Properties

Label 105.3.k.d.62.12
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 62.12
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.88692 - 1.88692i) q^{2} +(1.39918 + 2.65373i) q^{3} -3.12092i q^{4} +(4.96950 + 0.551428i) q^{5} +(7.64751 + 2.36725i) q^{6} +(-6.68054 + 2.09055i) q^{7} +(1.65875 + 1.65875i) q^{8} +(-5.08462 + 7.42608i) q^{9} +O(q^{10})\) \(q+(1.88692 - 1.88692i) q^{2} +(1.39918 + 2.65373i) 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} +(8.28210 - 4.36672i) q^{12} +(-11.1383 - 11.1383i) q^{13} +(-8.66093 + 16.5503i) q^{14} +(5.48986 + 13.9593i) q^{15} +18.7435 q^{16} +(-0.666845 - 0.666845i) q^{17} +(4.41815 + 23.6067i) q^{18} -10.8119 q^{19} +(1.72096 - 15.5094i) q^{20} +(-14.8950 - 14.8033i) 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} +(-26.8211 - 3.10283i) q^{27} +(6.52445 + 20.8494i) q^{28} -22.9708 q^{29} +(36.6989 + 15.9811i) q^{30} +26.1094i q^{31} +(28.7325 - 28.7325i) q^{32} +(47.5179 - 25.0537i) 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} +(-56.0383 + 0.173022i) q^{42} +(-37.6932 + 37.6932i) q^{43} -55.8834 q^{44} +(-29.3629 + 34.1001i) q^{45} -8.31847 q^{46} +(5.55606 + 5.55606i) q^{47} +(26.2255 + 49.7404i) 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} +(-15.1277 - 28.6918i) q^{57} +(-43.3441 + 43.3441i) q^{58} -99.8940i q^{59} +(43.5658 - 17.1334i) q^{60} -44.6768i q^{61} +(49.2664 + 49.2664i) q^{62} +(18.4433 - 60.2399i) 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} +(-20.7521 + 3.88391i) q^{72} +(55.3597 + 55.3597i) q^{73} +157.242 q^{74} +(19.5843 + 72.3979i) q^{75} +33.7430i q^{76} +(37.4336 + 119.622i) q^{77} +(-58.8133 - 111.548i) 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} +(-46.2000 + 46.4862i) q^{84} +(-2.94617 - 3.68160i) q^{85} +142.248i q^{86} +(-32.1402 - 60.9585i) q^{87} +(29.7017 - 29.7017i) q^{88} +58.4197i q^{89} +(8.93864 + 119.750i) q^{90} +(97.6954 + 51.1248i) q^{91} +(-6.87928 + 6.87928i) q^{92} +(-69.2875 + 36.5317i) 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 −0.0550258 0.998485i \(-0.517524\pi\)
0.998485 + 0.0550258i \(0.0175241\pi\)
\(3\) 1.39918 + 2.65373i 0.466392 + 0.884578i
\(4\) 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 \(-0.697334\pi\)
0.580989 0.813911i \(-0.302666\pi\)
\(12\) 8.28210 4.36672i 0.690175 0.363893i
\(13\) −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
\(15\) 5.48986 + 13.9593i 0.365991 + 0.930619i
\(16\) 18.7435 1.17147
\(17\) −0.666845 0.666845i −0.0392262 0.0392262i 0.687222 0.726448i \(-0.258830\pi\)
−0.726448 + 0.687222i \(0.758830\pi\)
\(18\) 4.41815 + 23.6067i 0.245453 + 1.31148i
\(19\) −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
\(21\) −14.8950 14.8033i −0.709287 0.704920i
\(22\) −33.7872 33.7872i −1.53578 1.53578i
\(23\) −2.20425 2.20425i −0.0958368 0.0958368i 0.657563 0.753400i \(-0.271587\pi\)
−0.753400 + 0.657563i \(0.771587\pi\)
\(24\) −2.08100 + 6.72276i −0.0867083 + 0.280115i
\(25\) 24.3919 + 5.48064i 0.975674 + 0.219226i
\(26\) −42.0343 −1.61670
\(27\) −26.8211 3.10283i −0.993375 0.114920i
\(28\) 6.52445 + 20.8494i 0.233016 + 0.744623i
\(29\) −22.9708 −0.792098 −0.396049 0.918229i \(-0.629619\pi\)
−0.396049 + 0.918229i \(0.629619\pi\)
\(30\) 36.6989 + 15.9811i 1.22330 + 0.532703i
\(31\) 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
\(33\) 47.5179 25.0537i 1.43994 0.759203i
\(34\) −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 \(-0.473340\pi\)
0.0836556 + 0.996495i \(0.473340\pi\)
