Properties

Label 177.7.c.a.58.5
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 58.5
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.56

$q$-expansion

\(f(q)\) \(=\) \(q-13.8068i q^{2} +15.5885 q^{3} -126.629 q^{4} +76.4303 q^{5} -215.227i q^{6} -5.71721 q^{7} +864.707i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-13.8068i q^{2} +15.5885 q^{3} -126.629 q^{4} +76.4303 q^{5} -215.227i q^{6} -5.71721 q^{7} +864.707i q^{8} +243.000 q^{9} -1055.26i q^{10} -701.846i q^{11} -1973.95 q^{12} -170.934i q^{13} +78.9366i q^{14} +1191.43 q^{15} +3834.62 q^{16} -6750.64 q^{17} -3355.06i q^{18} +1487.36 q^{19} -9678.28 q^{20} -89.1224 q^{21} -9690.27 q^{22} -23106.5i q^{23} +13479.4i q^{24} -9783.41 q^{25} -2360.05 q^{26} +3788.00 q^{27} +723.963 q^{28} -30946.9 q^{29} -16449.9i q^{30} +16180.0i q^{31} +2397.24i q^{32} -10940.7i q^{33} +93205.0i q^{34} -436.968 q^{35} -30770.8 q^{36} +66868.3i q^{37} -20535.8i q^{38} -2664.59i q^{39} +66089.8i q^{40} -50288.8 q^{41} +1230.50i q^{42} -62873.3i q^{43} +88873.9i q^{44} +18572.6 q^{45} -319028. q^{46} -73060.6i q^{47} +59775.8 q^{48} -117616. q^{49} +135078. i q^{50} -105232. q^{51} +21645.1i q^{52} -3796.98 q^{53} -52300.2i q^{54} -53642.3i q^{55} -4943.71i q^{56} +23185.7 q^{57} +427279. i q^{58} +(-24789.9 - 203877. i) q^{59} -150870. q^{60} +275330. i q^{61} +223395. q^{62} -1389.28 q^{63} +278514. q^{64} -13064.5i q^{65} -151056. q^{66} +22908.3i q^{67} +854826. q^{68} -360195. i q^{69} +6033.15i q^{70} +405836. q^{71} +210124. i q^{72} -156729. i q^{73} +923240. q^{74} -152508. q^{75} -188343. q^{76} +4012.60i q^{77} -36789.6 q^{78} +412146. q^{79} +293081. q^{80} +59049.0 q^{81} +694330. i q^{82} -95524.7i q^{83} +11285.5 q^{84} -515954. q^{85} -868082. q^{86} -482415. q^{87} +606891. q^{88} -187842. i q^{89} -256428. i q^{90} +977.263i q^{91} +2.92595e6i q^{92} +252222. i q^{93} -1.00874e6 q^{94} +113680. q^{95} +37369.2i q^{96} -706432. i q^{97} +1.62391e6i q^{98} -170548. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.8068i 1.72586i −0.505328 0.862928i \(-0.668628\pi\)
0.505328 0.862928i \(-0.331372\pi\)
\(3\) 15.5885 0.577350
\(4\) −126.629 −1.97858
\(5\) 76.4303 0.611443 0.305721 0.952121i \(-0.401102\pi\)
0.305721 + 0.952121i \(0.401102\pi\)
\(6\) 215.227i 0.996423i
\(7\) −5.71721 −0.0166682 −0.00833412 0.999965i \(-0.502653\pi\)
−0.00833412 + 0.999965i \(0.502653\pi\)
\(8\) 864.707i 1.68888i
\(9\) 243.000 0.333333
\(10\) 1055.26i 1.05526i
\(11\) 701.846i 0.527307i −0.964617 0.263653i \(-0.915072\pi\)
0.964617 0.263653i \(-0.0849275\pi\)
\(12\) −1973.95 −1.14233
\(13\) 170.934i 0.0778032i −0.999243 0.0389016i \(-0.987614\pi\)
0.999243 0.0389016i \(-0.0123859\pi\)
\(14\) 78.9366i 0.0287670i
\(15\) 1191.43 0.353017
\(16\) 3834.62 0.936187
\(17\) −6750.64 −1.37404 −0.687018 0.726640i \(-0.741081\pi\)
−0.687018 + 0.726640i \(0.741081\pi\)
\(18\) 3355.06i 0.575285i
\(19\) 1487.36 0.216849 0.108424 0.994105i \(-0.465419\pi\)
0.108424 + 0.994105i \(0.465419\pi\)
\(20\) −9678.28 −1.20979
\(21\) −89.1224 −0.00962341
\(22\) −9690.27 −0.910055
\(23\) 23106.5i 1.89911i −0.313593 0.949557i \(-0.601533\pi\)
0.313593 0.949557i \(-0.398467\pi\)
\(24\) 13479.4i 0.975075i
\(25\) −9783.41 −0.626138
\(26\) −2360.05 −0.134277
\(27\) 3788.00 0.192450
\(28\) 723.963 0.0329794
\(29\) −30946.9 −1.26889 −0.634444 0.772969i \(-0.718771\pi\)
−0.634444 + 0.772969i \(0.718771\pi\)
\(30\) 16449.9i 0.609255i
\(31\) 16180.0i 0.543118i 0.962422 + 0.271559i \(0.0875392\pi\)
−0.962422 + 0.271559i \(0.912461\pi\)
\(32\) 2397.24i 0.0731578i
\(33\) 10940.7i 0.304441i
\(34\) 93205.0i 2.37139i
\(35\) −436.968 −0.0101917
\(36\) −30770.8 −0.659525
\(37\) 66868.3i 1.32013i 0.751211 + 0.660063i \(0.229470\pi\)
−0.751211 + 0.660063i \(0.770530\pi\)
\(38\) 20535.8i 0.374249i
\(39\) 2664.59i 0.0449197i
\(40\) 66089.8i 1.03265i
\(41\) −50288.8 −0.729659 −0.364829 0.931074i \(-0.618873\pi\)
−0.364829 + 0.931074i \(0.618873\pi\)
\(42\) 1230.50i 0.0166086i
\(43\) 62873.3i 0.790790i −0.918511 0.395395i \(-0.870608\pi\)
0.918511 0.395395i \(-0.129392\pi\)
\(44\) 88873.9i 1.04332i
\(45\) 18572.6 0.203814
\(46\) −319028. −3.27760
\(47\) 73060.6i 0.703703i −0.936056 0.351852i \(-0.885552\pi\)
0.936056 0.351852i \(-0.114448\pi\)
\(48\) 59775.8 0.540508
\(49\) −117616. −0.999722
