Properties

Label 690.3.c.a.91.14
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 91.14
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.11

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +1.73205 q^{3} +2.00000 q^{4} +2.23607i q^{5} -2.44949 q^{6} +0.411309i q^{7} -2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +1.73205 q^{3} +2.00000 q^{4} +2.23607i q^{5} -2.44949 q^{6} +0.411309i q^{7} -2.82843 q^{8} +3.00000 q^{9} -3.16228i q^{10} -6.98697i q^{11} +3.46410 q^{12} -7.65791 q^{13} -0.581679i q^{14} +3.87298i q^{15} +4.00000 q^{16} -22.0292i q^{17} -4.24264 q^{18} -8.31107i q^{19} +4.47214i q^{20} +0.712409i q^{21} +9.88107i q^{22} +(17.3790 - 15.0656i) q^{23} -4.89898 q^{24} -5.00000 q^{25} +10.8299 q^{26} +5.19615 q^{27} +0.822619i q^{28} +32.6032 q^{29} -5.47723i q^{30} -17.7255 q^{31} -5.65685 q^{32} -12.1018i q^{33} +31.1540i q^{34} -0.919716 q^{35} +6.00000 q^{36} -22.9773i q^{37} +11.7536i q^{38} -13.2639 q^{39} -6.32456i q^{40} +28.8797 q^{41} -1.00750i q^{42} -7.58017i q^{43} -13.9739i q^{44} +6.70820i q^{45} +(-24.5776 + 21.3060i) q^{46} +49.4935 q^{47} +6.92820 q^{48} +48.8308 q^{49} +7.07107 q^{50} -38.1557i q^{51} -15.3158 q^{52} -17.5382i q^{53} -7.34847 q^{54} +15.6233 q^{55} -1.16336i q^{56} -14.3952i q^{57} -46.1078 q^{58} -33.8653 q^{59} +7.74597i q^{60} +39.2567i q^{61} +25.0676 q^{62} +1.23393i q^{63} +8.00000 q^{64} -17.1236i q^{65} +17.1145i q^{66} +70.8924i q^{67} -44.0585i q^{68} +(30.1012 - 26.0944i) q^{69} +1.30067 q^{70} +26.8165 q^{71} -8.48528 q^{72} -62.0148 q^{73} +32.4948i q^{74} -8.66025 q^{75} -16.6221i q^{76} +2.87381 q^{77} +18.7580 q^{78} -35.2805i q^{79} +8.94427i q^{80} +9.00000 q^{81} -40.8420 q^{82} -143.692i q^{83} +1.42482i q^{84} +49.2589 q^{85} +10.7200i q^{86} +56.4704 q^{87} +19.7621i q^{88} -73.4091i q^{89} -9.48683i q^{90} -3.14977i q^{91} +(34.7579 - 30.1312i) q^{92} -30.7014 q^{93} -69.9943 q^{94} +18.5841 q^{95} -9.79796 q^{96} +95.9147i q^{97} -69.0572 q^{98} -20.9609i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

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
\(7\) 0.411309i 0.0587585i 0.999568 + 0.0293792i \(0.00935305\pi\)
−0.999568 + 0.0293792i \(0.990647\pi\)
\(8\) −2.82843 −0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 6.98697i 0.635179i −0.948228 0.317589i \(-0.897127\pi\)
0.948228 0.317589i \(-0.102873\pi\)
\(12\) 3.46410 0.288675
\(13\) −7.65791 −0.589070 −0.294535 0.955641i \(-0.595165\pi\)
−0.294535 + 0.955641i \(0.595165\pi\)
\(14\) 0.581679i 0.0415485i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 22.0292i 1.29584i −0.761710 0.647918i \(-0.775640\pi\)
0.761710 0.647918i \(-0.224360\pi\)
\(18\) −4.24264 −0.235702
\(19\) 8.31107i 0.437425i −0.975789 0.218712i \(-0.929814\pi\)
0.975789 0.218712i \(-0.0701857\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 0.712409i 0.0339242i
\(22\) 9.88107i 0.449139i
\(23\) 17.3790 15.0656i 0.755607 0.655026i
\(24\) −4.89898 −0.204124
\(25\) −5.00000 −0.200000
\(26\) 10.8299 0.416535
\(27\) 5.19615 0.192450
\(28\) 0.822619i 0.0293792i
\(29\) 32.6032 1.12425 0.562124 0.827053i \(-0.309984\pi\)
0.562124 + 0.827053i \(0.309984\pi\)
\(30\) 5.47723i 0.182574i
\(31\) −17.7255 −0.571789 −0.285894 0.958261i \(-0.592291\pi\)
−0.285894 + 0.958261i \(0.592291\pi\)
\(32\) −5.65685 −0.176777
\(33\) 12.1018i 0.366721i
\(34\) 31.1540i 0.916295i
\(35\) −0.919716 −0.0262776
\(36\) 6.00000 0.166667
\(37\) 22.9773i 0.621008i −0.950572 0.310504i \(-0.899502\pi\)
0.950572 0.310504i \(-0.100498\pi\)
\(38\) 11.7536i 0.309306i
\(39\) −13.2639 −0.340100
\(40\) 6.32456i 0.158114i
\(41\) 28.8797 0.704382 0.352191 0.935928i \(-0.385437\pi\)
0.352191 + 0.935928i \(0.385437\pi\)
\(42\) 1.00750i 0.0239881i
\(43\) 7.58017i 0.176283i −0.996108 0.0881415i \(-0.971907\pi\)
0.996108 0.0881415i \(-0.0280928\pi\)
\(44\) 13.9739i 0.317589i
\(45\) 6.70820i 0.149071i
\(46\) −24.5776 + 21.3060i −0.534295 + 0.463173i
\(47\) 49.4935 1.05305 0.526526 0.850159i \(-0.323494\pi\)
0.526526 + 0.850159i \(0.323494\pi\)
\(48\) 6.92820 0.144338
\(49\) 48.8308 0.996547
\(50\) 7.07107 0.141421
\(51\) 38.1557i 0.748152i
\(52\) −15.3158 −0.294535
\(53\) 17.5382i 0.330910i −0.986217 0.165455i \(-0.947091\pi\)
0.986217 0.165455i \(-0.0529093\pi\)
