Properties

Label 105.3.k.d.62.6
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 62.6
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.88692 + 1.88692i) q^{2} +(2.65373 + 1.39918i) q^{3} -3.12092i q^{4} +(-4.96950 - 0.551428i) q^{5} +(-7.64751 + 2.36725i) q^{6} +(-6.68054 + 2.09055i) q^{7} +(-1.65875 - 1.65875i) q^{8} +(5.08462 + 7.42608i) q^{9} +O(q^{10})\) \(q+(-1.88692 + 1.88692i) q^{2} +(2.65373 + 1.39918i) q^{3} -3.12092i q^{4} +(-4.96950 - 0.551428i) q^{5} +(-7.64751 + 2.36725i) q^{6} +(-6.68054 + 2.09055i) q^{7} +(-1.65875 - 1.65875i) q^{8} +(5.08462 + 7.42608i) q^{9} +(10.4175 - 8.33654i) q^{10} +17.9060i q^{11} +(4.36672 - 8.28210i) q^{12} +(-11.1383 - 11.1383i) q^{13} +(8.66093 - 16.5503i) q^{14} +(-12.4162 - 8.41655i) q^{15} +18.7435 q^{16} +(0.666845 + 0.666845i) q^{17} +(-23.6067 - 4.41815i) q^{18} -10.8119 q^{19} +(-1.72096 + 15.5094i) q^{20} +(-20.6534 - 3.79947i) q^{21} +(-33.7872 - 33.7872i) q^{22} +(2.20425 + 2.20425i) q^{23} +(-2.08100 - 6.72276i) q^{24} +(24.3919 + 5.48064i) q^{25} +42.0343 q^{26} +(3.10283 + 26.8211i) q^{27} +(6.52445 + 20.8494i) q^{28} +22.9708 q^{29} +(39.3097 - 7.54700i) q^{30} +26.1094i q^{31} +(-28.7325 + 28.7325i) q^{32} +(-25.0537 + 47.5179i) q^{33} -2.51656 q^{34} +(34.3517 - 6.70517i) q^{35} +(23.1762 - 15.8687i) q^{36} +(41.6663 + 41.6663i) q^{37} +(20.4011 - 20.4011i) q^{38} +(-13.9737 - 45.1427i) q^{39} +(7.32848 + 9.15784i) q^{40} -6.85976 q^{41} +(46.1406 - 31.8020i) q^{42} +(-37.6932 + 37.6932i) q^{43} +55.8834 q^{44} +(-21.1730 - 39.7077i) q^{45} -8.31847 q^{46} +(-5.55606 - 5.55606i) q^{47} +(49.7404 + 26.2255i) q^{48} +(40.2592 - 27.9320i) q^{49} +(-56.3670 + 35.6839i) q^{50} +(0.836596 + 2.70266i) q^{51} +(-34.7619 + 34.7619i) q^{52} +(-32.4556 - 32.4556i) q^{53} +(-56.4640 - 44.7545i) q^{54} +(9.87390 - 88.9841i) q^{55} +(14.5490 + 7.61364i) q^{56} +(-28.6918 - 15.1277i) q^{57} +(-43.3441 + 43.3441i) q^{58} +99.8940i q^{59} +(-26.2674 + 38.7499i) q^{60} -44.6768i q^{61} +(-49.2664 - 49.2664i) q^{62} +(-49.4926 - 38.9806i) q^{63} -33.4577i q^{64} +(49.2100 + 61.4940i) q^{65} +(-42.3881 - 136.937i) q^{66} +(-18.0239 - 18.0239i) q^{67} +(2.08117 - 2.08117i) q^{68} +(2.76536 + 8.93362i) q^{69} +(-52.1668 + 77.4710i) q^{70} -6.35575i q^{71} +(3.88391 - 20.7521i) q^{72} +(55.3597 + 55.3597i) q^{73} -157.242 q^{74} +(57.0611 + 48.6727i) q^{75} +33.7430i q^{76} +(-37.4336 - 119.622i) q^{77} +(111.548 + 58.8133i) q^{78} -59.7832i q^{79} +(-93.1460 - 10.3357i) q^{80} +(-29.2934 + 75.5175i) q^{81} +(12.9438 - 12.9438i) q^{82} +(42.2387 - 42.2387i) q^{83} +(-11.8578 + 64.4577i) q^{84} +(-2.94617 - 3.68160i) q^{85} -142.248i q^{86} +(60.9585 + 32.1402i) q^{87} +(29.7017 - 29.7017i) q^{88} -58.4197i q^{89} +(114.877 + 34.9734i) q^{90} +(97.6954 + 51.1248i) q^{91} +(6.87928 - 6.87928i) q^{92} +(-36.5317 + 69.2875i) q^{93} +20.9677 q^{94} +(53.7296 + 5.96197i) q^{95} +(-116.450 + 36.0466i) q^{96} +(11.1921 - 11.1921i) q^{97} +(-23.2603 + 128.671i) q^{98} +(-132.972 + 91.0454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 48q^{15} - 24q^{16} - 92q^{18} - 60q^{21} + 112q^{22} - 72q^{25} + 88q^{28} - 108q^{30} + 416q^{36} + 72q^{37} + 300q^{42} - 328q^{43} + 32q^{46} + 148q^{51} - 748q^{57} - 392q^{58} + 544q^{60} - 220q^{63} - 648q^{67} - 8q^{70} - 8q^{72} + 500q^{78} - 948q^{81} + 672q^{85} + 1288q^{88} + 808q^{91} + 292q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88692 + 1.88692i −0.943459 + 0.943459i −0.998485 0.0550258i \(-0.982476\pi\)
0.0550258 + 0.998485i \(0.482476\pi\)
\(3\) 2.65373 + 1.39918i 0.884578 + 0.466392i
\(4\) 3.12092i 0.780230i
\(5\) −4.96950 0.551428i −0.993900 0.110286i
\(6\) −7.64751 + 2.36725i −1.27459 + 0.394542i
\(7\) −6.68054 + 2.09055i −0.954363 + 0.298651i
\(8\) −1.65875 1.65875i −0.207344 0.207344i
\(9\) 5.08462 + 7.42608i 0.564957 + 0.825120i
\(10\) 10.4175 8.33654i 1.04175 0.833654i
\(11\) 17.9060i 1.62782i 0.580989 + 0.813911i \(0.302666\pi\)
−0.580989 + 0.813911i \(0.697334\pi\)
\(12\) 4.36672 8.28210i 0.363893 0.690175i
\(13\) −11.1383 11.1383i −0.856796 0.856796i 0.134164 0.990959i \(-0.457165\pi\)
−0.990959 + 0.134164i \(0.957165\pi\)
\(14\) 8.66093 16.5503i 0.618638 1.18217i
\(15\) −12.4162 8.41655i −0.827746 0.561103i
\(16\) 18.7435 1.17147
\(17\) 0.666845 + 0.666845i 0.0392262 + 0.0392262i 0.726448 0.687222i \(-0.241170\pi\)
−0.687222 + 0.726448i \(0.741170\pi\)
\(18\) −23.6067 4.41815i −1.31148 0.245453i
\(19\) −10.8119 −0.569046 −0.284523 0.958669i \(-0.591835\pi\)
−0.284523 + 0.958669i \(0.591835\pi\)
\(20\) −1.72096 + 15.5094i −0.0860482 + 0.775471i
\(21\) −20.6534 3.79947i −0.983496 0.180927i
\(22\) −33.7872 33.7872i −1.53578 1.53578i
\(23\) 2.20425 + 2.20425i 0.0958368 + 0.0958368i 0.753400 0.657563i \(-0.228413\pi\)
−0.657563 + 0.753400i \(0.728413\pi\)
\(24\) −2.08100 6.72276i −0.0867083 0.280115i
\(25\) 24.3919 + 5.48064i 0.975674 + 0.219226i
\(26\) 42.0343 1.61670
\(27\) 3.10283 + 26.8211i 0.114920 + 0.993375i
\(28\) 6.52445 + 20.8494i 0.233016 + 0.744623i
\(29\) 22.9708 0.792098 0.396049 0.918229i \(-0.370381\pi\)
0.396049 + 0.918229i \(0.370381\pi\)
\(30\) 39.3097 7.54700i 1.31032 0.251567i
\(31\) 26.1094i 0.842240i 0.907005 + 0.421120i \(0.138363\pi\)
−0.907005 + 0.421120i \(0.861637\pi\)
\(32\) −28.7325 + 28.7325i −0.897891 + 0.897891i
\(33\) −25.0537 + 47.5179i −0.759203 + 1.43994i
\(34\) −2.51656 −0.0740166
\(35\) 34.3517 6.70517i 0.981478 0.191576i
\(36\) 23.1762 15.8687i 0.643784 0.440797i
\(37\) 41.6663 + 41.6663i 1.12612 + 1.12612i 0.990803 + 0.135314i \(0.0432044\pi\)
0.135314 + 0.990803i \(0.456796\pi\)
\(38\) 20.4011 20.4011i 0.536871 0.536871i
\(39\) −13.9737 45.1427i −0.358300 1.15751i
\(40\) 7.32848 + 9.15784i 0.183212 + 0.228946i
