Properties

Label 624.2.cn.c.305.2
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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 305.2
Root \(0.500000 + 1.56488i\) of defining polynomial
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.c.401.2

$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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 0.427694 0.903924i \(-0.359326\pi\)
−0.903924 + 0.427694i \(0.859326\pi\)
\(6\) 0 0
\(7\) −0.366025 + 1.36603i −0.138345 + 0.516309i 0.861617 + 0.507559i \(0.169452\pi\)
−0.999962 + 0.00875026i \(0.997215\pi\)
\(8\) 0 0
\(9\) 2.15351 2.08863i 0.717838 0.696210i
\(10\) 0 0
\(11\) −1.06488 3.97420i −0.321074 1.19826i −0.918200 0.396117i \(-0.870357\pi\)
0.597126 0.802148i \(-0.296309\pi\)
\(12\) 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 −0.991059 0.133424i \(-0.957403\pi\)
0.379981 0.924994i \(-0.375930\pi\)
\(18\) 0 0
\(19\) 3.73205 + 1.00000i 0.856191 + 0.229416i 0.660107 0.751171i \(-0.270511\pi\)
0.196084 + 0.980587i \(0.437177\pi\)
\(20\) 0 0
\(21\) 0.301143 + 2.43091i 0.0657148 + 0.530468i
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 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 0.949585 0.313509i \(-0.101505\pi\)
0.203286 + 0.979119i \(0.434838\pi\)
\(30\) 0 0
\(31\) 2.46410 2.46410i 0.442566 0.442566i −0.450308 0.892873i \(-0.648686\pi\)
0.892873 + 0.450308i \(0.148686\pi\)
\(32\) 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 −0.661821 0.749662i \(-0.730216\pi\)
−0.198323 + 0.980137i \(0.563549\pi\)
\(38\) 0 0
\(39\) 5.62477 2.71330i 0.900684 0.434476i
\(40\) 0 0
\(41\) −5.42885 + 1.45466i −0.847844 + 0.227179i −0.656483 0.754341i \(-0.727957\pi\)
−0.191361 + 0.981520i \(0.561290\pi\)
\(42\) 0 0
\(43\) −1.90192 + 1.09808i −0.290041 + 0.167455i −0.637960 0.770069i \(-0.720222\pi\)
0.347920 + 0.937524i \(0.386888\pi\)
\(44\) 0 0
\(45\) −4.51739 0.0690922i −0.673412 0.0102997i
\(46\) 0 0
\(47\) −4.25953 + 4.25953i −0.621316 + 0.621316i −0.945868 0.324552i \(-0.894787\pi\)
0.324552 + 0.945868i \(0.394787\pi\)
\(48\) 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 \(-0.982950\pi\)
0.998566 0.0535396i \(-0.0170503\pi\)
\(54\) 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 0.0644157 0.997923i \(-0.479482\pi\)
−0.443176 + 0.896435i \(0.646148\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 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 0.994050 + 0.108925i \(0.0347408\pi\)
−0.806410 + 0.591357i \(0.798593\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.779548 + 2.90931i −0.0925153 + 0.345272i −0.996631 0.0820158i \(-0.973864\pi\)
0.904116 + 0.427288i \(0.140531\pi\)
\(72\) 0 0
\(73\) −0.901924 0.901924i −0.105562 0.105562i 0.652353 0.757915i \(-0.273782\pi\)
−0.757915 + 0.652353i \(0.773782\pi\)
\(74\) 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 0.848513 0.529174i \(-0.177498\pi\)
−0.529174 + 0.848513i \(0.677498\pi\)
\(84\) 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 0.967531 + 0.252751i \(0.0813353\pi\)
−0.711531 + 0.702654i \(0.751998\pi\)
