Properties

Label 624.2.cn.c.401.2
Level $624$
Weight $2$
Character 624.401
Analytic conductor $4.983$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 401.2
Root \(0.500000 - 1.56488i\) of defining polynomial
Character \(\chi\) \(=\) 624.401
Dual form 624.2.cn.c.305.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.60523 + 0.650571i) q^{3} +(-1.06488 + 1.06488i) q^{5} +(-0.366025 - 1.36603i) q^{7} +(2.15351 + 2.08863i) q^{9} +O(q^{10})\) \(q+(1.60523 + 0.650571i) q^{3} +(-1.06488 + 1.06488i) q^{5} +(-0.366025 - 1.36603i) q^{7} +(2.15351 + 2.08863i) q^{9} +(-1.06488 + 3.97420i) q^{11} +(3.59808 + 0.232051i) q^{13} +(-2.40216 + 1.01660i) q^{15} +(-2.51954 + 4.36397i) q^{17} +(3.73205 - 1.00000i) q^{19} +(0.301143 - 2.43091i) q^{21} +2.73205i q^{25} +(2.09808 + 4.75374i) q^{27} +(6.20840 - 3.58442i) q^{29} +(2.46410 + 2.46410i) q^{31} +(-4.29488 + 5.68671i) q^{33} +(1.84443 + 1.06488i) q^{35} +(-5.23205 - 1.40192i) q^{37} +(5.62477 + 2.71330i) q^{39} +(-5.42885 - 1.45466i) q^{41} +(-1.90192 - 1.09808i) q^{43} +(-4.51739 + 0.0690922i) q^{45} +(-4.25953 - 4.25953i) q^{47} +(4.33013 - 2.50000i) q^{49} +(-6.88351 + 5.36603i) q^{51} +0.779548i q^{53} +(-3.09808 - 5.36603i) q^{55} +(6.64136 + 0.822738i) q^{57} +(-2.90931 + 0.779548i) q^{59} +(3.50000 - 6.06218i) q^{61} +(2.06488 - 3.70625i) q^{63} +(-4.07863 + 3.58442i) q^{65} +(1.53590 - 5.73205i) q^{67} +(-0.779548 - 2.90931i) q^{71} +(-0.901924 + 0.901924i) q^{73} +(-1.77739 + 4.38556i) q^{75} +5.81863 q^{77} -2.00000 q^{79} +(0.275241 + 8.99579i) q^{81} +(2.90931 - 2.90931i) q^{83} +(-1.96410 - 7.33013i) q^{85} +(12.2978 - 1.71481i) q^{87} +(2.41510 - 9.01327i) q^{89} +(-1.00000 - 5.00000i) q^{91} +(2.35237 + 5.55852i) q^{93} +(-2.90931 + 5.03908i) q^{95} +(1.63397 - 0.437822i) q^{97} +(-10.5939 + 6.33434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} + 4q^{7} + 4q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 4q^{7} + 4q^{9} + 8q^{13} + 14q^{15} + 16q^{19} + 4q^{21} - 4q^{27} - 8q^{31} + 16q^{33} - 28q^{37} + 14q^{39} - 36q^{43} - 20q^{45} - 4q^{55} + 16q^{57} + 28q^{61} + 8q^{63} + 40q^{67} - 28q^{73} - 12q^{75} - 16q^{79} + 4q^{81} + 12q^{85} + 34q^{87} - 8q^{91} + 4q^{93} + 20q^{97} - 40q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.60523 + 0.650571i 0.926779 + 0.375608i
\(4\) 0 0
\(5\) −1.06488 + 1.06488i −0.476230 + 0.476230i −0.903924 0.427694i \(-0.859326\pi\)
0.427694 + 0.903924i \(0.359326\pi\)
\(6\) 0 0
\(7\) −0.366025 1.36603i −0.138345 0.516309i −0.999962 0.00875026i \(-0.997215\pi\)
0.861617 0.507559i \(-0.169452\pi\)
\(8\) 0 0
\(9\) 2.15351 + 2.08863i 0.717838 + 0.696210i
\(10\) 0 0
\(11\) −1.06488 + 3.97420i −0.321074 + 1.19826i 0.597126 + 0.802148i \(0.296309\pi\)
−0.918200 + 0.396117i \(0.870357\pi\)
\(12\) 0 0
\(13\) 3.59808 + 0.232051i 0.997927 + 0.0643593i
\(14\) 0 0
\(15\) −2.40216 + 1.01660i −0.620235 + 0.262484i
\(16\) 0 0
\(17\) −2.51954 + 4.36397i −0.611078 + 1.05842i 0.379981 + 0.924994i \(0.375930\pi\)
−0.991059 + 0.133424i \(0.957403\pi\)
\(18\) 0 0
\(19\) 3.73205 1.00000i 0.856191 0.229416i 0.196084 0.980587i \(-0.437177\pi\)
0.660107 + 0.751171i \(0.270511\pi\)
\(20\) 0 0
\(21\) 0.301143 2.43091i 0.0657148 0.530468i
\(22\) 0 0
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 2.73205i 0.546410i
\(26\) 0 0
\(27\) 2.09808 + 4.75374i 0.403775 + 0.914858i
\(28\) 0 0
\(29\) 6.20840 3.58442i 1.15287 0.665610i 0.203286 0.979119i \(-0.434838\pi\)
0.949585 + 0.313509i \(0.101505\pi\)
\(30\) 0 0
\(31\) 2.46410 + 2.46410i 0.442566 + 0.442566i 0.892873 0.450308i \(-0.148686\pi\)
−0.450308 + 0.892873i \(0.648686\pi\)
\(32\) 0 0
\(33\) −4.29488 + 5.68671i −0.747642 + 0.989929i
\(34\) 0 0
\(35\) 1.84443 + 1.06488i 0.311766 + 0.179998i
\(36\) 0 0
\(37\) −5.23205 1.40192i −0.860144 0.230475i −0.198323 0.980137i \(-0.563549\pi\)
−0.661821 + 0.749662i \(0.730216\pi\)
\(38\) 0 0
\(39\) 5.62477 + 2.71330i 0.900684 + 0.434476i
\(40\) 0 0
\(41\) −5.42885 1.45466i −0.847844 0.227179i −0.191361 0.981520i \(-0.561290\pi\)
−0.656483 + 0.754341i \(0.727957\pi\)
\(42\) 0 0
\(43\) −1.90192 1.09808i −0.290041 0.167455i 0.347920 0.937524i \(-0.386888\pi\)
−0.637960 + 0.770069i \(0.720222\pi\)
\(44\) 0 0
\(45\) −4.51739 + 0.0690922i −0.673412 + 0.0102997i
\(46\) 0 0
\(47\) −4.25953 4.25953i −0.621316 0.621316i 0.324552 0.945868i \(-0.394787\pi\)
