Properties

Label 403.2.c.b.311.2
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.2
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.31

$q$-expansion

\(f(q)\) \(=\) \(q-2.67507i q^{2} -1.67043 q^{3} -5.15599 q^{4} -2.86564i q^{5} +4.46851i q^{6} -5.21058i q^{7} +8.44248i q^{8} -0.209666 q^{9} +O(q^{10})\) \(q-2.67507i q^{2} -1.67043 q^{3} -5.15599 q^{4} -2.86564i q^{5} +4.46851i q^{6} -5.21058i q^{7} +8.44248i q^{8} -0.209666 q^{9} -7.66579 q^{10} +0.107346i q^{11} +8.61271 q^{12} +(3.42522 + 1.12598i) q^{13} -13.9387 q^{14} +4.78685i q^{15} +12.2722 q^{16} -1.65501 q^{17} +0.560870i q^{18} -2.74920i q^{19} +14.7752i q^{20} +8.70391i q^{21} +0.287157 q^{22} +2.05031 q^{23} -14.1026i q^{24} -3.21190 q^{25} +(3.01208 - 9.16271i) q^{26} +5.36152 q^{27} +26.8657i q^{28} +8.54021 q^{29} +12.8052 q^{30} +1.00000i q^{31} -15.9441i q^{32} -0.179314i q^{33} +4.42728i q^{34} -14.9317 q^{35} +1.08103 q^{36} +7.15561i q^{37} -7.35430 q^{38} +(-5.72159 - 1.88088i) q^{39} +24.1931 q^{40} -9.28974i q^{41} +23.2835 q^{42} -7.32217 q^{43} -0.553474i q^{44} +0.600827i q^{45} -5.48472i q^{46} +4.70074i q^{47} -20.4999 q^{48} -20.1502 q^{49} +8.59206i q^{50} +2.76459 q^{51} +(-17.6604 - 5.80556i) q^{52} -3.04370 q^{53} -14.3424i q^{54} +0.307615 q^{55} +43.9902 q^{56} +4.59235i q^{57} -22.8456i q^{58} -11.4500i q^{59} -24.6809i q^{60} -5.46539 q^{61} +2.67507 q^{62} +1.09248i q^{63} -18.1070 q^{64} +(3.22667 - 9.81547i) q^{65} -0.479676 q^{66} -1.60563i q^{67} +8.53323 q^{68} -3.42490 q^{69} +39.9432i q^{70} -8.50173i q^{71} -1.77010i q^{72} +6.98159i q^{73} +19.1418 q^{74} +5.36526 q^{75} +14.1748i q^{76} +0.559334 q^{77} +(-5.03148 + 15.3057i) q^{78} -1.90261 q^{79} -35.1678i q^{80} -8.32704 q^{81} -24.8507 q^{82} -9.64608i q^{83} -44.8772i q^{84} +4.74268i q^{85} +19.5873i q^{86} -14.2658 q^{87} -0.906264 q^{88} +9.70043i q^{89} +1.60725 q^{90} +(5.86703 - 17.8474i) q^{91} -10.5714 q^{92} -1.67043i q^{93} +12.5748 q^{94} -7.87823 q^{95} +26.6334i q^{96} +14.1790i q^{97} +53.9030i q^{98} -0.0225067i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67507i 1.89156i −0.324810 0.945779i \(-0.605300\pi\)
0.324810 0.945779i \(-0.394700\pi\)
\(3\) −1.67043 −0.964423 −0.482211 0.876055i \(-0.660166\pi\)
−0.482211 + 0.876055i \(0.660166\pi\)
\(4\) −5.15599 −2.57799
\(5\) 2.86564i 1.28155i −0.767727 0.640777i \(-0.778612\pi\)
0.767727 0.640777i \(-0.221388\pi\)
\(6\) 4.46851i 1.82426i
\(7\) 5.21058i 1.96941i −0.174217 0.984707i \(-0.555739\pi\)
0.174217 0.984707i \(-0.444261\pi\)
\(8\) 8.44248i 2.98487i
\(9\) −0.209666 −0.0698885
\(10\) −7.66579 −2.42413
\(11\) 0.107346i 0.0323660i 0.999869 + 0.0161830i \(0.00515143\pi\)
−0.999869 + 0.0161830i \(0.994849\pi\)
\(12\) 8.61271 2.48628
\(13\) 3.42522 + 1.12598i 0.949986 + 0.312292i
\(14\) −13.9387 −3.72526
\(15\) 4.78685i 1.23596i
\(16\) 12.2722 3.06805
\(17\) −1.65501 −0.401400 −0.200700 0.979653i \(-0.564322\pi\)
−0.200700 + 0.979653i \(0.564322\pi\)
\(18\) 0.560870i 0.132198i
\(19\) 2.74920i 0.630710i −0.948974 0.315355i \(-0.897876\pi\)
0.948974 0.315355i \(-0.102124\pi\)
\(20\) 14.7752i 3.30384i
\(21\) 8.70391i 1.89935i
\(22\) 0.287157 0.0612221
\(23\) 2.05031 0.427519 0.213760 0.976886i \(-0.431429\pi\)
0.213760 + 0.976886i \(0.431429\pi\)
\(24\) 14.1026i 2.87867i
\(25\) −3.21190 −0.642381
\(26\) 3.01208 9.16271i 0.590718 1.79695i
\(27\) 5.36152 1.03182
\(28\) 26.8657i 5.07714i
\(29\) 8.54021 1.58588 0.792939 0.609302i \(-0.208550\pi\)
0.792939 + 0.609302i \(0.208550\pi\)
\(30\) 12.8052 2.33789
\(31\) 1.00000i 0.179605i
\(32\) 15.9441i 2.81854i
\(33\) 0.179314i 0.0312145i
\(34\) 4.42728i 0.759272i
\(35\) −14.9317 −2.52391
\(36\) 1.08103 0.180172
\(37\) 7.15561i 1.17638i 0.808724 + 0.588188i \(0.200158\pi\)
−0.808724 + 0.588188i \(0.799842\pi\)
\(38\) −7.35430 −1.19302
\(39\) −5.72159 1.88088i −0.916188 0.301181i
\(40\) 24.1931 3.82527
\(41\) 9.28974i 1.45081i −0.688320 0.725407i \(-0.741652\pi\)
0.688320 0.725407i \(-0.258348\pi\)
\(42\) 23.2835 3.59273
\(43\) −7.32217 −1.11662 −0.558311 0.829632i \(-0.688550\pi\)
−0.558311 + 0.829632i \(0.688550\pi\)
\(44\) 0.553474i 0.0834393i
\(45\) 0.600827i 0.0895659i
\(46\) 5.48472i 0.808678i
\(47\) 4.70074i 0.685674i 0.939395 + 0.342837i \(0.111388\pi\)
