Properties

Label 60.7.c.a.31.5
Level $60$
Weight $7$
Character 60.31
Analytic conductor $13.803$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.5
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.53904 - 7.17462i) q^{2} -15.5885i q^{3} +(-38.9505 + 50.7825i) q^{4} +55.9017 q^{5} +(-111.841 + 55.1681i) q^{6} +99.9522i q^{7} +(502.192 + 99.7338i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(-3.53904 - 7.17462i) q^{2} -15.5885i q^{3} +(-38.9505 + 50.7825i) q^{4} +55.9017 q^{5} +(-111.841 + 55.1681i) q^{6} +99.9522i q^{7} +(502.192 + 99.7338i) q^{8} -243.000 q^{9} +(-197.838 - 401.074i) q^{10} +2399.27i q^{11} +(791.621 + 607.177i) q^{12} +3619.28 q^{13} +(717.119 - 353.734i) q^{14} -871.421i q^{15} +(-1061.72 - 3956.00i) q^{16} -927.422 q^{17} +(859.986 + 1743.43i) q^{18} -773.488i q^{19} +(-2177.40 + 2838.83i) q^{20} +1558.10 q^{21} +(17213.9 - 8491.11i) q^{22} -12221.5i q^{23} +(1554.70 - 7828.40i) q^{24} +3125.00 q^{25} +(-12808.8 - 25967.0i) q^{26} +3788.00i q^{27} +(-5075.82 - 3893.18i) q^{28} +29029.7 q^{29} +(-6252.12 + 3083.99i) q^{30} -9560.97i q^{31} +(-24625.3 + 21617.9i) q^{32} +37401.0 q^{33} +(3282.18 + 6653.91i) q^{34} +5587.50i q^{35} +(9464.96 - 12340.1i) q^{36} +88644.4 q^{37} +(-5549.49 + 2737.40i) q^{38} -56419.0i q^{39} +(28073.4 + 5575.29i) q^{40} -53763.7 q^{41} +(-5514.17 - 11178.8i) q^{42} +140348. i q^{43} +(-121841. - 93452.8i) q^{44} -13584.1 q^{45} +(-87684.9 + 43252.5i) q^{46} +105555. i q^{47} +(-61668.0 + 16550.6i) q^{48} +107659. q^{49} +(-11059.5 - 22420.7i) q^{50} +14457.1i q^{51} +(-140973. + 183796. i) q^{52} -80965.8 q^{53} +(27177.4 - 13405.9i) q^{54} +134123. i q^{55} +(-9968.61 + 50195.2i) q^{56} -12057.5 q^{57} +(-102737. - 208277. i) q^{58} -59057.3i q^{59} +(44252.9 + 33942.3i) q^{60} +116330. q^{61} +(-68596.4 + 33836.6i) q^{62} -24288.4i q^{63} +(242250. + 100171. i) q^{64} +202324. q^{65} +(-132363. - 268338. i) q^{66} +134450. i q^{67} +(36123.5 - 47096.8i) q^{68} -190515. q^{69} +(40088.2 - 19774.4i) q^{70} +468387. i q^{71} +(-122033. - 24235.3i) q^{72} +79504.8 q^{73} +(-313716. - 635990. i) q^{74} -48713.9i q^{75} +(39279.7 + 30127.7i) q^{76} -239813. q^{77} +(-404785. + 199669. i) q^{78} -670660. i q^{79} +(-59352.2 - 221147. i) q^{80} +59049.0 q^{81} +(190272. + 385734. i) q^{82} -549656. i q^{83} +(-60688.7 + 79124.2i) q^{84} -51844.5 q^{85} +(1.00694e6 - 496695. i) q^{86} -452528. i q^{87} +(-239288. + 1.20490e6i) q^{88} +785334. q^{89} +(48074.7 + 97460.9i) q^{90} +361755. i q^{91} +(620640. + 476034. i) q^{92} -149041. q^{93} +(757314. - 373561. i) q^{94} -43239.3i q^{95} +(336990. + 383871. i) q^{96} +664400. q^{97} +(-381007. - 772410. i) q^{98} -583023. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} + O(q^{10}) \) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} - 750q^{10} + 5040q^{13} - 2596q^{14} + 4194q^{16} - 4860q^{18} + 7000q^{20} + 19440q^{21} + 45780q^{22} + 24786q^{24} + 75000q^{25} + 75852q^{26} + 54300q^{28} + 132800q^{29} - 10700q^{32} - 173484q^{34} + 59778q^{36} - 69840q^{37} + 215800q^{38} - 14250q^{40} - 70448q^{41} - 189540q^{42} - 395668q^{44} - 158760q^{46} + 252720q^{48} - 642984q^{49} + 62500q^{50} - 210240q^{52} - 644320q^{53} - 39366q^{54} - 917708q^{56} + 408240q^{57} - 1345020q^{58} + 222750q^{60} - 222864q^{61} + 1948520q^{62} + 935922q^{64} + 266000q^{65} - 640548q^{66} + 572680q^{68} - 541728q^{69} + 220500q^{70} + 82620q^{72} + 771120q^{73} - 589164q^{74} - 191544q^{76} + 1383840q^{77} - 693360q^{78} - 946000q^{80} + 1417176q^{81} + 2672520q^{82} + 1256796q^{84} - 372000q^{85} + 1781528q^{86} + 956940q^{88} - 1566224q^{89} + 182250q^{90} - 3040560q^{92} + 1496880q^{93} - 3788352q^{94} - 413262q^{96} - 1666800q^{97} - 2709660q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.53904 7.17462i −0.442379 0.896828i
\(3\) 15.5885i 0.577350i
\(4\) −38.9505 + 50.7825i −0.608601 + 0.793477i
\(5\) 55.9017 0.447214
\(6\) −111.841 + 55.1681i −0.517784 + 0.255408i
\(7\) 99.9522i 0.291406i 0.989328 + 0.145703i \(0.0465444\pi\)
−0.989328 + 0.145703i \(0.953456\pi\)
\(8\) 502.192 + 99.7338i 0.980844 + 0.194793i
\(9\) −243.000 −0.333333
\(10\) −197.838 401.074i −0.197838 0.401074i
\(11\) 2399.27i 1.80261i 0.433186 + 0.901304i \(0.357389\pi\)
−0.433186 + 0.901304i \(0.642611\pi\)
\(12\) 791.621 + 607.177i 0.458114 + 0.351376i
\(13\) 3619.28 1.64737 0.823687 0.567045i \(-0.191913\pi\)
0.823687 + 0.567045i \(0.191913\pi\)
\(14\) 717.119 353.734i 0.261341 0.128912i
\(15\) 871.421i 0.258199i
\(16\) −1061.72 3956.00i −0.259210 0.965821i
\(17\) −927.422 −0.188769 −0.0943845 0.995536i \(-0.530088\pi\)
−0.0943845 + 0.995536i \(0.530088\pi\)
\(18\) 859.986 + 1743.43i 0.147460 + 0.298943i
\(19\) 773.488i 0.112770i −0.998409 0.0563849i \(-0.982043\pi\)
0.998409 0.0563849i \(-0.0179574\pi\)
\(20\) −2177.40 + 2838.83i −0.272175 + 0.354854i
\(21\) 1558.10 0.168243
\(22\) 17213.9 8491.11i 1.61663 0.797437i
\(23\) 12221.5i 1.00448i −0.864728 0.502241i \(-0.832509\pi\)
0.864728 0.502241i \(-0.167491\pi\)
\(24\) 1554.70 7828.40i 0.112464 0.566291i
\(25\) 3125.00 0.200000
\(26\) −12808.8 25967.0i −0.728764 1.47741i
\(27\) 3788.00i 0.192450i
\(28\) −5075.82 3893.18i −0.231224 0.177350i
\(29\) 29029.7 1.19028 0.595139 0.803623i \(-0.297097\pi\)
0.595139 + 0.803623i \(0.297097\pi\)
\(30\) −6252.12 + 3083.99i −0.231560 + 0.114222i
\(31\) 9560.97i 0.320935i −0.987041 0.160467i \(-0.948700\pi\)
0.987041 0.160467i \(-0.0513002\pi\)
\(32\) −24625.3 + 21617.9i −0.751506 + 0.659726i
\(33\) 37401.0 1.04074
