Properties

Label 1110.2.u.f.191.9
Level $1110$
Weight $2$
Character 1110.191
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 191.9
Character \(\chi\) \(=\) 1110.191
Dual form 1110.2.u.f.401.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.65121 - 0.522966i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.53738 - 0.797792i) q^{6} +3.44243 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.45301 - 1.72706i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.65121 - 0.522966i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.53738 - 0.797792i) 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} +(0.797792 - 1.53738i) q^{15} -1.00000 q^{16} +(-1.58006 + 1.58006i) q^{17} +(-2.95576 - 0.513330i) 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} +(0.797792 - 1.53738i) 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} +(1.24312 + 0.645093i) q^{39} -1.00000i q^{40} -8.00829 q^{41} +(-5.29231 - 2.74634i) q^{42} +(3.17436 + 3.17436i) q^{43} +3.04782i q^{44} +(0.513330 - 2.95576i) 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} +(-1.78270 + 3.43533i) q^{51} +(-0.571765 + 0.571765i) q^{52} -12.4574i q^{53} +(-5.14904 + 0.698141i) q^{54} +(2.15513 - 2.15513i) q^{55} +(2.43416 - 2.43416i) q^{56} +(6.32020 + 3.27974i) q^{57} +2.59299i q^{58} +(2.00686 - 2.00686i) q^{59} +(1.53738 + 0.797792i) 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} +(-4.68565 - 2.43153i) q^{66} +9.46914i q^{67} +(-1.58006 - 1.58006i) q^{68} +(-2.31460 + 4.46033i) q^{69} -3.44243 q^{70} +11.8558i q^{71} +(0.513330 - 2.95576i) 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} +(-3.98641 - 2.06867i) 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} +(-7.15142 + 13.7811i) q^{93} +(-5.58775 + 5.58775i) q^{94} +4.11103 q^{95} +(1.53738 + 0.797792i) 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
\(6\) −1.53738 0.797792i −0.627632 0.325697i
\(7\) 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 \(-0.348037\pi\)
0.459476 + 0.888190i \(0.348037\pi\)
\(12\) 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
\(15\) 0.797792 1.53738i 0.205989 0.396949i
\(16\) −1.00000 −0.250000
\(17\) −1.58006 + 1.58006i −0.383220 + 0.383220i −0.872261 0.489041i \(-0.837347\pi\)
0.489041 + 0.872261i \(0.337347\pi\)
\(18\) −2.95576 0.513330i −0.696678 0.120993i
\(19\) 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 −0.887867 0.460100i \(-0.847814\pi\)
0.460100 + 0.887867i \(0.347814\pi\)
\(24\) 0.797792 1.53738i 0.162849 0.313816i
\(25\) 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 \(-0.327394\pi\)
−0.856546 + 0.516070i \(0.827394\pi\)
\(30\) −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
\(39\) 1.24312 + 0.645093i 0.199059 + 0.103298i
\(40\) 1.00000i 0.158114i
\(41\) −8.00829 −1.25069 −0.625343 0.780350i \(-0.715041\pi\)
−0.625343 + 0.780350i \(0.715041\pi\)
\(42\) −5.29231 2.74634i −0.816621 0.423769i
\(43\) 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
\(45\) 0.513330 2.95576i 0.0765227 0.440618i
\(46\) 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
\(51\) −1.78270 + 3.43533i −0.249627 + 0.481042i
\(52\) −0.571765 + 0.571765i −0.0792896 + 0.0792896i
\(53\) 12.4574i 1.71115i −0.517680 0.855574i \(-0.673204\pi\)
0.517680 0.855574i \(-0.326796\pi\)
\(54\) −5.14904 + 0.698141i −0.700695 + 0.0950049i
\(55\) 2.15513 2.15513i 0.290598 0.290598i
