Properties

Label 177.7.c.a.58.12
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 58.12
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.49

$q$-expansion

\(f(q)\) \(=\) \(q-10.4738i q^{2} -15.5885 q^{3} -45.7013 q^{4} +65.8108 q^{5} +163.271i q^{6} +49.8494 q^{7} -191.658i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-10.4738i q^{2} -15.5885 q^{3} -45.7013 q^{4} +65.8108 q^{5} +163.271i q^{6} +49.8494 q^{7} -191.658i q^{8} +243.000 q^{9} -689.291i q^{10} +359.481i q^{11} +712.413 q^{12} +1757.21i q^{13} -522.114i q^{14} -1025.89 q^{15} -4932.27 q^{16} -2676.91 q^{17} -2545.14i q^{18} +1226.97 q^{19} -3007.64 q^{20} -777.075 q^{21} +3765.14 q^{22} +17806.6i q^{23} +2987.65i q^{24} -11293.9 q^{25} +18404.8 q^{26} -3788.00 q^{27} -2278.18 q^{28} -11354.5 q^{29} +10745.0i q^{30} +40936.7i q^{31} +39393.8i q^{32} -5603.75i q^{33} +28037.5i q^{34} +3280.63 q^{35} -11105.4 q^{36} +48303.0i q^{37} -12851.1i q^{38} -27392.2i q^{39} -12613.1i q^{40} +116179. q^{41} +8138.96i q^{42} -84100.8i q^{43} -16428.7i q^{44} +15992.0 q^{45} +186503. q^{46} +121248. i q^{47} +76886.6 q^{48} -115164. q^{49} +118291. i q^{50} +41728.9 q^{51} -80306.8i q^{52} +265316. q^{53} +39674.8i q^{54} +23657.7i q^{55} -9554.02i q^{56} -19126.6 q^{57} +118925. i q^{58} +(-205323. + 4783.75i) q^{59} +46884.4 q^{60} -288153. i q^{61} +428764. q^{62} +12113.4 q^{63} +96938.3 q^{64} +115643. i q^{65} -58692.8 q^{66} +150364. i q^{67} +122338. q^{68} -277577. i q^{69} -34360.7i q^{70} -157139. q^{71} -46572.8i q^{72} -15652.5i q^{73} +505918. q^{74} +176055. q^{75} -56074.3 q^{76} +17919.9i q^{77} -286902. q^{78} +756230. q^{79} -324597. q^{80} +59049.0 q^{81} -1.21684e6i q^{82} -669157. i q^{83} +35513.3 q^{84} -176169. q^{85} -880859. q^{86} +176999. q^{87} +68897.2 q^{88} +802081. i q^{89} -167498. i q^{90} +87595.9i q^{91} -813785. i q^{92} -638139. i q^{93} +1.26993e6 q^{94} +80748.1 q^{95} -614088. i q^{96} +879496. i q^{97} +1.20621e6i q^{98} +87353.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.4738i 1.30923i −0.755963 0.654615i \(-0.772831\pi\)
0.755963 0.654615i \(-0.227169\pi\)
\(3\) −15.5885 −0.577350
\(4\) −45.7013 −0.714083
\(5\) 65.8108 0.526486 0.263243 0.964730i \(-0.415208\pi\)
0.263243 + 0.964730i \(0.415208\pi\)
\(6\) 163.271i 0.755884i
\(7\) 49.8494 0.145333 0.0726667 0.997356i \(-0.476849\pi\)
0.0726667 + 0.997356i \(0.476849\pi\)
\(8\) 191.658i 0.374331i
\(9\) 243.000 0.333333
\(10\) 689.291i 0.689291i
\(11\) 359.481i 0.270083i 0.990840 + 0.135042i \(0.0431168\pi\)
−0.990840 + 0.135042i \(0.956883\pi\)
\(12\) 712.413 0.412276
\(13\) 1757.21i 0.799823i 0.916554 + 0.399912i \(0.130959\pi\)
−0.916554 + 0.399912i \(0.869041\pi\)
\(14\) 522.114i 0.190275i
\(15\) −1025.89 −0.303967
\(16\) −4932.27 −1.20417
\(17\) −2676.91 −0.544862 −0.272431 0.962175i \(-0.587828\pi\)
−0.272431 + 0.962175i \(0.587828\pi\)
\(18\) 2545.14i 0.436410i
\(19\) 1226.97 0.178885 0.0894426 0.995992i \(-0.471491\pi\)
0.0894426 + 0.995992i \(0.471491\pi\)
\(20\) −3007.64 −0.375955
\(21\) −777.075 −0.0839083
\(22\) 3765.14 0.353601
\(23\) 17806.6i 1.46352i 0.681564 + 0.731758i \(0.261300\pi\)
−0.681564 + 0.731758i \(0.738700\pi\)
\(24\) 2987.65i 0.216120i
\(25\) −11293.9 −0.722812
\(26\) 18404.8 1.04715
\(27\) −3788.00 −0.192450
\(28\) −2278.18 −0.103780
\(29\) −11354.5 −0.465558 −0.232779 0.972530i \(-0.574782\pi\)
−0.232779 + 0.972530i \(0.574782\pi\)
\(30\) 10745.0i 0.397963i
\(31\) 40936.7i 1.37413i 0.726597 + 0.687064i \(0.241101\pi\)
−0.726597 + 0.687064i \(0.758899\pi\)
\(32\) 39393.8i 1.20220i
\(33\) 5603.75i 0.155933i
\(34\) 28037.5i 0.713350i
\(35\) 3280.63 0.0765161
\(36\) −11105.4 −0.238028
\(37\) 48303.0i 0.953606i 0.879010 + 0.476803i \(0.158204\pi\)
−0.879010 + 0.476803i \(0.841796\pi\)
\(38\) 12851.1i 0.234202i
\(39\) 27392.2i 0.461778i
\(40\) 12613.1i 0.197080i
\(41\) 116179. 1.68569 0.842844 0.538158i \(-0.180880\pi\)
0.842844 + 0.538158i \(0.180880\pi\)
\(42\) 8138.96i 0.109855i
\(43\) 84100.8i 1.05778i −0.848691 0.528889i \(-0.822609\pi\)
0.848691 0.528889i \(-0.177391\pi\)
\(44\) 16428.7i 0.192862i
\(45\) 15992.0 0.175495
\(46\) 186503. 1.91608
\(47\) 121248.i 1.16783i 0.811814 + 0.583917i \(0.198481\pi\)
−0.811814 + 0.583917i \(0.801519\pi\)
\(48\) 76886.6 0.695227
\(49\) −115164. −0.978878
\(50\) 118291.i 0.946327i
