Properties

Label 177.3.c.a.58.16
Level $177$
Weight $3$
Character 177.58
Analytic conductor $4.823$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.16
Root \(2.72775i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.5

$q$-expansion

\(f(q)\) \(=\) \(q+2.72775i q^{2} -1.73205 q^{3} -3.44061 q^{4} +5.71516 q^{5} -4.72460i q^{6} +8.69147 q^{7} +1.52587i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+2.72775i q^{2} -1.73205 q^{3} -3.44061 q^{4} +5.71516 q^{5} -4.72460i q^{6} +8.69147 q^{7} +1.52587i q^{8} +3.00000 q^{9} +15.5895i q^{10} +6.01328i q^{11} +5.95932 q^{12} -4.81519i q^{13} +23.7081i q^{14} -9.89894 q^{15} -17.9246 q^{16} +10.8327 q^{17} +8.18325i q^{18} -18.4655 q^{19} -19.6636 q^{20} -15.0541 q^{21} -16.4027 q^{22} +15.4084i q^{23} -2.64288i q^{24} +7.66303 q^{25} +13.1346 q^{26} -5.19615 q^{27} -29.9040 q^{28} +15.5293 q^{29} -27.0018i q^{30} -6.38687i q^{31} -42.7904i q^{32} -10.4153i q^{33} +29.5490i q^{34} +49.6731 q^{35} -10.3218 q^{36} -0.527041i q^{37} -50.3693i q^{38} +8.34016i q^{39} +8.72058i q^{40} +9.31080 q^{41} -41.0637i q^{42} +52.9611i q^{43} -20.6894i q^{44} +17.1455 q^{45} -42.0302 q^{46} -78.0549i q^{47} +31.0464 q^{48} +26.5417 q^{49} +20.9028i q^{50} -18.7628 q^{51} +16.5672i q^{52} -10.2232 q^{53} -14.1738i q^{54} +34.3668i q^{55} +13.2620i q^{56} +31.9832 q^{57} +42.3600i q^{58} +(29.4888 + 51.1020i) q^{59} +34.0584 q^{60} -41.5604i q^{61} +17.4218 q^{62} +26.0744 q^{63} +45.0230 q^{64} -27.5196i q^{65} +28.4103 q^{66} -92.4125i q^{67} -37.2712 q^{68} -26.6881i q^{69} +135.496i q^{70} +93.8038 q^{71} +4.57760i q^{72} -88.0161i q^{73} +1.43764 q^{74} -13.2728 q^{75} +63.5327 q^{76} +52.2642i q^{77} -22.7499 q^{78} -81.2111 q^{79} -102.442 q^{80} +9.00000 q^{81} +25.3975i q^{82} -2.92193i q^{83} +51.7952 q^{84} +61.9108 q^{85} -144.465 q^{86} -26.8975 q^{87} -9.17547 q^{88} -168.718i q^{89} +46.7685i q^{90} -41.8511i q^{91} -53.0143i q^{92} +11.0624i q^{93} +212.914 q^{94} -105.533 q^{95} +74.1152i q^{96} -169.166i q^{97} +72.3990i q^{98} +18.0398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.72775i 1.36387i 0.731411 + 0.681937i \(0.238862\pi\)
−0.731411 + 0.681937i \(0.761138\pi\)
\(3\) −1.73205 −0.577350
\(4\) −3.44061 −0.860153
\(5\) 5.71516 1.14303 0.571516 0.820591i \(-0.306356\pi\)
0.571516 + 0.820591i \(0.306356\pi\)
\(6\) 4.72460i 0.787433i
\(7\) 8.69147 1.24164 0.620819 0.783954i \(-0.286800\pi\)
0.620819 + 0.783954i \(0.286800\pi\)
\(8\) 1.52587i 0.190733i
\(9\) 3.00000 0.333333
\(10\) 15.5895i 1.55895i
\(11\) 6.01328i 0.546662i 0.961920 + 0.273331i \(0.0881254\pi\)
−0.961920 + 0.273331i \(0.911875\pi\)
\(12\) 5.95932 0.496610
\(13\) 4.81519i 0.370399i −0.982701 0.185200i \(-0.940707\pi\)
0.982701 0.185200i \(-0.0592932\pi\)
\(14\) 23.7081i 1.69344i
\(15\) −9.89894 −0.659930
\(16\) −17.9246 −1.12029
\(17\) 10.8327 0.637220 0.318610 0.947886i \(-0.396784\pi\)
0.318610 + 0.947886i \(0.396784\pi\)
\(18\) 8.18325i 0.454625i
\(19\) −18.4655 −0.971869 −0.485935 0.873995i \(-0.661521\pi\)
−0.485935 + 0.873995i \(0.661521\pi\)
\(20\) −19.6636 −0.983182
\(21\) −15.0541 −0.716860
\(22\) −16.4027 −0.745578
\(23\) 15.4084i 0.669930i 0.942231 + 0.334965i \(0.108724\pi\)
−0.942231 + 0.334965i \(0.891276\pi\)
\(24\) 2.64288i 0.110120i
\(25\) 7.66303 0.306521
\(26\) 13.1346 0.505178
\(27\) −5.19615 −0.192450
\(28\) −29.9040 −1.06800
\(29\) 15.5293 0.535492 0.267746 0.963489i \(-0.413721\pi\)
0.267746 + 0.963489i \(0.413721\pi\)
\(30\) 27.0018i 0.900061i
\(31\) 6.38687i 0.206028i −0.994680 0.103014i \(-0.967151\pi\)
0.994680 0.103014i \(-0.0328487\pi\)
\(32\) 42.7904i 1.33720i
\(33\) 10.4153i 0.315615i
\(34\) 29.5490i 0.869087i
\(35\) 49.6731 1.41923
\(36\) −10.3218 −0.286718
\(37\) 0.527041i 0.0142444i −0.999975 0.00712218i \(-0.997733\pi\)
0.999975 0.00712218i \(-0.00226708\pi\)
\(38\) 50.3693i 1.32551i
\(39\) 8.34016i 0.213850i
\(40\) 8.72058i 0.218014i
\(41\) 9.31080 0.227093 0.113546 0.993533i \(-0.463779\pi\)
0.113546 + 0.993533i \(0.463779\pi\)
\(42\) 41.0637i 0.977707i
\(43\) 52.9611i 1.23165i 0.787882 + 0.615827i \(0.211178\pi\)
−0.787882 + 0.615827i \(0.788822\pi\)
\(44\) 20.6894i 0.470213i
\(45\) 17.1455 0.381011