\(56\) 2.43416 2.43416i 0.325279 0.325279i
\(57\) 6.32020 + 3.27974i 0.837131 + 0.434413i
\(58\) 2.59299i 0.340476i
\(59\) 2.00686 2.00686i 0.261271 0.261271i −0.564300 0.825570i \(-0.690854\pi\)
0.825570 + 0.564300i \(0.190854\pi\)
\(60\) 1.53738 + 0.797792i 0.198475 + 0.102995i
\(61\) 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
\(66\) −4.68565 2.43153i −0.576763 0.299300i
\(67\) 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
\(69\) −2.31460 + 4.46033i −0.278645 + 0.536961i
\(70\) −3.44243 −0.411449
\(71\) 11.8558i 1.40702i 0.710685 + 0.703511i \(0.248385\pi\)
−0.710685 + 0.703511i \(0.751615\pi\)
\(72\) 0.513330 2.95576i 0.0604965 0.348339i
\(73\) 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 \(-0.797181\pi\)
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
\(87\) −3.98641 2.06867i −0.427388 0.221784i
\(88\) 2.15513 2.15513i 0.229738 0.229738i
\(89\) −9.90966 9.90966i −1.05042 1.05042i −0.998659 0.0517620i \(-0.983516\pi\)
−0.0517620 0.998659i \(-0.516484\pi\)
\(90\) −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
\(93\) −7.15142 + 13.7811i −0.741568 + 1.42903i
\(94\) −5.58775 + 5.58775i −0.576332 + 0.576332i
\(95\) 4.11103 0.421782
\(96\) 1.53738 + 0.797792i 0.156908 + 0.0814243i
\(97\) 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 \(-0.534507\pi\)
−0.108194 + 0.994130i \(0.534507\pi\)
\(102\) 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
\(105\) 2.74634 5.29231i 0.268015 0.516476i
\(106\) −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 0.537767 0.843094i \(-0.319268\pi\)
−0.843094 + 0.537767i \(0.819268\pi\)
\(110\) −3.04782 −0.290598
\(111\) −0.108737 + 10.5351i −0.0103208 + 0.999947i
\(112\) −3.44243 −0.325279
\(113\) −2.24895 2.24895i −0.211563 0.211563i 0.593368 0.804931i \(-0.297798\pi\)
−0.804931 + 0.593368i \(0.797798\pi\)
\(114\) −2.14992 6.78818i −0.201359 0.635772i
\(115\) 2.90126i 0.270544i
\(116\) 1.83352 1.83352i 0.170238 0.170238i
\(117\) 2.39002 + 0.415078i 0.220957 + 0.0383740i
\(118\) −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
\(126\) −10.1750 1.76710i −0.906458 0.157426i
\(127\) −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
\(129\) 6.90163 + 3.58147i 0.607655 + 0.315331i
\(130\) −0.571765 0.571765i −0.0501471 0.0501471i
\(131\) 9.42329 + 9.42329i 0.823317 + 0.823317i 0.986582 0.163265i \(-0.0522027\pi\)
−0.163265 + 0.986582i \(0.552203\pi\)
\(132\) 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
\(135\) −0.698141 5.14904i −0.0600864 0.443159i
\(136\) 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 \(-0.749237\pi\)
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 \(-0.847780\pi\)
0.887818 0.460194i \(-0.152220\pi\)
\(150\) −0.797792 + 1.53738i −0.0651394 + 0.125526i
\(151\) 18.1204i 1.47462i −0.675557 0.737308i \(-0.736097\pi\)
0.675557 0.737308i \(-0.263903\pi\)
\(152\) 4.11103 0.333448
\(153\) −1.14706 + 6.60475i −0.0927339 + 0.533962i
\(154\) −7.41889 7.41889i −0.597831 0.597831i
\(155\) 8.96401i 0.720007i
\(156\) −0.645093 + 1.24312i −0.0516488 + 0.0995293i
\(157\) 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
\(162\) −8.13706 + 3.84555i −0.639308 + 0.302135i
\(163\) 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
\(165\) 2.43153 4.68565i 0.189294 0.364777i
\(166\) −7.66511 + 7.66511i −0.594928 + 0.594928i
