Properties

Label 546.2.g.a.209.1
Level $546$
Weight $2$
Character 546.209
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.1
Root \(-0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 546.209
Dual form 546.2.g.a.209.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 - 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -1.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 - 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +1.23607i q^{10} +(1.61803 - 0.618034i) q^{12} +1.00000i q^{13} +(-2.61803 - 0.381966i) q^{14} +(2.00000 - 0.763932i) q^{15} +1.00000 q^{16} -6.47214 q^{17} +(-2.00000 - 2.23607i) q^{18} +6.00000i q^{19} +1.23607 q^{20} +(1.00000 + 4.47214i) q^{21} +1.23607i q^{23} +(-0.618034 - 1.61803i) q^{24} -3.47214 q^{25} +1.00000 q^{26} +(-2.38197 + 4.61803i) q^{27} +(-0.381966 + 2.61803i) q^{28} +7.70820i q^{29} +(-0.763932 - 2.00000i) q^{30} +2.76393i q^{31} -1.00000i q^{32} +6.47214i q^{34} +(-0.472136 + 3.23607i) q^{35} +(-2.23607 + 2.00000i) q^{36} -4.76393 q^{37} +6.00000 q^{38} +(-0.618034 - 1.61803i) q^{39} -1.23607i q^{40} -0.763932 q^{41} +(4.47214 - 1.00000i) q^{42} -1.52786 q^{43} +(-2.76393 + 2.47214i) q^{45} +1.23607 q^{46} +2.47214 q^{47} +(-1.61803 + 0.618034i) q^{48} +(-6.70820 - 2.00000i) q^{49} +3.47214i q^{50} +(10.4721 - 4.00000i) q^{51} -1.00000i q^{52} +1.23607i q^{53} +(4.61803 + 2.38197i) q^{54} +(2.61803 + 0.381966i) q^{56} +(-3.70820 - 9.70820i) q^{57} +7.70820 q^{58} +4.47214 q^{59} +(-2.00000 + 0.763932i) q^{60} -4.47214i q^{61} +2.76393 q^{62} +(-4.38197 - 6.61803i) q^{63} -1.00000 q^{64} -1.23607i q^{65} -10.9443 q^{67} +6.47214 q^{68} +(-0.763932 - 2.00000i) q^{69} +(3.23607 + 0.472136i) q^{70} +5.52786i q^{71} +(2.00000 + 2.23607i) q^{72} +1.23607i q^{73} +4.76393i q^{74} +(5.61803 - 2.14590i) q^{75} -6.00000i q^{76} +(-1.61803 + 0.618034i) q^{78} +8.94427 q^{79} -1.23607 q^{80} +(1.00000 - 8.94427i) q^{81} +0.763932i q^{82} +14.0000 q^{83} +(-1.00000 - 4.47214i) q^{84} +8.00000 q^{85} +1.52786i q^{86} +(-4.76393 - 12.4721i) q^{87} -16.1803 q^{89} +(2.47214 + 2.76393i) q^{90} +(2.61803 + 0.381966i) q^{91} -1.23607i q^{92} +(-1.70820 - 4.47214i) q^{93} -2.47214i q^{94} -7.41641i q^{95} +(0.618034 + 1.61803i) q^{96} -5.23607i q^{97} +(-2.00000 + 6.70820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 4q^{4} + 4q^{5} - 2q^{6} + 6q^{7} + O(q^{10}) \) \( 4q - 2q^{3} - 4q^{4} + 4q^{5} - 2q^{6} + 6q^{7} + 2q^{12} - 6q^{14} + 8q^{15} + 4q^{16} - 8q^{17} - 8q^{18} - 4q^{20} + 4q^{21} + 2q^{24} + 4q^{25} + 4q^{26} - 14q^{27} - 6q^{28} - 12q^{30} + 16q^{35} - 28q^{37} + 24q^{38} + 2q^{39} - 12q^{41} - 24q^{43} - 20q^{45} - 4q^{46} - 8q^{47} - 2q^{48} + 24q^{51} + 14q^{54} + 6q^{56} + 12q^{57} + 4q^{58} - 8q^{60} + 20q^{62} - 22q^{63} - 4q^{64} - 8q^{67} + 8q^{68} - 12q^{69} + 4q^{70} + 8q^{72} + 18q^{75} - 2q^{78} + 4q^{80} + 4q^{81} + 56q^{83} - 4q^{84} + 32q^{85} - 28q^{87} - 20q^{89} - 8q^{90} + 6q^{91} + 20q^{93} - 2q^{96} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.61803 + 0.618034i −0.934172 + 0.356822i
\(4\) −1.00000 −0.500000
\(5\) −1.23607 −0.552786 −0.276393 0.961045i \(-0.589139\pi\)
−0.276393 + 0.961045i \(0.589139\pi\)
\(6\) 0.618034 + 1.61803i 0.252311 + 0.660560i
\(7\) 0.381966 2.61803i 0.144370 0.989524i
\(8\) 1.00000i 0.353553i
\(9\) 2.23607 2.00000i 0.745356 0.666667i
\(10\) 1.23607i 0.390879i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 1.61803 0.618034i 0.467086 0.178411i
\(13\) 1.00000i 0.277350i
\(14\) −2.61803 0.381966i −0.699699 0.102085i
\(15\) 2.00000 0.763932i 0.516398 0.197246i
\(16\) 1.00000 0.250000
\(17\) −6.47214 −1.56972 −0.784862 0.619671i \(-0.787266\pi\)
−0.784862 + 0.619671i \(0.787266\pi\)
\(18\) −2.00000 2.23607i −0.471405 0.527046i
\(19\) 6.00000i 1.37649i 0.725476 + 0.688247i \(0.241620\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) 1.23607 0.276393
\(21\) 1.00000 + 4.47214i 0.218218 + 0.975900i
\(22\) 0 0
\(23\) 1.23607i 0.257738i 0.991662 + 0.128869i \(0.0411347\pi\)
−0.991662 + 0.128869i \(0.958865\pi\)
\(24\) −0.618034 1.61803i −0.126156 0.330280i
\(25\) −3.47214 −0.694427
\(26\) 1.00000 0.196116
\(27\) −2.38197 + 4.61803i −0.458410 + 0.888741i
\(28\) −0.381966 + 2.61803i −0.0721848 + 0.494762i
\(29\) 7.70820i 1.43138i 0.698419 + 0.715689i \(0.253887\pi\)
−0.698419 + 0.715689i \(0.746113\pi\)
\(30\) −0.763932 2.00000i −0.139474 0.365148i
\(31\) 2.76393i 0.496417i 0.968707 + 0.248208i \(0.0798418\pi\)
−0.968707 + 0.248208i \(0.920158\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 6.47214i 1.10996i
\(35\) −0.472136 + 3.23607i −0.0798055 + 0.546995i
\(36\) −2.23607 + 2.00000i −0.372678 + 0.333333i
\(37\) −4.76393 −0.783186 −0.391593 0.920139i \(-0.628076\pi\)
−0.391593 + 0.920139i \(0.628076\pi\)
\(38\) 6.00000 0.973329
\(39\) −0.618034 1.61803i −0.0989646 0.259093i
\(40\) 1.23607i 0.195440i
\(41\) −0.763932 −0.119306 −0.0596531 0.998219i \(-0.518999\pi\)
