Properties

Label 1110.2.u.f.401.15
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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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 401.15
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.f.191.15

$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

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 −0.623358 0.781937i \(-0.714232\pi\)
0.781937 + 0.623358i \(0.214232\pi\)
\(14\) 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 0.872261 0.489041i \(-0.162653\pi\)
−0.489041 + 0.872261i \(0.662653\pi\)
\(18\) 0.513330 2.95576i 0.120993 0.696678i
\(19\) 2.90693 2.90693i 0.666896 0.666896i −0.290100 0.956996i \(-0.593689\pi\)
0.956996 + 0.290100i \(0.0936885\pi\)
\(20\) −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 0.887867 0.460100i \(-0.152186\pi\)
−0.460100 + 0.887867i \(0.652186\pi\)
\(24\) 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 −0.516070 0.856546i \(-0.672606\pi\)
0.856546 + 0.516070i \(0.172606\pi\)
\(30\) 1.65121 0.522966i 0.301469 0.0954800i
\(31\) −6.33851 6.33851i −1.13843 1.13843i −0.988732 0.149699i \(-0.952169\pi\)
−0.149699 0.988732i \(-0.547831\pi\)
\(32\) −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 −0.422348 0.906434i \(-0.638794\pi\)
0.906434 + 0.422348i \(0.138794\pi\)
\(44\) 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 \(-0.804483\pi\)
0.817216 0.576332i \(-0.195517\pi\)
\(48\) 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 \(-0.673204\pi\)
0.517680 0.855574i \(-0.326796\pi\)
\(54\) 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 0.564300 0.825570i \(-0.309146\pi\)
−0.825570 + 0.564300i \(0.809146\pi\)
\(60\) 0.797792 1.53738i 0.102995 0.198475i
\(61\) 2.00335 + 2.00335i 0.256502 + 0.256502i 0.823630 0.567128i \(-0.191945\pi\)
−0.567128 + 0.823630i \(0.691945\pi\)
\(62\) −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 \(-0.803670\pi\)
0.815739 0.578420i \(-0.196330\pi\)
\(68\) 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 \(0.248385\pi\)
−0.710685 + 0.703511i \(0.751615\pi\)
\(72\) −2.95576 0.513330i −0.348339 0.0604965i
\(73\) 4.40734i 0.515841i 0.966166 + 0.257920i \(0.0830372\pi\)
−0.966166 + 0.257920i \(0.916963\pi\)
\(74\) −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 −0.997277 0.0737442i \(-0.976505\pi\)
0.0737442 + 0.997277i \(0.476505\pi\)
\(80\) 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 \(-0.797181\pi\)
0.803779 0.594928i \(-0.202819\pi\)
\(84\) 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 0.0517620 0.998659i \(-0.483516\pi\)
0.998659 0.0517620i \(-0.0164837\pi\)
\(90\) −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 −0.574479 0.818519i \(-0.694795\pi\)
0.818519 + 0.574479i \(0.194795\pi\)
\(98\) 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 0.682302 0.731070i \(-0.260979\pi\)
−0.731070 + 0.682302i \(0.760979\pi\)
\(104\) −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 \(0.00723272\pi\)
−0.999742 + 0.0227203i \(0.992767\pi\)
\(108\) 4.13458 + 3.14726i 0.397850 + 0.302845i
\(109\) −3.18770 + 3.18770i −0.305327 + 0.305327i −0.843094 0.537767i \(-0.819268\pi\)
0.537767 + 0.843094i \(0.319268\pi\)
\(110\) 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 −0.593368 0.804931i \(-0.702202\pi\)
0.804931 + 0.593368i \(0.202202\pi\)
\(114\) 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 −0.986582 0.163265i \(-0.947797\pi\)
0.163265 + 0.986582i \(0.447797\pi\)
\(132\) −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 \(0.213307\pi\)
−0.783745 + 0.621083i \(0.786693\pi\)
