Properties

Label 403.2.h.b.118.16
Level 403
Weight 2
Character 403.118
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 118.16
Character \(\chi\) \(=\) 403.118
Dual form 403.2.h.b.222.16

$q$-expansion

\(f(q)\) \(=\) \(q+2.53634 q^{2} +(-1.60552 - 2.78084i) q^{3} +4.43304 q^{4} +(1.34893 - 2.33641i) q^{5} +(-4.07215 - 7.05318i) q^{6} +(0.661783 + 1.14624i) q^{7} +6.17102 q^{8} +(-3.65540 + 6.33133i) q^{9} +O(q^{10})\) \(q+2.53634 q^{2} +(-1.60552 - 2.78084i) q^{3} +4.43304 q^{4} +(1.34893 - 2.33641i) q^{5} +(-4.07215 - 7.05318i) q^{6} +(0.661783 + 1.14624i) q^{7} +6.17102 q^{8} +(-3.65540 + 6.33133i) q^{9} +(3.42134 - 5.92593i) q^{10} +(-1.96273 + 3.39955i) q^{11} +(-7.11734 - 12.3276i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.67851 + 2.90726i) q^{14} -8.66291 q^{15} +6.78575 q^{16} +(-1.50918 - 2.61398i) q^{17} +(-9.27134 + 16.0584i) q^{18} +(2.04270 + 3.53806i) q^{19} +(5.97984 - 10.3574i) q^{20} +(2.12501 - 3.68063i) q^{21} +(-4.97816 + 8.62242i) q^{22} +6.92691 q^{23} +(-9.90771 - 17.1607i) q^{24} +(-1.13920 - 1.97315i) q^{25} +(-1.26817 + 2.19654i) q^{26} +13.8421 q^{27} +(2.93371 + 5.08134i) q^{28} -3.54948 q^{29} -21.9721 q^{30} +(-3.54638 - 4.29223i) q^{31} +4.86896 q^{32} +12.6048 q^{33} +(-3.82780 - 6.62994i) q^{34} +3.57078 q^{35} +(-16.2045 + 28.0670i) q^{36} +(-5.25632 - 9.10421i) q^{37} +(5.18099 + 8.97373i) q^{38} +3.21104 q^{39} +(8.32425 - 14.4180i) q^{40} +(-0.201439 + 0.348902i) q^{41} +(5.38977 - 9.33535i) q^{42} +(5.37367 + 9.30747i) q^{43} +(-8.70086 + 15.0703i) q^{44} +(9.86171 + 17.0810i) q^{45} +17.5690 q^{46} +3.91368 q^{47} +(-10.8947 - 18.8701i) q^{48} +(2.62409 - 4.54505i) q^{49} +(-2.88940 - 5.00458i) q^{50} +(-4.84604 + 8.39359i) q^{51} +(-2.21652 + 3.83912i) q^{52} +(-1.53201 + 2.65352i) q^{53} +35.1084 q^{54} +(5.29515 + 9.17147i) q^{55} +(4.08388 + 7.07349i) q^{56} +(6.55919 - 11.3609i) q^{57} -9.00271 q^{58} +(1.36289 + 2.36060i) q^{59} -38.4030 q^{60} -7.35204 q^{61} +(-8.99483 - 10.8866i) q^{62} -9.67632 q^{63} -1.22215 q^{64} +(1.34893 + 2.33641i) q^{65} +31.9702 q^{66} +(-6.80253 + 11.7823i) q^{67} +(-6.69025 - 11.5879i) q^{68} +(-11.1213 - 19.2627i) q^{69} +9.05674 q^{70} +(4.12093 - 7.13765i) q^{71} +(-22.5575 + 39.0708i) q^{72} +(-6.34066 + 10.9823i) q^{73} +(-13.3318 - 23.0914i) q^{74} +(-3.65801 + 6.33586i) q^{75} +(9.05537 + 15.6844i) q^{76} -5.19561 q^{77} +8.14431 q^{78} +(-3.53687 - 6.12604i) q^{79} +(9.15347 - 15.8543i) q^{80} +(-11.2577 - 19.4988i) q^{81} +(-0.510918 + 0.884936i) q^{82} +(1.35607 - 2.34878i) q^{83} +(9.42027 - 16.3164i) q^{84} -8.14308 q^{85} +(13.6295 + 23.6069i) q^{86} +(5.69877 + 9.87056i) q^{87} +(-12.1121 + 20.9787i) q^{88} +11.8364 q^{89} +(25.0127 + 43.3233i) q^{90} -1.32357 q^{91} +30.7073 q^{92} +(-6.24223 + 16.7532i) q^{93} +9.92643 q^{94} +11.0218 q^{95} +(-7.81722 - 13.5398i) q^{96} -1.84763 q^{97} +(6.65558 - 11.5278i) q^{98} +(-14.3491 - 24.8534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.53634 1.79347 0.896733 0.442572i \(-0.145934\pi\)
0.896733 + 0.442572i \(0.145934\pi\)
\(3\) −1.60552 2.78084i −0.926948 1.60552i −0.788398 0.615166i \(-0.789089\pi\)
−0.138550 0.990355i \(-0.544244\pi\)
\(4\) 4.43304 2.21652
\(5\) 1.34893 2.33641i 0.603258 1.04487i −0.389067 0.921210i \(-0.627202\pi\)
0.992324 0.123663i \(-0.0394642\pi\)
\(6\) −4.07215 7.05318i −1.66245 2.87945i
\(7\) 0.661783 + 1.14624i 0.250131 + 0.433239i 0.963562 0.267487i \(-0.0861931\pi\)
−0.713431 + 0.700725i \(0.752860\pi\)
\(8\) 6.17102 2.18179
\(9\) −3.65540 + 6.33133i −1.21847 + 2.11044i
\(10\) 3.42134 5.92593i 1.08192 1.87394i
\(11\) −1.96273 + 3.39955i −0.591786 + 1.02500i 0.402206 + 0.915549i \(0.368243\pi\)
−0.993992 + 0.109454i \(0.965090\pi\)
\(12\) −7.11734 12.3276i −2.05460 3.55867i
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) 1.67851 + 2.90726i 0.448601 + 0.776999i
\(15\) −8.66291 −2.23675
\(16\) 6.78575 1.69644
\(17\) −1.50918 2.61398i −0.366030 0.633983i 0.622911 0.782293i \(-0.285950\pi\)
−0.988941 + 0.148310i \(0.952617\pi\)
\(18\) −9.27134 + 16.0584i −2.18528 + 3.78501i
\(19\) 2.04270 + 3.53806i 0.468627 + 0.811686i 0.999357 0.0358547i \(-0.0114154\pi\)
−0.530730 + 0.847541i \(0.678082\pi\)
\(20\) 5.97984 10.3574i 1.33713 2.31598i
\(21\) 2.12501 3.68063i 0.463716 0.803180i
\(22\) −4.97816 + 8.62242i −1.06135 + 1.83831i
\(23\) 6.92691 1.44436 0.722180 0.691705i \(-0.243140\pi\)
0.722180 + 0.691705i \(0.243140\pi\)
\(24\) −9.90771 17.1607i −2.02240 3.50290i
\(25\) −1.13920 1.97315i −0.227839 0.394630i
\(26\) −1.26817 + 2.19654i −0.248709 + 0.430777i
\(27\) 13.8421 2.66392
\(28\) 2.93371 + 5.08134i 0.554419 + 0.960282i
\(29\) −3.54948 −0.659123 −0.329561 0.944134i \(-0.606901\pi\)
−0.329561 + 0.944134i \(0.606901\pi\)
\(30\) −21.9721 −4.01154
\(31\) −3.54638 4.29223i −0.636948 0.770907i
\(32\) 4.86896 0.860719
\(33\) 12.6048 2.19422
\(34\) −3.82780 6.62994i −0.656462 1.13703i
\(35\) 3.57078 0.603573
\(36\) −16.2045 + 28.0670i −2.70075 + 4.67784i
\(37\) −5.25632 9.10421i −0.864133 1.49672i −0.867905 0.496729i \(-0.834534\pi\)
0.00377244 0.999993i \(-0.498799\pi\)
\(38\) 5.18099 + 8.97373i 0.840467 + 1.45573i
\(39\) 3.21104 0.514178
\(40\) 8.32425 14.4180i 1.31618 2.27969i
\(41\) −0.201439 + 0.348902i −0.0314595 + 0.0544894i −0.881326 0.472508i \(-0.843349\pi\)
0.849867 + 0.526997i \(0.176682\pi\)
\(42\) 5.38977 9.33535i 0.831659 1.44048i
\(43\) 5.37367 + 9.30747i 0.819477 + 1.41938i 0.906068 + 0.423131i \(0.139069\pi\)
