Properties

Label 1050.2.b.c.251.3
Level $1050$
Weight $2$
Character 1050.251
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.3
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 1050.251
Dual form 1050.2.b.c.251.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +(-1.61803 - 0.618034i) q^{6} +(-0.381966 + 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000 q^{4} +(-1.61803 - 0.618034i) q^{6} +(-0.381966 + 2.61803i) q^{7} -1.00000i q^{8} +(-2.23607 - 2.00000i) q^{9} +4.47214i q^{11} +(0.618034 - 1.61803i) q^{12} +3.23607i q^{13} +(-2.61803 - 0.381966i) q^{14} +1.00000 q^{16} -0.763932 q^{17} +(2.00000 - 2.23607i) q^{18} +0.472136i q^{19} +(-4.00000 - 2.23607i) q^{21} -4.47214 q^{22} -4.00000i q^{23} +(1.61803 + 0.618034i) q^{24} -3.23607 q^{26} +(4.61803 - 2.38197i) q^{27} +(0.381966 - 2.61803i) q^{28} -5.70820i q^{29} +7.23607i q^{31} +1.00000i q^{32} +(-7.23607 - 2.76393i) q^{33} -0.763932i q^{34} +(2.23607 + 2.00000i) q^{36} -5.23607 q^{37} -0.472136 q^{38} +(-5.23607 - 2.00000i) q^{39} +6.47214 q^{41} +(2.23607 - 4.00000i) q^{42} -12.9443 q^{43} -4.47214i q^{44} +4.00000 q^{46} -2.47214 q^{47} +(-0.618034 + 1.61803i) q^{48} +(-6.70820 - 2.00000i) q^{49} +(0.472136 - 1.23607i) q^{51} -3.23607i q^{52} -8.47214i q^{53} +(2.38197 + 4.61803i) q^{54} +(2.61803 + 0.381966i) q^{56} +(-0.763932 - 0.291796i) q^{57} +5.70820 q^{58} -4.47214 q^{59} -2.76393i q^{61} -7.23607 q^{62} +(6.09017 - 5.09017i) q^{63} -1.00000 q^{64} +(2.76393 - 7.23607i) q^{66} +12.0000 q^{67} +0.763932 q^{68} +(6.47214 + 2.47214i) q^{69} +2.76393i q^{71} +(-2.00000 + 2.23607i) q^{72} -6.76393i q^{73} -5.23607i q^{74} -0.472136i q^{76} +(-11.7082 - 1.70820i) q^{77} +(2.00000 - 5.23607i) q^{78} +8.94427 q^{79} +(1.00000 + 8.94427i) q^{81} +6.47214i q^{82} +16.6525 q^{83} +(4.00000 + 2.23607i) q^{84} -12.9443i q^{86} +(9.23607 + 3.52786i) q^{87} +4.47214 q^{88} -14.4721 q^{89} +(-8.47214 - 1.23607i) q^{91} +4.00000i q^{92} +(-11.7082 - 4.47214i) q^{93} -2.47214i q^{94} +(-1.61803 - 0.618034i) q^{96} +5.23607i q^{97} +(2.00000 - 6.70820i) q^{98} +(8.94427 - 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} - 4q^{4} - 2q^{6} - 6q^{7} + O(q^{10}) \) \( 4q + 2q^{3} - 4q^{4} - 2q^{6} - 6q^{7} - 2q^{12} - 6q^{14} + 4q^{16} - 12q^{17} + 8q^{18} - 16q^{21} + 2q^{24} - 4q^{26} + 14q^{27} + 6q^{28} - 20q^{33} - 12q^{37} + 16q^{38} - 12q^{39} + 8q^{41} - 16q^{43} + 16q^{46} + 8q^{47} + 2q^{48} - 16q^{51} + 14q^{54} + 6q^{56} - 12q^{57} - 4q^{58} - 20q^{62} + 2q^{63} - 4q^{64} + 20q^{66} + 48q^{67} + 12q^{68} + 8q^{69} - 8q^{72} - 20q^{77} + 8q^{78} + 4q^{81} + 4q^{83} + 16q^{84} + 28q^{87} - 40q^{89} - 16q^{91} - 20q^{93} - 2q^{96} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.618034 + 1.61803i −0.356822 + 0.934172i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) −1.61803 0.618034i −0.660560 0.252311i
\(7\) −0.381966 + 2.61803i −0.144370 + 0.989524i
\(8\) 1.00000i 0.353553i
\(9\) −2.23607 2.00000i −0.745356 0.666667i
\(10\) 0 0
\(11\) 4.47214i 1.34840i 0.738549 + 0.674200i \(0.235511\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 0.618034 1.61803i 0.178411 0.467086i
\(13\) 3.23607i 0.897524i 0.893651 + 0.448762i \(0.148135\pi\)
−0.893651 + 0.448762i \(0.851865\pi\)
\(14\) −2.61803 0.381966i −0.699699 0.102085i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −0.763932 −0.185281 −0.0926404 0.995700i \(-0.529531\pi\)
−0.0926404 + 0.995700i \(0.529531\pi\)
\(18\) 2.00000 2.23607i 0.471405 0.527046i
\(19\) 0.472136i 0.108315i 0.998532 + 0.0541577i \(0.0172474\pi\)
−0.998532 + 0.0541577i \(0.982753\pi\)
\(20\) 0 0
\(21\) −4.00000 2.23607i −0.872872 0.487950i
\(22\) −4.47214 −0.953463
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 1.61803 + 0.618034i 0.330280 + 0.126156i
\(25\) 0 0
\(26\) −3.23607 −0.634645
\(27\) 4.61803 2.38197i 0.888741 0.458410i
\(28\) 0.381966 2.61803i 0.0721848 0.494762i
\(29\) 5.70820i 1.05999i −0.848002 0.529993i \(-0.822194\pi\)
0.848002 0.529993i \(-0.177806\pi\)
\(30\) 0 0
\(31\) 7.23607i 1.29964i 0.760090 + 0.649818i \(0.225155\pi\)
−0.760090 + 0.649818i \(0.774845\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −7.23607 2.76393i −1.25964 0.481139i
\(34\) 0.763932i 0.131013i
\(35\) 0 0
\(36\) 2.23607 + 2.00000i 0.372678 + 0.333333i
\(37\) −5.23607 −0.860804 −0.430402 0.902637i \(-0.641628\pi\)
−0.430402 + 0.902637i \(0.641628\pi\)
\(38\) −0.472136 −0.0765906
\(39\) −5.23607 2.00000i −0.838442 0.320256i
\(40\) 0 0
\(41\) 6.47214 1.01078 0.505389 0.862892i \(-0.331349\pi\)
0.505389 + 0.862892i \(0.331349\pi\)
\(42\) 2.23607 4.00000i 0.345033 0.617213i
