Properties

Label 177.7.c.a.58.17
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 58.17
Character \(\chi\) \(=\) 177.58
Dual form 177.7.c.a.58.44

$q$-expansion

\(f(q)\) \(=\) \(q-8.09269i q^{2} -15.5885 q^{3} -1.49168 q^{4} -181.057 q^{5} +126.153i q^{6} +502.973 q^{7} -505.861i q^{8} +243.000 q^{9} +O(q^{10})\) \(q-8.09269i q^{2} -15.5885 q^{3} -1.49168 q^{4} -181.057 q^{5} +126.153i q^{6} +502.973 q^{7} -505.861i q^{8} +243.000 q^{9} +1465.24i q^{10} +1074.07i q^{11} +23.2531 q^{12} -3240.18i q^{13} -4070.40i q^{14} +2822.40 q^{15} -4189.24 q^{16} -8984.93 q^{17} -1966.52i q^{18} -3953.23 q^{19} +270.080 q^{20} -7840.57 q^{21} +8692.12 q^{22} -8371.32i q^{23} +7885.59i q^{24} +17156.7 q^{25} -26221.8 q^{26} -3788.00 q^{27} -750.276 q^{28} +24362.4 q^{29} -22840.8i q^{30} +32425.1i q^{31} +1527.18i q^{32} -16743.1i q^{33} +72712.3i q^{34} -91066.9 q^{35} -362.479 q^{36} +6561.95i q^{37} +31992.2i q^{38} +50509.5i q^{39} +91589.8i q^{40} -33681.4 q^{41} +63451.3i q^{42} +29921.5i q^{43} -1602.17i q^{44} -43996.9 q^{45} -67746.5 q^{46} +43669.3i q^{47} +65303.8 q^{48} +135332. q^{49} -138844. i q^{50} +140061. q^{51} +4833.33i q^{52} +44950.7 q^{53} +30655.1i q^{54} -194468. i q^{55} -254434. i q^{56} +61624.7 q^{57} -197157. i q^{58} +(-74835.6 + 191259. i) q^{59} -4210.14 q^{60} +414592. i q^{61} +262406. q^{62} +122222. q^{63} -255753. q^{64} +586659. i q^{65} -135497. q^{66} +53813.1i q^{67} +13402.7 q^{68} +130496. i q^{69} +736976. i q^{70} -495039. q^{71} -122924. i q^{72} -388925. i q^{73} +53103.8 q^{74} -267447. q^{75} +5896.97 q^{76} +540228. i q^{77} +408757. q^{78} +490758. q^{79} +758493. q^{80} +59049.0 q^{81} +272573. i q^{82} +150512. i q^{83} +11695.7 q^{84} +1.62679e6 q^{85} +242145. q^{86} -379772. q^{87} +543330. q^{88} +1.05548e6i q^{89} +356054. i q^{90} -1.62972e6i q^{91} +12487.4i q^{92} -505457. i q^{93} +353402. q^{94} +715760. q^{95} -23806.3i q^{96} +358889. i q^{97} -1.09520e6i q^{98} +260999. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} + O(q^{10}) \) \( 60q - 1920q^{4} - 408q^{7} + 14580q^{9} - 1944q^{12} - 4536q^{15} + 56616q^{16} + 8480q^{17} + 11376q^{19} + 40796q^{20} - 8232q^{22} + 197940q^{25} + 147252q^{26} + 71640q^{28} + 63456q^{29} - 364432q^{35} - 466560q^{36} + 99632q^{41} - 470316q^{46} + 171072q^{48} + 1737420q^{49} + 60912q^{51} + 92240q^{53} + 186624q^{57} + 917264q^{59} + 1063368q^{60} - 115768q^{62} - 99144q^{63} - 1107444q^{64} + 1172232q^{66} - 4247232q^{68} + 1498048q^{71} + 1161448q^{74} - 1477440q^{75} - 1045320q^{76} - 1060452q^{78} - 90600q^{79} + 77096q^{80} + 3542940q^{81} - 2225880q^{84} - 693408q^{85} - 1567768q^{86} + 1821528q^{87} + 62892q^{88} + 5268696q^{94} + 296128q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.09269i 1.01159i −0.862655 0.505793i \(-0.831200\pi\)
0.862655 0.505793i \(-0.168800\pi\)
\(3\) −15.5885 −0.577350
\(4\) −1.49168 −0.0233076
\(5\) −181.057 −1.44846 −0.724229 0.689559i \(-0.757804\pi\)
−0.724229 + 0.689559i \(0.757804\pi\)
\(6\) 126.153i 0.584040i
\(7\) 502.973 1.46639 0.733196 0.680017i \(-0.238028\pi\)
0.733196 + 0.680017i \(0.238028\pi\)
\(8\) 505.861i 0.988009i
\(9\) 243.000 0.333333
\(10\) 1465.24i 1.46524i
\(11\) 1074.07i 0.806965i 0.914987 + 0.403482i \(0.132200\pi\)
−0.914987 + 0.403482i \(0.867800\pi\)
\(12\) 23.2531 0.0134566
\(13\) 3240.18i 1.47482i −0.675445 0.737411i \(-0.736048\pi\)
0.675445 0.737411i \(-0.263952\pi\)
\(14\) 4070.40i 1.48338i
\(15\) 2822.40 0.836268
\(16\) −4189.24 −1.02276
\(17\) −8984.93 −1.82881 −0.914404 0.404804i \(-0.867340\pi\)
−0.914404 + 0.404804i \(0.867340\pi\)
\(18\) 1966.52i 0.337196i
\(19\) −3953.23 −0.576356 −0.288178 0.957577i \(-0.593050\pi\)
−0.288178 + 0.957577i \(0.593050\pi\)
\(20\) 270.080 0.0337600
\(21\) −7840.57 −0.846622
\(22\) 8692.12 0.816315
\(23\) 8371.32i 0.688035i −0.938963 0.344017i \(-0.888212\pi\)
0.938963 0.344017i \(-0.111788\pi\)
\(24\) 7885.59i 0.570427i
\(25\) 17156.7 1.09803
\(26\) −26221.8 −1.49191
\(27\) −3788.00 −0.192450
\(28\) −750.276 −0.0341780
\(29\) 24362.4 0.998909 0.499454 0.866340i \(-0.333534\pi\)
0.499454 + 0.866340i \(0.333534\pi\)
\(30\) 22840.8i 0.845957i
\(31\) 32425.1i 1.08842i 0.838950 + 0.544209i \(0.183170\pi\)
−0.838950 + 0.544209i \(0.816830\pi\)
\(32\) 1527.18i 0.0466057i
\(33\) 16743.1i 0.465901i
\(34\) 72712.3i 1.85000i
\(35\) −91066.9 −2.12401
\(36\) −362.479 −0.00776919
