Properties

Label 105.3.k.d.62.11
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 62.11
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.88692 - 1.88692i) q^{2} +(-1.39918 - 2.65373i) q^{3} -3.12092i q^{4} +(-4.96950 - 0.551428i) q^{5} +(-7.64751 - 2.36725i) q^{6} +(2.09055 - 6.68054i) q^{7} +(1.65875 + 1.65875i) q^{8} +(-5.08462 + 7.42608i) q^{9} +O(q^{10})\) \(q+(1.88692 - 1.88692i) q^{2} +(-1.39918 - 2.65373i) 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} +(-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} +(-20.6534 + 3.79947i) q^{21} +(-33.7872 - 33.7872i) q^{22} +(-2.20425 - 2.20425i) q^{23} +(2.08100 - 6.72276i) q^{24} +(24.3919 + 5.48064i) q^{25} +42.0343 q^{26} +(26.8211 + 3.10283i) q^{27} +(-20.8494 - 6.52445i) 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} +(-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} +(-31.8020 + 46.1406i) 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} +(38.9806 + 49.4926i) 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} +(-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} +(-119.622 - 37.4336i) 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} +(11.8578 + 64.4577i) 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} +(-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 −0.0550258 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
\(7\) 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 \(-0.697334\pi\)
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 0.990959 0.134164i \(-0.0428348\pi\)
−0.134164 + 0.990959i \(0.542835\pi\)
\(14\) −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 0.726448 0.687222i \(-0.241170\pi\)
−0.687222 + 0.726448i \(0.741170\pi\)
\(18\) 4.41815 + 23.6067i 0.245453 + 1.31148i
\(19\) 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
\(21\) −20.6534 + 3.79947i −0.983496 + 0.180927i
\(22\) −33.7872 33.7872i −1.53578 1.53578i
\(23\) −2.20425 2.20425i −0.0958368 0.0958368i 0.657563 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
\(28\) −20.8494 6.52445i −0.744623 0.233016i
\(29\) −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 \(-0.861637\pi\)
0.907005 0.421120i \(-0.138363\pi\)
\(32\) 28.7325 28.7325i 0.897891 0.897891i
\(33\) −47.5179 + 25.0537i −1.43994 + 0.759203i
\(34\) 2.51656 0.0740166
\(35\) −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 \(-0.526660\pi\)
−0.0836556 + 0.996495i \(0.526660\pi\)
\(42\) −31.8020 + 46.1406i −0.757191 + 1.09859i
\(43\) −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 0.645525 0.763739i \(-0.276639\pi\)
−0.763739 + 0.645525i \(0.776639\pi\)
\(48\) −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 \(0.321330\pi\)
−0.532294 + 0.846559i \(0.678670\pi\)
\(60\) 43.5658 17.1334i 0.726097 0.285557i
\(61\) 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
\(63\) 38.9806 + 49.4926i 0.618739 + 0.785597i
\(64\) 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 \(0.0142519\pi\)
−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 0.217671 0.976022i \(-0.430154\pi\)
−0.976022 + 0.217671i \(0.930154\pi\)
\(74\) 157.242 2.12489
\(75\) −19.5843 72.3979i −0.261124 0.965305i
\(76\) 33.7430i 0.443987i
\(77\) −119.622 37.4336i −1.55353 0.486150i
\(78\) −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 −0.405289 0.914189i \(-0.632829\pi\)
0.914189 + 0.405289i \(0.132829\pi\)
\(84\) 11.8578 + 64.4577i 0.141165 + 0.767354i
\(85\) −2.94617 3.68160i −0.0346608 0.0433130i
\(86\) 142.248i 1.65405i
\(87\) 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 \(-0.893558\pi\)
0.944608 0.328200i \(-0.106442\pi\)
\(90\) −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 −0.762441 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 \(-0.518797\pi\)