\(50\) 135078.i 1.08062i
\(51\) −105232. −0.793300
\(52\) 21645.1i 0.153940i
\(53\) −3796.98 −0.0255042 −0.0127521 0.999919i \(-0.504059\pi\)
−0.0127521 + 0.999919i \(0.504059\pi\)
\(54\) 52300.2i 0.332141i
\(55\) 53642.3i 0.322418i
\(56\) 4943.71i 0.0281507i
\(57\) 23185.7 0.125198
\(58\) 427279.i 2.18992i
\(59\) −24789.9 203877.i −0.120703 0.992689i
\(60\) −150870. −0.698470
\(61\) 275330.i 1.21301i 0.795080 + 0.606504i \(0.207429\pi\)
−0.795080 + 0.606504i \(0.792571\pi\)
\(62\) 223395. 0.937343
\(63\) −1389.28 −0.00555608
\(64\) 278514. 1.06245
\(65\) 13064.5i 0.0475722i
\(66\) −151056. −0.525421
\(67\) 22908.3i 0.0761671i 0.999275 + 0.0380836i \(0.0121253\pi\)
−0.999275 + 0.0380836i \(0.987875\pi\)
\(68\) 854826. 2.71864
\(69\) 360195.i 1.09645i
\(70\) 6033.15i 0.0175893i
\(71\) 405836. 1.13390 0.566951 0.823751i \(-0.308123\pi\)
0.566951 + 0.823751i \(0.308123\pi\)
\(72\) 210124.i 0.562960i
\(73\) 156729.i 0.402885i −0.979500 0.201442i \(-0.935437\pi\)
0.979500 0.201442i \(-0.0645629\pi\)
\(74\) 923240. 2.27834
\(75\) −152508. −0.361501
\(76\) −188343. −0.429052
\(77\) 4012.60i 0.00878928i
\(78\) −36789.6 −0.0775249
\(79\) 412146. 0.835930 0.417965 0.908463i \(-0.362743\pi\)
0.417965 + 0.908463i \(0.362743\pi\)
\(80\) 293081. 0.572424
\(81\) 59049.0 0.111111
\(82\) 694330.i 1.25929i
\(83\) 95524.7i 0.167063i −0.996505 0.0835317i \(-0.973380\pi\)
0.996505 0.0835317i \(-0.0266200\pi\)
\(84\) 11285.5 0.0190407
\(85\) −515954. −0.840145
\(86\) −868082. −1.36479
\(87\) −482415. −0.732593
\(88\) 606891. 0.890558
\(89\) 187842.i 0.266454i −0.991086 0.133227i \(-0.957466\pi\)
0.991086 0.133227i \(-0.0425339\pi\)
\(90\) 256428.i 0.351754i
\(91\) 977.263i 0.00129684i
\(92\) 2.92595e6i 3.75754i
\(93\) 252222.i 0.313569i
\(94\) −1.00874e6 −1.21449
\(95\) 113680. 0.132590
\(96\) 37369.2i 0.0422377i
\(97\) 706432.i 0.774025i −0.922074 0.387012i \(-0.873507\pi\)
0.922074 0.387012i \(-0.126493\pi\)
\(98\) 1.62391e6i 1.72538i
\(99\) 170548.i 0.175769i
\(100\) 1.23886e6 1.23886
\(101\) 1.02971e6i 0.999431i 0.866190 + 0.499715i \(0.166562\pi\)
−0.866190 + 0.499715i \(0.833438\pi\)
\(102\) 1.45292e6i 1.36912i
\(103\) 720650.i 0.659497i 0.944069 + 0.329749i \(0.106964\pi\)
−0.944069 + 0.329749i \(0.893036\pi\)
\(104\) 147807. 0.131400
\(105\) −6811.66 −0.00588416
\(106\) 52424.3i 0.0440165i
\(107\) −159709. −0.130370 −0.0651850 0.997873i \(-0.520764\pi\)
−0.0651850 + 0.997873i \(0.520764\pi\)
\(108\) −479669. −0.380777
\(109\) 1.78282e6i 1.37666i −0.725395 0.688332i \(-0.758343\pi\)
0.725395 0.688332i \(-0.241657\pi\)
\(110\) −740630. −0.556447
\(111\) 1.04237e6i 0.762175i
\(112\) −21923.3 −0.0156046
\(113\) 446781.i 0.309642i 0.987943 + 0.154821i \(0.0494800\pi\)
−0.987943 + 0.154821i \(0.950520\pi\)
\(114\) 320122.i 0.216073i
\(115\) 1.76604e6i 1.16120i
\(116\) 3.91877e6 2.51059
\(117\) 41536.9i 0.0259344i
\(118\) −2.81490e6 + 342271.i −1.71324 + 0.208317i
\(119\) 38594.8 0.0229028
\(120\) 1.03024e6i 0.596203i
\(121\) 1.27897e6 0.721947
\(122\) 3.80143e6 2.09348
\(123\) −783925. −0.421269
\(124\) 2.04886e6i 1.07460i
\(125\) −1.94197e6 −0.994290
\(126\) 19181.6i 0.00958899i
\(127\) −3.17988e6 −1.55239 −0.776194 0.630494i \(-0.782852\pi\)
−0.776194 + 0.630494i \(0.782852\pi\)
\(128\) 3.69197e6i 1.76047i
\(129\) 980098.i 0.456563i
\(130\) −180380. −0.0821027
\(131\) 585371.i 0.260386i 0.991489 + 0.130193i \(0.0415597\pi\)
−0.991489 + 0.130193i \(0.958440\pi\)
\(132\) 1.38541e6i 0.602359i
\(133\) −8503.57 −0.00361449
\(134\) 316291. 0.131453
\(135\) 289518. 0.117672
\(136\) 5.83733e6i 2.32058i
\(137\) −1.59790e6 −0.621425 −0.310713 0.950504i \(-0.600568\pi\)
−0.310713 + 0.950504i \(0.600568\pi\)
\(138\) −4.97316e6 −1.89232
\(139\) −3.19302e6 −1.18893 −0.594466 0.804121i \(-0.702637\pi\)
−0.594466 + 0.804121i \(0.702637\pi\)
\(140\) 55332.7 0.0201650
\(141\) 1.13890e6i 0.406283i
\(142\) 5.60332e6i 1.95695i
\(143\) −119969. −0.0410262
\(144\) 931813. 0.312062
\(145\) −2.36528e6 −0.775852
\(146\) −2.16393e6 −0.695321
\(147\) −1.83346e6 −0.577190
\(148\) 8.46746e6i 2.61197i
\(149\) 2.29518e6i 0.693837i −0.937895 0.346919i \(-0.887228\pi\)
0.937895 0.346919i \(-0.112772\pi\)
\(150\) 2.10566e6i 0.623898i
\(151\) 458534.i 0.133181i −0.997780 0.0665903i \(-0.978788\pi\)
0.997780 0.0665903i \(-0.0212121\pi\)
\(152\) 1.28613e6i 0.366231i