\(34\) 3282.18 + 6653.91i 0.0835076 + 0.169293i
\(35\) 5587.50i 0.130321i
\(36\) 9464.96 12340.1i 0.202867 0.264492i
\(37\) 88644.4 1.75003 0.875016 0.484093i \(-0.160851\pi\)
0.875016 + 0.484093i \(0.160851\pi\)
\(38\) −5549.49 + 2737.40i −0.101135 + 0.0498870i
\(39\) 56419.0i 0.951112i
\(40\) 28073.4 + 5575.29i 0.438647 + 0.0871139i
\(41\) −53763.7 −0.780077 −0.390039 0.920799i \(-0.627538\pi\)
−0.390039 + 0.920799i \(0.627538\pi\)
\(42\) −5514.17 11178.8i −0.0744273 0.150885i
\(43\) 140348.i 1.76522i 0.470103 + 0.882612i \(0.344217\pi\)
−0.470103 + 0.882612i \(0.655783\pi\)
\(44\) −121841. 93452.8i −1.43033 1.09707i
\(45\) −13584.1 −0.149071
\(46\) −87684.9 + 43252.5i −0.900848 + 0.444362i
\(47\) 105555.i 1.01668i 0.861157 + 0.508339i \(0.169740\pi\)
−0.861157 + 0.508339i \(0.830260\pi\)
\(48\) −61668.0 + 16550.6i −0.557617 + 0.149655i
\(49\) 107659. 0.915083
\(50\) −11059.5 22420.7i −0.0884759 0.179366i
\(51\) 14457.1i 0.108986i
\(52\) −140973. + 183796.i −1.00259 + 1.30715i
\(53\) −80965.8 −0.543844 −0.271922 0.962319i \(-0.587659\pi\)
−0.271922 + 0.962319i \(0.587659\pi\)
\(54\) 27177.4 13405.9i 0.172595 0.0851360i
\(55\) 134123.i 0.806151i
\(56\) −9968.61 + 50195.2i −0.0567637 + 0.285824i
\(57\) −12057.5 −0.0651077
\(58\) −102737. 208277.i −0.526555 1.06747i
\(59\) 59057.3i 0.287553i −0.989610 0.143776i \(-0.954075\pi\)
0.989610 0.143776i \(-0.0459246\pi\)
\(60\) 44252.9 + 33942.3i 0.204875 + 0.157140i
\(61\) 116330. 0.512508 0.256254 0.966609i \(-0.417512\pi\)
0.256254 + 0.966609i \(0.417512\pi\)
\(62\) −68596.4 + 33836.6i −0.287823 + 0.141975i
\(63\) 24288.4i 0.0971353i
\(64\) 242250. + 100171.i 0.924112 + 0.382122i
\(65\) 202324. 0.736728
\(66\) −132363. 268338.i −0.460401 0.933362i
\(67\) 134450.i 0.447029i 0.974701 + 0.223514i \(0.0717529\pi\)
−0.974701 + 0.223514i \(0.928247\pi\)
\(68\) 36123.5 47096.8i 0.114885 0.149784i
\(69\) −190515. −0.579938
\(70\) 40088.2 19774.4i 0.116875 0.0576512i
\(71\) 468387.i 1.30867i 0.756206 + 0.654334i \(0.227051\pi\)
−0.756206 + 0.654334i \(0.772949\pi\)
\(72\) −122033. 24235.3i −0.326948 0.0649308i
\(73\) 79504.8 0.204373 0.102187 0.994765i \(-0.467416\pi\)
0.102187 + 0.994765i \(0.467416\pi\)
\(74\) −313716. 635990.i −0.774178 1.56948i
\(75\) 48713.9i 0.115470i
\(76\) 39279.7 + 30127.7i 0.0894802 + 0.0686318i
\(77\) −239813. −0.525291
\(78\) −404785. + 199669.i −0.852984 + 0.420752i
\(79\) 670660.i 1.36026i −0.733093 0.680129i \(-0.761924\pi\)
0.733093 0.680129i \(-0.238076\pi\)
\(80\) −59352.2 221147.i −0.115922 0.431928i
\(81\) 59049.0 0.111111
\(82\) 190272. + 385734.i 0.345090 + 0.699595i
\(83\) 549656.i 0.961296i −0.876914 0.480648i \(-0.840402\pi\)
0.876914 0.480648i \(-0.159598\pi\)
\(84\) −60688.7 + 79124.2i −0.102393 + 0.133497i
\(85\) −51844.5 −0.0844201
\(86\) 1.00694e6 496695.i 1.58310 0.780899i
\(87\) 452528.i 0.687207i
\(88\) −239288. + 1.20490e6i −0.351135 + 1.76808i
\(89\) 785334. 1.11400 0.556999 0.830513i \(-0.311953\pi\)
0.556999 + 0.830513i \(0.311953\pi\)
\(90\) 48074.7 + 97460.9i 0.0659460 + 0.133691i
\(91\) 361755.i 0.480054i
\(92\) 620640. + 476034.i 0.797033 + 0.611329i
\(93\) −149041. −0.185292
\(94\) 757314. 373561.i 0.911785 0.449757i
\(95\) 43239.3i 0.0504322i
\(96\) 336990. + 383871.i 0.380893 + 0.433882i
\(97\) 664400. 0.727972 0.363986 0.931404i \(-0.381416\pi\)
0.363986 + 0.931404i \(0.381416\pi\)
\(98\) −381007. 772410.i −0.404814 0.820672i
\(99\) 583023.i 0.600870i
\(100\) −121720. + 158695.i −0.121720 + 0.158695i
\(101\) −1.49801e6 −1.45396 −0.726978 0.686661i \(-0.759076\pi\)
−0.726978 + 0.686661i \(0.759076\pi\)
\(102\) 103724. 51164.1i 0.0977416 0.0482131i
\(103\) 799842.i 0.731968i 0.930621 + 0.365984i \(0.119268\pi\)
−0.930621 + 0.365984i \(0.880732\pi\)
\(104\) 1.81758e6 + 360965.i 1.61582 + 0.320896i
\(105\) 87100.5 0.0752406
\(106\) 286541. + 580899.i 0.240585 + 0.487734i
\(107\) 349292.i 0.285126i 0.989786 + 0.142563i \(0.0455344\pi\)
−0.989786 + 0.142563i \(0.954466\pi\)
\(108\) −192364. 147544.i −0.152705 0.117125i
\(109\) 680148. 0.525199 0.262599 0.964905i \(-0.415420\pi\)
0.262599 + 0.964905i \(0.415420\pi\)
\(110\) 962285. 474668.i 0.722979 0.356625i
\(111\) 1.38183e6i 1.01038i
\(112\) 395411. 106122.i 0.281446 0.0755353i
\(113\) −1.68229e6 −1.16591 −0.582955 0.812505i \(-0.698104\pi\)
−0.582955 + 0.812505i \(0.698104\pi\)
\(114\) 42671.9 + 86507.9i 0.0288023 + 0.0583904i
\(115\) 683205.i 0.449218i
\(116\) −1.13072e6 + 1.47420e6i −0.724404 + 0.944458i
\(117\) −879485. −0.549125
\(118\) −423714. + 209006.i −0.257886 + 0.127208i
\(119\) 92697.9i 0.0550084i
\(120\) 86910.1 437621.i 0.0502952 0.253253i
\(121\) −3.98495e6 −2.24940
\(122\) −411695. 834621.i −0.226723 0.459632i
\(123\) 838093.i 0.450378i
\(124\) 485530. + 372404.i 0.254654 + 0.195321i
\(125\) 174693. 0.0894427
\(126\) −174260. + 85957.4i −0.0871136 + 0.0429706i
\(127\) 2.92911e6i 1.42996i −0.699145 0.714980i \(-0.746436\pi\)
0.699145 0.714980i \(-0.253564\pi\)
\(128\) −138643. 2.09256e6i −0.0661101 0.997812i
\(129\) 2.18780e6 1.01915
\(130\) −716032. 1.45160e6i −0.325913 0.660718i
\(131\) 1.57652e6i 0.701272i 0.936512 + 0.350636i \(0.114035\pi\)
−0.936512 + 0.350636i \(0.885965\pi\)
\(132\) −1.45678e6 + 1.89931e6i −0.633393 + 0.825800i
\(133\) 77311.8 0.0328618
\(134\) 964626. 475822.i 0.400908 0.197756i
\(135\) 211755.i 0.0860663i
\(136\) −465744. 92495.3i −0.185153 0.0367708i
\(137\) −3.34075e6 −1.29922 −0.649609 0.760269i \(-0.725067\pi\)
−0.649609 + 0.760269i \(0.725067\pi\)
\(138\) 674239. + 1.36687e6i 0.256553 + 0.520105i
