Properties

Label 177.7.c.a.58.4
Level $177$
Weight $7$
Character 177.58
Analytic conductor $40.720$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(40.7195728007\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.4
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.57

$q$-expansion

\(f(q)\) \(=\) \(q-14.6202i q^{2} -15.5885 q^{3} -149.749 q^{4} -98.4329 q^{5} +227.906i q^{6} -154.279 q^{7} +1253.67i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-14.6202i q^{2} -15.5885 q^{3} -149.749 q^{4} -98.4329 q^{5} +227.906i q^{6} -154.279 q^{7} +1253.67i q^{8} +243.000 q^{9} +1439.11i q^{10} +1555.09i q^{11} +2334.36 q^{12} -1347.92i q^{13} +2255.59i q^{14} +1534.42 q^{15} +8744.86 q^{16} +345.025 q^{17} -3552.70i q^{18} +647.386 q^{19} +14740.2 q^{20} +2404.97 q^{21} +22735.6 q^{22} +8417.87i q^{23} -19542.7i q^{24} -5935.96 q^{25} -19706.8 q^{26} -3788.00 q^{27} +23103.2 q^{28} +194.502 q^{29} -22433.4i q^{30} +2402.92i q^{31} -47616.7i q^{32} -24241.4i q^{33} -5044.31i q^{34} +15186.1 q^{35} -36389.0 q^{36} +25370.8i q^{37} -9464.88i q^{38} +21012.0i q^{39} -123402. i q^{40} -79708.2 q^{41} -35161.1i q^{42} -29935.6i q^{43} -232873. i q^{44} -23919.2 q^{45} +123071. q^{46} -160549. i q^{47} -136319. q^{48} -93847.0 q^{49} +86784.7i q^{50} -5378.40 q^{51} +201850. i q^{52} +96330.9 q^{53} +55381.1i q^{54} -153072. i q^{55} -193415. i q^{56} -10091.7 q^{57} -2843.65i q^{58} +(155306. - 134390. i) q^{59} -229778. q^{60} +127221. i q^{61} +35131.1 q^{62} -37489.8 q^{63} -136492. q^{64} +132680. i q^{65} -354413. q^{66} +401421. i q^{67} -51667.1 q^{68} -131222. i q^{69} -222024. i q^{70} -108092. q^{71} +304641. i q^{72} +420503. i q^{73} +370925. q^{74} +92532.4 q^{75} -96945.4 q^{76} -239917. i q^{77} +307199. q^{78} +163438. q^{79} -860783. q^{80} +59049.0 q^{81} +1.16535e6i q^{82} -710122. i q^{83} -360143. q^{84} -33961.8 q^{85} -437663. q^{86} -3031.98 q^{87} -1.94956e6 q^{88} -405485. i q^{89} +349703. i q^{90} +207956. i q^{91} -1.26057e6i q^{92} -37457.8i q^{93} -2.34725e6 q^{94} -63724.1 q^{95} +742270. i q^{96} -366961. i q^{97} +1.37206e6i q^{98} +377886. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 14.6202i 1.82752i −0.406254 0.913760i \(-0.633165\pi\)
0.406254 0.913760i \(-0.366835\pi\)
\(3\) −15.5885 −0.577350
\(4\) −149.749 −2.33983
\(5\) −98.4329 −0.787463 −0.393732 0.919225i \(-0.628816\pi\)
−0.393732 + 0.919225i \(0.628816\pi\)
\(6\) 227.906i 1.05512i
\(7\) −154.279 −0.449793 −0.224897 0.974383i \(-0.572204\pi\)
−0.224897 + 0.974383i \(0.572204\pi\)
\(8\) 1253.67i 2.44857i
\(9\) 243.000 0.333333
\(10\) 1439.11i 1.43911i
\(11\) 1555.09i 1.16836i 0.811625 + 0.584179i \(0.198583\pi\)
−0.811625 + 0.584179i \(0.801417\pi\)
\(12\) 2334.36 1.35090
\(13\) 1347.92i 0.613528i −0.951786 0.306764i \(-0.900754\pi\)
0.951786 0.306764i \(-0.0992462\pi\)
\(14\) 2255.59i 0.822006i
\(15\) 1534.42 0.454642
\(16\) 8744.86 2.13498
\(17\) 345.025 0.0702269 0.0351134 0.999383i \(-0.488821\pi\)
0.0351134 + 0.999383i \(0.488821\pi\)
\(18\) 3552.70i 0.609173i
\(19\) 647.386 0.0943848 0.0471924 0.998886i \(-0.484973\pi\)
0.0471924 + 0.998886i \(0.484973\pi\)
\(20\) 14740.2 1.84253
\(21\) 2404.97 0.259688
\(22\) 22735.6 2.13520
\(23\) 8417.87i 0.691861i 0.938260 + 0.345931i \(0.112437\pi\)
−0.938260 + 0.345931i \(0.887563\pi\)
\(24\) 19542.7i 1.41368i
\(25\) −5935.96 −0.379901
\(26\) −19706.8 −1.12123
\(27\) −3788.00 −0.192450
\(28\) 23103.2 1.05244
\(29\) 194.502 0.00797498 0.00398749 0.999992i \(-0.498731\pi\)
0.00398749 + 0.999992i \(0.498731\pi\)
\(30\) 22433.4i 0.830868i
\(31\) 2402.92i 0.0806592i 0.999186 + 0.0403296i \(0.0128408\pi\)
−0.999186 + 0.0403296i \(0.987159\pi\)
\(32\) 47616.7i 1.45315i
\(33\) 24241.4i 0.674552i
\(34\) 5044.31i 0.128341i
\(35\) 15186.1 0.354196
\(36\) −36389.0 −0.779944
\(37\) 25370.8i 0.500875i 0.968133 + 0.250437i \(0.0805744\pi\)
−0.968133 + 0.250437i \(0.919426\pi\)
\(38\) 9464.88i 0.172490i
\(39\) 21012.0i 0.354220i
\(40\) 123402.i 1.92816i
\(41\) −79708.2 −1.15652 −0.578258 0.815854i \(-0.696267\pi\)
−0.578258 + 0.815854i \(0.696267\pi\)
\(42\) 35161.1i 0.474586i
\(43\) 29935.6i 0.376515i −0.982120 0.188258i \(-0.939716\pi\)
0.982120 0.188258i \(-0.0602840\pi\)
\(44\) 232873.i 2.73376i
\(45\) −23919.2 −0.262488
\(46\) 123071. 1.26439
