Properties

Label 720.2.t.b.541.1
Level $720$
Weight $2$
Character 720.541
Analytic conductor $5.749$
Analytic rank $0$
Dimension $8$
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] = [720,2,Mod(181,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.181");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.t (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 240)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 - 0.0297061i\) of defining polynomial
Character \(\chi\) \(=\) 720.541
Dual form 720.2.t.b.181.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.874559 + 1.11137i) q^{2} +(-0.470294 - 1.94392i) q^{4} +(-0.707107 + 0.707107i) q^{5} -1.41421i q^{7} +(2.57172 + 1.17740i) q^{8} +O(q^{10})\) \(q+(-0.874559 + 1.11137i) q^{2} +(-0.470294 - 1.94392i) q^{4} +(-0.707107 + 0.707107i) q^{5} -1.41421i q^{7} +(2.57172 + 1.17740i) q^{8} +(-0.167452 - 1.40426i) q^{10} +(0.808530 - 0.808530i) q^{11} +(-0.749118 - 0.749118i) q^{13} +(1.57172 + 1.23681i) q^{14} +(-3.55765 + 1.82843i) q^{16} -5.97186 q^{17} +(-1.88784 - 1.88784i) q^{19} +(1.70711 + 1.04201i) q^{20} +(0.191470 + 1.60568i) q^{22} +1.88118i q^{23} -1.00000i q^{25} +(1.48770 - 0.177401i) q^{26} +(-2.74912 + 0.665096i) q^{28} +(-5.88784 - 5.88784i) q^{29} +1.61040 q^{31} +(1.07931 - 5.55294i) q^{32} +(5.22274 - 6.63696i) q^{34} +(1.00000 + 1.00000i) q^{35} +(3.69637 - 3.69637i) q^{37} +(3.74912 - 0.447065i) q^{38} +(-2.65103 + 0.985930i) q^{40} -8.77215i q^{41} +(-0.744406 + 0.744406i) q^{43} +(-1.95196 - 1.19147i) q^{44} +(-2.09069 - 1.64520i) q^{46} -13.5608 q^{47} +5.00000 q^{49} +(1.11137 + 0.874559i) q^{50} +(-1.10392 + 1.80853i) q^{52} +(-0.863230 + 0.863230i) q^{53} +1.14343i q^{55} +(1.66510 - 3.63696i) q^{56} +(11.6928 - 1.39432i) q^{58} +(10.7523 - 10.7523i) q^{59} +(-9.05588 - 9.05588i) q^{61} +(-1.40839 + 1.78975i) q^{62} +(5.22746 + 6.05588i) q^{64} +1.05941 q^{65} +(-2.94725 - 2.94725i) q^{67} +(2.80853 + 11.6088i) q^{68} +(-1.98593 + 0.236813i) q^{70} +6.78863i q^{71} +2.32666i q^{73} +(0.875348 + 7.34073i) q^{74} +(-2.78197 + 4.55765i) q^{76} +(-1.14343 - 1.14343i) q^{77} -4.27078 q^{79} +(1.22274 - 3.80853i) q^{80} +(9.74912 + 7.67176i) q^{82} +(3.11529 + 3.11529i) q^{83} +(4.22274 - 4.22274i) q^{85} +(-0.176285 - 1.47834i) q^{86} +(3.03127 - 1.12735i) q^{88} -10.3172i q^{89} +(-1.05941 + 1.05941i) q^{91} +(3.65685 - 0.884705i) q^{92} +(11.8597 - 15.0711i) q^{94} +2.66981 q^{95} -3.72256 q^{97} +(-4.37279 + 5.55686i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{4} + 12 q^{8} - 8 q^{11} + 8 q^{13} + 4 q^{14} - 8 q^{17} + 8 q^{19} + 8 q^{20} + 16 q^{22} + 20 q^{26} - 8 q^{28} - 24 q^{29} + 8 q^{31} + 16 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{40} + 16 q^{44} + 24 q^{46} + 40 q^{49} - 4 q^{50} + 16 q^{52} + 16 q^{56} - 8 q^{59} - 16 q^{61} - 28 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{68} + 4 q^{70} + 36 q^{74} - 40 q^{76} + 8 q^{77} - 40 q^{79} - 16 q^{80} + 64 q^{82} - 32 q^{83} + 8 q^{85} - 16 q^{86} - 16 q^{88} - 8 q^{91} - 16 q^{92} + 32 q^{94} + 16 q^{95} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\) \(1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.874559 + 1.11137i −0.618406 + 0.785858i
\(3\) 0 0
\(4\) −0.470294 1.94392i −0.235147 0.971960i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) 0 0
\(7\) 1.41421i 0.534522i −0.963624 0.267261i \(-0.913881\pi\)
0.963624 0.267261i \(-0.0861187\pi\)
\(8\) 2.57172 + 1.17740i 0.909239 + 0.416274i
\(9\) 0 0
\(10\) −0.167452 1.40426i −0.0529530 0.444068i
\(11\) 0.808530 0.808530i 0.243781 0.243781i −0.574631 0.818412i \(-0.694855\pi\)
0.818412 + 0.574631i \(0.194855\pi\)
\(12\) 0 0
\(13\) −0.749118 0.749118i −0.207768 0.207768i 0.595550 0.803318i \(-0.296934\pi\)
−0.803318 + 0.595550i \(0.796934\pi\)
\(14\) 1.57172 + 1.23681i 0.420059 + 0.330552i
\(15\) 0 0
\(16\) −3.55765 + 1.82843i −0.889412 + 0.457107i
\(17\) −5.97186 −1.44839 −0.724195 0.689596i \(-0.757788\pi\)
−0.724195 + 0.689596i \(0.757788\pi\)
\(18\) 0 0
\(19\) −1.88784 1.88784i −0.433100 0.433100i 0.456582 0.889682i \(-0.349074\pi\)
−0.889682 + 0.456582i \(0.849074\pi\)
\(20\) 1.70711 + 1.04201i 0.381721 + 0.233001i
\(21\) 0 0
\(22\) 0.191470 + 1.60568i 0.0408216 + 0.342333i
\(23\) 1.88118i 0.392252i 0.980579 + 0.196126i \(0.0628362\pi\)
−0.980579 + 0.196126i \(0.937164\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) 1.48770 0.177401i 0.291761 0.0347911i
\(27\) 0 0
\(28\) −2.74912 + 0.665096i −0.519534 + 0.125691i
\(29\) −5.88784 5.88784i −1.09334 1.09334i −0.995169 0.0981752i \(-0.968699\pi\)
−0.0981752 0.995169i \(-0.531301\pi\)
\(30\) 0 0
\(31\) 1.61040 0.289236 0.144618 0.989488i \(-0.453805\pi\)
0.144618 + 0.989488i \(0.453805\pi\)
\(32\) 1.07931 5.55294i 0.190797 0.981630i
\(33\) 0 0
\(34\) 5.22274 6.63696i 0.895693 1.13823i
\(35\) 1.00000 + 1.00000i 0.169031 + 0.169031i
\(36\) 0 0
\(37\) 3.69637 3.69637i 0.607679 0.607679i −0.334660 0.942339i \(-0.608621\pi\)
0.942339 + 0.334660i \(0.108621\pi\)
\(38\) 3.74912 0.447065i 0.608187 0.0725235i
\(39\) 0 0
\(40\) −2.65103 + 0.985930i −0.419164 + 0.155889i
\(41\) 8.77215i 1.36998i −0.728553 0.684990i \(-0.759807\pi\)
0.728553 0.684990i \(-0.240193\pi\)
\(42\) 0 0
\(43\) −0.744406 + 0.744406i −0.113521 + 0.113521i −0.761585 0.648065i \(-0.775579\pi\)
0.648065 + 0.761585i \(0.275579\pi\)
\(44\) −1.95196 1.19147i −0.294270 0.179621i
\(45\) 0 0
\(46\) −2.09069 1.64520i −0.308255 0.242571i
\(47\) −13.5608 −1.97804 −0.989022 0.147771i \(-0.952790\pi\)
−0.989022 + 0.147771i \(0.952790\pi\)
\(48\) 0 0
\(49\) 5.00000 0.714286
\(50\) 1.11137 + 0.874559i 0.157172 + 0.123681i
\(51\) 0 0
\(52\) −1.10392 + 1.80853i −0.153086 + 0.250798i
\(53\) −0.863230 + 0.863230i −0.118574 + 0.118574i −0.763904 0.645330i \(-0.776720\pi\)
0.645330 + 0.763904i \(0.276720\pi\)
\(54\) 0 0
\(55\) 1.14343i 0.154181i
\(56\) 1.66510 3.63696i 0.222508 0.486009i
\(57\) 0 0
\(58\) 11.6928 1.39432i 1.53535 0.183083i
\(59\) 10.7523 10.7523i 1.39982 1.39982i 0.599298 0.800526i \(-0.295447\pi\)
0.800526 0.599298i \(-0.204553\pi\)
\(60\) 0 0
