Properties

Label 177.7.c.a.58.19
Level $177$
Weight $7$
Character 177.58
Analytic conductor $40.720$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 58.19
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.42

$q$-expansion

\(f(q)\) \(=\) \(q-7.02990i q^{2} -15.5885 q^{3} +14.5805 q^{4} +242.375 q^{5} +109.585i q^{6} +243.138 q^{7} -552.413i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-7.02990i q^{2} -15.5885 q^{3} +14.5805 q^{4} +242.375 q^{5} +109.585i q^{6} +243.138 q^{7} -552.413i q^{8} +243.000 q^{9} -1703.87i q^{10} -1556.52i q^{11} -227.288 q^{12} +1415.05i q^{13} -1709.23i q^{14} -3778.26 q^{15} -2950.26 q^{16} +3197.13 q^{17} -1708.27i q^{18} -454.920 q^{19} +3533.96 q^{20} -3790.14 q^{21} -10942.2 q^{22} +1158.71i q^{23} +8611.27i q^{24} +43120.8 q^{25} +9947.68 q^{26} -3788.00 q^{27} +3545.07 q^{28} +21964.5 q^{29} +26560.8i q^{30} +4418.81i q^{31} -14614.4i q^{32} +24263.8i q^{33} -22475.5i q^{34} +58930.6 q^{35} +3543.06 q^{36} +46436.0i q^{37} +3198.04i q^{38} -22058.5i q^{39} -133891. i q^{40} -132979. q^{41} +26644.3i q^{42} +157011. i q^{43} -22694.9i q^{44} +58897.2 q^{45} +8145.63 q^{46} -163691. i q^{47} +45989.9 q^{48} -58533.1 q^{49} -303135. i q^{50} -49838.3 q^{51} +20632.2i q^{52} +192890. q^{53} +26629.2i q^{54} -377263. i q^{55} -134312. i q^{56} +7091.50 q^{57} -154408. i q^{58} +(14748.1 - 204849. i) q^{59} -55088.9 q^{60} +340178. i q^{61} +31063.8 q^{62} +59082.4 q^{63} -291554. q^{64} +342974. i q^{65} +170572. q^{66} -237657. i q^{67} +46615.8 q^{68} -18062.5i q^{69} -414276. i q^{70} -352597. q^{71} -134236. i q^{72} -456696. i q^{73} +326441. q^{74} -672187. q^{75} -6632.97 q^{76} -378450. i q^{77} -155069. q^{78} +33053.2 q^{79} -715069. q^{80} +59049.0 q^{81} +934832. i q^{82} +40540.7i q^{83} -55262.2 q^{84} +774905. q^{85} +1.10377e6 q^{86} -342393. q^{87} -859844. q^{88} +1.07456e6i q^{89} -414041. i q^{90} +344053. i q^{91} +16894.6i q^{92} -68882.5i q^{93} -1.15073e6 q^{94} -110261. q^{95} +227817. i q^{96} -1.45966e6i q^{97} +411482. i q^{98} -378235. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.02990i 0.878737i −0.898307 0.439369i \(-0.855202\pi\)
0.898307 0.439369i \(-0.144798\pi\)
\(3\) −15.5885 −0.577350
\(4\) 14.5805 0.227821
\(5\) 242.375 1.93900 0.969501 0.245086i \(-0.0788163\pi\)
0.969501 + 0.245086i \(0.0788163\pi\)
\(6\) 109.585i 0.507339i
\(7\) 243.138 0.708856 0.354428 0.935083i \(-0.384676\pi\)
0.354428 + 0.935083i \(0.384676\pi\)
\(8\) 552.413i 1.07893i
\(9\) 243.000 0.333333
\(10\) 1703.87i 1.70387i
\(11\) 1556.52i 1.16944i −0.811235 0.584720i \(-0.801204\pi\)
0.811235 0.584720i \(-0.198796\pi\)
\(12\) −227.288 −0.131532
\(13\) 1415.05i 0.644084i 0.946725 + 0.322042i \(0.104369\pi\)
−0.946725 + 0.322042i \(0.895631\pi\)
\(14\) 1709.23i 0.622898i
\(15\) −3778.26 −1.11948
\(16\) −2950.26 −0.720277
\(17\) 3197.13 0.650749 0.325374 0.945585i \(-0.394510\pi\)
0.325374 + 0.945585i \(0.394510\pi\)
\(18\) 1708.27i 0.292912i
\(19\) −454.920 −0.0663245 −0.0331623 0.999450i \(-0.510558\pi\)
−0.0331623 + 0.999450i \(0.510558\pi\)
\(20\) 3533.96 0.441745
\(21\) −3790.14 −0.409258
\(22\) −10942.2 −1.02763
\(23\) 1158.71i 0.0952340i 0.998866 + 0.0476170i \(0.0151627\pi\)
−0.998866 + 0.0476170i \(0.984837\pi\)
\(24\) 8611.27i 0.622922i
\(25\) 43120.8 2.75973
\(26\) 9947.68 0.565981
\(27\) −3788.00 −0.192450
\(28\) 3545.07 0.161492
\(29\) 21964.5 0.900590 0.450295 0.892880i \(-0.351319\pi\)
0.450295 + 0.892880i \(0.351319\pi\)
\(30\) 26560.8i 0.983732i
\(31\) 4418.81i 0.148327i 0.997246 + 0.0741636i \(0.0236287\pi\)
−0.997246 + 0.0741636i \(0.976371\pi\)
\(32\) 14614.4i 0.445997i
\(33\) 24263.8i 0.675176i
\(34\) 22475.5i 0.571837i
\(35\) 58930.6 1.37447
\(36\) 3543.06 0.0759402
\(37\) 46436.0i 0.916748i 0.888760 + 0.458374i \(0.151568\pi\)
−0.888760 + 0.458374i \(0.848432\pi\)
\(38\) 3198.04i 0.0582818i
\(39\) 22058.5i 0.371862i
\(40\) 133891.i 2.09205i
\(41\) −132979. −1.92945 −0.964724 0.263264i \(-0.915201\pi\)
−0.964724 + 0.263264i \(0.915201\pi\)
\(42\) 26644.3i 0.359631i
\(43\) 157011.i 1.97481i 0.158219 + 0.987404i \(0.449425\pi\)
−0.158219 + 0.987404i \(0.550575\pi\)
\(44\) 22694.9i 0.266422i
\(45\) 58897.2 0.646334
\(46\) 8145.63 0.0836857
\(47\) 163691.i 1.57663i −0.615271 0.788316i \(-0.710953\pi\)
0.615271 0.788316i \(-0.289047\pi\)