−0.0596531 + 0.998219i \(0.518999\pi\)
\(42\) 4.47214 1.00000i 0.690066 0.154303i
\(43\) −1.52786 −0.232997 −0.116499 0.993191i \(-0.537167\pi\)
−0.116499 + 0.993191i \(0.537167\pi\)
\(44\) 0 0
\(45\) −2.76393 + 2.47214i −0.412023 + 0.368524i
\(46\) 1.23607 0.182248
\(47\) 2.47214 0.360598 0.180299 0.983612i \(-0.442293\pi\)
0.180299 + 0.983612i \(0.442293\pi\)
\(48\) −1.61803 + 0.618034i −0.233543 + 0.0892055i
\(49\) −6.70820 2.00000i −0.958315 0.285714i
\(50\) 3.47214i 0.491034i
\(51\) 10.4721 4.00000i 1.46639 0.560112i
\(52\) 1.00000i 0.138675i
\(53\) 1.23607i 0.169787i 0.996390 + 0.0848935i \(0.0270550\pi\)
−0.996390 + 0.0848935i \(0.972945\pi\)
\(54\) 4.61803 + 2.38197i 0.628435 + 0.324145i
\(55\) 0 0
\(56\) 2.61803 + 0.381966i 0.349850 + 0.0510424i
\(57\) −3.70820 9.70820i −0.491164 1.28588i
\(58\) 7.70820 1.01214
\(59\) 4.47214 0.582223 0.291111 0.956689i \(-0.405975\pi\)
0.291111 + 0.956689i \(0.405975\pi\)
\(60\) −2.00000 + 0.763932i −0.258199 + 0.0986232i
\(61\) 4.47214i 0.572598i −0.958140 0.286299i \(-0.907575\pi\)
0.958140 0.286299i \(-0.0924251\pi\)
\(62\) 2.76393 0.351020
\(63\) −4.38197 6.61803i −0.552076 0.833794i
\(64\) −1.00000 −0.125000
\(65\) 1.23607i 0.153315i
\(66\) 0 0
\(67\) −10.9443 −1.33706 −0.668528 0.743687i \(-0.733075\pi\)
−0.668528 + 0.743687i \(0.733075\pi\)
\(68\) 6.47214 0.784862
\(69\) −0.763932 2.00000i −0.0919666 0.240772i
\(70\) 3.23607 + 0.472136i 0.386784 + 0.0564310i
\(71\) 5.52786i 0.656037i 0.944671 + 0.328018i \(0.106381\pi\)
−0.944671 + 0.328018i \(0.893619\pi\)
\(72\) 2.00000 + 2.23607i 0.235702 + 0.263523i
\(73\) 1.23607i 0.144671i 0.997380 + 0.0723354i \(0.0230452\pi\)
−0.997380 + 0.0723354i \(0.976955\pi\)
\(74\) 4.76393i 0.553796i
\(75\) 5.61803 2.14590i 0.648715 0.247787i
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) −1.61803 + 0.618034i −0.183206 + 0.0699786i
\(79\) 8.94427 1.00631 0.503155 0.864196i \(-0.332173\pi\)
0.503155 + 0.864196i \(0.332173\pi\)
\(80\) −1.23607 −0.138197
\(81\) 1.00000 8.94427i 0.111111 0.993808i
\(82\) 0.763932i 0.0843622i
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) −1.00000 4.47214i −0.109109 0.487950i
\(85\) 8.00000 0.867722
\(86\) 1.52786i 0.164754i
\(87\) −4.76393 12.4721i −0.510747 1.33715i
\(88\) 0 0
\(89\) −16.1803 −1.71511 −0.857556 0.514390i \(-0.828018\pi\)
−0.857556 + 0.514390i \(0.828018\pi\)
\(90\) 2.47214 + 2.76393i 0.260586 + 0.291344i
\(91\) 2.61803 + 0.381966i 0.274445 + 0.0400409i
\(92\) 1.23607i 0.128869i
\(93\) −1.70820 4.47214i −0.177132 0.463739i
\(94\) 2.47214i 0.254981i
\(95\) 7.41641i 0.760907i
\(96\) 0.618034 + 1.61803i 0.0630778 + 0.165140i
\(97\) 5.23607i 0.531642i −0.964022 0.265821i \(-0.914357\pi\)
0.964022 0.265821i \(-0.0856430\pi\)
\(98\) −2.00000 + 6.70820i −0.202031 + 0.677631i
\(99\) 0 0
\(100\) 3.47214 0.347214
\(101\) −4.18034 −0.415959 −0.207980 0.978133i \(-0.566689\pi\)
−0.207980 + 0.978133i \(0.566689\pi\)
\(102\) −4.00000 10.4721i −0.396059 1.03690i
\(103\) 5.70820i 0.562446i 0.959642 + 0.281223i \(0.0907401\pi\)
−0.959642 + 0.281223i \(0.909260\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −1.23607 5.52786i −0.120628 0.539464i
\(106\) 1.23607 0.120058
\(107\) 6.47214i 0.625685i 0.949805 + 0.312842i \(0.101281\pi\)
−0.949805 + 0.312842i \(0.898719\pi\)
\(108\) 2.38197 4.61803i 0.229205 0.444371i
\(109\) −16.1803 −1.54980 −0.774898 0.632087i \(-0.782199\pi\)
−0.774898 + 0.632087i \(0.782199\pi\)
\(110\) 0 0
\(111\) 7.70820 2.94427i 0.731630 0.279458i
\(112\) 0.381966 2.61803i 0.0360924 0.247381i
\(113\) 16.0000i 1.50515i −0.658505 0.752577i \(-0.728811\pi\)
0.658505 0.752577i \(-0.271189\pi\)
\(114\) −9.70820 + 3.70820i −0.909257 + 0.347305i
\(115\) 1.52786i 0.142474i
\(116\) 7.70820i 0.715689i
\(117\) 2.00000 + 2.23607i 0.184900 + 0.206725i
\(118\) 4.47214i 0.411693i
\(119\) −2.47214 + 16.9443i −0.226620 + 1.55328i
\(120\) 0.763932 + 2.00000i 0.0697371 + 0.182574i
\(121\) 11.0000 1.00000
\(122\) −4.47214 −0.404888
\(123\) 1.23607 0.472136i 0.111452 0.0425711i
\(124\) 2.76393i 0.248208i
\(125\) 10.4721 0.936656
\(126\) −6.61803 + 4.38197i −0.589581 + 0.390377i
\(127\) −20.9443 −1.85850 −0.929252 0.369447i \(-0.879547\pi\)
−0.929252 + 0.369447i \(0.879547\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 2.47214 0.944272i 0.217659 0.0831385i
\(130\) −1.23607 −0.108410
\(131\) −0.763932 −0.0667451 −0.0333725 0.999443i \(-0.510625\pi\)
−0.0333725 + 0.999443i \(0.510625\pi\)
\(132\) 0 0
\(133\) 15.7082 + 2.29180i 1.36207 + 0.198724i
\(134\) 10.9443i 0.945441i
\(135\) 2.94427 5.70820i 0.253403 0.491284i
\(136\) 6.47214i 0.554981i
\(137\) 16.4721i 1.40731i 0.710542 + 0.703655i \(0.248450\pi\)
−0.710542 + 0.703655i \(0.751550\pi\)
\(138\) −2.00000 + 0.763932i −0.170251 + 0.0650302i
\(139\) 10.1803i 0.863485i −0.901997 0.431743i \(-0.857899\pi\)
0.901997 0.431743i \(-0.142101\pi\)
\(140\) 0.472136 3.23607i 0.0399028 0.273498i
\(141\) −4.00000 + 1.52786i −0.336861 + 0.128669i