\(51\) 41728.9 0.314576
\(52\) 80306.8i 0.571140i
\(53\) 265316. 1.78211 0.891056 0.453893i \(-0.149965\pi\)
0.891056 + 0.453893i \(0.149965\pi\)
\(54\) 39674.8i 0.251961i
\(55\) 23657.7i 0.142195i
\(56\) 9554.02i 0.0544029i
\(57\) −19126.6 −0.103279
\(58\) 118925.i 0.609522i
\(59\) −205323. + 4783.75i −0.999729 + 0.0232923i
\(60\) 46884.4 0.217058
\(61\) 288153.i 1.26950i −0.772716 0.634752i \(-0.781102\pi\)
0.772716 0.634752i \(-0.218898\pi\)
\(62\) 428764. 1.79905
\(63\) 12113.4 0.0484445
\(64\) 96938.3 0.369790
\(65\) 115643.i 0.421096i
\(66\) −58692.8 −0.204152
\(67\) 150364.i 0.499941i 0.968253 + 0.249971i \(0.0804210\pi\)
−0.968253 + 0.249971i \(0.919579\pi\)
\(68\) 122338. 0.389077
\(69\) 277577.i 0.844962i
\(70\) 34360.7i 0.100177i
\(71\) −157139. −0.439044 −0.219522 0.975608i \(-0.570450\pi\)
−0.219522 + 0.975608i \(0.570450\pi\)
\(72\) 46572.8i 0.124777i
\(73\) 15652.5i 0.0402361i −0.999798 0.0201181i \(-0.993596\pi\)
0.999798 0.0201181i \(-0.00640421\pi\)
\(74\) 505918. 1.24849
\(75\) 176055. 0.417316
\(76\) −56074.3 −0.127739
\(77\) 17919.9i 0.0392521i
\(78\) −286902. −0.604574
\(79\) 756230. 1.53381 0.766906 0.641759i \(-0.221795\pi\)
0.766906 + 0.641759i \(0.221795\pi\)
\(80\) −324597. −0.633978
\(81\) 59049.0 0.111111
\(82\) 1.21684e6i 2.20695i
\(83\) 669157.i 1.17029i −0.810929 0.585145i \(-0.801038\pi\)
0.810929 0.585145i \(-0.198962\pi\)
\(84\) 35513.3 0.0599175
\(85\) −176169. −0.286862
\(86\) −880859. −1.38488
\(87\) 176999. 0.268790
\(88\) 68897.2 0.101101
\(89\) 802081.i 1.13775i 0.822423 + 0.568877i \(0.192622\pi\)
−0.822423 + 0.568877i \(0.807378\pi\)
\(90\) 167498.i 0.229764i
\(91\) 87595.9i 0.116241i
\(92\) 813785.i 1.04507i
\(93\) 638139.i 0.793353i
\(94\) 1.26993e6 1.52896
\(95\) 80748.1 0.0941806
\(96\) 614088.i 0.694092i
\(97\) 879496.i 0.963649i 0.876268 + 0.481824i \(0.160026\pi\)
−0.876268 + 0.481824i \(0.839974\pi\)
\(98\) 1.20621e6i 1.28158i
\(99\) 87353.8i 0.0900277i
\(100\) 516148. 0.516148
\(101\) 958935.i 0.930733i 0.885118 + 0.465366i \(0.154077\pi\)
−0.885118 + 0.465366i \(0.845923\pi\)
\(102\) 437061.i 0.411853i
\(103\) 501320.i 0.458779i −0.973335 0.229389i \(-0.926327\pi\)
0.973335 0.229389i \(-0.0736729\pi\)
\(104\) 336783. 0.299399
\(105\) −51139.9 −0.0441766
\(106\) 2.77887e6i 2.33319i
\(107\) 1.15874e6 0.945878 0.472939 0.881095i \(-0.343193\pi\)
0.472939 + 0.881095i \(0.343193\pi\)
\(108\) 173116. 0.137425
\(109\) 369698.i 0.285474i −0.989761 0.142737i \(-0.954410\pi\)
0.989761 0.142737i \(-0.0455904\pi\)
\(110\) 247787. 0.186166
\(111\) 752969.i 0.550564i
\(112\) −245871. −0.175006
\(113\) 2.32947e6i 1.61444i 0.590253 + 0.807218i \(0.299028\pi\)
−0.590253 + 0.807218i \(0.700972\pi\)
\(114\) 200329.i 0.135216i
\(115\) 1.17187e6i 0.770521i
\(116\) 518915. 0.332447
\(117\) 427002.i 0.266608i
\(118\) 50104.2 + 2.15052e6i 0.0304950 + 1.30887i
\(119\) −133442. −0.0791867
\(120\) 196619.i 0.113784i
\(121\) 1.64233e6 0.927055
\(122\) −3.01807e6 −1.66207
\(123\) −1.81106e6 −0.973232
\(124\) 1.87086e6i 0.981241i
\(125\) −1.77156e6 −0.907037
\(126\) 126874.i 0.0634250i
\(127\) 2.36785e6 1.15596 0.577981 0.816050i \(-0.303841\pi\)
0.577981 + 0.816050i \(0.303841\pi\)
\(128\) 1.50588e6i 0.718062i
\(129\) 1.31100e6i 0.610709i
\(130\) 1.21123e6 0.551311
\(131\) 3.73876e6i 1.66308i 0.555463 + 0.831541i \(0.312541\pi\)
−0.555463 + 0.831541i \(0.687459\pi\)
\(132\) 256099.i 0.111349i
\(133\) 61163.9 0.0259980
\(134\) 1.57489e6 0.654538
\(135\) −249291. −0.101322
\(136\) 513050.i 0.203959i
\(137\) −4.53270e6 −1.76277 −0.881383 0.472402i \(-0.843387\pi\)
−0.881383 + 0.472402i \(0.843387\pi\)
\(138\) −2.90730e6 −1.10625
\(139\) −251519. −0.0936541 −0.0468271 0.998903i \(-0.514911\pi\)
−0.0468271 + 0.998903i \(0.514911\pi\)
\(140\) −149929. −0.0546388
\(141\) 1.89007e6i 0.674249i
\(142\) 1.64585e6i 0.574810i
\(143\) −631684. −0.216019
\(144\) −1.19854e6 −0.401390
\(145\) −747248. −0.245110
\(146\) −163942. −0.0526783
\(147\) 1.79523e6 0.565156
\(148\) 2.20751e6i 0.680953i
\(149\) 3.90999e6i 1.18200i 0.806673 + 0.590998i \(0.201266\pi\)
−0.806673 + 0.590998i \(0.798734\pi\)
\(150\) 1.84397e6i 0.546362i
\(151\) 2.04184e6i 0.593051i 0.955025 + 0.296525i \(0.0958279\pi\)
−0.955025 + 0.296525i \(0.904172\pi\)
\(152\) 235159.i 0.0669623i
\(153\) −650489. −0.181621
