Properties

Label 507.2.k.f.188.1
Level $507$
Weight $2$
Character 507.188
Analytic conductor $4.048$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.k (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: 8.0.56070144.2
Defining polynomial: \(x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 63 x^{4} - 74 x^{3} + 70 x^{2} - 38 x + 13\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 188.1
Root \(0.500000 + 2.19293i\) of defining polynomial
Character \(\chi\) \(=\) 507.188
Dual form 507.2.k.f.89.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.31259 + 0.619657i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(3.68825 + 1.89551i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +O(q^{10})\) \(q+(-2.31259 + 0.619657i) q^{2} +(-1.28311 - 1.16345i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(3.68825 + 1.89551i) q^{6} +(-0.366025 + 1.36603i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(0.292748 + 2.98568i) q^{9} +(-4.96410 - 2.86603i) q^{10} +(0.453620 + 1.69293i) q^{11} +(-6.31812 - 1.36603i) q^{12} -3.38587i q^{14} +(-0.202571 - 4.14187i) q^{15} +(1.23205 - 2.13397i) q^{16} +(-1.07328 - 1.85897i) q^{17} +(-2.52711 - 6.72326i) q^{18} +(-1.00000 - 0.267949i) q^{19} +(8.63071 + 2.31259i) q^{20} +(2.05896 - 1.32691i) q^{21} +(-2.09808 - 3.63397i) q^{22} +(7.17394 - 0.350863i) q^{24} +0.732051i q^{25} +(3.09808 - 4.17156i) q^{27} +(1.36603 + 5.09808i) q^{28} +(4.79122 + 2.76621i) q^{29} +(3.03500 + 9.45293i) q^{30} +(-4.46410 + 4.46410i) q^{31} +(0.619657 - 2.31259i) q^{32} +(1.38761 - 2.69999i) q^{33} +(3.63397 + 3.63397i) q^{34} +(-2.93225 + 1.69293i) q^{35} +(6.51754 + 9.10360i) q^{36} +(-6.59808 + 1.76795i) q^{37} +2.47863 q^{38} -9.92820 q^{40} +(0.619657 - 0.166037i) q^{41} +(-3.93930 + 4.34444i) q^{42} +(-7.09808 + 4.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(-4.55896 + 5.55017i) q^{45} +(-6.77174 + 6.77174i) q^{47} +(-4.06364 + 1.30469i) q^{48} +(4.33013 + 2.50000i) q^{49} +(-0.453620 - 1.69293i) q^{50} +(-0.785693 + 3.63397i) q^{51} +4.62518i q^{53} +(-4.57965 + 11.5669i) q^{54} +(-2.09808 + 3.63397i) q^{55} +(-2.93225 - 5.07880i) q^{56} +(0.971364 + 1.50726i) q^{57} +(-12.7942 - 3.42820i) q^{58} +(-4.62518 - 1.23931i) q^{59} +(-8.38356 - 13.0087i) q^{60} +(3.50000 + 6.06218i) q^{61} +(7.55743 - 13.0899i) q^{62} +(-4.18567 - 0.692934i) q^{63} +10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(-2.26795 - 8.46410i) q^{67} +(-6.93777 - 4.00552i) q^{68} +(5.73205 - 5.73205i) q^{70} +(-1.23931 + 4.62518i) q^{71} +(-9.61317 - 7.89635i) q^{72} +(6.09808 + 6.09808i) q^{73} +(14.1631 - 8.17709i) q^{74} +(0.851708 - 0.939303i) q^{75} +(-3.73205 + 1.00000i) q^{76} -2.47863 q^{77} +2.00000 q^{79} +(5.69846 - 1.52690i) q^{80} +(-8.82860 + 1.74811i) q^{81} +(-1.33013 + 0.767949i) q^{82} +(-1.23931 - 1.23931i) q^{83} +(4.17862 - 8.13071i) q^{84} +(1.33013 - 4.96410i) q^{85} +(13.8755 - 13.8755i) q^{86} +(-2.92931 - 9.12372i) q^{87} +(-6.29423 - 3.63397i) q^{88} +(2.60017 + 9.70398i) q^{89} +(7.10381 - 15.6603i) q^{90} +(10.9217 - 0.534160i) q^{93} +(11.4641 - 19.8564i) q^{94} +(-1.23931 - 2.14655i) q^{95} +(-3.48568 + 2.24637i) q^{96} +(12.5622 + 3.36603i) q^{97} +(-11.5630 - 3.09828i) q^{98} +(-4.92177 + 1.84997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} + 12q^{4} + 14q^{6} + 4q^{7} + 4q^{9} + O(q^{10}) \) \( 8q - 2q^{3} + 12q^{4} + 14q^{6} + 4q^{7} + 4q^{9} - 12q^{10} + 2q^{15} - 4q^{16} - 4q^{18} - 8q^{19} - 4q^{21} + 4q^{22} + 30q^{24} + 4q^{27} + 4q^{28} - 18q^{30} - 8q^{31} + 20q^{33} + 36q^{34} + 36q^{36} - 32q^{37} - 24q^{40} - 16q^{42} - 36q^{43} - 16q^{45} - 14q^{48} + 38q^{54} + 4q^{55} - 16q^{57} - 40q^{58} - 44q^{60} + 28q^{61} - 16q^{63} - 40q^{66} - 32q^{67} + 32q^{70} - 24q^{72} + 28q^{73} - 12q^{75} - 16q^{76} + 16q^{79} + 4q^{81} + 24q^{82} + 8q^{84} - 24q^{85} - 34q^{87} + 12q^{88} - 16q^{93} + 64q^{94} - 16q^{96} + 52q^{97} - 40q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31259 + 0.619657i −1.63525 + 0.438164i −0.955430 0.295217i \(-0.904608\pi\)
−0.679818 + 0.733380i \(0.737941\pi\)
\(3\) −1.28311 1.16345i −0.740805 0.671721i
\(4\) 3.23205 1.86603i 1.61603 0.933013i
\(5\) 1.69293 + 1.69293i 0.757103 + 0.757103i 0.975794 0.218691i \(-0.0701787\pi\)
−0.218691 + 0.975794i \(0.570179\pi\)
\(6\) 3.68825 + 1.89551i 1.50572 + 0.773837i
\(7\) −0.366025 + 1.36603i −0.138345 + 0.516309i 0.861617 + 0.507559i \(0.169452\pi\)
−0.999962 + 0.00875026i \(0.997215\pi\)
\(8\) −2.93225 + 2.93225i −1.03671 + 1.03671i
\(9\) 0.292748 + 2.98568i 0.0975828 + 0.995227i
\(10\) −4.96410 2.86603i −1.56979 0.906317i
\(11\) 0.453620 + 1.69293i 0.136772 + 0.510439i 0.999984 + 0.00559833i \(0.00178201\pi\)
−0.863213 + 0.504840i \(0.831551\pi\)
\(12\) −6.31812 1.36603i −1.82388 0.394338i
\(13\) 0 0
\(14\) 3.38587i 0.904911i
\(15\) −0.202571 4.14187i −0.0523036 1.06943i
\(16\) 1.23205 2.13397i 0.308013 0.533494i
\(17\) −1.07328 1.85897i −0.260308 0.450867i 0.706016 0.708196i \(-0.250491\pi\)
−0.966324 + 0.257330i \(0.917157\pi\)
\(18\) −2.52711 6.72326i −0.595644 1.58469i
\(19\) −1.00000 0.267949i −0.229416 0.0614718i 0.142280 0.989826i \(-0.454557\pi\)
−0.371695 + 0.928355i \(0.621223\pi\)
\(20\) 8.63071 + 2.31259i 1.92988 + 0.517111i
\(21\) 2.05896 1.32691i 0.449302 0.289555i
\(22\) −2.09808 3.63397i −0.447311 0.774766i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 7.17394 0.350863i 1.46437 0.0716197i
\(25\) 0.732051i 0.146410i
\(26\) 0 0
\(27\) 3.09808 4.17156i 0.596225 0.802817i
\(28\) 1.36603 + 5.09808i 0.258155 + 0.963446i
\(29\) 4.79122 + 2.76621i 0.889707 + 0.513673i 0.873847 0.486202i \(-0.161618\pi\)
0.0158603 + 0.999874i \(0.494951\pi\)
\(30\) 3.03500 + 9.45293i 0.554113 + 1.72586i