\(167\) −7.41766 + 7.41766i −0.573996 + 0.573996i −0.933243 0.359247i \(-0.883034\pi\)
0.359247 + 0.933243i \(0.383034\pi\)
\(168\) 2.74634 5.29231i 0.211885 0.408310i
\(169\) 12.3462i 0.949705i
\(170\) 1.58006 1.58006i 0.121185 0.121185i
\(171\) 12.1512 + 2.11031i 0.929225 + 0.161380i
\(172\) −3.17436 + 3.17436i −0.242043 + 0.242043i
\(173\) −22.1763 −1.68603 −0.843016 0.537889i \(-0.819222\pi\)
−0.843016 + 0.537889i \(0.819222\pi\)
\(174\) 1.35605 + 4.28158i 0.102802 + 0.324586i
\(175\) 3.44243i 0.260223i
\(176\) −3.04782 −0.229738
\(177\) 2.26423 4.36327i 0.170190 0.327963i
\(178\) 14.0144i 1.05042i
\(179\) −6.95933 6.95933i −0.520165 0.520165i 0.397456 0.917621i \(-0.369893\pi\)
−0.917621 + 0.397456i \(0.869893\pi\)
\(180\) 2.95576 + 0.513330i 0.220309 + 0.0382614i
\(181\) −0.826713 −0.0614491 −0.0307246 0.999528i \(-0.509781\pi\)
−0.0307246 + 0.999528i \(0.509781\pi\)
\(182\) 2.78354i 0.206330i
\(183\) 2.26027 4.35563i 0.167084 0.321978i
\(184\) 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 \(-0.778579\pi\)
0.640858 + 0.767659i \(0.278579\pi\)
\(192\) −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 \(0.219388\pi\)
−0.771738 + 0.635941i \(0.780612\pi\)
\(198\) −9.00861 1.56454i −0.640214 0.111187i
\(199\) 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
\(204\) −3.43533 1.78270i −0.240521 0.124814i
\(205\) −5.66272 + 5.66272i −0.395501 + 0.395501i
\(206\) 0.699945 0.0487675
\(207\) −1.48930 + 8.57542i −0.103514 + 0.596033i
\(208\) −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
\(216\) −0.698141 5.14904i −0.0475024 0.350348i
\(217\) −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
\(222\) 7.52632 7.37255i 0.505134 0.494813i
\(223\) 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 \(-0.856415\pi\)
0.435942 + 0.899975i \(0.356415\pi\)
\(228\) −3.27974 + 6.32020i −0.217206 + 0.418565i
\(229\) −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 \(-0.302682\pi\)
0.580949 + 0.813940i \(0.302682\pi\)
\(234\) −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
\(237\) −17.8468 9.26127i −1.15928 0.601584i
\(238\) 7.69223 0.498613
\(239\) −4.92552 + 4.92552i −0.318606 + 0.318606i −0.848231 0.529626i \(-0.822332\pi\)
0.529626 + 0.848231i \(0.322332\pi\)
\(240\) −0.797792 + 1.53738i −0.0514973 + 0.0992373i
\(241\) 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
\(246\) 12.3118 + 6.38895i 0.784969 + 0.407345i
\(247\) 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 \(-0.0148747\pi\)
−0.0467134 + 0.998908i \(0.514875\pi\)
\(252\) 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 \(-0.718965\pi\)
0.772581 + 0.634916i \(0.218965\pi\)
\(258\) −2.34771 7.41267i −0.146162 0.461493i
\(259\) −6.52803 + 19.8959i −0.405632 + 1.23627i
\(260\) 0.808598i 0.0501471i
\(261\) −7.66425 1.33106i −0.474405 0.0823906i
\(262\) 13.3265i 0.823317i
\(263\) 4.11676 0.253850 0.126925 0.991912i \(-0.459489\pi\)
0.126925 + 0.991912i \(0.459489\pi\)
\(264\) 2.43153 4.68565i 0.149650 0.288382i
\(265\) −8.80868 8.80868i −0.541113 0.541113i
\(266\) 14.1519i 0.867709i
\(267\) −21.5454 11.1806i −1.31856 0.684239i
\(268\) −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
\(273\) 4.27935 + 2.22069i 0.258998 + 0.134402i
\(274\) 10.2807 10.2807i 0.621083 0.621083i
\(275\) 3.04782i 0.183790i
\(276\) −4.46033 2.31460i −0.268480 0.139323i
