Properties

Label 507.2.k.e.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.e.89.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.31259 + 0.619657i) q^{2} +(1.64914 + 0.529480i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(-4.14187 - 0.202571i) q^{6} +(0.366025 - 1.36603i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(2.43930 + 1.74637i) q^{9} +O(q^{10})\) \(q+(-2.31259 + 0.619657i) q^{2} +(1.64914 + 0.529480i) q^{3} +(3.23205 - 1.86603i) q^{4} +(1.69293 + 1.69293i) q^{5} +(-4.14187 - 0.202571i) q^{6} +(0.366025 - 1.36603i) q^{7} +(-2.93225 + 2.93225i) q^{8} +(2.43930 + 1.74637i) q^{9} +(-4.96410 - 2.86603i) q^{10} +(0.453620 + 1.69293i) q^{11} +(6.31812 - 1.36603i) q^{12} +3.38587i q^{14} +(1.89551 + 3.68825i) q^{15} +(1.23205 - 2.13397i) q^{16} +(1.07328 + 1.85897i) q^{17} +(-6.72326 - 2.52711i) q^{18} +(1.00000 + 0.267949i) q^{19} +(8.63071 + 2.31259i) q^{20} +(1.32691 - 2.05896i) q^{21} +(-2.09808 - 3.63397i) q^{22} +(-6.38824 + 3.28311i) q^{24} +0.732051i q^{25} +(3.09808 + 4.17156i) q^{27} +(-1.36603 - 5.09808i) q^{28} +(-4.79122 - 2.76621i) q^{29} +(-6.66898 - 7.35486i) q^{30} +(4.46410 - 4.46410i) q^{31} +(0.619657 - 2.31259i) q^{32} +(-0.148292 + 3.03206i) q^{33} +(-3.63397 - 3.63397i) q^{34} +(2.93225 - 1.69293i) q^{35} +(11.1427 + 1.09255i) q^{36} +(6.59808 - 1.76795i) q^{37} -2.47863 q^{38} -9.92820 q^{40} +(0.619657 - 0.166037i) q^{41} +(-1.79275 + 5.58376i) q^{42} +(-7.09808 + 4.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(1.17309 + 7.08606i) q^{45} +(-6.77174 + 6.77174i) q^{47} +(3.16172 - 2.86687i) q^{48} +(4.33013 + 2.50000i) q^{49} +(-0.453620 - 1.69293i) q^{50} +(0.785693 + 3.63397i) q^{51} -4.62518i q^{53} +(-9.74952 - 7.72737i) q^{54} +(-2.09808 + 3.63397i) q^{55} +(2.93225 + 5.07880i) q^{56} +(1.50726 + 0.971364i) q^{57} +(12.7942 + 3.42820i) q^{58} +(-4.62518 - 1.23931i) q^{59} +(13.0087 + 8.38356i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-7.55743 + 13.0899i) q^{62} +(3.27843 - 2.69293i) 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} +(-12.2734 + 2.03185i) q^{72} +(-6.09808 - 6.09808i) q^{73} +(-14.1631 + 8.17709i) q^{74} +(-0.387606 + 1.20725i) q^{75} +(3.73205 - 1.00000i) q^{76} +2.47863 q^{77} +2.00000 q^{79} +(5.69846 - 1.52690i) q^{80} +(2.90039 + 8.51984i) q^{81} +(-1.33013 + 0.767949i) q^{82} +(-1.23931 - 1.23931i) q^{83} +(0.446565 - 9.13071i) q^{84} +(-1.33013 + 4.96410i) q^{85} +(13.8755 - 13.8755i) q^{86} +(-6.43672 - 7.09871i) q^{87} +(-6.29423 - 3.63397i) q^{88} +(2.60017 + 9.70398i) q^{89} +(-7.10381 - 15.6603i) q^{90} +(9.72556 - 4.99826i) q^{93} +(11.4641 - 19.8564i) q^{94} +(1.23931 + 2.14655i) q^{95} +(2.24637 - 3.48568i) q^{96} +(-12.5622 - 3.36603i) q^{97} +(-11.5630 - 3.09828i) q^{98} +(-1.84997 + 4.92177i) 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 \(0.737941\pi\)
\(3\) 1.64914 + 0.529480i 0.952129 + 0.305695i
\(4\) 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 \(0.570179\pi\)
\(6\) −4.14187 0.202571i −1.69091 0.0826993i
\(7\) 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
\(9\) 2.43930 + 1.74637i 0.813101 + 0.582123i
\(10\) −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
\(15\) 1.89551 + 3.68825i 0.489417 + 0.952303i
\(16\) 1.23205 2.13397i 0.308013 0.533494i
\(17\) 1.07328 + 1.85897i 0.260308 + 0.450867i 0.966324 0.257330i \(-0.0828426\pi\)
−0.706016 + 0.708196i \(0.749509\pi\)
\(18\) −6.72326 2.52711i −1.58469 0.595644i
\(19\) 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
\(21\) 1.32691 2.05896i 0.289555 0.449302i
\(22\) −2.09808 3.63397i −0.447311 0.774766i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −6.38824 + 3.28311i −1.30399 + 0.670162i