\(139\) 857823.i 0.319413i −0.987165 0.159707i \(-0.948945\pi\)
0.987165 0.159707i \(-0.0510549\pi\)
\(140\) −283747. 217636.i −0.103406 0.0793132i
\(141\) 1.64543e6 0.586979
\(142\) 3.36050e6 1.65764e6i 1.17365 0.578928i
\(143\) 8.68364e6i 2.96957i
\(144\) 257999. + 961309.i 0.0864034 + 0.321940i
\(145\) 1.62281e6 0.532309
\(146\) −281370. 570417.i −0.0904106 0.183288i
\(147\) 1.67823e6i 0.528323i
\(148\) −3.45274e6 + 4.50158e6i −1.06507 + 1.38861i
\(149\) −4.93323e6 −1.49133 −0.745663 0.666323i \(-0.767867\pi\)
−0.745663 + 0.666323i \(0.767867\pi\)
\(150\) −349504. + 172400.i −0.103557 + 0.0510816i
\(151\) 2.17991e6i 0.633151i −0.948567 0.316575i \(-0.897467\pi\)
0.948567 0.316575i \(-0.102533\pi\)
\(152\) 77142.9 388440.i 0.0219667 0.110610i
\(153\) 225364. 0.0629230
\(154\) 848705. + 1.72056e6i 0.232378 + 0.471095i
\(155\) 534475.i 0.143526i
\(156\) 2.86510e6 + 2.19755e6i 0.754685 + 0.578847i
\(157\) −561357. −0.145058 −0.0725288 0.997366i \(-0.523107\pi\)
−0.0725288 + 0.997366i \(0.523107\pi\)
\(158\) −4.81173e6 + 2.37349e6i −1.21992 + 0.601750i
\(159\) 1.26213e6i 0.313988i
\(160\) −1.37660e6 + 1.20848e6i −0.336084 + 0.295039i
\(161\) 1.22157e6 0.292712
\(162\) −208977. 423654.i −0.0491533 0.0996476i
\(163\) 3.42959e6i 0.791915i −0.918269 0.395958i \(-0.870413\pi\)
0.918269 0.395958i \(-0.129587\pi\)
\(164\) 2.09412e6 2.73025e6i 0.474756 0.618973i
\(165\) 2.09078e6 0.465432
\(166\) −3.94358e6 + 1.94525e6i −0.862117 + 0.425257i
\(167\) 4.96116e6i 1.06521i 0.846365 + 0.532603i \(0.178786\pi\)
−0.846365 + 0.532603i \(0.821214\pi\)
\(168\) 782466. + 155395.i 0.165020 + 0.0327725i
\(169\) 8.27239e6 1.71384
\(170\) 183479. + 371965.i 0.0373457 + 0.0757103i
\(171\) 187958.i 0.0375899i
\(172\) −7.12720e6 5.46660e6i −1.40066 1.07432i
\(173\) 1.02232e7 1.97447 0.987235 0.159271i \(-0.0509144\pi\)
0.987235 + 0.159271i \(0.0509144\pi\)
\(174\) −3.24672e6 + 1.60151e6i −0.616307 + 0.304006i
\(175\) 312351.i 0.0582812i
\(176\) 9.49153e6 2.54737e6i 1.74100 0.467254i
\(177\) −920613. −0.166019
\(178\) −2.77932e6 5.63447e6i −0.492810 0.999064i
\(179\) 162204.i 0.0282815i 0.999900 + 0.0141407i \(0.00450128\pi\)
−0.999900 + 0.0141407i \(0.995499\pi\)
\(180\) 529107. 689835.i 0.0907249 0.118285i
\(181\) −6.54734e6 −1.10415 −0.552076 0.833794i \(-0.686164\pi\)
−0.552076 + 0.833794i \(0.686164\pi\)
\(182\) 2.59546e6 1.28026e6i 0.430526 0.212366i
\(183\) 1.81340e6i 0.295897i
\(184\) 1.21890e6 6.13756e6i 0.195666 0.985241i
\(185\) 4.95537e6 0.782638
\(186\) 527461. + 1.06931e6i 0.0819693 + 0.166175i
\(187\) 2.22514e6i 0.340277i
\(188\) −5.36032e6 4.11140e6i −0.806710 0.618751i
\(189\) −378618. −0.0560811
\(190\) −310226. + 153025.i −0.0452290 + 0.0223102i
\(191\) 3.54149e6i 0.508260i −0.967170 0.254130i \(-0.918211\pi\)
0.967170 0.254130i \(-0.0817891\pi\)
\(192\) 1.56151e6 3.77631e6i 0.220618 0.533536i
\(193\) 8.80294e6 1.22449 0.612246 0.790667i \(-0.290266\pi\)
0.612246 + 0.790667i \(0.290266\pi\)
\(194\) −2.35134e6 4.76682e6i −0.322040 0.652865i
\(195\) 3.15392e6i 0.425350i
\(196\) −4.19335e6 + 5.46717e6i −0.556920 + 0.726097i
\(197\) 3.09941e6 0.405397 0.202698 0.979241i \(-0.435029\pi\)
0.202698 + 0.979241i \(0.435029\pi\)
\(198\) −4.18297e6 + 2.06334e6i −0.538877 + 0.265812i
\(199\) 852821.i 0.108218i 0.998535 + 0.0541089i \(0.0172318\pi\)
−0.998535 + 0.0541089i \(0.982768\pi\)
\(200\) 1.56935e6 + 311668.i 0.196169 + 0.0389585i
\(201\) 2.09586e6 0.258092
\(202\) 5.30152e6 + 1.07477e7i 0.643200 + 1.30395i
\(203\) 2.90158e6i 0.346854i
\(204\) −734167. 563110.i −0.0864777 0.0663289i
\(205\) −3.00548e6 −0.348861
\(206\) 5.73856e6 2.83067e6i 0.656450 0.323808i
\(207\) 2.96983e6i 0.334827i
\(208\) −3.84268e6 1.43179e7i −0.427016 1.59107i
\(209\) 1.85581e6 0.203280
\(210\) −308252. 624913.i −0.0332849 0.0674779i
\(211\) 1.07917e7i 1.14880i −0.818576 0.574399i \(-0.805236\pi\)
0.818576 0.574399i \(-0.194764\pi\)
\(212\) 3.15366e6 4.11165e6i 0.330984 0.431527i
\(213\) 7.30142e6 0.755560
\(214\) 2.50604e6 1.23616e6i 0.255709 0.126134i
\(215\) 7.84567e6i 0.789432i
\(216\) −377791. + 1.90230e6i −0.0374878 + 0.188764i
\(217\) 955640. 0.0935223
\(218\) −2.40707e6 4.87980e6i −0.232337 0.471013i
\(219\) 1.23936e6i 0.117995i
\(220\) −6.81112e6 5.22417e6i −0.639662 0.490624i
\(221\) −3.35660e6 −0.310973
\(222\) −9.91411e6 + 4.89034e6i −0.906139 + 0.446972i
\(223\) 1.42777e7i 1.28749i 0.765240 + 0.643745i \(0.222620\pi\)
−0.765240 + 0.643745i \(0.777380\pi\)
\(224\) −2.16076e6 2.46136e6i −0.192248 0.218993i
\(225\) −759375. −0.0666667
\(226\) 5.95368e6 + 1.20698e7i 0.515774 + 1.04562i
\(227\) 1.14371e7i 0.977776i 0.872347 + 0.488888i \(0.162597\pi\)
−0.872347 + 0.488888i \(0.837403\pi\)
\(228\) 469644. 612309.i 0.0396246 0.0516614i
\(229\) −1.28721e7 −1.07187 −0.535936 0.844258i \(-0.680041\pi\)
−0.535936 + 0.844258i \(0.680041\pi\)
\(230\) −4.90174e6 + 2.41789e6i −0.402871 + 0.198725i
\(231\) 3.73831e6i 0.303277i
\(232\) 1.45785e7 + 2.89524e6i 1.16748 + 0.231857i
\(233\) −9.25991e6 −0.732047 −0.366023 0.930606i \(-0.619281\pi\)
−0.366023 + 0.930606i \(0.619281\pi\)
\(234\) 3.11253e6 + 6.30998e6i 0.242921 + 0.492470i
\(235\) 5.90068e6i 0.454672i
\(236\) 2.99908e6 + 2.30031e6i 0.228167 + 0.175005i
\(237\) −1.04546e7 −0.785345
\(238\) −665073. + 328061.i −0.0493331 + 0.0243346i
\(239\) 4.26361e6i 0.312308i −0.987733 0.156154i \(-0.950090\pi\)
0.987733 0.156154i \(-0.0499097\pi\)
\(240\) −3.44734e6 + 925209.i −0.249374 + 0.0669278i
\(241\) −1.13558e7 −0.811271 −0.405636 0.914035i \(-0.632950\pi\)