\(31\) −4.46410 + 4.46410i −0.801776 + 0.801776i −0.983373 0.181597i \(-0.941873\pi\)
0.181597 + 0.983373i \(0.441873\pi\)
\(32\) 0.619657 2.31259i 0.109541 0.408812i
\(33\) 1.38761 2.69999i 0.241551 0.470008i
\(34\) 3.63397 + 3.63397i 0.623222 + 0.623222i
\(35\) −2.93225 + 1.69293i −0.495640 + 0.286158i
\(36\) 6.51754 + 9.10360i 1.08626 + 1.51727i
\(37\) −6.59808 + 1.76795i −1.08472 + 0.290649i −0.756527 0.653963i \(-0.773105\pi\)
−0.328190 + 0.944612i \(0.606439\pi\)
\(38\) 2.47863 0.402086
\(39\) 0 0
\(40\) −9.92820 −1.56979
\(41\) 0.619657 0.166037i 0.0967741 0.0259306i −0.210107 0.977678i \(-0.567381\pi\)
0.306881 + 0.951748i \(0.400715\pi\)
\(42\) −3.93930 + 4.34444i −0.607848 + 0.670362i
\(43\) −7.09808 + 4.09808i −1.08245 + 0.624951i −0.931555 0.363600i \(-0.881548\pi\)
−0.150891 + 0.988550i \(0.548214\pi\)
\(44\) 4.62518 + 4.62518i 0.697272 + 0.697272i
\(45\) −4.55896 + 5.55017i −0.679610 + 0.827370i
\(46\) 0 0
\(47\) −6.77174 + 6.77174i −0.987759 + 0.987759i −0.999926 0.0121668i \(-0.996127\pi\)
0.0121668 + 0.999926i \(0.496127\pi\)
\(48\) −4.06364 + 1.30469i −0.586536 + 0.188316i
\(49\) 4.33013 + 2.50000i 0.618590 + 0.357143i
\(50\) −0.453620 1.69293i −0.0641516 0.239417i
\(51\) −0.785693 + 3.63397i −0.110019 + 0.508858i
\(52\) 0 0
\(53\) 4.62518i 0.635318i 0.948205 + 0.317659i \(0.102897\pi\)
−0.948205 + 0.317659i \(0.897103\pi\)
\(54\) −4.57965 + 11.5669i −0.623211 + 1.57405i
\(55\) −2.09808 + 3.63397i −0.282905 + 0.490005i
\(56\) −2.93225 5.07880i −0.391838 0.678683i
\(57\) 0.971364 + 1.50726i 0.128660 + 0.199642i
\(58\) −12.7942 3.42820i −1.67996 0.450145i
\(59\) −4.62518 1.23931i −0.602147 0.161345i −0.0551484 0.998478i \(-0.517563\pi\)
−0.546999 + 0.837133i \(0.684230\pi\)
\(60\) −8.38356 13.0087i −1.08231 1.67942i
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 7.55743 13.0899i 0.959794 1.66241i
\(63\) −4.18567 0.692934i −0.527345 0.0873015i
\(64\) 10.6603i 1.33253i
\(65\) 0 0
\(66\) −1.53590 + 7.10381i −0.189056 + 0.874418i
\(67\) −2.26795 8.46410i −0.277074 1.03405i −0.954439 0.298407i \(-0.903545\pi\)
0.677365 0.735647i \(-0.263122\pi\)
\(68\) −6.93777 4.00552i −0.841328 0.485741i
\(69\) 0 0
\(70\) 5.73205 5.73205i 0.685111 0.685111i
\(71\) −1.23931 + 4.62518i −0.147079 + 0.548908i 0.852575 + 0.522606i \(0.175040\pi\)
−0.999654 + 0.0263025i \(0.991627\pi\)
\(72\) −9.61317 7.89635i −1.13292 0.930594i
\(73\) 6.09808 + 6.09808i 0.713726 + 0.713726i 0.967313 0.253587i \(-0.0816103\pi\)
−0.253587 + 0.967313i \(0.581610\pi\)
\(74\) 14.1631 8.17709i 1.64643 0.950567i
\(75\) 0.851708 0.939303i 0.0983467 0.108461i
\(76\) −3.73205 + 1.00000i −0.428096 + 0.114708i
\(77\) −2.47863 −0.282466
\(78\) 0 0
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) 5.69846 1.52690i 0.637107 0.170712i
\(81\) −8.82860 + 1.74811i −0.980955 + 0.194234i
\(82\) −1.33013 + 0.767949i −0.146888 + 0.0848058i
\(83\) −1.23931 1.23931i −0.136032 0.136032i 0.635812 0.771844i \(-0.280665\pi\)
−0.771844 + 0.635812i \(0.780665\pi\)
\(84\) 4.17862 8.13071i 0.455924 0.887133i
\(85\) 1.33013 4.96410i 0.144273 0.538432i
\(86\) 13.8755 13.8755i 1.49624 1.49624i
\(87\) −2.92931 9.12372i −0.314054 0.978165i
\(88\) −6.29423 3.63397i −0.670967 0.387383i
\(89\) 2.60017 + 9.70398i 0.275618 + 1.02862i 0.955426 + 0.295230i \(0.0953964\pi\)
−0.679808 + 0.733390i \(0.737937\pi\)
\(90\) 7.10381 15.6603i 0.748807 1.65074i
\(91\) 0 0
\(92\) 0 0
\(93\) 10.9217 0.534160i 1.13253 0.0553898i
\(94\) 11.4641 19.8564i 1.18243 2.04803i
\(95\) −1.23931 2.14655i −0.127151 0.220232i
\(96\) −3.48568 + 2.24637i −0.355756 + 0.229269i
\(97\) 12.5622 + 3.36603i 1.27550 + 0.341768i 0.832134 0.554575i \(-0.187119\pi\)
0.443362 + 0.896343i \(0.353786\pi\)
\(98\) −11.5630 3.09828i −1.16803 0.312974i
\(99\) −4.92177 + 1.84997i −0.494656 + 0.185929i
\(100\) 1.36603 + 2.36603i 0.136603 + 0.236603i
\(101\) −9.87002 + 17.0954i −0.982104 + 1.70105i −0.327944 + 0.944697i \(0.606356\pi\)
−0.654160 + 0.756356i \(0.726978\pi\)
\(102\) −0.434830 8.89076i −0.0430546 0.880316i
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) 0 0
\(105\) 5.73205 + 1.23931i 0.559391 + 0.120945i
\(106\) −2.86603 10.6962i −0.278373 1.03890i
\(107\) 14.4507 + 8.34312i 1.39700 + 0.806560i 0.994078 0.108673i \(-0.0346600\pi\)
0.402925 + 0.915233i \(0.367993\pi\)
\(108\) 2.22890 19.2638i 0.214476 1.85366i
\(109\) 2.80385 2.80385i 0.268560 0.268560i −0.559960 0.828520i \(-0.689183\pi\)
0.828520 + 0.559960i \(0.189183\pi\)
\(110\) 2.60017 9.70398i 0.247917 0.925239i
\(111\) 10.5230 + 5.40808i 0.998798 + 0.513313i
\(112\) 2.46410 + 2.46410i 0.232836 + 0.232836i
\(113\) −11.2309 + 6.48415i −1.05651 + 0.609978i −0.924465 0.381266i \(-0.875488\pi\)
−0.132047 + 0.991243i \(0.542155\pi\)
\(114\) −3.18035 2.88377i −0.297867 0.270090i
\(115\) 0 0
\(116\) 20.6473 1.91705
\(117\) 0 0
\(118\) 11.4641 1.05536
\(119\) 2.93225 0.785693i 0.268799 0.0720244i
\(120\) 12.7390 + 11.5510i 1.16291 + 1.05446i
\(121\) 6.86603 3.96410i 0.624184 0.360373i
\(122\) −11.8505 11.8505i −1.07290 1.07290i
\(123\) −0.988265 0.507899i −0.0891088 0.0457957i
\(124\) −6.09808 + 22.7583i −0.547623 + 2.04376i
\(125\) 7.22536 7.22536i 0.646255 0.646255i
\(126\) 10.1091 0.991207i 0.900592 0.0883037i
\(127\) −13.0981 7.56218i −1.16227 0.671035i −0.210420 0.977611i \(-0.567483\pi\)
−0.951846 + 0.306576i \(0.900817\pi\)
\(128\) −5.36639 20.0276i −0.474326 1.77021i
\(129\) 13.8755 + 3.00000i 1.22167 + 0.264135i
\(130\) 0 0
\(131\) 0.907241i 0.0792660i 0.999214 + 0.0396330i \(0.0126189\pi\)
−0.999214 + 0.0396330i \(0.987381\pi\)
\(132\) −0.553435 11.3158i −0.0481703 0.984915i
\(133\) 0.732051 1.26795i 0.0634769 0.109945i
\(134\) 10.4897 + 18.1687i 0.906170 + 1.56953i