−0.945868 + 0.324552i \(0.894787\pi\)
\(48\) 0 0
\(49\) 4.33013 2.50000i 0.618590 0.357143i
\(50\) 0 0
\(51\) −6.88351 + 5.36603i −0.963884 + 0.751394i
\(52\) 0 0
\(53\) 0.779548i 0.107079i 0.998566 + 0.0535396i \(0.0170503\pi\)
−0.998566 + 0.0535396i \(0.982950\pi\)
\(54\) 0 0
\(55\) −3.09808 5.36603i −0.417745 0.723555i
\(56\) 0 0
\(57\) 6.64136 + 0.822738i 0.879670 + 0.108974i
\(58\) 0 0
\(59\) −2.90931 + 0.779548i −0.378760 + 0.101489i −0.443176 0.896435i \(-0.646148\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(60\) 0 0
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 0 0
\(63\) 2.06488 3.70625i 0.260151 0.466943i
\(64\) 0 0
\(65\) −4.07863 + 3.58442i −0.505892 + 0.444593i
\(66\) 0 0
\(67\) 1.53590 5.73205i 0.187640 0.700281i −0.806410 0.591357i \(-0.798593\pi\)
0.994050 0.108925i \(-0.0347408\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.779548 2.90931i −0.0925153 0.345272i 0.904116 0.427288i \(-0.140531\pi\)
−0.996631 + 0.0820158i \(0.973864\pi\)
\(72\) 0 0
\(73\) −0.901924 + 0.901924i −0.105562 + 0.105562i −0.757915 0.652353i \(-0.773782\pi\)
0.652353 + 0.757915i \(0.273782\pi\)
\(74\) 0 0
\(75\) −1.77739 + 4.38556i −0.205236 + 0.506401i
\(76\) 0 0
\(77\) 5.81863 0.663094
\(78\) 0 0
\(79\) −2.00000 −0.225018 −0.112509 0.993651i \(-0.535889\pi\)
−0.112509 + 0.993651i \(0.535889\pi\)
\(80\) 0 0
\(81\) 0.275241 + 8.99579i 0.0305823 + 0.999532i
\(82\) 0 0
\(83\) 2.90931 2.90931i 0.319339 0.319339i −0.529174 0.848513i \(-0.677498\pi\)
0.848513 + 0.529174i \(0.177498\pi\)
\(84\) 0 0
\(85\) −1.96410 7.33013i −0.213037 0.795064i
\(86\) 0 0
\(87\) 12.2978 1.71481i 1.31846 0.183846i
\(88\) 0 0
\(89\) 2.41510 9.01327i 0.256000 0.955405i −0.711531 0.702654i \(-0.751998\pi\)
0.967531 0.252751i \(-0.0813353\pi\)
\(90\) 0 0
\(91\) −1.00000 5.00000i −0.104828 0.524142i
\(92\) 0 0
\(93\) 2.35237 + 5.55852i 0.243929 + 0.576392i
\(94\) 0 0
\(95\) −2.90931 + 5.03908i −0.298489 + 0.516998i
\(96\) 0 0
\(97\) 1.63397 0.437822i 0.165905 0.0444541i −0.174910 0.984584i \(-0.555964\pi\)
0.340815 + 0.940130i \(0.389297\pi\)
\(98\) 0 0
\(99\) −10.5939 + 6.33434i −1.06472 + 0.636625i
\(100\) 0 0
\(101\) 3.01375 + 5.21997i 0.299880 + 0.519407i 0.976108 0.217285i \(-0.0697202\pi\)
−0.676229 + 0.736692i \(0.736387\pi\)
\(102\) 0 0
\(103\) 6.92820i 0.682656i 0.939944 + 0.341328i \(0.110877\pi\)
−0.939944 + 0.341328i \(0.889123\pi\)
\(104\) 0 0
\(105\) 2.26795 + 2.90931i 0.221329 + 0.283920i
\(106\) 0 0
\(107\) 16.4675 9.50749i 1.59197 0.919123i 0.598999 0.800749i \(-0.295565\pi\)
0.992969 0.118374i \(-0.0377682\pi\)
\(108\) 0 0
\(109\) −13.1962 13.1962i −1.26396 1.26396i −0.949156 0.314806i \(-0.898060\pi\)
−0.314806 0.949156i \(-0.601940\pi\)
\(110\) 0 0
\(111\) −7.48658 5.65423i −0.710595 0.536676i
\(112\) 0 0
\(113\) 8.90883 + 5.14352i 0.838073 + 0.483861i 0.856609 0.515967i \(-0.172567\pi\)
−0.0185360 + 0.999828i \(0.505901\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 7.26384 + 8.01478i 0.671542 + 0.740967i
\(118\) 0 0
\(119\) 6.88351 + 1.84443i 0.631010 + 0.169079i
\(120\) 0 0
\(121\) −5.13397 2.96410i −0.466725 0.269464i
\(122\) 0 0
\(123\) −7.76819 5.86691i −0.700434 0.529002i
\(124\) 0 0
\(125\) −8.23373 8.23373i −0.736447 0.736447i
\(126\) 0 0
\(127\) −7.90192 + 4.56218i −0.701182 + 0.404828i −0.807788 0.589474i \(-0.799335\pi\)
0.106605 + 0.994301i \(0.466002\pi\)
\(128\) 0 0
\(129\) −2.33864 3.00000i −0.205906 0.264135i
\(130\) 0 0
\(131\) 7.94839i 0.694454i 0.937781 + 0.347227i \(0.112877\pi\)
−0.937781 + 0.347227i \(0.887123\pi\)
\(132\) 0 0
\(133\) −2.73205 4.73205i −0.236899 0.410321i
\(134\) 0 0
\(135\) −7.29638 2.82797i −0.627973 0.243393i
\(136\) 0 0
\(137\) −6.49373 + 1.73999i −0.554797 + 0.148657i −0.525315 0.850908i \(-0.676052\pi\)
−0.0294822 + 0.999565i \(0.509386\pi\)
\(138\) 0 0
\(139\) 9.19615 15.9282i 0.780007 1.35101i −0.151929 0.988391i \(-0.548549\pi\)
0.931937 0.362621i \(-0.118118\pi\)
\(140\) 0 0
\(141\) −4.06639 9.60864i −0.342452 0.809194i
\(142\) 0 0
\(143\) −4.75374 + 14.0524i −0.397528 + 1.17512i
\(144\) 0 0
\(145\) −2.79423 + 10.4282i −0.232048 + 0.866015i
\(146\) 0 0
\(147\) 8.57727 1.19601i 0.707441 0.0986455i
\(148\) 0 0
\(149\) −2.23420 8.33816i −0.183033 0.683089i −0.995043 0.0994454i \(-0.968293\pi\)
