Properties

Label 177.7.c.a.58.7
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 58.7
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.54

$q$-expansion

\(f(q)\) \(=\) \(q-13.2670i q^{2} +15.5885 q^{3} -112.012 q^{4} +130.160 q^{5} -206.811i q^{6} +304.309 q^{7} +636.976i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-13.2670i q^{2} +15.5885 q^{3} -112.012 q^{4} +130.160 q^{5} -206.811i q^{6} +304.309 q^{7} +636.976i q^{8} +243.000 q^{9} -1726.83i q^{10} -302.342i q^{11} -1746.10 q^{12} +3866.28i q^{13} -4037.26i q^{14} +2029.00 q^{15} +1281.96 q^{16} +4992.75 q^{17} -3223.87i q^{18} +11773.0 q^{19} -14579.5 q^{20} +4743.71 q^{21} -4011.16 q^{22} +17075.4i q^{23} +9929.48i q^{24} +1316.68 q^{25} +51293.8 q^{26} +3788.00 q^{27} -34086.3 q^{28} +34405.8 q^{29} -26918.6i q^{30} -35505.8i q^{31} +23758.8i q^{32} -4713.05i q^{33} -66238.6i q^{34} +39608.9 q^{35} -27219.0 q^{36} -32831.2i q^{37} -156193. i q^{38} +60269.3i q^{39} +82909.0i q^{40} -63683.4 q^{41} -62934.6i q^{42} -54194.2i q^{43} +33866.0i q^{44} +31628.9 q^{45} +226539. q^{46} +14109.8i q^{47} +19983.7 q^{48} -25045.0 q^{49} -17468.4i q^{50} +77829.2 q^{51} -433071. i q^{52} +86435.8 q^{53} -50255.2i q^{54} -39352.9i q^{55} +193838. i q^{56} +183524. q^{57} -456461. i q^{58} +(-55030.6 + 197869. i) q^{59} -227272. q^{60} +21873.5i q^{61} -471054. q^{62} +73947.1 q^{63} +397252. q^{64} +503236. i q^{65} -62527.8 q^{66} +351365. i q^{67} -559249. q^{68} +266180. i q^{69} -525490. i q^{70} -350770. q^{71} +154785. i q^{72} -216142. i q^{73} -435570. q^{74} +20525.0 q^{75} -1.31873e6 q^{76} -92005.5i q^{77} +799591. q^{78} -797387. q^{79} +166860. q^{80} +59049.0 q^{81} +844885. i q^{82} -710474. i q^{83} -531353. q^{84} +649857. q^{85} -718992. q^{86} +536334. q^{87} +192585. q^{88} -1.09404e6i q^{89} -419620. i q^{90} +1.17654e6i q^{91} -1.91266e6i q^{92} -553480. i q^{93} +187194. q^{94} +1.53238e6 q^{95} +370363. i q^{96} -1.57323e6i q^{97} +332271. i q^{98} -73469.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.2670i 1.65837i −0.558974 0.829185i \(-0.688805\pi\)
0.558974 0.829185i \(-0.311195\pi\)
\(3\) 15.5885 0.577350
\(4\) −112.012 −1.75019
\(5\) 130.160 1.04128 0.520641 0.853776i \(-0.325693\pi\)
0.520641 + 0.853776i \(0.325693\pi\)
\(6\) 206.811i 0.957460i
\(7\) 304.309 0.887198 0.443599 0.896225i \(-0.353701\pi\)
0.443599 + 0.896225i \(0.353701\pi\)
\(8\) 636.976i 1.24409i
\(9\) 243.000 0.333333
\(10\) 1726.83i 1.72683i
\(11\) 302.342i 0.227154i −0.993529 0.113577i \(-0.963769\pi\)
0.993529 0.113577i \(-0.0362309\pi\)
\(12\) −1746.10 −1.01047
\(13\) 3866.28i 1.75980i 0.475159 + 0.879900i \(0.342391\pi\)
−0.475159 + 0.879900i \(0.657609\pi\)
\(14\) 4037.26i 1.47130i
\(15\) 2029.00 0.601184
\(16\) 1281.96 0.312978
\(17\) 4992.75 1.01623 0.508116 0.861289i \(-0.330342\pi\)
0.508116 + 0.861289i \(0.330342\pi\)
\(18\) 3223.87i 0.552790i
\(19\) 11773.0 1.71644 0.858219 0.513284i \(-0.171571\pi\)
0.858219 + 0.513284i \(0.171571\pi\)
\(20\) −14579.5 −1.82244
\(21\) 4743.71 0.512224
\(22\) −4011.16 −0.376706
\(23\) 17075.4i 1.40342i 0.712461 + 0.701711i \(0.247580\pi\)
−0.712461 + 0.701711i \(0.752420\pi\)
\(24\) 9929.48i 0.718278i
\(25\) 1316.68 0.0842676
\(26\) 51293.8 2.91840
\(27\) 3788.00 0.192450
\(28\) −34086.3 −1.55277
\(29\) 34405.8 1.41071 0.705355 0.708854i \(-0.250787\pi\)
0.705355 + 0.708854i \(0.250787\pi\)
\(30\) 26918.6i 0.996986i
\(31\) 35505.8i 1.19183i −0.803048 0.595915i \(-0.796790\pi\)
0.803048 0.595915i \(-0.203210\pi\)
\(32\) 23758.8i 0.725062i
\(33\) 4713.05i 0.131148i
\(34\) 66238.6i 1.68529i
\(35\) 39608.9 0.923823
\(36\) −27219.0 −0.583397
\(37\) 32831.2i 0.648158i −0.946030 0.324079i \(-0.894946\pi\)
0.946030 0.324079i \(-0.105054\pi\)
\(38\) 156193.i 2.84649i
\(39\) 60269.3i 1.01602i
\(40\) 82909.0i 1.29545i
\(41\) −63683.4 −0.924006 −0.462003 0.886878i \(-0.652869\pi\)
−0.462003 + 0.886878i \(0.652869\pi\)
\(42\) 62934.6i 0.849457i
\(43\) 54194.2i 0.681628i −0.940131 0.340814i \(-0.889297\pi\)
0.940131 0.340814i \(-0.110703\pi\)
\(44\) 33866.0i 0.397563i
\(45\) 31628.9 0.347094
\(46\) 226539. 2.32739
\(47\) 14109.8i 0.135902i 0.997689 + 0.0679512i \(0.0216462\pi\)
−0.997689 + 0.0679512i \(0.978354\pi\)
\(48\) 19983.7 0.180698
\(49\) −25045.0 −0.212879
\(50\) 17468.4i 0.139747i