\(37\) 6561.95i 0.129547i 0.997900 + 0.0647735i \(0.0206325\pi\)
−0.997900 + 0.0647735i \(0.979368\pi\)
\(38\) 31992.2i 0.583034i
\(39\) 50509.5i 0.851489i
\(40\) 91589.8i 1.43109i
\(41\) −33681.4 −0.488696 −0.244348 0.969688i \(-0.578574\pi\)
−0.244348 + 0.969688i \(0.578574\pi\)
\(42\) 63451.3i 0.856432i
\(43\) 29921.5i 0.376338i 0.982137 + 0.188169i \(0.0602552\pi\)
−0.982137 + 0.188169i \(0.939745\pi\)
\(44\) 1602.17i 0.0188084i
\(45\) −43996.9 −0.482819
\(46\) −67746.5 −0.696007
\(47\) 43669.3i 0.420612i 0.977636 + 0.210306i \(0.0674461\pi\)
−0.977636 + 0.210306i \(0.932554\pi\)
\(48\) 65303.8 0.590493
\(49\) 135332. 1.15031
\(50\) 138844.i 1.11075i
\(51\) 140061. 1.05586
\(52\) 4833.33i 0.0343745i
\(53\) 44950.7 0.301932 0.150966 0.988539i \(-0.451762\pi\)
0.150966 + 0.988539i \(0.451762\pi\)
\(54\) 30655.1i 0.194680i
\(55\) 194468.i 1.16886i
\(56\) 254434.i 1.44881i
\(57\) 61624.7 0.332759
\(58\) 197157.i 1.01048i
\(59\) −74835.6 + 191259.i −0.364378 + 0.931251i
\(60\) −4210.14 −0.0194914
\(61\) 414592.i 1.82655i 0.407346 + 0.913274i \(0.366454\pi\)
−0.407346 + 0.913274i \(0.633546\pi\)
\(62\) 262406. 1.10103
\(63\) 122222. 0.488797
\(64\) −255753. −0.975619
\(65\) 586659.i 2.13622i
\(66\) −135497. −0.471300
\(67\) 53813.1i 0.178922i 0.995990 + 0.0894610i \(0.0285145\pi\)
−0.995990 + 0.0894610i \(0.971486\pi\)
\(68\) 13402.7 0.0426251
\(69\) 130496.i 0.397237i
\(70\) 736976.i 2.14862i
\(71\) −495039. −1.38313 −0.691567 0.722313i \(-0.743079\pi\)
−0.691567 + 0.722313i \(0.743079\pi\)
\(72\) 122924.i 0.329336i
\(73\) 388925.i 0.999764i −0.866093 0.499882i \(-0.833377\pi\)
0.866093 0.499882i \(-0.166623\pi\)
\(74\) 53103.8 0.131048
\(75\) −267447. −0.633949
\(76\) 5896.97 0.0134335
\(77\) 540228.i 1.18333i
\(78\) 408757. 0.861354
\(79\) 490758. 0.995374 0.497687 0.867357i \(-0.334183\pi\)
0.497687 + 0.867357i \(0.334183\pi\)
\(80\) 758493. 1.48143
\(81\) 59049.0 0.111111
\(82\) 272573.i 0.494359i
\(83\) 150512.i 0.263230i 0.991301 + 0.131615i \(0.0420163\pi\)
−0.991301 + 0.131615i \(0.957984\pi\)
\(84\) 11695.7 0.0197327
\(85\) 1.62679e6 2.64895
\(86\) 242145. 0.380698
\(87\) −379772. −0.576720
\(88\) 543330. 0.797289
\(89\) 1.05548e6i 1.49720i 0.663021 + 0.748601i \(0.269274\pi\)
−0.663021 + 0.748601i \(0.730726\pi\)
\(90\) 356054.i 0.488414i
\(91\) 1.62972e6i 2.16267i
\(92\) 12487.4i 0.0160364i
\(93\) 505457.i 0.628398i
\(94\) 353402. 0.425486
\(95\) 715760. 0.834828
\(96\) 23806.3i 0.0269078i
\(97\) 358889.i 0.393229i 0.980481 + 0.196614i \(0.0629947\pi\)
−0.980481 + 0.196614i \(0.937005\pi\)
\(98\) 1.09520e6i 1.16364i
\(99\) 260999.i 0.268988i
\(100\) −25592.4 −0.0255924
\(101\) 1.61640e6i 1.56886i 0.620217 + 0.784430i \(0.287045\pi\)
−0.620217 + 0.784430i \(0.712955\pi\)
\(102\) 1.13347e6i 1.06810i
\(103\) 142003.i 0.129953i −0.997887 0.0649766i \(-0.979303\pi\)
0.997887 0.0649766i \(-0.0206973\pi\)
\(104\) −1.63908e6 −1.45714
\(105\) 1.41959e6 1.22630
\(106\) 363772.i 0.305430i
\(107\) −2.21316e6 −1.80660 −0.903299 0.429012i \(-0.858862\pi\)
−0.903299 + 0.429012i \(0.858862\pi\)
\(108\) 5650.49 0.00448554
\(109\) 1.19205e6i 0.920483i 0.887794 + 0.460241i \(0.152237\pi\)
−0.887794 + 0.460241i \(0.847763\pi\)
\(110\) −1.57377e6 −1.18240
\(111\) 102291.i 0.0747940i
\(112\) −2.10707e6 −1.49977
\(113\) 2.60820e6i 1.80761i −0.427944 0.903805i \(-0.640762\pi\)
0.427944 0.903805i \(-0.359238\pi\)
\(114\) 498710.i 0.336615i
\(115\) 1.51569e6i 0.996590i
\(116\) −36341.0 −0.0232821
\(117\) 787364.i 0.491607i
\(118\) 1.54780e6 + 605621.i 0.942041 + 0.368600i
\(119\) −4.51917e6 −2.68175
\(120\) 1.42774e6i 0.826240i
\(121\) 617934. 0.348808
\(122\) 3.35516e6 1.84771
\(123\) 525041. 0.282149
\(124\) 48368.0i 0.0253684i
\(125\) −277333. −0.141995
\(126\) 989108.i 0.494461i
\(127\) −3.24582e6 −1.58458 −0.792289 0.610146i \(-0.791111\pi\)
−0.792289 + 0.610146i \(0.791111\pi\)
\(128\) 2.16747e6i 1.03353i
\(129\) 466430.i 0.217279i
\(130\) 4.74765e6 2.16097
\(131\) 2.05977e6i 0.916231i 0.888893 + 0.458116i \(0.151475\pi\)
−0.888893 + 0.458116i \(0.848525\pi\)
\(132\) 24975.4i 0.0108590i
\(133\) −1.98836e6 −0.845164
\(134\) 435493. 0.180995
\(135\) 685844. 0.278756
\(136\) 4.54512e6i 1.80688i
\(137\) −732623. −0.284917 −0.142459 0.989801i \(-0.545501\pi\)
−0.142459 + 0.989801i \(0.545501\pi\)
\(138\) 1.05606e6 0.401840
\(139\) 296030. 0.110228 0.0551140 0.998480i \(-0.482448\pi\)
0.0551140 + 0.998480i \(0.482448\pi\)