\(41\) −6.85976 −0.167311 −0.0836556 0.996495i \(-0.526660\pi\)
−0.0836556 + 0.996495i \(0.526660\pi\)
\(42\) 46.1406 31.8020i 1.09859 0.757191i
\(43\) −37.6932 + 37.6932i −0.876587 + 0.876587i −0.993180 0.116593i \(-0.962803\pi\)
0.116593 + 0.993180i \(0.462803\pi\)
\(44\) 55.8834 1.27008
\(45\) −21.1730 39.7077i −0.470512 0.882394i
\(46\) −8.31847 −0.180836
\(47\) −5.55606 5.55606i −0.118214 0.118214i 0.645525 0.763739i \(-0.276639\pi\)
−0.763739 + 0.645525i \(0.776639\pi\)
\(48\) 49.7404 + 26.2255i 1.03626 + 0.546364i
\(49\) 40.2592 27.9320i 0.821616 0.570042i
\(50\) −56.3670 + 35.6839i −1.12734 + 0.713678i
\(51\) 0.836596 + 2.70266i 0.0164038 + 0.0529934i
\(52\) −34.7619 + 34.7619i −0.668498 + 0.668498i
\(53\) −32.4556 32.4556i −0.612369 0.612369i 0.331194 0.943563i \(-0.392549\pi\)
−0.943563 + 0.331194i \(0.892549\pi\)
\(54\) −56.4640 44.7545i −1.04563 0.828787i
\(55\) 9.87390 88.9841i 0.179525 1.61789i
\(56\) 14.5490 + 7.61364i 0.259804 + 0.135958i
\(57\) −28.6918 15.1277i −0.503365 0.265398i
\(58\) −43.3441 + 43.3441i −0.747312 + 0.747312i
\(59\) 99.8940i 1.69312i 0.532294 + 0.846559i \(0.321330\pi\)
−0.532294 + 0.846559i \(0.678670\pi\)
\(60\) −26.2674 + 38.7499i −0.437790 + 0.645832i
\(61\) 44.6768i 0.732406i −0.930535 0.366203i \(-0.880658\pi\)
0.930535 0.366203i \(-0.119342\pi\)
\(62\) −49.2664 49.2664i −0.794619 0.794619i
\(63\) −49.4926 38.9806i −0.785597 0.618739i
\(64\) 33.4577i 0.522776i
\(65\) 49.2100 + 61.4940i 0.757077 + 0.946061i
\(66\) −42.3881 136.937i −0.642244 2.07480i
\(67\) −18.0239 18.0239i −0.269013 0.269013i 0.559689 0.828702i \(-0.310920\pi\)
−0.828702 + 0.559689i \(0.810920\pi\)
\(68\) 2.08117 2.08117i 0.0306054 0.0306054i
\(69\) 2.76536 + 8.93362i 0.0400777 + 0.129473i
\(70\) −52.1668 + 77.4710i −0.745240 + 1.10673i
\(71\) 6.35575i 0.0895177i −0.998998 0.0447588i \(-0.985748\pi\)
0.998998 0.0447588i \(-0.0142519\pi\)
\(72\) 3.88391 20.7521i 0.0539431 0.288224i
\(73\) 55.3597 + 55.3597i 0.758352 + 0.758352i 0.976022 0.217671i \(-0.0698458\pi\)
−0.217671 + 0.976022i \(0.569846\pi\)
\(74\) −157.242 −2.12489
\(75\) 57.0611 + 48.6727i 0.760815 + 0.648969i
\(76\) 33.7430i 0.443987i
\(77\) −37.4336 119.622i −0.486150 1.55353i
\(78\) 111.548 + 58.8133i 1.43010 + 0.754017i
\(79\) 59.7832i 0.756749i −0.925653 0.378375i \(-0.876483\pi\)
0.925653 0.378375i \(-0.123517\pi\)
\(80\) −93.1460 10.3357i −1.16432 0.129196i
\(81\) −29.2934 + 75.5175i −0.361646 + 0.932315i
\(82\) 12.9438 12.9438i 0.157851 0.157851i
\(83\) 42.2387 42.2387i 0.508900 0.508900i −0.405289 0.914189i \(-0.632829\pi\)
0.914189 + 0.405289i \(0.132829\pi\)
\(84\) −11.8578 + 64.4577i −0.141165 + 0.767354i
\(85\) −2.94617 3.68160i −0.0346608 0.0433130i
\(86\) 142.248i 1.65405i
\(87\) 60.9585 + 32.1402i 0.700673 + 0.369428i
\(88\) 29.7017 29.7017i 0.337519 0.337519i
\(89\) 58.4197i 0.656401i −0.944608 0.328200i \(-0.893558\pi\)
0.944608 0.328200i \(-0.106442\pi\)
\(90\) 114.877 + 34.9734i 1.27641 + 0.388593i
\(91\) 97.6954 + 51.1248i 1.07358 + 0.561811i
\(92\) 6.87928 6.87928i 0.0747748 0.0747748i
\(93\) −36.5317 + 69.2875i −0.392814 + 0.745027i
\(94\) 20.9677 0.223060
\(95\) 53.7296 + 5.96197i 0.565574 + 0.0627576i
\(96\) −116.450 + 36.0466i −1.21302 + 0.375486i
\(97\) 11.1921 11.1921i 0.115383 0.115383i −0.647058 0.762441i \(-0.724001\pi\)
0.762441 + 0.647058i \(0.224001\pi\)
\(98\) −23.2603 + 128.671i −0.237350 + 1.31297i
\(99\) −132.972 + 91.0454i −1.34315 + 0.919650i
\(100\) 17.1047 76.1251i 0.171047 0.761251i
\(101\) −11.9219 −0.118038 −0.0590191 0.998257i \(-0.518797\pi\)
−0.0590191 + 0.998257i \(0.518797\pi\)
\(102\) −6.67829 3.52111i −0.0654734 0.0345207i
\(103\) −24.4345 24.4345i −0.237229 0.237229i 0.578473 0.815702i \(-0.303649\pi\)
−0.815702 + 0.578473i \(0.803649\pi\)
\(104\) 36.9514i 0.355302i
\(105\) 100.542 + 30.2703i 0.957543 + 0.288289i
\(106\) 122.482 1.15549
\(107\) 36.8755 36.8755i 0.344631 0.344631i −0.513474 0.858105i \(-0.671642\pi\)
0.858105 + 0.513474i \(0.171642\pi\)
\(108\) 83.7066 9.68369i 0.775061 0.0896638i
\(109\) 53.8082i 0.493653i −0.969060 0.246827i \(-0.920612\pi\)
0.969060 0.246827i \(-0.0793879\pi\)
\(110\) 149.274 + 186.537i 1.35704 + 1.69579i
\(111\) 52.2729 + 168.870i 0.470927 + 1.52135i
\(112\) −125.217 + 39.1844i −1.11801 + 0.349860i
\(113\) −83.5360 83.5360i −0.739257 0.739257i 0.233177 0.972434i \(-0.425088\pi\)
−0.972434 + 0.233177i \(0.925088\pi\)
\(114\) 82.6839 25.5944i 0.725297 0.224512i
\(115\) −9.73852 12.1695i −0.0846828 0.105822i
\(116\) 71.6902i 0.618019i
\(117\) 26.0800 139.348i 0.222906 1.19101i
\(118\) −188.492 188.492i −1.59739 1.59739i
\(119\) −5.84896 3.06081i −0.0491509 0.0257211i
\(120\) 6.63441 + 34.5563i 0.0552867 + 0.287969i
\(121\) −199.627 −1.64981
\(122\) 84.3014 + 84.3014i 0.690995 + 0.690995i
\(123\) −18.2040 9.59801i −0.148000 0.0780326i
\(124\) 81.4855 0.657141
\(125\) −118.193 40.6864i −0.945545 0.325491i
\(126\) 166.942 19.8353i 1.32493 0.157423i
\(127\) 147.690 + 147.690i 1.16291 + 1.16291i 0.983835 + 0.179080i \(0.0573121\pi\)
0.179080 + 0.983835i \(0.442688\pi\)
\(128\) −51.7981 51.7981i −0.404673 0.404673i
\(129\) −152.767 + 47.2884i −1.18424 + 0.366577i
\(130\) −208.889 23.1789i −1.60684 0.178299i
\(131\) 131.274 1.00209 0.501046 0.865421i \(-0.332949\pi\)
0.501046 + 0.865421i \(0.332949\pi\)
\(132\) 148.300 + 78.1906i 1.12348 + 0.592353i
\(133\) 72.2291 22.6028i 0.543076 0.169946i
\(134\) 68.0192 0.507606
\(135\) −0.629594 134.999i −0.00466366 0.999989i
\(136\) 2.21226i 0.0162666i
\(137\) −68.1163 + 68.1163i −0.497199 + 0.497199i −0.910565 0.413366i \(-0.864353\pi\)
0.413366 + 0.910565i \(0.364353\pi\)
\(138\) −22.0750 11.6390i −0.159964 0.0843406i
\(139\) −30.1138 −0.216646 −0.108323 0.994116i \(-0.534548\pi\)
−0.108323 + 0.994116i \(0.534548\pi\)