−0.939395 + 0.342837i \(0.888612\pi\)
\(48\) −20.4999 −2.95890
\(49\) −20.1502 −2.87859
\(50\) 8.59206i 1.21510i
\(51\) 2.76459 0.387119
\(52\) −17.6604 5.80556i −2.44906 0.805086i
\(53\) −3.04370 −0.418084 −0.209042 0.977907i \(-0.567035\pi\)
−0.209042 + 0.977907i \(0.567035\pi\)
\(54\) 14.3424i 1.95176i
\(55\) 0.307615 0.0414788
\(56\) 43.9902 5.87844
\(57\) 4.59235i 0.608271i
\(58\) 22.8456i 2.99978i
\(59\) 11.4500i 1.49067i −0.666692 0.745333i \(-0.732290\pi\)
0.666692 0.745333i \(-0.267710\pi\)
\(60\) 24.6809i 3.18630i
\(61\) −5.46539 −0.699772 −0.349886 0.936792i \(-0.613780\pi\)
−0.349886 + 0.936792i \(0.613780\pi\)
\(62\) 2.67507 0.339734
\(63\) 1.09248i 0.137640i
\(64\) −18.1070 −2.26338
\(65\) 3.22667 9.81547i 0.400219 1.21746i
\(66\) −0.479676 −0.0590440
\(67\) 1.60563i 0.196159i −0.995179 0.0980796i \(-0.968730\pi\)
0.995179 0.0980796i \(-0.0312700\pi\)
\(68\) 8.53323 1.03481
\(69\) −3.42490 −0.412309
\(70\) 39.9432i 4.77413i
\(71\) 8.50173i 1.00897i −0.863421 0.504485i \(-0.831682\pi\)
0.863421 0.504485i \(-0.168318\pi\)
\(72\) 1.77010i 0.208608i
\(73\) 6.98159i 0.817133i 0.912729 + 0.408567i \(0.133971\pi\)
−0.912729 + 0.408567i \(0.866029\pi\)
\(74\) 19.1418 2.22518
\(75\) 5.36526 0.619527
\(76\) 14.1748i 1.62597i
\(77\) 0.559334 0.0637420
\(78\) −5.03148 + 15.3057i −0.569702 + 1.73302i
\(79\) −1.90261 −0.214061 −0.107030 0.994256i \(-0.534134\pi\)
−0.107030 + 0.994256i \(0.534134\pi\)
\(80\) 35.1678i 3.93188i
\(81\) −8.32704 −0.925227
\(82\) −24.8507 −2.74430
\(83\) 9.64608i 1.05880i −0.848374 0.529398i \(-0.822418\pi\)
0.848374 0.529398i \(-0.177582\pi\)
\(84\) 44.8772i 4.89651i
\(85\) 4.74268i 0.514416i
\(86\) 19.5873i 2.11215i
\(87\) −14.2658 −1.52946
\(88\) −0.906264 −0.0966081
\(89\) 9.70043i 1.02824i 0.857717 + 0.514122i \(0.171882\pi\)
−0.857717 + 0.514122i \(0.828118\pi\)
\(90\) 1.60725 0.169419
\(91\) 5.86703 17.8474i 0.615032 1.87092i
\(92\) −10.5714 −1.10214
\(93\) 1.67043i 0.173215i
\(94\) 12.5748 1.29699
\(95\) −7.87823 −0.808289
\(96\) 26.6334i 2.71826i
\(97\) 14.1790i 1.43966i 0.694150 + 0.719830i \(0.255780\pi\)
−0.694150 + 0.719830i \(0.744220\pi\)
\(98\) 53.9030i 5.44503i
\(99\) 0.0225067i 0.00226201i
\(100\) 16.5605 1.65605
\(101\) 3.99013 0.397032 0.198516 0.980098i \(-0.436388\pi\)
0.198516 + 0.980098i \(0.436388\pi\)
\(102\) 7.39545i 0.732259i
\(103\) 7.24951 0.714316 0.357158 0.934044i \(-0.383746\pi\)
0.357158 + 0.934044i \(0.383746\pi\)
\(104\) −9.50610 + 28.9174i −0.932150 + 2.83558i
\(105\) 24.9423 2.43412
\(106\) 8.14210i 0.790830i
\(107\) 2.56526 0.247993 0.123997 0.992283i \(-0.460429\pi\)
0.123997 + 0.992283i \(0.460429\pi\)
\(108\) −27.6439 −2.66004
\(109\) 6.50099i 0.622682i 0.950298 + 0.311341i \(0.100778\pi\)
−0.950298 + 0.311341i \(0.899222\pi\)
\(110\) 0.822890i 0.0784595i
\(111\) 11.9529i 1.13452i
\(112\) 63.9454i 6.04227i
\(113\) 6.19260 0.582551 0.291276 0.956639i \(-0.405920\pi\)
0.291276 + 0.956639i \(0.405920\pi\)
\(114\) 12.2848 1.15058
\(115\) 5.87546i 0.547889i
\(116\) −44.0332 −4.08838
\(117\) −0.718152 0.236080i −0.0663931 0.0218256i
\(118\) −30.6296 −2.81968
\(119\) 8.62359i 0.790523i
\(120\) −40.4129 −3.68918
\(121\) 10.9885 0.998952
\(122\) 14.6203i 1.32366i
\(123\) 15.5179i 1.39920i
\(124\) 5.15599i 0.463021i
\(125\) 5.12404i 0.458308i
\(126\) 2.92246 0.260353
\(127\) 4.47662 0.397236 0.198618 0.980077i \(-0.436355\pi\)
0.198618 + 0.980077i \(0.436355\pi\)
\(128\) 16.5493i 1.46277i
\(129\) 12.2312 1.07689
\(130\) −26.2570 8.63156i −2.30289 0.757038i
\(131\) 8.44606 0.737935 0.368968 0.929442i \(-0.379711\pi\)
0.368968 + 0.929442i \(0.379711\pi\)
\(132\) 0.924538i 0.0804707i
\(133\) −14.3249 −1.24213
\(134\) −4.29518 −0.371047
\(135\) 15.3642i 1.32234i
\(136\) 13.9724i 1.19813i
\(137\) 4.93436i 0.421571i 0.977532 + 0.210785i \(0.0676021\pi\)
−0.977532 + 0.210785i \(0.932398\pi\)
\(138\) 9.16184i 0.779907i
\(139\) −9.80769 −0.831877 −0.415938 0.909393i \(-0.636547\pi\)
−0.415938 + 0.909393i \(0.636547\pi\)
\(140\) 76.9874 6.50663
\(141\) 7.85226i 0.661280i
\(142\) −22.7427 −1.90852
\(143\) −0.120870 + 0.367683i −0.0101076 + 0.0307472i
\(144\) −2.57306 −0.214422
\(145\) 24.4732i 2.03239i
\(146\) 18.6762 1.54565
\(147\) 33.6594 2.77618
\(148\) 36.8943i 3.03269i
