Properties

Label 690.3.c.a.91.20
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 91.20
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.21

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} +3.95881i q^{7} +2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} +3.95881i q^{7} +2.82843 q^{8} +3.00000 q^{9} -3.16228i q^{10} -5.67111i q^{11} -3.46410 q^{12} +11.1376 q^{13} +5.59860i q^{14} +3.87298i q^{15} +4.00000 q^{16} +2.12953i q^{17} +4.24264 q^{18} -20.9865i q^{19} -4.47214i q^{20} -6.85686i q^{21} -8.02016i q^{22} +(-10.6801 + 20.3700i) q^{23} -4.89898 q^{24} -5.00000 q^{25} +15.7510 q^{26} -5.19615 q^{27} +7.91762i q^{28} +36.0592 q^{29} +5.47723i q^{30} +39.7941 q^{31} +5.65685 q^{32} +9.82265i q^{33} +3.01161i q^{34} +8.85217 q^{35} +6.00000 q^{36} -50.2613i q^{37} -29.6794i q^{38} -19.2910 q^{39} -6.32456i q^{40} +41.6563 q^{41} -9.69706i q^{42} -41.3234i q^{43} -11.3422i q^{44} -6.70820i q^{45} +(-15.1039 + 28.8075i) q^{46} +60.1764 q^{47} -6.92820 q^{48} +33.3278 q^{49} -7.07107 q^{50} -3.68845i q^{51} +22.2753 q^{52} -3.29435i q^{53} -7.34847 q^{54} -12.6810 q^{55} +11.1972i q^{56} +36.3497i q^{57} +50.9954 q^{58} -83.2918 q^{59} +7.74597i q^{60} -37.8857i q^{61} +56.2773 q^{62} +11.8764i q^{63} +8.00000 q^{64} -24.9045i q^{65} +13.8913i q^{66} +61.1024i q^{67} +4.25906i q^{68} +(18.4984 - 35.2819i) q^{69} +12.5189 q^{70} -0.572102 q^{71} +8.48528 q^{72} +40.8795 q^{73} -71.0803i q^{74} +8.66025 q^{75} -41.9730i q^{76} +22.4509 q^{77} -27.2815 q^{78} -86.8569i q^{79} -8.94427i q^{80} +9.00000 q^{81} +58.9109 q^{82} -84.6886i q^{83} -13.7137i q^{84} +4.76177 q^{85} -58.4401i q^{86} -62.4563 q^{87} -16.0403i q^{88} +94.7533i q^{89} -9.48683i q^{90} +44.0918i q^{91} +(-21.3601 + 40.7400i) q^{92} -68.9254 q^{93} +85.1023 q^{94} -46.9273 q^{95} -9.79796 q^{96} +171.701i q^{97} +47.1327 q^{98} -17.0133i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

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
\(7\) 3.95881i 0.565544i 0.959187 + 0.282772i \(0.0912540\pi\)
−0.959187 + 0.282772i \(0.908746\pi\)
\(8\) 2.82843 0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 5.67111i 0.515556i −0.966204 0.257778i \(-0.917010\pi\)
0.966204 0.257778i \(-0.0829903\pi\)
\(12\) −3.46410 −0.288675
\(13\) 11.1376 0.856742 0.428371 0.903603i \(-0.359088\pi\)
0.428371 + 0.903603i \(0.359088\pi\)
\(14\) 5.59860i 0.399900i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 2.12953i 0.125266i 0.998037 + 0.0626332i \(0.0199498\pi\)
−0.998037 + 0.0626332i \(0.980050\pi\)
\(18\) 4.24264 0.235702
\(19\) 20.9865i 1.10455i −0.833661 0.552277i \(-0.813759\pi\)
0.833661 0.552277i \(-0.186241\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 6.85686i 0.326517i
\(22\) 8.02016i 0.364553i
\(23\) −10.6801 + 20.3700i −0.464350 + 0.885652i
\(24\) −4.89898 −0.204124
\(25\) −5.00000 −0.200000
\(26\) 15.7510 0.605808
\(27\) −5.19615 −0.192450
\(28\) 7.91762i 0.282772i
\(29\) 36.0592 1.24342 0.621710 0.783248i \(-0.286438\pi\)
0.621710 + 0.783248i \(0.286438\pi\)
\(30\) 5.47723i 0.182574i
\(31\) 39.7941 1.28368 0.641840 0.766838i \(-0.278171\pi\)
0.641840 + 0.766838i \(0.278171\pi\)
\(32\) 5.65685 0.176777
\(33\) 9.82265i 0.297656i
\(34\) 3.01161i 0.0885767i
\(35\) 8.85217 0.252919
\(36\) 6.00000 0.166667
\(37\) 50.2613i 1.35841i −0.733946 0.679207i \(-0.762324\pi\)
0.733946 0.679207i \(-0.237676\pi\)
\(38\) 29.6794i 0.781037i
\(39\) −19.2910 −0.494640
\(40\) 6.32456i 0.158114i
\(41\) 41.6563 1.01601 0.508003 0.861355i \(-0.330384\pi\)
0.508003 + 0.861355i \(0.330384\pi\)
\(42\) 9.69706i 0.230882i
\(43\) 41.3234i 0.961009i −0.876992 0.480505i \(-0.840453\pi\)
0.876992 0.480505i \(-0.159547\pi\)
\(44\) 11.3422i 0.257778i
\(45\) 6.70820i 0.149071i
\(46\) −15.1039 + 28.8075i −0.328345 + 0.626250i
\(47\) 60.1764 1.28035 0.640175 0.768229i \(-0.278862\pi\)
0.640175 + 0.768229i \(0.278862\pi\)
\(48\) −6.92820 −0.144338
\(49\) 33.3278 0.680160
\(50\) −7.07107 −0.141421
\(51\) 3.68845i 0.0723226i
\(52\) 22.2753 0.428371
\(53\) 3.29435i 0.0621575i −0.999517 0.0310787i \(-0.990106\pi\)
0.999517 0.0310787i \(-0.00989427\pi\)
\(54\) −7.34847 −0.136083
\(55\) −12.6810 −0.230563
\(56\) 11.1972i 0.199950i
\(57\) 36.3497i 0.637714i