\(48\) 45989.9 0.415852
\(49\) −58533.1 −0.497523
\(50\) 303135.i 2.42508i
\(51\) −49838.3 −0.375710
\(52\) 20632.2i 0.146736i
\(53\) 192890. 1.29563 0.647816 0.761797i \(-0.275683\pi\)
0.647816 + 0.761797i \(0.275683\pi\)
\(54\) 26629.2i 0.169113i
\(55\) 377263.i 2.26755i
\(56\) 134312.i 0.764807i
\(57\) 7091.50 0.0382925
\(58\) 154408.i 0.791382i
\(59\) 14748.1 204849.i 0.0718094 0.997418i
\(60\) −55088.9 −0.255041
\(61\) 340178.i 1.49871i 0.662170 + 0.749354i \(0.269636\pi\)
−0.662170 + 0.749354i \(0.730364\pi\)
\(62\) 31063.8 0.130341
\(63\) 59082.4 0.236285
\(64\) −291554. −1.11219
\(65\) 342974.i 1.24888i
\(66\) 170572. 0.593303
\(67\) 237657.i 0.790180i −0.918643 0.395090i \(-0.870713\pi\)
0.918643 0.395090i \(-0.129287\pi\)
\(68\) 46615.8 0.148254
\(69\) 18062.5i 0.0549834i
\(70\) 414276.i 1.20780i
\(71\) −352597. −0.985151 −0.492576 0.870270i \(-0.663945\pi\)
−0.492576 + 0.870270i \(0.663945\pi\)
\(72\) 134236.i 0.359644i
\(73\) 456696.i 1.17398i −0.809596 0.586988i \(-0.800314\pi\)
0.809596 0.586988i \(-0.199686\pi\)
\(74\) 326441. 0.805580
\(75\) −672187. −1.59333
\(76\) −6632.97 −0.0151101
\(77\) 378450.i 0.828964i
\(78\) −155069. −0.326769
\(79\) 33053.2 0.0670398 0.0335199 0.999438i \(-0.489328\pi\)
0.0335199 + 0.999438i \(0.489328\pi\)
\(80\) −715069. −1.39662
\(81\) 59049.0 0.111111
\(82\) 934832.i 1.69548i
\(83\) 40540.7i 0.0709018i 0.999371 + 0.0354509i \(0.0112867\pi\)
−0.999371 + 0.0354509i \(0.988713\pi\)
\(84\) −55262.2 −0.0932374
\(85\) 774905. 1.26180
\(86\) 1.10377e6 1.73534
\(87\) −342393. −0.519956
\(88\) −859844. −1.26175
\(89\) 1.07456e6i 1.52427i 0.647420 + 0.762133i \(0.275848\pi\)
−0.647420 + 0.762133i \(0.724152\pi\)
\(90\) 414041.i 0.567958i
\(91\) 344053.i 0.456563i
\(92\) 16894.6i 0.0216963i
\(93\) 68882.5i 0.0856367i
\(94\) −1.15073e6 −1.38545
\(95\) −110261. −0.128603
\(96\) 227817.i 0.257497i
\(97\) 1.45966e6i 1.59932i −0.600454 0.799660i \(-0.705013\pi\)
0.600454 0.799660i \(-0.294987\pi\)
\(98\) 411482.i 0.437192i
\(99\) 378235.i 0.389813i
\(100\) 628723. 0.628723
\(101\) 264109.i 0.256341i 0.991752 + 0.128171i \(0.0409105\pi\)
−0.991752 + 0.128171i \(0.959089\pi\)
\(102\) 350358.i 0.330150i
\(103\) 410416.i 0.375589i −0.982208 0.187795i \(-0.939866\pi\)
0.982208 0.187795i \(-0.0601339\pi\)
\(104\) 781694. 0.694923
\(105\) −918636. −0.793553
\(106\) 1.35600e6i 1.13852i
\(107\) 1.11097e6 0.906879 0.453439 0.891287i \(-0.350197\pi\)
0.453439 + 0.891287i \(0.350197\pi\)
\(108\) −55230.9 −0.0438441
\(109\) 2.09796e6i 1.62001i −0.586422 0.810006i \(-0.699464\pi\)
0.586422 0.810006i \(-0.300536\pi\)
\(110\) −2.65212e6 −1.99258
\(111\) 723866.i 0.529284i
\(112\) −717318. −0.510573
\(113\) 266601.i 0.184768i 0.995723 + 0.0923839i \(0.0294487\pi\)
−0.995723 + 0.0923839i \(0.970551\pi\)
\(114\) 49852.5i 0.0336490i
\(115\) 280843.i 0.184659i
\(116\) 320254. 0.205173
\(117\) 343858.i 0.214695i
\(118\) −1.44007e6 103678.i −0.876469 0.0631016i
\(119\) 777342. 0.461287
\(120\) 2.08716e6i 1.20785i
\(121\) −651206. −0.367589
\(122\) 2.39142e6 1.31697
\(123\) 2.07294e6 1.11397
\(124\) 64428.6i 0.0337920i
\(125\) 6.66430e6 3.41212
\(126\) 415344.i 0.207633i
\(127\) −1.74962e6 −0.854148 −0.427074 0.904217i \(-0.640456\pi\)
−0.427074 + 0.904217i \(0.640456\pi\)
\(128\) 1.11427e6i 0.531327i
\(129\) 2.44756e6i 1.14016i
\(130\) 2.41107e6 1.09744
\(131\) 187240.i 0.0832886i −0.999132 0.0416443i \(-0.986740\pi\)
0.999132 0.0416443i \(-0.0132596\pi\)
\(132\) 353779.i 0.153819i
\(133\) −110608. −0.0470145
\(134\) −1.67070e6 −0.694360
\(135\) −918116. −0.373161
\(136\) 1.76614e6i 0.702114i
\(137\) −2.02527e6 −0.787628 −0.393814 0.919190i \(-0.628845\pi\)
−0.393814 + 0.919190i \(0.628845\pi\)
\(138\) −126978. −0.0483159
\(139\) −448349. −0.166944 −0.0834722 0.996510i \(-0.526601\pi\)
−0.0834722 + 0.996510i \(0.526601\pi\)
\(140\) 859238. 0.313133
\(141\) 2.55168e6i 0.910269i
\(142\) 2.47872e6i 0.865689i
\(143\) 2.20256e6 0.753218
\(144\) −716912. −0.240092
\(145\) 5.32365e6 1.74625
\(146\) −3.21053e6 −1.03162
\(147\) 912441. 0.287245
\(148\) 677061.i 0.208854i
\(149\) 1.99524e6i 0.603166i 0.953440 + 0.301583i \(0.0975150\pi\)
−0.953440 + 0.301583i \(0.902485\pi\)
\(150\) 4.72540e6i 1.40012i
\(151\) 2.13822e6i 0.621042i 0.950567 + 0.310521i \(0.100503\pi\)
−0.950567 + 0.310521i \(0.899497\pi\)
