | 18.2975i | 1.04662 | + | 0.760418i | ||||
\(580\) | 5.37879 | − | 16.5542i | 0.223342 | − | 0.687376i | ||||
\(581\) | −9.53937 | + | 29.3592i | −0.395760 | + | 1.21802i | ||||
\(582\) | −17.8106 | − | 54.8154i | −0.738273 | − | 2.27217i | ||||
\(583\) | −4.52708 | −0.187492 | ||||||||
\(584\) | 7.84653 | 0.324692 | ||||||||
\(585\) | −15.5230 | − | 47.7747i | −0.641795 | − | 1.97524i | ||||
\(586\) | 7.26649 | − | 5.27941i | 0.300176 | − | 0.218091i | ||||
\(587\) | −17.1362 | − | 12.4502i | −0.707287 | − | 0.513874i | 0.175010 | − | 0.984567i | \(-0.444004\pi\) |
−0.882297 | + | 0.470692i | \(0.844004\pi\) | |||||||
\(588\) | −2.01177 | −0.0829640 | ||||||||
\(589\) | 2.08292 | − | 0.845044i | 0.0858250 | − | 0.0348194i | ||||
\(590\) | 14.6114 | 0.601541 | ||||||||
\(591\) | 5.81098 | + | 4.22192i | 0.239032 | + | 0.173667i | ||||
\(592\) | −4.76454 | + | 3.46164i | −0.195821 | + | 0.142273i | ||||
\(593\) | 12.9021 | + | 39.7085i | 0.529824 | + | 1.63063i | 0.754574 | + | 0.656215i | \(0.227844\pi\) |
−0.224750 | + | 0.974417i | \(0.572156\pi\) | |||||||
\(594\) | 18.0415 | 0.740253 | ||||||||
\(595\) | 6.66013 | 0.273039 | ||||||||
\(596\) | −4.39690 | − | 13.5323i | −0.180104 | − | 0.554304i | ||||
\(597\) | −11.2940 | + | 34.7593i | −0.462232 | + | 1.42260i | ||||
\(598\) | −3.66447 | + | 11.2781i | −0.149851 | + | 0.461195i | ||||
\(599\) | 5.28226 | + | 3.83779i | 0.215827 | + | 0.156808i | 0.690446 | − | 0.723384i | \(-0.257414\pi\) |
−0.474619 | + | 0.880191i | \(0.657414\pi\) | |||||||
\(600\) | 5.87963 | + | 18.0956i | 0.240035 | + | 0.738751i | ||||
\(601\) | 4.23546 | + | 3.07724i | 0.172768 | + | 0.125523i | 0.670809 | − | 0.741630i | \(-0.265947\pi\) |
−0.498041 | + | 0.867154i | \(0.665947\pi\) | |||||||
\(602\) | −15.5824 | + | 11.3213i | −0.635093 | + | 0.461422i | ||||
\(603\) | −17.5664 | + | 54.0640i | −0.715361 | + | 2.20165i | ||||
\(604\) | 3.83136 | − | 2.78365i | 0.155896 | − | 0.113265i | ||||
\(605\) | −21.7580 | + | 15.8081i | −0.884590 | + | 0.642692i | ||||
\(606\) | −8.96564 | + | 27.5934i | −0.364204 | + | 1.12091i | ||||
\(607\) | −16.4180 | + | 11.9284i | −0.666386 | + | 0.484157i | −0.868813 | − | 0.495140i | \(-0.835117\pi\) |
0.202428 | + | 0.979297i | \(0.435117\pi\) | |||||||
\(608\) | −0.326615 | − | 0.237300i | −0.0132460 | − | 0.00962377i | ||||
\(609\) | −12.4213 | − | 38.2288i | −0.503336 | − | 1.54911i | ||||
\(610\) | 26.0172 | + | 18.9026i | 1.05341 | + | 0.765344i | ||||
\(611\) | −3.49892 | + | 10.7686i | −0.141551 | + | 0.435650i | ||||
\(612\) | −1.56623 | + | 4.82035i | −0.0633110 | + | 0.194851i | ||||
\(613\) | −0.456496 | − | 1.40495i | −0.0184377 | − | 0.0567454i | 0.941414 | − | 0.337252i | \(-0.109497\pi\) |
−0.959852 | + | 0.280507i | \(0.909497\pi\) | |||||||
\(614\) | −14.5413 | −0.586839 | ||||||||
\(615\) | −79.6648 | −3.21240 | ||||||||
\(616\) | 1.34005 | + | 4.12425i | 0.0539921 | + | 0.166171i | ||||
\(617\) | 16.6778 | − | 12.1171i | 0.671421 | − | 0.487816i | −0.199079 | − | 0.979983i | \(-0.563795\pi\) |
0.870501 | + | 0.492167i | \(0.163795\pi\) | |||||||
\(618\) | 3.24498 | + | 2.35762i | 0.130532 | + | 0.0948372i | ||||
\(619\) | −2.74094 | −0.110168 | −0.0550839 | − | 0.998482i | \(-0.517543\pi\) | ||||
−0.0550839 | + | 0.998482i | \(0.517543\pi\) | |||||||
\(620\) | 18.0870 | + | 4.48193i | 0.726391 | + | 0.179999i | ||||
\(621\) | −53.1131 | −2.13135 | ||||||||
\(622\) | 8.60777 | + | 6.25391i | 0.345140 | + | 0.250759i | ||||
\(623\) | −29.8412 | + | 21.6809i | −1.19556 | + | 0.868627i | ||||
\(624\) | 2.21847 | + | 6.82775i | 0.0888099 | + | 0.273329i | ||||
\(625\) | −17.5535 | −0.702142 | ||||||||
\(626\) | 3.37758 | 0.134995 | ||||||||
\(627\) | 0.659051 | + | 2.02835i | 0.0263200 | + | 0.0810046i | ||||
\(628\) | −5.67609 | + | 17.4692i | −0.226501 | + | 0.697098i | ||||
\(629\) | −1.43783 | + | 4.42520i | −0.0573302 | + | 0.176444i | ||||
\(630\) | 43.7509 | + | 31.7869i | 1.74308 | + | 1.26642i | ||||
\(631\) | −12.8289 | − | 39.4831i | −0.510709 | − | 1.57180i | −0.790957 | − | 0.611872i | \(-0.790417\pi\) |
0.280248 | − | 0.959928i | \(-0.409583\pi\) | |||||||
