Properties

Label 819.2.et.c.514.5
Level $819$
Weight $2$
Character 819.514
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(136,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 514.5
Character \(\chi\) \(=\) 819.514
Dual form 819.2.et.c.145.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.111217 - 0.111217i) q^{2} -1.97526i q^{4} +(2.13060 + 0.570893i) q^{5} +(-0.399954 + 2.61535i) q^{7} +(-0.442117 + 0.442117i) q^{8} +O(q^{10})\) \(q+(-0.111217 - 0.111217i) q^{2} -1.97526i q^{4} +(2.13060 + 0.570893i) q^{5} +(-0.399954 + 2.61535i) q^{7} +(-0.442117 + 0.442117i) q^{8} +(-0.173466 - 0.300452i) q^{10} +(5.42348 + 1.45322i) q^{11} +(-1.34030 - 3.34718i) q^{13} +(0.335353 - 0.246390i) q^{14} -3.85218 q^{16} +3.59112 q^{17} +(1.24688 + 4.65341i) q^{19} +(1.12766 - 4.20850i) q^{20} +(-0.441561 - 0.764807i) q^{22} +4.45466i q^{23} +(-0.116582 - 0.0673085i) q^{25} +(-0.223198 + 0.521328i) q^{26} +(5.16599 + 0.790013i) q^{28} +(-1.02264 + 1.77127i) q^{29} +(0.643610 + 2.40198i) q^{31} +(1.31266 + 1.31266i) q^{32} +(-0.399394 - 0.399394i) q^{34} +(-2.34523 + 5.34393i) q^{35} +(7.22320 - 7.22320i) q^{37} +(0.378865 - 0.656213i) q^{38} +(-1.19438 + 0.689574i) q^{40} +(-1.34422 - 5.01671i) q^{41} +(4.12300 - 2.38042i) q^{43} +(2.87049 - 10.7128i) q^{44} +(0.495434 - 0.495434i) q^{46} +(1.22397 - 4.56791i) q^{47} +(-6.68007 - 2.09204i) q^{49} +(0.00548003 + 0.0204517i) q^{50} +(-6.61155 + 2.64745i) q^{52} +(-0.201475 + 0.348965i) q^{53} +(10.7257 + 6.19246i) q^{55} +(-0.979463 - 1.33312i) q^{56} +(0.310731 - 0.0832601i) q^{58} +(1.93268 + 1.93268i) q^{59} +(1.61092 + 0.930065i) q^{61} +(0.195561 - 0.338722i) q^{62} +7.41238i q^{64} +(-0.944776 - 7.89667i) q^{65} +(1.78441 - 6.65951i) q^{67} -7.09340i q^{68} +(0.855166 - 0.333507i) q^{70} +(3.63562 - 13.5683i) q^{71} +(-4.45744 + 1.19437i) q^{73} -1.60669 q^{74} +(9.19171 - 2.46291i) q^{76} +(-5.96981 + 13.6031i) q^{77} +(-2.45889 - 4.25893i) q^{79} +(-8.20746 - 2.19918i) q^{80} +(-0.408443 + 0.707445i) q^{82} +(-10.3390 + 10.3390i) q^{83} +(7.65124 + 2.05014i) q^{85} +(-0.723291 - 0.193805i) q^{86} +(-3.04031 + 1.75532i) q^{88} +(12.7764 + 12.7764i) q^{89} +(9.29008 - 2.16664i) q^{91} +8.79911 q^{92} +(-0.644155 + 0.371903i) q^{94} +10.6264i q^{95} +(-3.52628 - 0.944864i) q^{97} +(0.510268 + 0.975608i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.111217 0.111217i −0.0786424 0.0786424i 0.666691 0.745334i \(-0.267710\pi\)
−0.745334 + 0.666691i \(0.767710\pi\)
\(3\) 0 0
\(4\) 1.97526i 0.987631i
\(5\) 2.13060 + 0.570893i 0.952834 + 0.255311i 0.701564 0.712606i \(-0.252485\pi\)
0.251270 + 0.967917i \(0.419152\pi\)
\(6\) 0 0
\(7\) −0.399954 + 2.61535i −0.151168 + 0.988508i
\(8\) −0.442117 + 0.442117i −0.156312 + 0.156312i
\(9\) 0 0
\(10\) −0.173466 0.300452i −0.0548548 0.0950114i
\(11\) 5.42348 + 1.45322i 1.63524 + 0.438162i 0.955428 0.295223i \(-0.0953940\pi\)
0.679814 + 0.733385i \(0.262061\pi\)
\(12\) 0 0
\(13\) −1.34030 3.34718i −0.371734 0.928339i
\(14\) 0.335353 0.246390i 0.0896268 0.0658504i
\(15\) 0 0
\(16\) −3.85218 −0.963045
\(17\) 3.59112 0.870974 0.435487 0.900195i \(-0.356576\pi\)
0.435487 + 0.900195i \(0.356576\pi\)
\(18\) 0 0
\(19\) 1.24688 + 4.65341i 0.286053 + 1.06757i 0.948066 + 0.318073i \(0.103036\pi\)
−0.662013 + 0.749493i \(0.730298\pi\)
\(20\) 1.12766 4.20850i 0.252153 0.941048i
\(21\) 0 0
\(22\) −0.441561 0.764807i −0.0941412 0.163057i
\(23\) 4.45466i 0.928860i 0.885610 + 0.464430i \(0.153741\pi\)
−0.885610 + 0.464430i \(0.846259\pi\)
\(24\) 0 0
\(25\) −0.116582 0.0673085i −0.0233164 0.0134617i
\(26\) −0.223198 + 0.521328i −0.0437728 + 0.102241i
\(27\) 0 0
\(28\) 5.16599 + 0.790013i 0.976281 + 0.149298i
\(29\) −1.02264 + 1.77127i −0.189900 + 0.328917i −0.945217 0.326443i \(-0.894150\pi\)
0.755317 + 0.655360i \(0.227483\pi\)
\(30\) 0 0
\(31\) 0.643610 + 2.40198i 0.115596 + 0.431409i 0.999331 0.0365784i \(-0.0116459\pi\)
−0.883735 + 0.467988i \(0.844979\pi\)
\(32\) 1.31266 + 1.31266i 0.232048 + 0.232048i
\(33\) 0 0
\(34\) −0.399394 0.399394i −0.0684955 0.0684955i
\(35\) −2.34523 + 5.34393i −0.396415 + 0.903289i
\(36\) 0 0
\(37\) 7.22320 7.22320i 1.18749 1.18749i 0.209727 0.977760i \(-0.432743\pi\)
0.977760 0.209727i \(-0.0672574\pi\)
\(38\) 0.378865 0.656213i 0.0614600 0.106452i
\(39\) 0 0
\(40\) −1.19438 + 0.689574i −0.188848 + 0.109031i
\(41\) −1.34422 5.01671i −0.209932 0.783479i −0.987889 0.155161i \(-0.950410\pi\)
0.777957 0.628318i \(-0.216256\pi\)
\(42\) 0 0
\(43\) 4.12300 2.38042i 0.628752 0.363010i −0.151517 0.988455i \(-0.548416\pi\)
0.780268 + 0.625445i \(0.215082\pi\)
\(44\) 2.87049 10.7128i 0.432742 1.61502i
\(45\) 0 0
\(46\) 0.495434 0.495434i 0.0730477 0.0730477i
\(47\) 1.22397 4.56791i 0.178534 0.666298i −0.817389 0.576087i \(-0.804579\pi\)
0.995923 0.0902113i \(-0.0287542\pi\)
\(48\) 0 0
\(49\) −6.68007 2.09204i −0.954296 0.298862i
\(50\) 0.00548003 + 0.0204517i 0.000774993 + 0.00289231i
\(51\) 0 0
\(52\) −6.61155 + 2.64745i −0.916857 + 0.367136i
\(53\) −0.201475 + 0.348965i −0.0276747 + 0.0479340i −0.879531 0.475841i \(-0.842144\pi\)
0.851856 + 0.523776i \(0.175477\pi\)
\(54\) 0 0
\(55\) 10.7257 + 6.19246i 1.44625 + 0.834991i
\(56\) −0.979463 1.33312i −0.130886 0.178145i
\(57\) 0 0
\(58\) 0.310731 0.0832601i 0.0408010 0.0109326i
\(59\) 1.93268 + 1.93268i 0.251614 + 0.251614i 0.821632 0.570018i \(-0.193064\pi\)
−0.570018 + 0.821632i \(0.693064\pi\)
\(60\) 0 0
\(61\) 1.61092 + 0.930065i 0.206257 + 0.119083i 0.599571 0.800322i \(-0.295338\pi\)
−0.393314 + 0.919404i \(0.628671\pi\)
\(62\) 0.195561 0.338722i 0.0248363 0.0430178i
\(63\) 0 0
\(64\) 7.41238i 0.926548i
\(65\) −0.944776 7.89667i −0.117185 0.979461i
\(66\) 0 0
\(67\) 1.78441 6.65951i 0.218000 0.813589i −0.767088 0.641542i \(-0.778295\pi\)
0.985089 0.172047i \(-0.0550381\pi\)
\(68\) 7.09340i 0.860201i
\(69\) 0 0
\(70\) 0.855166 0.333507i 0.102212 0.0398617i
\(71\) 3.63562 13.5683i 0.431469 1.61026i −0.317909 0.948121i \(-0.602981\pi\)
0.749378 0.662142i \(-0.230353\pi\)
\(72\) 0 0
\(73\) −4.45744 + 1.19437i −0.521704 + 0.139790i −0.510055 0.860142i \(-0.670375\pi\)
−0.0116493 + 0.999932i \(0.503708\pi\)
\(74\) −1.60669 −0.186773
\(75\) 0 0
\(76\) 9.19171 2.46291i 1.05436 0.282515i