\(140\) −20.9263 107.209i −0.149474 0.765779i
\(141\) −6.97041 22.5182i −0.0494355 0.159704i
\(142\) 11.9928 + 11.9928i 0.0844563 + 0.0844563i
\(143\) 199.444 199.444i 1.39471 1.39471i
\(144\) 95.3037 + 139.191i 0.661831 + 0.966604i
\(145\) −114.154 12.6668i −0.787266 0.0873570i
\(146\) −208.918 −1.43095
\(147\) 145.919 17.7946i 0.992646 0.121052i
\(148\) 130.037 130.037i 0.878631 0.878631i
\(149\) −92.4633 −0.620559 −0.310280 0.950645i \(-0.600423\pi\)
−0.310280 + 0.950645i \(0.600423\pi\)
\(150\) −199.511 + 15.8283i −1.33007 + 0.105522i
\(151\) −12.2683 −0.0812472 −0.0406236 0.999175i \(-0.512934\pi\)
−0.0406236 + 0.999175i \(0.512934\pi\)
\(152\) 17.9342 + 17.9342i 0.117988 + 0.117988i
\(153\) −1.56139 + 8.34269i −0.0102052 + 0.0545274i
\(154\) 296.351 + 155.083i 1.92436 + 1.00703i
\(155\) 14.3975 129.751i 0.0928870 0.837102i
\(156\) −140.887 + 43.6108i −0.903121 + 0.279557i
\(157\) −63.9309 + 63.9309i −0.407203 + 0.407203i −0.880762 0.473559i \(-0.842969\pi\)
0.473559 + 0.880762i \(0.342969\pi\)
\(158\) 112.806 + 112.806i 0.713962 + 0.713962i
\(159\) −40.7174 131.540i −0.256084 0.827292i
\(160\) 158.630 126.942i 0.991439 0.793390i
\(161\) −19.3337 10.1175i −0.120085 0.0628414i
\(162\) −87.2212 197.770i −0.538403 1.22080i
\(163\) −10.2931 + 10.2931i −0.0631481 + 0.0631481i −0.737976 0.674827i \(-0.764218\pi\)
0.674827 + 0.737976i \(0.264218\pi\)
\(164\) 21.4088i 0.130541i
\(165\) 150.707 222.325i 0.913376 1.34742i
\(166\) 159.402i 0.960253i
\(167\) 57.7311 + 57.7311i 0.345695 + 0.345695i 0.858503 0.512808i \(-0.171395\pi\)
−0.512808 + 0.858503i \(0.671395\pi\)
\(168\) 27.9565 + 40.5612i 0.166408 + 0.241436i
\(169\) 79.1253i 0.468197i
\(170\) 12.5061 + 1.38770i 0.0735650 + 0.00816296i
\(171\) −54.9742 80.2898i −0.321487 0.469531i
\(172\) 117.638 + 117.638i 0.683940 + 0.683940i
\(173\) −179.111 + 179.111i −1.03532 + 1.03532i −0.0359688 + 0.999353i \(0.511452\pi\)
−0.999353 + 0.0359688i \(0.988548\pi\)
\(174\) −175.670 + 54.3777i −1.00960 + 0.312516i
\(175\) −174.408 + 14.3788i −0.996619 + 0.0821647i
\(176\) 335.623i 1.90695i
\(177\) −139.769 + 265.092i −0.789657 + 1.49770i
\(178\) 110.233 + 110.233i 0.619287 + 0.619287i
\(179\) 307.914 1.72019 0.860095 0.510133i \(-0.170404\pi\)
0.860095 + 0.510133i \(0.170404\pi\)
\(180\) −123.925 + 66.0794i −0.688470 + 0.367108i
\(181\) 124.967i 0.690428i 0.938524 + 0.345214i \(0.112194\pi\)
−0.938524 + 0.345214i \(0.887806\pi\)
\(182\) −280.812 + 87.8749i −1.54292 + 0.482829i
\(183\) 62.5106 118.560i 0.341588 0.647870i
\(184\) 7.31259i 0.0397423i
\(185\) −184.085 230.037i −0.995053 1.24344i
\(186\) −61.8076 199.672i −0.332299 1.07351i
\(187\) −11.9406 + 11.9406i −0.0638532 + 0.0638532i
\(188\) −17.3400 + 17.3400i −0.0922342 + 0.0922342i
\(189\) −76.7996 172.693i −0.406347 0.913719i
\(190\) −112.633 + 90.1336i −0.592806 + 0.474387i
\(191\) 120.234i 0.629496i 0.949175 + 0.314748i \(0.101920\pi\)
−0.949175 + 0.314748i \(0.898080\pi\)
\(192\) 46.8132 88.7878i 0.243819 0.462437i
\(193\) −12.8649 + 12.8649i −0.0666576 + 0.0666576i −0.739650 0.672992i \(-0.765009\pi\)
0.672992 + 0.739650i \(0.265009\pi\)
\(194\) 42.2372i 0.217718i
\(195\) 44.5494 + 232.042i 0.228458 + 1.18996i
\(196\) −87.1737 125.646i −0.444764 0.641050i
\(197\) 7.82035 7.82035i 0.0396972 0.0396972i −0.686980 0.726677i \(-0.741064\pi\)
0.726677 + 0.686980i \(0.241064\pi\)
\(198\) 79.1117 422.702i 0.399554 2.13486i
\(199\) 301.160 1.51336 0.756682 0.653783i \(-0.226819\pi\)
0.756682 + 0.653783i \(0.226819\pi\)
\(200\) −31.3690 49.5510i −0.156845 0.247755i
\(201\) −22.6120 73.0491i −0.112498 0.363429i
\(202\) 22.4956 22.4956i 0.111364 0.111364i
\(203\) −153.458 + 48.0218i −0.755949 + 0.236560i
\(204\) 8.43479 2.61095i 0.0413470 0.0127988i
\(205\) 34.0896 + 3.78266i 0.166291 + 0.0184520i
\(206\) 92.2120 0.447631
\(207\) −5.16117 + 27.5767i −0.0249332 + 0.133221i
\(208\) −208.772 208.772i −1.00371 1.00371i
\(209\) 193.598i 0.926305i
\(210\) −246.832 + 132.597i −1.17539 + 0.631414i
\(211\) −363.605 −1.72325 −0.861623 0.507549i \(-0.830552\pi\)
−0.861623 + 0.507549i \(0.830552\pi\)
\(212\) −101.291 + 101.291i −0.477789 + 0.477789i
\(213\) 8.89282 16.8665i 0.0417503 0.0791854i
\(214\) 139.162i 0.650291i
\(215\) 208.102 166.531i 0.967915 0.774565i
\(216\) 39.3427 49.6363i 0.182142 0.229798i
\(217\) −54.5832 174.425i −0.251535 0.803802i
\(218\) 101.532 + 101.532i 0.465742 + 0.465742i
\(219\) 69.4520 + 224.368i 0.317132 + 1.02451i
\(220\) −277.712 30.8157i −1.26233 0.140071i
\(221\) 14.8551i 0.0672176i
\(222\) −417.278 220.009i −1.87963 0.991032i
\(223\) −21.1671 21.1671i −0.0949198 0.0949198i 0.658052 0.752972i \(-0.271381\pi\)
−0.752972 + 0.658052i \(0.771381\pi\)
\(224\) 131.882 252.016i 0.588758 1.12507i
\(225\) 83.3235 + 209.003i 0.370327 + 0.928902i
\(226\) 315.251 1.39492
\(227\) 190.960 + 190.960i 0.841234 + 0.841234i 0.989019 0.147785i \(-0.0472145\pi\)
−0.147785 + 0.989019i \(0.547215\pi\)
\(228\) −47.2124 + 89.5449i −0.207072 + 0.392741i
\(229\) 84.1627 0.367523 0.183761 0.982971i \(-0.441173\pi\)
0.183761 + 0.982971i \(0.441173\pi\)
\(230\) 41.3386 + 4.58704i 0.179733 + 0.0199436i
\(231\) 68.0335 369.821i 0.294517 1.60096i
\(232\) −38.1029 38.1029i −0.164237 0.164237i
\(233\) 227.465 + 227.465i 0.976246 + 0.976246i 0.999724 0.0234784i \(-0.00747408\pi\)
−0.0234784 + 0.999724i \(0.507474\pi\)
\(234\) 213.728 + 312.150i 0.913368 + 1.33397i
\(235\) 24.5471 + 30.6746i 0.104456 + 0.130530i
\(236\) 311.761 1.32102
\(237\) 83.6472 158.649i 0.352942 0.669404i
\(238\) 16.8120 5.26101i 0.0706386 0.0221051i
\(239\) −19.0852 −0.0798543 −0.0399272 0.999203i \(-0.512713\pi\)
−0.0399272 + 0.999203i \(0.512713\pi\)
\(240\) −232.723 157.756i −0.969680 0.657316i
\(241\) 345.423i 1.43329i −0.697438 0.716645i \(-0.745677\pi\)