\(47\) 160549.i 1.54637i −0.634179 0.773186i \(-0.718662\pi\)
0.634179 0.773186i \(-0.281338\pi\)
\(48\) −136319. −1.23263
\(49\) −93847.0 −0.797686
\(50\) 86784.7i 0.694277i
\(51\) −5378.40 −0.0405455
\(52\) 201850.i 1.43555i
\(53\) 96330.9 0.647050 0.323525 0.946220i \(-0.395132\pi\)
0.323525 + 0.946220i \(0.395132\pi\)
\(54\) 55381.1i 0.351706i
\(55\) 153072.i 0.920040i
\(56\) 193415.i 1.10135i
\(57\) −10091.7 −0.0544931
\(58\) 2843.65i 0.0145744i
\(59\) 155306. 134390.i 0.756191 0.654351i
\(60\) −229778. −1.06379
\(61\) 127221.i 0.560494i 0.959928 + 0.280247i \(0.0904164\pi\)
−0.959928 + 0.280247i \(0.909584\pi\)
\(62\) 35131.1 0.147406
\(63\) −37489.8 −0.149931
\(64\) −136492. −0.520676
\(65\) 132680.i 0.483131i
\(66\) −354413. −1.23276
\(67\) 401421.i 1.33467i 0.744755 + 0.667337i \(0.232566\pi\)
−0.744755 + 0.667337i \(0.767434\pi\)
\(68\) −51667.1 −0.164319
\(69\) 131222.i 0.399446i
\(70\) 222024.i 0.647300i
\(71\) −108092. −0.302008 −0.151004 0.988533i \(-0.548251\pi\)
−0.151004 + 0.988533i \(0.548251\pi\)
\(72\) 304641.i 0.816189i
\(73\) 420503.i 1.08094i 0.841364 + 0.540469i \(0.181753\pi\)
−0.841364 + 0.540469i \(0.818247\pi\)
\(74\) 370925. 0.915359
\(75\) 92532.4 0.219336
\(76\) −96945.4 −0.220845
\(77\) 239917.i 0.525520i
\(78\) 307199. 0.647345
\(79\) 163438. 0.331492 0.165746 0.986168i \(-0.446997\pi\)
0.165746 + 0.986168i \(0.446997\pi\)
\(80\) −860783. −1.68122
\(81\) 59049.0 0.111111
\(82\) 1.16535e6i 2.11356i
\(83\) 710122.i 1.24194i −0.783836 0.620968i \(-0.786740\pi\)
0.783836 0.620968i \(-0.213260\pi\)
\(84\) −360143. −0.607626
\(85\) −33961.8 −0.0553011
\(86\) −437663. −0.688089
\(87\) −3031.98 −0.00460436
\(88\) −1.94956e6 −2.86080
\(89\) 405485.i 0.575181i −0.957753 0.287591i \(-0.907146\pi\)
0.957753 0.287591i \(-0.0928543\pi\)
\(90\) 349703.i 0.479702i
\(91\) 207956.i 0.275961i
\(92\) 1.26057e6i 1.61884i
\(93\) 37457.8i 0.0465686i
\(94\) −2.34725e6 −2.82603
\(95\) −63724.1 −0.0743246
\(96\) 742270.i 0.838974i
\(97\) 366961.i 0.402072i −0.979584 0.201036i \(-0.935569\pi\)
0.979584 0.201036i \(-0.0644309\pi\)
\(98\) 1.37206e6i 1.45779i
\(99\) 377886.i 0.389453i
\(100\) 888905. 0.888905
\(101\) 185867.i 0.180401i −0.995924 0.0902006i \(-0.971249\pi\)
0.995924 0.0902006i \(-0.0287508\pi\)
\(102\) 78633.1i 0.0740977i
\(103\) 1.31011e6i 1.19893i −0.800399 0.599467i \(-0.795379\pi\)
0.800399 0.599467i \(-0.204621\pi\)
\(104\) 1.68984e6 1.50226
\(105\) −236729. −0.204495
\(106\) 1.40837e6i 1.18250i
\(107\) 1.51953e6 1.24039 0.620195 0.784448i \(-0.287054\pi\)
0.620195 + 0.784448i \(0.287054\pi\)
\(108\) 567249. 0.450301
\(109\) 228264.i 0.176262i 0.996109 + 0.0881309i \(0.0280894\pi\)
−0.996109 + 0.0881309i \(0.971911\pi\)
\(110\) −2.23793e6 −1.68139
\(111\) 395492.i 0.289180i
\(112\) −1.34915e6 −0.960298
\(113\) 287034.i 0.198929i −0.995041 0.0994643i \(-0.968287\pi\)
0.995041 0.0994643i \(-0.0317129\pi\)
\(114\) 147543.i 0.0995873i
\(115\) 828596.i 0.544815i
\(116\) −29126.5 −0.0186601
\(117\) 327545.i 0.204509i
\(118\) −1.96480e6 2.27060e6i −1.19584 1.38195i
\(119\) −53230.1 −0.0315876
\(120\) 1.92365e6i 1.11322i
\(121\) −646729. −0.365062
\(122\) 1.86000e6 1.02431
\(123\) 1.24253e6 0.667714
\(124\) 359835.i 0.188729i
\(125\) 2.12231e6 1.08662
\(126\) 548107.i 0.274002i
\(127\) −447324. −0.218379 −0.109190 0.994021i \(-0.534826\pi\)
−0.109190 + 0.994021i \(0.534826\pi\)
\(128\) 1.05193e6i 0.501599i
\(129\) 466650.i 0.217381i
\(130\) 1.93980e6 0.882931
\(131\) 2.31531e6i 1.02990i −0.857220 0.514950i \(-0.827811\pi\)
0.857220 0.514950i \(-0.172189\pi\)
\(132\) 3.63013e6i 1.57834i
\(133\) −99878.0 −0.0424537
\(134\) 5.86884e6 2.43915
\(135\) 372863. 0.151547
\(136\) 432546.i 0.171955i
\(137\) 3.74495e6 1.45641 0.728207 0.685358i \(-0.240354\pi\)
0.728207 + 0.685358i \(0.240354\pi\)
\(138\) −1.91848e6 −0.729996
\(139\) 4.17555e6 1.55478 0.777391 0.629018i \(-0.216543\pi\)
0.777391 + 0.629018i \(0.216543\pi\)
\(140\) −2.27411e6 −0.828758
\(141\) 2.50271e6i 0.892798i
\(142\) 1.58032e6i 0.551926i
\(143\) 2.09613e6 0.716820
\(144\) 2.12500e6 0.711659
\(145\) −19145.4 −0.00628001
\(146\) 6.14782e6 1.97543
\(147\) 1.46293e6 0.460544
\(148\) 3.79926e6i 1.17196i
\(149\) 1.07748e6i 0.325725i −0.986649 0.162862i \(-0.947927\pi\)
0.986649 0.162862i \(-0.0520726\pi\)
\(150\) 1.35284e6i 0.400841i
\(151\) 1.49993e6i 0.435653i −0.975987 0.217827i \(-0.930103\pi\)