\(43\) −12.9443 −1.97398 −0.986991 0.160773i \(-0.948601\pi\)
−0.986991 + 0.160773i \(0.948601\pi\)
\(44\) 4.47214i 0.674200i
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) −2.47214 −0.360598 −0.180299 0.983612i \(-0.557707\pi\)
−0.180299 + 0.983612i \(0.557707\pi\)
\(48\) −0.618034 + 1.61803i −0.0892055 + 0.233543i
\(49\) −6.70820 2.00000i −0.958315 0.285714i
\(50\) 0 0
\(51\) 0.472136 1.23607i 0.0661123 0.173084i
\(52\) 3.23607i 0.448762i
\(53\) 8.47214i 1.16374i −0.813283 0.581869i \(-0.802322\pi\)
0.813283 0.581869i \(-0.197678\pi\)
\(54\) 2.38197 + 4.61803i 0.324145 + 0.628435i
\(55\) 0 0
\(56\) 2.61803 + 0.381966i 0.349850 + 0.0510424i
\(57\) −0.763932 0.291796i −0.101185 0.0386493i
\(58\) 5.70820 0.749524
\(59\) −4.47214 −0.582223 −0.291111 0.956689i \(-0.594025\pi\)
−0.291111 + 0.956689i \(0.594025\pi\)
\(60\) 0 0
\(61\) 2.76393i 0.353885i −0.984221 0.176943i \(-0.943379\pi\)
0.984221 0.176943i \(-0.0566207\pi\)
\(62\) −7.23607 −0.918982
\(63\) 6.09017 5.09017i 0.767289 0.641301i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 2.76393 7.23607i 0.340217 0.890698i
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 0.763932 0.0926404
\(69\) 6.47214 + 2.47214i 0.779154 + 0.297610i
\(70\) 0 0
\(71\) 2.76393i 0.328018i 0.986459 + 0.164009i \(0.0524427\pi\)
−0.986459 + 0.164009i \(0.947557\pi\)
\(72\) −2.00000 + 2.23607i −0.235702 + 0.263523i
\(73\) 6.76393i 0.791658i −0.918324 0.395829i \(-0.870457\pi\)
0.918324 0.395829i \(-0.129543\pi\)
\(74\) 5.23607i 0.608681i
\(75\) 0 0
\(76\) 0.472136i 0.0541577i
\(77\) −11.7082 1.70820i −1.33427 0.194668i
\(78\) 2.00000 5.23607i 0.226455 0.592868i
\(79\) 8.94427 1.00631 0.503155 0.864196i \(-0.332173\pi\)
0.503155 + 0.864196i \(0.332173\pi\)
\(80\) 0 0
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 6.47214i 0.714728i
\(83\) 16.6525 1.82785 0.913923 0.405887i \(-0.133037\pi\)
0.913923 + 0.405887i \(0.133037\pi\)
\(84\) 4.00000 + 2.23607i 0.436436 + 0.243975i
\(85\) 0 0
\(86\) 12.9443i 1.39582i
\(87\) 9.23607 + 3.52786i 0.990210 + 0.378227i
\(88\) 4.47214 0.476731
\(89\) −14.4721 −1.53404 −0.767022 0.641621i \(-0.778262\pi\)
−0.767022 + 0.641621i \(0.778262\pi\)
\(90\) 0 0
\(91\) −8.47214 1.23607i −0.888121 0.129575i
\(92\) 4.00000i 0.417029i
\(93\) −11.7082 4.47214i −1.21408 0.463739i
\(94\) 2.47214i 0.254981i
\(95\) 0 0
\(96\) −1.61803 0.618034i −0.165140 0.0630778i
\(97\) 5.23607i 0.531642i 0.964022 + 0.265821i \(0.0856430\pi\)
−0.964022 + 0.265821i \(0.914357\pi\)
\(98\) 2.00000 6.70820i 0.202031 0.677631i
\(99\) 8.94427 10.0000i 0.898933 1.00504i
\(100\) 0 0
\(101\) −3.52786 −0.351036 −0.175518 0.984476i \(-0.556160\pi\)
−0.175518 + 0.984476i \(0.556160\pi\)
\(102\) 1.23607 + 0.472136i 0.122389 + 0.0467484i
\(103\) 16.6525i 1.64082i 0.571778 + 0.820409i \(0.306254\pi\)
−0.571778 + 0.820409i \(0.693746\pi\)
\(104\) 3.23607 0.317323
\(105\) 0 0
\(106\) 8.47214 0.822887
\(107\) 15.4164i 1.49036i −0.666863 0.745180i \(-0.732363\pi\)
0.666863 0.745180i \(-0.267637\pi\)
\(108\) −4.61803 + 2.38197i −0.444371 + 0.229205i
\(109\) −4.47214 −0.428353 −0.214176 0.976795i \(-0.568707\pi\)
−0.214176 + 0.976795i \(0.568707\pi\)
\(110\) 0 0
\(111\) 3.23607 8.47214i 0.307154 0.804140i
\(112\) −0.381966 + 2.61803i −0.0360924 + 0.247381i
\(113\) 14.9443i 1.40584i 0.711269 + 0.702919i \(0.248121\pi\)
−0.711269 + 0.702919i \(0.751879\pi\)
\(114\) 0.291796 0.763932i 0.0273292 0.0715488i
\(115\) 0 0
\(116\) 5.70820i 0.529993i
\(117\) 6.47214 7.23607i 0.598349 0.668975i
\(118\) 4.47214i 0.411693i
\(119\) 0.291796 2.00000i 0.0267489 0.183340i
\(120\) 0 0
\(121\) −9.00000 −0.818182
\(122\) 2.76393 0.250235
\(123\) −4.00000 + 10.4721i −0.360668 + 0.944241i
\(124\) 7.23607i 0.649818i
\(125\) 0 0
\(126\) 5.09017 + 6.09017i 0.453468 + 0.542555i
\(127\) 13.7082 1.21641 0.608203 0.793781i \(-0.291891\pi\)
0.608203 + 0.793781i \(0.291891\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.00000 20.9443i 0.704361 1.84404i
\(130\) 0 0
\(131\) −21.4164 −1.87116 −0.935580 0.353114i \(-0.885123\pi\)
−0.935580 + 0.353114i \(0.885123\pi\)
\(132\) 7.23607 + 2.76393i 0.629819 + 0.240569i
\(133\) −1.23607 0.180340i −0.107181 0.0156375i
\(134\) 12.0000i 1.03664i
\(135\) 0 0
\(136\) 0.763932i 0.0655066i
\(137\) 12.4721i 1.06557i 0.846252 + 0.532783i \(0.178854\pi\)
−0.846252 + 0.532783i \(0.821146\pi\)
\(138\) −2.47214 + 6.47214i −0.210442 + 0.550945i
\(139\) 20.4721i 1.73642i 0.496194 + 0.868212i \(0.334731\pi\)
−0.496194 + 0.868212i \(0.665269\pi\)
\(140\) 0 0
\(141\) 1.52786 4.00000i 0.128669 0.336861i
\(142\) −2.76393 −0.231944
\(143\) −14.4721 −1.21022
