Properties

Label 432.2.y.d.181.1
Level $432$
Weight $2$
Character 432.181
Analytic conductor $3.450$
Analytic rank $0$
Dimension $4$
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] = [432,2,Mod(37,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.y (of order \(12\), degree \(4\), not 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 181.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 432.181
Dual form 432.2.y.d.253.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(0.133975 - 0.500000i) q^{5} +(2.13397 + 1.23205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(0.133975 - 0.500000i) q^{5} +(2.13397 + 1.23205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(0.633975 - 0.366025i) q^{10} +(0.500000 - 0.133975i) q^{11} +(4.59808 + 1.23205i) q^{13} +(0.901924 + 3.36603i) q^{14} -4.00000 q^{16} -4.00000 q^{17} +(-3.00000 + 3.00000i) q^{19} +(1.00000 + 0.267949i) q^{20} +(0.633975 + 0.366025i) q^{22} +(0.401924 - 0.232051i) q^{23} +(4.09808 + 2.36603i) q^{25} +(3.36603 + 5.83013i) q^{26} +(-2.46410 + 4.26795i) q^{28} +(-0.866025 - 3.23205i) q^{29} +(0.598076 + 1.03590i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-4.00000 - 4.00000i) q^{34} +(0.901924 - 0.901924i) q^{35} +(-7.73205 - 7.73205i) q^{37} -6.00000 q^{38} +(0.732051 + 1.26795i) q^{40} +(9.69615 - 5.59808i) q^{41} +(8.69615 - 2.33013i) q^{43} +(0.267949 + 1.00000i) q^{44} +(0.633975 + 0.169873i) q^{46} +(-4.59808 + 7.96410i) q^{47} +(-0.464102 - 0.803848i) q^{49} +(1.73205 + 6.46410i) q^{50} +(-2.46410 + 9.19615i) q^{52} +(-2.26795 - 2.26795i) q^{53} -0.267949i q^{55} +(-6.73205 + 1.80385i) q^{56} +(2.36603 - 4.09808i) q^{58} +(1.50000 - 5.59808i) q^{59} +(-3.86603 - 14.4282i) q^{61} +(-0.437822 + 1.63397i) q^{62} -8.00000i q^{64} +(1.23205 - 2.13397i) q^{65} +(1.23205 + 0.330127i) q^{67} -8.00000i q^{68} +1.80385 q^{70} +10.9282i q^{71} -0.535898i q^{73} -15.4641i q^{74} +(-6.00000 - 6.00000i) q^{76} +(1.23205 + 0.330127i) q^{77} +(0.866025 - 1.50000i) q^{79} +(-0.535898 + 2.00000i) q^{80} +(15.2942 + 4.09808i) q^{82} +(-3.16025 - 11.7942i) q^{83} +(-0.535898 + 2.00000i) q^{85} +(11.0263 + 6.36603i) q^{86} +(-0.732051 + 1.26795i) q^{88} -11.8564i q^{89} +(8.29423 + 8.29423i) q^{91} +(0.464102 + 0.803848i) q^{92} +(-12.5622 + 3.36603i) q^{94} +(1.09808 + 1.90192i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(0.339746 - 1.26795i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{5} + 12 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 4 q^{5} + 12 q^{7} - 8 q^{8} + 6 q^{10} + 2 q^{11} + 8 q^{13} + 14 q^{14} - 16 q^{16} - 16 q^{17} - 12 q^{19} + 4 q^{20} + 6 q^{22} + 12 q^{23} + 6 q^{25} + 10 q^{26} + 4 q^{28} - 8 q^{31} - 16 q^{32} - 16 q^{34} + 14 q^{35} - 24 q^{37} - 24 q^{38} - 4 q^{40} + 18 q^{41} + 14 q^{43} + 8 q^{44} + 6 q^{46} - 8 q^{47} + 12 q^{49} + 4 q^{52} - 16 q^{53} - 20 q^{56} + 6 q^{58} + 6 q^{59} - 12 q^{61} - 26 q^{62} - 2 q^{65} - 2 q^{67} + 28 q^{70} - 24 q^{76} - 2 q^{77} - 16 q^{80} + 30 q^{82} + 22 q^{83} - 16 q^{85} + 6 q^{86} + 4 q^{88} + 2 q^{91} - 12 q^{92} - 26 q^{94} - 6 q^{95} - 2 q^{97} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.707107 + 0.707107i
\(3\) 0 0
\(4\) 2.00000i 1.00000i
\(5\) 0.133975 0.500000i 0.0599153 0.223607i −0.929476 0.368883i \(-0.879740\pi\)
0.989391 + 0.145276i \(0.0464070\pi\)
\(6\) 0 0
\(7\) 2.13397 + 1.23205i 0.806567 + 0.465671i 0.845762 0.533560i \(-0.179146\pi\)
−0.0391956 + 0.999232i \(0.512480\pi\)
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) 0.633975 0.366025i 0.200480 0.115747i
\(11\) 0.500000 0.133975i 0.150756 0.0403949i −0.182652 0.983178i \(-0.558468\pi\)
0.333408 + 0.942783i \(0.391801\pi\)
\(12\) 0 0
\(13\) 4.59808 + 1.23205i 1.27528 + 0.341709i 0.832050 0.554700i \(-0.187167\pi\)
0.443227 + 0.896410i \(0.353834\pi\)
\(14\) 0.901924 + 3.36603i 0.241049 + 0.899608i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 0 0
\(19\) −3.00000 + 3.00000i −0.688247 + 0.688247i −0.961844 0.273597i \(-0.911786\pi\)
0.273597 + 0.961844i \(0.411786\pi\)
\(20\) 1.00000 + 0.267949i 0.223607 + 0.0599153i
\(21\) 0 0
\(22\) 0.633975 + 0.366025i 0.135164 + 0.0780369i
\(23\) 0.401924 0.232051i 0.0838069 0.0483859i −0.457511 0.889204i \(-0.651259\pi\)
0.541318 + 0.840818i \(0.317926\pi\)
\(24\) 0 0
\(25\) 4.09808 + 2.36603i 0.819615 + 0.473205i
\(26\) 3.36603 + 5.83013i 0.660132 + 1.14338i
\(27\) 0 0
\(28\) −2.46410 + 4.26795i −0.465671 + 0.806567i
\(29\) −0.866025 3.23205i −0.160817 0.600177i −0.998537 0.0540766i \(-0.982778\pi\)
0.837720 0.546100i \(-0.183888\pi\)
\(30\) 0 0
\(31\) 0.598076 + 1.03590i 0.107418 + 0.186053i 0.914723 0.404081i \(-0.132408\pi\)
−0.807306 + 0.590133i \(0.799075\pi\)
\(32\) −4.00000 4.00000i −0.707107 0.707107i
\(33\) 0 0
\(34\) −4.00000 4.00000i −0.685994 0.685994i
\(35\) 0.901924 0.901924i 0.152453 0.152453i
\(36\) 0 0
\(37\) −7.73205 7.73205i −1.27114 1.27114i −0.945490 0.325651i \(-0.894416\pi\)
−0.325651 0.945490i \(-0.605584\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 0.732051 + 1.26795i 0.115747 + 0.200480i
\(41\) 9.69615 5.59808i 1.51428 0.874273i 0.514425 0.857536i \(-0.328006\pi\)
0.999860 0.0167371i \(-0.00532782\pi\)
\(42\) 0 0
\(43\) 8.69615 2.33013i 1.32615 0.355341i 0.474872 0.880055i \(-0.342494\pi\)
0.851279 + 0.524714i \(0.175828\pi\)
\(44\) 0.267949 + 1.00000i 0.0403949 + 0.150756i
\(45\) 0 0
\(46\) 0.633975 + 0.169873i 0.0934745 + 0.0250464i
\(47\) −4.59808 + 7.96410i −0.670698 + 1.16168i 0.307008 + 0.951707i \(0.400672\pi\)
−0.977706 + 0.209977i \(0.932661\pi\)
\(48\) 0 0
\(49\) −0.464102 0.803848i −0.0663002 0.114835i
\(50\) 1.73205 + 6.46410i 0.244949 + 0.914162i
\(51\) 0 0
\(52\) −2.46410 + 9.19615i −0.341709 + 1.27528i
\(53\) −2.26795 2.26795i −0.311527 0.311527i 0.533974 0.845501i \(-0.320698\pi\)
−0.845501 + 0.533974i \(0.820698\pi\)
\(54\) 0 0
\(55\) 0.267949i 0.0361303i
\(56\) −6.73205 + 1.80385i −0.899608 + 0.241049i
\(57\) 0 0
\(58\) 2.36603 4.09808i 0.310674 0.538104i
\(59\) 1.50000 5.59808i 0.195283 0.728807i −0.796910 0.604098i \(-0.793533\pi\)
0.992193 0.124709i \(-0.0397998\pi\)
\(60\) 0 0
\(61\) −3.86603 14.4282i −0.494994 1.84734i −0.530065 0.847957i \(-0.677832\pi\)
0.0350707 0.999385i \(-0.488834\pi\)
