Properties

Label 177.11.c.a.58.7
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.7
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.94

$q$-expansion

\(f(q)\) \(=\) \(q-56.3537i q^{2} -140.296 q^{3} -2151.73 q^{4} +3579.32 q^{5} +7906.20i q^{6} +7609.79 q^{7} +63551.9i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-56.3537i q^{2} -140.296 q^{3} -2151.73 q^{4} +3579.32 q^{5} +7906.20i q^{6} +7609.79 q^{7} +63551.9i q^{8} +19683.0 q^{9} -201708. i q^{10} +312528. i q^{11} +301880. q^{12} -359669. i q^{13} -428840. i q^{14} -502165. q^{15} +1.37801e6 q^{16} +567921. q^{17} -1.10921e6i q^{18} -397324. q^{19} -7.70175e6 q^{20} -1.06762e6 q^{21} +1.76121e7 q^{22} -1.14802e7i q^{23} -8.91609e6i q^{24} +3.04592e6 q^{25} -2.02686e7 q^{26} -2.76145e6 q^{27} -1.63743e7 q^{28} -1.45674e6 q^{29} +2.82988e7i q^{30} -1.04454e7i q^{31} -1.25786e7i q^{32} -4.38465e7i q^{33} -3.20044e7i q^{34} +2.72379e7 q^{35} -4.23526e7 q^{36} +1.11352e8i q^{37} +2.23906e7i q^{38} +5.04601e7i q^{39} +2.27473e8i q^{40} -1.09214e8 q^{41} +6.01645e7i q^{42} +2.71906e8i q^{43} -6.72478e8i q^{44} +7.04518e7 q^{45} -6.46953e8 q^{46} +1.44150e8i q^{47} -1.93329e8 q^{48} -2.24566e8 q^{49} -1.71649e8i q^{50} -7.96771e7 q^{51} +7.73911e8i q^{52} +1.14733e8 q^{53} +1.55618e8i q^{54} +1.11864e9i q^{55} +4.83617e8i q^{56} +5.57430e7 q^{57} +8.20924e7i q^{58} +(-7.13172e8 - 5.00283e7i) q^{59} +1.08053e9 q^{60} -7.51127e8i q^{61} -5.88636e8 q^{62} +1.49784e8 q^{63} +7.02230e8 q^{64} -1.28737e9i q^{65} -2.47091e9 q^{66} +6.46732e8i q^{67} -1.22201e9 q^{68} +1.61063e9i q^{69} -1.53495e9i q^{70} -1.38039e9 q^{71} +1.25089e9i q^{72} +2.57637e9i q^{73} +6.27507e9 q^{74} -4.27330e8 q^{75} +8.54935e8 q^{76} +2.37828e9i q^{77} +2.84361e9 q^{78} +4.01132e9 q^{79} +4.93233e9 q^{80} +3.87420e8 q^{81} +6.15460e9i q^{82} -1.17721e9i q^{83} +2.29724e9 q^{84} +2.03277e9 q^{85} +1.53229e10 q^{86} +2.04374e8 q^{87} -1.98618e10 q^{88} +5.40845e9i q^{89} -3.97022e9i q^{90} -2.73700e9i q^{91} +2.47024e10i q^{92} +1.46545e9i q^{93} +8.12336e9 q^{94} -1.42215e9 q^{95} +1.76473e9i q^{96} -8.97393e8i q^{97} +1.26551e10i q^{98} +6.15149e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 56.3537i 1.76105i −0.473998 0.880526i \(-0.657190\pi\)
0.473998 0.880526i \(-0.342810\pi\)
\(3\) −140.296 −0.577350
\(4\) −2151.73 −2.10130
\(5\) 3579.32 1.14538 0.572691 0.819771i \(-0.305899\pi\)
0.572691 + 0.819771i \(0.305899\pi\)
\(6\) 7906.20i 1.01674i
\(7\) 7609.79 0.452775 0.226388 0.974037i \(-0.427308\pi\)
0.226388 + 0.974037i \(0.427308\pi\)
\(8\) 63551.9i 1.93945i
\(9\) 19683.0 0.333333
\(10\) 201708.i 2.01708i
\(11\) 312528.i 1.94055i 0.241996 + 0.970277i \(0.422198\pi\)
−0.241996 + 0.970277i \(0.577802\pi\)
\(12\) 301880. 1.21319
\(13\) 359669.i 0.968692i −0.874877 0.484346i \(-0.839058\pi\)
0.874877 0.484346i \(-0.160942\pi\)
\(14\) 428840.i 0.797361i
\(15\) −502165. −0.661287
\(16\) 1.37801e6 1.31417
\(17\) 567921. 0.399984 0.199992 0.979797i \(-0.435908\pi\)
0.199992 + 0.979797i \(0.435908\pi\)
\(18\) 1.10921e6i 0.587017i
\(19\) −397324. −0.160464 −0.0802318 0.996776i \(-0.525566\pi\)
−0.0802318 + 0.996776i \(0.525566\pi\)
\(20\) −7.70175e6 −2.40680
\(21\) −1.06762e6 −0.261410
\(22\) 1.76121e7 3.41742
\(23\) 1.14802e7i 1.78366i −0.452373 0.891829i \(-0.649423\pi\)
0.452373 0.891829i \(-0.350577\pi\)
\(24\) 8.91609e6i 1.11974i
\(25\) 3.04592e6 0.311902
\(26\) −2.02686e7 −1.70592
\(27\) −2.76145e6 −0.192450
\(28\) −1.63743e7 −0.951418
\(29\) −1.45674e6 −0.0710216 −0.0355108 0.999369i \(-0.511306\pi\)
−0.0355108 + 0.999369i \(0.511306\pi\)
\(30\) 2.82988e7i 1.16456i
\(31\) 1.04454e7i 0.364852i −0.983220 0.182426i \(-0.941605\pi\)
0.983220 0.182426i \(-0.0583950\pi\)
\(32\) 1.25786e7i 0.374872i
\(33\) 4.38465e7i 1.12038i
\(34\) 3.20044e7i 0.704393i
\(35\) 2.72379e7 0.518601
\(36\) −4.23526e7 −0.700434
\(37\) 1.11352e8i 1.60579i 0.596122 + 0.802894i \(0.296707\pi\)
−0.596122 + 0.802894i \(0.703293\pi\)
\(38\) 2.23906e7i 0.282585i
\(39\) 5.04601e7i 0.559275i
\(40\) 2.27473e8i 2.22141i
\(41\) −1.09214e8 −0.942668 −0.471334 0.881955i \(-0.656227\pi\)
−0.471334 + 0.881955i \(0.656227\pi\)
\(42\) 6.01645e7i 0.460356i
\(43\) 2.71906e8i 1.84960i 0.380457 + 0.924799i \(0.375767\pi\)
−0.380457 + 0.924799i \(0.624233\pi\)
\(44\) 6.72478e8i 4.07769i
\(45\) 7.04518e7 0.381794
\(46\) −6.46953e8 −3.14111
\(47\) 1.44150e8i 0.628528i 0.949336 + 0.314264i \(0.101758\pi\)