\(46\) −42.0302 −0.913700
\(47\) 78.0549i 1.66074i −0.557211 0.830371i \(-0.688128\pi\)
0.557211 0.830371i \(-0.311872\pi\)
\(48\) 31.0464 0.646800
\(49\) 26.5417 0.541666
\(50\) 20.9028i 0.418056i
\(51\) −18.7628 −0.367899
\(52\) 16.5672i 0.318600i
\(53\) −10.2232 −0.192891 −0.0964457 0.995338i \(-0.530747\pi\)
−0.0964457 + 0.995338i \(0.530747\pi\)
\(54\) 14.1738i 0.262478i
\(55\) 34.3668i 0.624851i
\(56\) 13.2620i 0.236822i
\(57\) 31.9832 0.561109
\(58\) 42.3600i 0.730344i
\(59\) 29.4888 + 51.1020i 0.499810 + 0.866135i
\(60\) 34.0584 0.567641
\(61\) 41.5604i 0.681318i −0.940187 0.340659i \(-0.889350\pi\)
0.940187 0.340659i \(-0.110650\pi\)
\(62\) 17.4218 0.280997
\(63\) 26.0744 0.413880
\(64\) 45.0230 0.703484
\(65\) 27.5196i 0.423378i
\(66\) 28.4103 0.430460
\(67\) 92.4125i 1.37929i −0.724147 0.689646i \(-0.757766\pi\)
0.724147 0.689646i \(-0.242234\pi\)
\(68\) −37.2712 −0.548106
\(69\) 26.6881i 0.386784i
\(70\) 135.496i 1.93565i
\(71\) 93.8038 1.32118 0.660590 0.750747i \(-0.270306\pi\)
0.660590 + 0.750747i \(0.270306\pi\)
\(72\) 4.57760i 0.0635778i
\(73\) 88.0161i 1.20570i −0.797854 0.602850i \(-0.794032\pi\)
0.797854 0.602850i \(-0.205968\pi\)
\(74\) 1.43764 0.0194275
\(75\) −13.2728 −0.176970
\(76\) 63.5327 0.835957
\(77\) 52.2642i 0.678756i
\(78\) −22.7499 −0.291665
\(79\) −81.2111 −1.02799 −0.513994 0.857794i \(-0.671835\pi\)
−0.513994 + 0.857794i \(0.671835\pi\)
\(80\) −102.442 −1.28053
\(81\) 9.00000 0.111111
\(82\) 25.3975i 0.309726i
\(83\) 2.92193i 0.0352040i −0.999845 0.0176020i \(-0.994397\pi\)
0.999845 0.0176020i \(-0.00560318\pi\)
\(84\) 51.7952 0.616610
\(85\) 61.9108 0.728362
\(86\) −144.465 −1.67982
\(87\) −26.8975 −0.309167
\(88\) −9.17547 −0.104267
\(89\) 168.718i 1.89571i −0.318699 0.947856i \(-0.603246\pi\)
0.318699 0.947856i \(-0.396754\pi\)
\(90\) 46.7685i 0.519650i
\(91\) 41.8511i 0.459902i
\(92\) 53.0143i 0.576242i
\(93\) 11.0624i 0.118950i
\(94\) 212.914 2.26504
\(95\) −105.533 −1.11088
\(96\) 74.1152i 0.772033i
\(97\) 169.166i 1.74397i −0.489528 0.871987i \(-0.662831\pi\)
0.489528 0.871987i \(-0.337169\pi\)
\(98\) 72.3990i 0.738765i
\(99\) 18.0398i 0.182221i
\(100\) −26.3655 −0.263655
\(101\) 6.43636i 0.0637263i −0.999492 0.0318631i \(-0.989856\pi\)
0.999492 0.0318631i \(-0.0101441\pi\)
\(102\) 51.1803i 0.501768i
\(103\) 176.969i 1.71814i 0.511854 + 0.859072i \(0.328959\pi\)
−0.511854 + 0.859072i \(0.671041\pi\)
\(104\) 7.34735 0.0706476
\(105\) −86.0364 −0.819394
\(106\) 27.8864i 0.263080i
\(107\) −183.573 −1.71564 −0.857818 0.513953i \(-0.828181\pi\)
−0.857818 + 0.513953i \(0.828181\pi\)
\(108\) 17.8779 0.165537
\(109\) 105.308i 0.966132i −0.875584 0.483066i \(-0.839523\pi\)
0.875584 0.483066i \(-0.160477\pi\)
\(110\) −93.7441 −0.852219
\(111\) 0.912863i 0.00822399i
\(112\) −155.791 −1.39099
\(113\) 100.717i 0.891297i 0.895208 + 0.445648i \(0.147027\pi\)
−0.895208 + 0.445648i \(0.852973\pi\)
\(114\) 87.2422i 0.765282i
\(115\) 88.0614i 0.765751i
\(116\) −53.4302 −0.460606
\(117\) 14.4456i 0.123466i
\(118\) −139.393 + 80.4379i −1.18130 + 0.681677i
\(119\) 94.1524 0.791196
\(120\) 15.1045i 0.125871i
\(121\) 84.8405 0.701161
\(122\) 113.366 0.929233
\(123\) −16.1268 −0.131112
\(124\) 21.9748i 0.177216i
\(125\) −99.0835 −0.792668
\(126\) 71.1244i 0.564480i
\(127\) −206.165 −1.62335 −0.811675 0.584110i \(-0.801444\pi\)
−0.811675 + 0.584110i \(0.801444\pi\)
\(128\) 48.3503i 0.377737i
\(129\) 91.7313i 0.711095i
\(130\) 75.0665 0.577435
\(131\) 152.579i 1.16473i 0.812929 + 0.582363i \(0.197872\pi\)
−0.812929 + 0.582363i \(0.802128\pi\)
\(132\) 35.8350i 0.271477i
\(133\) −160.493 −1.20671
\(134\) 252.078 1.88118
\(135\) −29.6968 −0.219977
\(136\) 16.5293i 0.121539i
\(137\) 193.341 1.41125 0.705624 0.708586i \(-0.250667\pi\)
0.705624 + 0.708586i \(0.250667\pi\)
\(138\) 72.7985 0.527525
\(139\) 172.850 1.24353 0.621763 0.783206i \(-0.286417\pi\)
0.621763 + 0.783206i \(0.286417\pi\)
\(140\) −170.906 −1.22076
\(141\) 135.195i 0.958830i
\(142\) 255.873i 1.80192i
\(143\) 28.9551 0.202483
\(144\) −53.7739 −0.373430
\(145\) 88.7523 0.612085
\(146\) 240.086 1.64442
\(147\) −45.9715 −0.312731
\(148\) 1.81335i 0.0122523i
\(149\) 181.616i 1.21890i 0.792826 + 0.609448i \(0.208609\pi\)