\(58\) 50.9954 0.879231
\(59\) −83.2918 −1.41173 −0.705863 0.708349i \(-0.749440\pi\)
−0.705863 + 0.708349i \(0.749440\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 37.8857i 0.621077i −0.950561 0.310538i \(-0.899491\pi\)
0.950561 0.310538i \(-0.100509\pi\)
\(62\) 56.2773 0.907699
\(63\) 11.8764i 0.188515i
\(64\) 8.00000 0.125000
\(65\) 24.9045i 0.383147i
\(66\) 13.8913i 0.210475i
\(67\) 61.1024i 0.911975i 0.889986 + 0.455988i \(0.150714\pi\)
−0.889986 + 0.455988i \(0.849286\pi\)
\(68\) 4.25906i 0.0626332i
\(69\) 18.4984 35.2819i 0.268093 0.511331i
\(70\) 12.5189 0.178841
\(71\) −0.572102 −0.00805777 −0.00402888 0.999992i \(-0.501282\pi\)
−0.00402888 + 0.999992i \(0.501282\pi\)
\(72\) 8.48528 0.117851
\(73\) 40.8795 0.559994 0.279997 0.960001i \(-0.409667\pi\)
0.279997 + 0.960001i \(0.409667\pi\)
\(74\) 71.0803i 0.960544i
\(75\) 8.66025 0.115470
\(76\) 41.9730i 0.552277i
\(77\) 22.4509 0.291570
\(78\) −27.2815 −0.349763
\(79\) 86.8569i 1.09945i −0.835344 0.549727i \(-0.814732\pi\)
0.835344 0.549727i \(-0.185268\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) 58.9109 0.718425
\(83\) 84.6886i 1.02034i −0.860072 0.510172i \(-0.829582\pi\)
0.860072 0.510172i \(-0.170418\pi\)
\(84\) 13.7137i 0.163259i
\(85\) 4.76177 0.0560208
\(86\) 58.4401i 0.679536i
\(87\) −62.4563 −0.717889
\(88\) 16.0403i 0.182276i
\(89\) 94.7533i 1.06464i 0.846542 + 0.532322i \(0.178680\pi\)
−0.846542 + 0.532322i \(0.821320\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 44.0918i 0.484525i
\(92\) −21.3601 + 40.7400i −0.232175 + 0.442826i
\(93\) −68.9254 −0.741133
\(94\) 85.1023 0.905344
\(95\) −46.9273 −0.493971
\(96\) −9.79796 −0.102062
\(97\) 171.701i 1.77011i 0.465485 + 0.885056i \(0.345880\pi\)
−0.465485 + 0.885056i \(0.654120\pi\)
\(98\) 47.1327 0.480946
\(99\) 17.0133i 0.171852i
\(100\) −10.0000 −0.100000
\(101\) −48.8836 −0.483997 −0.241998 0.970277i \(-0.577803\pi\)
−0.241998 + 0.970277i \(0.577803\pi\)
\(102\) 5.21626i 0.0511398i
\(103\) 3.88018i 0.0376716i −0.999823 0.0188358i \(-0.994004\pi\)
0.999823 0.0188358i \(-0.00599598\pi\)
\(104\) 31.5020 0.302904
\(105\) −15.3324 −0.146023
\(106\) 4.65891i 0.0439520i
\(107\) 121.583i 1.13629i 0.822927 + 0.568147i \(0.192339\pi\)
−0.822927 + 0.568147i \(0.807661\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 140.035i 1.28473i −0.766401 0.642363i \(-0.777954\pi\)
0.766401 0.642363i \(-0.222046\pi\)
\(110\) −17.9336 −0.163033
\(111\) 87.0552i 0.784281i
\(112\) 15.8352i 0.141386i
\(113\) 3.73201i 0.0330267i 0.999864 + 0.0165133i \(0.00525660\pi\)
−0.999864 + 0.0165133i \(0.994743\pi\)
\(114\) 51.4063i 0.450932i
\(115\) 45.5487 + 23.8813i 0.396075 + 0.207664i
\(116\) 72.1184 0.621710
\(117\) 33.4129 0.285581
\(118\) −117.792 −0.998240
\(119\) −8.43040 −0.0708437
\(120\) 10.9545i 0.0912871i
\(121\) 88.8385 0.734202
\(122\) 53.5784i 0.439167i
\(123\) −72.1508 −0.586592
\(124\) 79.5882 0.641840
\(125\) 11.1803i 0.0894427i
\(126\) 16.7958i 0.133300i
\(127\) 189.032 1.48844 0.744221 0.667933i \(-0.232821\pi\)
0.744221 + 0.667933i \(0.232821\pi\)
\(128\) 11.3137 0.0883883
\(129\) 71.5742i 0.554839i
\(130\) 35.2203i 0.270926i
\(131\) −102.753 −0.784374 −0.392187 0.919885i \(-0.628281\pi\)
−0.392187 + 0.919885i \(0.628281\pi\)
\(132\) 19.6453i 0.148828i
\(133\) 83.0816 0.624674
\(134\) 86.4118i 0.644864i
\(135\) 11.6190i 0.0860663i
\(136\) 6.02322i 0.0442884i
\(137\) 53.0102i 0.386936i 0.981107 + 0.193468i \(0.0619736\pi\)
−0.981107 + 0.193468i \(0.938026\pi\)
\(138\) 26.1607 49.8961i 0.189570 0.361566i
\(139\) −230.317 −1.65696 −0.828478 0.560022i \(-0.810793\pi\)
−0.828478 + 0.560022i \(0.810793\pi\)
\(140\) 17.7043 0.126460
\(141\) −104.229 −0.739210
\(142\) −0.809074 −0.00569770
\(143\) 63.1628i 0.441698i
\(144\) 12.0000 0.0833333
\(145\) 80.6308i 0.556074i
\(146\) 57.8124 0.395975
\(147\) −57.7255 −0.392690
\(148\) 100.523i 0.679207i
\(149\) 34.0099i 0.228254i 0.993466 + 0.114127i \(0.0364071\pi\)
−0.993466 + 0.114127i \(0.963593\pi\)
\(150\) 12.2474 0.0816497
\(151\) −273.426 −1.81077 −0.905383 0.424596i \(-0.860416\pi\)
−0.905383 + 0.424596i \(0.860416\pi\)
\(152\) 59.3588i 0.390519i
\(153\) 6.38859i 0.0417555i
\(154\) 31.7503 0.206171
\(155\) 88.9823i 0.574079i
\(156\) −38.5819 −0.247320