\(77\) −5.96981 + 13.6031i −0.680323 + 1.55021i
\(78\) 0 0
\(79\) −2.45889 4.25893i −0.276647 0.479167i 0.693902 0.720069i \(-0.255890\pi\)
−0.970549 + 0.240902i \(0.922557\pi\)
\(80\) −8.20746 2.19918i −0.917622 0.245876i
\(81\) 0 0
\(82\) −0.408443 + 0.707445i −0.0451050 + 0.0781242i
\(83\) −10.3390 + 10.3390i −1.13485 + 1.13485i −0.145496 + 0.989359i \(0.546478\pi\)
−0.989359 + 0.145496i \(0.953522\pi\)
\(84\) 0 0
\(85\) 7.65124 + 2.05014i 0.829894 + 0.222369i
\(86\) −0.723291 0.193805i −0.0779945 0.0208986i
\(87\) 0 0
\(88\) −3.04031 + 1.75532i −0.324098 + 0.187118i
\(89\) 12.7764 + 12.7764i 1.35430 + 1.35430i 0.880787 + 0.473513i \(0.157014\pi\)
0.473513 + 0.880787i \(0.342986\pi\)
\(90\) 0 0
\(91\) 9.29008 2.16664i 0.973865 0.227126i
\(92\) 8.79911 0.917371
\(93\) 0 0
\(94\) −0.644155 + 0.371903i −0.0664396 + 0.0383589i
\(95\) 10.6264i 1.09025i
\(96\) 0 0
\(97\) −3.52628 0.944864i −0.358040 0.0959365i 0.0753153 0.997160i \(-0.476004\pi\)
−0.433355 + 0.901223i \(0.642670\pi\)
\(98\) 0.510268 + 0.975608i 0.0515449 + 0.0985513i
\(99\) 0 0
\(100\) −0.132952 + 0.230280i −0.0132952 + 0.0230280i
\(101\) 4.85620 + 8.41119i 0.483210 + 0.836945i 0.999814 0.0192798i \(-0.00613733\pi\)
−0.516604 + 0.856225i \(0.672804\pi\)
\(102\) 0 0
\(103\) −3.12086 5.40548i −0.307507 0.532618i 0.670309 0.742082i \(-0.266161\pi\)
−0.977816 + 0.209464i \(0.932828\pi\)
\(104\) 2.07241 + 0.887272i 0.203217 + 0.0870042i
\(105\) 0 0
\(106\) 0.0612184 0.0164034i 0.00594605 0.00159324i
\(107\) 4.47949 0.433049 0.216525 0.976277i \(-0.430528\pi\)
0.216525 + 0.976277i \(0.430528\pi\)
\(108\) 0 0
\(109\) −13.4448 + 3.60252i −1.28778 + 0.345059i −0.836815 0.547485i \(-0.815585\pi\)
−0.450961 + 0.892544i \(0.648919\pi\)
\(110\) −0.504169 1.88158i −0.0480706 0.179402i
\(111\) 0 0
\(112\) 1.54069 10.0748i 0.145582 0.951978i
\(113\) −4.28714 7.42555i −0.403301 0.698537i 0.590821 0.806802i \(-0.298804\pi\)
−0.994122 + 0.108265i \(0.965470\pi\)
\(114\) 0 0
\(115\) −2.54313 + 9.49110i −0.237148 + 0.885049i
\(116\) 3.49872 + 2.01999i 0.324848 + 0.187551i
\(117\) 0 0
\(118\) 0.429895i 0.0395750i
\(119\) −1.43628 + 9.39202i −0.131664 + 0.860965i
\(120\) 0 0
\(121\) 17.7761 + 10.2630i 1.61601 + 0.933001i
\(122\) −0.0757227 0.282601i −0.00685561 0.0255855i
\(123\) 0 0
\(124\) 4.74455 1.27130i 0.426073 0.114166i
\(125\) −8.00851 8.00851i −0.716303 0.716303i
\(126\) 0 0
\(127\) −8.25421 4.76557i −0.732443 0.422876i 0.0868725 0.996219i \(-0.472313\pi\)
−0.819315 + 0.573344i \(0.805646\pi\)
\(128\) 3.44971 3.44971i 0.304914 0.304914i
\(129\) 0 0
\(130\) −0.773169 + 0.983320i −0.0678114 + 0.0862428i
\(131\) −3.05542 + 1.76405i −0.266954 + 0.154126i −0.627502 0.778615i \(-0.715923\pi\)
0.360549 + 0.932740i \(0.382589\pi\)
\(132\) 0 0
\(133\) −12.6690 + 1.39987i −1.09854 + 0.121384i
\(134\) −0.939108 + 0.542194i −0.0811266 + 0.0468385i
\(135\) 0 0
\(136\) −1.58769 + 1.58769i −0.136144 + 0.136144i
\(137\) −7.14511 + 7.14511i −0.610448 + 0.610448i −0.943063 0.332615i \(-0.892069\pi\)
0.332615 + 0.943063i \(0.392069\pi\)
\(138\) 0 0
\(139\) −9.05971 + 5.23063i −0.768435 + 0.443656i −0.832316 0.554302i \(-0.812985\pi\)
0.0638813 + 0.997958i \(0.479652\pi\)
\(140\) 10.5557 + 4.63243i 0.892116 + 0.391512i
\(141\) 0 0
\(142\) −1.91337 + 1.10469i −0.160567 + 0.0927032i
\(143\) −2.40494 20.1011i −0.201111 1.68094i
\(144\) 0 0
\(145\) −3.19005 + 3.19005i −0.264919 + 0.264919i
\(146\) 0.628578 + 0.362909i 0.0520214 + 0.0300346i
\(147\) 0 0
\(148\) −14.2677 14.2677i −1.17280 1.17280i
\(149\) −0.428100 + 0.114709i −0.0350713 + 0.00939732i −0.276312 0.961068i \(-0.589112\pi\)
0.241241 + 0.970465i \(0.422446\pi\)
\(150\) 0 0
\(151\) 2.55428 + 9.53270i 0.207864 + 0.775760i 0.988557 + 0.150845i \(0.0481996\pi\)
−0.780693 + 0.624915i \(0.785134\pi\)
\(152\) −2.60862 1.50609i −0.211587 0.122160i
\(153\) 0 0
\(154\) 2.17684 0.848949i 0.175415 0.0684102i
\(155\) 5.48511i 0.440574i
\(156\) 0 0
\(157\) −19.2252 11.0997i −1.53434 0.885852i −0.999154 0.0411178i \(-0.986908\pi\)
−0.535186 0.844734i \(-0.679759\pi\)
\(158\) −0.200195 + 0.747137i −0.0159266 + 0.0594390i
\(159\) 0 0
\(160\) 2.04737 + 3.54615i 0.161859 + 0.280348i
\(161\) −11.6505 1.78166i −0.918185 0.140414i
\(162\) 0 0
\(163\) −0.722700 2.69715i −0.0566062 0.211257i 0.931830 0.362895i \(-0.118212\pi\)
−0.988436 + 0.151638i \(0.951545\pi\)
\(164\) −9.90932 + 2.65519i −0.773788 + 0.207336i
\(165\) 0 0
\(166\) 2.29975 0.178495
\(167\) −2.34772 + 0.629070i −0.181672 + 0.0486789i −0.348508 0.937306i \(-0.613312\pi\)
0.166836 + 0.985985i \(0.446645\pi\)
\(168\) 0 0
\(169\) −9.40717 + 8.97247i −0.723628 + 0.690190i
\(170\) −0.622938 1.07896i −0.0477772 0.0827525i
\(171\) 0 0
\(172\) −4.70194 8.14400i −0.358520 0.620974i
\(173\) −5.37379 + 9.30768i −0.408562 + 0.707650i −0.994729 0.102540i \(-0.967303\pi\)
0.586167 + 0.810190i \(0.300636\pi\)
\(174\) 0 0
\(175\) 0.222662 0.277981i 0.0168317 0.0210134i
\(176\) −20.8922 5.59806i −1.57481 0.421970i
\(177\) 0 0
\(178\) 2.84192i 0.213011i
\(179\) −16.5020 + 9.52742i −1.23342 + 0.712113i −0.967740 0.251950i \(-0.918928\pi\)
−0.265675 + 0.964063i \(0.585595\pi\)
\(180\) 0 0
\(181\) −20.5472 −1.52726 −0.763632 0.645652i \(-0.776586\pi\)
−0.763632 + 0.645652i \(0.776586\pi\)
\(182\) −1.27418 0.792248i −0.0944488 0.0587253i
\(183\) 0 0
\(184\) −1.96948 1.96948i −0.145192 0.145192i
\(185\) 19.5134 11.2661i 1.43466 0.828299i
\(186\) 0 0
\(187\) 19.4764 + 5.21868i 1.42425 + 0.381628i
\(188\) −9.02281 2.41766i −0.658056 0.176326i
\(189\) 0 0
\(190\) 1.18184 1.18184i 0.0857395 0.0857395i
\(191\) 9.70429 16.8083i 0.702178 1.21621i −0.265522 0.964105i \(-0.585544\pi\)
0.967700 0.252103i \(-0.0811222\pi\)
\(192\) 0 0
\(193\) −17.4662 4.68005i −1.25724 0.336877i −0.432112 0.901820i \(-0.642232\pi\)
−0.825130 + 0.564943i \(0.808898\pi\)
\(194\) 0.287098 + 0.497268i 0.0206124 + 0.0357018i
\(195\) 0 0
\(196\) −4.13232 + 13.1949i −0.295165 + 0.942492i
\(197\) 12.0770 3.23603i 0.860453 0.230558i 0.198498 0.980101i \(-0.436394\pi\)
0.661955 + 0.749544i \(0.269727\pi\)
\(198\) 0 0
\(199\) 20.9422 1.48455 0.742276 0.670094i \(-0.233746\pi\)
0.742276 + 0.670094i \(0.233746\pi\)
\(200\) 0.0813010 0.0217845i 0.00574885 0.00154040i
\(201\) 0 0