\(90\) 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 0.340815 0.940130i \(-0.389297\pi\)
−0.174910 + 0.984584i \(0.555964\pi\)
\(98\) 0 0
\(99\) −10.5939 6.33434i −1.06472 0.636625i
\(100\) 0 0
\(101\) 3.01375 5.21997i 0.299880 0.519407i −0.676229 0.736692i \(-0.736387\pi\)
0.976108 + 0.217285i \(0.0697202\pi\)
\(102\) 0 0
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) 0 0
\(105\) 2.26795 2.90931i 0.221329 0.283920i
\(106\) 0 0
\(107\) 16.4675 + 9.50749i 1.59197 + 0.919123i 0.992969 + 0.118374i \(0.0377682\pi\)
0.598999 + 0.800749i \(0.295565\pi\)
\(108\) 0 0
\(109\) −13.1962 + 13.1962i −1.26396 + 1.26396i −0.314806 + 0.949156i \(0.601940\pi\)
−0.949156 + 0.314806i \(0.898060\pi\)
\(110\) 0 0
\(111\) −7.48658 + 5.65423i −0.710595 + 0.536676i
\(112\) 0 0
\(113\) 8.90883 5.14352i 0.838073 0.483861i −0.0185360 0.999828i \(-0.505901\pi\)
0.856609 + 0.515967i \(0.172567\pi\)
\(114\) 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 0.106605 0.994301i \(-0.466002\pi\)
−0.807788 + 0.589474i \(0.799335\pi\)
\(128\) 0 0
\(129\) −2.33864 + 3.00000i −0.205906 + 0.264135i
\(130\) 0 0
\(131\) 7.94839i 0.694454i −0.937781 0.347227i \(-0.887123\pi\)
0.937781 0.347227i \(-0.112877\pi\)
\(132\) 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 −0.0294822 0.999565i \(-0.509386\pi\)
−0.525315 + 0.850908i \(0.676052\pi\)
\(138\) 0 0
\(139\) 9.19615 + 15.9282i 0.780007 + 1.35101i 0.931937 + 0.362621i \(0.118118\pi\)
−0.151929 + 0.988391i \(0.548549\pi\)
\(140\) 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 0.812010 + 0.583644i \(0.198374\pi\)
−0.995043 + 0.0994454i \(0.968293\pi\)
\(150\) 0 0
\(151\) −0.535898 0.535898i −0.0436108 0.0436108i 0.684965 0.728576i \(-0.259817\pi\)
−0.728576 + 0.684965i \(0.759817\pi\)
\(152\) 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 −0.911164 0.412045i \(-0.864815\pi\)
0.995113 + 0.0987406i \(0.0314814\pi\)
\(164\) 0 0
\(165\) −1.48214 + 10.6292i −0.115384 + 0.827483i
\(166\) 0 0
\(167\) 3.47998 + 12.9875i 0.269289 + 1.00500i 0.959573 + 0.281461i \(0.0908192\pi\)
−0.690283 + 0.723539i \(0.742514\pi\)
\(168\) 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 0.979670 + 0.200615i \(0.0642941\pi\)
−0.316097 + 0.948727i \(0.602373\pi\)
\(174\) 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 −0.387084 + 0.922045i \(0.626518\pi\)
−0.604972 + 0.796247i \(0.706816\pi\)
\(180\) 0 0
\(181\) 3.00000i 0.222988i 0.993765 + 0.111494i \(0.0355636\pi\)
−0.993765 + 0.111494i \(0.964436\pi\)
\(182\) 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 −0.340968 0.940075i \(-0.610755\pi\)
0.643645 + 0.765324i \(0.277421\pi\)
\(192\) 0 0
\(193\) 0.133975 0.0358984i 0.00964370 0.00258402i −0.253994 0.967206i \(-0.581744\pi\)
0.263638 + 0.964622i \(0.415078\pi\)
\(194\) 0 0
\(195\) −8.87906 3.10037i −0.635843 0.222022i
\(196\) 0 0
\(197\) 3.97420 1.06488i 0.283150 0.0758697i −0.114449 0.993429i \(-0.536510\pi\)
0.397599 + 0.917559i \(0.369844\pi\)
\(198\) 0 0
\(199\) −11.1962 + 6.46410i −0.793674 + 0.458228i −0.841254 0.540639i \(-0.818182\pi\)
0.0475802 + 0.998867i \(0.484849\pi\)