\(157\) 302.701i 1.92803i 0.265841 + 0.964017i \(0.414350\pi\)
−0.265841 + 0.964017i \(0.585650\pi\)
\(158\) 122.834i 0.777431i
\(159\) 5.70598i 0.0358866i
\(160\) 12.6491i 0.0790569i
\(161\) −80.6409 42.2803i −0.500875 0.262611i
\(162\) 12.7279 0.0785674
\(163\) −101.769 −0.624352 −0.312176 0.950024i \(-0.601058\pi\)
−0.312176 + 0.950024i \(0.601058\pi\)
\(164\) 83.3126 0.508003
\(165\) 21.9641 0.133116
\(166\) 119.768i 0.721493i
\(167\) −124.606 −0.746143 −0.373071 0.927803i \(-0.621695\pi\)
−0.373071 + 0.927803i \(0.621695\pi\)
\(168\) 19.3941i 0.115441i
\(169\) −44.9529 −0.265994
\(170\) 6.73416 0.0396127
\(171\) 62.9595i 0.368184i
\(172\) 82.6468i 0.480505i
\(173\) −278.331 −1.60885 −0.804425 0.594054i \(-0.797526\pi\)
−0.804425 + 0.594054i \(0.797526\pi\)
\(174\) −88.3266 −0.507624
\(175\) 19.7940i 0.113109i
\(176\) 22.6844i 0.128889i
\(177\) 144.266 0.815060
\(178\) 134.001i 0.752817i
\(179\) −22.7044 −0.126840 −0.0634202 0.997987i \(-0.520201\pi\)
−0.0634202 + 0.997987i \(0.520201\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 151.385i 0.836379i −0.908360 0.418189i \(-0.862665\pi\)
0.908360 0.418189i \(-0.137335\pi\)
\(182\) 62.3552i 0.342611i
\(183\) 65.6199i 0.358579i
\(184\) −30.2078 + 57.6150i −0.164173 + 0.313125i
\(185\) −112.388 −0.607502
\(186\) −97.4752 −0.524060
\(187\) 12.0768 0.0645818
\(188\) 120.353 0.640175
\(189\) 20.5706i 0.108839i
\(190\) −66.3652 −0.349290
\(191\) 68.1039i 0.356565i 0.983979 + 0.178282i \(0.0570541\pi\)
−0.983979 + 0.178282i \(0.942946\pi\)
\(192\) −13.8564 −0.0721688
\(193\) 243.269 1.26046 0.630230 0.776408i \(-0.282961\pi\)
0.630230 + 0.776408i \(0.282961\pi\)
\(194\) 242.822i 1.25166i
\(195\) 43.1359i 0.221210i
\(196\) 66.6556 0.340080
\(197\) −131.358 −0.666790 −0.333395 0.942787i \(-0.608194\pi\)
−0.333395 + 0.942787i \(0.608194\pi\)
\(198\) 24.0605i 0.121518i
\(199\) 313.700i 1.57638i 0.615432 + 0.788190i \(0.288982\pi\)
−0.615432 + 0.788190i \(0.711018\pi\)
\(200\) −14.1421 −0.0707107
\(201\) 105.832i 0.526529i
\(202\) −69.1319 −0.342237
\(203\) 142.751i 0.703209i
\(204\) 7.37690i 0.0361613i
\(205\) 93.1463i 0.454372i
\(206\) 5.48740i 0.0266379i
\(207\) −32.0402 + 61.1100i −0.154783 + 0.295217i
\(208\) 44.5506 0.214185
\(209\) −119.017 −0.569459
\(210\) −21.6833 −0.103254
\(211\) 75.8630 0.359540 0.179770 0.983709i \(-0.442465\pi\)
0.179770 + 0.983709i \(0.442465\pi\)
\(212\) 6.58869i 0.0310787i
\(213\) 0.990909 0.00465216
\(214\) 171.945i 0.803481i
\(215\) −92.4019 −0.429777
\(216\) −14.6969 −0.0680414
\(217\) 157.537i 0.725978i
\(218\) 198.040i 0.908438i
\(219\) −70.8054 −0.323313
\(220\) −25.3620 −0.115282
\(221\) 23.7179i 0.107321i
\(222\) 123.115i 0.554571i
\(223\) −165.794 −0.743472 −0.371736 0.928338i \(-0.621237\pi\)
−0.371736 + 0.928338i \(0.621237\pi\)
\(224\) 22.3944i 0.0999750i
\(225\) −15.0000 −0.0666667
\(226\) 5.27786i 0.0233534i
\(227\) 405.393i 1.78587i 0.450183 + 0.892937i \(0.351359\pi\)
−0.450183 + 0.892937i \(0.648641\pi\)
\(228\) 72.6994i 0.318857i
\(229\) 382.310i 1.66947i −0.550649 0.834737i \(-0.685620\pi\)
0.550649 0.834737i \(-0.314380\pi\)
\(230\) 64.4156 + 33.7733i 0.280068 + 0.146840i
\(231\) −38.8860 −0.168338
\(232\) 101.991 0.439615
\(233\) −125.133 −0.537050 −0.268525 0.963273i \(-0.586536\pi\)
−0.268525 + 0.963273i \(0.586536\pi\)
\(234\) 47.2530 0.201936
\(235\) 134.559i 0.572590i
\(236\) −166.584 −0.705863
\(237\) 150.441i 0.634770i
\(238\) −11.9224 −0.0500941
\(239\) −129.207 −0.540616 −0.270308 0.962774i \(-0.587126\pi\)
−0.270308 + 0.962774i \(0.587126\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 313.373i 1.30030i −0.759805 0.650151i \(-0.774705\pi\)
0.759805 0.650151i \(-0.225295\pi\)
\(242\) 125.637 0.519160
\(243\) −15.5885 −0.0641500
\(244\) 75.7713i 0.310538i
\(245\) 74.5233i 0.304177i
\(246\) −102.037 −0.414783
\(247\) 233.740i 0.946317i
\(248\) 112.555 0.453850
\(249\) 146.685i 0.589096i
\(250\) 15.8114i 0.0632456i
\(251\) 152.125i 0.606075i 0.952979 + 0.303037i \(0.0980007\pi\)
−0.952979 + 0.303037i \(0.901999\pi\)
\(252\) 23.7529i 0.0942574i
\(253\) 115.520 + 60.5678i 0.456603 + 0.239398i
\(254\) 267.332 1.05249
\(255\) −8.24763 −0.0323436
\(256\) 16.0000 0.0625000
\(257\) 19.5904 0.0762272 0.0381136 0.999273i \(-0.487865\pi\)