−0.949336 + 0.314264i \(0.898242\pi\)
\(48\) −1.93329e8 −0.758737
\(49\) −2.24566e8 −0.794995
\(50\) 1.71649e8i 0.549275i
\(51\) −7.96771e7 −0.230931
\(52\) 7.73911e8i 2.03552i
\(53\) 1.14733e8 0.274352 0.137176 0.990547i \(-0.456197\pi\)
0.137176 + 0.990547i \(0.456197\pi\)
\(54\) 1.55618e8i 0.338915i
\(55\) 1.11864e9i 2.22268i
\(56\) 4.83617e8i 0.878135i
\(57\) 5.57430e7 0.0926437
\(58\) 8.20924e7i 0.125073i
\(59\) −7.13172e8 5.00283e7i −0.997549 0.0699770i
\(60\) 1.08053e9 1.38956
\(61\) 7.51127e8i 0.889333i −0.895696 0.444667i \(-0.853322\pi\)
0.895696 0.444667i \(-0.146678\pi\)
\(62\) −5.88636e8 −0.642523
\(63\) 1.49784e8 0.150925
\(64\) 7.02230e8 0.654003
\(65\) 1.28737e9i 1.10952i
\(66\) −2.47091e9 −1.97305
\(67\) 6.46732e8i 0.479017i 0.970894 + 0.239508i \(0.0769862\pi\)
−0.970894 + 0.239508i \(0.923014\pi\)
\(68\) −1.22201e9 −0.840488
\(69\) 1.61063e9i 1.02980i
\(70\) 1.53495e9i 0.913283i
\(71\) −1.38039e9 −0.765088 −0.382544 0.923937i \(-0.624952\pi\)
−0.382544 + 0.923937i \(0.624952\pi\)
\(72\) 1.25089e9i 0.646484i
\(73\) 2.57637e9i 1.24278i 0.783502 + 0.621389i \(0.213431\pi\)
−0.783502 + 0.621389i \(0.786569\pi\)
\(74\) 6.27507e9 2.82787
\(75\) −4.27330e8 −0.180077
\(76\) 8.54935e8 0.337183
\(77\) 2.37828e9i 0.878635i
\(78\) 2.84361e9 0.984911
\(79\) 4.01132e9 1.30362 0.651811 0.758382i \(-0.274010\pi\)
0.651811 + 0.758382i \(0.274010\pi\)
\(80\) 4.93233e9 1.50523
\(81\) 3.87420e8 0.111111
\(82\) 6.15460e9i 1.66009i
\(83\) 1.17721e9i 0.298857i −0.988773 0.149428i \(-0.952257\pi\)
0.988773 0.149428i \(-0.0477434\pi\)
\(84\) 2.29724e9 0.549301
\(85\) 2.03277e9 0.458135
\(86\) 1.53229e10 3.25724
\(87\) 2.04374e8 0.0410044
\(88\) −1.98618e10 −3.76361
\(89\) 5.40845e9i 0.968551i 0.874915 + 0.484276i \(0.160917\pi\)
−0.874915 + 0.484276i \(0.839083\pi\)
\(90\) 3.97022e9i 0.672359i
\(91\) 2.73700e9i 0.438600i
\(92\) 2.47024e10i 3.74800i
\(93\) 1.46545e9i 0.210647i
\(94\) 8.12336e9 1.10687
\(95\) −1.42215e9 −0.183792
\(96\) 1.76473e9i 0.216432i
\(97\) 8.97393e8i 0.104502i −0.998634 0.0522509i \(-0.983360\pi\)
0.998634 0.0522509i \(-0.0166396\pi\)
\(98\) 1.26551e10i 1.40003i
\(99\) 6.15149e9i 0.646851i
\(100\) −6.55400e9 −0.655400
\(101\) 6.21405e9i 0.591245i −0.955305 0.295623i \(-0.904473\pi\)
0.955305 0.295623i \(-0.0955271\pi\)
\(102\) 4.49009e9i 0.406682i
\(103\) 8.01555e9i 0.691428i −0.938340 0.345714i \(-0.887637\pi\)
0.938340 0.345714i \(-0.112363\pi\)
\(104\) 2.28576e10 1.87873
\(105\) −3.82137e9 −0.299414
\(106\) 6.46561e9i 0.483148i
\(107\) −1.84063e10 −1.31234 −0.656171 0.754612i \(-0.727825\pi\)
−0.656171 + 0.754612i \(0.727825\pi\)
\(108\) 5.94190e9 0.404396
\(109\) 7.40048e9i 0.480981i 0.970652 + 0.240490i \(0.0773082\pi\)
−0.970652 + 0.240490i \(0.922692\pi\)
\(110\) 6.30394e10 3.91425
\(111\) 1.56222e10i 0.927102i
\(112\) 1.04864e10 0.595024
\(113\) 1.01481e10i 0.550798i 0.961330 + 0.275399i \(0.0888100\pi\)
−0.961330 + 0.275399i \(0.911190\pi\)
\(114\) 3.14132e9i 0.163150i
\(115\) 4.10914e10i 2.04297i
\(116\) 3.13451e9 0.149238
\(117\) 7.07936e9i 0.322897i
\(118\) −2.81928e9 + 4.01898e10i −0.123233 + 1.75673i
\(119\) 4.32176e9 0.181103
\(120\) 3.19136e10i 1.28253i
\(121\) −7.17365e10 −2.76575
\(122\) −4.23288e10 −1.56616
\(123\) 1.53223e10 0.544250
\(124\) 2.24757e10i 0.766664i
\(125\) −2.40520e10 −0.788136
\(126\) 8.44085e9i 0.265787i
\(127\) −1.88317e10 −0.569994 −0.284997 0.958528i \(-0.591993\pi\)
−0.284997 + 0.958528i \(0.591993\pi\)
\(128\) 5.24537e10i 1.52660i
\(129\) 3.81474e10i 1.06787i
\(130\) −7.25480e10 −1.95393
\(131\) 6.32170e10i 1.63862i 0.573352 + 0.819309i \(0.305643\pi\)
−0.573352 + 0.819309i \(0.694357\pi\)
\(132\) 9.43460e10i 2.35426i
\(133\) −3.02355e9 −0.0726539
\(134\) 3.64457e10 0.843573
\(135\) −9.88411e9 −0.220429
\(136\) 3.60925e10i 0.775750i
\(137\) 2.38705e10 0.494606 0.247303 0.968938i \(-0.420456\pi\)
0.247303 + 0.968938i \(0.420456\pi\)
\(138\) 9.07650e10 1.81352
\(139\) −1.68211e10 −0.324175 −0.162087 0.986776i \(-0.551823\pi\)
−0.162087 + 0.986776i \(0.551823\pi\)
\(140\) −5.86087e10 −1.08974
\(141\) 2.02236e10i 0.362881i
\(142\) 7.77903e10i 1.34736i
\(143\) 1.12407e11 1.87980
\(144\) 2.71233e10 0.438057
\(145\) −5.21412e9 −0.0813470
\(146\) 1.45188e11 2.18860
\(147\) 3.15058e10 0.458990
\(148\) 2.39599e11i 3.37425i
\(149\) 9.47892e10i 1.29071i −0.763884 0.645353i \(-0.776710\pi\)
0.763884 0.645353i \(-0.223290\pi\)
\(150\) 2.40816e10i 0.317124i