\(149\) 1.24011i 0.101593i −0.998709 0.0507967i \(-0.983824\pi\)
0.998709 0.0507967i \(-0.0161760\pi\)
\(150\) 14.3524i 1.17187i
\(151\) 4.52510i 0.368247i −0.982903 0.184124i \(-0.941055\pi\)
0.982903 0.184124i \(-0.0589447\pi\)
\(152\) 23.2101 1.88258
\(153\) 0.347000 0.0280533
\(154\) 1.49626i 0.120572i
\(155\) 2.86564 0.230174
\(156\) 29.5005 + 9.69778i 2.36193 + 0.776444i
\(157\) 7.78510 0.621319 0.310659 0.950521i \(-0.399450\pi\)
0.310659 + 0.950521i \(0.399450\pi\)
\(158\) 5.08961i 0.404908i
\(159\) 5.08428 0.403210
\(160\) −45.6900 −3.61211
\(161\) 10.6833i 0.841963i
\(162\) 22.2754i 1.75012i
\(163\) 1.90995i 0.149599i −0.997199 0.0747995i \(-0.976168\pi\)
0.997199 0.0747995i \(-0.0238317\pi\)
\(164\) 47.8978i 3.74019i
\(165\) −0.513849 −0.0400031
\(166\) −25.8039 −2.00277
\(167\) 20.1983i 1.56299i −0.623909 0.781497i \(-0.714457\pi\)
0.623909 0.781497i \(-0.285543\pi\)
\(168\) −73.4825 −5.66930
\(169\) 10.4643 + 7.71350i 0.804947 + 0.593346i
\(170\) 12.6870 0.973048
\(171\) 0.576413i 0.0440794i
\(172\) 37.7530 2.87864
\(173\) −2.87960 −0.218932 −0.109466 0.993991i \(-0.534914\pi\)
−0.109466 + 0.993991i \(0.534914\pi\)
\(174\) 38.1620i 2.89306i
\(175\) 16.7359i 1.26511i
\(176\) 1.31737i 0.0993006i
\(177\) 19.1265i 1.43763i
\(178\) 25.9493 1.94498
\(179\) −7.10080 −0.530739 −0.265369 0.964147i \(-0.585494\pi\)
−0.265369 + 0.964147i \(0.585494\pi\)
\(180\) 3.09785i 0.230900i
\(181\) −12.7730 −0.949409 −0.474704 0.880145i \(-0.657445\pi\)
−0.474704 + 0.880145i \(0.657445\pi\)
\(182\) −47.7430 15.6947i −3.53895 1.16337i
\(183\) 9.12955 0.674876
\(184\) 17.3097i 1.27609i
\(185\) 20.5054 1.50759
\(186\) −4.46851 −0.327647
\(187\) 0.177659i 0.0129917i
\(188\) 24.2370i 1.76766i
\(189\) 27.9366i 2.03209i
\(190\) 21.0748i 1.52893i
\(191\) −15.1982 −1.09970 −0.549850 0.835263i \(-0.685315\pi\)
−0.549850 + 0.835263i \(0.685315\pi\)
\(192\) 30.2465 2.18285
\(193\) 1.93144i 0.139028i −0.997581 0.0695142i \(-0.977855\pi\)
0.997581 0.0695142i \(-0.0221449\pi\)
\(194\) 37.9298 2.72320
\(195\) −5.38992 + 16.3960i −0.385980 + 1.17415i
\(196\) 103.894 7.42100
\(197\) 13.6030i 0.969176i 0.874742 + 0.484588i \(0.161031\pi\)
−0.874742 + 0.484588i \(0.838969\pi\)
\(198\) −0.0602070 −0.00427873
\(199\) 11.3269 0.802946 0.401473 0.915871i \(-0.368498\pi\)
0.401473 + 0.915871i \(0.368498\pi\)
\(200\) 27.1164i 1.91742i
\(201\) 2.68210i 0.189180i
\(202\) 10.6739i 0.751010i
\(203\) 44.4995i 3.12325i
\(204\) −14.2542 −0.997991
\(205\) −26.6211 −1.85930
\(206\) 19.3929i 1.35117i
\(207\) −0.429880 −0.0298787
\(208\) 42.0351 + 13.8183i 2.91461 + 0.958129i
\(209\) 0.295115 0.0204136
\(210\) 66.7223i 4.60428i
\(211\) −9.96107 −0.685749 −0.342874 0.939381i \(-0.611400\pi\)
−0.342874 + 0.939381i \(0.611400\pi\)
\(212\) 15.6933 1.07782
\(213\) 14.2015i 0.973073i
\(214\) 6.86225i 0.469094i
\(215\) 20.9827i 1.43101i
\(216\) 45.2645i 3.07986i
\(217\) 5.21058 0.353717
\(218\) 17.3906 1.17784
\(219\) 11.6623i 0.788062i
\(220\) −1.58606 −0.106932
\(221\) −5.66880 1.86352i −0.381324 0.125354i
\(222\) −31.9749 −2.14602
\(223\) 17.9002i 1.19869i 0.800491 + 0.599344i \(0.204572\pi\)
−0.800491 + 0.599344i \(0.795428\pi\)
\(224\) −83.0779 −5.55087
\(225\) 0.673426 0.0448951
\(226\) 16.5656i 1.10193i
\(227\) 1.72785i 0.114681i 0.998355 + 0.0573406i \(0.0182621\pi\)
−0.998355 + 0.0573406i \(0.981738\pi\)
\(228\) 23.6781i 1.56812i
\(229\) 13.4854i 0.891141i −0.895247 0.445570i \(-0.853001\pi\)
0.895247 0.445570i \(-0.146999\pi\)
\(230\) −15.7172 −1.03636
\(231\) −0.934328 −0.0614743
\(232\) 72.1005i 4.73363i
\(233\) 2.06862 0.135520 0.0677600 0.997702i \(-0.478415\pi\)
0.0677600 + 0.997702i \(0.478415\pi\)
\(234\) −0.631531 + 1.92110i −0.0412844 + 0.125587i
\(235\) 13.4706 0.878728
\(236\) 59.0362i 3.84293i
\(237\) 3.17818 0.206445
\(238\) 23.0687 1.49532
\(239\) 14.7921i 0.956823i −0.878136 0.478411i \(-0.841213\pi\)
0.878136 0.478411i \(-0.158787\pi\)
\(240\) 58.7453i 3.79199i
\(241\) 19.9764i 1.28679i 0.765532 + 0.643397i \(0.222476\pi\)
−0.765532 + 0.643397i \(0.777524\pi\)
\(242\) 29.3949i 1.88958i
\(243\) −2.17482 −0.139515
\(244\) 28.1795 1.80401
\(245\) 57.7431i 3.68907i
\(246\) 41.5113 2.64666
\(247\) 3.09556 9.41663i 0.196966 0.599166i
\(248\) −8.44248 −0.536098
\(249\) 16.1131i 1.02113i