0.812010 0.583644i \(-0.198374\pi\)
\(150\) 0 0
\(151\) −0.535898 + 0.535898i −0.0436108 + 0.0436108i −0.728576 0.684965i \(-0.759817\pi\)
0.684965 + 0.728576i \(0.259817\pi\)
\(152\) 0 0
\(153\) −14.5406 + 4.13548i −1.17554 + 0.334334i
\(154\) 0 0
\(155\) −5.24796 −0.421526
\(156\) 0 0
\(157\) −4.80385 −0.383389 −0.191694 0.981455i \(-0.561398\pi\)
−0.191694 + 0.981455i \(0.561398\pi\)
\(158\) 0 0
\(159\) −0.507152 + 1.25135i −0.0402197 + 0.0992387i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.07180 + 4.00000i 0.0839496 + 0.313304i 0.995113 0.0987406i \(-0.0314814\pi\)
−0.911164 + 0.412045i \(0.864815\pi\)
\(164\) 0 0
\(165\) −1.48214 10.6292i −0.115384 0.827483i
\(166\) 0 0
\(167\) 3.47998 12.9875i 0.269289 1.00500i −0.690283 0.723539i \(-0.742514\pi\)
0.959573 0.281461i \(-0.0908192\pi\)
\(168\) 0 0
\(169\) 12.8923 + 1.66987i 0.991716 + 0.128452i
\(170\) 0 0
\(171\) 10.1257 + 5.64136i 0.774328 + 0.431406i
\(172\) 0 0
\(173\) 8.72794 15.1172i 0.663573 1.14934i −0.316097 0.948727i \(-0.602373\pi\)
0.979670 0.200615i \(-0.0642941\pi\)
\(174\) 0 0
\(175\) 3.73205 1.00000i 0.282117 0.0755929i
\(176\) 0 0
\(177\) −5.17726 0.641364i −0.389147 0.0482078i
\(178\) 0 0
\(179\) −13.2728 22.9892i −0.992056 1.71829i −0.604972 0.796247i \(-0.706816\pi\)
−0.387084 0.922045i \(-0.626518\pi\)
\(180\) 0 0
\(181\) 3.00000i 0.222988i −0.993765 0.111494i \(-0.964436\pi\)
0.993765 0.111494i \(-0.0355636\pi\)
\(182\) 0 0
\(183\) 9.56218 7.45418i 0.706857 0.551029i
\(184\) 0 0
\(185\) 7.06440 4.07863i 0.519385 0.299867i
\(186\) 0 0
\(187\) −14.6603 14.6603i −1.07206 1.07206i
\(188\) 0 0
\(189\) 5.72579 4.60602i 0.416490 0.335038i
\(190\) 0 0
\(191\) 4.18307 + 2.41510i 0.302677 + 0.174750i 0.643645 0.765324i \(-0.277421\pi\)
−0.340968 + 0.940075i \(0.610755\pi\)
\(192\) 0 0
\(193\) 0.133975 + 0.0358984i 0.00964370 + 0.00258402i 0.263638 0.964622i \(-0.415078\pi\)
−0.253994 + 0.967206i \(0.581744\pi\)
\(194\) 0 0
\(195\) −8.87906 + 3.10037i −0.635843 + 0.222022i
\(196\) 0 0
\(197\) 3.97420 + 1.06488i 0.283150 + 0.0758697i 0.397599 0.917559i \(-0.369844\pi\)
−0.114449 + 0.993429i \(0.536510\pi\)
\(198\) 0 0
\(199\) −11.1962 6.46410i −0.793674 0.458228i 0.0475802 0.998867i \(-0.484849\pi\)
−0.841254 + 0.540639i \(0.818182\pi\)
\(200\) 0 0
\(201\) 6.19458 8.20204i 0.436932 0.578527i
\(202\) 0 0
\(203\) −7.16884 7.16884i −0.503154 0.503154i
\(204\) 0 0
\(205\) 7.33013 4.23205i 0.511958 0.295579i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 15.8968i 1.09960i
\(210\) 0 0
\(211\) −0.901924 1.56218i −0.0620910 0.107545i 0.833309 0.552808i \(-0.186444\pi\)
−0.895400 + 0.445263i \(0.853110\pi\)
\(212\) 0 0
\(213\) 0.641364 5.17726i 0.0439455 0.354740i
\(214\) 0 0
\(215\) 3.19465 0.856003i 0.217873 0.0583789i
\(216\) 0 0
\(217\) 2.46410 4.26795i 0.167274 0.289727i
\(218\) 0 0
\(219\) −2.03456 + 0.861027i −0.137483 + 0.0581828i
\(220\) 0 0
\(221\) −10.0782 + 15.1172i −0.677930 + 1.01690i
\(222\) 0 0
\(223\) −6.70577 + 25.0263i −0.449052 + 1.67588i 0.255960 + 0.966687i \(0.417609\pi\)
−0.705011 + 0.709196i \(0.749058\pi\)
\(224\) 0 0
\(225\) −5.70625 + 5.88351i −0.380416 + 0.392234i
\(226\) 0 0
\(227\) 5.24796 + 19.5856i 0.348319 + 1.29994i 0.888686 + 0.458515i \(0.151619\pi\)
−0.540367 + 0.841429i \(0.681715\pi\)
\(228\) 0 0
\(229\) −14.1244 + 14.1244i −0.933364 + 0.933364i −0.997914 0.0645507i \(-0.979439\pi\)
0.0645507 + 0.997914i \(0.479439\pi\)
\(230\) 0 0
\(231\) 9.34022 + 3.78543i 0.614541 + 0.249063i
\(232\) 0 0
\(233\) −17.4559 −1.14357 −0.571786 0.820403i \(-0.693749\pi\)
−0.571786 + 0.820403i \(0.693749\pi\)
\(234\) 0 0
\(235\) 9.07180 0.591779
\(236\) 0 0
\(237\) −3.21046 1.30114i −0.208542 0.0845183i
\(238\) 0 0
\(239\) 6.59817 6.59817i 0.426800 0.426800i −0.460737 0.887537i \(-0.652415\pi\)
0.887537 + 0.460737i \(0.152415\pi\)
\(240\) 0 0
\(241\) 3.76795 + 14.0622i 0.242715 + 0.905825i 0.974518 + 0.224309i \(0.0720123\pi\)
−0.731803 + 0.681516i \(0.761321\pi\)
\(242\) 0 0
\(243\) −5.41058 + 14.6194i −0.347089 + 0.937832i
\(244\) 0 0
\(245\) −1.94887 + 7.27328i −0.124509 + 0.464673i
\(246\) 0 0
\(247\) 13.6603 2.73205i 0.869181 0.173836i
\(248\) 0 0
\(249\) 6.56283 2.77739i 0.415902 0.176010i
\(250\) 0 0
\(251\) 0.494214 0.856003i 0.0311945 0.0540304i −0.850007 0.526772i \(-0.823402\pi\)