\(144\) −2.23607 2.00000i −0.186339 0.166667i
\(145\) 0 0
\(146\) 6.76393 0.559787
\(147\) 7.38197 9.61803i 0.608854 0.793282i
\(148\) 5.23607 0.430402
\(149\) 17.7082i 1.45071i 0.688374 + 0.725356i \(0.258325\pi\)
−0.688374 + 0.725356i \(0.741675\pi\)
\(150\) 0 0
\(151\) 3.05573 0.248672 0.124336 0.992240i \(-0.460320\pi\)
0.124336 + 0.992240i \(0.460320\pi\)
\(152\) 0.472136 0.0382953
\(153\) 1.70820 + 1.52786i 0.138100 + 0.123520i
\(154\) 1.70820 11.7082i 0.137651 0.943474i
\(155\) 0 0
\(156\) 5.23607 + 2.00000i 0.419221 + 0.160128i
\(157\) 4.76393i 0.380203i −0.981764 0.190102i \(-0.939118\pi\)
0.981764 0.190102i \(-0.0608817\pi\)
\(158\) 8.94427i 0.711568i
\(159\) 13.7082 + 5.23607i 1.08713 + 0.415247i
\(160\) 0 0
\(161\) 10.4721 + 1.52786i 0.825320 + 0.120413i
\(162\) −8.94427 + 1.00000i −0.702728 + 0.0785674i
\(163\) 1.52786 0.119672 0.0598358 0.998208i \(-0.480942\pi\)
0.0598358 + 0.998208i \(0.480942\pi\)
\(164\) −6.47214 −0.505389
\(165\) 0 0
\(166\) 16.6525i 1.29248i
\(167\) −16.9443 −1.31119 −0.655594 0.755114i \(-0.727582\pi\)
−0.655594 + 0.755114i \(0.727582\pi\)
\(168\) −2.23607 + 4.00000i −0.172516 + 0.308607i
\(169\) 2.52786 0.194451
\(170\) 0 0
\(171\) 0.944272 1.05573i 0.0722103 0.0807335i
\(172\) 12.9443 0.986991
\(173\) −17.4164 −1.32414 −0.662072 0.749440i \(-0.730323\pi\)
−0.662072 + 0.749440i \(0.730323\pi\)
\(174\) −3.52786 + 9.23607i −0.267447 + 0.700185i
\(175\) 0 0
\(176\) 4.47214i 0.337100i
\(177\) 2.76393 7.23607i 0.207750 0.543896i
\(178\) 14.4721i 1.08473i
\(179\) 2.94427i 0.220065i −0.993928 0.110033i \(-0.964904\pi\)
0.993928 0.110033i \(-0.0350955\pi\)
\(180\) 0 0
\(181\) 6.18034i 0.459381i −0.973264 0.229691i \(-0.926229\pi\)
0.973264 0.229691i \(-0.0737714\pi\)
\(182\) 1.23607 8.47214i 0.0916235 0.627996i
\(183\) 4.47214 + 1.70820i 0.330590 + 0.126274i
\(184\) −4.00000 −0.294884
\(185\) 0 0
\(186\) 4.47214 11.7082i 0.327913 0.858487i
\(187\) 3.41641i 0.249832i
\(188\) 2.47214 0.180299
\(189\) 4.47214 + 13.0000i 0.325300 + 0.945611i
\(190\) 0 0
\(191\) 2.76393i 0.199991i −0.994988 0.0999956i \(-0.968117\pi\)
0.994988 0.0999956i \(-0.0318829\pi\)
\(192\) 0.618034 1.61803i 0.0446028 0.116772i
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) −5.23607 −0.375928
\(195\) 0 0
\(196\) 6.70820 + 2.00000i 0.479157 + 0.142857i
\(197\) 12.4721i 0.888603i 0.895877 + 0.444301i \(0.146548\pi\)
−0.895877 + 0.444301i \(0.853452\pi\)
\(198\) 10.0000 + 8.94427i 0.710669 + 0.635642i
\(199\) 0.180340i 0.0127840i −0.999980 0.00639198i \(-0.997965\pi\)
0.999980 0.00639198i \(-0.00203464\pi\)
\(200\) 0 0
\(201\) −7.41641 + 19.4164i −0.523113 + 1.36953i
\(202\) 3.52786i 0.248220i
\(203\) 14.9443 + 2.18034i 1.04888 + 0.153030i
\(204\) −0.472136 + 1.23607i −0.0330561 + 0.0865421i
\(205\) 0 0
\(206\) −16.6525 −1.16023
\(207\) −8.00000 + 8.94427i −0.556038 + 0.621670i
\(208\) 3.23607i 0.224381i
\(209\) −2.11146 −0.146052
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 8.47214i 0.581869i
\(213\) −4.47214 1.70820i −0.306426 0.117044i
\(214\) 15.4164 1.05384
\(215\) 0 0
\(216\) −2.38197 4.61803i −0.162072 0.314217i
\(217\) −18.9443 2.76393i −1.28602 0.187628i
\(218\) 4.47214i 0.302891i
\(219\) 10.9443 + 4.18034i 0.739545 + 0.282481i
\(220\) 0 0
\(221\) 2.47214i 0.166294i
\(222\) 8.47214 + 3.23607i 0.568613 + 0.217191i
\(223\) 4.29180i 0.287400i 0.989621 + 0.143700i \(0.0459000\pi\)
−0.989621 + 0.143700i \(0.954100\pi\)
\(224\) −2.61803 0.381966i −0.174925 0.0255212i
\(225\) 0 0
\(226\) −14.9443 −0.994078
\(227\) −5.23607 −0.347530 −0.173765 0.984787i \(-0.555593\pi\)
−0.173765 + 0.984787i \(0.555593\pi\)
\(228\) 0.763932 + 0.291796i 0.0505926 + 0.0193247i
\(229\) 13.2361i 0.874664i 0.899300 + 0.437332i \(0.144077\pi\)
−0.899300 + 0.437332i \(0.855923\pi\)
\(230\) 0 0
\(231\) 10.0000 17.8885i 0.657952 1.17698i
\(232\) −5.70820 −0.374762
\(233\) 20.4721i 1.34117i 0.741831 + 0.670587i \(0.233958\pi\)
−0.741831 + 0.670587i \(0.766042\pi\)
\(234\) 7.23607 + 6.47214i 0.473037 + 0.423097i
\(235\) 0 0
\(236\) 4.47214 0.291111
\(237\) −5.52786 + 14.4721i −0.359073 + 0.940066i
\(238\) 2.00000 + 0.291796i 0.129641 + 0.0189143i
\(239\) 22.1803i 1.43473i 0.696699 + 0.717363i \(0.254651\pi\)
−0.696699 + 0.717363i \(0.745349\pi\)
\(240\) 0 0
\(241\) 17.8885i 1.15230i 0.817343 + 0.576151i \(0.195446\pi\)
−0.817343 + 0.576151i \(0.804554\pi\)
\(242\) 9.00000i 0.578542i
\(243\) −15.0902 3.90983i −0.968035 0.250816i
\(244\) 2.76393i 0.176943i
\(245\) 0 0
\(246\) −10.4721 4.00000i −0.667679 0.255031i
\(247\) −1.52786 −0.0972157
\(248\) 7.23607 0.459491
\(249\) −10.2918 + 26.9443i −0.652216 + 1.70752i