\(61\) −9.05588 9.05588i −1.15949 1.15949i −0.984586 0.174901i \(-0.944040\pi\)
−0.174901 0.984586i \(-0.555960\pi\)
\(62\) −1.40839 + 1.78975i −0.178865 + 0.227298i
\(63\) 0 0
\(64\) 5.22746 + 6.05588i 0.653432 + 0.756985i
\(65\) 1.05941 0.131404
\(66\) 0 0
\(67\) −2.94725 2.94725i −0.360064 0.360064i 0.503772 0.863836i \(-0.331945\pi\)
−0.863836 + 0.503772i \(0.831945\pi\)
\(68\) 2.80853 + 11.6088i 0.340584 + 1.40778i
\(69\) 0 0
\(70\) −1.98593 + 0.236813i −0.237364 + 0.0283046i
\(71\) 6.78863i 0.805662i 0.915274 + 0.402831i \(0.131974\pi\)
−0.915274 + 0.402831i \(0.868026\pi\)
\(72\) 0 0
\(73\) 2.32666i 0.272315i 0.990687 + 0.136158i \(0.0434754\pi\)
−0.990687 + 0.136158i \(0.956525\pi\)
\(74\) 0.875348 + 7.34073i 0.101757 + 0.853343i
\(75\) 0 0
\(76\) −2.78197 + 4.55765i −0.319114 + 0.522798i
\(77\) −1.14343 1.14343i −0.130306 0.130306i
\(78\) 0 0
\(79\) −4.27078 −0.480500 −0.240250 0.970711i \(-0.577229\pi\)
−0.240250 + 0.970711i \(0.577229\pi\)
\(80\) 1.22274 3.80853i 0.136707 0.425807i
\(81\) 0 0
\(82\) 9.74912 + 7.67176i 1.07661 + 0.847204i
\(83\) 3.11529 + 3.11529i 0.341948 + 0.341948i 0.857099 0.515151i \(-0.172264\pi\)
−0.515151 + 0.857099i \(0.672264\pi\)
\(84\) 0 0
\(85\) 4.22274 4.22274i 0.458021 0.458021i
\(86\) −0.176285 1.47834i −0.0190093 0.159413i
\(87\) 0 0
\(88\) 3.03127 1.12735i 0.323135 0.120175i
\(89\) 10.3172i 1.09363i −0.837255 0.546813i \(-0.815841\pi\)
0.837255 0.546813i \(-0.184159\pi\)
\(90\) 0 0
\(91\) −1.05941 + 1.05941i −0.111057 + 0.111057i
\(92\) 3.65685 0.884705i 0.381253 0.0922369i
\(93\) 0 0
\(94\) 11.8597 15.0711i 1.22323 1.55446i
\(95\) 2.66981 0.273917
\(96\) 0 0
\(97\) −3.72256 −0.377968 −0.188984 0.981980i \(-0.560519\pi\)
−0.188984 + 0.981980i \(0.560519\pi\)
\(98\) −4.37279 + 5.55686i −0.441719 + 0.561327i
\(99\) 0 0
\(100\) −1.94392 + 0.470294i −0.194392 + 0.0470294i
\(101\) 5.29539 5.29539i 0.526911 0.526911i −0.392739 0.919650i \(-0.628472\pi\)
0.919650 + 0.392739i \(0.128472\pi\)
\(102\) 0 0
\(103\) 15.8503i 1.56177i 0.624672 + 0.780887i \(0.285233\pi\)
−0.624672 + 0.780887i \(0.714767\pi\)
\(104\) −1.04451 2.80853i −0.102422 0.275399i
\(105\) 0 0
\(106\) −0.204424 1.71431i −0.0198554 0.166509i
\(107\) 1.33962 1.33962i 0.129506 0.129506i −0.639383 0.768888i \(-0.720810\pi\)
0.768888 + 0.639383i \(0.220810\pi\)
\(108\) 0 0
\(109\) −8.67294 8.67294i −0.830717 0.830717i 0.156898 0.987615i \(-0.449851\pi\)
−0.987615 + 0.156898i \(0.949851\pi\)
\(110\) −1.27078 1.00000i −0.121164 0.0953463i
\(111\) 0 0
\(112\) 2.58579 + 5.03127i 0.244334 + 0.475411i
\(113\) 15.3248 1.44164 0.720818 0.693124i \(-0.243766\pi\)
0.720818 + 0.693124i \(0.243766\pi\)
\(114\) 0 0
\(115\) −1.33019 1.33019i −0.124041 0.124041i
\(116\) −8.67647 + 14.2145i −0.805590 + 1.31978i
\(117\) 0 0
\(118\) 2.54627 + 21.3532i 0.234403 + 1.96572i
\(119\) 8.44549i 0.774196i
\(120\) 0 0
\(121\) 9.69256i 0.881142i
\(122\) 17.9844 2.14455i 1.62823 0.194158i
\(123\) 0 0
\(124\) −0.757359 3.13048i −0.0680129 0.281125i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) 4.18636 0.371480 0.185740 0.982599i \(-0.440532\pi\)
0.185740 + 0.982599i \(0.440532\pi\)
\(128\) −11.3021 + 0.513421i −0.998970 + 0.0453804i
\(129\) 0 0
\(130\) −0.926518 + 1.17740i −0.0812610 + 0.103265i
\(131\) −4.29734 4.29734i −0.375460 0.375460i 0.494001 0.869461i \(-0.335534\pi\)
−0.869461 + 0.494001i \(0.835534\pi\)
\(132\) 0 0
\(133\) −2.66981 + 2.66981i −0.231502 + 0.231502i
\(134\) 5.85304 0.697947i 0.505625 0.0602934i
\(135\) 0 0
\(136\) −15.3579 7.03127i −1.31693 0.602927i
\(137\) 7.68499i 0.656573i 0.944578 + 0.328287i \(0.106471\pi\)
−0.944578 + 0.328287i \(0.893529\pi\)
\(138\) 0 0
\(139\) −10.8776 + 10.8776i −0.922630 + 0.922630i −0.997215 0.0745848i \(-0.976237\pi\)
0.0745848 + 0.997215i \(0.476237\pi\)
\(140\) 1.47363 2.41421i 0.124544 0.204038i
\(141\) 0 0
\(142\) −7.54469 5.93706i −0.633137 0.498227i
\(143\) −1.21137 −0.101300
\(144\) 0 0
\(145\) 8.32666 0.691492
\(146\) −2.58579 2.03480i −0.214001 0.168401i
\(147\) 0 0
\(148\) −8.92382 5.44706i −0.733534 0.447746i
\(149\) −12.0559 + 12.0559i −0.987656 + 0.987656i −0.999925 0.0122684i \(-0.996095\pi\)
0.0122684 + 0.999925i \(0.496095\pi\)
\(150\) 0 0
\(151\) 4.21450i 0.342971i −0.985187 0.171486i \(-0.945143\pi\)
0.985187 0.171486i \(-0.0548567\pi\)
\(152\) −2.63224 7.07773i −0.213503 0.574080i
\(153\) 0 0
\(154\) 2.27078 0.270780i 0.182985 0.0218201i
\(155\) −1.13872 + 1.13872i −0.0914643 + 0.0914643i
\(156\) 0 0
\(157\) −9.53775 9.53775i −0.761195 0.761195i 0.215343 0.976538i \(-0.430913\pi\)
−0.976538 + 0.215343i \(0.930913\pi\)
\(158\) 3.73505 4.74642i 0.297144 0.377605i
\(159\) 0 0
\(160\) 3.16333 + 4.68971i 0.250083 + 0.370754i
\(161\) 2.66038 0.209668
\(162\) 0 0
\(163\) 11.0805 + 11.0805i 0.867891 + 0.867891i 0.992239 0.124348i \(-0.0396838\pi\)
−0.124348 + 0.992239i \(0.539684\pi\)
\(164\) −17.0524 + 4.12549i −1.33157 + 0.322146i
\(165\) 0 0
\(166\) −6.18676 + 0.737742i −0.480186 + 0.0572599i
\(167\) 11.7359i 0.908150i 0.890963 + 0.454075i \(0.150030\pi\)
−0.890963 + 0.454075i \(0.849970\pi\)
\(168\) 0 0
\(169\) 11.8776i 0.913665i
\(170\) 1.00000 + 8.38607i 0.0766965 + 0.643183i
\(171\) 0 0
\(172\) 1.79715 + 1.09698i 0.137032 + 0.0836436i
\(173\) −7.18766 7.18766i −0.546468 0.546468i 0.378950 0.925417i \(-0.376285\pi\)
−0.925417 + 0.378950i \(0.876285\pi\)
\(174\) 0 0
\(175\) −1.41421 −0.106904
\(176\) −1.39813 + 4.35480i −0.105388 + 0.328256i
\(177\) 0 0
\(178\) 11.4663 + 9.02303i 0.859434 + 0.676305i
\(179\) 6.84832 + 6.84832i 0.511868 + 0.511868i 0.915098 0.403231i \(-0.132113\pi\)
−0.403231 + 0.915098i \(0.632113\pi\)
\(180\) 0 0
\(181\) 8.26725 8.26725i 0.614500 0.614500i −0.329615 0.944115i \(-0.606919\pi\)
0.944115 + 0.329615i \(0.106919\pi\)
\(182\) −0.250882 2.10392i −0.0185966 0.155953i
\(183\) 0 0
\(184\) −2.21490 + 4.83785i −0.163284 + 0.356651i
\(185\) 5.22746i 0.384330i
\(186\) 0 0
\(187\) −4.82843 + 4.82843i −0.353090 + 0.353090i
\(188\) 6.37755 + 26.3611i 0.465131 + 1.92258i
\(189\) 0 0
\(190\) −2.33490 + 2.96715i −0.169392 + 0.215260i