0.881201 + 0.472741i \(0.156736\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 1.61594 13.0443i 0.101194 0.816867i
\(256\) 0 0
\(257\) −10.7533 18.6252i −0.670770 1.16181i −0.977686 0.210071i \(-0.932630\pi\)
0.306916 0.951737i \(-0.400703\pi\)
\(258\) 0 0
\(259\) 7.66025i 0.475985i
\(260\) 0 0
\(261\) 20.8564 + 5.24796i 1.29098 + 0.324840i
\(262\) 0 0
\(263\) −19.3003 + 11.1430i −1.19011 + 0.687109i −0.958331 0.285660i \(-0.907787\pi\)
−0.231777 + 0.972769i \(0.574454\pi\)
\(264\) 0 0
\(265\) −0.830127 0.830127i −0.0509943 0.0509943i
\(266\) 0 0
\(267\) 9.74056 12.8972i 0.596113 0.789294i
\(268\) 0 0
\(269\) 12.4168 + 7.16884i 0.757066 + 0.437092i 0.828241 0.560372i \(-0.189342\pi\)
−0.0711756 + 0.997464i \(0.522675\pi\)
\(270\) 0 0
\(271\) −7.46410 2.00000i −0.453412 0.121491i 0.0248835 0.999690i \(-0.492079\pi\)
−0.478295 + 0.878199i \(0.658745\pi\)
\(272\) 0 0
\(273\) 1.64763 8.67671i 0.0997191 0.525138i
\(274\) 0 0
\(275\) −10.8577 2.90931i −0.654744 0.175438i
\(276\) 0 0
\(277\) 23.8923 + 13.7942i 1.43555 + 0.828815i 0.997536 0.0701536i \(-0.0223490\pi\)
0.438013 + 0.898969i \(0.355682\pi\)
\(278\) 0 0
\(279\) 0.159877 + 10.4531i 0.00957158 + 0.625809i
\(280\) 0 0
\(281\) 12.1315 + 12.1315i 0.723703 + 0.723703i 0.969357 0.245655i \(-0.0790030\pi\)
−0.245655 + 0.969357i \(0.579003\pi\)
\(282\) 0 0
\(283\) 5.70577 3.29423i 0.339173 0.195822i −0.320733 0.947170i \(-0.603929\pi\)
0.659906 + 0.751348i \(0.270596\pi\)
\(284\) 0 0
\(285\) −7.94839 + 6.19615i −0.470822 + 0.367028i
\(286\) 0 0
\(287\) 7.94839i 0.469179i
\(288\) 0 0
\(289\) −4.19615 7.26795i −0.246832 0.427526i
\(290\) 0 0
\(291\) 2.90774 + 0.360213i 0.170455 + 0.0211161i
\(292\) 0 0
\(293\) 1.73999 0.466229i 0.101651 0.0272374i −0.207635 0.978206i \(-0.566577\pi\)
0.309286 + 0.950969i \(0.399910\pi\)
\(294\) 0 0
\(295\) 2.26795 3.92820i 0.132045 0.228709i
\(296\) 0 0
\(297\) −21.1265 + 3.27599i −1.22588 + 0.190092i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −0.803848 + 3.00000i −0.0463330 + 0.172917i
\(302\) 0 0
\(303\) 1.44179 + 10.3399i 0.0828289 + 0.594012i
\(304\) 0 0
\(305\) 2.72842 + 10.1826i 0.156229 + 0.583054i
\(306\) 0 0
\(307\) −8.39230 + 8.39230i −0.478974 + 0.478974i −0.904803 0.425829i \(-0.859982\pi\)
0.425829 + 0.904803i \(0.359982\pi\)
\(308\) 0 0
\(309\) −4.50729 + 11.1213i −0.256411 + 0.632671i
\(310\) 0 0
\(311\) 10.0782 0.571480 0.285740 0.958307i \(-0.407761\pi\)
0.285740 + 0.958307i \(0.407761\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) 1.74786 + 6.14557i 0.0984807 + 0.346264i
\(316\) 0 0
\(317\) 11.3519 11.3519i 0.637587 0.637587i −0.312373 0.949960i \(-0.601124\pi\)
0.949960 + 0.312373i \(0.101124\pi\)
\(318\) 0 0
\(319\) 7.63397 + 28.4904i 0.427421 + 1.59516i
\(320\) 0 0
\(321\) 32.6193 4.54843i 1.82063 0.253869i
\(322\) 0 0
\(323\) −5.03908 + 18.8061i −0.280382 + 1.04640i
\(324\) 0 0
\(325\) −0.633975 + 9.83013i −0.0351666 + 0.545277i
\(326\) 0 0
\(327\) −12.5978 29.7679i −0.696659 1.64617i
\(328\) 0 0
\(329\) −4.25953 + 7.37772i −0.234835 + 0.406747i
\(330\) 0 0
\(331\) 33.0526 8.85641i 1.81673 0.486792i 0.820357 0.571852i \(-0.193775\pi\)
0.996376 + 0.0850595i \(0.0271080\pi\)
\(332\) 0 0
\(333\) −8.33919 13.9469i −0.456985 0.764285i
\(334\) 0 0
\(335\) 4.46841 + 7.73951i 0.244135 + 0.422855i
\(336\) 0 0
\(337\) 18.4641i 1.00580i 0.864344 + 0.502902i \(0.167734\pi\)
−0.864344 + 0.502902i \(0.832266\pi\)
\(338\) 0 0
\(339\) 10.9545 + 14.0524i 0.594966 + 0.763219i
\(340\) 0 0
\(341\) −12.4168 + 7.16884i −0.672407 + 0.388215i
\(342\) 0 0
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 17.8177 + 10.2870i 0.956502 + 0.552237i 0.895095 0.445876i \(-0.147108\pi\)
0.0614076 + 0.998113i \(0.480441\pi\)
\(348\) 0 0
\(349\) 27.4904 + 7.36603i 1.47153 + 0.394294i 0.903454 0.428684i \(-0.141023\pi\)
0.568072 + 0.822979i \(0.307689\pi\)
\(350\) 0 0
\(351\) 6.44593 + 17.5912i 0.344058 + 0.938948i
\(352\) 0 0
\(353\) −13.6626 3.66088i −0.727186 0.194849i −0.123810 0.992306i \(-0.539511\pi\)
−0.603376 + 0.797457i \(0.706178\pi\)
\(354\) 0 0
\(355\) 3.92820 + 2.26795i 0.208487 + 0.120370i
\(356\) 0 0
\(357\) 9.84967 + 7.43895i 0.521300 + 0.393711i
\(358\) 0 0
\(359\) 18.2354 + 18.2354i 0.962429 + 0.962429i 0.999319 0.0368904i \(-0.0117452\pi\)
−0.0368904 + 0.999319i \(0.511745\pi\)
\(360\) 0 0