\(200\) 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 −0.895400 0.445263i \(-0.853110\pi\)
0.833309 + 0.552808i \(0.186444\pi\)
\(212\) 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 −0.705011 0.709196i \(-0.749058\pi\)
0.255960 0.966687i \(-0.417609\pi\)
\(224\) 0 0
\(225\) −5.70625 5.88351i −0.380416 0.392234i
\(226\) 0 0
\(227\) 5.24796 19.5856i 0.348319 1.29994i −0.540367 0.841429i \(-0.681715\pi\)
0.888686 0.458515i \(-0.151619\pi\)
\(228\) 0 0
\(229\) −14.1244 14.1244i −0.933364 0.933364i 0.0645507 0.997914i \(-0.479439\pi\)
−0.997914 + 0.0645507i \(0.979439\pi\)
\(230\) 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 0.887537 0.460737i \(-0.152415\pi\)
−0.460737 + 0.887537i \(0.652415\pi\)
\(240\) 0 0
\(241\) 3.76795 14.0622i 0.242715 0.905825i −0.731803 0.681516i \(-0.761321\pi\)
0.974518 0.224309i \(-0.0720123\pi\)
\(242\) 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 0.881201 0.472741i \(-0.156736\pi\)
−0.850007 + 0.526772i \(0.823402\pi\)
\(252\) 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 0.306916 + 0.951737i \(0.400703\pi\)
−0.977686 + 0.210071i \(0.932630\pi\)
\(258\) 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 −0.231777 0.972769i \(-0.574454\pi\)
−0.958331 + 0.285660i \(0.907787\pi\)
\(264\) 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 −0.0711756 0.997464i \(-0.522675\pi\)
0.828241 + 0.560372i \(0.189342\pi\)
\(270\) 0 0
\(271\) −7.46410 + 2.00000i −0.453412 + 0.121491i −0.478295 0.878199i \(-0.658745\pi\)
0.0248835 + 0.999690i \(0.492079\pi\)
\(272\) 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 0.438013 0.898969i \(-0.355682\pi\)
0.997536 + 0.0701536i \(0.0223490\pi\)
\(278\) 0 0
\(279\) 0.159877 10.4531i 0.00957158 0.625809i
\(280\) 0 0
\(281\) 12.1315 12.1315i 0.723703 0.723703i −0.245655 0.969357i \(-0.579003\pi\)
0.969357 + 0.245655i \(0.0790030\pi\)
\(282\) 0 0
\(283\) 5.70577 + 3.29423i 0.339173 + 0.195822i 0.659906 0.751348i \(-0.270596\pi\)
−0.320733 + 0.947170i \(0.603929\pi\)
\(284\) 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 0.309286 0.950969i \(-0.399910\pi\)
−0.207635 + 0.978206i \(0.566577\pi\)
\(294\) 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 0.425829 0.904803i \(-0.359982\pi\)
−0.904803 + 0.425829i \(0.859982\pi\)
\(308\) 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 0.949960 0.312373i \(-0.101124\pi\)
−0.312373 + 0.949960i \(0.601124\pi\)
\(318\) 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 0.996376 0.0850595i \(-0.0271080\pi\)
0.820357 + 0.571852i \(0.193775\pi\)
\(332\) 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 \(-0.832266\pi\)
0.864344 0.502902i \(-0.167734\pi\)
\(338\) 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 0.0614076 0.998113i \(-0.480441\pi\)
0.895095 + 0.445876i \(0.147108\pi\)
\(348\) 0 0
\(349\) 27.4904 7.36603i 1.47153 0.394294i 0.568072 0.822979i \(-0.307689\pi\)
0.903454 + 0.428684i \(0.141023\pi\)
\(350\) 0 0
\(351\) 6.44593 17.5912i 0.344058 0.938948i
\(352\) 0 0
\(353\) −13.6626 + 3.66088i −0.727186 + 0.194849i −0.603376 0.797457i \(-0.706178\pi\)
