Properties

Label 1110.2.u.f.401.14
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 401.14
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.f.191.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.392697 + 1.68695i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.47053 + 0.915172i) q^{6} -0.873718 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.69158 + 1.32492i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.392697 + 1.68695i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.47053 + 0.915172i) q^{6} -0.873718 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.69158 + 1.32492i) q^{9} -1.00000 q^{10} +3.24582 q^{11} +(1.68695 - 0.392697i) q^{12} +(2.80064 - 2.80064i) q^{13} +(-0.617812 + 0.617812i) q^{14} +(0.915172 - 1.47053i) q^{15} -1.00000 q^{16} +(2.67922 + 2.67922i) q^{17} +(-0.966374 + 2.84009i) q^{18} +(2.24528 - 2.24528i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(-0.343107 - 1.47392i) q^{21} +(2.29514 - 2.29514i) q^{22} +(3.93841 + 3.93841i) q^{23} +(0.915172 - 1.47053i) q^{24} +1.00000i q^{25} -3.96070i q^{26} +(-3.29204 - 4.02026i) q^{27} +0.873718i q^{28} +(0.0117303 - 0.0117303i) q^{29} +(-0.392697 - 1.68695i) q^{30} +(5.20171 + 5.20171i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.27463 + 5.47553i) q^{33} +3.78900 q^{34} +(0.617812 + 0.617812i) q^{35} +(1.32492 + 2.69158i) q^{36} +(-2.06314 - 5.72219i) q^{37} -3.17531i q^{38} +(5.82434 + 3.62473i) q^{39} +1.00000i q^{40} +12.1119 q^{41} +(-1.28483 - 0.799603i) q^{42} +(8.06425 - 8.06425i) q^{43} -3.24582i q^{44} +(2.84009 + 0.966374i) q^{45} +5.56975 q^{46} +3.06944i q^{47} +(-0.392697 - 1.68695i) q^{48} -6.23662 q^{49} +(0.707107 + 0.707107i) q^{50} +(-3.46758 + 5.57183i) q^{51} +(-2.80064 - 2.80064i) q^{52} +9.17714i q^{53} +(-5.17058 - 0.514925i) q^{54} +(-2.29514 - 2.29514i) q^{55} +(0.617812 + 0.617812i) q^{56} +(4.66939 + 2.90596i) q^{57} -0.0165891i q^{58} +(-7.96028 - 7.96028i) q^{59} +(-1.47053 - 0.915172i) q^{60} +(-6.64635 - 6.64635i) q^{61} +7.35632 q^{62} +(2.35168 - 1.15761i) q^{63} +1.00000i q^{64} -3.96070 q^{65} +(4.77308 + 2.97049i) q^{66} +7.74070i q^{67} +(2.67922 - 2.67922i) q^{68} +(-5.09728 + 8.19049i) q^{69} +0.873718 q^{70} -0.580983i q^{71} +(2.84009 + 0.966374i) q^{72} +11.0501i q^{73} +(-5.50506 - 2.58734i) q^{74} +(-1.68695 + 0.392697i) q^{75} +(-2.24528 - 2.24528i) q^{76} -2.83593 q^{77} +(6.68150 - 1.55536i) q^{78} +(0.763562 - 0.763562i) q^{79} +(0.707107 + 0.707107i) q^{80} +(5.48918 - 7.13224i) q^{81} +(8.56443 - 8.56443i) q^{82} +6.26833i q^{83} +(-1.47392 + 0.343107i) q^{84} -3.78900i q^{85} -11.4046i q^{86} +(0.0243948 + 0.0151819i) q^{87} +(-2.29514 - 2.29514i) q^{88} +(-6.49421 + 6.49421i) q^{89} +(2.69158 - 1.32492i) q^{90} +(-2.44697 + 2.44697i) q^{91} +(3.93841 - 3.93841i) q^{92} +(-6.73230 + 10.8177i) q^{93} +(2.17042 + 2.17042i) q^{94} -3.17531 q^{95} +(-1.47053 - 0.915172i) q^{96} +(7.15350 - 7.15350i) q^{97} +(-4.40995 + 4.40995i) q^{98} +(-8.73639 + 4.30045i) 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
