Properties

Label 1110.2.u.f.191.15
Level $1110$
Weight $2$
Character 1110.191
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 191.15
Character \(\chi\) \(=\) 1110.191
Dual form 1110.2.u.f.401.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.65121 - 0.522966i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.797792 - 1.53738i) q^{6} +3.44243 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.45301 + 1.72706i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.65121 - 0.522966i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.797792 - 1.53738i) q^{6} +3.44243 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.45301 + 1.72706i) q^{9} -1.00000 q^{10} -3.04782 q^{11} +(0.522966 - 1.65121i) q^{12} +(0.571765 + 0.571765i) q^{13} +(2.43416 + 2.43416i) q^{14} +(1.53738 - 0.797792i) q^{15} -1.00000 q^{16} +(1.58006 - 1.58006i) q^{17} +(0.513330 + 2.95576i) q^{18} +(2.90693 + 2.90693i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-5.68418 - 1.80027i) q^{21} +(-2.15513 - 2.15513i) q^{22} +(2.05150 - 2.05150i) q^{23} +(1.53738 - 0.797792i) q^{24} -1.00000i q^{25} +0.808598i q^{26} +(-3.14726 - 4.13458i) q^{27} +3.44243i q^{28} +(1.83352 + 1.83352i) q^{29} +(1.65121 + 0.522966i) q^{30} +(-6.33851 + 6.33851i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.03260 + 1.59390i) q^{33} +2.23454 q^{34} +(-2.43416 + 2.43416i) q^{35} +(-1.72706 + 2.45301i) q^{36} +(-1.89635 + 5.77961i) q^{37} +4.11103i q^{38} +(-0.645093 - 1.24312i) q^{39} -1.00000i q^{40} +8.00829 q^{41} +(-2.74634 - 5.29231i) q^{42} +(3.17436 + 3.17436i) q^{43} -3.04782i q^{44} +(-2.95576 + 0.513330i) q^{45} +2.90126 q^{46} +7.90227i q^{47} +(1.65121 + 0.522966i) q^{48} +4.85029 q^{49} +(0.707107 - 0.707107i) q^{50} +(-3.43533 + 1.78270i) q^{51} +(-0.571765 + 0.571765i) q^{52} +12.4574i q^{53} +(0.698141 - 5.14904i) q^{54} +(2.15513 - 2.15513i) q^{55} +(-2.43416 + 2.43416i) q^{56} +(-3.27974 - 6.32020i) q^{57} +2.59299i q^{58} +(-2.00686 + 2.00686i) q^{59} +(0.797792 + 1.53738i) q^{60} +(2.00335 - 2.00335i) q^{61} -8.96401 q^{62} +(8.44432 + 5.94526i) q^{63} -1.00000i q^{64} -0.808598 q^{65} +(2.43153 + 4.68565i) q^{66} +9.46914i q^{67} +(1.58006 + 1.58006i) q^{68} +(-4.46033 + 2.31460i) q^{69} -3.44243 q^{70} -11.8558i q^{71} +(-2.95576 + 0.513330i) q^{72} -4.40734i q^{73} +(-5.42772 + 2.74588i) q^{74} +(-0.522966 + 1.65121i) q^{75} +(-2.90693 + 2.90693i) q^{76} -10.4919 q^{77} +(0.422869 - 1.33517i) q^{78} +(-8.20854 - 8.20854i) q^{79} +(0.707107 - 0.707107i) q^{80} +(3.03456 + 8.47298i) q^{81} +(5.66272 + 5.66272i) q^{82} +10.8401i q^{83} +(1.80027 - 5.68418i) q^{84} +2.23454i q^{85} +4.48922i q^{86} +(-2.06867 - 3.98641i) q^{87} +(2.15513 - 2.15513i) q^{88} +(9.90966 + 9.90966i) q^{89} +(-2.45301 - 1.72706i) q^{90} +(1.96826 + 1.96826i) q^{91} +(2.05150 + 2.05150i) q^{92} +(13.7811 - 7.15142i) q^{93} +(-5.58775 + 5.58775i) q^{94} -4.11103 q^{95} +(0.797792 + 1.53738i) q^{96} +(2.40351 + 2.40351i) q^{97} +(3.42968 + 3.42968i) q^{98} +(-7.47635 - 5.26376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q + 24q^{7} - 8q^{9} - 40q^{10} + 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 16q^{22} - 8q^{31} + 24q^{33} + 24q^{34} + 32q^{37} + 16q^{39} + 12q^{42} + 32q^{43} + 8q^{45} - 56q^{46} - 32q^{49} - 44q^{51} - 16q^{52} - 24q^{54} + 16q^{55} + 8q^{57} - 72q^{61} + 24q^{63} - 28q^{66} + 16q^{69} - 24q^{70} + 8q^{72} - 16q^{76} - 48q^{79} + 120q^{81} - 24q^{82} - 24q^{84} + 20q^{87} + 16q^{88} + 8q^{90} - 92q^{93} - 8q^{94} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −1.65121 0.522966i −0.953329 0.301934i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) −0.797792 1.53738i −0.325697 0.627632i
\(7\) 3.44243 1.30111 0.650557 0.759457i \(-0.274535\pi\)
0.650557 + 0.759457i \(0.274535\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 2.45301 + 1.72706i 0.817671 + 0.575685i
\(10\) −1.00000 −0.316228
\(11\) −3.04782 −0.918952 −0.459476 0.888190i \(-0.651963\pi\)
−0.459476 + 0.888190i \(0.651963\pi\)
\(12\) 0.522966 1.65121i 0.150967 0.476664i
\(13\) 0.571765 + 0.571765i 0.158579 + 0.158579i 0.781937 0.623358i \(-0.214232\pi\)
−0.623358 + 0.781937i \(0.714232\pi\)
\(14\) 2.43416 + 2.43416i 0.650557 + 0.650557i
\(15\) 1.53738 0.797792i 0.396949 0.205989i
\(16\) −1.00000 −0.250000
\(17\) 1.58006 1.58006i 0.383220 0.383220i −0.489041 0.872261i \(-0.662653\pi\)
0.872261 + 0.489041i \(0.162653\pi\)
\(18\) 0.513330 + 2.95576i 0.120993 + 0.696678i
\(19\) 2.90693 + 2.90693i 0.666896 + 0.666896i 0.956996 0.290100i \(-0.0936885\pi\)
−0.290100 + 0.956996i \(0.593689\pi\)
\(20\) −0.707107 0.707107i −0.158114 0.158114i
\(21\) −5.68418 1.80027i −1.24039 0.392851i
\(22\) −2.15513 2.15513i −0.459476 0.459476i
\(23\) 2.05150 2.05150i 0.427768 0.427768i −0.460100 0.887867i \(-0.652186\pi\)
0.887867 + 0.460100i \(0.152186\pi\)
\(24\) 1.53738 0.797792i 0.313816 0.162849i
\(25\) 1.00000i 0.200000i
\(26\) 0.808598i 0.158579i
\(27\) −3.14726 4.13458i −0.605691 0.795700i
\(28\) 3.44243i 0.650557i
\(29\) 1.83352 + 1.83352i 0.340476 + 0.340476i 0.856546 0.516070i \(-0.172606\pi\)
−0.516070 + 0.856546i \(0.672606\pi\)
\(30\) 1.65121 + 0.522966i 0.301469 + 0.0954800i
\(31\) −6.33851 + 6.33851i −1.13843 + 1.13843i −0.149699 + 0.988732i \(0.547831\pi\)
−0.988732 + 0.149699i \(0.952169\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 5.03260 + 1.59390i 0.876064 + 0.277463i
\(34\) 2.23454 0.383220
\(35\) −2.43416 + 2.43416i −0.411449 + 0.411449i
\(36\) −1.72706 + 2.45301i −0.287843 + 0.408836i
\(37\) −1.89635 + 5.77961i −0.311757 + 0.950162i
\(38\) 4.11103i 0.666896i
\(39\) −0.645093 1.24312i −0.103298 0.199059i
