Properties

Label 177.7.c.a.58.14
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 58.14
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.47

$q$-expansion

\(f(q)\) \(=\) \(q-9.91595i q^{2} +15.5885 q^{3} -34.3260 q^{4} -70.2821 q^{5} -154.574i q^{6} +315.675 q^{7} -294.246i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-9.91595i q^{2} +15.5885 q^{3} -34.3260 q^{4} -70.2821 q^{5} -154.574i q^{6} +315.675 q^{7} -294.246i q^{8} +243.000 q^{9} +696.914i q^{10} +1757.73i q^{11} -535.089 q^{12} +3990.02i q^{13} -3130.21i q^{14} -1095.59 q^{15} -5114.59 q^{16} -2601.72 q^{17} -2409.57i q^{18} -12139.0 q^{19} +2412.50 q^{20} +4920.88 q^{21} +17429.6 q^{22} +8281.58i q^{23} -4586.84i q^{24} -10685.4 q^{25} +39564.8 q^{26} +3788.00 q^{27} -10835.8 q^{28} -31786.7 q^{29} +10863.8i q^{30} -194.726i q^{31} +31884.3i q^{32} +27400.4i q^{33} +25798.5i q^{34} -22186.3 q^{35} -8341.21 q^{36} -16186.6i q^{37} +120370. i q^{38} +62198.2i q^{39} +20680.2i q^{40} +82067.8 q^{41} -48795.2i q^{42} +134723. i q^{43} -60335.9i q^{44} -17078.6 q^{45} +82119.7 q^{46} -34502.7i q^{47} -79728.6 q^{48} -17998.4 q^{49} +105956. i q^{50} -40556.8 q^{51} -136961. i q^{52} +38215.6 q^{53} -37561.6i q^{54} -123537. i q^{55} -92886.0i q^{56} -189229. q^{57} +315195. i q^{58} +(156402. - 133112. i) q^{59} +37607.2 q^{60} +267542. i q^{61} -1930.89 q^{62} +76709.0 q^{63} -11171.2 q^{64} -280427. i q^{65} +271700. q^{66} +23922.1i q^{67} +89306.6 q^{68} +129097. i q^{69} +219998. i q^{70} +213558. q^{71} -71501.8i q^{72} -140860. i q^{73} -160506. q^{74} -166569. q^{75} +416684. q^{76} +554872. i q^{77} +616754. q^{78} +369365. q^{79} +359464. q^{80} +59049.0 q^{81} -813780. i q^{82} -201363. i q^{83} -168914. q^{84} +182854. q^{85} +1.33590e6 q^{86} -495505. q^{87} +517206. q^{88} -8376.32i q^{89} +169350. i q^{90} +1.25955e6i q^{91} -284273. i q^{92} -3035.47i q^{93} -342126. q^{94} +853156. q^{95} +497026. i q^{96} +738936. i q^{97} +178471. i q^{98} +427129. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.91595i 1.23949i −0.784802 0.619747i \(-0.787235\pi\)
0.784802 0.619747i \(-0.212765\pi\)
\(3\) 15.5885 0.577350
\(4\) −34.3260 −0.536344
\(5\) −70.2821 −0.562257 −0.281128 0.959670i \(-0.590709\pi\)
−0.281128 + 0.959670i \(0.590709\pi\)
\(6\) 154.574i 0.715622i
\(7\) 315.675 0.920335 0.460167 0.887832i \(-0.347789\pi\)
0.460167 + 0.887832i \(0.347789\pi\)
\(8\) 294.246i 0.574699i
\(9\) 243.000 0.333333
\(10\) 696.914i 0.696914i
\(11\) 1757.73i 1.32061i 0.750997 + 0.660306i \(0.229573\pi\)
−0.750997 + 0.660306i \(0.770427\pi\)
\(12\) −535.089 −0.309658
\(13\) 3990.02i 1.81612i 0.418839 + 0.908060i \(0.362437\pi\)
−0.418839 + 0.908060i \(0.637563\pi\)
\(14\) 3130.21i 1.14075i
\(15\) −1095.59 −0.324619
\(16\) −5114.59 −1.24868
\(17\) −2601.72 −0.529558 −0.264779 0.964309i \(-0.585299\pi\)
−0.264779 + 0.964309i \(0.585299\pi\)
\(18\) 2409.57i 0.413164i
\(19\) −12139.0 −1.76980 −0.884898 0.465785i \(-0.845772\pi\)
−0.884898 + 0.465785i \(0.845772\pi\)
\(20\) 2412.50 0.301563
\(21\) 4920.88 0.531356
\(22\) 17429.6 1.63689
\(23\) 8281.58i 0.680659i 0.940306 + 0.340330i \(0.110539\pi\)
−0.940306 + 0.340330i \(0.889461\pi\)
\(24\) 4586.84i 0.331803i
\(25\) −10685.4 −0.683867
\(26\) 39564.8 2.25107
\(27\) 3788.00 0.192450
\(28\) −10835.8 −0.493616
\(29\) −31786.7 −1.30332 −0.651660 0.758511i \(-0.725927\pi\)
−0.651660 + 0.758511i \(0.725927\pi\)
\(30\) 10863.8i 0.402363i
\(31\) 194.726i 0.00653639i −0.999995 0.00326819i \(-0.998960\pi\)
0.999995 0.00326819i \(-0.00104030\pi\)
\(32\) 31884.3i 0.973030i
\(33\) 27400.4i 0.762455i
\(34\) 25798.5i 0.656384i
\(35\) −22186.3 −0.517465
\(36\) −8341.21 −0.178781
\(37\) 16186.6i 0.319559i −0.987153 0.159779i \(-0.948922\pi\)
0.987153 0.159779i \(-0.0510783\pi\)
\(38\) 120370.i 2.19365i
\(39\) 62198.2i 1.04854i
\(40\) 20680.2i 0.323128i
\(41\) 82067.8 1.19075 0.595376 0.803447i \(-0.297003\pi\)
0.595376 + 0.803447i \(0.297003\pi\)
\(42\) 48795.2i 0.658612i
\(43\) 134723.i 1.69447i 0.531215 + 0.847237i \(0.321736\pi\)
−0.531215 + 0.847237i \(0.678264\pi\)
\(44\) 60335.9i 0.708301i
\(45\) −17078.6 −0.187419
\(46\) 82119.7 0.843673
\(47\) 34502.7i 0.332322i −0.986099 0.166161i \(-0.946863\pi\)
0.986099 0.166161i \(-0.0531371\pi\)
\(48\) −79728.6 −0.720925
\(49\) −17998.4 −0.152984