\(250\) −13.7072 −0.866917
\(251\) −4.64690 −0.293310 −0.146655 0.989188i \(-0.546851\pi\)
−0.146655 + 0.989188i \(0.546851\pi\)
\(252\) 5.63281i 0.354834i
\(253\) 0.220092i 0.0138371i
\(254\) 11.9753i 0.751394i
\(255\) 7.92231i 0.496114i
\(256\) 8.05659 0.503537
\(257\) 9.54021 0.595102 0.297551 0.954706i \(-0.403830\pi\)
0.297551 + 0.954706i \(0.403830\pi\)
\(258\) 32.7192i 2.03701i
\(259\) 37.2849 2.31677
\(260\) −16.6367 + 50.6084i −1.03176 + 3.13860i
\(261\) −1.79059 −0.110835
\(262\) 22.5938i 1.39585i
\(263\) −14.4929 −0.893672 −0.446836 0.894616i \(-0.647449\pi\)
−0.446836 + 0.894616i \(0.647449\pi\)
\(264\) 1.51385 0.0931711
\(265\) 8.72215i 0.535797i
\(266\) 38.3202i 2.34956i
\(267\) 16.2039i 0.991662i
\(268\) 8.27862i 0.505697i
\(269\) 27.3814 1.66947 0.834737 0.550648i \(-0.185619\pi\)
0.834737 + 0.550648i \(0.185619\pi\)
\(270\) −41.1003 −2.50128
\(271\) 13.3239i 0.809367i 0.914457 + 0.404683i \(0.132618\pi\)
−0.914457 + 0.404683i \(0.867382\pi\)
\(272\) −20.3107 −1.23152
\(273\) −9.80047 + 29.8128i −0.593151 + 1.80435i
\(274\) 13.1997 0.797426
\(275\) 0.344785i 0.0207913i
\(276\) 17.6587 1.06293
\(277\) −30.1947 −1.81422 −0.907112 0.420890i \(-0.861718\pi\)
−0.907112 + 0.420890i \(0.861718\pi\)
\(278\) 26.2362i 1.57354i
\(279\) 0.209666i 0.0125524i
\(280\) 126.060i 7.53354i
\(281\) 8.84908i 0.527892i −0.964537 0.263946i \(-0.914976\pi\)
0.964537 0.263946i \(-0.0850241\pi\)
\(282\) −21.0053 −1.25085
\(283\) −3.32142 −0.197438 −0.0987190 0.995115i \(-0.531474\pi\)
−0.0987190 + 0.995115i \(0.531474\pi\)
\(284\) 43.8348i 2.60112i
\(285\) 13.1600 0.779532
\(286\) 0.983578 + 0.323335i 0.0581602 + 0.0191192i
\(287\) −48.4049 −2.85725
\(288\) 3.34292i 0.196984i
\(289\) −14.2609 −0.838878
\(290\) −65.4674 −3.84438
\(291\) 23.6850i 1.38844i
\(292\) 35.9970i 2.10656i
\(293\) 24.8920i 1.45420i −0.686529 0.727102i \(-0.740867\pi\)
0.686529 0.727102i \(-0.259133\pi\)
\(294\) 90.0412i 5.25131i
\(295\) −32.8117 −1.91037
\(296\) −60.4111 −3.51132
\(297\) 0.575537i 0.0333960i
\(298\) −3.31736 −0.192170
\(299\) 7.02277 + 2.30862i 0.406137 + 0.133511i
\(300\) −27.6632 −1.59714
\(301\) 38.1528i 2.19909i
\(302\) −12.1049 −0.696561
\(303\) −6.66522 −0.382907
\(304\) 33.7388i 1.93505i
\(305\) 15.6619i 0.896796i
\(306\) 0.928247i 0.0530644i
\(307\) 4.47896i 0.255628i −0.991798 0.127814i \(-0.959204\pi\)
0.991798 0.127814i \(-0.0407960\pi\)
\(308\) −2.88392 −0.164327
\(309\) −12.1098 −0.688902
\(310\) 7.66579i 0.435387i
\(311\) 24.8980 1.41184 0.705918 0.708294i \(-0.250535\pi\)
0.705918 + 0.708294i \(0.250535\pi\)
\(312\) 15.8793 48.3044i 0.898986 2.73470i
\(313\) 21.0469 1.18964 0.594819 0.803860i \(-0.297224\pi\)
0.594819 + 0.803860i \(0.297224\pi\)
\(314\) 20.8257i 1.17526i
\(315\) 3.13066 0.176392
\(316\) 9.80984 0.551847
\(317\) 8.99093i 0.504981i −0.967599 0.252491i \(-0.918750\pi\)
0.967599 0.252491i \(-0.0812497\pi\)
\(318\) 13.6008i 0.762695i
\(319\) 0.916756i 0.0513285i
\(320\) 51.8882i 2.90064i
\(321\) −4.28509 −0.239170
\(322\) −28.5786 −1.59262
\(323\) 4.54997i 0.253167i
\(324\) 42.9341 2.38523
\(325\) −11.0015 3.61656i −0.610253 0.200610i
\(326\) −5.10925 −0.282975
\(327\) 10.8594i 0.600529i
\(328\) 78.4284 4.33048
\(329\) 24.4936 1.35038
\(330\) 1.37458i 0.0756681i
\(331\) 9.36893i 0.514963i −0.966283 0.257482i \(-0.917107\pi\)
0.966283 0.257482i \(-0.0828926\pi\)
\(332\) 49.7351i 2.72957i
\(333\) 1.50029i 0.0822152i
\(334\) −54.0319 −2.95649
\(335\) −4.60117 −0.251389
\(336\) 106.816i 5.82731i
\(337\) −20.3475 −1.10840 −0.554199 0.832384i \(-0.686975\pi\)
−0.554199 + 0.832384i \(0.686975\pi\)
\(338\) 20.6341 27.9928i 1.12235 1.52261i
\(339\) −10.3443 −0.561826
\(340\) 24.4532i 1.32616i
\(341\) −0.107346 −0.00581310
\(342\) 1.54194 0.0833788
\(343\) 68.5200i 3.69973i
\(344\) 61.8173i 3.33296i
\(345\) 9.81454i 0.528397i
\(346\) 7.70312i 0.414122i
\(347\) −12.1586 −0.652709 −0.326354 0.945248i \(-0.605820\pi\)
−0.326354 + 0.945248i \(0.605820\pi\)
\(348\) 73.5544 3.94293
\(349\) 30.9550i 1.65698i −0.560000 0.828492i \(-0.689199\pi\)
0.560000 0.828492i \(-0.310801\pi\)
\(350\) 44.7696 2.39304
\(351\) 18.3644 + 6.03699i 0.980219 + 0.322231i
\(352\) 1.71153 0.0912248
\(353\) 5.94598i 0.316472i −0.987401 0.158236i \(-0.949419\pi\)