\(51\) 77829.2 0.586722
\(52\) 433071.i 3.07999i
\(53\) 86435.8 0.580585 0.290293 0.956938i \(-0.406247\pi\)
0.290293 + 0.956938i \(0.406247\pi\)
\(54\) 50255.2i 0.319153i
\(55\) 39352.9i 0.236532i
\(56\) 193838.i 1.10376i
\(57\) 183524. 0.990986
\(58\) 456461.i 2.33948i
\(59\) −55030.6 + 197869.i −0.267947 + 0.963434i
\(60\) −227272. −1.05219
\(61\) 21873.5i 0.0963669i 0.998839 + 0.0481834i \(0.0153432\pi\)
−0.998839 + 0.0481834i \(0.984657\pi\)
\(62\) −471054. −1.97649
\(63\) 73947.1 0.295733
\(64\) 397252. 1.51540
\(65\) 503236.i 1.83245i
\(66\) −62527.8 −0.217491
\(67\) 351365.i 1.16824i 0.811666 + 0.584122i \(0.198561\pi\)
−0.811666 + 0.584122i \(0.801439\pi\)
\(68\) −559249. −1.77860
\(69\) 266180.i 0.810266i
\(70\) 525490.i 1.53204i
\(71\) −350770. −0.980047 −0.490024 0.871709i \(-0.663012\pi\)
−0.490024 + 0.871709i \(0.663012\pi\)
\(72\) 154785.i 0.414698i
\(73\) 216142.i 0.555611i −0.960637 0.277805i \(-0.910393\pi\)
0.960637 0.277805i \(-0.0896070\pi\)
\(74\) −435570. −1.07489
\(75\) 20525.0 0.0486519
\(76\) −1.31873e6 −3.00409
\(77\) 92005.5i 0.201531i
\(78\) 799591. 1.68494
\(79\) −797387. −1.61729 −0.808645 0.588297i \(-0.799799\pi\)
−0.808645 + 0.588297i \(0.799799\pi\)
\(80\) 166860. 0.325898
\(81\) 59049.0 0.111111
\(82\) 844885.i 1.53234i
\(83\) 710474.i 1.24255i −0.783593 0.621275i \(-0.786615\pi\)
0.783593 0.621275i \(-0.213385\pi\)
\(84\) −531353. −0.896490
\(85\) 649857. 1.05818
\(86\) −718992. −1.13039
\(87\) 536334. 0.814474
\(88\) 192585. 0.282601
\(89\) 1.09404e6i 1.55190i −0.630793 0.775951i \(-0.717270\pi\)
0.630793 0.775951i \(-0.282730\pi\)
\(90\) 419620.i 0.575610i
\(91\) 1.17654e6i 1.56129i
\(92\) 1.91266e6i 2.45626i
\(93\) 553480.i 0.688103i
\(94\) 187194. 0.225376
\(95\) 1.53238e6 1.78730
\(96\) 370363.i 0.418614i
\(97\) 1.57323e6i 1.72377i −0.507107 0.861883i \(-0.669285\pi\)
0.507107 0.861883i \(-0.330715\pi\)
\(98\) 332271.i 0.353032i
\(99\) 73469.2i 0.0757181i
\(100\) −147484. −0.147484
\(101\) 613316.i 0.595279i 0.954678 + 0.297639i \(0.0961993\pi\)
−0.954678 + 0.297639i \(0.903801\pi\)
\(102\) 1.03256e6i 0.973001i
\(103\) 1.07926e6i 0.987679i −0.869553 0.493839i \(-0.835593\pi\)
0.869553 0.493839i \(-0.164407\pi\)
\(104\) −2.46273e6 −2.18936
\(105\) 617442. 0.533370
\(106\) 1.14674e6i 0.962825i
\(107\) −1.82635e6 −1.49085 −0.745424 0.666591i \(-0.767753\pi\)
−0.745424 + 0.666591i \(0.767753\pi\)
\(108\) −424302. −0.336824
\(109\) 1.34684e6i 1.04001i 0.854164 + 0.520004i \(0.174069\pi\)
−0.854164 + 0.520004i \(0.825931\pi\)
\(110\) −522094. −0.392257
\(111\) 511787.i 0.374214i
\(112\) 390111. 0.277673
\(113\) 34952.4i 0.0242238i 0.999927 + 0.0121119i \(0.00385543\pi\)
−0.999927 + 0.0121119i \(0.996145\pi\)
\(114\) 2.43480e6i 1.64342i
\(115\) 2.22254e6i 1.46136i
\(116\) −3.85387e6 −2.46901
\(117\) 939506.i 0.586600i
\(118\) 2.62512e6 + 730089.i 1.59773 + 0.444355i
\(119\) 1.51934e6 0.901599
\(120\) 1.29242e6i 0.747930i
\(121\) 1.68015e6 0.948401
\(122\) 290194. 0.159812
\(123\) −992726. −0.533475
\(124\) 3.97708e6i 2.08593i
\(125\) −1.86237e6 −0.953535
\(126\) 981053.i 0.490434i
\(127\) −3.48711e6 −1.70237 −0.851185 0.524865i \(-0.824116\pi\)
−0.851185 + 0.524865i \(0.824116\pi\)
\(128\) 3.74977e6i 1.78803i
\(129\) 844804.i 0.393538i
\(130\) 6.67641e6 3.03888
\(131\) 396214.i 0.176245i 0.996110 + 0.0881223i \(0.0280866\pi\)
−0.996110 + 0.0881223i \(0.971913\pi\)
\(132\) 527919.i 0.229533i
\(133\) 3.58264e6 1.52282
\(134\) 4.66154e6 1.93738
\(135\) 493046. 0.200395
\(136\) 3.18026e6i 1.26429i
\(137\) 2.29114e6 0.891024 0.445512 0.895276i \(-0.353022\pi\)
0.445512 + 0.895276i \(0.353022\pi\)
\(138\) 3.53140e6 1.34372
\(139\) 4.70914e6 1.75347 0.876733 0.480978i \(-0.159718\pi\)
0.876733 + 0.480978i \(0.159718\pi\)
\(140\) −4.43668e6 −1.61687
\(141\) 219950.i 0.0784632i
\(142\) 4.65365e6i 1.62528i
\(143\) 1.16894e6 0.399746
\(144\) 311515. 0.104326
\(145\) 4.47827e6 1.46895
\(146\) −2.86755e6 −0.921408
\(147\) −390413. −0.122906
\(148\) 3.67749e6i 1.13440i
\(149\) 2.45902e6i 0.743366i 0.928360 + 0.371683i \(0.121219\pi\)
−0.928360 + 0.371683i \(0.878781\pi\)
\(150\) 272305.i 0.0806829i
\(151\) 629431.i 0.182817i 0.995813 + 0.0914086i \(0.0291369\pi\)
−0.995813 + 0.0914086i \(0.970863\pi\)
\(152\) 7.49915e6i 2.13541i
\(153\) 1.21324e6 0.338744