\(42\) −56.0383 + 0.173022i −1.33425 + 0.00411958i
\(43\) −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
\(45\) −29.3629 + 34.1001i −0.652510 + 0.757780i
\(46\) −8.31847 −0.180836
\(47\) 5.55606 + 5.55606i 0.118214 + 0.118214i 0.763739 0.645525i \(-0.223361\pi\)
−0.645525 + 0.763739i \(0.723361\pi\)
\(48\) 26.2255 + 49.7404i 0.546364 + 1.03626i
\(49\) 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 0.943563 0.331194i \(-0.107451\pi\)
−0.331194 + 0.943563i \(0.607451\pi\)
\(54\) −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
\(57\) −15.1277 28.6918i −0.265398 0.503365i
\(58\) −43.3441 + 43.3441i −0.747312 + 0.747312i
\(59\) 99.8940i 1.69312i −0.532294 0.846559i \(-0.678670\pi\)
0.532294 0.846559i \(-0.321330\pi\)
\(60\) 43.5658 17.1334i 0.726097 0.285557i
\(61\) 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
\(63\) 18.4433 60.2399i 0.292752 0.956189i
\(64\) 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 \(0.0142519\pi\)
−0.998998 + 0.0447588i \(0.985748\pi\)
\(72\) −20.7521 + 3.88391i −0.288224 + 0.0539431i
\(73\) 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
\(75\) 19.5843 + 72.3979i 0.261124 + 0.965305i
\(76\) 33.7430i 0.443987i
\(77\) 37.4336 + 119.622i 0.486150 + 1.55353i
\(78\) −58.8133 111.548i −0.754017 1.43010i
\(79\) 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 −0.914189 0.405289i \(-0.867171\pi\)
0.405289 + 0.914189i \(0.367171\pi\)
\(84\) −46.2000 + 46.4862i −0.550000 + 0.553407i
\(85\) −2.94617 3.68160i −0.0346608 0.0433130i
\(86\) 142.248i 1.65405i
\(87\) −32.1402 60.9585i −0.369428 0.700673i
\(88\) 29.7017 29.7017i 0.337519 0.337519i
\(89\) 58.4197i 0.656401i 0.944608 + 0.328200i \(0.106442\pi\)
−0.944608 + 0.328200i \(0.893558\pi\)
\(90\) 8.93864 + 119.750i 0.0993182 + 1.33055i
\(91\) 97.6954 + 51.1248i 1.07358 + 0.561811i
\(92\) −6.87928 + 6.87928i −0.0747748 + 0.0747748i
\(93\) −69.2875 + 36.5317i −0.745027 + 0.392814i
\(94\) 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 \(-0.481203\pi\)
0.0590191 + 0.998257i \(0.481203\pi\)
\(102\) −3.52111 6.67829i −0.0345207 0.0654734i
\(103\) −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
\(105\) −65.8578 81.7786i −0.627217 0.778844i
\(106\) 122.482 1.15549
\(107\) −36.8755 + 36.8755i −0.344631 + 0.344631i −0.858105 0.513474i \(-0.828358\pi\)
0.513474 + 0.858105i \(0.328358\pi\)
\(108\) −9.68369 + 83.7066i −0.0896638 + 0.775061i
\(109\) 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 0.972434 0.233177i \(-0.0749122\pi\)
−0.233177 + 0.972434i \(0.574912\pi\)
\(114\) −82.6839 25.5944i −0.725297 0.224512i
\(115\) −9.73852 12.1695i −0.0846828 0.105822i
\(116\) 71.6902i 0.618019i
\(117\) 139.348 26.0800i 1.19101 0.222906i
\(118\) −188.492 188.492i −1.59739 1.59739i
\(119\) 5.84896 + 3.06081i 0.0491509 + 0.0257211i
\(120\) −14.0486 + 32.2613i −0.117072 + 0.268844i
\(121\) −199.627 −1.64981
\(122\) −84.3014 84.3014i −0.690995 0.690995i
\(123\) 9.59801 + 18.2040i 0.0780326 + 0.148000i
\(124\) 81.4855 0.657141
\(125\) 118.193 + 40.6864i 0.945545 + 0.325491i
\(126\) −78.8666 148.469i −0.625926 1.17832i
\(127\) 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 \(-0.667051\pi\)
−0.501046 + 0.865421i \(0.667051\pi\)
\(132\) −78.1906 148.300i −0.592353 1.12348i
\(133\) 72.2291 22.6028i 0.543076 0.169946i
\(134\) −68.0192 −0.507606
\(135\) −131.577 30.2094i −0.974641 0.223774i
\(136\) 2.21226i 0.0162666i
\(137\) 68.1163 68.1163i 0.497199 0.497199i −0.413366 0.910565i \(-0.635647\pi\)
0.910565 + 0.413366i \(0.135647\pi\)
