Properties

Label 1050.2.d.d.1049.2
Level $1050$
Weight $2$
Character 1050.1049
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.d (of order \(2\), degree \(1\), not 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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1049.2
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 1050.1049
Dual form 1050.2.d.d.1049.1

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.61803 + 0.618034i −0.934172 + 0.356822i
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.61803 + 0.618034i −0.660560 + 0.252311i
\(7\) 2.61803 0.381966i 0.989524 0.144370i
\(8\) 1.00000 0.353553
\(9\) 2.23607 2.00000i 0.745356 0.666667i
\(10\) 0 0
\(11\) 4.47214i 1.34840i −0.738549 0.674200i \(-0.764489\pi\)
0.738549 0.674200i \(-0.235511\pi\)
\(12\) −1.61803 + 0.618034i −0.467086 + 0.178411i
\(13\) −3.23607 −0.897524 −0.448762 0.893651i \(-0.648135\pi\)
−0.448762 + 0.893651i \(0.648135\pi\)
\(14\) 2.61803 0.381966i 0.699699 0.102085i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.763932i 0.185281i −0.995700 0.0926404i \(-0.970469\pi\)
0.995700 0.0926404i \(-0.0295307\pi\)
\(18\) 2.23607 2.00000i 0.527046 0.471405i
\(19\) 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
\(22\) 4.47214i 0.953463i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) −1.61803 + 0.618034i −0.330280 + 0.126156i
\(25\) 0 0
\(26\) −3.23607 −0.634645
\(27\) −2.38197 + 4.61803i −0.458410 + 0.888741i
\(28\) 2.61803 0.381966i 0.494762 0.0721848i
\(29\) 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 \(-0.774845\pi\)
0.760090 0.649818i \(-0.225155\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.76393 + 7.23607i 0.481139 + 1.25964i
\(34\) 0.763932i 0.131013i
\(35\) 0 0
\(36\) 2.23607 2.00000i 0.372678 0.333333i
\(37\) 5.23607i 0.860804i −0.902637 0.430402i \(-0.858372\pi\)
0.902637 0.430402i \(-0.141628\pi\)
\(38\) 0.472136i 0.0765906i
\(39\) 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 \(0.331349\pi\)
\(42\) −4.00000 + 2.23607i −0.617213 + 0.345033i
\(43\) 12.9443i 1.97398i 0.160773 + 0.986991i \(0.448601\pi\)
−0.160773 + 0.986991i \(0.551399\pi\)
\(44\) 4.47214i 0.674200i
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) 2.47214i 0.360598i −0.983612 0.180299i \(-0.942293\pi\)
0.983612 0.180299i \(-0.0577065\pi\)
\(48\) −1.61803 + 0.618034i −0.233543 + 0.0892055i
\(49\) 6.70820 2.00000i 0.958315 0.285714i
\(50\) 0 0
\(51\) 0.472136 + 1.23607i 0.0661123 + 0.173084i
\(52\) −3.23607 −0.448762
\(53\) 8.47214 1.16374 0.581869 0.813283i \(-0.302322\pi\)
0.581869 + 0.813283i \(0.302322\pi\)
\(54\) −2.38197 + 4.61803i −0.324145 + 0.628435i
\(55\) 0 0
\(56\) 2.61803 0.381966i 0.349850 0.0510424i
\(57\) −0.291796 0.763932i −0.0386493 0.101185i
\(58\) 5.70820i 0.749524i
\(59\) 4.47214 0.582223 0.291111 0.956689i \(-0.405975\pi\)
0.291111 + 0.956689i \(0.405975\pi\)
\(60\) 0 0
\(61\) 2.76393i 0.353885i 0.984221 + 0.176943i \(0.0566207\pi\)
−0.984221 + 0.176943i \(0.943379\pi\)
\(62\) 7.23607i 0.918982i
\(63\) 5.09017 6.09017i 0.641301 0.767289i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 2.76393 + 7.23607i 0.340217 + 0.890698i
\(67\) 12.0000i 1.46603i 0.680211 + 0.733017i \(0.261888\pi\)
−0.680211 + 0.733017i \(0.738112\pi\)
\(68\) 0.763932i 0.0926404i
\(69\) −6.47214 + 2.47214i −0.779154 + 0.297610i
\(70\) 0 0
\(71\) 2.76393i 0.328018i −0.986459 0.164009i \(-0.947557\pi\)
0.986459 0.164009i \(-0.0524427\pi\)
\(72\) 2.23607 2.00000i 0.263523 0.235702i
\(73\) 6.76393 0.791658 0.395829 0.918324i \(-0.370457\pi\)
0.395829 + 0.918324i \(0.370457\pi\)
\(74\) 5.23607i 0.608681i
\(75\) 0 0
\(76\) 0.472136i 0.0541577i
\(77\) −1.70820 11.7082i −0.194668 1.33427i
\(78\) 5.23607 2.00000i 0.592868 0.226455i
\(79\) −8.94427 −1.00631 −0.503155 0.864196i \(-0.667827\pi\)
−0.503155 + 0.864196i \(0.667827\pi\)
\(80\) 0 0
\(81\) 1.00000 8.94427i 0.111111 0.993808i
\(82\) 6.47214 0.714728
\(83\) 16.6525i 1.82785i −0.405887 0.913923i \(-0.633037\pi\)