\(152\) 251304.i 0.0715596i
\(153\) 776902. 0.216916
\(154\) −2.66046e6 −0.728442
\(155\) 1.07101e6i 0.287607i
\(156\) 321624.i 0.0847178i
\(157\) 4.26617e6i 1.10240i 0.834373 + 0.551200i \(0.185830\pi\)
−0.834373 + 0.551200i \(0.814170\pi\)
\(158\) 232361.i 0.0589104i
\(159\) −3.00685e6 −0.748033
\(160\) 3.54218e6i 0.864790i
\(161\) 281726.i 0.0675072i
\(162\) 415109.i 0.0976375i
\(163\) −5.52187e6 −1.27504 −0.637519 0.770434i \(-0.720039\pi\)
−0.637519 + 0.770434i \(0.720039\pi\)
\(164\) −1.93891e6 −0.439568
\(165\) 5.88095e6i 1.30917i
\(166\) 284997. 0.0623041
\(167\) −1.59986e6 −0.343505 −0.171753 0.985140i \(-0.554943\pi\)
−0.171753 + 0.985140i \(0.554943\pi\)
\(168\) 2.09372e6i 0.441562i
\(169\) 2.82443e6 0.585155
\(170\) 5.44750e6i 1.10879i
\(171\) −110546. −0.0221082
\(172\) 2.28930e6i 0.449902i
\(173\) 4.65918e6i 0.899852i 0.893066 + 0.449926i \(0.148550\pi\)
−0.893066 + 0.449926i \(0.851450\pi\)
\(174\) 2.40699e6i 0.456905i
\(175\) 1.04843e7 1.95625
\(176\) 4.59214e6i 0.842321i
\(177\) −229901. + 3.19328e6i −0.0414592 + 0.575860i
\(178\) 7.55405e6 1.33943
\(179\) 8.35387e6i 1.45656i −0.685280 0.728280i \(-0.740320\pi\)
0.685280 0.728280i \(-0.259680\pi\)
\(180\) 858751. 0.147248
\(181\) −2.85135e6 −0.480855 −0.240427 0.970667i \(-0.577288\pi\)
−0.240427 + 0.970667i \(0.577288\pi\)
\(182\) 2.41866e6 0.401199
\(183\) 5.30285e6i 0.865279i
\(184\) 640088. 0.102751
\(185\) 1.12549e7i 1.77758i
\(186\) −484237. −0.0752522
\(187\) 4.97641e6i 0.761011i
\(188\) 2.38669e6i 0.359189i
\(189\) −921004. −0.136419
\(190\) 775126.i 0.113009i
\(191\) 9.07270e6i 1.30208i 0.759045 + 0.651038i \(0.225666\pi\)
−0.759045 + 0.651038i \(0.774334\pi\)
\(192\) 4.54488e6 0.642124
\(193\) −7.29522e6 −1.01477 −0.507384 0.861720i \(-0.669387\pi\)
−0.507384 + 0.861720i \(0.669387\pi\)
\(194\) −1.02612e7 −1.40538
\(195\) 5.34643e6i 0.721042i
\(196\) −853443. −0.113346
\(197\) 777089. 0.101642 0.0508209 0.998708i \(-0.483816\pi\)
0.0508209 + 0.998708i \(0.483816\pi\)
\(198\) −2.65896e6 −0.342543
\(199\) 7.75894e6 0.984562 0.492281 0.870436i \(-0.336163\pi\)
0.492281 + 0.870436i \(0.336163\pi\)
\(200\) 2.38205e7i 2.97756i
\(201\) 3.70470e6i 0.456210i
\(202\) 1.85666e6 0.225257
\(203\) 5.34040e6 0.638389
\(204\) −726668. −0.0855944
\(205\) −3.22309e7 −3.74120
\(206\) −2.88519e6 −0.330044
\(207\) 281567.i 0.0317447i
\(208\) 4.17477e6i 0.463919i
\(209\) 708094.i 0.0775625i
\(210\) 6.45792e6i 0.697324i
\(211\) 7.35347e6i 0.782789i −0.920223 0.391395i \(-0.871993\pi\)
0.920223 0.391395i \(-0.128007\pi\)
\(212\) 2.81243e6 0.295171
\(213\) 5.49644e6 0.568777
\(214\) 7.80997e6i 0.796908i
\(215\) 3.80556e7i 3.82916i
\(216\) 2.09254e6i 0.207641i
\(217\) 1.07438e6i 0.105143i
\(218\) −1.47485e7 −1.42356
\(219\) 7.11919e6i 0.677795i
\(220\) 5.50069e6i 0.516594i
\(221\) 4.52411e6i 0.419137i
\(222\) −5.08870e6 −0.465102
\(223\) −1.21133e7 −1.09232 −0.546159 0.837682i \(-0.683911\pi\)
−0.546159 + 0.837682i \(0.683911\pi\)
\(224\) 3.55332e6i 0.316148i
\(225\) 1.04784e7 0.919910
\(226\) 1.87418e6 0.162362
\(227\) 1.74805e7i 1.49443i 0.664580 + 0.747217i \(0.268610\pi\)
−0.664580 + 0.747217i \(0.731390\pi\)
\(228\) 103398. 0.00872381
\(229\) 1.33528e7i 1.11190i 0.831215 + 0.555952i \(0.187646\pi\)
−0.831215 + 0.555952i \(0.812354\pi\)
\(230\) 1.97430e6 0.162267
\(231\) 5.89944e6i 0.478603i
\(232\) 1.21335e7i 0.971676i
\(233\) 2.01747e6i 0.159492i 0.996815 + 0.0797462i \(0.0254110\pi\)
−0.996815 + 0.0797462i \(0.974589\pi\)
\(234\) 2.41729e6 0.188660
\(235\) 3.96746e7i 3.05709i
\(236\) 215035. 2.98680e6i 0.0163597 0.227232i
\(237\) −515249. −0.0387054
\(238\) 5.46464e6i 0.405350i
\(239\) 1.26466e7 0.926361 0.463180 0.886264i \(-0.346708\pi\)
0.463180 + 0.886264i \(0.346708\pi\)
\(240\) 1.11468e7 0.806339
\(241\) 2.18434e7 1.56052 0.780261 0.625454i \(-0.215086\pi\)
0.780261 + 0.625454i \(0.215086\pi\)
\(242\) 4.57791e6i 0.323014i
\(243\) −920483. −0.0641500
\(244\) 4.95997e6i 0.341436i
\(245\) −1.41870e7 −0.964699
\(246\) 1.45726e7i 0.978885i
\(247\) 643736.i 0.0427186i
\(248\) 2.44101e6 0.160035
\(249\) 631968.i 0.0409352i
\(250\) 4.68494e7i 2.99836i
\(251\) 1.43275e7 0.906042 0.453021 0.891500i \(-0.350346\pi\)
0.453021 + 0.891500i \(0.350346\pi\)
\(252\) 861452. 0.0538307
\(253\) 1.80356e6 0.111370
\(254\) 1.22997e7i 0.750571i
\(255\) −1.20796e7 −0.728503