\(25\) 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 −0.0158603 0.999874i \(-0.505049\pi\)
−0.873847 + 0.486202i \(0.838382\pi\)
\(30\) −6.66898 7.35486i −1.21758 1.34281i
\(31\) 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
\(33\) −0.148292 + 3.03206i −0.0258144 + 0.527814i
\(34\) −3.63397 3.63397i −0.623222 0.623222i
\(35\) 2.93225 1.69293i 0.495640 0.286158i
\(36\) 11.1427 + 1.09255i 1.85712 + 0.182092i
\(37\) 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 −0.210107 0.977678i \(-0.567381\pi\)
0.306881 + 0.951748i \(0.400715\pi\)
\(42\) −1.79275 + 5.58376i −0.276627 + 0.861593i
\(43\) −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
\(45\) 1.17309 + 7.08606i 0.174874 + 1.05633i
\(46\) 0 0
\(47\) −6.77174 + 6.77174i −0.987759 + 0.987759i −0.999926 0.0121668i \(-0.996127\pi\)
0.0121668 + 0.999926i \(0.496127\pi\)
\(48\) 3.16172 2.86687i 0.456354 0.413797i
\(49\) 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 \(-0.897103\pi\)
0.948205 0.317659i \(-0.102897\pi\)
\(54\) −9.74952 7.72737i −1.32674 1.05156i
\(55\) −2.09808 + 3.63397i −0.282905 + 0.490005i
\(56\) 2.93225 + 5.07880i 0.391838 + 0.678683i
\(57\) 1.50726 + 0.971364i 0.199642 + 0.128660i
\(58\) 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 \(0.684230\pi\)
\(60\) 13.0087 + 8.38356i 1.67942 + 1.08231i
\(61\) 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
\(63\) 3.27843 2.69293i 0.413043 0.339278i
\(64\) 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 \(0.175040\pi\)
−0.999654 + 0.0263025i \(0.991627\pi\)
\(72\) −12.2734 + 2.03185i −1.44644 + 0.239456i
\(73\) −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
\(75\) −0.387606 + 1.20725i −0.0447569 + 0.139401i
\(76\) 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
\(81\) 2.90039 + 8.51984i 0.322266 + 0.946649i
\(82\) −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 \(0.780665\pi\)
\(84\) 0.446565 9.13071i 0.0487243 0.996242i
\(85\) −1.33013 + 4.96410i −0.144273 + 0.538432i
\(86\) 13.8755 13.8755i 1.49624 1.49624i
\(87\) −6.43672 7.09871i −0.690089 0.761062i
\(88\) −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
\(93\) 9.72556 4.99826i 1.00849 0.518296i
\(94\) 11.4641 19.8564i 1.18243 2.04803i
\(95\) 1.23931 + 2.14655i 0.127151 + 0.220232i
\(96\) 2.24637 3.48568i 0.229269 0.355756i
\(97\) −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
\(99\) −1.84997 + 4.92177i −0.185929 + 0.494656i
\(100\) 1.36603 + 2.36603i 0.136603 + 0.236603i
\(101\) 9.87002 17.0954i 0.982104 1.70105i 0.327944 0.944697i \(-0.393644\pi\)
0.654160 0.756356i \(-0.273022\pi\)
\(102\) −4.06880 7.91704i −0.402872 0.783903i
\(103\) 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 −0.402925 0.915233i \(-0.632007\pi\)
−0.994078 + 0.108673i \(0.965340\pi\)
\(108\) 17.7974 + 7.70161i 1.71255 + 0.741088i
\(109\) −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
\(111\) 11.8172 + 0.577958i 1.12164 + 0.0548573i
\(112\) −2.46410 2.46410i −0.232836 0.232836i
\(113\) 11.2309 6.48415i 1.05651 0.609978i 0.132047 0.991243i \(-0.457845\pi\)
0.924465 + 0.381266i \(0.124512\pi\)
\(114\) −4.08759 1.31238i −0.382838 0.122916i
\(115\) 0 0
\(116\) −20.6473 −1.91705
\(117\) 0 0
\(118\) 11.4641 1.05536
\(119\) 2.93225 0.785693i 0.268799 0.0720244i
\(120\) −16.3730 5.25678i −1.49464 0.479876i
\(121\) 6.86603 3.96410i 0.624184 0.360373i
\(122\) −11.8505 11.8505i −1.07290 1.07290i
\(123\) 1.10981 + 0.0542788i 0.100068 + 0.00489415i
\(124\) 6.09808 22.7583i 0.547623 2.04376i
\(125\) 7.22536 7.22536i 0.646255 0.646255i
\(126\) −5.91297 + 8.25916i −0.526770 + 0.735784i
\(127\) −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 \(-0.987381\pi\)
0.999214 0.0396330i \(-0.0126189\pi\)