\(250\) 0 0
\(251\) −3.52786 −0.222677 −0.111338 0.993783i \(-0.535514\pi\)
−0.111338 + 0.993783i \(0.535514\pi\)
\(252\) −6.09017 + 5.09017i −0.383645 + 0.320651i
\(253\) 17.8885 1.12464
\(254\) 13.7082i 0.860129i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 8.18034 0.510276 0.255138 0.966905i \(-0.417879\pi\)
0.255138 + 0.966905i \(0.417879\pi\)
\(258\) 20.9443 + 8.00000i 1.30393 + 0.498058i
\(259\) 2.00000 13.7082i 0.124274 0.851786i
\(260\) 0 0
\(261\) −11.4164 + 12.7639i −0.706658 + 0.790068i
\(262\) 21.4164i 1.32311i
\(263\) 4.94427i 0.304877i 0.988313 + 0.152438i \(0.0487126\pi\)
−0.988313 + 0.152438i \(0.951287\pi\)
\(264\) −2.76393 + 7.23607i −0.170108 + 0.445349i
\(265\) 0 0
\(266\) 0.180340 1.23607i 0.0110573 0.0757882i
\(267\) 8.94427 23.4164i 0.547381 1.43306i
\(268\) −12.0000 −0.733017
\(269\) −4.47214 −0.272671 −0.136335 0.990663i \(-0.543533\pi\)
−0.136335 + 0.990663i \(0.543533\pi\)
\(270\) 0 0
\(271\) 18.2918i 1.11115i −0.831467 0.555574i \(-0.812499\pi\)
0.831467 0.555574i \(-0.187501\pi\)
\(272\) −0.763932 −0.0463202
\(273\) 7.23607 12.9443i 0.437947 0.783423i
\(274\) −12.4721 −0.753469
\(275\) 0 0
\(276\) −6.47214 2.47214i −0.389577 0.148805i
\(277\) −23.1246 −1.38942 −0.694712 0.719288i \(-0.744468\pi\)
−0.694712 + 0.719288i \(0.744468\pi\)
\(278\) −20.4721 −1.22784
\(279\) 14.4721 16.1803i 0.866424 0.968692i
\(280\) 0 0
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) 4.00000 + 1.52786i 0.238197 + 0.0909830i
\(283\) 8.76393i 0.520962i 0.965479 + 0.260481i \(0.0838811\pi\)
−0.965479 + 0.260481i \(0.916119\pi\)
\(284\) 2.76393i 0.164009i
\(285\) 0 0
\(286\) 14.4721i 0.855755i
\(287\) −2.47214 + 16.9443i −0.145926 + 1.00019i
\(288\) 2.00000 2.23607i 0.117851 0.131762i
\(289\) −16.4164 −0.965671
\(290\) 0 0
\(291\) −8.47214 3.23607i −0.496645 0.189702i
\(292\) 6.76393i 0.395829i
\(293\) 29.4164 1.71852 0.859262 0.511535i \(-0.170923\pi\)
0.859262 + 0.511535i \(0.170923\pi\)
\(294\) 9.61803 + 7.38197i 0.560935 + 0.430525i
\(295\) 0 0
\(296\) 5.23607i 0.304340i
\(297\) 10.6525 + 20.6525i 0.618119 + 1.19838i
\(298\) −17.7082 −1.02581
\(299\) 12.9443 0.748587
\(300\) 0 0
\(301\) 4.94427 33.8885i 0.284983 1.95330i
\(302\) 3.05573i 0.175837i
\(303\) 2.18034 5.70820i 0.125257 0.327928i
\(304\) 0.472136i 0.0270789i
\(305\) 0 0
\(306\) −1.52786 + 1.70820i −0.0873422 + 0.0976515i
\(307\) 4.18034i 0.238585i 0.992859 + 0.119292i \(0.0380626\pi\)
−0.992859 + 0.119292i \(0.961937\pi\)
\(308\) 11.7082 + 1.70820i 0.667137 + 0.0973340i
\(309\) −26.9443 10.2918i −1.53281 0.585480i
\(310\) 0 0
\(311\) 26.4721 1.50110 0.750549 0.660815i \(-0.229789\pi\)
0.750549 + 0.660815i \(0.229789\pi\)
\(312\) −2.00000 + 5.23607i −0.113228 + 0.296434i
\(313\) 7.70820i 0.435693i 0.975983 + 0.217847i \(0.0699033\pi\)
−0.975983 + 0.217847i \(0.930097\pi\)
\(314\) 4.76393 0.268844
\(315\) 0 0
\(316\) −8.94427 −0.503155
\(317\) 6.94427i 0.390029i 0.980800 + 0.195015i \(0.0624754\pi\)
−0.980800 + 0.195015i \(0.937525\pi\)
\(318\) −5.23607 + 13.7082i −0.293624 + 0.768718i
\(319\) 25.5279 1.42929
\(320\) 0 0
\(321\) 24.9443 + 9.52786i 1.39225 + 0.531794i
\(322\) −1.52786 + 10.4721i −0.0851445 + 0.583589i
\(323\) 0.360680i 0.0200688i
\(324\) −1.00000 8.94427i −0.0555556 0.496904i
\(325\) 0 0
\(326\) 1.52786i 0.0846206i
\(327\) 2.76393 7.23607i 0.152846 0.400155i
\(328\) 6.47214i 0.357364i
\(329\) 0.944272 6.47214i 0.0520594 0.356820i
\(330\) 0 0
\(331\) 20.9443 1.15120 0.575601 0.817731i \(-0.304768\pi\)
0.575601 + 0.817731i \(0.304768\pi\)
\(332\) −16.6525 −0.913923
\(333\) 11.7082 + 10.4721i 0.641606 + 0.573870i
\(334\) 16.9443i 0.927149i
\(335\) 0 0
\(336\) −4.00000 2.23607i −0.218218 0.121988i
\(337\) 5.41641 0.295051 0.147525 0.989058i \(-0.452869\pi\)
0.147525 + 0.989058i \(0.452869\pi\)
\(338\) 2.52786i 0.137498i
\(339\) −24.1803 9.23607i −1.31330 0.501634i
\(340\) 0 0
\(341\) −32.3607 −1.75243
\(342\) 1.05573 + 0.944272i 0.0570872 + 0.0510604i
\(343\) 7.79837 16.7984i 0.421073 0.907027i
\(344\) 12.9443i 0.697908i
\(345\) 0 0
\(346\) 17.4164i 0.936312i
\(347\) 6.47214i 0.347442i −0.984795 0.173721i \(-0.944421\pi\)
0.984795 0.173721i \(-0.0555792\pi\)
\(348\) −9.23607 3.52786i −0.495105 0.189113i
\(349\) 2.18034i 0.116711i 0.998296 + 0.0583555i \(0.0185857\pi\)
−0.998296 + 0.0583555i \(0.981414\pi\)
\(350\) 0 0
\(351\) 7.70820 + 14.9443i 0.411433 + 0.797666i
\(352\) −4.47214 −0.238366
\(353\) 14.2918 0.760676 0.380338 0.924848i \(-0.375808\pi\)
0.380338 + 0.924848i \(0.375808\pi\)
\(354\) 7.23607 + 2.76393i 0.384593 + 0.146901i
\(355\) 0 0
\(356\) 14.4721 0.767022