−0.0865916 + 0.996244i \(0.527598\pi\)
\(44\) −8.70086 + 15.0703i −1.31170 + 2.27194i
\(45\) 9.86171 + 17.0810i 1.47010 + 2.54628i
\(46\) 17.5690 2.59041
\(47\) 3.91368 0.570869 0.285434 0.958398i \(-0.407862\pi\)
0.285434 + 0.958398i \(0.407862\pi\)
\(48\) −10.8947 18.8701i −1.57251 2.72367i
\(49\) 2.62409 4.54505i 0.374869 0.649293i
\(50\) −2.88940 5.00458i −0.408622 0.707755i
\(51\) −4.84604 + 8.39359i −0.678582 + 1.17534i
\(52\) −2.21652 + 3.83912i −0.307376 + 0.532391i
\(53\) −1.53201 + 2.65352i −0.210438 + 0.364489i −0.951852 0.306559i \(-0.900822\pi\)
0.741414 + 0.671048i \(0.234156\pi\)
\(54\) 35.1084 4.77765
\(55\) 5.29515 + 9.17147i 0.713998 + 1.23668i
\(56\) 4.08388 + 7.07349i 0.545731 + 0.945234i
\(57\) 6.55919 11.3609i 0.868787 1.50478i
\(58\) −9.00271 −1.18211
\(59\) 1.36289 + 2.36060i 0.177434 + 0.307324i 0.941001 0.338404i \(-0.109887\pi\)
−0.763567 + 0.645728i \(0.776554\pi\)
\(60\) −38.4030 −4.95781
\(61\) −7.35204 −0.941332 −0.470666 0.882312i \(-0.655986\pi\)
−0.470666 + 0.882312i \(0.655986\pi\)
\(62\) −8.99483 10.8866i −1.14234 1.38259i
\(63\) −9.67632 −1.21910
\(64\) −1.22215 −0.152769
\(65\) 1.34893 + 2.33641i 0.167314 + 0.289796i
\(66\) 31.9702 3.93525
\(67\) −6.80253 + 11.7823i −0.831061 + 1.43944i 0.0661359 + 0.997811i \(0.478933\pi\)
−0.897197 + 0.441630i \(0.854400\pi\)
\(68\) −6.69025 11.5879i −0.811313 1.40523i
\(69\) −11.1213 19.2627i −1.33885 2.31895i
\(70\) 9.05674 1.08249
\(71\) 4.12093 7.13765i 0.489064 0.847084i −0.510857 0.859666i \(-0.670672\pi\)
0.999921 + 0.0125822i \(0.00400515\pi\)
\(72\) −22.5575 + 39.0708i −2.65843 + 4.60454i
\(73\) −6.34066 + 10.9823i −0.742118 + 1.28539i 0.209412 + 0.977828i \(0.432845\pi\)
−0.951529 + 0.307558i \(0.900488\pi\)
\(74\) −13.3318 23.0914i −1.54979 2.68432i
\(75\) −3.65801 + 6.33586i −0.422391 + 0.731602i
\(76\) 9.05537 + 15.6844i 1.03872 + 1.79912i
\(77\) −5.19561 −0.592095
\(78\) 8.14431 0.922161
\(79\) −3.53687 6.12604i −0.397929 0.689234i 0.595541 0.803325i \(-0.296938\pi\)
−0.993470 + 0.114091i \(0.963604\pi\)
\(80\) 9.15347 15.8543i 1.02339 1.77256i
\(81\) −11.2577 19.4988i −1.25085 2.16654i
\(82\) −0.510918 + 0.884936i −0.0564215 + 0.0977248i
\(83\) 1.35607 2.34878i 0.148848 0.257812i −0.781954 0.623336i \(-0.785777\pi\)
0.930802 + 0.365524i \(0.119110\pi\)
\(84\) 9.42027 16.3164i 1.02784 1.78026i
\(85\) −8.14308 −0.883242
\(86\) 13.6295 + 23.6069i 1.46970 + 2.54560i
\(87\) 5.69877 + 9.87056i 0.610973 + 1.05824i
\(88\) −12.1121 + 20.9787i −1.29115 + 2.23634i
\(89\) 11.8364 1.25465 0.627326 0.778757i \(-0.284149\pi\)
0.627326 + 0.778757i \(0.284149\pi\)
\(90\) 25.0127 + 43.3233i 2.63657 + 4.56667i
\(91\) −1.32357 −0.138747
\(92\) 30.7073 3.20145
\(93\) −6.24223 + 16.7532i −0.647289 + 1.73722i
\(94\) 9.92643 1.02383
\(95\) 11.0218 1.13081
\(96\) −7.81722 13.5398i −0.797842 1.38190i
\(97\) −1.84763 −0.187598 −0.0937991 0.995591i \(-0.529901\pi\)
−0.0937991 + 0.995591i \(0.529901\pi\)
\(98\) 6.65558 11.5278i 0.672315 1.16448i
\(99\) −14.3491 24.8534i −1.44214 2.49786i
\(100\) −5.05011 8.74704i −0.505011 0.874704i
\(101\) −18.2796 −1.81889 −0.909447 0.415821i \(-0.863494\pi\)
−0.909447 + 0.415821i \(0.863494\pi\)
\(102\) −12.2912 + 21.2890i −1.21701 + 2.10793i
\(103\) 5.41258 9.37486i 0.533317 0.923733i −0.465925 0.884824i \(-0.654279\pi\)
0.999243 0.0389087i \(-0.0123882\pi\)
\(104\) −3.08551 + 5.34426i −0.302559 + 0.524048i
\(105\) −5.73297 9.92980i −0.559481 0.969049i
\(106\) −3.88570 + 6.73024i −0.377413 + 0.653699i
\(107\) 0.390921 + 0.677094i 0.0377917 + 0.0654572i 0.884303 0.466914i \(-0.154634\pi\)
−0.846511 + 0.532371i \(0.821301\pi\)
\(108\) 61.3628 5.90463
\(109\) 4.95286 0.474398 0.237199 0.971461i \(-0.423771\pi\)
0.237199 + 0.971461i \(0.423771\pi\)
\(110\) 13.4303 + 23.2620i 1.28053 + 2.21795i
\(111\) −16.8783 + 29.2340i −1.60201 + 2.77477i
\(112\) 4.49070 + 7.77812i 0.424331 + 0.734963i
\(113\) −3.22750 + 5.59020i −0.303618 + 0.525882i −0.976953 0.213456i \(-0.931528\pi\)
0.673335 + 0.739338i \(0.264861\pi\)
\(114\) 16.6364 28.8150i 1.55814 2.69878i
\(115\) 9.34388 16.1841i 0.871321 1.50917i
\(116\) −15.7350 −1.46096
\(117\) −3.65540 6.33133i −0.337942 0.585332i
\(118\) 3.45677 + 5.98730i 0.318221 + 0.551175i
\(119\) 1.99750 3.45977i 0.183111 0.317157i
\(120\) −53.4590 −4.88012
\(121\) −2.20462 3.81852i −0.200420 0.347138i
\(122\) −18.6473 −1.68825
\(123\) 1.29366 0.116645
\(124\) −15.7212 19.0276i −1.41181 1.70873i
\(125\) 7.34248 0.656732
\(126\) −24.5425 −2.18642
\(127\) 2.27972 + 3.94860i 0.202293 + 0.350381i 0.949267 0.314472i \(-0.101827\pi\)
−0.746974 + 0.664853i \(0.768494\pi\)
\(128\) −12.8377 −1.13470
\(129\) 17.2551 29.8867i 1.51922 2.63137i
\(130\) 3.42134 + 5.92593i 0.300071 + 0.519738i
\(131\) −5.74729 9.95459i −0.502143 0.869737i −0.999997 0.00247595i \(-0.999212\pi\)
0.497854 0.867261i \(-0.334121\pi\)
\(132\) 55.8777 4.86353
\(133\) −2.70365 + 4.68286i −0.234436 + 0.406055i
\(134\) −17.2536 + 29.8840i −1.49048 + 2.58159i
\(135\) 18.6720 32.3409i 1.60703 2.78346i
\(136\) −9.31319 16.1309i −0.798599 1.38321i
\(137\) 9.17049 15.8838i 0.783488 1.35704i −0.146410 0.989224i \(-0.546772\pi\)
0.929898 0.367817i \(-0.119895\pi\)
\(138\) −28.2074 48.8567i −2.40118 4.15896i
\(139\) −2.30725 −0.195698 −0.0978492 0.995201i \(-0.531196\pi\)
−0.0978492 + 0.995201i \(0.531196\pi\)
\(140\) 15.8294 1.33783
\(141\) −6.28349 10.8833i −0.529166 0.916542i
\(142\) 10.4521 18.1035i 0.877119 1.51922i
\(143\) −1.96273 3.39955i −0.164132 0.284285i