0.405887 0.913923i \(-0.366963\pi\)
\(84\) −4.00000 + 2.23607i −0.436436 + 0.243975i
\(85\) 0 0
\(86\) 12.9443i 1.39582i
\(87\) 3.52786 + 9.23607i 0.378227 + 0.990210i
\(88\) 4.47214i 0.476731i
\(89\) 14.4721 1.53404 0.767022 0.641621i \(-0.221738\pi\)
0.767022 + 0.641621i \(0.221738\pi\)
\(90\) 0 0
\(91\) −8.47214 + 1.23607i −0.888121 + 0.129575i
\(92\) 4.00000 0.417029
\(93\) 4.47214 + 11.7082i 0.463739 + 1.21408i
\(94\) 2.47214i 0.254981i
\(95\) 0 0
\(96\) −1.61803 + 0.618034i −0.165140 + 0.0630778i
\(97\) 5.23607 0.531642 0.265821 0.964022i \(-0.414357\pi\)
0.265821 + 0.964022i \(0.414357\pi\)
\(98\) 6.70820 2.00000i 0.677631 0.202031i
\(99\) −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 \(0.556160\pi\)
\(102\) 0.472136 + 1.23607i 0.0467484 + 0.122389i
\(103\) −16.6525 −1.64082 −0.820409 0.571778i \(-0.806254\pi\)
−0.820409 + 0.571778i \(0.806254\pi\)
\(104\) −3.23607 −0.317323
\(105\) 0 0
\(106\) 8.47214 0.822887
\(107\) −15.4164 −1.49036 −0.745180 0.666863i \(-0.767637\pi\)
−0.745180 + 0.666863i \(0.767637\pi\)
\(108\) −2.38197 + 4.61803i −0.229205 + 0.444371i
\(109\) 4.47214 0.428353 0.214176 0.976795i \(-0.431293\pi\)
0.214176 + 0.976795i \(0.431293\pi\)
\(110\) 0 0
\(111\) 3.23607 + 8.47214i 0.307154 + 0.804140i
\(112\) 2.61803 0.381966i 0.247381 0.0360924i
\(113\) −14.9443 −1.40584 −0.702919 0.711269i \(-0.748121\pi\)
−0.702919 + 0.711269i \(0.748121\pi\)
\(114\) −0.291796 0.763932i −0.0273292 0.0715488i
\(115\) 0 0
\(116\) 5.70820i 0.529993i
\(117\) −7.23607 + 6.47214i −0.668975 + 0.598349i
\(118\) 4.47214 0.411693
\(119\) −0.291796 2.00000i −0.0267489 0.183340i
\(120\) 0 0
\(121\) −9.00000 −0.818182
\(122\) 2.76393i 0.250235i
\(123\) −10.4721 + 4.00000i −0.944241 + 0.360668i
\(124\) 7.23607i 0.649818i
\(125\) 0 0
\(126\) 5.09017 6.09017i 0.453468 0.542555i
\(127\) 13.7082i 1.21641i 0.793781 + 0.608203i \(0.208109\pi\)
−0.793781 + 0.608203i \(0.791891\pi\)
\(128\) 1.00000 0.0883883
\(129\) −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 \(0.885123\pi\)
\(132\) 2.76393 + 7.23607i 0.240569 + 0.629819i
\(133\) 0.180340 + 1.23607i 0.0156375 + 0.107181i
\(134\) 12.0000i 1.03664i
\(135\) 0 0
\(136\) 0.763932i 0.0655066i
\(137\) 12.4721 1.06557 0.532783 0.846252i \(-0.321146\pi\)
0.532783 + 0.846252i \(0.321146\pi\)
\(138\) −6.47214 + 2.47214i −0.550945 + 0.210442i
\(139\) 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
\(142\) 2.76393i 0.231944i
\(143\) 14.4721i 1.21022i
\(144\) 2.23607 2.00000i 0.186339 0.166667i
\(145\) 0 0
\(146\) 6.76393 0.559787
\(147\) −9.61803 + 7.38197i −0.793282 + 0.608854i
\(148\) 5.23607i 0.430402i
\(149\) 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 \(0.460320\pi\)
\(152\) 0.472136i 0.0382953i
\(153\) −1.52786 1.70820i −0.123520 0.138100i
\(154\) −1.70820 11.7082i −0.137651 0.943474i
\(155\) 0 0
\(156\) 5.23607 2.00000i 0.419221 0.160128i
\(157\) −4.76393 −0.380203 −0.190102 0.981764i \(-0.560882\pi\)
−0.190102 + 0.981764i \(0.560882\pi\)
\(158\) −8.94427 −0.711568
\(159\) −13.7082 + 5.23607i −1.08713 + 0.415247i
\(160\) 0 0
\(161\) 10.4721 1.52786i 0.825320 0.120413i
\(162\) 1.00000 8.94427i 0.0785674 0.702728i
\(163\) 1.52786i 0.119672i −0.998208 0.0598358i \(-0.980942\pi\)
0.998208 0.0598358i \(-0.0190577\pi\)
\(164\) 6.47214 0.505389
\(165\) 0 0
\(166\) 16.6525i 1.29248i
\(167\) 16.9443i 1.31119i −0.755114 0.655594i \(-0.772418\pi\)
0.755114 0.655594i \(-0.227582\pi\)
\(168\) −4.00000 + 2.23607i −0.308607 + 0.172516i
\(169\) −2.52786 −0.194451
\(170\) 0 0
\(171\) 0.944272 + 1.05573i 0.0722103 + 0.0807335i
\(172\) 12.9443i 0.986991i
\(173\) 17.4164i 1.32414i 0.749440 + 0.662072i \(0.230323\pi\)
−0.749440 + 0.662072i \(0.769677\pi\)
\(174\) 3.52786 + 9.23607i 0.267447 + 0.700185i
\(175\) 0 0
\(176\) 4.47214i 0.337100i
\(177\) −7.23607 + 2.76393i −0.543896 + 0.207750i
\(178\) 14.4721 1.08473
\(179\) 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 \(0.0737714\pi\)
−0.973264 + 0.229691i \(0.926229\pi\)