\(50\) 105956.i 0.847649i
\(51\) −40556.8 −0.305740
\(52\) 136961.i 0.974065i
\(53\) 38215.6 0.256692 0.128346 0.991729i \(-0.459033\pi\)
0.128346 + 0.991729i \(0.459033\pi\)
\(54\) 37561.6i 0.238541i
\(55\) 123537.i 0.742523i
\(56\) 92886.0i 0.528916i
\(57\) −189229. −1.02179
\(58\) 315195.i 1.61546i
\(59\) 156402. 133112.i 0.761531 0.648129i
\(60\) 37607.2 0.174107
\(61\) 267542.i 1.17870i 0.807879 + 0.589348i \(0.200615\pi\)
−0.807879 + 0.589348i \(0.799385\pi\)
\(62\) −1930.89 −0.00810181
\(63\) 76709.0 0.306778
\(64\) −11171.2 −0.0426146
\(65\) 280427.i 1.02113i
\(66\) 271700. 0.945058
\(67\) 23922.1i 0.0795381i 0.999209 + 0.0397691i \(0.0126622\pi\)
−0.999209 + 0.0397691i \(0.987338\pi\)
\(68\) 89306.6 0.284025
\(69\) 129097.i 0.392979i
\(70\) 219998.i 0.641394i
\(71\) 213558. 0.596680 0.298340 0.954460i \(-0.403567\pi\)
0.298340 + 0.954460i \(0.403567\pi\)
\(72\) 71501.8i 0.191566i
\(73\) 140860.i 0.362093i −0.983475 0.181046i \(-0.942052\pi\)
0.983475 0.181046i \(-0.0579484\pi\)
\(74\) −160506. −0.396091
\(75\) −166569. −0.394831
\(76\) 416684. 0.949218
\(77\) 554872.i 1.21540i
\(78\) 616754. 1.29966
\(79\) 369365. 0.749160 0.374580 0.927195i \(-0.377787\pi\)
0.374580 + 0.927195i \(0.377787\pi\)
\(80\) 359464. 0.702078
\(81\) 59049.0 0.111111
\(82\) 813780.i 1.47593i
\(83\) 201363.i 0.352165i −0.984375 0.176082i \(-0.943657\pi\)
0.984375 0.176082i \(-0.0563425\pi\)
\(84\) −168914. −0.284989
\(85\) 182854. 0.297748
\(86\) 1.33590e6 2.10029
\(87\) −495505. −0.752473
\(88\) 517206. 0.758954
\(89\) 8376.32i 0.0118818i −0.999982 0.00594091i \(-0.998109\pi\)
0.999982 0.00594091i \(-0.00189106\pi\)
\(90\) 169350.i 0.232305i
\(91\) 1.25955e6i 1.67144i
\(92\) 284273.i 0.365067i
\(93\) 3035.47i 0.00377379i
\(94\) −342126. −0.411911
\(95\) 853156. 0.995080
\(96\) 497026.i 0.561779i
\(97\) 738936.i 0.809639i 0.914397 + 0.404820i \(0.132666\pi\)
−0.914397 + 0.404820i \(0.867334\pi\)
\(98\) 178471.i 0.189623i
\(99\) 427129.i 0.440204i
\(100\) 366788. 0.366788
\(101\) 1.69788e6i 1.64795i −0.566630 0.823973i \(-0.691753\pi\)
0.566630 0.823973i \(-0.308247\pi\)
\(102\) 402159.i 0.378963i
\(103\) 98537.6i 0.0901758i 0.998983 + 0.0450879i \(0.0143568\pi\)
−0.998983 + 0.0450879i \(0.985643\pi\)
\(104\) 1.17405e6 1.04372
\(105\) −345850. −0.298758
\(106\) 378943.i 0.318168i
\(107\) −563327. −0.459842 −0.229921 0.973209i \(-0.573847\pi\)
−0.229921 + 0.973209i \(0.573847\pi\)
\(108\) −130027. −0.103219
\(109\) 219893.i 0.169798i 0.996390 + 0.0848988i \(0.0270567\pi\)
−0.996390 + 0.0848988i \(0.972943\pi\)
\(110\) −1.22499e6 −0.920352
\(111\) 252324.i 0.184497i
\(112\) −1.61455e6 −1.14920
\(113\) 1.22429e6i 0.848492i −0.905547 0.424246i \(-0.860539\pi\)
0.905547 0.424246i \(-0.139461\pi\)
\(114\) 1.87638e6i 1.26650i
\(115\) 582047.i 0.382705i
\(116\) 1.09111e6 0.699028
\(117\) 969574.i 0.605374i
\(118\) −1.31993e6 1.55088e6i −0.803352 0.943912i
\(119\) −821297. −0.487371
\(120\) 322373.i 0.186558i
\(121\) −1.31807e6 −0.744014
\(122\) 2.65293e6 1.46099
\(123\) 1.27931e6 0.687481
\(124\) 6684.15i 0.00350575i
\(125\) 1.84915e6 0.946766
\(126\) 760642.i 0.380250i
\(127\) −2.62983e6 −1.28386 −0.641929 0.766764i \(-0.721866\pi\)
−0.641929 + 0.766764i \(0.721866\pi\)
\(128\) 2.15137e6i 1.02585i
\(129\) 2.10012e6i 0.978305i
\(130\) −2.78070e6 −1.26568
\(131\) 2.92615e6i 1.30161i −0.759243 0.650807i \(-0.774431\pi\)
0.759243 0.650807i \(-0.225569\pi\)
\(132\) 940544.i 0.408938i
\(133\) −3.83199e6 −1.62880
\(134\) 237210. 0.0985870
\(135\) −266228. −0.108206
\(136\) 765545.i 0.304336i
\(137\) 1.96220e6 0.763101 0.381550 0.924348i \(-0.375390\pi\)
0.381550 + 0.924348i \(0.375390\pi\)
\(138\) 1.28012e6 0.487095
\(139\) −3.16846e6 −1.17979 −0.589893 0.807481i \(-0.700830\pi\)
−0.589893 + 0.807481i \(0.700830\pi\)
\(140\) 761566. 0.277539
\(141\) 537843.i 0.191866i
\(142\) 2.11763e6i 0.739581i
\(143\) −7.01339e6 −2.39839
\(144\) −1.24285e6 −0.416226
\(145\) 2.23404e6 0.732801
\(146\) −1.39676e6 −0.448811
\(147\) −280567. −0.0883253
\(148\) 555621.i 0.171393i
\(149\) 3.34972e6i 1.01263i 0.862350 + 0.506313i \(0.168992\pi\)
−0.862350 + 0.506313i \(0.831008\pi\)
\(150\) 1.65169e6i 0.489390i
\(151\) 3.55679e6i 1.03307i −0.856267 0.516533i \(-0.827222\pi\)
0.856267 0.516533i \(-0.172778\pi\)
\(152\) 3.57186e6i 1.01710i
\(153\) −632218. −0.176519