\(40\) 1.00000i 0.158114i
\(41\) 8.00829 1.25069 0.625343 0.780350i \(-0.284959\pi\)
0.625343 + 0.780350i \(0.284959\pi\)
\(42\) −2.74634 5.29231i −0.423769 0.816621i
\(43\) 3.17436 + 3.17436i 0.484086 + 0.484086i 0.906434 0.422348i \(-0.138794\pi\)
−0.422348 + 0.906434i \(0.638794\pi\)
\(44\) 3.04782i 0.459476i
\(45\) −2.95576 + 0.513330i −0.440618 + 0.0765227i
\(46\) 2.90126 0.427768
\(47\) 7.90227i 1.15266i 0.817216 + 0.576332i \(0.195517\pi\)
−0.817216 + 0.576332i \(0.804483\pi\)
\(48\) 1.65121 + 0.522966i 0.238332 + 0.0754836i
\(49\) 4.85029 0.692899
\(50\) 0.707107 0.707107i 0.100000 0.100000i
\(51\) −3.43533 + 1.78270i −0.481042 + 0.249627i
\(52\) −0.571765 + 0.571765i −0.0792896 + 0.0792896i
\(53\) 12.4574i 1.71115i 0.517680 + 0.855574i \(0.326796\pi\)
−0.517680 + 0.855574i \(0.673204\pi\)
\(54\) 0.698141 5.14904i 0.0950049 0.700695i
\(55\) 2.15513 2.15513i 0.290598 0.290598i
\(56\) −2.43416 + 2.43416i −0.325279 + 0.325279i
\(57\) −3.27974 6.32020i −0.434413 0.837131i
\(58\) 2.59299i 0.340476i
\(59\) −2.00686 + 2.00686i −0.261271 + 0.261271i −0.825570 0.564300i \(-0.809146\pi\)
0.564300 + 0.825570i \(0.309146\pi\)
\(60\) 0.797792 + 1.53738i 0.102995 + 0.198475i
\(61\) 2.00335 2.00335i 0.256502 0.256502i −0.567128 0.823630i \(-0.691945\pi\)
0.823630 + 0.567128i \(0.191945\pi\)
\(62\) −8.96401 −1.13843
\(63\) 8.44432 + 5.94526i 1.06388 + 0.749032i
\(64\) 1.00000i 0.125000i
\(65\) −0.808598 −0.100294
\(66\) 2.43153 + 4.68565i 0.299300 + 0.576763i
\(67\) 9.46914i 1.15684i 0.815739 + 0.578420i \(0.196330\pi\)
−0.815739 + 0.578420i \(0.803670\pi\)
\(68\) 1.58006 + 1.58006i 0.191610 + 0.191610i
\(69\) −4.46033 + 2.31460i −0.536961 + 0.278645i
\(70\) −3.44243 −0.411449
\(71\) 11.8558i 1.40702i −0.710685 0.703511i \(-0.751615\pi\)
0.710685 0.703511i \(-0.248385\pi\)
\(72\) −2.95576 + 0.513330i −0.348339 + 0.0604965i
\(73\) 4.40734i 0.515841i −0.966166 0.257920i \(-0.916963\pi\)
0.966166 0.257920i \(-0.0830372\pi\)
\(74\) −5.42772 + 2.74588i −0.630960 + 0.319202i
\(75\) −0.522966 + 1.65121i −0.0603869 + 0.190666i
\(76\) −2.90693 + 2.90693i −0.333448 + 0.333448i
\(77\) −10.4919 −1.19566
\(78\) 0.422869 1.33517i 0.0478805 0.151178i
\(79\) −8.20854 8.20854i −0.923533 0.923533i 0.0737442 0.997277i \(-0.476505\pi\)
−0.997277 + 0.0737442i \(0.976505\pi\)
\(80\) 0.707107 0.707107i 0.0790569 0.0790569i
\(81\) 3.03456 + 8.47298i 0.337173 + 0.941443i
\(82\) 5.66272 + 5.66272i 0.625343 + 0.625343i
\(83\) 10.8401i 1.18986i 0.803779 + 0.594928i \(0.202819\pi\)
−0.803779 + 0.594928i \(0.797181\pi\)
\(84\) 1.80027 5.68418i 0.196426 0.620195i
\(85\) 2.23454i 0.242370i
\(86\) 4.48922i 0.484086i
\(87\) −2.06867 3.98641i −0.221784 0.427388i
\(88\) 2.15513 2.15513i 0.229738 0.229738i
\(89\) 9.90966 + 9.90966i 1.05042 + 1.05042i 0.998659 + 0.0517620i \(0.0164837\pi\)
0.0517620 + 0.998659i \(0.483516\pi\)
\(90\) −2.45301 1.72706i −0.258570 0.182048i
\(91\) 1.96826 + 1.96826i 0.206330 + 0.206330i
\(92\) 2.05150 + 2.05150i 0.213884 + 0.213884i
\(93\) 13.7811 7.15142i 1.42903 0.741568i
\(94\) −5.58775 + 5.58775i −0.576332 + 0.576332i
\(95\) −4.11103 −0.421782
\(96\) 0.797792 + 1.53738i 0.0814243 + 0.156908i
\(97\) 2.40351 + 2.40351i 0.244040 + 0.244040i 0.818519 0.574479i \(-0.194795\pi\)
−0.574479 + 0.818519i \(0.694795\pi\)
\(98\) 3.42968 + 3.42968i 0.346450 + 0.346450i
\(99\) −7.47635 5.26376i −0.751401 0.529027i
\(100\) 1.00000 0.100000
\(101\) 2.17467 0.216387 0.108194 0.994130i \(-0.465493\pi\)
0.108194 + 0.994130i \(0.465493\pi\)
\(102\) −3.68970 1.16859i −0.365335 0.115707i
\(103\) −0.494936 + 0.494936i −0.0487675 + 0.0487675i −0.731070 0.682302i \(-0.760979\pi\)
0.682302 + 0.731070i \(0.260979\pi\)
\(104\) −0.808598 −0.0792896
\(105\) 5.29231 2.74634i 0.516476 0.268015i
\(106\) −8.80868 + 8.80868i −0.855574 + 0.855574i
\(107\) 0.470042i 0.0454406i −0.999742 0.0227203i \(-0.992767\pi\)
0.999742 0.0227203i \(-0.00723272\pi\)
\(108\) 4.13458 3.14726i 0.397850 0.302845i
\(109\) −3.18770 3.18770i −0.305327 0.305327i 0.537767 0.843094i \(-0.319268\pi\)
−0.843094 + 0.537767i \(0.819268\pi\)
\(110\) 3.04782 0.290598
\(111\) 6.15381 8.55165i 0.584094 0.811686i
\(112\) −3.44243 −0.325279
\(113\) 2.24895 + 2.24895i 0.211563 + 0.211563i 0.804931 0.593368i \(-0.202202\pi\)
−0.593368 + 0.804931i \(0.702202\pi\)
\(114\) 2.14992 6.78818i 0.201359 0.635772i
\(115\) 2.90126i 0.270544i
\(116\) −1.83352 + 1.83352i −0.170238 + 0.170238i
\(117\) 0.415078 + 2.39002i 0.0383740 + 0.220957i
\(118\) −2.83813 −0.261271
\(119\) 5.43923 5.43923i 0.498613 0.498613i
\(120\) −0.522966 + 1.65121i −0.0477400 + 0.150735i
\(121\) −1.71079 −0.155526
\(122\) 2.83316 0.256502
\(123\) −13.2234 4.18806i −1.19231 0.377625i
\(124\) −6.33851 6.33851i −0.569215 0.569215i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) 1.76710 + 10.1750i 0.157426 + 0.906458i
\(127\) −3.84862 −0.341510 −0.170755 0.985314i \(-0.554621\pi\)
−0.170755 + 0.985314i \(0.554621\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −3.58147 6.90163i −0.315331 0.607655i
\(130\) −0.571765 0.571765i −0.0501471 0.0501471i
\(131\) −9.42329 9.42329i −0.823317 0.823317i 0.163265 0.986582i \(-0.447797\pi\)
−0.986582 + 0.163265i \(0.947797\pi\)
\(132\) −1.59390 + 5.03260i −0.138732 + 0.438032i
\(133\) 10.0069 + 10.0069i 0.867709 + 0.867709i
\(134\) −6.69569 + 6.69569i −0.578420 + 0.578420i
\(135\) 5.14904 + 0.698141i 0.443159 + 0.0600864i
\(136\) 2.23454i 0.191610i
\(137\) 14.5392i 1.24217i −0.783745 0.621083i \(-0.786693\pi\)
0.783745 0.621083i \(-0.213307\pi\)
\(138\) −4.79060 1.51726i −0.407803 0.129158i
\(139\) 16.7132i 1.41760i −0.705410 0.708799i \(-0.749237\pi\)
0.705410 0.708799i \(-0.250763\pi\)