\(132\) 5.17862 + 10.0765i 0.450741 + 0.877046i
\(133\) 0.732051 1.26795i 0.0634769 0.109945i
\(134\) −10.4897 18.1687i −0.906170 1.56953i
\(135\) −1.81734 + 12.3070i −0.156412 + 1.05922i
\(136\) −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
\(141\) −14.7530 + 7.58202i −1.24243 + 0.638521i
\(142\) 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
\(147\) 5.81727 + 6.41556i 0.479800 + 0.529146i
\(148\) 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 \(0.0119392\pi\)
\(150\) 0.148292 3.03206i 0.0121080 0.247567i
\(151\) 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
\(153\) −0.628400 + 6.40893i −0.0508031 + 0.518131i
\(154\) −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
\(159\) 2.44894 7.62756i 0.194214 0.604905i
\(160\) 4.96410 2.86603i 0.392447 0.226579i
\(161\) 0 0
\(162\) −11.9868 17.9057i −0.941772 1.40680i
\(163\) 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
\(165\) −5.38413 + 4.88203i −0.419154 + 0.380066i
\(166\) 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
\(171\) 1.97136 + 2.39998i 0.150754 + 0.183531i
\(172\) −15.2942 + 26.4904i −1.16617 + 2.01987i
\(173\) 3.71794 + 6.43966i 0.282670 + 0.489598i 0.972041 0.234809i \(-0.0754466\pi\)
−0.689372 + 0.724408i \(0.742113\pi\)
\(174\) 19.2843 + 12.4279i 1.46194 + 0.942154i
\(175\) 1.00000 + 0.267949i 0.0755929 + 0.0202551i
\(176\) 4.17156 + 1.11777i 0.314443 + 0.0842548i
\(177\) −6.97136 4.49274i −0.524000 0.337695i
\(178\) −12.0263 20.8301i −0.901408 1.56128i
\(179\) −9.37191 + 16.2326i −0.700489 + 1.21328i 0.267805 + 0.963473i \(0.413702\pi\)
−0.968295 + 0.249810i \(0.919632\pi\)
\(180\) 17.0143 + 20.7135i 1.26817 + 1.54389i
\(181\) 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
\(186\) −19.3940 + 17.5854i −1.42204 + 1.28943i
\(187\) −2.66025 + 2.66025i −0.194537 + 0.194537i
\(188\) −9.25036 + 34.5228i −0.674652 + 2.51784i
\(189\) 6.83243 2.70515i 0.496986 0.196771i
\(190\) −4.19615 4.19615i −0.304421 0.304421i
\(191\) 16.8078 9.70398i 1.21617 0.702156i 0.252073 0.967708i \(-0.418888\pi\)
0.964096 + 0.265553i \(0.0855544\pi\)
\(192\) −5.64439 + 17.5802i −0.407349 + 1.26874i
\(193\) −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 −0.198006 0.980201i \(-0.563446\pi\)
0.318622 + 0.947882i \(0.396780\pi\)
\(198\) 1.22842 12.5284i 0.0872998 0.890353i
\(199\) −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
\(201\) −0.741412 + 15.1593i −0.0522952 + 1.06925i
\(202\) −12.2321 + 45.6506i −0.860644 + 3.21197i
\(203\) −5.53242 + 5.53242i −0.388300 + 0.388300i
\(204\) 9.32049 + 10.2791i 0.652565 + 0.719679i
\(205\) 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
\(210\) −12.4879 + 6.41793i −0.861750 + 0.442879i
\(211\) 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
\(213\) −4.49274 + 6.97136i −0.307837 + 0.477670i
\(214\) 38.5885 + 10.3397i 2.63785 + 0.706810i
\(215\) −18.9543 5.07880i −1.29268 0.346371i
\(216\) −21.3164 3.14772i −1.45040 0.214176i
\(217\) −4.46410 7.73205i −0.303043 0.524886i
\(218\) 4.74673 8.22158i 0.321489 0.556835i
\(219\) −6.82775 13.2854i −0.461377 0.897742i
\(220\) 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
\(225\) −1.27843 + 1.78569i −0.0852287 + 0.119046i
\(226\) −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 \(-0.0904735\pi\)
\(228\) 6.68414 + 0.326909i 0.442668 + 0.0216500i
\(229\) 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
\(231\) 4.08759 + 1.31238i 0.268944 + 0.0863485i
\(232\) 22.1603 5.93782i 1.45489 0.389837i
\(233\) −7.43588 −0.487141 −0.243570 0.969883i \(-0.578319\pi\)
−0.243570 + 0.969883i \(0.578319\pi\)
\(234\) 0 0
\(235\) −22.9282 −1.49567
\(236\) −17.2614 + 4.62518i −1.12362 + 0.301074i
\(237\) 3.29827 + 1.05896i 0.214246 + 0.0687868i