\(256\) −1.08262e7 −0.645295
\(257\) −8.65834e6 −0.510076 −0.255038 0.966931i \(-0.582088\pi\)
−0.255038 + 0.966931i \(0.582088\pi\)
\(258\) −1.72061e7 −1.00190
\(259\) 1.12903e7i 0.649842i
\(260\) 5.00074e6i 0.284521i
\(261\) 5.33737e6 0.300197
\(262\) −1.31628e6 −0.0731888
\(263\) −1.37885e7 −0.757965 −0.378982 0.925404i \(-0.623726\pi\)
−0.378982 + 0.925404i \(0.623726\pi\)
\(264\) 1.34036e7 0.728469
\(265\) 4.67517e7 2.51223
\(266\) 777564.i 0.0413134i
\(267\) 1.67507e7i 0.880036i
\(268\) 3.46516e6i 0.180019i
\(269\) 5.67928e6i 0.291767i −0.989302 0.145884i \(-0.953398\pi\)
0.989302 0.145884i \(-0.0466025\pi\)
\(270\) 6.45427e6i 0.327911i
\(271\) 1.92958e7 0.969515 0.484757 0.874649i \(-0.338908\pi\)
0.484757 + 0.874649i \(0.338908\pi\)
\(272\) −9.43235e6 −0.468720
\(273\) 5.36325e6i 0.263597i
\(274\) 1.42374e7i 0.692118i
\(275\) 6.71185e7i 3.22734i
\(276\) 263361.i 0.0125263i
\(277\) −2.29460e6 −0.107961 −0.0539805 0.998542i \(-0.517191\pi\)
−0.0539805 + 0.998542i \(0.517191\pi\)
\(278\) 3.15185e6i 0.146700i
\(279\) 1.07377e6i 0.0494424i
\(280\) 3.25540e7i 1.48296i
\(281\) −5.95760e6 −0.268505 −0.134252 0.990947i \(-0.542863\pi\)
−0.134252 + 0.990947i \(0.542863\pi\)
\(282\) 1.79381e7 0.799887
\(283\) 4.14139e6i 0.182720i −0.995818 0.0913602i \(-0.970879\pi\)
0.995818 0.0913602i \(-0.0291214\pi\)
\(284\) −5.14104e6 −0.224438
\(285\) 1.71880e6 0.0742492
\(286\) 1.54838e7i 0.661880i
\(287\) −3.23323e7 −1.36770
\(288\) 3.55131e6i 0.148666i
\(289\) −1.39159e7 −0.576526
\(290\) 3.74247e7i 1.53449i
\(291\) 2.27538e7i 0.923367i
\(292\) 6.65887e6i 0.267456i
\(293\) −1.53783e7 −0.611372 −0.305686 0.952132i \(-0.598886\pi\)
−0.305686 + 0.952132i \(0.598886\pi\)
\(294\) 6.41437e6i 0.252413i
\(295\) 3.57459e6 4.96503e7i 0.139239 1.93400i
\(296\) 2.56519e7 0.989108
\(297\) 5.89611e6i 0.225059i
\(298\) 1.40264e7 0.530025
\(299\) −1.63964e6 −0.0613387
\(300\) −9.80083e6 −0.362994
\(301\) 3.81753e7i 1.39985i
\(302\) 1.50314e7 0.545733
\(303\) 4.11705e6i 0.147999i
\(304\) 1.34213e6 0.0477721
\(305\) 8.24508e7i 2.90600i
\(306\) 5.46154e6i 0.190612i
\(307\) 1.16956e7 0.404210 0.202105 0.979364i \(-0.435222\pi\)
0.202105 + 0.979364i \(0.435222\pi\)
\(308\) 5.51799e6i 0.188855i
\(309\) 6.39776e6i 0.216846i
\(310\) 7.52910e6 0.252731
\(311\) 4.23584e7 1.40818 0.704090 0.710110i \(-0.251355\pi\)
0.704090 + 0.710110i \(0.251355\pi\)
\(312\) −1.21854e7 −0.401214
\(313\) 1.68961e7i 0.551002i −0.961301 0.275501i \(-0.911156\pi\)
0.961301 0.275501i \(-0.0888437\pi\)
\(314\) 2.99908e7 0.968721
\(315\) 1.43201e7 0.458158
\(316\) 481933. 0.0152730
\(317\) −1.41974e7 −0.445688 −0.222844 0.974854i \(-0.571534\pi\)
−0.222844 + 0.974854i \(0.571534\pi\)
\(318\) 2.11379e7i 0.657325i
\(319\) 3.41883e7i 1.05319i
\(320\) −7.06656e7 −2.15654
\(321\) −1.73182e7 −0.523587
\(322\) 1.98051e6 0.0593211
\(323\) −1.45444e6 −0.0431606
\(324\) 860965. 0.0253134
\(325\) 6.10182e7i 1.77750i
\(326\) 3.88182e7i 1.12042i
\(327\) 3.27040e7i 0.935314i
\(328\) 7.34596e7i 2.08174i
\(329\) 3.97993e7i 1.11760i
\(330\) 4.13425e7 1.15042
\(331\) −5.51311e7 −1.52024 −0.760121 0.649781i \(-0.774860\pi\)
−0.760121 + 0.649781i \(0.774860\pi\)
\(332\) 591105.i 0.0161529i
\(333\) 1.12840e7i 0.305583i
\(334\) 1.12469e7i 0.301851i
\(335\) 5.76021e7i 1.53216i
\(336\) 1.11819e7 0.294779
\(337\) 6.03833e7i 1.57771i 0.614580 + 0.788855i \(0.289326\pi\)
−0.614580 + 0.788855i \(0.710674\pi\)
\(338\) 1.98555e7i 0.514198i
\(339\) 4.15589e6i 0.106676i
\(340\) 1.12985e7 0.287465
\(341\) 6.87799e6 0.173460
\(342\) 777124.i 0.0194273i
\(343\) −4.28365e7 −1.06153
\(344\) 8.67350e7 2.13068
\(345\) 4.37791e6i 0.106613i
\(346\) 3.27536e7 0.790734
\(347\) 8.76068e6i 0.209676i 0.994489 + 0.104838i \(0.0334325\pi\)
−0.994489 + 0.104838i \(0.966568\pi\)
\(348\) −4.99226e6 −0.118457
\(349\) 4.14009e7i 0.973943i 0.873418 + 0.486971i \(0.161898\pi\)
−0.873418 + 0.486971i \(0.838102\pi\)
\(350\) 7.37035e7i 1.71903i
\(351\) 5.36021e6i 0.123954i
\(352\) −2.27477e7 −0.521567
\(353\) 3.12584e7i 0.710629i 0.934747 + 0.355315i \(0.115626\pi\)
−0.934747 + 0.355315i \(0.884374\pi\)
\(354\) 2.24484e7 + 1.61618e6i 0.506030 + 0.0364317i
\(355\) −8.54607e7 −1.91021
\(356\) 1.56676e7i 0.347259i
\(357\) −1.21176e7 −0.266324
\(358\) −5.87268e7 −1.27993
\(359\) −2.79538e7 −0.604168 −0.302084 0.953281i \(-0.597682\pi\)