\(632\) | 1.69477 | + | 1.23132i | 0.0674143 | + | 0.0489794i | ||||
\(633\) | −50.9134 | + | 36.9908i | −2.02363 | + | 1.47025i | ||||
\(634\) | 2.02016 | − | 6.21740i | 0.0802306 | − | 0.246924i | ||||
\(635\) | 11.3154 | − | 8.22109i | 0.449036 | − | 0.326244i | ||||
\(636\) | 6.52749 | − | 4.74250i | 0.258832 | − | 0.188052i | ||||
\(637\) | −0.474027 | + | 1.45890i | −0.0187816 | + | 0.0578039i | ||||
\(638\) | 7.24399 | − | 5.26307i | 0.286792 | − | 0.208367i | ||||
\(639\) | 61.7320 | + | 44.8509i | 2.44208 | + | 1.77427i | ||||
\(640\) | −1.03421 | − | 3.18297i | −0.0408807 | − | 0.125818i | ||||
\(641\) | 7.93753 | + | 5.76696i | 0.313514 | + | 0.227781i | 0.733403 | − | 0.679794i | \(-0.237931\pi\) |
−0.419889 | + | 0.907575i | \(0.637931\pi\) | |||||||
\(642\) | 14.2345 | − | 43.8092i | 0.561790 | − | 1.72901i | ||||
\(643\) | 11.7291 | − | 36.0983i | 0.462549 | − | 1.42358i | −0.399490 | − | 0.916738i | \(-0.630813\pi\) |
0.862039 | − | 0.506842i | \(-0.169187\pi\) | |||||||
\(644\) | −3.94502 | − | 12.1415i | −0.155455 | − | 0.478443i | ||||
\(645\) | −78.5280 | −3.09204 | ||||||||
\(646\) | −0.318964 | −0.0125495 | ||||||||
\(647\) | −9.54343 | − | 29.3717i | −0.375191 | − | 1.15472i | −0.943350 | − | 0.331800i | \(-0.892344\pi\) |
0.568159 | − | 0.822919i | \(-0.307656\pi\) | |||||||
\(648\) | −10.4437 | + | 7.58776i | −0.410266 | + | 0.298076i | ||||
\(649\) | 6.08089 | + | 4.41803i | 0.238696 | + | 0.173423i | ||||
\(650\) | 14.5081 | 0.569053 | ||||||||
\(651\) | 39.8751 | − | 16.1774i | 1.56283 | − | 0.634044i | ||||
\(652\) | −12.6774 | −0.496485 | ||||||||
\(653\) | 3.12889 | + | 2.27327i | 0.122443 | + | 0.0889601i | 0.647321 | − | 0.762217i | \(-0.275889\pi\) |
−0.524878 | + | 0.851177i | \(0.675889\pi\) | |||||||
\(654\) | −17.5309 | + | 12.7369i | −0.685512 | + | 0.498053i | ||||
\(655\) | −7.15933 | − | 22.0342i | −0.279738 | − | 0.860946i | ||||
\(656\) | 7.75758 | 0.302883 | ||||||||
\(657\) | 50.3370 | 1.96383 | ||||||||
\(658\) | −3.76679 | − | 11.5930i | −0.146845 | − | 0.451942i | ||||
\(659\) | 9.22225 | − | 28.3832i | 0.359248 | − | 1.10565i | −0.594258 | − | 0.804275i | \(-0.702554\pi\) |
0.953505 | − | 0.301376i | \(-0.0974460\pi\) | |||||||
\(660\) | −5.46345 | + | 16.8148i | −0.212665 | + | 0.654514i | ||||
\(661\) | −33.3584 | − | 24.2363i | −1.29749 | − | 0.942684i | −0.297565 | − | 0.954701i | \(-0.596175\pi\) |
−0.999928 | + | 0.0120174i | \(0.996175\pi\) | |||||||
\(662\) | 8.65382 | + | 26.6337i | 0.336340 | + | 1.03515i | ||||
\(663\) | 4.58872 | + | 3.33390i | 0.178211 | + | 0.129478i | ||||
\(664\) | 9.91519 | − | 7.20381i | 0.384784 | − | 0.279562i | ||||
\(665\) | −1.05167 | + | 3.23671i | −0.0407821 | + | 0.125514i | ||||
\(666\) | −30.5654 | + | 22.2071i | −1.18439 | + | 0.860507i | ||||
\(667\) | −21.3258 | + | 15.4941i | −0.825740 | + | 0.599935i | ||||
\(668\) | 7.12950 | − | 21.9424i | 0.275849 | − | 0.848975i | ||||
\(669\) | 8.77148 | − | 6.37285i | 0.339125 | − | 0.246389i | ||||
\(670\) | −23.9925 | − | 17.4316i | −0.926911 | − | 0.673441i | ||||
\(671\) | 5.11215 | + | 15.7336i | 0.197352 | + | 0.607388i | ||||
\(672\) | −6.25268 | − | 4.54284i | −0.241202 | − | 0.175244i | ||||
\(673\) | −12.5044 | + | 38.4845i | −0.482008 | + | 1.48347i | 0.354260 | + | 0.935147i | \(0.384733\pi\) |
−0.836268 | + | 0.548321i | \(0.815267\pi\) | |||||||
\(674\) | 9.18116 | − | 28.2567i | 0.353645 | − | 1.08841i | ||||
\(675\) | 20.0800 | + | 61.8000i | 0.772881 | + | 2.37868i | ||||
\(676\) | −7.52589 | −0.289457 | ||||||||
\(677\) | 43.9447 | 1.68893 | 0.844466 | − | 0.535609i | \(-0.179918\pi\) | ||||
0.844466 | + | 0.535609i | \(0.179918\pi\) | |||||||
\(678\) | 5.14855 | + | 15.8456i | 0.197729 | + | 0.608547i | ||||
\(679\) | 38.2766 | − | 27.8096i | 1.46892 | − | 1.06723i | ||||
\(680\) | −2.13918 | − | 1.55420i | −0.0820337 | − | 0.0596009i | ||||
\(681\) | 1.72165 | 0.0659737 | ||||||||
\(682\) | 6.17216 | + | 7.33421i | 0.236344 | + | 0.280841i | ||||
\(683\) | −4.87945 | −0.186707 | −0.0933535 | − | 0.995633i | \(-0.529759\pi\) | ||||
−0.0933535 | + | 0.995633i | \(0.529759\pi\) | |||||||