\(151\) 1.93435e9i 0.0246405i 0.999924 + 0.0123202i \(0.00392176\pi\)
−0.999924 + 0.0123202i \(0.996078\pi\)
\(152\) 2.52507e10i 0.311211i
\(153\) 1.11784e10 0.133328
\(154\) 1.34024e11 1.54732
\(155\) 3.73874e10i 0.417895i
\(156\) 1.08577e11i 1.17521i
\(157\) 6.15912e9i 0.0645684i −0.999479 0.0322842i \(-0.989722\pi\)
0.999479 0.0322842i \(-0.0102782\pi\)
\(158\) 2.26052e11i 2.29575i
\(159\) −1.60966e10 −0.158397
\(160\) 4.50229e10i 0.429372i
\(161\) 8.73622e10i 0.807596i
\(162\) 2.18326e10i 0.195672i
\(163\) 3.96458e9 0.0344555 0.0172278 0.999852i \(-0.494516\pi\)
0.0172278 + 0.999852i \(0.494516\pi\)
\(164\) 2.34999e11 1.98083
\(165\) 1.56941e11i 1.28326i
\(166\) −6.63400e10 −0.526302
\(167\) 4.04658e10 0.311534 0.155767 0.987794i \(-0.450215\pi\)
0.155767 + 0.987794i \(0.450215\pi\)
\(168\) 6.78496e10i 0.506992i
\(169\) 8.49702e9 0.0616358
\(170\) 1.14554e11i 0.806800i
\(171\) −7.82052e9 −0.0534878
\(172\) 5.85070e11i 3.88656i
\(173\) 2.16660e11i 1.39813i 0.715058 + 0.699065i \(0.246400\pi\)
−0.715058 + 0.699065i \(0.753600\pi\)
\(174\) 1.15172e10i 0.0722108i
\(175\) 2.31788e10 0.141221
\(176\) 4.30666e11i 2.55022i
\(177\) 1.00055e11 + 7.01877e9i 0.575935 + 0.0404013i
\(178\) 3.04786e11 1.70567
\(179\) 2.69806e11i 1.46820i 0.679039 + 0.734102i \(0.262397\pi\)
−0.679039 + 0.734102i \(0.737603\pi\)
\(180\) −1.51594e11 −0.802265
\(181\) 2.59874e11 1.33773 0.668867 0.743383i \(-0.266780\pi\)
0.668867 + 0.743383i \(0.266780\pi\)
\(182\) −1.54240e11 −0.772397
\(183\) 1.05380e11i 0.513457i
\(184\) 7.29591e11 3.45932
\(185\) 3.98563e11i 1.83924i
\(186\) 8.25834e10 0.370961
\(187\) 1.77491e11i 0.776191i
\(188\) 3.10172e11i 1.32073i
\(189\) −2.10141e10 −0.0871366
\(190\) 8.01433e10i 0.323668i
\(191\) 1.17487e11i 0.462191i 0.972931 + 0.231096i \(0.0742310\pi\)
−0.972931 + 0.231096i \(0.925769\pi\)
\(192\) −9.85201e10 −0.377589
\(193\) −3.98870e11 −1.48951 −0.744757 0.667336i \(-0.767435\pi\)
−0.744757 + 0.667336i \(0.767435\pi\)
\(194\) −5.05714e10 −0.184033
\(195\) 1.80613e11i 0.640584i
\(196\) 4.83207e11 1.67052
\(197\) −1.34625e11 −0.453726 −0.226863 0.973927i \(-0.572847\pi\)
−0.226863 + 0.973927i \(0.572847\pi\)
\(198\) 3.46659e11 1.13914
\(199\) −1.69369e11 −0.542710 −0.271355 0.962479i \(-0.587472\pi\)
−0.271355 + 0.962479i \(0.587472\pi\)
\(200\) 1.93574e11i 0.604918i
\(201\) 9.07340e10i 0.276560i
\(202\) −3.50184e11 −1.04121
\(203\) −1.10855e10 −0.0321568
\(204\) 1.71444e11 0.485256
\(205\) −3.90912e11 −1.07972
\(206\) −4.51706e11 −1.21764
\(207\) 2.25965e11i 0.594552i
\(208\) 4.95626e11i 1.27303i
\(209\) 1.24175e11i 0.311388i
\(210\) 2.15348e11i 0.527284i
\(211\) 7.72111e11i 1.84615i 0.384617 + 0.923076i \(0.374334\pi\)
−0.384617 + 0.923076i \(0.625666\pi\)
\(212\) −2.46874e11 −0.576496
\(213\) 1.93664e11 0.441724
\(214\) 1.03726e12i 2.31110i
\(215\) 9.73241e11i 2.11850i
\(216\) 1.75495e11i 0.373248i
\(217\) 7.94873e10i 0.165196i
\(218\) 4.17044e11 0.847032
\(219\) 3.61454e11i 0.717518i
\(220\) 2.40701e12i 4.67052i
\(221\) 2.04263e11i 0.387462i
\(222\) −8.80368e11 −1.63267
\(223\) 8.40189e11 1.52354 0.761768 0.647850i \(-0.224331\pi\)
0.761768 + 0.647850i \(0.224331\pi\)
\(224\) 9.57206e10i 0.169733i
\(225\) 5.99528e10 0.103967
\(226\) 5.71883e11 0.969984
\(227\) 8.38688e11i 1.39146i 0.718303 + 0.695731i \(0.244919\pi\)
−0.718303 + 0.695731i \(0.755081\pi\)
\(228\) −1.19944e11 −0.194672
\(229\) 8.90372e11i 1.41382i −0.707303 0.706910i \(-0.750088\pi\)
0.707303 0.706910i \(-0.249912\pi\)
\(230\) −2.31565e12 −3.59778
\(231\) 3.33663e11i 0.507280i
\(232\) 9.25784e10i 0.137743i
\(233\) 1.17803e12i 1.71544i −0.514117 0.857720i \(-0.671880\pi\)
0.514117 0.857720i \(-0.328120\pi\)
\(234\) −3.98948e11 −0.568639
\(235\) 5.15958e11i 0.719905i
\(236\) 1.53456e12 + 1.07648e11i 2.09615 + 0.147043i
\(237\) −5.62772e11 −0.752646
\(238\) 2.43547e11i 0.318932i
\(239\) 5.86280e11 0.751823 0.375911 0.926656i \(-0.377330\pi\)
0.375911 + 0.926656i \(0.377330\pi\)
\(240\) −6.91987e11 −0.869044
\(241\) 8.89255e11 1.09381 0.546904 0.837195i \(-0.315806\pi\)
0.546904 + 0.837195i \(0.315806\pi\)
\(242\) 4.04261e12i 4.87063i
\(243\) −5.43536e10 −0.0641500
\(244\) 1.61623e12i 1.86876i
\(245\) −8.03795e11 −0.910573
\(246\) 8.63467e11i 0.958452i
\(247\) 1.42905e11i 0.155440i
\(248\) 6.63825e11 0.707612
\(249\) 1.65158e11i 0.172545i
\(250\) 1.35542e12i 1.38795i
\(251\) 3.74763e11 0.376173 0.188087 0.982152i \(-0.439771\pi\)