−0.302084 + 0.953281i \(0.597682\pi\)
\(360\) 3.25356e7i 0.697351i
\(361\) −4.68389e7 −0.995601
\(362\) 2.00447e7i 0.422545i
\(363\) 1.01513e7 0.212227
\(364\) 5.01646e6i 0.104014i
\(365\) 1.10692e8i 2.27634i
\(366\) −3.72785e7 −0.760353
\(367\) 1.31779e7i 0.266592i −0.991076 0.133296i \(-0.957444\pi\)
0.991076 0.133296i \(-0.0425562\pi\)
\(368\) 3.41850e6i 0.0685949i
\(369\) −3.23140e7 −0.643149
\(370\) 7.91211e7 1.56202
\(371\) 4.68987e7 0.918416
\(372\) 1.00434e6i 0.0195098i
\(373\) 4.74124e7 0.913619 0.456810 0.889564i \(-0.348992\pi\)
0.456810 + 0.889564i \(0.348992\pi\)
\(374\) −3.49836e7 −0.668729
\(375\) −1.03886e8 −1.96999
\(376\) −9.04248e7 −1.70108
\(377\) 3.10809e7i 0.580056i
\(378\) 6.47457e6i 0.119877i
\(379\) 8.30070e7 1.52475 0.762373 0.647138i \(-0.224034\pi\)
0.762373 + 0.647138i \(0.224034\pi\)
\(380\) −1.60767e6 −0.0292985
\(381\) 2.72739e7 0.493142
\(382\) 6.37801e7 1.14418
\(383\) −5.00229e7 −0.890375 −0.445187 0.895437i \(-0.646863\pi\)
−0.445187 + 0.895437i \(0.646863\pi\)
\(384\) 1.73698e7i 0.306762i
\(385\) 9.17268e7i 1.60736i
\(386\) 5.12847e7i 0.891715i
\(387\) 3.81537e7i 0.658269i
\(388\) 2.12825e7i 0.364358i
\(389\) 5.23965e7 0.890131 0.445065 0.895498i \(-0.353180\pi\)
0.445065 + 0.895498i \(0.353180\pi\)
\(390\) −3.75849e7 −0.633606
\(391\) 3.70455e6i 0.0619734i
\(392\) 3.23344e7i 0.536794i
\(393\) 2.91879e6i 0.0480867i
\(394\) 5.46286e6i 0.0893164i
\(395\) 8.01129e6 0.129990
\(396\) 5.51487e6i 0.0888074i
\(397\) 3.41681e6i 0.0546072i 0.999627 + 0.0273036i \(0.00869209\pi\)
−0.999627 + 0.0273036i \(0.991308\pi\)
\(398\) 5.45446e7i 0.865172i
\(399\) 1.72421e6 0.0271439
\(400\) −1.27217e8 −1.98777
\(401\) 1.60966e7i 0.249633i 0.992180 + 0.124817i \(0.0398342\pi\)
−0.992180 + 0.124817i \(0.960166\pi\)
\(402\) 2.60437e7 0.400889
\(403\) −6.25286e6 −0.0955352
\(404\) 3.85084e6i 0.0583998i
\(405\) 1.43120e7 0.215445
\(406\) 3.75424e7i 0.560976i
\(407\) 7.22788e7 1.07208
\(408\) 2.75313e7i 0.405365i
\(409\) 6.15574e7i 0.899726i 0.893097 + 0.449863i \(0.148527\pi\)
−0.893097 + 0.449863i \(0.851473\pi\)
\(410\) 2.26580e8i 3.28754i
\(411\) 3.15708e7 0.454737
\(412\) 5.98408e6i 0.0855669i
\(413\) 3.58583e6 4.98064e7i 0.0509025 0.707026i
\(414\) 1.97939e6 0.0278952
\(415\) 9.82607e6i 0.137479i
\(416\) 2.06802e7 0.287260
\(417\) 6.98907e6 0.0963854
\(418\) 4.97783e6 0.0681571
\(419\) 8.43328e7i 1.14645i 0.819399 + 0.573224i \(0.194308\pi\)
−0.819399 + 0.573224i \(0.805692\pi\)
\(420\) −1.33942e7 −0.180788
\(421\) 1.10031e8i 1.47458i 0.675578 + 0.737288i \(0.263894\pi\)
−0.675578 + 0.737288i \(0.736106\pi\)
\(422\) −5.16941e7 −0.687866
\(423\) 3.97768e7i 0.525544i
\(424\) 1.06555e8i 1.39790i
\(425\) 1.37863e8 1.79589
\(426\) 3.86394e7i 0.499806i
\(427\) 8.27101e7i 1.06237i
\(428\) 1.61984e7 0.206606
\(429\) −3.43346e7 −0.434870
\(430\) 2.67527e8 3.36482
\(431\) 7.18805e7i 0.897799i −0.893582 0.448900i \(-0.851816\pi\)
0.893582 0.448900i \(-0.148184\pi\)
\(432\) 1.11756e7 0.138617
\(433\) −7.25464e7 −0.893618 −0.446809 0.894629i \(-0.647440\pi\)
−0.446809 + 0.894629i \(0.647440\pi\)
\(434\) 7.55278e6 0.0923927
\(435\) −8.29875e7 −1.00820
\(436\) 3.05894e7i 0.369072i
\(437\) 527121.i 0.00631635i
\(438\) 5.00472e7 0.595604
\(439\) 1.41616e7 0.167386 0.0836930 0.996492i \(-0.473328\pi\)
0.0836930 + 0.996492i \(0.473328\pi\)
\(440\) −2.08405e8 −2.44653
\(441\) −1.42235e7 −0.165841
\(442\) 3.18040e7 0.368311
\(443\) 1.02675e8i 1.18101i 0.807034 + 0.590504i \(0.201071\pi\)
−0.807034 + 0.590504i \(0.798929\pi\)
\(444\) 1.05543e7i 0.120582i
\(445\) 2.60447e8i 2.95556i
\(446\) 8.51555e7i 0.959861i
\(447\) 3.11028e7i 0.348238i
\(448\) −7.08878e7 −0.788384
\(449\) 2.43759e7 0.269290 0.134645 0.990894i \(-0.457011\pi\)
0.134645 + 0.990894i \(0.457011\pi\)
\(450\) 7.36618e7i 0.808360i
\(451\) 2.06986e8i 2.25637i
\(452\) 3.88718e6i 0.0420939i
\(453\) 3.33315e7i 0.358559i
\(454\) 1.22886e8 1.31322
\(455\) 8.33899e7i 0.885277i
\(456\) 3.91744e6i 0.0413150i
\(457\) 5.10616e7i 0.534990i −0.963559 0.267495i \(-0.913804\pi\)
0.963559 0.267495i \(-0.0861959\pi\)
\(458\) 9.38691e7 0.977071
\(459\) −1.21107e7 −0.125237
\(460\) 4.09484e6i 0.0420691i
\(461\) −1.05217e8 −1.07395 −0.536976 0.843598i \(-0.680433\pi\)
−0.536976 + 0.843598i \(0.680433\pi\)
\(462\) 4.14725e7 0.420566
\(463\) 9.27594e7i 0.934577i 0.884105 + 0.467288i \(0.154769\pi\)
