Properties

Label 624.2.cn.c.401.1
Level $624$
Weight $2$
Character 624.401
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 401.1
Root \(0.500000 + 0.564882i\) of defining polynomial
Character \(\chi\) \(=\) 624.401
Dual form 624.2.cn.c.305.1

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

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

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
\(3\) −0.239203 + 1.71545i −0.138104 + 0.990418i
\(4\) 0 0
\(5\) 1.06488 1.06488i 0.476230 0.476230i −0.427694 0.903924i \(-0.640674\pi\)
0.903924 + 0.427694i \(0.140674\pi\)
\(6\) 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
\(9\) −2.88556 0.820682i −0.961855 0.273561i
\(10\) 0 0
\(11\) 1.06488 3.97420i 0.321074 1.19826i −0.597126 0.802148i \(-0.703691\pi\)
0.918200 0.396117i \(-0.129643\pi\)
\(12\) 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 −0.379981 0.924994i \(-0.624070\pi\)
0.991059 0.133424i \(-0.0425971\pi\)
\(18\) 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
\(21\) 2.43091 0.301143i 0.530468 0.0657148i
\(22\) 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 −0.949585 0.313509i \(-0.898495\pi\)
−0.203286 + 0.979119i \(0.565162\pi\)
\(30\) 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
\(33\) 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 −0.198323 0.980137i \(-0.563549\pi\)
−0.661821 + 0.749662i \(0.730216\pi\)
\(38\) 0 0
\(39\) −1.25874 + 6.11683i −0.201560 + 0.979476i
\(40\) 0 0
\(41\) 5.42885 + 1.45466i 0.847844 + 0.227179i 0.656483 0.754341i \(-0.272043\pi\)
0.191361 + 0.981520i \(0.438710\pi\)
\(42\) 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
\(45\) −3.94672 + 2.19886i −0.588342 + 0.327786i
\(46\) 0 0
\(47\) 4.25953 + 4.25953i 0.621316 + 0.621316i 0.945868 0.324552i \(-0.105213\pi\)
−0.324552 + 0.945868i \(0.605213\pi\)
\(48\) 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
\(57\) 0.822738 + 6.64136i 0.108974 + 0.879670i
\(58\) 0 0
\(59\) 2.90931 0.779548i 0.378760 0.101489i −0.0644157 0.997923i \(-0.520518\pi\)
0.443176 + 0.896435i \(0.353852\pi\)
\(60\) 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
\(63\) −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 −0.806410 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 0.996631 0.0820158i \(-0.0261358\pi\)
−0.904116 + 0.427288i \(0.859469\pi\)
\(72\) 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
\(75\) −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 −0.848513 0.529174i \(-0.822502\pi\)
0.529174 + 0.848513i \(0.322502\pi\)
\(84\) 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 0.711531 + 0.702654i \(0.248002\pi\)
−0.967531 + 0.252751i \(0.918665\pi\)
\(90\) 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 −0.174910 0.984584i \(-0.555964\pi\)
0.340815 + 0.940130i \(0.389297\pi\)
\(98\) 0 0
\(99\) −6.33434 + 10.5939i −0.636625 + 1.06472i
\(100\) 0 0
\(101\) −3.01375 5.21997i −0.299880 0.519407i 0.676229 0.736692i \(-0.263613\pi\)
−0.976108 + 0.217285i \(0.930280\pi\)
\(102\) 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 \(0.704435\pi\)
−0.992969 + 0.118374i \(0.962232\pi\)
\(108\) 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
\(111\) 3.65646 8.64000i 0.347055 0.820072i
\(112\) 0 0
\(113\) −8.90883 5.14352i −0.838073 0.483861i 0.0185360 0.999828i \(-0.494099\pi\)
−0.856609 + 0.515967i \(0.827433\pi\)
\(114\) 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 −0.807788 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 \(-0.887123\pi\)
0.937781 0.347227i \(-0.112877\pi\)
\(132\) 0 0
\(133\) −2.73205 4.73205i −0.236899 0.410321i
\(134\) 0 0
\(135\) −2.82797 7.29638i −0.243393 0.627973i
\(136\) 0 0
\(137\) 6.49373 1.73999i 0.554797 0.148657i 0.0294822 0.999565i \(-0.490614\pi\)
0.525315 + 0.850908i \(0.323948\pi\)
\(138\) 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
\(141\) −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 0.995043 + 0.0994454i \(0.0317068\pi\)