\(154\) 5.50208e6 1.50649
\(155\) 13685.7i 0.00367513i
\(156\) 2.13502e6i 0.562376i
\(157\) 2.57388e6i 0.665104i 0.943085 + 0.332552i \(0.107910\pi\)
−0.943085 + 0.332552i \(0.892090\pi\)
\(158\) 3.66260e6i 0.928579i
\(159\) 595722. 0.148201
\(160\) 2.24089e6i 0.547093i
\(161\) 2.61429e6i 0.626434i
\(162\) 585527.i 0.137721i
\(163\) −1.21026e6 −0.279457 −0.139729 0.990190i \(-0.544623\pi\)
−0.139729 + 0.990190i \(0.544623\pi\)
\(164\) −2.81706e6 −0.638652
\(165\) 1.92575e6i 0.428696i
\(166\) −1.99671e6 −0.436506
\(167\) −6.75088e6 −1.44948 −0.724738 0.689024i \(-0.758039\pi\)
−0.724738 + 0.689024i \(0.758039\pi\)
\(168\) 1.44795e6i 0.305370i
\(169\) −1.10934e7 −2.29829
\(170\) 1.81317e6i 0.369056i
\(171\) −2.94978e6 −0.589932
\(172\) 4.62449e6i 0.908820i
\(173\) 4.51061e6i 0.871158i 0.900151 + 0.435579i \(0.143456\pi\)
−0.900151 + 0.435579i \(0.856544\pi\)
\(174\) 4.91340e6i 0.932685i
\(175\) −3.37312e6 −0.629387
\(176\) 8.99009e6i 1.64902i
\(177\) 2.43807e6 2.07501e6i 0.439670 0.374197i
\(178\) −83059.1 −0.0147274
\(179\) 2.01402e6i 0.351159i −0.984465 0.175579i \(-0.943820\pi\)
0.984465 0.175579i \(-0.0561799\pi\)
\(180\) 586238. 0.100521
\(181\) 5.72471e6 0.965424 0.482712 0.875779i \(-0.339652\pi\)
0.482712 + 0.875779i \(0.339652\pi\)
\(182\) 1.24896e7 2.07174
\(183\) 4.17056e6i 0.680521i
\(184\) 2.43682e6 0.391174
\(185\) 1.13763e6i 0.179674i
\(186\) −30099.6 −0.00467758
\(187\) 4.57313e6i 0.699340i
\(188\) 1.18434e6i 0.178239i
\(189\) 1.19577e6 0.177119
\(190\) 8.45985e6i 1.23339i
\(191\) 7.02854e6i 1.00871i 0.863497 + 0.504354i \(0.168269\pi\)
−0.863497 + 0.504354i \(0.831731\pi\)
\(192\) −174141. −0.0246035
\(193\) 1.27840e6 0.177825 0.0889126 0.996039i \(-0.471661\pi\)
0.0889126 + 0.996039i \(0.471661\pi\)
\(194\) 7.32725e6 1.00354
\(195\) 4.37142e6i 0.589548i
\(196\) 617813. 0.0820519
\(197\) 1.49210e7 1.95164 0.975819 0.218580i \(-0.0701425\pi\)
0.975819 + 0.218580i \(0.0701425\pi\)
\(198\) 4.23539e6 0.545630
\(199\) 1.18057e7 1.49807 0.749034 0.662532i \(-0.230518\pi\)
0.749034 + 0.662532i \(0.230518\pi\)
\(200\) 3.14414e6i 0.393018i
\(201\) 372909.i 0.0459214i
\(202\) −1.68361e7 −2.04262
\(203\) −1.00343e7 −1.19949
\(204\) 1.39215e6 0.163982
\(205\) −5.76790e6 −0.669509
\(206\) 977093. 0.111772
\(207\) 2.01242e6i 0.226886i
\(208\) 2.04073e7i 2.26775i
\(209\) 2.13372e7i 2.33721i
\(210\) 3.42943e6i 0.370309i
\(211\) 5.57655e6i 0.593633i 0.954935 + 0.296816i \(0.0959249\pi\)
−0.954935 + 0.296816i \(0.904075\pi\)
\(212\) −1.31179e6 −0.137675
\(213\) 3.32905e6 0.344493
\(214\) 5.58592e6i 0.569972i
\(215\) 9.46859e6i 0.952730i
\(216\) 1.11460e6i 0.110601i
\(217\) 61470.0i 0.00601567i
\(218\) 2.18044e6 0.210463
\(219\) 2.19579e6i 0.209054i
\(220\) 4.24054e6i 0.398247i
\(221\) 1.03809e7i 0.961741i
\(222\) −2.50203e6 −0.228683
\(223\) 1.19173e7 1.07464 0.537322 0.843377i \(-0.319436\pi\)
0.537322 + 0.843377i \(0.319436\pi\)
\(224\) 1.00651e7i 0.895514i
\(225\) −2.59656e6 −0.227956
\(226\) −1.21400e7 −1.05170
\(227\) 2.29320e7i 1.96049i 0.197790 + 0.980245i \(0.436624\pi\)
−0.197790 + 0.980245i \(0.563376\pi\)
\(228\) 6.49546e6 0.548032
\(229\) 2.08608e6i 0.173710i 0.996221 + 0.0868550i \(0.0276817\pi\)
−0.996221 + 0.0868550i \(0.972318\pi\)
\(230\) −5.77155e6 −0.474361
\(231\) 8.64960e6i 0.701714i
\(232\) 9.35310e6i 0.749017i
\(233\) 7.18787e6i 0.568241i 0.958789 + 0.284121i \(0.0917016\pi\)
−0.958789 + 0.284121i \(0.908298\pi\)
\(234\) 9.61425e6 0.750356
\(235\) 2.42492e6i 0.186850i
\(236\) −5.36867e6 + 4.56920e6i −0.408442 + 0.347620i
\(237\) 5.75783e6 0.432528
\(238\) 8.14394e6i 0.604093i
\(239\) −1.69825e7 −1.24397 −0.621983 0.783031i \(-0.713673\pi\)
−0.621983 + 0.783031i \(0.713673\pi\)
\(240\) 5.60349e6 0.405345
\(241\) 3.37071e6 0.240808 0.120404 0.992725i \(-0.461581\pi\)
0.120404 + 0.992725i \(0.461581\pi\)
\(242\) 1.30699e7i 0.922200i
\(243\) 920483. 0.0641500
\(244\) 9.18363e6i 0.632186i
\(245\) 1.26497e6 0.0860163
\(246\) 1.26856e7i 0.852128i
\(247\) 4.84349e7i 3.21416i
\(248\) −57297.2 −0.00375646
\(249\) 3.13894e6i 0.203323i
\(250\) 1.83361e7i 1.17351i
\(251\) −1.81189e7 −1.14580 −0.572901 0.819624i \(-0.694182\pi\)
−0.572901 + 0.819624i \(0.694182\pi\)
\(252\) −2.63311e6 −0.164539
\(253\) −1.45568e7 −0.898886
\(254\) 2.60773e7i 1.59133i
\(255\) 2.85042e6 0.171905