0.0381136 + 0.999273i \(0.487865\pi\)
\(258\) 101.221i 0.392330i
\(259\) 198.975 0.768244
\(260\) 49.8090i 0.191573i
\(261\) 108.178 0.414473
\(262\) −145.315 −0.554636
\(263\) 127.348i 0.484212i −0.970250 0.242106i \(-0.922162\pi\)
0.970250 0.242106i \(-0.0778381\pi\)
\(264\) 27.7827i 0.105237i
\(265\) −7.36638 −0.0277977
\(266\) 117.495 0.441711
\(267\) 164.118i 0.614672i
\(268\) 122.205i 0.455988i
\(269\) 142.959 0.531448 0.265724 0.964049i \(-0.414389\pi\)
0.265724 + 0.964049i \(0.414389\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) −63.7008 −0.235058 −0.117529 0.993069i \(-0.537497\pi\)
−0.117529 + 0.993069i \(0.537497\pi\)
\(272\) 8.51812i 0.0313166i
\(273\) 76.3692i 0.279741i
\(274\) 74.9678i 0.273605i
\(275\) 28.3556i 0.103111i
\(276\) 36.9968 70.5637i 0.134046 0.255666i
\(277\) 448.470 1.61903 0.809513 0.587101i \(-0.199731\pi\)
0.809513 + 0.587101i \(0.199731\pi\)
\(278\) −325.717 −1.17164
\(279\) 119.382 0.427893
\(280\) 25.0377 0.0894204
\(281\) 154.698i 0.550525i 0.961369 + 0.275263i \(0.0887648\pi\)
−0.961369 + 0.275263i \(0.911235\pi\)
\(282\) −147.402 −0.522701
\(283\) 19.1545i 0.0676837i −0.999427 0.0338418i \(-0.989226\pi\)
0.999427 0.0338418i \(-0.0107742\pi\)
\(284\) −1.14420 −0.00402888
\(285\) 81.2804 0.285194
\(286\) 89.3257i 0.312328i
\(287\) 164.909i 0.574597i
\(288\) 16.9706 0.0589256
\(289\) 284.465 0.984308
\(290\) 114.029i 0.393204i
\(291\) 297.395i 1.02197i
\(292\) 81.7591 0.279997
\(293\) 269.403i 0.919463i −0.888058 0.459732i \(-0.847946\pi\)
0.888058 0.459732i \(-0.152054\pi\)
\(294\) −81.6362 −0.277674
\(295\) 186.246i 0.631343i
\(296\) 142.161i 0.480272i
\(297\) 29.4680i 0.0992187i
\(298\) 48.0972i 0.161400i
\(299\) −118.951 + 226.874i −0.397828 + 0.758775i
\(300\) 17.3205 0.0577350
\(301\) 163.592 0.543493
\(302\) −386.682 −1.28040
\(303\) 84.6690 0.279436
\(304\) 83.9461i 0.276138i
\(305\) −84.7149 −0.277754
\(306\) 9.03483i 0.0295256i
\(307\) 331.722 1.08053 0.540263 0.841496i \(-0.318325\pi\)
0.540263 + 0.841496i \(0.318325\pi\)
\(308\) 44.9017 0.145785
\(309\) 6.72067i 0.0217497i
\(310\) 125.840i 0.405935i
\(311\) −397.584 −1.27840 −0.639202 0.769039i \(-0.720735\pi\)
−0.639202 + 0.769039i \(0.720735\pi\)
\(312\) −54.5631 −0.174882
\(313\) 124.944i 0.399181i −0.979879 0.199590i \(-0.936039\pi\)
0.979879 0.199590i \(-0.0639611\pi\)
\(314\) 428.084i 1.36333i
\(315\) 26.5565 0.0843064
\(316\) 173.714i 0.549727i
\(317\) 272.823 0.860642 0.430321 0.902676i \(-0.358400\pi\)
0.430321 + 0.902676i \(0.358400\pi\)
\(318\) 8.06947i 0.0253757i
\(319\) 204.496i 0.641052i
\(320\) 17.8885i 0.0559017i
\(321\) 210.589i 0.656039i
\(322\) −114.043 59.7934i −0.354172 0.185694i
\(323\) 44.6914 0.138363
\(324\) 18.0000 0.0555556
\(325\) −55.6882 −0.171348
\(326\) −143.924 −0.441483
\(327\) 242.548i 0.741737i
\(328\) 117.822 0.359213
\(329\) 238.227i 0.724094i
\(330\) 31.0620 0.0941271
\(331\) 158.093 0.477621 0.238811 0.971066i \(-0.423243\pi\)
0.238811 + 0.971066i \(0.423243\pi\)
\(332\) 169.377i 0.510172i
\(333\) 150.784i 0.452805i
\(334\) −176.219 −0.527603
\(335\) 136.629 0.407848
\(336\) 27.4274i 0.0816293i
\(337\) 187.915i 0.557610i −0.960348 0.278805i \(-0.910062\pi\)
0.960348 0.278805i \(-0.0899383\pi\)
\(338\) −63.5730 −0.188086
\(339\) 6.46404i 0.0190680i
\(340\) 9.52354 0.0280104
\(341\) 225.677i 0.661809i
\(342\) 89.0382i 0.260346i
\(343\) 325.920i 0.950205i
\(344\) 116.880i 0.339768i
\(345\) −78.8926 41.3637i −0.228674 0.119895i
\(346\) −393.620 −1.13763
\(347\) −313.436 −0.903274 −0.451637 0.892202i \(-0.649160\pi\)
−0.451637 + 0.892202i \(0.649160\pi\)
\(348\) −124.913 −0.358944
\(349\) 363.470 1.04146 0.520730 0.853721i \(-0.325660\pi\)
0.520730 + 0.853721i \(0.325660\pi\)
\(350\) 27.9930i 0.0799800i
\(351\) −57.8729 −0.164880
\(352\) 32.0807i 0.0911382i
\(353\) −524.725 −1.48647 −0.743236 0.669029i \(-0.766710\pi\)
−0.743236 + 0.669029i \(0.766710\pi\)
\(354\) 204.022 0.576334
\(355\) 1.27926i 0.00360354i
\(356\) 189.507i 0.532322i
\(357\) 14.6019 0.0409016
\(358\) −32.1089 −0.0896897
\(359\) 311.701i 0.868249i 0.900853 + 0.434124i \(0.142942\pi\)
−0.900853 + 0.434124i \(0.857058\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) −79.4338 −0.220038
\(362\) 214.090i 0.591409i
