Properties

Label 690.3.c.a.91.17
Level $690$
Weight $3$
Character 690.91
Analytic conductor $18.801$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.17
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.24

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} -11.8194i q^{7} +2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} -11.8194i q^{7} +2.82843 q^{8} +3.00000 q^{9} -3.16228i q^{10} +20.7652i q^{11} -3.46410 q^{12} +7.75559 q^{13} -16.7152i q^{14} +3.87298i q^{15} +4.00000 q^{16} -22.9081i q^{17} +4.24264 q^{18} -21.0098i q^{19} -4.47214i q^{20} +20.4719i q^{21} +29.3664i q^{22} +(-21.9968 - 6.71856i) q^{23} -4.89898 q^{24} -5.00000 q^{25} +10.9681 q^{26} -5.19615 q^{27} -23.6389i q^{28} -38.2483 q^{29} +5.47723i q^{30} +33.3493 q^{31} +5.65685 q^{32} -35.9663i q^{33} -32.3970i q^{34} -26.4291 q^{35} +6.00000 q^{36} -49.4326i q^{37} -29.7124i q^{38} -13.4331 q^{39} -6.32456i q^{40} -0.679308 q^{41} +28.9516i q^{42} +7.99696i q^{43} +41.5303i q^{44} -6.70820i q^{45} +(-31.1082 - 9.50148i) q^{46} -85.9436 q^{47} -6.92820 q^{48} -90.6993 q^{49} -7.07107 q^{50} +39.6780i q^{51} +15.5112 q^{52} -66.6981i q^{53} -7.34847 q^{54} +46.4323 q^{55} -33.4304i q^{56} +36.3901i q^{57} -54.0913 q^{58} +110.632 q^{59} +7.74597i q^{60} -16.6780i q^{61} +47.1630 q^{62} -35.4583i q^{63} +8.00000 q^{64} -17.3420i q^{65} -50.8640i q^{66} -117.857i q^{67} -45.8163i q^{68} +(38.0996 + 11.6369i) q^{69} -37.3764 q^{70} +28.9967 q^{71} +8.48528 q^{72} +31.0752 q^{73} -69.9083i q^{74} +8.66025 q^{75} -42.0196i q^{76} +245.433 q^{77} -18.9972 q^{78} +105.069i q^{79} -8.94427i q^{80} +9.00000 q^{81} -0.960687 q^{82} +43.1979i q^{83} +40.9438i q^{84} -51.2241 q^{85} +11.3094i q^{86} +66.2480 q^{87} +58.7327i q^{88} -49.1782i q^{89} -9.48683i q^{90} -91.6668i q^{91} +(-43.9937 - 13.4371i) q^{92} -57.7627 q^{93} -121.543 q^{94} -46.9794 q^{95} -9.79796 q^{96} -69.6738i q^{97} -128.268 q^{98} +62.2955i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) −1.73205 −0.577350
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) −2.44949 −0.408248
\(7\) 11.8194i 1.68849i −0.535955 0.844246i \(-0.680049\pi\)
0.535955 0.844246i \(-0.319951\pi\)
\(8\) 2.82843 0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 20.7652i 1.88774i 0.330315 + 0.943871i \(0.392845\pi\)
−0.330315 + 0.943871i \(0.607155\pi\)
\(12\) −3.46410 −0.288675
\(13\) 7.75559 0.596584 0.298292 0.954475i \(-0.403583\pi\)
0.298292 + 0.954475i \(0.403583\pi\)
\(14\) 16.7152i 1.19394i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 22.9081i 1.34754i −0.738943 0.673768i \(-0.764675\pi\)
0.738943 0.673768i \(-0.235325\pi\)
\(18\) 4.24264 0.235702
\(19\) 21.0098i 1.10578i −0.833255 0.552890i \(-0.813525\pi\)
0.833255 0.552890i \(-0.186475\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 20.4719i 0.974852i
\(22\) 29.3664i 1.33483i
\(23\) −21.9968 6.71856i −0.956384 0.292111i
\(24\) −4.89898 −0.204124
\(25\) −5.00000 −0.200000
\(26\) 10.9681 0.421848
\(27\) −5.19615 −0.192450
\(28\) 23.6389i 0.844246i
\(29\) −38.2483 −1.31891 −0.659454 0.751745i \(-0.729212\pi\)
−0.659454 + 0.751745i \(0.729212\pi\)
\(30\) 5.47723i 0.182574i
\(31\) 33.3493 1.07578 0.537892 0.843014i \(-0.319221\pi\)
0.537892 + 0.843014i \(0.319221\pi\)
\(32\) 5.65685 0.176777
\(33\) 35.9663i 1.08989i
\(34\) 32.3970i 0.952852i
\(35\) −26.4291 −0.755117
\(36\) 6.00000 0.166667
\(37\) 49.4326i 1.33602i −0.744154 0.668009i \(-0.767147\pi\)
0.744154 0.668009i \(-0.232853\pi\)
\(38\) 29.7124i 0.781904i
\(39\) −13.4331 −0.344438
\(40\) 6.32456i 0.158114i
\(41\) −0.679308 −0.0165685 −0.00828424 0.999966i \(-0.502637\pi\)
−0.00828424 + 0.999966i \(0.502637\pi\)
\(42\) 28.9516i 0.689324i
\(43\) 7.99696i 0.185976i 0.995667 + 0.0929879i \(0.0296418\pi\)
−0.995667 + 0.0929879i \(0.970358\pi\)
\(44\) 41.5303i 0.943871i
\(45\) 6.70820i 0.149071i
\(46\) −31.1082 9.50148i −0.676266 0.206554i
\(47\) −85.9436 −1.82859 −0.914294 0.405052i \(-0.867253\pi\)
−0.914294 + 0.405052i \(0.867253\pi\)
\(48\) −6.92820 −0.144338
\(49\) −90.6993 −1.85101
\(50\) −7.07107 −0.141421
\(51\) 39.6780i 0.778001i
\(52\) 15.5112 0.298292
\(53\) 66.6981i 1.25845i −0.777221 0.629227i \(-0.783371\pi\)
0.777221 0.629227i \(-0.216629\pi\)
\(54\) −7.34847 −0.136083