−0.792826 + 0.609448i \(0.791391\pi\)
\(150\) 36.2047i 0.241365i
\(151\) 1.21185i 0.00802549i −0.999992 0.00401275i \(-0.998723\pi\)
0.999992 0.00401275i \(-0.00127730\pi\)
\(152\) 28.1759i 0.185368i
\(153\) 32.4982 0.212407
\(154\) −142.564 −0.925738
\(155\) 36.5020i 0.235497i
\(156\) 28.6953i 0.183944i
\(157\) 184.394i 1.17449i −0.809410 0.587244i \(-0.800213\pi\)
0.809410 0.587244i \(-0.199787\pi\)
\(158\) 221.523i 1.40205i
\(159\) 17.7072 0.111366
\(160\) 244.554i 1.52846i
\(161\) 133.922i 0.831811i
\(162\) 24.5497i 0.151542i
\(163\) 8.96097 0.0549752 0.0274876 0.999622i \(-0.491249\pi\)
0.0274876 + 0.999622i \(0.491249\pi\)
\(164\) −32.0348 −0.195334
\(165\) 59.5251i 0.360758i
\(166\) 7.97030 0.0480139
\(167\) −143.336 −0.858298 −0.429149 0.903234i \(-0.641187\pi\)
−0.429149 + 0.903234i \(0.641187\pi\)
\(168\) 22.9705i 0.136729i
\(169\) 145.814 0.862804
\(170\) 168.877i 0.993394i
\(171\) −55.3966 −0.323956
\(172\) 182.219i 1.05941i
\(173\) 57.4482i 0.332070i 0.986120 + 0.166035i \(0.0530965\pi\)
−0.986120 + 0.166035i \(0.946903\pi\)
\(174\) 73.3696i 0.421665i
\(175\) 66.6030 0.380588
\(176\) 107.786i 0.612419i
\(177\) −51.0760 88.5112i −0.288565 0.500063i
\(178\) 460.221 2.58551
\(179\) 90.1857i 0.503831i 0.967749 + 0.251915i \(0.0810604\pi\)
−0.967749 + 0.251915i \(0.918940\pi\)
\(180\) −58.9909 −0.327727
\(181\) 123.939 0.684745 0.342373 0.939564i \(-0.388769\pi\)
0.342373 + 0.939564i \(0.388769\pi\)
\(182\) 114.159 0.627249
\(183\) 71.9848i 0.393359i
\(184\) −23.5112 −0.127778
\(185\) 3.01213i 0.0162818i
\(186\) −30.1754 −0.162233
\(187\) 65.1402i 0.348343i
\(188\) 268.557i 1.42849i
\(189\) −45.1622 −0.238953
\(190\) 287.868i 1.51510i
\(191\) 150.842i 0.789751i 0.918735 + 0.394876i \(0.129212\pi\)
−0.918735 + 0.394876i \(0.870788\pi\)
\(192\) −77.9821 −0.406157
\(193\) −84.8208 −0.439486 −0.219743 0.975558i \(-0.570522\pi\)
−0.219743 + 0.975558i \(0.570522\pi\)
\(194\) 461.441 2.37856
\(195\) 47.6653i 0.244438i
\(196\) −91.3195 −0.465916
\(197\) −190.721 −0.968127 −0.484063 0.875033i \(-0.660840\pi\)
−0.484063 + 0.875033i \(0.660840\pi\)
\(198\) −49.2081 −0.248526
\(199\) −200.054 −1.00529 −0.502647 0.864492i \(-0.667641\pi\)
−0.502647 + 0.864492i \(0.667641\pi\)
\(200\) 11.6928i 0.0584638i
\(201\) 160.063i 0.796334i
\(202\) 17.5568 0.0869147
\(203\) 134.972 0.664888
\(204\) 64.5557 0.316449
\(205\) 53.2127 0.259574
\(206\) −482.727 −2.34333
\(207\) 46.2252i 0.223310i
\(208\) 86.3106i 0.414955i
\(209\) 111.038i 0.531284i
\(210\) 234.686i 1.11755i
\(211\) 412.135i 1.95325i −0.214955 0.976624i \(-0.568961\pi\)
0.214955 0.976624i \(-0.431039\pi\)
\(212\) 35.1742 0.165916
\(213\) −162.473 −0.762784
\(214\) 500.741i 2.33991i
\(215\) 302.681i 1.40782i
\(216\) 7.92864i 0.0367067i
\(217\) 55.5113i 0.255813i
\(218\) 287.255 1.31768
\(219\) 152.448i 0.696111i
\(220\) 118.243i 0.537468i
\(221\) 52.1617i 0.236026i
\(222\) −2.49006 −0.0112165
\(223\) −22.4832 −0.100821 −0.0504107 0.998729i \(-0.516053\pi\)
−0.0504107 + 0.998729i \(0.516053\pi\)
\(224\) 371.912i 1.66032i
\(225\) 22.9891 0.102174
\(226\) −274.729 −1.21562
\(227\) 276.847i 1.21959i −0.792559 0.609795i \(-0.791252\pi\)
0.792559 0.609795i \(-0.208748\pi\)
\(228\) −110.042 −0.482640
\(229\) 160.926i 0.702732i 0.936238 + 0.351366i \(0.114283\pi\)
−0.936238 + 0.351366i \(0.885717\pi\)
\(230\) −240.209 −1.04439
\(231\) 90.5243i 0.391880i
\(232\) 23.6956i 0.102136i
\(233\) 10.6284i 0.0456153i −0.999740 0.0228076i \(-0.992739\pi\)
0.999740 0.0228076i \(-0.00726052\pi\)
\(234\) 39.4039 0.168393
\(235\) 446.096i 1.89828i
\(236\) −101.459 175.822i −0.429913 0.745009i
\(237\) 140.662 0.593510
\(238\) 256.824i 1.07909i
\(239\) 223.594 0.935540 0.467770 0.883850i \(-0.345058\pi\)
0.467770 + 0.883850i \(0.345058\pi\)
\(240\) 177.435 0.739312
\(241\) 64.6207 0.268136 0.134068 0.990972i \(-0.457196\pi\)
0.134068 + 0.990972i \(0.457196\pi\)
\(242\) 231.424i 0.956296i
\(243\) −15.5885 −0.0641500
\(244\) 142.993i 0.586038i
\(245\) 151.690 0.619142
\(246\) 43.9898i 0.178820i
\(247\) 88.9150i 0.359980i
\(248\) 9.74553 0.0392965
\(249\) 5.06094i 0.0203251i
\(250\) 270.275i 1.08110i
\(251\) −142.392 −0.567299 −0.283650 0.958928i \(-0.591545\pi\)
