Properties

Label 507.2.k.e.188.2
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 188.2
Root \(0.500000 - 1.19293i\) of defining polynomial
Character \(\chi\) \(=\) 507.188
Dual form 507.2.k.e.89.2

$q$-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 0.679818 0.733380i \(-0.262059\pi\)
0.955430 + 0.295217i \(0.0953919\pi\)
\(3\) −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 0.218691 0.975794i \(-0.429821\pi\)
−0.975794 + 0.218691i \(0.929821\pi\)
\(6\) −3.68825 1.89551i −1.50572 0.773837i
\(7\) 0.366025 1.36603i 0.138345 0.516309i −0.861617 0.507559i \(-0.830548\pi\)
0.999962 0.00875026i \(-0.00278533\pi\)
\(8\) 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 \(-0.998218\pi\)
0.863213 0.504840i \(-0.168449\pi\)
\(12\) −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 0.371695 0.928355i \(-0.378777\pi\)
−0.142280 + 0.989826i \(0.545443\pi\)
\(20\) −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 −0.181597 0.983373i \(-0.558127\pi\)
0.983373 + 0.181597i \(0.0581266\pi\)
\(32\) −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 0.328190 0.944612i \(-0.393561\pi\)
0.756527 + 0.653963i \(0.226895\pi\)
\(38\) 2.47863 0.402086
\(39\) 0 0
\(40\) −9.92820 −1.56979
\(41\) −0.619657 + 0.166037i −0.0967741 + 0.0259306i −0.306881 0.951748i \(-0.599285\pi\)
0.210107 + 0.977678i \(0.432619\pi\)
\(42\) −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 −0.0121668 0.999926i \(-0.503873\pi\)
0.999926 + 0.0121668i \(0.00387290\pi\)
\(48\) −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 0.546999 0.837133i \(-0.315770\pi\)
0.0551484 + 0.998478i \(0.482437\pi\)
\(60\) 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 \(0.0964553\pi\)
−0.677365 + 0.735647i \(0.736878\pi\)
\(68\) −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 \(-0.824960\pi\)
0.999654 0.0263025i \(-0.00837330\pi\)
\(72\) 9.61317 + 7.89635i 1.13292 + 0.930594i
\(73\) −6.09808 6.09808i −0.713726 0.713726i 0.253587 0.967313i \(-0.418390\pi\)
−0.967313 + 0.253587i \(0.918390\pi\)
\(74\) 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 0.771844 0.635812i \(-0.219335\pi\)
−0.635812 + 0.771844i \(0.719335\pi\)
\(84\) −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 \(-0.904604\pi\)
0.679808 0.733390i \(-0.262063\pi\)
\(90\) 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 −0.443362 0.896343i \(-0.646214\pi\)
−0.832134 + 0.554575i \(0.812881\pi\)
\(98\) 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 −0.828520 0.559960i \(-0.810817\pi\)
0.559960 + 0.828520i \(0.310817\pi\)
\(110\) −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 0.493891 0.869524i \(-0.335574\pi\)
−0.00703925 + 0.999975i \(0.502241\pi\)
\(138\) 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 −0.999297 0.0374992i \(-0.988061\pi\)
0.884166 + 0.467173i \(0.154728\pi\)
\(150\) 1.38761 2.69999i 0.113298 0.220453i
\(151\) 7.46410 + 7.46410i 0.607420 + 0.607420i 0.942271 0.334851i \(-0.108686\pi\)
−0.334851 + 0.942271i \(0.608686\pi\)
\(152\) 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 \(-0.709737\pi\)
0.925558 0.378606i \(-0.123596\pi\)
\(164\) −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 \(0.0675693\pi\)
−0.741244 + 0.671235i \(0.765764\pi\)
\(168\) −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 −0.500597 0.865680i \(-0.666886\pi\)
−0.000689767 1.00000i \(0.500220\pi\)
\(194\) −31.1370 −2.23550
\(195\) 0 0
\(196\) 18.6603 1.33288