\(357\) 3.05573 + 1.70820i 0.161726 + 0.0904077i
\(358\) 2.94427 0.155610
\(359\) 10.1803i 0.537298i −0.963238 0.268649i \(-0.913423\pi\)
0.963238 0.268649i \(-0.0865771\pi\)
\(360\) 0 0
\(361\) 18.7771 0.988268
\(362\) 6.18034 0.324831
\(363\) 5.56231 14.5623i 0.291945 0.764323i
\(364\) 8.47214 + 1.23607i 0.444061 + 0.0647876i
\(365\) 0 0
\(366\) −1.70820 + 4.47214i −0.0892892 + 0.233762i
\(367\) 14.1803i 0.740208i 0.928990 + 0.370104i \(0.120678\pi\)
−0.928990 + 0.370104i \(0.879322\pi\)
\(368\) 4.00000i 0.208514i
\(369\) −14.4721 12.9443i −0.753389 0.673852i
\(370\) 0 0
\(371\) 22.1803 + 3.23607i 1.15155 + 0.168008i
\(372\) 11.7082 + 4.47214i 0.607042 + 0.231869i
\(373\) 9.81966 0.508443 0.254221 0.967146i \(-0.418181\pi\)
0.254221 + 0.967146i \(0.418181\pi\)
\(374\) 3.41641 0.176658
\(375\) 0 0
\(376\) 2.47214i 0.127491i
\(377\) 18.4721 0.951363
\(378\) −13.0000 + 4.47214i −0.668648 + 0.230022i
\(379\) 17.8885 0.918873 0.459436 0.888211i \(-0.348051\pi\)
0.459436 + 0.888211i \(0.348051\pi\)
\(380\) 0 0
\(381\) −8.47214 + 22.1803i −0.434041 + 1.13633i
\(382\) 2.76393 0.141415
\(383\) −21.8885 −1.11845 −0.559226 0.829015i \(-0.688902\pi\)
−0.559226 + 0.829015i \(0.688902\pi\)
\(384\) 1.61803 + 0.618034i 0.0825700 + 0.0315389i
\(385\) 0 0
\(386\) 6.00000i 0.305392i
\(387\) 28.9443 + 25.8885i 1.47132 + 1.31599i
\(388\) 5.23607i 0.265821i
\(389\) 7.81966i 0.396473i −0.980154 0.198236i \(-0.936479\pi\)
0.980154 0.198236i \(-0.0635213\pi\)
\(390\) 0 0
\(391\) 3.05573i 0.154535i
\(392\) −2.00000 + 6.70820i −0.101015 + 0.338815i
\(393\) 13.2361 34.6525i 0.667671 1.74799i
\(394\) −12.4721 −0.628337
\(395\) 0 0
\(396\) −8.94427 + 10.0000i −0.449467 + 0.502519i
\(397\) 17.1246i 0.859460i −0.902958 0.429730i \(-0.858609\pi\)
0.902958 0.429730i \(-0.141391\pi\)
\(398\) 0.180340 0.00903962
\(399\) 1.05573 1.88854i 0.0528525 0.0945454i
\(400\) 0 0
\(401\) 5.52786i 0.276048i −0.990429 0.138024i \(-0.955925\pi\)
0.990429 0.138024i \(-0.0440752\pi\)
\(402\) −19.4164 7.41641i −0.968402 0.369897i
\(403\) −23.4164 −1.16645
\(404\) 3.52786 0.175518
\(405\) 0 0
\(406\) −2.18034 + 14.9443i −0.108208 + 0.741672i
\(407\) 23.4164i 1.16071i
\(408\) −1.23607 0.472136i −0.0611945 0.0233742i
\(409\) 19.4164i 0.960080i 0.877247 + 0.480040i \(0.159378\pi\)
−0.877247 + 0.480040i \(0.840622\pi\)
\(410\) 0 0
\(411\) −20.1803 7.70820i −0.995423 0.380218i
\(412\) 16.6525i 0.820409i
\(413\) 1.70820 11.7082i 0.0840552 0.576123i
\(414\) −8.94427 8.00000i −0.439587 0.393179i
\(415\) 0 0
\(416\) −3.23607 −0.158661
\(417\) −33.1246 12.6525i −1.62212 0.619594i
\(418\) 2.11146i 0.103275i
\(419\) −16.8328 −0.822337 −0.411168 0.911559i \(-0.634879\pi\)
−0.411168 + 0.911559i \(0.634879\pi\)
\(420\) 0 0
\(421\) −12.4721 −0.607855 −0.303927 0.952695i \(-0.598298\pi\)
−0.303927 + 0.952695i \(0.598298\pi\)
\(422\) 8.00000i 0.389434i
\(423\) 5.52786 + 4.94427i 0.268774 + 0.240399i
\(424\) −8.47214 −0.411443
\(425\) 0 0
\(426\) 1.70820 4.47214i 0.0827628 0.216676i
\(427\) 7.23607 + 1.05573i 0.350178 + 0.0510903i
\(428\) 15.4164i 0.745180i
\(429\) 8.94427 23.4164i 0.431834 1.13055i
\(430\) 0 0
\(431\) 9.59675i 0.462259i −0.972923 0.231130i \(-0.925758\pi\)
0.972923 0.231130i \(-0.0742421\pi\)
\(432\) 4.61803 2.38197i 0.222185 0.114602i
\(433\) 4.65248i 0.223584i −0.993732 0.111792i \(-0.964341\pi\)
0.993732 0.111792i \(-0.0356590\pi\)
\(434\) 2.76393 18.9443i 0.132673 0.909354i
\(435\) 0 0
\(436\) 4.47214 0.214176
\(437\) 1.88854 0.0903413
\(438\) −4.18034 + 10.9443i −0.199744 + 0.522938i
\(439\) 12.1803i 0.581336i 0.956824 + 0.290668i \(0.0938775\pi\)
−0.956824 + 0.290668i \(0.906123\pi\)
\(440\) 0 0
\(441\) 11.0000 + 17.8885i 0.523810 + 0.851835i
\(442\) 2.47214 0.117588
\(443\) 9.52786i 0.452682i −0.974048 0.226341i \(-0.927324\pi\)
0.974048 0.226341i \(-0.0726764\pi\)
\(444\) −3.23607 + 8.47214i −0.153577 + 0.402070i
\(445\) 0 0
\(446\) −4.29180 −0.203222
\(447\) −28.6525 10.9443i −1.35522 0.517646i
\(448\) 0.381966 2.61803i 0.0180462 0.123690i
\(449\) 1.52786i 0.0721044i 0.999350 + 0.0360522i \(0.0114783\pi\)
−0.999350 + 0.0360522i \(0.988522\pi\)
\(450\) 0 0
\(451\) 28.9443i 1.36293i
\(452\) 14.9443i 0.702919i
\(453\) −1.88854 + 4.94427i −0.0887315 + 0.232302i
\(454\) 5.23607i 0.245741i
\(455\) 0 0
\(456\) −0.291796 + 0.763932i −0.0136646 + 0.0357744i
\(457\) −9.05573 −0.423609 −0.211805 0.977312i \(-0.567934\pi\)
−0.211805 + 0.977312i \(0.567934\pi\)
\(458\) −13.2361 −0.618481
\(459\) −3.52786 + 1.81966i −0.164667 + 0.0849345i
\(460\) 0 0
\(461\) 10.9443 0.509726 0.254863 0.966977i \(-0.417970\pi\)
0.254863 + 0.966977i \(0.417970\pi\)