\(54\) −7.34847 −0.136083
\(55\) 15.6233 0.284061
\(56\) 1.16336i 0.0207743i
\(57\) 14.3952i 0.252547i
\(58\) −46.1078 −0.794963
\(59\) −33.8653 −0.573989 −0.286994 0.957932i \(-0.592656\pi\)
−0.286994 + 0.957932i \(0.592656\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 39.2567i 0.643552i 0.946816 + 0.321776i \(0.104280\pi\)
−0.946816 + 0.321776i \(0.895720\pi\)
\(62\) 25.0676 0.404316
\(63\) 1.23393i 0.0195862i
\(64\) 8.00000 0.125000
\(65\) 17.1236i 0.263440i
\(66\) 17.1145i 0.259311i
\(67\) 70.8924i 1.05810i 0.848592 + 0.529048i \(0.177451\pi\)
−0.848592 + 0.529048i \(0.822549\pi\)
\(68\) 44.0585i 0.647918i
\(69\) 30.1012 26.0944i 0.436250 0.378179i
\(70\) 1.30067 0.0185811
\(71\) 26.8165 0.377698 0.188849 0.982006i \(-0.439524\pi\)
0.188849 + 0.982006i \(0.439524\pi\)
\(72\) −8.48528 −0.117851
\(73\) −62.0148 −0.849518 −0.424759 0.905306i \(-0.639641\pi\)
−0.424759 + 0.905306i \(0.639641\pi\)
\(74\) 32.4948i 0.439119i
\(75\) −8.66025 −0.115470
\(76\) 16.6221i 0.218712i
\(77\) 2.87381 0.0373222
\(78\) 18.7580 0.240487
\(79\) 35.2805i 0.446589i −0.974751 0.223294i \(-0.928319\pi\)
0.974751 0.223294i \(-0.0716811\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) −40.8420 −0.498074
\(83\) 143.692i 1.73123i −0.500712 0.865614i \(-0.666928\pi\)
0.500712 0.865614i \(-0.333072\pi\)
\(84\) 1.42482i 0.0169621i
\(85\) 49.2589 0.579516
\(86\) 10.7200i 0.124651i
\(87\) 56.4704 0.649084
\(88\) 19.7621i 0.224570i
\(89\) 73.4091i 0.824821i −0.910998 0.412411i \(-0.864687\pi\)
0.910998 0.412411i \(-0.135313\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 3.14977i 0.0346129i
\(92\) 34.7579 30.1312i 0.377803 0.327513i
\(93\) −30.7014 −0.330123
\(94\) −69.9943 −0.744620
\(95\) 18.5841 0.195622
\(96\) −9.79796 −0.102062
\(97\) 95.9147i 0.988811i 0.869231 + 0.494405i \(0.164614\pi\)
−0.869231 + 0.494405i \(0.835386\pi\)
\(98\) −69.0572 −0.704665
\(99\) 20.9609i 0.211726i
\(100\) −10.0000 −0.100000
\(101\) 144.998 1.43563 0.717814 0.696235i \(-0.245143\pi\)
0.717814 + 0.696235i \(0.245143\pi\)
\(102\) 53.9604i 0.529023i
\(103\) 123.567i 1.19968i −0.800121 0.599838i \(-0.795232\pi\)
0.800121 0.599838i \(-0.204768\pi\)
\(104\) 21.6598 0.208268
\(105\) −1.59299 −0.0151714
\(106\) 24.8028i 0.233989i
\(107\) 92.0932i 0.860684i −0.902666 0.430342i \(-0.858393\pi\)
0.902666 0.430342i \(-0.141607\pi\)
\(108\) 10.3923 0.0962250
\(109\) 45.0093i 0.412929i −0.978454 0.206465i \(-0.933804\pi\)
0.978454 0.206465i \(-0.0661958\pi\)
\(110\) −22.0947 −0.200861
\(111\) 39.7978i 0.358539i
\(112\) 1.64524i 0.0146896i
\(113\) 54.3464i 0.480942i −0.970656 0.240471i \(-0.922698\pi\)
0.970656 0.240471i \(-0.0773018\pi\)
\(114\) 20.3579i 0.178578i
\(115\) 33.6877 + 38.8605i 0.292936 + 0.337918i
\(116\) 65.2063 0.562124
\(117\) −22.9737 −0.196357
\(118\) 47.8928 0.405871
\(119\) 9.06083 0.0761414
\(120\) 10.9545i 0.0912871i
\(121\) 72.1823 0.596548
\(122\) 55.5173i 0.455060i
\(123\) 50.0211 0.406675
\(124\) −35.4509 −0.285894
\(125\) 11.1803i 0.0894427i
\(126\) 1.74504i 0.0138495i
\(127\) 114.199 0.899203 0.449602 0.893229i \(-0.351566\pi\)
0.449602 + 0.893229i \(0.351566\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 13.1292i 0.101777i
\(130\) 24.2164i 0.186280i
\(131\) 87.1429 0.665213 0.332606 0.943066i \(-0.392072\pi\)
0.332606 + 0.943066i \(0.392072\pi\)
\(132\) 24.2036i 0.183360i
\(133\) 3.41842 0.0257024
\(134\) 100.257i 0.748186i
\(135\) 11.6190i 0.0860663i
\(136\) 62.3081i 0.458148i
\(137\) 3.00953i 0.0219674i −0.999940 0.0109837i \(-0.996504\pi\)
0.999940 0.0109837i \(-0.00349628\pi\)
\(138\) −42.5696 + 36.9030i −0.308475 + 0.267413i
\(139\) −124.206 −0.893567 −0.446783 0.894642i \(-0.647431\pi\)
−0.446783 + 0.894642i \(0.647431\pi\)
\(140\) −1.83943 −0.0131388
\(141\) 85.7252 0.607980
\(142\) −37.9243 −0.267073
\(143\) 53.5056i 0.374165i
\(144\) 12.0000 0.0833333
\(145\) 72.9029i 0.502779i
\(146\) 87.7022 0.600700
\(147\) 84.5775 0.575357
\(148\) 45.9546i 0.310504i
\(149\) 11.8453i 0.0794988i 0.999210 + 0.0397494i \(0.0126560\pi\)
−0.999210 + 0.0397494i \(0.987344\pi\)
\(150\) 12.2474 0.0816497
\(151\) 135.282 0.895908 0.447954 0.894057i \(-0.352153\pi\)
0.447954 + 0.894057i \(0.352153\pi\)
\(152\) 23.5073i 0.154653i
\(153\) 66.0877i 0.431946i