\(62\) −0.437822 + 1.63397i −0.0556035 + 0.207515i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 1.23205 2.13397i 0.152817 0.264687i
\(66\) 0 0
\(67\) 1.23205 + 0.330127i 0.150519 + 0.0403314i 0.333292 0.942824i \(-0.391841\pi\)
−0.182773 + 0.983155i \(0.558507\pi\)
\(68\) 8.00000i 0.970143i
\(69\) 0 0
\(70\) 1.80385 0.215601
\(71\) 10.9282i 1.29694i 0.761241 + 0.648470i \(0.224591\pi\)
−0.761241 + 0.648470i \(0.775409\pi\)
\(72\) 0 0
\(73\) 0.535898i 0.0627222i −0.999508 0.0313611i \(-0.990016\pi\)
0.999508 0.0313611i \(-0.00998418\pi\)
\(74\) 15.4641i 1.79767i
\(75\) 0 0
\(76\) −6.00000 6.00000i −0.688247 0.688247i
\(77\) 1.23205 + 0.330127i 0.140405 + 0.0376215i
\(78\) 0 0
\(79\) 0.866025 1.50000i 0.0974355 0.168763i −0.813187 0.582003i \(-0.802269\pi\)
0.910622 + 0.413239i \(0.135603\pi\)
\(80\) −0.535898 + 2.00000i −0.0599153 + 0.223607i
\(81\) 0 0
\(82\) 15.2942 + 4.09808i 1.68897 + 0.452557i
\(83\) −3.16025 11.7942i −0.346883 1.29458i −0.890397 0.455185i \(-0.849573\pi\)
0.543514 0.839400i \(-0.317093\pi\)
\(84\) 0 0
\(85\) −0.535898 + 2.00000i −0.0581263 + 0.216930i
\(86\) 11.0263 + 6.36603i 1.18899 + 0.686466i
\(87\) 0 0
\(88\) −0.732051 + 1.26795i −0.0780369 + 0.135164i
\(89\) 11.8564i 1.25678i −0.777900 0.628388i \(-0.783715\pi\)
0.777900 0.628388i \(-0.216285\pi\)
\(90\) 0 0
\(91\) 8.29423 + 8.29423i 0.869471 + 0.869471i
\(92\) 0.464102 + 0.803848i 0.0483859 + 0.0838069i
\(93\) 0 0
\(94\) −12.5622 + 3.36603i −1.29569 + 0.347179i
\(95\) 1.09808 + 1.90192i 0.112660 + 0.195133i
\(96\) 0 0
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0.339746 1.26795i 0.0343195 0.128082i
\(99\) 0 0
\(100\) −4.73205 + 8.19615i −0.473205 + 0.819615i
\(101\) 1.86603 0.500000i 0.185676 0.0497519i −0.164783 0.986330i \(-0.552692\pi\)
0.350459 + 0.936578i \(0.386026\pi\)
\(102\) 0 0
\(103\) −1.79423 + 1.03590i −0.176791 + 0.102070i −0.585784 0.810467i \(-0.699213\pi\)
0.408993 + 0.912537i \(0.365880\pi\)
\(104\) −11.6603 + 6.73205i −1.14338 + 0.660132i
\(105\) 0 0
\(106\) 4.53590i 0.440565i
\(107\) 11.3923 + 11.3923i 1.10134 + 1.10134i 0.994250 + 0.107086i \(0.0341520\pi\)
0.107086 + 0.994250i \(0.465848\pi\)
\(108\) 0 0
\(109\) 1.73205 1.73205i 0.165900 0.165900i −0.619274 0.785175i \(-0.712573\pi\)
0.785175 + 0.619274i \(0.212573\pi\)
\(110\) 0.267949 0.267949i 0.0255480 0.0255480i
\(111\) 0 0
\(112\) −8.53590 4.92820i −0.806567 0.465671i
\(113\) 2.76795 + 4.79423i 0.260387 + 0.451003i 0.966345 0.257251i \(-0.0828166\pi\)
−0.705958 + 0.708254i \(0.749483\pi\)
\(114\) 0 0
\(115\) −0.0621778 0.232051i −0.00579811 0.0216388i
\(116\) 6.46410 1.73205i 0.600177 0.160817i
\(117\) 0 0
\(118\) 7.09808 4.09808i 0.653431 0.377258i
\(119\) −8.53590 4.92820i −0.782485 0.451768i
\(120\) 0 0
\(121\) −9.29423 + 5.36603i −0.844930 + 0.487820i
\(122\) 10.5622 18.2942i 0.956255 1.65628i
\(123\) 0 0
\(124\) −2.07180 + 1.19615i −0.186053 + 0.107418i
\(125\) 3.56218 3.56218i 0.318611 0.318611i
\(126\) 0 0
\(127\) −20.3923 −1.80952 −0.904762 0.425917i \(-0.859952\pi\)
−0.904762 + 0.425917i \(0.859952\pi\)
\(128\) 8.00000 8.00000i 0.707107 0.707107i
\(129\) 0 0
\(130\) 3.36603 0.901924i 0.295220 0.0791039i
\(131\) −11.6962 3.13397i −1.02190 0.273817i −0.291305 0.956630i \(-0.594089\pi\)
−0.730593 + 0.682814i \(0.760756\pi\)
\(132\) 0 0
\(133\) −10.0981 + 2.70577i −0.875614 + 0.234620i
\(134\) 0.901924 + 1.56218i 0.0779143 + 0.134952i
\(135\) 0 0
\(136\) 8.00000 8.00000i 0.685994 0.685994i
\(137\) 14.4282 + 8.33013i 1.23268 + 0.711691i 0.967589 0.252531i \(-0.0812631\pi\)
0.265096 + 0.964222i \(0.414596\pi\)
\(138\) 0 0
\(139\) −1.16025 + 4.33013i −0.0984115 + 0.367277i −0.997515 0.0704603i \(-0.977553\pi\)
0.899103 + 0.437737i \(0.144220\pi\)
\(140\) 1.80385 + 1.80385i 0.152453 + 0.152453i
\(141\) 0 0
\(142\) −10.9282 + 10.9282i −0.917074 + 0.917074i
\(143\) 2.46410 0.206059
\(144\) 0 0
\(145\) −1.73205 −0.143839
\(146\) 0.535898 0.535898i 0.0443513 0.0443513i
\(147\) 0 0
\(148\) 15.4641 15.4641i 1.27114 1.27114i
\(149\) −3.93782 + 14.6962i −0.322599 + 1.20396i 0.594105 + 0.804388i \(0.297507\pi\)
−0.916704 + 0.399568i \(0.869160\pi\)
\(150\) 0 0
\(151\) 6.06218 + 3.50000i 0.493333 + 0.284826i 0.725956 0.687741i \(-0.241398\pi\)
−0.232623 + 0.972567i \(0.574731\pi\)
\(152\) 12.0000i 0.973329i
\(153\) 0 0
\(154\) 0.901924 + 1.56218i 0.0726791 + 0.125884i
\(155\) 0.598076 0.160254i 0.0480386 0.0128719i
\(156\) 0 0
\(157\) 0.866025 + 0.232051i 0.0691164 + 0.0185197i 0.293212 0.956048i \(-0.405276\pi\)
−0.224095 + 0.974567i \(0.571943\pi\)
\(158\) 2.36603 0.633975i 0.188231 0.0504363i
\(159\) 0 0
\(160\) −2.53590 + 1.46410i −0.200480 + 0.115747i
\(161\) 1.14359 0.0901278
\(162\) 0 0
\(163\) 11.9282 11.9282i 0.934289 0.934289i −0.0636813 0.997970i \(-0.520284\pi\)
0.997970 + 0.0636813i \(0.0202841\pi\)
\(164\) 11.1962 + 19.3923i 0.874273 + 1.51428i
\(165\) 0 0
\(166\) 8.63397 14.9545i 0.670126 1.16069i
\(167\) −8.25833 + 4.76795i −0.639049 + 0.368955i −0.784248 0.620447i \(-0.786951\pi\)
0.145199 + 0.989402i \(0.453618\pi\)
\(168\) 0 0
\(169\) 8.36603 + 4.83013i 0.643540 + 0.371548i
\(170\) −2.53590 + 1.46410i −0.194495 + 0.112291i
\(171\) 0 0
\(172\) 4.66025 + 17.3923i 0.355341 + 1.32615i
\(173\) −2.40192 8.96410i −0.182615 0.681528i −0.995129 0.0985859i \(-0.968568\pi\)
0.812514 0.582942i \(-0.198099\pi\)
\(174\) 0 0
\(175\) 5.83013 + 10.0981i 0.440716 + 0.763343i
\(176\) −2.00000 + 0.535898i −0.150756 + 0.0403949i
\(177\) 0 0
\(178\) 11.8564 11.8564i 0.888675 0.888675i
\(179\) −7.92820 + 7.92820i −0.592582 + 0.592582i −0.938328 0.345746i \(-0.887626\pi\)
0.345746 + 0.938328i \(0.387626\pi\)
\(180\) 0 0
\(181\) −4.26795 4.26795i −0.317234 0.317234i 0.530470 0.847704i \(-0.322016\pi\)
−0.847704 + 0.530470i \(0.822016\pi\)
\(182\) 16.5885i 1.22962i
\(183\) 0 0
\(184\) −0.339746 + 1.26795i −0.0250464 + 0.0934745i
\(185\) −4.90192 + 2.83013i −0.360397 + 0.208075i
\(186\) 0 0
\(187\) −2.00000 + 0.535898i −0.146254 + 0.0391888i
\(188\) −15.9282 9.19615i −1.16168 0.670698i
\(189\) 0 0
\(190\) −0.803848 + 3.00000i −0.0583172 + 0.217643i
\(191\) −6.59808 + 11.4282i −0.477420 + 0.826916i −0.999665 0.0258797i \(-0.991761\pi\)
0.522245 + 0.852795i \(0.325095\pi\)
\(192\) 0 0
\(193\) −1.23205 2.13397i −0.0886850 0.153607i 0.818271 0.574833i \(-0.194933\pi\)