\(140\) −2.43416 2.43416i −0.205724 0.205724i
\(141\) 4.13261 13.0483i 0.348029 1.09887i
\(142\) 8.38330 8.38330i 0.703511 0.703511i
\(143\) −1.74264 1.74264i −0.145727 0.145727i
\(144\) −2.45301 1.72706i −0.204418 0.143921i
\(145\) −2.59299 −0.215336
\(146\) 3.11646 3.11646i 0.257920 0.257920i
\(147\) −8.00887 2.53654i −0.660561 0.209210i
\(148\) −5.77961 1.89635i −0.475081 0.155879i
\(149\) 11.2348i 0.920388i 0.887818 + 0.460194i \(0.152220\pi\)
−0.887818 + 0.460194i \(0.847780\pi\)
\(150\) −1.53738 + 0.797792i −0.125526 + 0.0651394i
\(151\) 18.1204i 1.47462i −0.675557 0.737308i \(-0.736097\pi\)
0.675557 0.737308i \(-0.263903\pi\)
\(152\) −4.11103 −0.333448
\(153\) 6.60475 1.14706i 0.533962 0.0927339i
\(154\) −7.41889 7.41889i −0.597831 0.597831i
\(155\) 8.96401i 0.720007i
\(156\) 1.24312 0.645093i 0.0995293 0.0516488i
\(157\) 15.7039 1.25331 0.626653 0.779298i \(-0.284424\pi\)
0.626653 + 0.779298i \(0.284424\pi\)
\(158\) 11.6086i 0.923533i
\(159\) 6.51476 20.5697i 0.516654 1.63129i
\(160\) 1.00000 0.0790569
\(161\) 7.06214 7.06214i 0.556575 0.556575i
\(162\) −3.84555 + 8.13706i −0.302135 + 0.639308i
\(163\) 4.76257 4.76257i 0.373033 0.373033i −0.495548 0.868581i \(-0.665033\pi\)
0.868581 + 0.495548i \(0.165033\pi\)
\(164\) 8.00829i 0.625343i
\(165\) −4.68565 + 2.43153i −0.364777 + 0.189294i
\(166\) −7.66511 + 7.66511i −0.594928 + 0.594928i
\(167\) 7.41766 7.41766i 0.573996 0.573996i −0.359247 0.933243i \(-0.616966\pi\)
0.933243 + 0.359247i \(0.116966\pi\)
\(168\) 5.29231 2.74634i 0.408310 0.211885i
\(169\) 12.3462i 0.949705i
\(170\) −1.58006 + 1.58006i −0.121185 + 0.121185i
\(171\) 2.11031 + 12.1512i 0.161380 + 0.929225i
\(172\) −3.17436 + 3.17436i −0.242043 + 0.242043i
\(173\) 22.1763 1.68603 0.843016 0.537889i \(-0.180778\pi\)
0.843016 + 0.537889i \(0.180778\pi\)
\(174\) 1.35605 4.28158i 0.102802 0.324586i
\(175\) 3.44243i 0.260223i
\(176\) 3.04782 0.229738
\(177\) 4.36327 2.26423i 0.327963 0.170190i
\(178\) 14.0144i 1.05042i
\(179\) 6.95933 + 6.95933i 0.520165 + 0.520165i 0.917621 0.397456i \(-0.130107\pi\)
−0.397456 + 0.917621i \(0.630107\pi\)
\(180\) −0.513330 2.95576i −0.0382614 0.220309i
\(181\) −0.826713 −0.0614491 −0.0307246 0.999528i \(-0.509781\pi\)
−0.0307246 + 0.999528i \(0.509781\pi\)
\(182\) 2.78354i 0.206330i
\(183\) −4.35563 + 2.26027i −0.321978 + 0.167084i
\(184\) 2.90126i 0.213884i
\(185\) −2.74588 5.42772i −0.201881 0.399054i
\(186\) 14.8015 + 4.68787i 1.08530 + 0.343731i
\(187\) −4.81573 + 4.81573i −0.352161 + 0.352161i
\(188\) −7.90227 −0.576332
\(189\) −10.8342 14.2330i −0.788073 1.03530i
\(190\) −2.90693 2.90693i −0.210891 0.210891i
\(191\) 1.75243 1.75243i 0.126801 0.126801i −0.640858 0.767659i \(-0.721421\pi\)
0.767659 + 0.640858i \(0.221421\pi\)
\(192\) −0.522966 + 1.65121i −0.0377418 + 0.119166i
\(193\) 5.62234 + 5.62234i 0.404705 + 0.404705i 0.879887 0.475183i \(-0.157618\pi\)
−0.475183 + 0.879887i \(0.657618\pi\)
\(194\) 3.39908i 0.244040i
\(195\) 1.33517 + 0.422869i 0.0956134 + 0.0302823i
\(196\) 4.85029i 0.346450i
\(197\) 17.8517i 1.27188i −0.771738 0.635941i \(-0.780612\pi\)
0.771738 0.635941i \(-0.219388\pi\)
\(198\) −1.56454 9.00861i −0.111187 0.640214i
\(199\) 1.86996 1.86996i 0.132558 0.132558i −0.637715 0.770273i \(-0.720120\pi\)
0.770273 + 0.637715i \(0.220120\pi\)
\(200\) 0.707107 + 0.707107i 0.0500000 + 0.0500000i
\(201\) 4.95203 15.6356i 0.349290 1.10285i
\(202\) 1.53772 + 1.53772i 0.108194 + 0.108194i
\(203\) 6.31176 + 6.31176i 0.442999 + 0.442999i
\(204\) −1.78270 3.43533i −0.124814 0.240521i
\(205\) −5.66272 + 5.66272i −0.395501 + 0.395501i
\(206\) −0.699945 −0.0487675
\(207\) 8.57542 1.48930i 0.596033 0.103514i
\(208\) −0.571765 0.571765i −0.0396448 0.0396448i
\(209\) −8.85981 8.85981i −0.612846 0.612846i
\(210\) 5.68418 + 1.80027i 0.392246 + 0.124230i
\(211\) −19.4431 −1.33852 −0.669258 0.743030i \(-0.733388\pi\)
−0.669258 + 0.743030i \(0.733388\pi\)
\(212\) −12.4574 −0.855574
\(213\) −6.20016 + 19.5764i −0.424828 + 1.34135i
\(214\) 0.332370 0.332370i 0.0227203 0.0227203i
\(215\) −4.48922 −0.306163
\(216\) 5.14904 + 0.698141i 0.350348 + 0.0475024i
\(217\) −21.8199 + 21.8199i −1.48123 + 1.48123i
\(218\) 4.50809i 0.305327i
\(219\) −2.30489 + 7.27747i −0.155750 + 0.491766i
\(220\) 2.15513 + 2.15513i 0.145299 + 0.145299i
\(221\) 1.80684 0.121541
\(222\) 10.3983 1.69553i 0.697890 0.113796i
\(223\) 24.8953 1.66711 0.833555 0.552436i \(-0.186302\pi\)
0.833555 + 0.552436i \(0.186302\pi\)
\(224\) −2.43416 2.43416i −0.162639 0.162639i
\(225\) 1.72706 2.45301i 0.115137 0.163534i
\(226\) 3.18049i 0.211563i
\(227\) 6.99137 6.99137i 0.464033 0.464033i −0.435942 0.899975i \(-0.643585\pi\)
0.899975 + 0.435942i \(0.143585\pi\)
\(228\) 6.32020 3.27974i 0.418565 0.217206i
\(229\) −19.5563 −1.29232 −0.646158 0.763204i \(-0.723625\pi\)
−0.646158 + 0.763204i \(0.723625\pi\)
\(230\) −2.05150 + 2.05150i −0.135272 + 0.135272i
\(231\) 17.3244 + 5.48690i 1.13986 + 0.361011i
\(232\) −2.59299 −0.170238
\(233\) −17.7356 −1.16190 −0.580949 0.813940i \(-0.697318\pi\)
−0.580949 + 0.813940i \(0.697318\pi\)
\(234\) −1.39649 + 1.98350i −0.0912917 + 0.129666i
\(235\) −5.58775 5.58775i −0.364504 0.364504i
\(236\) −2.00686 2.00686i −0.130635 0.130635i
\(237\) 9.26127 + 17.8468i 0.601584 + 1.15928i
\(238\) 7.69223 0.498613
\(239\) 4.92552 4.92552i 0.318606 0.318606i −0.529626 0.848231i \(-0.677668\pi\)
0.848231 + 0.529626i \(0.177668\pi\)
\(240\) −1.53738 + 0.797792i −0.0992373 + 0.0514973i
\(241\) 18.5971 + 18.5971i 1.19794 + 1.19794i 0.974781 + 0.223163i \(0.0716383\pi\)
0.223163 + 0.974781i \(0.428362\pi\)
\(242\) −1.20971 1.20971i −0.0777632 0.0777632i