\(202\) 0.395375 1.47556i 0.0278185 0.103820i
\(203\) −4.22348 3.38299i −0.296430 0.237440i
\(204\) 0 0
\(205\) 11.4560i 0.800123i
\(206\) −0.254089 + 0.948274i −0.0177032 + 0.0660694i
\(207\) 0 0
\(208\) 5.16310 + 12.8939i 0.357996 + 0.894033i
\(209\) 27.0497i 1.87107i
\(210\) 0 0
\(211\) 8.85575 15.3386i 0.609655 1.05595i −0.381642 0.924310i \(-0.624641\pi\)
0.991297 0.131643i \(-0.0420253\pi\)
\(212\) 0.689297 + 0.397966i 0.0473411 + 0.0273324i
\(213\) 0 0
\(214\) −0.498196 0.498196i −0.0340560 0.0340560i
\(215\) 10.1434 2.71792i 0.691776 0.185361i
\(216\) 0 0
\(217\) −6.53944 + 0.722580i −0.443926 + 0.0490519i
\(218\) 1.89595 + 1.09463i 0.128410 + 0.0741375i
\(219\) 0 0
\(220\) 12.2317 21.1860i 0.824663 1.42836i
\(221\) −4.81319 12.0201i −0.323770 0.808560i
\(222\) 0 0
\(223\) 3.51328 + 13.1117i 0.235267 + 0.878027i 0.978029 + 0.208471i \(0.0668487\pi\)
−0.742762 + 0.669556i \(0.766485\pi\)
\(224\) −3.95807 + 2.90806i −0.264460 + 0.194303i
\(225\) 0 0
\(226\) −0.349045 + 1.30265i −0.0232181 + 0.0866511i
\(227\) 5.69257 5.69257i 0.377829 0.377829i −0.492489 0.870319i \(-0.663913\pi\)
0.870319 + 0.492489i \(0.163913\pi\)
\(228\) 0 0
\(229\) 0.157795 0.588900i 0.0104274 0.0389156i −0.960516 0.278224i \(-0.910254\pi\)
0.970944 + 0.239309i \(0.0769208\pi\)
\(230\) 1.33841 0.772732i 0.0882523 0.0509525i
\(231\) 0 0
\(232\) −0.330981 1.23524i −0.0217299 0.0810973i
\(233\) −20.5734 + 11.8780i −1.34781 + 0.778157i −0.987939 0.154846i \(-0.950512\pi\)
−0.359868 + 0.933003i \(0.617178\pi\)
\(234\) 0 0
\(235\) 5.21557 9.03364i 0.340227 0.589290i
\(236\) 3.81755 3.81755i 0.248502 0.248502i
\(237\) 0 0
\(238\) 1.20429 0.884814i 0.0780627 0.0573540i
\(239\) −8.02410 8.02410i −0.519036 0.519036i 0.398244 0.917280i \(-0.369620\pi\)
−0.917280 + 0.398244i \(0.869620\pi\)
\(240\) 0 0
\(241\) 9.76834 + 9.76834i 0.629234 + 0.629234i 0.947875 0.318641i \(-0.103227\pi\)
−0.318641 + 0.947875i \(0.603227\pi\)
\(242\) −0.835579 3.11842i −0.0537131 0.200460i
\(243\) 0 0
\(244\) 1.83712 3.18199i 0.117610 0.203706i
\(245\) −13.0382 8.27090i −0.832983 0.528409i
\(246\) 0 0
\(247\) 13.9046 10.4105i 0.884728 0.662405i
\(248\) −1.34651 0.777407i −0.0855034 0.0493654i
\(249\) 0 0
\(250\) 1.78137i 0.112663i
\(251\) 10.1546 + 17.5882i 0.640950 + 1.11016i 0.985221 + 0.171287i \(0.0547927\pi\)
−0.344271 + 0.938870i \(0.611874\pi\)
\(252\) 0 0
\(253\) −6.47359 + 24.1598i −0.406991 + 1.51891i
\(254\) 0.387996 + 1.44802i 0.0243450 + 0.0908570i
\(255\) 0 0
\(256\) 14.0574 0.878589
\(257\) 24.6914 1.54021 0.770105 0.637917i \(-0.220204\pi\)
0.770105 + 0.637917i \(0.220204\pi\)
\(258\) 0 0
\(259\) 16.0022 + 21.7801i 0.994330 + 1.35335i
\(260\) −15.5980 + 1.86618i −0.967346 + 0.115736i
\(261\) 0 0
\(262\) 0.536008 + 0.143623i 0.0331147 + 0.00887305i
\(263\) −15.1818 26.2956i −0.936148 1.62146i −0.772573 0.634925i \(-0.781031\pi\)
−0.163575 0.986531i \(-0.552302\pi\)
\(264\) 0 0
\(265\) −0.628485 + 0.628485i −0.0386075 + 0.0386075i
\(266\) 1.56470 + 1.25332i 0.0959377 + 0.0768458i
\(267\) 0 0
\(268\) −13.1543 3.52468i −0.803525 0.215304i
\(269\) 5.95292i 0.362956i 0.983395 + 0.181478i \(0.0580882\pi\)
−0.983395 + 0.181478i \(0.941912\pi\)
\(270\) 0 0
\(271\) −9.55925 9.55925i −0.580683 0.580683i 0.354408 0.935091i \(-0.384683\pi\)
−0.935091 + 0.354408i \(0.884683\pi\)
\(272\) −13.8336 −0.838788
\(273\) 0 0
\(274\) 1.58932 0.0960141
\(275\) −0.534466 0.534466i −0.0322295 0.0322295i
\(276\) 0 0
\(277\) 11.5559i 0.694326i 0.937805 + 0.347163i \(0.112855\pi\)
−0.937805 + 0.347163i \(0.887145\pi\)
\(278\) 1.58933 + 0.425860i 0.0953216 + 0.0255414i
\(279\) 0 0
\(280\) −1.32578 3.39951i −0.0792304 0.203159i
\(281\) −22.1034 + 22.1034i −1.31858 + 1.31858i −0.403672 + 0.914904i \(0.632266\pi\)
−0.914904 + 0.403672i \(0.867734\pi\)
\(282\) 0 0
\(283\) 11.2897 + 19.5544i 0.671105 + 1.16239i 0.977591 + 0.210513i \(0.0675136\pi\)
−0.306486 + 0.951875i \(0.599153\pi\)
\(284\) −26.8010 7.18130i −1.59035 0.426132i
\(285\) 0 0
\(286\) −1.96812 + 2.50306i −0.116377 + 0.148009i
\(287\) 13.6581 1.50916i 0.806210 0.0890828i
\(288\) 0 0
\(289\) −4.10387 −0.241404
\(290\) 0.709577 0.0416678
\(291\) 0 0
\(292\) 2.35919 + 8.80461i 0.138061 + 0.515251i
\(293\) 0.143904 0.537058i 0.00840697 0.0313752i −0.961595 0.274473i \(-0.911497\pi\)
0.970002 + 0.243097i \(0.0781634\pi\)
\(294\) 0 0
\(295\) 3.01442 + 5.22113i 0.175506 + 0.303986i
\(296\) 6.38700i 0.371237i
\(297\) 0 0
\(298\) 0.0603696 + 0.0348544i 0.00349712 + 0.00201906i
\(299\) 14.9105 5.97059i 0.862297 0.345288i
\(300\) 0 0
\(301\) 4.57660 + 11.7351i 0.263791 + 0.676402i
\(302\) 0.776119 1.34428i 0.0446607 0.0773545i
\(303\) 0 0
\(304\) −4.80320 17.9258i −0.275482 1.02811i
\(305\) 2.90126 + 2.90126i 0.166126 + 0.166126i
\(306\) 0 0
\(307\) −5.01312 5.01312i −0.286114 0.286114i 0.549427 0.835541i \(-0.314846\pi\)
−0.835541 + 0.549427i \(0.814846\pi\)
\(308\) 26.8696 + 11.7919i 1.53104 + 0.671908i
\(309\) 0 0
\(310\) 0.610037 0.610037i 0.0346478 0.0346478i
\(311\) −0.404846 + 0.701214i −0.0229567 + 0.0397622i −0.877276 0.479987i \(-0.840641\pi\)
0.854319 + 0.519749i \(0.173975\pi\)
\(312\) 0 0
\(313\) 0.914764 0.528139i 0.0517055 0.0298522i −0.473924 0.880566i \(-0.657163\pi\)
0.525630 + 0.850713i \(0.323830\pi\)
\(314\) 0.903699 + 3.37265i 0.0509987 + 0.190330i
\(315\) 0 0
\(316\) −8.41250 + 4.85696i −0.473240 + 0.273225i
\(317\) 8.45663 31.5606i 0.474972 1.77262i −0.146531 0.989206i \(-0.546811\pi\)
0.621503 0.783412i \(-0.286522\pi\)
\(318\) 0 0
\(319\) −8.12033 + 8.12033i −0.454651 + 0.454651i
\(320\) −4.23168 + 15.7928i −0.236558 + 0.882846i
\(321\) 0 0
\(322\) 1.09758 + 1.49388i 0.0611658 + 0.0832508i
\(323\) 4.47769 + 16.7110i 0.249145 + 0.929822i
\(324\) 0 0
\(325\) −0.0690384 + 0.480434i −0.00382956 + 0.0266497i
\(326\) −0.219593 + 0.380346i −0.0121621 + 0.0210654i
\(327\) 0 0
\(328\) 2.81228 + 1.62367i 0.155282 + 0.0896521i
\(329\) 11.4571 + 5.02805i 0.631652 + 0.277205i
\(330\) 0 0
\(331\) −23.2335 + 6.22540i −1.27703 + 0.342179i −0.832720 0.553695i \(-0.813217\pi\)
−0.444309 + 0.895874i \(0.646551\pi\)
\(332\) 20.4223 + 20.4223i 1.12082 + 1.12082i
\(333\) 0 0
\(334\) 0.331070 + 0.191143i 0.0181153 + 0.0104589i
\(335\) 7.60374 13.1701i 0.415436 0.719557i
