Properties

Label 403.2.c.b.311.3
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.3
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.30

$q$-expansion

\(f(q)\) \(=\) \(q-2.45635i q^{2} +2.80039 q^{3} -4.03363 q^{4} +3.48535i q^{5} -6.87871i q^{6} -3.54003i q^{7} +4.99531i q^{8} +4.84216 q^{9} +O(q^{10})\) \(q-2.45635i q^{2} +2.80039 q^{3} -4.03363 q^{4} +3.48535i q^{5} -6.87871i q^{6} -3.54003i q^{7} +4.99531i q^{8} +4.84216 q^{9} +8.56123 q^{10} -5.60543i q^{11} -11.2957 q^{12} +(3.17012 + 1.71765i) q^{13} -8.69555 q^{14} +9.76032i q^{15} +4.20294 q^{16} +2.47924 q^{17} -11.8940i q^{18} +2.94408i q^{19} -14.0586i q^{20} -9.91346i q^{21} -13.7689 q^{22} -1.33162 q^{23} +13.9888i q^{24} -7.14767 q^{25} +(4.21915 - 7.78691i) q^{26} +5.15875 q^{27} +14.2792i q^{28} -6.22251 q^{29} +23.9747 q^{30} -1.00000i q^{31} -0.333245i q^{32} -15.6974i q^{33} -6.08988i q^{34} +12.3383 q^{35} -19.5315 q^{36} +7.14956i q^{37} +7.23168 q^{38} +(8.87756 + 4.81009i) q^{39} -17.4104 q^{40} +4.88228i q^{41} -24.3509 q^{42} +0.926054 q^{43} +22.6103i q^{44} +16.8766i q^{45} +3.27093i q^{46} +11.4047i q^{47} +11.7698 q^{48} -5.53184 q^{49} +17.5571i q^{50} +6.94284 q^{51} +(-12.7871 - 6.92839i) q^{52} -9.27473 q^{53} -12.6717i q^{54} +19.5369 q^{55} +17.6836 q^{56} +8.24456i q^{57} +15.2846i q^{58} -6.89104i q^{59} -39.3696i q^{60} +5.72757 q^{61} -2.45635 q^{62} -17.1414i q^{63} +7.58730 q^{64} +(-5.98663 + 11.0490i) q^{65} -38.5582 q^{66} -9.27764i q^{67} -10.0004 q^{68} -3.72906 q^{69} -30.3070i q^{70} +0.850046i q^{71} +24.1881i q^{72} +8.68621i q^{73} +17.5618 q^{74} -20.0162 q^{75} -11.8753i q^{76} -19.8434 q^{77} +(11.8153 - 21.8064i) q^{78} -5.69838 q^{79} +14.6487i q^{80} -0.0799826 q^{81} +11.9926 q^{82} +10.1834i q^{83} +39.9873i q^{84} +8.64103i q^{85} -2.27471i q^{86} -17.4254 q^{87} +28.0009 q^{88} -3.72778i q^{89} +41.4548 q^{90} +(6.08056 - 11.2223i) q^{91} +5.37128 q^{92} -2.80039i q^{93} +28.0139 q^{94} -10.2611 q^{95} -0.933216i q^{96} -11.4074i q^{97} +13.5881i q^{98} -27.1424i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45635i 1.73690i −0.495778 0.868449i \(-0.665117\pi\)
0.495778 0.868449i \(-0.334883\pi\)
\(3\) 2.80039 1.61680 0.808402 0.588631i \(-0.200333\pi\)
0.808402 + 0.588631i \(0.200333\pi\)
\(4\) −4.03363 −2.01682
\(5\) 3.48535i 1.55870i 0.626591 + 0.779348i \(0.284450\pi\)
−0.626591 + 0.779348i \(0.715550\pi\)
\(6\) 6.87871i 2.80822i
\(7\) 3.54003i 1.33801i −0.743259 0.669004i \(-0.766721\pi\)
0.743259 0.669004i \(-0.233279\pi\)
\(8\) 4.99531i 1.76611i
\(9\) 4.84216 1.61405
\(10\) 8.56123 2.70730
\(11\) 5.60543i 1.69010i −0.534686 0.845051i \(-0.679570\pi\)
0.534686 0.845051i \(-0.320430\pi\)
\(12\) −11.2957 −3.26080
\(13\) 3.17012 + 1.71765i 0.879233 + 0.476392i
\(14\) −8.69555 −2.32398
\(15\) 9.76032i 2.52010i
\(16\) 4.20294 1.05073
\(17\) 2.47924 0.601305 0.300652 0.953734i \(-0.402796\pi\)
0.300652 + 0.953734i \(0.402796\pi\)
\(18\) 11.8940i 2.80345i
\(19\) 2.94408i 0.675418i 0.941251 + 0.337709i \(0.109652\pi\)
−0.941251 + 0.337709i \(0.890348\pi\)
\(20\) 14.0586i 3.14360i
\(21\) 9.91346i 2.16329i
\(22\) −13.7689 −2.93553
\(23\) −1.33162 −0.277663 −0.138831 0.990316i \(-0.544335\pi\)
−0.138831 + 0.990316i \(0.544335\pi\)
\(24\) 13.9888i 2.85545i
\(25\) −7.14767 −1.42953
\(26\) 4.21915 7.78691i 0.827444 1.52714i
\(27\) 5.15875 0.992802
\(28\) 14.2792i 2.69852i
\(29\) −6.22251 −1.15549 −0.577746 0.816217i \(-0.696067\pi\)
−0.577746 + 0.816217i \(0.696067\pi\)
\(30\) 23.9747 4.37717
\(31\) 1.00000i 0.179605i
\(32\) 0.333245i 0.0589100i
\(33\) 15.6974i 2.73256i
\(34\) 6.08988i 1.04441i
\(35\) 12.3383 2.08555
\(36\) −19.5315 −3.25525
\(37\) 7.14956i 1.17538i 0.809086 + 0.587691i \(0.199963\pi\)
−0.809086 + 0.587691i \(0.800037\pi\)
\(38\) 7.23168 1.17313
\(39\) 8.87756 + 4.81009i 1.42155 + 0.770232i
\(40\) −17.4104 −2.75283
\(41\) 4.88228i 0.762484i 0.924475 + 0.381242i \(0.124504\pi\)
−0.924475 + 0.381242i \(0.875496\pi\)
\(42\) −24.3509 −3.75742
\(43\) 0.926054 0.141222 0.0706110 0.997504i \(-0.477505\pi\)
0.0706110 + 0.997504i \(0.477505\pi\)
\(44\) 22.6103i 3.40862i
\(45\) 16.8766i 2.51582i
\(46\) 3.27093i 0.482272i
\(47\) 11.4047i 1.66355i 0.555116 + 0.831773i \(0.312674\pi\)