0.987401 0.158236i \(-0.0505808\pi\)
\(354\) 51.1646 2.71937
\(355\) −24.3629 −1.29305
\(356\) 50.0153i 2.65081i
\(357\) 14.4051i 0.762399i
\(358\) 18.9951i 1.00392i
\(359\) 29.5605i 1.56014i 0.625690 + 0.780072i \(0.284818\pi\)
−0.625690 + 0.780072i \(0.715182\pi\)
\(360\) −5.07246 −0.267342
\(361\) 11.4419 0.602205
\(362\) 34.1686i 1.79586i
\(363\) −18.3555 −0.963413
\(364\) −30.2503 + 92.0210i −1.58555 + 4.82321i
\(365\) 20.0067 1.04720
\(366\) 24.4222i 1.27657i
\(367\) 26.1640 1.36575 0.682874 0.730536i \(-0.260730\pi\)
0.682874 + 0.730536i \(0.260730\pi\)
\(368\) 25.1619 1.31165
\(369\) 1.94774i 0.101395i
\(370\) 54.8534i 2.85169i
\(371\) 15.8594i 0.823381i
\(372\) 8.61271i 0.446548i
\(373\) 8.69976 0.450456 0.225228 0.974306i \(-0.427687\pi\)
0.225228 + 0.974306i \(0.427687\pi\)
\(374\) −0.475250 −0.0245746
\(375\) 8.55935i 0.442003i
\(376\) −39.6859 −2.04664
\(377\) 29.2521 + 9.61614i 1.50656 + 0.495257i
\(378\) −74.7324 −3.84382
\(379\) 22.2845i 1.14468i −0.820018 0.572338i \(-0.806037\pi\)
0.820018 0.572338i \(-0.193963\pi\)
\(380\) 40.6200 2.08376
\(381\) −7.47788 −0.383103
\(382\) 40.6561i 2.08015i
\(383\) 21.8948i 1.11877i 0.828907 + 0.559387i \(0.188963\pi\)
−0.828907 + 0.559387i \(0.811037\pi\)
\(384\) 27.6445i 1.41073i
\(385\) 1.60285i 0.0816889i
\(386\) −5.16674 −0.262980
\(387\) 1.53521 0.0780390
\(388\) 73.1068i 3.71143i
\(389\) 18.6807 0.947150 0.473575 0.880754i \(-0.342963\pi\)
0.473575 + 0.880754i \(0.342963\pi\)
\(390\) 43.8605 + 14.4184i 2.22096 + 0.730104i
\(391\) −3.39329 −0.171606
\(392\) 170.117i 8.59222i
\(393\) −14.1085 −0.711682
\(394\) 36.3891 1.83325
\(395\) 5.45220i 0.274330i
\(396\) 0.116044i 0.00583145i
\(397\) 2.50967i 0.125957i −0.998015 0.0629783i \(-0.979940\pi\)
0.998015 0.0629783i \(-0.0200599\pi\)
\(398\) 30.3003i 1.51882i
\(399\) 23.9288 1.19794
\(400\) −39.4172 −1.97086
\(401\) 1.92212i 0.0959861i −0.998848 0.0479930i \(-0.984717\pi\)
0.998848 0.0479930i \(-0.0152825\pi\)
\(402\) 7.17479 0.357846
\(403\) −1.12598 + 3.42522i −0.0560893 + 0.170623i
\(404\) −20.5730 −1.02355
\(405\) 23.8623i 1.18573i
\(406\) −119.039 −5.90781
\(407\) −0.768125 −0.0380746
\(408\) 23.3399i 1.15550i
\(409\) 31.4091i 1.55308i −0.630068 0.776540i \(-0.716973\pi\)
0.630068 0.776540i \(-0.283027\pi\)
\(410\) 71.2132i 3.51697i
\(411\) 8.24250i 0.406572i
\(412\) −37.3784 −1.84150
\(413\) −59.6613 −2.93574
\(414\) 1.14996i 0.0565173i
\(415\) −27.6422 −1.35690
\(416\) 17.9528 54.6120i 0.880207 2.67757i
\(417\) 16.3830 0.802281
\(418\) 0.789453i 0.0386134i
\(419\) 30.6922 1.49941 0.749707 0.661770i \(-0.230195\pi\)
0.749707 + 0.661770i \(0.230195\pi\)
\(420\) −128.602 −6.27514
\(421\) 39.9412i 1.94662i −0.229504 0.973308i \(-0.573710\pi\)
0.229504 0.973308i \(-0.426290\pi\)
\(422\) 26.6465i 1.29713i
\(423\) 0.985584i 0.0479207i
\(424\) 25.6963i 1.24792i
\(425\) 5.31575 0.257852
\(426\) 37.9901 1.84062
\(427\) 28.4779i 1.37814i
\(428\) −13.2265 −0.639325
\(429\) 0.201904 0.614189i 0.00974804 0.0296533i
\(430\) 56.1302 2.70684
\(431\) 16.2333i 0.781931i −0.920405 0.390966i \(-0.872141\pi\)
0.920405 0.390966i \(-0.127859\pi\)
\(432\) 65.7978 3.16570
\(433\) 31.2313 1.50088 0.750439 0.660939i \(-0.229842\pi\)
0.750439 + 0.660939i \(0.229842\pi\)
\(434\) 13.9387i 0.669077i
\(435\) 40.8807i 1.96008i
\(436\) 33.5190i 1.60527i
\(437\) 5.63672i 0.269641i
\(438\) −31.1973 −1.49066
\(439\) 8.10748 0.386949 0.193475 0.981105i \(-0.438024\pi\)
0.193475 + 0.981105i \(0.438024\pi\)
\(440\) 2.59703i 0.123809i
\(441\) 4.22480 0.201181
\(442\) −4.98504 + 15.1644i −0.237114 + 0.721297i
\(443\) −1.90009 −0.0902762 −0.0451381 0.998981i \(-0.514373\pi\)
−0.0451381 + 0.998981i \(0.514373\pi\)
\(444\) 61.6292i 2.92479i
\(445\) 27.7980 1.31775
\(446\) 47.8843 2.26739
\(447\) 2.07151i 0.0979790i
\(448\) 94.3481i 4.45753i
\(449\) 7.08178i 0.334210i 0.985939 + 0.167105i \(0.0534419\pi\)
−0.985939 + 0.167105i \(0.946558\pi\)
\(450\) 1.80146i 0.0849216i
\(451\) 0.997215 0.0469570
\(452\) −31.9290 −1.50181
\(453\) 7.55885i 0.355146i
\(454\) 4.62210 0.216926
\(455\) −51.1443 16.8128i −2.39768 0.788197i
\(456\) −38.7708 −1.81561
\(457\) 3.80707i 0.178087i −0.996028 0.0890437i \(-0.971619\pi\)
0.996028 0.0890437i \(-0.0283811\pi\)
\(458\) −36.0744 −1.68565