\(135\) 12.3070 1.81734i 1.05922 0.156412i
\(136\) 8.59808 + 2.30385i 0.737279 + 0.197553i
\(137\) −5.69846 1.52690i −0.486852 0.130452i 0.00703925 0.999975i \(-0.497759\pi\)
−0.493891 + 0.869524i \(0.664426\pi\)
\(138\) 0 0
\(139\) 1.19615 + 2.07180i 0.101456 + 0.175728i 0.912285 0.409556i \(-0.134316\pi\)
−0.810829 + 0.585284i \(0.800983\pi\)
\(140\) −6.31812 + 10.9433i −0.533978 + 0.924877i
\(141\) 16.5675 0.810284i 1.39523 0.0682383i
\(142\) 11.4641i 0.962046i
\(143\) 0 0
\(144\) 6.73205 + 3.05379i 0.561004 + 0.254483i
\(145\) 3.42820 + 12.7942i 0.284697 + 1.06250i
\(146\) −17.8811 10.3236i −1.47985 0.854391i
\(147\) −2.64740 8.24568i −0.218354 0.680092i
\(148\) −18.0263 + 18.0263i −1.48175 + 1.48175i
\(149\) 1.40535 5.24484i 0.115131 0.429674i −0.884166 0.467173i \(-0.845272\pi\)
0.999297 + 0.0374992i \(0.0119392\pi\)
\(150\) −1.38761 + 2.69999i −0.113298 + 0.220453i
\(151\) −7.46410 7.46410i −0.607420 0.607420i 0.334851 0.942271i \(-0.391314\pi\)
−0.942271 + 0.334851i \(0.891314\pi\)
\(152\) 3.71794 2.14655i 0.301565 0.174109i
\(153\) 5.23610 3.74867i 0.423313 0.303062i
\(154\) 5.73205 1.53590i 0.461902 0.123766i
\(155\) −15.1149 −1.21405
\(156\) 0 0
\(157\) −15.1962 −1.21278 −0.606392 0.795165i \(-0.707384\pi\)
−0.606392 + 0.795165i \(0.707384\pi\)
\(158\) −4.62518 + 1.23931i −0.367960 + 0.0985945i
\(159\) 5.38119 5.93462i 0.426756 0.470646i
\(160\) 4.96410 2.86603i 0.392447 0.226579i
\(161\) 0 0
\(162\) 19.3337 9.51336i 1.51900 0.747440i
\(163\) −4.00000 + 14.9282i −0.313304 + 1.16927i 0.612254 + 0.790661i \(0.290263\pi\)
−0.925558 + 0.378606i \(0.876404\pi\)
\(164\) 1.69293 1.69293i 0.132196 0.132196i
\(165\) 6.92003 2.22178i 0.538723 0.172965i
\(166\) 3.63397 + 2.09808i 0.282051 + 0.162842i
\(167\) −3.05379 11.3969i −0.236310 0.881920i −0.977554 0.210685i \(-0.932431\pi\)
0.741244 0.671235i \(-0.234236\pi\)
\(168\) −2.14655 + 9.92820i −0.165610 + 0.765978i
\(169\) 0 0
\(170\) 12.3042i 0.943686i
\(171\) 0.507263 3.06412i 0.0387914 0.234319i
\(172\) −15.2942 + 26.4904i −1.16617 + 2.01987i
\(173\) −3.71794 6.43966i −0.282670 0.489598i 0.689372 0.724408i \(-0.257887\pi\)
−0.972041 + 0.234809i \(0.924553\pi\)
\(174\) 12.4279 + 19.2843i 0.942154 + 1.46194i
\(175\) −1.00000 0.267949i −0.0755929 0.0202551i
\(176\) 4.17156 + 1.11777i 0.314443 + 0.0842548i
\(177\) 4.49274 + 6.97136i 0.337695 + 0.524000i
\(178\) −12.0263 20.8301i −0.901408 1.56128i
\(179\) 9.37191 16.2326i 0.700489 1.21328i −0.267805 0.963473i \(-0.586298\pi\)
0.968295 0.249810i \(-0.0803683\pi\)
\(180\) −4.37804 + 26.4456i −0.326320 + 1.97114i
\(181\) 3.00000i 0.222988i 0.993765 + 0.111494i \(0.0355636\pi\)
−0.993765 + 0.111494i \(0.964436\pi\)
\(182\) 0 0
\(183\) 2.56218 11.8505i 0.189402 0.876017i
\(184\) 0 0
\(185\) −14.1631 8.17709i −1.04129 0.601191i
\(186\) −24.9265 + 8.00301i −1.82770 + 0.586809i
\(187\) 2.66025 2.66025i 0.194537 0.194537i
\(188\) −9.25036 + 34.5228i −0.674652 + 2.51784i
\(189\) 4.56448 + 5.75895i 0.332017 + 0.418902i
\(190\) 4.19615 + 4.19615i 0.304421 + 0.304421i
\(191\) −16.8078 + 9.70398i −1.21617 + 0.702156i −0.964096 0.265553i \(-0.914446\pi\)
−0.252073 + 0.967708i \(0.581112\pi\)
\(192\) 12.4027 13.6783i 0.895089 0.987146i
\(193\) 6.96410 1.86603i 0.501287 0.134319i 0.000689767 1.00000i \(-0.499780\pi\)
0.500597 + 0.865680i \(0.333114\pi\)
\(194\) −31.1370 −2.23550
\(195\) 0 0
\(196\) 18.6603 1.33288
\(197\) 1.69293 0.453620i 0.120617 0.0323191i −0.198006 0.980201i \(-0.563446\pi\)
0.318622 + 0.947882i \(0.396780\pi\)
\(198\) 10.2357 7.32803i 0.727418 0.520780i
\(199\) −0.803848 + 0.464102i −0.0569832 + 0.0328993i −0.528221 0.849107i \(-0.677141\pi\)
0.471238 + 0.882006i \(0.343807\pi\)
\(200\) −2.14655 2.14655i −0.151784 0.151784i
\(201\) −6.93756 + 13.4990i −0.489338 + 0.952149i
\(202\) 12.2321 45.6506i 0.860644 3.21197i
\(203\) −5.53242 + 5.53242i −0.388300 + 0.388300i
\(204\) 4.24169 + 13.2113i 0.296978 + 0.924977i
\(205\) 1.33013 + 0.767949i 0.0929001 + 0.0536359i
\(206\) 4.29311 + 16.0221i 0.299115 + 1.11631i
\(207\) 0 0
\(208\) 0 0
\(209\) 1.81448i 0.125510i
\(210\) −14.0238 + 0.685879i −0.967737 + 0.0473302i
\(211\) 6.09808 10.5622i 0.419809 0.727130i −0.576111 0.817371i \(-0.695430\pi\)
0.995920 + 0.0902411i \(0.0287638\pi\)
\(212\) 8.63071 + 14.9488i 0.592759 + 1.02669i
\(213\) 6.97136 4.49274i 0.477670 0.307837i
\(214\) −38.5885 10.3397i −2.63785 0.706810i
\(215\) −18.9543 5.07880i −1.29268 0.346371i
\(216\) 3.14772 + 21.3164i 0.214176 + 1.45040i
\(217\) −4.46410 7.73205i −0.303043 0.524886i
\(218\) −4.74673 + 8.22158i −0.321489 + 0.556835i
\(219\) −0.729677 14.9193i −0.0493070 1.00816i
\(220\) 15.6603i 1.05581i
\(221\) 0 0
\(222\) −27.6865 5.98604i −1.85820 0.401757i
\(223\) 5.97372 + 22.2942i 0.400030 + 1.49293i 0.813041 + 0.582206i \(0.197810\pi\)
−0.413011 + 0.910726i \(0.635523\pi\)
\(224\) 2.93225 + 1.69293i 0.195919 + 0.113114i
\(225\) −2.18567 + 0.214307i −0.145711 + 0.0142871i
\(226\) 21.9545 21.9545i 1.46039 1.46039i
\(227\) 4.05001 15.1149i 0.268809 1.00321i −0.691069 0.722789i \(-0.742860\pi\)
0.959878 0.280419i \(-0.0904735\pi\)
\(228\) 5.95209 + 3.05896i 0.394187 + 0.202585i
\(229\) −10.1244 10.1244i −0.669036 0.669036i 0.288457 0.957493i \(-0.406858\pi\)
−0.957493 + 0.288457i \(0.906858\pi\)
\(230\) 0 0
\(231\) 3.18035 + 2.88377i 0.209252 + 0.189738i
\(232\) −22.1603 + 5.93782i −1.45489 + 0.389837i
\(233\) 7.43588 0.487141 0.243570 0.969883i \(-0.421681\pi\)
0.243570 + 0.969883i \(0.421681\pi\)
\(234\) 0 0
\(235\) −22.9282 −1.49567
\(236\) −17.2614 + 4.62518i −1.12362 + 0.301074i
\(237\) −2.56622 2.32691i −0.166694 0.151149i
\(238\) −6.29423 + 3.63397i −0.407994 + 0.235556i
\(239\) −7.10381 7.10381i −0.459507 0.459507i 0.438986 0.898494i \(-0.355338\pi\)