−0.555116 + 0.831773i \(0.687326\pi\)
\(48\) 11.7698 1.69883
\(49\) −5.53184 −0.790263
\(50\) 17.5571i 2.48296i
\(51\) 6.94284 0.972191
\(52\) −12.7871 6.92839i −1.77325 0.960795i
\(53\) −9.27473 −1.27398 −0.636991 0.770871i \(-0.719821\pi\)
−0.636991 + 0.770871i \(0.719821\pi\)
\(54\) 12.6717i 1.72440i
\(55\) 19.5369 2.63435
\(56\) 17.6836 2.36307
\(57\) 8.24456i 1.09202i
\(58\) 15.2846i 2.00697i
\(59\) 6.89104i 0.897137i −0.893749 0.448568i \(-0.851934\pi\)
0.893749 0.448568i \(-0.148066\pi\)
\(60\) 39.3696i 5.08259i
\(61\) 5.72757 0.733340 0.366670 0.930351i \(-0.380498\pi\)
0.366670 + 0.930351i \(0.380498\pi\)
\(62\) −2.45635 −0.311956
\(63\) 17.1414i 2.15961i
\(64\) 7.58730 0.948413
\(65\) −5.98663 + 11.0490i −0.742550 + 1.37046i
\(66\) −38.5582 −4.74618
\(67\) 9.27764i 1.13344i −0.823909 0.566722i \(-0.808211\pi\)
0.823909 0.566722i \(-0.191789\pi\)
\(68\) −10.0004 −1.21272
\(69\) −3.72906 −0.448926
\(70\) 30.3070i 3.62238i
\(71\) 0.850046i 0.100882i 0.998727 + 0.0504410i \(0.0160627\pi\)
−0.998727 + 0.0504410i \(0.983937\pi\)
\(72\) 24.1881i 2.85059i
\(73\) 8.68621i 1.01664i 0.861167 + 0.508322i \(0.169734\pi\)
−0.861167 + 0.508322i \(0.830266\pi\)
\(74\) 17.5618 2.04152
\(75\) −20.0162 −2.31127
\(76\) 11.8753i 1.36219i
\(77\) −19.8434 −2.26137
\(78\) 11.8153 21.8064i 1.33781 2.46908i
\(79\) −5.69838 −0.641117 −0.320559 0.947229i \(-0.603871\pi\)
−0.320559 + 0.947229i \(0.603871\pi\)
\(80\) 14.6487i 1.63777i
\(81\) −0.0799826 −0.00888695
\(82\) 11.9926 1.32436
\(83\) 10.1834i 1.11778i 0.829243 + 0.558888i \(0.188772\pi\)
−0.829243 + 0.558888i \(0.811228\pi\)
\(84\) 39.9873i 4.36297i
\(85\) 8.64103i 0.937251i
\(86\) 2.27471i 0.245288i
\(87\) −17.4254 −1.86820
\(88\) 28.0009 2.98490
\(89\) 3.72778i 0.395144i −0.980288 0.197572i \(-0.936694\pi\)
0.980288 0.197572i \(-0.0633056\pi\)
\(90\) 41.4548 4.36972
\(91\) 6.08056 11.2223i 0.637415 1.17642i
\(92\) 5.37128 0.559995
\(93\) 2.80039i 0.290386i
\(94\) 28.0139 2.88941
\(95\) −10.2611 −1.05277
\(96\) 0.933216i 0.0952459i
\(97\) 11.4074i 1.15824i −0.815241 0.579122i \(-0.803396\pi\)
0.815241 0.579122i \(-0.196604\pi\)
\(98\) 13.5881i 1.37261i
\(99\) 27.1424i 2.72791i
\(100\) 28.8311 2.88311
\(101\) 6.14390 0.611341 0.305671 0.952137i \(-0.401119\pi\)
0.305671 + 0.952137i \(0.401119\pi\)
\(102\) 17.0540i 1.68860i
\(103\) 9.77159 0.962823 0.481412 0.876495i \(-0.340124\pi\)
0.481412 + 0.876495i \(0.340124\pi\)
\(104\) −8.58021 + 15.8357i −0.841359 + 1.55282i
\(105\) 34.5519 3.37192
\(106\) 22.7819i 2.21278i
\(107\) −0.0150159 −0.00145164 −0.000725821 1.00000i \(-0.500231\pi\)
−0.000725821 1.00000i \(0.500231\pi\)
\(108\) −20.8085 −2.00230
\(109\) 0.921927i 0.0883046i −0.999025 0.0441523i \(-0.985941\pi\)
0.999025 0.0441523i \(-0.0140587\pi\)
\(110\) 47.9894i 4.57561i
\(111\) 20.0215i 1.90036i
\(112\) 14.8785i 1.40589i
\(113\) −5.96949 −0.561562 −0.280781 0.959772i \(-0.590594\pi\)
−0.280781 + 0.959772i \(0.590594\pi\)
\(114\) 20.2515 1.89673
\(115\) 4.64118i 0.432792i
\(116\) 25.0993 2.33041
\(117\) 15.3502 + 8.31715i 1.41913 + 0.768921i
\(118\) −16.9268 −1.55824
\(119\) 8.77660i 0.804550i
\(120\) −48.7558 −4.45078
\(121\) −20.4209 −1.85644
\(122\) 14.0689i 1.27374i
\(123\) 13.6723i 1.23279i
\(124\) 4.03363i 0.362231i
\(125\) 7.48538i 0.669512i
\(126\) −42.1052 −3.75103
\(127\) −4.63997 −0.411731 −0.205865 0.978580i \(-0.566001\pi\)
−0.205865 + 0.978580i \(0.566001\pi\)
\(128\) 19.3035i 1.70621i
\(129\) 2.59331 0.228328
\(130\) 27.1401 + 14.7052i 2.38035 + 1.28973i
\(131\) −12.9817 −1.13421 −0.567107 0.823644i \(-0.691938\pi\)
−0.567107 + 0.823644i \(0.691938\pi\)
\(132\) 63.3174i 5.51108i
\(133\) 10.4221 0.903714
\(134\) −22.7891 −1.96868
\(135\) 17.9801i 1.54748i
\(136\) 12.3846i 1.06197i
\(137\) 4.66000i 0.398131i −0.979986 0.199065i \(-0.936209\pi\)
0.979986 0.199065i \(-0.0637906\pi\)
\(138\) 9.15986i 0.779739i
\(139\) 14.8173 1.25679 0.628393 0.777896i \(-0.283713\pi\)
0.628393 + 0.777896i \(0.283713\pi\)
\(140\) −49.7680 −4.20617
\(141\) 31.9375i 2.68963i
\(142\) 2.08801 0.175222
\(143\) 9.62820 17.7699i 0.805150 1.48599i
\(144\) 20.3513 1.69594
\(145\) 21.6876i 1.80106i
\(146\) 21.3363 1.76581
\(147\) −15.4913 −1.27770
\(148\) 28.8387i 2.37053i