−0.812010 + 0.583644i \(0.801626\pi\)
\(150\) 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
\(153\) −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 0.995113 0.0987406i \(-0.0314814\pi\)
−0.911164 + 0.412045i \(0.864815\pi\)
\(164\) 0 0
\(165\) 9.94624 4.03104i 0.774313 0.313816i
\(166\) 0 0
\(167\) −3.47998 + 12.9875i −0.269289 + 1.00500i 0.690283 + 0.723539i \(0.257486\pi\)
−0.959573 + 0.281461i \(0.909181\pi\)
\(168\) 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 0.316097 + 0.948727i \(0.397627\pi\)
−0.979670 + 0.200615i \(0.935706\pi\)
\(174\) 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 0.604972 + 0.796247i \(0.293184\pi\)
0.387084 + 0.922045i \(0.373482\pi\)
\(180\) 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
\(189\) −7.26168 1.12603i −0.528210 0.0819070i
\(190\) 0 0
\(191\) −4.18307 2.41510i −0.302677 0.174750i 0.340968 0.940075i \(-0.389245\pi\)
−0.643645 + 0.765324i \(0.722579\pi\)
\(192\) 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
\(195\) 5.17329 + 7.85411i 0.370467 + 0.562445i
\(196\) 0 0
\(197\) −3.97420 1.06488i −0.283150 0.0758697i 0.114449 0.993429i \(-0.463490\pi\)
−0.397599 + 0.917559i \(0.630156\pi\)
\(198\) 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
\(201\) 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 0.833309 0.552808i \(-0.186444\pi\)
−0.895400 + 0.445263i \(0.853110\pi\)
\(212\) 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 0.255960 + 0.966687i \(0.417609\pi\)
−0.705011 + 0.709196i \(0.749058\pi\)
\(224\) 0 0
\(225\) 2.24214 7.88351i 0.149476 0.525567i
\(226\) 0 0
\(227\) −5.24796 19.5856i −0.348319 1.29994i −0.888686 0.458515i \(-0.848381\pi\)
0.540367 0.841429i \(-0.318285\pi\)
\(228\) 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
\(231\) 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 −0.887537 0.460737i \(-0.847585\pi\)
0.460737 + 0.887537i \(0.347585\pi\)
\(240\) 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
\(243\) −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 −0.881201 0.472741i \(-0.843264\pi\)
0.850007 + 0.526772i \(0.176598\pi\)
\(252\) 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 0.977686 + 0.210071i \(0.0673696\pi\)
−0.306916 + 0.951737i \(0.599297\pi\)
\(258\) 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 \(-0.425546\pi\)
0.958331 + 0.285660i \(0.0922127\pi\)
\(264\) 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 0.0711756 0.997464i \(-0.477325\pi\)
−0.828241 + 0.560372i \(0.810658\pi\)
\(270\) 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
\(273\) 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 0.997536 0.0701536i \(-0.0223490\pi\)
0.438013 + 0.898969i \(0.355682\pi\)
\(278\) 0 0
\(279\) −5.08808 9.13257i −0.304615 0.546752i
\(280\) 0 0
\(281\) −12.1315 12.1315i −0.723703 0.723703i 0.245655 0.969357i \(-0.420997\pi\)
−0.969357 + 0.245655i \(0.920997\pi\)
\(282\) 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
\(291\) 0.360213 + 2.90774i 0.0211161 + 0.170455i
\(292\) 0 0
\(293\) −1.73999 + 0.466229i −0.101651 + 0.0272374i −0.309286 0.950969i \(-0.600090\pi\)
0.207635 + 0.978206i \(0.433423\pi\)
\(294\) 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 −0.904803 0.425829i \(-0.859982\pi\)
0.425829 + 0.904803i \(0.359982\pi\)
\(308\) 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 −0.949960 0.312373i \(-0.898876\pi\)
0.312373 + 0.949960i \(0.398876\pi\)
\(318\) 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 0.820357 0.571852i \(-0.193775\pi\)
0.996376 + 0.0850595i \(0.0271080\pi\)
\(332\) 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 \(0.167734\pi\)
−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 −0.0614076 0.998113i \(-0.519559\pi\)
−0.895095 + 0.445876i \(0.852892\pi\)
\(348\) 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
\(351\) 8.65215 16.6175i 0.461818 0.886975i
\(352\) 0 0
