Properties

Label 105.3.k.d.62.5
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 62.5
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.88692 + 1.88692i) q^{2} +(-2.65373 - 1.39918i) q^{3} -3.12092i q^{4} +(4.96950 + 0.551428i) q^{5} +(7.64751 - 2.36725i) q^{6} +(2.09055 - 6.68054i) q^{7} +(-1.65875 - 1.65875i) q^{8} +(5.08462 + 7.42608i) q^{9} +O(q^{10})\) \(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} +(2.09055 - 6.68054i) 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} +(-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} +(-3.10283 - 26.8211i) q^{27} +(-20.8494 - 6.52445i) 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} +(14.0728 - 32.0461i) 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} +(0.173022 - 56.0383i) 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} +(60.2399 - 18.4433i) 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} +(33.9141 + 87.0228i) 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} +(119.622 + 37.4336i) 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} +(46.2000 + 46.4862i) 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} +(128.671 - 23.2603i) 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
\(7\) 2.09055 6.68054i 0.298651 0.954363i
\(8\) −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 0.990959 0.134164i \(-0.0428348\pi\)
−0.134164 + 0.990959i \(0.542835\pi\)
\(14\) 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 0.687222 0.726448i \(-0.258830\pi\)
−0.726448 + 0.687222i \(0.758830\pi\)
\(18\) −23.6067 4.41815i −1.31148 0.245453i
\(19\) 10.8119 0.569046 0.284523 0.958669i \(-0.408165\pi\)
0.284523 + 0.958669i \(0.408165\pi\)
\(20\) 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 0.753400 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
\(28\) −20.8494 6.52445i −0.744623 0.233016i
\(29\) 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 \(-0.861637\pi\)
0.907005 0.421120i \(-0.138363\pi\)
\(32\) −28.7325 + 28.7325i −0.897891 + 0.897891i
\(33\) 25.0537 47.5179i 0.759203 1.43994i
\(34\) 2.51656 0.0740166
\(35\) 14.0728 32.0461i 0.402081 0.915604i
\(36\) 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 \(0.473340\pi\)
\(42\) 0.173022 56.0383i 0.00411958 1.33425i
\(43\) −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 0.763739 0.645525i \(-0.223361\pi\)
−0.645525 + 0.763739i \(0.723361\pi\)
\(48\) −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 \(-0.678670\pi\)
0.532294 0.846559i \(-0.321330\pi\)
\(60\) −26.2674 + 38.7499i −0.437790 + 0.645832i
\(61\) 44.6768i 0.732406i 0.930535 + 0.366203i \(0.119342\pi\)
−0.930535 + 0.366203i \(0.880658\pi\)
\(62\) 49.2664 + 49.2664i 0.794619 + 0.794619i
\(63\) 60.2399 18.4433i 0.956189 0.292752i
\(64\) 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
\(70\) 33.9141 + 87.0228i 0.484488 + 1.24318i
\(71\) 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 0.217671 0.976022i \(-0.430154\pi\)
−0.976022 + 0.217671i \(0.930154\pi\)
\(74\) −157.242 −2.12489
\(75\) −57.0611 48.6727i −0.760815 0.648969i
\(76\) 33.7430i 0.443987i
\(77\) 119.622 + 37.4336i 1.55353 + 0.486150i
\(78\) 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 −0.914189 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
\(87\) −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 \(0.106442\pi\)
−0.944608 + 0.328200i \(0.893558\pi\)
\(90\) −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 −0.762441 0.647058i \(-0.775999\pi\)
0.647058 + 0.762441i \(0.275999\pi\)
\(98\) 128.671 23.2603i 1.31297 0.237350i
\(99\) −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 \(0.481203\pi\)
\(102\) −6.67829 3.52111i −0.0654734 0.0345207i
\(103\) 24.4345 + 24.4345i 0.237229 + 0.237229i 0.815702 0.578473i \(-0.196351\pi\)
−0.578473 + 0.815702i \(0.696351\pi\)
\(104\) 36.9514i 0.355302i
\(105\) −82.1838 + 65.3516i −0.782703 + 0.622396i
\(106\) 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
\(112\) 39.1844 125.217i 0.349860 1.11801i
\(113\) −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