\(238\) −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 \(0.855338\pi\)
\(240\) 10.2060 + 0.499156i 0.658794 + 0.0322204i
\(241\) −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
\(243\) 0.272062 + 15.5861i 0.0174528 + 0.999848i
\(244\) 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
\(249\) −1.38761 2.69999i −0.0879360 0.171105i
\(250\) −12.2321 + 21.1865i −0.773623 + 1.33995i
\(251\) −10.9433 18.9543i −0.690735 1.19639i −0.971597 0.236640i \(-0.923954\pi\)
0.280863 0.959748i \(-0.409379\pi\)
\(252\) 5.57097 14.8213i 0.350938 0.933656i
\(253\) 0 0
\(254\) 34.9764 + 9.37191i 2.19462 + 0.588046i
\(255\) −4.82195 + 7.48221i −0.301962 + 0.468554i
\(256\) 14.1603 + 24.5263i 0.885016 + 1.53289i
\(257\) 8.29863 14.3737i 0.517655 0.896604i −0.482135 0.876097i \(-0.660139\pi\)
0.999790 0.0205071i \(-0.00652807\pi\)
\(258\) 30.2295 15.5358i 1.88201 0.967220i
\(259\) 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 0.145029 0.989427i \(-0.453673\pi\)
−0.784355 + 0.620312i \(0.787006\pi\)
\(264\) −8.45593 9.32559i −0.520426 0.573950i
\(265\) 7.83013 7.83013i 0.481001 0.481001i
\(266\) −0.907241 + 3.38587i −0.0556265 + 0.207601i
\(267\) −0.850019 + 17.3799i −0.0520203 + 1.06363i
\(268\) 23.1244 + 23.1244i 1.41254 + 1.41254i
\(269\) −9.58244 + 5.53242i −0.584251 + 0.337318i −0.762821 0.646610i \(-0.776186\pi\)
0.178570 + 0.983927i \(0.442853\pi\)
\(270\) −3.42336 29.5872i −0.208339 1.80062i
\(271\) −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
\(279\) 18.6853 3.09333i 1.11866 0.185193i
\(280\) −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 \(0.0159834\pi\)
\(282\) 29.4194 26.6759i 1.75190 1.58853i
\(283\) 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
\(288\) 5.55017 4.55896i 0.327047 0.268639i
\(289\) 6.19615 10.7321i 0.364480 0.631297i
\(290\) 15.8561 + 27.4635i 0.931100 + 1.61271i
\(291\) −18.9345 12.2025i −1.10996 0.715320i
\(292\) −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 \(0.360970\pi\)
\(294\) −17.4284 11.2318i −1.01645 0.655054i
\(295\) −5.73205 9.92820i −0.333733 0.578042i
\(296\) −14.1631 + 24.5313i −0.823215 + 1.42585i
\(297\) −5.65683 + 7.13714i −0.328242 + 0.414139i
\(298\) 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
\(303\) 25.3287 22.9666i 1.45509 1.31940i
\(304\) 1.80385 1.80385i 0.103458 0.103458i
\(305\) −4.33760 + 16.1881i −0.248370 + 0.926930i
\(306\) −2.51810 15.2106i −0.143950 0.869533i
\(307\) −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
\(309\) 3.66834 11.4256i 0.208685 0.649977i
\(310\) −34.9545 + 9.36603i −1.98528 + 0.531954i
\(311\) 4.29311 0.243440 0.121720 0.992564i \(-0.461159\pi\)
0.121720 + 0.992564i \(0.461159\pi\)
\(312\) 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
\(315\) 10.1091 + 0.991207i 0.569585 + 0.0558482i
\(316\) 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 \(0.602207\pi\)
\(318\) −0.936928 + 19.1569i −0.0525403 + 1.07427i
\(319\) 2.50962 9.36603i 0.140512 0.524397i
\(320\) −18.0471 + 18.0471i −1.00886 + 1.00886i
\(321\) −19.4137 21.4103i −1.08357 1.19501i
\(322\) 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
\(327\) −6.10851 + 3.13935i −0.337801 + 0.173606i
\(328\) −1.33013 + 2.30385i −0.0734440 + 0.127209i
\(329\) 6.77174 + 11.7290i 0.373338 + 0.646640i
\(330\) 9.42610 14.6265i 0.518890 0.805160i
\(331\) −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
\(333\) 19.1822 + 7.21011i 1.05118 + 0.395112i
\(334\) 14.1244 + 24.4641i 0.772850 + 1.33862i
\(335\) −10.4897 + 18.1687i −0.573112 + 0.992660i
\(336\) −2.75895 5.36833i −0.150513 0.292867i
\(337\) 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
\(342\) −6.04612 4.32860i −0.326937 0.234064i
