Properties

Label 624.2.cn.c.305.1
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 305.1
Root \(0.500000 - 0.564882i\) of defining polynomial
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.c.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.239203 - 1.71545i) q^{3} +(1.06488 + 1.06488i) q^{5} +(-0.366025 + 1.36603i) q^{7} +(-2.88556 + 0.820682i) q^{9} +O(q^{10})\) \(q+(-0.239203 - 1.71545i) q^{3} +(1.06488 + 1.06488i) q^{5} +(-0.366025 + 1.36603i) q^{7} +(-2.88556 + 0.820682i) q^{9} +(1.06488 + 3.97420i) q^{11} +(3.59808 - 0.232051i) q^{13} +(1.57203 - 2.08148i) q^{15} +(2.51954 + 4.36397i) q^{17} +(3.73205 + 1.00000i) q^{19} +(2.43091 + 0.301143i) q^{21} -2.73205i q^{25} +(2.09808 + 4.75374i) q^{27} +(-6.20840 - 3.58442i) q^{29} +(2.46410 - 2.46410i) q^{31} +(6.56283 - 2.77739i) q^{33} +(-1.84443 + 1.06488i) q^{35} +(-5.23205 + 1.40192i) q^{37} +(-1.25874 - 6.11683i) q^{39} +(5.42885 - 1.45466i) q^{41} +(-1.90192 + 1.09808i) q^{43} +(-3.94672 - 2.19886i) q^{45} +(4.25953 - 4.25953i) q^{47} +(4.33013 + 2.50000i) q^{49} +(6.88351 - 5.36603i) q^{51} +0.779548i q^{53} +(-3.09808 + 5.36603i) q^{55} +(0.822738 - 6.64136i) q^{57} +(2.90931 + 0.779548i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-0.0648824 - 4.24214i) q^{63} +(4.07863 + 3.58442i) q^{65} +(1.53590 + 5.73205i) q^{67} +(0.779548 - 2.90931i) q^{71} +(-0.901924 - 0.901924i) q^{73} +(-4.68671 + 0.653513i) q^{75} -5.81863 q^{77} -2.00000 q^{79} +(7.65296 - 4.73626i) q^{81} +(-2.90931 - 2.90931i) q^{83} +(-1.96410 + 7.33013i) q^{85} +(-4.66384 + 11.5076i) q^{87} +(-2.41510 - 9.01327i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(-4.81647 - 3.63763i) q^{93} +(2.90931 + 5.03908i) q^{95} +(1.63397 + 0.437822i) q^{97} +(-6.33434 - 10.5939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} + 4q^{7} + 4q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 4q^{7} + 4q^{9} + 8q^{13} + 14q^{15} + 16q^{19} + 4q^{21} - 4q^{27} - 8q^{31} + 16q^{33} - 28q^{37} + 14q^{39} - 36q^{43} - 20q^{45} - 4q^{55} + 16q^{57} + 28q^{61} + 8q^{63} + 40q^{67} - 28q^{73} - 12q^{75} - 16q^{79} + 4q^{81} + 12q^{85} + 34q^{87} - 8q^{91} + 4q^{93} + 20q^{97} - 40q^{99} + O(q^{100}) \)

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
\(3\) −0.239203 1.71545i −0.138104 0.990418i
\(4\) 0 0
\(5\) 1.06488 + 1.06488i 0.476230 + 0.476230i 0.903924 0.427694i \(-0.140674\pi\)
−0.427694 + 0.903924i \(0.640674\pi\)
\(6\) 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
\(9\) −2.88556 + 0.820682i −0.961855 + 0.273561i
\(10\) 0 0
\(11\) 1.06488 + 3.97420i 0.321074 + 1.19826i 0.918200 + 0.396117i \(0.129643\pi\)
−0.597126 + 0.802148i \(0.703691\pi\)
\(12\) 0 0
\(13\) 3.59808 0.232051i 0.997927 0.0643593i
\(14\) 0 0
\(15\) 1.57203 2.08148i 0.405897 0.537436i
\(16\) 0 0
\(17\) 2.51954 + 4.36397i 0.611078 + 1.05842i 0.991059 + 0.133424i \(0.0425971\pi\)
−0.379981 + 0.924994i \(0.624070\pi\)
\(18\) 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
\(21\) 2.43091 + 0.301143i 0.530468 + 0.0657148i
\(22\) 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 −0.203286 0.979119i \(-0.565162\pi\)
−0.949585 + 0.313509i \(0.898495\pi\)
\(30\) 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
\(33\) 6.56283 2.77739i 1.14244 0.483482i