\(126\) −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 \(0.667051\pi\)
\(132\) −148.300 78.1906i −1.12348 0.592353i
\(133\) 22.6028 72.2291i 0.169946 0.543076i
\(134\) 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 \(-0.465452\pi\)
0.108323 + 0.994116i \(0.465452\pi\)
\(140\) −100.013 43.9202i −0.714382 0.313716i
\(141\) −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
\(147\) 67.7553 + 130.454i 0.460921 + 0.887441i
\(148\) 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 −0.473559 0.880762i \(-0.657031\pi\)
0.880762 + 0.473559i \(0.157031\pi\)
\(158\) 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 0.512808 0.858503i \(-0.328605\pi\)
−0.858503 + 0.512808i \(0.828605\pi\)
\(168\) 49.2621 + 0.152100i 0.293227 + 0.000905359i
\(169\) 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
\(175\) 87.6061 151.493i 0.500606 0.865675i
\(176\) 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 \(-0.887806\pi\)
0.938524 0.345214i \(-0.112194\pi\)
\(182\) −87.8749 + 280.812i −0.482829 + 1.54292i
\(183\) 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
\(189\) −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 \(0.101920\pi\)
−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 \(-0.773181\pi\)
−0.756682 + 0.653783i \(0.773181\pi\)
\(200\) −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
\(203\) 48.0218 153.458i 0.236560 0.755949i
\(204\) 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
\(210\) 31.7610 278.387i 0.151243 1.32565i
\(211\) −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
\(217\) −174.425 54.5832i −0.803802 0.251535i
\(218\) 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 0.752972 0.658052i \(-0.228619\pi\)
−0.658052 + 0.752972i \(0.728619\pi\)
\(224\) 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 0.147785 0.989019i \(-0.452785\pi\)
−0.989019 + 0.147785i \(0.952785\pi\)
\(228\) −47.2124 + 89.5449i −0.207072 + 0.392741i
\(229\) −84.1627 −0.367523 −0.183761 0.982971i \(-0.558827\pi\)
−0.183761 + 0.982971i \(0.558827\pi\)
\(230\) −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 0.999724 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
\(238\) 5.26101 16.8120i 0.0221051 0.0706386i
\(239\) −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 \(0.254323\pi\)
−0.697438 + 0.716645i \(0.745677\pi\)
\(242\) 376.679 376.679i 1.55652 1.55652i
\(243\) 183.399 159.417i 0.754729 0.656037i
\(244\) 139.433 0.571445
\(245\) −184.665 161.008i −0.753736 0.657177i
\(246\) 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 \(0.331178\pi\)
\(252\) −57.5602 188.004i −0.228414 0.746047i
\(253\) −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 \(-0.947128\pi\)
−0.165340 0.986237i \(-0.552872\pi\)
\(258\) −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 \(-0.732320\pi\)
0.666761 0.745272i \(-0.267680\pi\)
\(270\) 255.919 + 253.543i 0.947849 + 0.939049i
\(271\) 395.831i 1.46063i −0.683109 0.730316i \(-0.739373\pi\)
0.683109 0.730316i \(-0.260627\pi\)
\(272\) −12.4990 12.4990i −0.0459523 0.0459523i
\(273\) −330.790 1.02134i −1.21169 0.00374117i
\(274\) 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
\(280\) −76.4999 + 29.8132i −0.273214 + 0.106476i
\(281\) 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 0.502078 0.864822i \(-0.332569\pi\)
−0.864822 + 0.502078i \(0.832569\pi\)
\(284\) −19.8358 −0.0698444
\(285\) −134.242 90.9986i −0.471025 0.319293i
\(286\) 752.668i 2.63171i
\(287\) 14.3407 45.8269i 0.0499676 0.159676i
\(288\) −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 −0.963767 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
\(297\) 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 −0.960770 0.277345i \(-0.910545\pi\)
0.277345 + 0.960770i \(0.410545\pi\)
\(308\) 116.827 373.331i 0.379309 1.21211i
\(309\) −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 \(0.267518\pi\)
\(312\) −51.7016 + 98.0593i −0.165710 + 0.314293i
\(313\) −6.05318 6.05318i −0.0193392 0.0193392i 0.697371 0.716710i \(-0.254353\pi\)
−0.716710 + 0.697371i \(0.754353\pi\)
\(314\) 241.265i 0.768359i