\(191\) −17.2435 −1.24770 −0.623849 0.781545i \(-0.714432\pi\)
−0.623849 + 0.781545i \(0.714432\pi\)
\(192\) 0 0
\(193\) −26.8347 −1.93160 −0.965802 0.259281i \(-0.916514\pi\)
−0.965802 + 0.259281i \(0.916514\pi\)
\(194\) 3.25559 4.13714i 0.233738 0.297030i
\(195\) 0 0
\(196\) −2.35147 9.71960i −0.167962 0.694257i
\(197\) −0.821763 + 0.821763i −0.0585482 + 0.0585482i −0.735775 0.677226i \(-0.763182\pi\)
0.677226 + 0.735775i \(0.263182\pi\)
\(198\) 0 0
\(199\) 20.3263i 1.44089i 0.693512 + 0.720445i \(0.256063\pi\)
−0.693512 + 0.720445i \(0.743937\pi\)
\(200\) 1.17740 2.57172i 0.0832548 0.181848i
\(201\) 0 0
\(202\) 1.25402 + 10.5163i 0.0882323 + 0.739922i
\(203\) −8.32666 + 8.32666i −0.584417 + 0.584417i
\(204\) 0 0
\(205\) 6.20285 + 6.20285i 0.433226 + 0.433226i
\(206\) −17.6155 13.8620i −1.22733 0.965811i
\(207\) 0 0
\(208\) 4.03480 + 1.29539i 0.279763 + 0.0898191i
\(209\) −3.05275 −0.211163
\(210\) 0 0
\(211\) 20.0625 + 20.0625i 1.38116 + 1.38116i 0.842560 + 0.538603i \(0.181048\pi\)
0.538603 + 0.842560i \(0.318952\pi\)
\(212\) 2.08402 + 1.27208i 0.143131 + 0.0873667i
\(213\) 0 0
\(214\) 0.317238 + 2.66038i 0.0216860 + 0.181860i
\(215\) 1.05275i 0.0717969i
\(216\) 0 0
\(217\) 2.27744i 0.154603i
\(218\) 17.2239 2.05386i 1.16655 0.139105i
\(219\) 0 0
\(220\) 2.22274 0.537750i 0.149857 0.0362551i
\(221\) 4.47363 + 4.47363i 0.300929 + 0.300929i
\(222\) 0 0
\(223\) 10.6787 0.715099 0.357549 0.933894i \(-0.383612\pi\)
0.357549 + 0.933894i \(0.383612\pi\)
\(224\) −7.85304 1.52637i −0.524703 0.101985i
\(225\) 0 0
\(226\) −13.4024 + 17.0316i −0.891517 + 1.13292i
\(227\) −17.5514 17.5514i −1.16492 1.16492i −0.983383 0.181541i \(-0.941891\pi\)
−0.181541 0.983383i \(-0.558109\pi\)
\(228\) 0 0
\(229\) −9.61077 + 9.61077i −0.635098 + 0.635098i −0.949342 0.314245i \(-0.898249\pi\)
0.314245 + 0.949342i \(0.398249\pi\)
\(230\) 2.64167 0.315007i 0.174186 0.0207709i
\(231\) 0 0
\(232\) −8.20951 22.0742i −0.538981 1.44924i
\(233\) 16.4268i 1.07615i 0.842896 + 0.538077i \(0.180849\pi\)
−0.842896 + 0.538077i \(0.819151\pi\)
\(234\) 0 0
\(235\) 9.58892 9.58892i 0.625512 0.625512i
\(236\) −25.9582 15.8448i −1.68974 1.03141i
\(237\) 0 0
\(238\) −9.38607 7.38607i −0.608409 0.478768i
\(239\) 14.6439 0.947235 0.473618 0.880731i \(-0.342948\pi\)
0.473618 + 0.880731i \(0.342948\pi\)
\(240\) 0 0
\(241\) 23.3529 1.50430 0.752148 0.658995i \(-0.229018\pi\)
0.752148 + 0.658995i \(0.229018\pi\)
\(242\) −10.7720 8.47671i −0.692453 0.544904i
\(243\) 0 0
\(244\) −13.3450 + 21.8628i −0.854325 + 1.39962i
\(245\) −3.53553 + 3.53553i −0.225877 + 0.225877i
\(246\) 0 0
\(247\) 2.82843i 0.179969i
\(248\) 4.14148 + 1.89608i 0.262984 + 0.120401i
\(249\) 0 0
\(250\) −1.40426 + 0.167452i −0.0888135 + 0.0105906i
\(251\) 12.8085 12.8085i 0.808467 0.808467i −0.175935 0.984402i \(-0.556295\pi\)
0.984402 + 0.175935i \(0.0562947\pi\)
\(252\) 0 0
\(253\) 1.52099 + 1.52099i 0.0956236 + 0.0956236i
\(254\) −3.66122 + 4.65260i −0.229725 + 0.291930i
\(255\) 0 0
\(256\) 9.31371 13.0098i 0.582107 0.813112i
\(257\) 22.3024 1.39119 0.695594 0.718436i \(-0.255141\pi\)
0.695594 + 0.718436i \(0.255141\pi\)
\(258\) 0 0
\(259\) −5.22746 5.22746i −0.324818 0.324818i
\(260\) −0.498235 2.05941i −0.0308992 0.127719i
\(261\) 0 0
\(262\) 8.53422 1.01767i 0.527246 0.0628716i
\(263\) 2.49471i 0.153830i 0.997038 + 0.0769151i \(0.0245070\pi\)
−0.997038 + 0.0769151i \(0.975493\pi\)
\(264\) 0 0
\(265\) 1.22079i 0.0749926i
\(266\) −0.632245 5.30205i −0.0387654 0.325090i
\(267\) 0 0
\(268\) −4.34315 + 7.11529i −0.265300 + 0.434636i
\(269\) −19.0031 19.0031i −1.15864 1.15864i −0.984768 0.173874i \(-0.944372\pi\)
−0.173874 0.984768i \(-0.555628\pi\)
\(270\) 0 0
\(271\) 21.7918 1.32376 0.661878 0.749612i \(-0.269760\pi\)
0.661878 + 0.749612i \(0.269760\pi\)
\(272\) 21.2458 10.9191i 1.28821 0.662068i
\(273\) 0 0
\(274\) −8.54088 6.72098i −0.515974 0.406029i
\(275\) −0.808530 0.808530i −0.0487562 0.0487562i
\(276\) 0 0
\(277\) −11.6401 + 11.6401i −0.699385 + 0.699385i −0.964278 0.264893i \(-0.914663\pi\)
0.264893 + 0.964278i \(0.414663\pi\)
\(278\) −2.57597 21.6022i −0.154496 1.29562i
\(279\) 0 0
\(280\) 1.39432 + 3.74912i 0.0833263 + 0.224053i
\(281\) 1.55136i 0.0925462i 0.998929 + 0.0462731i \(0.0147344\pi\)
−0.998929 + 0.0462731i \(0.985266\pi\)
\(282\) 0 0
\(283\) 18.5737 18.5737i 1.10409 1.10409i 0.110183 0.993911i \(-0.464856\pi\)
0.993911 0.110183i \(-0.0351436\pi\)
\(284\) 13.1966 3.19265i 0.783072 0.189449i
\(285\) 0 0
\(286\) 1.05941 1.34628i 0.0626444 0.0796072i
\(287\) −12.4057 −0.732285
\(288\) 0 0
\(289\) 18.6631 1.09783
\(290\) −7.28216 + 9.25402i −0.427623 + 0.543415i
\(291\) 0 0
\(292\) 4.52284 1.09422i 0.264679 0.0640341i
\(293\) 10.5671 10.5671i 0.617335 0.617335i −0.327512 0.944847i \(-0.606210\pi\)
0.944847 + 0.327512i \(0.106210\pi\)
\(294\) 0 0
\(295\) 15.2060i 0.885326i
\(296\) 13.8581 5.15391i 0.805487 0.299565i
\(297\) 0 0
\(298\) −2.85499 23.9421i −0.165385 1.38693i
\(299\) 1.40922 1.40922i 0.0814974 0.0814974i
\(300\) 0 0
\(301\) 1.05275 + 1.05275i 0.0606794 + 0.0606794i
\(302\) 4.68388 + 3.68583i 0.269527 + 0.212096i
\(303\) 0 0
\(304\) 10.1680 + 3.26449i 0.583177 + 0.187231i
\(305\) 12.8070 0.733324
\(306\) 0 0
\(307\) −11.4584 11.4584i −0.653968 0.653968i 0.299978 0.953946i \(-0.403021\pi\)
−0.953946 + 0.299978i \(0.903021\pi\)
\(308\) −1.68499 + 2.76049i −0.0960114 + 0.157294i
\(309\) 0 0
\(310\) −0.269664 2.26142i −0.0153159 0.128440i
\(311\) 6.80196i 0.385704i 0.981228 + 0.192852i \(0.0617737\pi\)
−0.981228 + 0.192852i \(0.938226\pi\)
\(312\) 0 0
\(313\) 15.8382i 0.895229i −0.894227 0.447615i \(-0.852274\pi\)
0.894227 0.447615i \(-0.147726\pi\)
\(314\) 18.9413 2.25866i 1.06892 0.127464i
\(315\) 0 0
\(316\) 2.00852 + 8.30205i 0.112988 + 0.467027i
\(317\) 9.37665 + 9.37665i 0.526645 + 0.526645i 0.919570 0.392925i \(-0.128537\pi\)
−0.392925 + 0.919570i \(0.628537\pi\)
\(318\) 0 0
\(319\) −9.52099 −0.533073
\(320\) −7.97852 0.585786i −0.446013 0.0327465i
\(321\) 0 0
\(322\) −2.32666 + 2.95668i −0.129660 + 0.164769i
\(323\) 11.2739 + 11.2739i 0.627297 + 0.627297i