\(55\) 46.4323 0.844224
\(56\) 33.4304i 0.596972i
\(57\) 36.3901i 0.638422i
\(58\) −54.0913 −0.932608
\(59\) 110.632 1.87512 0.937560 0.347823i \(-0.113079\pi\)
0.937560 + 0.347823i \(0.113079\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 16.6780i 0.273409i −0.990612 0.136705i \(-0.956349\pi\)
0.990612 0.136705i \(-0.0436511\pi\)
\(62\) 47.1630 0.760694
\(63\) 35.4583i 0.562831i
\(64\) 8.00000 0.125000
\(65\) 17.3420i 0.266800i
\(66\) 50.8640i 0.770667i
\(67\) 117.857i 1.75906i −0.475840 0.879532i \(-0.657856\pi\)
0.475840 0.879532i \(-0.342144\pi\)
\(68\) 45.8163i 0.673768i
\(69\) 38.0996 + 11.6369i 0.552169 + 0.168651i
\(70\) −37.3764 −0.533948
\(71\) 28.9967 0.408405 0.204202 0.978929i \(-0.434540\pi\)
0.204202 + 0.978929i \(0.434540\pi\)
\(72\) 8.48528 0.117851
\(73\) 31.0752 0.425688 0.212844 0.977086i \(-0.431727\pi\)
0.212844 + 0.977086i \(0.431727\pi\)
\(74\) 69.9083i 0.944707i
\(75\) 8.66025 0.115470
\(76\) 42.0196i 0.552890i
\(77\) 245.433 3.18744
\(78\) −18.9972 −0.243554
\(79\) 105.069i 1.32998i 0.746850 + 0.664992i \(0.231565\pi\)
−0.746850 + 0.664992i \(0.768435\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) −0.960687 −0.0117157
\(83\) 43.1979i 0.520456i 0.965547 + 0.260228i \(0.0837977\pi\)
−0.965547 + 0.260228i \(0.916202\pi\)
\(84\) 40.9438i 0.487426i
\(85\) −51.2241 −0.602637
\(86\) 11.3094i 0.131505i
\(87\) 66.2480 0.761471
\(88\) 58.7327i 0.667417i
\(89\) 49.1782i 0.552564i −0.961077 0.276282i \(-0.910898\pi\)
0.961077 0.276282i \(-0.0891023\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 91.6668i 1.00733i
\(92\) −43.9937 13.4371i −0.478192 0.146056i
\(93\) −57.7627 −0.621104
\(94\) −121.543 −1.29301
\(95\) −46.9794 −0.494520
\(96\) −9.79796 −0.102062
\(97\) 69.6738i 0.718287i −0.933282 0.359143i \(-0.883069\pi\)
0.933282 0.359143i \(-0.116931\pi\)
\(98\) −128.268 −1.30886
\(99\) 62.2955i 0.629247i
\(100\) −10.0000 −0.100000
\(101\) −17.2732 −0.171022 −0.0855111 0.996337i \(-0.527252\pi\)
−0.0855111 + 0.996337i \(0.527252\pi\)
\(102\) 56.1132i 0.550130i
\(103\) 51.7425i 0.502355i 0.967941 + 0.251177i \(0.0808177\pi\)
−0.967941 + 0.251177i \(0.919182\pi\)
\(104\) 21.9361 0.210924
\(105\) 45.7765 0.435967
\(106\) 94.3254i 0.889862i
\(107\) 54.2161i 0.506693i 0.967376 + 0.253346i \(0.0815313\pi\)
−0.967376 + 0.253346i \(0.918469\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 0.0647920i 0.000594422i 1.00000 0.000297211i \(9.46053e-5\pi\)
−1.00000 0.000297211i \(0.999905\pi\)
\(110\) 65.6652 0.596956
\(111\) 85.6198i 0.771350i
\(112\) 47.2778i 0.422123i
\(113\) 157.283i 1.39188i 0.718098 + 0.695942i \(0.245013\pi\)
−0.718098 + 0.695942i \(0.754987\pi\)
\(114\) 51.4633i 0.451432i
\(115\) −15.0232 + 49.1864i −0.130636 + 0.427708i
\(116\) −76.4966 −0.659454
\(117\) 23.2668 0.198861
\(118\) 156.457 1.32591
\(119\) −270.761 −2.27531
\(120\) 10.9545i 0.0912871i
\(121\) −310.192 −2.56357
\(122\) 23.5862i 0.193329i
\(123\) 1.17660 0.00956582
\(124\) 66.6986 0.537892
\(125\) 11.1803i 0.0894427i
\(126\) 50.1457i 0.397981i
\(127\) 133.370 1.05016 0.525080 0.851053i \(-0.324035\pi\)
0.525080 + 0.851053i \(0.324035\pi\)
\(128\) 11.3137 0.0883883
\(129\) 13.8511i 0.107373i
\(130\) 24.5253i 0.188656i
\(131\) 62.9089 0.480221 0.240110 0.970746i \(-0.422816\pi\)
0.240110 + 0.970746i \(0.422816\pi\)
\(132\) 71.9326i 0.544944i
\(133\) −248.324 −1.86710
\(134\) 166.675i 1.24385i
\(135\) 11.6190i 0.0860663i
\(136\) 64.7940i 0.476426i
\(137\) 152.155i 1.11062i 0.831643 + 0.555311i \(0.187401\pi\)
−0.831643 + 0.555311i \(0.812599\pi\)
\(138\) 53.8810 + 16.4570i 0.390442 + 0.119254i
\(139\) 63.6449 0.457877 0.228938 0.973441i \(-0.426475\pi\)
0.228938 + 0.973441i \(0.426475\pi\)
\(140\) −52.8582 −0.377558
\(141\) 148.859 1.05574
\(142\) 41.0076 0.288786
\(143\) 161.046i 1.12620i
\(144\) 12.0000 0.0833333
\(145\) 85.5258i 0.589833i
\(146\) 43.9470 0.301007
\(147\) 157.096 1.06868
\(148\) 98.8653i 0.668009i
\(149\) 133.418i 0.895421i −0.894178 0.447711i \(-0.852239\pi\)
0.894178 0.447711i \(-0.147761\pi\)
\(150\) 12.2474 0.0816497
\(151\) 133.515 0.884204 0.442102 0.896965i \(-0.354233\pi\)
0.442102 + 0.896965i \(0.354233\pi\)
\(152\) 59.4247i 0.390952i
\(153\) 68.7244i 0.449179i
\(154\) 347.094 2.25386