0.975987 0.217827i \(-0.0698967\pi\)
\(152\) 811606.i 0.231108i
\(153\) 83841.0 0.0234090
\(154\) −3.50763e6 −0.960398
\(155\) 236526.i 0.0635162i
\(156\) 3.14653e6i 0.828816i
\(157\) 974234.i 0.251747i −0.992046 0.125874i \(-0.959827\pi\)
0.992046 0.125874i \(-0.0401734\pi\)
\(158\) 2.38950e6i 0.605808i
\(159\) −1.50165e6 −0.373575
\(160\) 4.68705e6i 1.14430i
\(161\) 1.29870e6i 0.311194i
\(162\) 863306.i 0.203058i
\(163\) −4.02568e6 −0.929557 −0.464779 0.885427i \(-0.653866\pi\)
−0.464779 + 0.885427i \(0.653866\pi\)
\(164\) 1.19362e7 2.70605
\(165\) 2.38615e6i 0.531185i
\(166\) −1.03821e7 −2.26966
\(167\) −4.64702e6 −0.997758 −0.498879 0.866672i \(-0.666255\pi\)
−0.498879 + 0.866672i \(0.666255\pi\)
\(168\) 3.01503e6i 0.635864i
\(169\) 3.00992e6 0.623584
\(170\) 496527.i 0.101064i
\(171\) 157315. 0.0314616
\(172\) 4.48283e6i 0.880982i
\(173\) 3.95135e6i 0.763146i −0.924339 0.381573i \(-0.875383\pi\)
0.924339 0.381573i \(-0.124617\pi\)
\(174\) 44328.1i 0.00841456i
\(175\) 915794. 0.170877
\(176\) 1.35990e7i 2.49442i
\(177\) −2.42098e6 + 2.09493e6i −0.436587 + 0.377790i
\(178\) −5.92826e6 −1.05116
\(179\) 1.26718e6i 0.220943i −0.993879 0.110472i \(-0.964764\pi\)
0.993879 0.110472i \(-0.0352361\pi\)
\(180\) 3.58188e6 0.614177
\(181\) 295579. 0.0498469 0.0249235 0.999689i \(-0.492066\pi\)
0.0249235 + 0.999689i \(0.492066\pi\)
\(182\) 3.04035e6 0.504324
\(183\) 1.98319e6i 0.323601i
\(184\) −1.05532e7 −1.69407
\(185\) 2.49732e6i 0.394421i
\(186\) −547639. −0.0851051
\(187\) 536543.i 0.0820501i
\(188\) 2.40421e7i 3.61825i
\(189\) 584408. 0.0865627
\(190\) 931656.i 0.135830i
\(191\) 5.51720e6i 0.791806i 0.918292 + 0.395903i \(0.129568\pi\)
−0.918292 + 0.395903i \(0.870432\pi\)
\(192\) 2.12770e6 0.300612
\(193\) 1.00178e7 1.39347 0.696737 0.717326i \(-0.254634\pi\)
0.696737 + 0.717326i \(0.254634\pi\)
\(194\) −5.36502e6 −0.734796
\(195\) 2.06827e6i 0.278936i
\(196\) 1.40535e7 1.86645
\(197\) −7.50245e6 −0.981306 −0.490653 0.871355i \(-0.663242\pi\)
−0.490653 + 0.871355i \(0.663242\pi\)
\(198\) 5.52475e6 0.711733
\(199\) 2.22620e6 0.282492 0.141246 0.989975i \(-0.454889\pi\)
0.141246 + 0.989975i \(0.454889\pi\)
\(200\) 7.44171e6i 0.930214i
\(201\) 6.25753e6i 0.770575i
\(202\) −2.71741e6 −0.329687
\(203\) −30007.6 −0.00358709
\(204\) 805411. 0.0948696
\(205\) 7.84591e6 0.910714
\(206\) −1.91540e7 −2.19108
\(207\) 2.04554e6i 0.230620i
\(208\) 1.17874e7i 1.30987i
\(209\) 1.00674e6i 0.110275i
\(210\) 3.46101e6i 0.373719i
\(211\) 5.41139e6i 0.576052i 0.957623 + 0.288026i \(0.0929989\pi\)
−0.957623 + 0.288026i \(0.907001\pi\)
\(212\) −1.44255e7 −1.51399
\(213\) 1.68499e6 0.174364
\(214\) 2.22158e7i 2.26684i
\(215\) 2.94665e6i 0.296492i
\(216\) 4.74888e6i 0.471227i
\(217\) 370720.i 0.0362800i
\(218\) 3.33726e6 0.322122
\(219\) 6.55499e6i 0.624079i
\(220\) 2.29223e7i 2.15274i
\(221\) 465066.i 0.0430861i
\(222\) −5.78216e6 −0.528483
\(223\) 1.88110e7 1.69628 0.848140 0.529772i \(-0.177723\pi\)
0.848140 + 0.529772i \(0.177723\pi\)
\(224\) 7.34626e6i 0.653615i
\(225\) −1.44244e6 −0.126634
\(226\) −4.19648e6 −0.363546
\(227\) 9.53659e6i 0.815297i 0.913139 + 0.407648i \(0.133651\pi\)
−0.913139 + 0.407648i \(0.866349\pi\)
\(228\) 1.51123e6 0.127505
\(229\) 8.14845e6i 0.678529i 0.940691 + 0.339264i \(0.110178\pi\)
−0.940691 + 0.339264i \(0.889822\pi\)
\(230\) −1.21142e7 −0.995661
\(231\) 3.73994e6i 0.303409i
\(232\) 243841.i 0.0195273i
\(233\) 7.11460e6i 0.562449i 0.959642 + 0.281224i \(0.0907405\pi\)
−0.959642 + 0.281224i \(0.909260\pi\)
\(234\) −4.78876e6 −0.373745
\(235\) 1.58033e7i 1.21771i
\(236\) −2.32569e7 + 2.01248e7i −1.76936 + 1.53107i
\(237\) −2.54775e6 −0.191387
\(238\) 778232.i 0.0577269i
\(239\) −2.18707e6 −0.160202 −0.0801010 0.996787i \(-0.525524\pi\)
−0.0801010 + 0.996787i \(0.525524\pi\)
\(240\) 1.34183e7 0.970650
\(241\) 1.04964e7 0.749872 0.374936 0.927051i \(-0.377665\pi\)
0.374936 + 0.927051i \(0.377665\pi\)
\(242\) 9.45528e6i 0.667158i
\(243\) −920483. −0.0641500
\(244\) 1.90513e7i 1.31146i
\(245\) 9.23763e6 0.628149
\(246\) 1.81660e7i 1.22026i
\(247\) 872624.i 0.0579077i
\(248\) −3.01246e6 −0.197500
\(249\) 1.10697e7i 0.717032i
\(250\) 3.10285e7i 1.98582i
\(251\) −2.38289e7 −1.50689 −0.753447 0.657509i \(-0.771610\pi\)
−0.753447 + 0.657509i \(0.771610\pi\)
\(252\) 5.61407e6 0.350813