\(154\) 187690. 0.0513901
\(155\) 2.69407e6i 0.723460i
\(156\) 1.25186e6i 0.329748i
\(157\) 2.51585e6i 0.650109i −0.945695 0.325054i \(-0.894617\pi\)
0.945695 0.325054i \(-0.105383\pi\)
\(158\) 7.92063e6i 2.00811i
\(159\) −4.13586e6 −1.02890
\(160\) 2.59253e6i 0.632943i
\(161\) 887648.i 0.212698i
\(162\) 618470.i 0.145470i
\(163\) −356307. −0.0822739 −0.0411369 0.999154i \(-0.513098\pi\)
−0.0411369 + 0.999154i \(0.513098\pi\)
\(164\) −5.30954e6 −1.20372
\(165\) 368787.i 0.0820964i
\(166\) −7.00864e6 −1.53218
\(167\) −1.08155e6 −0.232218 −0.116109 0.993236i \(-0.537042\pi\)
−0.116109 + 0.993236i \(0.537042\pi\)
\(168\) 148932.i 0.0314095i
\(169\) 1.73902e6 0.360283
\(170\) 1.84517e6i 0.375569i
\(171\) 298155. 0.0596284
\(172\) 3.84352e6i 0.755342i
\(173\) 8.25269e6i 1.59389i −0.604054 0.796943i \(-0.706449\pi\)
0.604054 0.796943i \(-0.293551\pi\)
\(174\) 1.85386e6i 0.351908i
\(175\) −562996. −0.105049
\(176\) 1.77306e6i 0.325226i
\(177\) 3.20067e6 74571.3i 0.577194 0.0134478i
\(178\) 8.40087e6 1.48958
\(179\) 5.34005e6i 0.931078i 0.885027 + 0.465539i \(0.154140\pi\)
−0.885027 + 0.465539i \(0.845860\pi\)
\(180\) −730856. −0.125318
\(181\) −6.53227e6 −1.10161 −0.550806 0.834633i \(-0.685680\pi\)
−0.550806 + 0.834633i \(0.685680\pi\)
\(182\) 917465. 0.152186
\(183\) 4.49187e6i 0.732949i
\(184\) 3.41277e6 0.547840
\(185\) 3.17886e6i 0.502060i
\(186\) −6.68377e6 −1.03868
\(187\) 962297.i 0.147158i
\(188\) 5.54119e6i 0.833930i
\(189\) −188829. −0.0279694
\(190\) 845742.i 0.123304i
\(191\) 8.78274e6i 1.26046i −0.776407 0.630232i \(-0.782960\pi\)
0.776407 0.630232i \(-0.217040\pi\)
\(192\) −1.51112e6 −0.213498
\(193\) −7.18375e6 −0.999261 −0.499631 0.866239i \(-0.666531\pi\)
−0.499631 + 0.866239i \(0.666531\pi\)
\(194\) 9.21170e6 1.26164
\(195\) 1.80270e6i 0.243120i
\(196\) 5.26315e6 0.699000
\(197\) −1.13153e7 −1.48002 −0.740012 0.672594i \(-0.765180\pi\)
−0.740012 + 0.672594i \(0.765180\pi\)
\(198\) 914930. 0.117867
\(199\) −7.22619e6 −0.916960 −0.458480 0.888705i \(-0.651606\pi\)
−0.458480 + 0.888705i \(0.651606\pi\)
\(200\) 2.16457e6i 0.270571i
\(201\) 2.34394e6i 0.288641i
\(202\) 1.00437e7 1.21854
\(203\) −566014. −0.0676611
\(204\) −1.90706e6 −0.224634
\(205\) 7.64585e6 0.887491
\(206\) −5.25075e6 −0.600647
\(207\) 4.32700e6i 0.487839i
\(208\) 8.66705e6i 0.963122i
\(209\) 441073.i 0.0483139i
\(210\) 535631.i 0.0578373i
\(211\) 3.44063e6i 0.366261i −0.983089 0.183130i \(-0.941377\pi\)
0.983089 0.183130i \(-0.0586230\pi\)
\(212\) −1.21253e7 −1.27258
\(213\) 2.44955e6 0.253482
\(214\) 1.21365e7i 1.23837i
\(215\) 5.53474e6i 0.556906i
\(216\) 725998.i 0.0720401i
\(217\) 2.04067e6i 0.199707i
\(218\) −3.87215e6 −0.373752
\(219\) 243999.i 0.0232303i
\(220\) 1.08119e6i 0.101539i
\(221\) 4.70389e6i 0.435793i
\(222\) −7.88648e6 −0.720815
\(223\) 5.22189e6 0.470884 0.235442 0.971888i \(-0.424346\pi\)
0.235442 + 0.971888i \(0.424346\pi\)
\(224\) 1.96375e6i 0.174720i
\(225\) −2.74443e6 −0.240937
\(226\) 2.43984e7 2.11367
\(227\) 8.28804e6i 0.708556i −0.935140 0.354278i \(-0.884727\pi\)
0.935140 0.354278i \(-0.115273\pi\)
\(228\) 874111. 0.0737500
\(229\) 2.98348e6i 0.248438i −0.992255 0.124219i \(-0.960358\pi\)
0.992255 0.124219i \(-0.0396425\pi\)
\(230\) 1.22739e7 1.00879
\(231\) 279343.i 0.0226622i
\(232\) 2.17618e6i 0.174273i
\(233\) 1.71585e6i 0.135647i −0.997697 0.0678236i \(-0.978394\pi\)
0.997697 0.0678236i \(-0.0216055\pi\)
\(234\) 4.47235e6 0.349051
\(235\) 7.97942e6i 0.614848i
\(236\) 9.38354e6 218624.i 0.713889 0.0166326i
\(237\) −1.17885e7 −0.885547
\(238\) 1.39765e6i 0.103674i
\(239\) 1.30840e6 0.0958397 0.0479198 0.998851i \(-0.484741\pi\)
0.0479198 + 0.998851i \(0.484741\pi\)
\(240\) 5.05996e6 0.366027
\(241\) −1.93506e7 −1.38243 −0.691217 0.722647i \(-0.742925\pi\)
−0.691217 + 0.722647i \(0.742925\pi\)
\(242\) 1.72015e7i 1.21373i
\(243\) −920483. −0.0641500
\(244\) 1.31690e7i 0.906531i
\(245\) −7.57903e6 −0.515366
\(246\) 1.89687e7i 1.27418i
\(247\) 2.15605e6i 0.143077i
\(248\) 7.84582e6 0.514379
\(249\) 1.04311e7i 0.675667i
\(250\) 1.85550e7i 1.18752i
\(251\) −1.33473e7 −0.844058 −0.422029 0.906582i \(-0.638682\pi\)
−0.422029 + 0.906582i \(0.638682\pi\)
\(252\) −553598. −0.0345934
\(253\) −6.40113e6 −0.395271
\(254\) 2.48005e7i 1.51342i
\(255\) 2.74621e6 0.165620
\(256\) 2.19764e7 1.30990