0.188087 + 0.982152i \(0.439771\pi\)
\(252\) −3.22294e11 −0.317139
\(253\) 3.58790e12 3.46128
\(254\) 1.06123e12i 1.00379i
\(255\) −2.85190e11 −0.264505
\(256\) −2.23687e12 −2.03443
\(257\) −6.70538e11 −0.598078 −0.299039 0.954241i \(-0.596666\pi\)
−0.299039 + 0.954241i \(0.596666\pi\)
\(258\) −2.14975e12 −1.88057
\(259\) 8.47363e11i 0.727061i
\(260\) 2.77008e12i 2.33144i
\(261\) −2.86729e10 −0.0236739
\(262\) 3.56251e12 2.88569
\(263\) 1.25767e12 0.999510 0.499755 0.866167i \(-0.333423\pi\)
0.499755 + 0.866167i \(0.333423\pi\)
\(264\) 2.78653e12 2.17292
\(265\) 4.10665e11 0.314238
\(266\) 1.70388e11i 0.127947i
\(267\) 7.58784e11i 0.559193i
\(268\) 1.39160e12i 1.00656i
\(269\) 1.43473e12i 1.01861i 0.860586 + 0.509305i \(0.170097\pi\)
−0.860586 + 0.509305i \(0.829903\pi\)
\(270\) 5.57006e11i 0.388187i
\(271\) 1.13752e12 0.778240 0.389120 0.921187i \(-0.372779\pi\)
0.389120 + 0.921187i \(0.372779\pi\)
\(272\) 7.82599e11 0.525648
\(273\) 3.83991e11i 0.253226i
\(274\) 1.34519e12i 0.871027i
\(275\) 9.51935e11i 0.605263i
\(276\) 3.46565e12i 2.16391i
\(277\) −2.30586e12 −1.41395 −0.706974 0.707240i \(-0.749940\pi\)
−0.706974 + 0.707240i \(0.749940\pi\)
\(278\) 9.47928e11i 0.570889i
\(279\) 2.05597e11i 0.121617i
\(280\) 1.73102e12i 1.00580i
\(281\) 1.30397e12 0.744280 0.372140 0.928177i \(-0.378624\pi\)
0.372140 + 0.928177i \(0.378624\pi\)
\(282\) −1.13968e12 −0.639051
\(283\) 3.12895e12i 1.72372i 0.507149 + 0.861859i \(0.330699\pi\)
−0.507149 + 0.861859i \(0.669301\pi\)
\(284\) 2.97024e12 1.60768
\(285\) 1.99522e11 0.106112
\(286\) 6.33452e12i 3.31042i
\(287\) −8.31095e11 −0.426817
\(288\) 2.47585e11i 0.124957i
\(289\) −1.69346e12 −0.840012
\(290\) 2.93835e11i 0.143256i
\(291\) 1.25901e11i 0.0603342i
\(292\) 5.54366e12i 2.61145i
\(293\) −3.07266e12 −1.42291 −0.711454 0.702732i \(-0.751963\pi\)
−0.711454 + 0.702732i \(0.751963\pi\)
\(294\) 1.77547e12i 0.808306i
\(295\) −2.55267e12 1.79067e11i −1.14258 0.0801505i
\(296\) −7.07661e12 −3.11435
\(297\) 8.63031e11i 0.373460i
\(298\) −5.34172e12 −2.27300
\(299\) −4.12908e12 −1.72781
\(300\) 9.19501e11 0.378396
\(301\) 2.06915e12i 0.837452i
\(302\) 1.09007e11 0.0433932
\(303\) 8.71807e11i 0.341356i
\(304\) −5.47515e11 −0.210877
\(305\) 2.68853e12i 1.01863i
\(306\) 6.29943e11i 0.234798i
\(307\) 3.48971e12 1.27967 0.639835 0.768513i \(-0.279003\pi\)
0.639835 + 0.768513i \(0.279003\pi\)
\(308\) 5.11742e12i 1.84628i
\(309\) 1.12455e12i 0.399196i
\(310\) −2.10692e12 −0.735935
\(311\) 4.02825e12 1.38457 0.692284 0.721625i \(-0.256605\pi\)
0.692284 + 0.721625i \(0.256605\pi\)
\(312\) −3.20684e12 −1.08469
\(313\) 1.84973e12i 0.615724i −0.951431 0.307862i \(-0.900387\pi\)
0.951431 0.307862i \(-0.0996135\pi\)
\(314\) −3.47089e11 −0.113708
\(315\) 5.36123e11 0.172867
\(316\) −8.63129e12 −2.73930
\(317\) 1.74556e12 0.545304 0.272652 0.962113i \(-0.412099\pi\)
0.272652 + 0.962113i \(0.412099\pi\)
\(318\) 9.07100e11i 0.278945i
\(319\) 4.55271e11i 0.137821i
\(320\) 2.51351e12 0.749083
\(321\) 2.58233e12 0.757681
\(322\) −4.92318e12 −1.42222
\(323\) −2.25648e11 −0.0641829
\(324\) −8.33626e11 −0.233478
\(325\) 1.09552e12i 0.302137i
\(326\) 2.23418e11i 0.0606779i
\(327\) 1.03826e12i 0.277694i
\(328\) 6.94076e12i 1.82826i
\(329\) 1.09695e12i 0.284582i
\(330\) −8.84418e12 −2.25989
\(331\) −2.18072e12 −0.548859 −0.274429 0.961607i \(-0.588489\pi\)
−0.274429 + 0.961607i \(0.588489\pi\)
\(332\) 2.53304e12i 0.627989i
\(333\) 2.19173e12i 0.535262i
\(334\) 2.28040e12i 0.548628i
\(335\) 2.31486e12i 0.548657i
\(336\) −1.47120e12 −0.343537
\(337\) 2.89610e12i 0.666292i −0.942875 0.333146i \(-0.891890\pi\)
0.942875 0.333146i \(-0.108110\pi\)
\(338\) 4.78838e11i 0.108544i
\(339\) 1.42374e12i 0.318003i
\(340\) −4.37398e12 −0.962681
\(341\) 3.26448e12 0.708015
\(342\) 4.40715e11i 0.0941949i
\(343\) −3.85848e12 −0.812729
\(344\) −1.72802e13 −3.58720
\(345\) 5.76497e12i 1.17951i
\(346\) 1.22096e13 2.46218
\(347\) 4.24749e12i 0.844277i 0.906531 + 0.422138i \(0.138720\pi\)
−0.906531 + 0.422138i \(0.861280\pi\)
\(348\) −4.39759e11 −0.0861626
\(349\) 9.95896e12i 1.92348i 0.273969 + 0.961739i \(0.411663\pi\)
−0.273969 + 0.961739i \(0.588337\pi\)
\(350\) 1.30621e12i 0.248698i
\(351\) 9.93206e11i 0.186425i
\(352\) 3.93117e12 0.727459
\(353\) 2.06879e12i 0.377436i 0.982031 + 0.188718i \(0.0604332\pi\)
−0.982031 + 0.188718i \(0.939567\pi\)
\(354\) 3.95534e11 5.63848e12i 0.0711487 1.01425i