−0.0590191 + 0.998257i \(0.518797\pi\)
\(102\) −3.52111 6.67829i −0.0345207 0.0654734i
\(103\) 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
\(105\) 104.732 7.49259i 0.997451 0.0713580i
\(106\) 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
\(112\) 39.1844 125.217i 0.349860 1.11801i
\(113\) 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
\(126\) 166.942 + 19.8353i 1.32493 + 0.157423i
\(127\) 147.690 + 147.690i 1.16291 + 1.16291i 0.983835 + 0.179080i \(0.0573121\pi\)
0.179080 + 0.983835i \(0.442688\pi\)
\(128\) 51.7981 + 51.7981i 0.404673 + 0.404673i
\(129\) 152.767 + 47.2884i 1.18424 + 0.366577i
\(130\) −208.889 23.1789i −1.60684 0.178299i
\(131\) 131.274 1.00209 0.501046 0.865421i \(-0.332949\pi\)
0.501046 + 0.865421i \(0.332949\pi\)
\(132\) 78.1906 + 148.300i 0.592353 + 1.12348i
\(133\) 22.6028 72.2291i 0.169946 0.543076i
\(134\) −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 \(-0.465452\pi\)
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
\(147\) −17.7946 + 145.919i −0.121052 + 0.992646i
\(148\) 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 −0.473559 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
\(162\) −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 0.858503 0.512808i \(-0.171395\pi\)
−0.512808 + 0.858503i \(0.671395\pi\)
\(168\) −40.5612 27.9565i −0.241436 0.166408i
\(169\) 79.1253i 0.468197i
\(170\) −12.5061 1.38770i −0.0735650 0.00816296i
\(171\) −54.9742 + 80.2898i −0.321487 + 0.469531i
\(172\) 117.638 + 117.638i 0.683940 + 0.683940i
\(173\) −179.111 + 179.111i −1.03532 + 1.03532i −0.0359688 + 0.999353i \(0.511452\pi\)
−0.999353 + 0.0359688i \(0.988548\pi\)
\(174\) 175.670 + 54.3777i 1.00960 + 0.312516i
\(175\) 87.6061 151.493i 0.500606 0.865675i
\(176\) 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 \(-0.887806\pi\)
0.938524 0.345214i \(-0.112194\pi\)
\(182\) 87.8749 280.812i 0.482829 1.54292i
\(183\) 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
\(189\) 76.7996 172.693i 0.406347 0.913719i
\(190\) −112.633 + 90.1336i −0.592806 + 0.474387i
\(191\) 120.234i 0.629496i −0.949175 0.314748i \(-0.898080\pi\)
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 \(-0.773181\pi\)
−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
\(207\) 27.5767 5.16117i 0.133221 0.0249332i
\(208\) 208.772 + 208.772i 1.00371 + 1.00371i
\(209\) 193.598i 0.926305i
\(210\) 183.483 211.759i 0.873731 1.00838i
\(211\) −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
\(217\) −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
\(222\) −220.009 417.278i −0.991032 1.87963i
\(223\) 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
\(225\) −164.723 + 153.269i −0.732102 + 0.681195i
\(226\) 315.251 1.39492
\(227\) 190.960 + 190.960i 0.841234 + 0.841234i 0.989019 0.147785i \(-0.0472145\pi\)
−0.147785 + 0.989019i \(0.547215\pi\)
\(228\) −89.5449 + 47.2124i −0.392741 + 0.207072i
\(229\) −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
\(231\) 68.0335 + 369.821i 0.294517 + 1.60096i
\(232\) −38.1029 38.1029i −0.164237 0.164237i
\(233\) −227.465 227.465i −0.976246 0.976246i 0.0234784 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
\(238\) 5.26101 16.8120i 0.0221051 0.0706386i
\(239\) 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 \(0.254323\pi\)
−0.697438 + 0.716645i \(0.745677\pi\)
\(242\) −376.679 + 376.679i −1.55652 + 1.55652i
\(243\) −159.417 + 183.399i −0.656037 + 0.754729i
\(244\) 139.433 0.571445
\(245\) 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 \(-0.668822\pi\)
−0.505852 + 0.862620i \(0.668822\pi\)
\(252\) 154.462 121.655i 0.612946 0.482759i
\(253\) −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 \(0.0528721\pi\)
0.165340 + 0.986237i \(0.447128\pi\)