\(243\) −0.579624 15.5777i −0.0371829 0.999308i
\(244\) 2.00335 + 2.00335i 0.128251 + 0.128251i
\(245\) −3.42968 + 3.42968i −0.219114 + 0.219114i
\(246\) −6.38895 12.3118i −0.407345 0.784969i
\(247\) 3.32417i 0.211512i
\(248\) 8.96401i 0.569215i
\(249\) 5.66900 17.8993i 0.359258 1.13432i
\(250\) 1.00000i 0.0632456i
\(251\) −15.0856 15.0856i −0.952195 0.952195i 0.0467134 0.998908i \(-0.485125\pi\)
−0.998908 + 0.0467134i \(0.985125\pi\)
\(252\) −5.94526 + 8.44432i −0.374516 + 0.531942i
\(253\) −6.25261 + 6.25261i −0.393098 + 0.393098i
\(254\) −2.72139 2.72139i −0.170755 0.170755i
\(255\) 1.16859 3.68970i 0.0731797 0.231058i
\(256\) 1.00000 0.0625000
\(257\) −2.20693 + 2.20693i −0.137665 + 0.137665i −0.772581 0.634916i \(-0.781035\pi\)
0.634916 + 0.772581i \(0.281035\pi\)
\(258\) 2.34771 7.41267i 0.146162 0.461493i
\(259\) −6.52803 + 19.8959i −0.405632 + 1.23627i
\(260\) 0.808598i 0.0501471i
\(261\) 1.33106 + 7.66425i 0.0823906 + 0.474405i
\(262\) 13.3265i 0.823317i
\(263\) −4.11676 −0.253850 −0.126925 0.991912i \(-0.540511\pi\)
−0.126925 + 0.991912i \(0.540511\pi\)
\(264\) −4.68565 + 2.43153i −0.288382 + 0.149650i
\(265\) −8.80868 8.80868i −0.541113 0.541113i
\(266\) 14.1519i 0.867709i
\(267\) −11.1806 21.5454i −0.684239 1.31856i
\(268\) −9.46914 −0.578420
\(269\) 5.19624i 0.316820i −0.987373 0.158410i \(-0.949363\pi\)
0.987373 0.158410i \(-0.0506368\pi\)
\(270\) 3.14726 + 4.13458i 0.191536 + 0.251623i
\(271\) −4.74810 −0.288426 −0.144213 0.989547i \(-0.546065\pi\)
−0.144213 + 0.989547i \(0.546065\pi\)
\(272\) −1.58006 + 1.58006i −0.0958050 + 0.0958050i
\(273\) −2.22069 4.27935i −0.134402 0.258998i
\(274\) 10.2807 10.2807i 0.621083 0.621083i
\(275\) 3.04782i 0.183790i
\(276\) −2.31460 4.46033i −0.139323 0.268480i
\(277\) −2.25502 + 2.25502i −0.135491 + 0.135491i −0.771599 0.636109i \(-0.780543\pi\)
0.636109 + 0.771599i \(0.280543\pi\)
\(278\) 11.8180 11.8180i 0.708799 0.708799i
\(279\) −26.4954 + 4.60150i −1.58624 + 0.275484i
\(280\) 3.44243i 0.205724i
\(281\) 11.4729 11.4729i 0.684416 0.684416i −0.276576 0.960992i \(-0.589200\pi\)
0.960992 + 0.276576i \(0.0891999\pi\)
\(282\) 12.1488 6.30437i 0.723448 0.375420i
\(283\) −20.8649 + 20.8649i −1.24029 + 1.24029i −0.280407 + 0.959881i \(0.590469\pi\)
−0.959881 + 0.280407i \(0.909531\pi\)
\(284\) 11.8558 0.703511
\(285\) 6.78818 + 2.14992i 0.402097 + 0.127351i
\(286\) 2.46446i 0.145727i
\(287\) 27.5680 1.62728
\(288\) −0.513330 2.95576i −0.0302483 0.174170i
\(289\) 12.0068i 0.706285i
\(290\) −1.83352 1.83352i −0.107668 0.107668i
\(291\) −2.71176 5.22567i −0.158966 0.306334i
\(292\) 4.40734 0.257920
\(293\) 8.29342i 0.484507i −0.970213 0.242253i \(-0.922113\pi\)
0.970213 0.242253i \(-0.0778865\pi\)
\(294\) −3.86953 7.45673i −0.225675 0.434885i
\(295\) 2.83813i 0.165242i
\(296\) −2.74588 5.42772i −0.159601 0.315480i
\(297\) 9.59228 + 12.6015i 0.556601 + 0.731211i
\(298\) −7.94418 + 7.94418i −0.460194 + 0.460194i
\(299\) 2.34596 0.135670
\(300\) −1.65121 0.522966i −0.0953329 0.0301934i
\(301\) 10.9275 + 10.9275i 0.629851 + 0.629851i
\(302\) 12.8130 12.8130i 0.737308 0.737308i
\(303\) −3.59084 1.13727i −0.206288 0.0653347i
\(304\) −2.90693 2.90693i −0.166724 0.166724i
\(305\) 2.83316i 0.162226i
\(306\) 5.48135 + 3.85917i 0.313348 + 0.220614i
\(307\) 7.03890i 0.401731i −0.979619 0.200866i \(-0.935625\pi\)
0.979619 0.200866i \(-0.0643755\pi\)
\(308\) 10.4919i 0.597831i
\(309\) 1.07608 0.558411i 0.0612160 0.0317669i
\(310\) 6.33851 6.33851i 0.360003 0.360003i
\(311\) −5.36146 5.36146i −0.304020 0.304020i 0.538564 0.842585i \(-0.318967\pi\)
−0.842585 + 0.538564i \(0.818967\pi\)
\(312\) 1.33517 + 0.422869i 0.0755891 + 0.0239402i
\(313\) 16.4404 + 16.4404i 0.929266 + 0.929266i 0.997659 0.0683922i \(-0.0217869\pi\)
−0.0683922 + 0.997659i \(0.521787\pi\)
\(314\) 11.1043 + 11.1043i 0.626653 + 0.626653i
\(315\) −10.1750 + 1.76710i −0.573295 + 0.0995648i
\(316\) 8.20854 8.20854i 0.461766 0.461766i
\(317\) −19.4530 −1.09259 −0.546296 0.837592i \(-0.683963\pi\)
−0.546296 + 0.837592i \(0.683963\pi\)
\(318\) 19.1516 9.93838i 1.07397 0.557316i
\(319\) −5.58825 5.58825i −0.312882 0.312882i
\(320\) 0.707107 + 0.707107i 0.0395285 + 0.0395285i
\(321\) −0.245816 + 0.776139i −0.0137201 + 0.0433199i
\(322\) 9.98738 0.556575
\(323\) 9.18624 0.511136
\(324\) −8.47298 + 3.03456i −0.470721 + 0.168586i
\(325\) 0.571765 0.571765i 0.0317158 0.0317158i
\(326\) 6.73529 0.373033
\(327\) 3.59652 + 6.93064i 0.198888 + 0.383265i
\(328\) −5.66272 + 5.66272i −0.312671 + 0.312671i
\(329\) 27.2030i 1.49975i
\(330\) −5.03260 1.59390i −0.277036 0.0877416i
\(331\) −16.9551 16.9551i −0.931938 0.931938i 0.0658890 0.997827i \(-0.479012\pi\)
−0.997827 + 0.0658890i \(0.979012\pi\)
\(332\) −10.8401 −0.594928
\(333\) −14.6335 + 10.9024i −0.801909 + 0.597446i
\(334\) 10.4902 0.573996
\(335\) −6.69569 6.69569i −0.365825 0.365825i
\(336\) 5.68418 + 1.80027i 0.310097 + 0.0982128i
\(337\) 7.08308i 0.385840i 0.981214 + 0.192920i \(0.0617958\pi\)
−0.981214 + 0.192920i \(0.938204\pi\)
\(338\) 8.73006 8.73006i 0.474853 0.474853i
\(339\) −2.53737 4.88961i −0.137811 0.265567i
\(340\) −2.23454 −0.121185
\(341\) 19.3187 19.3187i 1.04616 1.04616i
\(342\) −7.09997 + 10.0844i −0.383922 + 0.545302i
\(343\) −7.40020 −0.399573
\(344\) −4.48922 −0.242043
\(345\) 1.51726 4.79060i 0.0816865 0.257917i
\(346\) 15.6810 + 15.6810i 0.843016 + 0.843016i
\(347\) −8.15272 8.15272i −0.437661 0.437661i 0.453563 0.891224i \(-0.350153\pi\)
−0.891224 + 0.453563i \(0.850153\pi\)
\(348\) 3.98641 2.06867i 0.213694 0.110892i
\(349\) −9.72270 −0.520444 −0.260222 0.965549i \(-0.583796\pi\)
−0.260222 + 0.965549i \(0.583796\pi\)
\(350\) 2.43416 2.43416i 0.130111 0.130111i