−0.405636 + 0.914035i \(0.632950\pi\)
\(242\) 1.41029e7 + 2.85905e7i 0.995088 + 2.01732i
\(243\) 920483.i 0.0641500i
\(244\) −4.53109e6 + 5.90751e6i −0.311913 + 0.406663i
\(245\) 6.01830e6 0.409237
\(246\) 6.01300e6 2.96604e6i 0.403911 0.199238i
\(247\) 2.79947e6i 0.185774i
\(248\) 953552. 4.80145e6i 0.0625157 0.314787i
\(249\) −8.56829e6 −0.555004
\(250\) −618244. 1.25336e6i −0.0395676 0.0802147i
\(251\) 2.40153e7i 1.51868i −0.650692 0.759342i \(-0.725521\pi\)
0.650692 0.759342i \(-0.274479\pi\)
\(252\) 1.23342e6 + 946043.i 0.0770746 + 0.0591166i
\(253\) 2.93228e7 1.81069
\(254\) −2.10152e7 + 1.03662e7i −1.28243 + 0.632585i
\(255\) 808176.i 0.0487400i
\(256\) −1.45227e7 + 8.40037e6i −0.865620 + 0.500701i
\(257\) −7.77314e6 −0.457928 −0.228964 0.973435i \(-0.573534\pi\)
−0.228964 + 0.973435i \(0.573534\pi\)
\(258\) −7.74271e6 1.56967e7i −0.450852 0.914004i
\(259\) 8.86020e6i 0.509970i
\(260\) −7.88061e6 + 1.02745e7i −0.448373 + 0.584576i
\(261\) −7.05421e6 −0.396759
\(262\) 1.13110e7 5.57938e6i 0.628921 0.310229i
\(263\) 2.33758e7i 1.28499i −0.766292 0.642493i \(-0.777900\pi\)
0.766292 0.642493i \(-0.222100\pi\)
\(264\) 1.87825e7 + 3.73014e6i 1.02080 + 0.202728i
\(265\) −4.52613e6 −0.243214
\(266\) −273609. 554683.i −0.0145374 0.0294714i
\(267\) 1.22421e7i 0.643167i
\(268\) −6.82769e6 5.23687e6i −0.354707 0.272062i
\(269\) −2.52755e7 −1.29850 −0.649252 0.760573i \(-0.724918\pi\)
−0.649252 + 0.760573i \(0.724918\pi\)
\(270\) 1.51927e6 749410.i 0.0771867 0.0380740i
\(271\) 1.98065e7i 0.995175i 0.867414 + 0.497588i \(0.165781\pi\)
−0.867414 + 0.497588i \(0.834219\pi\)
\(272\) 984667. + 3.66889e6i 0.0489308 + 0.182317i
\(273\) 5.63920e6 0.277159
\(274\) 1.18230e7 + 2.39686e7i 0.574747 + 1.16517i
\(275\) 7.49773e6i 0.360522i
\(276\) 7.42064e6 9.67482e6i 0.352951 0.460167i
\(277\) −1.96620e6 −0.0925101 −0.0462551 0.998930i \(-0.514729\pi\)
−0.0462551 + 0.998930i \(0.514729\pi\)
\(278\) −6.15456e6 + 3.03587e6i −0.286459 + 0.141302i
\(279\) 2.32332e6i 0.106978i
\(280\) −557262. + 2.80600e6i −0.0253855 + 0.127824i
\(281\) −3.71366e7 −1.67372 −0.836862 0.547414i \(-0.815612\pi\)
−0.836862 + 0.547414i \(0.815612\pi\)
\(282\) −5.82325e6 1.18054e7i −0.259668 0.526419i
\(283\) 1.30641e7i 0.576395i −0.957571 0.288197i \(-0.906944\pi\)
0.957571 0.288197i \(-0.0930559\pi\)
\(284\) −2.37858e7 1.82439e7i −1.03840 0.796456i
\(285\) −674034. −0.0291170
\(286\) 6.23019e7 3.07317e7i 2.66319 1.31368i
\(287\) 5.37380e6i 0.227319i
\(288\) 5.98396e6 5.25315e6i 0.250502 0.219909i
\(289\) −2.32775e7 −0.964366
\(290\) −5.74318e6 1.16430e7i −0.235482 0.477389i
\(291\) 1.03570e7i 0.420295i
\(292\) −3.09675e6 + 4.03745e6i −0.124382 + 0.162166i
\(293\) 2.99876e7 1.19217 0.596085 0.802921i \(-0.296722\pi\)
0.596085 + 0.802921i \(0.296722\pi\)
\(294\) −1.20407e7 + 5.93932e6i −0.473815 + 0.233719i
\(295\) 3.30141e6i 0.128598i
\(296\) 4.45165e7 + 8.84084e6i 1.71651 + 0.340893i
\(297\) −9.08843e6 −0.346912
\(298\) 1.74589e7 + 3.53941e7i 0.659732 + 1.33746i
\(299\) 4.42332e7i 1.65476i
\(300\) 2.47382e6 + 1.89743e6i 0.0916228 + 0.0702752i
\(301\) −1.40281e7 −0.514396
\(302\) −1.56400e7 + 7.71477e6i −0.567827 + 0.280093i
\(303\) 2.33517e7i 0.839442i
\(304\) −3.05992e6 + 821231.i −0.108915 + 0.0292311i
\(305\) 6.50302e6 0.229201
\(306\) −797570. 1.61690e6i −0.0278359 0.0564311i
\(307\) 2.02161e7i 0.698688i −0.936995 0.349344i \(-0.886404\pi\)
0.936995 0.349344i \(-0.113596\pi\)
\(308\) 9.34081e6 1.21783e7i 0.319692 0.416806i
\(309\) 1.24683e7 0.422602
\(310\) −3.83465e6 + 1.89152e6i −0.128719 + 0.0634932i
\(311\) 2.22851e6i 0.0740856i 0.999314 + 0.0370428i \(0.0117938\pi\)
−0.999314 + 0.0370428i \(0.988206\pi\)
\(312\) 5.62688e6 2.83332e7i 0.185269 0.932893i
\(313\) 5.08300e7 1.65763 0.828814 0.559525i \(-0.189016\pi\)
0.828814 + 0.559525i \(0.189016\pi\)
\(314\) 1.98666e6 + 4.02753e6i 0.0641705 + 0.130092i
\(315\) 1.35776e6i 0.0434402i
\(316\) 3.40578e7 + 2.61225e7i 1.07933 + 0.827854i
\(317\) 2.26114e7 0.709821 0.354911 0.934900i \(-0.384511\pi\)
0.354911 + 0.934900i \(0.384511\pi\)
\(318\) 9.05533e6 4.46673e6i 0.281594 0.138902i
\(319\) 6.96501e7i 2.14561i
\(320\) 1.35422e7 + 5.59973e6i 0.413275 + 0.170890i
\(321\) 5.44492e6 0.164618
\(322\) −4.32318e6 8.76430e6i −0.129490 0.262512i
\(323\) 717350.i 0.0212874i
\(324\) −2.29999e6 + 2.99866e6i −0.0676223 + 0.0881641i
\(325\) 1.13103e7 0.329475
\(326\) −2.46060e7 + 1.21374e7i −0.710212 + 0.350327i
\(327\) 1.06025e7i 0.303224i
\(328\) −2.69997e7 5.36206e6i −0.765134 0.151953i
\(329\) −1.05504e7 −0.296266
\(330\) −7.39933e6 1.50005e7i −0.205897 0.417412i
\(331\) 2.54747e7i 0.702467i −0.936288 0.351233i \(-0.885762\pi\)
0.936288 0.351233i \(-0.114238\pi\)
\(332\) 2.79129e7 + 2.14094e7i 0.762766 + 0.585045i
\(333\) −2.15406e7 −0.583344
\(334\) 3.55945e7 1.75577e7i 0.955307 0.471225i
\(335\) 7.51596e6i 0.199917i
\(336\) −1.65427e6 6.16385e6i −0.0436103 0.162493i
\(337\) −6.19868e7 −1.61961 −0.809803 0.586702i \(-0.800426\pi\)
−0.809803 + 0.586702i \(0.800426\pi\)
\(338\) −2.92763e7 5.93513e7i −0.758168 1.53702i
\(339\) 2.62243e7i 0.673138i
\(340\) 2.01937e6 2.63279e6i 0.0513781 0.0669854i
\(341\) 2.29394e7 0.578520
\(342\) 1.34852e6 665189.i 0.0337117 0.0166290i
\(343\) 2.25200e7i 0.558066i
\(344\) −1.39974e7 + 7.04815e7i −0.343852 + 1.73141i
\(345\) −1.06501e7 −0.259356
\(346\) −3.61804e7 7.33479e7i −0.873465 1.77076i
\(347\) 5.60089e7i 1.34051i −0.742133 0.670253i \(-0.766186\pi\)
0.742133 0.670253i \(-0.233814\pi\)
\(348\) 2.29805e7 + 1.76262e7i 0.545283 + 0.418235i