\(153\) −1.64041e6 −0.458012
\(154\) 55401.3 0.0151690
\(155\) 1.23665e6i 0.332086i
\(156\) 337414.i 0.0888770i
\(157\) 2.13679e6i 0.552157i −0.961135 0.276078i \(-0.910965\pi\)
0.961135 0.276078i \(-0.0890350\pi\)
\(158\) 5.69043e6i 1.44269i
\(159\) −59189.1 −0.0147248
\(160\) 183221.i 0.0447318i
\(161\) 132105.i 0.0316549i
\(162\) 815280.i 0.191762i
\(163\) 64149.9 0.0148127 0.00740633 0.999973i \(-0.497642\pi\)
0.00740633 + 0.999973i \(0.497642\pi\)
\(164\) 6.36802e6 1.44369
\(165\) 836200.i 0.186148i
\(166\) −1.31889e6 −0.288327
\(167\) 5.06205e6 1.08687 0.543434 0.839452i \(-0.317124\pi\)
0.543434 + 0.839452i \(0.317124\pi\)
\(168\) 77064.8i 0.0162528i
\(169\) 4.79759e6 0.993947
\(170\) 7.12369e6i 1.44997i
\(171\) 361430. 0.0722829
\(172\) 7.96158e6i 1.56464i
\(173\) 2.06522e6i 0.398867i −0.979911 0.199434i \(-0.936090\pi\)
0.979911 0.199434i \(-0.0639102\pi\)
\(174\) 6.66062e6i 1.26435i
\(175\) 55933.8 0.0104366
\(176\) 2.69131e6i 0.493658i
\(177\) −386437. 3.17813e6i −0.0696881 0.573129i
\(178\) −2.59350e6 −0.459860
\(179\) 4.01842e6i 0.700643i −0.936630 0.350321i \(-0.886072\pi\)
0.936630 0.350321i \(-0.113928\pi\)
\(180\) −2.35182e6 −0.403262
\(181\) −5.34348e6 −0.901133 −0.450566 0.892743i \(-0.648778\pi\)
−0.450566 + 0.892743i \(0.648778\pi\)
\(182\) 13492.9 0.00223816
\(183\) 4.29197e6i 0.700331i
\(184\) 1.99804e7 3.20738
\(185\) 5.11077e6i 0.807181i
\(186\) 3.48239e6 0.541175
\(187\) 4.73791e6i 0.724539i
\(188\) 9.25158e6i 1.39233i
\(189\) −21656.8 −0.00320780
\(190\) 1.56956e6i 0.228832i
\(191\) 901349.i 0.129358i 0.997906 + 0.0646789i \(0.0206023\pi\)
−0.997906 + 0.0646789i \(0.979398\pi\)
\(192\) 4.34160e6 0.613404
\(193\) −3.15087e6 −0.438287 −0.219144 0.975693i \(-0.570326\pi\)
−0.219144 + 0.975693i \(0.570326\pi\)
\(194\) −9.75359e6 −1.33585
\(195\) 203656.i 0.0274658i
\(196\) 1.48936e7 1.97803
\(197\) −5.44558e6 −0.712271 −0.356136 0.934434i \(-0.615906\pi\)
−0.356136 + 0.934434i \(0.615906\pi\)
\(198\) −2.35474e6 −0.303352
\(199\) −1.06370e7 −1.34977 −0.674884 0.737924i \(-0.735806\pi\)
−0.674884 + 0.737924i \(0.735806\pi\)
\(200\) 8.45978e6i 1.05747i
\(201\) 357104.i 0.0439751i
\(202\) 1.42171e7 1.72487
\(203\) 176930. 0.0211501
\(204\) 1.33254e7 1.56961
\(205\) −3.84359e6 −0.446145
\(206\) 9.94990e6 1.13820
\(207\) 5.61489e6i 0.633038i
\(208\) 655465.i 0.0728383i
\(209\) 1.04390e6i 0.114346i
\(210\) 94047.4i 0.0101552i
\(211\) 2.58627e6i 0.275313i 0.990480 + 0.137656i \(0.0439570\pi\)
−0.990480 + 0.137656i \(0.956043\pi\)
\(212\) 480808. 0.0504619
\(213\) 6.32636e6 0.654659
\(214\) 2.20507e6i 0.225000i
\(215\) 4.80543e6i 0.483522i
\(216\) 3.27550e6i 0.325025i
\(217\) 92504.6i 0.00905282i
\(218\) −2.46151e7 −2.37592
\(219\) 2.44316e6i 0.232606i
\(220\) 6.79266e6i 0.637928i
\(221\) 1.15391e6i 0.106904i
\(222\) 1.43919e7 1.31540
\(223\) 6.79409e6 0.612656 0.306328 0.951926i \(-0.400900\pi\)
0.306328 + 0.951926i \(0.400900\pi\)
\(224\) 13705.5i 0.00121941i
\(225\) −2.37737e6 −0.208713
\(226\) 6.16863e6 0.534397
\(227\) 4.99197e6i 0.426771i −0.976968 0.213385i \(-0.931551\pi\)
0.976968 0.213385i \(-0.0684490\pi\)
\(228\) −2.93598e6 −0.247713
\(229\) 6.25405e6i 0.520781i −0.965503 0.260391i \(-0.916149\pi\)
0.965503 0.260391i \(-0.0838513\pi\)
\(230\) −2.43834e7 −2.00406
\(231\) 62550.2i 0.00507449i
\(232\) 2.67600e7i 2.14300i
\(233\) 1.77129e7i 1.40030i −0.713994 0.700152i \(-0.753116\pi\)
0.713994 0.700152i \(-0.246884\pi\)
\(234\) −573493. −0.0447590
\(235\) 5.58404e6i 0.430274i
\(236\) 3.13912e6 + 2.58168e7i 0.238821 + 1.96411i
\(237\) 6.42472e6 0.482624
\(238\) 532873.i 0.0395269i
\(239\) 1.64830e7 1.20738 0.603689 0.797220i \(-0.293697\pi\)
0.603689 + 0.797220i \(0.293697\pi\)
\(240\) 4.56868e6 0.330489
\(241\) 2.38086e7 1.70092 0.850458 0.526043i \(-0.176325\pi\)
0.850458 + 0.526043i \(0.176325\pi\)
\(242\) 1.76586e7i 1.24598i
\(243\) 920483. 0.0641500
\(244\) 3.48647e7i 2.40003i
\(245\) −8.98945e6 −0.611273
\(246\) 1.08235e7i 0.727049i
\(247\) 254241.i 0.0168715i
\(248\) −1.39910e7 −0.917261
\(249\) 1.48908e6i 0.0964541i
\(250\) 2.68125e7i 1.71600i
\(251\) 1.81000e7 1.14461 0.572306 0.820040i \(-0.306049\pi\)
0.572306 + 0.820040i \(0.306049\pi\)
\(252\) 175923. 0.0109931
\(253\) −1.62172e7 −1.00142
\(254\) 4.39042e7i 2.67920i
\(255\) −8.04292e6 −0.485058
\(256\) −3.31496e7 −1.97587