\(684\) | −2.09530 | − | 1.52232i | −0.0801156 | − | 0.0582074i | ||||
\(685\) | −9.61744 | + | 6.98748i | −0.367463 | + | 0.266978i | ||||
\(686\) | −5.95879 | − | 18.3393i | −0.227507 | − | 0.700196i | ||||
\(687\) | 15.2475 | 0.581730 | ||||||||
\(688\) | 7.64688 | 0.291534 | ||||||||
\(689\) | −1.90114 | − | 5.85109i | −0.0724275 | − | 0.222909i | ||||
\(690\) | 16.0840 | − | 49.5016i | 0.612309 | − | 1.88449i | ||||
\(691\) | 11.0165 | − | 33.9054i | 0.419088 | − | 1.28982i | −0.489455 | − | 0.872029i | \(-0.662804\pi\) |
0.908543 | − | 0.417792i | \(-0.137196\pi\) | |||||||
\(692\) | 16.3838 | + | 11.9035i | 0.622818 | + | 0.452504i | ||||
\(693\) | 8.59666 | + | 26.4578i | 0.326560 | + | 1.00505i | ||||
\(694\) | 7.94487 | + | 5.77228i | 0.301583 | + | 0.219113i | ||||
\(695\) | −6.68168 | + | 4.85452i | −0.253451 | + | 0.184143i | ||||
\(696\) | −4.93143 | + | 15.1774i | −0.186925 | + | 0.575297i | ||||
\(697\) | 4.95846 | − | 3.60253i | 0.187815 | − | 0.136456i | ||||
\(698\) | −0.830159 | + | 0.603146i | −0.0314220 | + | 0.0228294i | ||||
\(699\) | −9.00830 | + | 27.7247i | −0.340725 | + | 1.04864i | ||||
\(700\) | −12.6358 | + | 9.18048i | −0.477590 | + | 0.346990i | ||||
\(701\) | 16.4492 | + | 11.9511i | 0.621279 | + | 0.451386i | 0.853368 | − | 0.521309i | \(-0.174556\pi\) |
−0.232089 | + | 0.972695i | \(0.574556\pi\) | |||||||
\(702\) | 7.57649 | + | 23.3180i | 0.285956 | + | 0.880083i | ||||
\(703\) | −1.92353 | − | 1.39753i | −0.0725474 | − | 0.0527087i | ||||
\(704\) | 0.532018 | − | 1.63738i | 0.0200512 | − | 0.0617112i | ||||
\(705\) | 15.3574 | − | 47.2652i | 0.578393 | − | 1.78011i | ||||
\(706\) | 6.49313 | + | 19.9838i | 0.244372 | + | 0.752100i | ||||
\(707\) | −23.8165 | −0.895713 | ||||||||
\(708\) | −13.3961 | −0.503458 | ||||||||
\(709\) | −2.96678 | − | 9.13080i | −0.111420 | − | 0.342914i | 0.879764 | − | 0.475411i | \(-0.157701\pi\) |
−0.991183 | + | 0.132497i | \(0.957701\pi\) | |||||||
\(710\) | −32.2052 | + | 23.3985i | −1.20864 | + | 0.878129i | ||||
\(711\) | 10.8723 | + | 7.89917i | 0.407742 | + | 0.296242i | ||||
\(712\) | 14.6442 | 0.548813 | ||||||||
\(713\) | −18.1704 | − | 21.5914i | −0.680488 | − | 0.808606i | ||||
\(714\) | −6.10621 | −0.228519 | ||||||||
\(715\) | 10.9065 | + | 7.92402i | 0.407879 | + | 0.296342i | ||||
\(716\) | 6.42033 | − | 4.66464i | 0.239939 | − | 0.174326i | ||||
\(717\) | −11.7210 | − | 36.0736i | −0.437730 | − | 1.34719i | ||||
\(718\) | −30.4196 | −1.13525 | ||||||||
\(719\) | −36.7351 | −1.36999 | −0.684994 | − | 0.728549i | \(-0.740195\pi\) | ||||
−0.684994 | + | 0.728549i | \(0.740195\pi\) | |||||||
\(720\) | −6.63465 | − | 20.4193i | −0.247259 | − | 0.760984i | ||||
\(721\) | −1.01746 | + | 3.13141i | −0.0378921 | + | 0.116620i | ||||
\(722\) | −5.82096 | + | 17.9151i | −0.216634 | + | 0.666730i | ||||
\(723\) | −49.4448 | − | 35.9238i | −1.83887 | − | 1.33602i | ||||
\(724\) | −7.50438 | − | 23.0961i | −0.278898 | − | 0.858360i | ||||
\(725\) | 26.0908 | + | 18.9560i | 0.968986 | + | 0.704010i | ||||
\(726\) | 19.9484 | − | 14.4934i | 0.740355 | − | 0.537899i | ||||
\(727\) | 5.13927 | − | 15.8170i | 0.190605 | − | 0.586622i | −0.809395 | − | 0.587265i | \(-0.800205\pi\) |
1.00000 | 0.000643148i | \(0.000204720\pi\) | ||||||||
\(728\) | −4.76769 | + | 3.46393i | −0.176702 | + | 0.128382i | ||||
\(729\) | 11.0429 | − | 8.02313i | 0.408996 | − | 0.297153i | ||||
\(730\) | −8.11495 | + | 24.9752i | −0.300348 | + | 0.924375i | ||||
\(731\) | 4.88770 | − | 3.55112i | 0.180778 | − | 0.131343i | ||||
\(732\) | −23.8533 | − | 17.3305i | −0.881645 | − | 0.640552i | ||||
\(733\) | 1.09540 | + | 3.37129i | 0.0404594 | + | 0.124521i | 0.969246 | − | 0.246093i | \(-0.0791470\pi\) |
−0.928787 | + | 0.370615i | \(0.879147\pi\) | |||||||
\(734\) | −20.8770 | − | 15.1681i | −0.770585 | − | 0.559863i | ||||
\(735\) | 2.08059 | − | 6.40340i | 0.0767437 | − | 0.236193i | ||||
\(736\) | −1.56623 | + | 4.82035i | −0.0577319 | + | 0.177681i | ||||
\(737\) | −4.71432 | − | 14.5092i | −0.173654 | − | 0.534452i | ||||
\(738\) | 49.7663 | 1.83192 | ||||||||
\(739\) | 9.42152 | 0.346576 | 0.173288 | − | 0.984871i | \(-0.444561\pi\) | ||||