\(459\) −8.87339 −0.414175
\(460\) 30.2938i 1.41245i
\(461\) 4.09587i 0.190764i −0.995441 0.0953818i \(-0.969593\pi\)
0.995441 0.0953818i \(-0.0304072\pi\)
\(462\) 2.49939i 0.116282i
\(463\) 23.3795i 1.08654i 0.839559 + 0.543269i \(0.182814\pi\)
−0.839559 + 0.543269i \(0.817186\pi\)
\(464\) 104.807 4.86556
\(465\) −4.78685 −0.221985
\(466\) 5.53371i 0.256344i
\(467\) 12.5818 0.582217 0.291108 0.956690i \(-0.405976\pi\)
0.291108 + 0.956690i \(0.405976\pi\)
\(468\) 3.70278 + 1.21723i 0.171161 + 0.0562663i
\(469\) −8.36628 −0.386319
\(470\) 36.0349i 1.66217i
\(471\) −13.0045 −0.599214
\(472\) 96.6666 4.44944
\(473\) 0.786005i 0.0361405i
\(474\) 8.50184i 0.390502i
\(475\) 8.83017i 0.405156i
\(476\) 44.4631i 2.03796i
\(477\) 0.638159 0.0292193
\(478\) −39.5699 −1.80989
\(479\) 22.2197i 1.01524i −0.861581 0.507621i \(-0.830525\pi\)
0.861581 0.507621i \(-0.169475\pi\)
\(480\) 76.3219 3.48360
\(481\) −8.05711 + 24.5096i −0.367373 + 1.11754i
\(482\) 53.4383 2.43405
\(483\) 17.8457i 0.812008i
\(484\) −56.6564 −2.57529
\(485\) 40.6320 1.84500
\(486\) 5.81779i 0.263900i
\(487\) 10.4466i 0.473381i −0.971585 0.236691i \(-0.923937\pi\)
0.971585 0.236691i \(-0.0760628\pi\)
\(488\) 46.1415i 2.08873i
\(489\) 3.19044i 0.144277i
\(490\) 154.467 6.97810
\(491\) −30.7514 −1.38779 −0.693895 0.720076i \(-0.744107\pi\)
−0.693895 + 0.720076i \(0.744107\pi\)
\(492\) 80.0098i 3.60712i
\(493\) −14.1342 −0.636571
\(494\) −25.1901 8.28083i −1.13336 0.372572i
\(495\) −0.0644962 −0.00289889
\(496\) 12.2722i 0.551039i
\(497\) −44.2989 −1.98708
\(498\) 43.1036 1.93152
\(499\) 39.9257i 1.78732i −0.448747 0.893659i \(-0.648129\pi\)
0.448747 0.893659i \(-0.351871\pi\)
\(500\) 26.4195i 1.18152i
\(501\) 33.7399i 1.50739i
\(502\) 12.4308i 0.554812i
\(503\) −37.8842 −1.68917 −0.844586 0.535420i \(-0.820153\pi\)
−0.844586 + 0.535420i \(0.820153\pi\)
\(504\) −9.22323 −0.410835
\(505\) 11.4343i 0.508819i
\(506\) 0.588762 0.0261737
\(507\) −17.4799 12.8849i −0.776310 0.572237i
\(508\) −23.0814 −1.02407
\(509\) 1.38770i 0.0615089i 0.999527 + 0.0307544i \(0.00979098\pi\)
−0.999527 + 0.0307544i \(0.990209\pi\)
\(510\) −21.1927 −0.938429
\(511\) 36.3781 1.60927
\(512\) 11.5468i 0.510299i
\(513\) 14.7399i 0.650782i
\(514\) 25.5207i 1.12567i
\(515\) 20.7745i 0.915434i
\(516\) −63.0638 −2.77623
\(517\) −0.504605 −0.0221925
\(518\) 99.7397i 4.38231i
\(519\) 4.81016 0.211143
\(520\) 82.8668 + 27.2411i 3.63395 + 1.19460i
\(521\) 17.5495 0.768857 0.384428 0.923155i \(-0.374399\pi\)
0.384428 + 0.923155i \(0.374399\pi\)
\(522\) 4.78994i 0.209650i
\(523\) −14.5271 −0.635224 −0.317612 0.948221i \(-0.602881\pi\)
−0.317612 + 0.948221i \(0.602881\pi\)
\(524\) −43.5478 −1.90239
\(525\) 27.9561i 1.22011i
\(526\) 38.7695i 1.69043i
\(527\) 1.65501i 0.0720936i
\(528\) 2.20058i 0.0957678i
\(529\) −18.7962 −0.817227
\(530\) 23.3323 1.01349
\(531\) 2.40068i 0.104180i
\(532\) 73.8592 3.20220
\(533\) 10.4601 31.8194i 0.453077 1.37825i
\(534\) −43.3465 −1.87579
\(535\) 7.35112i 0.317817i
\(536\) 13.5555 0.585509
\(537\) 11.8614 0.511857
\(538\) 73.2471i 3.15791i
\(539\) 2.16304i 0.0931685i
\(540\) 79.2176i 3.40898i
\(541\) 29.8000i 1.28120i 0.767875 + 0.640600i \(0.221314\pi\)
−0.767875 + 0.640600i \(0.778686\pi\)
\(542\) 35.6422 1.53096
\(543\) 21.3364 0.915632
\(544\) 26.3877i 1.13136i
\(545\) 18.6295 0.798001
\(546\) 79.7513 + 26.2169i 3.41304 + 1.12198i
\(547\) −22.7158 −0.971256 −0.485628 0.874166i \(-0.661409\pi\)
−0.485628 + 0.874166i \(0.661409\pi\)
\(548\) 25.4415i 1.08681i
\(549\) 1.14591 0.0489060
\(550\) −0.922322 −0.0393279
\(551\) 23.4788i 1.00023i
\(552\) 28.9146i 1.23069i
\(553\) 9.91371i 0.421574i
\(554\) 80.7728i 3.43171i
\(555\) −34.2529 −1.45395
\(556\) 50.5683 2.14457
\(557\) 12.5422i 0.531428i −0.964052 0.265714i \(-0.914392\pi\)
0.964052 0.265714i \(-0.0856077\pi\)
\(558\) −0.560870 −0.0237435
\(559\) −25.0801 8.24466i −1.06077 0.348712i
\(560\) −183.245 −7.74350
\(561\) 0.296767i 0.0125295i
\(562\) −23.6719 −0.998538
\(563\) 2.74698 0.115771 0.0578857 0.998323i \(-0.481564\pi\)
0.0578857 + 0.998323i \(0.481564\pi\)
\(564\) 40.4861i 1.70477i
\(565\) 17.7458i 0.746571i
\(566\) 8.88502i 0.373465i
\(567\) 43.3887i 1.82216i
\(568\) 71.7756 3.01164
\(569\) −5.85158 −0.245311 −0.122655 0.992449i \(-0.539141\pi\)