\(142\) 5.52786 0.463888
\(143\) 0 0
\(144\) 2.23607 2.00000i 0.186339 0.166667i
\(145\) 9.52786i 0.791246i
\(146\) 1.23607 0.102298
\(147\) 12.0902 0.909830i 0.997180 0.0750415i
\(148\) 4.76393 0.391593
\(149\) 9.41641i 0.771422i 0.922620 + 0.385711i \(0.126044\pi\)
−0.922620 + 0.385711i \(0.873956\pi\)
\(150\) −2.14590 5.61803i −0.175212 0.458711i
\(151\) −9.70820 −0.790042 −0.395021 0.918672i \(-0.629263\pi\)
−0.395021 + 0.918672i \(0.629263\pi\)
\(152\) −6.00000 −0.486664
\(153\) −14.4721 + 12.9443i −1.17000 + 1.04648i
\(154\) 0 0
\(155\) 3.41641i 0.274412i
\(156\) 0.618034 + 1.61803i 0.0494823 + 0.129546i
\(157\) 21.4164i 1.70922i −0.519274 0.854608i \(-0.673798\pi\)
0.519274 0.854608i \(-0.326202\pi\)
\(158\) 8.94427i 0.711568i
\(159\) −0.763932 2.00000i −0.0605838 0.158610i
\(160\) 1.23607i 0.0977198i
\(161\) 3.23607 + 0.472136i 0.255038 + 0.0372095i
\(162\) −8.94427 1.00000i −0.702728 0.0785674i
\(163\) 17.4164 1.36416 0.682079 0.731278i \(-0.261076\pi\)
0.682079 + 0.731278i \(0.261076\pi\)
\(164\) 0.763932 0.0596531
\(165\) 0 0
\(166\) 14.0000i 1.08661i
\(167\) −0.944272 −0.0730700 −0.0365350 0.999332i \(-0.511632\pi\)
−0.0365350 + 0.999332i \(0.511632\pi\)
\(168\) −4.47214 + 1.00000i −0.345033 + 0.0771517i
\(169\) −1.00000 −0.0769231
\(170\) 8.00000i 0.613572i
\(171\) 12.0000 + 13.4164i 0.917663 + 1.02598i
\(172\) 1.52786 0.116499
\(173\) −23.2361 −1.76661 −0.883303 0.468803i \(-0.844685\pi\)
−0.883303 + 0.468803i \(0.844685\pi\)
\(174\) −12.4721 + 4.76393i −0.945510 + 0.361153i
\(175\) −1.32624 + 9.09017i −0.100254 + 0.687152i
\(176\) 0 0
\(177\) −7.23607 + 2.76393i −0.543896 + 0.207750i
\(178\) 16.1803i 1.21277i
\(179\) 1.52786i 0.114198i 0.998369 + 0.0570990i \(0.0181851\pi\)
−0.998369 + 0.0570990i \(0.981815\pi\)
\(180\) 2.76393 2.47214i 0.206011 0.184262i
\(181\) 4.47214i 0.332411i −0.986091 0.166206i \(-0.946848\pi\)
0.986091 0.166206i \(-0.0531515\pi\)
\(182\) 0.381966 2.61803i 0.0283132 0.194062i
\(183\) 2.76393 + 7.23607i 0.204316 + 0.534906i
\(184\) −1.23607 −0.0911241
\(185\) 5.88854 0.432934
\(186\) −4.47214 + 1.70820i −0.327913 + 0.125252i
\(187\) 0 0
\(188\) −2.47214 −0.180299
\(189\) 11.1803 + 8.00000i 0.813250 + 0.581914i
\(190\) −7.41641 −0.538043
\(191\) 8.29180i 0.599973i −0.953943 0.299987i \(-0.903018\pi\)
0.953943 0.299987i \(-0.0969822\pi\)
\(192\) 1.61803 0.618034i 0.116772 0.0446028i
\(193\) −23.8885 −1.71954 −0.859768 0.510686i \(-0.829392\pi\)
−0.859768 + 0.510686i \(0.829392\pi\)
\(194\) −5.23607 −0.375928
\(195\) 0.763932 + 2.00000i 0.0547063 + 0.143223i
\(196\) 6.70820 + 2.00000i 0.479157 + 0.142857i
\(197\) 1.41641i 0.100915i −0.998726 0.0504574i \(-0.983932\pi\)
0.998726 0.0504574i \(-0.0160679\pi\)
\(198\) 0 0
\(199\) 14.2918i 1.01312i 0.862205 + 0.506559i \(0.169083\pi\)
−0.862205 + 0.506559i \(0.830917\pi\)
\(200\) 3.47214i 0.245517i
\(201\) 17.7082 6.76393i 1.24904 0.477091i
\(202\) 4.18034i 0.294128i
\(203\) 20.1803 + 2.94427i 1.41638 + 0.206647i
\(204\) −10.4721 + 4.00000i −0.733196 + 0.280056i
\(205\) 0.944272 0.0659508
\(206\) 5.70820 0.397709
\(207\) 2.47214 + 2.76393i 0.171825 + 0.192107i
\(208\) 1.00000i 0.0693375i
\(209\) 0 0
\(210\) −5.52786 + 1.23607i −0.381459 + 0.0852968i
\(211\) 9.88854 0.680755 0.340378 0.940289i \(-0.389445\pi\)
0.340378 + 0.940289i \(0.389445\pi\)
\(212\) 1.23607i 0.0848935i
\(213\) −3.41641 8.94427i −0.234088 0.612851i
\(214\) 6.47214 0.442426
\(215\) 1.88854 0.128798
\(216\) −4.61803 2.38197i −0.314217 0.162072i
\(217\) 7.23607 + 1.05573i 0.491216 + 0.0716675i
\(218\) 16.1803i 1.09587i
\(219\) −0.763932 2.00000i −0.0516217 0.135147i
\(220\) 0 0
\(221\) 6.47214i 0.435363i
\(222\) −2.94427 7.70820i −0.197607 0.517341i
\(223\) 13.2361i 0.886353i −0.896434 0.443176i \(-0.853852\pi\)
0.896434 0.443176i \(-0.146148\pi\)
\(224\) −2.61803 0.381966i −0.174925 0.0255212i
\(225\) −7.76393 + 6.94427i −0.517595 + 0.462951i
\(226\) −16.0000 −1.06430
\(227\) 12.4721 0.827805 0.413902 0.910321i \(-0.364165\pi\)
0.413902 + 0.910321i \(0.364165\pi\)
\(228\) 3.70820 + 9.70820i 0.245582 + 0.642942i
\(229\) 14.9443i 0.987545i 0.869591 + 0.493773i \(0.164382\pi\)
−0.869591 + 0.493773i \(0.835618\pi\)
\(230\) −1.52786 −0.100744
\(231\) 0 0
\(232\) −7.70820 −0.506068
\(233\) 24.9443i 1.63415i −0.576529 0.817077i \(-0.695593\pi\)
0.576529 0.817077i \(-0.304407\pi\)
\(234\) 2.23607 2.00000i 0.146176 0.130744i
\(235\) −3.05573 −0.199334
\(236\) −4.47214 −0.291111
\(237\) −14.4721 + 5.52786i −0.940066 + 0.359073i
\(238\) 16.9443 + 2.47214i 1.09833 + 0.160245i
\(239\) 27.4164i 1.77342i −0.462326 0.886710i \(-0.652985\pi\)
0.462326 0.886710i \(-0.347015\pi\)
\(240\) 2.00000 0.763932i 0.129099 0.0493116i
\(241\) 20.6525i 1.33034i 0.746691 + 0.665171i \(0.231642\pi\)
−0.746691 + 0.665171i \(0.768358\pi\)
\(242\) 11.0000i 0.707107i
\(243\) 3.90983 + 15.0902i 0.250816 + 0.968035i
\(244\) 4.47214i 0.286299i