\(149\) 2.85800i 0.234137i −0.993124 0.117068i \(-0.962650\pi\)
0.993124 0.117068i \(-0.0373496\pi\)
\(150\) 49.1668i 4.01445i
\(151\) 0.429054i 0.0349159i −0.999848 0.0174580i \(-0.994443\pi\)
0.999848 0.0174580i \(-0.00555732\pi\)
\(152\) −14.7066 −1.19286
\(153\) 12.0049 0.970537
\(154\) 48.7423i 3.92777i
\(155\) 3.48535 0.279950
\(156\) −35.8088 19.4022i −2.86700 1.55342i
\(157\) −4.78512 −0.381894 −0.190947 0.981600i \(-0.561156\pi\)
−0.190947 + 0.981600i \(0.561156\pi\)
\(158\) 13.9972i 1.11356i
\(159\) −25.9728 −2.05978
\(160\) 1.16148 0.0918228
\(161\) 4.71399i 0.371515i
\(162\) 0.196465i 0.0154357i
\(163\) 21.8453i 1.71105i −0.517758 0.855527i \(-0.673233\pi\)
0.517758 0.855527i \(-0.326767\pi\)
\(164\) 19.6933i 1.53779i
\(165\) 54.7108 4.25923
\(166\) 25.0140 1.94146
\(167\) 3.37083i 0.260843i −0.991459 0.130421i \(-0.958367\pi\)
0.991459 0.130421i \(-0.0416330\pi\)
\(168\) 49.5208 3.82061
\(169\) 7.09933 + 10.8903i 0.546102 + 0.837719i
\(170\) 21.2254 1.62791
\(171\) 14.2557i 1.09016i
\(172\) −3.73536 −0.284819
\(173\) −14.7745 −1.12329 −0.561643 0.827379i \(-0.689831\pi\)
−0.561643 + 0.827379i \(0.689831\pi\)
\(174\) 42.8029i 3.24488i
\(175\) 25.3030i 1.91273i
\(176\) 23.5593i 1.77585i
\(177\) 19.2976i 1.45049i
\(178\) −9.15671 −0.686325
\(179\) −24.6355 −1.84134 −0.920672 0.390337i \(-0.872359\pi\)
−0.920672 + 0.390337i \(0.872359\pi\)
\(180\) 68.0741i 5.07394i
\(181\) 5.26608 0.391425 0.195712 0.980661i \(-0.437298\pi\)
0.195712 + 0.980661i \(0.437298\pi\)
\(182\) −27.5659 14.9359i −2.04332 1.10713i
\(183\) 16.0394 1.18567
\(184\) 6.65187i 0.490383i
\(185\) −24.9187 −1.83206
\(186\) −6.87871 −0.504372
\(187\) 13.8972i 1.01627i
\(188\) 46.0024i 3.35507i
\(189\) 18.2622i 1.32838i
\(190\) 25.2049i 1.82856i
\(191\) −4.61535 −0.333955 −0.166978 0.985961i \(-0.553401\pi\)
−0.166978 + 0.985961i \(0.553401\pi\)
\(192\) 21.2474 1.53340
\(193\) 1.61977i 0.116594i 0.998299 + 0.0582969i \(0.0185670\pi\)
−0.998299 + 0.0582969i \(0.981433\pi\)
\(194\) −28.0205 −2.01175
\(195\) −16.7649 + 30.9414i −1.20056 + 2.21576i
\(196\) 22.3134 1.59382
\(197\) 8.32063i 0.592820i −0.955061 0.296410i \(-0.904210\pi\)
0.955061 0.296410i \(-0.0957896\pi\)
\(198\) −66.6711 −4.73811
\(199\) 23.6343 1.67539 0.837694 0.546140i \(-0.183903\pi\)
0.837694 + 0.546140i \(0.183903\pi\)
\(200\) 35.7048i 2.52471i
\(201\) 25.9810i 1.83256i
\(202\) 15.0916i 1.06184i
\(203\) 22.0279i 1.54606i
\(204\) −28.0049 −1.96073
\(205\) −17.0165 −1.18848
\(206\) 24.0024i 1.67233i
\(207\) −6.44793 −0.448162
\(208\) 13.3238 + 7.21919i 0.923840 + 0.500561i
\(209\) 16.5028 1.14153
\(210\) 84.8714i 5.85668i
\(211\) 22.5919 1.55529 0.777647 0.628701i \(-0.216413\pi\)
0.777647 + 0.628701i \(0.216413\pi\)
\(212\) 37.4109 2.56939
\(213\) 2.38046i 0.163106i
\(214\) 0.0368842i 0.00252135i
\(215\) 3.22762i 0.220122i
\(216\) 25.7696i 1.75340i
\(217\) −3.54003 −0.240313
\(218\) −2.26457 −0.153376
\(219\) 24.3247i 1.64371i
\(220\) −78.8047 −5.31301
\(221\) 7.85950 + 4.25848i 0.528687 + 0.286457i
\(222\) 49.1798 3.30073
\(223\) 24.0641i 1.61145i −0.592288 0.805726i \(-0.701775\pi\)
0.592288 0.805726i \(-0.298225\pi\)
\(224\) −1.17970 −0.0788220
\(225\) −34.6101 −2.30734
\(226\) 14.6631i 0.975377i
\(227\) 8.15313i 0.541142i 0.962700 + 0.270571i \(0.0872125\pi\)
−0.962700 + 0.270571i \(0.912787\pi\)
\(228\) 33.2555i 2.20240i
\(229\) 5.28147i 0.349010i 0.984656 + 0.174505i \(0.0558324\pi\)
−0.984656 + 0.174505i \(0.944168\pi\)
\(230\) −11.4003 −0.751716
\(231\) −55.5692 −3.65619
\(232\) 31.0834i 2.04072i
\(233\) 10.6469 0.697501 0.348750 0.937216i \(-0.386606\pi\)
0.348750 + 0.937216i \(0.386606\pi\)
\(234\) 20.4298 37.7055i 1.33554 2.46488i
\(235\) −39.7494 −2.59296
\(236\) 27.7959i 1.80936i
\(237\) −15.9576 −1.03656
\(238\) −21.5584 −1.39742
\(239\) 6.31548i 0.408514i 0.978917 + 0.204257i \(0.0654779\pi\)
−0.978917 + 0.204257i \(0.934522\pi\)
\(240\) 41.0220i 2.64796i
\(241\) 14.7695i 0.951389i −0.879610 0.475695i \(-0.842197\pi\)
0.879610 0.475695i \(-0.157803\pi\)
\(242\) 50.1607i 3.22445i
\(243\) −15.7002 −1.00717
\(244\) −23.1029 −1.47901
\(245\) 19.2804i 1.23178i
\(246\) 33.5838 2.14123
\(247\) −5.05691 + 9.33309i −0.321764 + 0.593850i
\(248\) 4.99531 0.317202
\(249\) 28.5175i 1.80723i
