Properties

Label 690.3.c.a.91.15
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 91.15
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +1.73205 q^{3} +2.00000 q^{4} +2.23607i q^{5} -2.44949 q^{6} +3.49916i q^{7} -2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +1.73205 q^{3} +2.00000 q^{4} +2.23607i q^{5} -2.44949 q^{6} +3.49916i q^{7} -2.82843 q^{8} +3.00000 q^{9} -3.16228i q^{10} -11.9699i q^{11} +3.46410 q^{12} -19.9639 q^{13} -4.94856i q^{14} +3.87298i q^{15} +4.00000 q^{16} +26.2299i q^{17} -4.24264 q^{18} -0.0297478i q^{19} +4.47214i q^{20} +6.06072i q^{21} +16.9280i q^{22} +(-9.54233 + 20.9271i) q^{23} -4.89898 q^{24} -5.00000 q^{25} +28.2332 q^{26} +5.19615 q^{27} +6.99832i q^{28} -41.0391 q^{29} -5.47723i q^{30} +29.7926 q^{31} -5.65685 q^{32} -20.7325i q^{33} -37.0947i q^{34} -7.82436 q^{35} +6.00000 q^{36} -51.3489i q^{37} +0.0420698i q^{38} -34.5785 q^{39} -6.32456i q^{40} -74.6506 q^{41} -8.57115i q^{42} +51.7973i q^{43} -23.9398i q^{44} +6.70820i q^{45} +(13.4949 - 29.5954i) q^{46} -27.5439 q^{47} +6.92820 q^{48} +36.7559 q^{49} +7.07107 q^{50} +45.4315i q^{51} -39.9278 q^{52} +15.0332i q^{53} -7.34847 q^{54} +26.7655 q^{55} -9.89712i q^{56} -0.0515248i q^{57} +58.0381 q^{58} +1.55359 q^{59} +7.74597i q^{60} +12.9254i q^{61} -42.1330 q^{62} +10.4975i q^{63} +8.00000 q^{64} -44.6406i q^{65} +29.3201i q^{66} -28.2878i q^{67} +52.4598i q^{68} +(-16.5278 + 36.2468i) q^{69} +11.0653 q^{70} -94.7727 q^{71} -8.48528 q^{72} -25.3868 q^{73} +72.6184i q^{74} -8.66025 q^{75} -0.0594957i q^{76} +41.8845 q^{77} +48.9013 q^{78} +80.5613i q^{79} +8.94427i q^{80} +9.00000 q^{81} +105.572 q^{82} -55.8397i q^{83} +12.1214i q^{84} -58.6518 q^{85} -73.2525i q^{86} -71.0818 q^{87} +33.8559i q^{88} +81.9490i q^{89} -9.48683i q^{90} -69.8568i q^{91} +(-19.0847 + 41.8542i) q^{92} +51.6022 q^{93} +38.9530 q^{94} +0.0665182 q^{95} -9.79796 q^{96} -4.03039i q^{97} -51.9807 q^{98} -35.9097i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

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
\(7\) 3.49916i 0.499880i 0.968261 + 0.249940i \(0.0804109\pi\)
−0.968261 + 0.249940i \(0.919589\pi\)
\(8\) −2.82843 −0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 11.9699i 1.08817i −0.839030 0.544086i \(-0.816877\pi\)
0.839030 0.544086i \(-0.183123\pi\)
\(12\) 3.46410 0.288675
\(13\) −19.9639 −1.53568 −0.767842 0.640640i \(-0.778669\pi\)
−0.767842 + 0.640640i \(0.778669\pi\)
\(14\) 4.94856i 0.353468i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 26.2299i 1.54293i 0.636269 + 0.771467i \(0.280477\pi\)
−0.636269 + 0.771467i \(0.719523\pi\)
\(18\) −4.24264 −0.235702
\(19\) 0.0297478i 0.00156568i −1.00000 0.000782838i \(-0.999751\pi\)
1.00000 0.000782838i \(-0.000249185\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 6.06072i 0.288606i
\(22\) 16.9280i 0.769453i
\(23\) −9.54233 + 20.9271i −0.414884 + 0.909874i
\(24\) −4.89898 −0.204124
\(25\) −5.00000 −0.200000
\(26\) 28.2332 1.08589
\(27\) 5.19615 0.192450
\(28\) 6.99832i 0.249940i
\(29\) −41.0391 −1.41514 −0.707571 0.706642i \(-0.750209\pi\)
−0.707571 + 0.706642i \(0.750209\pi\)
\(30\) 5.47723i 0.182574i
\(31\) 29.7926 0.961050 0.480525 0.876981i \(-0.340446\pi\)
0.480525 + 0.876981i \(0.340446\pi\)
\(32\) −5.65685 −0.176777
\(33\) 20.7325i 0.628256i
\(34\) 37.0947i 1.09102i
\(35\) −7.82436 −0.223553
\(36\) 6.00000 0.166667
\(37\) 51.3489i 1.38781i −0.720067 0.693905i \(-0.755889\pi\)
0.720067 0.693905i \(-0.244111\pi\)
\(38\) 0.0420698i 0.00110710i
\(39\) −34.5785 −0.886627
\(40\) 6.32456i 0.158114i
\(41\) −74.6506 −1.82075 −0.910373 0.413789i \(-0.864205\pi\)
−0.910373 + 0.413789i \(0.864205\pi\)
\(42\) 8.57115i 0.204075i
\(43\) 51.7973i 1.20459i 0.798274 + 0.602294i \(0.205747\pi\)
−0.798274 + 0.602294i \(0.794253\pi\)
\(44\) 23.9398i 0.544086i
\(45\) 6.70820i 0.149071i
\(46\) 13.4949 29.5954i 0.293367 0.643378i
\(47\) −27.5439 −0.586040 −0.293020 0.956106i \(-0.594660\pi\)
−0.293020 + 0.956106i \(0.594660\pi\)
\(48\) 6.92820 0.144338
\(49\) 36.7559 0.750120
\(50\) 7.07107 0.141421
\(51\) 45.4315i 0.890814i
\(52\) −39.9278 −0.767842
\(53\) 15.0332i 0.283645i 0.989892 + 0.141823i \(0.0452963\pi\)
−0.989892 + 0.141823i \(0.954704\pi\)
\(54\) −7.34847 −0.136083
\(55\) 26.7655 0.486645