\(245\) 8.29180 + 2.47214i 0.529743 + 0.157939i
\(246\) −0.472136 1.23607i −0.0301023 0.0788088i
\(247\) −6.00000 −0.381771
\(248\) −2.76393 −0.175510
\(249\) −22.6525 + 8.65248i −1.43554 + 0.548328i
\(250\) 10.4721i 0.662316i
\(251\) 19.2361 1.21417 0.607085 0.794637i \(-0.292339\pi\)
0.607085 + 0.794637i \(0.292339\pi\)
\(252\) 4.38197 + 6.61803i 0.276038 + 0.416897i
\(253\) 0 0
\(254\) 20.9443i 1.31416i
\(255\) −12.9443 + 4.94427i −0.810602 + 0.309622i
\(256\) 1.00000 0.0625000
\(257\) −6.47214 −0.403721 −0.201860 0.979414i \(-0.564699\pi\)
−0.201860 + 0.979414i \(0.564699\pi\)
\(258\) −0.944272 2.47214i −0.0587878 0.153908i
\(259\) −1.81966 + 12.4721i −0.113068 + 0.774981i
\(260\) 1.23607i 0.0766577i
\(261\) 15.4164 + 17.2361i 0.954252 + 1.06689i
\(262\) 0.763932i 0.0471959i
\(263\) 4.29180i 0.264643i −0.991207 0.132322i \(-0.957757\pi\)
0.991207 0.132322i \(-0.0422432\pi\)
\(264\) 0 0
\(265\) 1.52786i 0.0938559i
\(266\) 2.29180 15.7082i 0.140519 0.963132i
\(267\) 26.1803 10.0000i 1.60221 0.611990i
\(268\) 10.9443 0.668528
\(269\) 21.7082 1.32357 0.661786 0.749693i \(-0.269799\pi\)
0.661786 + 0.749693i \(0.269799\pi\)
\(270\) −5.70820 2.94427i −0.347390 0.179183i
\(271\) 26.1803i 1.59034i 0.606385 + 0.795171i \(0.292619\pi\)
−0.606385 + 0.795171i \(0.707381\pi\)
\(272\) −6.47214 −0.392431
\(273\) −4.47214 + 1.00000i −0.270666 + 0.0605228i
\(274\) 16.4721 0.995118
\(275\) 0 0
\(276\) 0.763932 + 2.00000i 0.0459833 + 0.120386i
\(277\) 23.5279 1.41365 0.706826 0.707387i \(-0.250126\pi\)
0.706826 + 0.707387i \(0.250126\pi\)
\(278\) −10.1803 −0.610576
\(279\) 5.52786 + 6.18034i 0.330945 + 0.370007i
\(280\) −3.23607 0.472136i −0.193392 0.0282155i
\(281\) 4.47214i 0.266785i 0.991063 + 0.133393i \(0.0425871\pi\)
−0.991063 + 0.133393i \(0.957413\pi\)
\(282\) 1.52786 + 4.00000i 0.0909830 + 0.238197i
\(283\) 19.1246i 1.13684i 0.822738 + 0.568420i \(0.192445\pi\)
−0.822738 + 0.568420i \(0.807555\pi\)
\(284\) 5.52786i 0.328018i
\(285\) 4.58359 + 12.0000i 0.271509 + 0.710819i
\(286\) 0 0
\(287\) −0.291796 + 2.00000i −0.0172242 + 0.118056i
\(288\) −2.00000 2.23607i −0.117851 0.131762i
\(289\) 24.8885 1.46403
\(290\) −9.52786 −0.559495
\(291\) 3.23607 + 8.47214i 0.189702 + 0.496645i
\(292\) 1.23607i 0.0723354i
\(293\) −27.7082 −1.61873 −0.809365 0.587306i \(-0.800189\pi\)
−0.809365 + 0.587306i \(0.800189\pi\)
\(294\) −0.909830 12.0902i −0.0530624 0.705113i
\(295\) −5.52786 −0.321845
\(296\) 4.76393i 0.276898i
\(297\) 0 0
\(298\) 9.41641 0.545478
\(299\) −1.23607 −0.0714837
\(300\) −5.61803 + 2.14590i −0.324357 + 0.123893i
\(301\) −0.583592 + 4.00000i −0.0336377 + 0.230556i
\(302\) 9.70820i 0.558644i
\(303\) 6.76393 2.58359i 0.388578 0.148423i
\(304\) 6.00000i 0.344124i
\(305\) 5.52786i 0.316525i
\(306\) 12.9443 + 14.4721i 0.739975 + 0.827317i
\(307\) 18.0000i 1.02731i −0.857996 0.513657i \(-0.828290\pi\)
0.857996 0.513657i \(-0.171710\pi\)
\(308\) 0 0
\(309\) −3.52786 9.23607i −0.200693 0.525422i
\(310\) −3.41641 −0.194039
\(311\) −13.5279 −0.767095 −0.383547 0.923521i \(-0.625298\pi\)
−0.383547 + 0.923521i \(0.625298\pi\)
\(312\) 1.61803 0.618034i 0.0916031 0.0349893i
\(313\) 1.52786i 0.0863600i −0.999067 0.0431800i \(-0.986251\pi\)
0.999067 0.0431800i \(-0.0137489\pi\)
\(314\) −21.4164 −1.20860
\(315\) 5.41641 + 8.18034i 0.305180 + 0.460910i
\(316\) −8.94427 −0.503155
\(317\) 10.9443i 0.614692i 0.951598 + 0.307346i \(0.0994408\pi\)
−0.951598 + 0.307346i \(0.900559\pi\)
\(318\) −2.00000 + 0.763932i −0.112154 + 0.0428392i
\(319\) 0 0
\(320\) 1.23607 0.0690983
\(321\) −4.00000 10.4721i −0.223258 0.584498i
\(322\) 0.472136 3.23607i 0.0263111 0.180339i
\(323\) 38.8328i 2.16072i
\(324\) −1.00000 + 8.94427i −0.0555556 + 0.496904i
\(325\) 3.47214i 0.192599i
\(326\) 17.4164i 0.964606i
\(327\) 26.1803 10.0000i 1.44778 0.553001i
\(328\) 0.763932i 0.0421811i
\(329\) 0.944272 6.47214i 0.0520594 0.356820i
\(330\) 0 0
\(331\) −30.3607 −1.66877 −0.834387 0.551179i \(-0.814178\pi\)
−0.834387 + 0.551179i \(0.814178\pi\)
\(332\) −14.0000 −0.768350
\(333\) −10.6525 + 9.52786i −0.583752 + 0.522124i
\(334\) 0.944272i 0.0516683i
\(335\) 13.5279 0.739106
\(336\) 1.00000 + 4.47214i 0.0545545 + 0.243975i
\(337\) 15.8885 0.865504 0.432752 0.901513i \(-0.357543\pi\)
0.432752 + 0.901513i \(0.357543\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 9.88854 + 25.8885i 0.537072 + 1.40607i
\(340\) −8.00000 −0.433861
\(341\) 0 0
\(342\) 13.4164 12.0000i 0.725476 0.648886i
\(343\) −7.79837 + 16.7984i −0.421073 + 0.907027i
\(344\) 1.52786i 0.0823769i
\(345\) 0.944272 + 2.47214i 0.0508379 + 0.133095i
\(346\) 23.2361i 1.24918i
\(347\) 20.3607i 1.09302i −0.837453 0.546509i \(-0.815956\pi\)
0.837453 0.546509i \(-0.184044\pi\)
\(348\) 4.76393 + 12.4721i 0.255374 + 0.668577i
\(349\) 27.3050i 1.46160i 0.682591 + 0.730800i \(0.260853\pi\)
−0.682591 + 0.730800i \(0.739147\pi\)
\(350\) 9.09017 + 1.32624i 0.485890 + 0.0708904i
\(351\) −4.61803 2.38197i −0.246492 0.127140i