−0.884105 + 0.467288i \(0.845231\pi\)
\(464\) −6.48009e7 −0.648675
\(465\) 1.66954e7i 0.166050i
\(466\) 1.41826e7 0.140152
\(467\) 9.12870e7i 0.896310i 0.893956 + 0.448155i \(0.147919\pi\)
−0.893956 + 0.448155i \(0.852081\pi\)
\(468\) 5.01362e6i 0.0489119i
\(469\) 5.77833e7i 0.560124i
\(470\) −2.78908e8 −2.68638
\(471\) 6.65031e7i 0.636471i
\(472\) −1.13161e8 8.14707e6i −1.07615 0.0774774i
\(473\) 2.44391e8 2.30942
\(474\) 3.62215e6i 0.0340119i
\(475\) −1.96165e7 −0.183038
\(476\) 1.13340e7 0.105091
\(477\) 4.68722e7 0.431877
\(478\) 8.89044e7i 0.814028i
\(479\) 1.64950e8 1.50088 0.750441 0.660938i \(-0.229841\pi\)
0.750441 + 0.660938i \(0.229841\pi\)
\(480\) 5.52171e7i 0.499287i
\(481\) −6.57094e7 −0.590463
\(482\) 1.53557e8i 1.37129i
\(483\) 4.39168e6i 0.0389753i
\(484\) −9.49492e6 −0.0837443
\(485\) 3.53784e8i 3.10108i
\(486\) 6.47090e6i 0.0563710i
\(487\) −1.45605e8 −1.26063 −0.630315 0.776339i \(-0.717074\pi\)
−0.630315 + 0.776339i \(0.717074\pi\)
\(488\) 1.87919e8 1.61700
\(489\) 8.60775e7 0.736144
\(490\) 9.97330e7i 0.847717i
\(491\) 1.50309e8 1.26981 0.634907 0.772589i \(-0.281038\pi\)
0.634907 + 0.772589i \(0.281038\pi\)
\(492\) 3.02246e7 0.253785
\(493\) 7.02233e7 0.586058
\(494\) −4.52540e6 −0.0375384
\(495\) 9.16749e7i 0.755849i
\(496\) 1.30366e7i 0.106837i
\(497\) −8.57295e7 −0.698331
\(498\) −4.44267e6 −0.0359713
\(499\) 7.21471e7 0.580654 0.290327 0.956927i \(-0.406236\pi\)
0.290327 + 0.956927i \(0.406236\pi\)
\(500\) 9.71689e7 0.777351
\(501\) 2.49394e7 0.198323
\(502\) 1.00721e8i 0.796173i
\(503\) 1.37613e8i 1.08132i −0.841240 0.540662i \(-0.818174\pi\)
0.841240 0.540662i \(-0.181826\pi\)
\(504\) 3.26379e7i 0.254936i
\(505\) 6.40134e7i 0.497046i
\(506\) 1.26789e7i 0.0978653i
\(507\) −4.40286e7 −0.337840
\(508\) −2.55104e7 −0.194592
\(509\) 9.86537e7i 0.748101i 0.927408 + 0.374050i \(0.122031\pi\)
−0.927408 + 0.374050i \(0.877969\pi\)
\(510\) 8.49182e7i 0.640162i
\(511\) 1.11040e8i 0.832180i
\(512\) 1.47421e8i 1.09837i
\(513\) 1.72323e6 0.0127642
\(514\) 6.08672e7i 0.448223i
\(515\) 9.94748e7i 0.728268i
\(516\) 3.56867e7i 0.259751i
\(517\) −2.54788e8 −1.84378
\(518\) 7.93700e7 0.571041
\(519\) 7.26294e7i 0.519530i
\(520\) 1.89463e8 1.34746
\(521\) −1.22686e8 −0.867524 −0.433762 0.901028i \(-0.642814\pi\)
−0.433762 + 0.901028i \(0.642814\pi\)
\(522\) 3.75212e7i 0.263794i
\(523\) 1.06812e8 0.746645 0.373323 0.927702i \(-0.378218\pi\)
0.373323 + 0.927702i \(0.378218\pi\)
\(524\) 2.73006e6i 0.0189749i
\(525\) −1.63434e8 −1.12944
\(526\) 9.69316e7i 0.666052i
\(527\) 1.41275e7i 0.0965237i
\(528\) 7.15844e7i 0.486314i
\(529\) 1.46693e8 0.990930
\(530\) 3.28660e8i 2.20759i
\(531\) 3.58380e6 4.97783e7i 0.0239365 0.332473i
\(532\) −1.61272e6 −0.0107109
\(533\) 1.88173e8i 1.24273i
\(534\) −1.17756e8 −0.773320
\(535\) 2.69271e8 1.75844
\(536\) −1.31285e8 −0.852550
\(537\) 1.30224e8i 0.840945i
\(538\) −3.99248e7 −0.256387
\(539\) 9.11082e7i 0.581823i
\(540\) −1.33866e7 −0.0850138
\(541\) 8.06570e7i 0.509390i 0.967021 + 0.254695i \(0.0819750\pi\)
−0.967021 + 0.254695i \(0.918025\pi\)
\(542\) 1.35647e8i 0.851949i
\(543\) 4.44481e7 0.277622
\(544\) 4.67242e7i 0.290232i
\(545\) 5.08494e8i 3.14121i
\(546\) −3.77031e7 −0.231632
\(547\) −8.28546e7 −0.506238 −0.253119 0.967435i \(-0.581456\pi\)
−0.253119 + 0.967435i \(0.581456\pi\)
\(548\) −2.95295e7 −0.179438
\(549\) 8.26633e7i 0.499569i
\(550\) −4.71837e8 −2.83598
\(551\) −9.99209e6 −0.0597312
\(552\) −9.97798e6 −0.0593233
\(553\) 8.03648e6 0.0475216
\(554\) 1.61308e7i 0.0948694i
\(555\) 1.75447e8i 1.02628i
\(556\) −6.53716e6 −0.0380334
\(557\) −1.37517e8 −0.795774 −0.397887 0.917434i \(-0.630256\pi\)
−0.397887 + 0.917434i \(0.630256\pi\)
\(558\) 7.54851e6 0.0434469
\(559\) −2.22179e8 −1.27194
\(560\) −1.73860e8 −0.990002
\(561\) 7.75745e7i 0.439370i
\(562\) 4.18813e7i 0.235945i
\(563\) 6.42052e6i 0.0359786i 0.999838 + 0.0179893i \(0.00572649\pi\)
−0.999838 + 0.0179893i \(0.994274\pi\)
\(564\) 3.72049e7i 0.207378i
\(565\) 6.46174e7i 0.358265i
\(566\) −2.91136e7 −0.160563
\(567\) 1.43570e7 0.0787618
\(568\) 1.94779e8i 1.06291i
\(569\) 9.06946e7i 0.492317i 0.969230 + 0.246158i \(0.0791684\pi\)
−0.969230 + 0.246158i \(0.920832\pi\)
\(570\) 1.20830e7i 0.0652456i
\(571\) 5.56109e7i 0.298711i −0.988784 0.149356i \(-0.952280\pi\)