\(250\) −18.3867 −1.16288
\(251\) −12.3317 −0.778372 −0.389186 0.921159i \(-0.627244\pi\)
−0.389186 + 0.921159i \(0.627244\pi\)
\(252\) 69.1421i 4.35555i
\(253\) 7.46433i 0.469278i
\(254\) 11.3974i 0.715135i
\(255\) 24.1982i 1.51535i
\(256\) −32.2415 −2.01510
\(257\) 27.5568 1.71895 0.859474 0.511180i \(-0.170791\pi\)
0.859474 + 0.511180i \(0.170791\pi\)
\(258\) 6.37006i 0.396583i
\(259\) 25.3097 1.57267
\(260\) 24.1479 44.5675i 1.49759 2.76396i
\(261\) −30.1304 −1.86502
\(262\) 31.8875i 1.97002i
\(263\) 26.3404 1.62422 0.812111 0.583503i \(-0.198319\pi\)
0.812111 + 0.583503i \(0.198319\pi\)
\(264\) 78.4132 4.82600
\(265\) 32.3257i 1.98575i
\(266\) 25.6004i 1.56966i
\(267\) 10.4392i 0.638870i
\(268\) 37.4226i 2.28595i
\(269\) −18.9927 −1.15801 −0.579004 0.815325i \(-0.696558\pi\)
−0.579004 + 0.815325i \(0.696558\pi\)
\(270\) 44.1652 2.68781
\(271\) 8.87920i 0.539373i 0.962948 + 0.269686i \(0.0869200\pi\)
−0.962948 + 0.269686i \(0.913080\pi\)
\(272\) 10.4201 0.631811
\(273\) 17.0279 31.4269i 1.03058 1.90204i
\(274\) −11.4466 −0.691513
\(275\) 40.0658i 2.41606i
\(276\) 15.0417 0.905402
\(277\) 0.263699 0.0158442 0.00792208 0.999969i \(-0.497478\pi\)
0.00792208 + 0.999969i \(0.497478\pi\)
\(278\) 36.3964i 2.18291i
\(279\) 4.84216i 0.289892i
\(280\) 61.6334i 3.68330i
\(281\) 6.28589i 0.374985i −0.982266 0.187492i \(-0.939964\pi\)
0.982266 0.187492i \(-0.0600360\pi\)
\(282\) 78.4497 4.67161
\(283\) 11.3137 0.672527 0.336264 0.941768i \(-0.390837\pi\)
0.336264 + 0.941768i \(0.390837\pi\)
\(284\) 3.42878i 0.203460i
\(285\) −28.7352 −1.70212
\(286\) −43.6490 23.6502i −2.58102 1.39846i
\(287\) 17.2834 1.02021
\(288\) 1.61363i 0.0950839i
\(289\) −10.8534 −0.638433
\(290\) −53.2723 −3.12826
\(291\) 31.9450i 1.87265i
\(292\) 35.0370i 2.05038i
\(293\) 19.5031i 1.13938i 0.821858 + 0.569692i \(0.192938\pi\)
−0.821858 + 0.569692i \(0.807062\pi\)
\(294\) 38.0520i 2.21924i
\(295\) 24.0177 1.39836
\(296\) −35.7143 −2.07585
\(297\) 28.9170i 1.67794i
\(298\) −7.02024 −0.406672
\(299\) −4.22141 2.28727i −0.244130 0.132276i
\(300\) 80.7381 4.66142
\(301\) 3.27826i 0.188956i
\(302\) −1.05390 −0.0606454
\(303\) 17.2053 0.988419
\(304\) 12.3738i 0.709685i
\(305\) 19.9626i 1.14305i
\(306\) 29.4881i 1.68573i
\(307\) 31.6864i 1.80844i −0.427069 0.904219i \(-0.640454\pi\)
0.427069 0.904219i \(-0.359546\pi\)
\(308\) 80.0411 4.56076
\(309\) 27.3642 1.55670
\(310\) 8.56123i 0.486245i
\(311\) −1.23362 −0.0699522 −0.0349761 0.999388i \(-0.511136\pi\)
−0.0349761 + 0.999388i \(0.511136\pi\)
\(312\) −24.0279 + 44.3461i −1.36031 + 2.51061i
\(313\) −19.5774 −1.10658 −0.553291 0.832988i \(-0.686628\pi\)
−0.553291 + 0.832988i \(0.686628\pi\)
\(314\) 11.7539i 0.663312i
\(315\) 59.7438 3.36618
\(316\) 22.9852 1.29302
\(317\) 2.05349i 0.115336i 0.998336 + 0.0576678i \(0.0183664\pi\)
−0.998336 + 0.0576678i \(0.981634\pi\)
\(318\) 63.7982i 3.57762i
\(319\) 34.8799i 1.95290i
\(320\) 26.4444i 1.47829i
\(321\) −0.0420503 −0.00234702
\(322\) 11.5792 0.645284
\(323\) 7.29909i 0.406132i
\(324\) 0.322620 0.0179234
\(325\) −22.6590 12.2772i −1.25689 0.681018i
\(326\) −53.6595 −2.97193
\(327\) 2.58175i 0.142771i
\(328\) −24.3885 −1.34663
\(329\) 40.3730 2.22584
\(330\) 134.389i 7.39785i
\(331\) 13.2618i 0.728933i 0.931216 + 0.364467i \(0.118749\pi\)
−0.931216 + 0.364467i \(0.881251\pi\)
\(332\) 41.0762i 2.25435i
\(333\) 34.6193i 1.89713i
\(334\) −8.27993 −0.453057
\(335\) 32.3358 1.76670
\(336\) 41.6656i 2.27305i
\(337\) 35.1836 1.91657 0.958287 0.285806i \(-0.0922613\pi\)
0.958287 + 0.285806i \(0.0922613\pi\)
\(338\) 26.7504 17.4384i 1.45503 0.948524i
\(339\) −16.7169 −0.907936
\(340\) 34.8548i 1.89026i
\(341\) −5.60543 −0.303551
\(342\) 35.0169 1.89350
\(343\) 5.19733i 0.280629i
\(344\) 4.62593i 0.249413i
\(345\) 12.9971i 0.699739i
\(346\) 36.2913i 1.95104i
\(347\) −12.0992 −0.649519 −0.324759 0.945797i \(-0.605283\pi\)
−0.324759 + 0.945797i \(0.605283\pi\)
\(348\) 70.2878 3.76782
\(349\) 28.7745i 1.54026i 0.637886 + 0.770131i \(0.279809\pi\)
−0.637886 + 0.770131i \(0.720191\pi\)
\(350\) 62.1529 3.32221
\(351\) 16.3539 + 8.86095i 0.872905 + 0.472963i
\(352\) −1.86798 −0.0995639
\(353\) 15.0930i 0.803321i 0.915789 + 0.401660i \(0.131567\pi\)
−0.915789 + 0.401660i \(0.868433\pi\)