\(257\) −1.69761e7 −1.00009 −0.500045 0.866000i \(-0.666683\pi\)
−0.500045 + 0.866000i \(0.666683\pi\)
\(258\) 1.37312e7 0.799558
\(259\) 2.40787e6i 0.138591i
\(260\) 5.28505e6i 0.300697i
\(261\) −2.75914e6 −0.155186
\(262\) 3.91592e7 2.17736
\(263\) 1.12084e6 0.0616135 0.0308068 0.999525i \(-0.490192\pi\)
0.0308068 + 0.999525i \(0.490192\pi\)
\(264\) −1.07400e6 −0.0583705
\(265\) 1.74606e7 0.938257
\(266\) 640620.i 0.0340374i
\(267\) 1.25032e7i 0.656883i
\(268\) 6.87182e6i 0.356999i
\(269\) 3.32729e7i 1.70936i 0.519155 + 0.854680i \(0.326247\pi\)
−0.519155 + 0.854680i \(0.673753\pi\)
\(270\) 2.61103e6i 0.132654i
\(271\) 3.33904e7 1.67770 0.838849 0.544365i \(-0.183229\pi\)
0.838849 + 0.544365i \(0.183229\pi\)
\(272\) 1.32032e7 0.656106
\(273\) 1.36549e6i 0.0671118i
\(274\) 4.74747e7i 2.30787i
\(275\) 4.05996e6i 0.195219i
\(276\) 1.26856e7i 0.603372i
\(277\) 1.66314e7 0.782509 0.391254 0.920283i \(-0.372041\pi\)
0.391254 + 0.920283i \(0.372041\pi\)
\(278\) 2.63437e6i 0.122615i
\(279\) 9.94761e6i 0.458043i
\(280\) 628757.i 0.0286424i
\(281\) 2.14792e7 0.968051 0.484026 0.875054i \(-0.339174\pi\)
0.484026 + 0.875054i \(0.339174\pi\)
\(282\) −1.97963e7 −0.882747
\(283\) 2.69660e7i 1.18975i 0.803816 + 0.594877i \(0.202799\pi\)
−0.803816 + 0.594877i \(0.797201\pi\)
\(284\) 7.18144e6 0.313514
\(285\) −1.25874e6 −0.0543752
\(286\) 6.61615e6i 0.282818i
\(287\) 5.79146e6 0.244987
\(288\) 9.57268e6i 0.400734i
\(289\) −1.69717e7 −0.703125
\(290\) 7.82655e6i 0.320905i
\(291\) 1.37100e7i 0.556363i
\(292\) 715341.i 0.0287319i
\(293\) 2.18049e7 0.866864 0.433432 0.901186i \(-0.357303\pi\)
0.433432 + 0.901186i \(0.357303\pi\)
\(294\) 1.88029e7i 0.739919i
\(295\) −1.35125e7 + 314822.i −0.526343 + 0.0122631i
\(296\) 9.25764e6 0.356965
\(297\) 1.36171e6i 0.0519775i
\(298\) 4.09526e7 1.54751
\(299\) −3.12900e7 −1.17055
\(300\) −8.04595e6 −0.297998
\(301\) 4.19237e6i 0.153731i
\(302\) 2.13860e7 0.776440
\(303\) 1.49483e7i 0.537359i
\(304\) −6.05177e6 −0.215408
\(305\) 1.89636e7i 0.668376i
\(306\) 6.81311e6i 0.237783i
\(307\) −1.81303e6 −0.0626600 −0.0313300 0.999509i \(-0.509974\pi\)
−0.0313300 + 0.999509i \(0.509974\pi\)
\(308\) 818962.i 0.0280293i
\(309\) 7.81481e6i 0.264876i
\(310\) 2.82173e7 0.947175
\(311\) 1.32810e7 0.441520 0.220760 0.975328i \(-0.429146\pi\)
0.220760 + 0.975328i \(0.429146\pi\)
\(312\) −5.24993e6 −0.172858
\(313\) 4.08372e7i 1.33175i −0.746062 0.665876i \(-0.768058\pi\)
0.746062 0.665876i \(-0.231942\pi\)
\(314\) −2.63506e7 −0.851142
\(315\) 797192. 0.0255054
\(316\) −3.45607e7 −1.09527
\(317\) −5.33718e7 −1.67546 −0.837730 0.546085i \(-0.816117\pi\)
−0.837730 + 0.546085i \(0.816117\pi\)
\(318\) 4.33183e7i 1.34707i
\(319\) 4.08172e6i 0.125739i
\(320\) 6.37958e6 0.194689
\(321\) −1.80630e7 −0.546103
\(322\) 9.29708e6 0.278470
\(323\) −3.28449e6 −0.0974678
\(324\) −2.69862e6 −0.0793425
\(325\) 1.98458e7i 0.578122i
\(326\) 3.73191e6i 0.107715i
\(327\) 5.76301e6i 0.164819i
\(328\) 2.22666e7i 0.631006i
\(329\) 6.04414e6i 0.169725i
\(330\) −3.86262e6 −0.107483
\(331\) 4.11069e7 1.13352 0.566762 0.823881i \(-0.308196\pi\)
0.566762 + 0.823881i \(0.308196\pi\)
\(332\) 3.05813e7i 0.835684i
\(333\) 1.17376e7i 0.317869i
\(334\) 1.13279e7i 0.304026i
\(335\) 9.89556e6i 0.263212i
\(336\) 3.83275e6 0.101040
\(337\) 5.40856e6i 0.141316i −0.997501 0.0706580i \(-0.977490\pi\)
0.997501 0.0706580i \(-0.0225099\pi\)
\(338\) 1.82142e7i 0.471693i
\(339\) 3.63128e7i 0.932095i
\(340\) 8.05117e6 0.204843
\(341\) −1.47159e7 −0.371129
\(342\) 3.12282e6i 0.0780673i
\(343\) −1.16056e7 −0.287597
\(344\) −1.61186e7 −0.395960
\(345\) 1.82676e7i 0.444861i
\(346\) −8.64374e7 −2.08676
\(347\) 1.65017e7i 0.394948i −0.980308 0.197474i \(-0.936726\pi\)
0.980308 0.197474i \(-0.0632738\pi\)
\(348\) −8.08908e6 −0.191938
\(349\) 7.68105e6i 0.180694i −0.995910 0.0903471i \(-0.971202\pi\)
0.995910 0.0903471i \(-0.0287977\pi\)
\(350\) 5.89673e6i 0.137533i
\(351\) 6.65631e6i 0.153926i
\(352\) −1.41613e7 −0.324695
\(353\) 2.36300e7i 0.537206i 0.963251 + 0.268603i \(0.0865619\pi\)
−0.963251 + 0.268603i \(0.913438\pi\)
\(354\) −781047. 3.35233e7i −0.0176063 0.755679i
\(355\) −1.03414e7 −0.231151
\(356\) 3.66562e7i 0.812451i
\(357\) 2.08016e6 0.0457185
\(358\) 5.59308e7 1.21900
\(359\) 3.66955e7 0.793102 0.396551 0.918013i \(-0.370207\pi\)
0.396551 + 0.918013i \(0.370207\pi\)