\(324\) 0 0
\(325\) −0.749118 + 0.749118i −0.0415536 + 0.0415536i
\(326\) −22.0051 + 2.62400i −1.21875 + 0.145330i
\(327\) 0 0
\(328\) 10.3283 22.5595i 0.570287 1.24564i
\(329\) 19.1778i 1.05731i
\(330\) 0 0
\(331\) 9.26059 9.26059i 0.509008 0.509008i −0.405214 0.914222i \(-0.632803\pi\)
0.914222 + 0.405214i \(0.132803\pi\)
\(332\) 4.59078 7.52099i 0.251952 0.412768i
\(333\) 0 0
\(334\) −13.0429 10.2637i −0.713677 0.561606i
\(335\) 4.16804 0.227725
\(336\) 0 0
\(337\) 2.99411 0.163099 0.0815497 0.996669i \(-0.474013\pi\)
0.0815497 + 0.996669i \(0.474013\pi\)
\(338\) 13.2005 + 10.3877i 0.718011 + 0.565016i
\(339\) 0 0
\(340\) −10.1946 6.22274i −0.552880 0.337476i
\(341\) 1.30205 1.30205i 0.0705101 0.0705101i
\(342\) 0 0
\(343\) 16.9706i 0.916324i
\(344\) −2.79086 + 1.03794i −0.150473 + 0.0559618i
\(345\) 0 0
\(346\) 14.2742 1.70213i 0.767385 0.0915071i
\(347\) 14.4455 14.4455i 0.775474 0.775474i −0.203583 0.979058i \(-0.565259\pi\)
0.979058 + 0.203583i \(0.0652588\pi\)
\(348\) 0 0
\(349\) −5.63668 5.63668i −0.301724 0.301724i 0.539964 0.841688i \(-0.318438\pi\)
−0.841688 + 0.539964i \(0.818438\pi\)
\(350\) 1.23681 1.57172i 0.0661104 0.0840118i
\(351\) 0 0
\(352\) −3.61706 5.36237i −0.192790 0.285815i
\(353\) 26.9058 1.43205 0.716025 0.698074i \(-0.245960\pi\)
0.716025 + 0.698074i \(0.245960\pi\)
\(354\) 0 0
\(355\) −4.80029 4.80029i −0.254773 0.254773i
\(356\) −20.0559 + 4.85213i −1.06296 + 0.257163i
\(357\) 0 0
\(358\) −13.6003 + 1.62177i −0.718798 + 0.0857133i
\(359\) 14.7533i 0.778649i 0.921101 + 0.389325i \(0.127292\pi\)
−0.921101 + 0.389325i \(0.872708\pi\)
\(360\) 0 0
\(361\) 11.8721i 0.624849i
\(362\) 1.95779 + 16.4182i 0.102899 + 0.862921i
\(363\) 0 0
\(364\) 2.55765 + 1.56118i 0.134057 + 0.0818279i
\(365\) −1.64520 1.64520i −0.0861136 0.0861136i
\(366\) 0 0
\(367\) −34.6779 −1.81017 −0.905086 0.425228i \(-0.860194\pi\)
−0.905086 + 0.425228i \(0.860194\pi\)
\(368\) −3.43959 6.69256i −0.179301 0.348874i
\(369\) 0 0
\(370\) −5.80965 4.57172i −0.302029 0.237672i
\(371\) 1.22079 + 1.22079i 0.0633803 + 0.0633803i
\(372\) 0 0
\(373\) 10.8679 10.8679i 0.562721 0.562721i −0.367359 0.930079i \(-0.619738\pi\)
0.930079 + 0.367359i \(0.119738\pi\)
\(374\) −1.14343 9.58892i −0.0591256 0.495831i
\(375\) 0 0
\(376\) −34.8745 15.9665i −1.79851 0.823408i
\(377\) 8.82137i 0.454324i
\(378\) 0 0
\(379\) 12.9374 12.9374i 0.664551 0.664551i −0.291898 0.956449i \(-0.594287\pi\)
0.956449 + 0.291898i \(0.0942868\pi\)
\(380\) −1.25559 5.18989i −0.0644106 0.266236i
\(381\) 0 0
\(382\) 15.0805 19.1640i 0.771585 0.980515i
\(383\) 12.1814 0.622439 0.311219 0.950338i \(-0.399263\pi\)
0.311219 + 0.950338i \(0.399263\pi\)
\(384\) 0 0
\(385\) 1.61706 0.0824130
\(386\) 23.4685 29.8233i 1.19452 1.51797i
\(387\) 0 0
\(388\) 1.75070 + 7.23635i 0.0888781 + 0.367370i
\(389\) 2.57246 2.57246i 0.130429 0.130429i −0.638879 0.769308i \(-0.720601\pi\)
0.769308 + 0.638879i \(0.220601\pi\)
\(390\) 0 0
\(391\) 11.2341i 0.568134i
\(392\) 12.8586 + 5.88700i 0.649457 + 0.297339i
\(393\) 0 0
\(394\) −0.194604 1.63196i −0.00980402 0.0822172i
\(395\) 3.01990 3.01990i 0.151948 0.151948i
\(396\) 0 0
\(397\) 8.94753 + 8.94753i 0.449064 + 0.449064i 0.895043 0.445979i \(-0.147145\pi\)
−0.445979 + 0.895043i \(0.647145\pi\)
\(398\) −22.5900 17.7765i −1.13234 0.891056i
\(399\) 0 0
\(400\) 1.82843 + 3.55765i 0.0914214 + 0.177882i
\(401\) −14.3306 −0.715634 −0.357817 0.933792i \(-0.616479\pi\)
−0.357817 + 0.933792i \(0.616479\pi\)
\(402\) 0 0
\(403\) −1.20638 1.20638i −0.0600939 0.0600939i
\(404\) −12.7842 7.80342i −0.636038 0.388235i
\(405\) 0 0
\(406\) −1.97186 16.5362i −0.0978618 0.820676i
\(407\) 5.97725i 0.296281i
\(408\) 0 0
\(409\) 11.2019i 0.553900i 0.960884 + 0.276950i \(0.0893237\pi\)
−0.960884 + 0.276950i \(0.910676\pi\)
\(410\) −12.3184 + 1.46891i −0.608363 + 0.0725445i
\(411\) 0 0
\(412\) 30.8117 7.45429i 1.51798 0.367246i
\(413\) −15.2060 15.2060i −0.748237 0.748237i
\(414\) 0 0
\(415\) −4.40569 −0.216267
\(416\) −4.96833 + 3.35127i −0.243592 + 0.164310i
\(417\) 0 0
\(418\) 2.66981 3.39274i 0.130585 0.165944i
\(419\) 12.6405 + 12.6405i 0.617528 + 0.617528i 0.944897 0.327369i \(-0.106162\pi\)
−0.327369 + 0.944897i \(0.606162\pi\)
\(420\) 0 0
\(421\) −2.83862 + 2.83862i −0.138346 + 0.138346i −0.772888 0.634542i \(-0.781189\pi\)
0.634542 + 0.772888i \(0.281189\pi\)
\(422\) −39.8428 + 4.75107i −1.93952 + 0.231278i
\(423\) 0 0
\(424\) −3.23635 + 1.20362i −0.157171 + 0.0584527i
\(425\) 5.97186i 0.289678i
\(426\) 0 0
\(427\) −12.8070 + 12.8070i −0.619772 + 0.619772i
\(428\) −3.23412 1.97409i −0.156327 0.0954214i
\(429\) 0 0
\(430\) 1.16999 + 0.920690i 0.0564222 + 0.0443996i
\(431\) 29.9874 1.44444 0.722222 0.691662i \(-0.243121\pi\)
0.722222 + 0.691662i \(0.243121\pi\)
\(432\) 0 0
\(433\) −23.2176 −1.11577 −0.557884 0.829919i \(-0.688387\pi\)
−0.557884 + 0.829919i \(0.688387\pi\)
\(434\) 2.53109 + 1.99176i 0.121496 + 0.0956075i
\(435\) 0 0
\(436\) −12.7807 + 20.9383i −0.612083 + 1.00276i
\(437\) 3.55136 3.55136i 0.169884 0.169884i
\(438\) 0 0
\(439\) 11.2110i 0.535070i 0.963548 + 0.267535i \(0.0862092\pi\)
−0.963548 + 0.267535i \(0.913791\pi\)
\(440\) −1.34628 + 2.94059i −0.0641814 + 0.140187i
\(441\) 0 0
\(442\) −8.88431 + 1.05941i −0.422584 + 0.0503911i
\(443\) −21.0684 + 21.0684i −1.00099 + 1.00099i −0.000992295 1.00000i \(0.500316\pi\)
−1.00000 0.000992295i \(0.999684\pi\)
\(444\) 0 0
\(445\) 7.29539 + 7.29539i 0.345835 + 0.345835i
\(446\) −9.33915 + 11.8680i −0.442222 + 0.561966i
\(447\) 0 0
\(448\) 8.56431 7.39274i 0.404626 0.349274i
\(449\) −20.6970 −0.976753 −0.488376 0.872633i \(-0.662411\pi\)
−0.488376 + 0.872633i \(0.662411\pi\)
\(450\) 0 0
\(451\) −7.09254 7.09254i −0.333975 0.333975i
\(452\) −7.20716 29.7902i −0.338996 1.40121i
\(453\) 0 0
\(454\) 34.8558 4.15639i 1.63586 0.195069i
\(455\) 1.49824i 0.0702383i
\(456\) 0 0
\(457\) 18.7986i 0.879362i 0.898154 + 0.439681i \(0.144909\pi\)
−0.898154 + 0.439681i \(0.855091\pi\)
\(458\) −2.27595 19.0863i −0.106348 0.891845i
\(459\) 0 0
\(460\) −1.96021 + 3.21137i −0.0913950 + 0.149731i