\(355\) −4.94087e12 −0.876319
\(356\) 1.16375e13i 2.03522i
\(357\) −6.06326e11 −0.104560
\(358\) 1.52046e13 2.58558
\(359\) −7.55431e12 −1.26684 −0.633421 0.773807i \(-0.718350\pi\)
−0.633421 + 0.773807i \(0.718350\pi\)
\(360\) 4.47735e12i 0.740471i
\(361\) −5.97320e12 −0.974251
\(362\) 1.46448e13i 2.35582i
\(363\) 1.00643e13 1.59681
\(364\) 5.88930e12i 0.921631i
\(365\) 9.22165e12i 1.42346i
\(366\) 5.93856e12 0.904224
\(367\) 5.34957e12i 0.803505i −0.915748 0.401752i \(-0.868401\pi\)
0.915748 0.401752i \(-0.131599\pi\)
\(368\) 1.58199e13i 2.34403i
\(369\) −2.14966e12 −0.314223
\(370\) 2.24605e13 3.23900
\(371\) 8.73092e11 0.124220
\(372\) 3.15326e12i 0.442634i
\(373\) −5.75490e12 −0.797064 −0.398532 0.917154i \(-0.630480\pi\)
−0.398532 + 0.917154i \(0.630480\pi\)
\(374\) 1.00023e13 1.36691
\(375\) 3.37440e12 0.455030
\(376\) −9.16099e12 −1.21900
\(377\) 5.23942e11i 0.0687981i
\(378\) 1.18422e12i 0.153452i
\(379\) 5.45963e11 0.0698180 0.0349090 0.999390i \(-0.488886\pi\)
0.0349090 + 0.999390i \(0.488886\pi\)
\(380\) 3.06009e12 0.386203
\(381\) 2.64201e12 0.329086
\(382\) 6.62080e12 0.813942
\(383\) 6.53010e11 0.0792367 0.0396183 0.999215i \(-0.487386\pi\)
0.0396183 + 0.999215i \(0.487386\pi\)
\(384\) 7.35905e12i 0.881385i
\(385\) 8.51261e12i 1.00637i
\(386\) 2.24778e13i 2.62311i
\(387\) 5.35193e12i 0.616532i
\(388\) 1.93095e12i 0.219590i
\(389\) −4.40465e12 −0.494496 −0.247248 0.968952i \(-0.579526\pi\)
−0.247248 + 0.968952i \(0.579526\pi\)
\(390\) 1.01782e13 1.12810
\(391\) 6.51986e12i 0.713435i
\(392\) 1.42716e13i 1.54185i
\(393\) 8.86910e12i 0.946056i
\(394\) 7.58660e12i 0.799036i
\(395\) 1.43578e13 1.49315
\(396\) 1.32364e13i 1.35923i
\(397\) 5.60159e12i 0.568014i 0.958822 + 0.284007i \(0.0916639\pi\)
−0.958822 + 0.284007i \(0.908336\pi\)
\(398\) 9.54455e12i 0.955740i
\(399\) 4.24192e11 0.0419468
\(400\) 4.19730e12 0.409892
\(401\) 1.14235e12i 0.110174i 0.998482 + 0.0550869i \(0.0175436\pi\)
−0.998482 + 0.0550869i \(0.982456\pi\)
\(402\) −5.11319e12 −0.487037
\(403\) −3.75688e12 −0.353429
\(404\) 1.33710e13i 1.24239i
\(405\) 1.38670e12 0.127265
\(406\) 6.24706e11i 0.0566298i
\(407\) −3.48005e13 −3.11612
\(408\) 5.06363e12i 0.447880i
\(409\) 1.51003e13i 1.31938i −0.751540 0.659688i \(-0.770689\pi\)
0.751540 0.659688i \(-0.229311\pi\)
\(410\) 2.20293e13i 1.90143i
\(411\) −3.34895e12 −0.285561
\(412\) 1.72473e13i 1.45290i
\(413\) −5.42709e12 3.80705e11i −0.451665 0.0316839i
\(414\) −1.27340e13 −1.04704
\(415\) 4.21361e12i 0.342305i
\(416\) −4.52413e12 −0.363135
\(417\) 2.35993e12 0.187163
\(418\) −6.99771e12 −0.548371
\(419\) 2.95169e12i 0.228560i −0.993449 0.114280i \(-0.963544\pi\)
0.993449 0.114280i \(-0.0364561\pi\)
\(420\) 8.22257e12 0.629160
\(421\) 2.32447e13i 1.75758i 0.477212 + 0.878788i \(0.341647\pi\)
−0.477212 + 0.878788i \(0.658353\pi\)
\(422\) 4.35113e13 3.25117
\(423\) 2.83730e12i 0.209509i
\(424\) 7.29149e12i 0.532092i
\(425\) 1.72984e12 0.124756
\(426\) 1.09137e13i 0.777898i
\(427\) 5.71592e12i 0.402668i
\(428\) 3.96054e13 2.75763
\(429\) −1.57702e13 −1.08530
\(430\) 5.48457e13 3.73078
\(431\) 7.31565e12i 0.491889i −0.969284 0.245944i \(-0.920902\pi\)
0.969284 0.245944i \(-0.0790980\pi\)
\(432\) −3.80530e12 −0.252912
\(433\) −6.64971e12 −0.436881 −0.218441 0.975850i \(-0.570097\pi\)
−0.218441 + 0.975850i \(0.570097\pi\)
\(434\) −4.47940e12 −0.290918
\(435\) 7.31521e11 0.0469657
\(436\) 1.59239e13i 1.01069i
\(437\) 4.56137e12i 0.286212i
\(438\) −2.03693e13 −1.26359
\(439\) 2.67460e13 1.64035 0.820173 0.572115i \(-0.193877\pi\)
0.820173 + 0.572115i \(0.193877\pi\)
\(440\) −7.10917e13 −4.31078
\(441\) −4.42014e12 −0.264998
\(442\) −1.15110e13 −0.682340
\(443\) 2.16431e13i 1.26853i 0.773116 + 0.634265i \(0.218697\pi\)
−0.773116 + 0.634265i \(0.781303\pi\)
\(444\) 3.36148e13i 1.94812i
\(445\) 1.93586e13i 1.10936i
\(446\) 4.73477e13i 2.68303i
\(447\) 1.32986e13i 0.745189i
\(448\) 5.34382e12 0.296116
\(449\) 1.39716e13 0.765623 0.382811 0.923827i \(-0.374956\pi\)
0.382811 + 0.923827i \(0.374956\pi\)
\(450\) 3.37856e12i 0.183092i
\(451\) 3.41324e13i 1.82930i
\(452\) 2.18360e13i 1.15739i
\(453\) 2.71381e11i 0.0142262i
\(454\) 4.72631e13 2.45044
\(455\) 9.79661e12i 0.502365i
\(456\) 3.54257e12i 0.179678i
\(457\) 9.56294e12i 0.479745i 0.970804 + 0.239872i \(0.0771056\pi\)
−0.970804 + 0.239872i \(0.922894\pi\)
\(458\) −5.01757e13 −2.48981
\(459\) −1.56828e12 −0.0769770
\(460\) 8.84178e13i 4.29290i