\(154\) −4.06418 −0.0263908
\(155\) 39.6353i 0.255712i
\(156\) −26.5278 −0.170050
\(157\) 172.890i 1.10121i −0.834765 0.550606i \(-0.814396\pi\)
0.834765 0.550606i \(-0.185604\pi\)
\(158\) 49.8942i 0.315786i
\(159\) 30.3771i 0.191051i
\(160\) 12.6491i 0.0790569i
\(161\) 6.19662 + 7.14813i 0.0384883 + 0.0443983i
\(162\) −12.7279 −0.0785674
\(163\) −247.308 −1.51723 −0.758613 0.651541i \(-0.774123\pi\)
−0.758613 + 0.651541i \(0.774123\pi\)
\(164\) 57.7594 0.352191
\(165\) 27.0604 0.164003
\(166\) 203.211i 1.22416i
\(167\) −218.390 −1.30773 −0.653863 0.756613i \(-0.726853\pi\)
−0.653863 + 0.756613i \(0.726853\pi\)
\(168\) 2.01500i 0.0119940i
\(169\) −110.356 −0.652997
\(170\) −69.6625 −0.409780
\(171\) 24.9332i 0.145808i
\(172\) 15.1603i 0.0881415i
\(173\) −172.122 −0.994927 −0.497463 0.867485i \(-0.665735\pi\)
−0.497463 + 0.867485i \(0.665735\pi\)
\(174\) −79.8611 −0.458972
\(175\) 2.05655i 0.0117517i
\(176\) 27.9479i 0.158795i
\(177\) −58.6565 −0.331392
\(178\) 103.816i 0.583237i
\(179\) 84.0652 0.469638 0.234819 0.972039i \(-0.424550\pi\)
0.234819 + 0.972039i \(0.424550\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 277.980i 1.53580i 0.640569 + 0.767901i \(0.278699\pi\)
−0.640569 + 0.767901i \(0.721301\pi\)
\(182\) 4.45445i 0.0244750i
\(183\) 67.9946i 0.371555i
\(184\) −49.1551 + 42.6119i −0.267147 + 0.231587i
\(185\) 51.3788 0.277723
\(186\) 43.4183 0.233432
\(187\) −153.918 −0.823088
\(188\) 98.9869 0.526526
\(189\) 2.13723i 0.0113081i
\(190\) −26.2819 −0.138326
\(191\) 66.0363i 0.345740i 0.984945 + 0.172870i \(0.0553040\pi\)
−0.984945 + 0.172870i \(0.944696\pi\)
\(192\) 13.8564 0.0721688
\(193\) −91.4052 −0.473602 −0.236801 0.971558i \(-0.576099\pi\)
−0.236801 + 0.971558i \(0.576099\pi\)
\(194\) 135.644i 0.699195i
\(195\) 29.6590i 0.152097i
\(196\) 97.6616 0.498274
\(197\) 34.0865 0.173028 0.0865140 0.996251i \(-0.472427\pi\)
0.0865140 + 0.996251i \(0.472427\pi\)
\(198\) 29.6432i 0.149713i
\(199\) 276.277i 1.38833i 0.719817 + 0.694164i \(0.244226\pi\)
−0.719817 + 0.694164i \(0.755774\pi\)
\(200\) 14.1421 0.0707107
\(201\) 122.789i 0.610892i
\(202\) −205.059 −1.01514
\(203\) 13.4100i 0.0660591i
\(204\) 76.3115i 0.374076i
\(205\) 64.5769i 0.315009i
\(206\) 174.750i 0.848299i
\(207\) 52.1369 45.1968i 0.251869 0.218342i
\(208\) −30.6316 −0.147267
\(209\) −58.0692 −0.277843
\(210\) 2.25283 0.0107278
\(211\) −159.869 −0.757675 −0.378838 0.925463i \(-0.623676\pi\)
−0.378838 + 0.925463i \(0.623676\pi\)
\(212\) 35.0765i 0.165455i
\(213\) 46.4476 0.218064
\(214\) 130.239i 0.608596i
\(215\) 16.9498 0.0788362
\(216\) −14.6969 −0.0680414
\(217\) 7.29065i 0.0335975i
\(218\) 63.6528i 0.291985i
\(219\) −107.413 −0.490470
\(220\) 31.2467 0.142030
\(221\) 168.698i 0.763339i
\(222\) 56.2826i 0.253525i
\(223\) −26.6387 −0.119456 −0.0597280 0.998215i \(-0.519023\pi\)
−0.0597280 + 0.998215i \(0.519023\pi\)
\(224\) 2.32672i 0.0103871i
\(225\) −15.0000 −0.0666667
\(226\) 76.8574i 0.340077i
\(227\) 209.504i 0.922924i 0.887160 + 0.461462i \(0.152675\pi\)
−0.887160 + 0.461462i \(0.847325\pi\)
\(228\) 28.7904i 0.126274i
\(229\) 80.8748i 0.353165i 0.984286 + 0.176583i \(0.0565043\pi\)
−0.984286 + 0.176583i \(0.943496\pi\)
\(230\) −47.6416 54.9571i −0.207137 0.238944i
\(231\) 4.97758 0.0215480
\(232\) −92.2157 −0.397481
\(233\) −174.793 −0.750184 −0.375092 0.926988i \(-0.622389\pi\)
−0.375092 + 0.926988i \(0.622389\pi\)
\(234\) 32.4898 0.138845
\(235\) 110.671i 0.470939i
\(236\) −67.7307 −0.286994
\(237\) 61.1077i 0.257838i
\(238\) −12.8139 −0.0538401
\(239\) 99.3102 0.415524 0.207762 0.978179i \(-0.433382\pi\)
0.207762 + 0.978179i \(0.433382\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 43.9106i 0.182202i 0.995842 + 0.0911008i \(0.0290386\pi\)
−0.995842 + 0.0911008i \(0.970961\pi\)
\(242\) −102.081 −0.421823
\(243\) 15.5885 0.0641500
\(244\) 78.5134i 0.321776i
\(245\) 109.189i 0.445670i
\(246\) −70.7405 −0.287563
\(247\) 63.6454i 0.257674i
\(248\) 50.1352 0.202158
\(249\) 248.882i 0.999525i
\(250\) 15.8114i 0.0632456i
\(251\) 419.272i 1.67041i 0.549940 + 0.835204i \(0.314651\pi\)
−0.549940 + 0.835204i \(0.685349\pi\)
\(252\) 2.46786i 0.00979308i
\(253\) −105.263 121.426i −0.416059 0.479945i
\(254\) −161.501 −0.635833
\(255\) 85.3188 0.334584
\(256\) 16.0000 0.0625000