\(3\) 0.392697 + 1.68695i 0.226724 + 0.973959i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) 1.47053 + 0.915172i 0.600341 + 0.373618i
\(7\) −0.873718 −0.330234 −0.165117 0.986274i \(-0.552800\pi\)
−0.165117 + 0.986274i \(0.552800\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −2.69158 + 1.32492i −0.897193 + 0.441640i
\(10\) −1.00000 −0.316228
\(11\) 3.24582 0.978653 0.489326 0.872101i \(-0.337243\pi\)
0.489326 + 0.872101i \(0.337243\pi\)
\(12\) 1.68695 0.392697i 0.486980 0.113362i
\(13\) 2.80064 2.80064i 0.776758 0.776758i −0.202520 0.979278i \(-0.564913\pi\)
0.979278 + 0.202520i \(0.0649131\pi\)
\(14\) −0.617812 + 0.617812i −0.165117 + 0.165117i
\(15\) 0.915172 1.47053i 0.236297 0.379689i
\(16\) −1.00000 −0.250000
\(17\) 2.67922 + 2.67922i 0.649807 + 0.649807i 0.952946 0.303139i \(-0.0980347\pi\)
−0.303139 + 0.952946i \(0.598035\pi\)
\(18\) −0.966374 + 2.84009i −0.227777 + 0.669416i
\(19\) 2.24528 2.24528i 0.515103 0.515103i −0.400982 0.916086i \(-0.631331\pi\)
0.916086 + 0.400982i \(0.131331\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) −0.343107 1.47392i −0.0748720 0.321635i
\(22\) 2.29514 2.29514i 0.489326 0.489326i
\(23\) 3.93841 + 3.93841i 0.821215 + 0.821215i 0.986282 0.165067i \(-0.0527842\pi\)
−0.165067 + 0.986282i \(0.552784\pi\)
\(24\) 0.915172 1.47053i 0.186809 0.300171i
\(25\) 1.00000i 0.200000i
\(26\) 3.96070i 0.776758i
\(27\) −3.29204 4.02026i −0.633554 0.773699i
\(28\) 0.873718i 0.165117i
\(29\) 0.0117303 0.0117303i 0.00217826 0.00217826i −0.706017 0.708195i \(-0.749510\pi\)
0.708195 + 0.706017i \(0.249510\pi\)
\(30\) −0.392697 1.68695i −0.0716964 0.307993i
\(31\) 5.20171 + 5.20171i 0.934254 + 0.934254i 0.997968 0.0637143i \(-0.0202946\pi\)
−0.0637143 + 0.997968i \(0.520295\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 1.27463 + 5.47553i 0.221884 + 0.953168i
\(34\) 3.78900 0.649807
\(35\) 0.617812 + 0.617812i 0.104429 + 0.104429i
\(36\) 1.32492 + 2.69158i 0.220820 + 0.448596i
\(37\) −2.06314 5.72219i −0.339179 0.940722i
\(38\) 3.17531i 0.515103i
\(39\) 5.82434 + 3.62473i 0.932640 + 0.580421i
\(40\) 1.00000i 0.158114i
\(41\) 12.1119 1.89157 0.945783 0.324799i \(-0.105297\pi\)
0.945783 + 0.324799i \(0.105297\pi\)
\(42\) −1.28483 0.799603i −0.198253 0.123381i
\(43\) 8.06425 8.06425i 1.22979 1.22979i 0.265743 0.964044i \(-0.414383\pi\)
0.964044 0.265743i \(-0.0856174\pi\)
\(44\) 3.24582i 0.489326i
\(45\) 2.84009 + 0.966374i 0.423376 + 0.144059i
\(46\) 5.56975 0.821215
\(47\) 3.06944i 0.447724i 0.974621 + 0.223862i \(0.0718666\pi\)
−0.974621 + 0.223862i \(0.928133\pi\)
\(48\) −0.392697 1.68695i −0.0566810 0.243490i
\(49\) −6.23662 −0.890945
\(50\) 0.707107 + 0.707107i 0.100000 + 0.100000i
\(51\) −3.46758 + 5.57183i −0.485559 + 0.780213i