−0.283650 + 0.958928i \(0.591545\pi\)
\(252\) −89.7119 −0.356000
\(253\) −92.6549 −0.366225
\(254\) 562.367i 2.21405i
\(255\) −107.233 −0.420520
\(256\) 311.979 1.21867
\(257\) 13.2725 0.0516440 0.0258220 0.999667i \(-0.491780\pi\)
0.0258220 + 0.999667i \(0.491780\pi\)
\(258\) 250.220 0.969844
\(259\) 4.58077i 0.0176864i
\(260\) 94.6843i 0.364170i
\(261\) 46.5878 0.178497
\(262\) −416.198 −1.58854
\(263\) −54.0179 −0.205391 −0.102696 0.994713i \(-0.532747\pi\)
−0.102696 + 0.994713i \(0.532747\pi\)
\(264\) 15.8924 0.0601984
\(265\) −58.4274 −0.220481
\(266\) 437.783i 1.64580i
\(267\) 292.229i 1.09449i
\(268\) 317.956i 1.18640i
\(269\) 372.720i 1.38558i 0.721140 + 0.692789i \(0.243618\pi\)
−0.721140 + 0.692789i \(0.756382\pi\)
\(270\) 81.0055i 0.300020i
\(271\) 531.359 1.96074 0.980368 0.197177i \(-0.0631773\pi\)
0.980368 + 0.197177i \(0.0631773\pi\)
\(272\) −194.173 −0.713871
\(273\) 72.4882i 0.265525i
\(274\) 527.386i 1.92477i
\(275\) 46.0799i 0.167563i
\(276\) 91.8235i 0.332694i
\(277\) 136.910 0.494260 0.247130 0.968982i \(-0.420512\pi\)
0.247130 + 0.968982i \(0.420512\pi\)
\(278\) 471.492i 1.69601i
\(279\) 19.1606i 0.0686761i
\(280\) 75.7946i 0.270695i
\(281\) −186.333 −0.663108 −0.331554 0.943436i \(-0.607573\pi\)
−0.331554 + 0.943436i \(0.607573\pi\)
\(282\) −368.778 −1.30772
\(283\) 370.038i 1.30755i 0.756687 + 0.653777i \(0.226817\pi\)
−0.756687 + 0.653777i \(0.773183\pi\)
\(284\) −322.743 −1.13642
\(285\) 182.789 0.641365
\(286\) 78.9822i 0.276162i
\(287\) 80.9245 0.281967
\(288\) 128.371i 0.445734i
\(289\) −171.652 −0.593951
\(290\) 242.094i 0.834807i
\(291\) 293.003i 1.00688i
\(292\) 302.829i 1.03709i
\(293\) 299.019 1.02054 0.510271 0.860013i \(-0.329545\pi\)
0.510271 + 0.860013i \(0.329545\pi\)
\(294\) 125.399i 0.426526i
\(295\) 168.533 + 292.056i 0.571298 + 0.990020i
\(296\) 0.804196 0.00271688
\(297\) 31.2459i 0.105205i
\(298\) −495.402 −1.66242
\(299\) 74.1944 0.248142
\(300\) 45.6664 0.152221
\(301\) 460.310i 1.52927i
\(302\) 3.30562 0.0109458
\(303\) 11.1481i 0.0367924i
\(304\) 330.988 1.08878
\(305\) 237.524i 0.778768i
\(306\) 88.6469i 0.289696i
\(307\) 27.6515 0.0900700 0.0450350 0.998985i \(-0.485660\pi\)
0.0450350 + 0.998985i \(0.485660\pi\)
\(308\) 179.821i 0.583834i
\(309\) 306.519i 0.991971i
\(310\) 99.5682 0.321188
\(311\) −364.708 −1.17269 −0.586347 0.810060i \(-0.699434\pi\)
−0.586347 + 0.810060i \(0.699434\pi\)
\(312\) −12.7260 −0.0407884
\(313\) 174.644i 0.557969i 0.960296 + 0.278984i \(0.0899978\pi\)
−0.960296 + 0.278984i \(0.910002\pi\)
\(314\) 502.982 1.60185
\(315\) 149.019 0.473077
\(316\) 279.416 0.884228
\(317\) −505.102 −1.59338 −0.796691 0.604387i \(-0.793418\pi\)
−0.796691 + 0.604387i \(0.793418\pi\)
\(318\) 48.3007i 0.151889i
\(319\) 93.3819i 0.292733i
\(320\) 257.313 0.804105
\(321\) 317.958 0.990523
\(322\) −365.304 −1.13449
\(323\) −200.032 −0.619294
\(324\) −30.9655 −0.0955726
\(325\) 36.8990i 0.113535i
\(326\) 24.4433i 0.0749793i
\(327\) 182.400i 0.557797i
\(328\) 14.2070i 0.0433142i
\(329\) 678.412i 2.06204i
\(330\) 162.370 0.492029
\(331\) 3.99311 0.0120638 0.00603188 0.999982i \(-0.498080\pi\)
0.00603188 + 0.999982i \(0.498080\pi\)
\(332\) 10.0532i 0.0302809i
\(333\) 1.58112i 0.00474812i
\(334\) 390.984i 1.17061i
\(335\) 528.152i 1.57657i
\(336\) 269.839 0.803091
\(337\) 347.538i 1.03127i −0.856808 0.515636i \(-0.827556\pi\)
0.856808 0.515636i \(-0.172444\pi\)
\(338\) 397.744i 1.17676i
\(339\) 174.446i 0.514591i
\(340\) −213.011 −0.626503
\(341\) 38.4060 0.112628
\(342\) 151.108i 0.441836i
\(343\) −195.196 −0.569085
\(344\) −80.8116 −0.234917
\(345\) 152.527i 0.442107i
\(346\) −156.704 −0.452902
\(347\) 587.431i 1.69289i 0.532480 + 0.846443i \(0.321260\pi\)
−0.532480 + 0.846443i \(0.678740\pi\)
\(348\) 92.5439 0.265931
\(349\) 395.445i 1.13308i 0.824034 + 0.566540i \(0.191718\pi\)
−0.824034 + 0.566540i \(0.808282\pi\)
\(350\) 181.676i 0.519075i
\(351\) 25.0205i 0.0712834i
\(352\) 257.311 0.730996
\(353\) 201.884i 0.571909i −0.958243 0.285955i \(-0.907689\pi\)
0.958243 0.285955i \(-0.0923106\pi\)
\(354\) 241.436 139.323i 0.682024 0.393567i
\(355\) 536.104 1.51015
\(356\) 580.494i 1.63060i
\(357\) −163.077 −0.456797