\(253\) −1.30905e7 −0.808342
\(254\) 6.53995e6i 0.399092i
\(255\) 529412. 0.0319281
\(256\) −2.41149e7 −1.43736
\(257\) 1.58733e7 0.935122 0.467561 0.883961i \(-0.345133\pi\)
0.467561 + 0.883961i \(0.345133\pi\)
\(258\) 6.82249e6 0.397268
\(259\) 3.91419e6i 0.225290i
\(260\) 1.98687e7i 1.13044i
\(261\) 47264.0 0.00265833
\(262\) −3.38502e7 −1.88216
\(263\) 3.26353e7 1.79399 0.896995 0.442041i \(-0.145745\pi\)
0.896995 + 0.442041i \(0.145745\pi\)
\(264\) 3.03906e7 1.65169
\(265\) −9.48213e6 −0.509528
\(266\) 1.46023e6i 0.0775849i
\(267\) 6.32089e6i 0.332081i
\(268\) 6.01124e7i 3.12291i
\(269\) 1.73683e7i 0.892277i −0.894964 0.446138i \(-0.852799\pi\)
0.894964 0.446138i \(-0.147201\pi\)
\(270\) 5.45132e6i 0.276956i
\(271\) −1.53995e7 −0.773746 −0.386873 0.922133i \(-0.626445\pi\)
−0.386873 + 0.922133i \(0.626445\pi\)
\(272\) 3.01719e6 0.149933
\(273\) 3.24171e6i 0.159326i
\(274\) 5.47518e7i 2.66163i
\(275\) 9.23092e6i 0.443861i
\(276\) 1.96503e7i 0.934636i
\(277\) 1.44727e7 0.680941 0.340470 0.940255i \(-0.389414\pi\)
0.340470 + 0.940255i \(0.389414\pi\)
\(278\) 6.10472e7i 2.84140i
\(279\) 583909.i 0.0268864i
\(280\) 1.90384e7i 0.867272i
\(281\) 2.79711e6 0.126064 0.0630319 0.998012i \(-0.479923\pi\)
0.0630319 + 0.998012i \(0.479923\pi\)
\(282\) 3.65900e7 1.63161
\(283\) 2.68560e7i 1.18490i 0.805607 + 0.592451i \(0.201840\pi\)
−0.805607 + 0.592451i \(0.798160\pi\)
\(284\) 1.61867e7 0.706648
\(285\) 993360. 0.0429113
\(286\) 3.06458e7i 1.31000i
\(287\) 1.22973e7 0.520193
\(288\) 1.15708e7i 0.484382i
\(289\) −2.40185e7 −0.995068
\(290\) 279909.i 0.0114768i
\(291\) 5.72035e6i 0.232137i
\(292\) 6.29700e7i 2.52921i
\(293\) 2.53416e7 1.00747 0.503735 0.863858i \(-0.331959\pi\)
0.503735 + 0.863858i \(0.331959\pi\)
\(294\) 2.13883e7i 0.841654i
\(295\) −1.52872e7 + 1.32284e7i −0.595473 + 0.515277i
\(296\) −3.18065e7 −1.22643
\(297\) 5.89066e6i 0.224851i
\(298\) −1.57529e7 −0.595268
\(299\) 1.13466e7 0.424476
\(300\) −1.38567e7 −0.513209
\(301\) 4.61843e6i 0.169354i
\(302\) −2.19293e7 −0.796165
\(303\) 2.89739e6i 0.104155i
\(304\) 5.66130e6 0.201509
\(305\) 1.25228e7i 0.441368i
\(306\) 1.22577e6i 0.0427803i
\(307\) 2.71219e7 0.937359 0.468679 0.883368i \(-0.344730\pi\)
0.468679 + 0.883368i \(0.344730\pi\)
\(308\) 3.59274e7i 1.22963i
\(309\) 2.04226e7i 0.692205i
\(310\) −3.45805e6 −0.116077
\(311\) −1.23118e7 −0.409300 −0.204650 0.978835i \(-0.565606\pi\)
−0.204650 + 0.978835i \(0.565606\pi\)
\(312\) −2.63420e7 −0.867332
\(313\) 1.98794e7i 0.648290i 0.946007 + 0.324145i \(0.105077\pi\)
−0.946007 + 0.324145i \(0.894923\pi\)
\(314\) −1.42435e7 −0.460073
\(315\) 3.69023e6 0.118065
\(316\) −2.44748e7 −0.775635
\(317\) 6.74191e6 0.211644 0.105822 0.994385i \(-0.466253\pi\)
0.105822 + 0.994385i \(0.466253\pi\)
\(318\) 2.19544e7i 0.682715i
\(319\) 302467.i 0.00931764i
\(320\) 1.34353e7 0.410013
\(321\) −2.36871e7 −0.716139
\(322\) −1.89872e7 −0.568714
\(323\) 223364. 0.00662835
\(324\) −8.84254e6 −0.259981
\(325\) 8.00120e6i 0.233080i
\(326\) 5.88561e7i 1.69879i
\(327\) 3.55829e6i 0.101765i
\(328\) 9.99275e7i 2.83181i
\(329\) 2.47694e7i 0.695548i
\(330\) 3.48859e7 0.970752
\(331\) −5.11403e7 −1.41019 −0.705097 0.709110i \(-0.749097\pi\)
−0.705097 + 0.709110i \(0.749097\pi\)
\(332\) 1.06340e8i 2.90592i
\(333\) 6.16511e6i 0.166958i
\(334\) 6.79402e7i 1.82342i
\(335\) 3.95130e7i 1.05101i
\(336\) 2.10312e7 0.554428
\(337\) 3.66422e7i 0.957397i 0.877979 + 0.478698i \(0.158891\pi\)
−0.877979 + 0.478698i \(0.841109\pi\)
\(338\) 4.40055e7i 1.13961i
\(339\) 4.47441e6i 0.114852i
\(340\) 5.08575e6 0.129395
\(341\) −3.73674e6 −0.0942389
\(342\) 2.29997e6i 0.0574967i
\(343\) 3.26294e7 0.808587
\(344\) 3.75292e7 0.921923
\(345\) 1.29165e7i 0.314549i
\(346\) −5.77694e7 −1.39466
\(347\) 3.17394e7i 0.759645i 0.925059 + 0.379822i \(0.124015\pi\)
−0.925059 + 0.379822i \(0.875985\pi\)
\(348\) 454037. 0.0107734
\(349\) 4.67911e7i 1.10075i −0.834919 0.550373i \(-0.814486\pi\)
0.834919 0.550373i \(-0.185514\pi\)
\(350\) 1.33891e7i 0.312281i
\(351\) 5.10591e6i 0.118073i
\(352\) 7.40480e7 1.69779
\(353\) 6.73316e7i 1.53072i 0.643605 + 0.765358i \(0.277438\pi\)
−0.643605 + 0.765358i \(0.722562\pi\)
\(354\) 3.06282e7 + 3.53951e7i 0.690418 + 0.797872i
\(355\) 1.06398e7 0.237820
\(356\) 6.07211e7i 1.34583i
\(357\) 829775. 0.0182371
\(358\) −1.85264e7 −0.403778