0.697438 0.716645i \(-0.254323\pi\)
\(242\) 376.679 376.679i 1.55652 1.55652i
\(243\) −183.399 + 159.417i −0.754729 + 0.656037i
\(244\) −139.433 −0.571445
\(245\) −215.470 + 116.608i −0.879471 + 0.475952i
\(246\) 52.4601 16.2388i 0.213252 0.0660112i
\(247\) 120.426 + 120.426i 0.487556 + 0.487556i
\(248\) 43.3090 43.3090i 0.174633 0.174633i
\(249\) 171.190 52.9910i 0.687509 0.212815i
\(250\) 299.793 146.249i 1.19917 0.584995i
\(251\) −253.938 −1.01170 −0.505852 0.862620i \(-0.668822\pi\)
−0.505852 + 0.862620i \(0.668822\pi\)
\(252\) −121.655 + 154.462i −0.482759 + 0.612946i
\(253\) −39.4694 + 39.4694i −0.156005 + 0.156005i
\(254\) −557.358 −2.19432
\(255\) −2.66714 13.8922i −0.0104594 0.0544792i
\(256\) 329.309 1.28636
\(257\) 295.955 + 295.955i 1.15158 + 1.15158i 0.986237 + 0.165340i \(0.0528721\pi\)
0.165340 + 0.986237i \(0.447128\pi\)
\(258\) 199.030 377.489i 0.771435 1.46313i
\(259\) −365.459 191.248i −1.41104 0.738408i
\(260\) 191.918 153.581i 0.738146 0.590694i
\(261\) 116.798 + 170.583i 0.447502 + 0.653576i
\(262\) −247.703 + 247.703i −0.945433 + 0.945433i
\(263\) 1.73180 + 1.73180i 0.00658477 + 0.00658477i 0.710392 0.703807i \(-0.248518\pi\)
−0.703807 + 0.710392i \(0.748518\pi\)
\(264\) 120.378 37.2625i 0.455978 0.141146i
\(265\) 143.391 + 179.185i 0.541098 + 0.676169i
\(266\) −93.6408 + 178.940i −0.352033 + 0.672707i
\(267\) 81.7394 155.030i 0.306140 0.580638i
\(268\) −56.2511 + 56.2511i −0.209892 + 0.209892i
\(269\) 400.956i 1.49054i 0.666761 + 0.745272i \(0.267680\pi\)
−0.666761 + 0.745272i \(0.732320\pi\)
\(270\) 255.919 + 253.543i 0.947849 + 0.939049i
\(271\) 395.831i 1.46063i 0.683109 + 0.730316i \(0.260627\pi\)
−0.683109 + 0.730316i \(0.739373\pi\)
\(272\) 12.4990 + 12.4990i 0.0459523 + 0.0459523i
\(273\) 187.725 + 272.365i 0.687638 + 0.997673i
\(274\) 257.060i 0.938174i
\(275\) −98.1367 + 436.762i −0.356861 + 1.58822i
\(276\) 27.8811 8.63047i 0.101019 0.0312698i
\(277\) −40.6213 40.6213i −0.146647 0.146647i 0.629971 0.776618i \(-0.283067\pi\)
−0.776618 + 0.629971i \(0.783067\pi\)
\(278\) 56.8222 56.8222i 0.204397 0.204397i
\(279\) −193.891 + 132.756i −0.694949 + 0.475830i
\(280\) −68.1031 45.8587i −0.243225 0.163781i
\(281\) 284.890i 1.01384i −0.861992 0.506922i \(-0.830783\pi\)
0.861992 0.506922i \(-0.169217\pi\)
\(282\) 55.6426 + 29.3374i 0.197314 + 0.104033i
\(283\) 102.657 + 102.657i 0.362744 + 0.362744i 0.864822 0.502078i \(-0.167431\pi\)
−0.502078 + 0.864822i \(0.667431\pi\)
\(284\) −19.8358 −0.0698444
\(285\) 134.242 + 90.9986i 0.471025 + 0.319293i
\(286\) 752.668i 2.63171i
\(287\) 45.8269 14.3407i 0.159676 0.0499676i
\(288\) −359.464 67.2762i −1.24814 0.233598i
\(289\) 288.111i 0.996923i
\(290\) 239.300 191.497i 0.825171 0.660336i
\(291\) 45.3606 14.0412i 0.155879 0.0482515i
\(292\) 172.773 172.773i 0.591689 0.591689i
\(293\) 204.227 204.227i 0.697021 0.697021i −0.266746 0.963767i \(-0.585948\pi\)
0.963767 + 0.266746i \(0.0859483\pi\)
\(294\) −241.760 + 308.914i −0.822314 + 1.05073i
\(295\) 55.0844 496.423i 0.186727 1.68279i
\(296\) 138.228i 0.466987i
\(297\) −480.260 + 55.5594i −1.61704 + 0.187069i
\(298\) 174.471 174.471i 0.585472 0.585472i
\(299\) 49.1033i 0.164225i
\(300\) 151.904 178.083i 0.506345 0.593611i
\(301\) 173.011 330.611i 0.574789 1.09838i
\(302\) 23.1493 23.1493i 0.0766534 0.0766534i
\(303\) −31.6374 16.6808i −0.104414 0.0550520i
\(304\) −202.653 −0.666621
\(305\) −24.6360 + 222.021i −0.0807738 + 0.727938i
\(306\) −12.7958 18.6882i −0.0418162 0.0610725i
\(307\) 209.811 209.811i 0.683425 0.683425i −0.277345 0.960770i \(-0.589455\pi\)
0.960770 + 0.277345i \(0.0894547\pi\)
\(308\) −373.331 + 116.827i −1.21211 + 0.379309i
\(309\) −30.6546 99.0310i −0.0992058 0.320489i
\(310\) 217.662 + 271.996i 0.702137 + 0.877407i
\(311\) −414.961 −1.33428 −0.667141 0.744932i \(-0.732482\pi\)
−0.667141 + 0.744932i \(0.732482\pi\)
\(312\) −51.7016 + 98.0593i −0.165710 + 0.314293i
\(313\) 6.05318 + 6.05318i 0.0193392 + 0.0193392i 0.716710 0.697371i \(-0.245647\pi\)
−0.697371 + 0.716710i \(0.745647\pi\)
\(314\) 241.265i 0.768359i
\(315\) 224.458 + 221.005i 0.712566 + 0.701605i
\(316\) −186.579 −0.590439
\(317\) 255.502 255.502i 0.805999 0.805999i −0.178027 0.984026i \(-0.556971\pi\)
0.984026 + 0.178027i \(0.0569714\pi\)
\(318\) 325.035 + 171.374i 1.02212 + 0.538911i
\(319\) 411.317i 1.28939i
\(320\) −18.4495 + 166.268i −0.0576547 + 0.519588i
\(321\) 149.453 46.2625i 0.465586 0.144120i
\(322\) 55.5719 17.3902i 0.172583 0.0540069i
\(323\) −7.20984 7.20984i −0.0223215 0.0223215i
\(324\) 235.684 + 91.4223i 0.727421 + 0.282168i
\(325\) −210.640 332.730i −0.648122 1.02378i
\(326\) 38.8446i 0.119155i
\(327\) 75.2872 142.793i 0.230236 0.436675i
\(328\) 11.3786 + 11.3786i 0.0346909 + 0.0346909i
\(329\) 48.7327 + 25.5022i 0.148124 + 0.0775144i
\(330\) 135.137 + 703.881i 0.409506 + 2.13297i
\(331\) 148.520 0.448702 0.224351 0.974508i \(-0.427974\pi\)
0.224351 + 0.974508i \(0.427974\pi\)
\(332\) −131.824 131.824i −0.397059 0.397059i
\(333\) −97.5603 + 521.275i −0.292974 + 1.56539i
\(334\) −217.868 −0.652299
\(335\) 79.6308 + 99.5085i 0.237704 + 0.297040i
\(336\) −387.118 71.2155i −1.15214 0.211951i
\(337\) 225.218 + 225.218i 0.668303 + 0.668303i 0.957323 0.289020i \(-0.0933294\pi\)
−0.289020 + 0.957323i \(0.593329\pi\)
\(338\) −149.303 149.303i −0.441725 0.441725i
\(339\) −104.801 338.564i −0.309147 0.998714i
\(340\) −11.4900 + 9.19476i −0.0337941 + 0.0270434i
\(341\) −467.517 −1.37102
\(342\) 255.232 + 47.7685i 0.746293 + 0.139674i
\(343\) −210.559 + 270.765i −0.613876 + 0.789402i
\(344\) 125.047 0.363510
\(345\) −8.81620 45.9205i −0.0255542 0.133103i
\(346\) 675.934i 1.95357i
\(347\) 81.8789 81.8789i 0.235962 0.235962i −0.579214 0.815176i \(-0.696640\pi\)