\(462\) 17.8885 + 10.0000i 0.832250 + 0.465242i
\(463\) −0.180340 −0.00838111 −0.00419055 0.999991i \(-0.501334\pi\)
−0.00419055 + 0.999991i \(0.501334\pi\)
\(464\) 5.70820i 0.264997i
\(465\) 0 0
\(466\) −20.4721 −0.948353
\(467\) 20.2918 0.938992 0.469496 0.882935i \(-0.344436\pi\)
0.469496 + 0.882935i \(0.344436\pi\)
\(468\) −6.47214 + 7.23607i −0.299175 + 0.334487i
\(469\) −4.58359 + 31.4164i −0.211651 + 1.45067i
\(470\) 0 0
\(471\) 7.70820 + 2.94427i 0.355175 + 0.135665i
\(472\) 4.47214i 0.205847i
\(473\) 57.8885i 2.66172i
\(474\) −14.4721 5.52786i −0.664727 0.253903i
\(475\) 0 0
\(476\) −0.291796 + 2.00000i −0.0133745 + 0.0916698i
\(477\) −16.9443 + 18.9443i −0.775825 + 0.867399i
\(478\) −22.1803 −1.01451
\(479\) 2.11146 0.0964749 0.0482374 0.998836i \(-0.484640\pi\)
0.0482374 + 0.998836i \(0.484640\pi\)
\(480\) 0 0
\(481\) 16.9443i 0.772592i
\(482\) −17.8885 −0.814801
\(483\) −8.94427 + 16.0000i −0.406978 + 0.728025i
\(484\) 9.00000 0.409091
\(485\) 0 0
\(486\) 3.90983 15.0902i 0.177353 0.684504i
\(487\) 31.5967 1.43179 0.715893 0.698210i \(-0.246020\pi\)
0.715893 + 0.698210i \(0.246020\pi\)
\(488\) −2.76393 −0.125117
\(489\) −0.944272 + 2.47214i −0.0427015 + 0.111794i
\(490\) 0 0
\(491\) 13.4164i 0.605474i 0.953074 + 0.302737i \(0.0979004\pi\)
−0.953074 + 0.302737i \(0.902100\pi\)
\(492\) 4.00000 10.4721i 0.180334 0.472120i
\(493\) 4.36068i 0.196395i
\(494\) 1.52786i 0.0687419i
\(495\) 0 0
\(496\) 7.23607i 0.324909i
\(497\) −7.23607 1.05573i −0.324582 0.0473559i
\(498\) −26.9443 10.2918i −1.20740 0.461186i
\(499\) −17.8885 −0.800801 −0.400401 0.916340i \(-0.631129\pi\)
−0.400401 + 0.916340i \(0.631129\pi\)
\(500\) 0 0
\(501\) 10.4721 27.4164i 0.467861 1.22487i
\(502\) 3.52786i 0.157456i
\(503\) −16.3607 −0.729487 −0.364743 0.931108i \(-0.618843\pi\)
−0.364743 + 0.931108i \(0.618843\pi\)
\(504\) −5.09017 6.09017i −0.226734 0.271278i
\(505\) 0 0
\(506\) 17.8885i 0.795243i
\(507\) −1.56231 + 4.09017i −0.0693844 + 0.181651i
\(508\) −13.7082 −0.608203
\(509\) 24.4721 1.08471 0.542354 0.840150i \(-0.317533\pi\)
0.542354 + 0.840150i \(0.317533\pi\)
\(510\) 0 0
\(511\) 17.7082 + 2.58359i 0.783365 + 0.114291i
\(512\) 1.00000i 0.0441942i
\(513\) 1.12461 + 2.18034i 0.0496528 + 0.0962644i
\(514\) 8.18034i 0.360819i
\(515\) 0 0
\(516\) −8.00000 + 20.9443i −0.352180 + 0.922020i
\(517\) 11.0557i 0.486230i
\(518\) 13.7082 + 2.00000i 0.602304 + 0.0878750i
\(519\) 10.7639 28.1803i 0.472484 1.23698i
\(520\) 0 0
\(521\) −19.0557 −0.834847 −0.417423 0.908712i \(-0.637067\pi\)
−0.417423 + 0.908712i \(0.637067\pi\)
\(522\) −12.7639 11.4164i −0.558662 0.499683i
\(523\) 24.5410i 1.07310i 0.843867 + 0.536552i \(0.180273\pi\)
−0.843867 + 0.536552i \(0.819727\pi\)
\(524\) 21.4164 0.935580
\(525\) 0 0
\(526\) −4.94427 −0.215580
\(527\) 5.52786i 0.240798i
\(528\) −7.23607 2.76393i −0.314909 0.120285i
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 10.0000 + 8.94427i 0.433963 + 0.388148i
\(532\) 1.23607 + 0.180340i 0.0535903 + 0.00781873i
\(533\) 20.9443i 0.907197i
\(534\) 23.4164 + 8.94427i 1.01333 + 0.387056i
\(535\) 0 0
\(536\) 12.0000i 0.518321i
\(537\) 4.76393 + 1.81966i 0.205579 + 0.0785241i
\(538\) 4.47214i 0.192807i
\(539\) 8.94427 30.0000i 0.385257 1.29219i
\(540\) 0 0
\(541\) 13.0557 0.561310 0.280655 0.959809i \(-0.409448\pi\)
0.280655 + 0.959809i \(0.409448\pi\)
\(542\) 18.2918 0.785700
\(543\) 10.0000 + 3.81966i 0.429141 + 0.163917i
\(544\) 0.763932i 0.0327533i
\(545\) 0 0
\(546\) 12.9443 + 7.23607i 0.553964 + 0.309675i
\(547\) 8.58359 0.367008 0.183504 0.983019i \(-0.441256\pi\)
0.183504 + 0.983019i \(0.441256\pi\)
\(548\) 12.4721i 0.532783i
\(549\) −5.52786 + 6.18034i −0.235923 + 0.263770i
\(550\) 0 0
\(551\) 2.69505 0.114813
\(552\) 2.47214 6.47214i 0.105221 0.275472i
\(553\) −3.41641 + 23.4164i −0.145280 + 0.995767i
\(554\) 23.1246i 0.982471i
\(555\) 0 0
\(556\) 20.4721i 0.868212i
\(557\) 16.4721i 0.697947i −0.937133 0.348973i \(-0.886530\pi\)
0.937133 0.348973i \(-0.113470\pi\)
\(558\) 16.1803 + 14.4721i 0.684968 + 0.612654i
\(559\) 41.8885i 1.77170i
\(560\) 0 0
\(561\) 5.52786 + 2.11146i 0.233387 + 0.0891457i
\(562\) 20.0000 0.843649
\(563\) −17.8197 −0.751009 −0.375505 0.926821i \(-0.622531\pi\)
−0.375505 + 0.926821i \(0.622531\pi\)
\(564\) −1.52786 + 4.00000i −0.0643347 + 0.168430i
\(565\) 0 0
\(566\) −8.76393 −0.368376
\(567\) −23.7984 0.798374i −0.999438 0.0335286i
\(568\) 2.76393 0.115972
\(569\) 18.4721i 0.774392i −0.921997 0.387196i \(-0.873444\pi\)
0.921997 0.387196i \(-0.126556\pi\)
\(570\) 0 0
\(571\) −34.8328 −1.45771 −0.728854 0.684669i \(-0.759947\pi\)
−0.728854 + 0.684669i \(0.759947\pi\)