\(56\) 9.89712i 0.176734i
\(57\) 0.0515248i 0.000903943i
\(58\) 58.0381 1.00066
\(59\) 1.55359 0.0263320 0.0131660 0.999913i \(-0.495809\pi\)
0.0131660 + 0.999913i \(0.495809\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 12.9254i 0.211892i 0.994372 + 0.105946i \(0.0337871\pi\)
−0.994372 + 0.105946i \(0.966213\pi\)
\(62\) −42.1330 −0.679565
\(63\) 10.4975i 0.166627i
\(64\) 8.00000 0.125000
\(65\) 44.6406i 0.686778i
\(66\) 29.3201i 0.444244i
\(67\) 28.2878i 0.422206i −0.977464 0.211103i \(-0.932294\pi\)
0.977464 0.211103i \(-0.0677055\pi\)
\(68\) 52.4598i 0.771467i
\(69\) −16.5278 + 36.2468i −0.239533 + 0.525316i
\(70\) 11.0653 0.158076
\(71\) −94.7727 −1.33483 −0.667413 0.744688i \(-0.732599\pi\)
−0.667413 + 0.744688i \(0.732599\pi\)
\(72\) −8.48528 −0.117851
\(73\) −25.3868 −0.347764 −0.173882 0.984766i \(-0.555631\pi\)
−0.173882 + 0.984766i \(0.555631\pi\)
\(74\) 72.6184i 0.981329i
\(75\) −8.66025 −0.115470
\(76\) 0.0594957i 0.000782838i
\(77\) 41.8845 0.543955
\(78\) 48.9013 0.626940
\(79\) 80.5613i 1.01976i 0.860245 + 0.509882i \(0.170311\pi\)
−0.860245 + 0.509882i \(0.829689\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) 105.572 1.28746
\(83\) 55.8397i 0.672767i −0.941725 0.336384i \(-0.890796\pi\)
0.941725 0.336384i \(-0.109204\pi\)
\(84\) 12.1214i 0.144303i
\(85\) −58.6518 −0.690021
\(86\) 73.2525i 0.851773i
\(87\) −71.0818 −0.817032
\(88\) 33.8559i 0.384727i
\(89\) 81.9490i 0.920775i 0.887718 + 0.460387i \(0.152290\pi\)
−0.887718 + 0.460387i \(0.847710\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 69.8568i 0.767657i
\(92\) −19.0847 + 41.8542i −0.207442 + 0.454937i
\(93\) 51.6022 0.554863
\(94\) 38.9530 0.414393
\(95\) 0.0665182 0.000700191
\(96\) −9.79796 −0.102062
\(97\) 4.03039i 0.0415504i −0.999784 0.0207752i \(-0.993387\pi\)
0.999784 0.0207752i \(-0.00661343\pi\)
\(98\) −51.9807 −0.530415
\(99\) 35.9097i 0.362724i
\(100\) −10.0000 −0.100000
\(101\) −162.974 −1.61360 −0.806801 0.590823i \(-0.798803\pi\)
−0.806801 + 0.590823i \(0.798803\pi\)
\(102\) 64.2498i 0.629900i
\(103\) 137.541i 1.33535i 0.744453 + 0.667675i \(0.232711\pi\)
−0.744453 + 0.667675i \(0.767289\pi\)
\(104\) 56.4664 0.542946
\(105\) −13.5522 −0.129068
\(106\) 21.2602i 0.200567i
\(107\) 66.5945i 0.622379i −0.950348 0.311189i \(-0.899273\pi\)
0.950348 0.311189i \(-0.100727\pi\)
\(108\) 10.3923 0.0962250
\(109\) 95.0049i 0.871605i −0.900042 0.435802i \(-0.856465\pi\)
0.900042 0.435802i \(-0.143535\pi\)
\(110\) −37.8521 −0.344110
\(111\) 88.9390i 0.801252i
\(112\) 13.9966i 0.124970i
\(113\) 194.493i 1.72118i 0.509300 + 0.860589i \(0.329904\pi\)
−0.509300 + 0.860589i \(0.670096\pi\)
\(114\) 0.0728670i 0.000639184i
\(115\) −46.7944 21.3373i −0.406908 0.185542i
\(116\) −82.0782 −0.707571
\(117\) −59.8916 −0.511894
\(118\) −2.19711 −0.0186195
\(119\) −91.7825 −0.771282
\(120\) 10.9545i 0.0912871i
\(121\) −22.2782 −0.184117
\(122\) 18.2793i 0.149830i
\(123\) −129.299 −1.05121
\(124\) 59.5851 0.480525
\(125\) 11.1803i 0.0894427i
\(126\) 14.8457i 0.117823i
\(127\) −139.254 −1.09649 −0.548244 0.836318i \(-0.684704\pi\)
−0.548244 + 0.836318i \(0.684704\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 89.7156i 0.695470i
\(130\) 63.1313i 0.485626i
\(131\) 87.8593 0.670682 0.335341 0.942097i \(-0.391149\pi\)
0.335341 + 0.942097i \(0.391149\pi\)
\(132\) 41.4649i 0.314128i
\(133\) 0.104092 0.000782650
\(134\) 40.0050i 0.298545i
\(135\) 11.6190i 0.0860663i
\(136\) 74.1893i 0.545510i
\(137\) 181.394i 1.32405i 0.749484 + 0.662023i \(0.230302\pi\)
−0.749484 + 0.662023i \(0.769698\pi\)
\(138\) 23.3738 51.2607i 0.169376 0.371455i
\(139\) −135.089 −0.971860 −0.485930 0.873998i \(-0.661519\pi\)
−0.485930 + 0.873998i \(0.661519\pi\)
\(140\) −15.6487 −0.111777
\(141\) −47.7074 −0.338351
\(142\) 134.029 0.943865
\(143\) 238.965i 1.67109i
\(144\) 12.0000 0.0833333
\(145\) 91.7662i 0.632871i
\(146\) 35.9023 0.245906
\(147\) 63.6631 0.433082
\(148\) 102.698i 0.693905i
\(149\) 56.7676i 0.380991i −0.981688 0.190495i \(-0.938991\pi\)
0.981688 0.190495i \(-0.0610094\pi\)
\(150\) 12.2474 0.0816497
\(151\) 36.4693 0.241519 0.120759 0.992682i \(-0.461467\pi\)
0.120759 + 0.992682i \(0.461467\pi\)
\(152\) 0.0841396i 0.000553550i
\(153\) 78.6897i 0.514312i
\(154\) −59.2337 −0.384634