\(353\) 13.6626 + 3.66088i 0.727186 + 0.194849i 0.603376 0.797457i \(-0.293822\pi\)
0.123810 + 0.992306i \(0.460489\pi\)
\(354\) 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 0.0368904 0.999319i \(-0.488255\pi\)
−0.999319 + 0.0368904i \(0.988255\pi\)
\(360\) 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
\(369\) −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 −0.976139 0.217148i \(-0.930325\pi\)
0.676125 + 0.736787i \(0.263658\pi\)
\(374\) 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 0.795069 + 0.606519i \(0.207435\pi\)
−0.991809 + 0.127726i \(0.959232\pi\)
\(380\) 0 0
\(381\) −5.93605 14.6467i −0.304113 0.750372i
\(382\) 0 0
\(383\) 8.51906 + 31.7936i 0.435304 + 1.62458i 0.740339 + 0.672234i \(0.234665\pi\)
−0.305035 + 0.952341i \(0.598668\pi\)
\(384\) 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 −0.995877 0.0907168i \(-0.971084\pi\)
0.817096 0.576501i \(-0.195582\pi\)
\(398\) 0 0
\(399\) 8.77113 3.55479i 0.439106 0.177962i
\(400\) 0 0
\(401\) −3.22263 + 12.0270i −0.160931 + 0.600601i 0.837594 + 0.546294i \(0.183962\pi\)
−0.998524 + 0.0543073i \(0.982705\pi\)
\(402\) 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 0.543236 0.839580i \(-0.317199\pi\)
0.890246 + 0.455480i \(0.150532\pi\)
\(410\) 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 −0.285208 0.958466i \(-0.592063\pi\)
0.687452 + 0.726230i \(0.258729\pi\)
\(420\) 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
\(423\) −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 0.986800 0.161944i \(-0.0517764\pi\)
0.773622 + 0.633648i \(0.218443\pi\)
\(432\) 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
\(435\) −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 −0.525975 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 \(0.0858762\pi\)
−0.963827 + 0.266527i \(0.914124\pi\)
\(444\) 0 0
\(445\) 7.02628 + 12.1699i 0.333078 + 0.576907i
\(446\) 0 0
\(447\) −14.8382 + 1.83816i −0.701821 + 0.0869422i
\(448\) 0 0
\(449\) −19.8710 + 5.32441i −0.937769 + 0.251275i −0.695165 0.718851i \(-0.744669\pi\)
−0.242605 + 0.970125i \(0.578002\pi\)
\(450\) 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 −0.985511 0.169611i \(-0.945749\pi\)
0.938283 + 0.345868i \(0.112416\pi\)
\(458\) 0 0
\(459\) −15.4590 21.1332i −0.721565 0.986412i
\(460\) 0 0
\(461\) −5.50531 20.5461i −0.256408 0.956927i −0.967302 0.253628i \(-0.918376\pi\)
0.710894 0.703299i \(-0.248290\pi\)
\(462\) 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
\(465\) −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 0.730962 + 0.682418i \(0.239072\pi\)
−0.974241 + 0.225510i \(0.927595\pi\)
\(480\) 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
\(489\) −7.11819 + 0.881808i −0.321896 + 0.0398767i
\(490\) 0 0
\(491\) −14.2612 24.7012i −0.643600 1.11475i −0.984623 0.174693i \(-0.944107\pi\)
0.341023 0.940055i \(-0.389227\pi\)
\(492\) 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
\(501\) −21.4470 9.07638i −0.958181 0.405503i
\(502\) 0 0
\(503\) 2.83286 + 1.63555i 0.126311 + 0.0729256i 0.561824 0.827257i \(-0.310100\pi\)
−0.435513 + 0.900182i \(0.643433\pi\)
\(504\) 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 0.558530 0.829484i \(-0.311366\pi\)
0.0689588 + 0.997620i \(0.478032\pi\)
\(510\) 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 \(-0.982618\pi\)
0.998509 0.0545785i \(-0.0173815\pi\)
\(522\) 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
\(525\) 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 −0.925118 0.379681i \(-0.876034\pi\)
0.379681 + 0.925118i \(0.376034\pi\)
\(542\) 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 −0.671123 0.741346i \(-0.734188\pi\)
0.951883 0.306462i \(-0.0991454\pi\)
\(558\) 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 −0.952456 0.304675i \(-0.901452\pi\)
0.740085 + 0.672514i \(0.234785\pi\)
\(564\) 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 0.892939 0.450178i \(-0.148639\pi\)