\(256\) 2.06179e7 1.22892
\(257\) −5.97124e6 −0.351775 −0.175887 0.984410i \(-0.556279\pi\)
−0.175887 + 0.984410i \(0.556279\pi\)
\(258\) 2.08246e7 1.21260
\(259\) 5.10971e6i 0.294101i
\(260\) 9.62593e6i 0.547675i
\(261\) −7.72416e6 −0.434440
\(262\) −2.90155e7 −1.61334
\(263\) 2.20924e7 1.21444 0.607220 0.794534i \(-0.292285\pi\)
0.607220 + 0.794534i \(0.292285\pi\)
\(264\) 8.06244e6 0.438182
\(265\) −2.68587e6 −0.144327
\(266\) 3.79978e7i 2.01889i
\(267\) 130574.i 0.00685997i
\(268\) 821151.i 0.0426598i
\(269\) 2.95123e7i 1.51616i 0.652159 + 0.758082i \(0.273863\pi\)
−0.652159 + 0.758082i \(0.726137\pi\)
\(270\) 2.63991e6i 0.134121i
\(271\) 2.45049e7 1.23125 0.615624 0.788040i \(-0.288904\pi\)
0.615624 + 0.788040i \(0.288904\pi\)
\(272\) 1.33067e7 0.661248
\(273\) 1.96344e7i 0.965006i
\(274\) 1.94571e7i 0.945858i
\(275\) 1.87821e7i 0.903123i
\(276\) 4.43139e6i 0.210772i
\(277\) −7.24719e6 −0.340981 −0.170491 0.985359i \(-0.554535\pi\)
−0.170491 + 0.985359i \(0.554535\pi\)
\(278\) 3.14182e7i 1.46234i
\(279\) 47318.3i 0.00217880i
\(280\) 6.52823e6i 0.297386i
\(281\) 4.38422e6 0.197594 0.0987969 0.995108i \(-0.468501\pi\)
0.0987969 + 0.995108i \(0.468501\pi\)
\(282\) −5.33322e6 −0.237817
\(283\) 6.34579e6i 0.279980i −0.990153 0.139990i \(-0.955293\pi\)
0.990153 0.139990i \(-0.0447070\pi\)
\(284\) −7.33060e6 −0.320025
\(285\) 1.32994e7 0.574510
\(286\) 6.95444e7i 2.97279i
\(287\) 2.59068e7 1.09589
\(288\) 7.74787e6i 0.324343i
\(289\) −1.73686e7 −0.719568
\(290\) 2.21526e7i 0.908302i
\(291\) 1.15189e7i 0.467445i
\(292\) 4.83516e6i 0.194206i
\(293\) 1.05299e7 0.418622 0.209311 0.977849i \(-0.432878\pi\)
0.209311 + 0.977849i \(0.432878\pi\)
\(294\) 2.78209e6i 0.109479i
\(295\) −1.09923e7 + 9.35540e6i −0.428176 + 0.364415i
\(296\) −4.76284e6 −0.183650
\(297\) 6.65829e6i 0.254152i
\(298\) 3.32156e7 1.25514
\(299\) −3.30437e7 −1.23616
\(300\) 5.71766e6 0.211765
\(301\) 4.25285e7i 1.55948i
\(302\) −3.52690e7 −1.28048
\(303\) 2.64673e7i 0.951442i
\(304\) 6.20861e7 2.20991
\(305\) 1.88034e7i 0.662730i
\(306\) 6.26904e6i 0.218795i
\(307\) −5.30124e7 −1.83215 −0.916077 0.401001i \(-0.868662\pi\)
−0.916077 + 0.401001i \(0.868662\pi\)
\(308\) 1.90465e7i 0.651874i
\(309\) 1.53605e6i 0.0520630i
\(310\) 135707. 0.00455530
\(311\) 2.41009e7 0.801219 0.400610 0.916249i \(-0.368798\pi\)
0.400610 + 0.916249i \(0.368798\pi\)
\(312\) 1.83016e7 0.602594
\(313\) 4.77031e7i 1.55566i 0.628477 + 0.777828i \(0.283679\pi\)
−0.628477 + 0.777828i \(0.716321\pi\)
\(314\) 2.55225e7 0.824393
\(315\) −5.39127e6 −0.172488
\(316\) −1.26788e7 −0.401807
\(317\) 1.81936e7 0.571137 0.285569 0.958358i \(-0.407818\pi\)
0.285569 + 0.958358i \(0.407818\pi\)
\(318\) 5.90714e6i 0.183695i
\(319\) 5.58725e7i 1.72118i
\(320\) 785133. 0.0239603
\(321\) −8.78139e6 −0.265490
\(322\) 2.59231e7 0.776461
\(323\) 3.15823e7 0.937209
\(324\) −2.02692e6 −0.0595937
\(325\) 4.26350e7i 1.24199i
\(326\) 1.20009e7i 0.346386i
\(327\) 3.42779e6i 0.0980326i
\(328\) 2.41481e7i 0.684324i
\(329\) 1.08916e7i 0.305847i
\(330\) −1.90957e7 −0.531365
\(331\) −6.20268e7 −1.71039 −0.855196 0.518305i \(-0.826563\pi\)
−0.855196 + 0.518305i \(0.826563\pi\)
\(332\) 6.91199e6i 0.188881i
\(333\) 3.93335e6i 0.106520i
\(334\) 6.69414e7i 1.79662i
\(335\) 1.68130e6i 0.0447209i
\(336\) −2.51683e7 −0.663493
\(337\) 5.85561e7i 1.52997i −0.644049 0.764984i \(-0.722747\pi\)
0.644049 0.764984i \(-0.277253\pi\)
\(338\) 1.10002e8i 2.84872i
\(339\) 1.90847e7i 0.489877i
\(340\) −6.27665e6 −0.159695
\(341\) 342276. 0.00863203
\(342\) 2.92499e7i 0.731217i
\(343\) −4.28205e7 −1.06113
\(344\) 3.96416e7 0.973813
\(345\) 9.07322e6i 0.220955i
\(346\) 4.47269e7 1.07979
\(347\) 7.33274e7i 1.75500i −0.479574 0.877501i \(-0.659209\pi\)
0.479574 0.877501i \(-0.340791\pi\)
\(348\) 1.70087e7 0.403584
\(349\) 1.37662e6i 0.0323845i −0.999869 0.0161923i \(-0.994846\pi\)
0.999869 0.0161923i \(-0.00515438\pi\)
\(350\) 3.34477e7i 0.780121i
\(351\) 1.51142e7i 0.349513i
\(352\) −5.60440e7 −1.28499
\(353\) 3.05310e7i 0.694091i −0.937848 0.347045i \(-0.887185\pi\)
0.937848 0.347045i \(-0.112815\pi\)
\(354\) −2.05757e7 2.41758e7i −0.463815 0.544968i
\(355\) −1.50093e7 −0.335487
\(356\) 287525.i 0.00637274i
\(357\) −1.28028e7 −0.281384
\(358\) −1.99709e7 −0.435259
\(359\) 4.05307e7 0.875993 0.437997 0.898977i \(-0.355688\pi\)