\(351\) 0.564515 4.16350i 0.0301316 0.222231i
\(352\) 2.15513 + 2.15513i 0.114869 + 0.114869i
\(353\) 0.400840 + 0.400840i 0.0213345 + 0.0213345i 0.717694 0.696359i \(-0.245198\pi\)
−0.696359 + 0.717694i \(0.745198\pi\)
\(354\) 4.68635 + 1.48424i 0.249077 + 0.0788866i
\(355\) 8.38330 + 8.38330i 0.444939 + 0.444939i
\(356\) −9.90966 + 9.90966i −0.525211 + 0.525211i
\(357\) −11.8259 + 6.13680i −0.625891 + 0.324794i
\(358\) 9.84198i 0.520165i
\(359\) 35.3458i 1.86548i −0.360548 0.932741i \(-0.617410\pi\)
0.360548 0.932741i \(-0.382590\pi\)
\(360\) 1.72706 2.45301i 0.0910238 0.129285i
\(361\) 2.09946i 0.110498i
\(362\) −0.584575 0.584575i −0.0307246 0.0307246i
\(363\) 2.82488 + 0.894685i 0.148268 + 0.0469588i
\(364\) −1.96826 + 1.96826i −0.103165 + 0.103165i
\(365\) 3.11646 + 3.11646i 0.163123 + 0.163123i
\(366\) −4.67815 1.48164i −0.244531 0.0774468i
\(367\) 4.27483 0.223144 0.111572 0.993756i \(-0.464411\pi\)
0.111572 + 0.993756i \(0.464411\pi\)
\(368\) −2.05150 + 2.05150i −0.106942 + 0.106942i
\(369\) 19.6445 + 13.8308i 1.02265 + 0.720001i
\(370\) 1.89635 5.77961i 0.0985863 0.300468i
\(371\) 42.8835i 2.22640i
\(372\) 7.15142 + 13.7811i 0.370784 + 0.714515i
\(373\) 32.8415i 1.70047i 0.526405 + 0.850234i \(0.323540\pi\)
−0.526405 + 0.850234i \(0.676460\pi\)
\(374\) −6.81047 −0.352161
\(375\) −0.797792 1.53738i −0.0411978 0.0793898i
\(376\) −5.58775 5.58775i −0.288166 0.288166i
\(377\) 2.09669i 0.107985i
\(378\) 2.40330 17.7252i 0.123612 0.911685i
\(379\) 7.66460 0.393704 0.196852 0.980433i \(-0.436928\pi\)
0.196852 + 0.980433i \(0.436928\pi\)
\(380\) 4.11103i 0.210891i
\(381\) 6.35490 + 2.01270i 0.325571 + 0.103114i
\(382\) 2.47831 0.126801
\(383\) −3.54407 + 3.54407i −0.181094 + 0.181094i −0.791832 0.610739i \(-0.790873\pi\)
0.610739 + 0.791832i \(0.290873\pi\)
\(384\) −1.53738 + 0.797792i −0.0784539 + 0.0407122i
\(385\) 7.41889 7.41889i 0.378102 0.378102i
\(386\) 7.95118i 0.404705i
\(387\) 2.30445 + 13.2691i 0.117142 + 0.674504i
\(388\) −2.40351 + 2.40351i −0.122020 + 0.122020i
\(389\) 18.3139 18.3139i 0.928551 0.928551i −0.0690616 0.997612i \(-0.522000\pi\)
0.997612 + 0.0690616i \(0.0220005\pi\)
\(390\) 0.645093 + 1.24312i 0.0326656 + 0.0629479i
\(391\) 6.48298i 0.327858i
\(392\) −3.42968 + 3.42968i −0.173225 + 0.173225i
\(393\) 10.6318 + 20.4879i 0.536304 + 1.03348i
\(394\) 12.6231 12.6231i 0.635941 0.635941i
\(395\) 11.6086 0.584094
\(396\) 5.26376 7.47635i 0.264514 0.375701i
\(397\) 0.886715i 0.0445029i −0.999752 0.0222515i \(-0.992917\pi\)
0.999752 0.0222515i \(-0.00708345\pi\)
\(398\) 2.64453 0.132558
\(399\) −11.2903 21.7568i −0.565221 1.08920i
\(400\) 1.00000i 0.0500000i
\(401\) 21.7682 + 21.7682i 1.08705 + 1.08705i 0.995831 + 0.0912209i \(0.0290769\pi\)
0.0912209 + 0.995831i \(0.470923\pi\)
\(402\) 14.5576 7.55440i 0.726069 0.376779i
\(403\) −7.24829 −0.361063
\(404\) 2.17467i 0.108194i
\(405\) −8.13706 3.84555i −0.404334 0.191087i
\(406\) 8.92618i 0.442999i
\(407\) 5.77972 17.6152i 0.286490 0.873153i
\(408\) 1.16859 3.68970i 0.0578536 0.182667i
\(409\) 9.72183 9.72183i 0.480713 0.480713i −0.424646 0.905359i \(-0.639601\pi\)
0.905359 + 0.424646i \(0.139601\pi\)
\(410\) −8.00829 −0.395501
\(411\) −7.60348 + 24.0073i −0.375052 + 1.18419i
\(412\) −0.494936 0.494936i −0.0243837 0.0243837i
\(413\) −6.90846 + 6.90846i −0.339943 + 0.339943i
\(414\) 7.11684 + 5.01064i 0.349773 + 0.246260i
\(415\) −7.66511 7.66511i −0.376266 0.376266i
\(416\) 0.808598i 0.0396448i
\(417\) −8.74045 + 27.5971i −0.428021 + 1.35144i
\(418\) 12.5297i 0.612846i
\(419\) 36.1112i 1.76415i 0.471109 + 0.882075i \(0.343854\pi\)
−0.471109 + 0.882075i \(0.656146\pi\)
\(420\) 2.74634 + 5.29231i 0.134008 + 0.258238i
\(421\) 16.4019 16.4019i 0.799382 0.799382i −0.183616 0.982998i \(-0.558780\pi\)
0.982998 + 0.183616i \(0.0587803\pi\)
\(422\) −13.7483 13.7483i −0.669258 0.669258i
\(423\) −13.6477 + 19.3844i −0.663572 + 0.942501i
\(424\) −8.80868 8.80868i −0.427787 0.427787i
\(425\) −1.58006 1.58006i −0.0766440 0.0766440i
\(426\) −18.2268 + 9.45844i −0.883091 + 0.458263i
\(427\) 6.89637 6.89637i 0.333739 0.333739i
\(428\) 0.470042 0.0227203
\(429\) 1.96613 + 3.78881i 0.0949256 + 0.182925i
\(430\) −3.17436 3.17436i −0.153081 0.153081i
\(431\) 18.1679 + 18.1679i 0.875118 + 0.875118i 0.993025 0.117906i \(-0.0376183\pi\)
−0.117906 + 0.993025i \(0.537618\pi\)
\(432\) 3.14726 + 4.13458i 0.151423 + 0.198925i
\(433\) 31.3276 1.50551 0.752755 0.658301i \(-0.228725\pi\)
0.752755 + 0.658301i \(0.228725\pi\)
\(434\) −30.8579 −1.48123
\(435\) 4.28158 + 1.35605i 0.205286 + 0.0650174i
\(436\) 3.18770 3.18770i 0.152663 0.152663i
\(437\) 11.9272 0.570553
\(438\) −6.77575 + 3.51614i −0.323758 + 0.168008i
\(439\) 21.7605 21.7605i 1.03857 1.03857i 0.0393487 0.999226i \(-0.487472\pi\)
0.999226 0.0393487i \(-0.0125283\pi\)
\(440\) 3.04782i 0.145299i
\(441\) 11.8978 + 8.37673i 0.566564 + 0.398892i
\(442\) 1.27763 + 1.27763i 0.0607707 + 0.0607707i
\(443\) −7.20883 −0.342502 −0.171251 0.985227i \(-0.554781\pi\)
−0.171251 + 0.985227i \(0.554781\pi\)
\(444\) 8.55165 + 6.15381i 0.405843 + 0.292047i
\(445\) −14.0144 −0.664345
\(446\) 17.6036 + 17.6036i 0.833555 + 0.833555i
\(447\) 5.87540 18.5510i 0.277897 0.877432i
\(448\) 3.44243i 0.162639i
\(449\) −2.23081 + 2.23081i −0.105278 + 0.105278i −0.757784 0.652506i \(-0.773718\pi\)
0.652506 + 0.757784i \(0.273718\pi\)
\(450\) 2.95576 0.513330i 0.139336 0.0241986i
\(451\) −24.4078 −1.14932
\(452\) −2.24895 + 2.24895i −0.105782 + 0.105782i
\(453\) −9.47633 + 29.9206i −0.445237 + 1.40579i
\(454\) 9.88729 0.464033
\(455\) −2.78354 −0.130494
\(456\) 6.78818 + 2.14992i 0.317886 + 0.100679i