−0.906956 + 0.421226i \(0.861600\pi\)
\(194\) −1.36603 + 0.366025i −0.0980749 + 0.0262791i
\(195\) 0 0
\(196\) 1.60770 0.928203i 0.114835 0.0663002i
\(197\) −10.4641 10.4641i −0.745536 0.745536i 0.228101 0.973637i \(-0.426748\pi\)
−0.973637 + 0.228101i \(0.926748\pi\)
\(198\) 0 0
\(199\) 5.85641i 0.415150i −0.978219 0.207575i \(-0.933443\pi\)
0.978219 0.207575i \(-0.0665570\pi\)
\(200\) −12.9282 + 3.46410i −0.914162 + 0.244949i
\(201\) 0 0
\(202\) 2.36603 + 1.36603i 0.166473 + 0.0961132i
\(203\) 2.13397 7.96410i 0.149776 0.558970i
\(204\) 0 0
\(205\) −1.50000 5.59808i −0.104765 0.390987i
\(206\) −2.83013 0.758330i −0.197184 0.0528354i
\(207\) 0 0
\(208\) −18.3923 4.92820i −1.27528 0.341709i
\(209\) −1.09808 + 1.90192i −0.0759555 + 0.131559i
\(210\) 0 0
\(211\) 1.96410 + 0.526279i 0.135214 + 0.0362306i 0.325791 0.945442i \(-0.394369\pi\)
−0.190577 + 0.981672i \(0.561036\pi\)
\(212\) 4.53590 4.53590i 0.311527 0.311527i
\(213\) 0 0
\(214\) 22.7846i 1.55752i
\(215\) 4.66025i 0.317827i
\(216\) 0 0
\(217\) 2.94744i 0.200085i
\(218\) 3.46410 0.234619
\(219\) 0 0
\(220\) 0.535898 0.0361303
\(221\) −18.3923 4.92820i −1.23720 0.331507i
\(222\) 0 0
\(223\) −7.79423 + 13.5000i −0.521940 + 0.904027i 0.477734 + 0.878504i \(0.341458\pi\)
−0.999674 + 0.0255224i \(0.991875\pi\)
\(224\) −3.60770 13.4641i −0.241049 0.899608i
\(225\) 0 0
\(226\) −2.02628 + 7.56218i −0.134786 + 0.503029i
\(227\) 4.62436 + 17.2583i 0.306929 + 1.14548i 0.931272 + 0.364325i \(0.118700\pi\)
−0.624343 + 0.781151i \(0.714633\pi\)
\(228\) 0 0
\(229\) −2.52628 + 9.42820i −0.166941 + 0.623033i 0.830843 + 0.556506i \(0.187858\pi\)
−0.997785 + 0.0665269i \(0.978808\pi\)
\(230\) 0.169873 0.294229i 0.0112011 0.0194009i
\(231\) 0 0
\(232\) 8.19615 + 4.73205i 0.538104 + 0.310674i
\(233\) 22.9282i 1.50208i 0.660259 + 0.751038i \(0.270447\pi\)
−0.660259 + 0.751038i \(0.729553\pi\)
\(234\) 0 0
\(235\) 3.36603 + 3.36603i 0.219575 + 0.219575i
\(236\) 11.1962 + 3.00000i 0.728807 + 0.195283i
\(237\) 0 0
\(238\) −3.60770 13.4641i −0.233852 0.872748i
\(239\) 5.59808 + 9.69615i 0.362109 + 0.627192i 0.988308 0.152472i \(-0.0487233\pi\)
−0.626198 + 0.779664i \(0.715390\pi\)
\(240\) 0 0
\(241\) −6.23205 + 10.7942i −0.401442 + 0.695317i −0.993900 0.110284i \(-0.964824\pi\)
0.592458 + 0.805601i \(0.298157\pi\)
\(242\) −14.6603 3.92820i −0.942397 0.252514i
\(243\) 0 0
\(244\) 28.8564 7.73205i 1.84734 0.494994i
\(245\) −0.464102 + 0.124356i −0.0296504 + 0.00794479i
\(246\) 0 0
\(247\) −17.4904 + 10.0981i −1.11289 + 0.642525i
\(248\) −3.26795 0.875644i −0.207515 0.0556035i
\(249\) 0 0
\(250\) 7.12436 0.450584
\(251\) −7.39230 7.39230i −0.466598 0.466598i 0.434212 0.900811i \(-0.357027\pi\)
−0.900811 + 0.434212i \(0.857027\pi\)
\(252\) 0 0
\(253\) 0.169873 0.169873i 0.0106798 0.0106798i
\(254\) −20.3923 20.3923i −1.27953 1.27953i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 5.16025 + 8.93782i 0.321888 + 0.557526i 0.980878 0.194626i \(-0.0623493\pi\)
−0.658990 + 0.752152i \(0.729016\pi\)
\(258\) 0 0
\(259\) −6.97372 26.0263i −0.433326 1.61719i
\(260\) 4.26795 + 2.46410i 0.264687 + 0.152817i
\(261\) 0 0
\(262\) −8.56218 14.8301i −0.528973 0.916208i
\(263\) 3.40192 + 1.96410i 0.209772 + 0.121112i 0.601205 0.799095i \(-0.294687\pi\)
−0.391434 + 0.920206i \(0.628021\pi\)
\(264\) 0 0
\(265\) −1.43782 + 0.830127i −0.0883247 + 0.0509943i
\(266\) −12.8038 7.39230i −0.785054 0.453251i
\(267\) 0 0
\(268\) −0.660254 + 2.46410i −0.0403314 + 0.150519i
\(269\) −7.73205 + 7.73205i −0.471431 + 0.471431i −0.902378 0.430946i \(-0.858180\pi\)
0.430946 + 0.902378i \(0.358180\pi\)
\(270\) 0 0
\(271\) −14.9282 −0.906824 −0.453412 0.891301i \(-0.649793\pi\)
−0.453412 + 0.891301i \(0.649793\pi\)
\(272\) 16.0000 0.970143
\(273\) 0 0
\(274\) 6.09808 + 22.7583i 0.368398 + 1.37488i
\(275\) 2.36603 + 0.633975i 0.142677 + 0.0382301i
\(276\) 0 0
\(277\) 13.7942 3.69615i 0.828815 0.222080i 0.180618 0.983553i \(-0.442190\pi\)
0.648197 + 0.761473i \(0.275523\pi\)
\(278\) −5.49038 + 3.16987i −0.329291 + 0.190116i
\(279\) 0 0
\(280\) 3.60770i 0.215601i
\(281\) 16.9641 + 9.79423i 1.01199 + 0.584275i 0.911775 0.410691i \(-0.134712\pi\)
0.100219 + 0.994965i \(0.468046\pi\)
\(282\) 0 0
\(283\) 4.16025 15.5263i 0.247301 0.922942i −0.724911 0.688842i \(-0.758119\pi\)
0.972213 0.234099i \(-0.0752141\pi\)
\(284\) −21.8564 −1.29694
\(285\) 0 0
\(286\) 2.46410 + 2.46410i 0.145705 + 0.145705i
\(287\) 27.5885 1.62850
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) −1.73205 1.73205i −0.101710 0.101710i
\(291\) 0 0
\(292\) 1.07180 0.0627222
\(293\) −3.86603 + 14.4282i −0.225856 + 0.842905i 0.756204 + 0.654336i \(0.227052\pi\)
−0.982060 + 0.188569i \(0.939615\pi\)
\(294\) 0 0
\(295\) −2.59808 1.50000i −0.151266 0.0873334i
\(296\) 30.9282 1.79767
\(297\) 0 0
\(298\) −18.6340 + 10.7583i −1.07944 + 0.623213i
\(299\) 2.13397 0.571797i 0.123411 0.0330679i
\(300\) 0 0
\(301\) 21.4282 + 5.74167i 1.23510 + 0.330944i
\(302\) 2.56218 + 9.56218i 0.147437 + 0.550242i
\(303\) 0 0
\(304\) 12.0000 12.0000i 0.688247 0.688247i
\(305\) −7.73205 −0.442736
\(306\) 0 0
\(307\) −5.92820 + 5.92820i −0.338340 + 0.338340i −0.855742 0.517402i \(-0.826899\pi\)
0.517402 + 0.855742i \(0.326899\pi\)
\(308\) −0.660254 + 2.46410i −0.0376215 + 0.140405i
\(309\) 0 0
\(310\) 0.758330 + 0.437822i 0.0430703 + 0.0248666i
\(311\) 27.1865 15.6962i 1.54161 0.890047i 0.542869 0.839817i \(-0.317338\pi\)
0.998738 0.0502299i \(-0.0159954\pi\)
\(312\) 0 0
\(313\) 7.83975 + 4.52628i 0.443129 + 0.255840i 0.704924 0.709283i \(-0.250981\pi\)
−0.261795 + 0.965123i \(0.584314\pi\)
\(314\) 0.633975 + 1.09808i 0.0357773 + 0.0619680i
\(315\) 0 0
\(316\) 3.00000 + 1.73205i 0.168763 + 0.0974355i
\(317\) 0.545517 + 2.03590i 0.0306393 + 0.114347i 0.979552 0.201192i \(-0.0644814\pi\)
−0.948913 + 0.315539i \(0.897815\pi\)
\(318\) 0 0
\(319\) −0.866025 1.50000i −0.0484881 0.0839839i
\(320\) −4.00000 1.07180i −0.223607 0.0599153i
\(321\) 0 0
\(322\) 1.14359 + 1.14359i 0.0637300 + 0.0637300i
\(323\) 12.0000 12.0000i 0.667698 0.667698i
\(324\) 0 0
\(325\) 15.9282 + 15.9282i 0.883538 + 0.883538i
\(326\) 23.8564 1.32128
\(327\) 0 0
\(328\) −8.19615 + 30.5885i −0.452557 + 1.68897i
\(329\) −19.6244 + 11.3301i −1.08193 + 0.624650i
\(330\) 0 0