\(155\) 66.6182i 0.429795i
\(156\) −69.1569 −0.443314
\(157\) 47.7035i 0.303844i −0.988392 0.151922i \(-0.951454\pi\)
0.988392 0.151922i \(-0.0485463\pi\)
\(158\) 113.931i 0.721081i
\(159\) 26.0383i 0.163763i
\(160\) 12.6491i 0.0790569i
\(161\) −73.2273 33.3901i −0.454828 0.207392i
\(162\) −12.7279 −0.0785674
\(163\) 118.851 0.729148 0.364574 0.931174i \(-0.381215\pi\)
0.364574 + 0.931174i \(0.381215\pi\)
\(164\) −149.301 −0.910373
\(165\) 46.3592 0.280965
\(166\) 78.9692i 0.475718i
\(167\) −108.318 −0.648610 −0.324305 0.945952i \(-0.605130\pi\)
−0.324305 + 0.945952i \(0.605130\pi\)
\(168\) 17.1423i 0.102038i
\(169\) 229.557 1.35832
\(170\) 82.9462 0.487919
\(171\) 0.0892435i 0.000521892i
\(172\) 103.595i 0.602294i
\(173\) 78.7417 0.455154 0.227577 0.973760i \(-0.426920\pi\)
0.227577 + 0.973760i \(0.426920\pi\)
\(174\) 100.525 0.577729
\(175\) 17.4958i 0.0999760i
\(176\) 47.8795i 0.272043i
\(177\) 2.69089 0.0152028
\(178\) 115.893i 0.651086i
\(179\) 225.677 1.26077 0.630383 0.776285i \(-0.282898\pi\)
0.630383 + 0.776285i \(0.282898\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 219.280i 1.21149i −0.795659 0.605745i \(-0.792875\pi\)
0.795659 0.605745i \(-0.207125\pi\)
\(182\) 98.7924i 0.542816i
\(183\) 22.3875i 0.122336i
\(184\) 26.9898 59.1908i 0.146684 0.321689i
\(185\) 114.820 0.620647
\(186\) −72.9766 −0.392347
\(187\) 313.969 1.67898
\(188\) −55.0878 −0.293020
\(189\) 18.1822i 0.0962019i
\(190\) −0.0940709 −0.000495110
\(191\) 240.006i 1.25658i −0.777981 0.628288i \(-0.783756\pi\)
0.777981 0.628288i \(-0.216244\pi\)
\(192\) 13.8564 0.0721688
\(193\) 368.019 1.90683 0.953417 0.301654i \(-0.0975388\pi\)
0.953417 + 0.301654i \(0.0975388\pi\)
\(194\) 5.69984i 0.0293806i
\(195\) 77.3198i 0.396512i
\(196\) 73.5118 0.375060
\(197\) −1.84737 −0.00937754 −0.00468877 0.999989i \(-0.501492\pi\)
−0.00468877 + 0.999989i \(0.501492\pi\)
\(198\) 50.7839i 0.256484i
\(199\) 56.5030i 0.283934i 0.989871 + 0.141967i \(0.0453428\pi\)
−0.989871 + 0.141967i \(0.954657\pi\)
\(200\) 14.1421 0.0707107
\(201\) 48.9959i 0.243761i
\(202\) 230.480 1.14099
\(203\) 143.602i 0.707401i
\(204\) 90.8630i 0.445407i
\(205\) 166.924i 0.814262i
\(206\) 194.513i 0.944236i
\(207\) −28.6270 + 62.7813i −0.138295 + 0.303291i
\(208\) −79.8555 −0.383921
\(209\) −0.356078 −0.00170372
\(210\) 19.1657 0.0912652
\(211\) −88.2861 −0.418418 −0.209209 0.977871i \(-0.567089\pi\)
−0.209209 + 0.977871i \(0.567089\pi\)
\(212\) 30.0664i 0.141823i
\(213\) −164.151 −0.770662
\(214\) 94.1788i 0.440088i
\(215\) −115.822 −0.538708
\(216\) −14.6969 −0.0680414
\(217\) 104.249i 0.480410i
\(218\) 134.357i 0.616317i
\(219\) −43.9712 −0.200782
\(220\) 53.5310 0.243323
\(221\) 523.650i 2.36946i
\(222\) 125.779i 0.566571i
\(223\) 129.548 0.580934 0.290467 0.956885i \(-0.406189\pi\)
0.290467 + 0.956885i \(0.406189\pi\)
\(224\) 19.7942i 0.0883671i
\(225\) −15.0000 −0.0666667
\(226\) 275.055i 1.21706i
\(227\) 76.1848i 0.335616i 0.985820 + 0.167808i \(0.0536688\pi\)
−0.985820 + 0.167808i \(0.946331\pi\)
\(228\) 0.103050i 0.000451972i
\(229\) 81.3519i 0.355248i 0.984098 + 0.177624i \(0.0568411\pi\)
−0.984098 + 0.177624i \(0.943159\pi\)
\(230\) 66.1773 + 30.1755i 0.287728 + 0.131198i
\(231\) 72.5461 0.314053
\(232\) 116.076 0.500328
\(233\) 229.590 0.985366 0.492683 0.870209i \(-0.336016\pi\)
0.492683 + 0.870209i \(0.336016\pi\)
\(234\) 84.6996 0.361964
\(235\) 61.5900i 0.262085i
\(236\) 3.10718 0.0131660
\(237\) 139.536i 0.588761i
\(238\) 129.800 0.545379
\(239\) −156.740 −0.655818 −0.327909 0.944709i \(-0.606344\pi\)
−0.327909 + 0.944709i \(0.606344\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 191.086i 0.792887i −0.918059 0.396444i \(-0.870244\pi\)
0.918059 0.396444i \(-0.129756\pi\)
\(242\) 31.5061 0.130190
\(243\) 15.5885 0.0641500
\(244\) 25.8508i 0.105946i
\(245\) 82.1887i 0.335464i
\(246\) 182.856 0.743316
\(247\) 0.593882i 0.00240438i
\(248\) −84.2661 −0.339783
\(249\) 96.7172i 0.388422i
\(250\) 15.8114i 0.0632456i
\(251\) 456.878i 1.82023i 0.414354 + 0.910116i \(0.364008\pi\)
−0.414354 + 0.910116i \(0.635992\pi\)
\(252\) 20.9950i 0.0833133i
\(253\) 250.495 + 114.221i 0.990099 + 0.451465i
\(254\) 196.935 0.775335
\(255\) −101.588 −0.398384
\(256\) 16.0000 0.0625000