\(138\) −4.79060 + 1.51726i −0.407803 + 0.129158i
\(139\) 16.7132i 1.41760i 0.705410 + 0.708799i \(0.250763\pi\)
−0.705410 + 0.708799i \(0.749237\pi\)
\(140\) −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 \(-0.847780\pi\)
0.887818 0.460194i \(-0.152220\pi\)
\(150\) −1.53738 0.797792i −0.125526 0.0651394i
\(151\) 18.1204i 1.47462i 0.675557 + 0.737308i \(0.263903\pi\)
−0.675557 + 0.737308i \(0.736097\pi\)
\(152\) −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 0.868581 0.495548i \(-0.165033\pi\)
−0.495548 + 0.868581i \(0.665033\pi\)
\(164\) 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 0.933243 0.359247i \(-0.116966\pi\)
−0.359247 + 0.933243i \(0.616966\pi\)
\(168\) 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 −0.397456 0.917621i \(-0.630107\pi\)
0.917621 + 0.397456i \(0.130107\pi\)
\(180\) −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 0.767659 0.640858i \(-0.221421\pi\)
−0.640858 + 0.767659i \(0.721421\pi\)
\(192\) −0.522966 1.65121i −0.0377418 0.119166i
\(193\) 5.62234 5.62234i 0.404705 0.404705i −0.475183 0.879887i \(-0.657618\pi\)
0.879887 + 0.475183i \(0.157618\pi\)
\(194\) 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 \(0.219388\pi\)
−0.771738 + 0.635941i \(0.780612\pi\)
\(198\) −1.56454 + 9.00861i −0.111187 + 0.640214i
\(199\) 1.86996 + 1.86996i 0.132558 + 0.132558i 0.770273 0.637715i \(-0.220120\pi\)
−0.637715 + 0.770273i \(0.720120\pi\)
\(200\) 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 0.899975 0.435942i \(-0.143585\pi\)
−0.435942 + 0.899975i \(0.643585\pi\)
\(228\) 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 0.848231 0.529626i \(-0.177668\pi\)
−0.529626 + 0.848231i \(0.677668\pi\)
\(240\) −1.53738 0.797792i −0.0992373 0.0514973i
\(241\) 18.5971 18.5971i 1.19794 1.19794i 0.223163 0.974781i \(-0.428362\pi\)
0.974781 0.223163i \(-0.0716383\pi\)
\(242\) −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 −0.998908 0.0467134i \(-0.985125\pi\)
0.0467134 + 0.998908i \(0.485125\pi\)
\(252\) −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 0.634916 0.772581i \(-0.281035\pi\)
−0.772581 + 0.634916i \(0.781035\pi\)
\(258\) 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 \(0.0506368\pi\)
−0.987373 + 0.158410i \(0.949363\pi\)
\(270\) 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 0.636109 0.771599i \(-0.280543\pi\)
−0.771599 + 0.636109i \(0.780543\pi\)
\(278\) 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 0.960992 0.276576i \(-0.0891999\pi\)
−0.276576 + 0.960992i \(0.589200\pi\)
\(282\) 12.1488 + 6.30437i 0.723448 + 0.375420i
\(283\) −20.8649 20.8649i −1.24029 1.24029i −0.959881 0.280407i \(-0.909531\pi\)
−0.280407 0.959881i \(-0.590469\pi\)
\(284\) 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 \(0.0778865\pi\)
−0.970213 + 0.242253i \(0.922113\pi\)
\(294\) −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 \(0.0643755\pi\)
−0.979619 + 0.200866i \(0.935625\pi\)
\(308\) 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 −0.842585 0.538564i \(-0.818967\pi\)
0.538564 + 0.842585i \(0.318967\pi\)
\(312\) 1.33517 0.422869i 0.0755891 0.0239402i
\(313\) 16.4404 16.4404i 0.929266 0.929266i −0.0683922 0.997659i \(-0.521787\pi\)
0.997659 + 0.0683922i \(0.0217869\pi\)
\(314\) 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 −0.997827 0.0658890i \(-0.979012\pi\)
0.0658890 + 0.997827i \(0.479012\pi\)
\(332\) −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 \(-0.938204\pi\)
0.981214 0.192920i \(-0.0617958\pi\)
\(338\) 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 −0.891224 0.453563i \(-0.850153\pi\)