\(360\) 3.06499e6i 0.0656934i
\(361\) −4.55404e7 −0.968000
\(362\) 6.84180e7i 1.44226i
\(363\) −2.56015e7 −0.535235
\(364\) 4.00325e6i 0.0830057i
\(365\) 1.03010e6i 0.0211838i
\(366\) 4.70471e7 0.959598
\(367\) 9.00008e7i 1.82074i −0.413795 0.910370i \(-0.635797\pi\)
0.413795 0.910370i \(-0.364203\pi\)
\(368\) 8.78271e7i 1.76232i
\(369\) 2.82316e7 0.561896
\(370\) 3.32948e7 0.657312
\(371\) 1.32258e7 0.259001
\(372\) 2.91638e7i 0.566520i
\(373\) −7.07018e7 −1.36240 −0.681199 0.732098i \(-0.738541\pi\)
−0.681199 + 0.732098i \(0.738541\pi\)
\(374\) −1.00789e7 −0.192664
\(375\) 2.76158e7 0.523678
\(376\) 2.32381e7 0.437157
\(377\) 1.99522e7i 0.372364i
\(378\) 1.97777e6i 0.0366184i
\(379\) −1.87827e7 −0.345017 −0.172509 0.985008i \(-0.555187\pi\)
−0.172509 + 0.985008i \(0.555187\pi\)
\(380\) −3.69029e6 −0.0672527
\(381\) −3.69112e7 −0.667395
\(382\) −9.19891e7 −1.65024
\(383\) 1.46187e7 0.260204 0.130102 0.991501i \(-0.458470\pi\)
0.130102 + 0.991501i \(0.458470\pi\)
\(384\) 2.34744e7i 0.414573i
\(385\) 1.17932e6i 0.0206657i
\(386\) 7.52414e7i 1.30826i
\(387\) 2.04365e7i 0.352593i
\(388\) 4.01941e7i 0.688125i
\(389\) 1.19705e7 0.203359 0.101679 0.994817i \(-0.467578\pi\)
0.101679 + 0.994817i \(0.467578\pi\)
\(390\) −1.88812e7 −0.318300
\(391\) 4.76666e7i 0.797415i
\(392\) 2.20721e7i 0.366425i
\(393\) 5.82815e7i 0.960181i
\(394\) 1.18515e8i 1.93769i
\(395\) 4.97680e7 0.807531
\(396\) 3.99218e6i 0.0642873i
\(397\) 7.88120e7i 1.25957i −0.776771 0.629783i \(-0.783144\pi\)
0.776771 0.629783i \(-0.216856\pi\)
\(398\) 7.56860e7i 1.20051i
\(399\) −953450. −0.0150100
\(400\) 5.57048e7 0.870388
\(401\) 2.81271e7i 0.436206i 0.975926 + 0.218103i \(0.0699868\pi\)
−0.975926 + 0.218103i \(0.930013\pi\)
\(402\) −2.45501e7 −0.377898
\(403\) −7.19344e7 −1.09906
\(404\) 4.38246e7i 0.664620i
\(405\) 3.88606e6 0.0584985
\(406\) 5.92834e6i 0.0885840i
\(407\) −1.73640e7 −0.257553
\(408\) 7.99766e6i 0.117756i
\(409\) 5.77299e7i 0.843783i 0.906646 + 0.421891i \(0.138634\pi\)
−0.906646 + 0.421891i \(0.861366\pi\)
\(410\) 8.00814e7i 1.16193i
\(411\) 7.06577e7 1.01773
\(412\) 2.29110e7i 0.327606i
\(413\) −1.02352e7 + 238467.i −0.145294 + 0.00338515i
\(414\) 4.53203e7 0.638693
\(415\) 4.40377e7i 0.616142i
\(416\) −6.92232e7 −0.961549
\(417\) 3.92080e6 0.0540712
\(418\) 4.61973e6 0.0632540
\(419\) 1.00992e8i 1.37292i 0.727167 + 0.686461i \(0.240837\pi\)
−0.727167 + 0.686461i \(0.759163\pi\)
\(420\) 2.33716e6 0.0315457
\(421\) 3.94968e7i 0.529317i 0.964342 + 0.264659i \(0.0852593\pi\)
−0.964342 + 0.264659i \(0.914741\pi\)
\(422\) −3.60366e7 −0.479519
\(423\) 2.94633e7i 0.389278i
\(424\) 5.08498e7i 0.667101i
\(425\) 3.02328e7 0.393833
\(426\) 2.56562e7i 0.331867i
\(427\) 1.43643e7i 0.184501i
\(428\) −5.29560e7 −0.675436
\(429\) 9.84698e6 0.124719
\(430\) −5.79700e7 −0.729118
\(431\) 6.54180e7i 0.817082i 0.912740 + 0.408541i \(0.133962\pi\)
−0.912740 + 0.408541i \(0.866038\pi\)
\(432\) 1.86834e7 0.231742
\(433\) −1.00605e8 −1.23924 −0.619619 0.784902i \(-0.712713\pi\)
−0.619619 + 0.784902i \(0.712713\pi\)
\(434\) 2.13736e7 0.261462
\(435\) 1.16484e7 0.141514
\(436\) 1.68957e7i 0.203852i
\(437\) 2.18482e7i 0.261801i
\(438\) 2.55560e6 0.0304138
\(439\) −4.18830e7 −0.495044 −0.247522 0.968882i \(-0.579616\pi\)
−0.247522 + 0.968882i \(0.579616\pi\)
\(440\) 4.53418e6 0.0532281
\(441\) −2.79849e7 −0.326293
\(442\) −4.92678e7 −0.570554
\(443\) 1.28585e8i 1.47903i 0.673139 + 0.739516i \(0.264946\pi\)
−0.673139 + 0.739516i \(0.735054\pi\)
\(444\) 3.44117e7i 0.393149i
\(445\) 5.27856e7i 0.599012i
\(446\) 5.46933e7i 0.616495i
\(447\) 6.09506e7i 0.682426i
\(448\) 4.83231e6 0.0537429
\(449\) −5.56187e7 −0.614443 −0.307221 0.951638i \(-0.599399\pi\)
−0.307221 + 0.951638i \(0.599399\pi\)
\(450\) 2.87447e7i 0.315442i
\(451\) 4.17642e7i 0.455276i
\(452\) 1.06460e8i 1.15284i
\(453\) 3.18292e7i 0.342398i
\(454\) −8.68076e7 −0.927663
\(455\) 5.76475e6i 0.0611993i
\(456\) 3.66576e6i 0.0386607i
\(457\) 7.70912e7i 0.807711i −0.914823 0.403855i \(-0.867670\pi\)
0.914823 0.403855i \(-0.132330\pi\)
\(458\) −3.12485e7 −0.325262
\(459\) 1.01401e7 0.104859
\(460\) 5.35558e7i 0.550216i
\(461\) −1.53553e7 −0.156731 −0.0783656 0.996925i \(-0.524970\pi\)
−0.0783656 + 0.996925i \(0.524970\pi\)
\(462\) −2.92580e6 −0.0296701
\(463\) 6.06121e6i 0.0610684i 0.999534 + 0.0305342i \(0.00972084\pi\)