−0.898494 + 0.438986i \(0.855338\pi\)
\(240\) −9.08823 4.67072i −0.586643 0.301493i
\(241\) 1.93782 7.23205i 0.124826 0.465857i −0.875007 0.484110i \(-0.839144\pi\)
0.999833 + 0.0182524i \(0.00581023\pi\)
\(242\) −13.4219 + 13.4219i −0.862794 + 0.862794i
\(243\) 13.3619 + 8.02865i 0.857167 + 0.515038i
\(244\) 22.6244 + 13.0622i 1.44838 + 0.836220i
\(245\) 3.09828 + 11.5630i 0.197942 + 0.738730i
\(246\) 2.60017 + 0.562178i 0.165781 + 0.0358431i
\(247\) 0 0
\(248\) 26.1797i 1.66241i
\(249\) 0.148292 + 3.03206i 0.00939765 + 0.192149i
\(250\) −12.2321 + 21.1865i −0.773623 + 1.33995i
\(251\) 10.9433 + 18.9543i 0.690735 + 1.19639i 0.971597 + 0.236640i \(0.0760461\pi\)
−0.280863 + 0.959748i \(0.590621\pi\)
\(252\) −14.8213 + 5.57097i −0.933656 + 0.350938i
\(253\) 0 0
\(254\) 34.9764 + 9.37191i 2.19462 + 0.588046i
\(255\) −7.48221 + 4.82195i −0.468554 + 0.301962i
\(256\) 14.1603 + 24.5263i 0.885016 + 1.53289i
\(257\) −8.29863 + 14.3737i −0.517655 + 0.896604i 0.482135 + 0.876097i \(0.339861\pi\)
−0.999790 + 0.0205071i \(0.993472\pi\)
\(258\) −33.9474 + 1.66030i −2.11347 + 0.103366i
\(259\) 9.66025i 0.600259i
\(260\) 0 0
\(261\) −6.85641 + 15.1149i −0.424401 + 0.935586i
\(262\) −0.562178 2.09808i −0.0347315 0.129620i
\(263\) 10.3681 + 5.98604i 0.639326 + 0.369115i 0.784355 0.620312i \(-0.212994\pi\)
−0.145029 + 0.989427i \(0.546327\pi\)
\(264\) 3.84823 + 11.9858i 0.236842 + 0.737677i
\(265\) −7.83013 + 7.83013i −0.481001 + 0.481001i
\(266\) −0.907241 + 3.38587i −0.0556265 + 0.207601i
\(267\) 7.95383 15.4765i 0.486766 0.947145i
\(268\) −23.1244 23.1244i −1.41254 1.41254i
\(269\) 9.58244 5.53242i 0.584251 0.337318i −0.178570 0.983927i \(-0.557147\pi\)
0.762821 + 0.646610i \(0.223814\pi\)
\(270\) −27.3350 + 11.8289i −1.66355 + 0.719883i
\(271\) 2.00000 0.535898i 0.121491 0.0325535i −0.197561 0.980291i \(-0.563302\pi\)
0.319052 + 0.947737i \(0.396635\pi\)
\(272\) −5.28933 −0.320713
\(273\) 0 0
\(274\) 14.1244 0.853284
\(275\) −1.23931 + 0.332073i −0.0747334 + 0.0200248i
\(276\) 0 0
\(277\) −3.10770 + 1.79423i −0.186723 + 0.107805i −0.590448 0.807076i \(-0.701049\pi\)
0.403724 + 0.914881i \(0.367715\pi\)
\(278\) −4.05001 4.05001i −0.242904 0.242904i
\(279\) −14.6352 12.0215i −0.876189 0.719710i
\(280\) 3.63397 13.5622i 0.217172 0.810495i
\(281\) 15.9006 15.9006i 0.948547 0.948547i −0.0501922 0.998740i \(-0.515983\pi\)
0.998740 + 0.0501922i \(0.0159834\pi\)
\(282\) −37.8117 + 12.1400i −2.25166 + 0.722928i
\(283\) 21.2942 + 12.2942i 1.26581 + 0.730816i 0.974192 0.225719i \(-0.0724731\pi\)
0.291618 + 0.956535i \(0.405806\pi\)
\(284\) 4.62518 + 17.2614i 0.274454 + 1.02428i
\(285\) −0.907241 + 4.19615i −0.0537403 + 0.248559i
\(286\) 0 0
\(287\) 0.907241i 0.0535527i
\(288\) 7.08606 + 1.17309i 0.417550 + 0.0691251i
\(289\) 6.19615 10.7321i 0.364480 0.631297i
\(290\) −15.8561 27.4635i −0.931100 1.61271i
\(291\) −12.2025 18.9345i −0.715320 1.10996i
\(292\) 31.0885 + 8.33013i 1.81931 + 0.487484i
\(293\) 21.2669 + 5.69846i 1.24243 + 0.332908i 0.819407 0.573212i \(-0.194303\pi\)
0.423021 + 0.906120i \(0.360970\pi\)
\(294\) 11.2318 + 17.4284i 0.655054 + 1.01645i
\(295\) −5.73205 9.92820i −0.333733 0.578042i
\(296\) 14.1631 24.5313i 0.823215 1.42585i
\(297\) 8.46753 + 3.35253i 0.491336 + 0.194534i
\(298\) 13.0000i 0.753070i
\(299\) 0 0
\(300\) 1.00000 4.62518i 0.0577350 0.267035i
\(301\) −3.00000 11.1962i −0.172917 0.645335i
\(302\) 21.8866 + 12.6362i 1.25943 + 0.727133i
\(303\) 32.5540 10.4520i 1.87018 0.600449i
\(304\) −1.80385 + 1.80385i −0.103458 + 0.103458i
\(305\) −4.33760 + 16.1881i −0.248370 + 0.926930i
\(306\) −9.78605 + 11.9137i −0.559431 + 0.681063i
\(307\) 12.3923 + 12.3923i 0.707266 + 0.707266i 0.965960 0.258693i \(-0.0832919\pi\)
−0.258693 + 0.965960i \(0.583292\pi\)
\(308\) −8.01105 + 4.62518i −0.456472 + 0.263544i
\(309\) −8.06065 + 8.88965i −0.458554 + 0.505715i
\(310\) 34.9545 9.36603i 1.98528 0.531954i
\(311\) −4.29311 −0.243440 −0.121720 0.992564i \(-0.538841\pi\)
−0.121720 + 0.992564i \(0.538841\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 35.1425 9.41640i 1.98321 0.531398i
\(315\) −5.91297 8.25916i −0.333158 0.465351i
\(316\) 6.46410 3.73205i 0.363634 0.209944i
\(317\) 11.2754 + 11.2754i 0.633288 + 0.633288i 0.948891 0.315603i \(-0.102207\pi\)
−0.315603 + 0.948891i \(0.602207\pi\)
\(318\) −8.76706 + 17.0588i −0.491632 + 0.956612i
\(319\) −2.50962 + 9.36603i −0.140512 + 0.524397i
\(320\) −18.0471 + 18.0471i −1.00886 + 1.00886i
\(321\) −8.83503 27.5179i −0.493123 1.53590i
\(322\) 0 0
\(323\) 0.575167 + 2.14655i 0.0320032 + 0.119437i
\(324\) −25.2725 + 22.1244i −1.40403 + 1.22913i
\(325\) 0 0
\(326\) 37.0015i 2.04932i
\(327\) −6.85980 + 0.335500i −0.379348 + 0.0185532i
\(328\) −1.33013 + 2.30385i −0.0734440 + 0.127209i
\(329\) −6.77174 11.7290i −0.373338 0.646640i
\(330\) −14.6265 + 9.42610i −0.805160 + 0.518890i
\(331\) 18.8564 + 5.05256i 1.03644 + 0.277714i 0.736638 0.676287i \(-0.236412\pi\)
0.299804 + 0.954001i \(0.403079\pi\)
\(332\) −6.31812 1.69293i −0.346752 0.0929118i
\(333\) −7.21011 19.1822i −0.395112 1.05118i
\(334\) 14.1244 + 24.4641i 0.772850 + 1.33862i
\(335\) 10.4897 18.1687i 0.573112 0.992660i
\(336\) −0.294847 6.02859i −0.0160852 0.328886i
\(337\) 11.5359i 0.628400i −0.949357 0.314200i \(-0.898264\pi\)
0.949357 0.314200i \(-0.101736\pi\)
\(338\) 0 0
\(339\) 21.9545 + 4.74673i 1.19240 + 0.257807i
\(340\) −4.96410 18.5263i −0.269216 1.00473i
\(341\) −9.58244 5.53242i −0.518918 0.299597i
\(342\) 0.725614 + 7.40039i 0.0392367 + 0.400167i
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 8.79674 32.8299i 0.474289 1.77007i
\(345\) 0 0
\(346\) 12.5885 + 12.5885i 0.676760 + 0.676760i