\(361\) −3.52628 + 2.03590i −0.185594 + 0.107153i
\(362\) 0 0
\(363\) −6.31284 8.09808i −0.331338 0.425039i
\(364\) 0 0
\(365\) 1.92089i 0.100544i
\(366\) 0 0
\(367\) 15.1962 + 26.3205i 0.793233 + 1.37392i 0.923955 + 0.382500i \(0.124937\pi\)
−0.130723 + 0.991419i \(0.541730\pi\)
\(368\) 0 0
\(369\) −8.65286 14.4715i −0.450450 0.753356i
\(370\) 0 0
\(371\) 1.06488 0.285334i 0.0552859 0.0148138i
\(372\) 0 0
\(373\) −5.79423 + 10.0359i −0.300014 + 0.519639i −0.976139 0.217148i \(-0.930325\pi\)
0.676125 + 0.736787i \(0.263658\pi\)
\(374\) 0 0
\(375\) −7.86038 18.5736i −0.405908 0.959138i
\(376\) 0 0
\(377\) 23.1701 11.4564i 1.19332 0.590032i
\(378\) 0 0
\(379\) −3.83013 + 14.2942i −0.196740 + 0.734245i 0.795069 + 0.606519i \(0.207435\pi\)
−0.991809 + 0.127726i \(0.959232\pi\)
\(380\) 0 0
\(381\) −15.6524 + 2.18257i −0.801897 + 0.111816i
\(382\) 0 0
\(383\) −8.51906 31.7936i −0.435304 1.62458i −0.740339 0.672234i \(-0.765335\pi\)
0.305035 0.952341i \(-0.401332\pi\)
\(384\) 0 0
\(385\) −6.19615 + 6.19615i −0.315785 + 0.315785i
\(386\) 0 0
\(387\) −1.80234 6.33714i −0.0916182 0.322135i
\(388\) 0 0
\(389\) −22.4950 −1.14054 −0.570270 0.821457i \(-0.693161\pi\)
−0.570270 + 0.821457i \(0.693161\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −5.17100 + 12.7590i −0.260842 + 0.643605i
\(394\) 0 0
\(395\) 2.12976 2.12976i 0.107160 0.107160i
\(396\) 0 0
\(397\) −3.56218 13.2942i −0.178781 0.667218i −0.995877 0.0907168i \(-0.971084\pi\)
0.817096 0.576501i \(-0.195582\pi\)
\(398\) 0 0
\(399\) −1.30703 9.37341i −0.0654332 0.469258i
\(400\) 0 0
\(401\) 3.22263 12.0270i 0.160931 0.600601i −0.837594 0.546294i \(-0.816038\pi\)
0.998524 0.0543073i \(-0.0172951\pi\)
\(402\) 0 0
\(403\) 8.29423 + 9.43782i 0.413165 + 0.470131i
\(404\) 0 0
\(405\) −9.87256 9.28636i −0.490571 0.461443i
\(406\) 0 0
\(407\) 11.1430 19.3003i 0.552340 0.956681i
\(408\) 0 0
\(409\) 28.9904 7.76795i 1.43348 0.384100i 0.543236 0.839580i \(-0.317199\pi\)
0.890246 + 0.455480i \(0.150532\pi\)
\(410\) 0 0
\(411\) −11.5559 1.43156i −0.570011 0.0706135i
\(412\) 0 0
\(413\) 2.12976 + 3.68886i 0.104799 + 0.181517i
\(414\) 0 0
\(415\) 6.19615i 0.304157i
\(416\) 0 0
\(417\) 25.1244 19.5856i 1.23034 0.959113i
\(418\) 0 0
\(419\) −8.23373 + 4.75374i −0.402244 + 0.232236i −0.687452 0.726230i \(-0.741271\pi\)
0.285208 + 0.958466i \(0.407937\pi\)
\(420\) 0 0
\(421\) −7.83013 7.83013i −0.381617 0.381617i 0.490067 0.871685i \(-0.336972\pi\)
−0.871685 + 0.490067i \(0.836972\pi\)
\(422\) 0 0
\(423\) −0.276369 18.0695i −0.0134375 0.878571i
\(424\) 0 0
\(425\) −11.9226 6.88351i −0.578330 0.333899i
\(426\) 0 0
\(427\) −9.56218 2.56218i −0.462746 0.123992i
\(428\) 0 0
\(429\) −16.7729 + 19.4646i −0.809803 + 0.939759i
\(430\) 0 0
\(431\) −36.5473 9.79282i −1.76042 0.471704i −0.773622 0.633648i \(-0.781557\pi\)
−0.986800 + 0.161944i \(0.948224\pi\)
\(432\) 0 0
\(433\) −26.8923 15.5263i −1.29236 0.746145i −0.313289 0.949658i \(-0.601431\pi\)
−0.979072 + 0.203512i \(0.934764\pi\)
\(434\) 0 0
\(435\) −11.2697 + 14.9218i −0.540339 + 0.715445i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.09808 + 0.633975i −0.0524083 + 0.0302580i −0.525975 0.850500i \(-0.676300\pi\)
0.473567 + 0.880758i \(0.342966\pi\)
\(440\) 0 0
\(441\) 14.5466 + 3.66025i 0.692694 + 0.174298i
\(442\) 0 0
\(443\) 11.2195i 0.533054i −0.963827 0.266527i \(-0.914124\pi\)
0.963827 0.266527i \(-0.0858762\pi\)
\(444\) 0 0
\(445\) 7.02628 + 12.1699i 0.333078 + 0.576907i
\(446\) 0 0
\(447\) 1.83816 14.8382i 0.0869422 0.701821i
\(448\) 0 0
\(449\) 19.8710 5.32441i 0.937769 0.251275i 0.242605 0.970125i \(-0.421998\pi\)
0.695165 + 0.718851i \(0.255331\pi\)
\(450\) 0 0
\(451\) 11.5622 20.0263i 0.544442 0.943001i
\(452\) 0 0
\(453\) −1.20888 + 0.511599i −0.0567981 + 0.0240370i
\(454\) 0 0
\(455\) 6.38929 + 4.25953i 0.299535 + 0.199690i
\(456\) 0 0
\(457\) −1.00962 + 3.76795i −0.0472280 + 0.176257i −0.985511 0.169611i \(-0.945749\pi\)
0.938283 + 0.345868i \(0.112416\pi\)
\(458\) 0 0
\(459\) −26.0314 2.82130i −1.21504 0.131687i
\(460\) 0 0
\(461\) 5.50531 + 20.5461i 0.256408 + 0.956927i 0.967302 + 0.253628i \(0.0816238\pi\)
−0.710894 + 0.703299i \(0.751710\pi\)
\(462\) 0 0
\(463\) −23.0526 + 23.0526i −1.07134 + 1.07134i −0.0740918 + 0.997251i \(0.523606\pi\)
−0.997251 + 0.0740918i \(0.976394\pi\)
\(464\) 0 0