\(331\) −26.3564 + 7.06218i −1.44868 + 0.388172i −0.895564 0.444933i \(-0.853228\pi\)
−0.553115 + 0.833105i \(0.686561\pi\)
\(332\) 23.5885 6.32051i 1.29458 0.346883i
\(333\) 0 0
\(334\) −13.0263 3.49038i −0.712766 0.190985i
\(335\) 0.330127 0.571797i 0.0180368 0.0312406i
\(336\) 0 0
\(337\) 0.696152 + 1.20577i 0.0379218 + 0.0656826i 0.884363 0.466799i \(-0.154593\pi\)
−0.846442 + 0.532482i \(0.821260\pi\)
\(338\) 3.53590 + 13.1962i 0.192328 + 0.717776i
\(339\) 0 0
\(340\) −4.00000 1.07180i −0.216930 0.0581263i
\(341\) 0.437822 + 0.437822i 0.0237094 + 0.0237094i
\(342\) 0 0
\(343\) 19.5359i 1.05484i
\(344\) −12.7321 + 22.0526i −0.686466 + 1.18899i
\(345\) 0 0
\(346\) 6.56218 11.3660i 0.352785 0.611041i
\(347\) 5.23205 19.5263i 0.280871 1.04823i −0.670933 0.741518i \(-0.734106\pi\)
0.951804 0.306707i \(-0.0992273\pi\)
\(348\) 0 0
\(349\) −2.13397 7.96410i −0.114229 0.426309i 0.884999 0.465593i \(-0.154159\pi\)
−0.999228 + 0.0392843i \(0.987492\pi\)
\(350\) −4.26795 + 15.9282i −0.228131 + 0.851398i
\(351\) 0 0
\(352\) −2.53590 1.46410i −0.135164 0.0780369i
\(353\) 15.2321 26.3827i 0.810720 1.40421i −0.101640 0.994821i \(-0.532409\pi\)
0.912361 0.409387i \(-0.134258\pi\)
\(354\) 0 0
\(355\) 5.46410 + 1.46410i 0.290004 + 0.0777064i
\(356\) 23.7128 1.25678
\(357\) 0 0
\(358\) −15.8564 −0.838037
\(359\) 15.0718i 0.795459i −0.917503 0.397730i \(-0.869798\pi\)
0.917503 0.397730i \(-0.130202\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 8.53590i 0.448637i
\(363\) 0 0
\(364\) −16.5885 + 16.5885i −0.869471 + 0.869471i
\(365\) −0.267949 0.0717968i −0.0140251 0.00375801i
\(366\) 0 0
\(367\) 15.4545 26.7679i 0.806717 1.39728i −0.108408 0.994106i \(-0.534575\pi\)
0.915125 0.403169i \(-0.132091\pi\)
\(368\) −1.60770 + 0.928203i −0.0838069 + 0.0483859i
\(369\) 0 0
\(370\) −7.73205 2.07180i −0.401970 0.107708i
\(371\) −2.04552 7.63397i −0.106198 0.396336i
\(372\) 0 0
\(373\) 3.59808 13.4282i 0.186301 0.695286i −0.808047 0.589118i \(-0.799475\pi\)
0.994348 0.106168i \(-0.0338581\pi\)
\(374\) −2.53590 1.46410i −0.131128 0.0757069i
\(375\) 0 0
\(376\) −6.73205 25.1244i −0.347179 1.29569i
\(377\) 15.9282i 0.820344i
\(378\) 0 0
\(379\) 15.5885 + 15.5885i 0.800725 + 0.800725i 0.983209 0.182484i \(-0.0584137\pi\)
−0.182484 + 0.983209i \(0.558414\pi\)
\(380\) −3.80385 + 2.19615i −0.195133 + 0.112660i
\(381\) 0 0
\(382\) −18.0263 + 4.83013i −0.922305 + 0.247131i
\(383\) −12.3301 21.3564i −0.630040 1.09126i −0.987543 0.157349i \(-0.949705\pi\)
0.357503 0.933912i \(-0.383628\pi\)
\(384\) 0 0
\(385\) 0.330127 0.571797i 0.0168248 0.0291415i
\(386\) 0.901924 3.36603i 0.0459067 0.171326i
\(387\) 0 0
\(388\) −1.73205 1.00000i −0.0879316 0.0507673i
\(389\) −7.59808 + 2.03590i −0.385238 + 0.103224i −0.446240 0.894914i \(-0.647237\pi\)
0.0610019 + 0.998138i \(0.480570\pi\)
\(390\) 0 0
\(391\) −1.60770 + 0.928203i −0.0813046 + 0.0469413i
\(392\) 2.53590 + 0.679492i 0.128082 + 0.0343195i
\(393\) 0 0
\(394\) 20.9282i 1.05435i
\(395\) −0.633975 0.633975i −0.0318987 0.0318987i
\(396\) 0 0
\(397\) −21.0526 + 21.0526i −1.05660 + 1.05660i −0.0582984 + 0.998299i \(0.518567\pi\)
−0.998299 + 0.0582984i \(0.981433\pi\)
\(398\) 5.85641 5.85641i 0.293555 0.293555i
\(399\) 0 0
\(400\) −16.3923 9.46410i −0.819615 0.473205i
\(401\) −1.16025 2.00962i −0.0579403 0.100356i 0.835600 0.549338i \(-0.185120\pi\)
−0.893541 + 0.448982i \(0.851787\pi\)
\(402\) 0 0
\(403\) 1.47372 + 5.50000i 0.0734112 + 0.273975i
\(404\) 1.00000 + 3.73205i 0.0497519 + 0.185676i
\(405\) 0 0
\(406\) 10.0981 5.83013i 0.501159 0.289344i
\(407\) −4.90192 2.83013i −0.242979 0.140284i
\(408\) 0 0
\(409\) 4.62436 2.66987i 0.228660 0.132017i −0.381294 0.924454i \(-0.624521\pi\)
0.609954 + 0.792437i \(0.291188\pi\)
\(410\) 4.09808 7.09808i 0.202390 0.350549i
\(411\) 0 0
\(412\) −2.07180 3.58846i −0.102070 0.176791i
\(413\) 10.0981 10.0981i 0.496894 0.496894i
\(414\) 0 0
\(415\) −6.32051 −0.310262
\(416\) −13.4641 23.3205i −0.660132 1.14338i
\(417\) 0 0
\(418\) −3.00000 + 0.803848i −0.146735 + 0.0393175i
\(419\) −1.96410 0.526279i −0.0959526 0.0257104i 0.210523 0.977589i \(-0.432483\pi\)
−0.306476 + 0.951878i \(0.599150\pi\)
\(420\) 0 0
\(421\) 10.7942 2.89230i 0.526079 0.140962i 0.0140017 0.999902i \(-0.495543\pi\)
0.512077 + 0.858940i \(0.328876\pi\)
\(422\) 1.43782 + 2.49038i 0.0699921 + 0.121230i
\(423\) 0 0
\(424\) 9.07180 0.440565
\(425\) −16.3923 9.46410i −0.795144 0.459076i
\(426\) 0 0
\(427\) 9.52628 35.5526i 0.461009 1.72051i
\(428\) −22.7846 + 22.7846i −1.10134 + 1.10134i
\(429\) 0 0
\(430\) 4.66025 4.66025i 0.224737 0.224737i
\(431\) −31.3205 −1.50866 −0.754328 0.656498i \(-0.772037\pi\)
−0.754328 + 0.656498i \(0.772037\pi\)
\(432\) 0 0
\(433\) 24.3923 1.17222 0.586110 0.810232i \(-0.300659\pi\)
0.586110 + 0.810232i \(0.300659\pi\)
\(434\) −2.94744 + 2.94744i −0.141482 + 0.141482i
\(435\) 0 0
\(436\) 3.46410 + 3.46410i 0.165900 + 0.165900i
\(437\) −0.509619 + 1.90192i −0.0243784 + 0.0909814i
\(438\) 0 0
\(439\) 18.0622 + 10.4282i 0.862061 + 0.497711i 0.864702 0.502286i \(-0.167507\pi\)
−0.00264111 + 0.999997i \(0.500841\pi\)
\(440\) 0.535898 + 0.535898i 0.0255480 + 0.0255480i
\(441\) 0 0
\(442\) −13.4641 23.3205i −0.640422 1.10924i
\(443\) −16.1603 + 4.33013i −0.767797 + 0.205731i −0.621398 0.783495i \(-0.713435\pi\)
−0.146399 + 0.989226i \(0.546768\pi\)
\(444\) 0 0
\(445\) −5.92820 1.58846i −0.281024 0.0753001i
\(446\) −21.2942 + 5.70577i −1.00831 + 0.270176i
\(447\) 0 0
\(448\) 9.85641 17.0718i 0.465671 0.806567i
\(449\) −0.679492 −0.0320672 −0.0160336 0.999871i \(-0.505104\pi\)
−0.0160336 + 0.999871i \(0.505104\pi\)
\(450\) 0 0
\(451\) 4.09808 4.09808i 0.192971 0.192971i
\(452\) −9.58846 + 5.53590i −0.451003 + 0.260387i
\(453\) 0 0
\(454\) −12.6340 + 21.8827i −0.592942 + 1.02701i
\(455\) 5.25833 3.03590i 0.246514 0.142325i
\(456\) 0 0
\(457\) 19.0359 + 10.9904i 0.890462 + 0.514108i 0.874094 0.485758i \(-0.161456\pi\)
0.0163683 + 0.999866i \(0.494790\pi\)
\(458\) −11.9545 + 6.90192i −0.558596 + 0.322506i
\(459\) 0 0
\(460\) 0.464102 0.124356i 0.0216388 0.00579811i
\(461\) 0.598076 + 2.23205i 0.0278552 + 0.103957i 0.978454 0.206466i \(-0.0661961\pi\)
−0.950599 + 0.310423i \(0.899529\pi\)
\(462\) 0 0
\(463\) 3.33013 + 5.76795i 0.154764 + 0.268059i 0.932973 0.359946i \(-0.117205\pi\)