\(347\) 22.4618 12.9683i 1.20581 0.696175i 0.243969 0.969783i \(-0.421550\pi\)
0.961841 + 0.273608i \(0.0882171\pi\)
\(348\) −26.4928 24.0222i −1.42016 1.28772i
\(349\) 5.63397 1.50962i 0.301580 0.0808080i −0.104856 0.994487i \(-0.533438\pi\)
0.406436 + 0.913679i \(0.366772\pi\)
\(350\) 2.47863 0.132488
\(351\) 0 0
\(352\) 4.19615 0.223656
\(353\) −26.3457 + 7.05932i −1.40224 + 0.375730i −0.879149 0.476546i \(-0.841889\pi\)
−0.523093 + 0.852276i \(0.675222\pi\)
\(354\) −14.7097 13.3380i −0.781813 0.708904i
\(355\) −9.92820 + 5.73205i −0.526934 + 0.304226i
\(356\) 26.5118 + 26.5118i 1.40512 + 1.40512i
\(357\) −4.67652 2.40340i −0.247508 0.127202i
\(358\) −11.6147 + 43.3468i −0.613858 + 2.29095i
\(359\) −12.0611 + 12.0611i −0.636559 + 0.636559i −0.949705 0.313146i \(-0.898617\pi\)
0.313146 + 0.949705i \(0.398617\pi\)
\(360\) −2.90646 29.6425i −0.153184 1.56229i
\(361\) −15.5263 8.96410i −0.817173 0.471795i
\(362\) −1.85897 6.93777i −0.0977053 0.364641i
\(363\) −13.4219 2.90192i −0.704468 0.152311i
\(364\) 0 0
\(365\) 20.6473i 1.08073i
\(366\) 1.41800 + 28.9931i 0.0741199 + 1.51549i
\(367\) −4.80385 + 8.32051i −0.250759 + 0.434327i −0.963735 0.266861i \(-0.914013\pi\)
0.712976 + 0.701188i \(0.247347\pi\)
\(368\) 0 0
\(369\) 0.677136 + 1.80149i 0.0352503 + 0.0937819i
\(370\) 37.8205 + 10.1340i 1.96619 + 0.526840i
\(371\) −6.31812 1.69293i −0.328020 0.0878928i
\(372\) 34.3028 22.1066i 1.77852 1.14618i
\(373\) 9.79423 + 16.9641i 0.507126 + 0.878368i 0.999966 + 0.00824796i \(0.00262544\pi\)
−0.492840 + 0.870120i \(0.664041\pi\)
\(374\) −4.50363 + 7.80052i −0.232877 + 0.403355i
\(375\) −17.6773 + 0.864563i −0.912852 + 0.0446459i
\(376\) 39.7128i 2.04803i
\(377\) 0 0
\(378\) −14.1244 10.4897i −0.726478 0.539531i
\(379\) −1.29423 4.83013i −0.0664801 0.248107i 0.924687 0.380729i \(-0.124327\pi\)
−0.991167 + 0.132622i \(0.957660\pi\)
\(380\) −8.01105 4.62518i −0.410958 0.237267i
\(381\) 8.00804 + 24.9421i 0.410264 + 1.27782i
\(382\) 32.8564 32.8564i 1.68108 1.68108i
\(383\) 3.62896 13.5435i 0.185431 0.692039i −0.809106 0.587662i \(-0.800048\pi\)
0.994538 0.104377i \(-0.0332849\pi\)
\(384\) −16.4156 + 31.9412i −0.837703 + 1.62999i
\(385\) −4.19615 4.19615i −0.213856 0.213856i
\(386\) −14.9488 + 8.63071i −0.760875 + 0.439291i
\(387\) −14.3135 19.9929i −0.727596 1.01630i
\(388\) 46.8827 12.5622i 2.38011 0.637748i
\(389\) 5.28933 0.268180 0.134090 0.990969i \(-0.457189\pi\)
0.134090 + 0.990969i \(0.457189\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −20.0276 + 5.36639i −1.01155 + 0.271043i
\(393\) 1.05553 1.16409i 0.0532446 0.0587206i
\(394\) −3.63397 + 2.09808i −0.183077 + 0.105700i
\(395\) 3.38587 + 3.38587i 0.170362 + 0.170362i
\(396\) −12.4553 + 15.1633i −0.625903 + 0.761986i
\(397\) 2.29423 8.56218i 0.115144 0.429723i −0.884154 0.467196i \(-0.845264\pi\)
0.999298 + 0.0374729i \(0.0119308\pi\)
\(398\) 1.57139 1.57139i 0.0787665 0.0787665i
\(399\) −2.41450 + 0.775212i −0.120876 + 0.0388091i
\(400\) 1.56218 + 0.901924i 0.0781089 + 0.0450962i
\(401\) −7.26985 27.1314i −0.363039 1.35488i −0.870060 0.492946i \(-0.835920\pi\)
0.507021 0.861933i \(-0.330747\pi\)
\(402\) 7.67898 35.5167i 0.382993 1.77141i
\(403\) 0 0
\(404\) 73.6708i 3.66526i
\(405\) −17.9057 11.9868i −0.889739 0.595629i
\(406\) 9.36603 16.2224i 0.464828 0.805106i
\(407\) −5.98604 10.3681i −0.296717 0.513929i
\(408\) −8.35187 12.9596i −0.413479 0.641594i
\(409\) 11.2321 + 3.00962i 0.555389 + 0.148816i 0.525587 0.850740i \(-0.323846\pi\)
0.0298020 + 0.999556i \(0.490512\pi\)
\(410\) −3.55190 0.951730i −0.175416 0.0470026i
\(411\) 5.53528 + 8.58908i 0.273035 + 0.423668i
\(412\) −12.9282 22.3923i −0.636927 1.10319i
\(413\) 3.38587 5.86450i 0.166608 0.288573i
\(414\) 0 0
\(415\) 4.19615i 0.205981i
\(416\) 0 0
\(417\) 0.875644 4.05001i 0.0428805 0.198330i
\(418\) 1.12436 + 4.19615i 0.0549940 + 0.205241i
\(419\) −7.22536 4.17156i −0.352982 0.203794i 0.313016 0.949748i \(-0.398661\pi\)
−0.665998 + 0.745954i \(0.731994\pi\)
\(420\) 20.8389 6.69063i 1.01683 0.326469i
\(421\) −0.830127 + 0.830127i −0.0404579 + 0.0404579i −0.727046 0.686588i \(-0.759107\pi\)
0.686588 + 0.727046i \(0.259107\pi\)
\(422\) −7.55743 + 28.2047i −0.367890 + 1.37298i
\(423\) −22.2007 18.2358i −1.07943 0.886657i
\(424\) −13.5622 13.5622i −0.658638 0.658638i
\(425\) 1.36086 0.785693i 0.0660114 0.0381117i
\(426\) −13.3380 + 14.7097i −0.646226 + 0.712688i
\(427\) −9.56218 + 2.56218i −0.462746 + 0.123992i
\(428\) 62.2739 3.01012
\(429\) 0 0
\(430\) 46.9808 2.26561
\(431\) −2.02501 + 0.542599i −0.0975412 + 0.0261361i −0.307260 0.951626i \(-0.599412\pi\)
0.209718 + 0.977762i \(0.432745\pi\)
\(432\) −5.08502 11.7508i −0.244653 0.565360i
\(433\) 6.10770 3.52628i 0.293517 0.169462i −0.346010 0.938231i \(-0.612464\pi\)
0.639527 + 0.768769i \(0.279130\pi\)
\(434\) 15.1149 + 15.1149i 0.725536 + 0.725536i
\(435\) 10.4867 20.4050i 0.502800 0.978344i
\(436\) 3.83013 14.2942i 0.183430 0.684569i
\(437\) 0 0
\(438\) 10.9323 + 34.0502i 0.522366 + 1.62698i
\(439\) 4.09808 + 2.36603i 0.195591 + 0.112924i 0.594597 0.804024i \(-0.297312\pi\)
−0.399007 + 0.916948i \(0.630645\pi\)
\(440\) −4.50363 16.8078i −0.214702 0.801280i
\(441\) −6.19657 + 13.6603i −0.295075 + 0.650488i
\(442\) 0 0
\(443\) 29.5656i 1.40470i −0.711830 0.702351i \(-0.752134\pi\)
0.711830 0.702351i \(-0.247866\pi\)
\(444\) 44.1025 2.15697i 2.09301 0.102365i
\(445\) −12.0263 + 20.8301i −0.570100 + 0.987443i
\(446\) −27.6295 47.8558i −1.30830 2.26604i
\(447\) −7.90535 + 5.09465i −0.373910 + 0.240969i
\(448\) −14.5622 3.90192i −0.687998 0.184349i
\(449\) 8.46467 + 2.26810i 0.399472 + 0.107038i 0.452961 0.891530i \(-0.350368\pi\)
−0.0534890 + 0.998568i \(0.517034\pi\)
\(450\) 4.92177 1.84997i 0.232014 0.0872084i