\(359\) 5.75944e7 1.24479 0.622397 0.782702i \(-0.286159\pi\)
0.622397 + 0.782702i \(0.286159\pi\)
\(360\) 2.99867e7i 0.642719i
\(361\) −4.66268e7 −0.991092
\(362\) 4.32142e6i 0.0910963i
\(363\) 1.00815e7 0.210768
\(364\) 3.11412e7i 0.645701i
\(365\) 4.13913e7i 0.851199i
\(366\) −2.89945e7 −0.591388
\(367\) 7.41560e7i 1.50020i 0.661326 + 0.750098i \(0.269994\pi\)
−0.661326 + 0.750098i \(0.730006\pi\)
\(368\) 7.36132e7i 1.47711i
\(369\) −1.93691e7 −0.385505
\(370\) −3.65113e7 −0.720812
\(371\) −1.48618e7 −0.291039
\(372\) 5.60927e6i 0.108963i
\(373\) −4.34155e7 −0.836600 −0.418300 0.908309i \(-0.637374\pi\)
−0.418300 + 0.908309i \(0.637374\pi\)
\(374\) 7.84434e6 0.149948
\(375\) −3.30835e7 −0.627361
\(376\) 2.01275e8 3.78640
\(377\) 262173.i 0.00489287i
\(378\) 8.54415e6i 0.158195i
\(379\) 3.61061e6 0.0663229 0.0331614 0.999450i \(-0.489442\pi\)
0.0331614 + 0.999450i \(0.489442\pi\)
\(380\) 9.54262e6 0.173907
\(381\) 6.97309e6 0.126081
\(382\) 8.06624e7 1.44704
\(383\) −6.55881e7 −1.16742 −0.583712 0.811961i \(-0.698400\pi\)
−0.583712 + 0.811961i \(0.698400\pi\)
\(384\) 1.63980e7i 0.289598i
\(385\) 2.36157e7i 0.413828i
\(386\) 1.46461e8i 2.54660i
\(387\) 7.27435e6i 0.125505i
\(388\) 5.49520e7i 0.940781i
\(389\) 8.08472e7 1.37346 0.686730 0.726912i \(-0.259045\pi\)
0.686730 + 0.726912i \(0.259045\pi\)
\(390\) −3.02385e7 −0.509760
\(391\) 2.90437e6i 0.0485872i
\(392\) 1.17653e8i 1.95319i
\(393\) 3.60921e7i 0.594613i
\(394\) 1.09687e8i 1.79336i
\(395\) −1.60877e7 −0.261038
\(396\) 5.65881e7i 0.911254i
\(397\) 1.19035e8i 1.90241i 0.308562 + 0.951204i \(0.400152\pi\)
−0.308562 + 0.951204i \(0.599848\pi\)
\(398\) 3.25475e7i 0.516259i
\(399\) 1.55694e6 0.0245106
\(400\) −5.19091e7 −0.811080
\(401\) 2.51016e7i 0.389286i −0.980874 0.194643i \(-0.937645\pi\)
0.980874 0.194643i \(-0.0623548\pi\)
\(402\) −9.14861e7 −1.40824
\(403\) 3.23894e6 0.0494867
\(404\) 2.78335e7i 0.422108i
\(405\) −5.81237e6 −0.0874959
\(406\) 438716.i 0.00655549i
\(407\) −3.94538e7 −0.585201
\(408\) 6.74272e6i 0.0992784i
\(409\) 9.64133e7i 1.40918i 0.709614 + 0.704591i \(0.248870\pi\)
−0.709614 + 0.704591i \(0.751130\pi\)
\(410\) 1.14708e8i 1.66435i
\(411\) −5.83780e7 −0.840861
\(412\) 1.96188e8i 2.80530i
\(413\) −2.39604e7 + 2.07336e7i −0.340130 + 0.294323i
\(414\) 2.99062e7 0.421463
\(415\) 6.98994e7i 0.977979i
\(416\) −6.41835e7 −0.891545
\(417\) −6.50904e7 −0.897654
\(418\) 1.47187e7 0.201530
\(419\) 5.91334e7i 0.803879i −0.915666 0.401939i \(-0.868336\pi\)
0.915666 0.401939i \(-0.131664\pi\)
\(420\) 3.54499e7 0.478484
\(421\) 5.51580e7i 0.739201i −0.929191 0.369600i \(-0.879495\pi\)
0.929191 0.369600i \(-0.120505\pi\)
\(422\) 7.91154e7 1.05275
\(423\) 3.90134e7i 0.515457i
\(424\) 1.20767e8i 1.58435i
\(425\) −2.04805e6 −0.0266793
\(426\) 2.46348e7i 0.318655i
\(427\) 1.96276e7i 0.252106i
\(428\) −2.27548e8 −2.90230
\(429\) −3.26754e7 −0.413856
\(430\) 4.30805e7 0.541845
\(431\) 1.45357e8i 1.81554i −0.419470 0.907769i \(-0.637784\pi\)
0.419470 0.907769i \(-0.362216\pi\)
\(432\) −3.31255e7 −0.410876
\(433\) 3.15671e7 0.388840 0.194420 0.980918i \(-0.437718\pi\)
0.194420 + 0.980918i \(0.437718\pi\)
\(434\) −5.41999e6 −0.0663024
\(435\) 298447. 0.00362576
\(436\) 3.41824e7i 0.412423i
\(437\) 5.44961e6i 0.0653012i
\(438\) −9.58351e7 −1.14052
\(439\) 3.52974e7 0.417205 0.208602 0.978001i \(-0.433109\pi\)
0.208602 + 0.978001i \(0.433109\pi\)
\(440\) 1.91901e8 2.25278
\(441\) −2.28048e7 −0.265895
\(442\) −6.79933e6 −0.0787407
\(443\) 1.02025e7i 0.117353i 0.998277 + 0.0586766i \(0.0186881\pi\)
−0.998277 + 0.0586766i \(0.981312\pi\)
\(444\) 5.92246e7i 0.676633i
\(445\) 3.99131e7i 0.452934i
\(446\) 2.75020e8i 3.09999i
\(447\) 1.67963e7i 0.188057i
\(448\) 2.10579e7 0.234197
\(449\) 1.64804e8 1.82066 0.910330 0.413884i \(-0.135828\pi\)
0.910330 + 0.413884i \(0.135828\pi\)
\(450\) 2.10887e7i 0.231426i
\(451\) 1.23953e8i 1.35122i
\(452\) 4.29830e7i 0.465459i
\(453\) 2.33816e7i 0.251525i
\(454\) 1.39427e8 1.48997
\(455\) 2.04697e7i 0.217309i
\(456\) 1.26517e7i 0.133430i
\(457\) 1.21465e8i 1.27263i −0.771428 0.636317i \(-0.780457\pi\)
0.771428 0.636317i \(-0.219543\pi\)
\(458\) 1.19132e8 1.24003
\(459\) −1.30695e6 −0.0135152
\(460\) 1.24082e8i 1.27478i
\(461\) 1.25615e8 1.28215 0.641073 0.767480i \(-0.278490\pi\)
0.641073 + 0.767480i \(0.278490\pi\)