\(155\) 74.5713i 0.481105i
\(156\) −26.8662 −0.172219
\(157\) 117.137i 0.746094i 0.927812 + 0.373047i \(0.121687\pi\)
−0.927812 + 0.373047i \(0.878313\pi\)
\(158\) 148.590i 0.940441i
\(159\) 115.524i 0.726569i
\(160\) 12.6491i 0.0790569i
\(161\) −79.4097 + 259.990i −0.493228 + 1.61485i
\(162\) 12.7279 0.0785674
\(163\) 34.3108 0.210496 0.105248 0.994446i \(-0.466436\pi\)
0.105248 + 0.994446i \(0.466436\pi\)
\(164\) −1.35862 −0.00828424
\(165\) −80.4231 −0.487413
\(166\) 61.0910i 0.368018i
\(167\) −33.8574 −0.202739 −0.101370 0.994849i \(-0.532322\pi\)
−0.101370 + 0.994849i \(0.532322\pi\)
\(168\) 57.9032i 0.344662i
\(169\) −108.851 −0.644088
\(170\) −72.4419 −0.426129
\(171\) 63.0294i 0.368593i
\(172\) 15.9939i 0.0929879i
\(173\) 207.140 1.19734 0.598670 0.800996i \(-0.295696\pi\)
0.598670 + 0.800996i \(0.295696\pi\)
\(174\) 93.6888 0.538442
\(175\) 59.0972i 0.337698i
\(176\) 83.0606i 0.471935i
\(177\) −191.620 −1.08260
\(178\) 69.5484i 0.390722i
\(179\) −74.8759 −0.418301 −0.209151 0.977883i \(-0.567070\pi\)
−0.209151 + 0.977883i \(0.567070\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 28.3027i 0.156369i 0.996939 + 0.0781844i \(0.0249123\pi\)
−0.996939 + 0.0781844i \(0.975088\pi\)
\(182\) 129.636i 0.712288i
\(183\) 28.8871i 0.157853i
\(184\) −62.2165 19.0030i −0.338133 0.103277i
\(185\) −110.535 −0.597485
\(186\) −81.6888 −0.439187
\(187\) 475.691 2.54380
\(188\) −171.887 −0.914294
\(189\) 61.4157i 0.324951i
\(190\) −66.4388 −0.349678
\(191\) 33.2592i 0.174132i 0.996203 + 0.0870659i \(0.0277491\pi\)
−0.996203 + 0.0870659i \(0.972251\pi\)
\(192\) −13.8564 −0.0721688
\(193\) 93.6041 0.484995 0.242498 0.970152i \(-0.422033\pi\)
0.242498 + 0.970152i \(0.422033\pi\)
\(194\) 98.5336i 0.507905i
\(195\) 30.0373i 0.154037i
\(196\) −181.399 −0.925503
\(197\) 372.604 1.89139 0.945696 0.325053i \(-0.105382\pi\)
0.945696 + 0.325053i \(0.105382\pi\)
\(198\) 88.0991i 0.444945i
\(199\) 59.8348i 0.300678i 0.988635 + 0.150339i \(0.0480364\pi\)
−0.988635 + 0.150339i \(0.951964\pi\)
\(200\) −14.1421 −0.0707107
\(201\) 204.135i 1.01560i
\(202\) −24.4281 −0.120931
\(203\) 452.074i 2.22696i
\(204\) 79.3561i 0.389000i
\(205\) 1.51898i 0.00740965i
\(206\) 73.1750i 0.355218i
\(207\) −65.9905 20.1557i −0.318795 0.0973704i
\(208\) 31.0224 0.149146
\(209\) 436.272 2.08743
\(210\) 64.7378 0.308275
\(211\) −152.649 −0.723455 −0.361728 0.932284i \(-0.617813\pi\)
−0.361728 + 0.932284i \(0.617813\pi\)
\(212\) 133.396i 0.629227i
\(213\) −50.2238 −0.235793
\(214\) 76.6732i 0.358286i
\(215\) 17.8817 0.0831709
\(216\) −14.6969 −0.0680414
\(217\) 394.170i 1.81645i
\(218\) 0.0916298i 0.000420320i
\(219\) −53.8239 −0.245771
\(220\) 92.8646 0.422112
\(221\) 177.666i 0.803919i
\(222\) 121.085i 0.545427i
\(223\) 205.883 0.923243 0.461622 0.887077i \(-0.347268\pi\)
0.461622 + 0.887077i \(0.347268\pi\)
\(224\) 66.8609i 0.298486i
\(225\) −15.0000 −0.0666667
\(226\) 222.432i 0.984210i
\(227\) 308.272i 1.35802i 0.734127 + 0.679012i \(0.237592\pi\)
−0.734127 + 0.679012i \(0.762408\pi\)
\(228\) 72.7801i 0.319211i
\(229\) 26.6431i 0.116346i 0.998307 + 0.0581728i \(0.0185274\pi\)
−0.998307 + 0.0581728i \(0.981473\pi\)
\(230\) −21.2460 + 69.5601i −0.0923737 + 0.302435i
\(231\) −425.102 −1.84027
\(232\) −108.183 −0.466304
\(233\) −362.883 −1.55744 −0.778720 0.627372i \(-0.784131\pi\)
−0.778720 + 0.627372i \(0.784131\pi\)
\(234\) 32.9042 0.140616
\(235\) 192.176i 0.817769i
\(236\) 221.264 0.937560
\(237\) 181.984i 0.767867i
\(238\) −382.914 −1.60888
\(239\) 375.990 1.57318 0.786591 0.617474i \(-0.211844\pi\)
0.786591 + 0.617474i \(0.211844\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 214.703i 0.890882i −0.895311 0.445441i \(-0.853047\pi\)
0.895311 0.445441i \(-0.146953\pi\)
\(242\) −438.677 −1.81272
\(243\) −15.5885 −0.0641500
\(244\) 33.3559i 0.136705i
\(245\) 202.810i 0.827795i
\(246\) 1.66396 0.00676406
\(247\) 162.943i 0.659690i
\(248\) 94.3261 0.380347
\(249\) 74.8209i 0.300485i
\(250\) 15.8114i 0.0632456i
\(251\) 164.214i 0.654237i 0.944983 + 0.327119i \(0.106078\pi\)
−0.944983 + 0.327119i \(0.893922\pi\)
\(252\) 70.9167i 0.281415i
\(253\) 139.512 456.768i 0.551431 1.80541i
\(254\) 188.614 0.742576
\(255\) 88.7228 0.347933
\(256\) 16.0000 0.0625000