\(257\) −207.444 −0.807176 −0.403588 0.914941i \(-0.632237\pi\)
−0.403588 + 0.914941i \(0.632237\pi\)
\(258\) 18.5676i 0.0719673i
\(259\) 9.45077 0.0364895
\(260\) 34.2472i 0.131720i
\(261\) 97.8095 0.374749
\(262\) −123.239 −0.470376
\(263\) 342.541i 1.30244i −0.758891 0.651218i \(-0.774258\pi\)
0.758891 0.651218i \(-0.225742\pi\)
\(264\) 34.2290i 0.129655i
\(265\) 39.2167 0.147987
\(266\) −4.83438 −0.0181744
\(267\) 127.148i 0.476211i
\(268\) 141.785i 0.529048i
\(269\) −403.239 −1.49903 −0.749514 0.661988i \(-0.769713\pi\)
−0.749514 + 0.661988i \(0.769713\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) 45.3290 0.167266 0.0836328 0.996497i \(-0.473348\pi\)
0.0836328 + 0.996497i \(0.473348\pi\)
\(272\) 88.1169i 0.323959i
\(273\) 5.45556i 0.0199837i
\(274\) 4.25612i 0.0155333i
\(275\) 34.9348i 0.127036i
\(276\) 60.2025 52.1887i 0.218125 0.189090i
\(277\) −241.667 −0.872446 −0.436223 0.899839i \(-0.643684\pi\)
−0.436223 + 0.899839i \(0.643684\pi\)
\(278\) 175.654 0.631847
\(279\) −53.1764 −0.190596
\(280\) 2.60135 0.00929053
\(281\) 231.673i 0.824459i 0.911080 + 0.412229i \(0.135250\pi\)
−0.911080 + 0.412229i \(0.864750\pi\)
\(282\) −121.234 −0.429907
\(283\) 175.141i 0.618874i −0.950920 0.309437i \(-0.899859\pi\)
0.950920 0.309437i \(-0.100141\pi\)
\(284\) 53.6331 0.188849
\(285\) 32.1886 0.112943
\(286\) 75.6683i 0.264575i
\(287\) 11.8785i 0.0413884i
\(288\) −16.9706 −0.0589256
\(289\) −196.287 −0.679194
\(290\) 103.100i 0.355518i
\(291\) 166.129i 0.570890i
\(292\) −124.030 −0.424759
\(293\) 306.727i 1.04685i 0.852072 + 0.523424i \(0.175346\pi\)
−0.852072 + 0.523424i \(0.824654\pi\)
\(294\) −119.611 −0.406839
\(295\) 75.7252i 0.256696i
\(296\) 64.9896i 0.219559i
\(297\) 36.3054i 0.122240i
\(298\) 16.7518i 0.0562141i
\(299\) −133.086 + 115.371i −0.445105 + 0.385856i
\(300\) −17.3205 −0.0577350
\(301\) 3.11780 0.0103581
\(302\) −191.318 −0.633503
\(303\) 251.145 0.828860
\(304\) 33.2443i 0.109356i
\(305\) −87.7806 −0.287805
\(306\) 93.4621i 0.305432i
\(307\) 106.431 0.346682 0.173341 0.984862i \(-0.444544\pi\)
0.173341 + 0.984862i \(0.444544\pi\)
\(308\) 5.74761 0.0186611
\(309\) 214.024i 0.692633i
\(310\) 56.0528i 0.180816i
\(311\) 604.165 1.94265 0.971327 0.237749i \(-0.0764097\pi\)
0.971327 + 0.237749i \(0.0764097\pi\)
\(312\) 37.5159 0.120243
\(313\) 505.257i 1.61424i 0.590388 + 0.807120i \(0.298975\pi\)
−0.590388 + 0.807120i \(0.701025\pi\)
\(314\) 244.504i 0.778675i
\(315\) −2.75915 −0.00875920
\(316\) 70.5611i 0.223294i
\(317\) 104.465 0.329544 0.164772 0.986332i \(-0.447311\pi\)
0.164772 + 0.986332i \(0.447311\pi\)
\(318\) 42.9597i 0.135093i
\(319\) 227.797i 0.714098i
\(320\) 17.8885i 0.0559017i
\(321\) 159.510i 0.496916i
\(322\) −8.76334 10.1090i −0.0272154 0.0313943i
\(323\) −183.086 −0.566831
\(324\) 18.0000 0.0555556
\(325\) 38.2895 0.117814
\(326\) 349.746 1.07284
\(327\) 77.9584i 0.238405i
\(328\) −81.6841 −0.249037
\(329\) 20.3571i 0.0618758i
\(330\) −38.2692 −0.115967
\(331\) −41.3629 −0.124963 −0.0624817 0.998046i \(-0.519902\pi\)
−0.0624817 + 0.998046i \(0.519902\pi\)
\(332\) 287.384i 0.865614i
\(333\) 68.9319i 0.207003i
\(334\) 308.851 0.924702
\(335\) −158.520 −0.473195
\(336\) 2.84964i 0.00848106i
\(337\) 181.417i 0.538331i 0.963094 + 0.269165i \(0.0867478\pi\)
−0.963094 + 0.269165i \(0.913252\pi\)
\(338\) 156.068 0.461738
\(339\) 94.1307i 0.277672i
\(340\) 98.5177 0.289758
\(341\) 123.847i 0.363188i
\(342\) 35.2609i 0.103102i
\(343\) 40.2387i 0.117314i
\(344\) 21.4400i 0.0623255i
\(345\) 58.3488 + 67.3084i 0.169127 + 0.195097i
\(346\) 243.418 0.703519
\(347\) 202.642 0.583984 0.291992 0.956421i \(-0.405682\pi\)
0.291992 + 0.956421i \(0.405682\pi\)
\(348\) 112.941 0.324542
\(349\) 319.984 0.916859 0.458430 0.888731i \(-0.348412\pi\)
0.458430 + 0.888731i \(0.348412\pi\)
\(350\) 2.90840i 0.00830971i
\(351\) −39.7917 −0.113367
\(352\) 39.5243i 0.112285i
\(353\) −308.167 −0.872994 −0.436497 0.899706i \(-0.643781\pi\)
−0.436497 + 0.899706i \(0.643781\pi\)
\(354\) 82.9528 0.234330
\(355\) 59.9636i 0.168912i
\(356\) 146.818i 0.412411i
\(357\) 15.6938 0.0439603
\(358\) −118.886 −0.332084
\(359\) 301.630i 0.840196i −0.907479 0.420098i \(-0.861996\pi\)
0.907479 0.420098i \(-0.138004\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 291.926 0.808660