\(257\) 7.51102e6 0.442486 0.221243 0.975219i \(-0.428989\pi\)
0.221243 + 0.975219i \(0.428989\pi\)
\(258\) −1.35321e7 −0.787961
\(259\) 382300.i 0.0220042i
\(260\) 1.65434e6i 0.0941252i
\(261\) −7.52010e6 −0.422963
\(262\) 8.08212e6 0.449388
\(263\) −3.00298e7 −1.65077 −0.825383 0.564573i \(-0.809041\pi\)
−0.825383 + 0.564573i \(0.809041\pi\)
\(264\) 9.46049e6 0.514164
\(265\) −290205. −0.0155943
\(266\) 117407.i 0.00623808i
\(267\) 2.92816e6i 0.153837i
\(268\) 2.90085e6i 0.150702i
\(269\) 9.50277e6i 0.488195i 0.969751 + 0.244097i \(0.0784917\pi\)
−0.969751 + 0.244097i \(0.921508\pi\)
\(270\) 3.99732e6i 0.203085i
\(271\) −3.58711e6 −0.180234 −0.0901170 0.995931i \(-0.528724\pi\)
−0.0901170 + 0.995931i \(0.528724\pi\)
\(272\) −2.58861e7 −1.28635
\(273\) 15234.0i 0.000748732i
\(274\) 2.20620e7i 1.07249i
\(275\) 6.86644e6i 0.330167i
\(276\) 4.56111e7i 2.16942i
\(277\) 1.06356e7 0.500406 0.250203 0.968193i \(-0.419503\pi\)
0.250203 + 0.968193i \(0.419503\pi\)
\(278\) 4.40855e7i 2.05192i
\(279\) 3.93175e6i 0.181039i
\(280\) 377849.i 0.0172125i
\(281\) 194792. 0.00877915 0.00438957 0.999990i \(-0.498603\pi\)
0.00438957 + 0.999990i \(0.498603\pi\)
\(282\) −1.57246e7 −0.701186
\(283\) 4.00849e7i 1.76857i −0.466952 0.884283i \(-0.654648\pi\)
0.466952 0.884283i \(-0.345352\pi\)
\(284\) −5.13906e7 −2.24351
\(285\) 1.77209e6 0.0765512
\(286\) 1.65639e6i 0.0708052i
\(287\) 287512. 0.0121621
\(288\) 582528.i 0.0243859i
\(289\) 2.14336e7 0.887977
\(290\) 3.26571e7i 1.33901i
\(291\) 1.10122e7i 0.446883i
\(292\) 1.98464e7i 0.797138i
\(293\) 4.09477e7 1.62790 0.813949 0.580937i \(-0.197314\pi\)
0.813949 + 0.580937i \(0.197314\pi\)
\(294\) 2.53142e7i 0.996146i
\(295\) −1.89470e6 1.55824e7i −0.0738032 0.606972i
\(296\) −5.78215e7 −2.22953
\(297\) 2.65859e6i 0.101480i
\(298\) −3.16892e7 −1.19746
\(299\) −3.94968e6 −0.147757
\(300\) 1.93119e7 0.715257
\(301\) 359460.i 0.0131811i
\(302\) −6.33091e6 −0.229851
\(303\) 1.60517e7i 0.577022i
\(304\) 5.70348e6 0.203011
\(305\) 2.10435e7i 0.741685i
\(306\) 2.26488e7i 0.790463i
\(307\) −1.52761e6 −0.0527955 −0.0263978 0.999652i \(-0.508404\pi\)
−0.0263978 + 0.999652i \(0.508404\pi\)
\(308\) 508110.i 0.0173903i
\(309\) 1.12338e7i 0.380761i
\(310\) 1.70742e7 0.573132
\(311\) 7.04493e6 0.234205 0.117102 0.993120i \(-0.462639\pi\)
0.117102 + 0.993120i \(0.462639\pi\)
\(312\) 2.30409e6 0.0758640
\(313\) 1.84231e7i 0.600801i 0.953813 + 0.300400i \(0.0971203\pi\)
−0.953813 + 0.300400i \(0.902880\pi\)
\(314\) −2.95023e7 −0.952943
\(315\) −106183. −0.00339722
\(316\) −5.21896e7 −1.65395
\(317\) 3.56499e7 1.11913 0.559565 0.828786i \(-0.310968\pi\)
0.559565 + 0.828786i \(0.310968\pi\)
\(318\) 817215.i 0.0254129i
\(319\) 2.17199e7i 0.669093i
\(320\) 2.12869e7 0.649625
\(321\) −2.48961e6 −0.0752691
\(322\) 1.82395e6 0.0546318
\(323\) −1.00407e7 −0.297958
\(324\) −7.47731e6 −0.219842
\(325\) 1.67231e6i 0.0487155i
\(326\) 885707.i 0.0255645i
\(327\) 2.77914e7i 0.794818i
\(328\) 4.34851e7i 1.23231i
\(329\) 417702.i 0.0117295i
\(330\) −1.15453e7 −0.321265
\(331\) 4.97150e7 1.37089 0.685447 0.728123i \(-0.259607\pi\)
0.685447 + 0.728123i \(0.259607\pi\)
\(332\) 1.20962e7i 0.330548i
\(333\) 1.62490e7i 0.440042i
\(334\) 6.98909e7i 1.87578i
\(335\) 1.75088e6i 0.0465718i
\(336\) −341751. −0.00900931
\(337\) 3.81569e6i 0.0996973i 0.998757 + 0.0498486i \(0.0158739\pi\)
−0.998757 + 0.0498486i \(0.984126\pi\)
\(338\) 6.62396e7i 1.71541i
\(339\) 6.96463e6i 0.178772i
\(340\) 6.53346e7 1.66229
\(341\) 1.13559e7 0.286390
\(342\) 4.99020e6i 0.124750i
\(343\) 1.34506e6 0.0333319
\(344\) 5.43670e7 1.33555
\(345\) 2.75298e7i 0.670419i
\(346\) −2.85142e7 −0.688387
\(347\) 6.39758e7i 1.53118i −0.643326 0.765592i \(-0.722446\pi\)
0.643326 0.765592i \(-0.277554\pi\)
\(348\) 6.10876e7 1.44949
\(349\) 5.89910e7i 1.38774i −0.720098 0.693872i \(-0.755903\pi\)
0.720098 0.693872i \(-0.244097\pi\)
\(350\) 772268.i 0.0180121i
\(351\) 647496.i 0.0149732i
\(352\) 1.68249e6 0.0385766
\(353\) 3.35328e7i 0.762335i −0.924506 0.381167i \(-0.875522\pi\)
0.924506 0.381167i \(-0.124478\pi\)
\(354\) −4.38800e7 + 5.33547e6i −0.989138 + 0.120272i
\(355\) 3.10182e7 0.693316
\(356\) 2.37862e7i 0.527199i
\(357\) 601634. 0.0132229
\(358\) −5.54817e7 −1.20921
\(359\) 4.94040e7 1.06777 0.533886 0.845556i \(-0.320731\pi\)
0.533886 + 0.845556i \(0.320731\pi\)