\(457\) 1.56539 + 1.56539i 0.0732256 + 0.0732256i 0.742771 0.669545i \(-0.233511\pi\)
−0.669545 + 0.742771i \(0.733511\pi\)
\(458\) −13.8284 13.8284i −0.646158 0.646158i
\(459\) −11.5057 1.56002i −0.537041 0.0728155i
\(460\) −2.90126 −0.135272
\(461\) 5.71858 5.71858i 0.266341 0.266341i −0.561283 0.827624i \(-0.689692\pi\)
0.827624 + 0.561283i \(0.189692\pi\)
\(462\) 8.37035 + 16.1300i 0.389424 + 0.750435i
\(463\) −24.0600 24.0600i −1.11816 1.11816i −0.992011 0.126154i \(-0.959737\pi\)
−0.126154 0.992011i \(-0.540263\pi\)
\(464\) −1.83352 1.83352i −0.0851191 0.0851191i
\(465\) −4.68787 + 14.8015i −0.217395 + 0.686403i
\(466\) −12.5410 12.5410i −0.580949 0.580949i
\(467\) 2.39895 2.39895i 0.111010 0.111010i −0.649420 0.760430i \(-0.724988\pi\)
0.760430 + 0.649420i \(0.224988\pi\)
\(468\) −2.39002 + 0.415078i −0.110479 + 0.0191870i
\(469\) 32.5968i 1.50518i
\(470\) 7.90227i 0.364504i
\(471\) −25.9305 8.21259i −1.19481 0.378416i
\(472\) 2.83813i 0.130635i
\(473\) −9.67488 9.67488i −0.444852 0.444852i
\(474\) −6.07091 + 19.1683i −0.278846 + 0.880431i
\(475\) 2.90693 2.90693i 0.133379 0.133379i
\(476\) 5.43923 + 5.43923i 0.249307 + 0.249307i
\(477\) −21.5145 + 30.5581i −0.985083 + 1.39916i
\(478\) 6.96574 0.318606
\(479\) −11.9467 + 11.9467i −0.545859 + 0.545859i −0.925240 0.379381i \(-0.876137\pi\)
0.379381 + 0.925240i \(0.376137\pi\)
\(480\) −1.65121 0.522966i −0.0753673 0.0238700i
\(481\) −4.38885 + 2.22032i −0.200114 + 0.101238i
\(482\) 26.3003i 1.19794i
\(483\) −15.3544 + 7.96785i −0.698648 + 0.362550i
\(484\) 1.71079i 0.0777632i
\(485\) −3.39908 −0.154344
\(486\) 10.6052 11.4249i 0.481063 0.518246i
\(487\) −13.5166 13.5166i −0.612496 0.612496i 0.331100 0.943596i \(-0.392580\pi\)
−0.943596 + 0.331100i \(0.892580\pi\)
\(488\) 2.83316i 0.128251i
\(489\) −10.3547 + 5.37336i −0.468255 + 0.242992i
\(490\) −4.85029 −0.219114
\(491\) 22.2070i 1.00219i −0.865392 0.501095i \(-0.832931\pi\)
0.865392 0.501095i \(-0.167069\pi\)
\(492\) 4.18806 13.2234i 0.188812 0.596157i
\(493\) 5.79414 0.260955
\(494\) −2.35054 + 2.35054i −0.105756 + 0.105756i
\(495\) 9.00861 1.56454i 0.404907 0.0703208i
\(496\) 6.33851 6.33851i 0.284608 0.284608i
\(497\) 40.8126i 1.83070i
\(498\) 16.6653 8.64815i 0.746791 0.387533i
\(499\) 14.5069 14.5069i 0.649417 0.649417i −0.303435 0.952852i \(-0.598134\pi\)
0.952852 + 0.303435i \(0.0981336\pi\)
\(500\) −0.707107 + 0.707107i −0.0316228 + 0.0316228i
\(501\) −16.1273 + 8.36896i −0.720516 + 0.373898i
\(502\) 21.3343i 0.952195i
\(503\) −29.5224 + 29.5224i −1.31634 + 1.31634i −0.399686 + 0.916652i \(0.630881\pi\)
−0.916652 + 0.399686i \(0.869119\pi\)
\(504\) −10.1750 + 1.76710i −0.453229 + 0.0787129i
\(505\) −1.53772 + 1.53772i −0.0684277 + 0.0684277i
\(506\) −8.84252 −0.393098
\(507\) −6.45662 + 20.3862i −0.286749 + 0.905381i
\(508\) 3.84862i 0.170755i
\(509\) 10.8887 0.482631 0.241316 0.970447i \(-0.422421\pi\)
0.241316 + 0.970447i \(0.422421\pi\)
\(510\) 3.43533 1.78270i 0.152119 0.0789391i
\(511\) 15.1720i 0.671168i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 2.87007 21.1678i 0.126717 0.934583i
\(514\) −3.12108 −0.137665
\(515\) 0.699945i 0.0308433i
\(516\) 6.90163 3.58147i 0.303827 0.157665i
\(517\) 24.0847i 1.05924i
\(518\) −18.6845 + 9.45249i −0.820951 + 0.415319i
\(519\) −36.6178 11.5974i −1.60734 0.509071i
\(520\) 0.571765 0.571765i 0.0250736 0.0250736i
\(521\) −3.34544 −0.146566 −0.0732831 0.997311i \(-0.523348\pi\)
−0.0732831 + 0.997311i \(0.523348\pi\)
\(522\) −4.47824 + 6.36064i −0.196007 + 0.278398i
\(523\) 13.0218 + 13.0218i 0.569405 + 0.569405i 0.931962 0.362557i \(-0.118096\pi\)
−0.362557 + 0.931962i \(0.618096\pi\)
\(524\) 9.42329 9.42329i 0.411658 0.411658i
\(525\) −1.80027 + 5.68418i −0.0785702 + 0.248078i
\(526\) −2.91099 2.91099i −0.126925 0.126925i
\(527\) 20.0304i 0.872539i
\(528\) −5.03260 1.59390i −0.219016 0.0693658i
\(529\) 14.5827i 0.634030i
\(530\) 12.4574i 0.541113i
\(531\) −8.38881 + 1.45690i −0.364043 + 0.0632239i
\(532\) −10.0069 + 10.0069i −0.433854 + 0.433854i
\(533\) 4.57887 + 4.57887i 0.198333 + 0.198333i
\(534\) 7.32903 23.1407i 0.317158 1.00140i
\(535\) 0.332370 + 0.332370i 0.0143696 + 0.0143696i
\(536\) −6.69569 6.69569i −0.289210 0.289210i
\(537\) −7.85185 15.1308i −0.338833 0.652944i
\(538\) 3.67429 3.67429i 0.158410 0.158410i
\(539\) −14.7828 −0.636741
\(540\) −0.698141 + 5.14904i −0.0300432 + 0.221579i
\(541\) 2.84989 + 2.84989i 0.122526 + 0.122526i 0.765711 0.643185i \(-0.222387\pi\)
−0.643185 + 0.765711i \(0.722387\pi\)
\(542\) −3.35741 3.35741i −0.144213 0.144213i
\(543\) 1.36508 + 0.432343i 0.0585812 + 0.0185536i
\(544\) −2.23454 −0.0958050
\(545\) 4.50809 0.193105
\(546\) 1.45570 4.59622i 0.0622980 0.196700i
\(547\) 31.6848 31.6848i 1.35474 1.35474i 0.474475 0.880269i \(-0.342638\pi\)
0.880269 0.474475i \(-0.157362\pi\)
\(548\) 14.5392 0.621083
\(549\) 8.37412 1.45435i 0.357399 0.0620700i
\(550\) −2.15513 + 2.15513i −0.0918952 + 0.0918952i
\(551\) 10.6599i 0.454125i
\(552\) 1.51726 4.79060i 0.0645789 0.203902i
\(553\) −28.2573 28.2573i −1.20162 1.20162i
\(554\) −3.18907 −0.135491
\(555\) 1.69553 + 10.3983i 0.0719711 + 0.441384i
\(556\) 16.7132 0.708799
\(557\) −30.2213 30.2213i −1.28052 1.28052i −0.940374 0.340143i \(-0.889525\pi\)
−0.340143 0.940374i \(-0.610475\pi\)
\(558\) −21.9889 15.4814i −0.930862 0.655378i
\(559\) 3.62998i 0.153532i
\(560\) 2.43416 2.43416i 0.102862 0.102862i
\(561\) 10.4703 5.43334i 0.442055 0.229396i
\(562\) 16.2251 0.684416
\(563\) −10.7209 + 10.7209i −0.451833 + 0.451833i −0.895963 0.444129i \(-0.853513\pi\)
0.444129 + 0.895963i \(0.353513\pi\)
\(564\) 13.0483 + 4.13261i 0.549434 + 0.174014i
\(565\) −3.18049 −0.133804