−0.836335 + 0.548219i \(0.815306\pi\)
\(570\) 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
\(579\) −0.0936291 + 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 −0.133164 0.991094i \(-0.542514\pi\)
−0.610871 + 0.791730i \(0.709181\pi\)
\(588\) 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 0.887119 0.461541i \(-0.152703\pi\)
−0.461541 + 0.887119i \(0.652703\pi\)
\(594\) 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 0.518668 0.854976i \(-0.326428\pi\)
−0.999765 + 0.0216919i \(0.993095\pi\)
\(602\) 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 −0.868009 0.496549i \(-0.834600\pi\)
0.864028 + 0.503444i \(0.167934\pi\)
\(608\) 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 0.218354 + 0.975870i \(0.429931\pi\)
−0.677035 + 0.735951i \(0.736735\pi\)
\(614\) 0 0
\(615\) 5.50650 + 13.5868i 0.222044 + 0.547873i
\(616\) 0 0
\(617\) −4.78173 17.8457i −0.192505 0.718439i −0.992899 0.118964i \(-0.962043\pi\)
0.800393 0.599475i \(-0.204624\pi\)
\(618\) 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
\(627\) 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 −0.981102 0.193493i \(-0.938018\pi\)
0.752912 0.658121i \(-0.228648\pi\)
\(632\) 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 −0.0626345 + 0.998037i \(0.519950\pi\)
−0.833008 + 0.553261i \(0.813383\pi\)
\(642\) 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
\(645\) −0.704266 5.68503i −0.0277305 0.223848i
\(646\) 0 0
\(647\) −8.23373 14.2612i −0.323701 0.560667i 0.657547 0.753413i \(-0.271594\pi\)
−0.981249 + 0.192746i \(0.938261\pi\)
\(648\) 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 \(-0.606135\pi\)
0.654683 + 0.755904i \(0.272802\pi\)
\(654\) 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 0.881967 0.471311i \(-0.156219\pi\)
0.0328158 + 0.999461i \(0.489553\pi\)
\(660\) 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
\(663\) 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 −0.996792 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 \(0.0594357\pi\)
−0.982618 + 0.185640i \(0.940564\pi\)
\(678\) 0 0
\(679\) −1.19615 2.07180i −0.0459041 0.0795083i
\(680\) 0 0
\(681\) 34.8536 4.31769i 1.33559 0.165454i
\(682\) 0 0
\(683\) −45.2752 + 12.1315i −1.73241 + 0.464198i −0.980736 0.195338i \(-0.937420\pi\)
−0.751673 + 0.659536i \(0.770753\pi\)
\(684\) 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 0.808723 + 0.588189i \(0.200159\pi\)
−0.994470 + 0.105025i \(0.966508\pi\)
\(692\) 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 0.885196 0.465219i \(-0.154024\pi\)
−0.999211 + 0.0397068i \(0.987358\pi\)
\(710\) 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 −0.926577 0.376106i \(-0.877263\pi\)
0.789005 + 0.614386i \(0.210596\pi\)
\(720\) 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 \(-0.882123\pi\)
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
\(735\) 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 0.457554 0.889182i \(-0.348726\pi\)
−0.0483378 + 0.998831i \(0.515392\pi\)
\(740\) 0 0
\(741\) 1.41914 + 24.0870i 0.0521334 + 0.884860i
\(742\) 0 0
\(743\) 8.51906 + 2.28268i 0.312534 + 0.0837432i 0.411677 0.911330i \(-0.364943\pi\)
−0.0991426 + 0.995073i \(0.531610\pi\)
\(744\) 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 0.140554 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 0.0775029 0.996992i \(-0.475305\pi\)
0.565616 + 0.824669i \(0.308639\pi\)
\(762\) 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 0.438694 + 0.898636i \(0.355441\pi\)
−0.829238 + 0.558895i \(0.811225\pi\)
\(770\) 0 0
\(771\) −34.5229 + 13.9915i −1.24331 + 0.503893i
\(772\) 0 0
\(773\) 11.1430 + 41.5864i 0.400787 + 1.49576i 0.811695 + 0.584081i \(0.198545\pi\)
−0.410908 + 0.911677i \(0.634788\pi\)
\(774\) 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 −0.999263 0.0383938i \(-0.987776\pi\)
0.846190 0.532881i \(-0.178891\pi\)
\(788\) 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