\(315\) 309.532 58.4362i 0.982642 0.185512i
\(316\) −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
\(322\) −17.3902 + 55.5719i −0.0540069 + 0.172583i
\(323\) −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
\(336\) −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
\(342\) −255.232 47.7685i −0.746293 0.139674i
\(343\) −270.765 + 210.559i −0.789402 + 0.613876i
\(344\) 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 \(-0.329279\pi\)
0.510989 + 0.859587i \(0.329279\pi\)
\(350\) 120.550 + 451.161i 0.344427 + 1.28903i
\(351\) 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
\(357\) 19.8042 + 0.0611469i 0.0554739 + 0.000171280i
\(358\) −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 −0.912976 0.408013i \(-0.866222\pi\)
0.408013 + 0.912976i \(0.366222\pi\)
\(368\) 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
\(378\) 417.025 283.649i 1.10324 0.750393i
\(379\) 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
\(385\) 573.820 + 251.989i 1.49044 + 0.654517i
\(386\) 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
\(392\) 20.4476 + 113.112i 0.0521623 + 0.288551i
\(393\) 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 \(-0.375143\pi\)
0.924051 0.382270i \(-0.124857\pi\)
\(398\) 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 \(-0.863695\pi\)
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 \(-0.782619\pi\)
−0.775732 + 0.631062i \(0.782619\pi\)
\(410\) −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
\(413\) −667.346 208.834i −1.61585 0.505651i
\(414\) −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 \(-0.835042\pi\)
0.868697 0.495343i \(-0.164958\pi\)
\(420\) 203.957 + 256.489i 0.485612 + 0.610688i
\(421\) 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
\(427\) 298.465 + 93.3992i 0.698981 + 0.218733i
\(428\) −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 0.120361 0.992730i \(-0.461595\pi\)
−0.992730 + 0.120361i \(0.961595\pi\)
\(434\) 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 \(-0.506841\pi\)
−0.0214894 + 0.999769i \(0.506841\pi\)
\(440\) 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 \(0.0314092\pi\)
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
\(448\) −223.515 69.9451i −0.498918 0.156127i
\(449\) 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
\(455\) 513.689 200.193i 1.12899 0.439984i
\(456\) 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 \(0.738179\pi\)
\(462\) 1003.43 + 3.09815i 2.17192 + 0.00670595i
\(463\) 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 0.402495 0.915422i \(-0.368143\pi\)
−0.915422 + 0.402495i \(0.868143\pi\)
\(468\) 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 \(0.361469\pi\)
−0.421598 + 0.906783i \(0.638531\pi\)
\(480\) 598.577 114.920i 1.24704 0.239416i
\(481\) 928.188i 1.92970i
\(482\) −651.785 651.785i −1.35225 1.35225i
\(483\) −65.4625 0.202120i −0.135533 0.000418468i
\(484\) 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
\(490\) 652.258 44.6390i 1.33114 0.0911000i
\(491\) 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
\(497\) −42.4599 13.2870i −0.0854323 0.0267345i
\(498\) −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 \(0.574636\pi\)
−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
\(507\) 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 \(-0.998779\pi\)
0.999993 0.00383697i \(-0.00122135\pi\)
\(510\) −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
\(518\) −328.723 + 1050.46i −0.634600 + 2.02792i
\(519\) −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 \(0.679317\pi\)
\(522\) −542.265 101.489i −1.03882 0.194423i
\(523\) 241.019 + 241.019i 0.460839 + 0.460839i 0.898930 0.438092i \(-0.144345\pi\)
−0.438092 + 0.898930i \(0.644345\pi\)
\(524\) 409.696i 0.781862i
\(525\) −444.449 + 279.446i −0.846569 + 0.532278i
\(526\) −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
\(532\) −225.421 70.5415i −0.423724 0.132597i
\(533\) 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
\(546\) 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