\(360\) 1.60598e7i 0.344218i
\(361\) −4.48336e7 −0.952977
\(362\) 7.37766e7i 1.55522i
\(363\) 1.99372e7 0.416816
\(364\) 123750.i 0.00256590i
\(365\) 1.19789e7i 0.246341i
\(366\) 5.92585e7 1.20867
\(367\) 4.35649e7i 0.881331i −0.897671 0.440665i \(-0.854743\pi\)
0.897671 0.440665i \(-0.145257\pi\)
\(368\) 8.86048e7i 1.77793i
\(369\) −1.22202e7 −0.243220
\(370\) 7.05635e7 1.39308
\(371\) 21708.1 0.000425110
\(372\) 3.19386e7i 0.620421i
\(373\) −3.99825e7 −0.770448 −0.385224 0.922823i \(-0.625876\pi\)
−0.385224 + 0.922823i \(0.625876\pi\)
\(374\) 6.54156e7 1.25045
\(375\) −3.02724e7 −0.574054
\(376\) 6.31760e7 1.18847
\(377\) 5.28987e6i 0.0987235i
\(378\) 299011.i 0.00553621i
\(379\) −8.61848e6 −0.158312 −0.0791558 0.996862i \(-0.525222\pi\)
−0.0791558 + 0.996862i \(0.525222\pi\)
\(380\) −1.43951e7 −0.262340
\(381\) −4.95695e7 −0.896271
\(382\) 1.24448e7 0.223253
\(383\) 8.27357e7 1.47264 0.736320 0.676633i \(-0.236562\pi\)
0.736320 + 0.676633i \(0.236562\pi\)
\(384\) 5.75522e7i 1.01641i
\(385\) 306684.i 0.00537414i
\(386\) 4.35036e7i 0.756420i
\(387\) 1.52782e7i 0.263597i
\(388\) 8.94546e7i 1.53147i
\(389\) 6.58216e7 1.11820 0.559100 0.829100i \(-0.311147\pi\)
0.559100 + 0.829100i \(0.311147\pi\)
\(390\) −2.81184e6 −0.0474020
\(391\) 1.55984e8i 2.60945i
\(392\) 1.01704e8i 1.68841i
\(393\) 9.12503e6i 0.150334i
\(394\) 7.51862e7i 1.22928i
\(395\) 3.15005e7 0.511123
\(396\) 2.15964e7i 0.347772i
\(397\) 1.83419e7i 0.293139i 0.989200 + 0.146570i \(0.0468232\pi\)
−0.989200 + 0.146570i \(0.953177\pi\)
\(398\) 1.46863e8i 2.32950i
\(399\) −132558. −0.00208682
\(400\) −3.75156e7 −0.586182
\(401\) 9.06964e7i 1.40656i −0.710915 0.703278i \(-0.751719\pi\)
0.710915 0.703278i \(-0.248281\pi\)
\(402\) 4.93048e6 0.0758947
\(403\) 2.76571e6 0.0422563
\(404\) 1.30392e8i 1.97745i
\(405\) 4.51313e6 0.0679381
\(406\) 2.44284e6i 0.0365021i
\(407\) 4.69312e7 0.696111
\(408\) 9.09949e7i 1.33979i
\(409\) 2.75611e7i 0.402835i −0.979506 0.201417i \(-0.935445\pi\)
0.979506 0.201417i \(-0.0645547\pi\)
\(410\) 5.30678e7i 0.769981i
\(411\) −2.49088e7 −0.358780
\(412\) 9.12551e7i 1.30487i
\(413\) 141729. + 1.16561e6i 0.00201191 + 0.0165464i
\(414\) −7.75238e7 −1.09253
\(415\) 7.30099e6i 0.102150i
\(416\) 409768. 0.00569191
\(417\) −4.97742e7 −0.686430
\(418\) −1.44130e7 −0.197344
\(419\) 1.36523e8i 1.85594i −0.372656 0.927969i \(-0.621553\pi\)
0.372656 0.927969i \(-0.378447\pi\)
\(420\) 862552. 0.0116423
\(421\) 3.01688e7i 0.404308i 0.979354 + 0.202154i \(0.0647942\pi\)
−0.979354 + 0.202154i \(0.935206\pi\)
\(422\) 3.57082e7 0.475150
\(423\) 1.77537e7i 0.234568i
\(424\) 3.28328e6i 0.0430735i
\(425\) 6.60443e7 0.860337
\(426\) 8.73470e7i 1.12985i
\(427\) 1.57412e6i 0.0202187i
\(428\) 2.02237e7 0.257947
\(429\) −1.87013e6 −0.0236865
\(430\) −6.63478e7 −0.834490
\(431\) 1.17705e8i 1.47015i 0.677983 + 0.735077i \(0.262854\pi\)
−0.677983 + 0.735077i \(0.737146\pi\)
\(432\) 1.45255e7 0.180169
\(433\) −7.96409e7 −0.981007 −0.490504 0.871439i \(-0.663187\pi\)
−0.490504 + 0.871439i \(0.663187\pi\)
\(434\) −1.27720e6 −0.0156239
\(435\) −3.68711e7 −0.447938
\(436\) 2.25757e8i 2.72384i
\(437\) 3.43678e7i 0.411821i
\(438\) −3.37324e7 −0.401444
\(439\) −1.60921e8 −1.90204 −0.951022 0.309125i \(-0.899964\pi\)
−0.951022 + 0.309125i \(0.899964\pi\)
\(440\) 4.63848e7 0.544525
\(441\) −2.85808e7 −0.333241
\(442\) 1.59319e7 0.184502
\(443\) 8.84927e7i 1.01788i 0.860802 + 0.508940i \(0.169962\pi\)
−0.860802 + 0.508940i \(0.830038\pi\)
\(444\) 1.31995e8i 1.50802i
\(445\) 1.43568e7i 0.162921i
\(446\) 9.38049e7i 1.05736i
\(447\) 3.57783e7i 0.400587i
\(448\) −1.59232e6 −0.0177091
\(449\) 4.69931e7 0.519153 0.259577 0.965723i \(-0.416417\pi\)
0.259577 + 0.965723i \(0.416417\pi\)
\(450\) 3.28239e7i 0.360208i
\(451\) 3.52950e7i 0.384754i
\(452\) 5.65754e7i 0.612649i
\(453\) 7.14785e6i 0.0768919i
\(454\) −6.89234e7 −0.736544
\(455\) 74692.5i 0.000792945i
\(456\) 2.00488e7i 0.211444i
\(457\) 8.23265e7i 0.862563i 0.902217 + 0.431282i \(0.141938\pi\)
−0.902217 + 0.431282i \(0.858062\pi\)
\(458\) −8.63487e7 −0.898793
\(459\) −2.55714e7 −0.264433
\(460\) 2.23632e8i 2.29752i
\(461\) 3.09968e7 0.316384 0.158192 0.987408i \(-0.449434\pi\)
0.158192 + 0.987408i \(0.449434\pi\)
\(462\) 863620. 0.00875784
\(463\) 1.96462e8i 1.97941i −0.143109 0.989707i \(-0.545710\pi\)