\(362\) 393.123i 1.08598i
\(363\) 125.023 0.344417
\(364\) 6.29954i 0.0173064i
\(365\) 138.669i 0.379916i
\(366\) 96.1588i 0.262729i
\(367\) 470.453i 1.28189i −0.767587 0.640945i \(-0.778543\pi\)
0.767587 0.640945i \(-0.221457\pi\)
\(368\) 69.5158 60.2624i 0.188902 0.163756i
\(369\) 86.6390 0.234794
\(370\) −72.6606 −0.196380
\(371\) 7.21364 0.0194438
\(372\) −61.4028 −0.165061
\(373\) 249.106i 0.667844i −0.942601 0.333922i \(-0.891628\pi\)
0.942601 0.333922i \(-0.108372\pi\)
\(374\) 217.672 0.582011
\(375\) 19.3649i 0.0516398i
\(376\) −139.989 −0.372310
\(377\) −249.672 −0.662260
\(378\) 3.02249i 0.00799602i
\(379\) 141.700i 0.373879i −0.982371 0.186940i \(-0.940143\pi\)
0.982371 0.186940i \(-0.0598569\pi\)
\(380\) 37.1682 0.0978112
\(381\) 197.798 0.519155
\(382\) 93.3895i 0.244475i
\(383\) 110.480i 0.288460i 0.989544 + 0.144230i \(0.0460705\pi\)
−0.989544 + 0.144230i \(0.953929\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 6.42603i 0.0166910i
\(386\) 129.266 0.334887
\(387\) 22.7405i 0.0587610i
\(388\) 191.829i 0.494405i
\(389\) 705.447i 1.81349i 0.421681 + 0.906744i \(0.361440\pi\)
−0.421681 + 0.906744i \(0.638560\pi\)
\(390\) 41.9441i 0.107549i
\(391\) −331.883 382.845i −0.848807 0.979143i
\(392\) −138.114 −0.352333
\(393\) 150.936 0.384061
\(394\) −48.2056 −0.122349
\(395\) 78.8897 0.199721
\(396\) 41.9218i 0.105863i
\(397\) 10.3766 0.0261376 0.0130688 0.999915i \(-0.495840\pi\)
0.0130688 + 0.999915i \(0.495840\pi\)
\(398\) 390.715i 0.981696i
\(399\) 5.92088 0.0148393
\(400\) −20.0000 −0.0500000
\(401\) 50.4144i 0.125722i −0.998022 0.0628609i \(-0.979978\pi\)
0.998022 0.0628609i \(-0.0200224\pi\)
\(402\) 173.650i 0.431966i
\(403\) 135.740 0.336824
\(404\) 289.997 0.717814
\(405\) 20.1246i 0.0496904i
\(406\) 18.9646i 0.0467108i
\(407\) −160.542 −0.394451
\(408\) 107.921i 0.264512i
\(409\) 71.8300 0.175624 0.0878118 0.996137i \(-0.472013\pi\)
0.0878118 + 0.996137i \(0.472013\pi\)
\(410\) 91.3256i 0.222745i
\(411\) 5.21266i 0.0126829i
\(412\) 247.133i 0.599838i
\(413\) 13.9291i 0.0337267i
\(414\) −73.7327 + 63.9179i −0.178098 + 0.154391i
\(415\) 321.305 0.774229
\(416\) 43.3197 0.104134
\(417\) −215.131 −0.515901
\(418\) 82.1222 0.196465
\(419\) 355.682i 0.848884i −0.905455 0.424442i \(-0.860470\pi\)
0.905455 0.424442i \(-0.139530\pi\)
\(420\) −3.18599 −0.00758569
\(421\) 277.750i 0.659738i −0.944027 0.329869i \(-0.892995\pi\)
0.944027 0.329869i \(-0.107005\pi\)
\(422\) 226.090 0.535757
\(423\) 148.480 0.351017
\(424\) 49.6056i 0.116994i
\(425\) 110.146i 0.259167i
\(426\) −65.6868 −0.154194
\(427\) −16.1466 −0.0378141
\(428\) 184.186i 0.430342i
\(429\) 92.6744i 0.216024i
\(430\) −23.9706 −0.0557456
\(431\) 219.586i 0.509481i 0.967009 + 0.254741i \(0.0819901\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(432\) 20.7846 0.0481125
\(433\) 284.730i 0.657574i 0.944404 + 0.328787i \(0.106640\pi\)
−0.944404 + 0.328787i \(0.893360\pi\)
\(434\) 10.3105i 0.0237570i
\(435\) 126.272i 0.290279i
\(436\) 90.0186i 0.206465i
\(437\) −125.211 144.438i −0.286524 0.330521i
\(438\) 151.905 0.346814
\(439\) −80.6153 −0.183634 −0.0918170 0.995776i \(-0.529267\pi\)
−0.0918170 + 0.995776i \(0.529267\pi\)
\(440\) −44.1895 −0.100431
\(441\) 146.492 0.332182
\(442\) 238.575i 0.539762i
\(443\) 208.114 0.469784 0.234892 0.972021i \(-0.424526\pi\)
0.234892 + 0.972021i \(0.424526\pi\)
\(444\) 79.5956i 0.179269i
\(445\) 164.148 0.368871
\(446\) 37.6728 0.0844681
\(447\) 20.5167i 0.0458986i
\(448\) 3.29048i 0.00734481i
\(449\) −409.241 −0.911450 −0.455725 0.890121i \(-0.650620\pi\)
−0.455725 + 0.890121i \(0.650620\pi\)
\(450\) 21.2132 0.0471405
\(451\) 201.781i 0.447409i
\(452\) 108.693i 0.240471i
\(453\) 234.316 0.517253
\(454\) 296.283i 0.652606i
\(455\) 7.04310 0.0154793
\(456\) 40.7158i 0.0892890i
\(457\) 310.013i 0.678365i 0.940721 + 0.339183i \(0.110151\pi\)
−0.940721 + 0.339183i \(0.889849\pi\)
\(458\) 114.374i 0.249726i
\(459\) 114.467i 0.249384i
\(460\) 67.3754 + 77.7210i 0.146468 + 0.168959i
\(461\) 463.484 1.00539 0.502694 0.864465i \(-0.332342\pi\)
0.502694 + 0.864465i \(0.332342\pi\)
\(462\) −7.03936 −0.0152367
\(463\) 604.690 1.30603 0.653013 0.757347i \(-0.273505\pi\)
0.653013 + 0.757347i \(0.273505\pi\)
\(464\) 130.413 0.281062