0.173288 | + | 0.984871i | \(0.444561\pi\) | |||||||
\(740\) | −6.09076 | − | 18.7454i | −0.223901 | − | 0.689096i | ||||
\(741\) | −2.34481 | + | 1.70360i | −0.0861386 | + | 0.0625834i | ||||
\(742\) | 5.35828 | + | 3.89302i | 0.196709 | + | 0.142917i | ||||
\(743\) | 0.492369 | 0.0180633 | 0.00903163 | − | 0.999959i | \(-0.497125\pi\) | ||||
0.00903163 | + | 0.999959i | \(0.497125\pi\) | |||||||
\(744\) | −16.5827 | − | 4.10917i | −0.607951 | − | 0.150649i | ||||
\(745\) | 47.6201 | 1.74467 | ||||||||
\(746\) | −10.1003 | − | 7.33829i | −0.369798 | − | 0.268674i | ||||
\(747\) | 63.6078 | − | 46.2138i | 2.32729 | − | 1.69087i | ||||
\(748\) | −0.420329 | − | 1.29364i | −0.0153688 | − | 0.0473002i | ||||
\(749\) | 37.8128 | 1.38165 | ||||||||
\(750\) | −12.3321 | −0.450305 | ||||||||
\(751\) | 12.6383 | + | 38.8968i | 0.461179 | + | 1.41936i | 0.863725 | + | 0.503964i | \(0.168125\pi\) |
−0.402546 | + | 0.915400i | \(0.631875\pi\) | |||||||
\(752\) | −1.49547 | + | 4.60258i | −0.0545341 | + | 0.167839i | ||||
\(753\) | −23.3405 | + | 71.8347i | −0.850575 | + | 2.61780i | ||||
\(754\) | 9.84443 | + | 7.15240i | 0.358513 | + | 0.260475i | ||||
\(755\) | 4.89783 | + | 15.0740i | 0.178250 | + | 0.548598i | ||||
\(756\) | −21.3541 | − | 15.5146i | −0.776640 | − | 0.564262i | ||||
\(757\) | 11.8157 | − | 8.58462i | 0.429449 | − | 0.312013i | −0.351979 | − | 0.936008i | \(-0.614491\pi\) |
0.781429 | + | 0.623995i | \(0.214491\pi\) | |||||||
\(758\) | 0.582244 | − | 1.79196i | 0.0211481 | − | 0.0650870i | ||||
\(759\) | 21.6615 | − | 15.7380i | 0.786263 | − | 0.571254i | ||||
\(760\) | 1.09310 | − | 0.794187i | 0.0396511 | − | 0.0288082i | ||||
\(761\) | 16.6393 | − | 51.2106i | 0.603175 | − | 1.85638i | 0.0942985 | − | 0.995544i | \(-0.469939\pi\) |
0.508877 | − | 0.860839i | \(-0.330061\pi\) | |||||||
\(762\) | −10.3743 | + | 7.53734i | −0.375820 | + | 0.273049i | ||||
\(763\) | −14.3907 | − | 10.4555i | −0.520980 | − | 0.378514i | ||||
\(764\) | 3.52016 | + | 10.8339i | 0.127355 | + | 0.391958i | ||||
\(765\) | −13.7232 | − | 9.97050i | −0.496164 | − | 0.360484i | ||||
\(766\) | 4.02861 | − | 12.3988i | 0.145560 | − | 0.447986i | ||||
\(767\) | −3.15649 | + | 9.71468i | −0.113974 | + | 0.350777i | ||||
\(768\) | 0.948193 | + | 2.91824i | 0.0342150 | + | 0.105303i | ||||
\(769\) | 41.8213 | 1.50811 | 0.754057 | − | 0.656809i | \(-0.228094\pi\) | ||||
0.754057 | + | 0.656809i | \(0.228094\pi\) | |||||||
\(770\) | −14.5132 | −0.523021 | ||||||||
\(771\) | 19.4405 | + | 59.8316i | 0.700132 | + | 2.15478i | ||||
\(772\) | 8.20759 | − | 5.96317i | 0.295398 | − | 0.214619i | ||||
\(773\) | −15.9544 | − | 11.5915i | −0.573839 | − | 0.416919i | 0.262658 | − | 0.964889i | \(-0.415401\pi\) |
−0.836498 | + | 0.547970i | \(0.815401\pi\) | |||||||
\(774\) | 49.0561 | 1.76329 | ||||||||
\(775\) | −18.2533 | + | 29.3052i | −0.655677 | + | 1.05267i | ||||
\(776\) | −18.7837 | −0.674296 | ||||||||
\(777\) | −36.8239 | − | 26.7541i | −1.32105 | − | 0.959799i | ||||
\(778\) | −8.35053 | + | 6.06702i | −0.299381 | + | 0.217513i | ||||
\(779\) | 0.967802 | + | 2.97859i | 0.0346751 | + | 0.106719i | ||||
\(780\) | −24.0269 | −0.860300 | ||||||||
\(781\) | −20.4780 | −0.732760 | ||||||||
\(782\) | 1.23742 | + | 3.80839i | 0.0442501 | + | 0.136188i | ||||
\(783\) | −16.8418 | + | 51.8336i | −0.601876 | + | 1.85238i | ||||
\(784\) | −0.202603 | + | 0.623548i | −0.00723583 | + | 0.0222696i | ||||
\(785\) | −49.7337 | − | 36.1336i | −1.77507 | − | 1.28967i | ||||
\(786\) | 6.56389 | + | 20.2016i | 0.234126 | + | 0.720566i | ||||
\(787\) | −3.06647 | − | 2.22792i | −0.109308 | − | 0.0794168i | 0.531789 | − | 0.846877i | \(-0.321520\pi\) |
−0.641096 | + | 0.767460i | \(0.721520\pi\) | |||||||
\(788\) | 1.89380 | − | 1.37593i | 0.0674640 | − | 0.0490154i | ||||
\(789\) | 4.80728 | − | 14.7953i | 0.171144 | − | 0.526726i | ||||
\(790\) | −5.67201 | + | 4.12095i | −0.201801 | + | 0.146617i | ||||
\(791\) | −11.0647 | + | 8.03897i | −0.393415 | + | 0.285833i | ||||
\(792\) | 3.41300 | − | 10.5041i | 0.121276 | − | 0.373248i | ||||
\(793\) | −18.1883 | + | 13.2145i | −0.645884 | + | 0.469262i | ||||