\(197\) −1.69293 + 0.453620i −0.120617 + 0.0323191i −0.318622 0.947882i \(-0.603220\pi\)
0.198006 + 0.980201i \(0.436554\pi\)
\(198\) 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 \(-0.802190\pi\)
0.413011 0.910726i \(-0.364477\pi\)
\(224\) 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 \(0.257140\pi\)
−0.959878 + 0.280419i \(0.909526\pi\)
\(228\) −5.95209 3.05896i −0.394187 0.202585i
\(229\) 10.1244 + 10.1244i 0.669036 + 0.669036i 0.957493 0.288457i \(-0.0931421\pi\)
−0.288457 + 0.957493i \(0.593142\pi\)
\(230\) 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 0.898494 0.438986i \(-0.144662\pi\)
−0.438986 + 0.898494i \(0.644662\pi\)
\(240\) 9.08823 + 4.67072i 0.586643 + 0.301493i
\(241\) −1.93782 + 7.23205i −0.124826 + 0.465857i −0.999833 0.0182524i \(-0.994190\pi\)
0.875007 + 0.484110i \(0.160856\pi\)
\(242\) 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 −0.319052 0.947737i \(-0.603365\pi\)
0.197561 + 0.980291i \(0.436698\pi\)
\(272\) −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 −0.998740 0.0501922i \(-0.984017\pi\)
0.0501922 + 0.998740i \(0.484017\pi\)
\(282\) −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 −0.423021 0.906120i \(-0.639030\pi\)
−0.819407 + 0.573212i \(0.805697\pi\)
\(294\) −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 0.258693 0.965960i \(-0.416708\pi\)
−0.965960 + 0.258693i \(0.916708\pi\)
\(308\) −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 0.315603 0.948891i \(-0.397793\pi\)
−0.948891 + 0.315603i \(0.897793\pi\)
\(318\) 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 −0.299804 0.954001i \(-0.596921\pi\)
−0.736638 + 0.676287i \(0.763588\pi\)
\(332\) 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 −0.406436 0.913679i \(-0.633228\pi\)
0.104856 + 0.994487i \(0.466562\pi\)
\(350\) 2.47863 0.132488
\(351\) 0 0
\(352\) 4.19615 0.223656
\(353\) 26.3457 7.05932i 1.40224 0.375730i 0.523093 0.852276i \(-0.324778\pi\)
0.879149 + 0.476546i \(0.158111\pi\)
\(354\) −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 −0.313146 0.949705i \(-0.601383\pi\)
0.949705 + 0.313146i \(0.101383\pi\)
\(360\) −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 0.991167 0.132622i \(-0.0423397\pi\)
−0.924687 + 0.380729i \(0.875673\pi\)
\(380\) −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 \(0.199952\pi\)
−0.994538 + 0.104377i \(0.966715\pi\)
\(384\) 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 −0.999298 0.0374729i \(-0.988069\pi\)
0.884154 + 0.467196i \(0.154736\pi\)
\(398\) −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 \(0.164080\pi\)
−0.507021 + 0.861933i \(0.669253\pi\)
\(402\) 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 −0.0298020 0.999556i \(-0.509488\pi\)
−0.525587 + 0.850740i \(0.676154\pi\)
\(410\) 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 −0.686588 0.727046i \(-0.740893\pi\)
0.727046 + 0.686588i \(0.240893\pi\)
\(422\) 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 −0.209718 0.977762i \(-0.567255\pi\)
0.307260 + 0.951626i \(0.400588\pi\)
\(432\) −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 0.0534890 0.998568i \(-0.482966\pi\)
−0.452961 + 0.891530i \(0.649632\pi\)
\(450\) −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 \(0.143387\pi\)
−0.561945 + 0.827175i \(0.689947\pi\)
\(458\) 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 \(0.274253\pi\)
−0.943422 + 0.331595i \(0.892413\pi\)
\(462\) 9.14181 + 4.69825i 0.425315 + 0.218582i