\(277\) −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
\(279\) −4.60150 + 26.4954i −0.275484 + 1.58624i
\(280\) 3.44243i 0.205724i
\(281\) −11.4729 + 11.4729i −0.684416 + 0.684416i −0.960992 0.276576i \(-0.910800\pi\)
0.276576 + 0.960992i \(0.410800\pi\)
\(282\) −6.30437 + 12.1488i −0.375420 + 0.723448i
\(283\) −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
\(288\) 2.95576 + 0.513330i 0.174170 + 0.0302483i
\(289\) 12.0068i 0.706285i
\(290\) 1.83352 + 1.83352i 0.107668 + 0.107668i
\(291\) 5.22567 + 2.71176i 0.306334 + 0.158966i
\(292\) 4.40734 0.257920
\(293\) 8.29342i 0.484507i 0.970213 + 0.242253i \(0.0778865\pi\)
−0.970213 + 0.242253i \(0.922113\pi\)
\(294\) −7.45673 3.86953i −0.434885 0.225675i
\(295\) 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
\(309\) −0.558411 + 1.07608i −0.0317669 + 0.0612160i
\(310\) 6.33851 6.33851i 0.360003 0.360003i
\(311\) 5.36146 + 5.36146i 0.304020 + 0.304020i 0.842585 0.538564i \(-0.181033\pi\)
−0.538564 + 0.842585i \(0.681033\pi\)
\(312\) 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
\(315\) 1.76710 10.1750i 0.0995648 0.573295i
\(316\) 8.20854 8.20854i 0.461766 0.461766i
\(317\) 19.4530 1.09259 0.546296 0.837592i \(-0.316037\pi\)
0.546296 + 0.837592i \(0.316037\pi\)
\(318\) −9.93838 + 19.1516i −0.557316 + 1.07397i
\(319\) −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
\(327\) −6.93064 3.59652i −0.383265 0.198888i
\(328\) −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
\(333\) 5.32994 + 17.4526i 0.292079 + 0.956394i
\(334\) 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
\(339\) −4.88961 2.53737i −0.265567 0.137811i
\(340\) −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 \(-0.149847\pi\)
−0.453563 + 0.891224i \(0.649847\pi\)
\(348\) 2.06867 3.98641i 0.110892 0.213694i
\(349\) −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
\(351\) 4.16350 0.564515i 0.222231 0.0301316i
\(352\) 2.15513 + 2.15513i 0.114869 + 0.114869i
\(353\) −0.400840 0.400840i −0.0213345 0.0213345i 0.696359 0.717694i \(-0.254802\pi\)
−0.717694 + 0.696359i \(0.754802\pi\)
\(354\) −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
\(357\) −6.13680 + 11.8259i −0.324794 + 0.625891i
\(358\) 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
\(372\) −13.7811 7.15142i −0.714515 0.370784i
\(373\) 32.8415i 1.70047i 0.526405 + 0.850234i \(0.323540\pi\)
−0.526405 + 0.850234i \(0.676460\pi\)
\(374\) 6.81047 0.352161
\(375\) −1.53738 0.797792i −0.0793898 0.0411978i
\(376\) −5.58775 5.58775i −0.288166 0.288166i
\(377\) 2.09669i 0.107985i
\(378\) −17.7252 + 2.40330i −0.911685 + 0.123612i
\(379\) 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 \(-0.709127\pi\)
0.791832 + 0.610739i \(0.209127\pi\)
\(384\) −0.797792 + 1.53738i −0.0407122 + 0.0784539i
\(385\) 7.41889 7.41889i 0.378102 0.378102i
\(386\) 7.95118i 0.404705i
\(387\) 13.2691 + 2.30445i 0.674504 + 0.117142i
\(388\) −2.40351 + 2.40351i −0.122020 + 0.122020i
\(389\) −18.3139 + 18.3139i −0.928551 + 0.928551i −0.997612 0.0690616i \(-0.978000\pi\)
0.0690616 + 0.997612i \(0.478000\pi\)
\(390\) −1.24312 0.645093i −0.0629479 0.0326656i
\(391\) 6.48298i 0.327858i
\(392\) 3.42968 3.42968i 0.173225 0.173225i
\(393\) 20.4879 + 10.6318i 1.03348 + 0.536304i
\(394\) 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
\(399\) 21.7568 + 11.2903i 1.08920 + 0.565221i
\(400\) 1.00000i 0.0500000i