\(358\) −246.004 −0.687162
\(359\) −529.552 −1.47507 −0.737537 0.675307i \(-0.764011\pi\)
−0.737537 + 0.675307i \(0.764011\pi\)
\(360\) 26.1617i 0.0726715i
\(361\) −20.0246 −0.0554698
\(362\) 338.074i 0.933906i
\(363\) −146.948 −0.404816
\(364\) 143.993i 0.395586i
\(365\) 503.026i 1.37815i
\(366\) −196.356 −0.536493
\(367\) 359.579i 0.979779i −0.871785 0.489889i \(-0.837037\pi\)
0.871785 0.489889i \(-0.162963\pi\)
\(368\) 276.190i 0.750516i
\(369\) 27.9324 0.0756975
\(370\) 8.21632 0.0222063
\(371\) −88.8550 −0.239501
\(372\) 38.0614i 0.102316i
\(373\) −439.679 −1.17876 −0.589382 0.807854i \(-0.700629\pi\)
−0.589382 + 0.807854i \(0.700629\pi\)
\(374\) −177.686 −0.475097
\(375\) 171.618 0.457647
\(376\) 119.101 0.316759
\(377\) 74.7765i 0.198346i
\(378\) 123.191i 0.325902i
\(379\) −580.426 −1.53147 −0.765734 0.643158i \(-0.777624\pi\)
−0.765734 + 0.643158i \(0.777624\pi\)
\(380\) 363.099 0.955525
\(381\) 357.089 0.937241
\(382\) −411.460 −1.07712
\(383\) −343.315 −0.896384 −0.448192 0.893937i \(-0.647932\pi\)
−0.448192 + 0.893937i \(0.647932\pi\)
\(384\) 83.7452i 0.218086i
\(385\) 298.698i 0.775840i
\(386\) 231.370i 0.599404i
\(387\) 158.883i 0.410551i
\(388\) 582.033i 1.50009i
\(389\) 303.425 0.780013 0.390007 0.920812i \(-0.372473\pi\)
0.390007 + 0.920812i \(0.372473\pi\)
\(390\) −130.019 −0.333382
\(391\) 166.915i 0.426893i
\(392\) 40.4991i 0.103314i
\(393\) 264.275i 0.672455i
\(394\) 520.239i 1.32040i
\(395\) −464.134 −1.17502
\(396\) 62.0681i 0.156738i
\(397\) 159.184i 0.400967i 0.979697 + 0.200484i \(0.0642513\pi\)
−0.979697 + 0.200484i \(0.935749\pi\)
\(398\) 545.696i 1.37110i
\(399\) 277.981 0.696695
\(400\) −137.357 −0.343392
\(401\) 421.293i 1.05061i −0.850915 0.525303i \(-0.823952\pi\)
0.850915 0.525303i \(-0.176048\pi\)
\(402\) −436.612 −1.08610
\(403\) −30.7540 −0.0763127
\(404\) 22.1450i 0.0548144i
\(405\) 51.4364 0.127004
\(406\) 368.170i 0.906824i
\(407\) 3.16925 0.00778685
\(408\) 28.6296i 0.0701706i
\(409\) 662.202i 1.61908i 0.587068 + 0.809538i \(0.300282\pi\)
−0.587068 + 0.809538i \(0.699718\pi\)
\(410\) 145.151i 0.354026i
\(411\) −334.877 −0.814785
\(412\) 608.881i 1.47787i
\(413\) 256.301 + 444.151i 0.620583 + 1.07543i
\(414\) −126.091 −0.304567
\(415\) 16.6993i 0.0402393i
\(416\) −206.044 −0.495299
\(417\) −299.385 −0.717950
\(418\) 302.885 0.724604
\(419\) 338.057i 0.806818i 0.915020 + 0.403409i \(0.132175\pi\)
−0.915020 + 0.403409i \(0.867825\pi\)
\(420\) 296.018 0.704804
\(421\) 101.363i 0.240766i 0.992727 + 0.120383i \(0.0384123\pi\)
−0.992727 + 0.120383i \(0.961588\pi\)
\(422\) 1124.20 2.66398
\(423\) 234.165i 0.553581i
\(424\) 15.5993i 0.0367908i
\(425\) 83.0115 0.195321
\(426\) 443.185i 1.04034i
\(427\) 361.221i 0.845951i
\(428\) 631.604 1.47571
\(429\) −50.1517 −0.116904
\(430\) −825.637 −1.92009
\(431\) 47.6635i 0.110588i −0.998470 0.0552941i \(-0.982390\pi\)
0.998470 0.0552941i \(-0.0176096\pi\)
\(432\) 93.1391 0.215600
\(433\) −172.895 −0.399294 −0.199647 0.979868i \(-0.563980\pi\)
−0.199647 + 0.979868i \(0.563980\pi\)
\(434\) 151.421 0.348896
\(435\) −153.723 −0.353387
\(436\) 362.325i 0.831022i
\(437\) 284.524i 0.651084i
\(438\) −415.841 −0.949409
\(439\) 384.161 0.875081 0.437540 0.899199i \(-0.355850\pi\)
0.437540 + 0.899199i \(0.355850\pi\)
\(440\) −52.4392 −0.119180
\(441\) 79.6250 0.180555
\(442\) 142.284 0.321910
\(443\) 172.202i 0.388717i −0.980931 0.194359i \(-0.937737\pi\)
0.980931 0.194359i \(-0.0622625\pi\)
\(444\) 3.14081i 0.00707389i
\(445\) 964.252i 2.16686i
\(446\) 61.3285i 0.137508i
\(447\) 314.567i 0.703730i
\(448\) 391.316 0.873473
\(449\) 613.309 1.36595 0.682973 0.730444i \(-0.260687\pi\)
0.682973 + 0.730444i \(0.260687\pi\)
\(450\) 62.7084i 0.139352i
\(451\) 55.9884i 0.124143i
\(452\) 346.527i 0.766652i
\(453\) 2.09898i 0.00463352i
\(454\) 755.168 1.66337
\(455\) 239.186i 0.525683i
\(456\) 48.8022i 0.107022i
\(457\) 279.448i 0.611484i 0.952114 + 0.305742i \(0.0989046\pi\)
−0.952114 + 0.305742i \(0.901095\pi\)
\(458\) −438.965 −0.958438
\(459\) −56.2885 −0.122633
\(460\) 302.985i 0.658663i
\(461\) −555.187 −1.20431 −0.602155 0.798379i \(-0.705691\pi\)
−0.602155 + 0.798379i \(0.705691\pi\)
\(462\) 246.928 0.534475