\(363\) −153.873 −0.423892
\(364\) 88.1836i 0.242263i
\(365\) 91.4094i 0.250437i
\(366\) 92.8006i 0.253553i
\(367\) 468.490i 1.27654i 0.769813 + 0.638269i \(0.220349\pi\)
−0.769813 + 0.638269i \(0.779651\pi\)
\(368\) −42.7202 + 81.4799i −0.116088 + 0.221413i
\(369\) 124.969 0.338669
\(370\) −158.940 −0.429568
\(371\) 13.0417 0.0351528
\(372\) −137.851 −0.370567
\(373\) 7.45302i 0.0199813i 0.999950 + 0.00999064i \(0.00318017\pi\)
−0.999950 + 0.00999064i \(0.996820\pi\)
\(374\) 17.0792 0.0456662
\(375\) 19.3649i 0.0516398i
\(376\) 170.205 0.452672
\(377\) 401.614 1.06529
\(378\) 29.0912i 0.0769608i
\(379\) 444.034i 1.17159i −0.810458 0.585796i \(-0.800782\pi\)
0.810458 0.585796i \(-0.199218\pi\)
\(380\) −93.8545 −0.246986
\(381\) −327.413 −0.859353
\(382\) 96.3134i 0.252129i
\(383\) 315.599i 0.824017i 0.911180 + 0.412009i \(0.135173\pi\)
−0.911180 + 0.412009i \(0.864827\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 50.2016i 0.130394i
\(386\) 344.034 0.891280
\(387\) 123.970i 0.320336i
\(388\) 343.402i 0.885056i
\(389\) 126.333i 0.324763i 0.986728 + 0.162381i \(0.0519175\pi\)
−0.986728 + 0.162381i \(0.948083\pi\)
\(390\) 61.0034i 0.156419i
\(391\) −43.3785 22.7435i −0.110942 0.0581675i
\(392\) 94.2653 0.240473
\(393\) 177.974 0.452859
\(394\) −185.768 −0.471492
\(395\) −194.218 −0.491691
\(396\) 34.0267i 0.0859259i
\(397\) −165.211 −0.416148 −0.208074 0.978113i \(-0.566719\pi\)
−0.208074 + 0.978113i \(0.566719\pi\)
\(398\) 443.638i 1.11467i
\(399\) −143.902 −0.360656
\(400\) −20.0000 −0.0500000
\(401\) 298.998i 0.745630i −0.927906 0.372815i \(-0.878393\pi\)
0.927906 0.372815i \(-0.121607\pi\)
\(402\) 149.670i 0.372312i
\(403\) 443.212 1.09978
\(404\) −97.7673 −0.241998
\(405\) 20.1246i 0.0496904i
\(406\) 201.881i 0.497244i
\(407\) −285.038 −0.700338
\(408\) 10.4325i 0.0255699i
\(409\) −55.5554 −0.135832 −0.0679162 0.997691i \(-0.521635\pi\)
−0.0679162 + 0.997691i \(0.521635\pi\)
\(410\) 131.729i 0.321290i
\(411\) 91.8164i 0.223398i
\(412\) 7.76036i 0.0188358i
\(413\) 329.736i 0.798393i
\(414\) −45.3117 + 86.4225i −0.109448 + 0.208750i
\(415\) −189.369 −0.456312
\(416\) 63.0040 0.151452
\(417\) 398.920 0.956644
\(418\) −168.315 −0.402668
\(419\) 422.645i 1.00870i −0.863500 0.504349i \(-0.831732\pi\)
0.863500 0.504349i \(-0.168268\pi\)
\(420\) −30.6648 −0.0730114
\(421\) 106.651i 0.253328i 0.991946 + 0.126664i \(0.0404269\pi\)
−0.991946 + 0.126664i \(0.959573\pi\)
\(422\) 107.287 0.254233
\(423\) 180.529 0.426783
\(424\) 9.31782i 0.0219760i
\(425\) 10.6476i 0.0250533i
\(426\) 1.40136 0.00328957
\(427\) 149.982 0.351246
\(428\) 243.167i 0.568147i
\(429\) 109.401i 0.255014i
\(430\) −130.676 −0.303898
\(431\) 305.614i 0.709080i −0.935041 0.354540i \(-0.884637\pi\)
0.935041 0.354540i \(-0.115363\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 285.890i 0.660254i 0.943936 + 0.330127i \(0.107092\pi\)
−0.943936 + 0.330127i \(0.892908\pi\)
\(434\) 222.791i 0.513344i
\(435\) 139.657i 0.321050i
\(436\) 280.070i 0.642363i
\(437\) 427.495 + 224.137i 0.978249 + 0.512900i
\(438\) −100.134 −0.228616
\(439\) −461.780 −1.05189 −0.525945 0.850519i \(-0.676288\pi\)
−0.525945 + 0.850519i \(0.676288\pi\)
\(440\) −35.8673 −0.0815165
\(441\) 99.9835 0.226720
\(442\) 33.5422i 0.0758874i
\(443\) −65.0709 −0.146887 −0.0734434 0.997299i \(-0.523399\pi\)
−0.0734434 + 0.997299i \(0.523399\pi\)
\(444\) 174.110i 0.392141i
\(445\) 211.875 0.476123
\(446\) −234.469 −0.525714
\(447\) 58.9068i 0.131783i
\(448\) 31.6705i 0.0706930i
\(449\) 547.308 1.21895 0.609475 0.792806i \(-0.291380\pi\)
0.609475 + 0.792806i \(0.291380\pi\)
\(450\) −21.2132 −0.0471405
\(451\) 236.237i 0.523808i
\(452\) 7.46403i 0.0165133i
\(453\) 473.587 1.04545
\(454\) 573.313i 1.26280i
\(455\) 98.5923 0.216686
\(456\) 102.813i 0.225466i
\(457\) 334.369i 0.731660i −0.930682 0.365830i \(-0.880785\pi\)
0.930682 0.365830i \(-0.119215\pi\)
\(458\) 540.667i 1.18050i
\(459\) 11.0654i 0.0241075i
\(460\) 91.0973 + 47.7627i 0.198038 + 0.103832i
\(461\) −384.546 −0.834156 −0.417078 0.908871i \(-0.636946\pi\)
−0.417078 + 0.908871i \(0.636946\pi\)
\(462\) −54.9931 −0.119033
\(463\) 741.501 1.60151 0.800757 0.598990i \(-0.204431\pi\)
0.800757 + 0.598990i \(0.204431\pi\)
\(464\) 144.237 0.310855