\(401\) −21.7682 21.7682i −1.08705 1.08705i −0.995831 0.0912209i \(-0.970923\pi\)
−0.0912209 0.995831i \(-0.529077\pi\)
\(402\) 7.55440 14.5576i 0.376779 0.726069i
\(403\) −7.24829 −0.361063
\(404\) 2.17467i 0.108194i
\(405\) −3.84555 8.13706i −0.191087 0.404334i
\(406\) 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 \(-0.656146\pi\)
0.471109 0.882075i \(-0.343854\pi\)
\(420\) 5.29231 + 2.74634i 0.258238 + 0.134008i
\(421\) 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
\(426\) 9.45844 18.2268i 0.458263 0.883091i
\(427\) 6.89637 6.89637i 0.333739 0.333739i
\(428\) −0.470042 −0.0227203
\(429\) 3.78881 + 1.96613i 0.182925 + 0.0949256i
\(430\) −3.17436 3.17436i −0.153081 0.153081i
\(431\) −18.1679 18.1679i −0.875118 0.875118i 0.117906 0.993025i \(-0.462382\pi\)
−0.993025 + 0.117906i \(0.962382\pi\)
\(432\) −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
\(438\) −3.51614 + 6.77575i −0.168008 + 0.323758i
\(439\) 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 \(-0.445219\pi\)
0.171251 + 0.985227i \(0.445219\pi\)
\(444\) −10.5351 0.108737i −0.499973 0.00516042i
\(445\) −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 \(-0.726282\pi\)
0.757784 + 0.652506i \(0.226282\pi\)
\(450\) −0.513330 + 2.95576i −0.0241986 + 0.139336i
\(451\) −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
\(459\) 1.56002 + 11.5057i 0.0728155 + 0.537041i
\(460\) −2.90126 −0.135272
\(461\) −5.71858 + 5.71858i −0.266341 + 0.266341i −0.827624 0.561283i \(-0.810308\pi\)
0.561283 + 0.827624i \(0.310308\pi\)
\(462\) −16.1300 8.37035i −0.750435 0.389424i
\(463\) −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 −0.760430 0.649420i \(-0.775012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(468\) −0.415078 + 2.39002i −0.0191870 + 0.110479i
\(469\) 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 \(-0.623863\pi\)
0.925240 + 0.379381i \(0.123863\pi\)
\(480\) 1.65121 0.522966i 0.0753673 0.0238700i
\(481\) −4.38885 + 2.22032i −0.200114 + 0.101238i
\(482\) 26.3003i 1.19794i
\(483\) −7.96785 + 15.3544i −0.362550 + 0.698648i
\(484\) 1.71079i 0.0777632i
\(485\) 3.39908 0.154344
\(486\) −11.4249 + 10.6052i −0.518246 + 0.481063i
\(487\) −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
\(489\) 5.37336 10.3547i 0.242992 0.468255i
\(490\) −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
\(495\) 1.56454 9.00861i 0.0703208 0.404907i
\(496\) 6.33851 6.33851i 0.284608 0.284608i
\(497\) 40.8126i 1.83070i
\(498\) −8.64815 + 16.6653i −0.387533 + 0.746791i
\(499\) 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
\(501\) −8.36896 + 16.1273i −0.373898 + 0.720516i
\(502\) 21.3343i 0.952195i
\(503\) 29.5224 29.5224i 1.31634 1.31634i 0.399686 0.916652i \(-0.369119\pi\)
0.916652 0.399686i \(-0.130881\pi\)
\(504\) 1.76710 10.1750i 0.0787129 0.453229i
\(505\) −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 \(-0.577579\pi\)
−0.241316 + 0.970447i \(0.577579\pi\)
\(510\) 1.78270 3.43533i 0.0789391 0.152119i
\(511\) 15.1720i 0.671168i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 21.1678 2.87007i 0.934583 0.126717i
\(514\) −3.12108 −0.137665
\(515\) 0.699945i 0.0308433i
\(516\) −3.58147 + 6.90163i −0.157665 + 0.303827i
\(517\) 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 \(-0.476652\pi\)
0.0732831 + 0.997311i \(0.476652\pi\)