\(794\) | −12.0223 | − | 8.73475i | −0.426657 | − | 0.309985i | ||||
\(795\) | 8.34443 | + | 25.6815i | 0.295946 | + | 0.910829i | ||||
\(796\) | 9.63624 | + | 7.00114i | 0.341548 | + | 0.248149i | ||||
\(797\) | 3.83584 | − | 11.8055i | 0.135872 | − | 0.418172i | −0.859852 | − | 0.510543i | \(-0.829444\pi\) |
0.995725 | + | 0.0923708i | \(0.0294445\pi\) | |||||||
\(798\) | 0.964204 | − | 2.96752i | 0.0341325 | − | 0.105049i | ||||
\(799\) | 1.18152 | + | 3.63634i | 0.0417991 | + | 0.128644i | ||||
\(800\) | 6.20087 | 0.219234 | ||||||||
\(801\) | 93.9451 | 3.31939 | ||||||||
\(802\) | 3.77616 | + | 11.6218i | 0.133341 | + | 0.410381i | ||||
\(803\) | −10.9290 | + | 7.94036i | −0.385675 | + | 0.280209i | ||||
\(804\) | 21.9970 | + | 15.9818i | 0.775776 | + | 0.563634i | ||||
\(805\) | 42.7260 | 1.50589 | ||||||||
\(806\) | −6.88723 | + | 11.0573i | −0.242592 | + | 0.389476i | ||||
\(807\) | −16.2546 | −0.572190 | ||||||||
\(808\) | 7.64966 | + | 5.55780i | 0.269114 | + | 0.195523i | ||||
\(809\) | 18.7740 | − | 13.6401i | 0.660059 | − | 0.479561i | −0.206624 | − | 0.978420i | \(-0.566248\pi\) |
0.866683 | + | 0.498859i | \(0.166248\pi\) | |||||||
\(810\) | −13.3507 | − | 41.0892i | −0.469095 | − | 1.44373i | ||||
\(811\) | 39.4836 | 1.38646 | 0.693228 | − | 0.720718i | \(-0.256188\pi\) | ||||
0.693228 | + | 0.720718i | \(0.256188\pi\) | |||||||
\(812\) | −13.1000 | −0.459719 | ||||||||
\(813\) | −7.40940 | − | 22.8038i | −0.259859 | − | 0.799763i | ||||
\(814\) | 3.13321 | − | 9.64304i | 0.109819 | − | 0.337988i | ||||
\(815\) | 13.1111 | − | 40.3517i | 0.459261 | − | 1.41346i | ||||
\(816\) | 1.96126 | + | 1.42494i | 0.0686578 | + | 0.0498828i | ||||
\(817\) | 0.953992 | + | 2.93608i | 0.0333759 | + | 0.102721i | ||||
\(818\) | −12.1077 | − | 8.79679i | −0.423337 | − | 0.307573i | ||||
\(819\) | −30.5857 | + | 22.2218i | −1.06875 | + | 0.776492i | ||||
\(820\) | −8.02296 | + | 24.6921i | −0.280174 | + | 0.862286i | ||||
\(821\) | 14.5456 | − | 10.5680i | 0.507644 | − | 0.368825i | −0.304285 | − | 0.952581i | \(-0.598418\pi\) |
0.811929 | + | 0.583756i | \(0.198418\pi\) | |||||||
\(822\) | 8.81755 | − | 6.40633i | 0.307547 | − | 0.223446i | ||||
\(823\) | 1.14856 | − | 3.53490i | 0.0400362 | − | 0.123219i | −0.929041 | − | 0.369977i | \(-0.879365\pi\) |
0.969077 | + | 0.246759i | \(0.0793654\pi\) | |||||||
\(824\) | 1.05754 | − | 0.768349i | 0.0368412 | − | 0.0267667i | ||||
\(825\) | −26.5014 | − | 19.2544i | −0.922661 | − | 0.670353i | ||||
\(826\) | −3.39814 | − | 10.4584i | −0.118237 | − | 0.363895i | ||||
\(827\) | −31.4516 | − | 22.8509i | −1.09368 | − | 0.794605i | −0.113663 | − | 0.993519i | \(-0.536259\pi\) |
−0.980017 | + | 0.198914i | \(0.936259\pi\) | |||||||
\(828\) | −10.0476 | + | 30.9235i | −0.349180 | + | 1.07466i | ||||
\(829\) | 6.49478 | − | 19.9889i | 0.225573 | − | 0.694243i | −0.772660 | − | 0.634820i | \(-0.781074\pi\) |
0.998233 | − | 0.0594223i | \(-0.0189259\pi\) | |||||||
\(830\) | 12.6751 | + | 39.0100i | 0.439959 | + | 1.35406i | ||||
\(831\) | −3.16148 | −0.109671 | ||||||||
\(832\) | 2.33968 | 0.0811139 | ||||||||
\(833\) | 0.160070 | + | 0.492644i | 0.00554609 | + | 0.0170691i | ||||
\(834\) | 6.12596 | − | 4.45077i | 0.212125 | − | 0.154118i | ||||
\(835\) | 62.4684 | + | 45.3860i | 2.16181 | + | 1.57065i | ||||
\(836\) | 0.695060 | 0.0240392 | ||||||||
\(837\) | −56.6330 | − | 14.0336i | −1.95752 | − | 0.485072i | ||||
\(838\) | 15.2903 | 0.528193 | ||||||||
\(839\) | −16.9514 | − | 12.3159i | −0.585227 | − | 0.425192i | 0.255378 | − | 0.966841i | \(-0.417800\pi\) |
−0.840605 | + | 0.541649i | \(0.817800\pi\) | |||||||
\(840\) | 20.9263 | − | 15.2038i | 0.722025 | − | 0.524582i | ||||
\(841\) | −0.602869 | − | 1.85544i | −0.0207886 | − | 0.0639807i | ||||
\(842\) | 21.4454 | 0.739057 | ||||||||
\(843\) | 21.6708 | 0.746380 | ||||||||
\(844\) | 6.33786 | + | 19.5059i | 0.218158 | + | 0.671422i | ||||
\(845\) | 7.78334 | − | 23.9547i | 0.267755 | − | 0.824066i | ||||
\(846\) | −9.59371 | + | 29.5264i | −0.329839 | + | 1.01514i | ||||
\(847\) | 16.3752 | + | 11.8973i | 0.562660 | + | 0.408796i | ||||
\(848\) | −0.812562 | − | 2.50081i | −0.0279035 | − | 0.0858781i | ||||