\(465\) 154.122i 0.331445i
\(466\) −176.964 −0.379752
\(467\) 183.855i 0.393695i 0.980434 + 0.196847i \(0.0630704\pi\)
−0.980434 + 0.196847i \(0.936930\pi\)
\(468\) 66.8259 0.142790
\(469\) −241.893 −0.515763
\(470\) 190.295i 0.404882i
\(471\) 524.294i 1.11315i
\(472\) −235.585 −0.499120
\(473\) −234.350 −0.495454
\(474\) 212.755i 0.448850i
\(475\) 104.933i 0.220911i
\(476\) −16.8608 −0.0354218
\(477\) 9.88304i 0.0207192i
\(478\) −182.727 −0.382273
\(479\) 643.670i 1.34378i 0.740652 + 0.671889i \(0.234517\pi\)
−0.740652 + 0.671889i \(0.765483\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 559.793i 1.16381i
\(482\) 443.176i 0.919453i
\(483\) 139.674 + 73.2317i 0.289180 + 0.151618i
\(484\) 177.677 0.367101
\(485\) 383.935 0.791618
\(486\) −22.0454 −0.0453609
\(487\) −404.712 −0.831031 −0.415516 0.909586i \(-0.636399\pi\)
−0.415516 + 0.909586i \(0.636399\pi\)
\(488\) 107.157i 0.219584i
\(489\) 176.270 0.360470
\(490\) 105.392i 0.215085i
\(491\) 173.587 0.353537 0.176769 0.984252i \(-0.443436\pi\)
0.176769 + 0.984252i \(0.443436\pi\)
\(492\) −144.302 −0.293296
\(493\) 76.7891i 0.155759i
\(494\) 330.559i 0.669147i
\(495\) −38.0430 −0.0768545
\(496\) 159.176 0.320920
\(497\) 2.26484i 0.00455703i
\(498\) 207.444i 0.416554i
\(499\) 6.44061 0.0129070 0.00645352 0.999979i \(-0.497946\pi\)
0.00645352 + 0.999979i \(0.497946\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 215.824 0.430786
\(502\) 215.137i 0.428559i
\(503\) 617.629i 1.22789i −0.789348 0.613945i \(-0.789581\pi\)
0.789348 0.613945i \(-0.210419\pi\)
\(504\) 33.5916i 0.0666500i
\(505\) 109.307i 0.216450i
\(506\) 163.371 + 85.6558i 0.322867 + 0.169280i
\(507\) 77.8608 0.153572
\(508\) 378.064 0.744221
\(509\) 200.449 0.393809 0.196904 0.980423i \(-0.436911\pi\)
0.196904 + 0.980423i \(0.436911\pi\)
\(510\) −11.6639 −0.0228704
\(511\) 161.834i 0.316701i
\(512\) 22.6274 0.0441942
\(513\) 109.049i 0.212571i
\(514\) 27.7050 0.0539008
\(515\) −8.67634 −0.0168473
\(516\) 143.148i 0.277420i
\(517\) 341.267i 0.660091i
\(518\) 281.393 0.543230
\(519\) 482.083 0.928870
\(520\) 70.4406i 0.135463i
\(521\) 201.610i 0.386968i 0.981103 + 0.193484i \(0.0619787\pi\)
−0.981103 + 0.193484i \(0.938021\pi\)
\(522\) 152.986 0.293077
\(523\) 678.779i 1.29786i 0.760850 + 0.648928i \(0.224782\pi\)
−0.760850 + 0.648928i \(0.775218\pi\)
\(524\) −205.506 −0.392187
\(525\) 34.2843i 0.0653034i
\(526\) 180.097i 0.342389i
\(527\) 84.7427i 0.160802i
\(528\) 39.2906i 0.0744140i
\(529\) −300.873 435.105i −0.568757 0.822505i
\(530\) −10.4176 −0.0196559
\(531\) −249.875 −0.470575
\(532\) 166.163 0.312337
\(533\) 463.953 0.870455
\(534\) 232.097i 0.434639i
\(535\) 271.869 0.508166
\(536\) 172.824i 0.322432i
\(537\) 39.3252 0.0732313
\(538\) 202.175 0.375790
\(539\) 189.006i 0.350660i
\(540\) 23.2379i 0.0430331i
\(541\) 465.332 0.860133 0.430067 0.902797i \(-0.358490\pi\)
0.430067 + 0.902797i \(0.358490\pi\)
\(542\) −90.0865 −0.166211
\(543\) 262.206i 0.482884i
\(544\) 12.0464i 0.0221442i
\(545\) −313.128 −0.574547
\(546\) 108.002i 0.197807i
\(547\) −309.522 −0.565853 −0.282926 0.959142i \(-0.591305\pi\)
−0.282926 + 0.959142i \(0.591305\pi\)
\(548\) 106.020i 0.193468i
\(549\) 113.657i 0.207026i
\(550\) 40.1008i 0.0729106i
\(551\) 756.756i 1.37342i
\(552\) 52.3214 99.7921i 0.0947851 0.180783i
\(553\) 343.850 0.621790
\(554\) 634.233 1.14482
\(555\) 194.661 0.350741
\(556\) −460.634 −0.828478
\(557\) 826.642i 1.48410i 0.670346 + 0.742049i \(0.266146\pi\)
−0.670346 + 0.742049i \(0.733854\pi\)
\(558\) 168.832 0.302566
\(559\) 460.245i 0.823337i
\(560\) 35.4087 0.0632298
\(561\) −20.9176 −0.0372863
\(562\) 218.775i 0.389280i
\(563\) 1018.64i 1.80931i −0.426140 0.904657i \(-0.640127\pi\)
0.426140 0.904657i \(-0.359873\pi\)
\(564\) −208.457 −0.369605
\(565\) 8.34503 0.0147700
\(566\) 27.0885i 0.0478596i
\(567\) 35.6293i 0.0628383i
\(568\) −1.61815 −0.00284885
\(569\) 766.176i 1.34653i −0.739401 0.673266i \(-0.764891\pi\)
0.739401 0.673266i \(-0.235109\pi\)
\(570\) 114.948 0.201663
\(571\) 119.265i 0.208870i −0.994532 0.104435i \(-0.966697\pi\)
0.994532 0.104435i \(-0.0333035\pi\)
\(572\) 126.326i 0.220849i
\(573\) 117.959i 0.205863i
\(574\) 233.217i 0.406301i
\(575\) 53.4003 101.850i 0.0928701 0.177130i