\(257\) 212.501 0.826851 0.413425 0.910538i \(-0.364332\pi\)
0.413425 + 0.910538i \(0.364332\pi\)
\(258\) 126.877i 0.491771i
\(259\) 179.678 0.693738
\(260\) 89.2812i 0.343389i
\(261\) −123.117 −0.471714
\(262\) −124.252 −0.474243
\(263\) 478.231i 1.81837i −0.416392 0.909185i \(-0.636706\pi\)
0.416392 0.909185i \(-0.363294\pi\)
\(264\) 58.6402i 0.222122i
\(265\) −33.6153 −0.126850
\(266\) −0.147209 −0.000553417
\(267\) 141.940i 0.531610i
\(268\) 56.5756i 0.211103i
\(269\) 525.346 1.95296 0.976479 0.215613i \(-0.0691750\pi\)
0.976479 + 0.215613i \(0.0691750\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) 374.732 1.38278 0.691388 0.722484i \(-0.257000\pi\)
0.691388 + 0.722484i \(0.257000\pi\)
\(272\) 104.920i 0.385734i
\(273\) 120.996i 0.443207i
\(274\) 256.530i 0.936241i
\(275\) 59.8494i 0.217634i
\(276\) −33.0556 + 72.4936i −0.119767 + 0.262658i
\(277\) −406.934 −1.46907 −0.734537 0.678569i \(-0.762601\pi\)
−0.734537 + 0.678569i \(0.762601\pi\)
\(278\) 191.044 0.687209
\(279\) 89.3777 0.320350
\(280\) 22.1306 0.0790379
\(281\) 189.257i 0.673511i −0.941592 0.336755i \(-0.890670\pi\)
0.941592 0.336755i \(-0.109330\pi\)
\(282\) 67.4685 0.239250
\(283\) 157.312i 0.555872i 0.960600 + 0.277936i \(0.0896503\pi\)
−0.960600 + 0.277936i \(0.910350\pi\)
\(284\) −189.545 −0.667413
\(285\) 0.115213 0.000404256
\(286\) 337.948i 1.18164i
\(287\) 261.214i 0.910154i
\(288\) −16.9706 −0.0589256
\(289\) −399.007 −1.38065
\(290\) 129.777i 0.447507i
\(291\) 6.98085i 0.0239892i
\(292\) −50.7736 −0.173882
\(293\) 463.682i 1.58253i 0.611472 + 0.791266i \(0.290578\pi\)
−0.611472 + 0.791266i \(0.709422\pi\)
\(294\) −90.0332 −0.306235
\(295\) 3.47393i 0.0117760i
\(296\) 145.237i 0.490665i
\(297\) 62.1974i 0.209419i
\(298\) 80.2815i 0.269401i
\(299\) 190.502 417.786i 0.637130 1.39728i
\(300\) −17.3205 −0.0577350
\(301\) −181.247 −0.602150
\(302\) −51.5754 −0.170780
\(303\) −282.279 −0.931614
\(304\) 0.118991i 0.000391419i
\(305\) −28.9021 −0.0947609
\(306\) 111.284i 0.363673i
\(307\) 350.361 1.14124 0.570620 0.821214i \(-0.306703\pi\)
0.570620 + 0.821214i \(0.306703\pi\)
\(308\) 83.7691 0.271977
\(309\) 238.228i 0.770965i
\(310\) 94.2123i 0.303911i
\(311\) 152.396 0.490018 0.245009 0.969521i \(-0.421209\pi\)
0.245009 + 0.969521i \(0.421209\pi\)
\(312\) 97.8027 0.313470
\(313\) 47.6313i 0.152177i −0.997101 0.0760884i \(-0.975757\pi\)
0.997101 0.0760884i \(-0.0242431\pi\)
\(314\) 67.4629i 0.214850i
\(315\) −23.4731 −0.0745177
\(316\) 161.123i 0.509882i
\(317\) 410.929 1.29631 0.648153 0.761511i \(-0.275542\pi\)
0.648153 + 0.761511i \(0.275542\pi\)
\(318\) 36.8237i 0.115798i
\(319\) 491.233i 1.53992i
\(320\) 17.8885i 0.0559017i
\(321\) 115.345i 0.359330i
\(322\) 103.559 + 47.2208i 0.321612 + 0.146648i
\(323\) 0.780282 0.00241573
\(324\) 18.0000 0.0555556
\(325\) 99.8194 0.307137
\(326\) −168.081 −0.515585
\(327\) 164.553i 0.503221i
\(328\) 211.144 0.643731
\(329\) 96.3805i 0.292950i
\(330\) −65.5618 −0.198672
\(331\) −392.356 −1.18537 −0.592683 0.805436i \(-0.701931\pi\)
−0.592683 + 0.805436i \(0.701931\pi\)
\(332\) 111.679i 0.336384i
\(333\) 154.047i 0.462603i
\(334\) 153.185 0.458637
\(335\) 63.2534 0.188816
\(336\) 24.2429i 0.0721514i
\(337\) 458.368i 1.36014i 0.733146 + 0.680071i \(0.238051\pi\)
−0.733146 + 0.680071i \(0.761949\pi\)
\(338\) −324.642 −0.960480
\(339\) 336.872i 0.993722i
\(340\) −117.304 −0.345011
\(341\) 356.614i 1.04579i
\(342\) 0.126209i 0.000369033i
\(343\) 300.073i 0.874850i
\(344\) 146.505i 0.425886i
\(345\) −81.0503 36.9573i −0.234929 0.107123i
\(346\) −111.358 −0.321843
\(347\) −178.744 −0.515112 −0.257556 0.966263i \(-0.582917\pi\)
−0.257556 + 0.966263i \(0.582917\pi\)
\(348\) −142.164 −0.408516
\(349\) −24.0318 −0.0688591 −0.0344295 0.999407i \(-0.510961\pi\)
−0.0344295 + 0.999407i \(0.510961\pi\)
\(350\) 24.7428i 0.0706937i
\(351\) −103.735 −0.295542
\(352\) 67.7119i 0.192363i
\(353\) −568.260 −1.60980 −0.804901 0.593409i \(-0.797782\pi\)
−0.804901 + 0.593409i \(0.797782\pi\)
\(354\) −3.80550 −0.0107500
\(355\) 211.918i 0.596953i
\(356\) 163.898i 0.460387i
\(357\) −158.972 −0.445300
\(358\) −319.155 −0.891496
\(359\) 540.074i 1.50438i 0.658945 + 0.752192i \(0.271003\pi\)
−0.658945 + 0.752192i \(0.728997\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 360.999 0.999998