\(182\) −8.47214 + 1.23607i −0.627996 + 0.0916235i
\(183\) −1.70820 4.47214i −0.126274 0.330590i
\(184\) 4.00000 0.294884
\(185\) 0 0
\(186\) 4.47214 + 11.7082i 0.327913 + 0.858487i
\(187\) −3.41641 −0.249832
\(188\) 2.47214i 0.180299i
\(189\) −4.47214 + 13.0000i −0.325300 + 0.945611i
\(190\) 0 0
\(191\) 2.76393i 0.199991i 0.994988 + 0.0999956i \(0.0318829\pi\)
−0.994988 + 0.0999956i \(0.968117\pi\)
\(192\) −1.61803 + 0.618034i −0.116772 + 0.0446028i
\(193\) 6.00000i 0.431889i −0.976406 0.215945i \(-0.930717\pi\)
0.976406 0.215945i \(-0.0692831\pi\)
\(194\) 5.23607 0.375928
\(195\) 0 0
\(196\) 6.70820 2.00000i 0.479157 0.142857i
\(197\) 12.4721 0.888603 0.444301 0.895877i \(-0.353452\pi\)
0.444301 + 0.895877i \(0.353452\pi\)
\(198\) −8.94427 10.0000i −0.635642 0.710669i
\(199\) 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
\(202\) −3.52786 −0.248220
\(203\) −2.18034 14.9443i −0.153030 1.04888i
\(204\) 0.472136 + 1.23607i 0.0330561 + 0.0865421i
\(205\) 0 0
\(206\) −16.6525 −1.16023
\(207\) 8.94427 8.00000i 0.621670 0.556038i
\(208\) −3.23607 −0.224381
\(209\) 2.11146 0.146052
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 8.47214 0.581869
\(213\) 1.70820 + 4.47214i 0.117044 + 0.306426i
\(214\) −15.4164 −1.05384
\(215\) 0 0
\(216\) −2.38197 + 4.61803i −0.162072 + 0.314217i
\(217\) −2.76393 18.9443i −0.187628 1.28602i
\(218\) 4.47214 0.302891
\(219\) −10.9443 + 4.18034i −0.739545 + 0.282481i
\(220\) 0 0
\(221\) 2.47214i 0.166294i
\(222\) 3.23607 + 8.47214i 0.217191 + 0.568613i
\(223\) −4.29180 −0.287400 −0.143700 0.989621i \(-0.545900\pi\)
−0.143700 + 0.989621i \(0.545900\pi\)
\(224\) 2.61803 0.381966i 0.174925 0.0255212i
\(225\) 0 0
\(226\) −14.9443 −0.994078
\(227\) 5.23607i 0.347530i −0.984787 0.173765i \(-0.944407\pi\)
0.984787 0.173765i \(-0.0555933\pi\)
\(228\) −0.291796 0.763932i −0.0193247 0.0505926i
\(229\) 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
\(232\) 5.70820i 0.374762i
\(233\) −20.4721 −1.34117 −0.670587 0.741831i \(-0.733958\pi\)
−0.670587 + 0.741831i \(0.733958\pi\)
\(234\) −7.23607 + 6.47214i −0.473037 + 0.423097i
\(235\) 0 0
\(236\) 4.47214 0.291111
\(237\) 14.4721 5.52786i 0.940066 0.359073i
\(238\) −0.291796 2.00000i −0.0189143 0.129641i
\(239\) 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 \(-0.804554\pi\)
0.817343 0.576151i \(-0.195446\pi\)
\(242\) −9.00000 −0.578542
\(243\) 3.90983 + 15.0902i 0.250816 + 0.968035i
\(244\) 2.76393i 0.176943i
\(245\) 0 0
\(246\) −10.4721 + 4.00000i −0.667679 + 0.255031i
\(247\) 1.52786i 0.0972157i
\(248\) 7.23607i 0.459491i
\(249\) 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 \(0.535514\pi\)
\(252\) 5.09017 6.09017i 0.320651 0.383645i
\(253\) 17.8885i 1.12464i
\(254\) 13.7082i 0.860129i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 8.18034i 0.510276i 0.966905 + 0.255138i \(0.0821208\pi\)
−0.966905 + 0.255138i \(0.917879\pi\)
\(258\) −8.00000 20.9443i −0.498058 1.30393i
\(259\) −2.00000 13.7082i −0.124274 0.851786i
\(260\) 0 0
\(261\) −11.4164 12.7639i −0.706658 0.790068i
\(262\) −21.4164 −1.32311
\(263\) −4.94427 −0.304877 −0.152438 0.988313i \(-0.548713\pi\)
−0.152438 + 0.988313i \(0.548713\pi\)
\(264\) 2.76393 + 7.23607i 0.170108 + 0.445349i
\(265\) 0 0
\(266\) 0.180340 + 1.23607i 0.0110573 + 0.0757882i
\(267\) −23.4164 + 8.94427i −1.43306 + 0.547381i
\(268\) 12.0000i 0.733017i
\(269\) 4.47214 0.272671 0.136335 0.990663i \(-0.456467\pi\)
0.136335 + 0.990663i \(0.456467\pi\)
\(270\) 0 0
\(271\) 18.2918i 1.11115i 0.831467 + 0.555574i \(0.187501\pi\)
−0.831467 + 0.555574i \(0.812499\pi\)
\(272\) 0.763932i 0.0463202i
\(273\) 12.9443 7.23607i 0.783423 0.437947i
\(274\) 12.4721 0.753469
\(275\) 0 0
\(276\) −6.47214 + 2.47214i −0.389577 + 0.148805i
\(277\) 23.1246i 1.38942i −0.719288 0.694712i \(-0.755532\pi\)
0.719288 0.694712i \(-0.244468\pi\)
\(278\) 20.4721i 1.22784i
\(279\) −14.4721 16.1803i −0.866424 0.968692i
\(280\) 0 0
\(281\) 20.0000i 1.19310i 0.802576 + 0.596550i \(0.203462\pi\)