\(352\) 0 0
\(353\) −21.1246 −1.12435 −0.562175 0.827018i \(-0.690035\pi\)
−0.562175 + 0.827018i \(0.690035\pi\)
\(354\) 2.76393 + 7.23607i 0.146901 + 0.384593i
\(355\) 6.83282i 0.362648i
\(356\) 16.1803 0.857556
\(357\) −6.47214 28.9443i −0.342542 1.53189i
\(358\) 1.52786 0.0807501
\(359\) 13.8885i 0.733009i 0.930416 + 0.366505i \(0.119446\pi\)
−0.930416 + 0.366505i \(0.880554\pi\)
\(360\) −2.47214 2.76393i −0.130293 0.145672i
\(361\) −17.0000 −0.894737
\(362\) −4.47214 −0.235050
\(363\) −17.7984 + 6.79837i −0.934172 + 0.356822i
\(364\) −2.61803 0.381966i −0.137222 0.0200205i
\(365\) 1.52786i 0.0799721i
\(366\) 7.23607 2.76393i 0.378235 0.144473i
\(367\) 18.6525i 0.973651i −0.873499 0.486826i \(-0.838155\pi\)
0.873499 0.486826i \(-0.161845\pi\)
\(368\) 1.23607i 0.0644345i
\(369\) −1.70820 + 1.52786i −0.0889255 + 0.0795374i
\(370\) 5.88854i 0.306131i
\(371\) 3.23607 + 0.472136i 0.168008 + 0.0245121i
\(372\) 1.70820 + 4.47214i 0.0885662 + 0.231869i
\(373\) −9.41641 −0.487563 −0.243782 0.969830i \(-0.578388\pi\)
−0.243782 + 0.969830i \(0.578388\pi\)
\(374\) 0 0
\(375\) −16.9443 + 6.47214i −0.874998 + 0.334220i
\(376\) 2.47214i 0.127491i
\(377\) −7.70820 −0.396993
\(378\) 8.00000 11.1803i 0.411476 0.575055i
\(379\) −30.0000 −1.54100 −0.770498 0.637442i \(-0.779993\pi\)
−0.770498 + 0.637442i \(0.779993\pi\)
\(380\) 7.41641i 0.380454i
\(381\) 33.8885 12.9443i 1.73616 0.663155i
\(382\) −8.29180 −0.424245
\(383\) −21.5279 −1.10002 −0.550011 0.835157i \(-0.685377\pi\)
−0.550011 + 0.835157i \(0.685377\pi\)
\(384\) −0.618034 1.61803i −0.0315389 0.0825700i
\(385\) 0 0
\(386\) 23.8885i 1.21589i
\(387\) −3.41641 + 3.05573i −0.173666 + 0.155331i
\(388\) 5.23607i 0.265821i
\(389\) 34.5410i 1.75130i 0.482947 + 0.875650i \(0.339566\pi\)
−0.482947 + 0.875650i \(0.660434\pi\)
\(390\) 2.00000 0.763932i 0.101274 0.0386832i
\(391\) 8.00000i 0.404577i
\(392\) 2.00000 6.70820i 0.101015 0.338815i
\(393\) 1.23607 0.472136i 0.0623514 0.0238161i
\(394\) −1.41641 −0.0713576
\(395\) −11.0557 −0.556274
\(396\) 0 0
\(397\) 24.8328i 1.24632i −0.782093 0.623162i \(-0.785848\pi\)
0.782093 0.623162i \(-0.214152\pi\)
\(398\) 14.2918 0.716383
\(399\) −26.8328 + 6.00000i −1.34332 + 0.300376i
\(400\) −3.47214 −0.173607
\(401\) 1.05573i 0.0527205i 0.999653 + 0.0263603i \(0.00839171\pi\)
−0.999653 + 0.0263603i \(0.991608\pi\)
\(402\) −6.76393 17.7082i −0.337354 0.883205i
\(403\) −2.76393 −0.137681
\(404\) 4.18034 0.207980
\(405\) −1.23607 + 11.0557i −0.0614207 + 0.549364i
\(406\) 2.94427 20.1803i 0.146122 1.00153i
\(407\) 0 0
\(408\) 4.00000 + 10.4721i 0.198030 + 0.518448i
\(409\) 7.70820i 0.381146i 0.981673 + 0.190573i \(0.0610346\pi\)
−0.981673 + 0.190573i \(0.938965\pi\)
\(410\) 0.944272i 0.0466343i
\(411\) −10.1803 26.6525i −0.502159 1.31467i
\(412\) 5.70820i 0.281223i
\(413\) 1.70820 11.7082i 0.0840552 0.576123i
\(414\) 2.76393 2.47214i 0.135840 0.121499i
\(415\) −17.3050 −0.849467
\(416\) 1.00000 0.0490290
\(417\) 6.29180 + 16.4721i 0.308111 + 0.806644i
\(418\) 0 0
\(419\) 1.70820 0.0834512 0.0417256 0.999129i \(-0.486714\pi\)
0.0417256 + 0.999129i \(0.486714\pi\)
\(420\) 1.23607 + 5.52786i 0.0603139 + 0.269732i
\(421\) 19.2361 0.937509 0.468754 0.883329i \(-0.344703\pi\)
0.468754 + 0.883329i \(0.344703\pi\)
\(422\) 9.88854i 0.481367i
\(423\) 5.52786 4.94427i 0.268774 0.240399i
\(424\) −1.23607 −0.0600288
\(425\) 22.4721 1.09006
\(426\) −8.94427 + 3.41641i −0.433351 + 0.165526i
\(427\) −11.7082 1.70820i −0.566600 0.0826658i
\(428\) 6.47214i 0.312842i
\(429\) 0 0
\(430\) 1.88854i 0.0910737i
\(431\) 20.0000i 0.963366i −0.876346 0.481683i \(-0.840026\pi\)
0.876346 0.481683i \(-0.159974\pi\)
\(432\) −2.38197 + 4.61803i −0.114602 + 0.222185i
\(433\) 7.41641i 0.356410i 0.983993 + 0.178205i \(0.0570290\pi\)
−0.983993 + 0.178205i \(0.942971\pi\)
\(434\) 1.05573 7.23607i 0.0506766 0.347342i
\(435\) 5.88854 + 15.4164i 0.282334 + 0.739160i
\(436\) 16.1803 0.774898
\(437\) −7.41641 −0.354775
\(438\) −2.00000 + 0.763932i −0.0955637 + 0.0365021i
\(439\) 32.5410i 1.55310i −0.630057 0.776549i \(-0.716968\pi\)
0.630057 0.776549i \(-0.283032\pi\)
\(440\) 0 0
\(441\) −19.0000 + 8.94427i −0.904762 + 0.425918i
\(442\) −6.47214 −0.307848
\(443\) 38.4721i 1.82787i 0.405865 + 0.913933i \(0.366970\pi\)
−0.405865 + 0.913933i \(0.633030\pi\)
\(444\) −7.70820 + 2.94427i −0.365815 + 0.139729i
\(445\) 20.0000 0.948091
\(446\) −13.2361 −0.626746
\(447\) −5.81966 15.2361i −0.275260 0.720641i
\(448\) −0.381966 + 2.61803i −0.0180462 + 0.123690i
\(449\) 26.3607i 1.24404i −0.783002 0.622019i \(-0.786313\pi\)
0.783002 0.622019i \(-0.213687\pi\)
\(450\) 6.94427 + 7.76393i 0.327356 + 0.365995i
\(451\) 0 0
\(452\) 16.0000i 0.752577i
\(453\) 15.7082 6.00000i 0.738036 0.281905i
\(454\) 12.4721i 0.585346i
\(455\) −3.23607 0.472136i −0.151709 0.0221341i
\(456\) 9.70820 3.70820i 0.454628 0.173653i
\(457\) 9.05573 0.423609 0.211805 0.977312i \(-0.432066\pi\)