\(354\) −47.4015 −2.51936
\(355\) −2.96271 −0.157244
\(356\) 15.0365i 0.796933i
\(357\) 24.5779i 1.30080i
\(358\) 60.5133i 3.19823i
\(359\) 2.92054i 0.154140i 0.997026 + 0.0770701i \(0.0245565\pi\)
−0.997026 + 0.0770701i \(0.975443\pi\)
\(360\) −84.3039 −4.44321
\(361\) 10.3324 0.543810
\(362\) 12.9353i 0.679865i
\(363\) −57.1863 −3.00150
\(364\) −24.5267 + 45.2668i −1.28555 + 2.37262i
\(365\) −30.2745 −1.58464
\(366\) 39.3983i 2.05938i
\(367\) 7.03364 0.367153 0.183576 0.983005i \(-0.441233\pi\)
0.183576 + 0.983005i \(0.441233\pi\)
\(368\) −5.59673 −0.291750
\(369\) 23.6408i 1.23069i
\(370\) 61.2090i 3.18211i
\(371\) 32.8328i 1.70460i
\(372\) 11.2957i 0.585656i
\(373\) −9.23107 −0.477967 −0.238983 0.971024i \(-0.576814\pi\)
−0.238983 + 0.971024i \(0.576814\pi\)
\(374\) −34.1364 −1.76515
\(375\) 20.9619i 1.08247i
\(376\) −56.9700 −2.93800
\(377\) −19.7261 10.6881i −1.01595 0.550466i
\(378\) −44.8582 −2.30726
\(379\) 14.1434i 0.726499i −0.931692 0.363249i \(-0.881667\pi\)
0.931692 0.363249i \(-0.118333\pi\)
\(380\) 41.3897 2.12325
\(381\) −12.9937 −0.665688
\(382\) 11.3369i 0.580046i
\(383\) 9.51959i 0.486428i 0.969973 + 0.243214i \(0.0782018\pi\)
−0.969973 + 0.243214i \(0.921798\pi\)
\(384\) 54.0573i 2.75860i
\(385\) 69.1613i 3.52478i
\(386\) 3.97872 0.202512
\(387\) 4.48410 0.227940
\(388\) 46.0132i 2.33596i
\(389\) 9.65776 0.489668 0.244834 0.969565i \(-0.421267\pi\)
0.244834 + 0.969565i \(0.421267\pi\)
\(390\) 76.0028 + 41.1803i 3.84855 + 2.08525i
\(391\) −3.30142 −0.166960
\(392\) 27.6333i 1.39569i
\(393\) −36.3537 −1.83380
\(394\) −20.4383 −1.02967
\(395\) 19.8608i 0.999307i
\(396\) 109.482i 5.50170i
\(397\) 13.1443i 0.659692i 0.944035 + 0.329846i \(0.106997\pi\)
−0.944035 + 0.329846i \(0.893003\pi\)
\(398\) 58.0539i 2.90998i
\(399\) 29.1860 1.46113
\(400\) −30.0412 −1.50206
\(401\) 22.7879i 1.13798i −0.822346 0.568988i \(-0.807335\pi\)
0.822346 0.568988i \(-0.192665\pi\)
\(402\) −63.8182 −3.18296
\(403\) 1.71765 3.17012i 0.0855625 0.157915i
\(404\) −24.7823 −1.23296
\(405\) 0.278767i 0.0138521i
\(406\) 54.1081 2.68534
\(407\) 40.0764 1.98651
\(408\) 34.6816i 1.71700i
\(409\) 20.1639i 0.997043i −0.866877 0.498521i \(-0.833877\pi\)
0.866877 0.498521i \(-0.166123\pi\)
\(410\) 41.7983i 2.06427i
\(411\) 13.0498i 0.643699i
\(412\) −39.4150 −1.94184
\(413\) −24.3945 −1.20038
\(414\) 15.8384i 0.778413i
\(415\) −35.4928 −1.74227
\(416\) 0.572401 1.05643i 0.0280642 0.0517957i
\(417\) 41.4941 2.03198
\(418\) 40.5367i 1.98271i
\(419\) 2.09350 0.102274 0.0511371 0.998692i \(-0.483715\pi\)
0.0511371 + 0.998692i \(0.483715\pi\)
\(420\) −139.370 −6.80054
\(421\) 15.1244i 0.737120i −0.929604 0.368560i \(-0.879851\pi\)
0.929604 0.368560i \(-0.120149\pi\)
\(422\) 55.4936i 2.70139i
\(423\) 55.2233i 2.68505i
\(424\) 46.3301i 2.24999i
\(425\) −17.7208 −0.859585
\(426\) 5.84723 0.283299
\(427\) 20.2758i 0.981214i
\(428\) 0.0605686 0.00292770
\(429\) 26.9627 49.7625i 1.30177 2.40256i
\(430\) 7.92816 0.382330
\(431\) 12.5939i 0.606628i 0.952891 + 0.303314i \(0.0980930\pi\)
−0.952891 + 0.303314i \(0.901907\pi\)
\(432\) 21.6819 1.04317
\(433\) −6.05166 −0.290824 −0.145412 0.989371i \(-0.546451\pi\)
−0.145412 + 0.989371i \(0.546451\pi\)
\(434\) 8.69555i 0.417400i
\(435\) 60.7337i 2.91196i
\(436\) 3.71872i 0.178094i
\(437\) 3.92041i 0.187539i
\(438\) 59.7499 2.85496
\(439\) 2.35627 0.112458 0.0562292 0.998418i \(-0.482092\pi\)
0.0562292 + 0.998418i \(0.482092\pi\)
\(440\) 97.5928i 4.65255i
\(441\) −26.7861 −1.27553
\(442\) 10.4603 19.3056i 0.497546 0.918276i
\(443\) 7.64035 0.363004 0.181502 0.983391i \(-0.441904\pi\)
0.181502 + 0.983391i \(0.441904\pi\)
\(444\) 80.7595i 3.83268i
\(445\) 12.9926 0.615909
\(446\) −59.1098 −2.79893
\(447\) 8.00351i 0.378553i
\(448\) 26.8593i 1.26898i
\(449\) 31.4131i 1.48247i −0.671243 0.741237i \(-0.734239\pi\)
0.671243 0.741237i \(-0.265761\pi\)
\(450\) 85.0145i 4.00762i
\(451\) 27.3673 1.28868
\(452\) 24.0787 1.13257
\(453\) 1.20152i 0.0564522i
\(454\) 20.0269 0.939909
\(455\) 39.1138 + 21.1929i 1.83368 + 0.993537i
\(456\) −41.1841 −1.92862
\(457\) 14.1833i 0.663466i −0.943373 0.331733i \(-0.892367\pi\)
0.943373 0.331733i \(-0.107633\pi\)
\(458\) 12.9731 0.606194
\(459\) 12.7898 0.596977
\(460\) 18.7208i 0.872862i