\(362\) 310.108i 0.856653i
\(363\) −38.5869 −0.106300
\(364\) 139.714i 0.383829i
\(365\) 56.7666i 0.155525i
\(366\) 31.6607i 0.0865045i
\(367\) 404.550i 1.10232i −0.834401 0.551158i \(-0.814186\pi\)
0.834401 0.551158i \(-0.185814\pi\)
\(368\) −38.1693 + 83.7084i −0.103721 + 0.227469i
\(369\) −223.952 −0.606915
\(370\) −162.380 −0.438864
\(371\) −52.6035 −0.141789
\(372\) 103.204 0.277431
\(373\) 192.435i 0.515911i −0.966157 0.257955i \(-0.916951\pi\)
0.966157 0.257955i \(-0.0830487\pi\)
\(374\) −444.019 −1.18722
\(375\) 19.3649i 0.0516398i
\(376\) 77.9059 0.207197
\(377\) 819.300 2.17321
\(378\) 25.7135i 0.0680250i
\(379\) 711.208i 1.87654i −0.345908 0.938269i \(-0.612429\pi\)
0.345908 0.938269i \(-0.387571\pi\)
\(380\) 0.133036 0.000350096
\(381\) −241.195 −0.633058
\(382\) 339.420i 0.888533i
\(383\) 308.566i 0.805655i 0.915276 + 0.402827i \(0.131973\pi\)
−0.915276 + 0.402827i \(0.868027\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 93.6567i 0.243264i
\(386\) −520.458 −1.34834
\(387\) 155.392i 0.401530i
\(388\) 8.06079i 0.0207752i
\(389\) 197.980i 0.508947i 0.967080 + 0.254474i \(0.0819022\pi\)
−0.967080 + 0.254474i \(0.918098\pi\)
\(390\) 109.347i 0.280376i
\(391\) −548.916 250.294i −1.40388 0.640139i
\(392\) −103.961 −0.265208
\(393\) 152.177 0.387218
\(394\) 2.61258 0.00663092
\(395\) −180.141 −0.456052
\(396\) 71.8193i 0.181362i
\(397\) 267.667 0.674224 0.337112 0.941465i \(-0.390550\pi\)
0.337112 + 0.941465i \(0.390550\pi\)
\(398\) 79.9073i 0.200772i
\(399\) 0.180293 0.000451863
\(400\) −20.0000 −0.0500000
\(401\) 749.856i 1.86997i −0.354694 0.934983i \(-0.615415\pi\)
0.354694 0.934983i \(-0.384585\pi\)
\(402\) 69.2906i 0.172365i
\(403\) −594.775 −1.47587
\(404\) −325.948 −0.806801
\(405\) 20.1246i 0.0496904i
\(406\) 203.084i 0.500208i
\(407\) −614.641 −1.51017
\(408\) 128.500i 0.314950i
\(409\) 291.243 0.712086 0.356043 0.934469i \(-0.384126\pi\)
0.356043 + 0.934469i \(0.384126\pi\)
\(410\) 236.066i 0.575770i
\(411\) 314.184i 0.764438i
\(412\) 275.082i 0.667675i
\(413\) 5.43625i 0.0131628i
\(414\) 40.4847 88.7862i 0.0977891 0.214459i
\(415\) 124.861 0.300871
\(416\) 112.933 0.271473
\(417\) −233.980 −0.561104
\(418\) 0.503571 0.00120471
\(419\) 334.184i 0.797574i 0.917044 + 0.398787i \(0.130569\pi\)
−0.917044 + 0.398787i \(0.869431\pi\)
\(420\) −27.1044 −0.0645342
\(421\) 414.441i 0.984422i 0.870476 + 0.492211i \(0.163811\pi\)
−0.870476 + 0.492211i \(0.836189\pi\)
\(422\) 124.855 0.295866
\(423\) −82.6317 −0.195347
\(424\) 42.5203i 0.100284i
\(425\) 131.149i 0.308587i
\(426\) 232.145 0.544941
\(427\) −45.2280 −0.105920
\(428\) 133.189i 0.311189i
\(429\) 413.900i 0.964802i
\(430\) 163.797 0.380924
\(431\) 721.242i 1.67342i −0.547649 0.836708i \(-0.684477\pi\)
0.547649 0.836708i \(-0.315523\pi\)
\(432\) 20.7846 0.0481125
\(433\) 231.360i 0.534319i −0.963652 0.267160i \(-0.913915\pi\)
0.963652 0.267160i \(-0.0860851\pi\)
\(434\) 147.430i 0.339701i
\(435\) 158.944i 0.365388i
\(436\) 190.010i 0.435802i
\(437\) 0.622536 + 0.283864i 0.00142457 + 0.000649574i
\(438\) 62.1847 0.141974
\(439\) 110.160 0.250935 0.125468 0.992098i \(-0.459957\pi\)
0.125468 + 0.992098i \(0.459957\pi\)
\(440\) −75.7042 −0.172055
\(441\) 110.268 0.250040
\(442\) 740.553i 1.67546i
\(443\) 140.713 0.317636 0.158818 0.987308i \(-0.449232\pi\)
0.158818 + 0.987308i \(0.449232\pi\)
\(444\) 177.878i 0.400626i
\(445\) −183.243 −0.411783
\(446\) −183.209 −0.410782
\(447\) 98.3244i 0.219965i
\(448\) 27.9933i 0.0624850i
\(449\) 222.010 0.494455 0.247227 0.968958i \(-0.420481\pi\)
0.247227 + 0.968958i \(0.420481\pi\)
\(450\) 21.2132 0.0471405
\(451\) 893.559i 1.98128i
\(452\) 388.986i 0.860589i
\(453\) 63.1668 0.139441
\(454\) 107.742i 0.237316i
\(455\) 156.205 0.343307
\(456\) 0.145734i 0.000319592i
\(457\) 448.070i 0.980460i 0.871593 + 0.490230i \(0.163087\pi\)
−0.871593 + 0.490230i \(0.836913\pi\)
\(458\) 115.049i 0.251199i
\(459\) 136.294i 0.296938i
\(460\) −93.5889 42.6746i −0.203454 0.0927709i
\(461\) 819.214 1.77704 0.888519 0.458841i \(-0.151735\pi\)
0.888519 + 0.458841i \(0.151735\pi\)
\(462\) −102.596 −0.222069
\(463\) −793.838 −1.71455 −0.857276 0.514857i \(-0.827845\pi\)
−0.857276 + 0.514857i \(0.827845\pi\)
\(464\) −164.156 −0.353785