\(349\) 4.87021e7 1.14570 0.572850 0.819660i \(-0.305838\pi\)
0.572850 + 0.819660i \(0.305838\pi\)
\(350\) 2.24100e6 1.10542e6i 0.0522682 0.0257824i
\(351\) 1.37098e7i 0.317037i
\(352\) −5.18673e7 5.90829e7i −1.18923 1.35467i
\(353\) 4.35162e7 0.989297 0.494649 0.869093i \(-0.335297\pi\)
0.494649 + 0.869093i \(0.335297\pi\)
\(354\) 3.25808e6 + 6.60505e6i 0.0734433 + 0.148890i
\(355\) 2.61836e7i 0.585254i
\(356\) −3.05891e7 + 3.98812e7i −0.677980 + 0.883931i
\(357\) −1.44502e6 −0.0317591
\(358\) 1.16375e6 574045.i 0.0253636 0.0125111i
\(359\) 1.34201e7i 0.290049i −0.989428 0.145025i \(-0.953674\pi\)
0.989428 0.145025i \(-0.0463261\pi\)
\(360\) −6.82184e6 1.35479e6i −0.146216 0.0290380i
\(361\) 4.64476e7 0.987283
\(362\) 2.31713e7 + 4.69747e7i 0.488454 + 0.990235i
\(363\) 6.21192e7i 1.29869i
\(364\) −1.83708e7 1.40905e7i −0.380912 0.292161i
\(365\) 4.44445e6 0.0913986
\(366\) −1.30105e7 + 6.41768e6i −0.265368 + 0.130899i
\(367\) 2.34709e7i 0.474823i −0.971409 0.237411i \(-0.923701\pi\)
0.971409 0.237411i \(-0.0762989\pi\)
\(368\) −4.83484e7 + 1.29759e7i −0.970150 + 0.260372i
\(369\) 1.30646e7 0.260026
\(370\) −1.75372e7 3.55529e7i −0.346223 0.701892i
\(371\) 8.09271e6i 0.158479i
\(372\) 5.80521e6 7.56867e6i 0.112769 0.147025i
\(373\) −5.34360e7 −1.02969 −0.514847 0.857282i \(-0.672151\pi\)
−0.514847 + 0.857282i \(0.672151\pi\)
\(374\) −1.59645e7 + 7.87485e6i −0.305170 + 0.150531i
\(375\) 2.72319e6i 0.0516398i
\(376\) −1.05274e7 + 5.30087e7i −0.198041 + 0.997203i
\(377\) 1.05067e8 1.96083
\(378\) 1.33994e6 + 2.71644e6i 0.0248091 + 0.0502951i
\(379\) 2.02671e7i 0.372285i 0.982523 + 0.186142i \(0.0595985\pi\)
−0.982523 + 0.186142i \(0.940401\pi\)
\(380\) 2.19580e6 + 1.68419e6i 0.0400168 + 0.0306931i
\(381\) −4.56602e7 −0.825588
\(382\) −2.54089e7 + 1.25335e7i −0.455822 + 0.224844i
\(383\) 5.58252e6i 0.0993651i −0.998765 0.0496826i \(-0.984179\pi\)
0.998765 0.0496826i \(-0.0158210\pi\)
\(384\) −3.26198e7 + 2.16123e6i −0.576087 + 0.0381687i
\(385\) −1.34059e7 −0.234917
\(386\) −3.11539e7 6.31578e7i −0.541690 1.09816i
\(387\) 3.41045e7i 0.588408i
\(388\) −2.58787e7 + 3.37399e7i −0.443044 + 0.577629i
\(389\) −1.05876e7 −0.179865 −0.0899327 0.995948i \(-0.528665\pi\)
−0.0899327 + 0.995948i \(0.528665\pi\)
\(390\) −2.26282e7 + 1.11618e7i −0.381466 + 0.188166i
\(391\) 1.13345e7i 0.189615i
\(392\) 5.40653e7 + 1.07372e7i 0.897554 + 0.178251i
\(393\) 2.45756e7 0.404880
\(394\) −1.09689e7 2.22371e7i −0.179339 0.363571i
\(395\) 3.74910e7i 0.608326i
\(396\) 2.96074e7 + 2.27090e7i 0.476776 + 0.365690i
\(397\) −1.89692e7 −0.303164 −0.151582 0.988445i \(-0.548437\pi\)
−0.151582 + 0.988445i \(0.548437\pi\)
\(398\) 6.11867e6 3.01817e6i 0.0970528 0.0478734i
\(399\) 1.20517e6i 0.0189728i
\(400\) −3.31789e6 1.23625e7i −0.0518420 0.193164i
\(401\) 9.20319e6 0.142727 0.0713634 0.997450i \(-0.477265\pi\)
0.0713634 + 0.997450i \(0.477265\pi\)
\(402\) −7.41733e6 1.50370e7i −0.114175 0.231464i
\(403\) 3.46038e7i 0.528700i
\(404\) 5.83482e7 7.60728e7i 0.884879 1.15368i
\(405\) 3.30094e6 0.0496904
\(406\) 2.08178e7 1.02688e7i 0.311068 0.153441i
\(407\) 2.12682e8i 3.15462i
\(408\) −1.44186e6 + 7.26024e6i −0.0212296 + 0.106898i
\(409\) −6.63022e7 −0.969076 −0.484538 0.874770i \(-0.661012\pi\)
−0.484538 + 0.874770i \(0.661012\pi\)
\(410\) 1.06365e7 + 2.15632e7i 0.154329 + 0.312868i
\(411\) 5.20771e7i 0.750103i
\(412\) −4.06180e7 3.11542e7i −0.580800 0.445477i
\(413\) 5.90291e6 0.0837946
\(414\) 2.13074e7 1.05103e7i 0.300283 0.148121i
\(415\) 3.07267e7i 0.429904i
\(416\) −8.91261e7 + 7.82413e7i −1.23801 + 1.08682i
\(417\) −1.33721e7 −0.184413
\(418\) −6.56777e6 1.33147e7i −0.0899268 0.182307i
\(419\) 1.06809e8i 1.45200i −0.687696 0.725999i \(-0.741378\pi\)
0.687696 0.725999i \(-0.258622\pi\)
\(420\) −3.39260e6 + 4.42318e6i −0.0457915 + 0.0597017i
\(421\) −3.11843e7 −0.417916 −0.208958 0.977925i \(-0.567007\pi\)
−0.208958 + 0.977925i \(0.567007\pi\)
\(422\) −7.74266e7 + 3.81923e7i −1.03027 + 0.508204i
\(423\) 2.56498e7i 0.338893i
\(424\) −4.06604e7 8.07503e6i −0.533426 0.105937i
\(425\) −2.89820e6 −0.0377538
\(426\) −2.58400e7 5.23850e7i −0.334244 0.677607i
\(427\) 1.16274e7i 0.149348i
\(428\) −1.77379e7 1.36051e7i −0.226241 0.173528i
\(429\) 1.35365e8 1.71448
\(430\) 5.62897e7 2.77661e7i 0.707985 0.349228i
\(431\) 9.72310e7i 1.21443i 0.794537 + 0.607215i \(0.207714\pi\)
−0.794537 + 0.607215i \(0.792286\pi\)
\(432\) 1.49853e7 4.02181e6i 0.185872 0.0498850i
\(433\) −6.52726e7 −0.804021 −0.402010 0.915635i \(-0.631688\pi\)
−0.402010 + 0.915635i \(0.631688\pi\)
\(434\) −3.38204e6 6.85636e6i −0.0413723 0.0838734i
\(435\) 2.52971e7i 0.307328i
\(436\) −2.64921e7 + 3.45396e7i −0.319636 + 0.416733i
\(437\) −9.45321e6 −0.113275
\(438\) −8.89192e6 + 4.38613e6i −0.105821 + 0.0521986i
\(439\) 8.96022e7i 1.05907i 0.848288 + 0.529536i \(0.177634\pi\)
−0.848288 + 0.529536i \(0.822366\pi\)
\(440\) −1.33766e7 + 6.73558e7i −0.157032 + 0.790709i
\(441\) −2.61610e7 −0.305028
\(442\) 1.18791e7 + 2.40824e7i 0.137568 + 0.278890i
\(443\) 5.37278e7i 0.617999i −0.951062 0.309000i \(-0.900006\pi\)
0.951062 0.309000i \(-0.0999942\pi\)
\(444\) 7.01728e7 + 5.38229e7i 0.801714 + 0.614919i
\(445\) 4.39015e7 0.498195
\(446\) 1.02437e8 5.05293e7i 1.15466 0.569560i
\(447\) 7.69015e7i 0.861018i
\(448\) −1.00123e7 + 2.42135e7i −0.111353 + 0.269292i
\(449\) 1.07640e8 1.18914 0.594571 0.804043i \(-0.297322\pi\)
0.594571 + 0.804043i \(0.297322\pi\)
\(450\) 2.68746e6 + 5.44823e6i 0.0294920 + 0.0597885i
\(451\) 1.28994e8i 1.40617i
\(452\) 6.55259e7 8.54308e7i 0.709573 0.925122i