\(257\) 92.0757 0.358271 0.179136 0.983824i \(-0.442670\pi\)
0.179136 + 0.983824i \(0.442670\pi\)
\(258\) 19.5885i 0.0759243i
\(259\) −584.266 −2.25586
\(260\) 34.6841i 0.133400i
\(261\) −114.745 −0.439636
\(262\) 88.9667 0.339567
\(263\) 340.726i 1.29554i 0.761837 + 0.647769i \(0.224298\pi\)
−0.761837 + 0.647769i \(0.775702\pi\)
\(264\) 101.728i 0.385334i
\(265\) −149.141 −0.562798
\(266\) −351.184 −1.32024
\(267\) 85.1791i 0.319023i
\(268\) 235.715i 0.879532i
\(269\) 253.330 0.941748 0.470874 0.882200i \(-0.343939\pi\)
0.470874 + 0.882200i \(0.343939\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) −21.6513 −0.0798939 −0.0399470 0.999202i \(-0.512719\pi\)
−0.0399470 + 0.999202i \(0.512719\pi\)
\(272\) 91.6325i 0.336884i
\(273\) 158.772i 0.581581i
\(274\) 215.180i 0.785328i
\(275\) 103.826i 0.377548i
\(276\) 76.1993 + 23.2738i 0.276084 + 0.0843253i
\(277\) 459.389 1.65844 0.829222 0.558919i \(-0.188784\pi\)
0.829222 + 0.558919i \(0.188784\pi\)
\(278\) 90.0074 0.323768
\(279\) 100.048 0.358595
\(280\) −74.7527 −0.266974
\(281\) 318.671i 1.13406i −0.823697 0.567030i \(-0.808092\pi\)
0.823697 0.567030i \(-0.191908\pi\)
\(282\) 210.518 0.746518
\(283\) 5.36172i 0.0189460i −0.999955 0.00947301i \(-0.996985\pi\)
0.999955 0.00947301i \(-0.00301540\pi\)
\(284\) 57.9935 0.204202
\(285\) 81.3706 0.285511
\(286\) 227.753i 0.796341i
\(287\) 8.02904i 0.0279758i
\(288\) 16.9706 0.0589256
\(289\) −235.782 −0.815856
\(290\) 120.952i 0.417075i
\(291\) 120.679i 0.414703i
\(292\) 62.1505 0.212844
\(293\) 519.450i 1.77287i −0.462854 0.886434i \(-0.653175\pi\)
0.462854 0.886434i \(-0.346825\pi\)
\(294\) 222.167 0.755670
\(295\) 247.381i 0.838579i
\(296\) 139.817i 0.472353i
\(297\) 107.899i 0.363296i
\(298\) 188.681i 0.633159i
\(299\) −170.598 52.1064i −0.570563 0.174269i
\(300\) 17.3205 0.0577350
\(301\) 94.5196 0.314019
\(302\) 188.818 0.625227
\(303\) 29.9181 0.0987397
\(304\) 84.0392i 0.276445i
\(305\) −37.2930 −0.122272
\(306\) 97.1910i 0.317617i
\(307\) −465.601 −1.51662 −0.758308 0.651897i \(-0.773974\pi\)
−0.758308 + 0.651897i \(0.773974\pi\)
\(308\) 490.865 1.59372
\(309\) 89.6207i 0.290035i
\(310\) 105.460i 0.340193i
\(311\) 299.817 0.964043 0.482021 0.876159i \(-0.339903\pi\)
0.482021 + 0.876159i \(0.339903\pi\)
\(312\) −37.9945 −0.121777
\(313\) 473.837i 1.51386i −0.653498 0.756928i \(-0.726699\pi\)
0.653498 0.756928i \(-0.273301\pi\)
\(314\) 165.656i 0.527568i
\(315\) −79.2873 −0.251706
\(316\) 210.138i 0.664992i
\(317\) 217.165 0.685065 0.342532 0.939506i \(-0.388715\pi\)
0.342532 + 0.939506i \(0.388715\pi\)
\(318\) 163.376i 0.513762i
\(319\) 794.232i 2.48976i
\(320\) 17.8885i 0.0559017i
\(321\) 93.9051i 0.292539i
\(322\) −112.302 + 367.682i −0.348765 + 1.14187i
\(323\) −481.295 −1.49008
\(324\) 18.0000 0.0555556
\(325\) −38.7779 −0.119317
\(326\) 48.5229 0.148843
\(327\) 0.112223i 0.000343190i
\(328\) −1.92137 −0.00585784
\(329\) 1015.81i 3.08756i
\(330\) −113.735 −0.344653
\(331\) −275.838 −0.833348 −0.416674 0.909056i \(-0.636804\pi\)
−0.416674 + 0.909056i \(0.636804\pi\)
\(332\) 86.3957i 0.260228i
\(333\) 148.298i 0.445339i
\(334\) −47.8816 −0.143358
\(335\) −263.537 −0.786677
\(336\) 81.8875i 0.243713i
\(337\) 201.315i 0.597374i 0.954351 + 0.298687i \(0.0965487\pi\)
−0.954351 + 0.298687i \(0.903451\pi\)
\(338\) −153.938 −0.455439
\(339\) 272.422i 0.803604i
\(340\) −102.448 −0.301318
\(341\) 692.503i 2.03080i
\(342\) 89.1371i 0.260635i
\(343\) 492.863i 1.43692i
\(344\) 22.6188i 0.0657524i
\(345\) 26.0209 85.1934i 0.0754228 0.246937i
\(346\) 292.940 0.846647
\(347\) 152.784 0.440300 0.220150 0.975466i \(-0.429345\pi\)
0.220150 + 0.975466i \(0.429345\pi\)
\(348\) 132.496 0.380736
\(349\) 599.141 1.71674 0.858368 0.513035i \(-0.171479\pi\)
0.858368 + 0.513035i \(0.171479\pi\)
\(350\) 83.5761i 0.238789i
\(351\) −40.2992 −0.114813
\(352\) 117.465i 0.333709i
\(353\) −574.915 −1.62865 −0.814327 0.580407i \(-0.802894\pi\)
−0.814327 + 0.580407i \(0.802894\pi\)
\(354\) −270.992 −0.765515
\(355\) 64.8387i 0.182644i
\(356\) 98.3563i 0.276282i
\(357\) 468.973 1.31365
\(358\) −105.890 −0.295783
\(359\) 165.976i 0.462330i 0.972915 + 0.231165i \(0.0742537\pi\)
−0.972915 + 0.231165i \(0.925746\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) −80.4119 −0.222748