\(465\) 115.386i 0.248142i
\(466\) −324.690 −0.696759
\(467\) 335.892i 0.719254i 0.933096 + 0.359627i \(0.117096\pi\)
−0.933096 + 0.359627i \(0.882904\pi\)
\(468\) −119.783 −0.255947
\(469\) 98.9835 0.211052
\(470\) 87.1015i 0.185322i
\(471\) 82.6249i 0.175424i
\(472\) −4.39421 −0.00930977
\(473\) 620.008 1.31080
\(474\) 197.334i 0.416317i
\(475\) 0.148739i 0.000313135i
\(476\) −183.565 −0.385641
\(477\) 45.0996i 0.0945484i
\(478\) 221.664 0.463733
\(479\) 578.078i 1.20684i 0.797422 + 0.603422i \(0.206196\pi\)
−0.797422 + 0.603422i \(0.793804\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 1025.12i 2.13124i
\(482\) 270.236i 0.560656i
\(483\) −126.833 57.8334i −0.262595 0.119738i
\(484\) −44.5563 −0.0920585
\(485\) 9.01223 0.0185819
\(486\) −22.0454 −0.0453609
\(487\) −921.262 −1.89171 −0.945854 0.324591i \(-0.894773\pi\)
−0.945854 + 0.324591i \(0.894773\pi\)
\(488\) 36.5586i 0.0749151i
\(489\) 205.856 0.420974
\(490\) 116.232i 0.237209i
\(491\) −830.923 −1.69231 −0.846153 0.532940i \(-0.821087\pi\)
−0.846153 + 0.532940i \(0.821087\pi\)
\(492\) −258.597 −0.525604
\(493\) 1076.45i 2.18347i
\(494\) 0.839876i 0.00170015i
\(495\) 80.2964 0.162215
\(496\) 119.170 0.240263
\(497\) 331.625i 0.667253i
\(498\) 136.779i 0.274656i
\(499\) −547.907 −1.09801 −0.549005 0.835819i \(-0.684993\pi\)
−0.549005 + 0.835819i \(0.684993\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −187.612 −0.374475
\(502\) 646.123i 1.28710i
\(503\) 40.5138i 0.0805443i 0.999189 + 0.0402722i \(0.0128225\pi\)
−0.999189 + 0.0402722i \(0.987178\pi\)
\(504\) 29.6913i 0.0589114i
\(505\) 364.420i 0.721625i
\(506\) −354.254 161.532i −0.700106 0.319234i
\(507\) 397.604 0.784228
\(508\) −278.508 −0.548244
\(509\) −943.330 −1.85330 −0.926650 0.375925i \(-0.877325\pi\)
−0.926650 + 0.375925i \(0.877325\pi\)
\(510\) 143.667 0.281700
\(511\) 88.8324i 0.173840i
\(512\) −22.6274 −0.0441942
\(513\) 0.154574i 0.000301314i
\(514\) −300.521 −0.584672
\(515\) −307.551 −0.597187
\(516\) 179.431i 0.347735i
\(517\) 329.697i 0.637712i
\(518\) −254.103 −0.490547
\(519\) 136.385 0.262783
\(520\) 126.263i 0.242813i
\(521\) 409.118i 0.785255i −0.919698 0.392628i \(-0.871566\pi\)
0.919698 0.392628i \(-0.128434\pi\)
\(522\) 174.114 0.333552
\(523\) 88.2598i 0.168757i 0.996434 + 0.0843784i \(0.0268904\pi\)
−0.996434 + 0.0843784i \(0.973110\pi\)
\(524\) 175.719 0.335341
\(525\) 30.3036i 0.0577211i
\(526\) 676.321i 1.28578i
\(527\) 781.455i 1.48284i
\(528\) 82.9298i 0.157064i
\(529\) −346.888 399.387i −0.655742 0.754985i
\(530\) 47.5391 0.0896965
\(531\) 4.66076 0.00877733
\(532\) 0.208185 0.000391325
\(533\) 1490.31 2.79609
\(534\) 200.733i 0.375905i
\(535\) 148.910 0.278336
\(536\) 80.0099i 0.149272i
\(537\) 390.884 0.727903
\(538\) −742.951 −1.38095
\(539\) 439.964i 0.816259i
\(540\) 23.2379i 0.0430331i
\(541\) 383.774 0.709380 0.354690 0.934984i \(-0.384586\pi\)
0.354690 + 0.934984i \(0.384586\pi\)
\(542\) −529.951 −0.977770
\(543\) 379.804i 0.699454i
\(544\) 148.379i 0.272755i
\(545\) 212.437 0.389793
\(546\) 171.114i 0.313395i
\(547\) −143.193 −0.261780 −0.130890 0.991397i \(-0.541783\pi\)
−0.130890 + 0.991397i \(0.541783\pi\)
\(548\) 362.788i 0.662023i
\(549\) 38.7762i 0.0706306i
\(550\) 84.6399i 0.153891i
\(551\) 1.22082i 0.00221565i
\(552\) 46.7477 102.521i 0.0846878 0.185727i
\(553\) −281.897 −0.509759
\(554\) 575.491 1.03879
\(555\) 198.874 0.358331
\(556\) −270.177 −0.485930
\(557\) 624.965i 1.12202i −0.827809 0.561010i \(-0.810413\pi\)
0.827809 0.561010i \(-0.189587\pi\)
\(558\) −126.399 −0.226522
\(559\) 1034.08i 1.84987i
\(560\) −31.2974 −0.0558883
\(561\) 543.810 0.969358
\(562\) 267.649i 0.476244i
\(563\) 697.193i 1.23835i 0.785251 + 0.619177i \(0.212534\pi\)
−0.785251 + 0.619177i \(0.787466\pi\)
\(564\) −95.4149 −0.169175
\(565\) −434.900 −0.769734
\(566\) 222.472i 0.393061i
\(567\) 31.4924i 0.0555422i
\(568\) 268.058 0.471932
\(569\) 943.778i 1.65866i 0.558759 + 0.829330i \(0.311278\pi\)
−0.558759 + 0.829330i \(0.688722\pi\)
\(570\) −0.162936 −0.000285852
\(571\) 159.659i 0.279613i −0.990179 0.139806i \(-0.955352\pi\)
0.990179 0.139806i \(-0.0446480\pi\)
\(572\) 477.931i 0.835543i
\(573\) 415.703i 0.725485i
\(574\) 369.413i 0.643576i
\(575\) 47.7117 104.636i 0.0829768 0.181975i