0.437997 + 0.898977i \(0.355688\pi\)
\(360\) 5.02529e6i 0.107709i
\(361\) 1.00310e8 2.13218
\(362\) 5.67660e7i 1.19664i
\(363\) −2.05466e7 −0.429557
\(364\) 4.32352e7i 0.896466i
\(365\) 9.89995e6i 0.203589i
\(366\) 4.13551e7 0.843501
\(367\) 2.60127e7i 0.526244i −0.964763 0.263122i \(-0.915248\pi\)
0.964763 0.263122i \(-0.0847522\pi\)
\(368\) 4.23569e7i 0.849925i
\(369\) 1.99425e7 0.396917
\(370\) 1.12807e7 0.222705
\(371\) 1.20637e7 0.236243
\(372\) 104196.i 0.00202405i
\(373\) −7.67396e7 −1.47874 −0.739372 0.673298i \(-0.764877\pi\)
−0.739372 + 0.673298i \(0.764877\pi\)
\(374\) −4.53469e7 −0.866827
\(375\) 2.88254e7 0.546616
\(376\) −1.01523e7 −0.190985
\(377\) 1.26829e8i 2.36699i
\(378\) 1.18572e7i 0.219537i
\(379\) 1.05935e8 1.94591 0.972955 0.230994i \(-0.0741979\pi\)
0.972955 + 0.230994i \(0.0741979\pi\)
\(380\) −2.92854e7 −0.533705
\(381\) −4.09950e7 −0.741235
\(382\) 6.96947e7 1.25029
\(383\) −7.76856e7 −1.38275 −0.691376 0.722495i \(-0.742995\pi\)
−0.691376 + 0.722495i \(0.742995\pi\)
\(384\) 3.35365e7i 0.592275i
\(385\) 3.89976e7i 0.683369i
\(386\) 1.26765e7i 0.220413i
\(387\) 3.27376e7i 0.564825i
\(388\) 2.53647e7i 0.434245i
\(389\) −1.60025e7 −0.271855 −0.135928 0.990719i \(-0.543401\pi\)
−0.135928 + 0.990719i \(0.543401\pi\)
\(390\) −4.33468e7 −0.730740
\(391\) 2.15463e7i 0.360449i
\(392\) 5.29596e6i 0.0879197i
\(393\) 4.56141e7i 0.751487i
\(394\) 1.47956e8i 2.41904i
\(395\) −2.59597e7 −0.421220
\(396\) 1.46616e7i 0.236100i
\(397\) 9.53672e7i 1.52415i 0.647489 + 0.762074i \(0.275819\pi\)
−0.647489 + 0.762074i \(0.724181\pi\)
\(398\) 1.17064e8i 1.85685i
\(399\) −5.97347e7 −0.940391
\(400\) 5.46516e7 0.853931
\(401\) 7.34361e7i 1.13888i −0.822034 0.569438i \(-0.807161\pi\)
0.822034 0.569438i \(-0.192839\pi\)
\(402\) 3.69775e6 0.0569192
\(403\) 776958. 0.0118709
\(404\) 5.82814e7i 0.883865i
\(405\) −4.15009e6 −0.0624730
\(406\) 9.94991e7i 1.48676i
\(407\) 2.84517e7 0.422013
\(408\) 1.19337e7i 0.175709i
\(409\) 6.32248e7i 0.924097i 0.886855 + 0.462048i \(0.152885\pi\)
−0.886855 + 0.462048i \(0.847115\pi\)
\(410\) 5.71942e7i 0.829851i
\(411\) 3.05877e7 0.440576
\(412\) 3.38240e6i 0.0483652i
\(413\) 4.93723e7 4.20201e7i 0.700863 0.596496i
\(414\) 1.99551e7 0.281224
\(415\) 1.41522e7i 0.198007i
\(416\) −1.27219e8 −1.76714
\(417\) −4.93913e7 −0.681150
\(418\) −2.11578e8 −2.89696
\(419\) 1.15918e7i 0.157583i 0.996891 + 0.0787916i \(0.0251062\pi\)
−0.996891 + 0.0787916i \(0.974894\pi\)
\(420\) 1.18716e7 0.160237
\(421\) 1.15562e8i 1.54870i 0.632755 + 0.774352i \(0.281924\pi\)
−0.632755 + 0.774352i \(0.718076\pi\)
\(422\) 5.52967e7 0.735804
\(423\) 8.38414e6i 0.110774i
\(424\) 1.12448e7i 0.147521i
\(425\) 2.78005e7 0.362147
\(426\) 3.30106e7i 0.426997i
\(427\) 8.44562e7i 1.08480i
\(428\) 1.93367e7 0.246634
\(429\) −1.09328e8 −1.38471
\(430\) −9.38900e7 −1.18090
\(431\) 3.80235e7i 0.474920i −0.971397 0.237460i \(-0.923685\pi\)
0.971397 0.237460i \(-0.0763149\pi\)
\(432\) −1.93740e7 −0.240308
\(433\) −4.82860e7 −0.594782 −0.297391 0.954756i \(-0.596117\pi\)
−0.297391 + 0.954756i \(0.596117\pi\)
\(434\) −609533. −0.00745638
\(435\) 3.48252e7 0.423083
\(436\) 7.54803e6i 0.0910698i
\(437\) 1.00530e8i 1.20463i
\(438\) −2.17734e7 −0.259121
\(439\) −5.04082e6 −0.0595809 −0.0297905 0.999556i \(-0.509484\pi\)
−0.0297905 + 0.999556i \(0.509484\pi\)
\(440\) −3.63503e7 −0.426727
\(441\) −4.37361e6 −0.0509946
\(442\) −1.02936e8 −1.19207
\(443\) 1.24562e8i 1.43276i 0.697711 + 0.716379i \(0.254202\pi\)
−0.697711 + 0.716379i \(0.745798\pi\)
\(444\) 8.66128e6i 0.0989540i
\(445\) 588705.i 0.00668064i
\(446\) 1.18172e8i 1.33201i
\(447\) 5.22169e7i 0.584640i
\(448\) −3.52645e6 −0.0392197
\(449\) 2.91679e7 0.322230 0.161115 0.986936i \(-0.448491\pi\)
0.161115 + 0.986936i \(0.448491\pi\)
\(450\) 2.57473e7i 0.282550i
\(451\) 1.44253e8i 1.57252i
\(452\) 4.20248e7i 0.455083i
\(453\) 5.54449e7i 0.596441i
\(454\) 2.27393e8 2.43001
\(455\) 8.85237e7i 0.939778i
\(456\) 5.56798e7i 0.587223i
\(457\) 1.21827e7i 0.127643i −0.997961 0.0638213i \(-0.979671\pi\)
0.997961 0.0638213i \(-0.0203288\pi\)
\(458\) 2.06855e7 0.215312
\(459\) −9.85530e6 −0.101913
\(460\) 1.99793e7i 0.205262i
\(461\) 3.02369e7 0.308628 0.154314 0.988022i \(-0.450683\pi\)
0.154314 + 0.988022i \(0.450683\pi\)
\(462\) 8.57690e7 0.869770