\(154\) −1.22063e6 −0.334213
\(155\) 4.62144e6i 1.24103i
\(156\) 6.75090e6i 1.77823i
\(157\) 4.88779e6i 1.26303i −0.775364 0.631514i \(-0.782434\pi\)
0.775364 0.631514i \(-0.217566\pi\)
\(158\) 1.05789e7i 2.68207i
\(159\) 1.34740e6 0.335201
\(160\) 3.09245e6i 0.754993i
\(161\) 5.19621e6i 1.24511i
\(162\) 783401.i 0.184263i
\(163\) 7.35509e6 1.69834 0.849171 0.528117i \(-0.177102\pi\)
0.849171 + 0.528117i \(0.177102\pi\)
\(164\) 7.13332e6 1.61719
\(165\) 613451.i 0.136562i
\(166\) −9.42583e6 −2.06061
\(167\) −3.16416e6 −0.679375 −0.339687 0.940538i \(-0.610321\pi\)
−0.339687 + 0.940538i \(0.610321\pi\)
\(168\) 3.02163e6i 0.637255i
\(169\) −1.01213e7 −2.09690
\(170\) 8.62162e6i 1.75486i
\(171\) 2.86085e6 0.572146
\(172\) 6.07041e6i 1.19298i
\(173\) 4.86437e6i 0.939481i 0.882805 + 0.469740i \(0.155652\pi\)
−0.882805 + 0.469740i \(0.844348\pi\)
\(174\) 7.11552e6i 1.35070i
\(175\) 400678. 0.0747621
\(176\) 387590.i 0.0710942i
\(177\) −857842. + 3.08447e6i −0.154699 + 0.556239i
\(178\) −1.45146e7 −2.57363
\(179\) 3.40368e6i 0.593458i −0.954962 0.296729i \(-0.904104\pi\)
0.954962 0.296729i \(-0.0958957\pi\)
\(180\) −3.54283e6 −0.607481
\(181\) 6.00041e6 1.01192 0.505959 0.862557i \(-0.331139\pi\)
0.505959 + 0.862557i \(0.331139\pi\)
\(182\) 1.56092e7 2.58920
\(183\) 340973.i 0.0556375i
\(184\) −1.08767e7 −1.74599
\(185\) 4.27331e6i 0.674915i
\(186\) −7.34300e6 −1.14113
\(187\) 1.50952e6i 0.230841i
\(188\) 1.58047e6i 0.237855i
\(189\) 1.15272e6 0.170741
\(190\) 2.03301e7i 2.96400i
\(191\) 5.95294e6i 0.854342i −0.904171 0.427171i \(-0.859510\pi\)
0.904171 0.427171i \(-0.140490\pi\)
\(192\) 6.19255e6 0.874915
\(193\) 8.14665e6 1.13320 0.566601 0.823992i \(-0.308258\pi\)
0.566601 + 0.823992i \(0.308258\pi\)
\(194\) −2.08720e7 −2.85864
\(195\) 7.84467e6i 1.05796i
\(196\) 2.80535e6 0.372579
\(197\) −6.88372e6 −0.900377 −0.450189 0.892934i \(-0.648643\pi\)
−0.450189 + 0.892934i \(0.648643\pi\)
\(198\) −974712. −0.125569
\(199\) −3.86736e6 −0.490744 −0.245372 0.969429i \(-0.578910\pi\)
−0.245372 + 0.969429i \(0.578910\pi\)
\(200\) 838695.i 0.104837i
\(201\) 5.47723e6i 0.674486i
\(202\) 8.13684e6 0.987192
\(203\) 1.04700e7 1.25158
\(204\) −8.71782e6 −1.02687
\(205\) −8.28905e6 −0.962151
\(206\) −1.43185e7 −1.63794
\(207\) 4.14933e6i 0.467808i
\(208\) 4.95640e6i 0.550778i
\(209\) 3.55949e6i 0.389896i
\(210\) 8.19158e6i 0.884524i
\(211\) 1.02663e7i 1.09287i 0.837502 + 0.546435i \(0.184015\pi\)
−0.837502 + 0.546435i \(0.815985\pi\)
\(212\) −9.68187e6 −1.01614
\(213\) −5.46796e6 −0.565831
\(214\) 2.42301e7i 2.47238i
\(215\) 7.05393e6i 0.709767i
\(216\) 2.41286e6i 0.239426i
\(217\) 1.08047e7i 1.05739i
\(218\) 1.78685e7 1.72472
\(219\) 3.36932e6i 0.320782i
\(220\) 4.40801e6i 0.413975i
\(221\) 1.93034e7i 1.78836i
\(222\) −6.78986e6 −0.620586
\(223\) 1.02204e7 0.921621 0.460811 0.887498i \(-0.347559\pi\)
0.460811 + 0.887498i \(0.347559\pi\)
\(224\) 7.23002e6i 0.643273i
\(225\) 319954. 0.0280892
\(226\) 463713. 0.0401720
\(227\) 4.14140e6i 0.354054i 0.984206 + 0.177027i \(0.0566480\pi\)
−0.984206 + 0.177027i \(0.943352\pi\)
\(228\) −2.05569e7 −1.73441
\(229\) 3.11497e6i 0.259387i 0.991554 + 0.129693i \(0.0413993\pi\)
−0.991554 + 0.129693i \(0.958601\pi\)
\(230\) 2.94864e7 2.42347
\(231\) 1.43422e6i 0.116354i
\(232\) 2.19157e7i 1.75506i
\(233\) 3.13161e6i 0.247571i −0.992309 0.123786i \(-0.960496\pi\)
0.992309 0.123786i \(-0.0395035\pi\)
\(234\) 1.24644e7 0.972800
\(235\) 1.83653e6i 0.141513i
\(236\) 6.16410e6 2.21638e7i 0.468958 1.68619i
\(237\) −1.24300e7 −0.933743
\(238\) 2.01570e7i 1.49518i
\(239\) 3.41855e6 0.250408 0.125204 0.992131i \(-0.460042\pi\)
0.125204 + 0.992131i \(0.460042\pi\)
\(240\) 2.60109e6 0.188157
\(241\) −7.48627e6 −0.534829 −0.267414 0.963582i \(-0.586169\pi\)
−0.267414 + 0.963582i \(0.586169\pi\)
\(242\) 2.22905e7i 1.57280i
\(243\) 920483. 0.0641500
\(244\) 2.45009e6i 0.168660i
\(245\) −3.25986e6 −0.221667
\(246\) 1.31705e7i 0.884699i
\(247\) 4.55179e7i 3.02059i
\(248\) 2.26163e7 1.48275
\(249\) 1.10752e7i 0.717387i
\(250\) 2.47080e7i 1.58131i
\(251\) 1.02216e7 0.646395 0.323197 0.946332i \(-0.395242\pi\)
0.323197 + 0.946332i \(0.395242\pi\)
\(252\) −8.28298e6 −0.517589
\(253\) 5.16263e6 0.318793
\(254\) 4.62633e7i 2.82316i
\(255\) 1.01303e7 0.610942
\(256\) −2.43239e7 −1.44982