−0.122655 + 0.992449i \(0.539141\pi\)
\(570\) 35.2039i 1.47453i
\(571\) 7.17387 0.300217 0.150109 0.988670i \(-0.452038\pi\)
0.150109 + 0.988670i \(0.452038\pi\)
\(572\) 0.623203 1.89577i 0.0260574 0.0792662i
\(573\) 25.3874 1.06058
\(574\) 129.486i 5.40466i
\(575\) −6.58540 −0.274630
\(576\) 3.79642 0.158184
\(577\) 11.4043i 0.474768i 0.971416 + 0.237384i \(0.0762899\pi\)
−0.971416 + 0.237384i \(0.923710\pi\)
\(578\) 38.1489i 1.58679i
\(579\) 3.22634i 0.134082i
\(580\) 126.183i 5.23948i
\(581\) −50.2617 −2.08521
\(582\) −63.3590 −2.62632
\(583\) 0.326728i 0.0135317i
\(584\) −58.9419 −2.43903
\(585\) −0.676522 + 2.05797i −0.0279707 + 0.0850864i
\(586\) −66.5877 −2.75071
\(587\) 26.0267i 1.07424i −0.843507 0.537119i \(-0.819513\pi\)
0.843507 0.537119i \(-0.180487\pi\)
\(588\) −173.547 −7.15698
\(589\) 2.74920 0.113279
\(590\) 87.7734i 3.61358i
\(591\) 22.7229i 0.934696i
\(592\) 87.8153i 3.60919i
\(593\) 32.6622i 1.34128i −0.741785 0.670638i \(-0.766020\pi\)
0.741785 0.670638i \(-0.233980\pi\)
\(594\) 1.53960 0.0631705
\(595\) 24.7121 1.01310
\(596\) 6.39396i 0.261907i
\(597\) −18.9209 −0.774379
\(598\) 6.17571 18.7864i 0.252544 0.768233i
\(599\) −39.3376 −1.60729 −0.803646 0.595108i \(-0.797109\pi\)
−0.803646 + 0.595108i \(0.797109\pi\)
\(600\) 45.2961i 1.84920i
\(601\) −41.5732 −1.69580 −0.847902 0.530153i \(-0.822135\pi\)
−0.847902 + 0.530153i \(0.822135\pi\)
\(602\) 102.061 4.15971
\(603\) 0.336646i 0.0137093i
\(604\) 23.3313i 0.949339i
\(605\) 31.4890i 1.28021i
\(606\) 17.8299i 0.724291i
\(607\) 8.85069 0.359238 0.179619 0.983736i \(-0.442513\pi\)
0.179619 + 0.983736i \(0.442513\pi\)
\(608\) −43.8334 −1.77768
\(609\) 74.3332i 3.01213i
\(610\) 41.8965 1.69634
\(611\) −5.29296 + 16.1011i −0.214130 + 0.651381i
\(612\) −1.78913 −0.0723211
\(613\) 7.46986i 0.301705i −0.988556 0.150852i \(-0.951798\pi\)
0.988556 0.150852i \(-0.0482018\pi\)
\(614\) −11.9815 −0.483535
\(615\) 44.4686 1.79315
\(616\) 4.72216i 0.190261i
\(617\) 29.5623i 1.19013i 0.803676 + 0.595067i \(0.202875\pi\)
−0.803676 + 0.595067i \(0.797125\pi\)
\(618\) 32.3945i 1.30310i
\(619\) 32.6410i 1.31195i 0.754782 + 0.655976i \(0.227743\pi\)
−0.754782 + 0.655976i \(0.772257\pi\)
\(620\) −14.7752 −0.593387
\(621\) 10.9928 0.441125
\(622\) 66.6038i 2.67057i
\(623\) 50.5449 2.02504
\(624\) −70.2167 23.0825i −2.81092 0.924041i
\(625\) −30.7432 −1.22973
\(626\) 56.3017i 2.25027i
\(627\) −0.492969 −0.0196873
\(628\) −40.1399 −1.60176
\(629\) 11.8426i 0.472197i
\(630\) 8.37472i 0.333657i
\(631\) 1.13759i 0.0452869i −0.999744 0.0226435i \(-0.992792\pi\)
0.999744 0.0226435i \(-0.00720825\pi\)
\(632\) 16.0628i 0.638942i
\(633\) 16.6393 0.661352
\(634\) −24.0513 −0.955201
\(635\) 12.8284i 0.509079i
\(636\) −26.2145 −1.03947
\(637\) −69.0188 22.6888i −2.73462 0.898962i
\(638\) 2.45238 0.0970908
\(639\) 1.78252i 0.0705154i
\(640\) 47.4245 1.87462
\(641\) −14.9135 −0.589049 −0.294525 0.955644i \(-0.595161\pi\)
−0.294525 + 0.955644i \(0.595161\pi\)
\(642\) 11.4629i 0.452405i
\(643\) 3.03312i 0.119615i −0.998210 0.0598073i \(-0.980951\pi\)
0.998210 0.0598073i \(-0.0190486\pi\)
\(644\) 55.0830i 2.17057i
\(645\) 35.0502i 1.38010i
\(646\) 12.1715 0.478880
\(647\) 28.4704 1.11929 0.559643 0.828734i \(-0.310938\pi\)
0.559643 + 0.828734i \(0.310938\pi\)
\(648\) 70.3009i 2.76168i
\(649\) 1.22911 0.0482469
\(650\) −9.67453 + 29.4297i −0.379466 + 1.15433i
\(651\) −8.70391 −0.341133
\(652\) 9.84769i 0.385665i
\(653\) 21.9746 0.859931 0.429966 0.902845i \(-0.358526\pi\)
0.429966 + 0.902845i \(0.358526\pi\)
\(654\) −29.0498 −1.13594
\(655\) 24.2034i 0.945704i
\(656\) 114.006i 4.45118i
\(657\) 1.46380i 0.0571082i
\(658\) 65.5220i 2.55432i
\(659\) 42.4003 1.65168 0.825841 0.563903i \(-0.190701\pi\)
0.825841 + 0.563903i \(0.190701\pi\)
\(660\) 2.64940 0.103128
\(661\) 35.4765i 1.37988i 0.723868 + 0.689939i \(0.242363\pi\)
−0.723868 + 0.689939i \(0.757637\pi\)
\(662\) −25.0625 −0.974083
\(663\) 9.46932 + 3.11288i 0.367758 + 0.120894i
\(664\) 81.4368 3.16036
\(665\) 41.0501i 1.59186i
\(666\) −4.01337 −0.155515
\(667\) 17.5101 0.677993
\(668\) 104.142i 4.02939i
\(669\) 29.9011i 1.15604i
\(670\) 12.3084i 0.475516i
\(671\) 0.586687i 0.0226488i
\(672\) 138.776 5.35339
\(673\) 45.4861 1.75336 0.876680 0.481074i \(-0.159753\pi\)