\(140\) 135843. 0.0495055
\(141\) 680736.i 0.242841i
\(142\) 4.00620e6i 1.39916i
\(143\) 3.48018e6 1.19013
\(144\) −1.01799e6 −0.340921
\(145\) −4.41099e6 −1.44688
\(146\) −3.14745e6 −1.01135
\(147\) −2.10962e6 −0.664130
\(148\) 9788.35i 0.00301943i
\(149\) 3.23510e6i 0.977977i −0.872290 0.488988i \(-0.837366\pi\)
0.872290 0.488988i \(-0.162634\pi\)
\(150\) 2.16437e6i 0.641294i
\(151\) 5.90713e6i 1.71572i −0.513887 0.857858i \(-0.671795\pi\)
0.513887 0.857858i \(-0.328205\pi\)
\(152\) 1.99978e6i 0.569445i
\(153\) −2.18334e6 −0.609602
\(154\) 4.37190e6 1.19704
\(155\) 5.87079e6i 1.57653i
\(156\) 75344.2i 0.0198461i
\(157\) 1.48706e6i 0.384265i 0.981369 + 0.192132i \(0.0615403\pi\)
−0.981369 + 0.192132i \(0.938460\pi\)
\(158\) 3.97156e6i 1.00691i
\(159\) −700712. −0.174320
\(160\) 276506.i 0.0675064i
\(161\) 4.21055e6i 1.00893i
\(162\) 477865.i 0.112399i
\(163\) −1.88948e6 −0.436293 −0.218147 0.975916i \(-0.570001\pi\)
−0.218147 + 0.975916i \(0.570001\pi\)
\(164\) 50242.1 0.0113903
\(165\) 3.03146e6i 0.674839i
\(166\) 1.21804e6 0.266280
\(167\) −5.60531e6 −1.20351 −0.601755 0.798680i \(-0.705532\pi\)
−0.601755 + 0.798680i \(0.705532\pi\)
\(168\) 3.96623e6i 0.836470i
\(169\) −5.67198e6 −1.17510
\(170\) 1.31651e7i 2.67964i
\(171\) −960634. −0.192119
\(172\) 44633.4i 0.00877152i
\(173\) 1.42134e6i 0.274511i 0.990536 + 0.137256i \(0.0438282\pi\)
−0.990536 + 0.137256i \(0.956172\pi\)
\(174\) 3.07338e6i 0.583402i
\(175\) 8.62937e6 1.61015
\(176\) 4.49954e6i 0.825335i
\(177\) 1.16657e6 2.98144e6i 0.210374 0.537658i
\(178\) 8.54168e6 1.51455
\(179\) 2.41255e6i 0.420647i 0.977632 + 0.210323i \(0.0674517\pi\)
−0.977632 + 0.210323i \(0.932548\pi\)
\(180\) 65629.5 0.0112533
\(181\) 3.67987e6 0.620579 0.310290 0.950642i \(-0.399574\pi\)
0.310290 + 0.950642i \(0.399574\pi\)
\(182\) −1.31889e7 −2.18773
\(183\) 6.46285e6i 1.05456i
\(184\) −4.23472e6 −0.679785
\(185\) 1.18809e6i 0.187644i
\(186\) −4.09051e6 −0.635679
\(187\) 9.65045e6i 1.47578i
\(188\) 65140.7i 0.00980346i
\(189\) −1.90526e6 −0.282207
\(190\) 5.79243e6i 0.844501i
\(191\) 1.06137e7i 1.52323i 0.648030 + 0.761614i \(0.275593\pi\)
−0.648030 + 0.761614i \(0.724407\pi\)
\(192\) 3.98679e6 0.563274
\(193\) −7.19890e6 −1.00137 −0.500684 0.865630i \(-0.666918\pi\)
−0.500684 + 0.865630i \(0.666918\pi\)
\(194\) 2.90438e6 0.397785
\(195\) 9.14510e6i 1.23335i
\(196\) −201873. −0.0268109
\(197\) 3.15905e6 0.413197 0.206598 0.978426i \(-0.433761\pi\)
0.206598 + 0.978426i \(0.433761\pi\)
\(198\) 2.11219e6 0.272105
\(199\) −1.07904e7 −1.36923 −0.684615 0.728905i \(-0.740030\pi\)
−0.684615 + 0.728905i \(0.740030\pi\)
\(200\) 8.67892e6i 1.08487i
\(201\) 838864.i 0.103301i
\(202\) 1.30810e7 1.58704
\(203\) 1.22536e7 1.46479
\(204\) −208927. −0.0246096
\(205\) 6.09827e6 0.707856
\(206\) −1.14919e6 −0.131459
\(207\) 2.03423e6i 0.229345i
\(208\) 1.35739e7i 1.50839i
\(209\) 4.24604e6i 0.465099i
\(210\) 1.14883e7i 1.24051i
\(211\) 7.52245e6i 0.800778i −0.916345 0.400389i \(-0.868875\pi\)
0.916345 0.400389i \(-0.131125\pi\)
\(212\) −67052.3 −0.00703730
\(213\) 7.71689e6 0.798552
\(214\) 1.79104e7i 1.82753i
\(215\) 5.41750e6i 0.545110i
\(216\) 1.91620e6i 0.190142i
\(217\) 1.63089e7i 1.59605i
\(218\) 9.64691e6 0.931148
\(219\) 6.06275e6i 0.577214i
\(220\) 290085.i 0.0272432i
\(221\) 2.91128e7i 2.69716i
\(222\) −827807. −0.0756606
\(223\) 1.15483e7 1.04136 0.520682 0.853751i \(-0.325678\pi\)
0.520682 + 0.853751i \(0.325678\pi\)
\(224\) 768128.i 0.0683423i
\(225\) 4.16909e6 0.366011
\(226\) −2.11073e7 −1.82855
\(227\) 2.29119e7i 1.95877i −0.202008 0.979384i \(-0.564747\pi\)
0.202008 0.979384i \(-0.435253\pi\)
\(228\) −91924.6 −0.00775581
\(229\) 2.08143e7i 1.73323i 0.498981 + 0.866613i \(0.333708\pi\)
−0.498981 + 0.866613i \(0.666292\pi\)
\(230\) 1.22660e7 1.00814
\(231\) 8.42132e6i 0.683194i
\(232\) 1.23240e7i 0.986931i
\(233\) 1.12126e7i 0.886417i −0.896419 0.443208i \(-0.853840\pi\)
0.896419 0.443208i \(-0.146160\pi\)
\(234\) −6.37190e6 −0.497303
\(235\) 7.90664e6i 0.609240i
\(236\) 111631. 285299.i 0.00849276 0.0217052i
\(237\) −7.65016e6 −0.574679
\(238\) 3.65723e7i 2.71282i
\(239\) 1.48994e7 1.09138 0.545690 0.837987i \(-0.316267\pi\)
0.545690 + 0.837987i \(0.316267\pi\)
\(240\) −1.18237e7 −0.855305
\(241\) 6.30441e6 0.450395 0.225197 0.974313i \(-0.427697\pi\)
0.225197 + 0.974313i \(0.427697\pi\)
\(242\) 5.00075e6i 0.352849i
\(243\) −920483. −0.0641500