0.143109 0.989707i \(-0.454290\pi\)
\(464\) −1.18670e8 −1.18792
\(465\) 1.92774e7i 0.191730i
\(466\) −2.44559e8 −2.41672
\(467\) 6.29578e7i 0.618157i 0.951037 + 0.309078i \(0.100021\pi\)
−0.951037 + 0.309078i \(0.899979\pi\)
\(468\) 5.25977e6i 0.0513132i
\(469\) 130971.i 0.00126957i
\(470\) −7.70980e7 −0.742591
\(471\) 3.33092e7i 0.318788i
\(472\) 1.76294e8 2.14360e7i 1.67653 0.203854i
\(473\) −4.41274e7 −0.416989
\(474\) 8.87051e7i 0.832940i
\(475\) −1.45515e7 −0.135777
\(476\) −4.88722e6 −0.0453149
\(477\) −922667. −0.00850139
\(478\) 2.27578e8i 2.08376i
\(479\) 1.93655e8 1.76207 0.881034 0.473052i \(-0.156848\pi\)
0.881034 + 0.473052i \(0.156848\pi\)
\(480\) 2.85614e6i 0.0258259i
\(481\) 1.14300e7 0.102710
\(482\) 3.28722e8i 2.93554i
\(483\) 2.05931e6i 0.0182760i
\(484\) −1.61955e8 −1.42843
\(485\) 5.39928e7i 0.473272i
\(486\) 1.27090e7i 0.110714i
\(487\) −1.45856e8 −1.26281 −0.631403 0.775455i \(-0.717521\pi\)
−0.631403 + 0.775455i \(0.717521\pi\)
\(488\) −2.38080e8 −2.04863
\(489\) 999998. 0.00855209
\(490\) 1.24116e8i 1.05497i
\(491\) −1.59916e8 −1.35098 −0.675489 0.737370i \(-0.736068\pi\)
−0.675489 + 0.737370i \(0.736068\pi\)
\(492\) 9.92675e7 0.833512
\(493\) 2.08912e8 1.74350
\(494\) −3.51026e6 −0.0291178
\(495\) 1.30351e7i 0.107473i
\(496\) 6.20443e7i 0.508460i
\(497\) −2.32025e6 −0.0189002
\(498\) −2.05595e7 −0.166466
\(499\) 6.15997e7 0.495766 0.247883 0.968790i \(-0.420265\pi\)
0.247883 + 0.968790i \(0.420265\pi\)
\(500\) 2.45910e8 1.96728
\(501\) 7.89095e7 0.627504
\(502\) 2.49904e8i 1.97543i
\(503\) 1.08230e8i 0.850444i −0.905089 0.425222i \(-0.860196\pi\)
0.905089 0.425222i \(-0.139804\pi\)
\(504\) 1.20132e6i 0.00938355i
\(505\) 7.87014e7i 0.611095i
\(506\) 2.23909e8i 1.72830i
\(507\) 7.47870e7 0.573855
\(508\) 4.02665e8 3.07152
\(509\) 1.22346e8i 0.927761i 0.885898 + 0.463881i \(0.153543\pi\)
−0.885898 + 0.463881i \(0.846457\pi\)
\(510\) 1.11047e8i 0.837139i
\(511\) 896052.i 0.00671538i
\(512\) 2.21405e8i 1.64960i
\(513\) 5.63413e6 0.0417325
\(514\) 1.03703e8i 0.763667i
\(515\) 5.50795e7i 0.403245i
\(516\) 1.24109e8i 0.903344i
\(517\) −5.12772e7 −0.371068
\(518\) −5.27835e6 −0.0379760
\(519\) 3.21936e7i 0.230286i
\(520\) 1.12970e7 0.0803437
\(521\) −1.00276e8 −0.709063 −0.354532 0.935044i \(-0.615360\pi\)
−0.354532 + 0.935044i \(0.615360\pi\)
\(522\) 1.03829e8i 0.729972i
\(523\) −9.60867e7 −0.671673 −0.335837 0.941920i \(-0.609019\pi\)
−0.335837 + 0.941920i \(0.609019\pi\)
\(524\) 7.41249e7i 0.515193i
\(525\) 871921. 0.00602558
\(526\) 4.14617e8i 2.84898i
\(527\) 1.09226e8i 0.746264i
\(528\) 4.19534e7i 0.285013i
\(529\) −3.85876e8 −2.60664
\(530\) 4.00681e6i 0.0269136i
\(531\) −6.02396e6 4.95422e7i −0.0402345 0.330896i
\(532\) 1.07680e6 0.00715153
\(533\) 8.59605e6i 0.0567698i
\(534\) −4.04286e7 −0.265500
\(535\) −1.22066e7 −0.0797137
\(536\) −1.98089e7 −0.128637
\(537\) 6.26410e7i 0.404516i
\(538\) 1.31203e8 0.842554
\(539\) 8.25485e7i 0.527160i
\(540\) −3.66613e7 −0.232823
\(541\) 2.95188e8i 1.86426i 0.362118 + 0.932132i \(0.382054\pi\)
−0.362118 + 0.932132i \(0.617946\pi\)
\(542\) 4.95267e7i 0.311058i
\(543\) −8.32967e7 −0.520269
\(544\) 1.61829e7i 0.100522i
\(545\) 1.36262e8i 0.841752i
\(546\) 210334. 0.00129220
\(547\) −6.18129e7 −0.377674 −0.188837 0.982008i \(-0.560472\pi\)
−0.188837 + 0.982008i \(0.560472\pi\)
\(548\) 2.02341e8 1.22954
\(549\) 6.69051e7i 0.404336i
\(550\) 9.48039e7 0.569820
\(551\) −4.60293e7 −0.275157
\(552\) 3.11463e8 1.85178
\(553\) −2.35632e6 −0.0139335
\(554\) 1.46844e8i 0.863628i
\(555\) 7.96689e7i 0.466026i
\(556\) 4.04328e8 2.35239
\(557\) −6.46982e6 −0.0374392 −0.0187196 0.999825i \(-0.505959\pi\)
−0.0187196 + 0.999825i \(0.505959\pi\)
\(558\) 5.42850e7 0.312448
\(559\) −1.07472e7 −0.0615260
\(560\) −1.67561e6 −0.00954131
\(561\) 7.38567e7i 0.418313i
\(562\) 2.68946e6i 0.0151515i
\(563\) 1.69126e8i 0.947733i 0.880597 + 0.473866i \(0.157142\pi\)
−0.880597 + 0.473866i \(0.842858\pi\)
\(564\) 1.44218e8i 0.803862i
\(565\) 3.41476e7i 0.189328i
\(566\) −5.53445e8 −3.05229
\(567\) −337595. −0.00185203
\(568\) 3.50929e8i 1.91503i
\(569\) 2.47807e8i 1.34517i 0.740021 + 0.672584i \(0.234816\pi\)
−0.740021 + 0.672584i \(0.765184\pi\)
\(570\) 2.44670e7i 0.132116i
\(571\) 4.00196e7i 0.214963i −0.994207 0.107482i \(-0.965721\pi\)
0.994207 0.107482i \(-0.0342787\pi\)