\(34\) 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
\(39\) −1.25874 6.11683i −0.201560 0.979476i
\(40\) 0 0
\(41\) 5.42885 1.45466i 0.847844 0.227179i 0.191361 0.981520i \(-0.438710\pi\)
0.656483 + 0.754341i \(0.272043\pi\)
\(42\) 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
\(45\) −3.94672 2.19886i −0.588342 0.327786i
\(46\) 0 0
\(47\) 4.25953 4.25953i 0.621316 0.621316i −0.324552 0.945868i \(-0.605213\pi\)
0.945868 + 0.324552i \(0.105213\pi\)
\(48\) 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
\(57\) 0.822738 6.64136i 0.108974 0.879670i
\(58\) 0 0
\(59\) 2.90931 + 0.779548i 0.378760 + 0.101489i 0.443176 0.896435i \(-0.353852\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(60\) 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
\(63\) −0.0648824 4.24214i −0.00817442 0.534460i
\(64\) 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 −0.904116 0.427288i \(-0.859469\pi\)
0.996631 + 0.0820158i \(0.0261358\pi\)
\(72\) 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
\(75\) −4.68671 + 0.653513i −0.541174 + 0.0754612i
\(76\) 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
\(81\) 7.65296 4.73626i 0.850329 0.526251i
\(82\) 0 0
\(83\) −2.90931 2.90931i −0.319339 0.319339i 0.529174 0.848513i \(-0.322502\pi\)
−0.848513 + 0.529174i \(0.822502\pi\)
\(84\) 0 0
\(85\) −1.96410 + 7.33013i −0.213037 + 0.795064i
\(86\) 0 0
\(87\) −4.66384 + 11.5076i −0.500017 + 1.23375i
\(88\) 0 0
\(89\) −2.41510 9.01327i −0.256000 0.955405i −0.967531 0.252751i \(-0.918665\pi\)
0.711531 0.702654i \(-0.248002\pi\)
\(90\) 0 0
\(91\) −1.00000 + 5.00000i −0.104828 + 0.524142i
\(92\) 0 0
\(93\) −4.81647 3.63763i −0.499445 0.377205i
\(94\) 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
\(99\) −6.33434 10.5939i −0.636625 1.06472i
\(100\) 0 0
\(101\) −3.01375 + 5.21997i −0.299880 + 0.519407i −0.976108 0.217285i \(-0.930280\pi\)
0.676229 + 0.736692i \(0.263613\pi\)
\(102\) 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 \(-0.962232\pi\)
−0.598999 0.800749i \(-0.704435\pi\)
\(108\) 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
\(111\) 3.65646 + 8.64000i 0.347055 + 0.820072i
\(112\) 0 0
\(113\) −8.90883 + 5.14352i −0.838073 + 0.483861i −0.856609 0.515967i \(-0.827433\pi\)
0.0185360 + 0.999828i \(0.494099\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −10.1920 + 3.62247i −0.942254 + 0.334898i
\(118\) 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
\(123\) −3.79399 8.96499i −0.342093 0.808346i
\(124\) 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 \(0.112877\pi\)
−0.937781 + 0.347227i \(0.887123\pi\)
\(132\) 0 0
\(133\) −2.73205 + 4.73205i −0.236899 + 0.410321i
\(134\) 0 0
\(135\) −2.82797 + 7.29638i −0.243393 + 0.627973i
\(136\) 0 0
\(137\) 6.49373 + 1.73999i 0.554797 + 0.148657i 0.525315 0.850908i \(-0.323948\pi\)
0.0294822 + 0.999565i \(0.490614\pi\)
\(138\) 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
\(141\) −8.32592 6.28814i −0.701169 0.529557i
\(142\) 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
\(147\) 3.25286 8.02614i 0.268291 0.661985i
\(148\) 0 0
\(149\) 2.23420 8.33816i 0.183033 0.683089i −0.812010 0.583644i \(-0.801626\pi\)
0.995043 0.0994454i \(-0.0317068\pi\)
\(150\) 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
\(153\) −10.8517 10.5248i −0.877310 0.850878i