0.815176 + 0.579214i \(0.196640\pi\)
\(348\) 100.307 190.247i 0.288239 0.546686i
\(349\) −356.670 −1.02198 −0.510989 0.859587i \(-0.670721\pi\)
−0.510989 + 0.859587i \(0.670721\pi\)
\(350\) 301.963 356.226i 0.862750 1.01779i
\(351\) 264.182 333.303i 0.752656 0.949582i
\(352\) −514.486 514.486i −1.46161 1.46161i
\(353\) −305.766 + 305.766i −0.866191 + 0.866191i −0.992048 0.125857i \(-0.959832\pi\)
0.125857 + 0.992048i \(0.459832\pi\)
\(354\) −236.474 763.940i −0.668006 2.15802i
\(355\) −3.50474 + 31.5849i −0.00987251 + 0.0889716i
\(356\) −182.323 −0.512144
\(357\) −11.2390 16.3063i −0.0314817 0.0456759i
\(358\) −581.009 + 581.009i −1.62293 + 1.62293i
\(359\) −356.776 −0.993806 −0.496903 0.867806i \(-0.665530\pi\)
−0.496903 + 0.867806i \(0.665530\pi\)
\(360\) −30.7444 + 100.986i −0.0854010 + 0.280516i
\(361\) −244.103 −0.676187
\(362\) −235.803 235.803i −0.651390 0.651390i
\(363\) −529.756 279.313i −1.45938 0.769456i
\(364\) 159.557 304.900i 0.438342 0.837637i
\(365\) −244.583 305.637i −0.670090 0.837361i
\(366\) 105.761 + 341.666i 0.288965 + 0.933514i
\(367\) 185.321 185.321i 0.504963 0.504963i −0.408013 0.912976i \(-0.633778\pi\)
0.912976 + 0.408013i \(0.133778\pi\)
\(368\) 41.3154 + 41.3154i 0.112270 + 0.112270i
\(369\) −34.8792 50.9411i −0.0945237 0.138052i
\(370\) 781.414 + 86.7076i 2.11193 + 0.234345i
\(371\) 284.671 + 148.971i 0.767307 + 0.401538i
\(372\) 216.241 + 114.013i 0.581293 + 0.306485i
\(373\) −231.949 + 231.949i −0.621848 + 0.621848i −0.946004 0.324155i \(-0.894920\pi\)
0.324155 + 0.946004i \(0.394920\pi\)
\(374\) 45.0617i 0.120486i
\(375\) −256.726 273.344i −0.684602 0.728917i
\(376\) 18.4322i 0.0490219i
\(377\) −255.857 255.857i −0.678666 0.678666i
\(378\) 470.772 + 180.943i 1.24543 + 0.478685i
\(379\) 33.7232i 0.0889794i −0.999010 0.0444897i \(-0.985834\pi\)
0.999010 0.0444897i \(-0.0141662\pi\)
\(380\) 18.6068 167.686i 0.0489654 0.441278i
\(381\) 185.286 + 598.575i 0.486315 + 1.57106i
\(382\) −226.871 226.871i −0.593904 0.593904i
\(383\) 353.025 353.025i 0.921735 0.921735i −0.0754169 0.997152i \(-0.524029\pi\)
0.997152 + 0.0754169i \(0.0240288\pi\)
\(384\) −64.9838 209.933i −0.169229 0.546701i
\(385\) 120.063 + 615.104i 0.311852 + 1.59767i
\(386\) 48.5501i 0.125777i
\(387\) −471.569 88.2574i −1.21852 0.228055i
\(388\) −34.9297 34.9297i −0.0900250 0.0900250i
\(389\) −222.963 −0.573170 −0.286585 0.958055i \(-0.592520\pi\)
−0.286585 + 0.958055i \(0.592520\pi\)
\(390\) −521.906 353.783i −1.33822 0.907137i
\(391\) 2.93978i 0.00751862i
\(392\) −113.112 20.4476i −0.288551 0.0521623i
\(393\) 348.366 + 183.675i 0.886429 + 0.467367i
\(394\) 29.5127i 0.0749054i
\(395\) −32.9661 + 297.093i −0.0834586 + 0.752133i
\(396\) 284.145 + 414.994i 0.717539 + 1.04797i
\(397\) −518.609 + 518.609i −1.30632 + 1.30632i −0.382270 + 0.924051i \(0.624857\pi\)
−0.924051 + 0.382270i \(0.875143\pi\)
\(398\) −568.264 + 568.264i −1.42780 + 1.42780i
\(399\) 223.302 + 41.0794i 0.559654 + 0.102956i
\(400\) 457.190 + 102.727i 1.14297 + 0.256817i
\(401\) 333.028i 0.830494i −0.909709 0.415247i \(-0.863695\pi\)
0.909709 0.415247i \(-0.136305\pi\)
\(402\) 180.505 + 95.1707i 0.449017 + 0.236743i
\(403\) 290.816 290.816i 0.721628 0.721628i
\(404\) 37.2072i 0.0920969i
\(405\) 187.216 359.131i 0.462261 0.886744i
\(406\) 198.949 380.175i 0.490022 0.936392i
\(407\) −746.079 + 746.079i −1.83312 + 1.83312i
\(408\) 3.09534 5.87074i 0.00758661 0.0143891i
\(409\) 634.549 1.55146 0.775732 0.631062i \(-0.217381\pi\)
0.775732 + 0.631062i \(0.217381\pi\)
\(410\) −71.4618 + 57.1866i −0.174297 + 0.139480i
\(411\) −276.069 + 85.4559i −0.671701 + 0.207922i
\(412\) −76.2583 + 76.2583i −0.185093 + 0.185093i
\(413\) −208.834 667.346i −0.505651 1.61585i
\(414\) −42.2962 61.7736i −0.102165 0.149212i
\(415\) −233.197 + 186.614i −0.561920 + 0.449671i
\(416\) 640.065 1.53862
\(417\) −79.9140 42.1345i −0.191640 0.101042i
\(418\) 365.303 + 365.303i 0.873931 + 0.873931i
\(419\) 415.098i 0.990687i 0.868697 + 0.495343i \(0.164958\pi\)
−0.868697 + 0.495343i \(0.835042\pi\)
\(420\) 94.4714 313.784i 0.224932 0.747104i
\(421\) 425.874 1.01158 0.505789 0.862657i \(-0.331201\pi\)
0.505789 + 0.862657i \(0.331201\pi\)
\(422\) 686.093 686.093i 1.62581 1.62581i
\(423\) 13.0093 69.5102i 0.0307549 0.164327i
\(424\) 107.671i 0.253942i
\(425\) 12.6108 + 19.9203i 0.0296726 + 0.0468713i
\(426\) 15.0457 + 48.6057i 0.0353185 + 0.114098i
\(427\) 93.3992 + 298.465i 0.218733 + 0.698981i
\(428\) −115.086 115.086i −0.268892 0.268892i
\(429\) 808.327 250.214i 1.88421 0.583249i
\(430\) −78.4396 + 706.902i −0.182418 + 1.64396i
\(431\) 217.914i 0.505600i 0.967519 + 0.252800i \(0.0813514\pi\)
−0.967519 + 0.252800i \(0.918649\pi\)
\(432\) 58.1580 + 502.723i 0.134625 + 1.16371i
\(433\) 377.736 + 377.736i 0.872369 + 0.872369i 0.992730 0.120361i \(-0.0384052\pi\)
−0.120361 + 0.992730i \(0.538405\pi\)
\(434\) 432.120 + 226.132i 0.995668 + 0.521041i
\(435\) −285.210 193.335i −0.655656 0.444449i
\(436\) −167.931 −0.385163
\(437\) −23.8320 23.8320i −0.0545355 0.0545355i
\(438\) −554.414 292.313i −1.26579 0.667382i
\(439\) 18.8677 0.0429789 0.0214894 0.999769i \(-0.493159\pi\)
0.0214894 + 0.999769i \(0.493159\pi\)
\(440\) −163.981 + 131.224i −0.372683 + 0.298236i
\(441\) 412.128 + 156.944i 0.934531 + 0.355882i
\(442\) 28.0303 + 28.0303i 0.0634171 + 0.0634171i
\(443\) 484.487 + 484.487i 1.09365 + 1.09365i 0.995136 + 0.0985149i \(0.0314092\pi\)
0.0985149 + 0.995136i \(0.468591\pi\)
\(444\) 527.030 163.140i 1.18700 0.367431i
\(445\) −32.2143 + 290.317i −0.0723916 + 0.652397i
\(446\) 79.8812 0.179106
\(447\) −245.373 129.372i −0.548933 0.289424i
\(448\) 69.9451 + 223.515i 0.156127 + 0.498918i
\(449\) 801.204 1.78442 0.892209 0.451623i \(-0.149155\pi\)
0.892209 + 0.451623i \(0.149155\pi\)