\(336\) 0 0
\(337\) 26.8501i 1.46262i −0.682046 0.731310i \(-0.738909\pi\)
0.682046 0.731310i \(-0.261091\pi\)
\(338\) 2.04413 + 0.0483460i 0.111186 + 0.00262968i
\(339\) 0 0
\(340\) 4.04957 15.1132i 0.219619 0.819629i
\(341\) 13.9624i 0.756108i
\(342\) 0 0
\(343\) 8.14312 16.6340i 0.439687 0.898151i
\(344\) −0.770426 + 2.87527i −0.0415386 + 0.155024i
\(345\) 0 0
\(346\) 1.63283 0.437516i 0.0877815 0.0235210i
\(347\) −23.0516 −1.23747 −0.618737 0.785598i \(-0.712355\pi\)
−0.618737 + 0.785598i \(0.712355\pi\)
\(348\) 0 0
\(349\) 5.97543 1.60111i 0.319858 0.0857056i −0.0953181 0.995447i \(-0.530387\pi\)
0.415176 + 0.909741i \(0.363720\pi\)
\(350\) −0.0556802 + 0.00615242i −0.00297623 + 0.000328861i
\(351\) 0 0
\(352\) 5.21162 + 9.02679i 0.277780 + 0.481129i
\(353\) −27.1270 7.26865i −1.44382 0.386871i −0.549952 0.835196i \(-0.685354\pi\)
−0.893871 + 0.448325i \(0.852021\pi\)
\(354\) 0 0
\(355\) 15.4921 26.8331i 0.822236 1.42416i
\(356\) 25.2368 25.2368i 1.33755 1.33755i
\(357\) 0 0
\(358\) 2.89491 + 0.775689i 0.153001 + 0.0409965i
\(359\) 7.64083 + 2.04735i 0.403268 + 0.108055i 0.454751 0.890619i \(-0.349728\pi\)
−0.0514834 + 0.998674i \(0.516395\pi\)
\(360\) 0 0
\(361\) −3.64506 + 2.10447i −0.191845 + 0.110762i
\(362\) 2.28520 + 2.28520i 0.120108 + 0.120108i
\(363\) 0 0
\(364\) −4.27969 18.3503i −0.224317 0.961819i
\(365\) −10.1789 −0.532787
\(366\) 0 0
\(367\) −7.92031 + 4.57279i −0.413437 + 0.238698i −0.692265 0.721643i \(-0.743387\pi\)
0.278829 + 0.960341i \(0.410054\pi\)
\(368\) 17.1601i 0.894534i
\(369\) 0 0
\(370\) −3.42321 0.917246i −0.177964 0.0476854i
\(371\) −0.832084 0.666497i −0.0431996 0.0346028i
\(372\) 0 0
\(373\) 16.4024 28.4099i 0.849286 1.47101i −0.0325601 0.999470i \(-0.510366\pi\)
0.881846 0.471537i \(-0.156301\pi\)
\(374\) −1.58570 2.74651i −0.0819946 0.142019i
\(375\) 0 0
\(376\) 1.47841 + 2.56069i 0.0762433 + 0.132057i
\(377\) 7.29941 + 1.04893i 0.375939 + 0.0540224i
\(378\) 0 0
\(379\) −16.9754 + 4.54854i −0.871967 + 0.233643i −0.666938 0.745113i \(-0.732395\pi\)
−0.205029 + 0.978756i \(0.565729\pi\)
\(380\) 20.9899 1.07676
\(381\) 0 0
\(382\) −2.94866 + 0.790090i −0.150866 + 0.0404245i
\(383\) 7.96025 + 29.7081i 0.406750 + 1.51801i 0.800806 + 0.598924i \(0.204405\pi\)
−0.394056 + 0.919087i \(0.628928\pi\)
\(384\) 0 0
\(385\) −20.4852 + 25.5746i −1.04402 + 1.30340i
\(386\) 1.42204 + 2.46304i 0.0723797 + 0.125365i
\(387\) 0 0
\(388\) −1.86635 + 6.96533i −0.0947498 + 0.353611i
\(389\) 13.1147 + 7.57176i 0.664940 + 0.383903i 0.794157 0.607713i \(-0.207913\pi\)
−0.129217 + 0.991616i \(0.541246\pi\)
\(390\) 0 0
\(391\) 15.9972i 0.809013i
\(392\) 3.87830 2.02845i 0.195884 0.102452i
\(393\) 0 0
\(394\) −1.70307 0.983270i −0.0857996 0.0495364i
\(395\) −2.80753 10.4778i −0.141262 0.527198i
\(396\) 0 0
\(397\) 7.79662 2.08910i 0.391301 0.104849i −0.0578036 0.998328i \(-0.518410\pi\)
0.449105 + 0.893479i \(0.351743\pi\)
\(398\) −2.32913 2.32913i −0.116749 0.116749i
\(399\) 0 0
\(400\) 0.449094 + 0.259285i 0.0224547 + 0.0129642i
\(401\) 12.1510 12.1510i 0.606791 0.606791i −0.335315 0.942106i \(-0.608843\pi\)
0.942106 + 0.335315i \(0.108843\pi\)
\(402\) 0 0
\(403\) 7.17723 5.37367i 0.357523 0.267681i
\(404\) 16.6143 9.59227i 0.826592 0.477233i
\(405\) 0 0
\(406\) 0.0934760 + 0.845969i 0.00463914 + 0.0419848i
\(407\) 49.6718 28.6780i 2.46214 1.42152i
\(408\) 0 0
\(409\) 21.6885 21.6885i 1.07243 1.07243i 0.0752633 0.997164i \(-0.476020\pi\)
0.997164 0.0752633i \(-0.0239797\pi\)
\(410\) −1.27411 + 1.27411i −0.0629236 + 0.0629236i
\(411\) 0 0
\(412\) −10.6772 + 6.16451i −0.526030 + 0.303703i
\(413\) −5.82762 + 4.28165i −0.286758 + 0.210686i
\(414\) 0 0
\(415\) −27.9308 + 16.1259i −1.37107 + 0.791587i
\(416\) 2.63434 6.15308i 0.129159 0.301679i
\(417\) 0 0
\(418\) 3.00839 3.00839i 0.147145 0.147145i
\(419\) 15.2013 + 8.77646i 0.742631 + 0.428758i 0.823025 0.568005i \(-0.192285\pi\)
−0.0803942 + 0.996763i \(0.525618\pi\)
\(420\) 0 0
\(421\) 15.5736 + 15.5736i 0.759010 + 0.759010i 0.976142 0.217132i \(-0.0696702\pi\)
−0.217132 + 0.976142i \(0.569670\pi\)
\(422\) −2.69083 + 0.721005i −0.130987 + 0.0350980i
\(423\) 0 0
\(424\) −0.0652078 0.243359i −0.00316677 0.0118186i
\(425\) −0.418659 0.241713i −0.0203079 0.0117248i
\(426\) 0 0
\(427\) −3.07674 + 3.84113i −0.148894 + 0.185885i
\(428\) 8.84817i 0.427693i
\(429\) 0 0
\(430\) −1.43040 0.825843i −0.0689801 0.0398257i
\(431\) −1.12224 + 4.18826i −0.0540564 + 0.201741i −0.987673 0.156533i \(-0.949968\pi\)
0.933616 + 0.358275i \(0.116635\pi\)
\(432\) 0 0
\(433\) −14.6114 25.3077i −0.702181 1.21621i −0.967699 0.252107i \(-0.918876\pi\)
0.265519 0.964106i \(-0.414457\pi\)
\(434\) 0.807660 + 0.646934i 0.0387689 + 0.0310538i
\(435\) 0 0
\(436\) 7.11591 + 26.5570i 0.340791 + 1.27185i
\(437\) −20.7293 + 5.55441i −0.991619 + 0.265704i
\(438\) 0 0
\(439\) −0.0638652 −0.00304812 −0.00152406 0.999999i \(-0.500485\pi\)
−0.00152406 + 0.999999i \(0.500485\pi\)
\(440\) −7.47978 + 2.00420i −0.356585 + 0.0955466i
\(441\) 0 0
\(442\) −0.801532 + 1.87215i −0.0381250 + 0.0890491i
\(443\) −8.77423 15.1974i −0.416876 0.722051i 0.578747 0.815507i \(-0.303542\pi\)
−0.995623 + 0.0934562i \(0.970208\pi\)
\(444\) 0 0
\(445\) 19.9275 + 34.5155i 0.944655 + 1.63619i
\(446\) 1.06751 1.84899i 0.0505482 0.0875520i
\(447\) 0 0
\(448\) −19.3859 2.96461i −0.915900 0.140065i
\(449\) 1.21603 + 0.325835i 0.0573881 + 0.0153771i 0.287399 0.957811i \(-0.407209\pi\)
−0.230011 + 0.973188i \(0.573876\pi\)
\(450\) 0 0
\(451\) 29.1615i 1.37316i
\(452\) −14.6674 + 8.46823i −0.689897 + 0.398312i
\(453\) 0 0
\(454\) −1.26622 −0.0594268
\(455\) 21.0304 + 0.687386i 0.985920 + 0.0322252i
\(456\) 0 0
\(457\) −5.23927 5.23927i −0.245083 0.245083i 0.573866 0.818949i \(-0.305443\pi\)
−0.818949 + 0.573866i \(0.805443\pi\)
\(458\) −0.0830452 + 0.0479462i −0.00388045 + 0.00224038i
\(459\) 0 0
\(460\) 18.7474 + 5.02335i 0.874102 + 0.234215i
\(461\) −17.9390 4.80674i −0.835502 0.223872i −0.184390 0.982853i \(-0.559031\pi\)
−0.651113 + 0.758981i \(0.725697\pi\)
\(462\) 0 0
\(463\) 10.9354 10.9354i 0.508209 0.508209i −0.405767 0.913976i \(-0.632996\pi\)
0.913976 + 0.405767i \(0.132996\pi\)
\(464\) 3.93941 6.82326i 0.182882 0.316762i
\(465\) 0 0