−0.778209 + 0.628005i \(0.783872\pi\)
\(464\) 3.46410 + 12.9282i 0.160817 + 0.600177i
\(465\) 0 0
\(466\) −22.9282 + 22.9282i −1.06213 + 1.06213i
\(467\) 19.7846 19.7846i 0.915523 0.915523i −0.0811771 0.996700i \(-0.525868\pi\)
0.996700 + 0.0811771i \(0.0258679\pi\)
\(468\) 0 0
\(469\) 2.22243 + 2.22243i 0.102622 + 0.102622i
\(470\) 6.73205i 0.310526i
\(471\) 0 0
\(472\) 8.19615 + 14.1962i 0.377258 + 0.653431i
\(473\) 4.03590 2.33013i 0.185571 0.107139i
\(474\) 0 0
\(475\) −19.3923 + 5.19615i −0.889780 + 0.238416i
\(476\) 9.85641 17.0718i 0.451768 0.782485i
\(477\) 0 0
\(478\) −4.09808 + 15.2942i −0.187442 + 0.699542i
\(479\) −0.669873 + 1.16025i −0.0306073 + 0.0530134i −0.880923 0.473259i \(-0.843077\pi\)
0.850316 + 0.526272i \(0.176411\pi\)
\(480\) 0 0
\(481\) −26.0263 45.0788i −1.18670 2.05542i
\(482\) −17.0263 + 4.56218i −0.775526 + 0.207802i
\(483\) 0 0
\(484\) −10.7321 18.5885i −0.487820 0.844930i
\(485\) 0.366025 + 0.366025i 0.0166204 + 0.0166204i
\(486\) 0 0
\(487\) 34.7846i 1.57624i −0.615521 0.788121i \(-0.711054\pi\)
0.615521 0.788121i \(-0.288946\pi\)
\(488\) 36.5885 + 21.1244i 1.65628 + 0.956255i
\(489\) 0 0
\(490\) −0.588457 0.339746i −0.0265838 0.0153482i
\(491\) −0.500000 + 1.86603i −0.0225647 + 0.0842125i −0.976290 0.216467i \(-0.930547\pi\)
0.953725 + 0.300679i \(0.0972134\pi\)
\(492\) 0 0
\(493\) 3.46410 + 12.9282i 0.156015 + 0.582257i
\(494\) −27.5885 7.39230i −1.24126 0.332596i
\(495\) 0 0
\(496\) −2.39230 4.14359i −0.107418 0.186053i
\(497\) −13.4641 + 23.3205i −0.603947 + 1.04607i
\(498\) 0 0
\(499\) −2.50000 0.669873i −0.111915 0.0299876i 0.202427 0.979297i \(-0.435117\pi\)
−0.314342 + 0.949310i \(0.601784\pi\)
\(500\) 7.12436 + 7.12436i 0.318611 + 0.318611i
\(501\) 0 0
\(502\) 14.7846i 0.659869i
\(503\) 13.8564i 0.617827i −0.951090 0.308913i \(-0.900035\pi\)
0.951090 0.308913i \(-0.0999653\pi\)
\(504\) 0 0
\(505\) 1.00000i 0.0444994i
\(506\) 0.339746 0.0151036
\(507\) 0 0
\(508\) 40.7846i 1.80952i
\(509\) 21.2583 + 5.69615i 0.942259 + 0.252478i 0.697074 0.716999i \(-0.254485\pi\)
0.245185 + 0.969476i \(0.421151\pi\)
\(510\) 0 0
\(511\) 0.660254 1.14359i 0.0292079 0.0505896i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 0 0
\(514\) −3.77757 + 14.0981i −0.166621 + 0.621839i
\(515\) 0.277568 + 1.03590i 0.0122311 + 0.0456471i
\(516\) 0 0
\(517\) −1.23205 + 4.59808i −0.0541855 + 0.202223i
\(518\) 19.0526 33.0000i 0.837121 1.44994i
\(519\) 0 0
\(520\) 1.80385 + 6.73205i 0.0791039 + 0.295220i
\(521\) 14.1436i 0.619642i −0.950795 0.309821i \(-0.899731\pi\)
0.950795 0.309821i \(-0.100269\pi\)
\(522\) 0 0
\(523\) −2.12436 2.12436i −0.0928916 0.0928916i 0.659134 0.752026i \(-0.270923\pi\)
−0.752026 + 0.659134i \(0.770923\pi\)
\(524\) 6.26795 23.3923i 0.273817 1.02190i
\(525\) 0 0
\(526\) 1.43782 + 5.36603i 0.0626920 + 0.233970i
\(527\) −2.39230 4.14359i −0.104210 0.180498i
\(528\) 0 0
\(529\) −11.3923 + 19.7321i −0.495318 + 0.857915i
\(530\) −2.26795 0.607695i −0.0985134 0.0263966i
\(531\) 0 0
\(532\) −5.41154 20.1962i −0.234620 0.875614i
\(533\) 51.4808 13.7942i 2.22988 0.597494i
\(534\) 0 0
\(535\) 7.22243 4.16987i 0.312253 0.180279i
\(536\) −3.12436 + 1.80385i −0.134952 + 0.0779143i
\(537\) 0 0
\(538\) −15.4641 −0.666705
\(539\) −0.339746 0.339746i −0.0146339 0.0146339i
\(540\) 0 0
\(541\) −15.0000 + 15.0000i −0.644900 + 0.644900i −0.951756 0.306856i \(-0.900723\pi\)
0.306856 + 0.951756i \(0.400723\pi\)
\(542\) −14.9282 14.9282i −0.641221 0.641221i
\(543\) 0 0
\(544\) 16.0000 + 16.0000i 0.685994 + 0.685994i
\(545\) −0.633975 1.09808i −0.0271565 0.0470364i
\(546\) 0 0
\(547\) 7.57180 + 28.2583i 0.323747 + 1.20824i 0.915566 + 0.402168i \(0.131743\pi\)
−0.591819 + 0.806071i \(0.701590\pi\)
\(548\) −16.6603 + 28.8564i −0.711691 + 1.23268i
\(549\) 0 0
\(550\) 1.73205 + 3.00000i 0.0738549 + 0.127920i
\(551\) 12.2942 + 7.09808i 0.523752 + 0.302388i
\(552\) 0 0
\(553\) 3.69615 2.13397i 0.157176 0.0907458i
\(554\) 17.4904 + 10.0981i 0.743095 + 0.429026i
\(555\) 0 0
\(556\) −8.66025 2.32051i −0.367277 0.0984115i
\(557\) −27.9808 + 27.9808i −1.18558 + 1.18558i −0.207307 + 0.978276i \(0.566470\pi\)
−0.978276 + 0.207307i \(0.933530\pi\)
\(558\) 0 0
\(559\) 42.8564 1.81263
\(560\) −3.60770 + 3.60770i −0.152453 + 0.152453i
\(561\) 0 0
\(562\) 7.16987 + 26.7583i 0.302443 + 1.12873i
\(563\) 29.3564 + 7.86603i 1.23723 + 0.331513i 0.817389 0.576086i \(-0.195421\pi\)
0.419836 + 0.907600i \(0.362088\pi\)
\(564\) 0 0
\(565\) 2.76795 0.741670i 0.116448 0.0312023i
\(566\) 19.6865 11.3660i 0.827487 0.477750i
\(567\) 0 0
\(568\) −21.8564 21.8564i −0.917074 0.917074i
\(569\) −24.4808 14.1340i −1.02629 0.592527i −0.110368 0.993891i \(-0.535203\pi\)
−0.915919 + 0.401364i \(0.868536\pi\)
\(570\) 0 0
\(571\) 1.44744 5.40192i 0.0605735 0.226063i −0.929003 0.370073i \(-0.879333\pi\)
0.989576 + 0.144009i \(0.0459995\pi\)
\(572\) 4.92820i 0.206059i
\(573\) 0 0
\(574\) 27.5885 + 27.5885i 1.15152 + 1.15152i
\(575\) 2.19615 0.0915859
\(576\) 0 0
\(577\) 37.1769 1.54770 0.773848 0.633372i \(-0.218330\pi\)
0.773848 + 0.633372i \(0.218330\pi\)
\(578\) −1.00000 1.00000i −0.0415945 0.0415945i
\(579\) 0 0
\(580\) 3.46410i 0.143839i
\(581\) 7.78719 29.0622i 0.323067 1.20570i
\(582\) 0 0
\(583\) −1.43782 0.830127i −0.0595485 0.0343803i
\(584\) 1.07180 + 1.07180i 0.0443513 + 0.0443513i
\(585\) 0 0
\(586\) −18.2942 + 10.5622i −0.755728 + 0.436320i
\(587\) 2.96410 0.794229i 0.122342 0.0327813i −0.197129 0.980378i \(-0.563162\pi\)
0.319470 + 0.947596i \(0.396495\pi\)
\(588\) 0 0
\(589\) −4.90192 1.31347i −0.201980 0.0541204i
\(590\) −1.09808 4.09808i −0.0452071 0.168715i
\(591\) 0 0
\(592\) 30.9282 + 30.9282i 1.27114 + 1.27114i
\(593\) −1.46410 −0.0601234 −0.0300617 0.999548i \(-0.509570\pi\)
−0.0300617 + 0.999548i \(0.509570\pi\)
\(594\) 0 0
\(595\) −3.60770 + 3.60770i −0.147901 + 0.147901i
\(596\) −29.3923 7.87564i −1.20396 0.322599i
\(597\) 0 0
\(598\) 2.70577 + 1.56218i 0.110647 + 0.0638822i
\(599\) −30.3109 + 17.5000i −1.23847 + 0.715031i −0.968781 0.247917i \(-0.920254\pi\)
−0.269688 + 0.962948i \(0.586921\pi\)
\(600\) 0 0
\(601\) −30.2321 17.4545i −1.23319 0.711983i −0.265497 0.964112i \(-0.585536\pi\)
−0.967694 + 0.252128i \(0.918869\pi\)
\(602\) 15.6865 + 27.1699i 0.639335 + 1.10736i
\(603\) 0 0