\(572\) 14.4721 0.605110
\(573\) 4.47214 + 1.70820i 0.186826 + 0.0713612i
\(574\) −16.9443 2.47214i −0.707240 0.103185i
\(575\) 0 0
\(576\) 2.23607 + 2.00000i 0.0931695 + 0.0833333i
\(577\) 14.1803i 0.590335i 0.955445 + 0.295168i \(0.0953755\pi\)
−0.955445 + 0.295168i \(0.904625\pi\)
\(578\) 16.4164i 0.682833i
\(579\) −3.70820 + 9.70820i −0.154108 + 0.403459i
\(580\) 0 0
\(581\) −6.36068 + 43.5967i −0.263885 + 1.80870i
\(582\) 3.23607 8.47214i 0.134139 0.351181i
\(583\) 37.8885 1.56918
\(584\) −6.76393 −0.279893
\(585\) 0 0
\(586\) 29.4164i 1.21518i
\(587\) 23.7082 0.978542 0.489271 0.872132i \(-0.337263\pi\)
0.489271 + 0.872132i \(0.337263\pi\)
\(588\) −7.38197 + 9.61803i −0.304427 + 0.396641i
\(589\) −3.41641 −0.140771
\(590\) 0 0
\(591\) −20.1803 7.70820i −0.830108 0.317073i
\(592\) −5.23607 −0.215201
\(593\) −47.0132 −1.93060 −0.965299 0.261145i \(-0.915900\pi\)
−0.965299 + 0.261145i \(0.915900\pi\)
\(594\) −20.6525 + 10.6525i −0.847381 + 0.437076i
\(595\) 0 0
\(596\) 17.7082i 0.725356i
\(597\) 0.291796 + 0.111456i 0.0119424 + 0.00456160i
\(598\) 12.9443i 0.529331i
\(599\) 41.2361i 1.68486i −0.538806 0.842430i \(-0.681124\pi\)
0.538806 0.842430i \(-0.318876\pi\)
\(600\) 0 0
\(601\) 14.4721i 0.590331i −0.955446 0.295165i \(-0.904625\pi\)
0.955446 0.295165i \(-0.0953747\pi\)
\(602\) 33.8885 + 4.94427i 1.38119 + 0.201513i
\(603\) −26.8328 24.0000i −1.09272 0.977356i
\(604\) −3.05573 −0.124336
\(605\) 0 0
\(606\) 5.70820 + 2.18034i 0.231880 + 0.0885703i
\(607\) 14.7639i 0.599250i −0.954057 0.299625i \(-0.903139\pi\)
0.954057 0.299625i \(-0.0968615\pi\)
\(608\) −0.472136 −0.0191476
\(609\) −12.7639 + 22.8328i −0.517221 + 0.925232i
\(610\) 0 0
\(611\) 8.00000i 0.323645i
\(612\) −1.70820 1.52786i −0.0690501 0.0617602i
\(613\) 20.0689 0.810575 0.405287 0.914189i \(-0.367171\pi\)
0.405287 + 0.914189i \(0.367171\pi\)
\(614\) −4.18034 −0.168705
\(615\) 0 0
\(616\) −1.70820 + 11.7082i −0.0688255 + 0.471737i
\(617\) 2.00000i 0.0805170i −0.999189 0.0402585i \(-0.987182\pi\)
0.999189 0.0402585i \(-0.0128181\pi\)
\(618\) 10.2918 26.9443i 0.413997 1.08386i
\(619\) 14.0000i 0.562708i −0.959604 0.281354i \(-0.909217\pi\)
0.959604 0.281354i \(-0.0907834\pi\)
\(620\) 0 0
\(621\) −9.52786 18.4721i −0.382340 0.741261i
\(622\) 26.4721i 1.06144i
\(623\) 5.52786 37.8885i 0.221469 1.51797i
\(624\) −5.23607 2.00000i −0.209610 0.0800641i
\(625\) 0 0
\(626\) −7.70820 −0.308082
\(627\) 1.30495 3.41641i 0.0521148 0.136438i
\(628\) 4.76393i 0.190102i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 29.8885 1.18984 0.594922 0.803783i \(-0.297183\pi\)
0.594922 + 0.803783i \(0.297183\pi\)
\(632\) 8.94427i 0.355784i
\(633\) 4.94427 12.9443i 0.196517 0.514489i
\(634\) −6.94427 −0.275792
\(635\) 0 0
\(636\) −13.7082 5.23607i −0.543566 0.207624i
\(637\) 6.47214 21.7082i 0.256435 0.860110i
\(638\) 25.5279i 1.01066i
\(639\) 5.52786 6.18034i 0.218679 0.244490i
\(640\) 0 0
\(641\) 3.41641i 0.134940i 0.997721 + 0.0674700i \(0.0214927\pi\)
−0.997721 + 0.0674700i \(0.978507\pi\)
\(642\) −9.52786 + 24.9443i −0.376035 + 0.984472i
\(643\) 25.7082i 1.01383i −0.861995 0.506916i \(-0.830785\pi\)
0.861995 0.506916i \(-0.169215\pi\)
\(644\) −10.4721 1.52786i −0.412660 0.0602063i
\(645\) 0 0
\(646\) 0.360680 0.0141908
\(647\) 18.8328 0.740394 0.370197 0.928953i \(-0.379290\pi\)
0.370197 + 0.928953i \(0.379290\pi\)
\(648\) 8.94427 1.00000i 0.351364 0.0392837i
\(649\) 20.0000i 0.785069i
\(650\) 0 0
\(651\) 16.1803 28.9443i 0.634158 1.13442i
\(652\) −1.52786 −0.0598358
\(653\) 11.8885i 0.465235i −0.972568 0.232617i \(-0.925271\pi\)
0.972568 0.232617i \(-0.0747290\pi\)
\(654\) 7.23607 + 2.76393i 0.282953 + 0.108078i
\(655\) 0 0
\(656\) 6.47214 0.252694
\(657\) −13.5279 + 15.1246i −0.527772 + 0.590067i
\(658\) 6.47214 + 0.944272i 0.252310 + 0.0368116i
\(659\) 40.4721i 1.57657i 0.615310 + 0.788285i \(0.289031\pi\)
−0.615310 + 0.788285i \(0.710969\pi\)
\(660\) 0 0
\(661\) 31.7082i 1.23331i −0.787235 0.616653i \(-0.788488\pi\)
0.787235 0.616653i \(-0.211512\pi\)
\(662\) 20.9443i 0.814022i
\(663\) 4.00000 + 1.52786i 0.155347 + 0.0593373i
\(664\) 16.6525i 0.646241i
\(665\) 0 0
\(666\) −10.4721 + 11.7082i −0.405787 + 0.453684i
\(667\) −22.8328 −0.884090
\(668\) 16.9443 0.655594
\(669\) −6.94427 2.65248i −0.268481 0.102551i
\(670\) 0 0
\(671\) 12.3607 0.477179
\(672\) 2.23607 4.00000i 0.0862582 0.154303i
\(673\) −28.4721 −1.09752 −0.548760 0.835980i \(-0.684900\pi\)
−0.548760 + 0.835980i \(0.684900\pi\)
\(674\) 5.41641i 0.208632i
\(675\) 0 0
\(676\) −2.52786 −0.0972255
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 9.23607 24.1803i 0.354709 0.928640i