\(463\) 2.77245e7i 0.279332i 0.990199 + 0.139666i \(0.0446028\pi\)
−0.990199 + 0.139666i \(0.955397\pi\)
\(464\) 1.62576e8 1.62743
\(465\) 213339.i 0.00212184i
\(466\) 7.12746e7 0.704331
\(467\) 8.09525e7i 0.794840i 0.917637 + 0.397420i \(0.130094\pi\)
−0.917637 + 0.397420i \(0.869906\pi\)
\(468\) 3.32816e7i 0.324688i
\(469\) 7.55161e6i 0.0732017i
\(470\) 2.40454e7 0.231600
\(471\) 4.01229e7i 0.383998i
\(472\) −3.91677e7 4.60208e7i −0.372479 0.437651i
\(473\) −2.36806e8 −2.23774
\(474\) 5.70943e7i 0.536115i
\(475\) 1.29711e8 1.21031
\(476\) 2.81918e7 0.261398
\(477\) 9.28638e6 0.0855641
\(478\) 1.68398e8i 1.54189i
\(479\) −1.78760e8 −1.62654 −0.813269 0.581888i \(-0.802314\pi\)
−0.813269 + 0.581888i \(0.802314\pi\)
\(480\) 3.49321e7i 0.315864i
\(481\) 6.45849e7 0.580357
\(482\) 3.34238e7i 0.298480i
\(483\) 4.07527e7i 0.361672i
\(484\) 4.52439e7 0.399047
\(485\) 5.19340e7i 0.455225i
\(486\) 9.12746e6i 0.0795135i
\(487\) 1.00111e8 0.866752 0.433376 0.901213i \(-0.357322\pi\)
0.433376 + 0.901213i \(0.357322\pi\)
\(488\) 7.87230e7 0.677396
\(489\) −1.88661e7 −0.161345
\(490\) 1.25433e7i 0.106617i
\(491\) 1.22140e8 1.03184 0.515920 0.856637i \(-0.327450\pi\)
0.515920 + 0.856637i \(0.327450\pi\)
\(492\) −4.39136e7 −0.368726
\(493\) 8.27000e7 0.690184
\(494\) −4.80278e8 −3.98393
\(495\) 3.00195e7i 0.247508i
\(496\) 995941.i 0.00816185i
\(497\) 6.74150e7 0.549145
\(498\) −3.11256e7 −0.252017
\(499\) −6.22366e7 −0.500892 −0.250446 0.968131i \(-0.580577\pi\)
−0.250446 + 0.968131i \(0.580577\pi\)
\(500\) −6.34740e7 −0.507792
\(501\) −1.05236e8 −0.836856
\(502\) 1.79666e8i 1.42021i
\(503\) 5.88439e7i 0.462378i −0.972909 0.231189i \(-0.925738\pi\)
0.972909 0.231189i \(-0.0742616\pi\)
\(504\) 2.25713e7i 0.176305i
\(505\) 1.19331e8i 0.926569i
\(506\) 1.44345e8i 1.11416i
\(507\) −1.72929e8 −1.32692
\(508\) 9.02716e7 0.688589
\(509\) 7.99767e6i 0.0606471i −0.999540 0.0303236i \(-0.990346\pi\)
0.999540 0.0303236i \(-0.00965377\pi\)
\(510\) 2.82646e7i 0.213075i
\(511\) 4.44660e7i 0.333246i
\(512\) 6.67583e7i 0.497388i
\(513\) −4.59826e7 −0.340597
\(514\) 5.92104e7i 0.436023i
\(515\) 6.92543e6i 0.0507020i
\(516\) 7.20886e7i 0.524708i
\(517\) 6.06465e7 0.438868
\(518\) −5.06676e7 −0.364536
\(519\) 7.03134e7i 0.502963i
\(520\) −8.25144e7 −0.586840
\(521\) 1.52735e8 1.08000 0.540002 0.841664i \(-0.318424\pi\)
0.540002 + 0.841664i \(0.318424\pi\)
\(522\) 7.65924e7i 0.538486i
\(523\) −1.44484e8 −1.00998 −0.504992 0.863124i \(-0.668504\pi\)
−0.504992 + 0.863124i \(0.668504\pi\)
\(524\) 1.00443e8i 0.698113i
\(525\) −5.25817e7 −0.363377
\(526\) 2.19067e8i 1.50529i
\(527\) 506621.i 0.00346140i
\(528\) 1.40142e8i 0.952062i
\(529\) 7.94513e7 0.536703
\(530\) 2.66329e7i 0.178892i
\(531\) 3.80058e7 3.23462e7i 0.253844 0.216043i
\(532\) 1.31537e8 0.873599
\(533\) 3.27452e8i 2.16255i
\(534\) −1.29476e6 −0.00850289
\(535\) 3.95918e7 0.258550
\(536\) 7.03899e6 0.0457105
\(537\) 3.13954e7i 0.202742i
\(538\) 2.92642e8 1.87927
\(539\) 3.16364e7i 0.202032i
\(540\) 9.13855e6 0.0580358
\(541\) 2.14241e8i 1.35304i −0.736423 0.676522i \(-0.763487\pi\)
0.736423 0.676522i \(-0.236513\pi\)
\(542\) 2.42990e8i 1.52612i
\(543\) 8.92395e7 0.557388
\(544\) 8.29539e7i 0.515276i
\(545\) 1.54545e7i 0.0954698i
\(546\) 1.94694e8 1.19612
\(547\) 2.40800e8 1.47128 0.735639 0.677373i \(-0.236882\pi\)
0.735639 + 0.677373i \(0.236882\pi\)
\(548\) −6.73545e7 −0.409284
\(549\) 6.50126e7i 0.392899i
\(550\) −1.86243e8 −1.11941
\(551\) 3.85859e8 2.30661
\(552\) 3.79863e7 0.225845
\(553\) 1.16599e8 0.689478
\(554\) 7.18627e7i 0.422644i
\(555\) 1.77339e7i 0.103735i
\(556\) 1.08760e8 0.632771
\(557\) −3.76529e7 −0.217888 −0.108944 0.994048i \(-0.534747\pi\)
−0.108944 + 0.994048i \(0.534747\pi\)
\(558\) −469206. −0.00270060
\(559\) −5.37545e8 −3.07737
\(560\) 1.13474e8 0.646147
\(561\) 7.12880e7i 0.403764i
\(562\) 4.34737e7i 0.244916i
\(563\) 1.25482e8i 0.703162i 0.936157 + 0.351581i \(0.114356\pi\)
−0.936157 + 0.351581i \(0.885644\pi\)
\(564\) 1.84620e7i 0.102906i
\(565\) 8.60454e7i 0.477070i
\(566\) −6.29245e7 −0.347033
\(567\) 1.86403e7 0.102259
\(568\) 6.28387e7i 0.342911i
\(569\) 1.90978e8i 1.03668i 0.855173 + 0.518342i \(0.173451\pi\)
−0.855173 + 0.518342i \(0.826549\pi\)
\(570\) 1.31876e8i 0.712101i
\(571\) 3.02963e8i 1.62735i 0.581321 + 0.813675i \(0.302536\pi\)
−0.581321 + 0.813675i \(0.697464\pi\)