−0.999534 + 0.0305342i \(0.990279\pi\)
\(464\) 5.60035e7 0.560610
\(465\) 4.19964e7i 0.417690i
\(466\) −1.79715e7 −0.177593
\(467\) 1.17824e8i 1.15686i 0.815731 + 0.578431i \(0.196335\pi\)
−0.815731 + 0.578431i \(0.803665\pi\)
\(468\) 1.95146e7i 0.190380i
\(469\) 7.49554e6i 0.0726582i
\(470\) 8.35752e7 0.804977
\(471\) 3.92182e7i 0.375340i
\(472\) 916842. + 3.93518e7i 0.00871904 + 0.374230i
\(473\) 3.02326e7 0.285688
\(474\) 1.23470e8i 1.15938i
\(475\) −1.38574e7 −0.129300
\(476\) 6.09848e6 0.0565459
\(477\) 6.44717e7 0.594037
\(478\) 1.37039e7i 0.125476i
\(479\) −1.66188e8 −1.51214 −0.756072 0.654488i \(-0.772884\pi\)
−0.756072 + 0.654488i \(0.772884\pi\)
\(480\) 4.04136e7i 0.365430i
\(481\) −8.48786e7 −0.762716
\(482\) 2.02676e8i 1.80992i
\(483\) 1.38371e7i 0.122801i
\(484\) −7.50568e7 −0.661994
\(485\) 5.78803e7i 0.507348i
\(486\) 9.64099e6i 0.0839871i
\(487\) −1.81382e8 −1.57039 −0.785194 0.619250i \(-0.787437\pi\)
−0.785194 + 0.619250i \(0.787437\pi\)
\(488\) −5.52268e7 −0.475215
\(489\) 5.55428e6 0.0475009
\(490\) 7.93816e7i 0.674732i
\(491\) 1.82057e8 1.53802 0.769010 0.639236i \(-0.220749\pi\)
0.769010 + 0.639236i \(0.220749\pi\)
\(492\) 8.27676e7 0.694968
\(493\) 3.03949e7 0.253665
\(494\) 2.25821e7 0.187320
\(495\) 5.74882e6i 0.0473984i
\(496\) 2.01911e8i 1.65468i
\(497\) −7.83327e6 −0.0638078
\(498\) 1.09254e8 0.884604
\(499\) 7.94846e7 0.639707 0.319854 0.947467i \(-0.396366\pi\)
0.319854 + 0.947467i \(0.396366\pi\)
\(500\) 8.09624e7 0.647699
\(501\) 1.68596e7 0.134071
\(502\) 1.39797e8i 1.10507i
\(503\) 6.89633e7i 0.541894i 0.962594 + 0.270947i \(0.0873368\pi\)
−0.962594 + 0.270947i \(0.912663\pi\)
\(504\) 2.32163e6i 0.0181343i
\(505\) 6.31083e7i 0.490018i
\(506\) 6.70444e7i 0.517501i
\(507\) −2.71086e7 −0.208009
\(508\) −1.08214e8 −0.825453
\(509\) 1.38066e8i 1.04697i 0.852034 + 0.523486i \(0.175369\pi\)
−0.852034 + 0.523486i \(0.824631\pi\)
\(510\) 2.87633e7i 0.216835i
\(511\) 780269.i 0.00584765i
\(512\) 1.33801e8i 0.996896i
\(513\) −4.64777e6 −0.0344265
\(514\) 1.77805e8i 1.30935i
\(515\) 3.29923e7i 0.241541i
\(516\) 5.99145e7i 0.436097i
\(517\) −4.35863e7 −0.315412
\(518\) 2.52197e7 0.181447
\(519\) 1.28647e8i 0.920231i
\(520\) 2.21640e7 0.157629
\(521\) 2.63461e8 1.86296 0.931479 0.363795i \(-0.118519\pi\)
0.931479 + 0.363795i \(0.118519\pi\)
\(522\) 2.88988e7i 0.203174i
\(523\) 2.27713e8 1.59178 0.795889 0.605443i \(-0.207004\pi\)
0.795889 + 0.605443i \(0.207004\pi\)
\(524\) 1.70866e8i 1.18758i
\(525\) 8.77624e6 0.0606500
\(526\) 1.17395e7i 0.0806662i
\(527\) 1.09584e8i 0.748711i
\(528\) 2.76392e7i 0.187769i
\(529\) −1.69039e8 −1.14188
\(530\) 1.82880e8i 1.22839i
\(531\) −4.98936e7 + 1.16245e6i −0.333243 + 0.00776410i
\(532\) −2.79527e6 −0.0185647
\(533\) 2.04152e8i 1.34825i
\(534\) −1.30957e8 −0.860010
\(535\) 7.62577e7 0.497992
\(536\) 2.88184e7 0.187144
\(537\) 8.32431e7i 0.537558i
\(538\) 3.48495e8 2.23795
\(539\) 4.13993e7i 0.264379i
\(540\) 1.13929e7 0.0723525
\(541\) 1.20606e8i 0.761687i −0.924640 0.380843i \(-0.875634\pi\)
0.924640 0.380843i \(-0.124366\pi\)
\(542\) 3.49726e8i 2.19649i
\(543\) 1.01828e8 0.636016
\(544\) 1.05453e8i 0.655034i
\(545\) 2.43301e7i 0.150298i
\(546\) −1.43019e7 −0.0878648
\(547\) 1.23169e8 0.752558 0.376279 0.926506i \(-0.377203\pi\)
0.376279 + 0.926506i \(0.377203\pi\)
\(548\) 2.07150e8 1.25876
\(549\) 7.00213e7i 0.423168i
\(550\) −4.25233e7 −0.255587
\(551\) −1.39317e7 −0.0832814
\(552\) −5.31999e7 −0.316296
\(553\) 3.76976e7 0.222914
\(554\) 1.74194e8i 1.02448i
\(555\) 4.95535e7i 0.289865i
\(556\) 1.14948e7 0.0668768
\(557\) −7.21947e7 −0.417772 −0.208886 0.977940i \(-0.566984\pi\)
−0.208886 + 0.977940i \(0.566984\pi\)
\(558\) 1.04190e8 0.599683
\(559\) 1.47783e8 0.846036
\(560\) −1.61809e7 −0.0921382
\(561\) 1.50007e7i 0.0849618i
\(562\) 2.24969e8i 1.26740i
\(563\) 8.89719e7i 0.498572i −0.968430 0.249286i \(-0.919804\pi\)
0.968430 0.249286i \(-0.0801958\pi\)
\(564\) 8.63786e7i 0.481469i
\(565\) 1.53304e8i 0.849978i
\(566\) 2.82438e8 1.55766
\(567\) 2.94356e6 0.0161482
\(568\) 3.01169e7i 0.164348i
\(569\) 1.17956e8i 0.640302i −0.947367 0.320151i \(-0.896266\pi\)
0.947367 0.320151i \(-0.103734\pi\)
\(570\) 1.31838e7i 0.0711896i
\(571\) 3.46617e7i 0.186184i 0.995658 + 0.0930918i \(0.0296750\pi\)
−0.995658 + 0.0930918i \(0.970325\pi\)