0.988784 0.149356i \(-0.0477199\pi\)
\(572\) 3.21145e7 0.171598
\(573\) 1.41429e8i 0.751754i
\(574\) 2.27293e8i 1.20185i
\(575\) 4.99646e7i 0.262820i
\(576\) −7.08477e7 −0.370731
\(577\) 1.05665e8 0.550050 0.275025 0.961437i \(-0.411314\pi\)
0.275025 + 0.961437i \(0.411314\pi\)
\(578\) 9.78277e7i 0.506615i
\(579\) 1.13721e8 0.585877
\(580\) 7.76216e7 0.397831
\(581\) 9.85698e6i 0.0502592i
\(582\) 1.59957e8 0.811397
\(583\) 3.00237e8i 1.51516i
\(584\) −2.52285e8 −1.26664
\(585\) 8.33427e7i 0.416294i
\(586\) 1.08108e8i 0.537236i
\(587\) 3.43340e8i 1.69750i −0.528792 0.848752i \(-0.677355\pi\)
0.528792 0.848752i \(-0.322645\pi\)
\(588\) 1.33039e7 0.0654403
\(589\) 2.01021e6i 0.00983773i
\(590\) −3.49037e8 2.51290e7i −1.69948 0.122354i
\(591\) −1.21136e7 −0.0586829
\(592\) 1.36998e8i 0.660312i
\(593\) 2.14834e8 1.03024 0.515121 0.857118i \(-0.327747\pi\)
0.515121 + 0.857118i \(0.327747\pi\)
\(594\) 4.14490e7 0.197768
\(595\) 1.88409e8 0.894437
\(596\) 2.90917e7i 0.137414i
\(597\) −1.20950e8 −0.568437
\(598\) 1.15265e7i 0.0539006i
\(599\) −3.49377e8 −1.62560 −0.812800 0.582543i \(-0.802058\pi\)
−0.812800 + 0.582543i \(0.802058\pi\)
\(600\) 3.71325e8i 1.71910i
\(601\) 1.07047e8i 0.493117i 0.969128 + 0.246558i \(0.0792997\pi\)
−0.969128 + 0.246558i \(0.920700\pi\)
\(602\) 2.68369e8 1.23010
\(603\) 5.77506e7i 0.263393i
\(604\) 3.11763e7i 0.141486i
\(605\) −1.57836e8 −0.712755
\(606\) −2.89424e7 −0.130052
\(607\) 1.14105e8 0.510197 0.255098 0.966915i \(-0.417892\pi\)
0.255098 + 0.966915i \(0.417892\pi\)
\(608\) 6.64840e6i 0.0295806i
\(609\) −8.32485e7 −0.368574
\(610\) 5.79621e8 2.55361
\(611\) 2.31631e8 1.01548
\(612\) 1.13276e7 0.0494180
\(613\) 2.88932e8i 1.25434i −0.778884 0.627169i \(-0.784214\pi\)
0.778884 0.627169i \(-0.215786\pi\)
\(614\) 8.22189e7i 0.355195i
\(615\) 5.02431e8 2.15998
\(616\) −2.09060e8 −0.894396
\(617\) −2.75011e8 −1.17083 −0.585415 0.810734i \(-0.699068\pi\)
−0.585415 + 0.810734i \(0.699068\pi\)
\(618\) 4.49756e7 0.190551
\(619\) −3.55949e8 −1.50078 −0.750388 0.660998i \(-0.770133\pi\)
−0.750388 + 0.660998i \(0.770133\pi\)
\(620\) 1.56159e7i 0.0655227i
\(621\) 4.38919e6i 0.0183278i
\(622\) 2.97775e8i 1.23742i
\(623\) 2.61266e8i 1.08049i
\(624\) 6.50782e7i 0.267844i
\(625\) 9.41500e8 3.85638
\(626\) −1.18778e8 −0.484186
\(627\) 1.10381e7i 0.0447807i
\(628\) 6.22030e7i 0.251150i
\(629\) 1.48462e8i 0.596572i
\(630\) 1.00669e8i 0.402600i
\(631\) −1.67383e8 −0.666228 −0.333114 0.942887i \(-0.608099\pi\)
−0.333114 + 0.942887i \(0.608099\pi\)
\(632\) 1.82590e7i 0.0723314i
\(633\) 1.14629e8i 0.451944i
\(634\) 9.98063e7i 0.391643i
\(635\) −4.24065e8 −1.65619
\(636\) −4.38415e7 −0.170417
\(637\) 8.28274e7i 0.320447i
\(638\) −2.40340e8 −0.925474
\(639\) −8.56810e7 −0.328384
\(640\) 2.70073e8i 1.03024i
\(641\) −2.37255e8 −0.900826 −0.450413 0.892820i \(-0.648723\pi\)
−0.450413 + 0.892820i \(0.648723\pi\)
\(642\) 1.21745e8i 0.460095i
\(643\) 6.55653e7 0.246627 0.123314 0.992368i \(-0.460648\pi\)
0.123314 + 0.992368i \(0.460648\pi\)
\(644\) 4.10772e6i 0.0153795i
\(645\) 5.93228e8i 2.21077i
\(646\) 1.02245e7i 0.0379268i
\(647\) −3.23977e8 −1.19619 −0.598096 0.801425i \(-0.704076\pi\)
−0.598096 + 0.801425i \(0.704076\pi\)
\(648\) 3.26194e7i 0.119881i
\(649\) −3.18852e8 2.29558e7i −1.16642 0.0839767i
\(650\) 4.28952e8 1.56195
\(651\) 1.67479e7i 0.0607041i
\(652\) −8.05117e7 −0.290480
\(653\) 3.44498e8 1.23722 0.618611 0.785697i \(-0.287696\pi\)
0.618611 + 0.785697i \(0.287696\pi\)
\(654\) 2.29906e8 0.821896
\(655\) 4.53824e7i 0.161497i
\(656\) 3.92323e8 1.38974
\(657\) 1.10977e8i 0.391325i
\(658\) −2.79785e8 −0.982081
\(659\) 9.99031e7i 0.349078i 0.984650 + 0.174539i \(0.0558436\pi\)
−0.984650 + 0.174539i \(0.944156\pi\)
\(660\) 8.57472e7i 0.298255i
\(661\) 2.49357e8 0.863409 0.431705 0.902015i \(-0.357912\pi\)
0.431705 + 0.902015i \(0.357912\pi\)
\(662\) 3.87566e8i 1.33589i
\(663\) 7.05238e7i 0.241989i
\(664\) 2.23952e7 0.0764982
\(665\) −2.68087e7 −0.0911613
\(666\) 7.93250e7 0.268527
\(667\) 2.54505e7i 0.0857668i
\(668\) −2.33268e7 −0.0782575
\(669\) 1.88828e8 0.630650
\(670\) −4.04937e8 −1.34637
\(671\) 5.29495e8 1.75265
\(672\) 5.53908e7i 0.182528i
\(673\) 9.58193e6i 0.0314346i 0.999876 + 0.0157173i \(0.00500317\pi\)
−0.999876 + 0.0157173i \(0.994997\pi\)
\(674\) 4.24488e8 1.38639
\(675\) −1.63341e8 −0.531110