\(450\) −551.596 237.147i −1.22577 0.526993i
\(451\) 122.831i 0.272353i
\(452\) −260.709 + 260.709i −0.576791 + 0.576791i
\(453\) −32.5569 17.1655i −0.0718695 0.0378930i
\(454\) −720.652 −1.58734
\(455\) −457.306 307.937i −1.00507 0.676784i
\(456\) 22.4995 + 72.6856i 0.0493410 + 0.159398i
\(457\) −407.879 407.879i −0.892515 0.892515i 0.102244 0.994759i \(-0.467398\pi\)
−0.994759 + 0.102244i \(0.967398\pi\)
\(458\) −158.808 + 158.808i −0.346743 + 0.346743i
\(459\) −15.8164 + 19.9546i −0.0344584 + 0.0434741i
\(460\) −37.9800 + 30.3932i −0.0825653 + 0.0660721i
\(461\) 627.296 1.36073 0.680365 0.732874i \(-0.261821\pi\)
0.680365 + 0.732874i \(0.261821\pi\)
\(462\) 569.449 + 826.196i 1.23257 + 1.78830i
\(463\) 576.012 576.012i 1.24409 1.24409i 0.285797 0.958290i \(-0.407742\pi\)
0.958290 0.285797i \(-0.0922584\pi\)
\(464\) 430.555 0.927920
\(465\) 219.751 324.180i 0.472584 0.697161i
\(466\) −858.417 −1.84210
\(467\) 239.537 + 239.537i 0.512928 + 0.512928i 0.915422 0.402495i \(-0.131857\pi\)
−0.402495 + 0.915422i \(0.631857\pi\)
\(468\) −434.895 81.3938i −0.929264 0.173918i
\(469\) 158.089 + 82.7293i 0.337077 + 0.176395i
\(470\) −104.199 11.5622i −0.221700 0.0246003i
\(471\) −259.106 + 80.2051i −0.550119 + 0.170287i
\(472\) 165.699 165.699i 0.351058 0.351058i
\(473\) −674.937 674.937i −1.42693 1.42693i
\(474\) 141.522 + 457.193i 0.298569 + 0.964542i
\(475\) −263.722 59.2560i −0.555203 0.124749i
\(476\) −9.55254 + 18.2541i −0.0200684 + 0.0383490i
\(477\) 75.9936 406.042i 0.159316 0.851241i
\(478\) 36.0122 36.0122i 0.0753393 0.0753393i
\(479\) 868.698i 1.81357i −0.421598 0.906783i \(-0.638531\pi\)
0.421598 0.906783i \(-0.361469\pi\)
\(480\) 598.577 114.920i 1.24704 0.239416i
\(481\) 928.188i 1.92970i
\(482\) 651.785 + 651.785i 1.35225 + 1.35225i
\(483\) −37.1503 53.9002i −0.0769157 0.111595i
\(484\) 623.019i 1.28723i
\(485\) −61.7909 + 49.4476i −0.127404 + 0.101954i
\(486\) 45.2524 646.866i 0.0931119 1.33100i
\(487\) 1.87718 + 1.87718i 0.00385458 + 0.00385458i 0.709031 0.705177i \(-0.249132\pi\)
−0.705177 + 0.709031i \(0.749132\pi\)
\(488\) −74.1076 + 74.1076i −0.151860 + 0.151860i
\(489\) −41.7171 + 12.9133i −0.0853111 + 0.0264077i
\(490\) 186.545 626.605i 0.380704 1.27879i
\(491\) 125.302i 0.255198i 0.991826 + 0.127599i \(0.0407270\pi\)
−0.991826 + 0.127599i \(0.959273\pi\)
\(492\) −29.9546 + 56.8132i −0.0608834 + 0.115474i
\(493\) 15.3180 + 15.3180i 0.0310710 + 0.0310710i
\(494\) −454.469 −0.919978
\(495\) 711.008 379.126i 1.43638 0.765910i
\(496\) 489.383i 0.986660i
\(497\) 13.2870 + 42.4599i 0.0267345 + 0.0854323i
\(498\) −223.031 + 423.011i −0.447854 + 0.849419i
\(499\) 426.549i 0.854807i 0.904061 + 0.427403i \(0.140572\pi\)
−0.904061 + 0.427403i \(0.859428\pi\)
\(500\) −126.979 + 368.871i −0.253958 + 0.737743i
\(501\) 72.4271 + 233.979i 0.144565 + 0.467024i
\(502\) 479.160 479.160i 0.954502 0.954502i
\(503\) 606.100 606.100i 1.20497 1.20497i 0.232335 0.972636i \(-0.425364\pi\)
0.972636 0.232335i \(-0.0746364\pi\)
\(504\) 17.4368 + 146.755i 0.0345969 + 0.291180i
\(505\) 59.2456 + 6.57404i 0.117318 + 0.0130179i
\(506\) 148.951i 0.294369i
\(507\) −110.710 + 209.978i −0.218363 + 0.414157i
\(508\) 460.929 460.929i 0.907341 0.907341i
\(509\) 3.90604i 0.00767394i 0.999993 + 0.00383697i \(0.00122135\pi\)
−0.999993 + 0.00383697i \(0.998779\pi\)
\(510\) 31.2461 + 21.1808i 0.0612669 + 0.0415309i
\(511\) −485.565 254.100i −0.950225 0.497260i
\(512\) −414.186 + 414.186i −0.808956 + 0.808956i
\(513\) −33.5474 289.986i −0.0653945 0.565276i
\(514\) −1116.89 −2.17293
\(515\) 107.954 + 134.901i 0.209619 + 0.261944i
\(516\) 147.583 + 476.775i 0.286014 + 0.923982i
\(517\) 99.4871 99.4871i 0.192431 0.192431i
\(518\) 1050.46 328.723i 2.02792 0.634600i
\(519\) −725.919 + 224.705i −1.39869 + 0.432957i
\(520\) 20.3761 183.630i 0.0391847 0.353135i
\(521\) 556.444 1.06803 0.534015 0.845475i \(-0.320683\pi\)
0.534015 + 0.845475i \(0.320683\pi\)
\(522\) −542.265 101.489i −1.03882 0.194423i
\(523\) −241.019 241.019i −0.460839 0.460839i 0.438092 0.898930i \(-0.355655\pi\)
−0.898930 + 0.438092i \(0.855655\pi\)
\(524\) 409.696i 0.781862i
\(525\) −482.952 205.870i −0.919908 0.392134i
\(526\) −6.53551 −0.0124249
\(527\) −17.4109 + 17.4109i −0.0330378 + 0.0330378i
\(528\) −469.595 + 890.653i −0.889384 + 1.68684i
\(529\) 519.283i 0.981631i
\(530\) −608.674 67.5400i −1.14844 0.127434i
\(531\) −741.821 + 507.923i −1.39703 + 0.956540i
\(532\) −70.5415 225.421i −0.132597 0.423724i
\(533\) 76.4063 + 76.4063i 0.143351 + 0.143351i
\(534\) 138.294 + 446.765i 0.258978 + 0.836639i
\(535\) −203.587 + 162.919i −0.380537 + 0.304521i
\(536\) 59.7942i 0.111556i
\(537\) 817.122 + 430.826i 1.52164 + 0.802283i
\(538\) −756.572 756.572i −1.40627 1.40627i
\(539\) 500.153 + 720.883i 0.927927 + 1.33744i
\(540\) −421.320 + 1.96491i −0.780222 + 0.00363873i
\(541\) 255.515 0.472302 0.236151 0.971716i \(-0.424114\pi\)
0.236151 + 0.971716i \(0.424114\pi\)
\(542\) −746.901 746.901i −1.37805 1.37805i
\(543\) −174.851 + 331.630i −0.322010 + 0.610737i
\(544\) −38.3203 −0.0704416
\(545\) −29.6714 + 267.400i −0.0544429 + 0.490642i
\(546\) −868.152 159.708i −1.59002 0.292506i
\(547\) −80.6313 80.6313i −0.147406 0.147406i 0.629552 0.776958i \(-0.283238\pi\)
−0.776958 + 0.629552i \(0.783238\pi\)
\(548\) 212.586 + 212.586i 0.387930 + 0.387930i
\(549\) 331.773 227.164i 0.604323 0.413778i
\(550\) −638.958 1009.31i −1.16174 1.83511i
\(551\) −248.358 −0.450740
\(552\) 10.2316 19.4057i 0.0185355 0.0351552i
\(553\) 124.980 + 399.384i 0.226004 + 0.722213i
\(554\) 153.298 0.276711
\(555\) −166.650 868.024i −0.300271 1.56401i
\(556\) 93.9827i 0.169034i
\(557\) −452.948 + 452.948i −0.813192 + 0.813192i −0.985111 0.171919i \(-0.945003\pi\)
0.171919 + 0.985111i \(0.445003\pi\)