\(257\) −1.51696e7 −0.893663 −0.446832 0.894618i \(-0.647448\pi\)
−0.446832 + 0.894618i \(0.647448\pi\)
\(258\) −1.12080e7 −0.652632
\(259\) 9.99082e6i 0.575045i
\(260\) 5.63686e7i 3.20713i
\(261\) 8.36062e6 0.470237
\(262\) 5.25656e6 0.292279
\(263\) −1.18718e6 −0.0652601 −0.0326301 0.999467i \(-0.510388\pi\)
−0.0326301 + 0.999467i \(0.510388\pi\)
\(264\) 3.00210e6 0.163160
\(265\) 1.12505e7 0.604553
\(266\) 4.75308e7i 2.52540i
\(267\) 1.70544e7i 0.895991i
\(268\) 3.93571e7i 2.04465i
\(269\) 2.00074e7i 1.02786i 0.857833 + 0.513929i \(0.171811\pi\)
−0.857833 + 0.513929i \(0.828189\pi\)
\(270\) 6.54122e6i 0.332329i
\(271\) −2.02889e7 −1.01941 −0.509706 0.860348i \(-0.670246\pi\)
−0.509706 + 0.860348i \(0.670246\pi\)
\(272\) 6.40048e6 0.318058
\(273\) 1.83405e7i 0.901412i
\(274\) 3.03964e7i 1.47765i
\(275\) 398088.i 0.0191417i
\(276\) 2.98154e7i 1.41812i
\(277\) 5.83030e6 0.274316 0.137158 0.990549i \(-0.456203\pi\)
0.137158 + 0.990549i \(0.456203\pi\)
\(278\) 6.24760e7i 2.90789i
\(279\) 8.62790e6i 0.397276i
\(280\) 2.52299e7i 1.14932i
\(281\) 1.21058e7 0.545601 0.272800 0.962071i \(-0.412050\pi\)
0.272800 + 0.962071i \(0.412050\pi\)
\(282\) 2.91807e6 0.130121
\(283\) 1.30713e7i 0.576711i −0.957523 0.288356i \(-0.906891\pi\)
0.957523 0.288356i \(-0.0931085\pi\)
\(284\) 3.92905e7 1.71527
\(285\) 2.38875e7 1.03190
\(286\) 1.55083e7i 0.662927i
\(287\) −1.93794e7 −0.819777
\(288\) 5.77339e6i 0.241687i
\(289\) 789935. 0.0327264
\(290\) 5.94130e7i 2.43606i
\(291\) 2.45243e7i 0.995217i
\(292\) 2.42105e7i 0.972425i
\(293\) 2.58060e7 1.02593 0.512966 0.858409i \(-0.328547\pi\)
0.512966 + 0.858409i \(0.328547\pi\)
\(294\) 5.17959e6i 0.203823i
\(295\) −7.16280e6 + 2.57547e7i −0.279008 + 1.00321i
\(296\) 2.09127e7 0.806370
\(297\) 1.14527e6i 0.0437158i
\(298\) 3.26237e7 1.23278
\(299\) −6.60184e7 −2.46974
\(300\) −2.29905e6 −0.0851502
\(301\) 1.64918e7i 0.604739i
\(302\) 8.35063e6 0.303179
\(303\) 9.56066e6i 0.343684i
\(304\) 1.50925e7 0.537207
\(305\) 2.84705e6i 0.100345i
\(306\) 1.60960e7i 0.561763i
\(307\) −2.55575e7 −0.883291 −0.441645 0.897190i \(-0.645605\pi\)
−0.441645 + 0.897190i \(0.645605\pi\)
\(308\) 1.03057e7i 0.352717i
\(309\) 1.68241e7i 0.570237i
\(310\) −6.13125e7 −2.05809
\(311\) −3.58308e7 −1.19117 −0.595587 0.803291i \(-0.703080\pi\)
−0.595587 + 0.803291i \(0.703080\pi\)
\(312\) −3.83901e7 −1.26403
\(313\) 2.94627e7i 0.960815i 0.877045 + 0.480408i \(0.159511\pi\)
−0.877045 + 0.480408i \(0.840489\pi\)
\(314\) −6.48461e7 −2.09457
\(315\) 9.62497e6 0.307941
\(316\) 8.93171e7 2.83057
\(317\) −2.81452e7 −0.883541 −0.441770 0.897128i \(-0.645649\pi\)
−0.441770 + 0.897128i \(0.645649\pi\)
\(318\) 1.78759e7i 0.555887i
\(319\) 1.04023e7i 0.320449i
\(320\) 5.17065e7 1.57796
\(321\) −2.84700e7 −0.860741
\(322\) 6.89379e7 2.06486
\(323\) 5.87798e7 1.74430
\(324\) −6.61421e6 −0.194466
\(325\) 5.09066e6i 0.148294i
\(326\) 9.75797e7i 2.81648i
\(327\) 2.09952e7i 0.600449i
\(328\) 4.05648e7i 1.14955i
\(329\) 4.29374e6i 0.120572i
\(330\) −8.13864e6 −0.226470
\(331\) 8.53611e6 0.235384 0.117692 0.993050i \(-0.462451\pi\)
0.117692 + 0.993050i \(0.462451\pi\)
\(332\) 7.95818e7i 2.17470i
\(333\) 7.97797e6i 0.216053i
\(334\) 4.19788e7i 1.12665i
\(335\) 4.57337e7i 1.21647i
\(336\) 6.08123e6 0.160315
\(337\) 5.17480e7i 1.35209i 0.736862 + 0.676043i \(0.236307\pi\)
−0.736862 + 0.676043i \(0.763693\pi\)
\(338\) 1.34279e8i 3.47743i
\(339\) 544855.i 0.0139856i
\(340\) −7.27919e7 −1.85202
\(341\) −1.07349e7 −0.270729
\(342\) 3.79548e7i 0.948830i
\(343\) −4.34231e7 −1.07606
\(344\) 3.45204e7 0.848009
\(345\) 3.46460e7i 0.843716i
\(346\) 6.45353e7 1.55801
\(347\) 4.80773e7i 1.15067i 0.817917 + 0.575336i \(0.195129\pi\)
−0.817917 + 0.575336i \(0.804871\pi\)
\(348\) −6.00759e7 −1.42549
\(349\) 4.31976e7i 1.01621i 0.861295 + 0.508104i \(0.169654\pi\)
−0.861295 + 0.508104i \(0.830346\pi\)
\(350\) 5.31578e6i 0.123983i
\(351\) 1.46455e7i 0.338674i
\(352\) 7.18329e6 0.164701
\(353\) 5.00314e7i 1.13741i −0.822540 0.568707i \(-0.807444\pi\)
0.822540 0.568707i \(-0.192556\pi\)
\(354\) 4.09216e7 + 1.13810e7i 0.922450 + 0.256548i
\(355\) −4.56563e7 −1.02051
\(356\) 1.22546e8i 2.71613i
\(357\) 2.36841e7 0.520538
\(358\) −4.51565e7 −0.984172
\(359\) 8.77345e6 0.189621 0.0948106 0.995495i \(-0.469775\pi\)
0.0948106 + 0.995495i \(0.469775\pi\)