\(465\) −8.42417 3.41417i −0.390661 0.158328i
\(466\) 0 0
\(467\) −19.1679 −0.886984 −0.443492 0.896278i \(-0.646261\pi\)
−0.443492 + 0.896278i \(0.646261\pi\)
\(468\) 0 0
\(469\) −8.39230 −0.387521
\(470\) 0 0
\(471\) −7.71127 3.12525i −0.355317 0.144004i
\(472\) 0 0
\(473\) 6.38929 6.38929i 0.293780 0.293780i
\(474\) 0 0
\(475\) 2.73205 + 10.1962i 0.125355 + 0.467832i
\(476\) 0 0
\(477\) −1.62819 + 1.67877i −0.0745496 + 0.0768655i
\(478\) 0 0
\(479\) 5.32441 19.8710i 0.243279 0.907928i −0.730962 0.682418i \(-0.760928\pi\)
0.974241 0.225510i \(-0.0724049\pi\)
\(480\) 0 0
\(481\) −18.5000 6.25833i −0.843527 0.285355i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.27376 + 2.20622i −0.0578385 + 0.100179i
\(486\) 0 0
\(487\) −5.56218 + 1.49038i −0.252046 + 0.0675356i −0.382630 0.923902i \(-0.624982\pi\)
0.130584 + 0.991437i \(0.458315\pi\)
\(488\) 0 0
\(489\) −0.881808 + 7.11819i −0.0398767 + 0.321896i
\(490\) 0 0
\(491\) 14.2612 + 24.7012i 0.643600 + 1.11475i 0.984623 + 0.174693i \(0.0558934\pi\)
−0.341023 + 0.940055i \(0.610773\pi\)
\(492\) 0 0
\(493\) 36.1244i 1.62696i
\(494\) 0 0
\(495\) 4.53590 18.0265i 0.203873 0.810233i
\(496\) 0 0
\(497\) −3.68886 + 2.12976i −0.165468 + 0.0955330i
\(498\) 0 0
\(499\) 2.46410 + 2.46410i 0.110308 + 0.110308i 0.760107 0.649798i \(-0.225147\pi\)
−0.649798 + 0.760107i \(0.725147\pi\)
\(500\) 0 0
\(501\) 14.0354 18.5839i 0.627057 0.830266i
\(502\) 0 0
\(503\) −2.83286 1.63555i −0.126311 0.0729256i 0.435513 0.900182i \(-0.356567\pi\)
−0.561824 + 0.827257i \(0.689900\pi\)
\(504\) 0 0
\(505\) −8.76795 2.34936i −0.390169 0.104545i
\(506\) 0 0
\(507\) 19.6087 + 11.0679i 0.870854 + 0.491542i
\(508\) 0 0
\(509\) −14.1568 3.79330i −0.627489 0.168135i −0.0689588 0.997620i \(-0.521968\pi\)
−0.558530 + 0.829484i \(0.688634\pi\)
\(510\) 0 0
\(511\) 1.56218 + 0.901924i 0.0691067 + 0.0398988i
\(512\) 0 0
\(513\) 12.5839 + 15.6431i 0.555591 + 0.690661i
\(514\) 0 0
\(515\) −7.37772 7.37772i −0.325101 0.325101i
\(516\) 0 0
\(517\) 21.4641 12.3923i 0.943990 0.545013i
\(518\) 0 0
\(519\) 23.8452 18.5885i 1.04669 0.815943i
\(520\) 0 0
\(521\) 2.49155i 0.109157i 0.998509 + 0.0545785i \(0.0173815\pi\)
−0.998509 + 0.0545785i \(0.982618\pi\)
\(522\) 0 0
\(523\) −19.4904 33.7583i −0.852255 1.47615i −0.879169 0.476511i \(-0.841901\pi\)
0.0269137 0.999638i \(-0.491432\pi\)
\(524\) 0 0
\(525\) 6.64136 + 0.822738i 0.289853 + 0.0359072i
\(526\) 0 0
\(527\) −16.9617 + 4.54486i −0.738862 + 0.197977i
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 0 0
\(531\) −7.89343 4.39771i −0.342546 0.190845i
\(532\) 0 0
\(533\) −19.1959 6.49373i −0.831465 0.281275i
\(534\) 0 0
\(535\) −7.41154 + 27.6603i −0.320429 + 1.19586i
\(536\) 0 0
\(537\) −6.34978 45.5378i −0.274013 1.96510i
\(538\) 0 0
\(539\) 5.32441 + 19.8710i 0.229339 + 0.855904i
\(540\) 0 0
\(541\) −12.6865 + 12.6865i −0.545437 + 0.545437i −0.925118 0.379681i \(-0.876034\pi\)
0.379681 + 0.925118i \(0.376034\pi\)
\(542\) 0 0
\(543\) 1.95171 4.81568i 0.0837561 0.206661i
\(544\) 0 0
\(545\) 28.1047 1.20387
\(546\) 0 0
\(547\) −2.00000 −0.0855138 −0.0427569 0.999086i \(-0.513614\pi\)
−0.0427569 + 0.999086i \(0.513614\pi\)
\(548\) 0 0
\(549\) 20.1990 5.74477i 0.862070 0.245181i
\(550\) 0 0
\(551\) 19.5856 19.5856i 0.834376 0.834376i
\(552\) 0 0
\(553\) 0.732051 + 2.73205i 0.0311300 + 0.116179i
\(554\) 0 0
\(555\) 13.9934 1.95124i 0.593988 0.0828255i
\(556\) 0 0
\(557\) −6.62616 + 24.7292i −0.280759 + 1.04781i 0.671123 + 0.741346i \(0.265812\pi\)
−0.951883 + 0.306462i \(0.900855\pi\)
\(558\) 0 0
\(559\) −6.58846 4.39230i −0.278662 0.185775i
\(560\) 0 0
\(561\) −13.9955 33.0706i −0.590891 1.39624i
\(562\) 0 0
\(563\) 5.03908 8.72794i 0.212372 0.367839i −0.740085 0.672514i \(-0.765215\pi\)
0.952456 + 0.304675i \(0.0985479\pi\)
\(564\) 0 0
\(565\) −14.9641 + 4.00962i −0.629544 + 0.168686i
\(566\) 0 0
\(567\) 12.1877 3.66867i 0.511837 0.154070i
\(568\) 0 0
\(569\) −1.35022 2.33864i −0.0566040 0.0980411i 0.836335 0.548219i \(-0.184694\pi\)
−0.892939 + 0.450178i \(0.851361\pi\)
\(570\) 0 0
\(571\) 1.94744i 0.0814979i 0.999169 + 0.0407489i \(0.0129744\pi\)
−0.999169 + 0.0407489i \(0.987026\pi\)
\(572\) 0 0
\(573\) 5.14359 + 6.59817i 0.214877 + 0.275643i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −22.4904 22.4904i −0.936287 0.936287i 0.0618016 0.998088i \(-0.480315\pi\)