\(144\) −24.8046 + 42.9629i −2.06705 + 3.58024i
\(145\) −4.78799 + 8.29304i −0.397621 + 0.688699i
\(146\) −16.0821 + 27.8550i −1.33096 + 2.30529i
\(147\) −16.8521 −1.38994
\(148\) −23.3015 40.3593i −1.91537 3.31751i
\(149\) −2.51736 4.36020i −0.206230 0.357201i 0.744294 0.667852i \(-0.232786\pi\)
−0.950524 + 0.310651i \(0.899453\pi\)
\(150\) −9.27797 + 16.0699i −0.757543 + 1.31210i
\(151\) −3.64011 −0.296228 −0.148114 0.988970i \(-0.547320\pi\)
−0.148114 + 0.988970i \(0.547320\pi\)
\(152\) 12.6055 + 21.8334i 1.02244 + 1.77093i
\(153\) 22.0666 1.78398
\(154\) −13.1779 −1.06190
\(155\) −14.8122 + 2.49588i −1.18974 + 0.200474i
\(156\) 14.2347 1.13969
\(157\) −13.0806 −1.04395 −0.521973 0.852962i \(-0.674804\pi\)
−0.521973 + 0.852962i \(0.674804\pi\)
\(158\) −8.97073 15.5378i −0.713673 1.23612i
\(159\) 9.83870 0.780260
\(160\) 6.56786 11.3759i 0.519235 0.899342i
\(161\) 4.58411 + 7.93992i 0.361279 + 0.625753i
\(162\) −28.5533 49.4558i −2.24336 3.88561i
\(163\) 8.52547 0.667766 0.333883 0.942615i \(-0.391641\pi\)
0.333883 + 0.942615i \(0.391641\pi\)
\(164\) −0.892986 + 1.54670i −0.0697305 + 0.120777i
\(165\) 17.0030 29.4500i 1.32368 2.29268i
\(166\) 3.43945 5.95730i 0.266953 0.462376i
\(167\) 7.58167 + 13.1318i 0.586687 + 1.01617i 0.994663 + 0.103179i \(0.0329015\pi\)
−0.407976 + 0.912993i \(0.633765\pi\)
\(168\) 13.1135 22.7133i 1.01173 1.75237i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) −20.6537 −1.58406
\(171\) −29.8675 −2.28403
\(172\) 23.8217 + 41.2604i 1.81639 + 3.14607i
\(173\) 4.68020 8.10634i 0.355829 0.616314i −0.631430 0.775432i \(-0.717532\pi\)
0.987259 + 0.159119i \(0.0508652\pi\)
\(174\) 14.4540 + 25.0351i 1.09576 + 1.89791i
\(175\) 1.50780 2.61159i 0.113979 0.197418i
\(176\) −13.3186 + 23.0685i −1.00393 + 1.73885i
\(177\) 4.37631 7.57999i 0.328944 0.569747i
\(178\) 30.0211 2.25017
\(179\) 4.96407 + 8.59803i 0.371032 + 0.642647i 0.989725 0.142987i \(-0.0456706\pi\)
−0.618692 + 0.785633i \(0.712337\pi\)
\(180\) 43.7174 + 75.7207i 3.25850 + 5.64389i
\(181\) −5.86310 + 10.1552i −0.435801 + 0.754829i −0.997361 0.0726068i \(-0.976868\pi\)
0.561560 + 0.827436i \(0.310202\pi\)
\(182\) −3.35702 −0.248839
\(183\) 11.8038 + 20.4449i 0.872566 + 1.51133i
\(184\) 42.7461 3.15128
\(185\) −28.3615 −2.08518
\(186\) −15.8324 + 42.4918i −1.16089 + 3.11565i
\(187\) 11.8485 0.866445
\(188\) 17.3495 1.26534
\(189\) 9.16050 + 15.8664i 0.666328 + 1.15411i
\(190\) 27.9551 2.02807
\(191\) −5.80338 + 10.0518i −0.419918 + 0.727320i −0.995931 0.0901212i \(-0.971275\pi\)
0.576013 + 0.817441i \(0.304608\pi\)
\(192\) 1.96219 + 3.39861i 0.141609 + 0.245274i
\(193\) −6.13269 10.6221i −0.441441 0.764598i 0.556356 0.830944i \(-0.312199\pi\)
−0.997797 + 0.0663461i \(0.978866\pi\)
\(194\) −4.68622 −0.336451
\(195\) 4.33146 7.50230i 0.310182 0.537251i
\(196\) 11.6327 20.1484i 0.830905 1.43917i
\(197\) 3.20203 5.54608i 0.228135 0.395142i −0.729120 0.684386i \(-0.760071\pi\)
0.957255 + 0.289244i \(0.0934039\pi\)
\(198\) −36.3943 63.0368i −2.58643 4.47983i
\(199\) −5.04216 + 8.73328i −0.357430 + 0.619086i −0.987531 0.157427i \(-0.949680\pi\)
0.630101 + 0.776513i \(0.283013\pi\)
\(200\) −7.03001 12.1763i −0.497097 0.860997i
\(201\) 43.6864 3.08140
\(202\) −46.3635 −3.26212
\(203\) −2.34899 4.06857i −0.164867 0.285558i
\(204\) −21.4827 + 37.2091i −1.50409 + 2.60516i
\(205\) 0.543452 + 0.941286i 0.0379563 + 0.0657423i
\(206\) 13.7282 23.7779i 0.956486 1.65668i
\(207\) −25.3206 + 43.8566i −1.75990 + 3.04824i
\(208\) −3.39288 + 5.87664i −0.235254 + 0.407471i
\(209\) −16.0371 −1.10931
\(210\) −14.5408 25.1854i −1.00341 1.73796i
\(211\) −3.48511 6.03639i −0.239925 0.415562i 0.720768 0.693177i \(-0.243789\pi\)
−0.960692 + 0.277615i \(0.910456\pi\)
\(212\) −6.79146 + 11.7632i −0.466439 + 0.807897i
\(213\) −26.4649 −1.81335
\(214\) 0.991509 + 1.71734i 0.0677782 + 0.117395i
\(215\) 28.9947 1.97742
\(216\) 85.4202 5.81211
\(217\) 2.57300 6.90553i 0.174667 0.468778i
\(218\) 12.5621 0.850816
\(219\) 40.7202 2.75162
\(220\) 23.4736 + 40.6575i 1.58259 + 2.74113i
\(221\) 3.01836 0.203037
\(222\) −42.8091 + 74.1475i −2.87316 + 4.97645i
\(223\) −5.49100 9.51068i −0.367704 0.636882i 0.621502 0.783413i \(-0.286523\pi\)
−0.989206 + 0.146530i \(0.953189\pi\)
\(224\) 3.22220 + 5.58101i 0.215292 + 0.372897i
\(225\) 16.6569 1.11046
\(226\) −8.18606 + 14.1787i −0.544528 + 0.943151i
\(227\) −3.85780 + 6.68190i −0.256051 + 0.443493i −0.965180 0.261585i \(-0.915755\pi\)
0.709129 + 0.705078i \(0.249088\pi\)
\(228\) 29.0772 50.3631i 1.92568 3.33538i
\(229\) −1.42695 2.47155i −0.0942955 0.163325i 0.815019 0.579434i \(-0.196727\pi\)
−0.909314 + 0.416110i \(0.863393\pi\)
\(230\) 23.6993 41.0484i 1.56268 2.70665i
\(231\) 8.34166 + 14.4482i 0.548841 + 0.950621i
\(232\) −21.9039 −1.43806
\(233\) 4.73257 0.310041 0.155020 0.987911i \(-0.450456\pi\)
0.155020 + 0.987911i \(0.450456\pi\)
\(234\) −9.27134 16.0584i −0.606087 1.04977i
\(235\) 5.27926 9.14394i 0.344381 0.596485i
\(236\) 6.04176 + 10.4646i 0.393285 + 0.681190i
\(237\) −11.3570 + 19.6710i −0.737720 + 1.27777i
\(238\) 5.06635 8.77517i 0.328403 0.568810i
\(239\) −8.08575 + 14.0049i −0.523024 + 0.905904i 0.476617 + 0.879111i \(0.341863\pi\)
−0.999641 + 0.0267928i \(0.991471\pi\)
\(240\) −58.7844 −3.79452
\(241\) −4.69186 8.12654i −0.302229 0.523477i 0.674411 0.738356i \(-0.264398\pi\)
−0.976641 + 0.214879i \(0.931064\pi\)
\(242\) −5.59168 9.68508i −0.359447 0.622580i
\(243\) −15.3856 + 26.6487i −0.986988 + 1.70951i