\(52\) −2.80064 2.80064i −0.388379 0.388379i
\(53\) 9.17714i 1.26058i 0.776361 + 0.630289i \(0.217063\pi\)
−0.776361 + 0.630289i \(0.782937\pi\)
\(54\) −5.17058 0.514925i −0.703626 0.0700724i
\(55\) −2.29514 2.29514i −0.309477 0.309477i
\(56\) 0.617812 + 0.617812i 0.0825586 + 0.0825586i
\(57\) 4.66939 + 2.90596i 0.618476 + 0.384903i
\(58\) 0.0165891i 0.00217826i
\(59\) −7.96028 7.96028i −1.03634 1.03634i −0.999314 0.0370254i \(-0.988212\pi\)
−0.0370254 0.999314i \(-0.511788\pi\)
\(60\) −1.47053 0.915172i −0.189845 0.118148i
\(61\) −6.64635 6.64635i −0.850978 0.850978i 0.139276 0.990254i \(-0.455522\pi\)
−0.990254 + 0.139276i \(0.955522\pi\)
\(62\) 7.35632 0.934254
\(63\) 2.35168 1.15761i 0.296284 0.145845i
\(64\) 1.00000i 0.125000i
\(65\) −3.96070 −0.491265
\(66\) 4.77308 + 2.97049i 0.587526 + 0.365642i
\(67\) 7.74070i 0.945677i 0.881149 + 0.472838i \(0.156771\pi\)
−0.881149 + 0.472838i \(0.843229\pi\)
\(68\) 2.67922 2.67922i 0.324904 0.324904i
\(69\) −5.09728 + 8.19049i −0.613641 + 0.986019i
\(70\) 0.873718 0.104429
\(71\) 0.580983i 0.0689500i −0.999406 0.0344750i \(-0.989024\pi\)
0.999406 0.0344750i \(-0.0109759\pi\)
\(72\) 2.84009 + 0.966374i 0.334708 + 0.113888i
\(73\) 11.0501i 1.29332i 0.762780 + 0.646658i \(0.223834\pi\)
−0.762780 + 0.646658i \(0.776166\pi\)
\(74\) −5.50506 2.58734i −0.639950 0.300772i
\(75\) −1.68695 + 0.392697i −0.194792 + 0.0453448i
\(76\) −2.24528 2.24528i −0.257552 0.257552i
\(77\) −2.83593 −0.323185
\(78\) 6.68150 1.55536i 0.756531 0.176110i
\(79\) 0.763562 0.763562i 0.0859075 0.0859075i −0.662847 0.748755i \(-0.730652\pi\)
0.748755 + 0.662847i \(0.230652\pi\)
\(80\) 0.707107 + 0.707107i 0.0790569 + 0.0790569i
\(81\) 5.48918 7.13224i 0.609909 0.792471i
\(82\) 8.56443 8.56443i 0.945783 0.945783i
\(83\) 6.26833i 0.688039i 0.938963 + 0.344019i \(0.111789\pi\)
−0.938963 + 0.344019i \(0.888211\pi\)
\(84\) −1.47392 + 0.343107i −0.160817 + 0.0374360i
\(85\) 3.78900i 0.410974i
\(86\) 11.4046i 1.22979i
\(87\) 0.0243948 + 0.0151819i 0.00261540 + 0.00162767i
\(88\) −2.29514 2.29514i −0.244663 0.244663i
\(89\) −6.49421 + 6.49421i −0.688385 + 0.688385i −0.961875 0.273490i \(-0.911822\pi\)
0.273490 + 0.961875i \(0.411822\pi\)
\(90\) 2.69158 1.32492i 0.283717 0.139659i
\(91\) −2.44697 + 2.44697i −0.256512 + 0.256512i
\(92\) 3.93841 3.93841i 0.410607 0.410607i
\(93\) −6.73230 + 10.8177i −0.698107 + 1.12174i
\(94\) 2.17042 + 2.17042i 0.223862 + 0.223862i
\(95\) −3.17531 −0.325780
\(96\) −1.47053 0.915172i −0.150085 0.0934044i
\(97\) 7.15350 7.15350i 0.726328 0.726328i −0.243558 0.969886i \(-0.578315\pi\)
0.969886 + 0.243558i \(0.0783147\pi\)
\(98\) −4.40995 + 4.40995i −0.445473 + 0.445473i
\(99\) −8.73639 + 4.30045i −0.878040 + 0.432212i
\(100\) 1.00000 0.100000
\(101\) −9.86993 −0.982095 −0.491048 0.871133i \(-0.663386\pi\)
−0.491048 + 0.871133i \(0.663386\pi\)
\(102\) 1.48793 + 6.39183i 0.147327 + 0.632886i