\(453\) −3.39814e7 −0.365550
\(454\) 8.20571e7 4.04764e7i 0.876897 0.432548i
\(455\) 2.02227e7i 0.214687i
\(456\) −6.05518e6 1.20254e6i −0.0638605 0.0126825i
\(457\) 5.35694e7 0.561266 0.280633 0.959815i \(-0.409456\pi\)
0.280633 + 0.959815i \(0.409456\pi\)
\(458\) 4.55548e7 + 9.23525e7i 0.474174 + 0.961285i
\(459\) 3.51307e6i 0.0363286i
\(460\) 3.46948e7 + 2.66111e7i 0.356444 + 0.273395i
\(461\) −5.79532e7 −0.591528 −0.295764 0.955261i \(-0.595574\pi\)
−0.295764 + 0.955261i \(0.595574\pi\)
\(462\) 2.68209e7 1.32300e7i 0.271987 0.134163i
\(463\) 5.12513e6i 0.0516371i 0.999667 + 0.0258185i \(0.00821921\pi\)
−0.999667 + 0.0258185i \(0.991781\pi\)
\(464\) −3.08215e7 1.14842e8i −0.308532 1.14960i
\(465\) −8.33164e6 −0.0828651
\(466\) 3.27711e7 + 6.64364e7i 0.323843 + 0.656520i
\(467\) 2.52747e7i 0.248162i 0.992272 + 0.124081i \(0.0395983\pi\)
−0.992272 + 0.124081i \(0.960402\pi\)
\(468\) 3.42563e7 4.46625e7i 0.334198 0.435718i
\(469\) −1.34385e7 −0.130267
\(470\) 4.23352e7 2.08827e7i 0.407763 0.201138i
\(471\) 8.75069e6i 0.0837490i
\(472\) 5.89001e6 2.96581e7i 0.0560132 0.282045i
\(473\) −3.36732e8 −3.18201
\(474\) 3.69991e7 + 7.50075e7i 0.347421 + 0.704320i
\(475\) 2.41715e6i 0.0225540i
\(476\) 4.70743e6 + 3.61062e6i 0.0436479 + 0.0334782i
\(477\) 1.96747e7 0.181281
\(478\) −3.05898e7 + 1.50891e7i −0.280087 + 0.138159i
\(479\) 1.83052e8i 1.66559i −0.553583 0.832794i \(-0.686740\pi\)
0.553583 0.832794i \(-0.313260\pi\)
\(480\) 1.88383e7 + 2.14591e7i 0.170341 + 0.194038i
\(481\) 3.20829e8 2.88296
\(482\) 4.01885e7 + 8.14735e7i 0.358890 + 0.727571i
\(483\) 1.90424e7i 0.168997i
\(484\) 1.55216e8 2.02366e8i 1.36899 1.78485i
\(485\) 3.71411e7 0.325559
\(486\) −6.60412e6 + 3.25762e6i −0.0575315 + 0.0283787i
\(487\) 7.19456e7i 0.622899i −0.950263 0.311449i \(-0.899186\pi\)
0.950263 0.311449i \(-0.100814\pi\)
\(488\) 5.84198e7 + 1.16020e7i 0.502691 + 0.0998327i
\(489\) −5.34619e7 −0.457213
\(490\) −2.12990e7 4.31790e7i −0.181038 0.367016i
\(491\) 5.86205e7i 0.495227i −0.968859 0.247614i \(-0.920354\pi\)
0.968859 0.247614i \(-0.0796464\pi\)
\(492\) −4.25605e7 3.26441e7i −0.357364 0.274100i
\(493\) −2.69228e7 −0.224688
\(494\) −2.00851e7 + 9.90743e6i −0.166607 + 0.0821826i
\(495\) 3.25920e7i 0.268717i
\(496\) −3.78232e7 + 1.01511e7i −0.309966 + 0.0831896i
\(497\) −4.68163e7 −0.381353
\(498\) 3.03235e7 + 6.14743e7i 0.245522 + 0.497743i
\(499\) 2.37768e8i 1.91360i −0.290743 0.956801i \(-0.593902\pi\)
0.290743 0.956801i \(-0.406098\pi\)
\(500\) −6.80436e6 + 8.87134e6i −0.0544349 + 0.0709707i
\(501\) 7.73368e7 0.614997
\(502\) −1.72301e8 + 8.49911e7i −1.36200 + 0.671834i
\(503\) 2.08303e8i 1.63678i 0.574660 + 0.818392i \(0.305134\pi\)
−0.574660 + 0.818392i \(0.694866\pi\)
\(504\) 2.42237e6 1.21974e7i 0.0189212 0.0952746i
\(505\) −8.37414e7 −0.650229
\(506\) −1.03774e8 2.10380e8i −0.801012 1.62388i
\(507\) 1.28954e8i 0.989487i
\(508\) 1.48747e8 + 1.14090e8i 1.13464 + 0.870275i
\(509\) −6.06760e7 −0.460112 −0.230056 0.973177i \(-0.573891\pi\)
−0.230056 + 0.973177i \(0.573891\pi\)
\(510\) 5.79836e6 2.86016e6i 0.0437114 0.0215616i
\(511\) 7.94667e6i 0.0595556i
\(512\) 1.11666e8 + 7.44657e7i 0.831975 + 0.554813i
\(513\) 2.92997e6 0.0217026
\(514\) 2.75094e7 + 5.57693e7i 0.202578 + 0.410682i
\(515\) 4.47125e7i 0.327346i
\(516\) −8.52159e7 + 1.11102e8i −0.620257 + 0.808673i
\(517\) −2.53254e8 −1.83267
\(518\) 6.35686e7 3.13566e7i 0.457355 0.225600i
\(519\) 1.59365e8i 1.13996i
\(520\) 1.01606e8 + 2.01785e7i 0.722616 + 0.143509i
\(521\) −4.23437e7 −0.299416 −0.149708 0.988730i \(-0.547833\pi\)
−0.149708 + 0.988730i \(0.547833\pi\)
\(522\) 2.49651e7 + 5.06113e7i 0.175518 + 0.355825i
\(523\) 2.64065e8i 1.84589i −0.384928 0.922947i \(-0.625774\pi\)
0.384928 0.922947i \(-0.374226\pi\)
\(524\) −8.00598e7 6.14063e7i −0.556443 0.426795i
\(525\) 4.86906e6 0.0336486
\(526\) −1.67712e8 + 8.27276e7i −1.15241 + 0.568451i
\(527\) 8.86706e6i 0.0605826i
\(528\) −3.97095e7 1.47958e8i −0.269769 1.00517i
\(529\) −1.33004e6 −0.00898459
\(530\) 1.60181e7 + 3.24733e7i 0.107593 + 0.218121i
\(531\) 1.43509e7i 0.0958510i
\(532\) −3.01133e6 + 3.92609e6i −0.0199997 + 0.0260750i
\(533\) −1.94586e8 −1.28508
\(534\) −8.78327e7 + 4.33254e7i −0.576810 + 0.284524i
\(535\) 1.95260e7i 0.127512i
\(536\) −1.34092e7 + 6.75196e7i −0.0870778 + 0.438465i
\(537\) 2.52851e6 0.0163283
\(538\) 8.94510e7 + 1.81342e8i 0.574432 + 1.16454i
\(539\) 2.58302e8i 1.64954i
\(540\) −1.07535e7 8.24797e6i −0.0682916 0.0523800i
\(541\) −4.99745e7 −0.315614 −0.157807 0.987470i \(-0.550442\pi\)
−0.157807 + 0.987470i \(0.550442\pi\)
\(542\) 1.42104e8 7.00958e7i 0.892501 0.440245i
\(543\) 1.02063e8i 0.637483i
\(544\) 2.28381e7 2.00489e7i 0.141861 0.124536i
\(545\) 3.80214e7 0.234876
\(546\) −1.99573e7 4.04592e7i −0.122610 0.248564i
\(547\) 2.70311e8i 1.65159i 0.563971 + 0.825795i \(0.309273\pi\)
−0.563971 + 0.825795i \(0.690727\pi\)
\(548\) 1.30124e8 1.69651e8i 0.790705 1.03090i
\(549\) −2.82681e7 −0.170836
\(550\) 5.37934e7 2.65347e7i 0.323326 0.159487i
\(551\) 2.24541e7i 0.134227i
\(552\) −9.56751e7 1.90008e7i −0.568829 0.112968i
\(553\) 6.70339e7 0.396387
\(554\) 6.95846e6 + 1.41068e7i 0.0409246 + 0.0829656i
\(555\) 7.72466e7i 0.451856i
\(556\) 4.35624e7 + 3.34126e7i 0.253447 + 0.194395i
\(557\) 1.75087e8 1.01319 0.506593 0.862185i \(-0.330905\pi\)
0.506593 + 0.862185i \(0.330905\pi\)
\(558\) 1.66689e7 8.22230e6i 0.0959412 0.0473250i
\(559\) 5.07957e8i 2.90798i
\(560\) 2.21042e7 5.93238e6i 0.125866 0.0337804i
\(561\) −3.46865e7 −0.196459
\(562\) 1.31428e8 + 2.66441e8i 0.740421 + 1.50104i