\(461\) −1.15043e13 −0.552531 −0.276265 0.961081i \(-0.589097\pi\)
−0.276265 + 0.961081i \(0.589097\pi\)
\(462\) −1.88031e13 −0.893346
\(463\) 1.08243e13i 0.508738i 0.967107 + 0.254369i \(0.0818678\pi\)
−0.967107 + 0.254369i \(0.918132\pi\)
\(464\) −2.00739e12 −0.0933346
\(465\) 5.24531e12i 0.241272i
\(466\) −6.63861e13 −3.02098
\(467\) 2.55968e13i 1.15239i 0.817311 + 0.576196i \(0.195464\pi\)
−0.817311 + 0.576196i \(0.804536\pi\)
\(468\) 1.52329e13i 0.678505i
\(469\) 4.92150e12i 0.216887i
\(470\) 2.90761e13 1.26779
\(471\) 8.64100e11i 0.0372786i
\(472\) 3.17939e12 4.53234e13i 0.135717 1.93470i
\(473\) −8.49784e13 −3.58924
\(474\) 3.17143e13i 1.32545i
\(475\) −1.21021e12 −0.0500489
\(476\) −9.29928e12 −0.380552
\(477\) 2.25828e12 0.0914506
\(478\) 3.30390e13i 1.32400i
\(479\) 5.80320e12 0.230139 0.115069 0.993357i \(-0.463291\pi\)
0.115069 + 0.993357i \(0.463291\pi\)
\(480\) 6.31653e12i 0.247898i
\(481\) 4.00497e13 1.55551
\(482\) 5.01128e13i 1.92625i
\(483\) 1.22566e13i 0.466266i
\(484\) 1.54358e14 5.81168
\(485\) 3.21206e12i 0.119695i
\(486\) 3.06302e12i 0.112972i
\(487\) −6.57773e12 −0.240121 −0.120061 0.992767i \(-0.538309\pi\)
−0.120061 + 0.992767i \(0.538309\pi\)
\(488\) 4.77356e13 1.72482
\(489\) −5.56215e11 −0.0198929
\(490\) 4.52968e13i 1.60357i
\(491\) 9.12416e12 0.319731 0.159866 0.987139i \(-0.448894\pi\)
0.159866 + 0.987139i \(0.448894\pi\)
\(492\) −3.29695e13 −1.14363
\(493\) −8.27310e11 −0.0284075
\(494\) 8.05321e12 0.273737
\(495\) 2.20182e13i 0.740893i
\(496\) 1.43938e13i 0.479478i
\(497\) −1.05045e13 −0.346413
\(498\) 9.30725e12 0.303861
\(499\) 4.19762e13 1.35675 0.678377 0.734714i \(-0.262684\pi\)
0.678377 + 0.734714i \(0.262684\pi\)
\(500\) 5.17535e13 1.65611
\(501\) −5.67719e12 −0.179864
\(502\) 2.11193e13i 0.662460i
\(503\) 2.75417e13i 0.855363i 0.903930 + 0.427681i \(0.140670\pi\)
−0.903930 + 0.427681i \(0.859330\pi\)
\(504\) 9.51904e12i 0.292712i
\(505\) 2.22421e13i 0.677202i
\(506\) 2.02191e14i 6.09550i
\(507\) −1.19210e12 −0.0355855
\(508\) 4.05208e13 1.19773
\(509\) 2.65671e13i 0.777597i −0.921323 0.388798i \(-0.872890\pi\)
0.921323 0.388798i \(-0.127110\pi\)
\(510\) 1.60715e13i 0.465806i
\(511\) 1.96056e13i 0.562699i
\(512\) 7.23435e13i 2.05613i
\(513\) 1.09719e12 0.0308812
\(514\) 3.77873e13i 1.05325i
\(515\) 2.86902e13i 0.791950i
\(516\) 8.20831e13i 2.24391i
\(517\) −4.50508e13 −1.21969
\(518\) 4.77520e13 1.28039
\(519\) 3.03965e13i 0.807210i
\(520\) 8.18148e13 2.15187
\(521\) 2.84427e13 0.740938 0.370469 0.928845i \(-0.379197\pi\)
0.370469 + 0.928845i \(0.379197\pi\)
\(522\) 1.61582e12i 0.0416909i
\(523\) 1.96961e13 0.503352 0.251676 0.967812i \(-0.419018\pi\)
0.251676 + 0.967812i \(0.419018\pi\)
\(524\) 1.36026e14i 3.44323i
\(525\) −3.25189e12 −0.0815342
\(526\) 7.08742e13i 1.76019i
\(527\) 5.93216e12i 0.145935i
\(528\) 6.04208e13i 1.47237i
\(529\) −9.03692e13 −2.18143
\(530\) 2.31425e13i 0.553389i
\(531\) −1.40374e13 9.84707e11i −0.332516 0.0233257i
\(532\) 6.50588e12 0.152668
\(533\) 3.92808e13i 0.913155i
\(534\) −4.27603e13 −0.984769
\(535\) −6.58820e13 −1.50313
\(536\) −4.11011e13 −0.929029
\(537\) 3.78527e13i 0.847668i
\(538\) 8.08521e13 1.79382
\(539\) 7.01833e13i 1.54273i
\(540\) 2.12680e13 0.463188
\(541\) 3.82714e12i 0.0825824i −0.999147 0.0412912i \(-0.986853\pi\)
0.999147 0.0412912i \(-0.0131471\pi\)
\(542\) 6.41036e13i 1.37052i
\(543\) −3.64593e13 −0.772341
\(544\) 7.14365e12i 0.149943i
\(545\) 2.64887e13i 0.550907i
\(546\) 2.16393e13 0.445943
\(547\) 4.19549e13 0.856733 0.428367 0.903605i \(-0.359089\pi\)
0.428367 + 0.903605i \(0.359089\pi\)
\(548\) −5.13631e13 −1.03932
\(549\) 1.47844e13i 0.296444i
\(550\) 5.36450e13 1.06590
\(551\) 5.78795e11 0.0113964
\(552\) −1.02359e14 −1.99724
\(553\) 3.05253e13 0.590248
\(554\) 1.29943e14i 2.49003i
\(555\) 5.59169e13i 1.06189i
\(556\) 3.61945e13 0.681190
\(557\) 9.01920e13 1.68225 0.841127 0.540837i \(-0.181892\pi\)
0.841127 + 0.540837i \(0.181892\pi\)
\(558\) −1.15861e13 −0.214174
\(559\) 9.77962e13 1.79169
\(560\) 3.75340e13 0.681530
\(561\) 2.49013e13i 0.448134i
\(562\) 7.34835e13i 1.31072i
\(563\) 4.13807e13i 0.731570i −0.930699 0.365785i \(-0.880800\pi\)
0.930699 0.365785i \(-0.119200\pi\)
\(564\) 4.35159e13i 0.762522i
\(565\) 3.63233e13i 0.630875i
\(566\) 1.76328e14 3.03555
\(567\) 2.94819e12 0.0503084
\(568\) 8.77267e13i 1.48385i
\(569\) 6.24035e13i 1.04628i 0.852247 + 0.523139i \(0.175239\pi\)