\(138\) −11.6390 22.0750i −0.0843406 0.159964i
\(139\) −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
\(147\) 130.454 + 67.7553i 0.887441 + 0.460921i
\(148\) 130.037 130.037i 0.878631 0.878631i
\(149\) 92.4633 0.620559 0.310280 0.950645i \(-0.399577\pi\)
0.310280 + 0.950645i \(0.399577\pi\)
\(150\) 173.563 + 99.6549i 1.15709 + 0.664366i
\(151\) −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
\(153\) 8.34269 1.56139i 0.0545274 0.0102052i
\(154\) 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
\(162\) −197.770 87.2212i −1.22080 0.538403i
\(163\) −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
\(165\) 249.955 98.3017i 1.51488 0.595768i
\(166\) 159.402i 0.960253i
\(167\) −57.7311 57.7311i −0.345695 0.345695i 0.512808 0.858503i \(-0.328605\pi\)
−0.858503 + 0.512808i \(0.828605\pi\)
\(168\) −0.152100 49.2621i −0.000905359 0.293227i
\(169\) 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 \(-0.488548\pi\)
0.999353 0.0359688i \(-0.0114517\pi\)
\(174\) −175.670 54.3777i −1.00960 0.312516i
\(175\) −174.408 + 14.3788i −0.996619 + 0.0821647i
\(176\) 335.623i 1.90695i
\(177\) 265.092 139.769i 1.49770 0.789657i
\(178\) 110.233 + 110.233i 0.619287 + 0.619287i
\(179\) −307.914 −1.72019 −0.860095 0.510133i \(-0.829596\pi\)
−0.860095 + 0.510133i \(0.829596\pi\)
\(180\) 106.424 + 91.6394i 0.591243 + 0.509108i
\(181\) 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
\(183\) 118.560 62.5106i 0.647870 0.341588i
\(184\) 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
\(189\) 185.666 35.3424i 0.982361 0.186997i
\(190\) −112.633 + 90.1336i −0.592806 + 0.474387i
\(191\) 120.234i 0.629496i −0.949175 0.314748i \(-0.898080\pi\)
0.949175 0.314748i \(-0.101920\pi\)
\(192\) 88.7878 46.8132i 0.462437 0.243819i
\(193\) −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
\(195\) 94.3353 216.631i 0.483771 1.11093i
\(196\) −87.1737 125.646i −0.444764 0.641050i
\(197\) −7.82035 + 7.82035i −0.0396972 + 0.0396972i −0.726677 0.686980i \(-0.758936\pi\)
0.686980 + 0.726677i \(0.258936\pi\)
\(198\) 422.702 79.1117i 2.13486 0.399554i
\(199\) 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
\(207\) 27.5767 5.16117i 0.133221 0.0249332i
\(208\) −208.772 208.772i −1.00371 1.00371i
\(209\) 193.598i 0.926305i
\(210\) −278.578 30.0413i −1.32656 0.143054i
\(211\) −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
\(213\) −16.8665 + 8.89282i −0.0791854 + 0.0417503i
\(214\) 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
\(222\) 220.009 + 417.278i 0.991032 + 1.87963i
\(223\) −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
\(225\) −164.723 + 153.269i −0.732102 + 0.681195i
\(226\) 315.251 1.39492
\(227\) −190.960 190.960i −0.841234 0.841234i 0.147785 0.989019i \(-0.452785\pi\)
−0.989019 + 0.147785i \(0.952785\pi\)
\(228\) −89.5449 + 47.2124i −0.392741 + 0.207072i
\(229\) 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
\(231\) −265.069 + 266.711i −1.14748 + 1.15459i
\(232\) −38.1029 38.1029i −0.164237 0.164237i
\(233\) −227.465 227.465i −0.976246 0.976246i 0.0234784 0.999724i \(-0.492526\pi\)
−0.999724 + 0.0234784i \(0.992526\pi\)
\(234\) 213.728 312.150i 0.913368 1.33397i
\(235\) 24.5471 + 30.6746i 0.104456 + 0.130530i
\(236\) −311.761 −1.32102
\(237\) 158.649 83.6472i 0.669404 0.352942i
\(238\) 16.8120 5.26101i 0.0706386 0.0221051i
\(239\) 19.0852 0.0798543 0.0399272 0.999203i \(-0.487287\pi\)
0.0399272 + 0.999203i \(0.487287\pi\)
\(240\) 102.899 + 261.646i 0.428747 + 1.09019i