\(343\) 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 −0.961841 0.273608i \(-0.911783\pi\)
−0.243969 + 0.969783i \(0.578450\pi\)
\(348\) −34.0502 10.9323i −1.82528 0.586034i
\(349\) −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 −0.879149 0.476546i \(-0.841889\pi\)
−0.523093 + 0.852276i \(0.675222\pi\)
\(354\) 18.9059 + 6.07001i 1.00484 + 0.322617i
\(355\) −9.92820 + 5.73205i −0.526934 + 0.304226i
\(356\) 26.5118 + 26.5118i 1.40512 + 1.40512i
\(357\) 5.25169 + 0.256850i 0.277949 + 0.0135939i
\(358\) 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 \(0.398617\pi\)
\(360\) −24.2179 17.3383i −1.27639 0.913809i
\(361\) −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
\(366\) −13.2685 25.8178i −0.693557 1.34952i
\(367\) −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
\(369\) 1.80149 + 0.677136i 0.0937819 + 0.0352503i
\(370\) −37.8205 10.1340i −1.96619 0.526840i
\(371\) −6.31812 1.69293i −0.328020 0.0878928i
\(372\) 22.1066 34.3028i 1.14618 1.77852i
\(373\) 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
\(375\) 15.7413 8.08992i 0.812876 0.417762i
\(376\) 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
\(381\) −17.5965 19.4062i −0.901496 0.994211i
\(382\) −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 \(-0.0332849\pi\)
\(384\) 1.75432 35.8697i 0.0895246 1.83047i
\(385\) 4.19615 + 4.19615i 0.213856 + 0.213856i
\(386\) 14.9488 8.63071i 0.760875 0.439291i
\(387\) −24.4711 2.39941i −1.24394 0.121969i
\(388\) −46.8827 + 12.5622i −2.38011 + 0.637748i
\(389\) −5.28933 −0.268180 −0.134090 0.990969i \(-0.542811\pi\)
−0.134090 + 0.990969i \(0.542811\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −20.0276 + 5.36639i −1.01155 + 0.271043i
\(393\) 0.480365 1.49616i 0.0242312 0.0754715i
\(394\) −3.63397 + 2.09808i −0.183077 + 0.105700i
\(395\) 3.38587 + 3.38587i 0.170362 + 0.170362i
\(396\) 3.20495 + 19.3595i 0.161055 + 0.972851i
\(397\) −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
\(399\) 1.87861 1.70342i 0.0940479 0.0852774i
\(400\) 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
\(405\) −9.51336 + 19.3337i −0.472722 + 0.960700i
\(406\) 9.36603 16.2224i 0.464828 0.805106i
\(407\) 5.98604 + 10.3681i 0.296717 + 0.513929i
\(408\) −12.9596 8.35187i −0.641594 0.413479i
\(409\) −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
\(411\) −8.58908 5.53528i −0.423668 0.273035i
\(412\) −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 0.665998 0.745954i \(-0.268006\pi\)
−0.313016 + 0.949748i \(0.601339\pi\)
\(420\) 16.2137 14.7017i 0.791147 0.717368i
\(421\) 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
\(423\) −28.3443 + 4.69237i −1.37815 + 0.228151i
\(424\) 13.5622 + 13.5622i 0.658638 + 0.658638i
\(425\) −1.36086 + 0.785693i −0.0660114 + 0.0381117i
\(426\) 6.07001 18.9059i 0.294093 0.915992i
\(427\) 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 \(0.432745\pi\)
\(432\) 12.7190 1.47164i 0.611943 0.0708043i
\(433\) 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
\(435\) 1.12071 22.9146i 0.0537339 1.09867i
\(436\) −3.83013 + 14.2942i −0.183430 + 0.684569i
\(437\) 0 0
\(438\) 24.0222 + 26.4928i 1.14782 + 1.26587i
\(439\) 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 \(0.247866\pi\)
−0.711830 + 0.702351i \(0.752134\pi\)
\(444\) 39.2723 20.1832i 1.86378 0.957855i
\(445\) −12.0263 + 20.8301i −0.570100 + 0.987443i
\(446\) 27.6295 + 47.8558i 1.30830 + 2.26604i
\(447\) 5.09465 7.90535i 0.240969 0.373910i
\(448\) 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 \(0.517034\pi\)
\(450\) 1.84997 4.92177i 0.0872084 0.232014i
\(451\) 0.562178 + 0.973721i 0.0264719 + 0.0458507i
\(452\) 24.1992 41.9142i 1.13823 1.97148i
\(453\) 8.35723 + 16.2614i 0.392657 + 0.764028i