\(572\) 1.51915e7 0.0811734
\(573\) 1.40506e7i 0.0746848i
\(574\) 3.96963e6i 0.0209901i
\(575\) 2.26061e8i 1.18911i
\(576\) 6.76789e7 0.354149
\(577\) 2.75991e8 1.43670 0.718351 0.695681i \(-0.244897\pi\)
0.718351 + 0.695681i \(0.244897\pi\)
\(578\) 2.95930e8i 1.53252i
\(579\) −4.91172e7 −0.253045
\(580\) 2.99513e8 1.53508
\(581\) 546135.i 0.00278465i
\(582\) −1.52043e8 −0.771256
\(583\) 2.66490e6i 0.0134485i
\(584\) 1.35525e8 0.680424
\(585\) 3.17468e6i 0.0158574i
\(586\) 5.65359e8i 2.80952i
\(587\) 183611.i 0.000907790i 1.00000 0.000453895i \(0.000144479\pi\)
−1.00000 0.000453895i \(0.999856\pi\)
\(588\) 2.32169e8 1.14201
\(589\) 2.40656e7i 0.117774i
\(590\) −2.15144e8 + 2.61599e7i −1.04755 + 0.127374i
\(591\) −8.48882e7 −0.411230
\(592\) 2.56415e8i 1.23588i
\(593\) −3.23810e8 −1.55284 −0.776420 0.630216i \(-0.782966\pi\)
−0.776420 + 0.630216i \(0.782966\pi\)
\(594\) −3.67067e7 −0.175140
\(595\) 2.94981e6 0.0140037
\(596\) 2.90636e8i 1.37281i
\(597\) −1.65814e8 −0.779289
\(598\) 5.45326e7i 0.255008i
\(599\) 8.19183e7 0.381154 0.190577 0.981672i \(-0.438964\pi\)
0.190577 + 0.981672i \(0.438964\pi\)
\(600\) 1.31875e8i 0.610532i
\(601\) 1.65135e8i 0.760706i 0.924841 + 0.380353i \(0.124198\pi\)
−0.924841 + 0.380353i \(0.875802\pi\)
\(602\) 4.96300e6 0.0227486
\(603\) 5.56670e6i 0.0253890i
\(604\) 5.80637e7i 0.263508i
\(605\) 9.77524e7 0.441429
\(606\) 2.21623e8 0.995856
\(607\) 1.07036e8 0.478589 0.239294 0.970947i \(-0.423084\pi\)
0.239294 + 0.970947i \(0.423084\pi\)
\(608\) 3.56556e6i 0.0158642i
\(609\) 2.75806e6 0.0122110
\(610\) 2.90545e8 1.28004
\(611\) −1.24885e7 −0.0547504
\(612\) 2.07723e8 0.906212
\(613\) 1.49782e8i 0.650246i −0.945672 0.325123i \(-0.894594\pi\)
0.945672 0.325123i \(-0.105406\pi\)
\(614\) 2.10915e7i 0.0911175i
\(615\) −5.99157e7 −0.257582
\(616\) −3.46972e6 −0.0148440
\(617\) 3.30963e8 1.40904 0.704522 0.709682i \(-0.251162\pi\)
0.704522 + 0.709682i \(0.251162\pi\)
\(618\) 1.55104e8 0.657138
\(619\) −2.05287e8 −0.865545 −0.432772 0.901503i \(-0.642465\pi\)
−0.432772 + 0.901503i \(0.642465\pi\)
\(620\) 1.56595e8i 0.657056i
\(621\) 8.75274e7i 0.365485i
\(622\) 9.72682e7i 0.404203i
\(623\) 1.07393e6i 0.00444131i
\(624\) 1.02177e7i 0.0420532i
\(625\) 4.44014e6 0.0181868
\(626\) 2.54365e8 1.03690
\(627\) 1.62728e7i 0.0660176i
\(628\) 2.70579e8i 1.09248i
\(629\) 4.51404e8i 1.81390i
\(630\) 1.46605e6i 0.00586312i
\(631\) −9.56680e7 −0.380784 −0.190392 0.981708i \(-0.560976\pi\)
−0.190392 + 0.981708i \(0.560976\pi\)
\(632\) 3.56385e8i 1.41179i
\(633\) 4.03159e7i 0.158952i
\(634\) 4.92213e8i 1.93146i
\(635\) −2.43040e8 −0.949196
\(636\) 7.49505e6 0.0291342
\(637\) 2.01046e7i 0.0777816i
\(638\) 2.99884e8 1.15476
\(639\) 9.86182e7 0.377968
\(640\) 2.82179e8i 1.07643i
\(641\) −2.42343e8 −0.920146 −0.460073 0.887881i \(-0.652177\pi\)
−0.460073 + 0.887881i \(0.652177\pi\)
\(642\) 3.43737e7i 0.129904i
\(643\) 2.67124e8 1.00480 0.502400 0.864635i \(-0.332450\pi\)
0.502400 + 0.864635i \(0.332450\pi\)
\(644\) 1.67283e7i 0.0626316i
\(645\) 7.49092e7i 0.279162i
\(646\) 1.38630e8i 0.514232i
\(647\) 9.87605e7 0.364645 0.182322 0.983239i \(-0.441639\pi\)
0.182322 + 0.983239i \(0.441639\pi\)
\(648\) 5.10601e7i 0.187653i
\(649\) −1.43090e8 + 1.73987e7i −0.523452 + 0.0636477i
\(650\) 2.30894e7 0.0840760
\(651\) 1.44200e6i 0.00522665i
\(652\) −8.12323e6 −0.0293080
\(653\) −7.27488e7 −0.261268 −0.130634 0.991431i \(-0.541701\pi\)
−0.130634 + 0.991431i \(0.541701\pi\)
\(654\) −3.83712e8 −1.37174
\(655\) 4.47401e7i 0.159211i
\(656\) −1.92839e8 −0.683097
\(657\) 3.80852e7i 0.134295i
\(658\) 5.76715e6 0.0202434
\(659\) 4.04397e8i 1.41303i 0.707698 + 0.706515i \(0.249734\pi\)
−0.707698 + 0.706515i \(0.750266\pi\)
\(660\) 1.05887e8i 0.368308i
\(661\) −1.92868e8 −0.667815 −0.333908 0.942606i \(-0.608367\pi\)
−0.333908 + 0.942606i \(0.608367\pi\)
\(662\) 6.86408e8i 2.36596i
\(663\) 1.79877e7i 0.0617213i
\(664\) 8.26009e7 0.282150
\(665\) −649931. −0.00221005
\(666\) 2.24347e8 0.759448
\(667\) 7.15076e8i 2.40976i
\(668\) −6.41002e8 −2.15045
\(669\) 1.05909e8 0.353717
\(670\) 2.41742e7 0.0803762
\(671\) 1.93239e8 0.639628
\(672\) 213647.i 0.000704028i
\(673\) 1.29241e8i 0.423989i −0.977271 0.211994i \(-0.932004\pi\)
0.977271 0.211994i \(-0.0679959\pi\)
\(674\) 5.26826e7 0.172063
\(675\) −3.70595e7 −0.120500