\(241\) 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
\(243\) 159.417 183.399i 0.656037 0.754729i
\(244\) −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 \(-0.331178\pi\)
0.505852 + 0.862620i \(0.331178\pi\)
\(252\) −188.004 57.5602i −0.746047 0.228414i
\(253\) −39.4694 + 39.4694i −0.156005 + 0.156005i
\(254\) 557.358 2.19432
\(255\) 5.64779 12.9696i 0.0221482 0.0508610i
\(256\) 329.309 1.28636
\(257\) −295.955 295.955i −1.15158 1.15158i −0.986237 0.165340i \(-0.947128\pi\)
−0.165340 0.986237i \(-0.552872\pi\)
\(258\) −377.489 + 199.030i −1.46313 + 0.771435i
\(259\) −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 0.703807 0.710392i \(-0.251482\pi\)
−0.710392 + 0.703807i \(0.751482\pi\)
\(264\) 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
\(267\) −155.030 + 81.7394i −0.580638 + 0.306140i
\(268\) −56.2511 + 56.2511i −0.209892 + 0.209892i
\(269\) 400.956i 1.49054i −0.666761 0.745272i \(-0.732320\pi\)
0.666761 0.745272i \(-0.267680\pi\)
\(270\) −305.277 + 191.271i −1.13066 + 0.708413i
\(271\) 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
\(273\) 1.02134 + 330.790i 0.00374117 + 1.21169i
\(274\) 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 \(0.169217\pi\)
−0.861992 + 0.506922i \(0.830783\pi\)
\(282\) 29.3374 + 55.6426i 0.104033 + 0.197314i
\(283\) 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
\(285\) −59.3556 150.926i −0.208265 0.529565i
\(286\) 752.668i 2.63171i
\(287\) −45.8269 + 14.3407i −0.159676 + 0.0499676i
\(288\) 67.2762 + 359.464i 0.233598 + 1.24814i
\(289\) 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 −0.963767 0.266746i \(-0.914052\pi\)
0.266746 + 0.963767i \(0.414052\pi\)
\(294\) 374.005 118.307i 1.27212 0.402405i
\(295\) 55.0844 496.423i 0.186727 1.68279i
\(296\) 138.228i 0.466987i
\(297\) −55.5594 + 480.260i −0.187069 + 1.61704i
\(298\) 174.471 174.471i 0.585472 0.585472i
\(299\) 49.1033i 0.164225i
\(300\) 225.948 61.1211i 0.753160 0.203737i
\(301\) 173.011 330.611i 0.574789 1.09838i
\(302\) −23.1493 + 23.1493i −0.0766534 + 0.0766534i
\(303\) 16.6808 + 31.6374i 0.0550520 + 0.104414i
\(304\) −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 \(-0.267518\pi\)
0.667141 + 0.744932i \(0.267518\pi\)
\(312\) 98.0593 51.7016i 0.314293 0.165710i
\(313\) 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
\(315\) 124.872 289.192i 0.396420 0.918069i
\(316\) −186.579 −0.590439
\(317\) −255.502 + 255.502i −0.805999 + 0.805999i −0.984026 0.178027i \(-0.943029\pi\)
0.178027 + 0.984026i \(0.443029\pi\)
\(318\) 171.374 + 325.035i 0.538911 + 1.02212i
\(319\) 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
\(327\) 142.793 75.2872i 0.436675 0.230236i
\(328\) 11.3786 + 11.3786i 0.0346909 + 0.0346909i
\(329\) −48.7327 25.5022i −0.148124 0.0775144i
\(330\) 286.158 657.133i 0.867147 1.99131i
\(331\) 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
\(333\) −521.275 + 97.5603i −1.56539 + 0.292974i
\(334\) −217.868 −0.652299
\(335\) −79.6308 99.5085i −0.237704 0.297040i
\(336\) −279.185 277.467i −0.830909 0.825794i
\(337\) 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
\(342\) −47.7685 255.232i −0.139674 0.746293i
\(343\) −210.559 + 270.765i −0.613876 + 0.789402i
\(344\) −125.047 −0.363510
\(345\) 18.6687 42.8707i 0.0541122 0.124263i
\(346\) 675.934i 1.95357i
\(347\) −81.8789 + 81.8789i −0.235962 + 0.235962i −0.815176 0.579214i \(-0.803360\pi\)
0.579214 + 0.815176i \(0.303360\pi\)
\(348\) −190.247 + 100.307i −0.546686 + 0.288239i