\(461\) 0.852165i 0.0396893i 0.999803 + 0.0198446i \(0.00631716\pi\)
−0.999803 + 0.0198446i \(0.993683\pi\)
\(462\) 136.497i 6.35043i
\(463\) 26.5817i 1.23535i −0.786432 0.617677i \(-0.788074\pi\)
0.786432 0.617677i \(-0.211926\pi\)
\(464\) −26.1528 −1.21411
\(465\) 9.76032 0.452624
\(466\) 26.1524i 1.21149i
\(467\) −26.5943 −1.23064 −0.615320 0.788278i \(-0.710973\pi\)
−0.615320 + 0.788278i \(0.710973\pi\)
\(468\) −61.9172 33.5484i −2.86212 1.55077i
\(469\) −32.8432 −1.51656
\(470\) 97.6382i 4.50371i
\(471\) −13.4002 −0.617448
\(472\) 34.4228 1.58444
\(473\) 5.19093i 0.238679i
\(474\) 39.1975i 1.80040i
\(475\) 21.0433i 0.965533i
\(476\) 35.4016i 1.62263i
\(477\) −44.9097 −2.05627
\(478\) 15.5130 0.709548
\(479\) 28.3556i 1.29560i −0.761809 0.647801i \(-0.775689\pi\)
0.761809 0.647801i \(-0.224311\pi\)
\(480\) 3.25258 0.148459
\(481\) −12.2805 + 22.6650i −0.559942 + 1.03343i
\(482\) −36.2791 −1.65247
\(483\) 13.2010i 0.600666i
\(484\) 82.3703 3.74410
\(485\) 39.7587 1.80535
\(486\) 38.5652i 1.74935i
\(487\) 30.9730i 1.40352i 0.712414 + 0.701760i \(0.247602\pi\)
−0.712414 + 0.701760i \(0.752398\pi\)
\(488\) 28.6110i 1.29516i
\(489\) 61.1752i 2.76644i
\(490\) −47.3593 −2.13948
\(491\) −2.33609 −0.105426 −0.0527131 0.998610i \(-0.516787\pi\)
−0.0527131 + 0.998610i \(0.516787\pi\)
\(492\) 55.1489i 2.48631i
\(493\) −15.4271 −0.694802
\(494\) 22.9253 + 12.4215i 1.03146 + 0.558871i
\(495\) 94.6007 4.25199
\(496\) 4.20294i 0.188717i
\(497\) 3.00919 0.134981
\(498\) 70.0489 3.13897
\(499\) 19.4432i 0.870396i 0.900335 + 0.435198i \(0.143322\pi\)
−0.900335 + 0.435198i \(0.856678\pi\)
\(500\) 30.1933i 1.35028i
\(501\) 9.43963i 0.421731i
\(502\) 30.2910i 1.35195i
\(503\) 10.6345 0.474170 0.237085 0.971489i \(-0.423808\pi\)
0.237085 + 0.971489i \(0.423808\pi\)
\(504\) 85.6266 3.81411
\(505\) 21.4137i 0.952895i
\(506\) 18.3350 0.815089
\(507\) 19.8808 + 30.4972i 0.882939 + 1.35443i
\(508\) 18.7159 0.830386
\(509\) 43.8547i 1.94383i −0.235338 0.971913i \(-0.575620\pi\)
0.235338 0.971913i \(-0.424380\pi\)
\(510\) 59.4392 2.63201
\(511\) 30.7495 1.36028
\(512\) 40.5893i 1.79381i
\(513\) 15.1878i 0.670557i
\(514\) 67.6891i 2.98564i
\(515\) 34.0574i 1.50075i
\(516\) −10.4605 −0.460496
\(517\) 63.9283 2.81156
\(518\) 62.1694i 2.73157i
\(519\) −41.3744 −1.81613
\(520\) −55.1931 29.9051i −2.42038 1.31142i
\(521\) 34.6533 1.51819 0.759095 0.650980i \(-0.225642\pi\)
0.759095 + 0.650980i \(0.225642\pi\)
\(522\) 74.0106i 3.23936i
\(523\) −13.5927 −0.594369 −0.297184 0.954820i \(-0.596048\pi\)
−0.297184 + 0.954820i \(0.596048\pi\)
\(524\) 52.3634 2.28750
\(525\) 70.8581i 3.09250i
\(526\) 64.7012i 2.82111i
\(527\) 2.47924i 0.107998i
\(528\) 65.9750i 2.87119i
\(529\) −21.2268 −0.922903
\(530\) −79.4030 −3.44905
\(531\) 33.3675i 1.44803i
\(532\) −42.0391 −1.82263
\(533\) −8.38607 + 15.4774i −0.363241 + 0.670401i
\(534\) −25.6423 −1.10965
\(535\) 0.0523357i 0.00226267i
\(536\) 46.3447 2.00179
\(537\) −68.9889 −2.97709
\(538\) 46.6527i 2.01134i
\(539\) 31.0084i 1.33562i
\(540\) 72.5250i 3.12098i
\(541\) 13.9830i 0.601178i −0.953754 0.300589i \(-0.902817\pi\)
0.953754 0.300589i \(-0.0971832\pi\)
\(542\) 21.8104 0.936836
\(543\) 14.7471 0.632857
\(544\) 0.826196i 0.0354229i
\(545\) 3.21324 0.137640
\(546\) −77.1952 41.8264i −3.30365 1.79000i
\(547\) −39.4448 −1.68654 −0.843269 0.537492i \(-0.819372\pi\)
−0.843269 + 0.537492i \(0.819372\pi\)
\(548\) 18.7967i 0.802957i
\(549\) 27.7338 1.18365
\(550\) 98.4154 4.19645
\(551\) 18.3196i 0.780440i
\(552\) 18.6278i 0.792852i
\(553\) 20.1724i 0.857820i
\(554\) 0.647737i 0.0275197i
\(555\) −69.7821 −2.96208
\(556\) −59.7676 −2.53471
\(557\) 27.8887i 1.18168i −0.806788 0.590841i \(-0.798796\pi\)
0.806788 0.590841i \(-0.201204\pi\)
\(558\) −11.8940 −0.503514
\(559\) 2.93570 + 1.59064i 0.124167 + 0.0672769i
\(560\) 51.8569 2.19135
\(561\) 38.9176i 1.64310i
\(562\) −15.4403 −0.651310
\(563\) −23.7172 −0.999559 −0.499780 0.866153i \(-0.666586\pi\)
−0.499780 + 0.866153i \(0.666586\pi\)
\(564\) 128.824i 5.42449i
\(565\) 20.8058i 0.875305i
\(566\) 27.7903i 1.16811i
\(567\) 0.283141i 0.0118908i
\(568\) −4.24624 −0.178168
\(569\) −15.1352 −0.634501 −0.317251 0.948342i \(-0.602760\pi\)
−0.317251 + 0.948342i \(0.602760\pi\)