\(849\) | −53.8247 | − | 39.1059i | −1.84726 | − | 1.34211i | ||||
\(850\) | 3.96345 | − | 2.87962i | 0.135945 | − | 0.0987700i | ||||
\(851\) | −9.22398 | + | 28.3885i | −0.316194 | + | 0.973145i | ||||
\(852\) | 29.5267 | − | 21.4524i | 1.01157 | − | 0.734948i | ||||
\(853\) | −43.0571 | + | 31.2828i | −1.47425 | + | 1.07110i | −0.494894 | + | 0.868954i | \(0.664793\pi\) |
−0.979355 | + | 0.202150i | \(0.935207\pi\) | |||||||
\(854\) | 7.47917 | − | 23.0185i | 0.255932 | − | 0.787677i | ||||
\(855\) | 7.01247 | − | 5.09486i | 0.239821 | − | 0.174241i | ||||
\(856\) | −12.1451 | − | 8.82395i | −0.415112 | − | 0.301596i | ||||
\(857\) | −4.36225 | − | 13.4256i | −0.149012 | − | 0.458611i | 0.848493 | − | 0.529206i | \(-0.177510\pi\) |
−0.997505 | + | 0.0705951i | \(0.977510\pi\) | |||||||
\(858\) | −9.99938 | − | 7.26498i | −0.341373 | − | 0.248022i | ||||
\(859\) | −6.54750 | + | 20.1511i | −0.223398 | + | 0.687548i | 0.775052 | + | 0.631897i | \(0.217723\pi\) |
−0.998450 | + | 0.0556511i | \(0.982277\pi\) | |||||||
\(860\) | −7.90847 | + | 24.3398i | −0.269676 | + | 0.829979i | ||||
\(861\) | 18.5275 | + | 57.0218i | 0.631416 | + | 1.94330i | ||||
\(862\) | 8.95255 | 0.304925 | ||||||||
\(863\) | 3.42261 | 0.116507 | 0.0582535 | − | 0.998302i | \(-0.481447\pi\) | ||||
0.0582535 | + | 0.998302i | \(0.481447\pi\) | |||||||
\(864\) | 3.23826 | + | 9.96634i | 0.110168 | + | 0.339062i | ||||
\(865\) | −54.8327 | + | 39.8383i | −1.86437 | + | 1.35454i | ||||
\(866\) | −4.19159 | − | 3.04537i | −0.142436 | − | 0.103486i | ||||
\(867\) | −50.2478 | −1.70650 | ||||||||
\(868\) | −0.998419 | − | 13.9885i | −0.0338886 | − | 0.474801i | ||||
\(869\) | −3.60659 | −0.122345 | ||||||||
\(870\) | −43.2090 | − | 31.3932i | −1.46492 | − | 1.06433i | ||||
\(871\) | 16.7728 | − | 12.1862i | 0.568326 | − | 0.412913i | ||||
\(872\) | 2.18230 | + | 6.71642i | 0.0739019 | + | 0.227447i | ||||
\(873\) | −120.501 | −4.07834 | ||||||||
\(874\) | −2.04621 | −0.0692141 | ||||||||
\(875\) | −3.12823 | − | 9.62771i | −0.105754 | − | 0.325476i | ||||
\(876\) | 7.44003 | − | 22.8980i | 0.251375 | − | 0.773653i | ||||
\(877\) | −15.1673 | + | 46.6803i | −0.512165 | + | 1.57628i | 0.276218 | + | 0.961095i | \(0.410919\pi\) |
−0.788382 | + | 0.615186i | \(0.789081\pi\) | |||||||
\(878\) | 1.83493 | + | 1.33316i | 0.0619260 | + | 0.0449919i | ||||
\(879\) | −8.51655 | − | 26.2113i | −0.287256 | − | 0.884084i | ||||
\(880\) | 4.66152 | + | 3.38679i | 0.157140 | + | 0.114169i | ||||
\(881\) | −21.4239 | + | 15.5654i | −0.721789 | + | 0.524411i | −0.886955 | − | 0.461855i | \(-0.847184\pi\) |
0.165166 | + | 0.986266i | \(0.447184\pi\) | |||||||
\(882\) | −1.29974 | + | 4.00018i | −0.0437644 | + | 0.134693i | ||||
\(883\) | −13.4921 | + | 9.80261i | −0.454047 | + | 0.329884i | −0.791191 | − | 0.611569i | \(-0.790539\pi\) |
0.337145 | + | 0.941453i | \(0.390539\pi\) | |||||||
\(884\) | 1.49547 | − | 1.08652i | 0.0502981 | − | 0.0365437i | ||||
\(885\) | 13.8544 | − | 42.6395i | 0.465711 | − | 1.43331i | ||||
\(886\) | 17.8944 | − | 13.0011i | 0.601175 | − | 0.436779i | ||||
\(887\) | −13.8834 | − | 10.0869i | −0.466160 | − | 0.338685i | 0.329783 | − | 0.944057i | \(-0.393024\pi\) |
−0.795943 | + | 0.605372i | \(0.793024\pi\) | |||||||
\(888\) | 5.58419 | + | 17.1864i | 0.187393 | + | 0.576737i | ||||
\(889\) | −8.51602 | − | 6.18725i | −0.285618 | − | 0.207514i | ||||
\(890\) | −15.1451 | + | 46.6119i | −0.507666 | + | 1.56243i | ||||
\(891\) | 6.86787 | − | 21.1371i | 0.230082 | − | 0.708120i | ||||
\(892\) | −1.09190 | − | 3.36052i | −0.0365595 | − | 0.112519i | ||||
\(893\) | −1.95377 | −0.0653804 | ||||||||
\(894\) | −43.6595 | −1.46019 | ||||||||
\(895\) | 8.20744 | + | 25.2599i | 0.274345 | + | 0.844346i | ||||
\(896\) | −2.03775 | + | 1.48051i | −0.0680766 | + | 0.0494605i | ||||
\(897\) | 29.4375 | + | 21.3876i | 0.982890 | + | 0.714112i | ||||
\(898\) | −16.6105 | −0.554298 | ||||||||
\(899\) | −26.8330 | + | 10.8862i | −0.894932 | + | 0.363076i | ||||
\(900\) | 39.7798 | 1.32599 | ||||||||
\(901\) | −1.68072 | − | 1.22111i | −0.0559928 | − | 0.0406811i | ||||