\(360\) 2.01469e7i 0.431818i
\(361\) 9.15587e7 1.94616
\(362\) 7.96072e7i 1.67813i
\(363\) 2.61909e7 0.547560
\(364\) 1.31787e8i 2.73256i
\(365\) 2.81331e7i 0.578547i
\(366\) 4.52368e6 0.0922675
\(367\) 6.37952e7i 1.29060i −0.763931 0.645298i \(-0.776733\pi\)
0.763931 0.645298i \(-0.223267\pi\)
\(368\) 2.18900e7i 0.439240i
\(369\) −1.54751e7 −0.308002
\(370\) −5.66938e7 −1.11926
\(371\) 2.63032e7 0.515094
\(372\) 6.19966e7i 1.20431i
\(373\) −7.33491e7 −1.41341 −0.706705 0.707508i \(-0.749819\pi\)
−0.706705 + 0.707508i \(0.749819\pi\)
\(374\) −2.00267e7 −0.382820
\(375\) −2.90315e7 −0.550524
\(376\) −8.98760e6 −0.169075
\(377\) 1.33023e8i 2.48257i
\(378\) 1.52931e7i 0.283152i
\(379\) 4.24353e7 0.779489 0.389745 0.920923i \(-0.372563\pi\)
0.389745 + 0.920923i \(0.372563\pi\)
\(380\) −1.71646e8 −3.12811
\(381\) −5.43586e7 −0.982864
\(382\) −7.89775e7 −1.41681
\(383\) −7.62200e7 −1.35667 −0.678333 0.734755i \(-0.737297\pi\)
−0.678333 + 0.734755i \(0.737297\pi\)
\(384\) 5.84531e7i 1.03232i
\(385\) 1.19755e7i 0.209850i
\(386\) 1.08081e8i 1.87927i
\(387\) 1.31692e7i 0.227209i
\(388\) 1.76222e8i 3.01692i
\(389\) −1.78271e7 −0.302854 −0.151427 0.988468i \(-0.548387\pi\)
−0.151427 + 0.988468i \(0.548387\pi\)
\(390\) 1.04075e8 1.75450
\(391\) 8.52533e7i 1.42620i
\(392\) 1.59531e7i 0.264842i
\(393\) 6.17637e6i 0.101755i
\(394\) 9.13260e7i 1.49316i
\(395\) −1.03788e8 −1.68405
\(396\) 8.22944e6i 0.132521i
\(397\) 4.58059e7i 0.732065i −0.930602 0.366033i \(-0.880716\pi\)
0.930602 0.366033i \(-0.119284\pi\)
\(398\) 5.13081e7i 0.813836i
\(399\) 5.58479e7 0.879201
\(400\) 1.68793e6 0.0263739
\(401\) 1.68612e7i 0.261491i −0.991416 0.130745i \(-0.958263\pi\)
0.991416 0.130745i \(-0.0417370\pi\)
\(402\) 7.26662e7 1.11855
\(403\) 1.37275e8 2.09738
\(404\) 6.86989e7i 1.04185i
\(405\) 7.68583e6 0.115698
\(406\) 1.38905e8i 2.07558i
\(407\) −9.92625e6 −0.147232
\(408\) 4.95754e7i 0.729937i
\(409\) 7.74091e7i 1.13142i −0.824606 0.565708i \(-0.808603\pi\)
0.824606 0.565708i \(-0.191397\pi\)
\(410\) 1.09970e8i 1.59560i
\(411\) 3.57153e7 0.514433
\(412\) 1.20891e8i 1.72863i
\(413\) −1.67463e7 + 6.02133e7i −0.237722 + 0.854757i
\(414\) 5.50490e7 0.775798
\(415\) 9.24755e7i 1.29384i
\(416\) −9.18582e7 −1.27596
\(417\) 7.34082e7 1.01236
\(418\) −4.72236e7 −0.646592
\(419\) 6.40310e7i 0.870459i −0.900319 0.435230i \(-0.856667\pi\)
0.900319 0.435230i \(-0.143333\pi\)
\(420\) −6.91611e7 −0.933499
\(421\) 1.06216e8i 1.42346i −0.702454 0.711730i \(-0.747912\pi\)
0.702454 0.711730i \(-0.252088\pi\)
\(422\) 1.36203e8 1.81238
\(423\) 3.42868e6i 0.0453008i
\(424\) 5.50576e7i 0.722303i
\(425\) 6.57385e6 0.0856354
\(426\) 7.25432e7i 0.938357i
\(427\) 6.65629e6i 0.0854965i
\(428\) 2.04574e8 2.60927
\(429\) 1.82220e7 0.230793
\(430\) −9.35842e7 −1.17706
\(431\) 4.74955e7i 0.593227i 0.954998 + 0.296613i \(0.0958573\pi\)
−0.954998 + 0.296613i \(0.904143\pi\)
\(432\) 4.85605e6 0.0602326
\(433\) −3.56448e7 −0.439068 −0.219534 0.975605i \(-0.570454\pi\)
−0.219534 + 0.975605i \(0.570454\pi\)
\(434\) −1.43346e8 −1.75354
\(435\) 6.98093e7 0.848097
\(436\) 1.50863e8i 1.82021i
\(437\) 2.01030e8i 2.40889i
\(438\) −4.47006e7 −0.531975
\(439\) 1.02332e8 1.20954 0.604770 0.796401i \(-0.293265\pi\)
0.604770 + 0.796401i \(0.293265\pi\)
\(440\) 2.50669e7 0.294268
\(441\) −6.08594e6 −0.0709597
\(442\) 2.56097e8 2.96577
\(443\) 3.68919e6i 0.0424345i −0.999775 0.0212173i \(-0.993246\pi\)
0.999775 0.0212173i \(-0.00675417\pi\)
\(444\) 5.73264e7i 0.654947i
\(445\) 1.42401e8i 1.61597i
\(446\) 1.35593e8i 1.52839i
\(447\) 3.83323e7i 0.429183i
\(448\) 1.20888e8 1.34446
\(449\) −7.44766e7 −0.822775 −0.411387 0.911461i \(-0.634956\pi\)
−0.411387 + 0.911461i \(0.634956\pi\)
\(450\) 4.24481e6i 0.0465823i
\(451\) 1.92542e7i 0.209892i
\(452\) 3.91510e6i 0.0423963i
\(453\) 9.81186e6i 0.105550i
\(454\) 5.49438e7 0.587152
\(455\) 1.53139e8i 1.62574i
\(456\) 1.16900e8i 1.23288i
\(457\) 5.98613e6i 0.0627188i −0.999508 0.0313594i \(-0.990016\pi\)
0.999508 0.0313594i \(-0.00998364\pi\)
\(458\) 4.13262e7 0.430159
\(459\) 1.89125e7 0.195574
\(460\) 2.48952e8i 2.55766i
\(461\) −5.41854e7 −0.553069 −0.276534 0.961004i \(-0.589186\pi\)
−0.276534 + 0.961004i \(0.589186\pi\)
\(462\) −1.90278e7 −0.192958
\(463\) 6.23169e6i 0.0627860i 0.999507 + 0.0313930i \(0.00999435\pi\)