\(349\) −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 −0.125857 0.992048i \(-0.540168\pi\)
0.992048 + 0.125857i \(0.0401681\pi\)
\(354\) 236.474 763.940i 0.668006 2.15802i
\(355\) −3.50474 + 31.5849i −0.00987251 + 0.0889716i
\(356\) 182.323 0.512144
\(357\) 0.0611469 + 19.8042i 0.000171280 + 0.0554739i
\(358\) −581.009 + 581.009i −1.62293 + 1.62293i
\(359\) 356.776 0.993806 0.496903 0.867806i \(-0.334470\pi\)
0.496903 + 0.867806i \(0.334470\pi\)
\(360\) −105.269 + 7.85776i −0.292415 + 0.0218271i
\(361\) −244.103 −0.676187
\(362\) 235.803 + 235.803i 0.651390 + 0.651390i
\(363\) −279.313 529.756i −0.769456 1.45938i
\(364\) 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
\(372\) 114.013 + 216.241i 0.306485 + 0.581293i
\(373\) −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
\(375\) 57.4020 + 370.581i 0.153072 + 0.988215i
\(376\) 18.4322i 0.0490219i
\(377\) 255.857 + 255.857i 0.678666 + 0.678666i
\(378\) 283.649 417.025i 0.750393 1.10324i
\(379\) 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 −0.997152 0.0754169i \(-0.975971\pi\)
0.0754169 + 0.997152i \(0.475971\pi\)
\(384\) −64.9838 + 209.933i −0.169229 + 0.546701i
\(385\) 120.063 + 615.104i 0.311852 + 1.59767i
\(386\) 48.5501i 0.125777i
\(387\) −88.2574 471.569i −0.228055 1.21852i
\(388\) −34.9297 34.9297i −0.0900250 0.0900250i
\(389\) 222.963 0.573170 0.286585 0.958055i \(-0.407480\pi\)
0.286585 + 0.958055i \(0.407480\pi\)
\(390\) −230.762 586.768i −0.591698 1.50453i
\(391\) 2.93978i 0.00751862i
\(392\) 113.112 + 20.4476i 0.288551 + 0.0521623i
\(393\) −183.675 348.366i −0.467367 0.886429i
\(394\) 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
\(399\) 161.043 + 160.052i 0.403617 + 0.401132i
\(400\) 457.190 + 102.727i 1.14297 + 0.256817i
\(401\) 333.028i 0.830494i 0.909709 + 0.415247i \(0.136305\pi\)
−0.909709 + 0.415247i \(0.863695\pi\)
\(402\) −95.1707 180.505i −0.236743 0.449017i
\(403\) 290.816 290.816i 0.721628 0.721628i
\(404\) 37.2072i 0.0920969i
\(405\) −103.931 391.438i −0.256619 0.966513i
\(406\) 198.949 380.175i 0.490022 0.936392i
\(407\) 746.079 746.079i 1.83312 1.83312i
\(408\) 5.87074 3.09534i 0.0143891 0.00758661i
\(409\) 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
\(417\) −42.1345 79.9140i −0.101042 0.191640i
\(418\) 365.303 + 365.303i 0.873931 + 0.873931i
\(419\) 415.098i 0.990687i −0.868697 0.495343i \(-0.835042\pi\)
0.868697 0.495343i \(-0.164958\pi\)
\(420\) −255.225 + 205.537i −0.607678 + 0.489374i
\(421\) 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
\(423\) −69.5102 + 13.0093i −0.164327 + 0.0307549i
\(424\) 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 \(-0.918649\pi\)
0.967519 0.252800i \(-0.0813514\pi\)
\(432\) −502.723 58.1580i −1.16371 0.134625i
\(433\) 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
\(435\) −126.107 320.656i −0.289900 0.737141i
\(436\) −167.931 −0.385163
\(437\) 23.8320 + 23.8320i 0.0545355 + 0.0545355i
\(438\) 292.313 + 554.414i 0.667382 + 1.26579i
\(439\) 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
\(441\) 2.72321 + 440.992i 0.00617509 + 0.999981i
\(442\) 28.0303 + 28.0303i 0.0634171 + 0.0634171i
\(443\) −484.487 484.487i −1.09365 1.09365i −0.995136 0.0985149i \(-0.968591\pi\)
−0.0985149 0.995136i \(-0.531409\pi\)
\(444\) 527.030 + 163.140i 1.18700 + 0.367431i
\(445\) −32.2143 + 290.317i −0.0723916 + 0.652397i
\(446\) −79.8812 −0.179106
\(447\) 129.372 + 245.373i 0.289424 + 0.548933i
\(448\) 69.9451 + 223.515i 0.156127 + 0.498918i
\(449\) −801.204 −1.78442 −0.892209 0.451623i \(-0.850845\pi\)