−0.802576 + 0.596550i \(0.796538\pi\)
\(282\) 1.52786 + 4.00000i 0.0909830 + 0.238197i
\(283\) −8.76393 −0.520962 −0.260481 0.965479i \(-0.583881\pi\)
−0.260481 + 0.965479i \(0.583881\pi\)
\(284\) 2.76393i 0.164009i
\(285\) 0 0
\(286\) 14.4721i 0.855755i
\(287\) 16.9443 2.47214i 1.00019 0.145926i
\(288\) 2.23607 2.00000i 0.131762 0.117851i
\(289\) 16.4164 0.965671
\(290\) 0 0
\(291\) −8.47214 + 3.23607i −0.496645 + 0.189702i
\(292\) 6.76393 0.395829
\(293\) 29.4164i 1.71852i −0.511535 0.859262i \(-0.670923\pi\)
0.511535 0.859262i \(-0.329077\pi\)
\(294\) −9.61803 + 7.38197i −0.560935 + 0.430525i
\(295\) 0 0
\(296\) 5.23607i 0.304340i
\(297\) 20.6525 + 10.6525i 1.19838 + 0.618119i
\(298\) 17.7082i 1.02581i
\(299\) −12.9443 −0.748587
\(300\) 0 0
\(301\) 4.94427 + 33.8885i 0.284983 + 1.95330i
\(302\) 3.05573 0.175837
\(303\) 5.70820 2.18034i 0.327928 0.125257i
\(304\) 0.472136i 0.0270789i
\(305\) 0 0
\(306\) −1.52786 1.70820i −0.0873422 0.0976515i
\(307\) 4.18034 0.238585 0.119292 0.992859i \(-0.461937\pi\)
0.119292 + 0.992859i \(0.461937\pi\)
\(308\) −1.70820 11.7082i −0.0973340 0.667137i
\(309\) 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 \(0.229789\pi\)
\(312\) 5.23607 2.00000i 0.296434 0.113228i
\(313\) −7.70820 −0.435693 −0.217847 0.975983i \(-0.569903\pi\)
−0.217847 + 0.975983i \(0.569903\pi\)
\(314\) −4.76393 −0.268844
\(315\) 0 0
\(316\) −8.94427 −0.503155
\(317\) 6.94427 0.390029 0.195015 0.980800i \(-0.437525\pi\)
0.195015 + 0.980800i \(0.437525\pi\)
\(318\) −13.7082 + 5.23607i −0.768718 + 0.293624i
\(319\) −25.5279 −1.42929
\(320\) 0 0
\(321\) 24.9443 9.52786i 1.39225 0.531794i
\(322\) 10.4721 1.52786i 0.583589 0.0851445i
\(323\) 0.360680 0.0200688
\(324\) 1.00000 8.94427i 0.0555556 0.496904i
\(325\) 0 0
\(326\) 1.52786i 0.0846206i
\(327\) −7.23607 + 2.76393i −0.400155 + 0.152846i
\(328\) 6.47214 0.357364
\(329\) −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 \(0.304768\pi\)
\(332\) 16.6525i 0.913923i
\(333\) −10.4721 11.7082i −0.573870 0.641606i
\(334\) 16.9443i 0.927149i
\(335\) 0 0
\(336\) −4.00000 + 2.23607i −0.218218 + 0.121988i
\(337\) 5.41641i 0.295051i 0.989058 + 0.147525i \(0.0471308\pi\)
−0.989058 + 0.147525i \(0.952869\pi\)
\(338\) −2.52786 −0.137498
\(339\) 24.1803 9.23607i 1.31330 0.501634i
\(340\) 0 0
\(341\) −32.3607 −1.75243
\(342\) 0.944272 + 1.05573i 0.0510604 + 0.0570872i
\(343\) 16.7984 7.79837i 0.907027 0.421073i
\(344\) 12.9443i 0.697908i
\(345\) 0 0
\(346\) 17.4164i 0.936312i
\(347\) −6.47214 −0.347442 −0.173721 0.984795i \(-0.555579\pi\)
−0.173721 + 0.984795i \(0.555579\pi\)
\(348\) 3.52786 + 9.23607i 0.189113 + 0.495105i
\(349\) 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
\(352\) 4.47214i 0.238366i
\(353\) 14.2918i 0.760676i −0.924848 0.380338i \(-0.875808\pi\)
0.924848 0.380338i \(-0.124192\pi\)
\(354\) −7.23607 + 2.76393i −0.384593 + 0.146901i
\(355\) 0 0
\(356\) 14.4721 0.767022
\(357\) 1.70820 + 3.05573i 0.0904077 + 0.161726i
\(358\) 2.94427i 0.155610i
\(359\) 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
\(362\) 6.18034i 0.324831i
\(363\) 14.5623 5.56231i 0.764323 0.291945i
\(364\) −8.47214 + 1.23607i −0.444061 + 0.0647876i
\(365\) 0 0
\(366\) −1.70820 4.47214i −0.0892892 0.233762i
\(367\) 14.1803 0.740208 0.370104 0.928990i \(-0.379322\pi\)
0.370104 + 0.928990i \(0.379322\pi\)
\(368\) 4.00000 0.208514
\(369\) 14.4721 12.9443i 0.753389 0.673852i
\(370\) 0 0
\(371\) 22.1803 3.23607i 1.15155 0.168008i
\(372\) 4.47214 + 11.7082i 0.231869 + 0.607042i
\(373\) 9.81966i 0.508443i −0.967146 0.254221i \(-0.918181\pi\)
0.967146 0.254221i \(-0.0818192\pi\)
\(374\) −3.41641 −0.176658
\(375\) 0 0
\(376\) 2.47214i 0.127491i
\(377\) 18.4721i 0.951363i
\(378\) −4.47214 + 13.0000i −0.230022 + 0.668648i
\(379\) −17.8885 −0.918873 −0.459436 0.888211i \(-0.651949\pi\)
−0.459436 + 0.888211i \(0.651949\pi\)
\(380\) 0 0
\(381\) −8.47214 22.1803i −0.434041 1.13633i
\(382\) 2.76393i 0.141415i