\(461\) 1.68943 + 1.68943i 0.0786844 + 0.0786844i 0.745354 0.666669i \(-0.232281\pi\)
−0.666669 + 0.745354i \(0.732281\pi\)
\(462\) 0 0
\(463\) −38.0434 −1.76803 −0.884014 0.467460i \(-0.845169\pi\)
−0.884014 + 0.467460i \(0.845169\pi\)
\(464\) 31.7123 + 10.1814i 1.47221 + 0.472658i
\(465\) 0 0
\(466\) −18.2562 14.3662i −0.845704 0.665500i
\(467\) −15.2247 15.2247i −0.704515 0.704515i 0.260861 0.965376i \(-0.415993\pi\)
−0.965376 + 0.260861i \(0.915993\pi\)
\(468\) 0 0
\(469\) −4.16804 + 4.16804i −0.192462 + 0.192462i
\(470\) 2.27078 + 19.0429i 0.104743 + 0.878385i
\(471\) 0 0
\(472\) 40.3115 14.9920i 1.85549 0.690064i
\(473\) 1.20375i 0.0553484i
\(474\) 0 0
\(475\) −1.88784 + 1.88784i −0.0866200 + 0.0866200i
\(476\) 16.4173 3.97186i 0.752488 0.182050i
\(477\) 0 0
\(478\) −12.8070 + 16.2748i −0.585776 + 0.744393i
\(479\) 13.0004 0.594002 0.297001 0.954877i \(-0.404013\pi\)
0.297001 + 0.954877i \(0.404013\pi\)
\(480\) 0 0
\(481\) −5.53803 −0.252512
\(482\) −20.4235 + 25.9538i −0.930266 + 1.18216i
\(483\) 0 0
\(484\) 18.8416 4.55835i 0.856434 0.207198i
\(485\) 2.63224 2.63224i 0.119524 0.119524i
\(486\) 0 0
\(487\) 16.1068i 0.729868i −0.931033 0.364934i \(-0.881092\pi\)
0.931033 0.364934i \(-0.118908\pi\)
\(488\) −12.6268 33.9516i −0.571587 1.53692i
\(489\) 0 0
\(490\) −0.837260 7.02132i −0.0378235 0.317191i
\(491\) 16.9993 16.9993i 0.767169 0.767169i −0.210438 0.977607i \(-0.567489\pi\)
0.977607 + 0.210438i \(0.0674891\pi\)
\(492\) 0 0
\(493\) 35.1614 + 35.1614i 1.58359 + 1.58359i
\(494\) −3.14343 2.47363i −0.141430 0.111294i
\(495\) 0 0
\(496\) −5.72922 + 2.94449i −0.257250 + 0.132212i
\(497\) 9.60058 0.430645
\(498\) 0 0
\(499\) −3.60373 3.60373i −0.161325 0.161325i 0.621828 0.783154i \(-0.286390\pi\)
−0.783154 + 0.621828i \(0.786390\pi\)
\(500\) 1.04201 1.70711i 0.0466001 0.0763441i
\(501\) 0 0
\(502\) 3.03322 + 25.4368i 0.135379 + 1.13530i
\(503\) 25.4482i 1.13468i −0.823484 0.567340i \(-0.807972\pi\)
0.823484 0.567340i \(-0.192028\pi\)
\(504\) 0 0
\(505\) 7.48881i 0.333248i
\(506\) −3.02057 + 0.360189i −0.134281 + 0.0160124i
\(507\) 0 0
\(508\) −1.96882 8.13795i −0.0873523 0.361063i
\(509\) −8.08087 8.08087i −0.358178 0.358178i 0.504963 0.863141i \(-0.331506\pi\)
−0.863141 + 0.504963i \(0.831506\pi\)
\(510\) 0 0
\(511\) 3.29040 0.145559
\(512\) 6.31333 + 21.7288i 0.279013 + 0.960287i
\(513\) 0 0
\(514\) −19.5048 + 24.7863i −0.860319 + 1.09328i
\(515\) −11.2078 11.2078i −0.493876 0.493876i
\(516\) 0 0
\(517\) −10.9643 + 10.9643i −0.482209 + 0.482209i
\(518\) 10.3814 1.23793i 0.456131 0.0543915i
\(519\) 0 0
\(520\) 2.72451 + 1.24735i 0.119478 + 0.0547000i
\(521\) 10.7981i 0.473071i 0.971623 + 0.236536i \(0.0760120\pi\)
−0.971623 + 0.236536i \(0.923988\pi\)
\(522\) 0 0
\(523\) 17.9785 17.9785i 0.786146 0.786146i −0.194714 0.980860i \(-0.562378\pi\)
0.980860 + 0.194714i \(0.0623779\pi\)
\(524\) −6.33267 + 10.3747i −0.276644 + 0.453221i
\(525\) 0 0
\(526\) −2.77254 2.18177i −0.120889 0.0951295i
\(527\) −9.61706 −0.418926
\(528\) 0 0
\(529\) 19.4612 0.846138
\(530\) 1.35675 + 1.06765i 0.0589336 + 0.0463759i
\(531\) 0 0
\(532\) 6.44549 + 3.93430i 0.279447 + 0.170573i
\(533\) −6.57137 + 6.57137i −0.284638 + 0.284638i
\(534\) 0 0
\(535\) 1.89450i 0.0819065i
\(536\) −4.10940 11.0496i −0.177499 0.477270i
\(537\) 0 0
\(538\) 37.7389 4.50019i 1.62704 0.194017i
\(539\) 4.04265 4.04265i 0.174129 0.174129i
\(540\) 0 0
\(541\) 6.61666 + 6.61666i 0.284473 + 0.284473i 0.834890 0.550417i \(-0.185531\pi\)
−0.550417 + 0.834890i \(0.685531\pi\)
\(542\) −19.0582 + 24.2188i −0.818619 + 1.04028i
\(543\) 0 0
\(544\) −6.44549 + 33.1614i −0.276348 + 1.42178i
\(545\) 12.2654 0.525392
\(546\) 0 0
\(547\) −9.62205 9.62205i −0.411409 0.411409i 0.470820 0.882229i \(-0.343958\pi\)
−0.882229 + 0.470820i \(0.843958\pi\)
\(548\) 14.9390 3.61421i 0.638163 0.154391i
\(549\) 0 0
\(550\) 1.60568 0.191470i 0.0684666 0.00816432i
\(551\) 22.2306i 0.947055i
\(552\) 0 0
\(553\) 6.03979i 0.256838i
\(554\) −2.75652 23.1164i −0.117113 0.982122i
\(555\) 0 0
\(556\) 26.2610 + 16.0296i 1.11371 + 0.679806i
\(557\) 2.50137 + 2.50137i 0.105986 + 0.105986i 0.758111 0.652125i \(-0.226122\pi\)
−0.652125 + 0.758111i \(0.726122\pi\)
\(558\) 0 0
\(559\) 1.11529 0.0471719
\(560\) −5.38607 1.72922i −0.227603 0.0730729i
\(561\) 0 0
\(562\) −1.72413 1.35675i −0.0727282 0.0572312i
\(563\) 2.20547 + 2.20547i 0.0929496 + 0.0929496i 0.752053 0.659103i \(-0.229064\pi\)
−0.659103 + 0.752053i \(0.729064\pi\)
\(564\) 0 0
\(565\) −10.8363 + 10.8363i −0.455885 + 0.455885i
\(566\) 4.39850 + 36.8861i 0.184883 + 1.55044i
\(567\) 0 0
\(568\) −7.99294 + 17.4584i −0.335376 + 0.732540i
\(569\) 17.5569i 0.736023i −0.929821 0.368011i \(-0.880039\pi\)
0.929821 0.368011i \(-0.119961\pi\)
\(570\) 0 0
\(571\) −5.36237 + 5.36237i −0.224408 + 0.224408i −0.810352 0.585944i \(-0.800724\pi\)
0.585944 + 0.810352i \(0.300724\pi\)
\(572\) 0.569699 + 2.35480i 0.0238203 + 0.0984592i
\(573\) 0 0
\(574\) 10.8495 13.7873i 0.452850 0.575472i
\(575\) 1.88118 0.0784504
\(576\) 0 0
\(577\) 13.7422 0.572093 0.286047 0.958216i \(-0.407659\pi\)
0.286047 + 0.958216i \(0.407659\pi\)
\(578\) −16.3220 + 20.7417i −0.678906 + 0.862740i
\(579\) 0 0
\(580\) −3.91598 16.1864i −0.162602 0.672102i
\(581\) 4.40569 4.40569i 0.182779 0.182779i
\(582\) 0 0
\(583\) 1.39589i 0.0578120i
\(584\) −2.73941 + 5.98352i −0.113358 + 0.247600i
\(585\) 0 0
\(586\) 2.50242 + 20.9855i 0.103374 + 0.866902i
\(587\) −17.5608 + 17.5608i −0.724811 + 0.724811i −0.969581 0.244770i \(-0.921288\pi\)
0.244770 + 0.969581i \(0.421288\pi\)
\(588\) 0 0
\(589\) −3.04017 3.04017i −0.125268 0.125268i
\(590\) −16.8995 13.2985i −0.695741 0.547492i
\(591\) 0 0
\(592\) −6.39184 + 19.9089i −0.262703 + 0.818252i
\(593\) −41.3973 −1.69998 −0.849992 0.526795i \(-0.823394\pi\)
−0.849992 + 0.526795i \(0.823394\pi\)
\(594\) 0 0
\(595\) −5.97186 5.97186i −0.244822 0.244822i
\(596\) 29.1055 + 17.7659i 1.19221 + 0.727718i
\(597\) 0 0
\(598\) 0.333722 + 2.79862i 0.0136469 + 0.114444i
\(599\) 36.7651i 1.50218i 0.660199 + 0.751090i \(0.270472\pi\)
−0.660199 + 0.751090i \(0.729528\pi\)