−0.998088 + 0.0618016i \(0.980315\pi\)
\(578\) 0 0
\(579\) 0.191705 + 0.144785i 0.00796700 + 0.00601707i
\(580\) 0 0
\(581\) −5.03908 2.90931i −0.209056 0.120699i
\(582\) 0 0
\(583\) −3.09808 0.830127i −0.128309 0.0343803i
\(584\) 0 0
\(585\) −16.2699 0.799664i −0.672679 0.0330620i
\(586\) 0 0
\(587\) 18.0265 + 4.83020i 0.744035 + 0.199364i 0.610871 0.791730i \(-0.290819\pi\)
0.133164 + 0.991094i \(0.457486\pi\)
\(588\) 0 0
\(589\) 11.6603 + 6.73205i 0.480452 + 0.277389i
\(590\) 0 0
\(591\) 5.68671 + 4.29488i 0.233920 + 0.176668i
\(592\) 0 0
\(593\) −10.3635 10.3635i −0.425578 0.425578i 0.461541 0.887119i \(-0.347297\pi\)
−0.887119 + 0.461541i \(0.847297\pi\)
\(594\) 0 0
\(595\) −9.29423 + 5.36603i −0.381026 + 0.219986i
\(596\) 0 0
\(597\) −13.7670 17.6603i −0.563446 0.722786i
\(598\) 0 0
\(599\) 20.7270i 0.846881i 0.905924 + 0.423441i \(0.139178\pi\)
−0.905924 + 0.423441i \(0.860822\pi\)
\(600\) 0 0
\(601\) −11.7942 20.4282i −0.481097 0.833284i 0.518668 0.854976i \(-0.326428\pi\)
−0.999765 + 0.0216919i \(0.993095\pi\)
\(602\) 0 0
\(603\) 15.2797 9.13612i 0.622238 0.372052i
\(604\) 0 0
\(605\) 8.62350 2.31066i 0.350595 0.0939417i
\(606\) 0 0
\(607\) −0.0980762 + 0.169873i −0.00398079 + 0.00689493i −0.868009 0.496549i \(-0.834600\pi\)
0.864028 + 0.503444i \(0.167934\pi\)
\(608\) 0 0
\(609\) −6.84378 16.1715i −0.277324 0.655301i
\(610\) 0 0
\(611\) −14.3377 16.3145i −0.580041 0.660016i
\(612\) 0 0
\(613\) −11.3564 + 42.3827i −0.458681 + 1.71182i 0.218354 + 0.975870i \(0.429931\pi\)
−0.677035 + 0.735951i \(0.736735\pi\)
\(614\) 0 0
\(615\) 14.5198 2.02463i 0.585494 0.0816411i
\(616\) 0 0
\(617\) 4.78173 + 17.8457i 0.192505 + 0.718439i 0.992899 + 0.118964i \(0.0379573\pi\)
−0.800393 + 0.599475i \(0.795376\pi\)
\(618\) 0 0
\(619\) 31.6603 31.6603i 1.27253 1.27253i 0.327778 0.944755i \(-0.393700\pi\)
0.944755 0.327778i \(-0.106300\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −13.1963 −0.528701
\(624\) 0 0
\(625\) 3.87564 0.155026
\(626\) 0 0
\(627\) −10.3420 + 25.5180i −0.413019 + 1.01909i
\(628\) 0 0
\(629\) 19.3003 19.3003i 0.769554 0.769554i
\(630\) 0 0
\(631\) −5.73205 21.3923i −0.228189 0.851614i −0.981102 0.193493i \(-0.938018\pi\)
0.752912 0.658121i \(-0.228648\pi\)
\(632\) 0 0
\(633\) −0.431485 3.09442i −0.0171500 0.122992i
\(634\) 0 0
\(635\) 3.55644 13.2728i 0.141133 0.526715i
\(636\) 0 0
\(637\) 16.1603 7.99038i 0.640293 0.316590i
\(638\) 0 0
\(639\) 4.39771 7.89343i 0.173971 0.312259i
\(640\) 0 0
\(641\) 22.6758 39.2757i 0.895642 1.55130i 0.0626345 0.998037i \(-0.480050\pi\)
0.833008 0.553261i \(-0.186617\pi\)
\(642\) 0 0
\(643\) −7.00000 + 1.87564i −0.276053 + 0.0739682i −0.394190 0.919029i \(-0.628975\pi\)
0.118136 + 0.992997i \(0.462308\pi\)
\(644\) 0 0
\(645\) 5.68503 + 0.704266i 0.223848 + 0.0277305i
\(646\) 0 0
\(647\) 8.23373 + 14.2612i 0.323701 + 0.560667i 0.981249 0.192746i \(-0.0617394\pi\)
−0.657547 + 0.753413i \(0.728406\pi\)
\(648\) 0 0
\(649\) 12.3923i 0.486441i
\(650\) 0 0
\(651\) 6.73205 5.24796i 0.263850 0.205684i
\(652\) 0 0
\(653\) −8.36615 + 4.83020i −0.327393 + 0.189020i −0.654683 0.755904i \(-0.727198\pi\)
0.327290 + 0.944924i \(0.393865\pi\)
\(654\) 0 0
\(655\) −8.46410 8.46410i −0.330720 0.330720i
\(656\) 0 0
\(657\) −3.82609 + 0.0585190i −0.149270 + 0.00228304i
\(658\) 0 0
\(659\) −23.4834 13.5581i −0.914783 0.528150i −0.0328158 0.999461i \(-0.510447\pi\)
−0.881967 + 0.471311i \(0.843781\pi\)
\(660\) 0 0
\(661\) 9.42820 + 2.52628i 0.366715 + 0.0982609i 0.437470 0.899233i \(-0.355874\pi\)
−0.0707559 + 0.997494i \(0.522541\pi\)
\(662\) 0 0
\(663\) −26.0126 + 17.7100i −1.01024 + 0.687801i
\(664\) 0 0
\(665\) 7.94839 + 2.12976i 0.308225 + 0.0825887i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −27.0457 + 35.8103i −1.04565 + 1.38451i
\(670\) 0 0
\(671\) 20.3652 + 20.3652i 0.786189 + 0.786189i
\(672\) 0 0
\(673\) −36.9904 + 21.3564i −1.42587 + 0.823229i −0.996792 0.0800364i \(-0.974496\pi\)
−0.429082 + 0.903265i \(0.641163\pi\)
\(674\) 0 0
\(675\) −12.9875 + 5.73205i −0.499888 + 0.220627i
\(676\) 0 0
\(677\) 9.66040i 0.371279i −0.982618 0.185640i \(-0.940564\pi\)
0.982618 0.185640i \(-0.0594357\pi\)
\(678\) 0 0
\(679\) −1.19615 2.07180i −0.0459041 0.0795083i
\(680\) 0 0
\(681\) −4.31769 + 34.8536i −0.165454 + 1.33559i
\(682\) 0 0