\(383\) 21.8885i 1.11845i 0.829015 + 0.559226i \(0.188902\pi\)
−0.829015 + 0.559226i \(0.811098\pi\)
\(384\) −1.61803 + 0.618034i −0.0825700 + 0.0315389i
\(385\) 0 0
\(386\) 6.00000i 0.305392i
\(387\) 25.8885 + 28.9443i 1.31599 + 1.47132i
\(388\) 5.23607 0.265821
\(389\) 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
\(392\) 6.70820 2.00000i 0.338815 0.101015i
\(393\) 34.6525 13.2361i 1.74799 0.667671i
\(394\) 12.4721 0.628337
\(395\) 0 0
\(396\) −8.94427 10.0000i −0.449467 0.502519i
\(397\) −17.1246 −0.859460 −0.429730 0.902958i \(-0.641391\pi\)
−0.429730 + 0.902958i \(0.641391\pi\)
\(398\) 0.180340i 0.00903962i
\(399\) −1.05573 1.88854i −0.0528525 0.0945454i
\(400\) 0 0
\(401\) 5.52786i 0.276048i 0.990429 + 0.138024i \(0.0440752\pi\)
−0.990429 + 0.138024i \(0.955925\pi\)
\(402\) −7.41641 19.4164i −0.369897 0.968402i
\(403\) 23.4164i 1.16645i
\(404\) −3.52786 −0.175518
\(405\) 0 0
\(406\) −2.18034 14.9443i −0.108208 0.741672i
\(407\) −23.4164 −1.16071
\(408\) 0.472136 + 1.23607i 0.0233742 + 0.0611945i
\(409\) 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
\(412\) −16.6525 −0.820409
\(413\) 11.7082 1.70820i 0.576123 0.0840552i
\(414\) 8.94427 8.00000i 0.439587 0.393179i
\(415\) 0 0
\(416\) −3.23607 −0.158661
\(417\) −12.6525 33.1246i −0.619594 1.62212i
\(418\) 2.11146 0.103275
\(419\) 16.8328 0.822337 0.411168 0.911559i \(-0.365121\pi\)
0.411168 + 0.911559i \(0.365121\pi\)
\(420\) 0 0
\(421\) −12.4721 −0.607855 −0.303927 0.952695i \(-0.598298\pi\)
−0.303927 + 0.952695i \(0.598298\pi\)
\(422\) −8.00000 −0.389434
\(423\) −4.94427 5.52786i −0.240399 0.268774i
\(424\) 8.47214 0.411443
\(425\) 0 0
\(426\) 1.70820 + 4.47214i 0.0827628 + 0.216676i
\(427\) 1.05573 + 7.23607i 0.0510903 + 0.350178i
\(428\) −15.4164 −0.745180
\(429\) −8.94427 23.4164i −0.431834 1.13055i
\(430\) 0 0
\(431\) 9.59675i 0.462259i 0.972923 + 0.231130i \(0.0742421\pi\)
−0.972923 + 0.231130i \(0.925758\pi\)
\(432\) −2.38197 + 4.61803i −0.114602 + 0.222185i
\(433\) 4.65248 0.223584 0.111792 0.993732i \(-0.464341\pi\)
0.111792 + 0.993732i \(0.464341\pi\)
\(434\) −2.76393 18.9443i −0.132673 0.909354i
\(435\) 0 0
\(436\) 4.47214 0.214176
\(437\) 1.88854i 0.0903413i
\(438\) −10.9443 + 4.18034i −0.522938 + 0.199744i
\(439\) 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
\(442\) 2.47214i 0.117588i
\(443\) 9.52786 0.452682 0.226341 0.974048i \(-0.427324\pi\)
0.226341 + 0.974048i \(0.427324\pi\)
\(444\) 3.23607 + 8.47214i 0.153577 + 0.402070i
\(445\) 0 0
\(446\) −4.29180 −0.203222
\(447\) −10.9443 28.6525i −0.517646 1.35522i
\(448\) 2.61803 0.381966i 0.123690 0.0180462i
\(449\) 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
\(452\) −14.9443 −0.702919
\(453\) −4.94427 + 1.88854i −0.232302 + 0.0887315i
\(454\) 5.23607i 0.245741i
\(455\) 0 0
\(456\) −0.291796 0.763932i −0.0136646 0.0357744i
\(457\) 9.05573i 0.423609i −0.977312 0.211805i \(-0.932066\pi\)
0.977312 0.211805i \(-0.0679340\pi\)
\(458\) 13.2361i 0.618481i
\(459\) 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 \(0.417970\pi\)
\(462\) 10.0000 + 17.8885i 0.465242 + 0.832250i
\(463\) 0.180340i 0.00838111i 0.999991 + 0.00419055i \(0.00133390\pi\)
−0.999991 + 0.00419055i \(0.998666\pi\)
\(464\) 5.70820i 0.264997i
\(465\) 0 0
\(466\) −20.4721 −0.948353
\(467\) 20.2918i 0.938992i 0.882935 + 0.469496i \(0.155564\pi\)
−0.882935 + 0.469496i \(0.844436\pi\)
\(468\) −7.23607 + 6.47214i −0.334487 + 0.299175i
\(469\) 4.58359 + 31.4164i 0.211651 + 1.45067i
\(470\) 0 0
\(471\) 7.70820 2.94427i 0.355175 0.135665i
\(472\) 4.47214 0.205847
\(473\) 57.8885 2.66172
\(474\) 14.4721 5.52786i 0.664727 0.253903i
\(475\) 0 0
\(476\) −0.291796 2.00000i −0.0133745 0.0916698i
\(477\) 18.9443 16.9443i 0.867399 0.775825i
\(478\) 22.1803i 1.01451i
\(479\) −2.11146 −0.0964749 −0.0482374 0.998836i \(-0.515360\pi\)
−0.0482374 + 0.998836i \(0.515360\pi\)
\(480\) 0 0
\(481\) 16.9443i 0.772592i
\(482\) 17.8885i 0.814801i
\(483\) −16.0000 + 8.94427i −0.728025 + 0.406978i
\(484\) −9.00000 −0.409091