\(244\) −32.5919 −2.08648
\(245\) −7.07939 12.2619i −0.452286 0.783382i
\(246\) 3.28116 0.209199
\(247\) −4.08540 −0.259948
\(248\) −21.8848 26.4874i −1.38968 1.68195i
\(249\) −8.70878 −0.551896
\(250\) 18.6231 1.17783
\(251\) 4.30920 + 7.46376i 0.271995 + 0.471108i 0.969372 0.245595i \(-0.0789834\pi\)
−0.697378 + 0.716704i \(0.745650\pi\)
\(252\) −42.8955 −2.70216
\(253\) −13.5957 + 23.5484i −0.854752 + 1.48047i
\(254\) 5.78216 + 10.0150i 0.362805 + 0.628397i
\(255\) 13.0739 + 22.6447i 0.818719 + 1.41806i
\(256\) −30.1166 −1.88229
\(257\) 6.23222 10.7945i 0.388755 0.673344i −0.603527 0.797342i \(-0.706239\pi\)
0.992282 + 0.123999i \(0.0395718\pi\)
\(258\) 43.7648 75.8029i 2.72468 4.71928i
\(259\) 6.95708 12.0500i 0.432292 0.748752i
\(260\) 5.97984 + 10.3574i 0.370854 + 0.642337i
\(261\) 12.9748 22.4730i 0.803118 1.39104i
\(262\) −14.5771 25.2483i −0.900576 1.55984i
\(263\) −25.3680 −1.56426 −0.782128 0.623118i \(-0.785866\pi\)
−0.782128 + 0.623118i \(0.785866\pi\)
\(264\) 77.7846 4.78731
\(265\) 4.13313 + 7.15880i 0.253896 + 0.439762i
\(266\) −6.85738 + 11.8773i −0.420453 + 0.728246i
\(267\) −19.0035 32.9151i −1.16300 2.01437i
\(268\) −30.1559 + 52.2315i −1.84206 + 3.19055i
\(269\) 8.05991 13.9602i 0.491422 0.851167i −0.508530 0.861044i \(-0.669811\pi\)
0.999951 + 0.00987735i \(0.00314411\pi\)
\(270\) 47.3586 82.0276i 2.88215 4.99204i
\(271\) −4.66859 −0.283597 −0.141798 0.989896i \(-0.545288\pi\)
−0.141798 + 0.989896i \(0.545288\pi\)
\(272\) −10.2409 17.7378i −0.620947 1.07551i
\(273\) 2.12501 + 3.68063i 0.128612 + 0.222762i
\(274\) 23.2595 40.2867i 1.40516 2.43381i
\(275\) 8.94375 0.539328
\(276\) −49.3011 85.3921i −2.96758 5.14000i
\(277\) 23.8493 1.43296 0.716482 0.697605i \(-0.245751\pi\)
0.716482 + 0.697605i \(0.245751\pi\)
\(278\) −5.85198 −0.350978
\(279\) 40.1389 6.76350i 2.40306 0.404920i
\(280\) 22.0354 1.31687
\(281\) 19.8631 1.18493 0.592465 0.805596i \(-0.298155\pi\)
0.592465 + 0.805596i \(0.298155\pi\)
\(282\) −15.9371 27.6039i −0.949040 1.64379i
\(283\) −17.2634 −1.02620 −0.513102 0.858328i \(-0.671504\pi\)
−0.513102 + 0.858328i \(0.671504\pi\)
\(284\) 18.2682 31.6415i 1.08402 1.87758i
\(285\) −17.6957 30.6499i −1.04820 1.81554i
\(286\) −4.97816 8.62242i −0.294365 0.509855i
\(287\) −0.533235 −0.0314759
\(288\) −17.7980 + 30.8270i −1.04876 + 1.81650i
\(289\) 3.94475 6.83251i 0.232044 0.401912i
\(290\) −12.1440 + 21.0340i −0.713119 + 1.23516i
\(291\) 2.96640 + 5.13796i 0.173894 + 0.301193i
\(292\) −28.1084 + 48.6851i −1.64492 + 2.84908i
\(293\) −1.05232 1.82267i −0.0614772 0.106482i 0.833649 0.552295i \(-0.186248\pi\)
−0.895126 + 0.445813i \(0.852914\pi\)
\(294\) −42.7427 −2.49281
\(295\) 7.35377 0.428153
\(296\) −32.4368 56.1823i −1.88535 3.26553i
\(297\) −27.1684 + 47.0570i −1.57647 + 2.73053i
\(298\) −6.38490 11.0590i −0.369867 0.640629i
\(299\) −3.46345 + 5.99888i −0.200297 + 0.346924i
\(300\) −16.2161 + 28.0871i −0.936237 + 1.62161i
\(301\) −7.11241 + 12.3191i −0.409952 + 0.710058i
\(302\) −9.23256 −0.531274
\(303\) 29.3484 + 50.8329i 1.68602 + 2.92027i
\(304\) 13.8613 + 24.0084i 0.794998 + 1.37698i
\(305\) −9.91734 + 17.1773i −0.567866 + 0.983572i
\(306\) 55.9685 3.19951
\(307\) 0.445440 + 0.771526i 0.0254226 + 0.0440333i 0.878457 0.477822i \(-0.158574\pi\)
−0.853034 + 0.521855i \(0.825240\pi\)
\(308\) −23.0323 −1.31239
\(309\) −34.7600 −1.97743
\(310\) −37.5688 + 6.33042i −2.13376 + 0.359544i
\(311\) −12.3220 −0.698715 −0.349358 0.936989i \(-0.613600\pi\)
−0.349358 + 0.936989i \(0.613600\pi\)
\(312\) 19.8154 1.12183
\(313\) 9.81751 + 17.0044i 0.554919 + 0.961147i 0.997910 + 0.0646212i \(0.0205839\pi\)
−0.442991 + 0.896526i \(0.646083\pi\)
\(314\) −33.1769 −1.87228
\(315\) −13.0526 + 22.6078i −0.735433 + 1.27381i
\(316\) −15.6791 27.1570i −0.882018 1.52770i
\(317\) 7.26417 + 12.5819i 0.407997 + 0.706671i 0.994665 0.103156i \(-0.0328942\pi\)
−0.586669 + 0.809827i \(0.699561\pi\)
\(318\) 24.9543 1.39937
\(319\) 6.96668 12.0666i 0.390059 0.675603i
\(320\) −1.64859 + 2.85544i −0.0921591 + 0.159624i
\(321\) 1.25526 2.17418i 0.0700619 0.121351i
\(322\) 11.6269 + 20.1384i 0.647941 + 1.12227i
\(323\) 6.16560 10.6791i 0.343063 0.594203i
\(324\) −49.9057 86.4391i −2.77254 4.80217i
\(325\) 2.27839 0.126383
\(326\) 21.6235 1.19762
\(327\) −7.95192 13.7731i −0.439742 0.761655i
\(328\) −1.24308 + 2.15308i −0.0686378 + 0.118884i
\(329\) 2.59001 + 4.48602i 0.142792 + 0.247322i
\(330\) 43.1254 74.6953i 2.37397 4.11184i
\(331\) 5.50182 9.52943i 0.302407 0.523785i −0.674273 0.738482i \(-0.735543\pi\)
0.976681 + 0.214697i \(0.0688764\pi\)
\(332\) 6.01150 10.4122i 0.329924 0.571445i
\(333\) 76.8557 4.21167
\(334\) 19.2297 + 33.3068i 1.05220 + 1.82247i
\(335\) 18.3522 + 31.7870i 1.00269 + 1.73671i
\(336\) 14.4198 24.9759i 0.786666 1.36255i
\(337\) −8.75126 −0.476711 −0.238356 0.971178i \(-0.576608\pi\)
−0.238356 + 0.971178i \(0.576608\pi\)
\(338\) −1.26817 2.19654i −0.0689795 0.119476i
\(339\) 20.7273 1.12575
\(340\) −36.0986 −1.95772
\(341\) 21.5522 3.63160i 1.16712 0.196662i
\(342\) −75.7543 −4.09632
\(343\) 16.2113 0.875326
\(344\) 33.1610 + 57.4366i 1.78792 + 3.09677i
\(345\) −60.0072 −3.23068
\(346\) 11.8706 20.5605i 0.638167 1.10534i
\(347\) 6.26088 + 10.8442i 0.336102 + 0.582145i 0.983696 0.179840i \(-0.0575580\pi\)
−0.647594 + 0.761986i \(0.724225\pi\)
\(348\) 25.2629 + 43.7566i 1.35423 + 2.34560i
\(349\) −21.0030 −1.12427 −0.562134 0.827046i \(-0.690019\pi\)
−0.562134 + 0.827046i \(0.690019\pi\)