−0.123810 + 0.992306i \(0.539511\pi\)
\(354\) 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 −0.0368904 0.999319i \(-0.511745\pi\)
0.999319 + 0.0368904i \(0.0117452\pi\)
\(360\) 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 −0.130723 0.991419i \(-0.541730\pi\)
0.923955 0.382500i \(-0.124937\pi\)
\(368\) 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 0.676125 0.736787i \(-0.263658\pi\)
−0.976139 + 0.217148i \(0.930325\pi\)
\(374\) 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 −0.991809 0.127726i \(-0.959232\pi\)
0.795069 0.606519i \(-0.207435\pi\)
\(380\) 0 0
\(381\) −15.6524 2.18257i −0.801897 0.111816i
\(382\) 0 0
\(383\) −8.51906 + 31.7936i −0.435304 + 1.62458i 0.305035 + 0.952341i \(0.401332\pi\)
−0.740339 + 0.672234i \(0.765335\pi\)
\(384\) 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 0.817096 + 0.576501i \(0.195582\pi\)
−0.995877 + 0.0907168i \(0.971084\pi\)
\(398\) 0 0
\(399\) −1.30703 + 9.37341i −0.0654332 + 0.469258i
\(400\) 0 0
\(401\) 3.22263 + 12.0270i 0.160931 + 0.600601i 0.998524 + 0.0543073i \(0.0172951\pi\)
−0.837594 + 0.546294i \(0.816038\pi\)
\(402\) 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 0.890246 0.455480i \(-0.150532\pi\)
0.543236 + 0.839580i \(0.317199\pi\)
\(410\) 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 0.285208 0.958466i \(-0.407937\pi\)
−0.687452 + 0.726230i \(0.741271\pi\)
\(420\) 0 0
\(421\) −7.83013 + 7.83013i −0.381617 + 0.381617i −0.871685 0.490067i \(-0.836972\pi\)
0.490067 + 0.871685i \(0.336972\pi\)
\(422\) 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 −0.986800 0.161944i \(-0.948224\pi\)
−0.773622 + 0.633648i \(0.781557\pi\)
\(432\) 0 0
\(433\) −26.8923 + 15.5263i −1.29236 + 0.746145i −0.979072 0.203512i \(-0.934764\pi\)
−0.313289 + 0.949658i \(0.601431\pi\)
\(434\) 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 0.473567 0.880758i \(-0.342966\pi\)
−0.525975 + 0.850500i \(0.676300\pi\)
\(440\) 0 0
\(441\) 14.5466 3.66025i 0.692694 0.174298i
\(442\) 0 0
\(443\) 11.2195i 0.533054i 0.963827 + 0.266527i \(0.0858762\pi\)
−0.963827 + 0.266527i \(0.914124\pi\)
\(444\) 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 0.695165 0.718851i \(-0.255331\pi\)
0.242605 + 0.970125i \(0.421998\pi\)
\(450\) 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 0.938283 0.345868i \(-0.112416\pi\)
−0.985511 + 0.169611i \(0.945749\pi\)
\(458\) 0 0
\(459\) −26.0314 + 2.82130i −1.21504 + 0.131687i
\(460\) 0 0
\(461\) 5.50531 20.5461i 0.256408 0.956927i −0.710894 0.703299i \(-0.751710\pi\)
0.967302 0.253628i \(-0.0816238\pi\)
\(462\) 0 0
\(463\) −23.0526 23.0526i −1.07134 1.07134i −0.997251 0.0740918i \(-0.976394\pi\)
−0.0740918 0.997251i \(-0.523606\pi\)
\(464\) 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 0.974241 + 0.225510i \(0.0724049\pi\)
−0.730962 + 0.682418i \(0.760928\pi\)
\(480\) 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 0.130584 0.991437i \(-0.458315\pi\)
−0.382630 + 0.923902i \(0.624982\pi\)
\(488\) 0 0
\(489\) −0.881808 7.11819i −0.0398767 0.321896i
\(490\) 0 0