\(362\) 40.0261i 0.110569i
\(363\) 537.268 1.48008
\(364\) 183.334i 0.503664i
\(365\) 69.4863i 0.190373i
\(366\) 40.8525i 0.111619i
\(367\) 433.965i 1.18247i 0.806501 + 0.591233i \(0.201358\pi\)
−0.806501 + 0.591233i \(0.798642\pi\)
\(368\) −87.9874 26.8742i −0.239096 0.0730278i
\(369\) −2.03792 −0.00552283
\(370\) −156.320 −0.422486
\(371\) −788.335 −2.12489
\(372\) −115.525 −0.310552
\(373\) 342.059i 0.917048i −0.888682 0.458524i \(-0.848378\pi\)
0.888682 0.458524i \(-0.151622\pi\)
\(374\) 672.728 1.79874
\(375\) 19.3649i 0.0516398i
\(376\) −243.085 −0.646503
\(377\) −296.638 −0.786839
\(378\) 86.8548i 0.229775i
\(379\) 76.7922i 0.202618i −0.994855 0.101309i \(-0.967697\pi\)
0.994855 0.101309i \(-0.0323031\pi\)
\(380\) −93.9587 −0.247260
\(381\) −231.004 −0.606310
\(382\) 47.0356i 0.123130i
\(383\) 78.7390i 0.205585i 0.994703 + 0.102792i \(0.0327777\pi\)
−0.994703 + 0.102792i \(0.967222\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 548.804i 1.42547i
\(386\) 132.376 0.342944
\(387\) 23.9909i 0.0619919i
\(388\) 139.348i 0.359143i
\(389\) 65.8586i 0.169302i −0.996411 0.0846511i \(-0.973022\pi\)
0.996411 0.0846511i \(-0.0269776\pi\)
\(390\) 42.4791i 0.108921i
\(391\) −153.910 + 503.906i −0.393631 + 1.28876i
\(392\) −256.536 −0.654430
\(393\) −108.961 −0.277256
\(394\) 526.942 1.33742
\(395\) 234.941 0.594787
\(396\) 124.591i 0.314624i
\(397\) −261.799 −0.659443 −0.329721 0.944078i \(-0.606955\pi\)
−0.329721 + 0.944078i \(0.606955\pi\)
\(398\) 84.6192i 0.212611i
\(399\) 430.110 1.07797
\(400\) −20.0000 −0.0500000
\(401\) 136.192i 0.339630i −0.985476 0.169815i \(-0.945683\pi\)
0.985476 0.169815i \(-0.0543171\pi\)
\(402\) 288.690i 0.718135i
\(403\) 258.644 0.641795
\(404\) −34.5465 −0.0855111
\(405\) 20.1246i 0.0496904i
\(406\) 639.329i 1.57470i
\(407\) 1026.48 2.52205
\(408\) 112.226i 0.275065i
\(409\) −162.202 −0.396583 −0.198291 0.980143i \(-0.563539\pi\)
−0.198291 + 0.980143i \(0.563539\pi\)
\(410\) 2.14816i 0.00523942i
\(411\) 263.540i 0.641217i
\(412\) 103.485i 0.251177i
\(413\) 1307.61i 3.16613i
\(414\) −93.3247 28.5044i −0.225422 0.0688513i
\(415\) 96.5933 0.232755
\(416\) 43.8722 0.105462
\(417\) −110.236 −0.264355
\(418\) 616.982 1.47603
\(419\) 746.726i 1.78216i 0.453844 + 0.891081i \(0.350052\pi\)
−0.453844 + 0.891081i \(0.649948\pi\)
\(420\) 91.5530 0.217983
\(421\) 675.466i 1.60443i −0.597033 0.802216i \(-0.703654\pi\)
0.597033 0.802216i \(-0.296346\pi\)
\(422\) −215.878 −0.511560
\(423\) −257.831 −0.609529
\(424\) 188.651i 0.444931i
\(425\) 114.541i 0.269507i
\(426\) −71.0272 −0.166730
\(427\) −197.124 −0.461649
\(428\) 108.432i 0.253346i
\(429\) 278.940i 0.650210i
\(430\) 25.2886 0.0588107
\(431\) 270.979i 0.628721i −0.949304 0.314360i \(-0.898210\pi\)
0.949304 0.314360i \(-0.101790\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 549.884i 1.26994i 0.772537 + 0.634970i \(0.218988\pi\)
−0.772537 + 0.634970i \(0.781012\pi\)
\(434\) 557.441i 1.28443i
\(435\) 148.135i 0.340540i
\(436\) 0.129584i 0.000297211i
\(437\) −141.156 + 462.149i −0.323011 + 1.05755i
\(438\) −76.1184 −0.173786
\(439\) 342.257 0.779628 0.389814 0.920894i \(-0.372539\pi\)
0.389814 + 0.920894i \(0.372539\pi\)
\(440\) 131.330 0.298478
\(441\) −272.098 −0.617002
\(442\) 251.258i 0.568456i
\(443\) 476.091 1.07470 0.537349 0.843360i \(-0.319426\pi\)
0.537349 + 0.843360i \(0.319426\pi\)
\(444\) 171.240i 0.385675i
\(445\) −109.966 −0.247114
\(446\) 291.163 0.652832
\(447\) 231.086i 0.516972i
\(448\) 94.5556i 0.211062i
\(449\) 554.189 1.23427 0.617137 0.786855i \(-0.288292\pi\)
0.617137 + 0.786855i \(0.288292\pi\)
\(450\) −21.2132 −0.0471405
\(451\) 14.1059i 0.0312770i
\(452\) 314.566i 0.695942i
\(453\) −231.254 −0.510496
\(454\) 435.962i 0.960269i
\(455\) −204.973 −0.450490
\(456\) 102.927i 0.225716i
\(457\) 142.050i 0.310832i 0.987849 + 0.155416i \(0.0496718\pi\)
−0.987849 + 0.155416i \(0.950328\pi\)
\(458\) 37.6791i 0.0822688i
\(459\) 119.034i 0.259334i
\(460\) −30.0463 + 98.3729i −0.0653181 + 0.213854i
\(461\) −618.196 −1.34099 −0.670495 0.741914i \(-0.733918\pi\)
−0.670495 + 0.741914i \(0.733918\pi\)
\(462\) −601.185 −1.30127
\(463\) 115.319 0.249069 0.124534 0.992215i \(-0.460256\pi\)
0.124534 + 0.992215i \(0.460256\pi\)