−0.892209 + 0.451623i \(0.850845\pi\)
\(450\) −21.6128 + 600.025i −0.0480283 + 1.33339i
\(451\) 122.831i 0.272353i
\(452\) 260.709 260.709i 0.576791 0.576791i
\(453\) −17.1655 32.5569i −0.0378930 0.0718695i
\(454\) −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 \(-0.738179\pi\)
−0.680365 + 0.732874i \(0.738179\pi\)
\(462\) 3.09815 + 1003.43i 0.00670595 + 2.17192i
\(463\) 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
\(465\) −364.469 + 143.337i −0.783804 + 0.308252i
\(466\) −858.417 −1.84210
\(467\) −239.537 239.537i −0.512928 0.512928i 0.402495 0.915422i \(-0.368143\pi\)
−0.915422 + 0.402495i \(0.868143\pi\)
\(468\) −81.3938 434.895i −0.173918 0.929264i
\(469\) 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
\(477\) −406.042 + 75.9936i −0.851241 + 0.159316i
\(478\) 36.0122 36.0122i 0.0753393 0.0753393i
\(479\) 868.698i 1.81357i 0.421598 + 0.906783i \(0.361469\pi\)
−0.421598 + 0.906783i \(0.638531\pi\)
\(480\) 558.823 + 243.348i 1.16421 + 0.506975i
\(481\) 928.188i 1.92970i
\(482\) −651.785 651.785i −1.35225 1.35225i
\(483\) 0.202120 + 65.4625i 0.000418468 + 0.135533i
\(484\) 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 \(-0.959273\pi\)
0.991826 0.127599i \(-0.0407270\pi\)
\(492\) 56.8132 29.9546i 0.115474 0.0608834i
\(493\) 15.3180 + 15.3180i 0.0310710 + 0.0310710i
\(494\) 454.469 0.919978
\(495\) 610.598 + 525.774i 1.23353 + 1.06217i
\(496\) 489.383i 0.986660i
\(497\) −13.2870 42.4599i −0.0267345 0.0854323i
\(498\) −423.011 + 223.031i −0.849419 + 0.447854i
\(499\) 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 \(0.574636\pi\)
−0.972636 + 0.232335i \(0.925364\pi\)
\(504\) 130.516 69.3300i 0.258960 0.137559i
\(505\) 59.2456 + 6.57404i 0.117318 + 0.0130179i
\(506\) 148.951i 0.294369i
\(507\) −209.978 + 110.710i −0.414157 + 0.218363i
\(508\) 460.929 460.929i 0.907341 0.907341i
\(509\) 3.90604i 0.00767394i −0.999993 0.00383697i \(-0.998779\pi\)
0.999993 0.00383697i \(-0.00122135\pi\)
\(510\) −13.8156 35.1294i −0.0270894 0.0688812i
\(511\) −485.565 254.100i −0.950225 0.497260i
\(512\) 414.186 414.186i 0.808956 0.808956i
\(513\) 289.986 + 33.5474i 0.565276 + 0.0653945i
\(514\) −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 \(-0.679317\pi\)
−0.534015 + 0.845475i \(0.679317\pi\)
\(522\) −101.489 542.265i −0.194423 1.03882i
\(523\) −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
\(525\) −282.185 442.715i −0.537496 0.843266i
\(526\) −6.53551 −0.0124249
\(527\) 17.4109 17.4109i 0.0330378 0.0330378i
\(528\) 890.653 469.595i 1.68684 0.889384i
\(529\) 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
\(537\) −430.826 817.122i −0.802283 1.52164i
\(538\) −756.572 756.572i −1.40627 1.40627i
\(539\) −500.153 720.883i −0.927927 1.33744i
\(540\) −94.2813 + 410.640i −0.174595 + 0.760445i
\(541\) 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
\(543\) −331.630 + 174.851i −0.610737 + 0.322010i
\(544\) −38.3203 −0.0704416
\(545\) 29.6714 267.400i 0.0544429 0.490642i
\(546\) 626.101 + 622.247i 1.14671 + 1.13965i
\(547\) −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
\(552\) 19.4057 10.2316i 0.0351552 0.0185355i
\(553\) 124.980 + 399.384i 0.226004 + 0.722213i
\(554\) −153.298 −0.276711
\(555\) −352.890 + 810.374i −0.635837 + 1.46013i
\(556\) 93.9827i 0.169034i
\(557\) 452.948 452.948i 0.813192 0.813192i −0.171919 0.985111i \(-0.554997\pi\)
0.985111 + 0.171919i \(0.0549967\pi\)
\(558\) −616.357 + 115.356i −1.10458 + 0.206730i