\(466\) 3.60915 + 0.967070i 0.167191 + 0.0447986i
\(467\) 8.85362 + 15.3349i 0.409697 + 0.709616i 0.994856 0.101303i \(-0.0323011\pi\)
−0.585159 + 0.810919i \(0.698968\pi\)
\(468\) 0 0
\(469\) 16.7032 + 7.33035i 0.771284 + 0.338484i
\(470\) −1.58476 + 0.424634i −0.0730993 + 0.0195869i
\(471\) 0 0
\(472\) −1.70894 −0.0786605
\(473\) 25.8203 6.91853i 1.18722 0.318114i
\(474\) 0 0
\(475\) 0.167851 0.626429i 0.00770153 0.0287425i
\(476\) 18.5517 + 2.83703i 0.850316 + 0.130035i
\(477\) 0 0
\(478\) 1.78483i 0.0816364i
\(479\) −4.37332 + 16.3215i −0.199822 + 0.745747i 0.791143 + 0.611631i \(0.209486\pi\)
−0.990966 + 0.134116i \(0.957181\pi\)
\(480\) 0 0
\(481\) −33.8586 14.4960i −1.54382 0.660962i
\(482\) 2.17281i 0.0989689i
\(483\) 0 0
\(484\) 20.2721 35.1124i 0.921461 1.59602i
\(485\) −6.97369 4.02626i −0.316659 0.182823i
\(486\) 0 0
\(487\) −1.58169 1.58169i −0.0716733 0.0716733i 0.670361 0.742035i \(-0.266139\pi\)
−0.742035 + 0.670361i \(0.766139\pi\)
\(488\) −1.12341 + 0.301017i −0.0508545 + 0.0136264i
\(489\) 0 0
\(490\) 0.530210 + 2.36994i 0.0239525 + 0.107063i
\(491\) 28.4705 + 16.4375i 1.28486 + 0.741812i 0.977732 0.209858i \(-0.0673000\pi\)
0.307124 + 0.951669i \(0.400633\pi\)
\(492\) 0 0
\(493\) −3.67243 + 6.36084i −0.165398 + 0.286478i
\(494\) −2.70425 0.388602i −0.121670 0.0174840i
\(495\) 0 0
\(496\) −2.47930 9.25288i −0.111324 0.415467i
\(497\) 34.0318 + 14.9351i 1.52653 + 0.669931i
\(498\) 0 0
\(499\) 7.97619 29.7675i 0.357063 1.33258i −0.520805 0.853676i \(-0.674368\pi\)
0.877868 0.478902i \(-0.158965\pi\)
\(500\) −15.8189 + 15.8189i −0.707443 + 0.707443i
\(501\) 0 0
\(502\) 0.826749 3.08547i 0.0368996 0.137711i
\(503\) 9.25091 5.34101i 0.412478 0.238144i −0.279376 0.960182i \(-0.590128\pi\)
0.691854 + 0.722038i \(0.256794\pi\)
\(504\) 0 0
\(505\) 5.54475 + 20.6933i 0.246738 + 0.920838i
\(506\) 3.40695 1.96700i 0.151457 0.0874440i
\(507\) 0 0
\(508\) −9.41325 + 16.3042i −0.417645 + 0.723383i
\(509\) 16.6654 16.6654i 0.738681 0.738681i −0.233641 0.972323i \(-0.575064\pi\)
0.972323 + 0.233641i \(0.0750642\pi\)
\(510\) 0 0
\(511\) −1.34091 12.1354i −0.0593186 0.536840i
\(512\) −8.46284 8.46284i −0.374008 0.374008i
\(513\) 0 0
\(514\) −2.74611 2.74611i −0.121126 0.121126i
\(515\) −3.56335 13.2986i −0.157020 0.586006i
\(516\) 0 0
\(517\) 13.2763 22.9953i 0.583893 1.01133i
\(518\) 0.642600 4.20204i 0.0282342 0.184627i
\(519\) 0 0
\(520\) 3.90895 + 3.07355i 0.171419 + 0.134784i
\(521\) −27.2035 15.7059i −1.19180 0.688089i −0.233089 0.972455i \(-0.574883\pi\)
−0.958716 + 0.284367i \(0.908217\pi\)
\(522\) 0 0
\(523\) 7.66261i 0.335062i 0.985867 + 0.167531i \(0.0535795\pi\)
−0.985867 + 0.167531i \(0.946420\pi\)
\(524\) 3.48446 + 6.03526i 0.152219 + 0.263652i
\(525\) 0 0
\(526\) −1.23605 + 4.61299i −0.0538942 + 0.201136i
\(527\) 2.31128 + 8.62581i 0.100681 + 0.375746i
\(528\) 0 0
\(529\) 3.15604 0.137219
\(530\) 0.139797 0.00607237
\(531\) 0 0
\(532\) 2.76511 + 25.0245i 0.119883 + 1.08495i
\(533\) −14.9901 + 11.2233i −0.649295 + 0.486134i
\(534\) 0 0
\(535\) 9.54402 + 2.55731i 0.412624 + 0.110562i
\(536\) 2.15536 + 3.73320i 0.0930976 + 0.161250i
\(537\) 0 0
\(538\) 0.662067 0.662067i 0.0285437 0.0285437i
\(539\) −33.1891 21.0537i −1.42956 0.906848i
\(540\) 0 0
\(541\) 21.5302 + 5.76899i 0.925654 + 0.248028i 0.690001 0.723809i \(-0.257610\pi\)
0.235654 + 0.971837i \(0.424277\pi\)
\(542\) 2.12630i 0.0913326i
\(543\) 0 0
\(544\) 4.71393 + 4.71393i 0.202108 + 0.202108i
\(545\) −30.7021 −1.31513
\(546\) 0 0
\(547\) 18.1017 0.773971 0.386986 0.922086i \(-0.373516\pi\)
0.386986 + 0.922086i \(0.373516\pi\)
\(548\) 14.1135 + 14.1135i 0.602897 + 0.602897i
\(549\) 0 0
\(550\) 0.118883i 0.00506920i
\(551\) −9.51756 2.55022i −0.405462 0.108643i
\(552\) 0 0
\(553\) 12.1220 4.72749i 0.515481 0.201033i
\(554\) 1.28521 1.28521i 0.0546035 0.0546035i
\(555\) 0 0
\(556\) 10.3319 + 17.8953i 0.438168 + 0.758930i
\(557\) −0.603665 0.161752i −0.0255781 0.00685364i 0.246007 0.969268i \(-0.420881\pi\)
−0.271585 + 0.962414i \(0.587548\pi\)
\(558\) 0 0
\(559\) −13.4937 10.6099i −0.570724 0.448752i
\(560\) 9.03423 20.5858i 0.381766 0.869908i
\(561\) 0 0
\(562\) 4.91654 0.207392
\(563\) 6.32497 0.266566 0.133283 0.991078i \(-0.457448\pi\)
0.133283 + 0.991078i \(0.457448\pi\)
\(564\) 0 0
\(565\) −4.89500 18.2684i −0.205934 0.768557i
\(566\) 0.919172 3.43040i 0.0386357 0.144190i
\(567\) 0 0
\(568\) 4.39142 + 7.60615i 0.184260 + 0.319147i
\(569\) 7.32323i 0.307006i 0.988148 + 0.153503i \(0.0490554\pi\)
−0.988148 + 0.153503i \(0.950945\pi\)
\(570\) 0 0
\(571\) 24.3352 + 14.0500i 1.01840 + 0.587972i 0.913639 0.406526i \(-0.133260\pi\)
0.104758 + 0.994498i \(0.466593\pi\)
\(572\) −39.7049 + 4.75039i −1.66015 + 0.198624i
\(573\) 0 0
\(574\) −1.68685 1.35117i −0.0704079 0.0563966i
\(575\) 0.299836 0.519332i 0.0125040 0.0216576i
\(576\) 0 0
\(577\) −9.18425 34.2761i −0.382345 1.42693i −0.842309 0.538995i \(-0.818804\pi\)
0.459964 0.887938i \(-0.347862\pi\)
\(578\) 0.456420 + 0.456420i 0.0189846 + 0.0189846i
\(579\) 0 0
\(580\) 6.30119 + 6.30119i 0.261643 + 0.261643i
\(581\) −22.9050 31.1753i −0.950259 1.29337i
\(582\) 0 0
\(583\) −1.59982 + 1.59982i −0.0662578 + 0.0662578i
\(584\) 1.44266 2.49876i 0.0596977 0.103399i
\(585\) 0 0
\(586\) −0.0757346 + 0.0437254i −0.00312857 + 0.00180628i
\(587\) 4.40846 + 16.4526i 0.181957 + 0.679071i 0.995262 + 0.0972337i \(0.0309994\pi\)
−0.813305 + 0.581838i \(0.802334\pi\)
\(588\) 0 0
\(589\) −10.3749 + 5.98996i −0.427491 + 0.246812i
\(590\) 0.245424 0.915934i 0.0101039 0.0377084i
\(591\) 0 0
\(592\) −27.8251 + 27.8251i −1.14360 + 1.14360i
\(593\) 3.60164 13.4415i 0.147901 0.551976i −0.851708 0.524017i \(-0.824433\pi\)
0.999609 0.0279585i \(-0.00890063\pi\)
\(594\) 0 0
\(595\) −8.42198 + 19.1907i −0.345268 + 0.786742i
\(596\) 0.226580 + 0.845609i 0.00928109 + 0.0346375i
\(597\) 0 0
\(598\) −2.32234 0.994272i −0.0949674 0.0406588i
\(599\) 8.84405 15.3183i 0.361358 0.625890i −0.626827 0.779159i \(-0.715647\pi\)
0.988185 + 0.153268i \(0.0489799\pi\)
\(600\) 0 0
\(601\) 23.8753 + 13.7844i 0.973894 + 0.562278i 0.900421 0.435019i \(-0.143258\pi\)
0.0734732 + 0.997297i \(0.476592\pi\)
\(602\) 0.796151 1.81414i 0.0324487 0.0739389i
\(603\) 0 0
\(604\) 18.8296 5.04537i 0.766164 0.205293i