\(464\) −152.993 −0.329727
\(465\) 129.161i 0.277766i
\(466\) −513.195 −1.10128
\(467\) 778.924i 1.66793i −0.551817 0.833966i \(-0.686065\pi\)
0.551817 0.833966i \(-0.313935\pi\)
\(468\) 46.5335 0.0994306
\(469\) −1393.01 −2.97017
\(470\) 271.777i 0.578250i
\(471\) 202.887i 0.430757i
\(472\) 312.915 0.662955
\(473\) −166.058 −0.351074
\(474\) 257.365i 0.542964i
\(475\) 105.049i 0.221156i
\(476\) −541.523 −1.13765
\(477\) 200.094i 0.419485i
\(478\) 531.731 1.11241
\(479\) 18.0817i 0.0377488i −0.999822 0.0188744i \(-0.993992\pi\)
0.999822 0.0188744i \(-0.00600826\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 383.379i 0.797046i
\(482\) 303.635i 0.629949i
\(483\) 137.542 450.317i 0.284765 0.932333i
\(484\) −620.383 −1.28178
\(485\) −155.795 −0.321228
\(486\) −22.0454 −0.0453609
\(487\) 522.588 1.07308 0.536538 0.843876i \(-0.319732\pi\)
0.536538 + 0.843876i \(0.319732\pi\)
\(488\) 47.1724i 0.0966647i
\(489\) −59.4281 −0.121530
\(490\) 286.816i 0.585340i
\(491\) 524.138 1.06749 0.533746 0.845645i \(-0.320784\pi\)
0.533746 + 0.845645i \(0.320784\pi\)
\(492\) 2.35319 0.00478291
\(493\) 876.197i 1.77728i
\(494\) 230.437i 0.466471i
\(495\) 139.297 0.281408
\(496\) 133.397 0.268946
\(497\) 342.725i 0.689588i
\(498\) 105.813i 0.212475i
\(499\) −384.131 −0.769801 −0.384900 0.922958i \(-0.625764\pi\)
−0.384900 + 0.922958i \(0.625764\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 58.6428 0.117052
\(502\) 232.233i 0.462616i
\(503\) 815.894i 1.62206i 0.585007 + 0.811028i \(0.301092\pi\)
−0.585007 + 0.811028i \(0.698908\pi\)
\(504\) 100.291i 0.198991i
\(505\) 38.6241i 0.0764835i
\(506\) 197.300 645.967i 0.389920 1.27661i
\(507\) 188.535 0.371864
\(508\) 266.741 0.525080
\(509\) −138.733 −0.272560 −0.136280 0.990670i \(-0.543515\pi\)
−0.136280 + 0.990670i \(0.543515\pi\)
\(510\) 125.473 0.246025
\(511\) 367.292i 0.718771i
\(512\) 22.6274 0.0441942
\(513\) 109.170i 0.212807i
\(514\) 130.215 0.253336
\(515\) 115.700 0.224660
\(516\) 27.7023i 0.0536866i
\(517\) 1784.63i 3.45190i
\(518\) −826.278 −1.59513
\(519\) −358.777 −0.691285
\(520\) 49.0507i 0.0943282i
\(521\) 79.0746i 0.151775i 0.997116 + 0.0758873i \(0.0241789\pi\)
−0.997116 + 0.0758873i \(0.975821\pi\)
\(522\) −162.274 −0.310869
\(523\) 188.376i 0.360184i −0.983650 0.180092i \(-0.942360\pi\)
0.983650 0.180092i \(-0.0576396\pi\)
\(524\) 125.818 0.240110
\(525\) 102.359i 0.194970i
\(526\) 481.860i 0.916083i
\(527\) 763.970i 1.44966i
\(528\) 143.865i 0.272472i
\(529\) 438.722 + 295.574i 0.829342 + 0.558741i
\(530\) −210.918 −0.397958
\(531\) 331.896 0.625040
\(532\) −496.649 −0.933550
\(533\) −5.26843 −0.00988449
\(534\) 120.461i 0.225583i
\(535\) 121.231 0.226600
\(536\) 333.351i 0.621923i
\(537\) 129.689 0.241506
\(538\) 358.263 0.665917
\(539\) 1883.39i 3.49422i
\(540\) 23.2379i 0.0430331i
\(541\) −362.416 −0.669900 −0.334950 0.942236i \(-0.608719\pi\)
−0.334950 + 0.942236i \(0.608719\pi\)
\(542\) −30.6195 −0.0564935
\(543\) 49.0218i 0.0902795i
\(544\) 129.588i 0.238213i
\(545\) 0.144879 0.000265834
\(546\) 224.537i 0.411240i
\(547\) −593.659 −1.08530 −0.542650 0.839959i \(-0.682579\pi\)
−0.542650 + 0.839959i \(0.682579\pi\)
\(548\) 304.310i 0.555311i
\(549\) 50.0339i 0.0911364i
\(550\) 146.832i 0.266967i
\(551\) 803.589i 1.45842i
\(552\) 107.762 + 32.9141i 0.195221 + 0.0596270i
\(553\) 1241.85 2.24567
\(554\) 649.674 1.17270
\(555\) 191.452 0.344958
\(556\) 127.290 0.228938
\(557\) 183.937i 0.330229i −0.986274 0.165114i \(-0.947201\pi\)
0.986274 0.165114i \(-0.0527993\pi\)
\(558\) 141.489 0.253565
\(559\) 62.0211i 0.110950i
\(560\) −105.716 −0.188779
\(561\) −823.921 −1.46866
\(562\) 450.668i 0.801901i
\(563\) 447.708i 0.795218i −0.917555 0.397609i \(-0.869840\pi\)
0.917555 0.397609i \(-0.130160\pi\)
\(564\) 297.717 0.527868
\(565\) 351.695 0.622469
\(566\) 7.58262i 0.0133969i
\(567\) 106.375i 0.187610i
\(568\) 82.0151 0.144393
\(569\) 334.865i 0.588515i 0.955726 + 0.294258i \(0.0950724\pi\)
−0.955726 + 0.294258i \(0.904928\pi\)
\(570\) 115.075 0.201887
\(571\) 644.554i 1.12882i 0.825496 + 0.564408i \(0.190896\pi\)
−0.825496 + 0.564408i \(0.809104\pi\)
\(572\) 322.092i 0.563098i
\(573\) 57.6066i 0.100535i
\(574\) 11.3548i 0.0197819i
\(575\) 109.984 + 33.5928i 0.191277 + 0.0584223i