\(572\) 2.88688e7 0.154255
\(573\) 1.36909e8i 0.727729i
\(574\) 6.06589e7i 0.320744i
\(575\) 2.01107e8i 1.05785i
\(576\) 2.35560e7 0.123263
\(577\) −8.59270e7 −0.447303 −0.223652 0.974669i \(-0.571798\pi\)
−0.223652 + 0.974669i \(0.571798\pi\)
\(578\) 1.77759e8i 0.920552i
\(579\) 1.11984e8 0.576924
\(580\) 3.41502e7 0.175029
\(581\) 3.33570e7i 0.170082i
\(582\) −1.43596e8 −0.728407
\(583\) 9.53758e7i 0.481319i
\(584\) −2.99993e6 −0.0150616
\(585\) 2.81014e7i 0.140365i
\(586\) 2.28381e8i 1.13492i
\(587\) 3.82513e7i 0.189118i −0.995519 0.0945589i \(-0.969856\pi\)
0.995519 0.0945589i \(-0.0301441\pi\)
\(588\) −8.20443e7 −0.403568
\(589\) 5.02282e7i 0.245811i
\(590\) 3.29740e6 + 1.41528e8i 0.0160552 + 0.689104i
\(591\) 1.76389e8 0.854492
\(592\) 2.38244e8i 1.14830i
\(593\) 1.54007e8 0.738543 0.369271 0.929322i \(-0.379607\pi\)
0.369271 + 0.929322i \(0.379607\pi\)
\(594\) −1.42623e7 −0.0680505
\(595\) −8.78193e6 −0.0416907
\(596\) 1.78691e8i 0.844044i
\(597\) 1.12645e8 0.529407
\(598\) 3.27726e8i 1.53252i
\(599\) 2.97305e8 1.38332 0.691658 0.722225i \(-0.256881\pi\)
0.691658 + 0.722225i \(0.256881\pi\)
\(600\) 3.37423e7i 0.156214i
\(601\) 2.74162e8i 1.26294i 0.775399 + 0.631472i \(0.217549\pi\)
−0.775399 + 0.631472i \(0.782451\pi\)
\(602\) −4.39102e7 −0.201269
\(603\) 3.65384e7i 0.166647i
\(604\) 9.33149e7i 0.423487i
\(605\) 1.08083e8 0.488082
\(606\) −1.56566e8 −0.703526
\(607\) −7.44553e7 −0.332912 −0.166456 0.986049i \(-0.553232\pi\)
−0.166456 + 0.986049i \(0.553232\pi\)
\(608\) 4.83351e7i 0.215056i
\(609\) 8.82329e6 0.0390642
\(610\) −1.98622e8 −0.875058
\(611\) −2.13058e8 −0.934060
\(612\) 2.97282e7 0.129692
\(613\) 1.19319e8i 0.517997i −0.965878 0.258998i \(-0.916608\pi\)
0.965878 0.258998i \(-0.0833924\pi\)
\(614\) 1.89894e7i 0.0820364i
\(615\) −1.19187e8 −0.512393
\(616\) 3.43449e6 0.0146933
\(617\) −4.67089e7 −0.198859 −0.0994293 0.995045i \(-0.531702\pi\)
−0.0994293 + 0.995045i \(0.531702\pi\)
\(618\) 8.18510e7 0.346784
\(619\) −3.82262e8 −1.61172 −0.805859 0.592107i \(-0.798296\pi\)
−0.805859 + 0.592107i \(0.798296\pi\)
\(620\) 1.23123e8i 0.516610i
\(621\) 6.74513e7i 0.281654i
\(622\) 1.39103e8i 0.578051i
\(623\) 3.99833e7i 0.165354i
\(624\) 1.35106e8i 0.556059i
\(625\) 5.98804e7 0.245270
\(626\) −4.27723e8 −1.74357
\(627\) 6.87565e6i 0.0278940i
\(628\) 1.14978e8i 0.464231i
\(629\) 1.29303e8i 0.519584i
\(630\) 8.34966e6i 0.0333924i
\(631\) 3.27902e8 1.30514 0.652568 0.757730i \(-0.273692\pi\)
0.652568 + 0.757730i \(0.273692\pi\)
\(632\) 1.44937e8i 0.574154i
\(633\) 5.36341e7i 0.211461i
\(634\) 5.59007e8i 2.19356i
\(635\) 1.55830e8 0.608598
\(636\) 1.89014e8 0.734722
\(637\) 2.02368e8i 0.782929i
\(638\) −4.27513e7 −0.164622
\(639\) −3.81847e7 −0.146348
\(640\) 9.91034e7i 0.378050i
\(641\) −1.03508e8 −0.393005 −0.196503 0.980503i \(-0.562958\pi\)
−0.196503 + 0.980503i \(0.562958\pi\)
\(642\) 1.89189e8i 0.714975i
\(643\) −1.45263e8 −0.546413 −0.273207 0.961955i \(-0.588084\pi\)
−0.273207 + 0.961955i \(0.588084\pi\)
\(644\) 4.05667e7i 0.151884i
\(645\) 8.62781e7i 0.321530i
\(646\) 3.44013e7i 0.127608i
\(647\) −4.05992e7 −0.149901 −0.0749505 0.997187i \(-0.523880\pi\)
−0.0749505 + 0.997187i \(0.523880\pi\)
\(648\) 1.13172e7i 0.0415924i
\(649\) −1.71967e6 7.38098e7i −0.00629086 0.270010i
\(650\) −2.07862e8 −0.756895
\(651\) 3.18108e7i 0.115301i
\(652\) 1.62837e7 0.0587504
\(653\) 2.85932e8 1.02689 0.513445 0.858123i \(-0.328369\pi\)
0.513445 + 0.858123i \(0.328369\pi\)
\(654\) 6.03609e7 0.215786
\(655\) 2.46051e8i 0.875590i
\(656\) −5.73028e8 −2.02985
\(657\) 3.80356e6i 0.0134120i
\(658\) 6.33053e7 0.222209
\(659\) 1.76873e8i 0.618024i −0.951058 0.309012i \(-0.900002\pi\)
0.951058 0.309012i \(-0.0999983\pi\)
\(660\) 1.68540e7i 0.0586236i
\(661\) −7.79873e7 −0.270035 −0.135017 0.990843i \(-0.543109\pi\)
−0.135017 + 0.990843i \(0.543109\pi\)
\(662\) 4.30547e8i 1.48404i
\(663\) 7.33264e7i 0.251605i
\(664\) −1.28249e8 −0.438076
\(665\) 4.02524e6 0.0136876
\(666\) 1.22938e8 0.416163
\(667\) 2.02185e8i 0.681352i
\(668\) 4.94280e7 0.165823
\(669\) −8.14013e7 −0.271865
\(670\) 1.03644e8 0.344605
\(671\) 1.03586e8 0.342872
\(672\) 3.06119e7i 0.100875i
\(673\) 2.77194e8i 0.909367i −0.890653 0.454684i \(-0.849752\pi\)
0.890653 0.454684i \(-0.150248\pi\)
\(674\) −5.66483e7 −0.185015
\(675\) 4.27814e7 0.139105