\(522\) 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
\(531\) 1.45690 8.38881i 0.0632239 0.364043i
\(532\) −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
\(537\) −15.1308 7.85185i −0.652944 0.338833i
\(538\) 3.67429 3.67429i 0.158410 0.158410i
\(539\) 14.7828 0.636741
\(540\) 5.14904 0.698141i 0.221579 0.0300432i
\(541\) 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
\(549\) 1.45435 8.37412i 0.0620700 0.357399i
\(550\) −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
\(555\) 7.37255 + 7.52632i 0.312947 + 0.319475i
\(556\) 16.7132 0.708799
\(557\) 30.2213 + 30.2213i 1.28052 + 1.28052i 0.940374 + 0.340143i \(0.110475\pi\)
0.340143 + 0.940374i \(0.389525\pi\)
\(558\) 21.9889 15.4814i 0.930862 0.655378i
\(559\) 3.62998i 0.153532i
\(560\) −2.43416 + 2.43416i −0.102862 + 0.102862i
\(561\) −5.43334 + 10.4703i −0.229396 + 0.442055i
\(562\) 16.2251 0.684416
\(563\) 10.7209 10.7209i 0.451833 0.451833i −0.444129 0.895963i \(-0.646487\pi\)
0.895963 + 0.444129i \(0.146487\pi\)
\(564\) 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 \(0.105761\pi\)
0.326179 + 0.945308i \(0.394239\pi\)
\(570\) −6.32020 3.27974i −0.264724 0.137373i
\(571\) 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
\(573\) −1.97718 + 3.81010i −0.0825978 + 0.159169i
\(574\) 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
\(579\) 12.2240 + 6.34339i 0.508011 + 0.263622i
\(580\) 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 \(-0.314006\pi\)
−0.834088 + 0.551631i \(0.814006\pi\)
\(588\) 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 \(0.821881\pi\)
\(594\) −15.6933 + 2.12781i −0.643906 + 0.0873050i
\(595\) 7.69223i 0.315351i
\(596\) 11.2348 0.460194
\(597\) 2.10978 4.06564i 0.0863477 0.166395i
\(598\) 1.65884 + 1.65884i 0.0678351 + 0.0678351i
\(599\) 28.9337i 1.18220i −0.806598 0.591100i \(-0.798694\pi\)
0.806598 0.591100i \(-0.201306\pi\)
\(600\) −1.53738 0.797792i −0.0627632 0.0325697i
\(601\) −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
\(606\) 3.34328 + 1.73493i 0.135811 + 0.0704767i
\(607\) −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
\(609\) −13.7229 7.12124i −0.556080 0.288567i
\(610\) −2.00335 + 2.00335i −0.0811131 + 0.0811131i
\(611\) 4.51824 4.51824i 0.182789 0.182789i
\(612\) −6.60475 1.14706i −0.266981 0.0463670i
\(613\) 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
\(615\) −6.38895 + 12.3118i −0.257627 + 0.496458i
\(616\) 7.41889 7.41889i 0.298916 0.298916i
\(617\) 25.4539 1.02474 0.512369 0.858766i \(-0.328768\pi\)
0.512369 + 0.858766i \(0.328768\pi\)
\(618\) 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
\(621\) 2.02549 + 14.9387i 0.0812800 + 0.599470i
\(622\) 7.58225i 0.304020i
\(623\) −34.1133 34.1133i −1.36672 1.36672i
\(624\) −1.24312 0.645093i −0.0497647 0.0258244i
\(625\) −1.00000 −0.0400000
\(626\) 23.2502i 0.929266i
\(627\) 19.2628 + 9.99607i 0.769283 + 0.399205i
\(628\) 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 \(0.0353980\pi\)
−0.993823 + 0.110977i \(0.964602\pi\)
\(642\) 0.374995 0.722631i 0.0147999 0.0285200i
\(643\) 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 \(-0.991046\pi\)
−0.0281258 0.999604i \(-0.508954\pi\)
\(648\) −3.84555 8.13706i −0.151067 0.319654i
\(649\) 6.11654 6.11654i 0.240095 0.240095i
\(650\) −0.808598 −0.0317158
\(651\) −24.6182 + 47.4403i −0.964864 + 1.85933i