\(244\) 618440.i 0.0425724i
\(245\) −2.45029e7 −1.66617
\(246\) 4.24900e6i 0.285418i
\(247\) 1.28092e7i 0.850022i
\(248\) 1.64026e7 1.07537
\(249\) 2.34624e6i 0.151976i
\(250\) 2.24437e6i 0.143640i
\(251\) 4.31335e6 0.272768 0.136384 0.990656i \(-0.456452\pi\)
0.136384 + 0.990656i \(0.456452\pi\)
\(252\) −182317. −0.0113927
\(253\) 8.99139e6 0.555220
\(254\) 2.62674e7i 1.60294i
\(255\) −2.53591e7 −1.52937
\(256\) 1.17248e6 0.0698850
\(257\) 509644. 0.0300239 0.0150120 0.999887i \(-0.495221\pi\)
0.0150120 + 0.999887i \(0.495221\pi\)
\(258\) −3.77467e6 −0.219796
\(259\) 3.30048e6i 0.189967i
\(260\) 875110.i 0.0497900i
\(261\) 5.92006e6 0.332970
\(262\) 1.66691e7 0.926847
\(263\) 1.62201e6 0.0891631 0.0445815 0.999006i \(-0.485805\pi\)
0.0445815 + 0.999006i \(0.485805\pi\)
\(264\) −8.46967e6 −0.460315
\(265\) −8.13865e6 −0.437336
\(266\) 1.60912e7i 0.854957i
\(267\) 1.64533e7i 0.864410i
\(268\) 80272.2i 0.00417024i
\(269\) 1.49664e7i 0.768881i −0.923150 0.384440i \(-0.874394\pi\)
0.923150 0.384440i \(-0.125606\pi\)
\(270\) 5.55033e6i 0.281986i
\(271\) −2.85453e7 −1.43426 −0.717129 0.696940i \(-0.754544\pi\)
−0.717129 + 0.696940i \(0.754544\pi\)
\(272\) 3.76400e7 1.87044
\(273\) 2.54049e7i 1.24862i
\(274\) 5.92890e6i 0.288219i
\(275\) 1.84275e7i 0.886073i
\(276\) 194659.i 0.00925863i
\(277\) −1.84671e7 −0.868880 −0.434440 0.900701i \(-0.643054\pi\)
−0.434440 + 0.900701i \(0.643054\pi\)
\(278\) 2.39568e6i 0.111505i
\(279\) 7.87929e6i 0.362806i
\(280\) 4.60671e7i 2.09854i
\(281\) 1.41891e7 0.639494 0.319747 0.947503i \(-0.396402\pi\)
0.319747 + 0.947503i \(0.396402\pi\)
\(282\) −5.50899e6 −0.245654
\(283\) 1.59920e7i 0.705576i 0.935703 + 0.352788i \(0.114766\pi\)
−0.935703 + 0.352788i \(0.885234\pi\)
\(284\) 738441. 0.0322375
\(285\) −1.11576e7 −0.481988
\(286\) 2.81641e7i 1.20392i
\(287\) −1.69408e7 −0.716620
\(288\) 371104.i 0.0155352i
\(289\) 5.65914e7 2.34454
\(290\) 3.56968e7i 1.46364i
\(291\) 5.59453e6i 0.227031i
\(292\) 580154.i 0.0233021i
\(293\) −2.92252e7 −1.16186 −0.580932 0.813952i \(-0.697312\pi\)
−0.580932 + 0.813952i \(0.697312\pi\)
\(294\) 1.70725e7i 0.671825i
\(295\) 1.35495e7 3.46289e7i 0.527786 1.34888i
\(296\) 3.31943e6 0.127994
\(297\) 4.06857e6i 0.155300i
\(298\) −2.61807e7 −0.989308
\(299\) −2.71246e7 −1.01473
\(300\) 398947. 0.0147758
\(301\) 1.50497e7i 0.551859i
\(302\) −4.78046e7 −1.73560
\(303\) 2.51972e7i 0.905782i
\(304\) 1.65610e7 0.589476
\(305\) 7.50649e7i 2.64568i
\(306\) 1.76691e7i 0.616666i
\(307\) 1.48404e7 0.512898 0.256449 0.966558i \(-0.417447\pi\)
0.256449 + 0.966558i \(0.417447\pi\)
\(308\) 805850.i 0.0275805i
\(309\) 2.21361e6i 0.0750285i
\(310\) −4.75105e7 −1.59479
\(311\) −2.14470e7 −0.712994 −0.356497 0.934296i \(-0.616029\pi\)
−0.356497 + 0.934296i \(0.616029\pi\)
\(312\) 2.55507e7 0.841278
\(313\) 9.09563e6i 0.296620i 0.988941 + 0.148310i \(0.0473833\pi\)
−0.988941 + 0.148310i \(0.952617\pi\)
\(314\) 1.20344e7 0.388717
\(315\) −2.21292e7 −0.708003
\(316\) −732056. −0.0231997
\(317\) 8.24643e6 0.258874 0.129437 0.991588i \(-0.458683\pi\)
0.129437 + 0.991588i \(0.458683\pi\)
\(318\) 5.67065e6i 0.176340i
\(319\) 2.61669e7i 0.806084i
\(320\) 4.63059e7 1.41314
\(321\) 3.44997e7 1.04304
\(322\) −3.40747e7 −1.02062
\(323\) 3.55195e7 1.05404
\(324\) −88082.5 −0.00258973
\(325\) 5.55910e7i 1.61940i
\(326\) 1.52909e7i 0.441348i
\(327\) 1.85822e7i 0.531441i
\(328\) 1.70381e7i 0.482836i
\(329\) 2.19644e7i 0.616783i
\(330\) 2.45327e7 0.682658
\(331\) 1.87982e6 0.0518360 0.0259180 0.999664i \(-0.491749\pi\)
0.0259180 + 0.999664i \(0.491749\pi\)
\(332\) 224516.i 0.00613525i
\(333\) 1.59455e6i 0.0431823i
\(334\) 4.53620e7i 1.21746i
\(335\) 9.74326e6i 0.259161i
\(336\) 3.28460e7 0.865895
\(337\) 1.28467e7i 0.335661i 0.985816 + 0.167831i \(0.0536762\pi\)
−0.985816 + 0.167831i \(0.946324\pi\)
\(338\) 4.59016e7i 1.18871i
\(339\) 4.06577e7i 1.04362i
\(340\) −2.42665e6 −0.0617406
\(341\) −3.48268e7 −0.878315
\(342\) 7.77412e6i 0.194345i
\(343\) 8.89429e6 0.220409
\(344\) 1.51361e7 0.371825
\(345\) 2.36273e7i 0.575382i
\(346\) 1.15025e7 0.277692
\(347\) 3.81906e7i 0.914047i −0.889455 0.457023i \(-0.848916\pi\)
0.889455 0.457023i \(-0.151084\pi\)
\(348\) 566500. 0.0134419
\(349\) 5.47515e7i 1.28801i −0.765021 0.644006i \(-0.777271\pi\)
0.765021 0.644006i \(-0.222729\pi\)
\(350\) 6.98349e7i 1.62880i
\(351\) 1.22738e7i 0.283830i
\(352\) −1.64029e6 −0.0376092