\(558\) 115.356 616.357i 0.206730 1.10458i
\(559\) 839.680 1.50211
\(560\) 643.873 125.679i 1.14977 0.224426i
\(561\) −48.3940 + 14.9801i −0.0862638 + 0.0267025i
\(562\) 537.564 + 537.564i 0.956520 + 0.956520i
\(563\) −534.797 + 534.797i −0.949906 + 0.949906i −0.998804 0.0488978i \(-0.984429\pi\)
0.0488978 + 0.998804i \(0.484429\pi\)
\(564\) −70.2776 + 21.7541i −0.124606 + 0.0385711i
\(565\) 369.068 + 461.196i 0.653218 + 0.816277i
\(566\) −387.409 −0.684468
\(567\) 37.8220 565.737i 0.0667054 0.997773i
\(568\) −10.5426 + 10.5426i −0.0185609 + 0.0185609i
\(569\) −527.903 −0.927773 −0.463886 0.885895i \(-0.653545\pi\)
−0.463886 + 0.885895i \(0.653545\pi\)
\(570\) −425.011 + 81.5972i −0.745633 + 0.143153i
\(571\) 249.965 0.437767 0.218884 0.975751i \(-0.429759\pi\)
0.218884 + 0.975751i \(0.429759\pi\)
\(572\) −622.448 622.448i −1.08820 1.08820i
\(573\) −168.228 + 319.069i −0.293592 + 0.556839i
\(574\) −59.4118 + 113.531i −0.103505 + 0.197790i
\(575\) 41.6850 + 65.8464i 0.0724956 + 0.114515i
\(576\) 248.460 170.120i 0.431353 0.295346i
\(577\) −63.8107 + 63.8107i −0.110590 + 0.110590i −0.760237 0.649646i \(-0.774917\pi\)
0.649646 + 0.760237i \(0.274917\pi\)
\(578\) 543.641 + 543.641i 0.940556 + 0.940556i
\(579\) −52.1404 + 16.1398i −0.0900524 + 0.0278753i
\(580\) −39.5320 + 356.264i −0.0681586 + 0.614249i
\(581\) −193.875 + 370.480i −0.333692 + 0.637658i
\(582\) −59.0973 + 112.086i −0.101542 + 0.192588i
\(583\) 581.151 581.151i 0.996828 0.996828i
\(584\) 183.656i 0.314479i
\(585\) −206.445 + 678.111i −0.352898 + 1.15916i
\(586\) 770.720i 1.31522i
\(587\) −748.348 748.348i −1.27487 1.27487i −0.943502 0.331366i \(-0.892491\pi\)
−0.331366 0.943502i \(-0.607509\pi\)
\(588\) −55.5355 455.402i −0.0944481 0.774493i
\(589\) 282.292i 0.479273i
\(590\) 832.770 + 1040.65i 1.41148 + 1.76381i
\(591\) 31.6952 9.81110i 0.0536298 0.0166008i
\(592\) 780.974 + 780.974i 1.31921 + 1.31921i
\(593\) 88.6544 88.6544i 0.149502 0.149502i −0.628394 0.777895i \(-0.716287\pi\)
0.777895 + 0.628394i \(0.216287\pi\)
\(594\) 801.376 1011.05i 1.34912 1.70210i
\(595\) 27.3786 + 18.4360i 0.0460144 + 0.0309848i
\(596\) 288.571i 0.484179i
\(597\) 799.198 + 421.375i 1.33869 + 0.705821i
\(598\) 92.6540 + 92.6540i 0.154940 + 0.154940i
\(599\) −512.160 −0.855025 −0.427512 0.904009i \(-0.640610\pi\)
−0.427512 + 0.904009i \(0.640610\pi\)
\(600\) −13.9144 175.386i −0.0231906 0.292310i
\(601\) 148.766i 0.247530i 0.992312 + 0.123765i \(0.0394969\pi\)
−0.992312 + 0.123765i \(0.960503\pi\)
\(602\) 297.377 + 950.294i 0.493982 + 1.57856i
\(603\) 42.2023 225.491i 0.0699872 0.373949i
\(604\) 38.2885i 0.0633915i
\(605\) 992.044 + 110.080i 1.63974 + 0.181950i
\(606\) 91.1725 28.2220i 0.150450 0.0465710i
\(607\) 336.268 336.268i 0.553984 0.553984i −0.373604 0.927588i \(-0.621878\pi\)
0.927588 + 0.373604i \(0.121878\pi\)
\(608\) 310.652 310.652i 0.510941 0.510941i
\(609\) −474.427 87.2770i −0.779026 0.143312i
\(610\) −372.450 465.422i −0.610573 0.762987i
\(611\) 123.771i 0.202571i
\(612\) 26.0369 + 4.87299i 0.0425439 + 0.00796240i
\(613\) −289.428 + 289.428i −0.472151 + 0.472151i −0.902610 0.430459i \(-0.858352\pi\)
0.430459 + 0.902610i \(0.358352\pi\)
\(614\) 791.794i 1.28957i
\(615\) 85.1720 + 57.7355i 0.138491 + 0.0938788i
\(616\) −136.330 + 260.516i −0.221315 + 0.422915i
\(617\) 759.979 759.979i 1.23173 1.23173i 0.268434 0.963298i \(-0.413494\pi\)
0.963298 0.268434i \(-0.0865062\pi\)
\(618\) 244.706 + 129.021i 0.395965 + 0.208771i
\(619\) 509.592 0.823251 0.411626 0.911353i \(-0.364961\pi\)
0.411626 + 0.911353i \(0.364961\pi\)
\(620\) −404.942 44.9334i −0.653133 0.0724732i
\(621\) −52.2810 + 65.9598i −0.0841884 + 0.106215i
\(622\) 782.998 782.998i 1.25884 1.25884i
\(623\) 122.129 + 390.275i 0.196034 + 0.626444i
\(624\) −261.917 846.134i −0.419738 1.35598i
\(625\) 564.925 + 267.366i 0.903880 + 0.427786i
\(626\) −22.8437 −0.0364915
\(627\) 270.877 513.757i 0.432021 0.819390i
\(628\) 199.523 + 199.523i 0.317712 + 0.317712i
\(629\) 55.5699i 0.0883465i
\(630\) −840.554 + 6.51546i −1.33421 + 0.0103420i
\(631\) −647.514 −1.02617 −0.513086 0.858337i \(-0.671498\pi\)
−0.513086 + 0.858337i \(0.671498\pi\)
\(632\) −99.1654 + 99.1654i −0.156907 + 0.156907i
\(633\) −964.911 508.747i −1.52435 0.803708i
\(634\) 964.221i 1.52085i
\(635\) −652.506 815.387i −1.02757 1.28407i
\(636\) −410.524 + 127.076i −0.645479 + 0.199805i
\(637\) −759.537 137.304i −1.19237 0.215547i
\(638\) −776.122 776.122i −1.21649 1.21649i
\(639\) 47.1983 32.3166i 0.0738628 0.0505737i
\(640\) 228.848 + 285.974i 0.357575 + 0.446834i
\(641\) 428.281i 0.668145i −0.942547 0.334072i \(-0.891577\pi\)
0.942547 0.334072i \(-0.108423\pi\)
\(642\) −194.712 + 369.300i −0.303290 + 0.575233i
\(643\) −251.455 251.455i −0.391065 0.391065i 0.484002 0.875067i \(-0.339183\pi\)
−0.875067 + 0.484002i \(0.839183\pi\)
\(644\) −31.5758 + 60.3388i −0.0490307 + 0.0936938i
\(645\) 785.253 150.760i 1.21745 0.233736i
\(646\) 27.2087 0.0421188
\(647\) −245.105 245.105i −0.378832 0.378832i 0.491848 0.870681i \(-0.336321\pi\)
−0.870681 + 0.491848i \(0.836321\pi\)
\(648\) 173.855 76.6743i 0.268295 0.118325i
\(649\) −1788.71 −2.75610
\(650\) 1025.29 + 230.375i 1.57738 + 0.354423i
\(651\) 99.2021 539.249i 0.152384 0.828340i
\(652\) 32.1241 + 32.1241i 0.0492700 + 0.0492700i
\(653\) −253.883 253.883i −0.388794 0.388794i 0.485463 0.874257i \(-0.338651\pi\)
−0.874257 + 0.485463i \(0.838651\pi\)
\(654\) 127.378 + 411.499i 0.194767 + 0.629203i
\(655\) −652.366 72.3882i −0.995979 0.110516i
\(656\) −128.576 −0.196000
\(657\) −129.623 + 692.588i −0.197295 + 1.05417i
\(658\) −140.075 + 43.8340i −0.212880 + 0.0666170i
\(659\) −508.205 −0.771176 −0.385588 0.922671i \(-0.626001\pi\)
−0.385588 + 0.922671i \(0.626001\pi\)