\(552\) −10.2316 + 19.4057i −0.0185355 + 0.0351552i
\(553\) −399.384 124.980i −0.722213 0.226004i
\(554\) 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
\(560\) 263.775 600.658i 0.471026 1.07260i
\(561\) −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
\(567\) 443.258 + 353.569i 0.781761 + 0.623578i
\(568\) −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 −0.649646 0.760237i \(-0.725083\pi\)
0.760237 + 0.649646i \(0.225083\pi\)
\(578\) 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 \(0.107509\pi\)
0.331366 + 0.943502i \(0.392491\pi\)
\(588\) 407.136 211.459i 0.692409 0.359624i
\(589\) 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
\(595\) −30.7542 + 11.9854i −0.0516877 + 0.0201435i
\(596\) 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 \(-0.960503\pi\)
0.992312 0.123765i \(-0.0394969\pi\)
\(602\) −950.294 297.377i −1.57856 0.493982i
\(603\) 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 −0.927588 0.373604i \(-0.878122\pi\)
0.373604 + 0.927588i \(0.378122\pi\)
\(608\) −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
\(612\) −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 \(-0.635039\pi\)
−0.411626 + 0.911353i \(0.635039\pi\)
\(620\) −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
\(623\) 390.275 + 122.129i 0.626444 + 0.196034i
\(624\) −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
\(630\) −473.798 + 694.326i −0.752060 + 1.10211i
\(631\) −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
\(637\) −137.304 759.537i −0.215547 1.19237i
\(638\) −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 0.875067 0.484002i \(-0.160817\pi\)
−0.484002 + 0.875067i \(0.660817\pi\)
\(644\) −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 0.870681 0.491848i \(-0.163679\pi\)
−0.491848 + 0.870681i \(0.663679\pi\)
\(648\) 173.855 76.6743i 0.268295 0.118325i
\(649\) 1788.71 2.75610
\(650\) −1025.29 230.375i −1.57738 0.354423i
\(651\) 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 0.485463 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
\(658\) −43.8340 + 140.075i −0.0666170 + 0.212880i
\(659\) −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 \(-0.904118\pi\)
0.954975 0.296687i \(-0.0958817\pi\)
\(662\) −280.246 + 280.246i −0.423332 + 0.423332i
\(663\) −20.7849 + 39.4215i −0.0313497 + 0.0594592i
\(664\) 140.127 0.211034
\(665\) 152.154 346.479i 0.228803 0.521021i
\(666\) −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
\(672\) 2.63465 853.308i 0.00392061 1.26980i
\(673\) 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 0.574825 0.818277i \(-0.305070\pi\)
−0.818277 + 0.574825i \(0.805070\pi\)
\(678\) −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 \(0.143800\pi\)
−0.899680 + 0.436550i \(0.856200\pi\)
\(692\) −558.990 558.990i −0.807789 0.807789i
\(693\) 330.247 + 1078.66i 0.476548 + 1.55651i
\(694\) 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
\(700\) −472.798 273.412i −0.675426 0.390588i
\(701\) 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
\(707\) 24.9233 79.6444i 0.0352521 0.112651i
\(708\) 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
\(714\) −37.4843 + 37.2535i −0.0524990 + 0.0521758i
\(715\) −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 \(0.0979843\pi\)
−0.952994 + 0.302988i \(0.902016\pi\)
\(720\) 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 \(-0.486410\pi\)
0.999089 0.0426819i \(-0.0135902\pi\)
\(728\) −246.856 77.2490i −0.339087 0.106111i
\(729\) −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 0.0794540 0.996839i \(-0.474682\pi\)
−0.996839 + 0.0794540i \(0.974682\pi\)
\(734\) 699.372i 0.952823i
\(735\) 264.774 + 685.653i 0.360237 + 0.932861i
\(736\) −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
\(742\) 256.055 818.246i 0.345088 1.10276i
\(743\) 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
\(756\) −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 \(0.276060\pi\)
\(762\) 1479.08 + 779.842i 1.94105 + 1.02342i
\(763\) −359.468 112.489i −0.471124 0.147430i
\(764\) 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