−0.852247 + 0.523139i \(0.824761\pi\)
\(570\) 1.12438e13i 0.186870i
\(571\) 7.43307e13i 1.22458i −0.790632 0.612291i \(-0.790248\pi\)
0.790632 0.612291i \(-0.209752\pi\)
\(572\) −2.41869e14 −3.95003
\(573\) 1.64829e13i 0.266846i
\(574\) 4.68353e13i 0.751646i
\(575\) 3.49678e13i 0.556326i
\(576\) 1.38220e13 0.218001
\(577\) −2.05474e13 −0.321276 −0.160638 0.987013i \(-0.551355\pi\)
−0.160638 + 0.987013i \(0.551355\pi\)
\(578\) 9.54327e13i 1.47931i
\(579\) 5.59599e13 0.859971
\(580\) 1.12194e13 0.170935
\(581\) 8.95832e12i 0.135315i
\(582\) 7.09497e12 0.106252
\(583\) 3.58572e13i 0.532395i
\(584\) −1.63733e14 −2.41031
\(585\) 2.53393e13i 0.369841i
\(586\) 1.73156e14i 2.50582i
\(587\) 1.16216e14i 1.66753i −0.552117 0.833767i \(-0.686180\pi\)
0.552117 0.833767i \(-0.313820\pi\)
\(588\) −6.77921e13 −0.964478
\(589\) 4.15020e12i 0.0585454i
\(590\) −1.00911e13 + 1.43852e14i −0.141149 + 2.01213i
\(591\) 1.88873e13 0.261959
\(592\) 1.53443e14i 2.11028i
\(593\) −8.87027e13 −1.20966 −0.604830 0.796355i \(-0.706759\pi\)
−0.604830 + 0.796355i \(0.706759\pi\)
\(594\) −4.86349e13 −0.657682
\(595\) 1.54690e13 0.207432
\(596\) 2.03961e14i 2.71216i
\(597\) 2.37618e13 0.313334
\(598\) 2.32689e14i 3.04277i
\(599\) −8.18429e12 −0.106132 −0.0530661 0.998591i \(-0.516899\pi\)
−0.0530661 + 0.998591i \(0.516899\pi\)
\(600\) 2.71577e13i 0.349250i
\(601\) 1.31722e14i 1.67991i −0.542654 0.839956i \(-0.682581\pi\)
0.542654 0.839956i \(-0.317419\pi\)
\(602\) 1.16604e14 1.47480
\(603\) 1.27296e13i 0.159672i
\(604\) 4.16220e12i 0.0517771i
\(605\) −2.56768e14 −3.16784
\(606\) 4.91295e13 0.601145
\(607\) −5.27923e13 −0.640660 −0.320330 0.947306i \(-0.603794\pi\)
−0.320330 + 0.947306i \(0.603794\pi\)
\(608\) 4.99778e12i 0.0601532i
\(609\) 1.55525e12 0.0185658
\(610\) −1.51508e14 −1.79385
\(611\) 5.18461e13 0.608850
\(612\) −2.40529e13 −0.280163
\(613\) 1.53901e14i 1.77803i −0.457878 0.889015i \(-0.651390\pi\)
0.457878 0.889015i \(-0.348610\pi\)
\(614\) 1.96658e14i 2.25356i
\(615\) 5.48434e13 0.623374
\(616\) −1.51144e14 −1.70407
\(617\) 2.31009e13 0.258346 0.129173 0.991622i \(-0.458768\pi\)
0.129173 + 0.991622i \(0.458768\pi\)
\(618\) 6.33725e13 0.703005
\(619\) −1.38207e14 −1.52081 −0.760407 0.649446i \(-0.775001\pi\)
−0.760407 + 0.649446i \(0.775001\pi\)
\(620\) 8.04478e13i 0.878124i
\(621\) 3.17021e13i 0.343265i
\(622\) 2.27006e14i 2.43830i
\(623\) 4.11572e13i 0.438536i
\(624\) 6.95344e13i 0.734982i
\(625\) −1.15835e14 −1.21462
\(626\) −1.04239e14 −1.08432
\(627\) 1.74212e13i 0.179780i
\(628\) 1.32528e13i 0.135678i
\(629\) 6.32389e13i 0.642290i
\(630\) 3.02125e13i 0.304428i
\(631\) −3.14987e13 −0.314880 −0.157440 0.987529i \(-0.550324\pi\)
−0.157440 + 0.987529i \(0.550324\pi\)
\(632\) 2.54927e14i 2.52831i
\(633\) 1.08324e14i 1.06588i
\(634\) 9.83688e13i 0.960309i
\(635\) −6.74046e13 −0.652862
\(636\) 3.46355e13 0.332840
\(637\) 8.07694e13i 0.770105i
\(638\) −2.56562e13 −0.242711
\(639\) −2.71703e13 −0.255029
\(640\) 1.87749e14i 1.74855i
\(641\) 8.70942e13 0.804820 0.402410 0.915459i \(-0.368173\pi\)
0.402410 + 0.915459i \(0.368173\pi\)
\(642\) 1.45524e14i 1.33432i
\(643\) −1.32562e14 −1.20605 −0.603025 0.797722i \(-0.706038\pi\)
−0.603025 + 0.797722i \(0.706038\pi\)
\(644\) 1.87980e14i 1.69700i
\(645\) 1.36542e14i 1.22311i
\(646\) 1.27161e13i 0.113029i
\(647\) −5.81938e13 −0.513282 −0.256641 0.966507i \(-0.582616\pi\)
−0.256641 + 0.966507i \(0.582616\pi\)
\(648\) 2.46213e13i 0.215495i
\(649\) 1.56353e13 2.22886e14i 0.135794 1.93580i
\(650\) −6.17366e13 −0.532079
\(651\) 1.11518e13i 0.0953759i
\(652\) −8.53071e12 −0.0724015
\(653\) 1.55543e14 1.31004 0.655021 0.755611i \(-0.272660\pi\)
0.655021 + 0.755611i \(0.272660\pi\)
\(654\) −5.85097e13 −0.489034
\(655\) 2.26274e14i 1.87684i
\(656\) −1.50498e14 −1.23883
\(657\) 5.07107e13i 0.414259i
\(658\) 6.18171e13 0.501163
\(659\) 7.04034e12i 0.0566457i −0.999599 0.0283228i \(-0.990983\pi\)
0.999599 0.0283228i \(-0.00901664\pi\)
\(660\) 3.37695e14i 2.69653i
\(661\) −1.59800e14 −1.26639 −0.633196 0.773991i \(-0.718257\pi\)
−0.633196 + 0.773991i \(0.718257\pi\)
\(662\) 1.22892e14i 0.966569i
\(663\) 2.86573e13i 0.223701i
\(664\) 7.48139e13 0.579618
\(665\) −1.08223e13 −0.0832165
\(666\) 1.23512e14 0.942625
\(667\) 1.67237e13i 0.126678i
\(668\) −8.70716e13 −0.654628
\(669\) −1.17875e14 −0.879614
\(670\) 1.30451e14 0.966214
\(671\) 2.34749e14 1.72580
\(672\) 1.34292e13i 0.0979952i