\(451\) 0.562178 + 0.973721i 0.0264719 + 0.0458507i
\(452\) −24.1992 + 41.9142i −1.13823 + 1.97148i
\(453\) 0.893131 + 18.2614i 0.0419629 + 0.857996i
\(454\) 37.4641i 1.75828i
\(455\) 0 0
\(456\) −7.26795 1.57139i −0.340353 0.0735869i
\(457\) −7.23205 26.9904i −0.338301 1.26256i −0.900246 0.435382i \(-0.856613\pi\)
0.561945 0.827175i \(-0.310053\pi\)
\(458\) 29.6871 + 17.1399i 1.38719 + 0.800893i
\(459\) −11.0799 1.28199i −0.517166 0.0598382i
\(460\) 0 0
\(461\) 6.27363 23.4135i 0.292192 1.09048i −0.651230 0.758880i \(-0.725747\pi\)
0.943422 0.331595i \(-0.107587\pi\)
\(462\) −9.14181 4.69825i −0.425315 0.218582i
\(463\) 15.0526 + 15.0526i 0.699552 + 0.699552i 0.964314 0.264762i \(-0.0852934\pi\)
−0.264762 + 0.964314i \(0.585293\pi\)
\(464\) 11.8060 6.81623i 0.548082 0.316435i
\(465\) 19.3940 + 17.5854i 0.899377 + 0.815506i
\(466\) −17.1962 + 4.60770i −0.796596 + 0.213447i
\(467\) 30.4728 1.41011 0.705057 0.709151i \(-0.250921\pi\)
0.705057 + 0.709151i \(0.250921\pi\)
\(468\) 0 0
\(469\) 12.3923 0.572223
\(470\) 53.0236 14.2076i 2.44579 0.655349i
\(471\) 19.4984 + 17.6800i 0.898437 + 0.814653i
\(472\) 17.1962 9.92820i 0.791517 0.456983i
\(473\) −10.1576 10.1576i −0.467047 0.467047i
\(474\) 7.37651 + 3.79101i 0.338814 + 0.174127i
\(475\) 0.196152 0.732051i 0.00900009 0.0335888i
\(476\) 8.01105 8.01105i 0.367186 0.367186i
\(477\) −13.8093 + 1.35401i −0.632285 + 0.0619960i
\(478\) 20.8301 + 12.0263i 0.952748 + 0.550069i
\(479\) −2.26810 8.46467i −0.103632 0.386761i 0.894554 0.446959i \(-0.147493\pi\)
−0.998186 + 0.0601988i \(0.980827\pi\)
\(480\) −9.70398 2.09808i −0.442924 0.0957636i
\(481\) 0 0
\(482\) 17.9256i 0.816487i
\(483\) 0 0
\(484\) 14.7942 25.6244i 0.672465 1.16474i
\(485\) 15.5685 + 26.9654i 0.706928 + 1.22444i
\(486\) −35.8756 10.2872i −1.62735 0.466636i
\(487\) −24.4904 6.56218i −1.10977 0.297361i −0.343030 0.939324i \(-0.611453\pi\)
−0.766735 + 0.641964i \(0.778120\pi\)
\(488\) −28.0387 7.51294i −1.26925 0.340095i
\(489\) 22.5007 14.5007i 1.01752 0.655746i
\(490\) −14.3301 24.8205i −0.647369 1.12128i
\(491\) 12.5147 21.6761i 0.564780 0.978227i −0.432290 0.901734i \(-0.642294\pi\)
0.997070 0.0764928i \(-0.0243722\pi\)
\(492\) −4.14187 + 0.202571i −0.186730 + 0.00913261i
\(493\) 11.8756i 0.534852i
\(494\) 0 0
\(495\) −11.4641 5.20035i −0.515273 0.233738i
\(496\) 4.02628 + 15.0263i 0.180785 + 0.674700i
\(497\) −5.86450 3.38587i −0.263059 0.151877i
\(498\) −2.22178 6.92003i −0.0995602 0.310094i
\(499\) −4.46410 + 4.46410i −0.199841 + 0.199841i −0.799932 0.600091i \(-0.795131\pi\)
0.600091 + 0.799932i \(0.295131\pi\)
\(500\) 9.87002 36.8354i 0.441401 1.64733i
\(501\) −9.34143 + 18.1765i −0.417345 + 0.812064i
\(502\) −37.0526 37.0526i −1.65374 1.65374i
\(503\) 24.8188 14.3292i 1.10662 0.638906i 0.168666 0.985673i \(-0.446054\pi\)
0.937951 + 0.346767i \(0.112721\pi\)
\(504\) 14.3053 10.2416i 0.637208 0.456196i
\(505\) −45.6506 + 12.2321i −2.03143 + 0.544319i
\(506\) 0 0
\(507\) 0 0
\(508\) −56.4449 −2.50434
\(509\) 14.4952 3.88398i 0.642489 0.172154i 0.0771582 0.997019i \(-0.475415\pi\)
0.565330 + 0.824865i \(0.308749\pi\)
\(510\) 14.3153 15.7876i 0.633893 0.699087i
\(511\) −10.5622 + 6.09808i −0.467243 + 0.269763i
\(512\) −18.6223 18.6223i −0.822996 0.822996i
\(513\) −4.21584 + 3.34143i −0.186134 + 0.147528i
\(514\) 10.2846 38.3827i 0.453635 1.69299i
\(515\) 11.7290 11.7290i 0.516841 0.516841i
\(516\) 50.4445 16.1960i 2.22070 0.712988i
\(517\) −14.5359 8.39230i −0.639288 0.369093i
\(518\) 5.98604 + 22.3402i 0.263012 + 0.981573i
\(519\) −2.72172 + 12.5885i −0.119470 + 0.552572i
\(520\) 0 0
\(521\) 33.2835i 1.45818i −0.684419 0.729089i \(-0.739944\pi\)
0.684419 0.729089i \(-0.260056\pi\)
\(522\) 6.49004 39.2031i 0.284061 1.71587i
\(523\) −6.49038 + 11.2417i −0.283805 + 0.491564i −0.972319 0.233659i \(-0.924930\pi\)
0.688514 + 0.725223i \(0.258263\pi\)
\(524\) 1.69293 + 2.93225i 0.0739562 + 0.128096i
\(525\) 0.971364 + 1.50726i 0.0423938 + 0.0657823i
\(526\) −27.6865 7.41858i −1.20719 0.323466i
\(527\) 13.0899 + 3.50742i 0.570203 + 0.152785i
\(528\) −4.05211 6.28764i −0.176345 0.273634i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 13.2559 22.9599i 0.575799 0.997313i
\(531\) 2.34618 14.1721i 0.101816 0.615018i
\(532\) 5.46410i 0.236899i
\(533\) 0 0
\(534\) −8.80385 + 40.7194i −0.380980 + 1.76210i
\(535\) 10.3397 + 38.5885i 0.447026 + 1.66832i
\(536\) 31.4690 + 18.1687i 1.35926 + 0.784766i
\(537\) −30.9111 + 9.92447i −1.33391 + 0.428273i
\(538\) −18.7321 + 18.7321i −0.807596 + 0.807596i
\(539\) −2.26810 + 8.46467i −0.0976940 + 0.364599i
\(540\) 36.3857 28.8389i 1.56579 1.24103i
\(541\) −23.6865 23.6865i −1.01836 1.01836i −0.999828 0.0185354i \(-0.994100\pi\)
−0.0185354 0.999828i \(-0.505900\pi\)
\(542\) −4.29311 + 2.47863i −0.184405 + 0.106466i
\(543\) 3.49036 3.84933i 0.149786 0.165191i
\(544\) −4.96410 + 1.33013i −0.212834 + 0.0570287i
\(545\) 9.49346 0.406655
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −21.2669 + 5.69846i −0.908479 + 0.243426i
\(549\) −17.0751 + 12.2246i −0.728748 + 0.521732i
\(550\) 2.66025 1.53590i 0.113434 0.0654909i
\(551\) −4.05001 4.05001i −0.172536 0.172536i
\(552\) 0 0
\(553\) −0.732051 + 2.73205i −0.0311300 + 0.116179i
\(554\) 6.07502 6.07502i 0.258103 0.258103i
\(555\) 8.65920 + 26.9703i 0.367563 + 1.14482i
\(556\) 7.73205 + 4.46410i 0.327912 + 0.189320i
\(557\) 10.5342 + 39.3140i 0.446347 + 1.66579i 0.712355 + 0.701819i \(0.247628\pi\)
−0.266009 + 0.963971i \(0.585705\pi\)
\(558\) 41.2946 + 18.7321i 1.74814 + 0.792991i
\(559\) 0 0
\(560\) 8.34312i 0.352561i
\(561\) −6.50849 + 0.318318i −0.274788 + 0.0134394i
\(562\) −26.9186 + 46.6244i −1.13549 + 1.96673i