\(572\) 2.40741e8 1.28636
\(573\) 1.09564e8i 0.582378i
\(574\) 2.56890e8i 1.35835i
\(575\) 8.84922e7i 0.465481i
\(576\) −2.71459e6 −0.0142049
\(577\) 2.82315e8 1.46962 0.734812 0.678271i \(-0.237271\pi\)
0.734812 + 0.678271i \(0.237271\pi\)
\(578\) 1.72226e8i 0.891900i
\(579\) 1.99282e7 0.102667
\(580\) −7.66855e7 −0.393033
\(581\) 6.35653e7i 0.324110i
\(582\) 1.14220e8 0.579395
\(583\) 6.71728e7i 0.338991i
\(584\) −4.14475e7 −0.208094
\(585\) 6.81437e7i 0.340375i
\(586\) 1.04414e8i 0.518880i
\(587\) 3.55786e7i 0.175904i −0.996125 0.0879518i \(-0.971968\pi\)
0.996125 0.0879518i \(-0.0280321\pi\)
\(588\) 9.63075e6 0.0473727
\(589\) 2.36378e6i 0.0115681i
\(590\) 9.27676e7 + 1.08999e8i 0.451690 + 0.530721i
\(591\) 2.32595e8 1.12678
\(592\) 8.27879e7i 0.399026i
\(593\) −2.37978e8 −1.14123 −0.570614 0.821218i \(-0.693295\pi\)
−0.570614 + 0.821218i \(0.693295\pi\)
\(594\) 6.60232e7 0.315019
\(595\) 5.77225e7 0.274027
\(596\) 1.14982e8i 0.543116i
\(597\) 1.84032e8 0.864910
\(598\) 3.27659e8i 1.53221i
\(599\) −3.35138e8 −1.55935 −0.779674 0.626185i \(-0.784615\pi\)
−0.779674 + 0.626185i \(0.784615\pi\)
\(600\) 4.90123e7i 0.226909i
\(601\) 5.73297e7i 0.264093i −0.991244 0.132046i \(-0.957845\pi\)
0.991244 0.132046i \(-0.0421548\pi\)
\(602\) 4.21711e8 1.93297
\(603\) 5.81308e6i 0.0265127i
\(604\) 1.22090e8i 0.554078i
\(605\) 9.26364e7 0.418327
\(606\) −2.62449e8 −1.17931
\(607\) −5.69967e7 −0.254849 −0.127425 0.991848i \(-0.540671\pi\)
−0.127425 + 0.991848i \(0.540671\pi\)
\(608\) 3.87044e8i 1.72206i
\(609\) −1.56419e8 −0.692527
\(610\) −1.86453e8 −0.821449
\(611\) 1.37666e8 0.603537
\(612\) 2.17015e7 0.0946750
\(613\) 1.77064e8i 0.768685i 0.923191 + 0.384342i \(0.125572\pi\)
−0.923191 + 0.384342i \(0.874428\pi\)
\(614\) 5.25668e8i 2.27094i
\(615\) −8.99127e7 −0.386541
\(616\) 1.63269e8 0.698492
\(617\) −1.07770e8 −0.458820 −0.229410 0.973330i \(-0.573680\pi\)
−0.229410 + 0.973330i \(0.573680\pi\)
\(618\) 1.52314e7 0.0645318
\(619\) 2.76526e8 1.16591 0.582953 0.812506i \(-0.301897\pi\)
0.582953 + 0.812506i \(0.301897\pi\)
\(620\) 469776.i 0.00197113i
\(621\) 3.13706e7i 0.130993i
\(622\) 2.38983e8i 0.993106i
\(623\) 2.64419e6i 0.0109353i
\(624\) 3.18118e8i 1.30929i
\(625\) 3.69975e7 0.151542
\(626\) 4.73021e8 1.92823
\(627\) 3.32614e8i 1.34939i
\(628\) 8.83511e7i 0.356724i
\(629\) 4.21130e7i 0.169225i
\(630\) 5.34595e7i 0.213798i
\(631\) 2.00851e8 0.799442 0.399721 0.916637i \(-0.369107\pi\)
0.399721 + 0.916637i \(0.369107\pi\)
\(632\) 1.08684e8i 0.430541i
\(633\) 8.69297e7i 0.342734i
\(634\) 1.80407e8i 0.707921i
\(635\) 1.84830e8 0.721858
\(636\) −2.04487e7 −0.0794868
\(637\) 7.18139e7i 0.277837i
\(638\) −5.54029e8 −2.13339
\(639\) 5.18947e7 0.198893
\(640\) 1.51202e8i 0.576792i
\(641\) −3.76806e8 −1.43068 −0.715341 0.698775i \(-0.753729\pi\)
−0.715341 + 0.698775i \(0.753729\pi\)
\(642\) 8.70758e7i 0.329073i
\(643\) 1.11916e8 0.420979 0.210489 0.977596i \(-0.432494\pi\)
0.210489 + 0.977596i \(0.432494\pi\)
\(644\) 8.97380e7i 0.335984i
\(645\) 1.47601e8i 0.550059i
\(646\) 3.13169e8i 1.16166i
\(647\) 9.73243e7 0.359342 0.179671 0.983727i \(-0.442497\pi\)
0.179671 + 0.983727i \(0.442497\pi\)
\(648\) 1.73749e7i 0.0638554i
\(649\) 2.33976e8 + 2.74914e8i 0.855926 + 1.00569i
\(650\) −4.22767e8 −1.53943
\(651\) 958222.i 0.00347315i
\(652\) 4.15434e7 0.149885
\(653\) −7.12719e7 −0.255964 −0.127982 0.991777i \(-0.540850\pi\)
−0.127982 + 0.991777i \(0.540850\pi\)
\(654\) 3.39898e7 0.121511
\(655\) 2.05656e8i 0.731842i
\(656\) −4.19743e8 −1.48687
\(657\) 3.42290e7i 0.120698i
\(658\) −1.08001e8 −0.379096
\(659\) 1.41719e8i 0.495190i 0.968864 + 0.247595i \(0.0796402\pi\)
−0.968864 + 0.247595i \(0.920360\pi\)
\(660\) 6.61034e7i 0.229928i
\(661\) −3.46865e8 −1.20104 −0.600519 0.799611i \(-0.705039\pi\)
−0.600519 + 0.799611i \(0.705039\pi\)
\(662\) 6.15055e8i 2.12002i
\(663\) 1.61822e8i 0.555262i
\(664\) −5.92503e7 −0.202389
\(665\) 2.69320e8 0.915806
\(666\) −3.90028e7 −0.132030
\(667\) 2.63244e8i 0.887117i
\(668\) 2.31731e8 0.777417
\(669\) 1.85773e8 0.620445
\(670\) −1.66717e7 −0.0554312
\(671\) −4.70267e8 −1.55660
\(672\) 1.56899e8i 0.517025i
\(673\) 1.27064e8i 0.416849i −0.978038 0.208424i \(-0.933166\pi\)
0.978038 0.208424i \(-0.0668336\pi\)
\(674\) −5.80639e8 −1.89639
\(675\) −4.04763e7 −0.131610