\(491\) 14.2612 24.7012i 0.643600 1.11475i −0.341023 0.940055i \(-0.610773\pi\)
0.984623 0.174693i \(-0.0558934\pi\)
\(492\) 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 −0.649798 0.760107i \(-0.725147\pi\)
0.760107 + 0.649798i \(0.225147\pi\)
\(500\) 0 0
\(501\) 14.0354 + 18.5839i 0.627057 + 0.830266i
\(502\) 0 0
\(503\) −2.83286 + 1.63555i −0.126311 + 0.0729256i −0.561824 0.827257i \(-0.689900\pi\)
0.435513 + 0.900182i \(0.356567\pi\)
\(504\) 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 −0.558530 0.829484i \(-0.688634\pi\)
−0.0689588 + 0.997620i \(0.521968\pi\)
\(510\) 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 \(-0.982618\pi\)
0.998509 0.0545785i \(-0.0173815\pi\)
\(522\) 0 0
\(523\) −19.4904 + 33.7583i −0.852255 + 1.47615i 0.0269137 + 0.999638i \(0.491432\pi\)
−0.879169 + 0.476511i \(0.841901\pi\)
\(524\) 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 0.379681 0.925118i \(-0.376034\pi\)
−0.925118 + 0.379681i \(0.876034\pi\)
\(542\) 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 −0.951883 0.306462i \(-0.900855\pi\)
0.671123 0.741346i \(-0.265812\pi\)
\(558\) 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 0.952456 0.304675i \(-0.0985479\pi\)
−0.740085 + 0.672514i \(0.765215\pi\)
\(564\) 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 −0.892939 0.450178i \(-0.851361\pi\)
0.836335 + 0.548219i \(0.184694\pi\)
\(570\) 0 0
\(571\) 1.94744i 0.0814979i −0.999169 0.0407489i \(-0.987026\pi\)
0.999169 0.0407489i \(-0.0129744\pi\)
\(572\) 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 −0.998088 0.0618016i \(-0.980315\pi\)
0.0618016 + 0.998088i \(0.480315\pi\)
\(578\) 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 0.133164 0.991094i \(-0.457486\pi\)
0.610871 + 0.791730i \(0.290819\pi\)
\(588\) 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 −0.887119 0.461541i \(-0.847297\pi\)
0.461541 + 0.887119i \(0.347297\pi\)
\(594\) 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 \(-0.860822\pi\)
0.905924 0.423441i \(-0.139178\pi\)
\(600\) 0 0
\(601\) −11.7942 + 20.4282i −0.481097 + 0.833284i −0.999765 0.0216919i \(-0.993095\pi\)
0.518668 + 0.854976i \(0.326428\pi\)
\(602\) 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 0.864028 0.503444i \(-0.167934\pi\)
−0.868009 + 0.496549i \(0.834600\pi\)
\(608\) 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 −0.677035 0.735951i \(-0.736735\pi\)
0.218354 0.975870i \(-0.429931\pi\)
\(614\) 0 0
\(615\) 14.5198 + 2.02463i 0.585494 + 0.0816411i
\(616\) 0 0
\(617\) 4.78173 17.8457i 0.192505 0.718439i −0.800393 0.599475i \(-0.795376\pi\)
0.992899 0.118964i \(-0.0379573\pi\)
\(618\) 0 0
\(619\) 31.6603 + 31.6603i 1.27253 + 1.27253i 0.944755 + 0.327778i \(0.106300\pi\)
0.327778 + 0.944755i \(0.393700\pi\)
\(620\) 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 0.752912 + 0.658121i \(0.228648\pi\)
−0.981102 + 0.193493i \(0.938018\pi\)
\(632\) 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 0.833008 + 0.553261i \(0.186617\pi\)
0.0626345 + 0.998037i \(0.480050\pi\)
\(642\) 0 0
\(643\) −7.00000 1.87564i −0.276053 0.0739682i 0.118136 0.992997i \(-0.462308\pi\)