\(463\) −15.0526 15.0526i −0.699552 0.699552i 0.264762 0.964314i \(-0.414707\pi\)
−0.964314 + 0.264762i \(0.914707\pi\)
\(464\) 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 0.998186 0.0601988i \(-0.0191735\pi\)
−0.894554 + 0.446959i \(0.852507\pi\)
\(480\) −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 0.766735 0.641964i \(-0.221880\pi\)
0.343030 + 0.939324i \(0.388547\pi\)
\(488\) 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 −0.600091 0.799932i \(-0.704869\pi\)
0.799932 + 0.600091i \(0.204869\pi\)
\(500\) −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 −0.565330 0.824865i \(-0.691251\pi\)
−0.0771582 + 0.997019i \(0.524585\pi\)
\(510\) 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 \(0.00590034\pi\)
0.0185354 + 0.999828i \(0.494100\pi\)
\(542\) −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 \(-0.752372\pi\)
0.266009 0.963971i \(-0.414295\pi\)
\(558\) 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 −0.630711 0.776018i \(-0.717237\pi\)
0.776018 + 0.630711i \(0.217237\pi\)
\(578\) 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 0.165006 0.986292i \(-0.447235\pi\)
0.636046 + 0.771651i \(0.280569\pi\)
\(588\) −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 −0.890579 0.454828i \(-0.849701\pi\)
0.454828 + 0.890579i \(0.349701\pi\)
\(594\) −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 \(-0.972240\pi\)
0.819185 0.573530i \(-0.194426\pi\)
\(614\) −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 \(-0.642759\pi\)
0.826066 0.563574i \(-0.190574\pi\)
\(618\) −13.1324 + 25.5530i −0.528264 + 1.02789i
\(619\) −14.3397 14.3397i −0.576363 0.576363i 0.357536 0.933899i \(-0.383617\pi\)
−0.933899 + 0.357536i \(0.883617\pi\)
\(620\) −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 −0.976966 0.213393i \(-0.931548\pi\)
0.952774 + 0.303679i \(0.0982151\pi\)
\(632\) 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 −0.296179 0.955132i \(-0.595713\pi\)
−0.734065 + 0.679079i \(0.762379\pi\)
\(644\) 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 0.0773274 0.997006i \(-0.475361\pi\)
0.565470 + 0.824769i \(0.308695\pi\)
\(662\) −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 −0.0585607 0.998284i \(-0.518651\pi\)
−0.549857 + 0.835259i \(0.685318\pi\)
\(684\) 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 \(0.225350\pi\)
−0.332770 + 0.943008i \(0.607983\pi\)
\(692\) −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 −0.897496 0.441022i \(-0.854616\pi\)
0.997766 + 0.0668121i \(0.0212828\pi\)
\(710\) −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 \(0.644958\pi\)
−0.898086 + 0.439820i \(0.855042\pi\)
\(734\) −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 −0.994255 0.107037i \(-0.965864\pi\)
−0.807531 + 0.589825i \(0.799197\pi\)
\(740\) −61.0346 −2.24368
\(741\) 0 0
\(742\) 15.6603 0.574906
\(743\) −50.5449 + 13.5435i −1.85431 + 0.496862i −0.999747 0.0224808i \(-0.992844\pi\)
−0.854566 + 0.519343i \(0.826177\pi\)
\(744\) −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 0.182415 0.983222i \(-0.441608\pi\)
−0.333634 + 0.942703i \(0.608275\pi\)
\(762\) 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 0.975616 0.219483i \(-0.0704370\pi\)
−0.954650 + 0.297730i \(0.903770\pi\)
\(770\) 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 −0.931063 0.364858i \(-0.881117\pi\)
0.988753 + 0.149555i \(0.0477842\pi\)
\(774\) −45.4900 37.3659i −1.63510 1.34309i
\(775\) 3.26795 + 3.26795i 0.117388 + 0.117388i