\(154\) 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
\(159\) 1.33728 0.186470i 0.106053 0.0147880i
\(160\) 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
\(165\) 9.94624 + 4.03104i 0.774313 + 0.313816i
\(166\) 0 0
\(167\) −3.47998 12.9875i −0.269289 1.00500i −0.959573 0.281461i \(-0.909181\pi\)
0.690283 0.723539i \(-0.257486\pi\)
\(168\) 0 0
\(169\) 12.8923 1.66987i 0.991716 0.128452i
\(170\) 0 0
\(171\) −11.5898 + 0.177262i −0.886291 + 0.0135556i
\(172\) 0 0
\(173\) −8.72794 15.1172i −0.663573 1.14934i −0.979670 0.200615i \(-0.935706\pi\)
0.316097 0.948727i \(-0.397627\pi\)
\(174\) 0 0
\(175\) 3.73205 + 1.00000i 0.282117 + 0.0755929i
\(176\) 0 0
\(177\) 0.641364 5.17726i 0.0482078 0.389147i
\(178\) 0 0
\(179\) 13.2728 22.9892i 0.992056 1.71829i 0.387084 0.922045i \(-0.373482\pi\)
0.604972 0.796247i \(-0.293184\pi\)
\(180\) 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
\(189\) −7.26168 + 1.12603i −0.528210 + 0.0819070i
\(190\) 0 0
\(191\) −4.18307 + 2.41510i −0.302677 + 0.174750i −0.643645 0.765324i \(-0.722579\pi\)
0.340968 + 0.940075i \(0.389245\pi\)
\(192\) 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
\(195\) 5.17329 7.85411i 0.370467 0.562445i
\(196\) 0 0
\(197\) −3.97420 + 1.06488i −0.283150 + 0.0758697i −0.397599 0.917559i \(-0.630156\pi\)
0.114449 + 0.993429i \(0.463490\pi\)
\(198\) 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
\(201\) 9.46568 4.00588i 0.667657 0.282553i
\(202\) 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
\(213\) −5.17726 0.641364i −0.354740 0.0439455i
\(214\) 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
\(219\) −1.33147 + 1.76295i −0.0899722 + 0.119129i
\(220\) 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
\(225\) 2.24214 + 7.88351i 0.149476 + 0.525567i
\(226\) 0 0
\(227\) −5.24796 + 19.5856i −0.348319 + 1.29994i 0.540367 + 0.841429i \(0.318285\pi\)
−0.888686 + 0.458515i \(0.848381\pi\)
\(228\) 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
\(231\) 1.39183 + 9.98158i 0.0915757 + 0.656740i
\(232\) 0 0
\(233\) 17.4559 1.14357 0.571786 0.820403i \(-0.306251\pi\)
0.571786 + 0.820403i \(0.306251\pi\)
\(234\) 0 0
\(235\) 9.07180 0.591779
\(236\) 0 0
\(237\) 0.478405 + 3.43091i 0.0310757 + 0.222861i
\(238\) 0 0
\(239\) −6.59817 6.59817i −0.426800 0.426800i 0.460737 0.887537i \(-0.347585\pi\)
−0.887537 + 0.460737i \(0.847585\pi\)
\(240\) 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
\(243\) −9.95544 11.9954i −0.638642 0.769504i
\(244\) 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
\(249\) −4.29488 + 5.68671i −0.272177 + 0.360380i
\(250\) 0 0
\(251\) −0.494214 0.856003i −0.0311945 0.0540304i 0.850007 0.526772i \(-0.176598\pi\)
−0.881201 + 0.472741i \(0.843264\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 13.0443 + 1.61594i 0.816867 + 0.101194i
\(256\) 0 0
\(257\) 10.7533 18.6252i 0.670770 1.16181i −0.306916 0.951737i \(-0.599297\pi\)
0.977686 0.210071i \(-0.0673696\pi\)
\(258\) 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 \(-0.0922127\pi\)
0.231777 + 0.972769i \(0.425546\pi\)
\(264\) 0 0
\(265\) −0.830127 + 0.830127i −0.0509943 + 0.0509943i
\(266\) 0 0
\(267\) −14.8842 + 6.29899i −0.910896 + 0.385492i
\(268\) 0 0
\(269\) −12.4168 + 7.16884i −0.757066 + 0.437092i −0.828241 0.560372i \(-0.810658\pi\)