\(902\) | −10.8051 | + | 7.85035i | −0.359770 | + | 0.261388i | ||||
\(903\) | 18.2631 | + | 56.2081i | 0.607758 | + | 1.87049i | ||||
\(904\) | 5.42985 | 0.180594 | ||||||||
\(905\) | 81.2753 | 2.70168 | ||||||||
\(906\) | −4.49048 | − | 13.8203i | −0.149186 | − | 0.459148i | ||||
\(907\) | −11.5936 | + | 35.6815i | −0.384960 | + | 1.18479i | 0.551549 | + | 0.834143i | \(0.314037\pi\) |
−0.936509 | + | 0.350643i | \(0.885963\pi\) | |||||||
\(908\) | 0.173385 | − | 0.533625i | 0.00575399 | − | 0.0177090i | ||||
\(909\) | 49.0740 | + | 35.6544i | 1.62768 | + | 1.18258i | ||||
\(910\) | −6.09479 | − | 18.7578i | −0.202040 | − | 0.621817i | ||||
\(911\) | 21.1009 | + | 15.3307i | 0.699104 | + | 0.507929i | 0.879640 | − | 0.475640i | \(-0.157783\pi\) |
−0.180536 | + | 0.983568i | \(0.557783\pi\) | |||||||
\(912\) | −1.00219 | + | 0.728134i | −0.0331858 | + | 0.0241109i | ||||
\(913\) | −6.52033 | + | 20.0675i | −0.215792 | + | 0.664138i | ||||
\(914\) | 29.4312 | − | 21.3830i | 0.973497 | − | 0.707287i | ||||
\(915\) | 79.8316 | − | 58.0011i | 2.63915 | − | 1.91746i | ||||
\(916\) | 1.53556 | − | 4.72598i | 0.0507364 | − | 0.156151i | ||||
\(917\) | −14.1064 | + | 10.2489i | −0.465834 | + | 0.338448i | ||||
\(918\) | 6.69807 | + | 4.86643i | 0.221069 | + | 0.160616i | ||||
\(919\) | −15.6792 | − | 48.2557i | −0.517210 | − | 1.59181i | −0.779225 | − | 0.626744i | \(-0.784387\pi\) |
0.262016 | − | 0.965064i | \(-0.415613\pi\) | |||||||
\(920\) | −13.7232 | − | 9.97050i | −0.452441 | − | 0.328718i | ||||
\(921\) | −13.7880 | + | 42.4350i | −0.454328 | + | 1.39828i | ||||
\(922\) | 1.07920 | − | 3.32144i | 0.0355416 | − | 0.109386i | ||||
\(923\) | −8.59968 | − | 26.4671i | −0.283062 | − | 0.871175i | ||||
\(924\) | 13.3062 | 0.437741 | ||||||||
\(925\) | 36.5188 | 1.20073 | ||||||||
\(926\) | 1.87450 | + | 5.76912i | 0.0615999 | + | 0.189585i | ||||
\(927\) | 6.78433 | − | 4.92910i | 0.222827 | − | 0.161893i | ||||
\(928\) | 4.20759 | + | 3.05700i | 0.138121 | + | 0.100351i | ||||
\(929\) | −46.0097 | −1.50953 | −0.754764 | − | 0.655996i | \(-0.772249\pi\) | ||||
−0.754764 | + | 0.655996i | \(0.772249\pi\) | |||||||
\(930\) | 30.2293 | − | 48.5324i | 0.991258 | − | 1.59144i | ||||
\(931\) | −0.264693 | −0.00867495 | ||||||||
\(932\) | 7.68606 | + | 5.58425i | 0.251765 | + | 0.182918i | ||||
\(933\) | 26.4122 | − | 19.1896i | 0.864698 | − | 0.628240i | ||||
\(934\) | 0.947526 | + | 2.91619i | 0.0310040 | + | 0.0954205i | ||||
\(935\) | 4.55232 | 0.148877 | ||||||||
\(936\) | 15.0095 | 0.490601 | ||||||||
\(937\) | 11.1062 | + | 34.1815i | 0.362825 | + | 1.11666i | 0.951332 | + | 0.308168i | \(0.0997158\pi\) |
−0.588507 | + | 0.808492i | \(0.700284\pi\) | |||||||
\(938\) | −6.89713 | + | 21.2272i | −0.225199 | + | 0.693092i | ||||
\(939\) | 3.20260 | − | 9.85660i | 0.104513 | − | 0.321658i | ||||
\(940\) | −13.1032 | − | 9.52006i | −0.427380 | − | 0.310510i | ||||
\(941\) | 5.65993 | + | 17.4195i | 0.184509 | + | 0.567859i | 0.999940 | − | 0.0109954i | \(-0.00350002\pi\) |
−0.815431 | + | 0.578854i | \(0.803500\pi\) | |||||||
\(942\) | 45.5973 | + | 33.1284i | 1.48564 | + | 1.07938i | ||||
\(943\) | 31.8095 | − | 23.1109i | 1.03586 | − | 0.752595i | ||||
\(944\) | −1.34911 | + | 4.15214i | −0.0439098 | + | 0.135141i | ||||
\(945\) | 71.4672 | − | 51.9240i | 2.32483 | − | 1.68909i | ||||
\(946\) | −10.6509 | + | 7.73832i | −0.346290 | + | 0.251595i | ||||
\(947\) | −16.2732 | + | 50.0836i | −0.528807 | + | 1.62750i | 0.227857 | + | 0.973695i | \(0.426828\pi\) |
−0.756663 | + | 0.653805i | \(0.773172\pi\) | |||||||
\(948\) | 5.20026 | − | 3.77821i | 0.168897 | − | 0.122711i | ||||
\(949\) | −14.8522 | − | 10.7908i | −0.482124 | − | 0.350284i | ||||
\(950\) | 0.773594 | + | 2.38088i | 0.0250987 | + | 0.0772459i | ||||
\(951\) | −16.2284 | − | 11.7906i | −0.526241 | − | 0.382336i | ||||
\(952\) | −0.614949 | + | 1.89262i | −0.0199306 | + | 0.0613402i | ||||
\(953\) | 15.3296 | − | 47.1796i | 0.496574 | − | 1.52830i | −0.317915 | − | 0.948119i | \(-0.602983\pi\) |
0.814489 | − | 0.580178i | \(-0.197017\pi\) | |||||||
\(954\) | −5.21274 | − | 16.0431i | −0.168769 | − | 0.519416i | ||||