\(566\) −29.5074 −1.24029
\(567\) 10.4462 + 29.1676i 0.438701 + 1.22492i
\(568\) 8.38330 + 8.38330i 0.351755 + 0.351755i
\(569\) −30.3297 30.3297i −1.27149 1.27149i −0.945308 0.326179i \(-0.894239\pi\)
−0.326179 0.945308i \(-0.605761\pi\)
\(570\) 3.27974 + 6.32020i 0.137373 + 0.264724i
\(571\) 26.1370 1.09380 0.546900 0.837198i \(-0.315808\pi\)
0.546900 + 0.837198i \(0.315808\pi\)
\(572\) 1.74264 1.74264i 0.0728634 0.0728634i
\(573\) −3.81010 + 1.97718i −0.159169 + 0.0825978i
\(574\) 19.4935 + 19.4935i 0.813642 + 0.813642i
\(575\) −2.05150 2.05150i −0.0855535 0.0855535i
\(576\) 1.72706 2.45301i 0.0719607 0.102209i
\(577\) 18.6883 + 18.6883i 0.778004 + 0.778004i 0.979491 0.201487i \(-0.0645775\pi\)
−0.201487 + 0.979491i \(0.564578\pi\)
\(578\) −8.49012 + 8.49012i −0.353142 + 0.353142i
\(579\) −6.34339 12.2240i −0.263622 0.508011i
\(580\) 2.59299i 0.107668i
\(581\) 37.3163i 1.54814i
\(582\) 1.77760 5.61261i 0.0736840 0.232650i
\(583\) 37.9678i 1.57246i
\(584\) 3.11646 + 3.11646i 0.128960 + 0.128960i
\(585\) −1.98350 1.39649i −0.0820078 0.0577379i
\(586\) 5.86433 5.86433i 0.242253 0.242253i
\(587\) 6.84341 + 6.84341i 0.282458 + 0.282458i 0.834088 0.551631i \(-0.185994\pi\)
−0.551631 + 0.834088i \(0.685994\pi\)
\(588\) 2.53654 8.00887i 0.104605 0.330280i
\(589\) −36.8513 −1.51843
\(590\) 2.00686 2.00686i 0.0826210 0.0826210i
\(591\) −9.33583 + 29.4770i −0.384025 + 1.21252i
\(592\) 1.89635 5.77961i 0.0779393 0.237540i
\(593\) 25.8530i 1.06166i −0.847480 0.530828i \(-0.821881\pi\)
0.847480 0.530828i \(-0.178119\pi\)
\(594\) −2.12781 + 15.6933i −0.0873050 + 0.643906i
\(595\) 7.69223i 0.315351i
\(596\) −11.2348 −0.460194
\(597\) −4.06564 + 2.10978i −0.166395 + 0.0863477i
\(598\) 1.65884 + 1.65884i 0.0678351 + 0.0678351i
\(599\) 28.9337i 1.18220i 0.806598 + 0.591100i \(0.201306\pi\)
−0.806598 + 0.591100i \(0.798694\pi\)
\(600\) −0.797792 1.53738i −0.0325697 0.0627632i
\(601\) −6.17236 −0.251776 −0.125888 0.992044i \(-0.540178\pi\)
−0.125888 + 0.992044i \(0.540178\pi\)
\(602\) 15.4538i 0.629851i
\(603\) −16.3537 + 23.2279i −0.665976 + 0.945915i
\(604\) 18.1204 0.737308
\(605\) 1.20971 1.20971i 0.0491818 0.0491818i
\(606\) −1.73493 3.34328i −0.0704767 0.135811i
\(607\) −9.27354 + 9.27354i −0.376401 + 0.376401i −0.869802 0.493401i \(-0.835754\pi\)
0.493401 + 0.869802i \(0.335754\pi\)
\(608\) 4.11103i 0.166724i
\(609\) −7.12124 13.7229i −0.288567 0.556080i
\(610\) −2.00335 + 2.00335i −0.0811131 + 0.0811131i
\(611\) −4.51824 + 4.51824i −0.182789 + 0.182789i
\(612\) 1.14706 + 6.60475i 0.0463670 + 0.266981i
\(613\) 3.85367i 0.155648i −0.996967 0.0778241i \(-0.975203\pi\)
0.996967 0.0778241i \(-0.0247973\pi\)
\(614\) 4.97725 4.97725i 0.200866 0.200866i
\(615\) 12.3118 6.38895i 0.496458 0.257627i
\(616\) 7.41889 7.41889i 0.298916 0.298916i
\(617\) −25.4539 −1.02474 −0.512369 0.858766i \(-0.671232\pi\)
−0.512369 + 0.858766i \(0.671232\pi\)
\(618\) 1.15576 + 0.366047i 0.0464914 + 0.0147246i
\(619\) 13.3502i 0.536588i −0.963337 0.268294i \(-0.913540\pi\)
0.963337 0.268294i \(-0.0864599\pi\)
\(620\) 8.96401 0.360003
\(621\) −14.9387 2.02549i −0.599470 0.0812800i
\(622\) 7.58225i 0.304020i
\(623\) 34.1133 + 34.1133i 1.36672 + 1.36672i
\(624\) 0.645093 + 1.24312i 0.0258244 + 0.0497647i
\(625\) −1.00000 −0.0400000
\(626\) 23.2502i 0.929266i
\(627\) 9.99607 + 19.2628i 0.399205 + 0.769283i
\(628\) 15.7039i 0.626653i
\(629\) 6.13577 + 12.1284i 0.244649 + 0.483593i
\(630\) −8.44432 5.94526i −0.336430 0.236865i
\(631\) −34.7483 + 34.7483i −1.38331 + 1.38331i −0.544631 + 0.838676i \(0.683330\pi\)
−0.838676 + 0.544631i \(0.816670\pi\)
\(632\) 11.6086 0.461766
\(633\) 32.1047 + 10.1681i 1.27605 + 0.404144i
\(634\) −13.7554 13.7554i −0.546296 0.546296i
\(635\) 2.72139 2.72139i 0.107995 0.107995i
\(636\) 20.5697 + 6.51476i 0.815644 + 0.258327i
\(637\) 2.77323 + 2.77323i 0.109879 + 0.109879i
\(638\) 7.90297i 0.312882i
\(639\) 20.4756 29.0824i 0.810001 1.15048i
\(640\) 1.00000i 0.0395285i
\(641\) 5.61943i 0.221954i −0.993823 0.110977i \(-0.964602\pi\)
0.993823 0.110977i \(-0.0353980\pi\)
\(642\) −0.722631 + 0.374995i −0.0285200 + 0.0147999i
\(643\) 20.4006 20.4006i 0.804522 0.804522i −0.179277 0.983799i \(-0.557376\pi\)
0.983799 + 0.179277i \(0.0573757\pi\)
\(644\) 7.06214 + 7.06214i 0.278287 + 0.278287i
\(645\) 7.41267 + 2.34771i 0.291874 + 0.0924410i
\(646\) 6.49565 + 6.49565i 0.255568 + 0.255568i
\(647\) 26.1415 + 26.1415i 1.02773 + 1.02773i 0.999604 + 0.0281258i \(0.00895389\pi\)
0.0281258 + 0.999604i \(0.491046\pi\)
\(648\) −8.13706 3.84555i −0.319654 0.151067i
\(649\) 6.11654 6.11654i 0.240095 0.240095i
\(650\) 0.808598 0.0317158
\(651\) 47.4403 24.6182i 1.85933 0.964864i
\(652\) 4.76257 + 4.76257i 0.186517 + 0.186517i
\(653\) 21.1720 + 21.1720i 0.828525 + 0.828525i 0.987313 0.158788i \(-0.0507585\pi\)
−0.158788 + 0.987313i \(0.550758\pi\)
\(654\) −2.35758 + 7.44383i −0.0921886 + 0.291077i
\(655\) 13.3265 0.520711
\(656\) −8.00829 −0.312671
\(657\) 7.61173 10.8113i 0.296962 0.421788i
\(658\) −19.2354 + 19.2354i −0.749874 + 0.749874i
\(659\) −28.6785 −1.11716 −0.558578 0.829452i \(-0.688653\pi\)
−0.558578 + 0.829452i \(0.688653\pi\)
\(660\) −2.43153 4.68565i −0.0946471 0.182389i
\(661\) −9.63627 + 9.63627i −0.374807 + 0.374807i −0.869225 0.494417i \(-0.835382\pi\)
0.494417 + 0.869225i \(0.335382\pi\)
\(662\) 23.9782i 0.931938i
\(663\) −2.98348 0.944917i −0.115869 0.0366975i
\(664\) −7.66511 7.66511i −0.297464 0.297464i
\(665\) −14.1519 −0.548787
\(666\) −18.0566 2.63829i −0.699678 0.102232i
\(667\) 7.52295 0.291290
\(668\) 7.41766 + 7.41766i 0.286998 + 0.286998i
\(669\) −41.1074 13.0194i −1.58930 0.503358i