\(485\) 0 0
\(486\) 3.90983 + 15.0902i 0.177353 + 0.684504i
\(487\) 31.5967i 1.43179i 0.698210 + 0.715893i \(0.253980\pi\)
−0.698210 + 0.715893i \(0.746020\pi\)
\(488\) 2.76393i 0.125117i
\(489\) 0.944272 + 2.47214i 0.0427015 + 0.111794i
\(490\) 0 0
\(491\) 13.4164i 0.605474i −0.953074 0.302737i \(-0.902100\pi\)
0.953074 0.302737i \(-0.0979004\pi\)
\(492\) −10.4721 + 4.00000i −0.472120 + 0.180334i
\(493\) −4.36068 −0.196395
\(494\) 1.52786i 0.0687419i
\(495\) 0 0
\(496\) 7.23607i 0.324909i
\(497\) −1.05573 7.23607i −0.0473559 0.324582i
\(498\) 10.2918 + 26.9443i 0.461186 + 1.20740i
\(499\) 17.8885 0.800801 0.400401 0.916340i \(-0.368871\pi\)
0.400401 + 0.916340i \(0.368871\pi\)
\(500\) 0 0
\(501\) 10.4721 + 27.4164i 0.467861 + 1.22487i
\(502\) −3.52786 −0.157456
\(503\) 16.3607i 0.729487i 0.931108 + 0.364743i \(0.118843\pi\)
−0.931108 + 0.364743i \(0.881157\pi\)
\(504\) 5.09017 6.09017i 0.226734 0.271278i
\(505\) 0 0
\(506\) 17.8885i 0.795243i
\(507\) 4.09017 1.56231i 0.181651 0.0693844i
\(508\) 13.7082i 0.608203i
\(509\) −24.4721 −1.08471 −0.542354 0.840150i \(-0.682467\pi\)
−0.542354 + 0.840150i \(0.682467\pi\)
\(510\) 0 0
\(511\) 17.7082 2.58359i 0.783365 0.114291i
\(512\) 1.00000 0.0441942
\(513\) −2.18034 1.12461i −0.0962644 0.0496528i
\(514\) 8.18034i 0.360819i
\(515\) 0 0
\(516\) −8.00000 20.9443i −0.352180 0.922020i
\(517\) −11.0557 −0.486230
\(518\) −2.00000 13.7082i −0.0878750 0.602304i
\(519\) −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 \(0.637067\pi\)
\(522\) −11.4164 12.7639i −0.499683 0.558662i
\(523\) −24.5410 −1.07310 −0.536552 0.843867i \(-0.680273\pi\)
−0.536552 + 0.843867i \(0.680273\pi\)
\(524\) −21.4164 −0.935580
\(525\) 0 0
\(526\) −4.94427 −0.215580
\(527\) −5.52786 −0.240798
\(528\) 2.76393 + 7.23607i 0.120285 + 0.314909i
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 10.0000 8.94427i 0.433963 0.388148i
\(532\) 0.180340 + 1.23607i 0.00781873 + 0.0535903i
\(533\) −20.9443 −0.907197
\(534\) −23.4164 + 8.94427i −1.01333 + 0.387056i
\(535\) 0 0
\(536\) 12.0000i 0.518321i
\(537\) 1.81966 + 4.76393i 0.0785241 + 0.205579i
\(538\) 4.47214 0.192807
\(539\) −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 \(0.409448\pi\)
\(542\) 18.2918i 0.785700i
\(543\) −3.81966 10.0000i −0.163917 0.429141i
\(544\) 0.763932i 0.0327533i
\(545\) 0 0
\(546\) 12.9443 7.23607i 0.553964 0.309675i
\(547\) 8.58359i 0.367008i 0.983019 + 0.183504i \(0.0587440\pi\)
−0.983019 + 0.183504i \(0.941256\pi\)
\(548\) 12.4721 0.532783
\(549\) 5.52786 + 6.18034i 0.235923 + 0.263770i
\(550\) 0 0
\(551\) 2.69505 0.114813
\(552\) −6.47214 + 2.47214i −0.275472 + 0.105221i
\(553\) −23.4164 + 3.41641i −0.995767 + 0.145280i
\(554\) 23.1246i 0.982471i
\(555\) 0 0
\(556\) 20.4721i 0.868212i
\(557\) −16.4721 −0.697947 −0.348973 0.937133i \(-0.613470\pi\)
−0.348973 + 0.937133i \(0.613470\pi\)
\(558\) −14.4721 16.1803i −0.612654 0.684968i
\(559\) 41.8885i 1.77170i
\(560\) 0 0
\(561\) 5.52786 2.11146i 0.233387 0.0891457i
\(562\) 20.0000i 0.843649i
\(563\) 17.8197i 0.751009i 0.926821 + 0.375505i \(0.122531\pi\)
−0.926821 + 0.375505i \(0.877469\pi\)
\(564\) 1.52786 + 4.00000i 0.0643347 + 0.168430i
\(565\) 0 0
\(566\) −8.76393 −0.368376
\(567\) −0.798374 23.7984i −0.0335286 0.999438i
\(568\) 2.76393i 0.115972i
\(569\) 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 \(0.759947\pi\)
\(572\) 14.4721i 0.605110i
\(573\) −1.70820 4.47214i −0.0713612 0.186826i
\(574\) 16.9443 2.47214i 0.707240 0.103185i
\(575\) 0 0
\(576\) 2.23607 2.00000i 0.0931695 0.0833333i
\(577\) 14.1803 0.590335 0.295168 0.955445i \(-0.404625\pi\)
0.295168 + 0.955445i \(0.404625\pi\)
\(578\) 16.4164 0.682833
\(579\) 3.70820 + 9.70820i 0.154108 + 0.403459i
\(580\) 0 0
\(581\) −6.36068 43.5967i −0.263885 1.80870i
\(582\) −8.47214 + 3.23607i −0.351181 + 0.134139i
\(583\) 37.8885i 1.56918i
\(584\) 6.76393 0.279893
\(585\) 0 0
\(586\) 29.4164i 1.21518i
\(587\) 23.7082i 0.978542i 0.872132 + 0.489271i \(0.162737\pi\)