\(350\) 3.82431 6.62390i 0.204418 0.354062i
\(351\) −6.92107 + 11.9876i −0.369419 + 0.639853i
\(352\) −9.55646 + 16.5523i −0.509361 + 0.882239i
\(353\) 1.69858 + 2.94203i 0.0904064 + 0.156588i 0.907682 0.419658i \(-0.137850\pi\)
−0.817276 + 0.576247i \(0.804517\pi\)
\(354\) 11.0998 19.2255i 0.589949 1.02182i
\(355\) −11.1176 19.2563i −0.590063 1.02202i
\(356\) 52.4710 2.78096
\(357\) −12.8281 −0.678936
\(358\) 12.5906 + 21.8075i 0.665434 + 1.15256i
\(359\) 9.00334 15.5942i 0.475178 0.823033i −0.524418 0.851461i \(-0.675717\pi\)
0.999596 + 0.0284283i \(0.00905024\pi\)
\(360\) 60.8568 + 105.407i 3.20744 + 5.55544i
\(361\) 1.15476 2.00010i 0.0607767 0.105268i
\(362\) −14.8708 + 25.7571i −0.781594 + 1.35376i
\(363\) −7.07914 + 12.2614i −0.371558 + 0.643558i
\(364\) −5.86742 −0.307536
\(365\) 17.1061 + 29.6287i 0.895376 + 1.55084i
\(366\) 29.9386 + 51.8552i 1.56492 + 2.71052i
\(367\) 15.9948 27.7037i 0.834919 1.44612i −0.0591768 0.998248i \(-0.518848\pi\)
0.894096 0.447875i \(-0.147819\pi\)
\(368\) 47.0043 2.45027
\(369\) −1.47268 2.55075i −0.0766645 0.132787i
\(370\) −71.9345 −3.73970
\(371\) −4.05544 −0.210548
\(372\) −27.6721 + 74.2675i −1.43473 + 3.85059i
\(373\) −15.7687 −0.816472 −0.408236 0.912877i \(-0.633856\pi\)
−0.408236 + 0.912877i \(0.633856\pi\)
\(374\) 30.0518 1.55394
\(375\) −11.7885 20.4183i −0.608756 1.05440i
\(376\) 24.1514 1.24551
\(377\) 1.77474 3.07394i 0.0914039 0.158316i
\(378\) 23.2342 + 40.2428i 1.19504 + 2.06986i
\(379\) −11.2412 19.4704i −0.577423 1.00013i −0.995774 0.0918406i \(-0.970725\pi\)
0.418351 0.908286i \(-0.362608\pi\)
\(380\) 48.8600 2.50647
\(381\) 7.32029 12.6791i 0.375030 0.649571i
\(382\) −14.7194 + 25.4947i −0.753109 + 1.30442i
\(383\) 18.0275 31.2245i 0.921161 1.59550i 0.123539 0.992340i \(-0.460576\pi\)
0.797622 0.603158i \(-0.206091\pi\)
\(384\) 20.6112 + 35.6997i 1.05181 + 1.82179i
\(385\) −7.00849 + 12.1391i −0.357186 + 0.618664i
\(386\) −15.5546 26.9414i −0.791709 1.37128i
\(387\) −78.5716 −3.99402
\(388\) −8.19060 −0.415815
\(389\) 16.6509 + 28.8401i 0.844232 + 1.46225i 0.886286 + 0.463138i \(0.153276\pi\)
−0.0420544 + 0.999115i \(0.513390\pi\)
\(390\) 10.9861 19.0284i 0.556301 0.963541i
\(391\) −10.4540 18.1068i −0.528679 0.915699i
\(392\) 16.1933 28.0476i 0.817885 1.41662i
\(393\) −18.4548 + 31.9646i −0.930920 + 1.61240i
\(394\) 8.12145 14.0668i 0.409153 0.708673i
\(395\) −19.0839 −0.960216
\(396\) −63.6102 110.176i −3.19653 5.53656i
\(397\) −12.2408 21.2016i −0.614346 1.06408i −0.990499 0.137521i \(-0.956087\pi\)
0.376153 0.926558i \(-0.377247\pi\)
\(398\) −12.7887 + 22.1506i −0.641038 + 1.11031i
\(399\) 17.3631 0.869240
\(400\) −7.73031 13.3893i −0.386516 0.669465i
\(401\) 36.1390 1.80469 0.902347 0.431009i \(-0.141842\pi\)
0.902347 + 0.431009i \(0.141842\pi\)
\(402\) 110.804 5.52639
\(403\) 5.49037 0.925138i 0.273495 0.0460844i
\(404\) −81.0344 −4.03161
\(405\) −60.7430 −3.01834
\(406\) −5.95784 10.3193i −0.295683 0.512138i
\(407\) 41.2669 2.04553
\(408\) −29.9050 + 51.7970i −1.48052 + 2.56434i
\(409\) 1.54622 + 2.67814i 0.0764559 + 0.132425i 0.901718 0.432324i \(-0.142306\pi\)
−0.825263 + 0.564749i \(0.808973\pi\)
\(410\) 1.37838 + 2.38742i 0.0680733 + 0.117906i
\(411\) −58.8937 −2.90501
\(412\) 23.9942 41.5591i 1.18211 2.04747i
\(413\) −1.80388 + 3.12441i −0.0887632 + 0.153742i
\(414\) −64.2217 + 111.235i −3.15633 + 5.46692i
\(415\) −3.65846 6.33665i −0.179587 0.311054i
\(416\) −2.43448 + 4.21664i −0.119360 + 0.206738i
\(417\) 3.70434 + 6.41610i 0.181402 + 0.314198i
\(418\) −40.6755 −1.98951
\(419\) 5.40393 0.263999 0.132000 0.991250i \(-0.457860\pi\)
0.132000 + 0.991250i \(0.457860\pi\)
\(420\) −25.4145 44.0192i −1.24010 2.14792i
\(421\) 10.1550 17.5890i 0.494926 0.857237i −0.505057 0.863086i \(-0.668528\pi\)
0.999983 + 0.00584889i \(0.00186177\pi\)
\(422\) −8.83944 15.3104i −0.430297 0.745296i
\(423\) −14.3060 + 24.7788i −0.695584 + 1.20479i
\(424\) −9.45407 + 16.3749i −0.459130 + 0.795237i
\(425\) −3.43851 + 5.95567i −0.166792 + 0.288892i
\(426\) −67.1242 −3.25218
\(427\) −4.86545 8.42721i −0.235456 0.407822i
\(428\) 1.73297 + 3.00159i 0.0837661 + 0.145087i
\(429\) −6.30241 + 10.9161i −0.304283 + 0.527034i
\(430\) 73.5405 3.54644
\(431\) 9.15912 + 15.8641i 0.441180 + 0.764145i 0.997777 0.0666368i \(-0.0212269\pi\)
−0.556598 + 0.830782i \(0.687894\pi\)
\(432\) 93.9294 4.51918
\(433\) 19.3182 0.928372 0.464186 0.885738i \(-0.346347\pi\)
0.464186 + 0.885738i \(0.346347\pi\)
\(434\) 6.52601 17.5148i 0.313259 0.840737i
\(435\) 30.7489 1.47430
\(436\) 21.9562 1.05151
\(437\) 14.1496 + 24.5078i 0.676867 + 1.17237i
\(438\) 103.281 4.93493
\(439\) 8.33676 14.4397i 0.397892 0.689169i −0.595574 0.803301i \(-0.703075\pi\)
0.993466 + 0.114132i \(0.0364085\pi\)
\(440\) 32.6765 + 56.5974i 1.55779 + 2.69817i
\(441\) 19.1841 + 33.2279i 0.913531 + 1.58228i
\(442\) 7.65560 0.364140
\(443\) −8.20919 + 14.2187i −0.390030 + 0.675552i −0.992453 0.122625i \(-0.960869\pi\)
0.602423 + 0.798177i \(0.294202\pi\)
\(444\) −74.8220 + 129.595i −3.55089 + 6.15033i
\(445\) 15.9664 27.6545i 0.756878 1.31095i
\(446\) −13.9271 24.1224i −0.659465 1.14223i
\(447\) −8.08336 + 14.0008i −0.382330 + 0.662214i
\(448\) −0.808800 1.40088i −0.0382122 0.0661855i
\(449\) 19.5215 0.921275 0.460638 0.887588i \(-0.347621\pi\)
0.460638 + 0.887588i \(0.347621\pi\)
\(450\) 42.2476 1.99157
\(451\) −0.790740 1.36960i −0.0372345 0.0644920i
\(452\) −14.3076 + 24.7816i −0.672975 + 1.16563i
\(453\) 5.84427 + 10.1226i 0.274588 + 0.475600i