\(676\) −6.07513e8 −1.96660
\(677\) −3.69410e8 −1.19053 −0.595267 0.803528i \(-0.702954\pi\)
−0.595267 + 0.803528i \(0.702954\pi\)
\(678\) 9.61595e7 0.308534
\(679\) 4.03882e6i 0.0129016i
\(680\) 4.46149e8i 1.41890i
\(681\) 7.78171e7i 0.246396i
\(682\) 1.56789e8i 0.494268i
\(683\) 4.64586e8i 1.45816i −0.684430 0.729079i \(-0.739949\pi\)
0.684430 0.729079i \(-0.260051\pi\)
\(684\) −4.57674e7 −0.143017
\(685\) −1.22128e8 −0.379966
\(686\) 1.85710e7i 0.0575259i
\(687\) 9.74911e7i 0.300673i
\(688\) 2.41095e8i 0.740327i
\(689\) 649032.i 0.00198431i
\(690\) −3.80100e8 −1.15705
\(691\) 5.05263e8i 1.53138i 0.643209 + 0.765691i \(0.277603\pi\)
−0.643209 + 0.765691i \(0.722397\pi\)
\(692\) 2.61517e8i 0.789189i
\(693\) 975061.i 0.00292976i
\(694\) −8.83304e8 −2.64260
\(695\) −2.44043e8 −0.726964
\(696\) 4.17147e8i 1.23726i
\(697\) 3.39482e8 1.00258
\(698\) −8.14479e8 −2.39505
\(699\) 2.76117e8i 0.808466i
\(700\) −7.08283e6 −0.0206496
\(701\) 3.46156e8i 1.00489i −0.864610 0.502444i \(-0.832434\pi\)
0.864610 0.502444i \(-0.167566\pi\)
\(702\) −8.93987e6 −0.0258416
\(703\) 9.94576e7i 0.286267i
\(704\) 1.95474e8i 0.560235i
\(705\) 8.70466e7i 0.248419i
\(706\) −4.62982e8 −1.31568
\(707\) 5.88709e6i 0.0166588i
\(708\) 4.89341e7 + 4.02443e8i 0.137883 + 1.13398i
\(709\) −4.52162e8 −1.26869 −0.634345 0.773050i \(-0.718730\pi\)
−0.634345 + 0.773050i \(0.718730\pi\)
\(710\) 4.28263e8i 1.19656i
\(711\) 1.00151e8 0.278643
\(712\) 1.62428e8 0.450008
\(713\) 3.73864e8 1.03144
\(714\) 8.30666e6i 0.0228208i
\(715\) −9.16927e6 −0.0250851
\(716\) 5.08848e8i 1.38627i
\(717\) 2.56945e8 0.697080
\(718\) 6.82113e8i 1.84282i
\(719\) 1.71324e8i 0.460925i 0.973081 + 0.230463i \(0.0740239\pi\)
−0.973081 + 0.230463i \(0.925976\pi\)
\(720\) 7.12187e7 0.190808
\(721\) 4.12011e6i 0.0109927i
\(722\) 6.19011e8i 1.64470i
\(723\) 3.71140e8 0.982024
\(724\) 6.76639e8 1.78296
\(725\) 3.02766e8 0.794499
\(726\) 2.75270e8i 0.719365i
\(727\) 3.72134e8 0.968493 0.484247 0.874932i \(-0.339094\pi\)
0.484247 + 0.874932i \(0.339094\pi\)
\(728\) −845046. −0.00219021
\(729\) 1.43489e7 0.0370370
\(730\) −1.65390e8 −0.425149
\(731\) 4.24435e8i 1.08657i
\(732\) 5.43487e8i 1.38566i
\(733\) 1.44204e8 0.366155 0.183078 0.983098i \(-0.441394\pi\)
0.183078 + 0.983098i \(0.441394\pi\)
\(734\) −6.01494e8 −1.52105
\(735\) −1.40132e8 −0.352918
\(736\) 5.53918e7 0.138935
\(737\) 1.60781e7 0.0401635
\(738\) 1.68722e8i 0.419762i
\(739\) 5.87245e7i 0.145508i −0.997350 0.0727538i \(-0.976821\pi\)
0.997350 0.0727538i \(-0.0231787\pi\)
\(740\) 6.47170e8i 1.59707i
\(741\) 3.96322e6i 0.00974078i
\(742\) 299721.i 0.000733677i
\(743\) −6.34696e8 −1.54739 −0.773694 0.633560i \(-0.781593\pi\)
−0.773694 + 0.633560i \(0.781593\pi\)
\(744\) −2.18098e8 −0.529581
\(745\) 1.75421e8i 0.424242i
\(746\) 5.52032e8i 1.32968i
\(747\) 2.32125e7i 0.0556878i
\(748\) 5.99956e8i 1.43356i
\(749\) 913088. 0.00217304
\(750\) 4.17966e8i 0.990733i
\(751\) 7.55144e8i 1.78283i 0.453187 + 0.891415i \(0.350287\pi\)
−0.453187 + 0.891415i \(0.649713\pi\)
\(752\) 2.80160e8i 0.658797i
\(753\) 2.82152e8 0.660842
\(754\) 7.30363e7 0.170383
\(755\) 3.50459e7i 0.0814323i
\(756\) 2.74237e6 0.00634688
\(757\) 6.07614e8 1.40068 0.700342 0.713807i \(-0.253031\pi\)
0.700342 + 0.713807i \(0.253031\pi\)
\(758\) 1.18994e8i 0.273223i
\(759\) −2.52801e8 −0.578168
\(760\) 9.82997e7i 0.223929i
\(761\) 5.84643e8 1.32659 0.663295 0.748358i \(-0.269157\pi\)
0.663295 + 0.748358i \(0.269157\pi\)
\(762\) 6.84398e8i 1.54683i
\(763\) 1.01928e7i 0.0229466i
\(764\) 1.14137e8i 0.255944i
\(765\) −1.25377e8 −0.280048
\(766\) 1.14232e9i 2.54156i
\(767\) −3.48495e7 + 4.23743e6i −0.0772343 + 0.00939111i
\(768\) −5.16751e8 −1.14077
\(769\) 2.44620e8i 0.537914i 0.963152 + 0.268957i \(0.0866789\pi\)
−0.963152 + 0.268957i \(0.913321\pi\)
\(770\) 4.23434e6 0.00927499
\(771\) 1.17085e8 0.255469
\(772\) 3.98991e8 0.867185
\(773\) 2.90161e8i 0.628203i 0.949389 + 0.314102i \(0.101703\pi\)
−0.949389 + 0.314102i \(0.898297\pi\)
\(774\) −2.10944e8 −0.454929
\(775\) 1.58296e8i 0.340067i
\(776\) 6.10856e8 1.30724
\(777\) 5.95947e6i 0.0127041i
\(778\) 9.08789e8i 1.92985i
\(779\) −7.47978e7 −0.158226
\(780\) 2.57887e7i 0.0543432i
\(781\) 2.84834e8i 0.597915i
\(782\) 2.15365e9 4.50354
\(783\) −1.17227e8 −0.244198
\(784\) −4.51014e8 −0.935926
\(785\) 1.63315e8i 0.337612i