\(570\) 70.5835i 2.95642i
\(571\) −33.0021 −1.38109 −0.690547 0.723288i \(-0.742630\pi\)
−0.690547 + 0.723288i \(0.742630\pi\)
\(572\) −38.8366 + 71.6772i −1.62384 + 2.99698i
\(573\) −12.9248 −0.539940
\(574\) 42.4541i 1.77200i
\(575\) 9.51801 0.396928
\(576\) 36.7389 1.53079
\(577\) 15.1583i 0.631049i 0.948917 + 0.315525i \(0.102181\pi\)
−0.948917 + 0.315525i \(0.897819\pi\)
\(578\) 26.6596i 1.10889i
\(579\) 4.53599i 0.188509i
\(580\) 87.4800i 3.63241i
\(581\) 36.0497 1.49559
\(582\) −78.4681 −3.25261
\(583\) 51.9888i 2.15316i
\(584\) −43.3903 −1.79550
\(585\) −28.9882 + 53.5009i −1.19851 + 2.21199i
\(586\) 47.9064 1.97899
\(587\) 7.05245i 0.291086i −0.989352 0.145543i \(-0.953507\pi\)
0.989352 0.145543i \(-0.0464929\pi\)
\(588\) 62.4862 2.57689
\(589\) 2.94408 0.121309
\(590\) 58.9957i 2.42882i
\(591\) 23.3010i 0.958474i
\(592\) 30.0492i 1.23501i
\(593\) 21.3706i 0.877584i −0.898589 0.438792i \(-0.855407\pi\)
0.898589 0.438792i \(-0.144593\pi\)
\(594\) −71.0302 −2.91440
\(595\) 30.5895 1.25405
\(596\) 11.5281i 0.472211i
\(597\) 66.1850 2.70877
\(598\) −5.61833 + 10.3692i −0.229750 + 0.424030i
\(599\) 21.7134 0.887184 0.443592 0.896229i \(-0.353704\pi\)
0.443592 + 0.896229i \(0.353704\pi\)
\(600\) 99.9872i 4.08196i
\(601\) 6.23220 0.254217 0.127108 0.991889i \(-0.459430\pi\)
0.127108 + 0.991889i \(0.459430\pi\)
\(602\) −8.05255 −0.328197
\(603\) 44.9238i 1.82944i
\(604\) 1.73065i 0.0704190i
\(605\) 71.1739i 2.89363i
\(606\) 42.2622i 1.71678i
\(607\) −6.62821 −0.269031 −0.134515 0.990912i \(-0.542948\pi\)
−0.134515 + 0.990912i \(0.542948\pi\)
\(608\) 0.981101 0.0397889
\(609\) 61.6866i 2.49967i
\(610\) 49.0350 1.98537
\(611\) −19.5893 + 36.1543i −0.792500 + 1.46265i
\(612\) −48.4233 −1.95740
\(613\) 15.3431i 0.619700i 0.950785 + 0.309850i \(0.100279\pi\)
−0.950785 + 0.309850i \(0.899721\pi\)
\(614\) −77.8327 −3.14107
\(615\) −47.6526 −1.92154
\(616\) 99.1240i 3.99382i
\(617\) 10.2734i 0.413592i 0.978384 + 0.206796i \(0.0663037\pi\)
−0.978384 + 0.206796i \(0.933696\pi\)
\(618\) 67.2160i 2.70382i
\(619\) 39.0227i 1.56845i 0.620474 + 0.784227i \(0.286940\pi\)
−0.620474 + 0.784227i \(0.713060\pi\)
\(620\) −14.0586 −0.564608
\(621\) −6.86952 −0.275664
\(622\) 3.03020i 0.121500i
\(623\) −13.1965 −0.528705
\(624\) 37.3118 + 20.2165i 1.49367 + 0.809308i
\(625\) −9.64918 −0.385967
\(626\) 48.0889i 1.92202i
\(627\) 46.2143 1.84562
\(628\) 19.3014 0.770211
\(629\) 17.7255i 0.706762i
\(630\) 146.751i 5.84672i
\(631\) 0.624321i 0.0248538i 0.999923 + 0.0124269i \(0.00395571\pi\)
−0.999923 + 0.0124269i \(0.996044\pi\)
\(632\) 28.4651i 1.13228i
\(633\) 63.2662 2.51460
\(634\) 5.04409 0.200326
\(635\) 16.1719i 0.641763i
\(636\) 104.765 4.15419
\(637\) −17.5366 9.50179i −0.694826 0.376475i
\(638\) 85.6770 3.39198
\(639\) 4.11606i 0.162829i
\(640\) 67.2796 2.65946
\(641\) −15.3676 −0.606983 −0.303492 0.952834i \(-0.598152\pi\)
−0.303492 + 0.952834i \(0.598152\pi\)
\(642\) 0.103290i 0.00407653i
\(643\) 37.6317i 1.48405i 0.670372 + 0.742025i \(0.266135\pi\)
−0.670372 + 0.742025i \(0.733865\pi\)
\(644\) 19.0145i 0.749277i
\(645\) 9.03859i 0.355894i
\(646\) 17.9291 0.705410
\(647\) −31.8747 −1.25312 −0.626562 0.779372i \(-0.715538\pi\)
−0.626562 + 0.779372i \(0.715538\pi\)
\(648\) 0.399538i 0.0156953i
\(649\) −38.6272 −1.51625
\(650\) −30.1571 + 55.6583i −1.18286 + 2.18310i
\(651\) −9.91346 −0.388539
\(652\) 88.1158i 3.45088i
\(653\) 37.9437 1.48485 0.742426 0.669928i \(-0.233675\pi\)
0.742426 + 0.669928i \(0.233675\pi\)
\(654\) −6.34167 −0.247979
\(655\) 45.2457i 1.76790i
\(656\) 20.5199i 0.801168i
\(657\) 42.0600i 1.64092i
\(658\) 99.1701i 3.86605i
\(659\) 34.4697 1.34275 0.671374 0.741119i \(-0.265705\pi\)
0.671374 + 0.741119i \(0.265705\pi\)
\(660\) −220.683 −8.59009
\(661\) 26.3201i 1.02373i 0.859065 + 0.511867i \(0.171046\pi\)
−0.859065 + 0.511867i \(0.828954\pi\)
\(662\) 32.5755 1.26608
\(663\) 22.0096 + 11.9254i 0.854783 + 0.463144i
\(664\) −50.8694 −1.97411
\(665\) 36.3248i 1.40862i
\(666\) 85.0370 3.29512
\(667\) 8.28605 0.320837
\(668\) 13.5967i 0.526072i
\(669\) 67.3888i 2.60540i
\(670\) 79.4280i 3.06857i
\(671\) 32.1055i 1.23942i
\(672\) −3.30362 −0.127440
\(673\) 22.6031 0.871284 0.435642 0.900120i \(-0.356521\pi\)