0.453563 + 0.891224i \(0.350153\pi\)
\(348\) 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 −0.696359 0.717694i \(-0.745198\pi\)
0.717694 + 0.696359i \(0.245198\pi\)
\(354\) 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 \(0.382590\pi\)
−0.360548 + 0.932741i \(0.617410\pi\)
\(360\) 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 \(-0.676460\pi\)
0.526405 0.850234i \(-0.323540\pi\)
\(374\) −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 0.610739 0.791832i \(-0.290873\pi\)
−0.791832 + 0.610739i \(0.790873\pi\)
\(384\) −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 0.997612 0.0690616i \(-0.0220005\pi\)
−0.0690616 + 0.997612i \(0.522000\pi\)
\(390\) 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 \(0.00708345\pi\)
−0.999752 + 0.0222515i \(0.992917\pi\)
\(398\) 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 0.0912209 0.995831i \(-0.470923\pi\)
0.995831 0.0912209i \(-0.0290769\pi\)
\(402\) 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 0.905359 0.424646i \(-0.139601\pi\)
−0.424646 + 0.905359i \(0.639601\pi\)
\(410\) −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 \(-0.656146\pi\)
0.471109 0.882075i \(-0.343854\pi\)
\(420\) 2.74634 5.29231i 0.134008 0.258238i
\(421\) 16.4019 + 16.4019i 0.799382 + 0.799382i 0.982998 0.183616i \(-0.0587803\pi\)
−0.183616 + 0.982998i \(0.558780\pi\)
\(422\) −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 −0.117906 0.993025i \(-0.537618\pi\)
0.993025 + 0.117906i \(0.0376183\pi\)
\(432\) 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 0.999226 + 0.0393487i \(0.0125283\pi\)
0.0393487 + 0.999226i \(0.487472\pi\)
\(440\) 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 0.652506 0.757784i \(-0.273718\pi\)
−0.757784 + 0.652506i \(0.773718\pi\)
\(450\) 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 −0.669545 0.742771i \(-0.733511\pi\)
0.742771 + 0.669545i \(0.233511\pi\)
\(458\) −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 0.827624 0.561283i \(-0.189692\pi\)
−0.561283 + 0.827624i \(0.689692\pi\)
\(462\) 8.37035 16.1300i 0.389424 0.750435i
\(463\) −24.0600 + 24.0600i −1.11816 + 1.11816i −0.126154 + 0.992011i \(0.540263\pi\)
−0.992011 + 0.126154i \(0.959737\pi\)
\(464\) −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 0.760430 0.649420i \(-0.224988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(468\) −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 0.379381 0.925240i \(-0.376137\pi\)
−0.925240 + 0.379381i \(0.876137\pi\)
\(480\) −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 −0.943596 0.331100i \(-0.892580\pi\)
0.331100 + 0.943596i \(0.392580\pi\)
\(488\) 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 \(0.167069\pi\)
−0.865392 + 0.501095i \(0.832931\pi\)
\(492\) 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 0.952852 0.303435i \(-0.0981336\pi\)
−0.303435 + 0.952852i \(0.598134\pi\)
\(500\) −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 −0.916652 0.399686i \(-0.869119\pi\)
−0.399686 0.916652i \(-0.630881\pi\)
\(504\) −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 −0.362557 0.931962i \(-0.618096\pi\)
0.931962 + 0.362557i \(0.118096\pi\)
\(524\) 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 −0.643185 0.765711i \(-0.722387\pi\)
0.765711 + 0.643185i \(0.222387\pi\)
\(542\) −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 0.880269 + 0.474475i \(0.157362\pi\)
0.474475 + 0.880269i \(0.342638\pi\)
\(548\) 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 −0.340143 + 0.940374i \(0.610475\pi\)
−0.940374 + 0.340143i \(0.889525\pi\)