\(605\) 32.0146 + 32.0146i 1.30158 + 1.30158i
\(606\) 0 0
\(607\) 17.6565 + 10.1940i 0.716657 + 0.413762i 0.813521 0.581536i \(-0.197548\pi\)
−0.0968642 + 0.995298i \(0.530881\pi\)
\(608\) −4.47163 + 7.74509i −0.181348 + 0.314105i
\(609\) 0 0
\(610\) 0.645339i 0.0261290i
\(611\) −16.9301 + 2.02555i −0.684918 + 0.0819451i
\(612\) 0 0
\(613\) 5.69586 21.2573i 0.230054 0.858572i −0.750263 0.661140i \(-0.770073\pi\)
0.980316 0.197433i \(-0.0632603\pi\)
\(614\) 1.11509i 0.0450014i
\(615\) 0 0
\(616\) −3.37479 8.65350i −0.135974 0.348660i
\(617\) −2.77212 + 10.3457i −0.111602 + 0.416503i −0.999010 0.0444809i \(-0.985837\pi\)
0.887409 + 0.460984i \(0.152503\pi\)
\(618\) 0 0
\(619\) −46.3466 + 12.4185i −1.86283 + 0.499143i −0.999980 0.00631894i \(-0.997989\pi\)
−0.862849 + 0.505462i \(0.831322\pi\)
\(620\) 10.8345 0.435125
\(621\) 0 0
\(622\) 0.123013 0.0329612i 0.00493236 0.00132162i
\(623\) −38.5248 + 28.3048i −1.54346 + 1.13401i
\(624\) 0 0
\(625\) −12.1544 21.0520i −0.486176 0.842081i
\(626\) −0.160476 0.0429993i −0.00641389 0.00171860i
\(627\) 0 0
\(628\) −21.9248 + 37.9749i −0.874895 + 1.51536i
\(629\) 25.9394 25.9394i 1.03427 1.03427i
\(630\) 0 0
\(631\) −28.4576 7.62520i −1.13288 0.303554i −0.356795 0.934183i \(-0.616131\pi\)
−0.776085 + 0.630628i \(0.782797\pi\)
\(632\) 2.97006 + 0.795826i 0.118143 + 0.0316563i
\(633\) 0 0
\(634\) −4.45060 + 2.56955i −0.176756 + 0.102050i
\(635\) −14.8658 14.8658i −0.589931 0.589931i
\(636\) 0 0
\(637\) 1.95092 + 25.1633i 0.0772984 + 0.997008i
\(638\) 1.80624 0.0715097
\(639\) 0 0
\(640\) 9.31937 5.38054i 0.368380 0.212685i
\(641\) 3.78962i 0.149681i 0.997196 + 0.0748405i \(0.0238448\pi\)
−0.997196 + 0.0748405i \(0.976155\pi\)
\(642\) 0 0
\(643\) −9.08002 2.43298i −0.358081 0.0959475i 0.0752936 0.997161i \(-0.476011\pi\)
−0.433375 + 0.901214i \(0.642677\pi\)
\(644\) −3.51924 + 23.0127i −0.138677 + 0.906828i
\(645\) 0 0
\(646\) 1.36055 2.35654i 0.0535301 0.0927168i
\(647\) −14.8089 25.6498i −0.582199 1.00840i −0.995218 0.0976755i \(-0.968859\pi\)
0.413020 0.910722i \(-0.364474\pi\)
\(648\) 0 0
\(649\) 7.67327 + 13.2905i 0.301202 + 0.521697i
\(650\) 0.0611107 0.0457542i 0.00239696 0.00179463i
\(651\) 0 0
\(652\) −5.32758 + 1.42752i −0.208644 + 0.0559060i
\(653\) −42.5984 −1.66700 −0.833502 0.552516i \(-0.813668\pi\)
−0.833502 + 0.552516i \(0.813668\pi\)
\(654\) 0 0
\(655\) −7.51697 + 2.01417i −0.293712 + 0.0787000i
\(656\) 5.17819 + 19.3253i 0.202174 + 0.754525i
\(657\) 0 0
\(658\) −0.715024 1.83343i −0.0278745 0.0714747i
\(659\) −0.832186 1.44139i −0.0324173 0.0561485i 0.849362 0.527811i \(-0.176987\pi\)
−0.881779 + 0.471663i \(0.843654\pi\)
\(660\) 0 0
\(661\) −2.43629 + 9.09235i −0.0947606 + 0.353651i −0.996983 0.0776197i \(-0.975268\pi\)
0.902222 + 0.431271i \(0.141935\pi\)
\(662\) 3.27633 + 1.89159i 0.127338 + 0.0735188i
\(663\) 0 0
\(664\) 9.14211i 0.354783i
\(665\) −27.7917 4.25007i −1.07772 0.164811i
\(666\) 0 0
\(667\) −7.89040 4.55552i −0.305518 0.176391i
\(668\) 1.24258 + 4.63736i 0.0480768 + 0.179425i
\(669\) 0 0
\(670\) −2.31040 + 0.619070i −0.0892586 + 0.0239168i
\(671\) 7.38521 + 7.38521i 0.285103 + 0.285103i
\(672\) 0 0
\(673\) 2.15591 + 1.24472i 0.0831043 + 0.0479803i 0.540976 0.841038i \(-0.318055\pi\)
−0.457872 + 0.889018i \(0.651388\pi\)
\(674\) −2.98619 + 2.98619i −0.115024 + 0.115024i
\(675\) 0 0
\(676\) 17.7230 + 18.5816i 0.681653 + 0.714678i
\(677\) −18.2860 + 10.5574i −0.702789 + 0.405756i −0.808385 0.588654i \(-0.799658\pi\)
0.105596 + 0.994409i \(0.466325\pi\)
\(678\) 0 0
\(679\) 3.88150 8.84455i 0.148958 0.339423i
\(680\) −4.28915 + 2.47634i −0.164481 + 0.0949633i
\(681\) 0 0
\(682\) 1.55286 1.55286i 0.0594621 0.0594621i
\(683\) −3.90071 + 3.90071i −0.149257 + 0.149257i −0.777786 0.628529i \(-0.783657\pi\)
0.628529 + 0.777786i \(0.283657\pi\)
\(684\) 0 0
\(685\) −19.3025 + 11.1443i −0.737510 + 0.425801i
\(686\) −2.75564 + 0.944330i −0.105211 + 0.0360547i
\(687\) 0 0
\(688\) −15.8825 + 9.16979i −0.605516 + 0.349595i
\(689\) 1.43809 + 0.206653i 0.0547867 + 0.00787285i
\(690\) 0 0
\(691\) −11.4634 + 11.4634i −0.436089 + 0.436089i −0.890694 0.454604i \(-0.849781\pi\)
0.454604 + 0.890694i \(0.349781\pi\)
\(692\) 18.3851 + 10.6146i 0.698897 + 0.403508i
\(693\) 0 0
\(694\) 2.56373 + 2.56373i 0.0973179 + 0.0973179i
\(695\) −22.2888 + 5.97226i −0.845461 + 0.226541i
\(696\) 0 0
\(697\) −4.82727 18.0156i −0.182846 0.682390i
\(698\) −0.842641 0.486499i −0.0318944 0.0184143i
\(699\) 0 0
\(700\) −0.549086 0.439817i −0.0207535 0.0166235i
\(701\) 11.5049i 0.434534i −0.976112 0.217267i \(-0.930286\pi\)
0.976112 0.217267i \(-0.0697142\pi\)
\(702\) 0 0
\(703\) 42.6190 + 24.6061i 1.60741 + 0.928036i
\(704\) −10.7718 + 40.2009i −0.405978 + 1.51513i
\(705\) 0 0
\(706\) 2.20858 + 3.82538i 0.0831212 + 0.143970i
\(707\) −23.9404 + 9.33657i −0.900373 + 0.351138i
\(708\) 0 0
\(709\) −0.0992239 0.370309i −0.00372643 0.0139072i 0.964038 0.265766i \(-0.0856248\pi\)
−0.967764 + 0.251859i \(0.918958\pi\)
\(710\) −4.70729 + 1.26132i −0.176662 + 0.0473363i
\(711\) 0 0
\(712\) −11.2974 −0.423387
\(713\) −10.7000 + 2.86706i −0.400719 + 0.107372i
\(714\) 0 0
\(715\) 6.35161 44.2004i 0.237537 1.65300i
\(716\) 18.8191 + 32.5957i 0.703304 + 1.21816i
\(717\) 0 0
\(718\) −0.622090 1.07749i −0.0232162 0.0402116i
\(719\) 11.9136 20.6350i 0.444304 0.769557i −0.553699 0.832717i \(-0.686784\pi\)
0.998003 + 0.0631593i \(0.0201176\pi\)
\(720\) 0 0
\(721\) 15.3854 6.00018i 0.572982 0.223458i
\(722\) 0.639446 + 0.171339i 0.0237977 + 0.00637658i
\(723\) 0 0
\(724\) 40.5862i 1.50837i
\(725\) 0.238443 0.137665i 0.00885556 0.00511276i
\(726\) 0 0
\(727\) −0.135408 −0.00502200 −0.00251100 0.999997i \(-0.500799\pi\)
−0.00251100 + 0.999997i \(0.500799\pi\)
\(728\) −3.14939 + 5.06521i −0.116724 + 0.187729i
\(729\) 0 0
\(730\) 1.13207 + 1.13207i 0.0418996 + 0.0418996i
\(731\) 14.8062 8.54835i 0.547626 0.316172i
\(732\) 0 0
\(733\) −37.2352 9.97714i −1.37531 0.368514i −0.505897 0.862594i \(-0.668838\pi\)
−0.869417 + 0.494080i \(0.835505\pi\)
\(734\) 1.38945 + 0.372301i 0.0512854 + 0.0137419i
\(735\) 0 0
\(736\) −5.84746 + 5.84746i −0.215540 + 0.215540i
\(737\) 19.3554 33.5246i 0.712967 1.23489i
\(738\) 0 0