\(462\) 5.46785e7 0.554486
\(463\) 9.50535e7i 0.957690i −0.877899 0.478845i \(-0.841056\pi\)
0.877899 0.478845i \(-0.158944\pi\)
\(464\) 1.70089e6 0.0170264
\(465\) 3.68708e6i 0.0366711i
\(466\) 1.04017e8 1.02789
\(467\) 1.11809e8i 1.09781i −0.835884 0.548906i \(-0.815045\pi\)
0.835884 0.548906i \(-0.184955\pi\)
\(468\) 4.90495e7i 0.478517i
\(469\) 6.19308e7i 0.600328i
\(470\) 2.31047e8 2.22539
\(471\) 1.51868e7i 0.145346i
\(472\) 1.68480e8 + 1.94702e8i 1.60222 + 1.85159i
\(473\) 4.65524e7 0.439905
\(474\) 3.72486e7i 0.349763i
\(475\) −3.84285e6 −0.0358569
\(476\) 7.97116e6 0.0739095
\(477\) 2.34084e7 0.215683
\(478\) 3.19753e7i 0.292773i
\(479\) 1.79395e8 1.63231 0.816157 0.577831i \(-0.196101\pi\)
0.816157 + 0.577831i \(0.196101\pi\)
\(480\) 7.30638e7i 0.660661i
\(481\) 3.41978e7 0.307301
\(482\) 1.53458e8i 1.37041i
\(483\) 2.02448e7i 0.179668i
\(484\) 9.68471e7 0.854182
\(485\) 3.61210e7i 0.316617i
\(486\) 1.34576e7i 0.117235i
\(487\) 5.56871e6 0.0482134 0.0241067 0.999709i \(-0.492326\pi\)
0.0241067 + 0.999709i \(0.492326\pi\)
\(488\) −1.59493e8 −1.37241
\(489\) 6.27541e7 0.536680
\(490\) 1.35056e8i 1.14795i
\(491\) −1.62969e8 −1.37677 −0.688384 0.725347i \(-0.741679\pi\)
−0.688384 + 0.725347i \(0.741679\pi\)
\(492\) −1.86067e8 −1.56234
\(493\) 67107.9 0.000560058
\(494\) −1.27579e7 −0.105827
\(495\) 3.71964e7i 0.306680i
\(496\) 2.10132e7i 0.172206i
\(497\) 1.66763e7 0.135841
\(498\) 1.61841e8 1.31039
\(499\) −1.15293e8 −0.927897 −0.463949 0.885862i \(-0.653568\pi\)
−0.463949 + 0.885862i \(0.653568\pi\)
\(500\) −3.17814e8 −2.54251
\(501\) 7.24399e7 0.576056
\(502\) 3.48382e8i 2.75388i
\(503\) 5.21389e7i 0.409693i 0.978794 + 0.204846i \(0.0656694\pi\)
−0.978794 + 0.204846i \(0.934331\pi\)
\(504\) 4.69997e7i 0.367116i
\(505\) 1.82955e7i 0.142059i
\(506\) 1.91385e8i 1.47726i
\(507\) −4.69200e7 −0.360026
\(508\) 6.69864e7 0.510970
\(509\) 2.31503e8i 1.75551i −0.479107 0.877757i \(-0.659039\pi\)
0.479107 0.877757i \(-0.340961\pi\)
\(510\) 7.74008e6i 0.0583492i
\(511\) 6.48748e7i 0.486198i
\(512\) 2.85240e8i 2.12520i
\(513\) −2.45229e6 −0.0181644
\(514\) 2.32070e8i 1.70895i
\(515\) 1.28958e8i 0.944117i
\(516\) 6.98804e7i 0.508635i
\(517\) 2.49667e8 1.80672
\(518\) −5.72260e7 −0.411722
\(519\) 6.15955e7i 0.440602i
\(520\) −1.66336e8 −1.18298
\(521\) −1.05626e8 −0.746891 −0.373445 0.927652i \(-0.621824\pi\)
−0.373445 + 0.927652i \(0.621824\pi\)
\(522\) 691007.i 0.00485815i
\(523\) 2.56497e7 0.179299 0.0896494 0.995973i \(-0.471425\pi\)
0.0896494 + 0.995973i \(0.471425\pi\)
\(524\) 3.46715e8i 2.40979i
\(525\) −1.42758e7 −0.0986559
\(526\) 4.77133e8i 3.27855i
\(527\) 829066.i 0.00566444i
\(528\) 2.11988e8i 1.44015i
\(529\) 7.71753e7 0.521328
\(530\) 1.38630e8i 0.931173i
\(531\) 3.77393e7 3.26567e7i 0.252064 0.218117i
\(532\) 1.49567e7 0.0993344
\(533\) 1.07440e8i 0.709554i
\(534\) 9.24124e7 0.606885
\(535\) −1.49572e8 −0.976761
\(536\) −5.03248e8 −3.26804
\(537\) 1.97535e7i 0.127562i
\(538\) −2.53927e8 −1.63065
\(539\) 1.45940e8i 0.931983i
\(540\) −5.58360e7 −0.354595
\(541\) 3.67500e7i 0.232095i −0.993244 0.116047i \(-0.962978\pi\)
0.993244 0.116047i \(-0.0370224\pi\)
\(542\) 2.25143e8i 1.41404i
\(543\) −4.60763e6 −0.0287791
\(544\) 1.64289e7i 0.102050i
\(545\) 2.24687e7i 0.138800i
\(546\) −4.73943e7 −0.291171
\(547\) 4.91319e7 0.300194 0.150097 0.988671i \(-0.452041\pi\)
0.150097 + 0.988671i \(0.452041\pi\)
\(548\) −5.60804e8 −3.40776
\(549\) 3.09148e7i 0.186831i
\(550\) −1.34958e8 −0.811165
\(551\) 125918. 0.000752718
\(552\) 1.64508e8 0.978071
\(553\) −2.52151e7 −0.149103
\(554\) 2.11593e8i 1.24443i
\(555\) 3.89294e7i 0.227719i
\(556\) −6.25285e8 −3.63793
\(557\) 2.64230e8 1.52903 0.764516 0.644605i \(-0.222978\pi\)
0.764516 + 0.644605i \(0.222978\pi\)
\(558\) 8.53685e6 0.0491355
\(559\) −4.03508e7 −0.231002
\(560\) 1.32801e8 0.756200
\(561\) 8.36387e6i 0.0473717i
\(562\) 4.08942e7i 0.230384i
\(563\) 7.91202e7i 0.443366i −0.975119 0.221683i \(-0.928845\pi\)
0.975119 0.221683i \(-0.0711550\pi\)
\(564\) 3.74779e8i 2.08900i
\(565\) 2.82536e7i 0.156649i
\(566\) 3.92639e8 2.16543
\(567\) −9.11003e6 −0.0499770
\(568\) 1.35511e8i 0.739487i
\(569\) 1.27333e8i 0.691199i −0.938382 0.345600i \(-0.887676\pi\)
0.938382 0.345600i \(-0.112324\pi\)
\(570\) 1.45231e7i 0.0784213i
\(571\) 2.14936e7i 0.115452i −0.998332 0.0577258i \(-0.981615\pi\)