\(676\) −7.94753e7 −0.257272
\(677\) 3.25221e8 1.04812 0.524061 0.851681i \(-0.324416\pi\)
0.524061 + 0.851681i \(0.324416\pi\)
\(678\) −3.80334e8 −1.22033
\(679\) 4.38423e7i 0.140050i
\(680\) 3.37642e7i 0.107382i
\(681\) 1.29198e8i 0.409085i
\(682\) 1.54132e8i 0.485893i
\(683\) 1.09553e8i 0.343844i 0.985111 + 0.171922i \(0.0549977\pi\)
−0.985111 + 0.171922i \(0.945002\pi\)
\(684\) −1.36260e7 −0.0425796
\(685\) −2.98300e8 −0.928072
\(686\) 1.21555e8i 0.376531i
\(687\) 4.65079e7i 0.143436i
\(688\) 4.14808e8i 1.27374i
\(689\) 4.66216e8i 1.42537i
\(690\) −1.91332e8 −0.582425
\(691\) 2.79823e8i 0.848105i 0.905638 + 0.424052i \(0.139393\pi\)
−0.905638 + 0.424052i \(0.860607\pi\)
\(692\) 3.77159e8i 1.13817i
\(693\) 4.35453e6i 0.0130840i
\(694\) −1.72836e8 −0.517078
\(695\) −1.65527e7 −0.0493076
\(696\) 3.39232e7i 0.100617i
\(697\) −3.11001e8 −0.918467
\(698\) −8.04501e7 −0.236570
\(699\) 2.67474e7i 0.0783159i
\(700\) 2.57296e7 0.0750136
\(701\) 2.76329e8i 0.802181i −0.916038 0.401091i \(-0.868631\pi\)
0.916038 0.401091i \(-0.131369\pi\)
\(702\) −6.97171e7 −0.201525
\(703\) 5.92665e7i 0.170586i
\(704\) 3.48474e7i 0.0998741i
\(705\) 1.24387e8i 0.354983i
\(706\) 2.47497e8 0.703326
\(707\) 4.78023e7i 0.135267i
\(708\) −1.46275e8 + 3.40800e6i −0.412164 + 0.00960285i
\(709\) 5.87199e8 1.64758 0.823791 0.566894i \(-0.191855\pi\)
0.823791 + 0.566894i \(0.191855\pi\)
\(710\) 1.08314e8i 0.302629i
\(711\) 1.83764e8 0.511271
\(712\) 1.53725e8 0.425897
\(713\) −7.28943e8 −2.01106
\(714\) 2.17872e7i 0.0598560i
\(715\) −4.15716e7 −0.113731
\(716\) 2.44047e8i 0.664867i
\(717\) −2.03959e7 −0.0553331
\(718\) 3.84342e8i 1.03835i
\(719\) 1.61463e8i 0.434395i 0.976128 + 0.217198i \(0.0696916\pi\)
−0.976128 + 0.217198i \(0.930308\pi\)
\(720\) −7.88770e7 −0.211326
\(721\) 2.49905e7i 0.0666759i
\(722\) 4.76983e8i 1.26733i
\(723\) 3.01647e8 0.798148
\(724\) 2.98533e8 0.786642
\(725\) 1.28237e8 0.336511
\(726\) 2.68146e8i 0.700746i
\(727\) 2.22627e8 0.579394 0.289697 0.957118i \(-0.406446\pi\)
0.289697 + 0.957118i \(0.406446\pi\)
\(728\) 1.67884e7 0.0435127
\(729\) 1.43489e7 0.0370370
\(730\) −1.07892e7 −0.0277344
\(731\) 2.25130e8i 0.576344i
\(732\) 2.05284e8i 0.523386i
\(733\) 2.35665e8 0.598388 0.299194 0.954192i \(-0.403282\pi\)
0.299194 + 0.954192i \(0.403282\pi\)
\(734\) −9.42653e8 −2.38377
\(735\) 1.18145e8 0.297547
\(736\) −7.01469e8 −1.75944
\(737\) −5.40529e7 −0.135026
\(738\) 2.95693e8i 0.735651i
\(739\) 6.19496e8i 1.53499i −0.641055 0.767495i \(-0.721503\pi\)
0.641055 0.767495i \(-0.278497\pi\)
\(740\) 1.45278e8i 0.358512i
\(741\) 3.36095e7i 0.0826053i
\(742\) 1.38525e8i 0.339091i
\(743\) 3.35713e8 0.818469 0.409234 0.912429i \(-0.365796\pi\)
0.409234 + 0.912429i \(0.365796\pi\)
\(744\) −1.22304e8 −0.296977
\(745\) 2.57319e8i 0.622305i
\(746\) 7.40519e8i 1.78369i
\(747\) 1.62605e8i 0.390097i
\(748\) 4.39782e7i 0.105083i
\(749\) 5.77626e7 0.137468
\(750\) 2.89244e8i 0.685615i
\(751\) 6.69314e8i 1.58019i 0.612982 + 0.790097i \(0.289970\pi\)
−0.612982 + 0.790097i \(0.710030\pi\)
\(752\) 5.98028e8i 1.40627i
\(753\) 2.08064e8 0.487317
\(754\) −2.08977e8 −0.487510
\(755\) 1.34375e8i 0.312233i
\(756\) 8.62974e6 0.0199725
\(757\) −8.01456e8 −1.84753 −0.923767 0.382956i \(-0.874906\pi\)
−0.923767 + 0.382956i \(0.874906\pi\)
\(758\) 1.96727e8i 0.451707i
\(759\) 9.97838e7 0.228210
\(760\) 1.54760e7i 0.0352547i
\(761\) −1.79814e8 −0.408008 −0.204004 0.978970i \(-0.565396\pi\)
−0.204004 + 0.978970i \(0.565396\pi\)
\(762\) 3.86602e8i 0.873774i
\(763\) 1.84292e7i 0.0414890i
\(764\) 4.01383e8i 0.900075i
\(765\) −4.28092e7 −0.0956208
\(766\) 1.53114e8i 0.340667i
\(767\) −8.40606e6 3.60796e8i −0.0186297 0.799606i
\(768\) −3.42579e8 −0.756270
\(769\) 7.98304e8i 1.75545i 0.479161 + 0.877727i \(0.340941\pi\)
−0.479161 + 0.877727i \(0.659059\pi\)
\(770\) 1.23520e7 0.0270562
\(771\) 2.64631e8 0.577402
\(772\) 3.28306e8 0.713555
\(773\) 5.06230e8i 1.09600i −0.836479 0.547998i \(-0.815390\pi\)
0.836479 0.547998i \(-0.184610\pi\)
\(774\) −2.14049e8 −0.461625
\(775\) 4.62336e8i 0.993237i
\(776\) 1.68562e8 0.360724
\(777\) 3.75350e7i 0.0800154i
\(778\) 1.25377e8i 0.266243i
\(779\) 1.42549e8 0.301544
\(780\) 8.23859e7i 0.173608i
\(781\) 5.64884e7i 0.118578i
\(782\) −4.99253e8 −1.04400
\(783\) 4.30108e7 0.0895967
\(784\) 5.68021e8 1.17873
\(785\) 1.65570e8i 0.342273i