\(670\) 9.46914i 0.365825i
\(671\) −6.10584 + 6.10584i −0.235713 + 0.235713i
\(672\) 2.74634 + 5.29231i 0.105942 + 0.204155i
\(673\) −32.2049 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(674\) −5.00850 + 5.00850i −0.192920 + 0.192920i
\(675\) −4.13458 + 3.14726i −0.159140 + 0.121138i
\(676\) 12.3462 0.474853
\(677\) 4.54053 0.174507 0.0872533 0.996186i \(-0.472191\pi\)
0.0872533 + 0.996186i \(0.472191\pi\)
\(678\) 1.66329 5.25167i 0.0638782 0.201689i
\(679\) 8.27392 + 8.27392i 0.317524 + 0.317524i
\(680\) −1.58006 1.58006i −0.0605924 0.0605924i
\(681\) −15.2005 + 7.88800i −0.582484 + 0.302269i
\(682\) 27.3207 1.04616
\(683\) 17.4943 17.4943i 0.669399 0.669399i −0.288178 0.957577i \(-0.593049\pi\)
0.957577 + 0.288178i \(0.0930493\pi\)
\(684\) −12.1512 + 2.11031i −0.464612 + 0.0806899i
\(685\) 10.2807 + 10.2807i 0.392807 + 0.392807i
\(686\) −5.23273 5.23273i −0.199787 0.199787i
\(687\) 32.2916 + 10.2273i 1.23200 + 0.390194i
\(688\) −3.17436 3.17436i −0.121021 0.121021i
\(689\) −7.12268 + 7.12268i −0.271353 + 0.271353i
\(690\) 4.46033 2.31460i 0.169802 0.0881154i
\(691\) 5.34751i 0.203429i −0.994814 0.101714i \(-0.967567\pi\)
0.994814 0.101714i \(-0.0324328\pi\)
\(692\) 22.1763i 0.843016i
\(693\) −25.7368 18.1201i −0.977659 0.688325i
\(694\) 11.5297i 0.437661i
\(695\) 11.8180 + 11.8180i 0.448284 + 0.448284i
\(696\) 4.28158 + 1.35605i 0.162293 + 0.0514008i
\(697\) 12.6536 12.6536i 0.479288 0.479288i
\(698\) −6.87499 6.87499i −0.260222 0.260222i
\(699\) 29.2853 + 9.27511i 1.10767 + 0.350817i
\(700\) 3.44243 0.130111
\(701\) 14.9583 14.9583i 0.564967 0.564967i −0.365747 0.930714i \(-0.619186\pi\)
0.930714 + 0.365747i \(0.119186\pi\)
\(702\) 3.34322 2.54487i 0.126182 0.0960499i
\(703\) −22.3135 + 11.2884i −0.841569 + 0.425750i
\(704\) 3.04782i 0.114869i
\(705\) 6.30437 + 12.1488i 0.237436 + 0.457549i
\(706\) 0.566873i 0.0213345i
\(707\) 7.48612 0.281545
\(708\) 2.26423 + 4.36327i 0.0850951 + 0.163982i
\(709\) −30.3690 30.3690i −1.14053 1.14053i −0.988353 0.152178i \(-0.951371\pi\)
−0.152178 0.988353i \(-0.548629\pi\)
\(710\) 11.8558i 0.444939i
\(711\) −5.95906 34.3123i −0.223482 1.28681i
\(712\) −14.0144 −0.525211
\(713\) 26.0069i 0.973968i
\(714\) −12.7015 4.02277i −0.475342 0.150548i
\(715\) 2.46446 0.0921657
\(716\) −6.95933 + 6.95933i −0.260082 + 0.260082i
\(717\) −10.7090 + 5.55721i −0.399934 + 0.207538i
\(718\) 24.9933 24.9933i 0.932741 0.932741i
\(719\) 12.6121i 0.470351i 0.971953 + 0.235175i \(0.0755665\pi\)
−0.971953 + 0.235175i \(0.924434\pi\)
\(720\) 2.95576 0.513330i 0.110155 0.0191307i
\(721\) −1.70378 + 1.70378i −0.0634521 + 0.0634521i
\(722\) 1.48455 1.48455i 0.0552491 0.0552491i
\(723\) −20.9821 40.4334i −0.780334 1.50374i
\(724\) 0.826713i 0.0307246i
\(725\) 1.83352 1.83352i 0.0680953 0.0680953i
\(726\) 1.36486 + 2.63013i 0.0506545 + 0.0976133i
\(727\) −0.256819 + 0.256819i −0.00952488 + 0.00952488i −0.711853 0.702328i \(-0.752144\pi\)
0.702328 + 0.711853i \(0.252144\pi\)
\(728\) −2.78354 −0.103165
\(729\) −7.18951 + 26.0252i −0.266278 + 0.963896i
\(730\) 4.40734i 0.163123i
\(731\) 10.0313 0.371022
\(732\) −2.26027 4.35563i −0.0835420 0.160989i
\(733\) 12.0159i 0.443816i −0.975068 0.221908i \(-0.928771\pi\)
0.975068 0.221908i \(-0.0712285\pi\)
\(734\) 3.02276 + 3.02276i 0.111572 + 0.111572i
\(735\) 7.45673 3.86953i 0.275046 0.142730i
\(736\) −2.90126 −0.106942
\(737\) 28.8602i 1.06308i
\(738\) 4.11090 + 23.6706i 0.151324 + 0.871325i
\(739\) 44.3596i 1.63179i 0.578198 + 0.815896i \(0.303756\pi\)
−0.578198 + 0.815896i \(0.696244\pi\)
\(740\) 5.42772 2.74588i 0.199527 0.100941i
\(741\) 1.73843 5.48891i 0.0638627 0.201640i
\(742\) −30.3232 + 30.3232i −1.11320 + 1.11320i
\(743\) −40.0701 −1.47003 −0.735014 0.678052i \(-0.762824\pi\)
−0.735014 + 0.678052i \(0.762824\pi\)
\(744\) −4.68787 + 14.8015i −0.171866 + 0.542649i
\(745\) −7.94418 7.94418i −0.291052 0.291052i
\(746\) −23.2224 + 23.2224i −0.850234 + 0.850234i
\(747\) −18.7215 + 26.5909i −0.684983 + 0.972911i
\(748\) −4.81573 4.81573i −0.176080 0.176080i
\(749\) 1.61808i 0.0591235i
\(750\) 0.522966 1.65121i 0.0190960 0.0602938i
\(751\) 44.0250i 1.60650i −0.595645 0.803248i \(-0.703103\pi\)
0.595645 0.803248i \(-0.296897\pi\)
\(752\) 7.90227i 0.288166i
\(753\) 17.0203 + 32.7988i 0.620255 + 1.19526i
\(754\) −1.48258 + 1.48258i −0.0539925 + 0.0539925i
\(755\) 12.8130 + 12.8130i 0.466314 + 0.466314i
\(756\) 14.2330 10.8342i 0.517649 0.394036i
\(757\) 4.69837 + 4.69837i 0.170765 + 0.170765i 0.787315 0.616550i \(-0.211470\pi\)
−0.616550 + 0.787315i \(0.711470\pi\)
\(758\) 5.41969 + 5.41969i 0.196852 + 0.196852i
\(759\) 13.5943 7.05449i 0.493442 0.256062i
\(760\) 2.90693 2.90693i 0.105446 0.105446i
\(761\) −10.9188 −0.395805 −0.197902 0.980222i \(-0.563413\pi\)
−0.197902 + 0.980222i \(0.563413\pi\)
\(762\) 3.07040 + 5.91678i 0.111229 + 0.214342i
\(763\) −10.9734 10.9734i −0.397265 0.397265i
\(764\) 1.75243 + 1.75243i 0.0634007 + 0.0634007i
\(765\) −3.85917 + 5.48135i −0.139529 + 0.198179i
\(766\) −5.01207 −0.181094
\(767\) −2.29490 −0.0828642
\(768\) −1.65121 0.522966i −0.0595830 0.0188709i
\(769\) 32.6754 32.6754i 1.17830 1.17830i 0.198128 0.980176i \(-0.436514\pi\)
0.980176 0.198128i \(-0.0634863\pi\)
\(770\) 10.4919 0.378102
\(771\) 4.79827 2.48997i 0.172806 0.0896741i
\(772\) −5.62234 + 5.62234i −0.202352 + 0.202352i
\(773\) 46.7775i 1.68247i −0.540669 0.841235i \(-0.681829\pi\)
0.540669 0.841235i \(-0.318171\pi\)
\(774\) −7.75314 + 11.0121i −0.278681 + 0.395823i
\(775\) 6.33851 + 6.33851i 0.227686 + 0.227686i
\(776\) −3.39908 −0.122020
\(777\) 21.1840 29.4384i 0.759973 1.05610i
\(778\) 25.8997 0.928551
\(779\) 23.2796 + 23.2796i 0.834078