\(600\) 0 0
\(601\) 13.3396i 0.544134i 0.962278 + 0.272067i \(0.0877073\pi\)
−0.962278 + 0.272067i \(0.912293\pi\)
\(602\) −2.09069 + 0.249304i −0.0852100 + 0.0101609i
\(603\) 0 0
\(604\) −8.19265 + 1.98205i −0.333354 + 0.0806486i
\(605\) −6.85367 6.85367i −0.278641 0.278641i
\(606\) 0 0
\(607\) −17.5393 −0.711898 −0.355949 0.934505i \(-0.615842\pi\)
−0.355949 + 0.934505i \(0.615842\pi\)
\(608\) −12.5206 + 8.44549i −0.507778 + 0.342510i
\(609\) 0 0
\(610\) −11.2004 + 14.2333i −0.453492 + 0.576289i
\(611\) 10.1586 + 10.1586i 0.410974 + 0.410974i
\(612\) 0 0
\(613\) 14.9538 14.9538i 0.603978 0.603978i −0.337388 0.941366i \(-0.609543\pi\)
0.941366 + 0.337388i \(0.109543\pi\)
\(614\) 22.7557 2.71351i 0.918344 0.109508i
\(615\) 0 0
\(616\) −1.59431 4.28687i −0.0642365 0.172723i
\(617\) 7.04165i 0.283486i 0.989903 + 0.141743i \(0.0452707\pi\)
−0.989903 + 0.141743i \(0.954729\pi\)
\(618\) 0 0
\(619\) 14.2931 14.2931i 0.574490 0.574490i −0.358890 0.933380i \(-0.616845\pi\)
0.933380 + 0.358890i \(0.116845\pi\)
\(620\) 2.74912 + 1.67805i 0.110407 + 0.0673921i
\(621\) 0 0
\(622\) −7.55951 5.94871i −0.303109 0.238522i
\(623\) −14.5908 −0.584567
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 17.6022 + 13.8515i 0.703524 + 0.553616i
\(627\) 0 0
\(628\) −14.0551 + 23.0262i −0.560859 + 0.918844i
\(629\) −22.0742 + 22.0742i −0.880156 + 0.880156i
\(630\) 0 0
\(631\) 41.3531i 1.64624i −0.567867 0.823121i \(-0.692231\pi\)
0.567867 0.823121i \(-0.307769\pi\)
\(632\) −10.9832 5.02842i −0.436890 0.200020i
\(633\) 0 0
\(634\) −18.6214 + 2.22051i −0.739549 + 0.0881878i
\(635\) −2.96021 + 2.96021i −0.117472 + 0.117472i
\(636\) 0 0
\(637\) −3.74559 3.74559i −0.148406 0.148406i
\(638\) 8.32666 10.5814i 0.329656 0.418920i
\(639\) 0 0
\(640\) 7.62872 8.35480i 0.301551 0.330253i
\(641\) 14.3228 0.565715 0.282857 0.959162i \(-0.408718\pi\)
0.282857 + 0.959162i \(0.408718\pi\)
\(642\) 0 0
\(643\) 13.4370 + 13.4370i 0.529902 + 0.529902i 0.920543 0.390641i \(-0.127747\pi\)
−0.390641 + 0.920543i \(0.627747\pi\)
\(644\) −1.25116 5.17157i −0.0493027 0.203789i
\(645\) 0 0
\(646\) −22.3892 + 2.66981i −0.880892 + 0.105042i
\(647\) 17.3231i 0.681043i −0.940237 0.340521i \(-0.889396\pi\)
0.940237 0.340521i \(-0.110604\pi\)
\(648\) 0 0
\(649\) 17.3870i 0.682501i
\(650\) −0.177401 1.48770i −0.00695823 0.0583522i
\(651\) 0 0
\(652\) 16.3285 26.7507i 0.639473 1.04764i
\(653\) −31.0148 31.0148i −1.21370 1.21370i −0.969800 0.243903i \(-0.921572\pi\)
−0.243903 0.969800i \(-0.578428\pi\)
\(654\) 0 0
\(655\) 6.07736 0.237462
\(656\) 16.0392 + 31.2082i 0.626227 + 1.21848i
\(657\) 0 0
\(658\) −21.3137 16.7721i −0.830895 0.653846i
\(659\) −29.8050 29.8050i −1.16104 1.16104i −0.984249 0.176789i \(-0.943429\pi\)
−0.176789 0.984249i \(-0.556571\pi\)
\(660\) 0 0
\(661\) −3.86546 + 3.86546i −0.150349 + 0.150349i −0.778274 0.627925i \(-0.783904\pi\)
0.627925 + 0.778274i \(0.283904\pi\)
\(662\) 2.19303 + 18.3909i 0.0852344 + 0.714782i
\(663\) 0 0
\(664\) 4.34371 + 11.6796i 0.168568 + 0.453257i
\(665\) 3.77568i 0.146415i
\(666\) 0 0
\(667\) 11.0761 11.0761i 0.428867 0.428867i
\(668\) 22.8136 5.51931i 0.882685 0.213549i
\(669\) 0 0
\(670\) −3.64520 + 4.63224i −0.140826 + 0.178959i
\(671\) −14.6439 −0.565322
\(672\) 0 0
\(673\) −24.2478 −0.934685 −0.467342 0.884076i \(-0.654788\pi\)
−0.467342 + 0.884076i \(0.654788\pi\)
\(674\) −2.61852 + 3.32756i −0.100862 + 0.128173i
\(675\) 0 0
\(676\) −23.0892 + 5.58598i −0.888046 + 0.214846i
\(677\) 9.11030 9.11030i 0.350137 0.350137i −0.510023 0.860161i \(-0.670363\pi\)
0.860161 + 0.510023i \(0.170363\pi\)
\(678\) 0 0
\(679\) 5.26449i 0.202033i
\(680\) 15.8316 5.88784i 0.607113 0.225788i
\(681\) 0 0
\(682\) 0.308343 + 2.58579i 0.0118071 + 0.0990149i
\(683\) 6.43216 6.43216i 0.246120 0.246120i −0.573256 0.819376i \(-0.694320\pi\)
0.819376 + 0.573256i \(0.194320\pi\)
\(684\) 0 0
\(685\) −5.43411 5.43411i −0.207627 0.207627i
\(686\) 18.8606 + 14.8418i 0.720101 + 0.566661i
\(687\) 0 0
\(688\) 1.28724 4.00942i 0.0490756 0.152858i
\(689\) 1.29332 0.0492716
\(690\) 0 0
\(691\) 8.79586 + 8.79586i 0.334610 + 0.334610i 0.854334 0.519724i \(-0.173965\pi\)
−0.519724 + 0.854334i \(0.673965\pi\)
\(692\) −10.5919 + 17.3525i −0.402644 + 0.659645i
\(693\) 0 0
\(694\) 3.42088 + 28.6877i 0.129855 + 1.08897i
\(695\) 15.3833i 0.583522i
\(696\) 0 0
\(697\) 52.3861i 1.98426i
\(698\) 11.1940 1.33484i 0.423701 0.0505244i
\(699\) 0 0
\(700\) 0.665096 + 2.74912i 0.0251383 + 0.103907i
\(701\) 27.7073 + 27.7073i 1.04649 + 1.04649i 0.998865 + 0.0476269i \(0.0151659\pi\)
0.0476269 + 0.998865i \(0.484834\pi\)
\(702\) 0 0
\(703\) −13.9563 −0.526372
\(704\) 9.12291 + 0.669808i 0.343833 + 0.0252443i
\(705\) 0 0
\(706\) −23.5307 + 29.9023i −0.885589 + 1.12539i
\(707\) −7.48881 7.48881i −0.281646 0.281646i
\(708\) 0 0
\(709\) −25.2865 + 25.2865i −0.949653 + 0.949653i −0.998792 0.0491386i \(-0.984352\pi\)
0.0491386 + 0.998792i \(0.484352\pi\)
\(710\) 9.53304 1.13677i 0.357769 0.0426622i
\(711\) 0 0
\(712\) 12.1475 26.5330i 0.455248 0.994367i
\(713\) 3.02944i 0.113453i
\(714\) 0 0
\(715\) 0.856566 0.856566i 0.0320338 0.0320338i
\(716\) 10.0919 16.5333i 0.377151 0.617879i
\(717\) 0 0
\(718\) −16.3964 12.9026i −0.611908 0.481522i
\(719\) −9.43253 −0.351774 −0.175887 0.984410i \(-0.556279\pi\)
−0.175887 + 0.984410i \(0.556279\pi\)
\(720\) 0 0
\(721\) 22.4157 0.834803
\(722\) 13.1943 + 10.3829i 0.491043 + 0.386410i
\(723\) 0 0
\(724\) −19.9589 12.1828i −0.741767 0.452771i
\(725\) −5.88784 + 5.88784i −0.218669 + 0.218669i
\(726\) 0 0
\(727\) 1.10144i 0.0408501i −0.999791 0.0204250i \(-0.993498\pi\)
0.999791 0.0204250i \(-0.00650195\pi\)
\(728\) −3.97186 + 1.47716i −0.147207 + 0.0547470i
\(729\) 0 0
\(730\) 3.26725 0.389604i 0.120926 0.0144199i
\(731\) 4.44549 4.44549i 0.164422 0.164422i
\(732\) 0 0
\(733\) −18.2214 18.2214i −0.673024 0.673024i 0.285388 0.958412i \(-0.407878\pi\)
−0.958412 + 0.285388i \(0.907878\pi\)
\(734\) 30.3279 38.5400i 1.11942 1.42254i
\(735\) 0 0
\(736\) 10.4460 + 2.03037i 0.385046 + 0.0748405i
\(737\) −4.76588 −0.175553
\(738\) 0 0