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) 1.43782 + 5.36603i 0.0584558 + 0.218160i
\(606\) 0 0
\(607\) −4.59808 7.96410i −0.186630 0.323253i 0.757494 0.652842i \(-0.226423\pi\)
−0.944125 + 0.329589i \(0.893090\pi\)
\(608\) 24.0000 0.973329
\(609\) 0 0
\(610\) −7.73205 7.73205i −0.313062 0.313062i
\(611\) −30.9545 + 30.9545i −1.25228 + 1.25228i
\(612\) 0 0
\(613\) −7.58846 7.58846i −0.306495 0.306495i 0.537053 0.843548i \(-0.319537\pi\)
−0.843548 + 0.537053i \(0.819537\pi\)
\(614\) −11.8564 −0.478486
\(615\) 0 0
\(616\) −3.12436 + 1.80385i −0.125884 + 0.0726791i
\(617\) 8.08846 4.66987i 0.325629 0.188002i −0.328270 0.944584i \(-0.606466\pi\)
0.653899 + 0.756582i \(0.273132\pi\)
\(618\) 0 0
\(619\) −33.0885 + 8.86603i −1.32994 + 0.356356i −0.852692 0.522414i \(-0.825031\pi\)
−0.477246 + 0.878770i \(0.658365\pi\)
\(620\) 0.320508 + 1.19615i 0.0128719 + 0.0480386i
\(621\) 0 0
\(622\) 42.8827 + 11.4904i 1.71944 + 0.460722i
\(623\) 14.6077 25.3013i 0.585245 1.01367i
\(624\) 0 0
\(625\) 10.5263 + 18.2321i 0.421051 + 0.729282i
\(626\) 3.31347 + 12.3660i 0.132433 + 0.494246i
\(627\) 0 0
\(628\) −0.464102 + 1.73205i −0.0185197 + 0.0691164i
\(629\) 30.9282 + 30.9282i 1.23319 + 1.23319i
\(630\) 0 0
\(631\) 32.2487i 1.28380i 0.766788 + 0.641900i \(0.221854\pi\)
−0.766788 + 0.641900i \(0.778146\pi\)
\(632\) 1.26795 + 4.73205i 0.0504363 + 0.188231i
\(633\) 0 0
\(634\) −1.49038 + 2.58142i −0.0591906 + 0.102521i
\(635\) −2.73205 + 10.1962i −0.108418 + 0.404622i
\(636\) 0 0
\(637\) −1.14359 4.26795i −0.0453108 0.169102i
\(638\) 0.633975 2.36603i 0.0250993 0.0936718i
\(639\) 0 0
\(640\) −2.92820 5.07180i −0.115747 0.200480i
\(641\) −5.76795 + 9.99038i −0.227820 + 0.394596i −0.957162 0.289553i \(-0.906493\pi\)
0.729342 + 0.684150i \(0.239827\pi\)
\(642\) 0 0
\(643\) 1.03590 + 0.277568i 0.0408518 + 0.0109462i 0.279187 0.960237i \(-0.409935\pi\)
−0.238335 + 0.971183i \(0.576602\pi\)
\(644\) 2.28719i 0.0901278i
\(645\) 0 0
\(646\) 24.0000 0.944267
\(647\) 46.3923i 1.82387i 0.410335 + 0.911935i \(0.365412\pi\)
−0.410335 + 0.911935i \(0.634588\pi\)
\(648\) 0 0
\(649\) 3.00000i 0.117760i
\(650\) 31.8564i 1.24951i
\(651\) 0 0
\(652\) 23.8564 + 23.8564i 0.934289 + 0.934289i
\(653\) 21.3301 + 5.71539i 0.834712 + 0.223661i 0.650768 0.759276i \(-0.274447\pi\)
0.183944 + 0.982937i \(0.441114\pi\)
\(654\) 0 0
\(655\) −3.13397 + 5.42820i −0.122455 + 0.212097i
\(656\) −38.7846 + 22.3923i −1.51428 + 0.874273i
\(657\) 0 0
\(658\) −30.9545 8.29423i −1.20673 0.323343i
\(659\) 2.23205 + 8.33013i 0.0869484 + 0.324496i 0.995676 0.0928939i \(-0.0296117\pi\)
−0.908728 + 0.417390i \(0.862945\pi\)
\(660\) 0 0
\(661\) 4.20577 15.6962i 0.163586 0.610510i −0.834631 0.550810i \(-0.814319\pi\)
0.998216 0.0596998i \(-0.0190143\pi\)
\(662\) −33.4186 19.2942i −1.29885 0.749891i
\(663\) 0 0
\(664\) 29.9090 + 17.2679i 1.16069 + 0.670126i
\(665\) 5.41154i 0.209851i
\(666\) 0 0
\(667\) −1.09808 1.09808i −0.0425177 0.0425177i
\(668\) −9.53590 16.5167i −0.368955 0.639049i
\(669\) 0 0
\(670\) 0.901924 0.241670i 0.0348444 0.00933652i
\(671\) −3.86603 6.69615i −0.149246 0.258502i
\(672\) 0 0
\(673\) 3.83975 6.65064i 0.148011 0.256363i −0.782481 0.622674i \(-0.786046\pi\)
0.930492 + 0.366311i \(0.119379\pi\)
\(674\) −0.509619 + 1.90192i −0.0196298 + 0.0732594i
\(675\) 0 0
\(676\) −9.66025 + 16.7321i −0.371548 + 0.643540i
\(677\) −45.6506 + 12.2321i −1.75450 + 0.470116i −0.985577 0.169229i \(-0.945872\pi\)
−0.768920 + 0.639345i \(0.779205\pi\)
\(678\) 0 0
\(679\) −2.13397 + 1.23205i −0.0818944 + 0.0472818i
\(680\) −2.92820 5.07180i −0.112291 0.194495i
\(681\) 0 0
\(682\) 0.875644i 0.0335302i
\(683\) 5.39230 + 5.39230i 0.206331 + 0.206331i 0.802706 0.596375i \(-0.203393\pi\)
−0.596375 + 0.802706i \(0.703393\pi\)
\(684\) 0 0
\(685\) 6.09808 6.09808i 0.232996 0.232996i
\(686\) 19.5359 19.5359i 0.745884 0.745884i
\(687\) 0 0
\(688\) −34.7846 + 9.32051i −1.32615 + 0.355341i
\(689\) −7.63397 13.2224i −0.290831 0.503735i
\(690\) 0 0
\(691\) 4.96410 + 18.5263i 0.188843 + 0.704773i 0.993775 + 0.111405i \(0.0355352\pi\)
−0.804932 + 0.593367i \(0.797798\pi\)
\(692\) 17.9282 4.80385i 0.681528 0.182615i
\(693\) 0 0
\(694\) 24.7583 14.2942i 0.939813 0.542601i
\(695\) 2.00962 + 1.16025i 0.0762292 + 0.0440109i
\(696\) 0 0
\(697\) −38.7846 + 22.3923i −1.46907 + 0.848169i
\(698\) 5.83013 10.0981i 0.220674 0.382218i
\(699\) 0 0
\(700\) −20.1962 + 11.6603i −0.763343 + 0.440716i
\(701\) 21.0526 21.0526i 0.795144 0.795144i −0.187181 0.982325i \(-0.559935\pi\)
0.982325 + 0.187181i \(0.0599352\pi\)
\(702\) 0 0
\(703\) 46.3923 1.74972
\(704\) −1.07180 4.00000i −0.0403949 0.150756i
\(705\) 0 0
\(706\) 41.6147 11.1506i 1.56619 0.419660i
\(707\) 4.59808 + 1.23205i 0.172928 + 0.0463360i
\(708\) 0 0
\(709\) −40.1147 + 10.7487i −1.50654 + 0.403676i −0.915285 0.402808i \(-0.868034\pi\)
−0.591256 + 0.806484i \(0.701368\pi\)
\(710\) 4.00000 + 6.92820i 0.150117 + 0.260011i
\(711\) 0 0
\(712\) 23.7128 + 23.7128i 0.888675 + 0.888675i
\(713\) 0.480762 + 0.277568i 0.0180047 + 0.0103950i
\(714\) 0 0
\(715\) 0.330127 1.23205i 0.0123461 0.0460761i
\(716\) −15.8564 15.8564i −0.592582 0.592582i
\(717\) 0 0
\(718\) 15.0718 15.0718i 0.562474 0.562474i
\(719\) −23.3205 −0.869708 −0.434854 0.900501i \(-0.643200\pi\)
−0.434854 + 0.900501i \(0.643200\pi\)
\(720\) 0 0
\(721\) −5.10512 −0.190125
\(722\) −1.00000 + 1.00000i −0.0372161 + 0.0372161i
\(723\) 0 0
\(724\) 8.53590 8.53590i 0.317234 0.317234i
\(725\) 4.09808 15.2942i 0.152199 0.568013i
\(726\) 0 0
\(727\) −9.06218 5.23205i −0.336098 0.194046i 0.322447 0.946587i \(-0.395494\pi\)
−0.658545 + 0.752541i \(0.728828\pi\)
\(728\) −33.1769 −1.22962
\(729\) 0 0
\(730\) −0.196152 0.339746i −0.00725993 0.0125746i
\(731\) −34.7846 + 9.32051i −1.28656 + 0.344731i
\(732\) 0 0
\(733\) 27.5263 + 7.37564i 1.01671 + 0.272426i 0.728429 0.685121i \(-0.240251\pi\)
0.288277 + 0.957547i \(0.406917\pi\)
\(734\) 42.2224 11.3135i 1.55846 0.417588i
\(735\) 0 0
\(736\) −2.53590 0.679492i −0.0934745 0.0250464i
\(737\) 0.660254 0.0243208
\(738\) 0 0
\(739\) −29.7321 + 29.7321i −1.09371 + 1.09371i −0.0985823 + 0.995129i \(0.531431\pi\)
−0.995129 + 0.0985823i \(0.968569\pi\)
\(740\) −5.66025 9.80385i −0.208075 0.360397i
\(741\) 0 0
\(742\) 5.58846 9.67949i 0.205159 0.355345i