\(454\) −9.78470 + 16.9476i −0.459219 + 0.795390i
\(455\) −1.78539 + 3.09239i −0.0837005 + 0.144973i
\(456\) 40.4769 70.1081i 1.89551 3.28311i
\(457\) −14.4428 −0.675607 −0.337804 0.941217i \(-0.609684\pi\)
−0.337804 + 0.941217i \(0.609684\pi\)
\(458\) −3.61924 6.26870i −0.169116 0.292917i
\(459\) −20.8903 36.1830i −0.975075 1.68888i
\(460\) 41.4218 71.7446i 1.93130 3.34511i
\(461\) −24.4176 −1.13724 −0.568620 0.822600i \(-0.692523\pi\)
−0.568620 + 0.822600i \(0.692523\pi\)
\(462\) 21.1573 + 36.6456i 0.984328 + 1.70491i
\(463\) −40.4577 −1.88023 −0.940115 0.340859i \(-0.889282\pi\)
−0.940115 + 0.340859i \(0.889282\pi\)
\(464\) −24.0859 −1.11816
\(465\) 30.7219 + 37.1832i 1.42470 + 1.72433i
\(466\) 12.0034 0.556048
\(467\) 40.6648 1.88174 0.940872 0.338763i \(-0.110008\pi\)
0.940872 + 0.338763i \(0.110008\pi\)
\(468\) −16.2045 28.0670i −0.749054 1.29740i
\(469\) −18.0072 −0.831496
\(470\) 13.3900 23.1922i 0.617635 1.06978i
\(471\) 21.0012 + 36.3752i 0.967685 + 1.67608i
\(472\) 8.41045 + 14.5673i 0.387122 + 0.670515i
\(473\) −42.1883 −1.93982
\(474\) −28.8054 + 49.8924i −1.32307 + 2.29163i
\(475\) 4.65408 8.06110i 0.213544 0.369868i
\(476\) 8.85500 15.3373i 0.405868 0.702984i
\(477\) −11.2002 19.3993i −0.512822 0.888235i
\(478\) −20.5082 + 35.5213i −0.938025 + 1.62471i
\(479\) −3.09715 5.36442i −0.141512 0.245107i 0.786554 0.617522i \(-0.211863\pi\)
−0.928066 + 0.372415i \(0.878530\pi\)
\(480\) −42.1794 −1.92522
\(481\) 10.5126 0.479335
\(482\) −11.9002 20.6117i −0.542038 0.938837i
\(483\) 14.7198 25.4954i 0.669773 1.16008i
\(484\) −9.77318 16.9276i −0.444235 0.769438i
\(485\) −2.49231 + 4.31681i −0.113170 + 0.196016i
\(486\) −39.0232 + 67.5902i −1.77013 + 3.06595i
\(487\) −3.19517 + 5.53419i −0.144787 + 0.250778i −0.929293 0.369342i \(-0.879583\pi\)
0.784507 + 0.620121i \(0.212916\pi\)
\(488\) −45.3696 −2.05378
\(489\) −13.6878 23.7080i −0.618984 1.07211i
\(490\) −17.9558 31.1003i −0.811159 1.40497i
\(491\) 12.6940 21.9867i 0.572874 0.992246i −0.423395 0.905945i \(-0.639162\pi\)
0.996269 0.0863014i \(-0.0275048\pi\)
\(492\) 5.73483 0.258546
\(493\) 5.35681 + 9.27827i 0.241259 + 0.417872i
\(494\) −10.3620 −0.466207
\(495\) −77.4235 −3.47993
\(496\) −24.0648 29.1260i −1.08054 1.30780i
\(497\) 10.9086 0.489319
\(498\) −22.0884 −0.989807
\(499\) 8.73906 + 15.1365i 0.391214 + 0.677602i 0.992610 0.121349i \(-0.0387220\pi\)
−0.601396 + 0.798951i \(0.705389\pi\)
\(500\) 32.5495 1.45566
\(501\) 24.3451 42.1669i 1.08766 1.88388i
\(502\) 10.9296 + 18.9307i 0.487813 + 0.844917i
\(503\) 7.06495 + 12.2369i 0.315011 + 0.545615i 0.979440 0.201737i \(-0.0646585\pi\)
−0.664429 + 0.747351i \(0.731325\pi\)
\(504\) −59.7128 −2.65982
\(505\) −24.6579 + 42.7087i −1.09726 + 1.90051i
\(506\) −34.4833 + 59.7267i −1.53297 + 2.65518i
\(507\) −1.60552 + 2.78084i −0.0713037 + 0.123502i
\(508\) 10.1061 + 17.5043i 0.448386 + 0.776627i
\(509\) 14.9241 25.8493i 0.661500 1.14575i −0.318722 0.947848i \(-0.603254\pi\)
0.980222 0.197903i \(-0.0634130\pi\)
\(510\) 33.1599 + 57.4346i 1.46834 + 2.54325i
\(511\) −16.7846 −0.742505
\(512\) −50.7105 −2.24111
\(513\) 28.2753 + 48.9743i 1.24839 + 2.16227i
\(514\) 15.8071 27.3786i 0.697219 1.20762i
\(515\) −14.6023 25.2920i −0.643455 1.11450i
\(516\) 76.4924 132.489i 3.36739 5.83249i
\(517\) −7.68150 + 13.3047i −0.337832 + 0.585142i
\(518\) 17.6456 30.5630i 0.775301 1.34286i
\(519\) −30.0566 −1.31934
\(520\) 8.32425 + 14.4180i 0.365042 + 0.632272i
\(521\) 7.41822 + 12.8487i 0.324998 + 0.562913i 0.981512 0.191401i \(-0.0613030\pi\)
−0.656514 + 0.754314i \(0.727970\pi\)
\(522\) 32.9085 56.9992i 1.44037 2.49479i
\(523\) −38.6872 −1.69167 −0.845836 0.533443i \(-0.820898\pi\)
−0.845836 + 0.533443i \(0.820898\pi\)
\(524\) −25.4779 44.1291i −1.11301 1.92779i
\(525\) −9.68324 −0.422611
\(526\) −64.3419 −2.80544
\(527\) −5.86766 + 15.7479i −0.255599 + 0.685989i
\(528\) 85.5332 3.72236
\(529\) 24.9821 1.08618
\(530\) 10.4830 + 18.1572i 0.455355 + 0.788697i
\(531\) −19.9277 −0.864787
\(532\) −11.9854 + 20.7593i −0.519632 + 0.900029i
\(533\) −0.201439 0.348902i −0.00872528 0.0151126i
\(534\) −48.1995 83.4839i −2.08579 3.61270i
\(535\) 2.10929 0.0911926
\(536\) −41.9786 + 72.7090i −1.81320 + 3.14055i
\(537\) 15.9398 27.6086i 0.687855 1.19140i
\(538\) 20.4427 35.4078i 0.881348 1.52654i
\(539\) 10.3007 + 17.8414i 0.443685 + 0.768484i
\(540\) 82.7737 143.368i 3.56201 6.16959i
\(541\) −5.23022 9.05901i −0.224865 0.389477i 0.731414 0.681934i \(-0.238861\pi\)
−0.956279 + 0.292456i \(0.905527\pi\)
\(542\) −11.8412 −0.508621
\(543\) 37.6533 1.61586
\(544\) −7.34814 12.7274i −0.315049 0.545681i
\(545\) 6.68103 11.5719i 0.286184 0.495685i
\(546\) 5.38977 + 9.33535i 0.230661 + 0.399516i
\(547\) −15.0413 + 26.0523i −0.643120 + 1.11392i 0.341612 + 0.939841i \(0.389027\pi\)
−0.984732 + 0.174075i \(0.944306\pi\)
\(548\) 40.6531 70.4133i 1.73662 3.00791i
\(549\) 26.8746 46.5482i 1.14698 1.98663i
\(550\) 22.6844 0.967267
\(551\) −7.25053 12.5583i −0.308883 0.535001i
\(552\) −68.6298 118.870i −2.92108 5.05945i
\(553\) 4.68129 8.10823i 0.199069 0.344797i
\(554\) 60.4900 2.56997
\(555\) 45.5350 + 78.8689i 1.93285 + 3.34780i
\(556\) −10.2281 −0.433769
\(557\) 2.86306 0.121312 0.0606559 0.998159i \(-0.480681\pi\)
0.0606559 + 0.998159i \(0.480681\pi\)
\(558\) 101.806 17.1545i 4.30980 0.726210i
\(559\) −10.7473 −0.454564
\(560\) 24.2305 1.02392
\(561\) −19.0230 32.9487i −0.803150 1.39110i
\(562\) 50.3795 2.12513
\(563\) −14.0275 + 24.2963i −0.591187 + 1.02397i 0.402886 + 0.915250i \(0.368007\pi\)