0.998332 0.0577258i \(-0.0183849\pi\)
\(572\) −3.13894e8 −1.67724
\(573\) 8.60047e7i 0.457150i
\(574\) 1.79789e8i 0.950663i
\(575\) 4.99681e7i 0.262839i
\(576\) −3.31676e7 −0.173559
\(577\) −1.75877e8 −0.915549 −0.457774 0.889068i \(-0.651353\pi\)
−0.457774 + 0.889068i \(0.651353\pi\)
\(578\) 3.51155e8i 1.81851i
\(579\) −1.56162e8 −0.804523
\(580\) 2.86701e6 0.0146942
\(581\) 1.09557e8i 0.558614i
\(582\) 8.36325e7 0.424234
\(583\) 1.49803e8i 0.755986i
\(584\) −5.27171e8 −2.64675
\(585\) 3.22412e7i 0.161044i
\(586\) 3.70499e8i 1.84117i
\(587\) 3.63690e8i 1.79811i −0.437834 0.899056i \(-0.644254\pi\)
0.437834 0.899056i \(-0.355746\pi\)
\(588\) −2.19072e8 −1.07760
\(589\) 1.55562e6i 0.00761301i
\(590\) 1.93401e8 + 2.23501e8i 0.941680 + 1.08824i
\(591\) 1.16952e8 0.566557
\(592\) 2.21864e8i 1.06936i
\(593\) −3.10986e7 −0.149134 −0.0745670 0.997216i \(-0.523757\pi\)
−0.0745670 + 0.997216i \(0.523757\pi\)
\(594\) −8.61223e7 −0.410919
\(595\) 5.23959e6 0.0248741
\(596\) 1.61352e8i 0.762140i
\(597\) −3.47031e7 −0.163097
\(598\) 1.65889e8i 0.775738i
\(599\) −3.39747e8 −1.58079 −0.790397 0.612595i \(-0.790126\pi\)
−0.790397 + 0.612595i \(0.790126\pi\)
\(600\) 1.16005e8i 0.537059i
\(601\) 3.43788e8i 1.58368i 0.610728 + 0.791840i \(0.290877\pi\)
−0.610728 + 0.791840i \(0.709123\pi\)
\(602\) 6.75223e7 0.309498
\(603\) 9.75453e7i 0.444892i
\(604\) 2.24614e8i 1.01935i
\(605\) 6.36594e7 0.287473
\(606\) 4.23603e7 0.190345
\(607\) 2.24070e7 0.100188 0.0500942 0.998744i \(-0.484048\pi\)
0.0500942 + 0.998744i \(0.484048\pi\)
\(608\) 3.08263e7i 0.137155i
\(609\) 467772. 0.00207101
\(610\) −1.83085e8 −0.806610
\(611\) −2.16407e8 −0.948742
\(612\) −1.25551e7 −0.0547730
\(613\) 9.41425e7i 0.408700i −0.978898 0.204350i \(-0.934492\pi\)
0.978898 0.204350i \(-0.0655080\pi\)
\(614\) 3.96527e8i 1.71304i
\(615\) −1.22306e8 −0.525801
\(616\) 3.00776e8 1.28677
\(617\) 6.71253e7 0.285779 0.142890 0.989739i \(-0.454361\pi\)
0.142890 + 0.989739i \(0.454361\pi\)
\(618\) 2.98581e8 1.26502
\(619\) −2.50796e8 −1.05742 −0.528712 0.848801i \(-0.677325\pi\)
−0.528712 + 0.848801i \(0.677325\pi\)
\(620\) 3.54196e7i 0.148617i
\(621\) 3.18869e7i 0.133149i
\(622\) 1.80001e8i 0.748004i
\(623\) 6.25579e7i 0.258713i
\(624\) 1.83747e8i 0.756252i
\(625\) −1.16156e8 −0.475774
\(626\) 2.90639e8 1.18476
\(627\) 1.56935e7i 0.0636675i
\(628\) 1.45891e8i 0.589046i
\(629\) 8.75355e6i 0.0351749i
\(630\) 5.39518e7i 0.215767i
\(631\) 3.43892e8 1.36878 0.684391 0.729115i \(-0.260068\pi\)
0.684391 + 0.729115i \(0.260068\pi\)
\(632\) 2.04897e8i 0.811680i
\(633\) 8.43552e7i 0.332584i
\(634\) 9.85679e7i 0.386783i
\(635\) 4.40314e7 0.171966
\(636\) 2.24871e8 0.874101
\(637\) 1.26498e8i 0.489402i
\(638\) 4.42212e6 0.0170282
\(639\) −2.62664e7 −0.100669
\(640\) 1.03545e8i 0.394991i
\(641\) 1.75124e8 0.664922 0.332461 0.943117i \(-0.392121\pi\)
0.332461 + 0.943117i \(0.392121\pi\)
\(642\) 3.46310e8i 1.30876i
\(643\) 2.40631e8 0.905144 0.452572 0.891728i \(-0.350507\pi\)
0.452572 + 0.891728i \(0.350507\pi\)
\(644\) 1.94479e8i 0.728142i
\(645\) 4.59337e7i 0.171180i
\(646\) 3.26562e6i 0.0121134i
\(647\) 2.99942e8 1.10745 0.553726 0.832699i \(-0.313206\pi\)
0.553726 + 0.832699i \(0.313206\pi\)
\(648\) 7.40278e7i 0.272063i
\(649\) 2.08988e8 + 2.41514e8i 0.764516 + 0.883502i
\(650\) 1.16979e8 0.425958
\(651\) 5.77896e6i 0.0209463i
\(652\) 6.02842e8 2.17501
\(653\) 1.69558e8 0.608947 0.304473 0.952521i \(-0.401520\pi\)
0.304473 + 0.952521i \(0.401520\pi\)
\(654\) −5.20227e7 −0.185977
\(655\) 2.27903e8i 0.811008i
\(656\) −6.97037e8 −2.46913
\(657\) 1.02182e8i 0.360312i
\(658\) 3.62132e8 1.27113
\(659\) 4.22378e8i 1.47586i −0.674878 0.737929i \(-0.735804\pi\)
0.674878 0.737929i \(-0.264196\pi\)
\(660\) 3.57324e8i 1.24288i
\(661\) 3.36981e8 1.16681 0.583407 0.812180i \(-0.301719\pi\)
0.583407 + 0.812180i \(0.301719\pi\)
\(662\) 7.47679e8i 2.57716i
\(663\) 7.24965e6i 0.0248758i
\(664\) 8.90257e8 3.04096
\(665\) 9.83129e6 0.0334307
\(666\) 9.01349e7 0.305120
\(667\) 1.63729e6i 0.00551758i
\(668\) 6.95887e8 2.33458
\(669\) −2.93235e8 −0.979348
\(670\) −5.77687e8 −1.92074
\(671\) −1.97840e8 −0.654858
\(672\) 1.14517e8i 0.377365i
\(673\) 5.80418e8i 1.90413i −0.305900 0.952064i \(-0.598957\pi\)
0.305900 0.952064i \(-0.401043\pi\)
\(674\) 5.35715e8 1.74966
\(675\) 2.24854e7 0.0731120