\(739\) −39.9013 10.6915i −1.46779 0.393294i −0.565620 0.824666i \(-0.691363\pi\)
−0.902174 + 0.431372i \(0.858030\pi\)
\(740\) −22.2535 38.5441i −0.818054 1.41691i
\(741\) 0 0
\(742\) 0.0184161 + 0.166668i 0.000676076 + 0.00611857i
\(743\) 29.7830 7.98032i 1.09263 0.292769i 0.332870 0.942973i \(-0.391983\pi\)
0.759760 + 0.650203i \(0.225316\pi\)
\(744\) 0 0
\(745\) −0.977597 −0.0358164
\(746\) −4.98389 + 1.33543i −0.182473 + 0.0488936i
\(747\) 0 0
\(748\) 10.3083 38.4709i 0.376907 1.40664i
\(749\) −1.79159 + 11.7154i −0.0654633 + 0.428072i
\(750\) 0 0
\(751\) 32.6954i 1.19307i 0.802586 + 0.596536i \(0.203457\pi\)
−0.802586 + 0.596536i \(0.796543\pi\)
\(752\) −4.71494 + 17.5964i −0.171936 + 0.641675i
\(753\) 0 0
\(754\) −0.695160 0.928477i −0.0253162 0.0338131i
\(755\) 21.7686i 0.792241i
\(756\) 0 0
\(757\) 4.04055 6.99844i 0.146856 0.254363i −0.783208 0.621760i \(-0.786418\pi\)
0.930064 + 0.367398i \(0.119751\pi\)
\(758\) 2.39383 + 1.38208i 0.0869477 + 0.0501993i
\(759\) 0 0
\(760\) −4.69811 4.69811i −0.170418 0.170418i
\(761\) 13.8024 3.69833i 0.500335 0.134064i 0.000179461 1.00000i \(-0.499943\pi\)
0.500155 + 0.865936i \(0.333276\pi\)
\(762\) 0 0
\(763\) −4.04454 36.6036i −0.146422 1.32514i
\(764\) −33.2008 19.1685i −1.20116 0.693493i
\(765\) 0 0
\(766\) 2.41873 4.18936i 0.0873922 0.151368i
\(767\) 3.87865 9.05941i 0.140050 0.327116i
\(768\) 0 0
\(769\) 0.992641 + 3.70459i 0.0357955 + 0.133591i 0.981511 0.191404i \(-0.0613041\pi\)
−0.945716 + 0.324995i \(0.894637\pi\)
\(770\) 5.12264 0.566029i 0.184607 0.0203983i
\(771\) 0 0
\(772\) −9.24431 + 34.5003i −0.332710 + 1.24169i
\(773\) 0.986845 0.986845i 0.0354943 0.0354943i −0.689137 0.724631i \(-0.742010\pi\)
0.724631 + 0.689137i \(0.242010\pi\)
\(774\) 0 0
\(775\) 0.0866409 0.323348i 0.00311223 0.0116150i
\(776\) 1.97677 1.14129i 0.0709619 0.0409699i
\(777\) 0 0
\(778\) −0.616466 2.30068i −0.0221014 0.0824835i
\(779\) 21.6687 12.5105i 0.776363 0.448234i
\(780\) 0 0
\(781\) 39.4355 68.3042i 1.41111 2.44412i
\(782\) 1.77916 1.77916i 0.0636227 0.0636227i
\(783\) 0 0
\(784\) 25.7329 + 8.05890i 0.919031 + 0.287818i
\(785\) −34.6246 34.6246i −1.23580 1.23580i
\(786\) 0 0
\(787\) −23.6123 23.6123i −0.841686 0.841686i 0.147392 0.989078i \(-0.452912\pi\)
−0.989078 + 0.147392i \(0.952912\pi\)
\(788\) −6.39201 23.8553i −0.227706 0.849809i
\(789\) 0 0
\(790\) −0.853070 + 1.47756i −0.0303509 + 0.0525693i
\(791\) 21.1351 8.24249i 0.751476 0.293069i
\(792\) 0 0
\(793\) 0.953968 6.63860i 0.0338764 0.235744i
\(794\) −1.09946 0.634774i −0.0390184 0.0225273i
\(795\) 0 0
\(796\) 41.3663i 1.46619i
\(797\) 13.5213 + 23.4196i 0.478950 + 0.829566i 0.999709 0.0241380i \(-0.00768412\pi\)
−0.520758 + 0.853704i \(0.674351\pi\)
\(798\) 0 0
\(799\) 4.39541 16.4039i 0.155498 0.580328i
\(800\) −0.0646792 0.241386i −0.00228675 0.00853428i
\(801\) 0 0
\(802\) −2.70279 −0.0954389
\(803\) −25.9105 −0.914363
\(804\) 0 0
\(805\) −23.8054 10.4472i −0.839029 0.368214i
\(806\) −1.39587 0.200587i −0.0491676 0.00706539i
\(807\) 0 0
\(808\) −5.86574 1.57172i −0.206356 0.0552929i
\(809\) 4.12773 + 7.14944i 0.145123 + 0.251361i 0.929419 0.369026i \(-0.120309\pi\)
−0.784296 + 0.620387i \(0.786975\pi\)
\(810\) 0 0
\(811\) 17.4673 17.4673i 0.613359 0.613359i −0.330461 0.943820i \(-0.607204\pi\)
0.943820 + 0.330461i \(0.107204\pi\)
\(812\) −6.68230 + 8.34247i −0.234503 + 0.292763i
\(813\) 0 0
\(814\) −8.71384 2.33487i −0.305420 0.0818370i
\(815\) 6.15914i 0.215745i
\(816\) 0 0
\(817\) 16.2179 + 16.2179i 0.567394 + 0.567394i
\(818\) −4.82426 −0.168676
\(819\) 0 0
\(820\) −22.6286 −0.790226
\(821\) 25.3099 + 25.3099i 0.883322 + 0.883322i 0.993871 0.110549i \(-0.0352608\pi\)
−0.110549 + 0.993871i \(0.535261\pi\)
\(822\) 0 0
\(823\) 4.02596i 0.140336i −0.997535 0.0701681i \(-0.977646\pi\)
0.997535 0.0701681i \(-0.0223536\pi\)
\(824\) 3.76964 + 1.01007i 0.131322 + 0.0351875i
\(825\) 0 0
\(826\) 1.12432 + 0.171938i 0.0391202 + 0.00598249i
\(827\) −1.28533 + 1.28533i −0.0446954 + 0.0446954i −0.729101 0.684406i \(-0.760062\pi\)
0.684406 + 0.729101i \(0.260062\pi\)
\(828\) 0 0
\(829\) 9.96119 + 17.2533i 0.345967 + 0.599232i 0.985529 0.169508i \(-0.0542177\pi\)
−0.639562 + 0.768739i \(0.720884\pi\)
\(830\) 4.89985 + 1.31291i 0.170076 + 0.0455718i
\(831\) 0 0
\(832\) 24.8105 9.93485i 0.860151 0.344429i
\(833\) −23.9889 7.51275i −0.831167 0.260301i
\(834\) 0 0
\(835\) −5.36119 −0.185532
\(836\) 53.4302 1.84792
\(837\) 0 0
\(838\) −0.714549 2.66673i −0.0246837 0.0921208i
\(839\) 13.3275 49.7391i 0.460118 1.71718i −0.212471 0.977167i \(-0.568151\pi\)
0.672589 0.740016i \(-0.265182\pi\)
\(840\) 0 0
\(841\) 12.4084 + 21.4920i 0.427876 + 0.741103i
\(842\) 3.46410i 0.119381i
\(843\) 0 0
\(844\) −30.2978 17.4924i −1.04289 0.602114i
\(845\) −25.1652 + 13.7463i −0.865711 + 0.472886i
\(846\) 0 0
\(847\) −33.9509 + 42.3858i −1.16657 + 1.45639i
\(848\) 0.776119 1.34428i 0.0266520 0.0461627i
\(849\) 0 0
\(850\) 0.0196794 + 0.0734446i 0.000674999 + 0.00251913i
\(851\) 32.1769 + 32.1769i 1.10301 + 1.10301i
\(852\) 0 0
\(853\) 11.4061 + 11.4061i 0.390537 + 0.390537i 0.874879 0.484342i \(-0.160941\pi\)
−0.484342 + 0.874879i \(0.660941\pi\)
\(854\) 0.769385 0.0850137i 0.0263278 0.00290911i
\(855\) 0 0
\(856\) −1.98046 + 1.98046i −0.0676907 + 0.0676907i
\(857\) −5.11355 + 8.85693i −0.174676 + 0.302547i −0.940049 0.341040i \(-0.889221\pi\)
0.765373 + 0.643586i \(0.222554\pi\)
\(858\) 0 0
\(859\) −20.0305 + 11.5646i −0.683433 + 0.394580i −0.801147 0.598467i \(-0.795777\pi\)
0.117714 + 0.993048i \(0.462443\pi\)
\(860\) −5.36861 20.0359i −0.183068 0.683220i
\(861\) 0 0
\(862\) 0.590618 0.340994i 0.0201165 0.0116143i
\(863\) −2.58806 + 9.65877i −0.0880986 + 0.328788i −0.995883 0.0906489i \(-0.971106\pi\)
0.907784 + 0.419437i \(0.137773\pi\)
\(864\) 0 0
\(865\) −16.7631 + 16.7631i −0.569963 + 0.569963i
\(866\) −1.18961 + 4.43969i −0.0404247 + 0.150867i
\(867\) 0 0
\(868\) 1.42728 + 12.9171i 0.0484452 + 0.438435i
\(869\) −7.14662 26.6715i −0.242432 0.904770i
\(870\) 0 0
\(871\) −24.6822 + 2.95304i −0.836324 + 0.100060i
\(872\) 4.35143 7.53690i 0.147358 0.255232i
\(873\) 0 0
\(874\) 2.92320 + 1.68771i 0.0988788 + 0.0570877i
\(875\) 24.1481 17.7420i 0.816353 0.599789i
\(876\) 0 0