\(465\) 68.6504i 0.147635i
\(466\) 247.194 0.530460
\(467\) 271.585i 0.581551i −0.956791 0.290776i \(-0.906087\pi\)
0.956791 0.290776i \(-0.0939134\pi\)
\(468\) −45.9475 −0.0981783
\(469\) −29.1587 −0.0621721
\(470\) 156.512i 0.333004i
\(471\) 299.455i 0.635786i
\(472\) 95.7856 0.202936
\(473\) −52.9624 −0.111971
\(474\) 86.4193i 0.182319i
\(475\) 41.5554i 0.0874850i
\(476\) 18.1217 0.0380707
\(477\) 52.6147i 0.110303i
\(478\) −140.446 −0.293820
\(479\) 793.694i 1.65698i −0.560003 0.828491i \(-0.689200\pi\)
0.560003 0.828491i \(-0.310800\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 175.958i 0.365817i
\(482\) 62.0990i 0.128836i
\(483\) 10.7329 + 12.3809i 0.0222212 + 0.0256334i
\(484\) 144.365 0.298274
\(485\) −214.472 −0.442210
\(486\) −22.0454 −0.0453609
\(487\) −434.574 −0.892350 −0.446175 0.894946i \(-0.647214\pi\)
−0.446175 + 0.894946i \(0.647214\pi\)
\(488\) 111.035i 0.227530i
\(489\) −428.350 −0.875971
\(490\) 154.417i 0.315136i
\(491\) 95.0833 0.193652 0.0968261 0.995301i \(-0.469131\pi\)
0.0968261 + 0.995301i \(0.469131\pi\)
\(492\) 100.042 0.203338
\(493\) 718.223i 1.45684i
\(494\) 90.0082i 0.182203i
\(495\) 46.8700 0.0946869
\(496\) −70.9018 −0.142947
\(497\) 11.0299i 0.0221929i
\(498\) 351.972i 0.706771i
\(499\) 826.993 1.65730 0.828650 0.559767i \(-0.189109\pi\)
0.828650 + 0.559767i \(0.189109\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −378.263 −0.755016
\(502\) 592.941i 1.18116i
\(503\) 424.858i 0.844648i 0.906445 + 0.422324i \(0.138785\pi\)
−0.906445 + 0.422324i \(0.861215\pi\)
\(504\) 3.49008i 0.00692475i
\(505\) 324.226i 0.642032i
\(506\) 148.864 + 171.723i 0.294198 + 0.339373i
\(507\) −191.143 −0.377008
\(508\) 228.398 0.449602
\(509\) −786.116 −1.54443 −0.772216 0.635360i \(-0.780852\pi\)
−0.772216 + 0.635360i \(0.780852\pi\)
\(510\) −120.659 −0.236586
\(511\) 25.5073i 0.0499164i
\(512\) −22.6274 −0.0441942
\(513\) 43.1856i 0.0841824i
\(514\) 293.371 0.570760
\(515\) 276.303 0.536511
\(516\) 26.2585i 0.0508885i
\(517\) 345.809i 0.668877i
\(518\) −13.3654 −0.0258020
\(519\) −298.125 −0.574421
\(520\) 48.4329i 0.0931401i
\(521\) 792.323i 1.52077i 0.649471 + 0.760387i \(0.274991\pi\)
−0.649471 + 0.760387i \(0.725009\pi\)
\(522\) −138.324 −0.264988
\(523\) 123.543i 0.236220i −0.993001 0.118110i \(-0.962316\pi\)
0.993001 0.118110i \(-0.0376835\pi\)
\(524\) 174.286 0.332606
\(525\) 3.56204i 0.00678485i
\(526\) 484.425i 0.920961i
\(527\) 390.478i 0.740945i
\(528\) 48.4071i 0.0916802i
\(529\) 75.0560 523.648i 0.141883 0.989883i
\(530\) −55.4608 −0.104643
\(531\) −101.596 −0.191330
\(532\) 6.83684 0.0128512
\(533\) −221.158 −0.414930
\(534\) 179.815i 0.336732i
\(535\) 205.927 0.384910
\(536\) 200.514i 0.374093i
\(537\) 145.605 0.271145
\(538\) 570.266 1.05997
\(539\) 341.179i 0.632986i
\(540\) 23.2379i 0.0430331i
\(541\) −746.830 −1.38046 −0.690231 0.723589i \(-0.742491\pi\)
−0.690231 + 0.723589i \(0.742491\pi\)
\(542\) −64.1048 −0.118275
\(543\) 481.476i 0.886696i
\(544\) 124.616i 0.229074i
\(545\) 100.644 0.184668
\(546\) 7.71533i 0.0141306i
\(547\) 760.793 1.39085 0.695423 0.718600i \(-0.255217\pi\)
0.695423 + 0.718600i \(0.255217\pi\)
\(548\) 6.01906i 0.0109837i
\(549\) 117.770i 0.214517i
\(550\) 49.4053i 0.0898279i
\(551\) 270.967i 0.491774i
\(552\) −85.1391 + 73.8060i −0.154238 + 0.133707i
\(553\) 14.5112 0.0262409
\(554\) 341.769 0.616912
\(555\) 88.9906 0.160343
\(556\) −248.412 −0.446783
\(557\) 619.940i 1.11300i 0.830848 + 0.556499i \(0.187856\pi\)
−0.830848 + 0.556499i \(0.812144\pi\)
\(558\) 75.2028 0.134772
\(559\) 58.0483i 0.103843i
\(560\) −3.67886 −0.00656940
\(561\) −266.593 −0.475210
\(562\) 327.635i 0.582980i
\(563\) 674.480i 1.19801i −0.800745 0.599006i \(-0.795563\pi\)
0.800745 0.599006i \(-0.204437\pi\)
\(564\) 171.450 0.303990
\(565\) 121.522 0.215084
\(566\) 247.687i 0.437610i
\(567\) 3.70178i 0.00652872i
\(568\) −75.8486 −0.133536
\(569\) 456.740i 0.802706i 0.915923 + 0.401353i \(0.131460\pi\)
−0.915923 + 0.401353i \(0.868540\pi\)
\(570\) −45.5216 −0.0798625
\(571\) 484.210i 0.848004i −0.905661 0.424002i \(-0.860625\pi\)
0.905661 0.424002i \(-0.139375\pi\)
\(572\) 107.011i 0.187082i
\(573\) 114.378i 0.199613i
\(574\) 16.7987i 0.0292660i
\(575\) −86.8948 + 75.3280i −0.151121 + 0.131005i