0.0711756 + 0.997464i \(0.477325\pi\)
\(270\) 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
\(273\) 8.81647 + 0.519441i 0.533597 + 0.0314380i
\(274\) 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
\(279\) −5.08808 + 9.13257i −0.304615 + 0.546752i
\(280\) 0 0
\(281\) −12.1315 + 12.1315i −0.723703 + 0.723703i −0.969357 0.245655i \(-0.920997\pi\)
0.245655 + 0.969357i \(0.420997\pi\)
\(282\) 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
\(291\) 0.360213 2.90774i 0.0211161 0.170455i
\(292\) 0 0
\(293\) −1.73999 0.466229i −0.101651 0.0272374i 0.207635 0.978206i \(-0.433423\pi\)
−0.309286 + 0.950969i \(0.600090\pi\)
\(294\) 0 0
\(295\) 2.26795 + 3.92820i 0.132045 + 0.228709i
\(296\) 0 0
\(297\) −16.6581 + 13.4003i −0.966601 + 0.777567i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −0.803848 3.00000i −0.0463330 0.172917i
\(302\) 0 0
\(303\) 9.67552 + 3.92132i 0.555844 + 0.225274i
\(304\) 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
\(309\) −11.8850 + 1.65724i −0.676115 + 0.0942773i
\(310\) 0 0
\(311\) −10.0782 −0.571480 −0.285740 0.958307i \(-0.592239\pi\)
−0.285740 + 0.958307i \(0.592239\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) 4.44829 4.58648i 0.250633 0.258419i
\(316\) 0 0
\(317\) −11.3519 11.3519i −0.637587 0.637587i 0.312373 0.949960i \(-0.398876\pi\)
−0.949960 + 0.312373i \(0.898876\pi\)
\(318\) 0 0
\(319\) 7.63397 28.4904i 0.427421 1.59516i
\(320\) 0 0
\(321\) −12.3706 + 30.5234i −0.690460 + 1.70365i
\(322\) 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
\(327\) 25.7939 + 19.4808i 1.42641 + 1.07729i
\(328\) 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
\(333\) 13.9469 8.33919i 0.764285 0.456985i
\(334\) 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 −0.895095 0.445876i \(-0.852892\pi\)
−0.0614076 + 0.998113i \(0.519559\pi\)
\(348\) 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
\(351\) 8.65215 + 16.6175i 0.461818 + 0.886975i
\(352\) 0 0
\(353\) 13.6626 3.66088i 0.727186 0.194849i 0.123810 0.992306i \(-0.460489\pi\)
0.603376 + 0.797457i \(0.293822\pi\)
\(354\) 0 0
\(355\) 3.92820 2.26795i 0.208487 0.120370i
\(356\) 0 0
\(357\) 4.81059 + 11.3671i 0.254603 + 0.601613i
\(358\) 0 0
\(359\) −18.2354 + 18.2354i −0.962429 + 0.962429i −0.999319 0.0368904i \(-0.988255\pi\)
0.0368904 + 0.999319i \(0.488255\pi\)
\(360\) 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
\(369\) −14.4715 + 8.65286i −0.753356 + 0.450450i
\(370\) 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
\(375\) −16.0941 12.1550i −0.831096 0.627684i
\(376\) 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
\(381\) −5.93605 + 14.6467i −0.304113 + 0.750372i
\(382\) 0 0
\(383\) 8.51906 31.7936i 0.435304 1.62458i −0.305035 0.952341i \(-0.598668\pi\)
0.740339 0.672234i \(-0.234665\pi\)
\(384\) 0 0
\(385\) −6.19615 6.19615i −0.315785 0.315785i
\(386\) 0 0
\(387\) 4.58695 4.72944i 0.233168 0.240411i
\(388\) 0 0
\(389\) 22.4950 1.14054 0.570270 0.821457i \(-0.306839\pi\)
0.570270 + 0.821457i \(0.306839\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 13.6351 1.90128i 0.687800 0.0959066i
\(394\) 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
\(399\) 8.77113 + 3.55479i 0.439106 + 0.177962i
\(400\) 0 0