\(676\) 3.80793e8 1.23268
\(677\) −4.88993e8 −1.57593 −0.787964 0.615722i \(-0.788865\pi\)
−0.787964 + 0.615722i \(0.788865\pi\)
\(678\) −1.89243e8 −0.607199
\(679\) 2.33263e8i 0.745139i
\(680\) 5.38041e7i 0.171115i
\(681\) 3.57475e8i 1.13189i
\(682\) 3.39399e6i 0.0106993i
\(683\) 3.15064e8i 0.988864i −0.869216 0.494432i \(-0.835376\pi\)
0.869216 0.494432i \(-0.164624\pi\)
\(684\) 1.01254e8 0.316406
\(685\) −1.37908e8 −0.429058
\(686\) 4.24605e8i 1.31526i
\(687\) 3.25188e7i 0.100292i
\(688\) 6.89051e8i 2.11585i
\(689\) 1.52481e8i 0.466184i
\(690\) −8.99695e7 −0.273872
\(691\) 6.17270e8i 1.87086i 0.353513 + 0.935430i \(0.384987\pi\)
−0.353513 + 0.935430i \(0.615013\pi\)
\(692\) 1.54831e8i 0.467240i
\(693\) 1.34834e8i 0.405135i
\(694\) −7.27110e8 −2.17531
\(695\) 2.22686e8 0.663343
\(696\) 1.45800e8i 0.432445i
\(697\) −2.13517e8 −0.630572
\(698\) −1.36505e7 −0.0401404
\(699\) 1.12048e8i 0.328074i
\(700\) 1.15786e8 0.337568
\(701\) 4.33185e8i 1.25753i 0.777594 + 0.628766i \(0.216440\pi\)
−0.777594 + 0.628766i \(0.783560\pi\)
\(702\) 1.49871e8 0.433219
\(703\) 1.96490e8i 0.565554i
\(704\) 1.96359e7i 0.0562773i
\(705\) 3.78007e7i 0.107878i
\(706\) −3.02743e8 −0.860321
\(707\) 5.35978e8i 1.51666i
\(708\) −8.36892e7 + 7.12268e7i −0.235814 + 0.200698i
\(709\) −5.33293e7 −0.149633 −0.0748165 0.997197i \(-0.523837\pi\)
−0.0748165 + 0.997197i \(0.523837\pi\)
\(710\) 1.48832e8i 0.415834i
\(711\) 8.97557e7 0.249720
\(712\) −2.46470e6 −0.00682847
\(713\) 1.61264e6 0.00444905
\(714\) 1.26951e8i 0.348773i
\(715\) 4.92916e8 1.34851
\(716\) 6.91331e7i 0.188342i
\(717\) −2.64731e8 −0.718204
\(718\) 4.01900e8i 1.08579i
\(719\) 1.43489e8i 0.386039i 0.981195 + 0.193020i \(0.0618281\pi\)
−0.981195 + 0.193020i \(0.938172\pi\)
\(720\) 8.73498e7 0.234026
\(721\) 3.11058e7i 0.0829920i
\(722\) 9.94670e8i 2.64282i
\(723\) 5.25442e7 0.139030
\(724\) −1.96506e8 −0.517799
\(725\) 3.39654e8 0.891298
\(726\) 2.03739e8i 0.532432i
\(727\) −3.66892e8 −0.954850 −0.477425 0.878672i \(-0.658430\pi\)
−0.477425 + 0.878672i \(0.658430\pi\)
\(728\) 3.70617e8 0.960574
\(729\) 1.43489e7 0.0370370
\(730\) 9.81674e7 0.252347
\(731\) 3.50510e8i 0.897322i
\(732\) 1.43159e8i 0.364993i
\(733\) 3.01738e8 0.766158 0.383079 0.923715i \(-0.374864\pi\)
0.383079 + 0.923715i \(0.374864\pi\)
\(734\) −2.57940e8 −0.652276
\(735\) 1.97189e7 0.0496615
\(736\) −2.64052e8 −0.662302
\(737\) −4.20487e7 −0.105039
\(738\) 1.97749e8i 0.491976i
\(739\) 4.84655e8i 1.20088i 0.799670 + 0.600440i \(0.205008\pi\)
−0.799670 + 0.600440i \(0.794992\pi\)
\(740\) 3.90502e7i 0.0963670i
\(741\) 7.55026e8i 1.85570i
\(742\) 1.19623e8i 0.292821i
\(743\) 7.54774e8 1.84014 0.920069 0.391755i \(-0.128132\pi\)
0.920069 + 0.391755i \(0.128132\pi\)
\(744\) −893175. −0.00216879
\(745\) 2.35425e8i 0.569356i
\(746\) 7.60945e8i 1.83289i
\(747\) 4.89313e7i 0.117388i
\(748\) 1.56977e8i 0.375087i
\(749\) −1.77828e8 −0.423209
\(750\) 2.85831e8i 0.677526i
\(751\) 2.39183e8i 0.564691i −0.959313 0.282345i \(-0.908888\pi\)
0.959313 0.282345i \(-0.0911124\pi\)
\(752\) 1.76467e8i 0.414963i
\(753\) −2.82445e8 −0.661529
\(754\) −1.25763e9 −2.93387
\(755\) 2.49979e8i 0.580848i
\(756\) −4.10461e7 −0.0949964
\(757\) 1.77949e8 0.410211 0.205106 0.978740i \(-0.434246\pi\)
0.205106 + 0.978740i \(0.434246\pi\)
\(758\) 1.05045e9i 2.41194i
\(759\) −2.26918e8 −0.518972
\(760\) 2.51038e8i 0.571871i
\(761\) 7.08378e7 0.160735 0.0803676 0.996765i \(-0.474391\pi\)
0.0803676 + 0.996765i \(0.474391\pi\)
\(762\) 4.06504e8i 0.918756i
\(763\) 6.94146e7i 0.156271i
\(764\) 2.41262e8i 0.541014i
\(765\) 4.44336e7 0.0992492
\(766\) 7.70326e8i 1.71391i
\(767\) 5.31120e8 + 6.24048e8i 1.17708 + 1.38303i
\(768\) 3.21401e8 0.709518
\(769\) 7.07471e8i 1.55571i −0.628441 0.777857i \(-0.716307\pi\)
0.628441 0.777857i \(-0.283693\pi\)
\(770\) −3.86698e8 −0.847032
\(771\) −9.30823e7 −0.203097
\(772\) −4.38822e7 −0.0953754
\(773\) 7.54245e8i 1.63295i −0.577378 0.816477i \(-0.695924\pi\)
0.577378 0.816477i \(-0.304076\pi\)
\(774\) 3.24624e8 0.700097
\(775\) 2.08073e6i 0.00447002i
\(776\) 2.17429e8 0.465299
\(777\) 7.96524e7i 0.169799i
\(778\) 1.58680e8i 0.336963i
\(779\) −9.96224e8 −2.10739
\(780\) 1.50053e8i 0.316200i
\(781\) 3.75379e8i 0.787982i
\(782\) −2.13652e8 −0.446774
\(783\) −1.20408e8 −0.250824
\(784\) 9.20545e7 0.191028
\(785\) 1.80898e8i