0.876680 + 0.481074i \(0.159753\pi\)
\(674\) 54.4309i 2.09660i
\(675\) −17.2207 −0.662825
\(676\) −53.9539 39.7707i −2.07515 1.52964i
\(677\) −11.7990 −0.453471 −0.226735 0.973956i \(-0.572805\pi\)
−0.226735 + 0.973956i \(0.572805\pi\)
\(678\) 27.6717i 1.06273i
\(679\) 73.8809 2.83529
\(680\) −40.0400 −1.53546
\(681\) 2.88624i 0.110601i
\(682\) 0.287157i 0.0109958i
\(683\) 23.9204i 0.915288i 0.889135 + 0.457644i \(0.151307\pi\)
−0.889135 + 0.457644i \(0.848693\pi\)
\(684\) 2.97198i 0.113636i
\(685\) 14.1401 0.540266
\(686\) 183.296 6.99826
\(687\) 22.5264i 0.859437i
\(688\) −89.8593 −3.42585
\(689\) −10.4253 3.42716i −0.397174 0.130564i
\(690\) 26.2545 0.999493
\(691\) 17.3715i 0.660842i 0.943834 + 0.330421i \(0.107191\pi\)
−0.943834 + 0.330421i \(0.892809\pi\)
\(692\) 14.8472 0.564405
\(693\) −0.117273 −0.00445484
\(694\) 32.5251i 1.23464i
\(695\) 28.1053i 1.06610i
\(696\) 120.439i 4.56522i
\(697\) 15.3747i 0.582357i
\(698\) −82.8068 −3.13428
\(699\) −3.45549 −0.130699
\(700\) 86.2900i 3.26146i
\(701\) 32.9874 1.24592 0.622958 0.782256i \(-0.285931\pi\)
0.622958 + 0.782256i \(0.285931\pi\)
\(702\) 16.1494 49.1260i 0.609518 1.85414i
\(703\) 19.6722 0.741952
\(704\) 1.94371i 0.0732564i
\(705\) −22.5018 −0.847465
\(706\) −15.9059 −0.598626
\(707\) 20.7909i 0.781921i
\(708\) 98.6158i 3.70621i
\(709\) 21.3761i 0.802797i 0.915904 + 0.401398i \(0.131476\pi\)
−0.915904 + 0.401398i \(0.868524\pi\)
\(710\) 65.1724i 2.44588i
\(711\) 0.398912 0.0149604
\(712\) −81.8957 −3.06917
\(713\) 2.05031i 0.0767847i
\(714\) −38.5346 −1.44212
\(715\) 1.05365 + 0.346369i 0.0394042 + 0.0129535i
\(716\) 36.6116 1.36824
\(717\) 24.7092i 0.922782i
\(718\) 79.0764 2.95110
\(719\) 42.6299 1.58983 0.794913 0.606723i \(-0.207516\pi\)
0.794913 + 0.606723i \(0.207516\pi\)
\(720\) 7.37348i 0.274793i
\(721\) 37.7742i 1.40678i
\(722\) 30.6078i 1.13911i
\(723\) 33.3692i 1.24101i
\(724\) 65.8574 2.44757
\(725\) −27.4303 −1.01874
\(726\) 49.1021i 1.82235i
\(727\) 38.9647 1.44512 0.722561 0.691308i \(-0.242965\pi\)
0.722561 + 0.691308i \(0.242965\pi\)
\(728\) 150.676 + 49.5323i 5.58444 + 1.83579i
\(729\) 28.6140 1.05978
\(730\) 53.5194i 1.98084i
\(731\) 12.1183 0.448212
\(732\) −47.0719 −1.73983
\(733\) 15.6365i 0.577548i −0.957397 0.288774i \(-0.906752\pi\)
0.957397 0.288774i \(-0.0932476\pi\)
\(734\) 69.9904i 2.58339i
\(735\) 96.4558i 3.55783i
\(736\) 32.6903i 1.20498i
\(737\) 0.172358 0.00634889
\(738\) 5.21033 0.191795
\(739\) 3.68292i 0.135478i −0.997703 0.0677392i \(-0.978421\pi\)
0.997703 0.0677392i \(-0.0215786\pi\)
\(740\) −105.726 −3.88655
\(741\) −5.17091 + 15.7298i −0.189958 + 0.577849i
\(742\) 42.4251 1.55747
\(743\) 50.2368i 1.84301i 0.388367 + 0.921505i \(0.373039\pi\)
−0.388367 + 0.921505i \(0.626961\pi\)
\(744\) 14.1026 0.517025
\(745\) −3.55370 −0.130197
\(746\) 23.2724i 0.852065i
\(747\) 2.02245i 0.0739977i
\(748\) 0.916007i 0.0334925i
\(749\) 13.3665i 0.488402i
\(750\) 22.8968 0.836074
\(751\) −5.96827 −0.217785 −0.108893 0.994054i \(-0.534730\pi\)
−0.108893 + 0.994054i \(0.534730\pi\)
\(752\) 57.6885i 2.10368i
\(753\) 7.76232 0.282875
\(754\) 25.7238 78.2514i 0.936807 2.84975i
\(755\) −12.9673 −0.471929
\(756\) 144.041i 5.23872i
\(757\) −37.6489 −1.36837 −0.684187 0.729307i \(-0.739843\pi\)
−0.684187 + 0.729307i \(0.739843\pi\)
\(758\) −59.6124 −2.16522
\(759\) 0.367649i 0.0133448i
\(760\) 66.5117i 2.41263i
\(761\) 22.9366i 0.831451i −0.909490 0.415726i \(-0.863528\pi\)
0.909490 0.415726i \(-0.136472\pi\)
\(762\) 20.0038i 0.724662i
\(763\) 33.8739 1.22632
\(764\) 78.3615 2.83502
\(765\) 0.994377i 0.0359518i
\(766\) 58.5702 2.11623
\(767\) 12.8926 39.2189i 0.465523 1.41611i
\(768\) −13.4580 −0.485623
\(769\) 24.0231i 0.866295i 0.901323 + 0.433148i \(0.142597\pi\)
−0.901323 + 0.433148i \(0.857403\pi\)
\(770\) −4.28774 −0.154519
\(771\) −15.9362 −0.573930
\(772\) 9.95850i 0.358414i
\(773\) 24.5940i 0.884585i 0.896871 + 0.442292i \(0.145835\pi\)
−0.896871 + 0.442292i \(0.854165\pi\)
\(774\) 4.10679i 0.147615i
\(775\) 3.21190i 0.115375i
\(776\) −119.706 −4.29719
\(777\) −62.2818 −2.23435
\(778\) 49.9722i 1.79159i
\(779\) −25.5394 −0.915043
\(780\) 27.7904 84.5378i 0.995055 3.02694i
\(781\) 0.912625 0.0326563
\(782\) 9.07729i 0.324603i