\(401\) −3.22263 12.0270i −0.160931 0.600601i −0.998524 0.0543073i \(-0.982705\pi\)
0.837594 0.546294i \(-0.183962\pi\)
\(402\) 0 0
\(403\) 8.29423 9.43782i 0.413165 0.470131i
\(404\) 0 0
\(405\) 13.1931 + 3.10594i 0.655569 + 0.154336i
\(406\) 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
\(411\) 1.43156 11.5559i 0.0706135 0.570011i
\(412\) 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 \(-0.258729\pi\)
−0.285208 + 0.958466i \(0.592063\pi\)
\(420\) 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
\(423\) −8.79543 + 15.7869i −0.427648 + 0.767584i
\(424\) 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
\(429\) 22.9691 11.5162i 1.10896 0.556007i
\(430\) 0 0
\(431\) 36.5473 9.79282i 1.76042 0.471704i 0.773622 0.633648i \(-0.218443\pi\)
0.986800 + 0.161944i \(0.0517764\pi\)
\(432\) 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
\(435\) −17.2207 + 7.28782i −0.825670 + 0.349424i
\(436\) 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 \(-0.914124\pi\)
0.963827 0.266527i \(-0.0858762\pi\)
\(444\) 0 0
\(445\) 7.02628 12.1699i 0.333078 0.576907i
\(446\) 0 0
\(447\) −14.8382 1.83816i −0.701821 0.0869422i
\(448\) 0 0
\(449\) −19.8710 5.32441i −0.937769 0.251275i −0.242605 0.970125i \(-0.578002\pi\)
−0.695165 + 0.718851i \(0.744669\pi\)
\(450\) 0 0
\(451\) 11.5622 + 20.0263i 0.544442 + 0.943001i
\(452\) 0 0
\(453\) −0.791121 + 1.04750i −0.0371701 + 0.0492157i
\(454\) 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
\(459\) −15.4590 + 21.1332i −0.721565 + 0.986412i
\(460\) 0 0
\(461\) −5.50531 + 20.5461i −0.256408 + 0.956927i 0.710894 + 0.703299i \(0.248290\pi\)
−0.967302 + 0.253628i \(0.918376\pi\)
\(462\) 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
\(465\) −1.25532 9.00263i −0.0582143 0.417487i
\(466\) 0 0
\(467\) 19.1679 0.886984 0.443492 0.896278i \(-0.353739\pi\)
0.443492 + 0.896278i \(0.353739\pi\)
\(468\) 0 0
\(469\) −8.39230 −0.387521
\(470\) 0 0
\(471\) 1.14909 + 8.24078i 0.0529474 + 0.379715i
\(472\) 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
\(477\) −0.639761 2.24944i −0.0292926 0.102995i
\(478\) 0 0
\(479\) −5.32441 19.8710i −0.243279 0.907928i −0.974241 0.225510i \(-0.927595\pi\)
0.730962 0.682418i \(-0.239072\pi\)
\(480\) 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
\(489\) −7.11819 0.881808i −0.321896 0.0398767i
\(490\) 0 0
\(491\) −14.2612 + 24.7012i −0.643600 + 1.11475i 0.341023 + 0.940055i \(0.389227\pi\)
−0.984623 + 0.174693i \(0.944107\pi\)
\(492\) 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
\(501\) −21.4470 + 9.07638i −0.958181 + 0.405503i
\(502\) 0 0
\(503\) 2.83286 1.63555i 0.126311 0.0729256i −0.435513 0.900182i \(-0.643433\pi\)
0.561824 + 0.827257i \(0.310100\pi\)
\(504\) 0 0
\(505\) −8.76795 + 2.34936i −0.390169 + 0.104545i
\(506\) 0 0
\(507\) −5.94846 21.7167i −0.264180 0.964473i
\(508\) 0 0
\(509\) 14.1568 3.79330i 0.627489 0.168135i 0.0689588 0.997620i \(-0.478032\pi\)
0.558530 + 0.829484i \(0.311366\pi\)
\(510\) 0 0
\(511\) 1.56218 0.901924i 0.0691067 0.0398988i
\(512\) 0 0
\(513\) 3.07638 + 19.8393i 0.135826 + 0.875926i
\(514\) 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 0.0269137 + 0.999638i \(0.491432\pi\)
−0.879169 + 0.476511i \(0.841901\pi\)
\(524\) 0 0
\(525\) 0.822738 6.64136i 0.0359072 0.289853i