\(563\) −2.14655 3.71794i −0.0904665 0.156693i 0.817241 0.576296i \(-0.195502\pi\)
−0.907708 + 0.419603i \(0.862169\pi\)
\(564\) 52.0350 33.5342i 2.19107 1.41205i
\(565\) −29.9904 8.03590i −1.26170 0.338073i
\(566\) −56.8630 15.2364i −2.39013 0.640434i
\(567\) 0.843533 12.6999i 0.0354250 0.533347i
\(568\) −9.92820 17.1962i −0.416578 0.721535i
\(569\) −8.01105 + 13.8755i −0.335841 + 0.581693i −0.983646 0.180113i \(-0.942354\pi\)
0.647805 + 0.761806i \(0.275687\pi\)
\(570\) −0.502098 10.2662i −0.0210306 0.430002i
\(571\) 40.0526i 1.67615i 0.545557 + 0.838074i \(0.316318\pi\)
−0.545557 + 0.838074i \(0.683682\pi\)
\(572\) 0 0
\(573\) 32.8564 + 7.10381i 1.37260 + 0.296766i
\(574\) −0.562178 2.09808i −0.0234648 0.0875720i
\(575\) 0 0
\(576\) −31.8281 + 3.12077i −1.32617 + 0.130032i
\(577\) −3.49038 + 3.49038i −0.145306 + 0.145306i −0.776018 0.630711i \(-0.782763\pi\)
0.630711 + 0.776018i \(0.282763\pi\)
\(578\) −7.67898 + 28.6583i −0.319403 + 1.19203i
\(579\) −11.1068 5.70810i −0.461581 0.237220i
\(580\) 34.9545 + 34.9545i 1.45141 + 1.45141i
\(581\) 2.14655 1.23931i 0.0890541 0.0514154i
\(582\) 39.9522 + 36.2264i 1.65607 + 1.50163i
\(583\) −7.83013 + 2.09808i −0.324291 + 0.0868934i
\(584\) −35.7621 −1.47985
\(585\) 0 0
\(586\) −52.7128 −2.17755
\(587\) −19.4080 + 5.20035i −0.801053 + 0.214641i −0.636046 0.771651i \(-0.719431\pi\)
−0.165006 + 0.986292i \(0.552765\pi\)
\(588\) −23.9432 21.7104i −0.987400 0.895320i
\(589\) 5.66025 3.26795i 0.233227 0.134654i
\(590\) 19.4080 + 19.4080i 0.799013 + 0.799013i
\(591\) −2.69999 1.38761i −0.111063 0.0570785i
\(592\) −4.35641 + 16.2583i −0.179047 + 0.668213i
\(593\) 10.6112 10.6112i 0.435751 0.435751i −0.454828 0.890579i \(-0.650299\pi\)
0.890579 + 0.454828i \(0.150299\pi\)
\(594\) −21.6593 2.50608i −0.888694 0.102826i
\(595\) 6.29423 + 3.63397i 0.258038 + 0.148978i
\(596\) −5.24484 19.5740i −0.214837 0.801782i
\(597\) 1.57139 + 0.339746i 0.0643126 + 0.0139049i
\(598\) 0 0
\(599\) 21.2224i 0.867126i 0.901123 + 0.433563i \(0.142744\pi\)
−0.901123 + 0.433563i \(0.857256\pi\)
\(600\) 0.256850 + 5.25169i 0.0104859 + 0.214399i
\(601\) 3.79423 6.57180i 0.154770 0.268069i −0.778205 0.628010i \(-0.783870\pi\)
0.932975 + 0.359941i \(0.117203\pi\)
\(602\) 13.8755 + 24.0331i 0.565525 + 0.979518i
\(603\) 24.6072 9.24923i 1.00208 0.376658i
\(604\) −38.0526 10.1962i −1.54834 0.414876i
\(605\) 18.3347 + 4.91277i 0.745411 + 0.199732i
\(606\) −68.8075 + 44.3434i −2.79511 + 1.80133i
\(607\) −5.09808 8.83013i −0.206925 0.358404i 0.743820 0.668380i \(-0.233012\pi\)
−0.950744 + 0.309977i \(0.899679\pi\)
\(608\) −1.23931 + 2.14655i −0.0502608 + 0.0870543i
\(609\) 13.5354 0.661992i 0.548483 0.0268253i
\(610\) 40.1244i 1.62459i
\(611\) 0 0
\(612\) 9.92820 21.8866i 0.401324 0.884713i
\(613\) 4.38269 + 16.3564i 0.177015 + 0.660629i 0.996200 + 0.0870991i \(0.0277597\pi\)
−0.819185 + 0.573530i \(0.805574\pi\)
\(614\) −36.3373 20.9794i −1.46645 0.846658i
\(615\) −0.813227 2.53291i −0.0327925 0.102137i
\(616\) 7.26795 7.26795i 0.292834 0.292834i
\(617\) −9.74847 + 36.3818i −0.392459 + 1.46468i 0.433607 + 0.901102i \(0.357241\pi\)
−0.826066 + 0.563574i \(0.809426\pi\)
\(618\) 13.1324 25.5530i 0.528264 1.02789i
\(619\) 14.3397 + 14.3397i 0.576363 + 0.576363i 0.933899 0.357536i \(-0.116383\pi\)
−0.357536 + 0.933899i \(0.616383\pi\)
\(620\) −48.8520 + 28.2047i −1.96194 + 1.13273i
\(621\) 0 0
\(622\) 9.92820 2.66025i 0.398085 0.106666i
\(623\) −14.2076 −0.569216
\(624\) 0 0
\(625\) 28.1244 1.12497
\(626\) −4.62518 + 1.23931i −0.184859 + 0.0495329i
\(627\) −2.11107 + 2.32818i −0.0843078 + 0.0929786i
\(628\) −49.1147 + 28.3564i −1.95989 + 1.13154i
\(629\) 10.3681 + 10.3681i 0.413404 + 0.413404i
\(630\) 18.7921 + 15.4360i 0.748696 + 0.614986i
\(631\) 0.607695 2.26795i 0.0241920 0.0902856i −0.952774 0.303679i \(-0.901785\pi\)
0.976966 + 0.213393i \(0.0684516\pi\)
\(632\) −5.86450 + 5.86450i −0.233277 + 0.233277i
\(633\) −20.1131 + 6.45761i −0.799425 + 0.256667i
\(634\) −33.0622 19.0885i −1.31307 0.758099i
\(635\) −9.37191 34.9764i −0.371913 1.38800i
\(636\) 6.31812 29.2224i 0.250530 1.15874i
\(637\) 0 0
\(638\) 23.2149i 0.919086i
\(639\) −14.1721 2.34618i −0.560641 0.0928136i
\(640\) 24.8205 42.9904i 0.981117 1.69934i
\(641\) 9.65949 + 16.7307i 0.381527 + 0.660824i 0.991281 0.131767i \(-0.0420650\pi\)
−0.609754 + 0.792591i \(0.708732\pi\)
\(642\) 37.4835 + 58.1629i 1.47935 + 2.29551i
\(643\) 26.1244 + 7.00000i 1.03024 + 0.276053i 0.734065 0.679079i \(-0.237621\pi\)
0.296179 + 0.955132i \(0.404287\pi\)
\(644\) 0 0
\(645\) 18.4116 + 28.5692i 0.724955 + 1.12491i
\(646\) −2.66025 4.60770i −0.104666 0.181287i
\(647\) −7.22536 + 12.5147i −0.284058 + 0.492003i −0.972380 0.233402i \(-0.925014\pi\)
0.688322 + 0.725405i \(0.258348\pi\)
\(648\) 20.7618 31.0135i 0.815599 1.21833i
\(649\) 8.39230i 0.329427i
\(650\) 0 0
\(651\) −3.26795 + 15.1149i −0.128081 + 0.592398i
\(652\) 14.9282 + 55.7128i 0.584634 + 2.18188i
\(653\) −33.6156 19.4080i −1.31548 0.759492i −0.332482 0.943110i \(-0.607886\pi\)
−0.982998 + 0.183617i \(0.941219\pi\)
\(654\) 15.6560 5.02659i 0.612198 0.196555i
\(655\) −1.53590 + 1.53590i −0.0600125 + 0.0600125i
\(656\) 0.409131 1.52690i 0.0159739 0.0596153i
\(657\) −16.4217 + 19.9921i −0.640672 + 0.779967i
\(658\) 22.9282 + 22.9282i 0.893834 + 0.893834i
\(659\) 27.1759 15.6900i 1.05862 0.611197i 0.133572 0.991039i \(-0.457355\pi\)
0.925051 + 0.379842i \(0.124022\pi\)
\(660\) 18.2200 20.0938i 0.709212 0.782152i
\(661\) −16.5263 + 4.42820i −0.642798 + 0.172237i −0.565470 0.824769i \(-0.691305\pi\)
−0.0773274 + 0.997006i \(0.524639\pi\)
\(662\) −46.7380 −1.81652
\(663\) 0 0
\(664\) 7.26795 0.282051
\(665\) 3.38587 0.907241i 0.131298 0.0351813i
\(666\) 28.5604 + 39.8928i 1.10669 + 1.54581i