\(673\) 1.57352e14i 1.13971i 0.821744 + 0.569857i \(0.193001\pi\)
−0.821744 + 0.569857i \(0.806999\pi\)
\(674\) −1.63206e14 −1.17337
\(675\) −8.41114e12 −0.0600255
\(676\) −1.82833e13 −0.129516
\(677\) −3.79219e12 −0.0266653 −0.0133326 0.999911i \(-0.504244\pi\)
−0.0133326 + 0.999911i \(0.504244\pi\)
\(678\) −8.02329e13 −0.560021
\(679\) 6.82898e12i 0.0473159i
\(680\) 1.29187e14i 0.888531i
\(681\) 1.17665e14i 0.803361i
\(682\) 1.83965e14i 1.24685i
\(683\) 3.83847e12i 0.0258258i 0.999917 + 0.0129129i \(0.00411042\pi\)
−0.999917 + 0.0129129i \(0.995890\pi\)
\(684\) 1.68277e13 0.112394
\(685\) 8.54404e13 0.566513
\(686\) 2.17440e14i 1.43126i
\(687\) 1.24916e14i 0.816270i
\(688\) 3.74689e14i 2.43069i
\(689\) 4.12657e13i 0.265762i
\(690\) 3.24877e14 2.07718
\(691\) 9.70769e13i 0.616206i 0.951353 + 0.308103i \(0.0996941\pi\)
−0.951353 + 0.308103i \(0.900306\pi\)
\(692\) 4.66194e14i 2.93789i
\(693\) 4.68116e13i 0.292878i
\(694\) 2.39361e14 1.48681
\(695\) −6.02080e13 −0.371304
\(696\) 1.29884e13i 0.0795260i
\(697\) −6.20248e13 −0.377052
\(698\) 5.61224e14 3.38734
\(699\) 1.65273e14i 0.990410i
\(700\) −4.98746e13 −0.296749
\(701\) 1.58415e14i 0.935848i 0.883769 + 0.467924i \(0.154998\pi\)
−0.883769 + 0.467924i \(0.845002\pi\)
\(702\) 5.59708e13 0.328304
\(703\) 4.42426e13i 0.257670i
\(704\) 2.19467e14i 1.26913i
\(705\) 7.23869e13i 0.415637i
\(706\) 1.16584e14 0.664685
\(707\) 4.72876e13i 0.267701i
\(708\) −2.15292e14 1.51025e13i −1.21021 0.0848953i
\(709\) −1.37774e14 −0.769019 −0.384509 0.923121i \(-0.625629\pi\)
−0.384509 + 0.923121i \(0.625629\pi\)
\(710\) 2.78436e14i 1.54324i
\(711\) 7.89548e13 0.434541
\(712\) −3.43717e14 −1.87846
\(713\) −1.19916e14 −0.650771
\(714\) 3.41687e13i 0.184135i
\(715\) 4.02339e14 2.15309
\(716\) 5.80551e14i 3.08514i
\(717\) −8.22528e13 −0.434065
\(718\) 4.25713e14i 2.23097i
\(719\) 4.09687e13i 0.213210i −0.994301 0.106605i \(-0.966002\pi\)
0.994301 0.106605i \(-0.0339980\pi\)
\(720\) 9.70831e13 0.501743
\(721\) 6.09967e13i 0.313062i
\(722\) 3.36612e14i 1.71571i
\(723\) −1.24759e14 −0.631511
\(724\) −5.59179e14 −2.81098
\(725\) −4.43709e12 −0.0221518
\(726\) 5.67163e14i 2.81206i
\(727\) 1.18643e14 0.584213 0.292107 0.956386i \(-0.405644\pi\)
0.292107 + 0.956386i \(0.405644\pi\)
\(728\) 1.73942e14 0.850643
\(729\) 7.62560e12 0.0370370
\(730\) 5.19674e14 2.50678
\(731\) 1.54421e14i 0.739810i
\(732\) 2.26750e14i 1.07893i
\(733\) −2.44546e14 −1.15569 −0.577843 0.816148i \(-0.696106\pi\)
−0.577843 + 0.816148i \(0.696106\pi\)
\(734\) −3.01468e14 −1.41501
\(735\) 1.12769e14 0.525720
\(736\) −1.44405e14 −0.668643
\(737\) −2.02122e14 −0.929558
\(738\) 1.21141e14i 0.553362i
\(739\) 1.15757e14i 0.525200i −0.964905 0.262600i \(-0.915420\pi\)
0.964905 0.262600i \(-0.0845800\pi\)
\(740\) 8.57602e14i 3.86480i
\(741\) 2.00490e13i 0.0897432i
\(742\) 4.92019e13i 0.218757i
\(743\) 1.02803e14 0.454008 0.227004 0.973894i \(-0.427107\pi\)
0.227004 + 0.973894i \(0.427107\pi\)
\(744\) −9.31321e13 −0.408540
\(745\) 3.39281e14i 1.47835i
\(746\) 3.24309e14i 1.40367i
\(747\) 2.31710e13i 0.0996189i
\(748\) 3.81914e14i 1.63101i
\(749\) −1.40068e14 −0.594196
\(750\) 1.90160e14i 0.801332i
\(751\) 1.66524e14i 0.697071i −0.937296 0.348536i \(-0.886679\pi\)
0.937296 0.348536i \(-0.113321\pi\)
\(752\) 1.98639e14i 0.825993i
\(753\) −5.25778e13 −0.217184
\(754\) 2.95260e13 0.121157
\(755\) 6.92365e12i 0.0282228i
\(756\) 4.52167e13 0.183100
\(757\) 1.05660e14 0.425039 0.212520 0.977157i \(-0.431833\pi\)
0.212520 + 0.977157i \(0.431833\pi\)
\(758\) 3.07670e13i 0.122953i
\(759\) −5.03368e14 −1.99837
\(760\) 9.03803e13i 0.356456i
\(761\) 2.80348e14 1.09843 0.549217 0.835680i \(-0.314926\pi\)
0.549217 + 0.835680i \(0.314926\pi\)
\(762\) 1.48887e14i 0.579538i
\(763\) 5.63161e13i 0.217776i
\(764\) 2.52800e14i 0.971204i
\(765\) 4.00110e13 0.152712
\(766\) 3.67995e13i 0.139540i
\(767\) −1.79936e13 + 2.56505e14i −0.0677862 + 0.966317i
\(768\) 3.13825e14 1.17458
\(769\) 1.98347e14i 0.737555i 0.929518 + 0.368777i \(0.120224\pi\)
−0.929518 + 0.368777i \(0.879776\pi\)
\(770\) 4.79717e14 1.77228
\(771\) 9.40739e13 0.345301
\(772\) 8.58262e14 3.12992
\(773\) 1.64588e14i 0.596348i 0.954511 + 0.298174i \(0.0963776\pi\)
−0.954511 + 0.298174i \(0.903622\pi\)
\(774\) 3.01601e14 1.08575
\(775\) 3.18158e13i 0.113798i
\(776\) 5.70311e13 0.202676
\(777\) 1.18882e14i 0.419769i
\(778\) 2.48218e14i 0.870834i
\(779\) 4.33933e13 0.151264
\(780\)