−0.994073 + 0.108716i \(0.965326\pi\)
\(564\) −27.8550 48.2462i −1.17291 2.03153i
\(565\) 8.70732 + 15.0815i 0.366320 + 0.634484i
\(566\) −43.7859 −1.84046
\(567\) 14.9003 25.8080i 0.625752 1.08383i
\(568\) 25.4303 44.0466i 1.06703 1.84815i
\(569\) 16.3668 28.3482i 0.686133 1.18842i −0.286946 0.957947i \(-0.592640\pi\)
0.973079 0.230470i \(-0.0740265\pi\)
\(570\) −44.8824 77.7387i −1.87992 3.25611i
\(571\) −15.5051 + 26.8557i −0.648870 + 1.12388i 0.334523 + 0.942388i \(0.391425\pi\)
−0.983393 + 0.181488i \(0.941909\pi\)
\(572\) −8.70086 15.0703i −0.363801 0.630122i
\(573\) 37.2698 1.55697
\(574\) −1.35247 −0.0564509
\(575\) −7.89112 13.6678i −0.329082 0.569987i
\(576\) 4.46745 7.73785i 0.186144 0.322410i
\(577\) 18.0839 + 31.3222i 0.752842 + 1.30396i 0.946440 + 0.322879i \(0.104651\pi\)
−0.193599 + 0.981081i \(0.562016\pi\)
\(578\) 10.0052 17.3296i 0.416163 0.720816i
\(579\) −19.6923 + 34.1081i −0.818386 + 1.41749i
\(580\) −21.2253 + 36.7634i −0.881334 + 1.52652i
\(581\) 3.58969 0.148925
\(582\) 7.52382 + 13.0316i 0.311872 + 0.540179i
\(583\) −6.01385 10.4163i −0.249068 0.431399i
\(584\) −39.1283 + 67.7723i −1.61914 + 2.80444i
\(585\) −19.7234 −0.815463
\(586\) −2.66905 4.62293i −0.110257 0.190971i
\(587\) −2.69150 −0.111090 −0.0555450 0.998456i \(-0.517690\pi\)
−0.0555450 + 0.998456i \(0.517690\pi\)
\(588\) −74.7060 −3.08082
\(589\) 7.94197 21.3150i 0.327243 0.878270i
\(590\) 18.6517 0.767877
\(591\) −20.5637 −0.845878
\(592\) −35.6681 61.7789i −1.46595 2.53910i
\(593\) 2.01622 0.0827961 0.0413980 0.999143i \(-0.486819\pi\)
0.0413980 + 0.999143i \(0.486819\pi\)
\(594\) −68.9084 + 119.353i −2.82735 + 4.89711i
\(595\) −5.38896 9.33395i −0.220926 0.382655i
\(596\) −11.1596 19.3289i −0.457114 0.791744i
\(597\) 32.3812 1.32527
\(598\) −8.78451 + 15.2152i −0.359225 + 0.622197i
\(599\) −3.62657 + 6.28140i −0.148177 + 0.256651i −0.930554 0.366155i \(-0.880674\pi\)
0.782376 + 0.622806i \(0.214007\pi\)
\(600\) −22.5737 + 39.0987i −0.921566 + 1.59620i
\(601\) 3.50141 + 6.06463i 0.142826 + 0.247381i 0.928560 0.371183i \(-0.121048\pi\)
−0.785734 + 0.618565i \(0.787715\pi\)
\(602\) −18.0395 + 31.2453i −0.735236 + 1.27347i
\(603\) −49.7319 86.1382i −2.02524 3.50782i
\(604\) −16.1367 −0.656594
\(605\) −11.8955 −0.483620
\(606\) 74.4375 + 128.930i 3.02382 + 5.23741i
\(607\) 7.48155 12.9584i 0.303667 0.525966i −0.673297 0.739372i \(-0.735122\pi\)
0.976964 + 0.213406i \(0.0684557\pi\)
\(608\) 9.94582 + 17.2267i 0.403356 + 0.698634i
\(609\) −7.54271 + 13.0643i −0.305646 + 0.529394i
\(610\) −25.1538 + 43.5676i −1.01845 + 1.76400i
\(611\) −1.95684 + 3.38934i −0.0791652 + 0.137118i
\(612\) 97.8221 3.95423
\(613\) −9.81686 17.0033i −0.396499 0.686757i 0.596792 0.802396i \(-0.296442\pi\)
−0.993291 + 0.115639i \(0.963108\pi\)
\(614\) 1.12979 + 1.95685i 0.0455946 + 0.0789722i
\(615\) 1.74505 3.02251i 0.0703671 0.121879i
\(616\) −32.0622 −1.29182
\(617\) 2.68524 + 4.65097i 0.108104 + 0.187241i 0.915002 0.403449i \(-0.132189\pi\)
−0.806898 + 0.590690i \(0.798855\pi\)
\(618\) −88.1634 −3.54645
\(619\) 20.9725 0.842956 0.421478 0.906839i \(-0.361511\pi\)
0.421478 + 0.906839i \(0.361511\pi\)
\(620\) −65.6630 + 11.0644i −2.63709 + 0.444355i
\(621\) 95.8833 3.84766
\(622\) −31.2528 −1.25312
\(623\) 7.83310 + 13.5673i 0.313827 + 0.543564i
\(624\) 21.7893 0.872272
\(625\) 15.6004 27.0208i 0.624018 1.08083i
\(626\) 24.9006 + 43.1291i 0.995227 + 1.72378i
\(627\) 25.7479 + 44.5966i 1.02827 + 1.78102i
\(628\) −57.9869 −2.31393
\(629\) −15.8655 + 27.4798i −0.632597 + 1.09569i
\(630\) −33.1060 + 57.3412i −1.31897 + 2.28453i
\(631\) 3.53980 6.13111i 0.140917 0.244076i −0.786925 0.617048i \(-0.788328\pi\)
0.927842 + 0.372973i \(0.121662\pi\)
\(632\) −21.8261 37.8040i −0.868196 1.50376i
\(633\) −11.1908 + 19.3831i −0.444796 + 0.770409i
\(634\) 18.4244 + 31.9121i 0.731728 + 1.26739i
\(635\) 12.3007 0.488139
\(636\) 43.6153 1.72946
\(637\) 2.62409 + 4.54505i 0.103970 + 0.180081i
\(638\) 17.6699 30.6052i 0.699558 1.21167i
\(639\) 30.1272 + 52.1819i 1.19182 + 2.06428i
\(640\) −17.3171 + 29.9941i −0.684519 + 1.18562i
\(641\) −11.1351 + 19.2866i −0.439810 + 0.761773i −0.997674 0.0681588i \(-0.978288\pi\)
0.557865 + 0.829932i \(0.311621\pi\)
\(642\) 3.18378 5.51447i 0.125654 0.217639i
\(643\) 42.1022 1.66035 0.830174 0.557505i \(-0.188241\pi\)
0.830174 + 0.557505i \(0.188241\pi\)
\(644\) 20.3215 + 35.1980i 0.800781 + 1.38699i
\(645\) −46.5516 80.6298i −1.83297 3.17479i
\(646\) 15.6381 27.0860i 0.615272 1.06568i
\(647\) 42.3591 1.66531 0.832654 0.553793i \(-0.186820\pi\)
0.832654 + 0.553793i \(0.186820\pi\)
\(648\) −69.4713 120.328i −2.72909 4.72692i
\(649\) −10.7000 −0.420011
\(650\) 5.77879 0.226663
\(651\) −23.3342 + 3.93186i −0.914540 + 0.154102i
\(652\) 37.7937 1.48012
\(653\) 6.20158 0.242687 0.121343 0.992611i \(-0.461280\pi\)
0.121343 + 0.992611i \(0.461280\pi\)
\(654\) −20.1688 34.9334i −0.788662 1.36600i
\(655\) −31.0106 −1.21169
\(656\) −1.36691 + 2.36756i −0.0533690 + 0.0924379i
\(657\) −46.3552 80.2896i −1.80849 3.13240i
\(658\) 6.56915 + 11.3781i 0.256092 + 0.443564i
\(659\) −2.77132 −0.107955 −0.0539777 0.998542i \(-0.517190\pi\)
−0.0539777 + 0.998542i \(0.517190\pi\)
\(660\) 75.3748 130.553i 2.93396 5.08177i
\(661\) 17.6335 30.5422i 0.685865 1.18795i −0.287299 0.957841i \(-0.592757\pi\)
0.973164 0.230112i \(-0.0739093\pi\)
\(662\) 13.9545 24.1699i 0.542357 0.939390i
\(663\) −4.84604 8.39359i −0.188205 0.325980i