\(739\) −22.0953 22.0953i −0.812788 0.812788i 0.172263 0.985051i \(-0.444892\pi\)
−0.985051 + 0.172263i \(0.944892\pi\)
\(740\) 10.1618 2.45844i 0.373553 0.0903741i
\(741\) 0 0
\(742\) −2.42441 + 0.289099i −0.0890028 + 0.0106132i
\(743\) 47.3029i 1.73538i −0.497109 0.867688i \(-0.665605\pi\)
0.497109 0.867688i \(-0.334395\pi\)
\(744\) 0 0
\(745\) 17.0496i 0.624649i
\(746\) 2.57367 + 21.5830i 0.0942287 + 0.790209i
\(747\) 0 0
\(748\) 11.6569 + 7.11529i 0.426217 + 0.260161i
\(749\) −1.89450 1.89450i −0.0692236 0.0692236i
\(750\) 0 0
\(751\) −4.81234 −0.175605 −0.0878024 0.996138i \(-0.527984\pi\)
−0.0878024 + 0.996138i \(0.527984\pi\)
\(752\) 48.2445 24.7949i 1.75930 0.904177i
\(753\) 0 0
\(754\) −9.80382 7.71480i −0.357034 0.280957i
\(755\) 2.98010 + 2.98010i 0.108457 + 0.108457i
\(756\) 0 0
\(757\) 19.5838 19.5838i 0.711786 0.711786i −0.255123 0.966909i \(-0.582116\pi\)
0.966909 + 0.255123i \(0.0821159\pi\)
\(758\) 3.06375 + 25.6928i 0.111280 + 0.933206i
\(759\) 0 0
\(760\) 6.86599 + 3.14343i 0.249056 + 0.114024i
\(761\) 0.278003i 0.0100776i 0.999987 + 0.00503881i \(0.00160391\pi\)
−0.999987 + 0.00503881i \(0.998396\pi\)
\(762\) 0 0
\(763\) −12.2654 + 12.2654i −0.444037 + 0.444037i
\(764\) 8.10953 + 33.5201i 0.293393 + 1.21271i
\(765\) 0 0
\(766\) −10.6533 + 13.5380i −0.384920 + 0.489149i
\(767\) −16.1094 −0.581677
\(768\) 0 0
\(769\) −20.5808 −0.742162 −0.371081 0.928600i \(-0.621013\pi\)
−0.371081 + 0.928600i \(0.621013\pi\)
\(770\) −1.41421 + 1.79715i −0.0509647 + 0.0647649i
\(771\) 0 0
\(772\) 12.6202 + 52.1645i 0.454211 + 1.87744i
\(773\) −18.3427 + 18.3427i −0.659743 + 0.659743i −0.955319 0.295576i \(-0.904488\pi\)
0.295576 + 0.955319i \(0.404488\pi\)
\(774\) 0 0
\(775\) 1.61040i 0.0578471i
\(776\) −9.57336 4.38294i −0.343664 0.157338i
\(777\) 0 0
\(778\) 0.609191 + 5.10872i 0.0218406 + 0.183157i
\(779\) −16.5604 + 16.5604i −0.593338 + 0.593338i
\(780\) 0 0
\(781\) 5.48881 + 5.48881i 0.196405 + 0.196405i
\(782\) 12.4853 + 9.82490i 0.446473 + 0.351338i
\(783\) 0 0
\(784\) −17.7882 + 9.14214i −0.635294 + 0.326505i
\(785\) 13.4884 0.481422
\(786\) 0 0
\(787\) 21.0313 + 21.0313i 0.749684 + 0.749684i 0.974420 0.224736i \(-0.0721519\pi\)
−0.224736 + 0.974420i \(0.572152\pi\)
\(788\) 1.98391 + 1.21097i 0.0706740 + 0.0431391i
\(789\) 0 0
\(790\) 0.715151 + 5.99731i 0.0254439 + 0.213375i
\(791\) 21.6725i 0.770587i
\(792\) 0 0
\(793\) 13.5678i 0.481808i
\(794\) −17.7692 + 2.11889i −0.630604 + 0.0751966i
\(795\) 0 0
\(796\) 39.5126 9.55932i 1.40049 0.338821i
\(797\) 34.4451 + 34.4451i 1.22011 + 1.22011i 0.967593 + 0.252515i \(0.0812576\pi\)
0.252515 + 0.967593i \(0.418742\pi\)
\(798\) 0 0
\(799\) 80.9831 2.86498
\(800\) −5.55294 1.07931i −0.196326 0.0381594i
\(801\) 0 0
\(802\) 12.5329 15.9266i 0.442553 0.562387i
\(803\) 1.88118 + 1.88118i 0.0663852 + 0.0663852i
\(804\) 0 0
\(805\) −1.88118 + 1.88118i −0.0663027 + 0.0663027i
\(806\) 2.39578 0.285685i 0.0843877 0.0100628i
\(807\) 0 0
\(808\) 19.8530 7.38345i 0.698427 0.259749i
\(809\) 4.84727i 0.170421i −0.996363 0.0852106i \(-0.972844\pi\)
0.996363 0.0852106i \(-0.0271563\pi\)
\(810\) 0 0
\(811\) −37.5774 + 37.5774i −1.31952 + 1.31952i −0.405369 + 0.914153i \(0.632857\pi\)
−0.914153 + 0.405369i \(0.867143\pi\)
\(812\) 20.1023 + 12.2704i 0.705454 + 0.430606i
\(813\) 0 0
\(814\) 6.64294 + 5.22746i 0.232835 + 0.183222i
\(815\) −15.6702 −0.548903
\(816\) 0 0
\(817\) 2.81064 0.0983317
\(818\) −12.4495 9.79676i −0.435287 0.342536i
\(819\) 0 0
\(820\) 9.14067 14.9750i 0.319206 0.522950i
\(821\) 6.23725 6.23725i 0.217682 0.217682i −0.589839 0.807521i \(-0.700809\pi\)
0.807521 + 0.589839i \(0.200809\pi\)
\(822\) 0 0
\(823\) 20.6905i 0.721225i −0.932716 0.360613i \(-0.882568\pi\)
0.932716 0.360613i \(-0.117432\pi\)
\(824\) −18.6621 + 40.7624i −0.650126 + 1.42003i
\(825\) 0 0
\(826\) 30.1980 3.60097i 1.05072 0.125294i
\(827\) 5.53413 5.53413i 0.192440 0.192440i −0.604309 0.796750i \(-0.706551\pi\)
0.796750 + 0.604309i \(0.206551\pi\)
\(828\) 0 0
\(829\) −21.2582 21.2582i −0.738328 0.738328i 0.233926 0.972254i \(-0.424842\pi\)
−0.972254 + 0.233926i \(0.924842\pi\)
\(830\) 3.85304 4.89636i 0.133741 0.169955i
\(831\) 0 0
\(832\) 0.620589 8.45255i 0.0215151 0.293039i
\(833\) −29.8593 −1.03456
\(834\) 0 0
\(835\) −8.29852 8.29852i −0.287182 0.287182i
\(836\) 1.43569 + 5.93430i 0.0496543 + 0.205242i
\(837\) 0 0
\(838\) −25.1031 + 2.99343i −0.867173 + 0.103406i
\(839\) 3.55688i 0.122797i 0.998113 + 0.0613985i \(0.0195561\pi\)
−0.998113 + 0.0613985i \(0.980444\pi\)
\(840\) 0 0
\(841\) 40.3333i 1.39080i
\(842\) −0.672222 5.63730i −0.0231663 0.194274i
\(843\) 0 0
\(844\) 29.5647 48.4353i 1.01766 1.66721i
\(845\) 8.39876 + 8.39876i 0.288926 + 0.288926i
\(846\) 0 0
\(847\) 13.7073 0.470990
\(848\) 1.49271 4.64942i 0.0512600 0.159662i
\(849\) 0 0
\(850\) −6.63696 5.22274i −0.227646 0.179139i
\(851\) 6.95352 + 6.95352i 0.238364 + 0.238364i
\(852\) 0 0
\(853\) 7.41187 7.41187i 0.253777 0.253777i −0.568740 0.822517i \(-0.692569\pi\)
0.822517 + 0.568740i \(0.192569\pi\)
\(854\) −3.03285 25.4337i −0.103782 0.870324i
\(855\) 0 0
\(856\) 5.02238 1.86785i 0.171661 0.0638417i
\(857\) 31.1426i 1.06381i −0.846803 0.531906i \(-0.821476\pi\)
0.846803 0.531906i \(-0.178524\pi\)
\(858\) 0 0
\(859\) 32.0035 32.0035i 1.09195 1.09195i 0.0966247 0.995321i \(-0.469195\pi\)
0.995321 0.0966247i \(-0.0308047\pi\)
\(860\) −2.04646 + 0.495101i −0.0697837 + 0.0168828i
\(861\) 0 0
\(862\) −26.2258 + 33.3272i −0.893253 + 1.13513i
\(863\) 29.2347 0.995160 0.497580 0.867418i \(-0.334222\pi\)
0.497580 + 0.867418i \(0.334222\pi\)
\(864\) 0 0
\(865\) 10.1649 0.345617
\(866\) 20.3052 25.8034i 0.689998 0.876836i
\(867\) 0 0
\(868\) −4.42717 + 1.07107i −0.150268 + 0.0363544i
\(869\) −3.45305 + 3.45305i −0.117137 + 0.117137i
\(870\) 0 0
\(871\) 4.41568i 0.149619i
\(872\) −12.0928 32.5159i −0.409515 1.10113i
\(873\) 0 0
\(874\) 0.841007 + 7.05275i 0.0284475 + 0.238563i
\(875\) 1.00000 1.00000i 0.0338062 0.0338062i
\(876\) 0 0
\(877\) 11.9832 + 11.9832i 0.404645 + 0.404645i 0.879866 0.475221i \(-0.157632\pi\)