\(576\) 24.0000 0.0416667
\(577\) 72.0514 0.124872 0.0624362 0.998049i \(-0.480113\pi\)
0.0624362 + 0.998049i \(0.480113\pi\)
\(578\) 277.592 0.480262
\(579\) −158.318 −0.273434
\(580\) 145.806i 0.251389i
\(581\) 59.1018 0.101724
\(582\) 234.942i 0.403680i
\(583\) −122.539 −0.210187
\(584\) 175.404 0.300350
\(585\) 51.3708i 0.0878134i
\(586\) 433.777i 0.740234i
\(587\) −119.743 −0.203991 −0.101995 0.994785i \(-0.532523\pi\)
−0.101995 + 0.994785i \(0.532523\pi\)
\(588\) 169.155 0.287678
\(589\) 147.318i 0.250115i
\(590\) 107.092i 0.181511i
\(591\) 59.0396 0.0998978
\(592\) 91.9091i 0.155252i
\(593\) −648.197 −1.09308 −0.546540 0.837433i \(-0.684055\pi\)
−0.546540 + 0.837433i \(0.684055\pi\)
\(594\) 51.3435i 0.0864369i
\(595\) 20.2606i 0.0340515i
\(596\) 23.6906i 0.0397494i
\(597\) 478.526i 0.801551i
\(598\) 188.213 163.159i 0.314737 0.272841i
\(599\) 269.000 0.449082 0.224541 0.974465i \(-0.427912\pi\)
0.224541 + 0.974465i \(0.427912\pi\)
\(600\) 24.4949 0.0408248
\(601\) −339.169 −0.564340 −0.282170 0.959364i \(-0.591054\pi\)
−0.282170 + 0.959364i \(0.591054\pi\)
\(602\) −4.40923 −0.00732430
\(603\) 212.677i 0.352698i
\(604\) 270.564 0.447954
\(605\) 161.404i 0.266784i
\(606\) −355.172 −0.586093
\(607\) 372.696 0.613997 0.306998 0.951710i \(-0.400675\pi\)
0.306998 + 0.951710i \(0.400675\pi\)
\(608\) 47.0145i 0.0773265i
\(609\) 23.2268i 0.0381392i
\(610\) 124.141 0.203509
\(611\) −379.016 −0.620322
\(612\) 132.175i 0.215973i
\(613\) 125.657i 0.204987i −0.994734 0.102493i \(-0.967318\pi\)
0.994734 0.102493i \(-0.0326820\pi\)
\(614\) −150.517 −0.245141
\(615\) 111.851i 0.181871i
\(616\) −8.12835 −0.0131954
\(617\) 702.136i 1.13798i 0.822343 + 0.568992i \(0.192667\pi\)
−0.822343 + 0.568992i \(0.807333\pi\)
\(618\) 302.675i 0.489766i
\(619\) 888.543i 1.43545i 0.696327 + 0.717724i \(0.254816\pi\)
−0.696327 + 0.717724i \(0.745184\pi\)
\(620\) 79.2707i 0.127856i
\(621\) 90.3037 78.2831i 0.145417 0.126060i
\(622\) −854.418 −1.37366
\(623\) 30.1938 0.0484652
\(624\) −53.0556 −0.0850249
\(625\) 25.0000 0.0400000
\(626\) 714.541i 1.14144i
\(627\) −100.579 −0.160413
\(628\) 345.781i 0.550606i
\(629\) −506.172 −0.804725
\(630\) 3.90202 0.00619369
\(631\) 189.781i 0.300763i −0.988628 0.150381i \(-0.951950\pi\)
0.988628 0.150381i \(-0.0480501\pi\)
\(632\) 99.7884i 0.157893i
\(633\) −276.902 −0.437444
\(634\) −147.736 −0.233023
\(635\) 255.356i 0.402136i
\(636\) 60.7542i 0.0955255i
\(637\) −373.942 −0.587036
\(638\) 322.154i 0.504944i
\(639\) 80.4496 0.125899
\(640\) 25.2982i 0.0395285i
\(641\) 682.549i 1.06482i 0.846487 + 0.532410i \(0.178713\pi\)
−0.846487 + 0.532410i \(0.821287\pi\)
\(642\) 225.581i 0.351373i
\(643\) 436.832i 0.679365i 0.940540 + 0.339682i \(0.110320\pi\)
−0.940540 + 0.339682i \(0.889680\pi\)
\(644\) 12.3932 + 14.2963i 0.0192442 + 0.0221992i
\(645\) 29.3579 0.0455161
\(646\) 258.923 0.400810
\(647\) 853.291 1.31884 0.659421 0.751774i \(-0.270801\pi\)
0.659421 + 0.751774i \(0.270801\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 236.616i 0.364586i
\(650\) −54.1496 −0.0833071
\(651\) 12.6278i 0.0193975i
\(652\) −494.616 −0.758613
\(653\) −502.550 −0.769601 −0.384801 0.923000i \(-0.625730\pi\)
−0.384801 + 0.923000i \(0.625730\pi\)
\(654\) 110.250i 0.168578i
\(655\) 194.857i 0.297492i
\(656\) 115.519 0.176096
\(657\) −186.044 −0.283173
\(658\) 28.7893i 0.0437528i
\(659\) 325.726i 0.494273i −0.968981 0.247136i \(-0.920510\pi\)
0.968981 0.247136i \(-0.0794895\pi\)
\(660\) 54.1208 0.0820013
\(661\) 578.734i 0.875543i −0.899086 0.437771i \(-0.855768\pi\)
0.899086 0.437771i \(-0.144232\pi\)
\(662\) 58.4960 0.0883625
\(663\) 292.193i 0.440714i
\(664\) 406.422i 0.612081i
\(665\) 7.64382i 0.0114945i
\(666\) 97.4844i 0.146373i
\(667\) 566.609 491.186i 0.849489 0.736411i
\(668\) −436.781 −0.653863
\(669\) −46.1396 −0.0689679
\(670\) 224.181 0.334599
\(671\) 274.285 0.408771
\(672\) 4.02999i 0.00599701i
\(673\) 787.850 1.17065 0.585327 0.810798i \(-0.300966\pi\)
0.585327 + 0.810798i \(0.300966\pi\)
\(674\) 256.563i 0.380657i
\(675\) −25.9808 −0.0384900
\(676\) −220.713 −0.326498
\(677\) 1053.03i 1.55543i −0.628616 0.777716i \(-0.716378\pi\)
0.628616 0.777716i \(-0.283622\pi\)
\(678\) 133.121i 0.196344i
\(679\) −39.4506 −0.0581010
\(680\) −139.325 −0.204890