\(683\) 45.2752 12.1315i 1.73241 0.464198i 0.751673 0.659536i \(-0.229247\pi\)
0.980736 + 0.195338i \(0.0625804\pi\)
\(684\) 0 0
\(685\) 5.06218 8.76795i 0.193416 0.335006i
\(686\) 0 0
\(687\) −31.8617 + 13.4839i −1.21560 + 0.514443i
\(688\) 0 0
\(689\) −0.180895 + 2.80487i −0.00689154 + 0.106857i
\(690\) 0 0
\(691\) −4.88269 + 18.2224i −0.185746 + 0.693214i 0.808723 + 0.588189i \(0.200159\pi\)
−0.994470 + 0.105025i \(0.966508\pi\)
\(692\) 0 0
\(693\) 12.5305 + 12.1530i 0.475994 + 0.461653i
\(694\) 0 0
\(695\) 7.16884 + 26.7545i 0.271930 + 1.01486i
\(696\) 0 0
\(697\) 20.0263 20.0263i 0.758549 0.758549i
\(698\) 0 0
\(699\) −28.0207 11.3563i −1.05984 0.429535i
\(700\) 0 0
\(701\) −12.7786 −0.482641 −0.241320 0.970446i \(-0.577580\pi\)
−0.241320 + 0.970446i \(0.577580\pi\)
\(702\) 0 0
\(703\) −20.9282 −0.789322
\(704\) 0 0
\(705\) 14.5623 + 5.90185i 0.548448 + 0.222277i
\(706\) 0 0
\(707\) 6.02751 6.02751i 0.226688 0.226688i
\(708\) 0 0
\(709\) −3.03590 11.3301i −0.114016 0.425512i 0.885196 0.465219i \(-0.154024\pi\)
−0.999211 + 0.0397068i \(0.987358\pi\)
\(710\) 0 0
\(711\) −4.30703 4.17726i −0.161526 0.156660i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −9.90192 20.0263i −0.370311 0.748940i
\(716\) 0 0
\(717\) 14.8842 6.29899i 0.555859 0.235240i
\(718\) 0 0
\(719\) 3.68886 6.38929i 0.137571 0.238280i −0.789005 0.614386i \(-0.789404\pi\)
0.926577 + 0.376106i \(0.122737\pi\)
\(720\) 0 0
\(721\) 9.46410 2.53590i 0.352462 0.0944418i
\(722\) 0 0
\(723\) −3.10003 + 25.0243i −0.115292 + 0.930665i
\(724\) 0 0
\(725\) 9.79282 + 16.9617i 0.363696 + 0.629940i
\(726\) 0 0
\(727\) 19.5167i 0.723833i −0.932211 0.361916i \(-0.882123\pi\)
0.932211 0.361916i \(-0.117877\pi\)
\(728\) 0 0
\(729\) −18.1962 + 19.9474i −0.673932 + 0.738794i
\(730\) 0 0
\(731\) 9.58394 5.53329i 0.354475 0.204656i
\(732\) 0 0
\(733\) −6.77757 6.77757i −0.250335 0.250335i 0.570773 0.821108i \(-0.306644\pi\)
−0.821108 + 0.570773i \(0.806644\pi\)
\(734\) 0 0
\(735\) −7.86017 + 10.4074i −0.289927 + 0.383883i
\(736\) 0 0
\(737\) 21.1447 + 12.2079i 0.778876 + 0.449685i
\(738\) 0 0
\(739\) 11.1244 + 2.98076i 0.409216 + 0.109649i 0.457554 0.889182i \(-0.348726\pi\)
−0.0483378 + 0.998831i \(0.515392\pi\)
\(740\) 0 0
\(741\) 23.7052 + 4.50141i 0.870833 + 0.165363i
\(742\) 0 0
\(743\) −8.51906 2.28268i −0.312534 0.0837432i 0.0991426 0.995073i \(-0.468390\pi\)
−0.411677 + 0.911330i \(0.635057\pi\)
\(744\) 0 0
\(745\) 11.2583 + 6.50000i 0.412473 + 0.238142i
\(746\) 0 0
\(747\) 12.3417 0.188763i 0.451560 0.00690649i
\(748\) 0 0
\(749\) −19.0150 19.0150i −0.694792 0.694792i
\(750\) 0 0
\(751\) 29.2750 16.9019i 1.06826 0.616760i 0.140554 0.990073i \(-0.455112\pi\)
0.927705 + 0.373313i \(0.121778\pi\)
\(752\) 0 0
\(753\) 1.35022 1.05256i 0.0492046 0.0383574i
\(754\) 0 0
\(755\) 1.14134i 0.0415375i
\(756\) 0 0
\(757\) −8.39230 14.5359i −0.305024 0.528316i 0.672243 0.740331i \(-0.265331\pi\)
−0.977267 + 0.212014i \(0.931998\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −17.7412 + 4.75374i −0.643118 + 0.172323i −0.565616 0.824669i \(-0.691361\pi\)
−0.0775029 + 0.996992i \(0.524695\pi\)
\(762\) 0 0
\(763\) −13.1962 + 22.8564i −0.477733 + 0.827457i
\(764\) 0 0
\(765\) 11.0802 19.8878i 0.400606 0.719045i
\(766\) 0 0
\(767\) −10.6488 + 2.12976i −0.384507 + 0.0769014i
\(768\) 0 0
\(769\) −10.8301 + 40.4186i −0.390544 + 1.45753i 0.438694 + 0.898636i \(0.355441\pi\)
−0.829238 + 0.558895i \(0.811225\pi\)
\(770\) 0 0
\(771\) −5.14442 36.8935i −0.185272 1.32869i
\(772\) 0 0
\(773\) −11.1430 41.5864i −0.400787 1.49576i −0.811695 0.584081i \(-0.801455\pi\)
0.410908 0.911677i \(-0.365212\pi\)
\(774\) 0 0
\(775\) −6.73205 + 6.73205i −0.241822 + 0.241822i
\(776\) 0 0
\(777\) −4.98354 + 12.2965i −0.178784 + 0.441133i
\(778\) 0 0
\(779\) −21.7154 −0.778035
\(780\) 0 0
\(781\) 12.3923 0.443432
\(782\) 0 0
\(783\) 30.0651 + 21.9928i 1.07444 + 0.785957i
\(784\) 0 0
\(785\) 5.11553 5.11553i 0.182581 0.182581i
\(786\) 0 0
\(787\) −4.29423 16.0263i −0.153073 0.571275i −0.999263 0.0383938i \(-0.987776\pi\)
0.846190 0.532881i \(-0.178891\pi\)
\(788\) 0 0
\(789\) −38.2307 + 5.33089i −1.36105 + 0.189785i
\(790\) 0 0
\(791\) 3.76532 14.0524i 0.133879 0.499644i
\(792\) 0 0
\(793\) 14.0000 21.0000i 0.497155 0.745732i
\(794\) 0 0
\(795\) −0.792486 1.87260i −0.0281066