\(576\) 24.0000 0.0416667
\(577\) −73.2216 −0.126901 −0.0634503 0.997985i \(-0.520210\pi\)
−0.0634503 + 0.997985i \(0.520210\pi\)
\(578\) 402.294 0.696011
\(579\) −421.354 −0.727727
\(580\) 161.262i 0.278037i
\(581\) 335.266 0.577050
\(582\) 420.579i 0.722645i
\(583\) −18.6826 −0.0320456
\(584\) 115.625 0.197988
\(585\) 74.7136i 0.127716i
\(586\) 380.993i 0.650159i
\(587\) 829.222 1.41264 0.706322 0.707891i \(-0.250353\pi\)
0.706322 + 0.707891i \(0.250353\pi\)
\(588\) −115.451 −0.196345
\(589\) 835.139i 1.41789i
\(590\) 263.392i 0.446427i
\(591\) 227.518 0.384972
\(592\) 201.045i 0.339604i
\(593\) 82.6719 0.139413 0.0697065 0.997568i \(-0.477794\pi\)
0.0697065 + 0.997568i \(0.477794\pi\)
\(594\) 41.6740i 0.0701582i
\(595\) 18.8509i 0.0316823i
\(596\) 68.0198i 0.114127i
\(597\) 543.344i 0.910123i
\(598\) −168.222 + 320.848i −0.281307 + 0.536535i
\(599\) 390.672 0.652208 0.326104 0.945334i \(-0.394264\pi\)
0.326104 + 0.945334i \(0.394264\pi\)
\(600\) 24.4949 0.0408248
\(601\) −726.400 −1.20865 −0.604326 0.796737i \(-0.706558\pi\)
−0.604326 + 0.796737i \(0.706558\pi\)
\(602\) 231.353 0.384308
\(603\) 183.307i 0.303992i
\(604\) −546.851 −0.905383
\(605\) 198.649i 0.328345i
\(606\) 119.740 0.197591
\(607\) −289.612 −0.477120 −0.238560 0.971128i \(-0.576675\pi\)
−0.238560 + 0.971128i \(0.576675\pi\)
\(608\) 118.718i 0.195259i
\(609\) 247.253i 0.405998i
\(610\) −119.805 −0.196402
\(611\) 670.224 1.09693
\(612\) 12.7772i 0.0208777i
\(613\) 457.354i 0.746091i 0.927813 + 0.373045i \(0.121686\pi\)
−0.927813 + 0.373045i \(0.878314\pi\)
\(614\) 469.125 0.764048
\(615\) 161.334i 0.262332i
\(616\) 63.5006 0.103085
\(617\) 934.894i 1.51523i 0.652705 + 0.757613i \(0.273634\pi\)
−0.652705 + 0.757613i \(0.726366\pi\)
\(618\) 9.50446i 0.0153794i
\(619\) 79.2136i 0.127970i −0.997951 0.0639851i \(-0.979619\pi\)
0.997951 0.0639851i \(-0.0203810\pi\)
\(620\) 177.965i 0.287040i
\(621\) 55.4952 105.846i 0.0893643 0.170444i
\(622\) −562.268 −0.903968
\(623\) −375.110 −0.602103
\(624\) −77.1638 −0.123660
\(625\) 25.0000 0.0400000
\(626\) 176.697i 0.282263i
\(627\) 206.143 0.328777
\(628\) 605.403i 0.964017i
\(629\) 107.033 0.170164
\(630\) 37.5566 0.0596136
\(631\) 405.115i 0.642021i 0.947076 + 0.321011i \(0.104023\pi\)
−0.947076 + 0.321011i \(0.895977\pi\)
\(632\) 245.668i 0.388716i
\(633\) −131.399 −0.207581
\(634\) 385.831 0.608566
\(635\) 422.689i 0.665652i
\(636\) 11.4120i 0.0179433i
\(637\) 371.193 0.582721
\(638\) 289.200i 0.453292i
\(639\) −1.71630 −0.00268592
\(640\) 25.2982i 0.0395285i
\(641\) 984.727i 1.53623i 0.640309 + 0.768117i \(0.278806\pi\)
−0.640309 + 0.768117i \(0.721194\pi\)
\(642\) 297.817i 0.463890i
\(643\) 330.197i 0.513526i 0.966474 + 0.256763i \(0.0826560\pi\)
−0.966474 + 0.256763i \(0.917344\pi\)
\(644\) −161.282 84.5606i −0.250438 0.131305i
\(645\) 160.045 0.248132
\(646\) 63.2032 0.0978377
\(647\) 948.869 1.46657 0.733284 0.679923i \(-0.237987\pi\)
0.733284 + 0.679923i \(0.237987\pi\)
\(648\) 25.4558 0.0392837
\(649\) 472.357i 0.727823i
\(650\) −78.7550 −0.121162
\(651\) 272.863i 0.419144i
\(652\) −203.539 −0.312176
\(653\) −378.498 −0.579630 −0.289815 0.957083i \(-0.593594\pi\)
−0.289815 + 0.957083i \(0.593594\pi\)
\(654\) 343.014i 0.524487i
\(655\) 229.763i 0.350783i
\(656\) 166.625 0.254002
\(657\) 122.639 0.186665
\(658\) 336.904i 0.512012i
\(659\) 470.040i 0.713262i −0.934245 0.356631i \(-0.883925\pi\)
0.934245 0.356631i \(-0.116075\pi\)
\(660\) 43.9282 0.0665579
\(661\) 244.609i 0.370058i −0.982733 0.185029i \(-0.940762\pi\)
0.982733 0.185029i \(-0.0592380\pi\)
\(662\) 223.577 0.337729
\(663\) 41.0807i 0.0619618i
\(664\) 239.536i 0.360746i
\(665\) 185.776i 0.279363i
\(666\) 213.241i 0.320181i
\(667\) −385.114 + 734.525i −0.577383 + 1.10124i
\(668\) −249.212 −0.373071
\(669\) 287.164 0.429244
\(670\) 193.223 0.288392
\(671\) −214.854 −0.320199
\(672\) 38.7883i 0.0577206i
\(673\) 297.873 0.442605 0.221302 0.975205i \(-0.428969\pi\)
0.221302 + 0.975205i \(0.428969\pi\)
\(674\) 265.751i 0.394290i
\(675\) 25.9808 0.0384900
\(676\) −89.9059 −0.132997
\(677\) 306.899i 0.453322i 0.973974 + 0.226661i \(0.0727809\pi\)
−0.973974 + 0.226661i \(0.927219\pi\)
\(678\) 9.14153i 0.0134831i
\(679\) −679.731 −1.00108
\(680\) 13.4683 0.0198064