\(676\) 4.11817e7 0.133310
\(677\) −4.60108e8 −1.48284 −0.741420 0.671042i \(-0.765847\pi\)
−0.741420 + 0.671042i \(0.765847\pi\)
\(678\) −2.92155e7 −0.0937399
\(679\) 3.54897e8i 1.13369i
\(680\) 4.28068e8i 1.36140i
\(681\) 2.72494e8i 0.862812i
\(682\) 4.83516e7i 0.152425i
\(683\) 3.83112e8i 1.20244i 0.799083 + 0.601221i \(0.205319\pi\)
−0.799083 + 0.601221i \(0.794681\pi\)
\(684\) −1.61181e6 −0.00503670
\(685\) −4.90875e8 −1.52721
\(686\) 3.01136e8i 0.932805i
\(687\) 2.08150e8i 0.641958i
\(688\) 4.63223e8i 1.42241i
\(689\) 2.72949e8i 0.834496i
\(690\) −3.07763e7 −0.0936847
\(691\) 3.91705e8i 1.18720i 0.804759 + 0.593602i \(0.202294\pi\)
−0.804759 + 0.593602i \(0.797706\pi\)
\(692\) 6.79332e7i 0.205005i
\(693\) 9.19632e7i 0.276321i
\(694\) 6.15867e7 0.184250
\(695\) −1.08669e8 −0.323706
\(696\) 1.89142e8i 0.560997i
\(697\) −4.25152e8 −1.25559
\(698\) 2.91044e8 0.855840
\(699\) 3.14493e7i 0.0920829i
\(700\) 1.52866e8 0.445674
\(701\) 5.84516e8i 1.69685i −0.529318 0.848423i \(-0.677552\pi\)
0.529318 0.848423i \(-0.322448\pi\)
\(702\) −3.76818e7 −0.108923
\(703\) 2.11247e7i 0.0608029i
\(704\) 4.53811e8i 1.30064i
\(705\) 6.18465e8i 1.76501i
\(706\) 2.19744e8 0.624456
\(707\) 6.42148e7i 0.181709i
\(708\) −3.35207e6 + 4.65596e7i −0.00944525 + 0.131193i
\(709\) 1.79681e8 0.504154 0.252077 0.967707i \(-0.418886\pi\)
0.252077 + 0.967707i \(0.418886\pi\)
\(710\) 6.00780e8i 1.67857i
\(711\) 8.03193e6 0.0223466
\(712\) 5.93601e8 1.64458
\(713\) −5.12013e6 −0.0141258
\(714\) 8.51853e7i 0.234029i
\(715\) 5.33847e8 1.46049
\(716\) 1.21804e8i 0.331834i
\(717\) −1.97141e8 −0.534835
\(718\) 1.96512e8i 0.530905i
\(719\) 4.43984e7i 0.119448i 0.998215 + 0.0597242i \(0.0190221\pi\)
−0.998215 + 0.0597242i \(0.980978\pi\)
\(720\) −1.73762e8 −0.465540
\(721\) 9.97877e7i 0.266239i
\(722\) 3.29273e8i 0.874872i
\(723\) −3.40505e8 −0.900968
\(724\) −4.15741e7 −0.109549
\(725\) 9.47127e8 2.48539
\(726\) 7.13626e7i 0.186492i
\(727\) −1.40640e8 −0.366021 −0.183011 0.983111i \(-0.558584\pi\)
−0.183011 + 0.983111i \(0.558584\pi\)
\(728\) 1.90059e8 0.492600
\(729\) 1.43489e7 0.0370370
\(730\) −7.78153e8 −2.00031
\(731\) 5.01985e8i 1.28510i
\(732\) 7.73183e7i 0.197128i
\(733\) 3.63182e8 0.922173 0.461087 0.887355i \(-0.347460\pi\)
0.461087 + 0.887355i \(0.347460\pi\)
\(734\) −9.26393e7 −0.234265
\(735\) 2.21153e8 0.556969
\(736\) 1.69339e7 0.0424741
\(737\) −3.69918e8 −0.924067
\(738\) 2.27164e8i 0.565159i
\(739\) 5.57713e6i 0.0138190i −0.999976 0.00690951i \(-0.997801\pi\)
0.999976 0.00690951i \(-0.00219938\pi\)
\(740\) 1.64103e8i 0.404968i
\(741\) 1.00348e7i 0.0246636i
\(742\) 3.29693e8i 0.807047i
\(743\) 3.32916e8 0.811648 0.405824 0.913951i \(-0.366985\pi\)
0.405824 + 0.913951i \(0.366985\pi\)
\(744\) −3.80516e7 −0.0923962
\(745\) 4.83597e8i 1.16954i
\(746\) 3.33304e8i 0.802832i
\(747\) 9.85140e6i 0.0236339i
\(748\) 7.25586e7i 0.173374i
\(749\) 2.70117e8 0.642846
\(750\) 7.30309e8i 1.73110i
\(751\) 3.17334e8i 0.749199i −0.927187 0.374599i \(-0.877780\pi\)
0.927187 0.374599i \(-0.122220\pi\)
\(752\) 4.82929e8i 1.13561i
\(753\) −2.23343e8 −0.523104
\(754\) 2.18496e8 0.509717
\(755\) 5.18251e8i 1.20420i
\(756\) −1.34287e7 −0.0310791
\(757\) −4.60544e8 −1.06165 −0.530827 0.847480i \(-0.678119\pi\)
−0.530827 + 0.847480i \(0.678119\pi\)
\(758\) 5.83531e8i 1.33985i
\(759\) −2.81148e7 −0.0642997
\(760\) 6.09098e7i 0.138754i
\(761\) 6.75942e8 1.53375 0.766877 0.641795i \(-0.221810\pi\)
0.766877 + 0.641795i \(0.221810\pi\)
\(762\) 1.91733e8i 0.433343i
\(763\) 5.10094e8i 1.14836i
\(764\) 1.32285e8i 0.296640i
\(765\) 1.88302e8 0.420601
\(766\) 3.51656e8i 0.782405i
\(767\) 2.89872e8 + 2.08694e7i 0.642421 + 0.0462513i
\(768\) 1.68764e8 0.372561
\(769\) 6.34399e8i 1.39503i 0.716571 + 0.697514i \(0.245711\pi\)
−0.716571 + 0.697514i \(0.754289\pi\)
\(770\) −6.44830e8 −1.41245
\(771\) 1.34970e8 0.294493
\(772\) −1.06368e8 −0.231185
\(773\) 8.78120e8i 1.90115i −0.310501 0.950573i \(-0.600497\pi\)
0.310501 0.950573i \(-0.399503\pi\)
\(774\) 2.68217e8 0.578446
\(775\) 1.90543e8i 0.409343i
\(776\) −8.06333e8 −1.72556
\(777\) 1.75999e8i 0.375186i
\(778\) 3.68342e8i 0.782191i
\(779\) 6.04950e7 0.127970
\(780\) 7.79538e7i 0.164268i
\(781\) 5.48825e8i 1.15207i
\(782\) 2.60426e7 0.0544583
\(783\) −8.32014e7 −0.173319
\(784\) 1.72688e8 0.358355
\(785\) 1.03402e9i 2.13756i
\(786\)