\(258\) 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 \(0.267680\pi\)
−0.666761 + 0.745272i \(0.732320\pi\)
\(270\) −305.277 + 191.271i −1.13066 + 0.708413i
\(271\) 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
\(273\) −272.365 187.725i −0.997673 0.687638i
\(274\) 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 \(0.169217\pi\)
−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 0.502078 0.864822i \(-0.332569\pi\)
−0.864822 + 0.502078i \(0.832569\pi\)
\(284\) 19.8358 0.0698444
\(285\) 59.3556 + 150.926i 0.208265 + 0.529565i
\(286\) 752.668i 2.63171i
\(287\) −14.3407 + 45.8269i −0.0499676 + 0.159676i
\(288\) 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 −0.266746 0.963767i \(-0.585948\pi\)
0.963767 + 0.266746i \(0.0859483\pi\)
\(294\) 241.760 + 308.914i 0.822314 + 1.05073i
\(295\) 55.0844 496.423i 0.186727 1.68279i
\(296\) 138.228i 0.466987i
\(297\) 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 −0.960770 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 \(-0.732482\pi\)
−0.667141 + 0.744932i \(0.732482\pi\)
\(312\) 98.0593 51.7016i 0.314293 0.165710i
\(313\) −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
\(315\) −166.422 267.448i −0.528325 0.849042i
\(316\) −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
\(322\) −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
\(327\) −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
\(336\) −387.118 + 71.2155i −1.15214 + 0.211951i
\(337\) 225.218 + 225.218i 0.668303 + 0.668303i 0.957323 0.289020i \(-0.0933294\pi\)
−0.289020 + 0.957323i \(0.593329\pi\)
\(338\) 149.303 + 149.303i 0.441725 + 0.441725i
\(339\) 104.801 338.564i 0.309147 0.998714i
\(340\) −11.4900 + 9.19476i −0.0337941 + 0.0270434i
\(341\) −467.517 −1.37102
\(342\) 47.7685 + 255.232i 0.139674 + 0.746293i
\(343\) −270.765 + 210.559i −0.789402 + 0.613876i
\(344\) −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 \(-0.329279\pi\)
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 −0.992048 0.125857i \(-0.959832\pi\)
0.125857 + 0.992048i \(0.459832\pi\)
\(354\) 236.474 763.940i 0.668006 2.15802i
\(355\) 3.50474 31.5849i 0.00987251 0.0889716i
\(356\) −182.323 −0.512144
\(357\) −16.3063 11.2390i −0.0456759 0.0314817i
\(358\) −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 −0.912976 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
\(372\) 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
\(378\) −180.943 470.772i −0.478685 1.24543i
\(379\) 33.7232i 0.0889794i −0.999010 0.0444897i \(-0.985834\pi\)
0.999010 0.0444897i \(-0.0141662\pi\)
\(380\) −18.6068 + 167.686i −0.0489654 + 0.441278i
\(381\) 185.286 598.575i 0.486315 1.57106i
\(382\) −226.871 226.871i −0.593904 0.593904i
\(383\) 353.025 353.025i 0.921735 0.921735i −0.0754169 0.997152i \(-0.524029\pi\)
0.997152 + 0.0754169i \(0.0240288\pi\)
\(384\) 64.9838 209.933i 0.169229 0.546701i
\(385\) 573.820 + 251.989i 1.49044 + 0.654517i
\(386\) 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
\(392\) −20.4476 113.112i −0.0521623 0.288551i
\(393\) −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 \(-0.375143\pi\)
0.924051 0.382270i \(-0.124857\pi\)
\(398\) −568.264 + 568.264i −1.42780 + 1.42780i
\(399\) −223.302 + 41.0794i −0.559654 + 0.102956i
\(400\) 457.190 + 102.727i 1.14297 + 0.256817i
\(401\) 333.028i 0.830494i 0.909709 + 0.415247i \(0.136305\pi\)
−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 \(-0.782619\pi\)
−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
\(417\) −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 \(0.164958\pi\)
−0.868697 + 0.495343i \(0.835042\pi\)
\(420\) −23.3838 326.861i −0.0556756 0.778241i
\(421\) 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
\(427\) 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 \(-0.918649\pi\)