\(454\) 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
\(459\) −4.42972 + 10.2365i −0.206761 + 0.477798i
\(460\) 0 0
\(461\) 6.27363 23.4135i 0.292192 1.09048i −0.651230 0.758880i \(-0.725747\pi\)
0.943422 0.331595i \(-0.107587\pi\)
\(462\) −10.2662 0.502098i −0.477625 0.0233597i
\(463\) −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
\(465\) 24.9265 + 8.00301i 1.15594 + 0.371131i
\(466\) 17.1962 4.60770i 0.796596 0.213447i
\(467\) −30.4728 −1.41011 −0.705057 0.709151i \(-0.749079\pi\)
−0.705057 + 0.709151i \(0.749079\pi\)
\(468\) 0 0
\(469\) 12.3923 0.572223
\(470\) 53.0236 14.2076i 2.44579 0.655349i
\(471\) −25.0605 8.04605i −1.15473 0.370743i
\(472\) 17.1962 9.92820i 0.791517 0.456983i
\(473\) −10.1576 10.1576i −0.467047 0.467047i
\(474\) −8.28375 0.405142i −0.380485 0.0186088i
\(475\) −0.196152 + 0.732051i −0.00900009 + 0.0335888i
\(476\) 8.01105 8.01105i 0.367186 0.367186i
\(477\) 8.07727 11.2822i 0.369833 0.516577i
\(478\) 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
\(486\) −10.2872 35.8756i −0.466636 1.62735i
\(487\) 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
\(489\) 14.5007 22.5007i 0.655746 1.01752i
\(490\) −14.3301 24.8205i −0.647369 1.12128i
\(491\) −12.5147 + 21.6761i −0.564780 + 0.978227i 0.432290 + 0.901734i \(0.357706\pi\)
−0.997070 + 0.0764928i \(0.975628\pi\)
\(492\) 3.68825 1.89551i 0.166279 0.0854560i
\(493\) 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
\(498\) 4.88203 + 5.38413i 0.218769 + 0.241269i
\(499\) 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
\(501\) 0.998312 20.4120i 0.0446013 0.911941i
\(502\) 37.0526 + 37.0526i 1.65374 + 1.65374i
\(503\) −24.8188 + 14.3292i −1.10662 + 0.638906i −0.937951 0.346767i \(-0.887279\pi\)
−0.168666 + 0.985673i \(0.553946\pi\)
\(504\) −1.71682 + 17.5095i −0.0764733 + 0.779936i
\(505\) 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 \(0.308749\pi\)
\(510\) 6.51480 20.2912i 0.288480 0.898511i
\(511\) −10.5622 + 6.09808i −0.467243 + 0.269763i
\(512\) −18.6223 18.6223i −0.822996 0.822996i
\(513\) 1.98031 + 5.00169i 0.0874328 + 0.220830i
\(514\) −10.2846 + 38.3827i −0.453635 + 1.69299i
\(515\) 11.7290 11.7290i 0.516841 0.516841i
\(516\) −39.2484 + 35.5883i −1.72781 + 1.56669i
\(517\) −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 \(0.260056\pi\)
−0.684419 + 0.729089i \(0.739944\pi\)
\(522\) 25.2221 + 30.7059i 1.10394 + 1.34396i
\(523\) −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
\(525\) 1.50726 + 0.971364i 0.0657823 + 0.0423938i
\(526\) 27.6865 + 7.41858i 1.20719 + 0.323466i
\(527\) 13.0899 + 3.50742i 0.570203 + 0.152785i
\(528\) 6.28764 + 4.05211i 0.273634 + 0.176345i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) −13.2559 + 22.9599i −0.575799 + 0.997313i
\(531\) −9.11792 11.1003i −0.395684 0.481713i
\(532\) 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
\(537\) −24.0504 + 21.8076i −1.03785 + 0.941066i
\(538\) 18.7321 18.7321i 0.807596 0.807596i
\(539\) −2.26810 + 8.46467i −0.0976940 + 0.364599i
\(540\) 17.0915 + 43.1681i 0.735500 + 1.85766i
\(541\) 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
\(543\) −1.58844 + 4.94741i −0.0681664 + 0.212314i
\(544\) 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
\(549\) −2.04924 + 20.8998i −0.0874593 + 0.891981i
\(550\) 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
\(555\) 19.0273 + 20.9842i 0.807665 + 0.890731i
\(556\) 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
\(561\) −5.79567 + 2.97857i −0.244693 + 0.125755i
\(562\) −26.9186 + 46.6244i −1.13549 + 1.96673i
\(563\) 2.14655 + 3.71794i 0.0904665 + 0.156693i 0.907708 0.419603i \(-0.137831\pi\)
−0.817241 + 0.576296i \(0.804498\pi\)