\(558\) −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 0.444129 0.895963i \(-0.353513\pi\)
−0.895963 + 0.444129i \(0.853513\pi\)
\(564\) 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 −0.326179 + 0.945308i \(0.605761\pi\)
−0.945308 + 0.326179i \(0.894239\pi\)
\(570\) 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 −0.201487 0.979491i \(-0.564578\pi\)
0.979491 + 0.201487i \(0.0645775\pi\)
\(578\) −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 −0.551631 0.834088i \(-0.685994\pi\)
0.834088 + 0.551631i \(0.185994\pi\)
\(588\) 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 \(0.178119\pi\)
−0.847480 + 0.530828i \(0.821881\pi\)
\(594\) −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 \(-0.798694\pi\)
0.806598 0.591100i \(-0.201306\pi\)
\(600\) −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 0.493401 0.869802i \(-0.335754\pi\)
−0.869802 + 0.493401i \(0.835754\pi\)
\(608\) 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 \(0.0247973\pi\)
−0.996967 + 0.0778241i \(0.975203\pi\)
\(614\) 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 \(0.0864599\pi\)
−0.963337 + 0.268294i \(0.913540\pi\)
\(620\) 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 −0.838676 0.544631i \(-0.816670\pi\)
−0.544631 0.838676i \(-0.683330\pi\)
\(632\) 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 \(0.0353980\pi\)
−0.993823 + 0.110977i \(0.964602\pi\)
\(642\) −0.722631 0.374995i −0.0285200 0.0147999i
\(643\) 20.4006 + 20.4006i 0.804522 + 0.804522i 0.983799 0.179277i \(-0.0573757\pi\)
−0.179277 + 0.983799i \(0.557376\pi\)
\(644\) 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 0.0281258 0.999604i \(-0.491046\pi\)
0.999604 0.0281258i \(-0.00895389\pi\)
\(648\) −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 −0.158788 0.987313i \(-0.550758\pi\)
0.987313 + 0.158788i \(0.0507585\pi\)
\(654\) −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 0.494417 0.869225i \(-0.335382\pi\)
−0.869225 + 0.494417i \(0.835382\pi\)
\(662\) 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 0.957577 0.288178i \(-0.0930493\pi\)
−0.288178 + 0.957577i \(0.593049\pi\)
\(684\) −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 \(0.0324328\pi\)
−0.994814 + 0.101714i \(0.967567\pi\)
\(692\) 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 0.930714 0.365747i \(-0.119186\pi\)
−0.365747 + 0.930714i \(0.619186\pi\)
\(702\) 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 −0.152178 + 0.988353i \(0.548629\pi\)
−0.988353 + 0.152178i \(0.951371\pi\)
\(710\) 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 \(-0.924434\pi\)
0.971953 0.235175i \(-0.0755665\pi\)
\(720\) 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 0.702328 0.711853i \(-0.252144\pi\)
−0.711853 + 0.702328i \(0.752144\pi\)
\(728\) −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 \(0.0712285\pi\)
−0.975068 + 0.221908i \(0.928771\pi\)
\(734\) 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 \(-0.696244\pi\)
0.578198 0.815896i \(-0.303756\pi\)
\(740\) 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 \(0.296897\pi\)
−0.595645 + 0.803248i \(0.703103\pi\)
\(752\) 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 −0.616550 0.787315i \(-0.711470\pi\)
0.787315 + 0.616550i \(0.211470\pi\)
\(758\) 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 0.980176 + 0.198128i \(0.0634863\pi\)
0.198128 + 0.980176i \(0.436514\pi\)
\(770\) 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 \(0.318171\pi\)
−0.540669 + 0.841235i \(0.681829\pi\)
\(774\) −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