\(576\) 24.0000 0.0416667
\(577\) 82.7980 0.143497 0.0717487 0.997423i \(-0.477142\pi\)
0.0717487 + 0.997423i \(0.477142\pi\)
\(578\) −333.447 −0.576897
\(579\) −162.127 −0.280012
\(580\) 171.052i 0.294917i
\(581\) 510.575 0.878786
\(582\) 170.665i 0.293239i
\(583\) 1385.00 2.37564
\(584\) 87.8940 0.150503
\(585\) 52.0261i 0.0889335i
\(586\) 734.614i 1.25361i
\(587\) 48.0652 0.0818827 0.0409414 0.999162i \(-0.486964\pi\)
0.0409414 + 0.999162i \(0.486964\pi\)
\(588\) 314.192 0.534340
\(589\) 700.662i 1.18958i
\(590\) 349.849i 0.592965i
\(591\) −645.369 −1.09200
\(592\) 197.731i 0.334004i
\(593\) −115.147 −0.194176 −0.0970882 0.995276i \(-0.530953\pi\)
−0.0970882 + 0.995276i \(0.530953\pi\)
\(594\) 152.592i 0.256889i
\(595\) 605.441i 1.01755i
\(596\) 266.836i 0.447711i
\(597\) 103.637i 0.173596i
\(598\) −241.263 73.6896i −0.403449 0.123227i
\(599\) −813.749 −1.35851 −0.679256 0.733901i \(-0.737697\pi\)
−0.679256 + 0.733901i \(0.737697\pi\)
\(600\) 24.4949 0.0408248
\(601\) −550.200 −0.915474 −0.457737 0.889088i \(-0.651340\pi\)
−0.457737 + 0.889088i \(0.651340\pi\)
\(602\) 133.671 0.222045
\(603\) 353.572i 0.586355i
\(604\) 267.030 0.442102
\(605\) 693.609i 1.14646i
\(606\) 42.3106 0.0698195
\(607\) 287.538 0.473703 0.236851 0.971546i \(-0.423885\pi\)
0.236851 + 0.971546i \(0.423885\pi\)
\(608\) 118.849i 0.195476i
\(609\) 783.015i 1.28574i
\(610\) −52.7403 −0.0864596
\(611\) −666.543 −1.09091
\(612\) 137.449i 0.224589i
\(613\) 573.173i 0.935029i 0.883985 + 0.467514i \(0.154850\pi\)
−0.883985 + 0.467514i \(0.845150\pi\)
\(614\) −658.459 −1.07241
\(615\) 2.63095i 0.00427796i
\(616\) 694.188 1.12693
\(617\) 1156.17i 1.87385i −0.349525 0.936927i \(-0.613657\pi\)
0.349525 0.936927i \(-0.386343\pi\)
\(618\) 126.743i 0.205085i
\(619\) 14.9600i 0.0241680i 0.999927 + 0.0120840i \(0.00384655\pi\)
−0.999927 + 0.0120840i \(0.996153\pi\)
\(620\) 149.143i 0.240553i
\(621\) 114.299 + 34.9107i 0.184056 + 0.0562168i
\(622\) 424.006 0.681681
\(623\) −581.259 −0.933000
\(624\) −53.7323 −0.0861095
\(625\) 25.0000 0.0400000
\(626\) 670.107i 1.07046i
\(627\) −755.645 −1.20518
\(628\) 234.273i 0.373047i
\(629\) −1132.41 −1.80033
\(630\) −112.129 −0.177983
\(631\) 361.056i 0.572196i −0.958200 0.286098i \(-0.907642\pi\)
0.958200 0.286098i \(-0.0923583\pi\)
\(632\) 297.179i 0.470220i
\(633\) 264.396 0.417687
\(634\) 307.118 0.484414
\(635\) 298.225i 0.469646i
\(636\) 231.049i 0.363285i
\(637\) −703.427 −1.10428
\(638\) 1123.21i 1.76052i
\(639\) 86.9902 0.136135
\(640\) 25.2982i 0.0395285i
\(641\) 1132.34i 1.76652i −0.468881 0.883261i \(-0.655343\pi\)
0.468881 0.883261i \(-0.344657\pi\)
\(642\) 132.802i 0.206856i
\(643\) 753.140i 1.17129i −0.810567 0.585645i \(-0.800841\pi\)
0.810567 0.585645i \(-0.199159\pi\)
\(644\) −158.819 + 519.981i −0.246614 + 0.807424i
\(645\) −30.9721 −0.0480187
\(646\) −680.654 −1.05364
\(647\) −32.8271 −0.0507375 −0.0253687 0.999678i \(-0.508076\pi\)
−0.0253687 + 0.999678i \(0.508076\pi\)
\(648\) 25.4558 0.0392837
\(649\) 2297.29i 3.53974i
\(650\) −54.8403 −0.0843697
\(651\) 682.723i 1.04873i
\(652\) 68.6217 0.105248
\(653\) −1288.05 −1.97251 −0.986257 0.165219i \(-0.947167\pi\)
−0.986257 + 0.165219i \(0.947167\pi\)
\(654\) 0.158707i 0.000242672i
\(655\) 140.669i 0.214761i
\(656\) −2.71723 −0.00414212
\(657\) 93.2257 0.141896
\(658\) 1436.57i 2.18323i
\(659\) 101.045i 0.153330i −0.997057 0.0766652i \(-0.975573\pi\)
0.997057 0.0766652i \(-0.0244273\pi\)
\(660\) −160.846 −0.243706
\(661\) 597.593i 0.904074i 0.891999 + 0.452037i \(0.149302\pi\)
−0.891999 + 0.452037i \(0.850698\pi\)
\(662\) −390.094 −0.589266
\(663\) 307.727i 0.464143i
\(664\) 122.182i 0.184009i
\(665\) 555.270i 0.834992i
\(666\) 209.725i 0.314902i
\(667\) 841.342 + 256.974i 1.26138 + 0.385268i
\(668\) −67.7149 −0.101370
\(669\) −356.600 −0.533035
\(670\) −372.697 −0.556265
\(671\) 346.320 0.516126
\(672\) 115.806i 0.172331i
\(673\) 178.729 0.265570 0.132785 0.991145i \(-0.457608\pi\)
0.132785 + 0.991145i \(0.457608\pi\)
\(674\) 284.703i 0.422407i
\(675\) 25.9808 0.0384900
\(676\) −217.702 −0.322044
\(677\) 1197.98i 1.76955i 0.466023 + 0.884773i \(0.345686\pi\)
−0.466023 + 0.884773i \(0.654314\pi\)
\(678\) 385.263i 0.568234i
\(679\) −823.506 −1.21282
\(680\) −144.884 −0.213064