\(564\) −33.5342 + 52.0350i −1.41205 + 2.19107i
\(565\) 29.9904 + 8.03590i 1.26170 + 0.338073i
\(566\) −56.8630 15.2364i −2.39013 0.640434i
\(567\) 12.6999 0.843533i 0.533347 0.0354250i
\(568\) −9.92820 17.1962i −0.416578 0.721535i
\(569\) 8.01105 13.8755i 0.335841 0.581693i −0.647805 0.761806i \(-0.724313\pi\)
0.983646 + 0.180113i \(0.0576463\pi\)
\(570\) −4.69825 9.14181i −0.196788 0.382908i
\(571\) 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
\(576\) −18.6167 + 26.0036i −0.775697 + 1.08348i
\(577\) 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
\(579\) −12.4728 0.610020i −0.518351 0.0253516i
\(580\) −34.9545 34.9545i −1.45141 1.45141i
\(581\) −2.14655 + 1.23931i −0.0890541 + 0.0514154i
\(582\) 51.3491 + 16.4864i 2.12849 + 0.683383i
\(583\) 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 \(0.552765\pi\)
\(588\) 30.7733 + 9.88023i 1.26907 + 0.407454i
\(589\) 5.66025 3.26795i 0.233227 0.134654i
\(590\) 19.4080 + 19.4080i 0.799013 + 0.799013i
\(591\) 3.03206 + 0.148292i 0.124722 + 0.00609993i
\(592\) 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 \(0.150299\pi\)
\(594\) 8.65935 20.0106i 0.355297 0.821044i
\(595\) 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 \(-0.857256\pi\)
0.901123 0.433563i \(-0.142744\pi\)
\(600\) −2.40340 4.67652i −0.0981186 0.190918i
\(601\) 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
\(603\) −9.24923 + 24.6072i −0.376658 + 1.00208i
\(604\) 38.0526 + 10.1962i 1.54834 + 0.414876i
\(605\) 18.3347 + 4.91277i 0.745411 + 0.199732i
\(606\) −44.3434 + 68.8075i −1.80133 + 2.79511i
\(607\) −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
\(609\) −12.0530 + 6.19441i −0.488413 + 0.251010i
\(610\) 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
\(615\) 1.78695 + 1.97073i 0.0720567 + 0.0794674i
\(616\) −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 \(0.809426\pi\)
\(618\) −1.40345 + 28.6957i −0.0564552 + 1.15431i
\(619\) −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
\(627\) −0.960731 + 2.99233i −0.0383679 + 0.119502i
\(628\) −49.1147 + 28.3564i −1.95989 + 1.13154i
\(629\) 10.3681 + 10.3681i 0.413404 + 0.413404i
\(630\) −23.9925 + 3.97193i −0.955883 + 0.158246i
\(631\) −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
\(633\) 15.6490 14.1897i 0.621993 0.563989i
\(634\) −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
\(639\) −11.1003 + 9.11792i −0.439122 + 0.360699i
\(640\) 24.8205 42.9904i 0.981117 1.69934i
\(641\) −9.65949 16.7307i −0.381527 0.660824i 0.609754 0.792591i \(-0.291268\pi\)
−0.991281 + 0.131767i \(0.957935\pi\)
\(642\) 58.1629 + 37.4835i 2.29551 + 1.47935i
\(643\) −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
\(645\) −28.5692 18.4116i −1.12491 0.724955i
\(646\) −2.66025 4.60770i −0.104666 0.181287i
\(647\) 7.22536 12.5147i 0.284058 0.492003i −0.688322 0.725405i \(-0.741652\pi\)
0.972380 + 0.233402i \(0.0749858\pi\)
\(648\) −33.4870 16.4776i −1.31549 0.647302i
\(649\) 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 0.982998 0.183617i \(-0.0587807\pi\)
0.332482 + 0.943110i \(0.392114\pi\)
\(654\) 12.1812 11.0452i 0.476321 0.431902i
\(655\) 1.53590 1.53590i 0.0600125 0.0600125i
\(656\) 0.409131 1.52690i 0.0159739 0.0596153i
\(657\) −4.22556 25.5245i −0.164855 0.995807i
\(658\) −22.9282 22.9282i −0.893834 0.893834i
\(659\) −27.1759 + 15.6900i −1.05862 + 0.611197i −0.925051 0.379842i \(-0.875978\pi\)
−0.133572 + 0.991039i \(0.542645\pi\)
\(660\) −8.29179 + 25.8259i −0.322757 + 1.00527i
\(661\) 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
\(666\) −48.8284 4.78766i −1.89206 0.185518i
\(667\) 0 0
\(668\) −31.1370 31.1370i −1.20473 1.20473i
\(669\) 1.95286 39.9292i 0.0755019 1.54375i