−0.872132 + 0.489271i \(0.837263\pi\)
\(588\) −9.61803 + 7.38197i −0.396641 + 0.304427i
\(589\) 3.41641 0.140771
\(590\) 0 0
\(591\) −20.1803 + 7.70820i −0.830108 + 0.317073i
\(592\) 5.23607i 0.215201i
\(593\) 47.0132i 1.93060i 0.261145 + 0.965299i \(0.415900\pi\)
−0.261145 + 0.965299i \(0.584100\pi\)
\(594\) 20.6525 + 10.6525i 0.847381 + 0.437076i
\(595\) 0 0
\(596\) 17.7082i 0.725356i
\(597\) 0.111456 + 0.291796i 0.00456160 + 0.0119424i
\(598\) −12.9443 −0.529331
\(599\) 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 \(0.0953747\pi\)
−0.955446 + 0.295165i \(0.904625\pi\)
\(602\) 4.94427 + 33.8885i 0.201513 + 1.38119i
\(603\) 24.0000 + 26.8328i 0.977356 + 1.09272i
\(604\) 3.05573 0.124336
\(605\) 0 0
\(606\) 5.70820 2.18034i 0.231880 0.0885703i
\(607\) −14.7639 −0.599250 −0.299625 0.954057i \(-0.596861\pi\)
−0.299625 + 0.954057i \(0.596861\pi\)
\(608\) 0.472136i 0.0191476i
\(609\) 12.7639 + 22.8328i 0.517221 + 0.925232i
\(610\) 0 0
\(611\) 8.00000i 0.323645i
\(612\) −1.52786 1.70820i −0.0617602 0.0690501i
\(613\) 20.0689i 0.810575i −0.914189 0.405287i \(-0.867171\pi\)
0.914189 0.405287i \(-0.132829\pi\)
\(614\) 4.18034 0.168705
\(615\) 0 0
\(616\) −1.70820 11.7082i −0.0688255 0.471737i
\(617\) −2.00000 −0.0805170 −0.0402585 0.999189i \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 26.9443 10.2918i 1.08386 0.413997i
\(619\) 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
\(622\) 26.4721 1.06144
\(623\) 37.8885 5.52786i 1.51797 0.221469i
\(624\) 5.23607 2.00000i 0.209610 0.0800641i
\(625\) 0 0
\(626\) −7.70820 −0.308082
\(627\) −3.41641 + 1.30495i −0.136438 + 0.0521148i
\(628\) −4.76393 −0.190102
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 29.8885 1.18984 0.594922 0.803783i \(-0.297183\pi\)
0.594922 + 0.803783i \(0.297183\pi\)
\(632\) −8.94427 −0.355784
\(633\) 12.9443 4.94427i 0.514489 0.196517i
\(634\) 6.94427 0.275792
\(635\) 0 0
\(636\) −13.7082 + 5.23607i −0.543566 + 0.207624i
\(637\) −21.7082 + 6.47214i −0.860110 + 0.256435i
\(638\) −25.5279 −1.01066
\(639\) −5.52786 6.18034i −0.218679 0.244490i
\(640\) 0 0
\(641\) 3.41641i 0.134940i −0.997721 0.0674700i \(-0.978507\pi\)
0.997721 0.0674700i \(-0.0214927\pi\)
\(642\) 24.9443 9.52786i 0.984472 0.376035i
\(643\) 25.7082 1.01383 0.506916 0.861995i \(-0.330785\pi\)
0.506916 + 0.861995i \(0.330785\pi\)
\(644\) 10.4721 1.52786i 0.412660 0.0602063i
\(645\) 0 0
\(646\) 0.360680 0.0141908
\(647\) 18.8328i 0.740394i 0.928953 + 0.370197i \(0.120710\pi\)
−0.928953 + 0.370197i \(0.879290\pi\)
\(648\) 1.00000 8.94427i 0.0392837 0.351364i
\(649\) 20.0000i 0.785069i
\(650\) 0 0
\(651\) 16.1803 + 28.9443i 0.634158 + 1.13442i
\(652\) 1.52786i 0.0598358i
\(653\) 11.8885 0.465235 0.232617 0.972568i \(-0.425271\pi\)
0.232617 + 0.972568i \(0.425271\pi\)
\(654\) −7.23607 + 2.76393i −0.282953 + 0.108078i
\(655\) 0 0
\(656\) 6.47214 0.252694
\(657\) 15.1246 13.5279i 0.590067 0.527772i
\(658\) −0.944272 6.47214i −0.0368116 0.252310i
\(659\) 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 \(0.211512\pi\)
−0.787235 + 0.616653i \(0.788488\pi\)
\(662\) 20.9443 0.814022
\(663\) −1.52786 4.00000i −0.0593373 0.155347i
\(664\) 16.6525i 0.646241i
\(665\) 0 0
\(666\) −10.4721 11.7082i −0.405787 0.453684i
\(667\) 22.8328i 0.884090i
\(668\) 16.9443i 0.655594i
\(669\) 6.94427 2.65248i 0.268481 0.102551i
\(670\) 0 0
\(671\) 12.3607 0.477179
\(672\) −4.00000 + 2.23607i −0.154303 + 0.0862582i
\(673\) 28.4721i 1.09752i 0.835980 + 0.548760i \(0.184900\pi\)
−0.835980 + 0.548760i \(0.815100\pi\)
\(674\) 5.41641i 0.208632i
\(675\) 0 0
\(676\) −2.52786 −0.0972255
\(677\) 18.0000i 0.691796i −0.938272 0.345898i \(-0.887574\pi\)
0.938272 0.345898i \(-0.112426\pi\)
\(678\) 24.1803 9.23607i 0.928640 0.354709i
\(679\) 13.7082 2.00000i 0.526073 0.0767530i
\(680\) 0 0
\(681\) 3.23607 + 8.47214i 0.124006 + 0.324653i
\(682\) −32.3607 −1.23915
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0.944272 + 1.05573i 0.0361051 + 0.0403668i