\(353\) 6.62688e7i 1.50656i −0.657703 0.753278i \(-0.728472\pi\)
0.657703 0.753278i \(-0.271528\pi\)
\(354\) −2.41279e7 9.44070e6i −0.543888 0.212811i
\(355\) 8.96304e7 2.00341
\(356\) 1.57444e6i 0.0348961i
\(357\) 7.04469e7 1.54831
\(358\) 1.95240e7 0.425520
\(359\) −2.03844e7 −0.440570 −0.220285 0.975436i \(-0.570699\pi\)
−0.220285 + 0.975436i \(0.570699\pi\)
\(360\) 2.22563e7i 0.477030i
\(361\) −3.14179e7 −0.667814
\(362\) 2.97801e7i 0.627770i
\(363\) −9.63264e6 −0.201384
\(364\) 2.43103e6i 0.0504065i
\(365\) 7.04178e7i 1.44812i
\(366\) −5.23018e7 −1.06678
\(367\) 3.15331e7i 0.637924i 0.947768 + 0.318962i \(0.103334\pi\)
−0.947768 + 0.318962i \(0.896666\pi\)
\(368\) 3.50695e7i 0.703698i
\(369\) −8.18459e6 −0.162899
\(370\) −9.61483e6 −0.189818
\(371\) 2.26090e7 0.442751
\(372\) 753982.i 0.0146464i
\(373\) −8.34425e7 −1.60791 −0.803953 0.594692i \(-0.797274\pi\)
−0.803953 + 0.594692i \(0.797274\pi\)
\(374\) −7.80981e7 −1.49288
\(375\) 4.32320e6 0.0819807
\(376\) 2.20906e7 0.415569
\(377\) 7.89386e7i 1.47321i
\(378\) 1.54187e7i 0.285477i
\(379\) 2.24835e7 0.412997 0.206499 0.978447i \(-0.433793\pi\)
0.206499 + 0.978447i \(0.433793\pi\)
\(380\) −1.06769e6 −0.0194578
\(381\) 5.05973e7 0.914856
\(382\) 8.58931e7 1.54088
\(383\) −4.67001e6 −0.0831231 −0.0415615 0.999136i \(-0.513233\pi\)
−0.0415615 + 0.999136i \(0.513233\pi\)
\(384\) 3.37875e7i 0.596708i
\(385\) 9.78122e7i 1.71400i
\(386\) 5.82585e7i 1.01297i
\(387\) 7.27092e6i 0.125446i
\(388\) 535349.i 0.00916520i
\(389\) 1.10798e8 1.88228 0.941141 0.338015i \(-0.109755\pi\)
0.941141 + 0.338015i \(0.109755\pi\)
\(390\) −7.40085e7 −1.24764
\(391\) 7.52157e7i 1.25828i
\(392\) 6.84594e7i 1.13651i
\(393\) 3.21087e7i 0.528986i
\(394\) 2.55652e7i 0.417985i
\(395\) −8.88553e7 −1.44176
\(396\) 389328.i 0.00626946i
\(397\) 8.45514e7i 1.35129i −0.737226 0.675646i \(-0.763865\pi\)
0.737226 0.675646i \(-0.236135\pi\)
\(398\) 8.73230e7i 1.38509i
\(399\) 3.09955e7 0.487956
\(400\) −7.18738e7 −1.12303
\(401\) 1.95146e7i 0.302640i 0.988485 + 0.151320i \(0.0483524\pi\)
−0.988485 + 0.151320i \(0.951648\pi\)
\(402\) −6.78867e6 −0.104498
\(403\) 1.05063e8 1.60522
\(404\) 2.41116e6i 0.0365663i
\(405\) −1.06913e7 −0.160940
\(406\) 9.91647e7i 1.48176i
\(407\) −7.04799e6 −0.104540
\(408\) 7.08514e7i 1.04320i
\(409\) 1.29898e8i 1.89860i −0.314369 0.949301i \(-0.601793\pi\)
0.314369 0.949301i \(-0.398207\pi\)
\(410\) 4.93514e7i 0.716058i
\(411\) 1.14205e7 0.164497
\(412\) 211824.i 0.00302889i
\(413\) −3.76402e7 + 9.61983e7i −0.534321 + 1.36558i
\(414\) −1.64624e7 −0.232002
\(415\) 2.72512e7i 0.381278i
\(416\) 4.94833e6 0.0687351
\(417\) −4.61466e6 −0.0636401
\(418\) −3.43619e7 −0.470488
\(419\) 8.50090e7i 1.15564i −0.816164 0.577820i \(-0.803903\pi\)
0.816164 0.577820i \(-0.196097\pi\)
\(420\) −2.11758e6 −0.0285820
\(421\) 6.79876e7i 0.911137i −0.890201 0.455568i \(-0.849436\pi\)
0.890201 0.455568i \(-0.150564\pi\)
\(422\) −6.08769e7 −0.810056
\(423\) 1.06116e7i 0.140204i
\(424\) 2.27388e7i 0.298311i
\(425\) −1.54152e8 −2.00809
\(426\) 6.24504e7i 0.807805i
\(427\) 2.08528e8i 2.67844i
\(428\) 3.30134e6 0.0421074
\(429\) −5.42507e7 −0.687121
\(430\) −4.38422e7 −0.551426
\(431\) 1.14061e8i 1.42464i 0.701855 + 0.712320i \(0.252355\pi\)
−0.701855 + 0.712320i \(0.747645\pi\)
\(432\) 1.58688e7 0.196831
\(433\) 4.10358e6 0.0505474 0.0252737 0.999681i \(-0.491954\pi\)
0.0252737 + 0.999681i \(0.491954\pi\)
\(434\) 1.31983e8 1.61454
\(435\) 6.87605e7 0.835355
\(436\) 1.77817e6i 0.0214542i
\(437\) 3.30937e7i 0.396553i
\(438\) 4.90639e7 0.583902
\(439\) −7.48938e7 −0.885223 −0.442611 0.896714i \(-0.645948\pi\)
−0.442611 + 0.896714i \(0.645948\pi\)
\(440\) −9.83738e7 −1.15484
\(441\) 3.28858e7 0.383436
\(442\) 2.35601e8 2.72842
\(443\) 1.15108e8i 1.32402i −0.749495 0.662011i \(-0.769703\pi\)
0.749495 0.662011i \(-0.230297\pi\)
\(444\) 152585.i 0.00174327i
\(445\) 1.91103e8i 2.16863i
\(446\) 9.34566e7i 1.05343i
\(447\) 5.04302e7i 0.564635i
\(448\) −1.28637e8 −1.43064
\(449\) −4.15193e7 −0.458681 −0.229341 0.973346i \(-0.573657\pi\)
−0.229341 + 0.973346i \(0.573657\pi\)
\(450\) 3.37392e7i 0.370251i
\(451\) 3.61762e7i 0.394361i
\(452\) 3.89061e6i 0.0421310i
\(453\) 9.20830e7i 0.990569i
\(454\) −1.85419e8 −1.98146
\(455\) 2.95073e8i 3.13253i
\(456\) 3.11735e7i 0.328769i
\(457\) 6.26855e7i 0.656778i 0.944543 + 0.328389i \(0.106506\pi\)
−0.944543 + 0.328389i \(0.893494\pi\)
\(458\) 1.68444e8 1.75331