\(526\) 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
\(531\) −9.03477 + 0.138184i −0.392076 + 0.00599669i
\(532\) 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
\(537\) −42.6117 17.2698i −1.83883 0.745247i
\(538\) 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
\(543\) 5.14636 0.717608i 0.220852 0.0307955i
\(544\) 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
\(549\) −15.0746 14.6204i −0.643368 0.623984i
\(550\) 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
\(555\) −5.30689 + 13.0943i −0.225265 + 0.555821i
\(556\) 0 0
\(557\) 6.62616 + 24.7292i 0.280759 + 1.04781i 0.951883 + 0.306462i \(0.0991454\pi\)
−0.671123 + 0.741346i \(0.734188\pi\)
\(558\) 0 0
\(559\) −6.58846 + 4.39230i −0.278662 + 0.185775i
\(560\) 0 0
\(561\) 28.6558 + 21.6422i 1.20985 + 0.913735i
\(562\) 0 0
\(563\) −5.03908 8.72794i −0.212372 0.367839i 0.740085 0.672514i \(-0.234785\pi\)
−0.952456 + 0.304675i \(0.901452\pi\)
\(564\) 0 0
\(565\) −14.9641 4.00962i −0.629544 0.168686i
\(566\) 0 0
\(567\) 3.66867 + 12.1877i 0.154070 + 0.511837i
\(568\) 0 0
\(569\) 1.35022 2.33864i 0.0566040 0.0980411i −0.836335 0.548219i \(-0.815306\pi\)
0.892939 + 0.450178i \(0.148639\pi\)
\(570\) 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
\(579\) −0.0936291 0.221240i −0.00389109 0.00919443i
\(580\) 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
\(585\) −14.7108 6.99582i −0.608218 0.289241i
\(586\) 0 0
\(587\) −18.0265 + 4.83020i −0.744035 + 0.199364i −0.610871 0.791730i \(-0.709181\pi\)
−0.133164 + 0.991094i \(0.542514\pi\)
\(588\) 0 0
\(589\) 11.6603 6.73205i 0.480452 0.277389i
\(590\) 0 0
\(591\) 2.77739 + 6.56283i 0.114247 + 0.269959i
\(592\) 0 0
\(593\) 10.3635 10.3635i 0.425578 0.425578i −0.461541 0.887119i \(-0.652703\pi\)
0.887119 + 0.461541i \(0.152703\pi\)
\(594\) 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 −0.999765 0.0216919i \(-0.993095\pi\)
0.518668 + 0.854976i \(0.326428\pi\)
\(602\) 0 0
\(603\) −9.13612 15.2797i −0.372052 0.622238i
\(604\) 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
\(609\) −14.0126 10.5830i −0.567820 0.428845i
\(610\) 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
\(615\) 5.50650 13.5868i 0.222044 0.547873i
\(616\) 0 0
\(617\) −4.78173 + 17.8457i −0.192505 + 0.718439i 0.800393 + 0.599475i \(0.204624\pi\)
−0.992899 + 0.118964i \(0.962043\pi\)
\(618\) 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
\(627\) 27.2702 3.80255i 1.08907 0.151859i
\(628\) 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
\(633\) 2.89559 + 1.17353i 0.115089 + 0.0466437i
\(634\) 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
\(639\) 0.138184 + 9.03477i 0.00546649 + 0.357410i
\(640\) 0 0
\(641\) −22.6758 39.2757i −0.895642 1.55130i −0.833008 0.553261i \(-0.813383\pi\)
−0.0626345 0.998037i \(-0.519950\pi\)
\(642\) 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
\(645\) −0.704266 + 5.68503i −0.0277305 + 0.223848i
\(646\) 0 0
\(647\) −8.23373 + 14.2612i −0.323701 + 0.560667i −0.981249 0.192746i \(-0.938261\pi\)
0.657547 + 0.753413i \(0.271594\pi\)
\(648\) 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 \(-0.272802\pi\)
−0.327290 + 0.944924i \(0.606135\pi\)
\(654\) 0 0
\(655\) −8.46410 + 8.46410i −0.330720 + 0.330720i
\(656\) 0 0