−0.999507 + 0.0313930i \(0.990006\pi\)
\(464\) 4.41068e7 0.441521
\(465\) 7.20411e7i 0.716509i
\(466\) −4.15470e7 −0.410565
\(467\) 1.39127e8i 1.36603i 0.730405 + 0.683014i \(0.239331\pi\)
−0.730405 + 0.683014i \(0.760669\pi\)
\(468\) 1.05236e8i 1.02666i
\(469\) 1.06923e8i 1.03646i
\(470\) 2.43652e7 0.234680
\(471\) 7.61930e7i 0.729210i
\(472\) −1.26038e8 3.50532e7i −1.19860 0.333351i
\(473\) −1.63852e7 −0.154835
\(474\) 1.64909e8i 1.54849i
\(475\) 1.55013e7 0.144640
\(476\) −1.70184e8 −1.57797
\(477\) 2.10039e7 0.193528
\(478\) 4.53537e7i 0.415269i
\(479\) −2.07373e7 −0.188688 −0.0943442 0.995540i \(-0.530075\pi\)
−0.0943442 + 0.995540i \(0.530075\pi\)
\(480\) 4.82066e7i 0.435896i
\(481\) 1.26934e8 1.14063
\(482\) 9.93201e7i 0.886944i
\(483\) 8.10009e7i 0.718867i
\(484\) −1.88197e8 −1.65988
\(485\) 2.04773e8i 1.79493i
\(486\) 1.22120e7i 0.106384i
\(487\) −1.57737e8 −1.36567 −0.682835 0.730573i \(-0.739253\pi\)
−0.682835 + 0.730573i \(0.739253\pi\)
\(488\) −1.39329e7 −0.119890
\(489\) 1.14655e8 0.980539
\(490\) 4.32485e7i 0.367606i
\(491\) −1.05877e8 −0.894451 −0.447226 0.894421i \(-0.647588\pi\)
−0.447226 + 0.894421i \(0.647588\pi\)
\(492\) 1.11197e8 0.933683
\(493\) 1.71780e8 1.43361
\(494\) 6.03884e8 5.00925
\(495\) 9.56276e6i 0.0788438i
\(496\) 4.55169e7i 0.373016i
\(497\) −1.06742e8 −0.869496
\(498\) −1.46934e8 −1.18969
\(499\) 1.18761e8 0.955808 0.477904 0.878412i \(-0.341397\pi\)
0.477904 + 0.878412i \(0.341397\pi\)
\(500\) 2.08609e8 1.66887
\(501\) −4.93244e7 −0.392237
\(502\) 1.35610e8i 1.07196i
\(503\) 1.90458e8i 1.49657i −0.663380 0.748283i \(-0.730878\pi\)
0.663380 0.748283i \(-0.269122\pi\)
\(504\) 4.71025e7i 0.367919i
\(505\) 7.98294e7i 0.619853i
\(506\) 6.84924e7i 0.528677i
\(507\) −1.57776e8 −1.21064
\(508\) 3.90599e8 2.97947
\(509\) 2.50692e8i 1.90102i 0.310690 + 0.950511i \(0.399440\pi\)
−0.310690 + 0.950511i \(0.600560\pi\)
\(510\) 1.34398e8i 1.01317i
\(511\) 6.57740e7i 0.492937i
\(512\) 8.27186e7i 0.616302i
\(513\) 4.45962e7 0.330329
\(514\) 2.01254e8i 1.48202i
\(515\) 1.40477e8i 1.02845i
\(516\) 9.46283e7i 0.688767i
\(517\) 4.26598e6 0.0308708
\(518\) −1.32548e8 −0.953637
\(519\) 7.58280e7i 0.542409i
\(520\) −3.20549e8 −2.27974
\(521\) 3.29248e7 0.232815 0.116407 0.993202i \(-0.462862\pi\)
0.116407 + 0.993202i \(0.462862\pi\)
\(522\) 1.10920e8i 0.779827i
\(523\) −8.55987e7 −0.598360 −0.299180 0.954197i \(-0.596713\pi\)
−0.299180 + 0.954197i \(0.596713\pi\)
\(524\) 4.43808e7i 0.308462i
\(525\) 6.24595e6 0.0431639
\(526\) 1.57502e7i 0.108225i
\(527\) 1.77271e8i 1.21117i
\(528\) 6.04192e6i 0.0410463i
\(529\) −1.43535e8 −0.969595
\(530\) 1.49260e8i 1.00257i
\(531\) −1.33724e7 + 4.80822e7i −0.0893155 + 0.321145i
\(532\) −4.01300e8 −2.66523
\(533\) 2.46218e8i 1.62607i
\(534\) −2.26261e8 −1.48589
\(535\) −2.37718e8 −1.55239
\(536\) −2.23811e8 −1.45341
\(537\) 5.30581e7i 0.342633i
\(538\) 2.65437e8 1.70457
\(539\) 7.57216e6i 0.0483564i
\(540\) −5.52272e7 −0.350729
\(541\) 2.89276e8i 1.82693i −0.406920 0.913464i \(-0.633397\pi\)
0.406920 0.913464i \(-0.366603\pi\)
\(542\) 2.69172e8i 1.69056i
\(543\) 9.35372e7 0.584231
\(544\) 1.18622e8i 0.736830i
\(545\) 1.75305e8i 1.08294i
\(546\) 2.43323e8 1.49487
\(547\) 3.21322e8 1.96327 0.981633 0.190779i \(-0.0611014\pi\)
0.981633 + 0.190779i \(0.0611014\pi\)
\(548\) −2.56635e8 −1.55946
\(549\) 5.31525e6i 0.0321223i
\(550\) −5.28142e6 −0.0317441
\(551\) 4.05061e8 2.42140
\(552\) −1.69550e8 −1.00805
\(553\) −2.42652e8 −1.43486
\(554\) 7.73503e7i 0.454918i
\(555\) 6.66143e7i 0.389663i
\(556\) −5.27481e8 −3.06890
\(557\) 1.42874e8 0.826778 0.413389 0.910555i \(-0.364345\pi\)
0.413389 + 0.910555i \(0.364345\pi\)
\(558\) −1.14466e8 −0.658831
\(559\) 2.09530e8 1.19953
\(560\) 5.07769e7 0.289136
\(561\) 2.35311e7i 0.133276i
\(562\) 1.60607e8i 0.904808i
\(563\) 9.47478e7i 0.530938i 0.964119 + 0.265469i \(0.0855268\pi\)
−0.964119 + 0.265469i \(0.914473\pi\)
\(564\) 2.46371e7i 0.137326i
\(565\) 4.54942e6i 0.0252238i
\(566\) −1.73416e8 −0.956401
\(567\) 1.79691e7 0.0985776
\(568\) 2.23432e8i 1.21927i
\(569\) 1.29523e8i 0.703087i 0.936172 + 0.351543i \(0.114343\pi\)
−0.936172 + 0.351543i \(0.885657\pi\)
\(570\) 3.16914e8i 1.71126i
\(571\) 4.87058e7i 0.261621i −0.991407 0.130811i \(-0.958242\pi\)
0.991407 0.130811i \(-0.0417580\pi\)