−0.394190 + 0.919029i \(0.628975\pi\)
\(644\) 0 0
\(645\) 5.68503 0.704266i 0.223848 0.0277305i
\(646\) 0 0
\(647\) 8.23373 14.2612i 0.323701 0.560667i −0.657547 0.753413i \(-0.728406\pi\)
0.981249 + 0.192746i \(0.0617394\pi\)
\(648\) 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 0.327290 0.944924i \(-0.393865\pi\)
−0.654683 + 0.755904i \(0.727198\pi\)
\(654\) 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 −0.881967 0.471311i \(-0.843781\pi\)
−0.0328158 + 0.999461i \(0.510447\pi\)
\(660\) 0 0
\(661\) 9.42820 2.52628i 0.366715 0.0982609i −0.0707559 0.997494i \(-0.522541\pi\)
0.437470 + 0.899233i \(0.355874\pi\)
\(662\) 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 −0.429082 0.903265i \(-0.641163\pi\)
−0.996792 + 0.0800364i \(0.974496\pi\)
\(674\) 0 0
\(675\) −12.9875 5.73205i −0.499888 0.220627i
\(676\) 0 0
\(677\) 9.66040i 0.371279i 0.982618 + 0.185640i \(0.0594357\pi\)
−0.982618 + 0.185640i \(0.940564\pi\)
\(678\) 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 0.980736 0.195338i \(-0.0625804\pi\)
0.751673 + 0.659536i \(0.229247\pi\)
\(684\) 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 −0.994470 0.105025i \(-0.966508\pi\)
0.808723 0.588189i \(-0.200159\pi\)
\(692\) 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 −0.999211 0.0397068i \(-0.987358\pi\)
0.885196 + 0.465219i \(0.154024\pi\)
\(710\) 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 0.926577 0.376106i \(-0.122737\pi\)
−0.789005 + 0.614386i \(0.789404\pi\)
\(720\) 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 \(0.117877\pi\)
−0.932211 + 0.361916i \(0.882123\pi\)
\(728\) 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 −0.821108 0.570773i \(-0.806644\pi\)
0.570773 + 0.821108i \(0.306644\pi\)
\(734\) 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 −0.0483378 0.998831i \(-0.515392\pi\)
0.457554 + 0.889182i \(0.348726\pi\)
\(740\) 0 0
\(741\) 23.7052 4.50141i 0.870833 0.165363i
\(742\) 0 0
\(743\) −8.51906 + 2.28268i −0.312534 + 0.0837432i −0.411677 0.911330i \(-0.635057\pi\)
0.0991426 + 0.995073i \(0.468390\pi\)
\(744\) 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 0.927705 0.373313i \(-0.121778\pi\)
0.140554 + 0.990073i \(0.455112\pi\)
\(752\) 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 −0.977267 0.212014i \(-0.931998\pi\)
0.672243 + 0.740331i \(0.265331\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −17.7412 4.75374i −0.643118 0.172323i −0.0775029 0.996992i \(-0.524695\pi\)
−0.565616 + 0.824669i \(0.691361\pi\)
\(762\) 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 −0.829238 0.558895i \(-0.811225\pi\)
0.438694 0.898636i \(-0.355441\pi\)
\(770\) 0 0
\(771\) −5.14442 + 36.8935i −0.185272 + 1.32869i
\(772\) 0 0
\(773\) −11.1430 + 41.5864i −0.400787 + 1.49576i 0.410908 + 0.911677i \(0.365212\pi\)
−0.811695 + 0.584081i \(0.801455\pi\)
\(774\) 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 0.846190 + 0.532881i \(0.178891\pi\)
−0.999263 + 0.0383938i \(0.987776\pi\)
\(788\) 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 + 0.0664143i