\(463\) 672.785i 1.45310i −0.687114 0.726550i \(-0.741123\pi\)
0.687114 0.726550i \(-0.258877\pi\)
\(464\) −278.357 −0.599907
\(465\) 63.2233i 0.135964i
\(466\) 28.9915 0.0622135
\(467\) 436.023i 0.933669i 0.884345 + 0.466834i \(0.154606\pi\)
−0.884345 + 0.466834i \(0.845394\pi\)
\(468\) 49.7016i 0.106200i
\(469\) 803.201i 1.71258i
\(470\) 1216.84 2.58902
\(471\) 319.381i 0.678090i
\(472\) −77.9749 + 44.9960i −0.165201 + 0.0953304i
\(473\) −318.470 −0.673297
\(474\) 383.690i 0.809472i
\(475\) −141.502 −0.297899
\(476\) −323.942 −0.680550
\(477\) −30.6697 −0.0642971
\(478\) 609.908i 1.27596i
\(479\) 620.966 1.29638 0.648190 0.761479i \(-0.275526\pi\)
0.648190 + 0.761479i \(0.275526\pi\)
\(480\) 423.580i 0.882458i
\(481\) −2.53781 −0.00527611
\(482\) 176.269i 0.365704i
\(483\) 231.959i 0.480246i
\(484\) −291.903 −0.603106
\(485\) 966.808i 1.99342i
\(486\) 42.5214i 0.0874926i
\(487\) 683.788 1.40408 0.702041 0.712136i \(-0.252272\pi\)
0.702041 + 0.712136i \(0.252272\pi\)
\(488\) 63.4157 0.129950
\(489\) −15.5208 −0.0317400
\(490\) 413.771i 0.844432i
\(491\) 650.610 1.32507 0.662536 0.749030i \(-0.269480\pi\)
0.662536 + 0.749030i \(0.269480\pi\)
\(492\) 55.4860 0.112776
\(493\) 168.225 0.341226
\(494\) −242.538 −0.490967
\(495\) 103.100i 0.208284i
\(496\) 114.482i 0.230811i
\(497\) 815.293 1.64043
\(498\) −13.8050 −0.0277208
\(499\) −503.786 −1.00959 −0.504796 0.863239i \(-0.668432\pi\)
−0.504796 + 0.863239i \(0.668432\pi\)
\(500\) 340.908 0.681816
\(501\) 248.265 0.495539
\(502\) 388.410i 0.773725i
\(503\) 622.714i 1.23800i 0.785391 + 0.619000i \(0.212462\pi\)
−0.785391 + 0.619000i \(0.787538\pi\)
\(504\) 39.7861i 0.0789407i
\(505\) 36.7848i 0.0728412i
\(506\) 252.739i 0.499485i
\(507\) −252.557 −0.498140
\(508\) 709.335 1.39633
\(509\) 338.691i 0.665405i 0.943032 + 0.332702i \(0.107960\pi\)
−0.943032 + 0.332702i \(0.892040\pi\)
\(510\) 292.504i 0.573536i
\(511\) 764.990i 1.49704i
\(512\) 657.600i 1.28438i
\(513\) 95.9497 0.187036
\(514\) 36.2041i 0.0704360i
\(515\) 1011.41i 1.96389i
\(516\) 315.612i 0.611651i
\(517\) 469.366 0.907864
\(518\) 12.4952 0.0241220
\(519\) 99.5032i 0.191721i
\(520\) 41.9913 0.0807524
\(521\) 144.363 0.277088 0.138544 0.990356i \(-0.455758\pi\)
0.138544 + 0.990356i \(0.455758\pi\)
\(522\) 127.080i 0.243448i
\(523\) −81.3990 −0.155639 −0.0778193 0.996967i \(-0.524796\pi\)
−0.0778193 + 0.996967i \(0.524796\pi\)
\(524\) 524.966i 1.00184i
\(525\) −115.360 −0.219733
\(526\) 147.347i 0.280128i
\(527\) 69.1873i 0.131285i
\(528\) 186.690i 0.353580i
\(529\) 291.582 0.551194
\(530\) 159.375i 0.300708i
\(531\) 88.4663 + 153.306i 0.166603 + 0.288712i
\(532\) 552.193 1.03796
\(533\) 44.8333i 0.0841150i
\(534\) −797.127 −1.49275
\(535\) −1049.15 −1.96103
\(536\) 141.009 0.263077
\(537\) 156.206i 0.290887i
\(538\) −1016.69 −1.88975
\(539\) 159.602i 0.296108i
\(540\) 102.175 0.189214
\(541\) 52.0841i 0.0962738i 0.998841 + 0.0481369i \(0.0153284\pi\)
−0.998841 + 0.0481369i \(0.984672\pi\)
\(542\) 1449.41i 2.67420i
\(543\) −214.668 −0.395338
\(544\) 463.537i 0.852091i
\(545\) 601.854i 1.10432i
\(546\) −197.730 −0.362142
\(547\) 477.454 0.872859 0.436429 0.899738i \(-0.356243\pi\)
0.436429 + 0.899738i \(0.356243\pi\)
\(548\) −665.212 −1.21389
\(549\) 124.681i 0.227106i
\(550\) −125.694 −0.228535
\(551\) −286.756 −0.520429
\(552\) 40.7225 0.0737727
\(553\) −705.844 −1.27639
\(554\) 373.456i 0.674109i
\(555\) 5.21715i 0.00940028i
\(556\) −594.710 −1.06962
\(557\) 313.535 0.562899 0.281449 0.959576i \(-0.409185\pi\)
0.281449 + 0.959576i \(0.409185\pi\)
\(558\) 52.2654 0.0936655
\(559\) 255.018 0.456204
\(560\) −890.373 −1.58995
\(561\) 112.826i 0.201116i
\(562\) 508.270i 0.904395i
\(563\) 49.8387i 0.0885234i 0.999020 + 0.0442617i \(0.0140935\pi\)
−0.999020 + 0.0442617i \(0.985906\pi\)
\(564\) 465.154i 0.824741i
\(565\) 575.611i 1.01878i
\(566\) −1009.37 −1.78334
\(567\) 78.2232 0.137960
\(568\) 143.132i 0.251993i
\(569\) 197.517i 0.347131i 0.984822 + 0.173565i \(0.0555288\pi\)
−0.984822 + 0.173565i \(0.944471\pi\)
\(570\) 498.603i 0.874742i
\(571\) 18.9985i 0.0332723i −0.999862 0.0166362i \(-0.994704\pi\)
0.999862 0.0166362i \(-0.00529570\pi\)
\(572\) −99.6233 −0.174167
\(573\) 261.267i 0.455963i