\(955\) | −38.1246 | −1.23368 | ||||||||
\(956\) | −12.3614 | −0.399797 | ||||||||
\(957\) | −8.49019 | − | 26.1301i | −0.274449 | − | 0.844667i | ||||
\(958\) | −4.25051 | + | 3.08818i | −0.137328 | + | 0.0997745i | ||||
\(959\) | 7.23815 | + | 5.25882i | 0.233732 | + | 0.169816i | ||||
\(960\) | −10.2693 | −0.331440 | ||||||||
\(961\) | −13.6697 | − | 27.8234i | −0.440958 | − | 0.897528i | ||||
\(962\) | 13.7791 | 0.444255 | ||||||||
\(963\) | −77.9133 | − | 56.6073i | −2.51072 | − | 1.82415i | ||||
\(964\) | −16.1141 | + | 11.7076i | −0.519001 | + | 0.377076i | ||||
\(965\) | 10.4922 | + | 32.2917i | 0.337756 | + | 1.03951i | ||||
\(966\) | −39.1725 | −1.26035 | ||||||||
\(967\) | 56.5038 | 1.81704 | 0.908520 | − | 0.417841i | \(-0.137213\pi\) | ||||
0.908520 | + | 0.417841i | \(0.137213\pi\) | |||||||
\(968\) | −2.48324 | − | 7.64262i | −0.0798143 | − | 0.245643i | ||||
\(969\) | −0.302439 | + | 0.930812i | −0.00971575 | + | 0.0299020i | ||||
\(970\) | 19.4263 | − | 59.7879i | 0.623740 | − | 1.91968i | ||||
\(971\) | 1.37242 | + | 0.997121i | 0.0440430 | + | 0.0319991i | 0.609589 | − | 0.792718i | \(-0.291335\pi\) |
−0.565546 | + | 0.824717i | \(0.691335\pi\) | |||||||
\(972\) | 2.52552 | + | 7.77276i | 0.0810062 | + | 0.249311i | ||||
\(973\) | 5.02868 | + | 3.65355i | 0.161212 | + | 0.117127i | ||||
\(974\) | 5.49742 | − | 3.99411i | 0.176149 | − | 0.127979i | ||||
\(975\) | 13.7565 | − | 42.3380i | 0.440559 | − | 1.35590i | ||||
\(976\) | −7.77382 | + | 5.64801i | −0.248834 | + | 0.180788i | ||||
\(977\) | 16.5809 | − | 12.0467i | 0.530470 | − | 0.385409i | −0.290064 | − | 0.957007i | \(-0.593677\pi\) |
0.820533 | + | 0.571599i | \(0.193677\pi\) | |||||||
\(978\) | −12.0206 | + | 36.9957i | −0.384377 | + | 1.18299i | ||||
\(979\) | −20.3970 | + | 14.8193i | −0.651891 | + | 0.473627i | ||||
\(980\) | −1.77520 | − | 1.28976i | −0.0567067 | − | 0.0411998i | ||||
\(981\) | 13.9999 | + | 43.0871i | 0.446981 | + | 1.37567i | ||||
\(982\) | −18.6890 | − | 13.5784i | −0.596390 | − | 0.433303i | ||||
\(983\) | 3.38925 | − | 10.4310i | 0.108100 | − | 0.332699i | −0.882345 | − | 0.470603i | \(-0.844037\pi\) |
0.990446 | + | 0.137904i | \(0.0440365\pi\) | |||||||
\(984\) | 7.35568 | − | 22.6385i | 0.234491 | − | 0.721688i | ||||
\(985\) | 2.42095 | + | 7.45091i | 0.0771378 | + | 0.237406i | ||||
\(986\) | 4.10903 | 0.130858 | ||||||||
\(987\) | −37.4027 | −1.19054 | ||||||||
\(988\) | 0.291889 | + | 0.898341i | 0.00928622 | + | 0.0285800i | ||||
\(989\) | 31.3555 | − | 22.7811i | 0.997048 | − | 0.724398i | ||||
\(990\) | 29.9045 | + | 21.7269i | 0.950429 | + | 0.690527i | ||||
\(991\) | −32.5863 | −1.03514 | −0.517569 | − | 0.855642i | \(-0.673163\pi\) | ||||
−0.517569 | + | 0.855642i | \(0.673163\pi\) | |||||||
\(992\) | −2.94366 | + | 4.72598i | −0.0934614 | + | 0.150050i | ||||
\(993\) | 85.9291 | 2.72688 | ||||||||
\(994\) | 24.2379 | + | 17.6099i | 0.768779 | + | 0.558551i | ||||
\(995\) | −32.2503 | + | 23.4312i | −1.02240 | + | 0.742819i | ||||
\(996\) | −11.6209 | − | 35.7655i | −0.368223 | − | 1.13327i | ||||
\(997\) | −33.2453 | −1.05289 | −0.526445 | − | 0.850209i | \(-0.676475\pi\) | ||||
−0.526445 | + | 0.850209i | \(0.676475\pi\) | |||||||
\(998\) | 25.1701 | 0.796744 | ||||||||
\(999\) | 19.0711 | + | 58.6947i | 0.603382 | + | 1.85702i |
(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 | 62.2.d.a.33.1 | ✓ | 8 | |
3.2 | odd | 2 | 558.2.i.i.343.2 | 8 | |||
4.3 | odd | 2 | 496.2.n.e.33.2 | 8 | |||
31.4 | even | 5 | 1922.2.a.r.1.4 | 4 | |||
31.16 | even | 5 | inner | 62.2.d.a.47.1 | yes | 8 | |
31.27 | odd | 10 | 1922.2.a.n.1.1 | 4 | |||
93.47 | odd | 10 | 558.2.i.i.109.2 | 8 | |||
124.47 | odd | 10 | 496.2.n.e.481.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
62.2.d.a.33.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
62.2.d.a.47.1 | yes | 8 | 31.16 | even | 5 | inner | |
496.2.n.e.33.2 | 8 | 4.3 | odd | 2 | |||
496.2.n.e.481.2 | 8 | 124.47 | odd | 10 | |||
558.2.i.i.109.2 | 8 | 93.47 | odd | 10 | |||
558.2.i.i.343.2 | 8 | 3.2 | odd | 2 | |||
1922.2.a.n.1.1 | 4 | 31.27 | odd | 10 | |||
1922.2.a.r.1.4 | 4 | 31.4 | even | 5 |