\(670\) 13.0000 48.5167i 0.502234 1.87436i
\(671\) −8.67520 + 8.67520i −0.334902 + 0.334902i
\(672\) −3.93930 4.34444i −0.151962 0.167591i
\(673\) 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 \(-0.732015\pi\)
0.666048 0.745909i \(-0.267985\pi\)
\(678\) −47.8304 + 24.5815i −1.83692 + 0.944046i
\(679\) −9.19615 + 15.9282i −0.352916 + 0.611268i
\(680\) −10.6557 18.4562i −0.408628 0.707764i
\(681\) 14.6820 22.7821i 0.562617 0.873011i
\(682\) −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 \(0.481349\pi\)
\(684\) 10.8500 + 4.07823i 0.414859 + 0.155935i
\(685\) −7.06218 12.2321i −0.269832 0.467363i
\(686\) −20.3152 + 35.1870i −0.775638 + 1.34344i
\(687\) 11.3358 + 22.0571i 0.432488 + 0.841530i
\(688\) 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
\(693\) 6.04612 + 4.32860i 0.229673 + 0.164430i
\(694\) 43.9090 43.9090i 1.66676 1.66676i
\(695\) −1.48241 + 5.53242i −0.0562309 + 0.209857i
\(696\) 39.6892 + 1.94112i 1.50442 + 0.0735781i
\(697\) 0.973721 + 0.973721i 0.0368823 + 0.0368823i
\(698\) 12.0936 6.98226i 0.457751 0.264283i
\(699\) −12.2628 3.93715i −0.463821 0.148917i
\(700\) 3.73205 1.00000i 0.141058 0.0377964i
\(701\) 20.3152 0.767295 0.383647 0.923480i \(-0.374668\pi\)
0.383647 + 0.923480i \(0.374668\pi\)
\(702\) 0 0
\(703\) 7.07180 0.266718
\(704\) −18.0471 + 4.83571i −0.680176 + 0.182253i
\(705\) −37.8117 12.1400i −1.42407 0.457220i
\(706\) 56.5526 32.6506i 2.12838 1.22882i
\(707\) −19.7400 19.7400i −0.742401 0.742401i
\(708\) −30.9154 1.51201i −1.16187 0.0568249i
\(709\) 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
\(711\) 4.87861 + 3.49274i 0.182962 + 0.130988i
\(712\) −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
\(717\) −7.95383 15.4765i −0.297041 0.577979i
\(718\) 20.4186 35.3660i 0.762015 1.31985i
\(719\) −5.86450 10.1576i −0.218709 0.378815i 0.735705 0.677302i \(-0.236851\pi\)
−0.954413 + 0.298488i \(0.903518\pi\)
\(720\) 16.5668 + 6.22704i 0.617408 + 0.232068i
\(721\) −9.46410 2.53590i −0.352462 0.0944418i
\(722\) 41.4606 + 11.1093i 1.54300 + 0.413447i
\(723\) −7.02496 + 10.9006i −0.261261 + 0.405398i
\(724\) 5.59808 + 9.69615i 0.208051 + 0.360355i
\(725\) 2.02501 3.50742i 0.0752069 0.130262i
\(726\) −29.2412 + 15.0279i −1.08524 + 0.557740i
\(727\) 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
\(732\) 30.3945 + 33.5205i 1.12341 + 1.23895i
\(733\) −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
\(735\) −1.01286 + 20.7094i −0.0373597 + 0.763877i
\(736\) 0 0
\(737\) −13.3004 + 7.67898i −0.489926 + 0.282859i
\(738\) −4.58570 0.449632i −0.168802 0.0165512i
\(739\) −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 0.854566 0.519343i \(-0.173823\pi\)
0.999747 + 0.0224808i \(0.00715645\pi\)
\(744\) −13.8616 + 43.1739i −0.508192 + 1.58283i
\(745\) 11.2583 6.50000i 0.412473 0.238142i
\(746\) −33.1620 33.1620i −1.21415 1.21415i
\(747\) −0.858763 5.18736i −0.0314205 0.189796i
\(748\) −3.63397 + 13.5622i −0.132871 + 0.495882i
\(749\) −16.6862 + 16.6862i −0.609702 + 0.609702i
\(750\) −31.3902 + 28.4629i −1.14621 + 1.03932i
\(751\) −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
\(756\) 17.0349 21.4927i 0.619553 0.781681i
\(757\) 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 \(0.558392\pi\)
\(762\) 52.7187 + 33.9749i 1.90980 + 1.23078i
\(763\) 2.80385 + 4.85641i 0.101506 + 0.175814i
\(764\) 36.2158 62.7275i 1.31024 2.26940i
\(765\) −11.9137 + 9.78605i −0.430742 + 0.353816i
\(766\) 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
\(771\) 21.2961 19.3102i 0.766962 0.695438i
\(772\) −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 \(0.118883\pi\)
\(774\) 58.0785 9.61484i 2.08759 0.345598i
\(775\) 3.26795 + 3.26795i 0.117388 + 0.117388i