\(559\) 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 −0.0488978 0.998804i \(-0.515571\pi\)
0.998804 + 0.0488978i \(0.0155709\pi\)
\(564\) 70.2776 + 21.7541i 0.124606 + 0.0385711i
\(565\) 369.068 + 461.196i 0.653218 + 0.816277i
\(566\) 387.409 0.684468
\(567\) 353.569 + 443.258i 0.623578 + 0.781761i
\(568\) −10.5426 + 10.5426i −0.0185609 + 0.0185609i
\(569\) 527.903 0.927773 0.463886 0.885895i \(-0.346455\pi\)
0.463886 + 0.885895i \(0.346455\pi\)
\(570\) −396.784 172.786i −0.696112 0.303133i
\(571\) 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
\(573\) 319.069 168.228i 0.556839 0.293592i
\(574\) −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
\(582\) 112.086 59.0973i 0.192588 0.101542i
\(583\) 581.151 581.151i 0.996828 0.996828i
\(584\) 183.656i 0.314479i
\(585\) 706.873 52.7641i 1.20833 0.0901951i
\(586\) 770.720i 1.31522i
\(587\) 748.348 + 748.348i 1.27487 + 1.27487i 0.943502 + 0.331366i \(0.107509\pi\)
0.331366 + 0.943502i \(0.392491\pi\)
\(588\) 211.459 407.136i 0.359624 0.692409i
\(589\) 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 −0.777895 0.628394i \(-0.783713\pi\)
0.628394 + 0.777895i \(0.283713\pi\)
\(594\) 801.376 + 1011.05i 1.34912 + 1.70210i
\(595\) 27.3786 + 18.4360i 0.0460144 + 0.0309848i
\(596\) 288.571i 0.484179i
\(597\) 421.375 + 799.198i 0.705821 + 1.33869i
\(598\) 92.6540 + 92.6540i 0.154940 + 0.154940i
\(599\) 512.160 0.855025 0.427512 0.904009i \(-0.359390\pi\)
0.427512 + 0.904009i \(0.359390\pi\)
\(600\) −87.6045 + 152.575i −0.146008 + 0.254292i
\(601\) 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
\(603\) 225.491 42.2023i 0.373949 0.0699872i
\(604\) 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
\(609\) 342.151 + 340.045i 0.561825 + 0.558366i
\(610\) −372.450 465.422i −0.610573 0.762987i
\(611\) 123.771i 0.202571i
\(612\) −4.87299 26.0369i −0.00796240 0.0425439i
\(613\) −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
\(615\) 37.6591 + 95.7573i 0.0612343 + 0.155703i
\(616\) −136.330 + 260.516i −0.221315 + 0.422915i
\(617\) −759.979 + 759.979i −1.23173 + 1.23173i −0.268434 + 0.963298i \(0.586506\pi\)
−0.963298 + 0.268434i \(0.913494\pi\)
\(618\) −129.021 244.706i −0.208771 0.395965i
\(619\) 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
\(627\) −513.757 + 270.877i −0.819390 + 0.432021i
\(628\) 199.523 + 199.523i 0.317712 + 0.317712i
\(629\) 55.5699i 0.0883465i
\(630\) −310.058 781.305i −0.492155 1.24017i
\(631\) −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
\(633\) −508.747 964.911i −0.803708 1.52435i
\(634\) 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 \(0.108423\pi\)
−0.942547 + 0.334072i \(0.891577\pi\)
\(642\) −369.300 + 194.712i −0.575233 + 0.303290i
\(643\) −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
\(645\) −733.101 319.240i −1.13659 0.494946i
\(646\) 27.2087 0.0421188
\(647\) 245.105 + 245.105i 0.378832 + 0.378832i 0.870681 0.491848i \(-0.163679\pi\)
−0.491848 + 0.870681i \(0.663679\pi\)
\(648\) 76.6743 173.855i 0.118325 0.268295i
\(649\) −1788.71 −2.75610
\(650\) −1025.29 230.375i −1.57738 0.354423i
\(651\) 386.507 388.901i 0.593712 0.597390i
\(652\) 32.1241 + 32.1241i 0.0492700 + 0.0492700i
\(653\) 253.883 + 253.883i 0.388794 + 0.388794i 0.874257 0.485463i \(-0.161349\pi\)
−0.485463 + 0.874257i \(0.661349\pi\)
\(654\) 127.378 411.499i 0.194767 0.629203i
\(655\) −652.366 72.3882i −0.995979 0.110516i
\(656\) 128.576 0.196000
\(657\) −692.588 + 129.623i −1.05417 + 0.197295i
\(658\) −140.075 + 43.8340i −0.212880 + 0.0666170i