\(572\) −1.30936e8 −0.699632
\(573\) 9.27972e7i 0.493254i
\(574\) 2.57106e8i 1.35949i
\(575\) 2.24829e7i 0.118263i
\(576\) 9.65324e7 0.505133
\(577\) 4.43975e7 0.231117 0.115558 0.993301i \(-0.463134\pi\)
0.115558 + 0.993301i \(0.463134\pi\)
\(578\) 1.04800e7i 0.0542724i
\(579\) 1.26994e8 0.654254
\(580\) −5.01621e8 −2.57094
\(581\) 2.16204e8i 1.10239i
\(582\) −3.25363e8 −1.65044
\(583\) 2.61332e7i 0.131882i
\(584\) 1.37677e8 0.691232
\(585\) 1.22286e8i 0.610816i
\(586\) 3.42368e8i 1.70137i
\(587\) 2.32647e8i 1.15022i −0.818075 0.575112i \(-0.804958\pi\)
0.818075 0.575112i \(-0.195042\pi\)
\(588\) 4.37310e7 0.215109
\(589\) 4.18011e8i 2.04570i
\(590\) 3.41686e8 + 9.50285e7i 1.66369 + 0.462698i
\(591\) −1.07307e8 −0.519833
\(592\) 4.20881e7i 0.202859i
\(593\) −7.02595e7 −0.336931 −0.168466 0.985708i \(-0.553881\pi\)
−0.168466 + 0.985708i \(0.553881\pi\)
\(594\) −1.51943e7 −0.0724970
\(595\) 1.97757e8 0.938818
\(596\) 2.75440e8i 1.30103i
\(597\) −6.02862e7 −0.283331
\(598\) 8.75864e8i 4.09575i
\(599\) 1.26550e8 0.588817 0.294408 0.955680i \(-0.404877\pi\)
0.294408 + 0.955680i \(0.404877\pi\)
\(600\) 1.30740e7i 0.0605276i
\(601\) 1.51823e8i 0.699381i −0.936865 0.349690i \(-0.886287\pi\)
0.936865 0.349690i \(-0.113713\pi\)
\(602\) −2.18796e8 −1.00288
\(603\) 8.53816e7i 0.389415i
\(604\) 7.05040e7i 0.319965i
\(605\) 2.18689e8 0.987553
\(606\) 1.26841e8 0.569956
\(607\) 2.49091e8 1.11376 0.556881 0.830593i \(-0.311998\pi\)
0.556881 + 0.830593i \(0.311998\pi\)
\(608\) 2.79714e8i 1.24452i
\(609\) 1.63211e8 0.722600
\(610\) 3.77717e7 0.166409
\(611\) −5.45524e7 −0.239161
\(612\) −1.35897e8 −0.592866
\(613\) 1.65012e8i 0.716363i 0.933652 + 0.358181i \(0.116603\pi\)
−0.933652 + 0.358181i \(0.883397\pi\)
\(614\) 3.39071e8i 1.46482i
\(615\) −1.29213e8 −0.555498
\(616\) 5.86053e7 0.250723
\(617\) −3.28492e8 −1.39852 −0.699262 0.714866i \(-0.746488\pi\)
−0.699262 + 0.714866i \(0.746488\pi\)
\(618\) −2.23204e8 −0.945663
\(619\) −1.14198e6 −0.00481490 −0.00240745 0.999997i \(-0.500766\pi\)
−0.00240745 + 0.999997i \(0.500766\pi\)
\(620\) 5.17658e8i 2.17204i
\(621\) 6.46817e7i 0.270089i
\(622\) 4.75365e8i 1.97541i
\(623\) 3.32927e8i 1.37685i
\(624\) 7.72627e7i 0.317992i
\(625\) −2.62980e8 −1.07717
\(626\) 3.90881e8 1.59339
\(627\) 5.54869e7i 0.225107i
\(628\) 5.47492e8i 2.21054i
\(629\) 1.63918e8i 0.658679i
\(630\) 1.27694e8i 0.510680i
\(631\) −4.22819e8 −1.68293 −0.841465 0.540312i \(-0.818306\pi\)
−0.841465 + 0.540312i \(0.818306\pi\)
\(632\) 5.07917e8i 2.01206i
\(633\) 1.60036e8i 0.630969i
\(634\) 3.73401e8i 1.46524i
\(635\) −4.53883e8 −1.77265
\(636\) −1.50925e8 −0.586666
\(637\) 9.68310e7i 0.374625i
\(638\) −1.38007e8 −0.531423
\(639\) −8.52371e7 −0.326682
\(640\) 4.88071e8i 1.86184i
\(641\) 1.89312e8 0.718792 0.359396 0.933185i \(-0.382983\pi\)
0.359396 + 0.933185i \(0.382983\pi\)
\(642\) 3.77711e8i 1.42743i
\(643\) 2.27620e7 0.0856205 0.0428102 0.999083i \(-0.486369\pi\)
0.0428102 + 0.999083i \(0.486369\pi\)
\(644\) 5.82039e8i 2.17919i
\(645\) 1.09960e8i 0.409784i
\(646\) 7.79829e8i 2.89269i
\(647\) −1.90979e8 −0.705134 −0.352567 0.935787i \(-0.614691\pi\)
−0.352567 + 0.935787i \(0.614691\pi\)
\(648\) 3.76128e7i 0.138233i
\(649\) 5.98242e7 + 1.66381e7i 0.218848 + 0.0608652i
\(650\) 6.75376e7 0.245926
\(651\) 1.68429e8i 0.610484i
\(652\) −8.23860e8 −2.97242
\(653\) 2.90721e8 1.04409 0.522043 0.852919i \(-0.325170\pi\)
0.522043 + 0.852919i \(0.325170\pi\)
\(654\) 2.78542e8 0.995766
\(655\) 5.15713e7i 0.183520i
\(656\) −8.16394e7 −0.289193
\(657\) 5.25225e7i 0.185204i
\(658\) 5.69648e7 0.199954
\(659\) 4.08241e7i 0.142646i 0.997453 + 0.0713231i \(0.0227222\pi\)
−0.997453 + 0.0713231i \(0.977278\pi\)
\(660\) 6.87141e7i 0.239009i
\(661\) −4.20379e8 −1.45558 −0.727791 0.685799i \(-0.759453\pi\)
−0.727791 + 0.685799i \(0.759453\pi\)
\(662\) 1.13248e8i 0.390353i
\(663\) 3.00909e8i 1.03251i
\(664\) 4.52555e8 1.54585
\(665\) 4.66318e8 1.58569
\(666\) −1.05843e8 −0.358295
\(667\) 5.87495e8i 1.97982i
\(668\) 3.54425e8 1.18904
\(669\) 1.59320e8 0.532098
\(670\) 6.06747e8 2.01736
\(671\) 6.61327e6 0.0218901
\(672\) 1.12705e8i 0.371394i
\(673\) 3.44287e8i 1.12947i −0.825271 0.564737i \(-0.808978\pi\)
0.825271 0.564737i \(-0.191022\pi\)
\(674\) 6.86539e8 2.24226
\(675\) 4.98758e6 0.0162173
\(676\) 1.13371e9 3.66997