\(576\) 24.0000 0.0416667
\(577\) 689.947 1.19575 0.597874 0.801590i \(-0.296012\pi\)
0.597874 + 0.801590i \(0.296012\pi\)
\(578\) 564.281 0.976265
\(579\) 637.428 1.10091
\(580\) 183.532i 0.316435i
\(581\) 195.392 0.336303
\(582\) 9.87241i 0.0169629i
\(583\) 179.946 0.308655
\(584\) 71.8047 0.122953
\(585\) 133.922i 0.228926i
\(586\) 655.745i 1.11902i
\(587\) 46.9308 0.0799502 0.0399751 0.999201i \(-0.487272\pi\)
0.0399751 + 0.999201i \(0.487272\pi\)
\(588\) 127.326 0.216541
\(589\) 0.886264i 0.00150469i
\(590\) 4.91288i 0.00832691i
\(591\) −3.19975 −0.00541412
\(592\) 205.396i 0.346952i
\(593\) 52.6508 0.0887871 0.0443936 0.999014i \(-0.485864\pi\)
0.0443936 + 0.999014i \(0.485864\pi\)
\(594\) 87.9603i 0.148081i
\(595\) 205.232i 0.344928i
\(596\) 113.535i 0.190495i
\(597\) 97.8660i 0.163930i
\(598\) −269.411 + 590.839i −0.450519 + 0.988025i
\(599\) −208.189 −0.347560 −0.173780 0.984784i \(-0.555598\pi\)
−0.173780 + 0.984784i \(0.555598\pi\)
\(600\) 24.4949 0.0408248
\(601\) 116.243 0.193417 0.0967083 0.995313i \(-0.469169\pi\)
0.0967083 + 0.995313i \(0.469169\pi\)
\(602\) 256.322 0.425784
\(603\) 84.8634i 0.140735i
\(604\) 72.9387 0.120759
\(605\) 49.8155i 0.0823396i
\(606\) 399.203 0.658750
\(607\) −211.295 −0.348097 −0.174048 0.984737i \(-0.555685\pi\)
−0.174048 + 0.984737i \(0.555685\pi\)
\(608\) 0.168279i 0.000276775i
\(609\) 248.727i 0.408418i
\(610\) 40.8737 0.0670061
\(611\) 549.883 0.899973
\(612\) 157.379i 0.257156i
\(613\) 939.938i 1.53334i 0.642040 + 0.766671i \(0.278088\pi\)
−0.642040 + 0.766671i \(0.721912\pi\)
\(614\) −495.485 −0.806979
\(615\) 289.120i 0.470114i
\(616\) −118.467 −0.192317
\(617\) 571.784i 0.926717i −0.886171 0.463359i \(-0.846644\pi\)
0.886171 0.463359i \(-0.153356\pi\)
\(618\) 336.906i 0.545155i
\(619\) 944.586i 1.52599i 0.646406 + 0.762994i \(0.276271\pi\)
−0.646406 + 0.762994i \(0.723729\pi\)
\(620\) 133.236i 0.214897i
\(621\) −49.5834 + 108.740i −0.0798445 + 0.175105i
\(622\) −215.520 −0.346495
\(623\) −286.752 −0.460277
\(624\) −138.314 −0.221657
\(625\) 25.0000 0.0400000
\(626\) 67.3608i 0.107605i
\(627\) −0.616745 −0.000983645
\(628\) 95.4070i 0.151922i
\(629\) 1346.88 2.14130
\(630\) 33.1959 0.0526920
\(631\) 1035.90i 1.64169i 0.571154 + 0.820843i \(0.306496\pi\)
−0.571154 + 0.820843i \(0.693504\pi\)
\(632\) 227.862i 0.360541i
\(633\) −152.916 −0.241574
\(634\) −581.141 −0.916626
\(635\) 311.382i 0.490365i
\(636\) 52.0765i 0.0818813i
\(637\) −733.790 −1.15195
\(638\) 694.709i 1.08889i
\(639\) −284.318 −0.444942
\(640\) 25.2982i 0.0395285i
\(641\) 291.199i 0.454289i −0.973861 0.227144i \(-0.927061\pi\)
0.973861 0.227144i \(-0.0729389\pi\)
\(642\) 163.123i 0.254085i
\(643\) 183.214i 0.284936i 0.989799 + 0.142468i \(0.0455038\pi\)
−0.989799 + 0.142468i \(0.954496\pi\)
\(644\) −146.455 66.7803i −0.227414 0.103696i
\(645\) −200.610 −0.311023
\(646\) −1.10349 −0.00170818
\(647\) −196.253 −0.303328 −0.151664 0.988432i \(-0.548463\pi\)
−0.151664 + 0.988432i \(0.548463\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 18.5963i 0.0286537i
\(650\) −141.166 −0.217178
\(651\) 180.564i 0.277365i
\(652\) 237.702 0.364574
\(653\) −215.371 −0.329818 −0.164909 0.986309i \(-0.552733\pi\)
−0.164909 + 0.986309i \(0.552733\pi\)
\(654\) 232.714i 0.355831i
\(655\) 196.459i 0.299938i
\(656\) −298.602 −0.455186
\(657\) −76.1604 −0.115921
\(658\) 136.303i 0.207147i
\(659\) 144.360i 0.219059i 0.993984 + 0.109529i \(0.0349344\pi\)
−0.993984 + 0.109529i \(0.965066\pi\)
\(660\) 92.7183 0.140482
\(661\) 639.386i 0.967301i −0.875261 0.483650i \(-0.839311\pi\)
0.875261 0.483650i \(-0.160689\pi\)
\(662\) 554.876 0.838181
\(663\) 906.989i 1.36801i
\(664\) 157.938i 0.237859i
\(665\) 0.232758i 0.000350012i
\(666\) 217.855i 0.327110i
\(667\) 391.609 858.830i 0.587120 1.28760i
\(668\) −216.636 −0.324305
\(669\) 224.384 0.335402
\(670\) −89.4538 −0.133513
\(671\) 154.716 0.230575
\(672\) 34.2846i 0.0510188i
\(673\) 594.376 0.883174 0.441587 0.897218i \(-0.354416\pi\)
0.441587 + 0.897218i \(0.354416\pi\)
\(674\) 648.230i 0.961766i
\(675\) −25.9808 −0.0384900
\(676\) 459.113 0.679162
\(677\) 514.242i 0.759590i −0.925071 0.379795i \(-0.875995\pi\)
0.925071 0.379795i \(-0.124005\pi\)
\(678\) 476.409i 0.702668i
\(679\) 14.1030 0.0207702