\(459\) 3.40349e7 0.351954
\(460\) 2.26093e6i 0.0232281i
\(461\) 7.66005e7 0.781860 0.390930 0.920420i \(-0.372153\pi\)
0.390930 + 0.920420i \(0.372153\pi\)
\(462\) −6.81512e7 −0.691110
\(463\) 5.27702e7i 0.531674i −0.964018 0.265837i \(-0.914352\pi\)
0.964018 0.265837i \(-0.0856483\pi\)
\(464\) −1.02060e8 −1.02165
\(465\) 9.15166e7i 0.910209i
\(466\) −9.07400e7 −0.896688
\(467\) 1.77663e8i 1.74440i 0.489150 + 0.872200i \(0.337307\pi\)
−0.489150 + 0.872200i \(0.662693\pi\)
\(468\) 1.17450e6i 0.0114582i
\(469\) 2.70665e7i 0.262370i
\(470\) −6.39860e7 −0.616299
\(471\) 2.31810e7i 0.221855i
\(472\) 9.67506e7 + 3.78564e7i 0.920085 + 0.360009i
\(473\) −3.21378e7 −0.303691
\(474\) 6.19104e7i 0.581338i
\(475\) −6.78245e7 −0.632857
\(476\) 6.74118e6 0.0625051
\(477\) 1.09230e7 0.100644
\(478\) 1.20577e8i 1.10403i
\(479\) −6.15345e7 −0.559902 −0.279951 0.960014i \(-0.590318\pi\)
−0.279951 + 0.960014i \(0.590318\pi\)
\(480\) 4.31031e6i 0.0389749i
\(481\) 2.12619e7 0.191059
\(482\) 5.10197e7i 0.455613i
\(483\) 6.56359e7i 0.582506i
\(484\) −921763. −0.00812986
\(485\) 6.49795e7i 0.569575i
\(486\) 7.44919e6i 0.0648933i
\(487\) −2.91174e7 −0.252096 −0.126048 0.992024i \(-0.540229\pi\)
−0.126048 + 0.992024i \(0.540229\pi\)
\(488\) 2.09726e8 1.80465
\(489\) 2.94540e7 0.251894
\(490\) 1.98295e8i 1.68548i
\(491\) 1.87066e8 1.58034 0.790168 0.612891i \(-0.209993\pi\)
0.790168 + 0.612891i \(0.209993\pi\)
\(492\) −783196. −0.00657620
\(493\) −2.18894e8 −1.82681
\(494\) 1.03661e8 0.859871
\(495\) 4.72558e7i 0.389618i
\(496\) 1.35836e8i 1.11320i
\(497\) −2.48991e8 −2.02822
\(498\) −1.89874e7 −0.153737
\(499\) −1.67013e8 −1.34415 −0.672077 0.740481i \(-0.734598\pi\)
−0.672077 + 0.740481i \(0.734598\pi\)
\(500\) 413694. 0.00330955
\(501\) 8.73781e7 0.694847
\(502\) 3.49066e7i 0.275928i
\(503\) 8.91849e7i 0.700789i 0.936602 + 0.350395i \(0.113953\pi\)
−0.936602 + 0.350395i \(0.886047\pi\)
\(504\) 6.18275e7i 0.482936i
\(505\) 2.92661e8i 2.27243i
\(506\) 7.27645e7i 0.561653i
\(507\) 8.84174e7 0.678443
\(508\) 4.84174e6 0.0369326
\(509\) 9.46235e7i 0.717539i 0.933426 + 0.358770i \(0.116804\pi\)
−0.933426 + 0.358770i \(0.883196\pi\)
\(510\) 2.05223e8i 1.54709i
\(511\) 1.95619e8i 1.46605i
\(512\) 1.29229e8i 0.962834i
\(513\) 1.49748e7 0.110920
\(514\) 4.12439e6i 0.0303718i
\(515\) 2.57107e7i 0.188232i
\(516\) 695766.i 0.00506424i
\(517\) −4.69038e7 −0.339420
\(518\) 2.67098e7 0.192168
\(519\) 2.21565e7i 0.158489i
\(520\) 2.96768e8 2.11060
\(521\) −2.18083e8 −1.54209 −0.771044 0.636782i \(-0.780265\pi\)
−0.771044 + 0.636782i \(0.780265\pi\)
\(522\) 4.79092e7i 0.336828i
\(523\) −2.69917e8 −1.88680 −0.943399 0.331660i \(-0.892391\pi\)
−0.943399 + 0.331660i \(0.892391\pi\)
\(524\) 3.07253e6i 0.0213551i
\(525\) −1.34519e8 −0.929618
\(526\) 1.31264e7i 0.0901962i
\(527\) 2.91337e8i 1.99051i
\(528\) 7.01409e7i 0.476507i
\(529\) 7.79569e7 0.526608
\(530\) 6.58636e7i 0.442403i
\(531\) −1.81850e7 + 4.64760e7i −0.121459 + 0.310417i
\(532\) 2.96601e6 0.0196987
\(533\) 1.09134e8i 0.720740i
\(534\) −1.33152e8 −0.874425
\(535\) 4.00709e8 2.61678
\(536\) 2.72219e7 0.176777
\(537\) 3.76079e7i 0.242860i
\(538\) −1.21118e8 −0.777790
\(539\) 1.45357e8i 0.928257i
\(540\) −1.02306e6 −0.00649712
\(541\) 4.97524e7i 0.314211i 0.987582 + 0.157106i \(0.0502163\pi\)
−0.987582 + 0.157106i \(0.949784\pi\)
\(542\) 2.31009e8i 1.45088i
\(543\) −5.73636e7 −0.358292
\(544\) 1.37216e7i 0.0852329i
\(545\) 2.15830e8i 1.33328i
\(546\) 2.05594e8 1.26308
\(547\) −1.70686e8 −1.04289 −0.521443 0.853286i \(-0.674606\pi\)
−0.521443 + 0.853286i \(0.674606\pi\)
\(548\) 1.09284e6 0.00664073
\(549\) 1.00746e8i 0.608849i
\(550\) 1.49128e8 0.896340
\(551\) −9.63100e7 −0.575727
\(552\) 6.60128e7 0.392474
\(553\) 2.46838e8 1.45961
\(554\) 1.49449e8i 0.878947i
\(555\) 1.85205e7i 0.108336i
\(556\) −441584. −0.00256915
\(557\) 2.82753e8 1.63622 0.818109 0.575063i \(-0.195023\pi\)
0.818109 + 0.575063i \(0.195023\pi\)
\(558\) 6.37647e7 0.367010
\(559\) 9.69511e7 0.555031
\(560\) 3.81501e8 2.17236
\(561\) 1.50436e8i 0.852044i
\(562\) 1.14828e8i 0.646904i
\(563\) 9.96556e7i 0.558440i 0.960227 + 0.279220i \(0.0900759\pi\)
−0.960227 + 0.279220i \(0.909924\pi\)
\(564\) 1.01544e6i 0.00566003i
\(565\) 4.72233e8i 2.61825i
\(566\) 1.29418e8 0.713751
\(567\) 2.97000e7 0.162932
\(568\) 2.50421e8i 1.36655i
\(569\) 2.02184e8i 1.09751i −0.835982 0.548757i \(-0.815101\pi\)