\(664\) 8.36832 14.4944i 0.324754 0.562490i
\(665\) 7.29404 + 12.6336i 0.282851 + 0.489912i
\(666\) 194.932 7.55348
\(667\) −24.5870 −0.952011
\(668\) 33.6098 + 58.2139i 1.30040 + 2.25236i
\(669\) −17.6318 + 30.5392i −0.681686 + 1.18071i
\(670\) 46.5475 + 80.6226i 1.79829 + 3.11472i
\(671\) 14.4301 24.9936i 0.557067 0.964868i
\(672\) 10.3466 17.9209i 0.399129 0.691312i
\(673\) −8.07757 + 13.9908i −0.311368 + 0.539305i −0.978659 0.205492i \(-0.934120\pi\)
0.667291 + 0.744797i \(0.267454\pi\)
\(674\) −22.1962 −0.854965
\(675\) −15.7689 27.3126i −0.606946 1.05126i
\(676\) −2.21652 3.83912i −0.0852507 0.147659i
\(677\) −5.38720 + 9.33091i −0.207047 + 0.358616i −0.950783 0.309858i \(-0.899719\pi\)
0.743736 + 0.668473i \(0.233052\pi\)
\(678\) 52.5715 2.01900
\(679\) −1.22273 2.11783i −0.0469240 0.0812748i
\(680\) −50.2512 −1.92704
\(681\) 24.7751 0.949384
\(682\) 54.6638 9.21097i 2.09319 0.352706i
\(683\) −19.2309 −0.735849 −0.367924 0.929856i \(-0.619932\pi\)
−0.367924 + 0.929856i \(0.619932\pi\)
\(684\) −132.404 −5.06259
\(685\) −24.7406 42.8520i −0.945290 1.63729i
\(686\) 41.1174 1.56987
\(687\) −4.58200 + 7.93625i −0.174814 + 0.302787i
\(688\) 36.4644 + 63.1582i 1.39019 + 2.40788i
\(689\) −1.53201 2.65352i −0.0583649 0.101091i
\(690\) −152.199 −5.79411
\(691\) 15.9965 27.7068i 0.608537 1.05402i −0.382945 0.923771i \(-0.625090\pi\)
0.991482 0.130246i \(-0.0415767\pi\)
\(692\) 20.7475 35.9357i 0.788702 1.36607i
\(693\) 18.9920 32.8951i 0.721447 1.24958i
\(694\) 15.8798 + 27.5045i 0.602787 + 1.04406i
\(695\) −3.11231 + 5.39067i −0.118056 + 0.204480i
\(696\) 35.1673 + 60.9115i 1.33301 + 2.30884i
\(697\) 1.21603 0.0460604
\(698\) −53.2709 −2.01633
\(699\) −7.59824 13.1605i −0.287392 0.497777i
\(700\) 6.68415 11.5773i 0.252637 0.437580i
\(701\) 18.9555 + 32.8319i 0.715941 + 1.24005i 0.962596 + 0.270942i \(0.0873352\pi\)
−0.246655 + 0.969103i \(0.579331\pi\)
\(702\) −17.5542 + 30.4048i −0.662541 + 1.14755i
\(703\) 21.4741 37.1943i 0.809913 1.40281i
\(704\) 2.39876 4.15477i 0.0904065 0.156589i
\(705\) −33.9038 −1.27689
\(706\) 4.30819 + 7.46200i 0.162141 + 0.280836i
\(707\) −12.0972 20.9529i −0.454961 0.788015i
\(708\) 19.4003 33.6024i 0.729110 1.26286i
\(709\) 6.36760 0.239140 0.119570 0.992826i \(-0.461848\pi\)
0.119570 + 0.992826i \(0.461848\pi\)
\(710\) −28.1982 48.8406i −1.05826 1.83296i
\(711\) 51.7147 1.93945
\(712\) 73.0424 2.73738
\(713\) −24.5654 29.7319i −0.919982 1.11347i
\(714\) −32.5365 −1.21765
\(715\) −10.5903 −0.396055
\(716\) 22.0059 + 38.1154i 0.822400 + 1.42444i
\(717\) 51.9274 1.93926
\(718\) 22.8356 39.5524i 0.852216 1.47608i
\(719\) −10.7247 18.5758i −0.399965 0.692759i 0.593756 0.804645i \(-0.297644\pi\)
−0.993721 + 0.111886i \(0.964311\pi\)
\(720\) 66.9192 + 115.907i 2.49393 + 4.31961i
\(721\) 14.3278 0.533596
\(722\) 2.92886 5.07294i 0.109001 0.188795i
\(723\) −15.0658 + 26.0947i −0.560302 + 0.970471i
\(724\) −25.9914 + 45.0184i −0.965961 + 1.67309i
\(725\) 4.04356 + 7.00366i 0.150174 + 0.260109i
\(726\) −17.9551 + 31.0992i −0.666377 + 1.15420i
\(727\) −2.42708 4.20383i −0.0900156 0.155912i 0.817502 0.575926i \(-0.195358\pi\)
−0.907517 + 0.420014i \(0.862025\pi\)
\(728\) −8.16776 −0.302717
\(729\) 31.2618 1.15784
\(730\) 43.3870 + 75.1486i 1.60583 + 2.78137i
\(731\) 16.2197 28.0933i 0.599906 1.03907i
\(732\) 52.3269 + 90.6329i 1.93406 + 3.34989i
\(733\) −11.1530 + 19.3175i −0.411944 + 0.713508i −0.995102 0.0988503i \(-0.968484\pi\)
0.583158 + 0.812359i \(0.301817\pi\)
\(734\) 40.5682 70.2662i 1.49740 2.59357i
\(735\) −22.7322 + 39.3734i −0.838491 + 1.45231i
\(736\) 33.7268 1.24319
\(737\) −26.7031 46.2511i −0.983620 1.70368i
\(738\) −3.73522 6.46958i −0.137495 0.238149i
\(739\) 0.152502 0.264141i 0.00560986 0.00971657i −0.863207 0.504850i \(-0.831548\pi\)
0.868817 + 0.495134i \(0.164881\pi\)
\(740\) −125.728 −4.62184
\(741\) 6.55919 + 11.3609i 0.240958 + 0.417352i
\(742\) −10.2860 −0.377610
\(743\) 12.1732 0.446591 0.223296 0.974751i \(-0.428318\pi\)
0.223296 + 0.974751i \(0.428318\pi\)
\(744\) −38.5210 + 103.384i −1.41225 + 3.79025i
\(745\) −13.5829 −0.497640
\(746\) −39.9948 −1.46431
\(747\) 9.91392 + 17.1714i 0.362731 + 0.628269i
\(748\) 52.5247 1.92049
\(749\) −0.517410 + 0.896180i −0.0189057 + 0.0327457i
\(750\) −29.8997 51.7878i −1.09178 1.89102i
\(751\) −4.69962 8.13999i −0.171492 0.297032i 0.767450 0.641109i \(-0.221525\pi\)
−0.938942 + 0.344077i \(0.888192\pi\)
\(752\) 26.5573 0.968443
\(753\) 13.8370 23.9665i 0.504250 0.873386i
\(754\) 4.50136 7.79658i 0.163930 0.283935i
\(755\) −4.91023 + 8.50477i −0.178702 + 0.309520i
\(756\) 40.6088 + 70.3366i 1.47693 + 2.55812i
\(757\) −15.8545 + 27.4608i −0.576242 + 0.998080i 0.419664 + 0.907680i \(0.362148\pi\)
−0.995906 + 0.0904002i \(0.971185\pi\)
\(758\) −28.5116 49.3836i −1.03559 1.79369i
\(759\) 87.3125 3.16924
\(760\) 68.0157 2.46719
\(761\) −4.85926 8.41649i −0.176148 0.305097i 0.764410 0.644731i \(-0.223030\pi\)
−0.940558 + 0.339633i \(0.889697\pi\)
\(762\) 18.5668 32.1586i 0.672603 1.16498i
\(763\) 3.27772 + 5.67717i 0.118661 + 0.205527i
\(764\) −25.7266 + 44.5598i −0.930757 + 1.61212i
\(765\) 29.7662 51.5566i 1.07620 1.86403i
\(766\) 45.7239 79.1961i 1.65207 2.86147i
\(767\) −2.72579 −0.0984225
\(768\) 48.3528 + 83.7495i 1.74478 + 3.02205i
\(769\) −14.6585 25.3892i −0.528598 0.915559i −0.999444 0.0333434i \(-0.989384\pi\)
0.470846 0.882216i \(-0.343949\pi\)
\(770\) −17.7759 + 30.7888i −0.640600 + 1.10955i
\(771\) −40.0238 −1.44142
\(772\) −27.1865