\(679\) −13.7082 2.00000i −0.526073 0.0767530i
\(680\) 0 0
\(681\) 3.23607 8.47214i 0.124006 0.324653i
\(682\) 32.3607i 1.23915i
\(683\) 36.0000i 1.37750i 0.724998 + 0.688751i \(0.241841\pi\)
−0.724998 + 0.688751i \(0.758159\pi\)
\(684\) −0.944272 + 1.05573i −0.0361051 + 0.0403668i
\(685\) 0 0
\(686\) 16.7984 + 7.79837i 0.641365 + 0.297743i
\(687\) −21.4164 8.18034i −0.817087 0.312099i
\(688\) −12.9443 −0.493496
\(689\) 27.4164 1.04448
\(690\) 0 0
\(691\) 38.9443i 1.48151i 0.671775 + 0.740755i \(0.265532\pi\)
−0.671775 + 0.740755i \(0.734468\pi\)
\(692\) 17.4164 0.662072
\(693\) 22.7639 + 27.2361i 0.864730 + 1.03461i
\(694\) 6.47214 0.245679
\(695\) 0 0
\(696\) 3.52786 9.23607i 0.133723 0.350092i
\(697\) −4.94427 −0.187278
\(698\) −2.18034 −0.0825271
\(699\) −33.1246 12.6525i −1.25289 0.478561i
\(700\) 0 0
\(701\) 14.0689i 0.531374i −0.964059 0.265687i \(-0.914401\pi\)
0.964059 0.265687i \(-0.0855988\pi\)
\(702\) −14.9443 + 7.70820i −0.564035 + 0.290927i
\(703\) 2.47214i 0.0932384i
\(704\) 4.47214i 0.168550i
\(705\) 0 0
\(706\) 14.2918i 0.537879i
\(707\) 1.34752 9.23607i 0.0506789 0.347358i
\(708\) −2.76393 + 7.23607i −0.103875 + 0.271948i
\(709\) −24.4721 −0.919070 −0.459535 0.888160i \(-0.651984\pi\)
−0.459535 + 0.888160i \(0.651984\pi\)
\(710\) 0 0
\(711\) −20.0000 17.8885i −0.750059 0.670873i
\(712\) 14.4721i 0.542366i
\(713\) 28.9443 1.08397
\(714\) −1.70820 + 3.05573i −0.0639279 + 0.114358i
\(715\) 0 0
\(716\) 2.94427i 0.110033i
\(717\) −35.8885 13.7082i −1.34028 0.511942i
\(718\) 10.1803 0.379927
\(719\) −25.5279 −0.952029 −0.476014 0.879438i \(-0.657919\pi\)
−0.476014 + 0.879438i \(0.657919\pi\)
\(720\) 0 0
\(721\) −43.5967 6.36068i −1.62363 0.236884i
\(722\) 18.7771i 0.698811i
\(723\) −28.9443 11.0557i −1.07645 0.411167i
\(724\) 6.18034i 0.229691i
\(725\) 0 0
\(726\) 14.5623 + 5.56231i 0.540458 + 0.206437i
\(727\) 39.7082i 1.47270i 0.676603 + 0.736348i \(0.263451\pi\)
−0.676603 + 0.736348i \(0.736549\pi\)
\(728\) −1.23607 + 8.47214i −0.0458117 + 0.313998i
\(729\) 15.6525 22.0000i 0.579721 0.814815i
\(730\) 0 0
\(731\) 9.88854 0.365741
\(732\) −4.47214 1.70820i −0.165295 0.0631370i
\(733\) 38.0689i 1.40611i −0.711137 0.703053i \(-0.751820\pi\)
0.711137 0.703053i \(-0.248180\pi\)
\(734\) −14.1803 −0.523406
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 53.6656i 1.97680i
\(738\) 12.9443 14.4721i 0.476485 0.532727i
\(739\) −8.94427 −0.329020 −0.164510 0.986375i \(-0.552604\pi\)
−0.164510 + 0.986375i \(0.552604\pi\)
\(740\) 0 0
\(741\) 0.944272 2.47214i 0.0346887 0.0908162i
\(742\) −3.23607 + 22.1803i −0.118800 + 0.814266i
\(743\) 1.52786i 0.0560519i 0.999607 + 0.0280259i \(0.00892210\pi\)
−0.999607 + 0.0280259i \(0.991078\pi\)
\(744\) −4.47214 + 11.7082i −0.163956 + 0.429244i
\(745\) 0 0
\(746\) 9.81966i 0.359523i
\(747\) −37.2361 33.3050i −1.36240 1.21856i
\(748\) 3.41641i 0.124916i
\(749\) 40.3607 + 5.88854i 1.47475 + 0.215163i
\(750\) 0 0
\(751\) 35.4164 1.29236 0.646182 0.763184i \(-0.276365\pi\)
0.646182 + 0.763184i \(0.276365\pi\)
\(752\) −2.47214 −0.0901495
\(753\) 2.18034 5.70820i 0.0794560 0.208019i
\(754\) 18.4721i 0.672716i
\(755\) 0 0
\(756\) −4.47214 13.0000i −0.162650 0.472805i
\(757\) −28.6525 −1.04139 −0.520696 0.853742i \(-0.674327\pi\)
−0.520696 + 0.853742i \(0.674327\pi\)
\(758\) 17.8885i 0.649741i
\(759\) −11.0557 + 28.9443i −0.401298 + 1.05061i
\(760\) 0 0
\(761\) 29.8885 1.08346 0.541729 0.840553i \(-0.317770\pi\)
0.541729 + 0.840553i \(0.317770\pi\)
\(762\) −22.1803 8.47214i −0.803509 0.306913i
\(763\) 1.70820 11.7082i 0.0618411 0.423865i
\(764\) 2.76393i 0.0999956i
\(765\) 0 0
\(766\) 21.8885i 0.790865i
\(767\) 14.4721i 0.522559i
\(768\) −0.618034 + 1.61803i −0.0223014 + 0.0583858i
\(769\) 36.0000i 1.29819i 0.760706 + 0.649097i \(0.224853\pi\)
−0.760706 + 0.649097i \(0.775147\pi\)
\(770\) 0 0
\(771\) −5.05573 + 13.2361i −0.182078 + 0.476685i
\(772\) −6.00000 −0.215945
\(773\) −37.4164 −1.34577 −0.672887 0.739745i \(-0.734946\pi\)
−0.672887 + 0.739745i \(0.734946\pi\)
\(774\) −25.8885 + 28.9443i −0.930544 + 1.04038i
\(775\) 0 0
\(776\) 5.23607 0.187964
\(777\) 20.9443 + 11.7082i 0.751372 + 0.420029i
\(778\) 7.81966 0.280348
\(779\) 3.05573i 0.109483i
\(780\) 0 0
\(781\) −12.3607 −0.442300
\(782\) −3.05573 −0.109273
\(783\) −13.5967 26.3607i −0.485908 0.942054i
\(784\) −6.70820 2.00000i −0.239579 0.0714286i
\(785\) 0 0
\(786\) 34.6525 + 13.2361i 1.23601 + 0.472115i
\(787\) 49.7082i 1.77191i 0.463775 + 0.885953i \(0.346495\pi\)
−0.463775 + 0.885953i \(0.653505\pi\)
\(788\) 12.4721i 0.444301i
\(789\) −8.00000 3.05573i −0.284808