\(563\) 1.20097e7i 0.0672989i −0.999434 0.0336495i \(-0.989287\pi\)
0.999434 0.0336495i \(-0.0107130\pi\)
\(564\) −6.40904e7 + 8.35592e7i −0.357236 + 0.465754i
\(565\) −9.40427e7 −0.521411
\(566\) −9.37299e7 + 4.62343e7i −0.516927 + 0.254985i
\(567\) 5.90208e6i 0.0323784i
\(568\) −4.67140e7 + 2.35220e8i −0.254919 + 1.28360i
\(569\) 1.60968e8 0.873781 0.436891 0.899515i \(-0.356080\pi\)
0.436891 + 0.899515i \(0.356080\pi\)
\(570\) 2.38543e6 + 4.83594e6i 0.0128808 + 0.0261130i
\(571\) 3.01355e8i 1.61871i 0.587319 + 0.809356i \(0.300184\pi\)
−0.587319 + 0.809356i \(0.699816\pi\)
\(572\) −4.40977e8 3.38232e8i −2.35629 1.80728i
\(573\) −5.52064e7 −0.293444
\(574\) −3.85550e7 + 1.90181e7i −0.203866 + 0.100561i
\(575\) 3.81923e7i 0.200896i
\(576\) −5.88668e7 2.43416e7i −0.308037 0.127374i
\(577\) 3.49901e8 1.82145 0.910726 0.413012i \(-0.135523\pi\)
0.910726 + 0.413012i \(0.135523\pi\)
\(578\) 8.23798e7 + 1.67007e8i 0.426616 + 0.864871i
\(579\) 1.37224e8i 0.706961i
\(580\) −6.32091e7 + 8.24103e7i −0.323963 + 0.422374i
\(581\) 5.49393e7 0.280127
\(582\) −7.43074e7 + 3.66537e7i −0.376932 + 0.185930i
\(583\) 1.94259e8i 0.980338i
\(584\) 3.99267e7 + 7.92931e6i 0.200459 + 0.0398104i
\(585\) −4.91647e7 −0.245576
\(586\) −1.06127e8 2.15149e8i −0.527392 1.06917i
\(587\) 3.88340e7i 0.191998i 0.995381 + 0.0959992i \(0.0306046\pi\)
−0.995381 + 0.0959992i \(0.969395\pi\)
\(588\) 8.52248e7 + 6.53679e7i 0.419212 + 0.321538i
\(589\) −7.39530e6 −0.0361918
\(590\) −2.36863e7 + 1.16838e7i −0.115330 + 0.0568889i
\(591\) 4.83150e7i 0.234056i
\(592\) −9.41159e7 3.50677e8i −0.453626 1.69022i
\(593\) −1.76851e8 −0.848091 −0.424046 0.905641i \(-0.639390\pi\)
−0.424046 + 0.905641i \(0.639390\pi\)
\(594\) 3.21643e7 + 6.52061e7i 0.153467 + 0.311121i
\(595\) 5.18197e6i 0.0246005i
\(596\) 1.92152e8 2.50522e8i 0.907622 1.18333i
\(597\) 1.32942e7 0.0624796
\(598\) −3.17356e8 + 1.56543e8i −1.48403 + 0.732031i
\(599\) 1.77934e8i 0.827900i −0.910300 0.413950i \(-0.864149\pi\)
0.910300 0.413950i \(-0.135851\pi\)
\(600\) 4.85842e6 2.44638e7i 0.0224927 0.113258i
\(601\) −1.37416e8 −0.633016 −0.316508 0.948590i \(-0.602510\pi\)
−0.316508 + 0.948590i \(0.602510\pi\)
\(602\) 4.96458e7 + 1.00646e8i 0.227558 + 0.461325i
\(603\) 3.26713e7i 0.149010i
\(604\) 1.10701e8 + 8.49084e7i 0.502390 + 0.385336i
\(605\) −2.22765e8 −1.00596
\(606\) 1.67540e8 8.26425e7i 0.752835 0.371352i
\(607\) 3.25760e8i 1.45657i −0.685275 0.728284i \(-0.740318\pi\)
0.685275 0.728284i \(-0.259682\pi\)
\(608\) 1.67212e7 + 1.90474e7i 0.0743972 + 0.0847472i
\(609\) 4.52312e7 0.200256
\(610\) −2.30144e7 4.66567e7i −0.101394 0.205553i
\(611\) 3.82032e8i 1.67485i
\(612\) −8.77802e6 + 1.14445e7i −0.0382950 + 0.0499279i
\(613\) 1.79249e8 0.778173 0.389087 0.921201i \(-0.372791\pi\)
0.389087 + 0.921201i \(0.372791\pi\)
\(614\) −1.45043e8 + 7.15457e7i −0.626603 + 0.309085i
\(615\) 4.68508e7i 0.201415i
\(616\) −1.20432e8 2.39174e7i −0.515228 0.102323i
\(617\) −4.40621e7 −0.187590 −0.0937951 0.995592i \(-0.529900\pi\)
−0.0937951 + 0.995592i \(0.529900\pi\)
\(618\) −4.41257e7 8.94553e7i −0.186951 0.379001i
\(619\) 3.99677e8i 1.68515i 0.538582 + 0.842573i \(0.318960\pi\)
−0.538582 + 0.842573i \(0.681040\pi\)
\(620\) 2.71420e7 + 2.08180e7i 0.113885 + 0.0873503i
\(621\) 4.62951e7 0.193313
\(622\) 1.59887e7 7.88678e6i 0.0664420 0.0327739i
\(623\) 7.84958e7i 0.324625i
\(624\) −2.23194e8 + 5.99014e7i −0.918604 + 0.246538i
\(625\) 9.76562e6 0.0400000
\(626\) −1.79889e8 3.64686e8i −0.733300 1.48661i
\(627\) 2.89292e7i 0.117364i
\(628\) 2.18651e7 2.85071e7i 0.0882821 0.115100i
\(629\) −8.22108e7 −0.330352
\(630\) −9.74143e6 + 4.80517e6i −0.0389584 + 0.0192171i
\(631\) 1.34075e8i 0.533654i −0.963744 0.266827i \(-0.914025\pi\)
0.963744 0.266827i \(-0.0859753\pi\)
\(632\) 6.68875e7 3.36800e8i 0.264968 1.33420i
\(633\) −1.68226e8 −0.663258
\(634\) −8.00224e7 1.62228e8i −0.314010 0.636587i
\(635\) 1.63742e8i 0.639498i
\(636\) −6.40942e7 4.91606e7i −0.249142 0.191094i
\(637\) 3.89647e8 1.50748
\(638\) 4.99714e8 2.46494e8i 1.92424 0.949172i
\(639\) 1.13818e8i 0.436223i
\(640\) −7.75038e6 1.16978e8i −0.0295653 0.446235i
\(641\) 4.99004e8 1.89466 0.947328 0.320266i \(-0.103772\pi\)
0.947328 + 0.320266i \(0.103772\pi\)
\(642\) −1.92698e7 3.90653e7i −0.0728235 0.147634i
\(643\) 4.27044e8i 1.60635i −0.595745 0.803174i \(-0.703143\pi\)
0.595745 0.803174i \(-0.296857\pi\)
\(644\) −4.75807e7 + 6.20343e7i −0.178145 + 0.232260i
\(645\) 1.22302e8 0.455779
\(646\) 5.14672e6 2.53873e6i 0.0190912 0.00941713i
\(647\) 2.61812e7i 0.0966666i −0.998831 0.0483333i \(-0.984609\pi\)
0.998831 0.0483333i \(-0.0153910\pi\)
\(648\) 2.96540e7 + 5.88918e6i 0.108983 + 0.0216436i
\(649\) 1.41695e8 0.518346
\(650\) −4.00274e7 8.11468e7i −0.145753 0.295482i
\(651\) 1.48970e7i 0.0539951i
\(652\) 1.74163e8 + 1.33584e8i 0.628366 + 0.481960i
\(653\) 4.83197e8 1.73534 0.867671 0.497139i \(-0.165616\pi\)
0.867671 + 0.497139i \(0.165616\pi\)
\(654\) −7.60686e7 + 3.75225e7i −0.271939 + 0.134140i
\(655\) 8.81304e7i 0.313619i
\(656\) 5.70822e7 + 2.12689e8i 0.202204 + 0.753415i
\(657\) −1.93197e7 −0.0681245
\(658\) 3.73383e7 + 7.56952e7i 0.131062 + 0.265700i
\(659\) 2.51071e6i 0.00877283i −0.999990 0.00438642i \(-0.998604\pi\)
0.999990 0.00438642i \(-0.00139624\pi\)
\(660\) −8.14367e7 + 1.06175e8i −0.283262 + 0.369309i
\(661\) 4.38678e8 1.51894 0.759472 0.650540i \(-0.225458\pi\)
0.759472 + 0.650540i \(0.225458\pi\)
\(662\) −1.82772e8 + 9.01560e7i −0.629992 + 0.310757i
\(663\) 5.23243e7i 0.179540i