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 0.120361 0.992730i \(-0.461595\pi\)
−0.992730 + 0.120361i \(0.961595\pi\)
\(434\) −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 \(-0.506841\pi\)
−0.0214894 + 0.999769i \(0.506841\pi\)
\(440\) −163.981 + 131.224i −0.372683 + 0.298236i
\(441\) 412.128 156.944i 0.934531 0.355882i
\(442\) 28.0303 + 28.0303i 0.0634171 + 0.0634171i
\(443\) −484.487 484.487i −1.09365 1.09365i −0.995136 0.0985149i \(-0.968591\pi\)
−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
\(448\) −223.515 69.9451i −0.498918 0.156127i
\(449\) −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
\(455\) −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 \(-0.261821\pi\)
0.680365 + 0.732874i \(0.261821\pi\)
\(462\) 826.196 + 569.449i 1.78830 + 1.23257i
\(463\) 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 0.915422 0.402495i \(-0.131857\pi\)
−0.402495 + 0.915422i \(0.631857\pi\)
\(468\) 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 \(-0.638531\pi\)
0.421598 0.906783i \(-0.361469\pi\)
\(480\) 558.823 + 243.348i 1.16421 + 0.506975i
\(481\) 928.188i 1.92970i
\(482\) 651.785 + 651.785i 1.35225 + 1.35225i
\(483\) 53.9002 + 37.1503i 0.111595 + 0.0769157i
\(484\) 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 \(-0.959273\pi\)
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
\(497\) 42.4599 + 13.2870i 0.0854323 + 0.0267345i
\(498\) −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 \(-0.425364\pi\)
0.972636 0.232335i \(-0.0746364\pi\)
\(504\) −17.4368 + 146.755i −0.0345969 + 0.291180i
\(505\) 59.2456 + 6.57404i 0.117318 + 0.0130179i
\(506\) 148.951i 0.294369i
\(507\) 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 \(0.00122135\pi\)
−0.999993 + 0.00383697i \(0.998779\pi\)
\(510\) 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
\(518\) 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 \(-0.320683\pi\)
0.534015 + 0.845475i \(0.320683\pi\)
\(522\) −101.489 542.265i −0.194423 1.03882i
\(523\) 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
\(525\) −524.599 20.5180i −0.999236 0.0390818i
\(526\) −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
\(532\) −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
\(537\) 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
\(546\) −868.152 + 159.708i −1.59002 + 0.292506i
\(547\) −80.6313 80.6313i −0.147406 0.147406i 0.629552 0.776958i \(-0.283238\pi\)
−0.776958 + 0.629552i \(0.783238\pi\)
\(548\) −212.586 212.586i −0.387930 0.387930i
\(549\) −331.773 227.164i −0.604323 0.413778i
\(550\) −638.958 1009.31i −1.16174 1.83511i
\(551\) −248.358 −0.450740
\(552\) −19.4057 + 10.2316i −0.0351552 + 0.0185355i
\(553\) −399.384 124.980i −0.722213 0.226004i
\(554\) −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
\(560\) −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 −0.998804 0.0488978i \(-0.984429\pi\)
0.0488978 + 0.998804i \(0.484429\pi\)
\(564\) 70.2776 + 21.7541i 0.124606 + 0.0385711i
\(565\) −369.068 461.196i −0.653218 0.816277i
\(566\) −387.409 −0.684468
\(567\) −565.737 + 37.8220i −0.997773 + 0.0667054i
\(568\) −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 −0.649646 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
\(582\) 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 \(-0.892491\pi\)
−0.331366 0.943502i \(-0.607509\pi\)
\(588\) 455.402 + 55.5355i 0.774493 + 0.0944481i
\(589\) 282.292i 0.479273i
\(590\) −832.770 1040.65i −1.41148 1.76381i
\(591\) 31.6952 + 9.81110i 0.0536298 + 0.0166008i
\(592\) 780.974 + 780.974i 1.31921 + 1.31921i
\(593\) 88.6544 88.6544i 0.149502 0.149502i −0.628394 0.777895i \(-0.716287\pi\)
0.777895 + 0.628394i \(0.216287\pi\)
\(594\) −801.376 1011.05i −1.34912 1.70210i