0.211805 + 0.977312i \(0.432066\pi\)
\(458\) 14.9443 0.698300
\(459\) 15.4164 29.8885i 0.719576 1.39508i
\(460\) 1.52786i 0.0712370i
\(461\) −25.2361 −1.17536 −0.587680 0.809093i \(-0.699959\pi\)
−0.587680 + 0.809093i \(0.699959\pi\)
\(462\) 0 0
\(463\) 2.29180 0.106509 0.0532544 0.998581i \(-0.483041\pi\)
0.0532544 + 0.998581i \(0.483041\pi\)
\(464\) 7.70820i 0.357844i
\(465\) 2.11146 + 5.52786i 0.0979164 + 0.256349i
\(466\) −24.9443 −1.15552
\(467\) 4.18034 0.193443 0.0967215 0.995311i \(-0.469164\pi\)
0.0967215 + 0.995311i \(0.469164\pi\)
\(468\) −2.00000 2.23607i −0.0924500 0.103362i
\(469\) −4.18034 + 28.6525i −0.193030 + 1.32305i
\(470\) 3.05573i 0.140950i
\(471\) 13.2361 + 34.6525i 0.609886 + 1.59670i
\(472\) 4.47214i 0.205847i
\(473\) 0 0
\(474\) 5.52786 + 14.4721i 0.253903 + 0.664727i
\(475\) 20.8328i 0.955875i
\(476\) 2.47214 16.9443i 0.113310 0.776639i
\(477\) 2.47214 + 2.76393i 0.113191 + 0.126552i
\(478\) −27.4164 −1.25400
\(479\) 5.52786 0.252575 0.126287 0.991994i \(-0.459694\pi\)
0.126287 + 0.991994i \(0.459694\pi\)
\(480\) −0.763932 2.00000i −0.0348686 0.0912871i
\(481\) 4.76393i 0.217217i
\(482\) 20.6525 0.940694
\(483\) −5.52786 + 1.23607i −0.251527 + 0.0562430i
\(484\) −11.0000 −0.500000
\(485\) 6.47214i 0.293885i
\(486\) 15.0902 3.90983i 0.684504 0.177353i
\(487\) 15.2361 0.690412 0.345206 0.938527i \(-0.387809\pi\)
0.345206 + 0.938527i \(0.387809\pi\)
\(488\) 4.47214 0.202444
\(489\) −28.1803 + 10.7639i −1.27436 + 0.486762i
\(490\) 2.47214 8.29180i 0.111680 0.374585i
\(491\) 23.4164i 1.05677i −0.849006 0.528384i \(-0.822798\pi\)
0.849006 0.528384i \(-0.177202\pi\)
\(492\) −1.23607 + 0.472136i −0.0557262 + 0.0212855i
\(493\) 49.8885i 2.24687i
\(494\) 6.00000i 0.269953i
\(495\) 0 0
\(496\) 2.76393i 0.124104i
\(497\) 14.4721 + 2.11146i 0.649164 + 0.0947118i
\(498\) 8.65248 + 22.6525i 0.387727 + 1.01508i
\(499\) −10.0000 −0.447661 −0.223831 0.974628i \(-0.571856\pi\)
−0.223831 + 0.974628i \(0.571856\pi\)
\(500\) −10.4721 −0.468328
\(501\) 1.52786 0.583592i 0.0682599 0.0260730i
\(502\) 19.2361i 0.858548i
\(503\) 12.9443 0.577157 0.288578 0.957456i \(-0.406817\pi\)
0.288578 + 0.957456i \(0.406817\pi\)
\(504\) 6.61803 4.38197i 0.294791 0.195188i
\(505\) 5.16718 0.229937
\(506\) 0 0
\(507\) 1.61803 0.618034i 0.0718594 0.0274479i
\(508\) 20.9443 0.929252
\(509\) −2.76393 −0.122509 −0.0612546 0.998122i \(-0.519510\pi\)
−0.0612546 + 0.998122i \(0.519510\pi\)
\(510\) 4.94427 + 12.9443i 0.218936 + 0.573182i
\(511\) 3.23607 + 0.472136i 0.143155 + 0.0208861i
\(512\) 1.00000i 0.0441942i
\(513\) −27.7082 14.2918i −1.22335 0.630998i
\(514\) 6.47214i 0.285474i
\(515\) 7.05573i 0.310913i
\(516\) −2.47214 + 0.944272i −0.108830 + 0.0415693i
\(517\) 0 0
\(518\) 12.4721 + 1.81966i 0.547994 + 0.0799513i
\(519\) 37.5967 14.3607i 1.65031 0.630364i
\(520\) 1.23607 0.0542052
\(521\) 18.8328 0.825081 0.412540 0.910939i \(-0.364642\pi\)
0.412540 + 0.910939i \(0.364642\pi\)
\(522\) 17.2361 15.4164i 0.754402 0.674758i
\(523\) 15.7082i 0.686872i 0.939176 + 0.343436i \(0.111591\pi\)
−0.939176 + 0.343436i \(0.888409\pi\)
\(524\) 0.763932 0.0333725
\(525\) −3.47214 15.5279i −0.151536 0.677692i
\(526\) −4.29180 −0.187131
\(527\) 17.8885i 0.779237i
\(528\) 0 0
\(529\) 21.4721 0.933571
\(530\) −1.52786 −0.0663662
\(531\) 10.0000 8.94427i 0.433963 0.388148i
\(532\) −15.7082 2.29180i −0.681037 0.0993620i
\(533\) 0.763932i 0.0330896i
\(534\) −10.0000 26.1803i −0.432742 1.13293i
\(535\) 8.00000i 0.345870i
\(536\) 10.9443i 0.472721i
\(537\) −0.944272 2.47214i −0.0407483 0.106681i
\(538\) 21.7082i 0.935907i
\(539\) 0 0
\(540\) −2.94427 + 5.70820i −0.126701 + 0.245642i
\(541\) 2.65248 0.114039 0.0570194 0.998373i \(-0.481840\pi\)
0.0570194 + 0.998373i \(0.481840\pi\)
\(542\) 26.1803 1.12454
\(543\) 2.76393 + 7.23607i 0.118612 + 0.310529i
\(544\) 6.47214i 0.277491i
\(545\) 20.0000 0.856706
\(546\) 1.00000 + 4.47214i 0.0427960 + 0.191390i
\(547\) 13.5279 0.578410 0.289205 0.957267i \(-0.406609\pi\)
0.289205 + 0.957267i \(0.406609\pi\)
\(548\) 16.4721i 0.703655i
\(549\) −8.94427 10.0000i −0.381732 0.426790i
\(550\) 0 0
\(551\) −46.2492 −1.97028
\(552\) 2.00000 0.763932i 0.0851257 0.0325151i
\(553\) 3.41641 23.4164i 0.145280 0.995767i
\(554\) 23.5279i 0.999603i
\(555\) −9.52786 + 3.63932i −0.404435 + 0.154481i
\(556\) 10.1803i 0.431743i
\(557\) 22.0000i 0.932170i 0.884740 + 0.466085i \(0.154336\pi\)
−0.884740 + 0.466085i \(0.845664\pi\)
\(558\) 6.18034 5.52786i 0.261635 0.234013i
\(559\) 1.52786i 0.0646218i
\(560\) −0.472136 + 3.23607i −0.0199514 + 0.136749i
\(561\) 0 0
\(562\) 4.47214 0.188646
\(563\) −32.1803 −1.35624 −0.678120 0.734951i \(-0.737205\pi\)
−0.678120 + 0.734951i \(0.737205\pi\)
\(564\) 4.00000 1.52786i 0.168430 0.0643347i
\(565\) 19.7771i 0.832028i
\(566\) 19.1246 0.803867
\(567\) −23.0344 6.03444i −0.967356 0.253423i
\(568\) −5.52786 −0.231944
\(569\) 36.3607i 1.52432i −0.647389 0.762159i \(-0.724139\pi\)