\(681\) 702.162i 1.03107i
\(682\) 319.155i 0.467969i
\(683\) 270.473 0.396007 0.198003 0.980201i \(-0.436554\pi\)
0.198003 + 0.980201i \(0.436554\pi\)
\(684\) 125.919i 0.184092i
\(685\) 118.534 0.173043
\(686\) 460.921i 0.671896i
\(687\) 662.180i 0.963871i
\(688\) 165.294i 0.240252i
\(689\) 36.6913i 0.0532529i
\(690\) −111.571 58.4971i −0.161697 0.0847784i
\(691\) −994.734 −1.43956 −0.719779 0.694204i \(-0.755757\pi\)
−0.719779 + 0.694204i \(0.755757\pi\)
\(692\) −556.662 −0.804425
\(693\) 67.3526 0.0971898
\(694\) −443.266 −0.638711
\(695\) 515.004i 0.741013i
\(696\) −176.653 −0.253812
\(697\) 88.7082i 0.127272i
\(698\) 514.024 0.736424
\(699\) 216.736 0.310066
\(700\) 39.5881i 0.0565544i
\(701\) 615.121i 0.877490i −0.898612 0.438745i \(-0.855423\pi\)
0.898612 0.438745i \(-0.144577\pi\)
\(702\) −81.8446 −0.116588
\(703\) −1054.81 −1.50044
\(704\) 45.3689i 0.0644444i
\(705\) 233.062i 0.330585i
\(706\) −742.073 −1.05109
\(707\) 193.521i 0.273721i
\(708\) 288.531 0.407530
\(709\) 768.270i 1.08360i 0.840509 + 0.541798i \(0.182256\pi\)
−0.840509 + 0.541798i \(0.817744\pi\)
\(710\) 1.80914i 0.00254809i
\(711\) 260.571i 0.366485i
\(712\) 268.003i 0.376408i
\(713\) −425.003 + 810.605i −0.596078 + 1.13689i
\(714\) 20.6502 0.0289218
\(715\) −141.236 −0.197533
\(716\) −45.4088 −0.0634202
\(717\) 223.793 0.312125
\(718\) 440.812i 0.613944i
\(719\) −613.243 −0.852910 −0.426455 0.904509i \(-0.640238\pi\)
−0.426455 + 0.904509i \(0.640238\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 15.3609 0.0213050
\(722\) −112.336 −0.155590
\(723\) 542.778i 0.750730i
\(724\) 302.769i 0.418189i
\(725\) −180.296 −0.248684
\(726\) −217.609 −0.299737
\(727\) 1148.29i 1.57949i −0.613436 0.789744i \(-0.710213\pi\)
0.613436 0.789744i \(-0.289787\pi\)
\(728\) 124.710i 0.171306i
\(729\) 27.0000 0.0370370
\(730\) 129.272i 0.177086i
\(731\) 87.9994 0.120382
\(732\) 131.240i 0.179289i
\(733\) 570.538i 0.778361i 0.921162 + 0.389180i \(0.127242\pi\)
−0.921162 + 0.389180i \(0.872758\pi\)
\(734\) 662.544i 0.902649i
\(735\) 129.078i 0.175616i
\(736\) −60.4155 + 115.230i −0.0820863 + 0.156563i
\(737\) 346.518 0.470174
\(738\) 176.733 0.239475
\(739\) −1062.30 −1.43749 −0.718744 0.695275i \(-0.755283\pi\)
−0.718744 + 0.695275i \(0.755283\pi\)
\(740\) −224.776 −0.303751
\(741\) 404.850i 0.546356i
\(742\) 18.4437 0.0248568
\(743\) 166.131i 0.223595i −0.993731 0.111797i \(-0.964339\pi\)
0.993731 0.111797i \(-0.0356608\pi\)
\(744\) −194.950 −0.262030
\(745\) 76.0484 0.102078
\(746\) 10.5402i 0.0141289i
\(747\) 254.066i 0.340115i
\(748\) 24.1536 0.0322909
\(749\) −481.325 −0.642624
\(750\) 27.3861i 0.0365148i
\(751\) 1210.26i 1.61153i 0.592236 + 0.805765i \(0.298245\pi\)
−0.592236 + 0.805765i \(0.701755\pi\)
\(752\) 240.706 0.320087
\(753\) 263.488i 0.349917i
\(754\) 567.968 0.753274
\(755\) 611.398i 0.809799i
\(756\) 41.1412i 0.0544195i
\(757\) 500.893i 0.661681i 0.943687 + 0.330841i \(0.107332\pi\)
−0.943687 + 0.330841i \(0.892668\pi\)
\(758\) 627.958i 0.828441i
\(759\) −200.087 104.907i −0.263620 0.138217i
\(760\) −132.730 −0.174645
\(761\) 788.375 1.03597 0.517987 0.855389i \(-0.326682\pi\)
0.517987 + 0.855389i \(0.326682\pi\)
\(762\) −463.032 −0.607654
\(763\) 554.372 0.726569
\(764\) 136.208i 0.178282i
\(765\) 14.2853 0.0186736
\(766\) 446.324i 0.582668i
\(767\) −927.674 −1.20948
\(768\) −27.7128 −0.0360844
\(769\) 115.079i 0.149647i −0.997197 0.0748237i \(-0.976161\pi\)
0.997197 0.0748237i \(-0.0238394\pi\)
\(770\) 70.9958i 0.0922024i
\(771\) −33.9315 −0.0440098
\(772\) 486.538 0.630230
\(773\) 1396.31i 1.80635i −0.429272 0.903175i \(-0.641230\pi\)
0.429272 0.903175i \(-0.358770\pi\)
\(774\) 175.320i 0.226512i
\(775\) −198.970 −0.256736
\(776\) 485.643i 0.625829i
\(777\) −344.635 −0.443546
\(778\) 178.661i 0.229642i
\(779\) 874.220i 1.12223i
\(780\) 86.2718i 0.110605i
\(781\) 3.24445i 0.00415423i
\(782\) −61.3464 32.1642i −0.0784481 0.0411306i
\(783\) −187.369 −0.239296
\(784\) 133.311 0.170040
\(785\) 676.861 0.862243
\(786\) 251.693 0.320220
\(787\) 608.869i 0.773659i 0.922151 + 0.386829i \(0.126430\pi\)
−0.922151 + 0.386829i \(0.873570\pi\)
\(788\) −262.715 −0.333395
\(789\) 220.573i 0.279560i
\(790\) −274.666 −0.347678
\(791\) −14.7743 −0.0186780
\(792\) 48.1210i