0.835982 0.548757i \(-0.184899\pi\)
\(570\) 9.02950e7i 0.487573i
\(571\) 1.98397e8i 1.06568i 0.846216 + 0.532840i \(0.178875\pi\)
−0.846216 + 0.532840i \(0.821125\pi\)
\(572\) −5.19134e6 −0.0277390
\(573\) 1.65451e8i 0.879437i
\(574\) 1.37097e8i 0.724924i
\(575\) 1.43625e8i 0.755484i
\(576\) −6.21479e7 −0.325206
\(577\) −8.58467e7 −0.446885 −0.223443 0.974717i \(-0.571730\pi\)
−0.223443 + 0.974717i \(0.571730\pi\)
\(578\) 4.57977e8i 2.37170i
\(579\) 1.12220e8 0.578140
\(580\) 6.57980e6 0.0337232
\(581\) 7.57032e7i 0.385999i
\(582\) −4.52748e7 −0.229661
\(583\) 4.82802e7i 0.243648i
\(584\) −1.96742e8 −0.987776
\(585\) 1.42558e8i 0.712072i
\(586\) 2.36511e8i 1.17533i
\(587\) 1.87040e8i 0.924744i 0.886686 + 0.462372i \(0.153001\pi\)
−0.886686 + 0.462372i \(0.846999\pi\)
\(588\) 3.14689e6 0.0154793
\(589\) 1.28184e8i 0.627316i
\(590\) −2.80241e8 1.09652e8i −1.36451 0.533901i
\(591\) −4.92446e7 −0.238559
\(592\) 2.74896e7i 0.132496i
\(593\) 1.21559e8 0.582941 0.291470 0.956580i \(-0.405856\pi\)
0.291470 + 0.956580i \(0.405856\pi\)
\(594\) −3.29257e7 −0.157100
\(595\) 8.18229e8 3.88440
\(596\) 4.82575e6i 0.0227943i
\(597\) 1.68205e8 0.790525
\(598\) 2.19511e8i 1.02649i
\(599\) 3.22698e8 1.50147 0.750733 0.660606i \(-0.229701\pi\)
0.750733 + 0.660606i \(0.229701\pi\)
\(600\) 1.35291e8i 0.626347i
\(601\) 2.44614e8i 1.12683i −0.826175 0.563413i \(-0.809488\pi\)
0.826175 0.563413i \(-0.190512\pi\)
\(602\) 1.21793e8 0.558253
\(603\) 1.30766e7i 0.0596407i
\(604\) 8.81157e6i 0.0399892i
\(605\) −1.11881e8 −0.505233
\(606\) −2.03913e8 −0.916277
\(607\) −1.85485e7 −0.0829358 −0.0414679 0.999140i \(-0.513203\pi\)
−0.0414679 + 0.999140i \(0.513203\pi\)
\(608\) 6.03727e6i 0.0268615i
\(609\) −1.91015e8 −0.845698
\(610\) −6.07477e8 −2.67633
\(611\) 1.41496e8 0.620328
\(612\) 3.25685e6 0.0142084
\(613\) 2.82096e8i 1.22466i 0.790602 + 0.612330i \(0.209768\pi\)
−0.790602 + 0.612330i \(0.790232\pi\)
\(614\) 1.20099e8i 0.518841i
\(615\) −9.50626e7 −0.408681
\(616\) 2.73280e8 1.16914
\(617\) 3.38596e8 1.44154 0.720770 0.693174i \(-0.243788\pi\)
0.720770 + 0.693174i \(0.243788\pi\)
\(618\) 1.79141e7 0.0758978
\(619\) −1.86438e8 −0.786071 −0.393036 0.919523i \(-0.628575\pi\)
−0.393036 + 0.919523i \(0.628575\pi\)
\(620\) 8.75737e6i 0.0367450i
\(621\) 3.17105e7i 0.132412i
\(622\) 1.73564e8i 0.721256i
\(623\) 5.30878e8i 2.19549i
\(624\) 2.11596e8i 0.870872i
\(625\) −2.17861e8 −0.892358
\(626\) 7.36082e7 0.300057
\(627\) 6.61893e7i 0.268525i
\(628\) 2.21823e6i 0.00895628i
\(629\) 5.89586e7i 0.236917i
\(630\) 1.79085e8i 0.716206i
\(631\) −3.44905e8 −1.37281 −0.686407 0.727218i \(-0.740813\pi\)
−0.686407 + 0.727218i \(0.740813\pi\)
\(632\) 2.48255e8i 0.983438i
\(633\) 1.17263e8i 0.462329i
\(634\) 6.67358e7i 0.261873i
\(635\) 5.87680e8 2.29519
\(636\) 1.04524e6 0.00406299
\(637\) 4.38502e8i 1.69650i
\(638\) 2.11761e8 0.815424
\(639\) −1.20294e8 −0.461044
\(640\) 3.92436e8i 1.49702i
\(641\) −4.28085e8 −1.62538 −0.812691 0.582694i \(-0.801999\pi\)
−0.812691 + 0.582694i \(0.801999\pi\)
\(642\) 2.79196e8i 1.05512i
\(643\) −4.70703e8 −1.77057 −0.885286 0.465047i \(-0.846038\pi\)
−0.885286 + 0.465047i \(0.846038\pi\)
\(644\) 6.28081e6i 0.0235157i
\(645\) 8.44505e7i 0.314719i
\(646\) 2.87448e8i 1.06626i
\(647\) −1.81727e8 −0.670975 −0.335487 0.942045i \(-0.608901\pi\)
−0.335487 + 0.942045i \(0.608901\pi\)
\(648\) 2.98706e7i 0.109779i
\(649\) −2.05426e8 8.03787e7i −0.751487 0.294040i
\(650\) −4.49881e8 −1.63816
\(651\) 2.54231e8i 0.921479i
\(652\) 2.81850e6 0.0101689
\(653\) −1.64342e8 −0.590213 −0.295106 0.955464i \(-0.595355\pi\)
−0.295106 + 0.955464i \(0.595355\pi\)
\(654\) −1.50380e8 −0.537599
\(655\) 3.72937e8i 1.32712i
\(656\) 1.41100e8 0.499821
\(657\) 9.45089e7i 0.333255i
\(658\) 1.77751e8 0.623929
\(659\) 1.34126e8i 0.468659i 0.972157 + 0.234329i \(0.0752894\pi\)
−0.972157 + 0.234329i \(0.924711\pi\)
\(660\) 4.52198e6i 0.0157289i
\(661\) −3.06053e8 −1.05972 −0.529862 0.848084i \(-0.677756\pi\)
−0.529862 + 0.848084i \(0.677756\pi\)
\(662\) 1.52128e7i 0.0524366i
\(663\) 4.53824e8i 1.55721i
\(664\) 7.61379e7 0.260074
\(665\) 3.60008e8 1.22419
\(666\) 1.29042e7 0.0436827
\(667\) 2.03945e8i 0.687284i
\(668\) 8.36135e6 0.0280509
\(669\) −1.80020e8 −0.601231
\(670\) −7.88492e7 −0.262164
\(671\) −4.45301e8 −1.47396
\(672\) 1.19739e7i 0.0394574i
\(673\) 6.88272e7i 0.225795i 0.993607 + 0.112898i \(0.0360132\pi\)
−0.993607 + 0.112898i \(0.963987\pi\)