\(595\) −30.7542 + 11.9854i −0.0516877 + 0.0201435i
\(596\) 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 \(-0.960503\pi\)
0.992312 0.123765i \(-0.0394969\pi\)
\(602\) 950.294 + 297.377i 1.57856 + 0.493982i
\(603\) 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 −0.927588 0.373604i \(-0.878122\pi\)
0.373604 + 0.927588i \(0.378122\pi\)
\(608\) 310.652 310.652i 0.510941 0.510941i
\(609\) 474.427 87.2770i 0.779026 0.143312i
\(610\) −372.450 465.422i −0.610573 0.762987i
\(611\) 123.771i 0.202571i
\(612\) 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 \(-0.635039\pi\)
−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
\(627\) −513.757 + 270.877i −0.819390 + 0.432021i
\(628\) −199.523 199.523i −0.317712 0.317712i
\(629\) 55.5699i 0.0883465i
\(630\) −818.678 190.628i −1.29949 0.302584i
\(631\) −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
\(637\) −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 \(0.108423\pi\)
−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 0.875067 0.484002i \(-0.160817\pi\)
−0.484002 + 0.875067i \(0.660817\pi\)
\(644\) 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 0.491848 0.870681i \(-0.336321\pi\)
−0.870681 + 0.491848i \(0.836321\pi\)
\(648\) 76.6743 173.855i 0.118325 0.268295i
\(649\) 1788.71 2.75610
\(650\) 1025.29 + 230.375i 1.57738 + 0.354423i
\(651\) 99.2021 + 539.249i 0.152384 + 0.828340i
\(652\) 32.1241 + 32.1241i 0.0492700 + 0.0492700i
\(653\) 253.883 + 253.883i 0.388794 + 0.388794i 0.874257 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
\(658\) −43.8340 + 140.075i −0.0666170 + 0.212880i
\(659\) 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 \(-0.904118\pi\)
0.954975 0.296687i \(-0.0958817\pi\)
\(662\) 280.246 280.246i 0.423332 0.423332i
\(663\) 39.4215 20.7849i 0.0594592 0.0313497i
\(664\) 140.127 0.211034
\(665\) −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
\(672\) −484.257 + 702.593i −0.720620 + 1.04553i
\(673\) 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 0.818277 0.574825i \(-0.194930\pi\)
−0.574825 + 0.818277i \(0.694930\pi\)
\(678\) −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 \(0.143800\pi\)
−0.899680 + 0.436550i \(0.856200\pi\)
\(692\) 558.990 + 558.990i 0.807789 + 0.807789i
\(693\) 886.217 697.988i 1.27881 1.00720i
\(694\) 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 \(-0.918516\pi\)
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
\(707\) −24.9233 + 79.6444i −0.0352521 + 0.112651i
\(708\) −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
\(714\) −51.9756 + 9.56161i −0.0727950 + 0.0133916i
\(715\) −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 \(-0.902016\pi\)
0.952994 0.302988i \(-0.0979843\pi\)
\(720\) 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 \(-0.486410\pi\)
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
\(732\) −195.091 370.017i −0.266517 0.505488i
\(733\) −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
\(735\) 168.894 715.332i 0.229788 0.973241i
\(736\) −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
\(742\) 256.055 818.246i 0.345088 1.10276i
\(743\) −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
\(756\) −538.961 239.685i −0.712911 0.317044i
\(757\) −328.630 328.630i −0.434121 0.434121i 0.455906 0.890028i \(-0.349315\pi\)
−0.890028 + 0.455906i \(0.849315\pi\)
\(758\) −63.6329 63.6329i −0.0839484 0.0839484i
\(759\) 159.966 + 49.5166i 0.210759 + 0.0652393i
\(760\) −79.2345 99.0133i −0.104256 0.130281i
\(761\) −984.602 −1.29383 −0.646913 0.762564i \(-0.723940\pi\)
−0.646913 + 0.762564i \(0.723940\pi\)
\(762\) −779.842 1479.08i −1.02342 1.94105i
\(763\) −359.468 112.489i −0.471124 0.147430i
\(764\) −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