\(657\) 3.34275 + 1.86237i 0.130413 + 0.0726578i
\(658\) 0 0
\(659\) 23.4834 13.5581i 0.914783 0.528150i 0.0328158 0.999461i \(-0.489553\pi\)
0.881967 + 0.471311i \(0.156219\pi\)
\(660\) 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
\(663\) 23.5222 20.9047i 0.913526 0.811871i
\(664\) 0 0
\(665\) −7.94839 + 2.12976i −0.308225 + 0.0825887i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −41.3274 + 17.4898i −1.59781 + 0.676194i
\(670\) 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 \(-0.940564\pi\)
0.982618 0.185640i \(-0.0594357\pi\)
\(678\) 0 0
\(679\) −1.19615 + 2.07180i −0.0459041 + 0.0795083i
\(680\) 0 0
\(681\) 34.8536 + 4.31769i 1.33559 + 0.165454i
\(682\) 0 0
\(683\) −45.2752 12.1315i −1.73241 0.464198i −0.751673 0.659536i \(-0.770753\pi\)
−0.980736 + 0.195338i \(0.937420\pi\)
\(684\) 0 0
\(685\) 5.06218 + 8.76795i 0.193416 + 0.335006i
\(686\) 0 0
\(687\) −20.8511 + 27.6083i −0.795519 + 1.05332i
\(688\) 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
\(693\) 16.7900 4.77524i 0.637800 0.181396i
\(694\) 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
\(699\) −4.17549 29.9448i −0.157932 1.13261i
\(700\) 0 0
\(701\) 12.7786 0.482641 0.241320 0.970446i \(-0.422420\pi\)
0.241320 + 0.970446i \(0.422420\pi\)
\(702\) 0 0
\(703\) −20.9282 −0.789322
\(704\) 0 0
\(705\) −2.17000 15.5622i −0.0817268 0.586108i
\(706\) 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
\(711\) 5.77113 1.64136i 0.216434 0.0615559i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −9.90192 + 20.0263i −0.370311 + 0.748940i
\(716\) 0 0
\(717\) −9.74056 + 12.8972i −0.363768 + 0.481653i
\(718\) 0 0
\(719\) −3.68886 6.38929i −0.137571 0.238280i 0.789005 0.614386i \(-0.210596\pi\)
−0.926577 + 0.376106i \(0.877263\pi\)
\(720\) 0 0
\(721\) 9.46410 + 2.53590i 0.352462 + 0.0944418i
\(722\) 0 0
\(723\) −25.0243 3.10003i −0.930665 0.115292i
\(724\) 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
\(735\) 12.0108 5.08298i 0.443025 0.187489i
\(736\) 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
\(741\) 1.41914 24.0870i 0.0521334 0.884860i
\(742\) 0 0
\(743\) 8.51906 2.28268i 0.312534 0.0837432i −0.0991426 0.995073i \(-0.531610\pi\)
0.411677 + 0.911330i \(0.364943\pi\)
\(744\) 0 0
\(745\) 11.2583 6.50000i 0.412473 0.238142i
\(746\) 0 0
\(747\) 10.7826 + 6.00739i 0.394516 + 0.219799i
\(748\) 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 0.565616 0.824669i \(-0.308639\pi\)
0.0775029 + 0.996992i \(0.475305\pi\)
\(762\) 0 0
\(763\) −13.1962 22.8564i −0.477733 0.827457i
\(764\) 0 0
\(765\) −0.348161 22.7635i −0.0125878 0.823014i
\(766\) 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
\(771\) −34.5229 13.9915i −1.24331 0.503893i
\(772\) 0 0
\(773\) 11.1430 41.5864i 0.400787 1.49576i −0.410908 0.911677i \(-0.634788\pi\)
0.811695 0.584081i \(-0.198545\pi\)
\(774\) 0 0
\(775\) −6.73205 6.73205i −0.241822 0.241822i
\(776\) 0 0
\(777\) −13.1408 + 1.83235i −0.471424 + 0.0657353i
\(778\) 0 0
\(779\) 21.7154 0.778035
\(780\) 0 0
\(781\) 12.3923 0.443432
\(782\) 0 0
\(783\) 4.01372 37.0335i 0.143439 1.32347i
\(784\) 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
\(789\) 14.4987 35.7742i 0.516167 1.27360i
\(790\) 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
\(795\) 1.62261 + 1.22548i 0.0575482 + 0.0434632i