\(674\) 1.03964e8 0.339550
\(675\) −6.49897e7 −0.211316
\(676\) 8.46080e6 0.0273887
\(677\) 2.16960e8 0.699221 0.349611 0.936895i \(-0.386314\pi\)
0.349611 + 0.936895i \(0.386314\pi\)
\(678\) 3.29031e8 1.05572
\(679\) 1.80511e8i 0.576627i
\(680\) 8.22927e8i 2.61719i
\(681\) 3.57161e8i 1.13090i
\(682\) 2.81843e8i 0.888492i
\(683\) 4.96754e8i 1.55912i 0.626328 + 0.779560i \(0.284557\pi\)
−0.626328 + 0.779560i \(0.715443\pi\)
\(684\) 1.43296e6 0.00447782
\(685\) 1.32647e8 0.412691
\(686\) 7.19788e7i 0.222963i
\(687\) 3.24463e8i 1.00068i
\(688\) 1.25348e8i 0.384905i
\(689\) 1.45649e8i 0.445296i
\(690\) −1.91208e8 −0.582048
\(691\) 2.16699e8i 0.656785i 0.944541 + 0.328392i \(0.106507\pi\)
−0.944541 + 0.328392i \(0.893493\pi\)
\(692\) 2.12020e6i 0.00639820i
\(693\) 1.31275e8i 0.394442i
\(694\) −3.09065e8 −0.924637
\(695\) −5.35985e7 −0.159661
\(696\) 1.92112e8i 0.569805i
\(697\) 3.02625e8 0.893731
\(698\) −4.43087e8 −1.30293
\(699\) 1.74787e8i 0.511773i
\(700\) −1.28723e7 −0.0375286
\(701\) 3.80877e8i 1.10568i 0.833286 + 0.552842i \(0.186457\pi\)
−0.833286 + 0.552842i \(0.813543\pi\)
\(702\) 9.93281e7 0.287118
\(703\) 2.59409e7i 0.0746652i
\(704\) 2.74696e8i 0.787290i
\(705\) 1.23252e8i 0.351745i
\(706\) −5.36293e8 −1.52401
\(707\) 8.13004e8i 2.30057i
\(708\) −1.74016e6 + 4.44737e6i −0.00490330 + 0.0125315i
\(709\) 6.14643e8 1.72458 0.862292 0.506412i \(-0.169028\pi\)
0.862292 + 0.506412i \(0.169028\pi\)
\(710\) 7.25351e8i 2.02662i
\(711\) 1.19254e8 0.331791
\(712\) 5.33926e8 1.47925
\(713\) 2.71441e8 0.748870
\(714\) 5.70105e8i 1.56625i
\(715\) −6.30113e8 −1.72385
\(716\) 3.59876e6i 0.00980425i
\(717\) −2.32259e8 −0.630109
\(718\) 1.64965e8i 0.445675i
\(719\) 2.89336e8i 0.778423i −0.921148 0.389211i \(-0.872748\pi\)
0.921148 0.389211i \(-0.127252\pi\)
\(720\) 1.84314e8 0.493811
\(721\) 7.14238e7i 0.190562i
\(722\) 2.54255e8i 0.675551i
\(723\) −9.82761e7 −0.260036
\(724\) −5.48921e6 −0.0144642
\(725\) 4.17979e8 1.09683
\(726\) 7.79540e7i 0.203718i
\(727\) 1.60533e8 0.417793 0.208896 0.977938i \(-0.433013\pi\)
0.208896 + 0.977938i \(0.433013\pi\)
\(728\) −8.24413e8 −2.13673
\(729\) 1.43489e7 0.0370370
\(730\) 5.69869e8 1.46490
\(731\) 2.68842e8i 0.688249i
\(732\) 9.64053e6i 0.0245792i
\(733\) 1.67584e8 0.425519 0.212760 0.977105i \(-0.431755\pi\)
0.212760 + 0.977105i \(0.431755\pi\)
\(734\) 2.55188e8 0.645315
\(735\) 3.81963e8 0.961965
\(736\) 1.27845e7 0.0320664
\(737\) −5.77991e7 −0.144384
\(738\) 6.62354e7i 0.164786i
\(739\) 1.50914e8i 0.373934i 0.982366 + 0.186967i \(0.0598658\pi\)
−0.982366 + 0.186967i \(0.940134\pi\)
\(740\) 1.77225e6i 0.00437351i
\(741\) 1.99675e8i 0.490761i
\(742\) 1.82967e8i 0.447881i
\(743\) −5.60788e8 −1.36720 −0.683601 0.729856i \(-0.739587\pi\)
−0.683601 + 0.729856i \(0.739587\pi\)
\(744\) −2.55691e8 −0.620863
\(745\) 5.85738e8i 1.41656i
\(746\) 6.75275e8i 1.62654i
\(747\) 3.65743e7i 0.0877434i
\(748\) 1.43954e7i 0.0343969i
\(749\) −1.11316e9 −2.64918
\(750\) 3.49863e7i 0.0829305i
\(751\) 4.66632e8i 1.10168i −0.834612 0.550839i \(-0.814308\pi\)
0.834612 0.550839i \(-0.185692\pi\)
\(752\) 1.82941e8i 0.430187i
\(753\) −6.72384e7 −0.157483
\(754\) −6.38826e8 −1.49028
\(755\) 1.06953e9i 2.48514i
\(756\) 2.84204e6 0.00657757
\(757\) −5.19434e8 −1.19741 −0.598705 0.800969i \(-0.704318\pi\)
−0.598705 + 0.800969i \(0.704318\pi\)
\(758\) 1.81952e8i 0.417783i
\(759\) −1.40162e8 −0.320556
\(760\) 3.62075e8i 0.824817i
\(761\) 3.22688e8 0.732198 0.366099 0.930576i \(-0.380693\pi\)
0.366099 + 0.930576i \(0.380693\pi\)
\(762\) 4.09469e8i 0.925456i
\(763\) 5.99569e8i 1.34979i
\(764\) 1.58322e7i 0.0355028i
\(765\) 3.95309e8 0.882984
\(766\) 3.77930e7i 0.0840862i
\(767\) 6.19716e8 + 2.42481e8i 1.37343 + 0.537392i
\(768\) −1.82771e7 −0.0403481
\(769\) 7.22488e7i 0.158874i 0.996840 + 0.0794368i \(0.0253122\pi\)
−0.996840 + 0.0794368i \(0.974688\pi\)
\(770\) −7.91564e8 −1.73386
\(771\) −7.94456e6 −0.0173343
\(772\) 1.07385e7 0.0233395
\(773\) 6.92238e7i 0.149871i 0.997188 + 0.0749354i \(0.0238751\pi\)
−0.997188 + 0.0749354i \(0.976125\pi\)
\(774\) 5.88413e7 0.126899
\(775\) 5.56308e8i 1.19512i
\(776\) 1.81548e8 0.388513
\(777\) 5.14494e7i 0.109677i
\(778\) 8.96657e8i 1.90409i
\(779\) 1.33150e8 0.281663
\(780\) 1.36416e7i 0.0287463i
\(781\) 5.31706e8i 1.11614i
\(782\) 6.08698e8 1.27286
\(783\) −9.22846e7 −0.192240
\(784\) −5.66940e8 −1.17649
\(785\) 2.69244e8i 0.556592i
\(786\)