\(743\) 25.1147 14.5000i 0.921370 0.531953i 0.0372984 0.999304i \(-0.488125\pi\)
0.884072 + 0.467351i \(0.154791\pi\)
\(744\) 0 0
\(745\) 6.82051 + 3.93782i 0.249884 + 0.144271i
\(746\) 17.0263 9.83013i 0.623376 0.359907i
\(747\) 0 0
\(748\) −1.07180 4.00000i −0.0391888 0.146254i
\(749\) 10.2750 + 38.3468i 0.375440 + 1.40116i
\(750\) 0 0
\(751\) 4.72243 + 8.17949i 0.172324 + 0.298474i 0.939232 0.343283i \(-0.111539\pi\)
−0.766908 + 0.641757i \(0.778206\pi\)
\(752\) 18.3923 31.8564i 0.670698 1.16168i
\(753\) 0 0
\(754\) 15.9282 15.9282i 0.580071 0.580071i
\(755\) 2.56218 2.56218i 0.0932472 0.0932472i
\(756\) 0 0
\(757\) 8.46410 + 8.46410i 0.307633 + 0.307633i 0.843991 0.536358i \(-0.180200\pi\)
−0.536358 + 0.843991i \(0.680200\pi\)
\(758\) 31.1769i 1.13240i
\(759\) 0 0
\(760\) −6.00000 1.60770i −0.217643 0.0583172i
\(761\) −25.2846 + 14.5981i −0.916566 + 0.529180i −0.882538 0.470241i \(-0.844167\pi\)
−0.0340283 + 0.999421i \(0.510834\pi\)
\(762\) 0 0
\(763\) 5.83013 1.56218i 0.211065 0.0565546i
\(764\) −22.8564 13.1962i −0.826916 0.477420i
\(765\) 0 0
\(766\) 9.02628 33.6865i 0.326133 1.21714i
\(767\) 13.7942 23.8923i 0.498081 0.862701i
\(768\) 0 0
\(769\) −3.50000 6.06218i −0.126213 0.218608i 0.795993 0.605305i \(-0.206949\pi\)
−0.922207 + 0.386698i \(0.873616\pi\)
\(770\) 0.901924 0.241670i 0.0325031 0.00870917i
\(771\) 0 0
\(772\) 4.26795 2.46410i 0.153607 0.0886850i
\(773\) −7.58846 7.58846i −0.272938 0.272938i 0.557344 0.830282i \(-0.311821\pi\)
−0.830282 + 0.557344i \(0.811821\pi\)
\(774\) 0 0
\(775\) 5.66025i 0.203322i
\(776\) −0.732051 2.73205i −0.0262791 0.0980749i
\(777\) 0 0
\(778\) −9.63397 5.56218i −0.345395 0.199414i
\(779\) −12.2942 + 45.8827i −0.440486 + 1.64392i
\(780\) 0 0
\(781\) 1.46410 + 5.46410i 0.0523897 + 0.195521i
\(782\) −2.53590 0.679492i −0.0906835 0.0242986i
\(783\) 0 0
\(784\) 1.85641 + 3.21539i 0.0663002 + 0.114835i
\(785\) 0.232051 0.401924i 0.00828225 0.0143453i
\(786\) 0 0
\(787\) −33.8205 9.06218i −1.20557 0.323032i −0.400548 0.916276i \(-0.631180\pi\)
−0.805023 + 0.593244i \(0.797847\pi\)
\(788\) 20.9282 20.9282i 0.745536 0.745536i
\(789\) 0 0
\(790\) 1.26795i 0.0451116i
\(791\) 13.6410i 0.485019i
\(792\) 0 0
\(793\) 71.1051i 2.52502i
\(794\) −42.1051 −1.49425
\(795\) 0 0
\(796\) 11.7128 0.415150
\(797\) 1.06218 + 0.284610i 0.0376243 + 0.0100814i 0.277582 0.960702i \(-0.410467\pi\)
−0.239958 + 0.970783i \(0.577134\pi\)
\(798\) 0 0
\(799\) 18.3923 31.8564i 0.650673 1.12700i
\(800\) −6.92820 25.8564i −0.244949 0.914162i
\(801\) 0 0
\(802\) 0.849365 3.16987i 0.0299921 0.111932i
\(803\) −0.0717968 0.267949i −0.00253365 0.00945572i
\(804\) 0 0
\(805\) 0.153212 0.571797i 0.00540003 0.0201532i
\(806\) −4.02628 + 6.97372i −0.141820 + 0.245639i
\(807\) 0 0
\(808\) −2.73205 + 4.73205i −0.0961132 + 0.166473i
\(809\) 32.6410i 1.14760i 0.818997 + 0.573799i \(0.194531\pi\)
−0.818997 + 0.573799i \(0.805469\pi\)
\(810\) 0 0
\(811\) −11.5359 11.5359i −0.405080 0.405080i 0.474939 0.880019i \(-0.342470\pi\)
−0.880019 + 0.474939i \(0.842470\pi\)
\(812\) 15.9282 + 4.26795i 0.558970 + 0.149776i
\(813\) 0 0
\(814\) −2.07180 7.73205i −0.0726164 0.271008i
\(815\) −4.36603 7.56218i −0.152935 0.264892i
\(816\) 0 0
\(817\) −19.0981 + 33.0788i −0.668157 + 1.15728i
\(818\) 7.29423 + 1.95448i 0.255037 + 0.0683369i
\(819\) 0 0
\(820\) 11.1962 3.00000i 0.390987 0.104765i
\(821\) 18.7224 5.01666i 0.653417 0.175083i 0.0831439 0.996538i \(-0.473504\pi\)
0.570273 + 0.821455i \(0.306837\pi\)
\(822\) 0 0
\(823\) −6.65064 + 3.83975i −0.231827 + 0.133845i −0.611414 0.791311i \(-0.709399\pi\)
0.379588 + 0.925156i \(0.376066\pi\)
\(824\) 1.51666 5.66025i 0.0528354 0.197184i
\(825\) 0 0
\(826\) 20.1962 0.702714
\(827\) 10.6077 + 10.6077i 0.368866 + 0.368866i 0.867063 0.498198i \(-0.166005\pi\)
−0.498198 + 0.867063i \(0.666005\pi\)
\(828\) 0 0
\(829\) −17.7321 + 17.7321i −0.615860 + 0.615860i −0.944467 0.328607i \(-0.893421\pi\)
0.328607 + 0.944467i \(0.393421\pi\)
\(830\) −6.32051 6.32051i −0.219388 0.219388i
\(831\) 0 0
\(832\) 9.85641 36.7846i 0.341709 1.27528i
\(833\) 1.85641 + 3.21539i 0.0643207 + 0.111407i
\(834\) 0 0
\(835\) 1.27757 + 4.76795i 0.0442121 + 0.165002i
\(836\) −3.80385 2.19615i −0.131559 0.0759555i
\(837\) 0 0
\(838\) −1.43782 2.49038i −0.0496687 0.0860288i
\(839\) −29.2583 16.8923i −1.01011 0.583187i −0.0988859 0.995099i \(-0.531528\pi\)
−0.911224 + 0.411912i \(0.864861\pi\)
\(840\) 0 0
\(841\) 15.4186 8.90192i 0.531675 0.306963i
\(842\) 13.6865 + 7.90192i 0.471669 + 0.272318i
\(843\) 0 0
\(844\) −1.05256 + 3.92820i −0.0362306 + 0.135214i
\(845\) 3.53590 3.53590i 0.121639 0.121639i
\(846\) 0 0
\(847\) −26.4449 −0.908656
\(848\) 9.07180 + 9.07180i 0.311527 + 0.311527i
\(849\) 0 0
\(850\) −6.92820 25.8564i −0.237635 0.886867i
\(851\) −4.90192 1.31347i −0.168036 0.0450251i
\(852\) 0 0
\(853\) 10.0622 2.69615i 0.344522 0.0923145i −0.0824088 0.996599i \(-0.526261\pi\)
0.426931 + 0.904284i \(0.359595\pi\)
\(854\) 45.0788 26.0263i 1.54257 0.890601i
\(855\) 0 0
\(856\) −45.5692 −1.55752
\(857\) −42.3564 24.4545i −1.44687 0.835349i −0.448574 0.893746i \(-0.648068\pi\)
−0.998293 + 0.0583966i \(0.981401\pi\)
\(858\) 0 0
\(859\) −4.50000 + 16.7942i −0.153538 + 0.573012i 0.845688 + 0.533677i \(0.179190\pi\)
−0.999226 + 0.0393342i \(0.987476\pi\)
\(860\) 9.32051 0.317827
\(861\) 0 0
\(862\) −31.3205 31.3205i −1.06678 1.06678i
\(863\) 33.4641 1.13913 0.569566 0.821946i \(-0.307111\pi\)
0.569566 + 0.821946i \(0.307111\pi\)
\(864\) 0 0
\(865\) −4.80385 −0.163336
\(866\) 24.3923 + 24.3923i 0.828884 + 0.828884i
\(867\) 0 0
\(868\) −5.89488 −0.200085
\(869\) 0.232051 0.866025i 0.00787178 0.0293779i
\(870\) 0 0
\(871\) 5.25833 + 3.03590i 0.178172 + 0.102867i
\(872\) 6.92820i 0.234619i
\(873\) 0 0
\(874\) −2.41154 + 1.39230i −0.0815716 + 0.0470954i
\(875\) 11.9904 3.21281i 0.405349 0.108613i
\(876\) 0 0
\(877\) 33.3827 + 8.94486i 1.12725 + 0.302047i 0.773815 0.633411i \(-0.218346\pi\)
0.353438 + 0.935458i \(0.385013\pi\)
\(878\) 7.63397 + 28.4904i 0.257634 + 0.961504i
\(879\) 0 0
\(880\) 1.07180i 0.0361303i
\(881\) 3.32051 0.111871 0.0559354 0.998434i \(-0.482186\pi\)
0.0559354 + 0.998434i \(0.482186\pi\)
\(882\) 0 0
\(883\) −3.00000 + 3.00000i −0.100958 + 0.100958i −0.755782 0.654824i \(-0.772743\pi\)