\(659\) 508.205 0.771176 0.385588 0.922671i \(-0.373999\pi\)
0.385588 + 0.922671i \(0.373999\pi\)
\(660\) −306.792 780.091i −0.464836 1.18196i
\(661\) 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
\(663\) −39.4215 + 20.7849i −0.0594592 + 0.0313497i
\(664\) −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
\(672\) −853.308 + 2.63465i −1.26980 + 0.00392061i
\(673\) 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
\(675\) −637.211 222.681i −0.944017 0.329897i
\(676\) 246.944 0.365302
\(677\) −164.817 164.817i −0.243452 0.243452i 0.574825 0.818277i \(-0.305070\pi\)
−0.818277 + 0.574825i \(0.805070\pi\)
\(678\) 441.092 + 836.593i 0.650578 + 1.23391i
\(679\) −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 \(-0.988213\pi\)
−0.0370224 0.999314i \(-0.511787\pi\)
\(684\) −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
\(687\) 117.758 + 223.346i 0.171410 + 0.325103i
\(688\) −706.505 + 706.505i −1.02690 + 1.02690i
\(689\) 723.002i 1.04935i
\(690\) −45.6672 116.120i −0.0661844 0.168290i
\(691\) 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
\(693\) −1078.66 330.247i −1.55651 0.476548i
\(694\) 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 \(-0.918516\pi\)
0.967413 0.253203i \(-0.0814841\pi\)
\(702\) 1127.41 + 130.425i 1.60599 + 0.185791i
\(703\) −450.491 450.491i −0.640812 0.640812i
\(704\) −599.095 −0.850987
\(705\) −47.0566 + 108.061i −0.0667470 + 0.153277i
\(706\) 1153.91i 1.63443i
\(707\) −79.6444 + 24.9233i −0.112651 + 0.0352521i
\(708\) −436.209 827.332i −0.616114 1.16855i
\(709\) 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
\(714\) 37.4843 + 37.2535i 0.0524990 + 0.0521758i
\(715\) −1101.11 + 881.156i −1.54002 + 1.23239i
\(716\) 960.976i 1.34215i
\(717\) 26.7035 + 50.6470i 0.0372434 + 0.0706374i
\(718\) 673.208 673.208i 0.937616 0.937616i
\(719\) 435.697i 0.605976i 0.952994 + 0.302988i \(0.0979843\pi\)
−0.952994 + 0.302988i \(0.902016\pi\)
\(720\) −550.365 + 639.157i −0.764396 + 0.887717i
\(721\) 214.318 + 112.154i 0.297251 + 0.155554i
\(722\) −460.603 + 460.603i −0.637955 + 0.637955i
\(723\) 916.661 483.307i 1.26786 0.668475i
\(724\) 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
\(732\) −195.091 370.017i −0.266517 0.505488i
\(733\) 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
\(735\) 610.928 + 408.646i 0.831195 + 0.555981i
\(736\) −126.667 −0.172102
\(737\) −322.736 + 322.736i −0.437906 + 0.437906i
\(738\) 30.3075 + 161.936i 0.0410670 + 0.219425i
\(739\) 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 0.587960 0.808890i \(-0.299931\pi\)
−0.808890 + 0.587960i \(0.799931\pi\)
\(744\) −175.528 54.3337i −0.235924 0.0730292i
\(745\) 459.497 + 50.9869i 0.616774 + 0.0684388i
\(746\) 875.339i 1.17338i
\(747\) −98.9005 528.436i −0.132397 0.707411i
\(748\) 37.2655 + 37.2655i 0.0498202 + 0.0498202i
\(749\) 169.258 323.439i 0.225979 0.431827i
\(750\) 807.568 + 590.943i 1.07676 + 0.787923i
\(751\) −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
\(753\) 355.304 + 673.883i 0.471851 + 0.894932i
\(754\) 965.563 1.28059
\(755\) −60.9674 6.76510i −0.0807515 0.00896039i
\(756\) −110.301 579.449i −0.145901 0.766467i
\(757\) −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 \(-0.276060\pi\)
0.646913 + 0.762564i \(0.276060\pi\)
\(762\) 779.842 + 1479.08i 1.02342 + 1.94105i
\(763\) 112.489 + 359.468i 0.147430 + 0.471124i
\(764\) −375.240 −0.491152
\(765\) 42.3200 3.15895i 0.0553203 0.00412935i
\(766\) 1332.26i 1.73924i
\(767\) −1112.65 + 1112.65i −1.45066 +