0.435642 + 0.900120i \(0.356521\pi\)
\(674\) 86.4232i 3.32890i
\(675\) −36.8730 −1.41924
\(676\) −28.6361 43.9277i −1.10139 1.68953i
\(677\) 22.8439 0.877962 0.438981 0.898496i \(-0.355339\pi\)
0.438981 + 0.898496i \(0.355339\pi\)
\(678\) 41.0624i 1.57699i
\(679\) −40.3825 −1.54974
\(680\) −43.1646 −1.65529
\(681\) 22.8319i 0.874921i
\(682\) 13.7689i 0.527238i
\(683\) 19.3530i 0.740523i 0.928927 + 0.370262i \(0.120732\pi\)
−0.928927 + 0.370262i \(0.879268\pi\)
\(684\) 57.5023i 2.19865i
\(685\) 16.2417 0.620565
\(686\) −12.7664 −0.487425
\(687\) 14.7902i 0.564280i
\(688\) 3.89215 0.148387
\(689\) −29.4020 15.9308i −1.12013 0.606914i
\(690\) −31.9253 −1.21538
\(691\) 33.9864i 1.29290i −0.762955 0.646452i \(-0.776252\pi\)
0.762955 0.646452i \(-0.223748\pi\)
\(692\) 59.5950 2.26546
\(693\) −96.0850 −3.64997
\(694\) 29.7198i 1.12815i
\(695\) 51.6435i 1.95895i
\(696\) 87.0454i 3.29945i
\(697\) 12.1044i 0.458485i
\(698\) 70.6800 2.67528
\(699\) 29.8154 1.12772
\(700\) 102.063i 3.85762i
\(701\) −14.0298 −0.529898 −0.264949 0.964262i \(-0.585355\pi\)
−0.264949 + 0.964262i \(0.585355\pi\)
\(702\) 21.7656 40.1707i 0.821488 1.51615i
\(703\) −21.0489 −0.793874
\(704\) 42.5301i 1.60291i
\(705\) −111.314 −4.19231
\(706\) 37.0737 1.39529
\(707\) 21.7496i 0.817979i
\(708\) 77.8393i 2.92538i
\(709\) 6.14179i 0.230660i −0.993327 0.115330i \(-0.963207\pi\)
0.993327 0.115330i \(-0.0367925\pi\)
\(710\) 7.27744i 0.273117i
\(711\) −27.5924 −1.03480
\(712\) 18.6214 0.697867
\(713\) 1.33162i 0.0498697i
\(714\) −60.3718 −2.25936
\(715\) 61.9343 + 33.5576i 2.31621 + 1.25498i
\(716\) 99.3706 3.71365
\(717\) 17.6858i 0.660487i
\(718\) 7.17386 0.267726
\(719\) −8.98548 −0.335102 −0.167551 0.985863i \(-0.553586\pi\)
−0.167551 + 0.985863i \(0.553586\pi\)
\(720\) 70.9313i 2.64345i
\(721\) 34.5918i 1.28826i
\(722\) 25.3799i 0.944543i
\(723\) 41.3604i 1.53821i
\(724\) −21.2414 −0.789432
\(725\) 44.4764 1.65181
\(726\) 140.469i 5.21330i
\(727\) 30.2413 1.12159 0.560795 0.827955i \(-0.310496\pi\)
0.560795 + 0.827955i \(0.310496\pi\)
\(728\) 56.0590 + 30.3742i 2.07769 + 1.12574i
\(729\) −43.7268 −1.61951
\(730\) 74.3646i 2.75236i
\(731\) 2.29591 0.0849174
\(732\) −64.6971 −2.39127
\(733\) 51.5640i 1.90456i 0.305227 + 0.952280i \(0.401268\pi\)
−0.305227 + 0.952280i \(0.598732\pi\)
\(734\) 17.2770i 0.637707i
\(735\) 53.9926i 1.99155i
\(736\) 0.443758i 0.0163571i
\(737\) −52.0052 −1.91564
\(738\) 58.0699 2.13758
\(739\) 10.0098i 0.368216i −0.982906 0.184108i \(-0.941060\pi\)
0.982906 0.184108i \(-0.0589397\pi\)
\(740\) 100.513 3.69493
\(741\) −14.1613 + 26.1362i −0.520228 + 0.960139i
\(742\) 80.6488 2.96071
\(743\) 16.9940i 0.623449i 0.950173 + 0.311724i \(0.100907\pi\)
−0.950173 + 0.311724i \(0.899093\pi\)
\(744\) 13.9888 0.512854
\(745\) 9.96114 0.364948
\(746\) 22.6747i 0.830179i
\(747\) 49.3098i 1.80415i
\(748\) 56.0563i 2.04962i
\(749\) 0.0531568i 0.00194231i
\(750\) −51.4898 −1.88014
\(751\) −37.7192 −1.37639 −0.688196 0.725524i \(-0.741597\pi\)
−0.688196 + 0.725524i \(0.741597\pi\)
\(752\) 47.9332i 1.74794i
\(753\) −34.5336 −1.25847
\(754\) −26.2537 + 48.4541i −0.956104 + 1.76460i
\(755\) 1.49540 0.0544233
\(756\) 73.6628i 2.67909i
\(757\) −5.31555 −0.193197 −0.0965984 0.995323i \(-0.530796\pi\)
−0.0965984 + 0.995323i \(0.530796\pi\)
\(758\) −34.7411 −1.26186
\(759\) 20.9030i 0.758731i
\(760\) 51.2576i 1.85931i
\(761\) 29.2832i 1.06152i 0.847524 + 0.530758i \(0.178093\pi\)
−0.847524 + 0.530758i \(0.821907\pi\)
\(762\) 31.9170i 1.15623i
\(763\) −3.26365 −0.118152
\(764\) 18.6166 0.673527
\(765\) 41.8412i 1.51277i
\(766\) 23.3834 0.844877
\(767\) 11.8364 21.8454i 0.427388 0.788792i
\(768\) −90.2887 −3.25801
\(769\) 29.7376i 1.07237i 0.844102 + 0.536183i \(0.180134\pi\)
−0.844102 + 0.536183i \(0.819866\pi\)
\(770\) −169.884 −6.12219
\(771\) 77.1697 2.77920
\(772\) 6.53357i 0.235148i
\(773\) 1.75024i 0.0629517i −0.999505 0.0314758i \(-0.989979\pi\)
0.999505 0.0314758i \(-0.0100207\pi\)
\(774\) 11.0145i 0.395908i
\(775\) 7.14767i 0.256752i
\(776\) 56.9833 2.04558
\(777\) 70.8769 2.54270
\(778\) 23.7228i 0.850503i
\(779\) −14.3738 −0.514996
\(780\) 67.6233 124.806i 2.42130 4.46878i
\(781\) 4.76488 0.170501
\(782\) 8.10943i 0.289993i
\(783\) −32.1004 −1.14717