\(681\) 533.942i 0.784056i
\(682\) 979.348i 1.43599i
\(683\) 264.345 0.387035 0.193518 0.981097i \(-0.438010\pi\)
0.193518 + 0.981097i \(0.438010\pi\)
\(684\) 126.059i 0.184297i
\(685\) 340.229 0.496685
\(686\) 697.014i 1.01605i
\(687\) 46.1473i 0.0671722i
\(688\) 31.9878i 0.0464939i
\(689\) 517.283i 0.750774i
\(690\) 36.7991 120.482i 0.0533320 0.174611i
\(691\) 236.685 0.342525 0.171262 0.985225i \(-0.445215\pi\)
0.171262 + 0.985225i \(0.445215\pi\)
\(692\) 414.280 0.598670
\(693\) 736.298 1.06248
\(694\) 216.069 0.311339
\(695\) 142.314i 0.204769i
\(696\) 187.378 0.269221
\(697\) 15.5617i 0.0223266i
\(698\) 847.313 1.21392
\(699\) 628.533 0.899188
\(700\) 118.194i 0.168849i
\(701\) 322.720i 0.460371i 0.973147 + 0.230186i \(0.0739334\pi\)
−0.973147 + 0.230186i \(0.926067\pi\)
\(702\) −56.9917 −0.0811848
\(703\) −1038.57 −1.47734
\(704\) 166.121i 0.235968i
\(705\) 332.858i 0.472139i
\(706\) −813.052 −1.15163
\(707\) 204.160i 0.288770i
\(708\) −383.241 −0.541301
\(709\) 100.401i 0.141609i 0.997490 + 0.0708046i \(0.0225567\pi\)
−0.997490 + 0.0708046i \(0.977443\pi\)
\(710\) 91.6957i 0.129149i
\(711\) 315.206i 0.443328i
\(712\) 139.097i 0.195361i
\(713\) −733.579 224.059i −1.02886 0.314249i
\(714\) 663.227 0.928890
\(715\) 360.110 0.503650
\(716\) −149.752 −0.209151
\(717\) −651.235 −0.908277
\(718\) 234.726i 0.326917i
\(719\) 1250.73 1.73953 0.869767 0.493462i \(-0.164269\pi\)
0.869767 + 0.493462i \(0.164269\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 611.568 0.848222
\(722\) −113.720 −0.157506
\(723\) 371.876i 0.514351i
\(724\) 56.6055i 0.0781844i
\(725\) 191.242 0.263781
\(726\) 759.811 1.04657
\(727\) 528.487i 0.726942i 0.931605 + 0.363471i \(0.118408\pi\)
−0.931605 + 0.363471i \(0.881592\pi\)
\(728\) 259.273i 0.356144i
\(729\) 27.0000 0.0370370
\(730\) 98.2685i 0.134614i
\(731\) 183.195 0.250609
\(732\) 57.7741i 0.0789264i
\(733\) 37.5960i 0.0512905i 0.999671 + 0.0256453i \(0.00816403\pi\)
−0.999671 + 0.0256453i \(0.991836\pi\)
\(734\) 613.719i 0.836129i
\(735\) 351.277i 0.477928i
\(736\) −124.433 38.0059i −0.169066 0.0516385i
\(737\) 2447.32 3.32066
\(738\) −2.88206 −0.00390523
\(739\) −1383.68 −1.87237 −0.936187 0.351502i \(-0.885671\pi\)
−0.936187 + 0.351502i \(0.885671\pi\)
\(740\) −221.069 −0.298743
\(741\) 282.226i 0.380872i
\(742\) −1114.87 −1.50253
\(743\) 143.332i 0.192909i −0.995337 0.0964547i \(-0.969250\pi\)
0.995337 0.0964547i \(-0.0307503\pi\)
\(744\) −163.378 −0.219593
\(745\) −298.331 −0.400445
\(746\) 483.745i 0.648451i
\(747\) 129.594i 0.173485i
\(748\) 951.382 1.27190
\(749\) 640.805 0.855547
\(750\) 27.3861i 0.0365148i
\(751\) 1057.29i 1.40784i 0.710277 + 0.703922i \(0.248569\pi\)
−0.710277 + 0.703922i \(0.751431\pi\)
\(752\) −343.774 −0.457147
\(753\) 284.426i 0.377724i
\(754\) −419.510 −0.556379
\(755\) 298.548i 0.395428i
\(756\) 122.831i 0.162475i
\(757\) 85.5898i 0.113065i −0.998401 0.0565323i \(-0.981996\pi\)
0.998401 0.0565323i \(-0.0180044\pi\)
\(758\) 108.601i 0.143272i
\(759\) −241.642 + 791.145i −0.318369 + 1.04235i
\(760\) −132.878 −0.174839
\(761\) −751.679 −0.987752 −0.493876 0.869532i \(-0.664420\pi\)
−0.493876 + 0.869532i \(0.664420\pi\)
\(762\) −326.689 −0.428726
\(763\) 0.765806 0.00100368
\(764\) 66.5184i 0.0870659i
\(765\) −153.672 −0.200879
\(766\) 111.354i 0.145370i
\(767\) 858.017 1.11867
\(768\) −27.7128 −0.0360844
\(769\) 80.5080i 0.104692i −0.998629 0.0523459i \(-0.983330\pi\)
0.998629 0.0523459i \(-0.0166698\pi\)
\(770\) 776.126i 1.00796i
\(771\) −159.480 −0.206848
\(772\) 187.208 0.242498
\(773\) 1038.03i 1.34286i −0.741070 0.671428i \(-0.765681\pi\)
0.741070 0.671428i \(-0.234319\pi\)
\(774\) 33.9282i 0.0438349i
\(775\) −166.747 −0.215157
\(776\) 197.067i 0.253953i
\(777\) 1011.98 1.30242
\(778\) 93.1381i 0.119715i
\(779\) 14.2721i 0.0183211i
\(780\) 60.0745i 0.0770186i
\(781\) 602.122i 0.770962i
\(782\) −217.661 + 712.631i −0.278339 + 0.911293i
\(783\) 198.744 0.253824
\(784\) −362.797 −0.462752
\(785\) 261.926 0.333663
\(786\) −154.095 −0.196049
\(787\) 1078.55i 1.37045i 0.728330 + 0.685227i \(0.240297\pi\)
−0.728330 + 0.685227i \(0.759703\pi\)
\(788\) 745.208 0.945696
\(789\) 590.155i 0.747979i
\(790\) 332.257 0.420578
\(791\) 1859.00 2.35019
\(792\) 176.198i