\(677\) −5.11470e8 −1.64837 −0.824184 0.566322i \(-0.808366\pi\)
−0.824184 + 0.566322i \(0.808366\pi\)
\(678\) 7.22856e6 0.0231933
\(679\) 4.78750e8i 1.52932i
\(680\) 4.13943e8i 1.31648i
\(681\) 6.45580e7i 0.204413i
\(682\) 1.42419e8i 0.448969i
\(683\) 1.47287e8i 0.462276i 0.972921 + 0.231138i \(0.0742448\pi\)
−0.972921 + 0.231138i \(0.925755\pi\)
\(684\) −3.20450e8 −1.00136
\(685\) 2.98215e8 0.927807
\(686\) 5.76092e8i 1.78451i
\(687\) 4.85576e7i 0.149757i
\(688\) 6.94746e7i 0.213334i
\(689\) 3.34185e8i 1.02171i
\(690\) 4.59647e8 1.39919
\(691\) 2.22376e8i 0.673989i 0.941507 + 0.336995i \(0.109410\pi\)
−0.941507 + 0.336995i \(0.890590\pi\)
\(692\) 5.44868e8i 1.64427i
\(693\) 2.23573e7i 0.0671769i
\(694\) 6.37840e8 1.90824
\(695\) 6.12943e8 1.82585
\(696\) 3.41632e8i 1.01328i
\(697\) −3.17955e8 −0.939004
\(698\) 5.73100e8 1.68525
\(699\) 4.88170e7i 0.142935i
\(700\) −4.48808e7 −0.130848
\(701\) 1.91012e8i 0.554507i 0.960797 + 0.277254i \(0.0894242\pi\)
−0.960797 + 0.277254i \(0.910576\pi\)
\(702\) 1.94301e8 0.561646
\(703\) 3.86523e8i 1.11252i
\(704\) 1.20106e8i 0.344229i
\(705\) 2.86287e7i 0.0817023i
\(706\) −6.63764e8 −1.88625
\(707\) 1.86638e8i 0.528130i
\(708\) 9.60888e7 3.45499e8i 0.270753 0.973524i
\(709\) −9.36384e7 −0.262733 −0.131367 0.991334i \(-0.541937\pi\)
−0.131367 + 0.991334i \(0.541937\pi\)
\(710\) 6.05720e8i 1.69238i
\(711\) −1.93765e8 −0.539097
\(712\) 6.96880e8 1.93071
\(713\) 6.06277e8 1.67264
\(714\) 3.14216e8i 0.863245i
\(715\) 1.52149e8 0.416248
\(716\) 3.81254e8i 1.03866i
\(717\) 5.32898e7 0.144573
\(718\) 1.16397e8i 0.314462i
\(719\) 5.79765e8i 1.55979i −0.625913 0.779893i \(-0.715273\pi\)
0.625913 0.779893i \(-0.284727\pi\)
\(720\) 4.05469e7 0.108633
\(721\) 3.28430e8i 0.876267i
\(722\) 1.21471e9i 3.22745i
\(723\) −1.16699e8 −0.308783
\(724\) −6.72120e8 −1.77105
\(725\) 4.53015e7 0.118877
\(726\) 3.47474e8i 0.908056i
\(727\) −6.49571e7 −0.169053 −0.0845266 0.996421i \(-0.526938\pi\)
−0.0845266 + 0.996421i \(0.526938\pi\)
\(728\) −7.49431e8 −1.94239
\(729\) 1.43489e7 0.0370370
\(730\) −3.73241e8 −0.959445
\(731\) 2.70578e8i 0.692692i
\(732\) 3.81932e7i 0.0973762i
\(733\) 2.57152e7 0.0652946 0.0326473 0.999467i \(-0.489606\pi\)
0.0326473 + 0.999467i \(0.489606\pi\)
\(734\) −8.46369e8 −2.14028
\(735\) −5.08162e7 −0.127980
\(736\) −4.05692e8 −1.01757
\(737\) 1.06232e8 0.265372
\(738\) 2.05307e8i 0.510781i
\(739\) 6.36740e6i 0.0157772i 0.999969 + 0.00788858i \(0.00251104\pi\)
−0.999969 + 0.00788858i \(0.997489\pi\)
\(740\) 4.78663e8i 1.18123i
\(741\) 7.09554e8i 1.74394i
\(742\) 3.48963e8i 0.854217i
\(743\) −6.88384e8 −1.67828 −0.839140 0.543916i \(-0.816941\pi\)
−0.839140 + 0.543916i \(0.816941\pi\)
\(744\) 3.52554e8 0.856065
\(745\) 3.20066e8i 0.774054i
\(746\) 9.73119e8i 2.34396i
\(747\) 1.72645e8i 0.414183i
\(748\) 1.69084e8i 0.404016i
\(749\) −5.55776e8 −1.32268
\(750\) 3.85160e8i 0.912972i
\(751\) 6.76662e8i 1.59754i −0.601637 0.798770i \(-0.705484\pi\)
0.601637 0.798770i \(-0.294516\pi\)
\(752\) 1.80881e7i 0.0425344i
\(753\) 1.59339e8 0.373196
\(754\) 1.76480e9 4.11702
\(755\) 8.19269e7i 0.190364i
\(756\) −1.29119e8 −0.298830
\(757\) 2.15394e8 0.496530 0.248265 0.968692i \(-0.420140\pi\)
0.248265 + 0.968692i \(0.420140\pi\)
\(758\) 5.62988e8i 1.29268i
\(759\) 8.04774e7 0.184055
\(760\) 9.76091e8i 2.22356i
\(761\) 3.83354e8 0.869852 0.434926 0.900466i \(-0.356774\pi\)
0.434926 + 0.900466i \(0.356774\pi\)
\(762\) 7.21174e8i 1.62995i
\(763\) 4.09856e8i 0.922693i
\(764\) 6.66802e8i 1.49526i
\(765\) 1.57915e8 0.352728
\(766\) 1.01121e9i 2.24985i
\(767\) −7.65017e8 2.12764e8i −1.69545 0.471532i
\(768\) −3.79172e8 −0.837051
\(769\) 4.83594e8i 1.06341i 0.846929 + 0.531706i \(0.178449\pi\)
−0.846929 + 0.531706i \(0.821551\pi\)
\(770\) −1.58878e8 −0.348010
\(771\) −2.36470e8 −0.515957
\(772\) −9.12524e8 −1.98332
\(773\) 1.06726e7i 0.0231064i 0.999933 + 0.0115532i \(0.00367758\pi\)
−0.999933 + 0.0115532i \(0.996322\pi\)
\(774\) −1.74715e8 −0.376797
\(775\) 4.67498e7i 0.100433i
\(776\) 1.00211e9 2.14453
\(777\) 1.55741e8i 0.332002i
\(778\) 2.36512e8i 0.502244i
\(779\) −7.49748e8 −1.58600
\(780\) 8.78699e8i 1.85164i
\(781\) 1.06053e8i 0.222622i
\(782\) 1.13105e9 2.36517
\(783\) 1.30329e8 0.271491
\(784\) −3.21066e7 −0.0666264
\(785\) 6.36195e8i 1.31517i
\(786\) 8.19416e7