\(676\) −4.50733e8 −1.45908
\(677\) −2.93634e8 −0.946326 −0.473163 0.880975i \(-0.656888\pi\)
−0.473163 + 0.880975i \(0.656888\pi\)
\(678\) 6.54166e7 0.209893
\(679\) 5.66144e7i 0.180849i
\(680\) 4.25767e7i 0.135408i
\(681\) 1.48661e8i 0.470712i
\(682\) 5.46318e7i 0.172224i
\(683\) 1.75942e8i 0.552214i −0.961127 0.276107i \(-0.910956\pi\)
0.961127 0.276107i \(-0.0890444\pi\)
\(684\) −2.35577e7 −0.0736148
\(685\) −3.68627e8 −1.14687
\(686\) 4.77047e8i 1.47771i
\(687\) 1.27022e8i 0.391749i
\(688\) 2.61783e8i 0.803851i
\(689\) 1.29846e8i 0.396983i
\(690\) 1.88842e8 0.574845
\(691\) 2.69736e8i 0.817531i −0.912639 0.408766i \(-0.865959\pi\)
0.912639 0.408766i \(-0.134041\pi\)
\(692\) 5.91712e8i 1.78563i
\(693\) 5.82999e7i 0.175173i
\(694\) 4.64035e8 1.38827
\(695\) −4.11012e8 −1.22433
\(696\) 3.80110e6i 0.0112741i
\(697\) −2.75013e7 −0.0812184
\(698\) −6.84094e8 −2.01164
\(699\) 1.10906e8i 0.324730i
\(700\) −1.37139e8 −0.399823
\(701\) 3.13562e8i 0.910267i 0.890423 + 0.455133i \(0.150408\pi\)
−0.890423 + 0.455133i \(0.849592\pi\)
\(702\) 7.46493e7 0.215782
\(703\) 1.64247e7i 0.0472750i
\(704\) 2.12257e8i 0.608336i
\(705\) 2.46349e8i 0.703046i
\(706\) 9.84399e8 2.79742
\(707\) 2.86755e7i 0.0811432i
\(708\) 3.62539e8 3.13714e8i 1.02154 0.883964i
\(709\) 5.67397e8 1.59202 0.796010 0.605284i \(-0.206940\pi\)
0.796010 + 0.605284i \(0.206940\pi\)
\(710\) 1.55556e8i 0.434621i
\(711\) 3.97155e7 0.110497
\(712\) 5.08343e8 1.40837
\(713\) −2.02275e7 −0.0558050
\(714\) 1.21314e7i 0.0333287i
\(715\) −2.06328e8 −0.564470
\(716\) 1.89760e8i 0.516970i
\(717\) 3.40930e7 0.0924927
\(718\) 8.42040e8i 2.27489i
\(719\) 6.89644e8i 1.85540i −0.373324 0.927701i \(-0.621782\pi\)
0.373324 0.927701i \(-0.378218\pi\)
\(720\) −2.09170e8 −0.560405
\(721\) 2.02122e8i 0.539273i
\(722\) 6.81691e8i 1.81124i
\(723\) −1.63622e8 −0.432939
\(724\) −4.42628e7 −0.116633
\(725\) −1.15456e6 −0.00302971
\(726\) 1.47393e8i 0.385184i
\(727\) 3.00693e8 0.782564 0.391282 0.920271i \(-0.372032\pi\)
0.391282 + 0.920271i \(0.372032\pi\)
\(728\) −2.60707e8 −0.675708
\(729\) 1.43489e7 0.0370370
\(730\) −6.05148e8 −1.55558
\(731\) 1.03285e7i 0.0264415i
\(732\) 2.96981e8i 0.757172i
\(733\) −3.35833e8 −0.852729 −0.426364 0.904551i \(-0.640206\pi\)
−0.426364 + 0.904551i \(0.640206\pi\)
\(734\) 1.08417e9 2.74164
\(735\) −1.44000e8 −0.362662
\(736\) 4.00831e8 1.00537
\(737\) −6.24244e8 −1.55938
\(738\) 2.83179e8i 0.704518i
\(739\) 6.36157e8i 1.57627i 0.615501 + 0.788136i \(0.288954\pi\)
−0.615501 + 0.788136i \(0.711046\pi\)
\(740\) 3.73972e8i 0.922878i
\(741\) 1.36029e7i 0.0334330i
\(742\) 2.17283e8i 0.531879i
\(743\) −5.72867e8 −1.39665 −0.698325 0.715781i \(-0.746071\pi\)
−0.698325 + 0.715781i \(0.746071\pi\)
\(744\) 4.69596e7 0.114026
\(745\) 1.06060e8i 0.256496i
\(746\) 6.34741e8i 1.52890i
\(747\) 1.72560e8i 0.413978i
\(748\) 8.03468e7i 0.191983i
\(749\) −2.34432e8 −0.557919
\(750\) 4.83686e8i 1.14652i
\(751\) 3.15394e8i 0.744619i −0.928109 0.372310i \(-0.878566\pi\)
0.928109 0.372310i \(-0.121434\pi\)
\(752\) 1.40398e9i 3.30147i
\(753\) 3.71456e8 0.870006
\(754\) −3.83301e6 −0.00894182
\(755\) 1.47643e8i 0.343061i
\(756\) −8.75147e7 −0.202542
\(757\) −6.71386e8 −1.54769 −0.773847 0.633373i \(-0.781670\pi\)
−0.773847 + 0.633373i \(0.781670\pi\)
\(758\) 5.27878e7i 0.121206i
\(759\) 2.04061e8 0.466696
\(760\) 7.98887e7i 0.181989i
\(761\) −1.89435e8 −0.429840 −0.214920 0.976632i \(-0.568949\pi\)
−0.214920 + 0.976632i \(0.568949\pi\)
\(762\) 1.01948e8i 0.230416i
\(763\) 3.52164e7i 0.0792814i
\(764\) 8.26197e8i 1.85269i
\(765\) −8.25271e6 −0.0184337
\(766\) 9.58909e8i 2.13349i
\(767\) −1.81147e8 2.09340e8i −0.401462 0.463944i
\(768\) 3.75914e8 0.829859
\(769\) 1.56205e8i 0.343492i 0.985141 + 0.171746i \(0.0549408\pi\)
−0.985141 + 0.171746i \(0.945059\pi\)
\(770\) 3.45266e8 0.756278
\(771\) −2.47440e8 −0.539893
\(772\) −1.50015e9 −3.26049
\(773\) 3.30339e8i 0.715190i −0.933877 0.357595i \(-0.883597\pi\)
0.933877 0.357595i \(-0.116403\pi\)
\(774\) −1.06352e8 −0.229363
\(775\) 1.42636e7i 0.0306426i
\(776\) 4.60046e8 0.984501
\(777\) 6.10161e7i 0.130071i
\(778\) 1.18200e9i 2.51003i
\(779\) −5.16019e7 −0.109158
\(780\) 3.09722e8i 0.652662i
\(781\) 1.68092e8i 0.352854i
\(782\) 4.24624e7 0.0887941
\(783\) −736772. −0.00153479
\(784\) −8.20679e8 −1.70304
\(785\) 9.58967e7i