\(652\) 4.76257 + 4.76257i 0.186517 + 0.186517i
\(653\) −21.1720 21.1720i −0.828525 0.828525i 0.158788 0.987313i \(-0.449242\pi\)
−0.987313 + 0.158788i \(0.949242\pi\)
\(654\) 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 \(-0.311347\pi\)
0.558578 + 0.829452i \(0.311347\pi\)
\(660\) 4.68565 + 2.43153i 0.182389 + 0.0946471i
\(661\) −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
\(666\) 8.57198 16.1097i 0.332158 0.624237i
\(667\) 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
\(672\) 5.29231 + 2.74634i 0.204155 + 0.105942i
\(673\) −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 \(-0.527809\pi\)
−0.0872533 + 0.996186i \(0.527809\pi\)
\(678\) 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
\(681\) −7.88800 + 15.2005i −0.302269 + 0.582484i
\(682\) 27.3207 1.04616
\(683\) −17.4943 + 17.4943i −0.669399 + 0.669399i −0.957577 0.288178i \(-0.906951\pi\)
0.288178 + 0.957577i \(0.406951\pi\)
\(684\) −2.11031 + 12.1512i −0.0806899 + 0.464612i
\(685\) 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
\(690\) 2.31460 4.46033i 0.0881154 0.169802i
\(691\) 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 −0.930714 0.365747i \(-0.880814\pi\)
0.365747 + 0.930714i \(0.380814\pi\)
\(702\) −3.34322 2.54487i −0.126182 0.0960499i
\(703\) −22.3135 + 11.2884i −0.841569 + 0.425750i
\(704\) 3.04782i 0.114869i
\(705\) −12.1488 6.30437i −0.457549 0.237436i
\(706\) 0.566873i 0.0213345i
\(707\) −7.48612 −0.281545
\(708\) 4.36327 + 2.26423i 0.163982 + 0.0850951i
\(709\) −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
\(711\) −34.3123 5.95906i −1.28681 0.223482i
\(712\) −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
\(717\) −5.55721 + 10.7090i −0.207538 + 0.399934i
\(718\) 24.9933 24.9933i 0.932741 0.932741i
\(719\) 12.6121i 0.470351i −0.971953 0.235175i \(-0.924434\pi\)
0.971953 0.235175i \(-0.0755665\pi\)
\(720\) −0.513330 + 2.95576i −0.0191307 + 0.110155i
\(721\) −1.70378 + 1.70378i −0.0634521 + 0.0634521i
\(722\) −1.48455 + 1.48455i −0.0552491 + 0.0552491i
\(723\) 40.4334 + 20.9821i 1.50374 + 0.780334i
\(724\) 0.826713i 0.0307246i
\(725\) −1.83352 + 1.83352i −0.0680953 + 0.0680953i
\(726\) 2.63013 + 1.36486i 0.0976133 + 0.0506545i
\(727\) −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
\(732\) 4.35563 + 2.26027i 0.160989 + 0.0835420i
\(733\) 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
\(735\) 3.86953 7.45673i 0.142730 0.275046i
\(736\) −2.90126 −0.106942
\(737\) 28.8602i 1.06308i
\(738\) 23.6706 + 4.11090i 0.871325 + 0.151324i
\(739\) 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 \(-0.237176\pi\)
0.735014 + 0.678052i \(0.237176\pi\)
\(744\) 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
\(753\) 32.7988 + 17.0203i 1.19526 + 0.620255i
\(754\) −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
\(759\) −7.05449 + 13.5943i −0.256062 + 0.493442i
\(760\) 2.90693 2.90693i 0.105446 0.105446i
\(761\) 10.9188 0.395805 0.197902 0.980222i \(-0.436587\pi\)
0.197902 + 0.980222i \(0.436587\pi\)
\(762\) 5.91678 + 3.07040i 0.214342 + 0.111229i
\(763\) −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
\(771\) 2.48997 4.79827i 0.0896741 0.172806i
\(772\) −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
\(777\) −0.374319 + 36.2663i −0.0134286 + 1.30105i
\(778\) 25.8997 0.928551
\(779\) −23.2796 23.2796i −0.834078 0.834078i