0.647389 0.762159i \(-0.275861\pi\)
\(570\) 12.0000 4.58359i 0.502625 0.191986i
\(571\) −13.5279 −0.566123 −0.283062 0.959102i \(-0.591350\pi\)
−0.283062 + 0.959102i \(0.591350\pi\)
\(572\) 0 0
\(573\) 5.12461 + 13.4164i 0.214084 + 0.560478i
\(574\) 2.00000 + 0.291796i 0.0834784 + 0.0121793i
\(575\) 4.29180i 0.178980i
\(576\) −2.23607 + 2.00000i −0.0931695 + 0.0833333i
\(577\) 43.1246i 1.79530i −0.440708 0.897651i \(-0.645273\pi\)
0.440708 0.897651i \(-0.354727\pi\)
\(578\) 24.8885i 1.03523i
\(579\) 38.6525 14.7639i 1.60634 0.613568i
\(580\) 9.52786i 0.395623i
\(581\) 5.34752 36.6525i 0.221853 1.52060i
\(582\) 8.47214 3.23607i 0.351181 0.134139i
\(583\) 0 0
\(584\) −1.23607 −0.0511489
\(585\) −2.47214 2.76393i −0.102210 0.114275i
\(586\) 27.7082i 1.14462i
\(587\) 21.4164 0.883950 0.441975 0.897027i \(-0.354278\pi\)
0.441975 + 0.897027i \(0.354278\pi\)
\(588\) −12.0902 + 0.909830i −0.498590 + 0.0375208i
\(589\) −16.5836 −0.683315
\(590\) 5.52786i 0.227579i
\(591\) 0.875388 + 2.29180i 0.0360087 + 0.0942719i
\(592\) −4.76393 −0.195796
\(593\) 18.0689 0.742000 0.371000 0.928633i \(-0.379015\pi\)
0.371000 + 0.928633i \(0.379015\pi\)
\(594\) 0 0
\(595\) 3.05573 20.9443i 0.125273 0.858631i
\(596\) 9.41641i 0.385711i
\(597\) −8.83282 23.1246i −0.361503 0.946427i
\(598\) 1.23607i 0.0505466i
\(599\) 34.5410i 1.41131i 0.708557 + 0.705654i \(0.249347\pi\)
−0.708557 + 0.705654i \(0.750653\pi\)
\(600\) 2.14590 + 5.61803i 0.0876059 + 0.229355i
\(601\) 23.4164i 0.955175i 0.878584 + 0.477588i \(0.158489\pi\)
−0.878584 + 0.477588i \(0.841511\pi\)
\(602\) 4.00000 + 0.583592i 0.163028 + 0.0237854i
\(603\) −24.4721 + 21.8885i −0.996582 + 0.891370i
\(604\) 9.70820 0.395021
\(605\) −13.5967 −0.552786
\(606\) −2.58359 6.76393i −0.104951 0.274766i
\(607\) 17.1246i 0.695067i 0.937668 + 0.347533i \(0.112981\pi\)
−0.937668 + 0.347533i \(0.887019\pi\)
\(608\) 6.00000 0.243332
\(609\) −34.4721 + 7.70820i −1.39688 + 0.312352i
\(610\) 5.52786 0.223817
\(611\) 2.47214i 0.100012i
\(612\) 14.4721 12.9443i 0.585001 0.523241i
\(613\) 2.29180 0.0925648 0.0462824 0.998928i \(-0.485263\pi\)
0.0462824 + 0.998928i \(0.485263\pi\)
\(614\) −18.0000 −0.726421
\(615\) −1.52786 + 0.583592i −0.0616094 + 0.0235327i
\(616\) 0 0
\(617\) 37.7771i 1.52085i 0.649427 + 0.760424i \(0.275009\pi\)
−0.649427 + 0.760424i \(0.724991\pi\)
\(618\) −9.23607 + 3.52786i −0.371529 + 0.141912i
\(619\) 0.472136i 0.0189767i 0.999955 + 0.00948837i \(0.00302029\pi\)
−0.999955 + 0.00948837i \(0.996980\pi\)
\(620\) 3.41641i 0.137206i
\(621\) −5.70820 2.94427i −0.229062 0.118150i
\(622\) 13.5279i 0.542418i
\(623\) −6.18034 + 42.3607i −0.247610 + 1.69714i
\(624\) −0.618034 1.61803i −0.0247412 0.0647732i
\(625\) 4.41641 0.176656
\(626\) −1.52786 −0.0610657
\(627\) 0 0
\(628\) 21.4164i 0.854608i
\(629\) 30.8328 1.22938
\(630\) 8.18034 5.41641i 0.325913 0.215795i
\(631\) 48.1803 1.91803 0.959015 0.283357i \(-0.0914481\pi\)
0.959015 + 0.283357i \(0.0914481\pi\)
\(632\) 8.94427i 0.355784i
\(633\) −16.0000 + 6.11146i −0.635943 + 0.242909i
\(634\) 10.9443 0.434653
\(635\) 25.8885 1.02736
\(636\) 0.763932 + 2.00000i 0.0302919 + 0.0793052i
\(637\) 2.00000 6.70820i 0.0792429 0.265789i
\(638\) 0 0
\(639\) 11.0557 + 12.3607i 0.437358 + 0.488981i
\(640\) 1.23607i 0.0488599i
\(641\) 25.5279i 1.00829i 0.863619 + 0.504145i \(0.168192\pi\)
−0.863619 + 0.504145i \(0.831808\pi\)
\(642\) −10.4721 + 4.00000i −0.413302 + 0.157867i
\(643\) 3.88854i 0.153349i −0.997056 0.0766746i \(-0.975570\pi\)
0.997056 0.0766746i \(-0.0244303\pi\)
\(644\) −3.23607 0.472136i −0.127519 0.0186048i
\(645\) −3.05573 + 1.16718i −0.120319 + 0.0459578i
\(646\) −38.8328 −1.52786
\(647\) −24.3607 −0.957717 −0.478859 0.877892i \(-0.658949\pi\)
−0.478859 + 0.877892i \(0.658949\pi\)
\(648\) 8.94427 + 1.00000i 0.351364 + 0.0392837i
\(649\) 0 0
\(650\) −3.47214 −0.136188
\(651\) −12.3607 + 2.76393i −0.484453 + 0.108327i
\(652\) −17.4164 −0.682079
\(653\) 36.6525i 1.43432i −0.696907 0.717161i \(-0.745441\pi\)
0.696907 0.717161i \(-0.254559\pi\)
\(654\) −10.0000 26.1803i −0.391031 1.02373i
\(655\) 0.944272 0.0368958
\(656\) −0.763932 −0.0298265
\(657\) 2.47214 + 2.76393i 0.0964472 + 0.107831i
\(658\) −6.47214 0.944272i −0.252310 0.0368116i
\(659\) 33.8885i 1.32011i 0.751217 + 0.660055i \(0.229467\pi\)
−0.751217 + 0.660055i \(0.770533\pi\)
\(660\) 0 0
\(661\) 6.58359i 0.256072i 0.991770 + 0.128036i \(0.0408673\pi\)
−0.991770 + 0.128036i \(0.959133\pi\)
\(662\) 30.3607i 1.18000i
\(663\) 4.00000 + 10.4721i 0.155347 + 0.406704i
\(664\) 14.0000i 0.543305i
\(665\) −19.4164 2.83282i −0.752936 0.109852i
\(666\) 9.52786 + 10.6525i 0.369197 + 0.412775i
\(667\) −9.52786 −0.368920
\(668\) 0.944272 0.0365350
\(669\) 8.18034 + 21.4164i 0.316270 + 0.828006i
\(670\) 13.5279i 0.522627i
\(671\) 0 0
\(672\) 4.47214 1.00000i 0.172516 0.0385758i
\(673\) 40.8328 1.57399 0.786995 0.616960i \(-0.211636\pi\)
0.786995 + 0.616960i \(0.211636\pi\)