\(664\) 5.48193e7 2.76033e8i 0.187253 0.942881i
\(665\) 4.32186e6 0.0146962
\(666\) 7.62329e7 + 1.54546e8i 0.258059 + 0.523159i
\(667\) 3.54787e8i 1.19561i
\(668\) −2.51940e8 1.93239e8i −0.845216 0.648285i
\(669\) 2.22568e8 0.743333
\(670\) 5.39242e7 2.65993e7i 0.179291 0.0884393i
\(671\) 2.79106e8i 0.923852i
\(672\) −3.83688e7 + 3.36829e7i −0.126436 + 0.110994i
\(673\) −1.98183e8 −0.650160 −0.325080 0.945686i \(-0.605391\pi\)
−0.325080 + 0.945686i \(0.605391\pi\)
\(674\) 2.19373e8 + 4.44732e8i 0.716480 + 1.45251i
\(675\) 1.18375e7i 0.0384900i
\(676\) −3.22213e8 + 4.20092e8i −1.04305 + 1.35989i
\(677\) −1.73607e8 −0.559500 −0.279750 0.960073i \(-0.590252\pi\)
−0.279750 + 0.960073i \(0.590252\pi\)
\(678\) 1.88149e8 9.28086e7i 0.603689 0.297783i
\(679\) 6.64082e7i 0.212135i
\(680\) −2.60359e7 5.17065e6i −0.0828030 0.0164444i
\(681\) 1.78287e8 0.564519
\(682\) −8.11833e7 1.64581e8i −0.255925 0.518833i
\(683\) 1.59479e8i 0.500544i 0.968176 + 0.250272i \(0.0805200\pi\)
−0.968176 + 0.250272i \(0.919480\pi\)
\(684\) −9.54496e6 7.32103e6i −0.0298267 0.0228773i
\(685\) −1.86753e8 −0.581028
\(686\) 1.61572e8 7.96990e7i 0.500489 0.246877i
\(687\) 2.00656e8i 0.618846i
\(688\) 5.55216e8 1.49011e8i 1.70489 0.457564i
\(689\) −2.93038e8 −0.895914
\(690\) 3.76911e7 + 7.64105e7i 0.114734 + 0.232598i
\(691\) 3.01483e8i 0.913753i −0.889530 0.456877i \(-0.848968\pi\)
0.889530 0.456877i \(-0.151032\pi\)
\(692\) −3.98200e8 + 5.19162e8i −1.20166 + 1.56670i
\(693\) 5.82744e7 0.175097
\(694\) −4.01843e8 + 1.98218e8i −1.20220 + 0.593012i
\(695\) 4.79538e7i 0.142846i
\(696\) 4.51323e7 2.27256e8i 0.133863 0.674044i
\(697\) 4.98617e7 0.147254
\(698\) −1.72358e8 3.49419e8i −0.506834 1.02750i
\(699\) 1.44348e8i 0.422647i
\(700\) −1.58619e7 1.21662e7i −0.0462447 0.0354700i
\(701\) 1.33555e8 0.387710 0.193855 0.981030i \(-0.437901\pi\)
0.193855 + 0.981030i \(0.437901\pi\)
\(702\) 9.83628e7 4.85195e7i 0.284328 0.140251i
\(703\) 6.85654e7i 0.197351i
\(704\) −2.40338e8 + 5.81225e8i −0.688817 + 1.66581i
\(705\) 9.19825e7 0.262505
\(706\) −1.54005e8 3.12212e8i −0.437645 0.887229i
\(707\) 1.49730e8i 0.423691i
\(708\) 3.58583e7 4.67510e7i 0.101039 0.131732i
\(709\) −6.26975e8 −1.75919 −0.879593 0.475728i \(-0.842185\pi\)
−0.879593 + 0.475728i \(0.842185\pi\)
\(710\) 1.87858e8 9.26647e7i 0.524872 0.258904i
\(711\) 1.62970e8i 0.453419i
\(712\) 3.94389e8 + 7.83243e7i 1.09266 + 0.216998i
\(713\) −1.16850e8 −0.322373
\(714\) 5.11397e6 + 1.03675e7i 0.0140496 + 0.0284825i
\(715\) 4.85430e8i 1.32803i
\(716\) −8.23711e6 6.31791e6i −0.0224407 0.0172121i
\(717\) −6.64631e7 −0.180311
\(718\) −9.62840e7 + 4.74941e7i −0.260124 + 0.128312i
\(719\) 1.61719e8i 0.435084i 0.976051 + 0.217542i \(0.0698039\pi\)
−0.976051 + 0.217542i \(0.930196\pi\)
\(720\) 1.44226e7 + 5.37388e7i 0.0386408 + 0.143976i
\(721\) −7.99459e7 −0.213300
\(722\) −1.64380e8 3.33244e8i −0.436754 0.885423i
\(723\) 1.77019e8i 0.468388i
\(724\) 2.55022e8 3.32490e8i 0.671988 0.876119i
\(725\) 9.07178e7 0.238056
\(726\) 4.45682e8 2.19842e8i 1.16470 0.574514i
\(727\) 2.51088e8i 0.653466i 0.945117 + 0.326733i \(0.105948\pi\)
−0.945117 + 0.326733i \(0.894052\pi\)
\(728\) −3.60792e7 + 1.81671e8i −0.0935110 + 0.470859i
\(729\) −1.43489e7 −0.0370370
\(730\) −1.57291e7 3.18873e7i −0.0404329 0.0819688i
\(731\) 1.30162e8i 0.333220i
\(732\) 9.20889e7 + 7.06327e7i 0.234787 + 0.180083i
\(733\) 1.62811e8 0.413400 0.206700 0.978404i \(-0.433728\pi\)
0.206700 + 0.978404i \(0.433728\pi\)
\(734\) −1.68395e8 + 8.30643e7i −0.425834 + 0.210052i
\(735\) 9.38160e7i 0.236273i
\(736\) 2.64204e8 + 3.00960e8i 0.662683 + 0.754874i
\(737\) −3.22581e8 −0.805818
\(738\) −4.62360e7 9.37334e7i −0.115030 0.233198i
\(739\) 1.02236e8i 0.253320i 0.991946 + 0.126660i \(0.0404257\pi\)
−0.991946 + 0.126660i \(0.959574\pi\)
\(740\) −1.93014e8 + 2.51646e8i −0.476314 + 0.621005i
\(741\) −4.36394e7 −0.107257
\(742\) −5.80622e7 + 2.86404e7i −0.142129 + 0.0701080i
\(743\) 4.84447e8i 1.18108i −0.807008 0.590540i \(-0.798915\pi\)
0.807008 0.590540i \(-0.201085\pi\)
\(744\) −7.48472e7 1.48644e7i −0.181743 0.0360935i
\(745\) −2.75776e8 −0.666941
\(746\) 1.89112e8 + 3.83384e8i 0.455515 + 0.923458i
\(747\) 1.33566e8i 0.320432i
\(748\) 1.12998e8 + 8.66702e7i 0.270002 + 0.207093i
\(749\) −3.49125e7 −0.0830874
\(750\) −1.95379e7 + 9.63747e6i −0.0463120 + 0.0228444i
\(751\) 5.03888e8i 1.18964i −0.803860 0.594818i \(-0.797224\pi\)
0.803860 0.594818i \(-0.202776\pi\)
\(752\) 4.17574e8 1.12070e8i 0.981929 0.263533i
\(753\) −3.74362e8 −0.876812
\(754\) −3.71834e8 7.53813e8i −0.867432 1.75853i
\(755\) 1.21861e8i 0.283154i
\(756\) 1.47474e7 1.92272e7i 0.0341310 0.0444990i
\(757\) −1.36114e8 −0.313772 −0.156886 0.987617i \(-0.550145\pi\)
−0.156886 + 0.987617i \(0.550145\pi\)
\(758\) 1.45409e8 7.17262e7i 0.333875 0.164691i
\(759\) 4.57097e8i 1.04540i
\(760\) 4.31242e6 2.17144e7i 0.00982381 0.0494661i
\(761\) −6.36763e8 −1.44485 −0.722426 0.691448i \(-0.756973\pi\)
−0.722426 + 0.691448i \(0.756973\pi\)
\(762\) 1.61593e8 + 3.27595e8i 0.365223 + 0.740410i
\(763\) 6.79822e7i 0.153046i
\(764\) 1.79846e8 + 1.37943e8i 0.403292 + 0.309328i
\(765\) 1.25982e7 0.0281400
\(766\) −4.00525e7 + 1.97567e7i −0.0891134 + 0.0439571i
\(767\) 2.13745e8i 0.473707i
\(768\) 1.30949e8 + 2.26386e8i 0.289080 + 0.499766i
\(769\) −3.95443e8 −0.869570 −0.434785 0.900534i \(-0.643176\pi\)
−0.434785 + 0.900534i \(0.643176\pi\)
\(770\) 4.74441e7 + 9.61825e7i 0.103923 + 0.210680i
\(771\) 1.21171e8i 0.264385i
\(772\) −3.42879e8 + 4.47035e8i −0.745227 + 0.971606i
\(773\) 4.24812e8 0.919725