\(574\) 220.742i 0.384567i
\(575\) 118.075i 0.205348i
\(576\) 135.069 0.234495
\(577\) −248.509 −0.430691 −0.215346 0.976538i \(-0.569088\pi\)
−0.215346 + 0.976538i \(0.569088\pi\)
\(578\) 468.223i 0.810075i
\(579\) 146.914 0.253737
\(580\) −305.362 −0.526487
\(581\) 25.3959i 0.0437107i
\(582\) −799.239 −1.37326
\(583\) 61.4752i 0.105446i
\(584\) 134.301 0.229967
\(585\) 82.5588i 0.141126i
\(586\) 815.649i 1.39189i
\(587\) 736.598i 1.25485i 0.778676 + 0.627426i \(0.215892\pi\)
−0.778676 + 0.627426i \(0.784108\pi\)
\(588\) 158.170 0.268997
\(589\) 117.937i 0.200232i
\(590\) −796.655 + 459.716i −1.35026 + 0.779179i
\(591\) 330.338 0.558948
\(592\) 9.44703i 0.0159578i
\(593\) −83.9607 −0.141586 −0.0707932 0.997491i \(-0.522553\pi\)
−0.0707932 + 0.997491i \(0.522553\pi\)
\(594\) 85.2310 0.143487
\(595\) 538.096 0.904362
\(596\) 624.869i 1.04844i
\(597\) 346.503 0.580407
\(598\) 202.384i 0.338434i
\(599\) −93.6816 −0.156397 −0.0781983 0.996938i \(-0.524917\pi\)
−0.0781983 + 0.996938i \(0.524917\pi\)
\(600\) 20.2525i 0.0337541i
\(601\) 931.300i 1.54958i 0.632216 + 0.774792i \(0.282146\pi\)
−0.632216 + 0.774792i \(0.717854\pi\)
\(602\) −1255.61 −2.08573
\(603\) 277.238i 0.459764i
\(604\) 4.16950i 0.00690315i
\(605\) 484.877 0.801449
\(606\) −30.4092 −0.0501802
\(607\) −217.894 −0.358969 −0.179484 0.983761i \(-0.557443\pi\)
−0.179484 + 0.983761i \(0.557443\pi\)
\(608\) 790.147i 1.29958i
\(609\) −233.779 −0.383873
\(610\) 647.907 1.06214
\(611\) −375.849 −0.615138
\(612\) −111.814 −0.182702
\(613\) 46.8619i 0.0764468i 0.999269 + 0.0382234i \(0.0121698\pi\)
−0.999269 + 0.0382234i \(0.987830\pi\)
\(614\) 75.4263i 0.122844i
\(615\) −92.1670 −0.149865
\(616\) −79.7483 −0.129462
\(617\) 994.661 1.61209 0.806046 0.591853i \(-0.201603\pi\)
0.806046 + 0.591853i \(0.201603\pi\)
\(618\) 836.107 1.35292
\(619\) 801.130 1.29423 0.647116 0.762391i \(-0.275975\pi\)
0.647116 + 0.762391i \(0.275975\pi\)
\(620\) 125.589i 0.202563i
\(621\) 80.0643i 0.128928i
\(622\) 994.831i 1.59941i
\(623\) 1466.41i 2.35379i
\(624\) 149.494i 0.239574i
\(625\) −757.854 −1.21257
\(626\) −476.385 −0.760999
\(627\) 192.324i 0.306737i
\(628\) 634.430i 1.01024i
\(629\) 5.70930i 0.00907679i
\(630\) 406.487i 0.645218i
\(631\) 891.594 1.41299 0.706493 0.707720i \(-0.250276\pi\)
0.706493 + 0.707720i \(0.250276\pi\)
\(632\) 123.917i 0.196072i
\(633\) 713.839i 1.12771i
\(634\) 1377.79i 2.17317i
\(635\) −1178.27 −1.85554
\(636\) −60.9235 −0.0957917
\(637\) 127.803i 0.200633i
\(638\) −254.722 −0.399251
\(639\) 281.411 0.440394
\(640\) 276.330i 0.431765i
\(641\) −790.983 −1.23398 −0.616991 0.786970i \(-0.711649\pi\)
−0.616991 + 0.786970i \(0.711649\pi\)
\(642\) 867.309i 1.35095i
\(643\) −348.723 −0.542337 −0.271169 0.962532i \(-0.587410\pi\)
−0.271169 + 0.962532i \(0.587410\pi\)
\(644\) 460.772i 0.715485i
\(645\) 524.259i 0.812804i
\(646\) 545.637i 0.844639i
\(647\) 746.195 1.15332 0.576658 0.816986i \(-0.304357\pi\)
0.576658 + 0.816986i \(0.304357\pi\)
\(648\) 13.7328i 0.0211926i
\(649\) −307.290 + 177.324i −0.473483 + 0.273227i
\(650\) 100.651 0.154848
\(651\) 96.1484i 0.147693i
\(652\) −30.8312 −0.0472871
\(653\) −945.003 −1.44717 −0.723586 0.690234i \(-0.757507\pi\)
−0.723586 + 0.690234i \(0.757507\pi\)
\(654\) −497.540 −0.760765
\(655\) 872.014i 1.33132i
\(656\) −166.893 −0.254409
\(657\) 264.048i 0.401900i
\(658\) 1850.54 2.81237
\(659\) 907.745i 1.37746i −0.725018 0.688729i \(-0.758169\pi\)
0.725018 0.688729i \(-0.241831\pi\)
\(660\) 204.803i 0.310307i
\(661\) −1024.26 −1.54957 −0.774783 0.632227i \(-0.782141\pi\)
−0.774783 + 0.632227i \(0.782141\pi\)
\(662\) 10.8922i 0.0164535i
\(663\) 90.3467i 0.136270i
\(664\) 4.45849 0.00671459
\(665\) −917.240 −1.37931
\(666\) 4.31291 0.00647584
\(667\) 239.281i 0.358742i
\(668\) 493.163 0.738268
\(669\) 38.9420 0.0582093
\(670\) 1440.67 2.15025
\(671\) 249.914 0.372451
\(672\) 644.170i 0.958586i
\(673\) 629.364i 0.935163i 0.883950 + 0.467581i \(0.154874\pi\)
−0.883950 + 0.467581i \(0.845126\pi\)
\(674\) 947.997 1.40652
\(675\) −39.8183 −0.0589900
\(676\) −501.689 −0.742144
\(677\) 671.976 0.992579 0.496289 0.868157i \(-0.334695\pi\)
0.496289 + 0.868157i \(0.334695\pi\)
\(678\) 475.845 0.701837