\(674\) 15.8885i 0.612004i
\(675\) 8.27051 16.0344i 0.318332 0.617166i
\(676\) 1.00000 0.0384615
\(677\) −22.6525 −0.870605 −0.435303 0.900284i \(-0.643359\pi\)
−0.435303 + 0.900284i \(0.643359\pi\)
\(678\) 25.8885 9.88854i 0.994244 0.379767i
\(679\) −13.7082 2.00000i −0.526073 0.0767530i
\(680\) 8.00000i 0.306786i
\(681\) −20.1803 + 7.70820i −0.773312 + 0.295379i
\(682\) 0 0
\(683\) 10.8328i 0.414506i 0.978287 + 0.207253i \(0.0664524\pi\)
−0.978287 + 0.207253i \(0.933548\pi\)
\(684\) −12.0000 13.4164i −0.458831 0.512989i
\(685\) 20.3607i 0.777942i
\(686\) 16.7984 + 7.79837i 0.641365 + 0.297743i
\(687\) −9.23607 24.1803i −0.352378 0.922538i
\(688\) −1.52786 −0.0582493
\(689\) −1.23607 −0.0470904
\(690\) 2.47214 0.944272i 0.0941126 0.0359478i
\(691\) 10.0000i 0.380418i 0.981744 + 0.190209i \(0.0609166\pi\)
−0.981744 + 0.190209i \(0.939083\pi\)
\(692\) 23.2361 0.883303
\(693\) 0 0
\(694\) −20.3607 −0.772881
\(695\) 12.5836i 0.477323i
\(696\) 12.4721 4.76393i 0.472755 0.180576i
\(697\) 4.94427 0.187278
\(698\) 27.3050 1.03351
\(699\) 15.4164 + 40.3607i 0.583102 + 1.52658i
\(700\) 1.32624 9.09017i 0.0501271 0.343576i
\(701\) 17.2361i 0.650997i −0.945543 0.325499i \(-0.894468\pi\)
0.945543 0.325499i \(-0.105532\pi\)
\(702\) −2.38197 + 4.61803i −0.0899015 + 0.174296i
\(703\) 28.5836i 1.07805i
\(704\) 0 0
\(705\) 4.94427 1.88854i 0.186212 0.0711267i
\(706\) 21.1246i 0.795035i
\(707\) −1.59675 + 10.9443i −0.0600519 + 0.411602i
\(708\) 7.23607 2.76393i 0.271948 0.103875i
\(709\) 7.23607 0.271756 0.135878 0.990726i \(-0.456614\pi\)
0.135878 + 0.990726i \(0.456614\pi\)
\(710\) −6.83282 −0.256431
\(711\) 20.0000 17.8885i 0.750059 0.670873i
\(712\) 16.1803i 0.606384i
\(713\) −3.41641 −0.127945
\(714\) −28.9443 + 6.47214i −1.08321 + 0.242214i
\(715\) 0 0
\(716\) 1.52786i 0.0570990i
\(717\) 16.9443 + 44.3607i 0.632795 + 1.65668i
\(718\) 13.8885 0.518316
\(719\) −44.7214 −1.66783 −0.833913 0.551896i \(-0.813904\pi\)
−0.833913 + 0.551896i \(0.813904\pi\)
\(720\) −2.76393 + 2.47214i −0.103006 + 0.0921311i
\(721\) 14.9443 + 2.18034i 0.556554 + 0.0812001i
\(722\) 17.0000i 0.632674i
\(723\) −12.7639 33.4164i −0.474696 1.24277i
\(724\) 4.47214i 0.166206i
\(725\) 26.7639i 0.993987i
\(726\) 6.79837 + 17.7984i 0.252311 + 0.660560i
\(727\) 15.8197i 0.586719i 0.956002 + 0.293359i \(0.0947732\pi\)
−0.956002 + 0.293359i \(0.905227\pi\)
\(728\) −0.381966 + 2.61803i −0.0141566 + 0.0970308i
\(729\) −15.6525 22.0000i −0.579721 0.814815i
\(730\) −1.52786 −0.0565488
\(731\) 9.88854 0.365741
\(732\) −2.76393 7.23607i −0.102158 0.267453i
\(733\) 14.0000i 0.517102i 0.965998 + 0.258551i \(0.0832450\pi\)
−0.965998 + 0.258551i \(0.916755\pi\)
\(734\) −18.6525 −0.688475
\(735\) −14.9443 + 1.12461i −0.551228 + 0.0414819i
\(736\) 1.23607 0.0455621
\(737\) 0 0
\(738\) 1.52786 + 1.70820i 0.0562415 + 0.0628799i
\(739\) 36.8328 1.35492 0.677459 0.735561i \(-0.263081\pi\)
0.677459 + 0.735561i \(0.263081\pi\)
\(740\) −5.88854 −0.216467
\(741\) 9.70820 3.70820i 0.356640 0.136224i
\(742\) 0.472136 3.23607i 0.0173327 0.118800i
\(743\) 45.3050i 1.66208i 0.556215 + 0.831039i \(0.312253\pi\)
−0.556215 + 0.831039i \(0.687747\pi\)
\(744\) 4.47214 1.70820i 0.163956 0.0626258i
\(745\) 11.6393i 0.426432i
\(746\) 9.41641i 0.344759i
\(747\) 31.3050 28.0000i 1.14539 1.02447i
\(748\) 0 0
\(749\) 16.9443 + 2.47214i 0.619130 + 0.0903299i
\(750\) 6.47214 + 16.9443i 0.236329 + 0.618717i
\(751\) −29.3050 −1.06935 −0.534676 0.845057i \(-0.679567\pi\)
−0.534676 + 0.845057i \(0.679567\pi\)
\(752\) 2.47214 0.0901495
\(753\) −31.1246 + 11.8885i −1.13424 + 0.433243i
\(754\) 7.70820i 0.280716i
\(755\) 12.0000 0.436725
\(756\) −11.1803 8.00000i −0.406625 0.290957i
\(757\) −34.3607 −1.24886 −0.624430 0.781081i \(-0.714669\pi\)
−0.624430 + 0.781081i \(0.714669\pi\)
\(758\) 30.0000i 1.08965i
\(759\) 0 0
\(760\) 7.41641 0.269021
\(761\) −26.2918 −0.953077 −0.476538 0.879154i \(-0.658109\pi\)
−0.476538 + 0.879154i \(0.658109\pi\)
\(762\) −12.9443 33.8885i −0.468921 1.22765i
\(763\) −6.18034 + 42.3607i −0.223743 + 1.53356i
\(764\) 8.29180i 0.299987i
\(765\) 17.8885 16.0000i 0.646762 0.578481i
\(766\) 21.5279i 0.777833i
\(767\) 4.47214i 0.161479i
\(768\) −1.61803 + 0.618034i −0.0583858 + 0.0223014i
\(769\) 14.5410i 0.524363i 0.965019 + 0.262181i \(0.0844418\pi\)
−0.965019 + 0.262181i \(0.915558\pi\)
\(770\) 0 0
\(771\) 10.4721 4.00000i 0.377145 0.144056i
\(772\) 23.8885 0.859768
\(773\) −27.7082 −0.996595 −0.498297 0.867006i \(-0.666041\pi\)
−0.498297 + 0.867006i \(0.666041\pi\)
\(774\) 3.05573 + 3.41641i 0.109836 + 0.122800i
\(775\) 9.59675i 0.344725i
\(776\) 5.23607 0.187964
\(777\) −4.76393 21.3050i −0.170905 0.764311i
\(778\) 34.5410 1.23836
\(779\) 4.58359i 0.164224i
\(780\) −0.763932 2.00000i −0.0273532 0.0716115i
\(781\) 0 0
\(782\) −8.00000 −0.286079
\(783\) −35.5967 18.3607i −1.27212 0.656157i
\(784\) −6.70820 2.00000i −0.239579 0.0714286i
\(785\) 26.4721i 0.944831i