\(667\) 0 0
\(668\) −31.1370 31.1370i −1.20473 1.20473i
\(669\) 18.2734 35.5561i 0.706489 1.37468i
\(670\) −13.0000 + 48.5167i −0.502234 + 1.87436i
\(671\) −8.67520 + 8.67520i −0.334902 + 0.334902i
\(672\) −1.79275 5.58376i −0.0691568 0.215398i
\(673\) 11.0096 + 6.35641i 0.424390 + 0.245021i 0.696954 0.717116i \(-0.254538\pi\)
−0.272564 + 0.962138i \(0.587872\pi\)
\(674\) 7.14830 + 26.6778i 0.275342 + 1.02759i
\(675\) 3.05379 + 2.26795i 0.117541 + 0.0872934i
\(676\) 0 0
\(677\) 38.8159i 1.49182i 0.666048 + 0.745909i \(0.267985\pi\)
−0.666048 + 0.745909i \(0.732015\pi\)
\(678\) −53.7131 + 2.62700i −2.06284 + 0.100889i
\(679\) −9.19615 + 15.9282i −0.352916 + 0.611268i
\(680\) 10.6557 + 18.4562i 0.408628 + 0.707764i
\(681\) −22.7821 + 14.6820i −0.873011 + 0.562617i
\(682\) 25.5885 + 6.85641i 0.979833 + 0.262545i
\(683\) 15.9006 + 4.26054i 0.608418 + 0.163025i 0.549857 0.835259i \(-0.314682\pi\)
0.0585607 + 0.998284i \(0.481349\pi\)
\(684\) −4.07823 10.8500i −0.155935 0.414859i
\(685\) −7.06218 12.2321i −0.269832 0.467363i
\(686\) 20.3152 35.1870i 0.775638 1.34344i
\(687\) 1.21145 + 24.7699i 0.0462196 + 0.945031i
\(688\) 20.1962i 0.769971i
\(689\) 0 0
\(690\) 0 0
\(691\) −11.2224 41.8827i −0.426921 1.59329i −0.759691 0.650284i \(-0.774650\pi\)
0.332770 0.943008i \(-0.392017\pi\)
\(692\) −24.0331 13.8755i −0.913603 0.527469i
\(693\) −0.725614 7.40039i −0.0275638 0.281118i
\(694\) −43.9090 + 43.9090i −1.66676 + 1.66676i
\(695\) −1.48241 + 5.53242i −0.0562309 + 0.209857i
\(696\) 35.3425 + 18.1636i 1.33965 + 0.688488i
\(697\) −0.973721 0.973721i −0.0368823 0.0368823i
\(698\) −12.0936 + 6.98226i −0.457751 + 0.264283i
\(699\) −9.54106 8.65131i −0.360876 0.327223i
\(700\) −3.73205 + 1.00000i −0.141058 + 0.0377964i
\(701\) −20.3152 −0.767295 −0.383647 0.923480i \(-0.625332\pi\)
−0.383647 + 0.923480i \(0.625332\pi\)
\(702\) 0 0
\(703\) 7.07180 0.266718
\(704\) −18.0471 + 4.83571i −0.680176 + 0.182253i
\(705\) 29.4194 + 26.6759i 1.10800 + 1.00467i
\(706\) 56.5526 32.6506i 2.12838 1.22882i
\(707\) −19.7400 19.7400i −0.742401 0.742401i
\(708\) 27.5295 + 14.1482i 1.03462 + 0.531724i
\(709\) −2.66987 + 9.96410i −0.100269 + 0.374210i −0.997766 0.0668121i \(-0.978717\pi\)
0.897496 + 0.441022i \(0.145384\pi\)
\(710\) 19.4080 19.4080i 0.728368 0.728368i
\(711\) 0.585497 + 5.97136i 0.0219578 + 0.223944i
\(712\) −36.0788 20.8301i −1.35211 0.780642i
\(713\) 0 0
\(714\) 12.3042 + 2.66025i 0.460472 + 0.0995575i
\(715\) 0 0
\(716\) 69.9529i 2.61426i
\(717\) 0.850019 + 17.3799i 0.0317446 + 0.649065i
\(718\) 20.4186 35.3660i 0.762015 1.31985i
\(719\) 5.86450 + 10.1576i 0.218709 + 0.378815i 0.954413 0.298488i \(-0.0964822\pi\)
−0.735705 + 0.677302i \(0.763149\pi\)
\(720\) 6.22704 + 16.5668i 0.232068 + 0.617408i
\(721\) 9.46410 + 2.53590i 0.352462 + 0.0944418i
\(722\) 41.4606 + 11.1093i 1.54300 + 0.413447i
\(723\) −10.9006 + 7.02496i −0.405398 + 0.261261i
\(724\) 5.59808 + 9.69615i 0.208051 + 0.360355i
\(725\) −2.02501 + 3.50742i −0.0752069 + 0.130262i
\(726\) 32.8376 1.60603i 1.21872 0.0596052i
\(727\) 25.5167i 0.946361i 0.880966 + 0.473180i \(0.156894\pi\)
−0.880966 + 0.473180i \(0.843106\pi\)
\(728\) 0 0
\(729\) −7.80385 25.8476i −0.289031 0.957320i
\(730\) −12.7942 47.7487i −0.473536 1.76726i
\(731\) 15.2364 + 8.79674i 0.563539 + 0.325359i
\(732\) −13.8323 43.0826i −0.511257 1.59238i
\(733\) 36.2224 36.2224i 1.33791 1.33791i 0.439820 0.898086i \(-0.355042\pi\)
0.898086 0.439820i \(-0.144958\pi\)
\(734\) 5.95347 22.2187i 0.219747 0.820106i
\(735\) 9.47753 18.4413i 0.349584 0.680216i
\(736\) 0 0
\(737\) 13.3004 7.67898i 0.489926 0.282859i
\(738\) −2.68224 3.74652i −0.0987348 0.137911i
\(739\) 48.9808 13.1244i 1.80179 0.482787i 0.807531 0.589825i \(-0.200803\pi\)
0.994255 + 0.107037i \(0.0341364\pi\)
\(740\) −61.0346 −2.24368
\(741\) 0 0
\(742\) 15.6603 0.574906
\(743\) 50.5449 13.5435i 1.85431 0.496862i 0.854566 0.519343i \(-0.173823\pi\)
0.999747 + 0.0224808i \(0.00715645\pi\)
\(744\) −30.4589 + 33.5915i −1.11668 + 1.23152i
\(745\) 11.2583 6.50000i 0.412473 0.238142i
\(746\) −33.1620 33.1620i −1.21415 1.21415i
\(747\) 3.33739 4.06300i 0.122109 0.148658i
\(748\) 3.63397 13.5622i 0.132871 0.495882i
\(749\) −16.6862 + 16.6862i −0.609702 + 0.609702i
\(750\) 40.3446 12.9532i 1.47318 0.472986i
\(751\) −38.2750 22.0981i −1.39667 0.806370i −0.402632 0.915362i \(-0.631904\pi\)
−0.994043 + 0.108992i \(0.965238\pi\)
\(752\) 6.10759 + 22.7938i 0.222721 + 0.831206i
\(753\) 8.01105 37.0526i 0.291939 1.35027i
\(754\) 0 0
\(755\) 25.2725i 0.919759i
\(756\) 25.4990 + 10.0958i 0.927389 + 0.367180i
\(757\) 12.3923 21.4641i 0.450406 0.780126i −0.548005 0.836475i \(-0.684613\pi\)
0.998411 + 0.0563489i \(0.0179459\pi\)
\(758\) 5.98604 + 10.3681i 0.217423 + 0.376587i
\(759\) 0 0
\(760\) 9.92820 + 2.66025i 0.360134 + 0.0964976i
\(761\) 4.17156 + 1.11777i 0.151219 + 0.0405190i 0.333634 0.942703i \(-0.391725\pi\)
−0.182415 + 0.983222i \(0.558392\pi\)
\(762\) −33.9749 52.7187i −1.23078 1.90980i
\(763\) 2.80385 + 4.85641i 0.101506 + 0.175814i
\(764\) −36.2158 + 62.7275i −1.31024 + 2.26940i
\(765\) 15.2106 + 2.51810i 0.549941 + 0.0910423i
\(766\) 33.5692i 1.21291i
\(767\) 0 0
\(768\) 10.3660 47.9447i 0.374052 1.73006i
\(769\) −0.581416 2.16987i −0.0209664 0.0782476i 0.954650 0.297730i \(-0.0962297\pi\)
−0.975616 + 0.219483i \(0.929563\pi\)
\(770\) 12.3042 + 7.10381i 0.443411 + 0.256004i
\(771\) 27.3712 8.78792i 0.985748 0.316489i
\(772\) 19.0263 19.0263i 0.684771 0.684771i
\(773\) −1.60396 + 5.98604i −0.0576903 + 0.215303i −0.988753 0.149555i \(-0.952216\pi\)
0.931063 + 0.364858i \(0.118883\pi\)
\(774\) 45.4900 + 37.3659i 1.63510 + 1.34309i
\(775\) −3.26795 3.26795i −0.117388 0.117388i