\(680\) 165.892 0.243959
\(681\) 131.956i 0.193768i
\(682\) 504.328i 0.739483i
\(683\) 304.332 0.445581 0.222790 0.974866i \(-0.428483\pi\)
0.222790 + 0.974866i \(0.428483\pi\)
\(684\) 0.178487i 0.000260946i
\(685\) −405.610 −0.592131
\(686\) 424.368i 0.618612i
\(687\) 140.906i 0.205103i
\(688\) 207.189i 0.301147i
\(689\) 300.121i 0.435589i
\(690\) 114.622 + 52.2655i 0.166120 + 0.0757471i
\(691\) 845.096 1.22300 0.611502 0.791243i \(-0.290566\pi\)
0.611502 + 0.791243i \(0.290566\pi\)
\(692\) 157.483 0.227577
\(693\) 125.654 0.181318
\(694\) 252.782 0.364239
\(695\) 302.067i 0.434629i
\(696\) 201.050 0.288865
\(697\) 1958.08i 2.80929i
\(698\) 33.9861 0.0486907
\(699\) 397.662 0.568901
\(700\) 34.9916i 0.0499880i
\(701\) 192.249i 0.274250i 0.990554 + 0.137125i \(0.0437861\pi\)
−0.990554 + 0.137125i \(0.956214\pi\)
\(702\) 146.704 0.208980
\(703\) −1.52752 −0.00217286
\(704\) 95.7591i 0.136021i
\(705\) 106.677i 0.151315i
\(706\) 803.641 1.13830
\(707\) 570.271i 0.806607i
\(708\) 5.38179 0.00760139
\(709\) 1303.54i 1.83856i 0.393599 + 0.919282i \(0.371230\pi\)
−0.393599 + 0.919282i \(0.628770\pi\)
\(710\) 299.698i 0.422109i
\(711\) 241.684i 0.339921i
\(712\) 231.787i 0.325543i
\(713\) −284.291 + 623.472i −0.398724 + 0.874435i
\(714\) 224.820 0.314874
\(715\) −534.343 −0.747333
\(716\) 451.354 0.630383
\(717\) −271.482 −0.378637
\(718\) 763.779i 1.06376i
\(719\) 359.296 0.499717 0.249858 0.968282i \(-0.419616\pi\)
0.249858 + 0.968282i \(0.419616\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −481.278 −0.667515
\(722\) −510.530 −0.707105
\(723\) 330.970i 0.457774i
\(724\) 438.560i 0.605745i
\(725\) 205.196 0.283028
\(726\) 54.5701 0.0751655
\(727\) 1033.74i 1.42193i 0.703227 + 0.710966i \(0.251742\pi\)
−0.703227 + 0.710966i \(0.748258\pi\)
\(728\) 197.585i 0.271408i
\(729\) 27.0000 0.0370370
\(730\) 80.2801i 0.109973i
\(731\) −1358.64 −1.85860
\(732\) 44.7749i 0.0611679i
\(733\) 88.8871i 0.121265i 0.998160 + 0.0606324i \(0.0193117\pi\)
−0.998160 + 0.0606324i \(0.980688\pi\)
\(734\) 572.120i 0.779455i
\(735\) 142.355i 0.193680i
\(736\) 53.9796 118.382i 0.0733418 0.160845i
\(737\) −338.602 −0.459432
\(738\) 316.715 0.429154
\(739\) 284.091 0.384426 0.192213 0.981353i \(-0.438434\pi\)
0.192213 + 0.981353i \(0.438434\pi\)
\(740\) 229.639 0.310324
\(741\) 1.02863i 0.00138817i
\(742\) 74.3927 0.100260
\(743\) 972.637i 1.30907i −0.756033 0.654534i \(-0.772865\pi\)
0.756033 0.654534i \(-0.227135\pi\)
\(744\) −145.953 −0.196174
\(745\) 126.936 0.170384
\(746\) 272.144i 0.364804i
\(747\) 167.519i 0.224256i
\(748\) 627.937 0.839489
\(749\) 233.025 0.311114
\(750\) 27.3861i 0.0365148i
\(751\) 85.8549i 0.114321i 0.998365 + 0.0571604i \(0.0182046\pi\)
−0.998365 + 0.0571604i \(0.981795\pi\)
\(752\) −110.176 −0.146510
\(753\) 791.336i 1.05091i
\(754\) −1158.67 −1.53669
\(755\) 81.5479i 0.108010i
\(756\) 36.3643i 0.0481010i
\(757\) 130.267i 0.172084i 0.996292 + 0.0860419i \(0.0274219\pi\)
−0.996292 + 0.0860419i \(0.972578\pi\)
\(758\) 1005.80i 1.32691i
\(759\) 433.870 + 197.836i 0.571634 + 0.260653i
\(760\) −0.188142 −0.000247555
\(761\) −255.675 −0.335973 −0.167987 0.985789i \(-0.553727\pi\)
−0.167987 + 0.985789i \(0.553727\pi\)
\(762\) 341.101 0.447640
\(763\) 332.437 0.435698
\(764\) 480.012i 0.628288i
\(765\) −175.955 −0.230007
\(766\) 436.378i 0.569684i
\(767\) −31.0156 −0.0404376
\(768\) 27.7128 0.0360844
\(769\) 254.418i 0.330843i −0.986223 0.165421i \(-0.947102\pi\)
0.986223 0.165421i \(-0.0528984\pi\)
\(770\) 132.451i 0.172014i
\(771\) 368.062 0.477383
\(772\) 736.038 0.953417
\(773\) 849.508i 1.09898i 0.835502 + 0.549488i \(0.185177\pi\)
−0.835502 + 0.549488i \(0.814823\pi\)
\(774\) 219.757i 0.283924i
\(775\) −148.963 −0.192210
\(776\) 11.3997i 0.0146903i
\(777\) 311.212 0.400530
\(778\) 279.987i 0.359880i
\(779\) 2.22069i 0.00285070i
\(780\) 154.640i 0.198256i
\(781\) 1134.42i 1.45252i
\(782\) 776.284 + 353.970i 0.992691 + 0.452647i
\(783\) −213.245 −0.272344
\(784\) 147.024 0.187530
\(785\) 106.668 0.135883
\(786\) −215.210 −0.273805
\(787\) 911.783i 1.15856i 0.815130 + 0.579278i \(0.196665\pi\)
−0.815130 + 0.579278i \(0.803335\pi\)
\(788\) −3.69475 −0.00468877
\(789\) 828.321i 1.04984i
\(790\) 254.757 0.322477
\(791\) −680.562 −0.860382
\(792\) 101.568i