\(685\) 0 0
\(686\) 16.7984 7.79837i 0.641365 0.297743i
\(687\) −8.18034 21.4164i −0.312099 0.817087i
\(688\) 12.9443i 0.493496i
\(689\) −27.4164 −1.04448
\(690\) 0 0
\(691\) 38.9443i 1.48151i −0.671775 0.740755i \(-0.734468\pi\)
0.671775 0.740755i \(-0.265532\pi\)
\(692\) 17.4164i 0.662072i
\(693\) −27.2361 22.7639i −1.03461 0.864730i
\(694\) −6.47214 −0.245679
\(695\) 0 0
\(696\) 3.52786 + 9.23607i 0.133723 + 0.350092i
\(697\) 4.94427i 0.187278i
\(698\) 2.18034i 0.0825271i
\(699\) 33.1246 12.6525i 1.25289 0.478561i
\(700\) 0 0
\(701\) 14.0689i 0.531374i 0.964059 + 0.265687i \(0.0855988\pi\)
−0.964059 + 0.265687i \(0.914401\pi\)
\(702\) 7.70820 14.9443i 0.290927 0.564035i
\(703\) 2.47214 0.0932384
\(704\) 4.47214i 0.168550i
\(705\) 0 0
\(706\) 14.2918i 0.537879i
\(707\) −9.23607 + 1.34752i −0.347358 + 0.0506789i
\(708\) −7.23607 + 2.76393i −0.271948 + 0.103875i
\(709\) 24.4721 0.919070 0.459535 0.888160i \(-0.348016\pi\)
0.459535 + 0.888160i \(0.348016\pi\)
\(710\) 0 0
\(711\) −20.0000 + 17.8885i −0.750059 + 0.670873i
\(712\) 14.4721 0.542366
\(713\) 28.9443i 1.08397i
\(714\) 1.70820 + 3.05573i 0.0639279 + 0.114358i
\(715\) 0 0
\(716\) 2.94427i 0.110033i
\(717\) −13.7082 35.8885i −0.511942 1.34028i
\(718\) 10.1803i 0.379927i
\(719\) 25.5279 0.952029 0.476014 0.879438i \(-0.342081\pi\)
0.476014 + 0.879438i \(0.342081\pi\)
\(720\) 0 0
\(721\) −43.5967 + 6.36068i −1.62363 + 0.236884i
\(722\) 18.7771 0.698811
\(723\) 11.0557 + 28.9443i 0.411167 + 1.07645i
\(724\) 6.18034i 0.229691i
\(725\) 0 0
\(726\) 14.5623 5.56231i 0.540458 0.206437i
\(727\) 39.7082 1.47270 0.736348 0.676603i \(-0.236549\pi\)
0.736348 + 0.676603i \(0.236549\pi\)
\(728\) −8.47214 + 1.23607i −0.313998 + 0.0458117i
\(729\) −15.6525 22.0000i −0.579721 0.814815i
\(730\) 0 0
\(731\) 9.88854 0.365741
\(732\) −1.70820 4.47214i −0.0631370 0.165295i
\(733\) 38.0689 1.40611 0.703053 0.711137i \(-0.251820\pi\)
0.703053 + 0.711137i \(0.251820\pi\)
\(734\) 14.1803 0.523406
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 53.6656 1.97680
\(738\) 14.4721 12.9443i 0.532727 0.476485i
\(739\) 8.94427 0.329020 0.164510 0.986375i \(-0.447396\pi\)
0.164510 + 0.986375i \(0.447396\pi\)
\(740\) 0 0
\(741\) 0.944272 + 2.47214i 0.0346887 + 0.0908162i
\(742\) 22.1803 3.23607i 0.814266 0.118800i
\(743\) −1.52786 −0.0560519 −0.0280259 0.999607i \(-0.508922\pi\)
−0.0280259 + 0.999607i \(0.508922\pi\)
\(744\) 4.47214 + 11.7082i 0.163956 + 0.429244i
\(745\) 0 0
\(746\) 9.81966i 0.359523i
\(747\) −33.3050 37.2361i −1.21856 1.36240i
\(748\) −3.41641 −0.124916
\(749\) −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 \(0.276365\pi\)
\(752\) 2.47214i 0.0901495i
\(753\) 5.70820 2.18034i 0.208019 0.0794560i
\(754\) 18.4721i 0.672716i
\(755\) 0 0
\(756\) −4.47214 + 13.0000i −0.162650 + 0.472805i
\(757\) 28.6525i 1.04139i −0.853742 0.520696i \(-0.825673\pi\)
0.853742 0.520696i \(-0.174327\pi\)
\(758\) −17.8885 −0.649741
\(759\) 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 \(0.317770\pi\)
\(762\) −8.47214 22.1803i −0.306913 0.803509i
\(763\) 11.7082 1.70820i 0.423865 0.0618411i
\(764\) 2.76393i 0.0999956i
\(765\) 0 0
\(766\) 21.8885i 0.790865i
\(767\) −14.4721 −0.522559
\(768\) −1.61803 + 0.618034i −0.0583858 + 0.0223014i
\(769\) 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
\(772\) 6.00000i 0.215945i
\(773\) 37.4164i 1.34577i 0.739745 + 0.672887i \(0.234946\pi\)
−0.739745 + 0.672887i \(0.765054\pi\)
\(774\) 25.8885 + 28.9443i 0.930544 + 1.04038i
\(775\) 0 0
\(776\) 5.23607 0.187964
\(777\) 11.7082 + 20.9443i 0.420029 + 0.751372i
\(778\) 7.81966i 0.280348i
\(779\) 3.05573i 0.109483i
\(780\) 0 0
\(781\) −12.3607 −0.442300
\(782\) 3.05573i 0.109273i
\(783\) 26.3607 + 13.5967i 0.942054 + 0.485908i
\(784\) 6.70820 2.00000i 0.239579 0.0714286i
\(785\) 0 0
\(786\) 34.6525 13.2361i 1.23601 0.472115i
\(787\) 49.7082 1.77191 0.885953 0.463775i \(-0.153505\pi\)
0.885953 + 0.463775i \(0.153505\pi\)
\(788\) 12.4721 0.444301
\(789\) 8.