\(679\) 1470.30i 2.16539i
\(680\) 94.4677i 0.138923i
\(681\) 479.513i 0.704130i
\(682\) 104.762i 0.153610i
\(683\) 683.994i 1.00145i 0.865605 + 0.500727i \(0.166934\pi\)
−0.865605 + 0.500727i \(0.833066\pi\)
\(684\) 190.598 0.278652
\(685\) 1104.97 1.61310
\(686\) 532.446i 0.776160i
\(687\) 278.731i 0.405722i
\(688\) 949.308i 1.37981i
\(689\) 49.2269i 0.0714468i
\(690\) 416.055 0.602978
\(691\) 69.2046i 0.100151i −0.998745 0.0500757i \(-0.984054\pi\)
0.998745 0.0500757i \(-0.0159463\pi\)
\(692\) 197.657i 0.285631i
\(693\) 156.793i 0.226252i
\(694\) −1602.36 −2.30888
\(695\) 987.865 1.42139
\(696\) 41.0420i 0.0589685i
\(697\) 100.861 0.144708
\(698\) −1078.67 −1.54538
\(699\) 18.4088i 0.0263360i
\(700\) −229.155 −0.327364
\(701\) 1173.53i 1.67408i 0.547143 + 0.837039i \(0.315715\pi\)
−0.547143 + 0.837039i \(0.684285\pi\)
\(702\) −68.2496 −0.0972216
\(703\) 9.73209i 0.0138437i
\(704\) 270.736i 0.384568i
\(705\) 772.661i 1.09597i
\(706\) 550.689 0.780012
\(707\) 55.9414i 0.0791250i
\(708\) 175.733 + 304.533i 0.248210 + 0.430131i
\(709\) −291.385 −0.410980 −0.205490 0.978659i \(-0.565879\pi\)
−0.205490 + 0.978659i \(0.565879\pi\)
\(710\) 1462.36i 2.05966i
\(711\) −243.633 −0.342663
\(712\) 257.442 0.361576
\(713\) 98.4114 0.138024
\(714\) 444.832i 0.623014i
\(715\) 165.483 0.231445
\(716\) 310.294i 0.433371i
\(717\) −387.276 −0.540134
\(718\) 1444.48i 2.01182i
\(719\) 1045.70i 1.45438i −0.686434 0.727192i \(-0.740825\pi\)
0.686434 0.727192i \(-0.259175\pi\)
\(720\) −307.326 −0.426842
\(721\) 1538.12i 2.13331i
\(722\) 54.6221i 0.0756538i
\(723\) −111.926 −0.154808
\(724\) −426.426 −0.588986
\(725\) 119.001 0.164140
\(726\) 400.837i 0.552118i
\(727\) −96.8300 −0.133191 −0.0665956 0.997780i \(-0.521214\pi\)
−0.0665956 + 0.997780i \(0.521214\pi\)
\(728\) 63.8593 0.0877188
\(729\) 27.0000 0.0370370
\(730\) 1372.13 1.87963
\(731\) 573.713i 0.784833i
\(732\) 247.672i 0.338349i
\(733\) 63.9954 0.0873061 0.0436531 0.999047i \(-0.486100\pi\)
0.0436531 + 0.999047i \(0.486100\pi\)
\(734\) 980.840 1.33629
\(735\) −262.734 −0.357462
\(736\) 659.332 0.895831
\(737\) 555.702 0.754006
\(738\) 76.1925i 0.103242i
\(739\) 234.644i 0.317515i 0.987318 + 0.158758i \(0.0507489\pi\)
−0.987318 + 0.158758i \(0.949251\pi\)
\(740\) 10.3636i 0.0140048i
\(741\) 154.005i 0.207835i
\(742\) 242.374i 0.326650i
\(743\) 724.236 0.974746 0.487373 0.873194i \(-0.337955\pi\)
0.487373 + 0.873194i \(0.337955\pi\)
\(744\) −16.8797 −0.0226878
\(745\) 1037.96i 1.39324i
\(746\) 1199.33i 1.60769i
\(747\) 8.76580i 0.0117347i
\(748\) 224.122i 0.299629i
\(749\) −1595.52 −2.13020
\(750\) 468.130i 0.624173i
\(751\) 539.064i 0.717795i −0.933377 0.358897i \(-0.883153\pi\)
0.933377 0.358897i \(-0.116847\pi\)
\(752\) 1399.11i 1.86051i
\(753\) 246.630 0.327531
\(754\) 203.971 0.270519
\(755\) 6.92591i 0.00917339i
\(756\) 155.386 0.205537
\(757\) 669.143 0.883941 0.441970 0.897030i \(-0.354280\pi\)
0.441970 + 0.897030i \(0.354280\pi\)
\(758\) 1583.26i 2.08873i
\(759\) 160.483 0.211440
\(760\) 161.030i 0.211882i
\(761\) 896.609 1.17820 0.589099 0.808061i \(-0.299483\pi\)
0.589099 + 0.808061i \(0.299483\pi\)
\(762\) 974.049i 1.27828i
\(763\) 915.285i 1.19959i
\(764\) 518.990i 0.679307i
\(765\) 185.732 0.242787
\(766\) 936.477i 1.22255i
\(767\) 246.066 141.994i 0.320816 0.185129i
\(768\) −540.364 −0.703599
\(769\) 294.155i 0.382516i 0.981540 + 0.191258i \(0.0612567\pi\)
−0.981540 + 0.191258i \(0.938743\pi\)
\(770\) −814.774 −1.05815
\(771\) −22.9887 −0.0298167
\(772\) 291.836 0.378025
\(773\) 118.806i 0.153694i −0.997043 0.0768471i \(-0.975515\pi\)
0.997043 0.0768471i \(-0.0244853\pi\)
\(774\) −433.394 −0.559940
\(775\) 48.9428i 0.0631520i
\(776\) 258.124 0.332634
\(777\) 7.93412i 0.0102112i
\(778\) 827.668i 1.06384i
\(779\) −171.929 −0.220704
\(780\) 163.998i 0.210254i
\(781\) 564.068i 0.722239i
\(782\) −455.302 −0.582228
\(783\) −80.6925 −0.103056
\(784\) −475.749 −0.606823
\(785\) 1053.84i 1.34248i
\(786\) 720.876 0.917144
\(787\) 67.0954 0.0852546 0.0426273 0.999091i \(-0.486427\pi\)
0.0426273 + 0.999091i \(0.486427\pi\)
\(788\) 656.197 0.832737
\(789\) 93.5618 0.118583
\(790\) 1266.04i 1.60258i
\(791\) 875.375i 1.10667i
\(792\) </