\(877\) 7.23964 1.93986i 0.244465 0.0655043i −0.134506 0.990913i \(-0.542945\pi\)
0.378971 + 0.925409i \(0.376278\pi\)
\(878\) 0.00710290 + 0.00710290i 0.000239711 + 0.000239711i
\(879\) 0 0
\(880\) −41.3172 23.8545i −1.39280 0.804134i
\(881\) −10.1686 + 17.6125i −0.342589 + 0.593381i −0.984913 0.173052i \(-0.944637\pi\)
0.642324 + 0.766433i \(0.277970\pi\)
\(882\) 0 0
\(883\) 31.9023i 1.07360i 0.843710 + 0.536799i \(0.180367\pi\)
−0.843710 + 0.536799i \(0.819633\pi\)
\(884\) −23.7429 + 9.50731i −0.798558 + 0.319766i
\(885\) 0 0
\(886\) −0.714368 + 2.66606i −0.0239996 + 0.0895679i
\(887\) 43.1400i 1.44850i 0.689538 + 0.724249i \(0.257814\pi\)
−0.689538 + 0.724249i \(0.742186\pi\)
\(888\) 0 0
\(889\) 15.7649 19.6816i 0.528738 0.660100i
\(890\) 1.62243 6.05499i 0.0543840 0.202964i
\(891\) 0 0
\(892\) 25.8991 6.93964i 0.867166 0.232356i
\(893\) 22.7825 0.762387
\(894\) 0 0
\(895\) −40.5983 + 10.8783i −1.35705 + 0.363620i
\(896\) 7.64246 + 10.4019i 0.255317 + 0.347503i
\(897\) 0 0
\(898\) −0.0990052 0.171482i −0.00330385 0.00572243i
\(899\) −4.91275 1.31637i −0.163849 0.0439033i
\(900\) 0 0
\(901\) −0.723521 + 1.25318i −0.0241040 + 0.0417493i
\(902\) −3.24326 + 3.24326i −0.107989 + 0.107989i
\(903\) 0 0
\(904\) 5.17838 + 1.38754i 0.172230 + 0.0461490i
\(905\) −43.7780 11.7303i −1.45523 0.389927i
\(906\) 0 0
\(907\) 38.7355 22.3639i 1.28619 0.742583i 0.308218 0.951316i \(-0.400267\pi\)
0.977973 + 0.208733i \(0.0669340\pi\)
\(908\) −11.2443 11.2443i −0.373156 0.373156i
\(909\) 0 0
\(910\) −2.26249 2.41539i −0.0750008 0.0800693i
\(911\) −19.2491 −0.637751 −0.318875 0.947797i \(-0.603305\pi\)
−0.318875 + 0.947797i \(0.603305\pi\)
\(912\) 0 0
\(913\) −71.0984 + 41.0487i −2.35301 + 1.35851i
\(914\) 1.16539i 0.0385478i
\(915\) 0 0
\(916\) −1.16323 0.311687i −0.0384342 0.0102984i
\(917\) −3.39157 8.69653i −0.112000 0.287185i
\(918\) 0 0
\(919\) 2.95449 5.11733i 0.0974596 0.168805i −0.813173 0.582022i \(-0.802262\pi\)
0.910632 + 0.413217i \(0.135595\pi\)
\(920\) −3.07181 5.32054i −0.101275 0.175413i
\(921\) 0 0
\(922\) 1.46053 + 2.52971i 0.0481000 + 0.0833117i
\(923\) −50.2884 + 6.01662i −1.65526 + 0.198039i
\(924\) 0 0
\(925\) −1.32828 + 0.355911i −0.0436735 + 0.0117023i
\(926\) −2.43240 −0.0799335
\(927\) 0 0
\(928\) −3.66747 + 0.982694i −0.120390 + 0.0322585i
\(929\) −6.93438 25.8795i −0.227510 0.849077i −0.981384 0.192058i \(-0.938484\pi\)
0.753874 0.657019i \(-0.228183\pi\)
\(930\) 0 0
\(931\) 1.40587 33.6937i 0.0460754 1.10426i
\(932\) 23.4623 + 40.6378i 0.768532 + 1.33114i
\(933\) 0 0
\(934\) 0.720832 2.69018i 0.0235863 0.0880254i
\(935\) 38.5171 + 22.2379i 1.25964 + 0.727256i
\(936\) 0 0
\(937\) 33.5545i 1.09618i 0.836420 + 0.548089i \(0.184644\pi\)
−0.836420 + 0.548089i \(0.815356\pi\)
\(938\) −1.04243 2.67295i −0.0340364 0.0872748i
\(939\) 0 0
\(940\) −17.8438 10.3021i −0.582001 0.336018i
\(941\) 0.902282 + 3.36736i 0.0294135 + 0.109773i 0.979072 0.203514i \(-0.0652364\pi\)
−0.949658 + 0.313287i \(0.898570\pi\)
\(942\) 0 0
\(943\) 22.3477 5.98805i 0.727742 0.194998i
\(944\) −7.44504 7.44504i −0.242316 0.242316i
\(945\) 0 0
\(946\) −3.64112 2.10220i −0.118383 0.0683484i
\(947\) 4.56102 4.56102i 0.148213 0.148213i −0.629106 0.777319i \(-0.716579\pi\)
0.777319 + 0.629106i \(0.216579\pi\)
\(948\) 0 0
\(949\) 9.97208 + 13.3190i 0.323708 + 0.432354i
\(950\) −0.0883375 + 0.0510017i −0.00286605 + 0.00165471i
\(951\) 0 0
\(952\) −3.51737 4.78738i −0.113999 0.155160i
\(953\) −21.7137 + 12.5364i −0.703376 + 0.406094i −0.808604 0.588354i \(-0.799776\pi\)
0.105228 + 0.994448i \(0.466443\pi\)
\(954\) 0 0
\(955\) 30.2717 30.2717i 0.979570 0.979570i
\(956\) −15.8497 + 15.8497i −0.512616 + 0.512616i
\(957\) 0 0
\(958\) 2.30161 1.32884i 0.0743618 0.0429328i
\(959\) −15.8292 21.5447i −0.511152 0.695713i
\(960\) 0 0
\(961\) 21.4915 12.4081i 0.693274 0.400262i
\(962\) 2.15345 + 5.37786i 0.0694300 + 0.173389i
\(963\) 0 0
\(964\) 19.2950 19.2950i 0.621451 0.621451i
\(965\) −34.5416 19.9426i −1.11193 0.641976i
\(966\) 0 0
\(967\) 15.8740 + 15.8740i 0.510473 + 0.510473i 0.914671 0.404199i \(-0.132450\pi\)
−0.404199 + 0.914671i \(0.632450\pi\)
\(968\) −12.3966 + 3.32165i −0.398440 + 0.106762i
\(969\) 0 0
\(970\) 0.327804 + 1.22338i 0.0105252 + 0.0392804i
\(971\) −32.4502 18.7352i −1.04138 0.601240i −0.121155 0.992634i \(-0.538660\pi\)
−0.920223 + 0.391394i \(0.871993\pi\)
\(972\) 0 0
\(973\) −10.0564 25.7863i −0.322394 0.826670i
\(974\) 0.351822i 0.0112731i
\(975\) 0 0
\(976\) −6.20555 3.58278i −0.198635 0.114682i
\(977\) −6.13522 + 22.8970i −0.196283 + 0.732539i 0.795648 + 0.605759i \(0.207131\pi\)
−0.991931 + 0.126779i \(0.959536\pi\)
\(978\) 0 0
\(979\) 50.7259 + 87.8598i 1.62121 + 2.80801i
\(980\) −16.3372 + 25.7540i −0.521873 + 0.822680i
\(981\) 0 0
\(982\) −1.33828 4.99453i −0.0427063 0.159382i
\(983\) −5.27840 + 1.41434i −0.168355 + 0.0451105i −0.342012 0.939696i \(-0.611108\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(984\) 0 0
\(985\) 27.5788 0.878732
\(986\) 1.11587 0.298997i 0.0355366 0.00952200i
\(987\) 0 0
\(988\) −20.5635 27.4652i −0.654211 0.873785i
\(989\) 10.6039 + 18.3665i 0.337185 + 0.584022i
\(990\) 0 0
\(991\) 4.31507 + 7.47392i 0.137073 + 0.237417i 0.926387 0.376572i \(-0.122897\pi\)
−0.789315 + 0.613989i \(0.789564\pi\)
\(992\) −2.30815 + 3.99784i −0.0732839 + 0.126931i
\(993\) 0 0
\(994\) −2.12388 5.44595i −0.0673653 0.172735i
\(995\) 44.6195 + 11.9558i 1.41453 + 0.379023i
\(996\) 0 0
\(997\) 15.6402i 0.495330i 0.968846 + 0.247665i \(0.0796633\pi\)
−0.968846 + 0.247665i \(0.920337\pi\)
\(998\) −4.19775 + 2.42357i −0.132877 + 0.0767168i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 819.2.et.c.514.5 36
3.2 odd 2 273.2.bt.a.241.5 yes 36
7.5 odd 6 819.2.gh.c.397.5 36
13.2 odd 12 819.2.gh.c.262.5 36
21.5 even 6 273.2.cg.a.124.5 yes 36
39.2 even 12 273.2.cg.a.262.5 yes 36
91.54 even 12 inner 819.2.et.c.145.5 36
273.236 odd 12 273.2.bt.a.145.5 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bt.a.145.5 36 273.236 odd 12
273.2.bt.a.241.5 yes 36 3.2 odd 2
273.2.cg.a.124.5 yes 36 21.5 even 6
273.2.cg.a.262.5 yes 36 39.2 even 12
819.2.et.c.145.5 36 91.54 even 12 inner
819.2.et.c.514.5 36 1.1 even 1 trivial
819.2.gh.c.262.5 36 13.2 odd 12
819.2.gh.c.397.5 36 7.5 odd 6