−0.475221 + 0.879866i \(0.657632\pi\)
\(878\) −12.4596 9.80465i −0.420490 0.330891i
\(879\) 0 0
\(880\) −2.09069 4.06793i −0.0704770 0.137130i
\(881\) −31.6194 −1.06529 −0.532643 0.846340i \(-0.678801\pi\)
−0.532643 + 0.846340i \(0.678801\pi\)
\(882\) 0 0
\(883\) −9.32520 9.32520i −0.313818 0.313818i 0.532569 0.846387i \(-0.321227\pi\)
−0.846387 + 0.532569i \(0.821227\pi\)
\(884\) 6.59245 10.8003i 0.221728 0.363253i
\(885\) 0 0
\(886\) −4.98928 41.8405i −0.167618 1.40566i
\(887\) 44.8049i 1.50440i −0.658934 0.752200i \(-0.728993\pi\)
0.658934 0.752200i \(-0.271007\pi\)
\(888\) 0 0
\(889\) 5.92041i 0.198564i
\(890\) −14.4881 + 1.72764i −0.485643 + 0.0579107i
\(891\) 0 0
\(892\) −5.02213 20.7585i −0.168153 0.695047i
\(893\) 25.6006 + 25.6006i 0.856691 + 0.856691i
\(894\) 0 0
\(895\) −9.68499 −0.323734
\(896\) 0.726086 + 15.9835i 0.0242568 + 0.533972i
\(897\) 0 0
\(898\) 18.1008 23.0021i 0.604030 0.767589i
\(899\) −9.48175 9.48175i −0.316234 0.316234i
\(900\) 0 0
\(901\) 5.15509 5.15509i 0.171741 0.171741i
\(902\) 14.0853 1.67961i 0.468989 0.0559247i
\(903\) 0 0
\(904\) 39.4111 + 18.0434i 1.31079 + 0.600116i
\(905\) 11.6917i 0.388644i
\(906\) 0 0
\(907\) −19.4040 + 19.4040i −0.644299 + 0.644299i −0.951609 0.307310i \(-0.900571\pi\)
0.307310 + 0.951609i \(0.400571\pi\)
\(908\) −25.8641 + 42.3727i −0.858331 + 1.40619i
\(909\) 0 0
\(910\) 1.66510 + 1.31029i 0.0551974 + 0.0434358i
\(911\) −44.4094 −1.47135 −0.735674 0.677336i \(-0.763134\pi\)
−0.735674 + 0.677336i \(0.763134\pi\)
\(912\) 0 0
\(913\) 5.03762 0.166721
\(914\) −20.8922 16.4405i −0.691054 0.543803i
\(915\) 0 0
\(916\) 23.2025 + 14.1627i 0.766631 + 0.467948i
\(917\) −6.07736 + 6.07736i −0.200692 + 0.200692i
\(918\) 0 0
\(919\) 26.3092i 0.867861i 0.900946 + 0.433931i \(0.142874\pi\)
−0.900946 + 0.433931i \(0.857126\pi\)
\(920\) −1.85471 4.98705i −0.0611479 0.164418i
\(921\) 0 0
\(922\) −3.35508 + 0.400078i −0.110494 + 0.0131759i
\(923\) 5.08548 5.08548i 0.167391 0.167391i
\(924\) 0 0
\(925\) −3.69637 3.69637i −0.121536 0.121536i
\(926\) 33.2712 42.2804i 1.09336 1.38942i
\(927\) 0 0
\(928\) −39.0496 + 26.3400i −1.28187 + 0.864653i
\(929\) 41.9008 1.37472 0.687360 0.726317i \(-0.258770\pi\)
0.687360 + 0.726317i \(0.258770\pi\)
\(930\) 0 0
\(931\) −9.43920 9.43920i −0.309357 0.309357i
\(932\) 31.9323 7.72541i 1.04598 0.253054i
\(933\) 0 0
\(934\) 30.2352 3.60540i 0.989325 0.117972i
\(935\) 6.82843i 0.223313i
\(936\) 0 0
\(937\) 50.1251i 1.63752i −0.574139 0.818758i \(-0.694663\pi\)
0.574139 0.818758i \(-0.305337\pi\)
\(938\) −0.987046 8.27744i −0.0322282 0.270268i
\(939\) 0 0
\(940\) −23.1497 14.1305i −0.755060 0.460885i
\(941\) −17.7315 17.7315i −0.578029 0.578029i 0.356331 0.934360i \(-0.384028\pi\)
−0.934360 + 0.356331i \(0.884028\pi\)
\(942\) 0 0
\(943\) 16.5020 0.537378
\(944\) −18.5930 + 57.9124i −0.605151 + 1.88489i
\(945\) 0 0
\(946\) −1.33781 1.05275i −0.0434960 0.0342278i
\(947\) 8.29393 + 8.29393i 0.269516 + 0.269516i 0.828905 0.559389i \(-0.188964\pi\)
−0.559389 + 0.828905i \(0.688964\pi\)
\(948\) 0 0
\(949\) 1.74294 1.74294i 0.0565783 0.0565783i
\(950\) −0.447065 3.74912i −0.0145047 0.121637i
\(951\) 0 0
\(952\) −9.94372 + 21.7194i −0.322278 + 0.703930i
\(953\) 22.6285i 0.733010i −0.930416 0.366505i \(-0.880554\pi\)
0.930416 0.366505i \(-0.119446\pi\)
\(954\) 0 0
\(955\) 12.1930 12.1930i 0.394557 0.394557i
\(956\) −6.88694 28.4666i −0.222739 0.920675i
\(957\) 0 0
\(958\) −11.3696 + 14.4482i −0.367335 + 0.466802i
\(959\) 10.8682 0.350953
\(960\) 0 0
\(961\) −28.4066 −0.916343
\(962\) 4.84333 6.15481i 0.156155 0.198439i
\(963\) 0 0
\(964\) −10.9827 45.3962i −0.353730 1.46211i
\(965\) 18.9750 18.9750i 0.610827 0.610827i
\(966\) 0 0
\(967\) 41.6144i 1.33823i −0.743159 0.669115i \(-0.766673\pi\)
0.743159 0.669115i \(-0.233327\pi\)
\(968\) −11.4120 + 24.9265i −0.366796 + 0.801169i
\(969\) 0 0
\(970\) 0.623349 + 5.22746i 0.0200145 + 0.167843i
\(971\) −21.7691 + 21.7691i −0.698604 + 0.698604i −0.964109 0.265505i \(-0.914461\pi\)
0.265505 + 0.964109i \(0.414461\pi\)
\(972\) 0 0
\(973\) 15.3833 + 15.3833i 0.493166 + 0.493166i
\(974\) 17.9006 + 14.0863i 0.573573 + 0.451355i
\(975\) 0 0
\(976\) 48.7757 + 15.6596i 1.56127 + 0.501252i
\(977\) −17.3840 −0.556164 −0.278082 0.960557i \(-0.589699\pi\)
−0.278082 + 0.960557i \(0.589699\pi\)
\(978\) 0 0
\(979\) −8.34179 8.34179i −0.266605 0.266605i
\(980\) 8.53553 + 5.21005i 0.272658 + 0.166429i
\(981\) 0 0
\(982\) 4.02566 + 33.7595i 0.128464 + 1.07731i
\(983\) 4.91428i 0.156741i −0.996924 0.0783707i \(-0.975028\pi\)
0.996924 0.0783707i \(-0.0249718\pi\)
\(984\) 0 0
\(985\) 1.16215i 0.0370291i
\(986\) −69.8280 + 8.32666i −2.22378 + 0.265175i
\(987\) 0 0
\(988\) 5.49824 1.33019i 0.174922 0.0423190i
\(989\) −1.40036 1.40036i −0.0445288 0.0445288i
\(990\) 0 0
\(991\) 23.5415 0.747822 0.373911 0.927465i \(-0.378017\pi\)
0.373911 + 0.927465i \(0.378017\pi\)
\(992\) 1.73812 8.94242i 0.0551852 0.283922i
\(993\) 0 0
\(994\) −8.39627 + 10.6698i −0.266313 + 0.338426i
\(995\) −14.3728 14.3728i −0.455650 0.455650i
\(996\) 0 0
\(997\) −19.6097 + 19.6097i −0.621046 + 0.621046i −0.945799 0.324753i \(-0.894719\pi\)
0.324753 + 0.945799i \(0.394719\pi\)
\(998\) 7.15676 0.853410i 0.226543 0.0270142i
\(999\) 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 720.2.t.b.541.1 8
3.2 odd 2 240.2.s.b.61.4 8
4.3 odd 2 2880.2.t.b.721.1 8
12.11 even 2 960.2.s.b.721.4 8
16.5 even 4 inner 720.2.t.b.181.1 8
16.11 odd 4 2880.2.t.b.2161.1 8
24.5 odd 2 1920.2.s.c.1441.4 8
24.11 even 2 1920.2.s.d.1441.1 8
48.5 odd 4 240.2.s.b.181.4 yes 8
48.11 even 4 960.2.s.b.241.4 8
48.29 odd 4 1920.2.s.c.481.4 8
48.35 even 4 1920.2.s.d.481.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.s.b.61.4 8 3.2 odd 2
240.2.s.b.181.4 yes 8 48.5 odd 4
720.2.t.b.181.1 8 16.5 even 4 inner
720.2.t.b.541.1 8 1.1 even 1 trivial
960.2.s.b.241.4 8 48.11 even 4
960.2.s.b.721.4 8 12.11 even 2
1920.2.s.c.481.4 8 48.29 odd 4
1920.2.s.c.1441.4 8 24.5 odd 2
1920.2.s.d.481.1 8 48.35 even 4
1920.2.s.d.1441.1 8 24.11 even 2
2880.2.t.b.721.1 8 4.3 odd 2
2880.2.t.b.2161.1 8 16.11 odd 4