\(681\) 362.871i 0.532850i
\(682\) 175.146i 0.256813i
\(683\) −416.716 −0.610127 −0.305063 0.952332i \(-0.598678\pi\)
−0.305063 + 0.952332i \(0.598678\pi\)
\(684\) 49.8664i 0.0729041i
\(685\) 6.72951 0.00982410
\(686\) 56.9062i 0.0829536i
\(687\) 140.079i 0.203900i
\(688\) 30.3207i 0.0440708i
\(689\) 134.306i 0.194929i
\(690\) −82.5176 95.1884i −0.119591 0.137954i
\(691\) 144.765 0.209500 0.104750 0.994499i \(-0.466596\pi\)
0.104750 + 0.994499i \(0.466596\pi\)
\(692\) −344.245 −0.497463
\(693\) 8.62142 0.0124407
\(694\) −286.580 −0.412939
\(695\) 277.733i 0.399615i
\(696\) −159.722 −0.229486
\(697\) 636.197i 0.912765i
\(698\) −452.525 −0.648317
\(699\) −302.750 −0.433119
\(700\) 4.11309i 0.00587585i
\(701\) 723.630i 1.03228i 0.856503 + 0.516142i \(0.172632\pi\)
−0.856503 + 0.516142i \(0.827368\pi\)
\(702\) 56.2739 0.0801623
\(703\) −190.966 −0.271644
\(704\) 55.8958i 0.0793974i
\(705\) 191.687i 0.271897i
\(706\) 435.814 0.617300
\(707\) 59.6392i 0.0843553i
\(708\) −117.313 −0.165696
\(709\) 4.77044i 0.00672841i −0.999994 0.00336420i \(-0.998929\pi\)
0.999994 0.00336420i \(-0.00107086\pi\)
\(710\) 84.8013i 0.119438i
\(711\) 105.842i 0.148863i
\(712\) 207.632i 0.291618i
\(713\) −308.050 + 267.044i −0.432048 + 0.374536i
\(714\) −22.1944 −0.0310846
\(715\) −119.642 −0.167332
\(716\) 168.130 0.234819
\(717\) 172.010 0.239903
\(718\) 426.570i 0.594108i
\(719\) −163.295 −0.227115 −0.113557 0.993531i \(-0.536225\pi\)
−0.113557 + 0.993531i \(0.536225\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 50.8241 0.0704911
\(722\) −412.846 −0.571809
\(723\) 76.0554i 0.105194i
\(724\) 555.960i 0.767901i
\(725\) −163.016 −0.224849
\(726\) −176.810 −0.243540
\(727\) 1100.34i 1.51354i 0.653683 + 0.756769i \(0.273223\pi\)
−0.653683 + 0.756769i \(0.726777\pi\)
\(728\) 8.90890i 0.0122375i
\(729\) 27.0000 0.0370370
\(730\) 196.108i 0.268641i
\(731\) −166.985 −0.228434
\(732\) 135.989i 0.185777i
\(733\) 362.979i 0.495197i 0.968863 + 0.247599i \(0.0796414\pi\)
−0.968863 + 0.247599i \(0.920359\pi\)
\(734\) 665.321i 0.906432i
\(735\) 189.121i 0.257307i
\(736\) −98.3102 + 85.2238i −0.133574 + 0.115793i
\(737\) 495.323 0.672080
\(738\) −122.526 −0.166025
\(739\) −475.365 −0.643254 −0.321627 0.946866i \(-0.604230\pi\)
−0.321627 + 0.946866i \(0.604230\pi\)
\(740\) 102.758 0.138862
\(741\) 110.237i 0.148768i
\(742\) −10.2016 −0.0137488
\(743\) 691.352i 0.930487i −0.885183 0.465244i \(-0.845967\pi\)
0.885183 0.465244i \(-0.154033\pi\)
\(744\) 86.8367 0.116716
\(745\) −26.4869 −0.0355529
\(746\) 352.289i 0.472237i
\(747\) 431.076i 0.577076i
\(748\) −307.835 −0.411544
\(749\) 37.8788 0.0505725
\(750\) 27.3861i 0.0365148i
\(751\) 971.631i 1.29378i −0.762582 0.646892i \(-0.776069\pi\)
0.762582 0.646892i \(-0.223931\pi\)
\(752\) 197.974 0.263263
\(753\) 726.201i 0.964411i
\(754\) 353.090 0.468289
\(755\) 302.500i 0.400662i
\(756\) 4.27445i 0.00565404i
\(757\) 983.792i 1.29959i 0.760108 + 0.649797i \(0.225146\pi\)
−0.760108 + 0.649797i \(0.774854\pi\)
\(758\) 200.394i 0.264373i
\(759\) −182.321 210.316i −0.240212 0.277097i
\(760\) −52.5638 −0.0691629
\(761\) −73.1433 −0.0961147 −0.0480574 0.998845i \(-0.515303\pi\)
−0.0480574 + 0.998845i \(0.515303\pi\)
\(762\) −279.729 −0.367098
\(763\) 18.5127 0.0242631
\(764\) 132.073i 0.172870i
\(765\) 147.777 0.193172
\(766\) 156.243i 0.203972i
\(767\) 259.338 0.338119
\(768\) 27.7128 0.0360844
\(769\) 687.166i 0.893584i −0.894638 0.446792i \(-0.852566\pi\)
0.894638 0.446792i \(-0.147434\pi\)
\(770\) 9.08777i 0.0118023i
\(771\) −359.304 −0.466023
\(772\) −182.810 −0.236801
\(773\) 56.9245i 0.0736411i 0.999322 + 0.0368205i \(0.0117230\pi\)
−0.999322 + 0.0368205i \(0.988277\pi\)
\(774\) 32.1599i 0.0415503i
\(775\) 88.6273 0.114358
\(776\) 271.288i 0.349597i
\(777\) 16.3692 0.0210672
\(778\) 997.653i 1.28233i
\(779\) 240.021i 0.308114i
\(780\) 59.3179i 0.0760486i
\(781\) 187.366i 0.239906i
\(782\) 469.354 + 541.424i 0.600197 + 0.692359i
\(783\) 169.411 0.216361
\(784\) 195.323 0.249137
\(785\) 386.595 0.492477
\(786\) −213.456 −0.271572
\(787\) 339.738i 0.431688i −0.976428 0.215844i \(-0.930750\pi\)
0.976428 0.215844i \(-0.0692502\pi\)
\(788\) 68.1730 0.0865140
\(789\) 593.298i 0.751961i
\(790\) −111.567 −0.141224
\(791\) 22.3532 0.0282594
\(792\)