0.654824 + 0.755782i \(0.272743\pi\)
\(884\) 9.85641 36.7846i 0.331507 1.23720i
\(885\) 0 0
\(886\) −20.4904 11.8301i −0.688388 0.397441i
\(887\) −21.0622 + 12.1603i −0.707199 + 0.408301i −0.810023 0.586398i \(-0.800545\pi\)
0.102824 + 0.994700i \(0.467212\pi\)
\(888\) 0 0
\(889\) −43.5167 25.1244i −1.45950 0.842644i
\(890\) −4.33975 7.51666i −0.145469 0.251959i
\(891\) 0 0
\(892\) −27.0000 15.5885i −0.904027 0.521940i
\(893\) −10.0981 37.6865i −0.337919 1.26113i
\(894\) 0 0
\(895\) 2.90192 + 5.02628i 0.0970006 + 0.168010i
\(896\) 26.9282 7.21539i 0.899608 0.241049i
\(897\) 0 0
\(898\) −0.679492 0.679492i −0.0226749 0.0226749i
\(899\) 2.83013 2.83013i 0.0943900 0.0943900i
\(900\) 0 0
\(901\) 9.07180 + 9.07180i 0.302225 + 0.302225i
\(902\) 8.19615 0.272902
\(903\) 0 0
\(904\) −15.1244 4.05256i −0.503029 0.134786i
\(905\) −2.70577 + 1.56218i −0.0899429 + 0.0519285i
\(906\) 0 0
\(907\) 11.4282 3.06218i 0.379467 0.101678i −0.0640432 0.997947i \(-0.520400\pi\)
0.443510 + 0.896269i \(0.353733\pi\)
\(908\) −34.5167 + 9.24871i −1.14548 + 0.306929i
\(909\) 0 0
\(910\) 8.29423 + 2.22243i 0.274951 + 0.0736729i
\(911\) 5.86603 10.1603i 0.194350 0.336624i −0.752337 0.658778i \(-0.771074\pi\)
0.946687 + 0.322154i \(0.104407\pi\)
\(912\) 0 0
\(913\) −3.16025 5.47372i −0.104589 0.181154i
\(914\) 8.04552 + 30.0263i 0.266122 + 0.993181i
\(915\) 0 0
\(916\) −18.8564 5.05256i −0.623033 0.166941i
\(917\) −21.0981 21.0981i −0.696720 0.696720i
\(918\) 0 0
\(919\) 43.4641i 1.43375i 0.697203 + 0.716874i \(0.254428\pi\)
−0.697203 + 0.716874i \(0.745572\pi\)
\(920\) 0.588457 + 0.339746i 0.0194009 + 0.0112011i
\(921\) 0 0
\(922\) −1.63397 + 2.83013i −0.0538121 + 0.0932053i
\(923\) −13.4641 + 50.2487i −0.443176 + 1.65396i
\(924\) 0 0
\(925\) −13.3923 49.9808i −0.440336 1.64336i
\(926\) −2.43782 + 9.09808i −0.0801118 + 0.298981i
\(927\) 0 0
\(928\) −9.46410 + 16.3923i −0.310674 + 0.538104i
\(929\) 18.3564 31.7942i 0.602254 1.04313i −0.390225 0.920720i \(-0.627603\pi\)
0.992479 0.122415i \(-0.0390640\pi\)
\(930\) 0 0
\(931\) 3.80385 + 1.01924i 0.124666 + 0.0334042i
\(932\) −45.8564 −1.50208
\(933\) 0 0
\(934\) 39.5692 1.29474
\(935\) 1.07180i 0.0350515i
\(936\) 0 0
\(937\) 32.9282i 1.07572i −0.843035 0.537859i \(-0.819233\pi\)
0.843035 0.537859i \(-0.180767\pi\)
\(938\) 4.44486i 0.145130i
\(939\) 0 0
\(940\) −6.73205 + 6.73205i −0.219575 + 0.219575i
\(941\) −10.8660 2.91154i −0.354222 0.0949136i 0.0773199 0.997006i \(-0.475364\pi\)
−0.431542 + 0.902093i \(0.642030\pi\)
\(942\) 0 0
\(943\) 2.59808 4.50000i 0.0846050 0.146540i
\(944\) −6.00000 + 22.3923i −0.195283 + 0.728807i
\(945\) 0 0
\(946\) 6.36603 + 1.70577i 0.206977 + 0.0554594i
\(947\) −4.01666 14.9904i −0.130524 0.487122i 0.869452 0.494017i \(-0.164472\pi\)
−0.999976 + 0.00689497i \(0.997805\pi\)
\(948\) 0 0
\(949\) 0.660254 2.46410i 0.0214328 0.0799881i
\(950\) −24.5885 14.1962i −0.797755 0.460584i
\(951\) 0 0
\(952\) 26.9282 7.21539i 0.872748 0.233852i
\(953\) 39.4641i 1.27837i −0.769054 0.639184i \(-0.779272\pi\)
0.769054 0.639184i \(-0.220728\pi\)
\(954\) 0 0
\(955\) 4.83013 + 4.83013i 0.156299 + 0.156299i
\(956\) −19.3923 + 11.1962i −0.627192 + 0.362109i
\(957\) 0 0
\(958\) −1.83013 + 0.490381i −0.0591287 + 0.0158435i
\(959\) 20.5263 + 35.5526i 0.662828 + 1.14805i
\(960\) 0 0
\(961\) 14.7846 25.6077i 0.476923 0.826055i
\(962\) 19.0526 71.1051i 0.614279 2.29252i
\(963\) 0 0
\(964\) −21.5885 12.4641i −0.695317 0.401442i
\(965\) −1.23205 + 0.330127i −0.0396611 + 0.0106272i
\(966\) 0 0
\(967\) −14.9378 + 8.62436i −0.480368 + 0.277341i −0.720570 0.693382i \(-0.756120\pi\)
0.240202 + 0.970723i \(0.422786\pi\)
\(968\) 7.85641 29.3205i 0.252514 0.942397i
\(969\) 0 0
\(970\) 0.732051i 0.0235047i
\(971\) −27.9808 27.9808i −0.897945 0.897945i 0.0973088 0.995254i \(-0.468977\pi\)
−0.995254 + 0.0973088i \(0.968977\pi\)
\(972\) 0 0
\(973\) −7.81089 + 7.81089i −0.250406 + 0.250406i
\(974\) 34.7846 34.7846i 1.11457 1.11457i
\(975\) 0 0
\(976\) 15.4641 + 57.7128i 0.494994 + 1.84734i
\(977\) −17.2846 29.9378i −0.552984 0.957796i −0.998057 0.0623018i \(-0.980156\pi\)
0.445074 0.895494i \(-0.353177\pi\)
\(978\) 0 0
\(979\) −1.58846 5.92820i −0.0507673 0.189466i
\(980\) −0.248711 0.928203i −0.00794479 0.0296504i
\(981\) 0 0
\(982\) −2.36603 + 1.36603i −0.0755029 + 0.0435916i
\(983\) 40.9186 + 23.6244i 1.30510 + 0.753500i 0.981274 0.192617i \(-0.0616974\pi\)
0.323826 + 0.946117i \(0.395031\pi\)
\(984\) 0 0
\(985\) −6.63397 + 3.83013i −0.211376 + 0.122038i
\(986\) −9.46410 + 16.3923i −0.301398 + 0.522037i
\(987\) 0 0
\(988\) −20.1962 34.9808i −0.642525 1.11289i
\(989\) 2.95448 2.95448i 0.0939471 0.0939471i
\(990\) 0 0
\(991\) −23.6077 −0.749923 −0.374962 0.927040i \(-0.622344\pi\)
−0.374962 + 0.927040i \(0.622344\pi\)
\(992\) 1.75129 6.53590i 0.0556035 0.207515i
\(993\) 0 0
\(994\) −36.7846 + 9.85641i −1.16674 + 0.312626i
\(995\) −2.92820 0.784610i −0.0928303 0.0248738i
\(996\) 0 0
\(997\) 11.0622 2.96410i 0.350343 0.0938740i −0.0793561 0.996846i \(-0.525286\pi\)
0.429699 + 0.902972i \(0.358620\pi\)
\(998\) −1.83013 3.16987i −0.0579317 0.100341i
\(999\) 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 432.2.y.d.181.1 4
3.2 odd 2 144.2.x.a.133.1 yes 4
4.3 odd 2 1728.2.bc.c.1585.1 4
9.4 even 3 432.2.y.a.37.1 4
9.5 odd 6 144.2.x.d.85.1 yes 4
12.11 even 2 576.2.bb.a.241.1 4
16.3 odd 4 1728.2.bc.b.721.1 4
16.13 even 4 432.2.y.a.397.1 4
36.23 even 6 576.2.bb.b.49.1 4
36.31 odd 6 1728.2.bc.b.1009.1 4
48.29 odd 4 144.2.x.d.61.1 yes 4
48.35 even 4 576.2.bb.b.529.1 4
144.13 even 12 inner 432.2.y.d.253.1 4
144.67 odd 12 1728.2.bc.c.145.1 4
144.77 odd 12 144.2.x.a.13.1 4
144.131 even 12 576.2.bb.a.337.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.a.13.1 4 144.77 odd 12
144.2.x.a.133.1 yes 4 3.2 odd 2
144.2.x.d.61.1 yes 4 48.29 odd 4
144.2.x.d.85.1 yes 4 9.5 odd 6
432.2.y.a.37.1 4 9.4 even 3
432.2.y.a.397.1 4 16.13 even 4
432.2.y.d.181.1 4 1.1 even 1 trivial
432.2.y.d.253.1 4 144.13 even 12 inner
576.2.bb.a.241.1 4 12.11 even 2
576.2.bb.a.337.1 4 144.131 even 12
576.2.bb.b.49.1 4 36.23 even 6
576.2.bb.b.529.1 4 48.35 even 4
1728.2.bc.b.721.1 4 16.3 odd 4
1728.2.bc.b.1009.1 4 36.31 odd 6
1728.2.bc.c.145.1 4 144.67 odd 12
1728.2.bc.c.1585.1 4 4.3 odd 2