\(660\) −693.858 470.345i −1.05130 0.712644i
\(661\) 392.220i 0.593373i 0.954975 + 0.296687i \(0.0958817\pi\)
−0.954975 + 0.296687i \(0.904118\pi\)
\(662\) −280.246 + 280.246i −0.423332 + 0.423332i
\(663\) 20.7849 39.4215i 0.0313497 0.0594592i
\(664\) −140.127 −0.211034
\(665\) −371.406 + 72.4954i −0.558506 + 0.109016i
\(666\) −799.515 1167.69i −1.20047 1.75329i
\(667\) 50.6334 + 50.6334i 0.0759122 + 0.0759122i
\(668\) 180.174 180.174i 0.269722 0.269722i
\(669\) −26.5554 85.7884i −0.0396942 0.128234i
\(670\) −338.021 37.5077i −0.504509 0.0559816i
\(671\) 799.984 1.19223
\(672\) 702.593 484.257i 1.04553 0.720620i
\(673\) 335.327 335.327i 0.498257 0.498257i −0.412638 0.910895i \(-0.635393\pi\)
0.910895 + 0.412638i \(0.135393\pi\)
\(674\) −849.936 −1.26103
\(675\) −71.3132 + 671.222i −0.105649 + 0.994403i
\(676\) 246.944 0.365302
\(677\) 164.817 + 164.817i 0.243452 + 0.243452i 0.818277 0.574825i \(-0.194930\pi\)
−0.574825 + 0.818277i \(0.694930\pi\)
\(678\) 836.593 + 441.092i 1.23391 + 0.650578i
\(679\) −51.3716 + 98.1671i −0.0756578 + 0.144576i
\(680\) −1.21990 + 10.9938i −0.00179397 + 0.0161674i
\(681\) 239.571 + 773.944i 0.351793 + 1.13648i
\(682\) 882.166 882.166i 1.29350 1.29350i
\(683\) 707.818 + 707.818i 1.03634 + 1.03634i 0.999314 + 0.0370224i \(0.0117873\pi\)
0.0370224 + 0.999314i \(0.488213\pi\)
\(684\) −250.578 + 171.570i −0.366342 + 0.250834i
\(685\) 376.065 300.943i 0.549000 0.439332i
\(686\) −113.603 908.220i −0.165602 1.32394i
\(687\) 223.346 + 117.758i 0.325103 + 0.171410i
\(688\) −706.505 + 706.505i −1.02690 + 1.02690i
\(689\) 723.002i 1.04935i
\(690\) 103.284 + 70.0128i 0.149687 + 0.101468i
\(691\) 603.312i 0.873101i −0.899680 0.436550i \(-0.856200\pi\)
0.899680 0.436550i \(-0.143800\pi\)
\(692\) 558.990 + 558.990i 0.807789 + 0.807789i
\(693\) 697.988 886.217i 1.00720 1.27881i
\(694\) 308.998i 0.445242i
\(695\) 149.650 + 16.6056i 0.215324 + 0.0238929i
\(696\) −47.8023 154.428i −0.0686815 0.221879i
\(697\) −4.57439 4.57439i −0.00656297 0.00656297i
\(698\) 673.008 673.008i 0.964195 0.964195i
\(699\) 285.369 + 921.896i 0.408253 + 1.31888i
\(700\) 44.8752 + 544.315i 0.0641074 + 0.777592i
\(701\) 354.991i 0.506406i 0.967413 + 0.253203i \(0.0814841\pi\)
−0.967413 + 0.253203i \(0.918516\pi\)
\(702\) 130.425 + 1127.41i 0.185791 + 1.60599i
\(703\) −450.491 450.491i −0.640812 0.640812i
\(704\) 599.095 0.850987
\(705\) 22.2223 + 115.748i 0.0315209 + 0.164181i
\(706\) 1153.91i 1.63443i
\(707\) 79.6444 24.9233i 0.112651 0.0352521i
\(708\) 827.332 + 436.209i 1.16855 + 0.616114i
\(709\) 637.022i 0.898479i 0.893411 + 0.449240i \(0.148305\pi\)
−0.893411 + 0.449240i \(0.851695\pi\)
\(710\) −52.9850 66.2113i −0.0746268 0.0932554i
\(711\) 443.955 303.975i 0.624409 0.427531i
\(712\) −96.9036 + 96.9036i −0.136101 + 0.136101i
\(713\) −57.5517 + 57.5517i −0.0807176 + 0.0807176i
\(714\) 51.9756 + 9.56161i 0.0727950 + 0.0133916i
\(715\) −1101.11 + 881.156i −1.54002 + 1.23239i
\(716\) 960.976i 1.34215i
\(717\) −50.6470 26.7035i −0.0706374 0.0372434i
\(718\) 673.208 673.208i 0.937616 0.937616i
\(719\) 435.697i 0.605976i −0.952994 0.302988i \(-0.902016\pi\)
0.952994 0.302988i \(-0.0979843\pi\)
\(720\) −396.858 744.263i −0.551191 1.03370i
\(721\) 214.318 + 112.154i 0.297251 + 0.155554i
\(722\) 460.603 460.603i 0.637955 0.637955i
\(723\) 483.307 916.661i 0.668475 1.26786i
\(724\) 390.014 0.538693
\(725\) 560.301 + 125.895i 0.772830 + 0.173648i
\(726\) 1526.65 472.566i 2.10282 0.650917i
\(727\) −757.367 + 757.367i −1.04177 + 1.04177i −0.0426819 + 0.999089i \(0.513590\pi\)
−0.999089 + 0.0426819i \(0.986410\pi\)
\(728\) −77.2490 246.856i −0.106111 0.339087i
\(729\) −709.745 + 166.443i −0.973587 + 0.228317i
\(730\) 1038.22 + 115.203i 1.42222 + 0.157813i
\(731\) −50.2711 −0.0687703
\(732\) −370.017 195.091i −0.505488 0.266517i
\(733\) 672.443 + 672.443i 0.917385 + 0.917385i 0.996839 0.0794540i \(-0.0253177\pi\)
−0.0794540 + 0.996839i \(0.525318\pi\)
\(734\) 699.372i 0.952823i
\(735\) −734.957 + 7.96636i −0.999941 + 0.0108386i
\(736\) −126.667 −0.172102
\(737\) 322.736 322.736i 0.437906 0.437906i
\(738\) 161.936 + 30.3075i 0.219425 + 0.0410670i
\(739\) 540.207i 0.730997i 0.930812 + 0.365498i \(0.119101\pi\)
−0.930812 + 0.365498i \(0.880899\pi\)
\(740\) −717.927 + 574.514i −0.970171 + 0.776371i
\(741\) 151.082 + 488.077i 0.203889 + 0.658673i
\(742\) −818.246 + 256.055i −1.10276 + 0.345088i
\(743\) 164.151 + 164.151i 0.220931 + 0.220931i 0.808890 0.587960i \(-0.200069\pi\)
−0.587960 + 0.808890i \(0.700069\pi\)
\(744\) 175.528 54.3337i 0.235924 0.0730292i
\(745\) 459.497 + 50.9869i 0.616774 + 0.0684388i
\(746\) 875.339i 1.17338i
\(747\) 528.436 + 98.9005i 0.707411 + 0.132397i
\(748\) 37.2655 + 37.2655i 0.0498202 + 0.0498202i
\(749\) −169.258 + 323.439i −0.225979 + 0.431827i
\(750\) 1000.20 + 31.3570i 1.33360 + 0.0418094i
\(751\) −12.8996 −0.0171766 −0.00858830 0.999963i \(-0.502734\pi\)
−0.00858830 + 0.999963i \(0.502734\pi\)
\(752\) −104.140 104.140i −0.138484 0.138484i
\(753\) −673.883 355.304i −0.894932 0.471851i
\(754\) 965.563 1.28059
\(755\) 60.9674 + 6.76510i 0.0807515 + 0.00896039i
\(756\) −538.961 + 239.685i −0.712911 + 0.317044i
\(757\) −328.630 328.630i −0.434121 0.434121i 0.455906 0.890028i \(-0.349315\pi\)
−0.890028 + 0.455906i \(0.849315\pi\)
\(758\) 63.6329 + 63.6329i 0.0839484 + 0.0839484i
\(759\) −159.966 + 49.5166i −0.210759 + 0.0652393i
\(760\) −79.2345 99.0133i −0.104256 0.130281i
\(761\) −984.602 −1.29383 −0.646913 0.762564i \(-0.723940\pi\)
−0.646913 + 0.762564i \(0.723940\pi\)
\(762\) −1479.08 779.842i −1.94105 1.02342i
\(763\) 112.489 + 359.468i 0.147430 + 0.471124i
\(764\) 375.240 0.491152
\(765\) 12.3597 40.5980i 0.0161565 0.0530693i
\(766\) 1332.26i 1.73924i
\(767\) 1112.65 1112.65i 1.45066 1.45066i