\(103\) −4.80415 4.80415i −0.473367 0.473367i 0.429636 0.903002i \(-0.358642\pi\)
−0.903002 + 0.429636i \(0.858642\pi\)
\(104\) −3.96070 −0.388379
\(105\) −0.799603 + 1.28483i −0.0780332 + 0.125386i
\(106\) 6.48922 + 6.48922i 0.630289 + 0.630289i
\(107\) 14.7208i 1.42312i −0.702628 0.711558i \(-0.747990\pi\)
0.702628 0.711558i \(-0.252010\pi\)
\(108\) −4.02026 + 3.29204i −0.386849 + 0.316777i
\(109\) 12.8578 12.8578i 1.23155 1.23155i 0.268184 0.963368i \(-0.413577\pi\)
0.963368 0.268184i \(-0.0864235\pi\)
\(110\) −3.24582 −0.309477
\(111\) 8.84284 5.72750i 0.839325 0.543630i
\(112\) 0.873718 0.0825586
\(113\) −3.10020 + 3.10020i −0.291643 + 0.291643i −0.837729 0.546086i \(-0.816117\pi\)
0.546086 + 0.837729i \(0.316117\pi\)
\(114\) 5.35658 1.24694i 0.501690 0.116786i
\(115\) 5.56975i 0.519382i
\(116\) −0.0117303 0.0117303i −0.00108913 0.00108913i
\(117\) −3.82752 + 11.2488i −0.353854 + 1.03995i
\(118\) −11.2575 −1.03634
\(119\) −2.34089 2.34089i −0.214589 0.214589i
\(120\) −1.68695 + 0.392697i −0.153996 + 0.0358482i
\(121\) −0.464630 −0.0422391
\(122\) −9.39935 −0.850978
\(123\) 4.75632 + 20.4322i 0.428863 + 1.84231i
\(124\) 5.20171 5.20171i 0.467127 0.467127i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) 0.844338 2.48144i 0.0752196 0.221064i
\(127\) −0.948940 −0.0842048 −0.0421024 0.999113i \(-0.513406\pi\)
−0.0421024 + 0.999113i \(0.513406\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 16.7708 + 10.4372i 1.47658 + 0.918940i
\(130\) −2.80064 + 2.80064i −0.245632 + 0.245632i
\(131\) 11.7356 11.7356i 1.02535 1.02535i 0.0256765 0.999670i \(-0.491826\pi\)
0.999670 0.0256765i \(-0.00817399\pi\)
\(132\) 5.47553 1.27463i 0.476584 0.110942i
\(133\) −1.96174 + 1.96174i −0.170105 + 0.170105i
\(134\) 5.47350 + 5.47350i 0.472838 + 0.472838i
\(135\) −0.514925 + 5.17058i −0.0443177 + 0.445012i
\(136\) 3.78900i 0.324904i
\(137\) 21.3281i 1.82218i 0.412209 + 0.911089i \(0.364757\pi\)
−0.412209 + 0.911089i \(0.635243\pi\)
\(138\) 2.18723 + 9.39587i 0.186189 + 0.799830i
\(139\) 14.6182i 1.23990i 0.784641 + 0.619951i \(0.212847\pi\)
−0.784641 + 0.619951i \(0.787153\pi\)
\(140\) 0.617812 0.617812i 0.0522146 0.0522146i
\(141\) −5.17799 + 1.20536i −0.436065 + 0.101510i
\(142\) −0.410817 0.410817i −0.0344750 0.0344750i
\(143\) 9.09039 9.09039i 0.760176 0.760176i
\(144\) 2.69158 1.32492i 0.224298 0.110410i
\(145\) −0.0165891 −0.00137765
\(146\) 7.81360 + 7.81360i 0.646658 + 0.646658i
\(147\) −2.44910 10.5208i −0.201999 0.867744i
\(148\) −5.72219 + 2.06314i −0.470361 + 0.169589i
\(149\) 4.27966i 0.350604i −0.984515 0.175302i \(-0.943910\pi\)
0.984515 0.175302i \(-0.0560902\pi\)
\(150\) −0.915172 + 1.47053i −0.0747235 + 0.120068i
\(151\) 16.2675i 1.32383i −0.749577 0.661917i \(-0.769743\pi\)
0.749577 0.661917i \(-0.230257\pi\)
\(152\) −3.17531 −0.257552
\(153\) −10.7611 3.66159i −0.869983 0.296022i
\(154\) −2.00531 + 2.00531i −0.161592 + 0.161592i
\(155\) 7.35632i 0.590874i
\(156\) 3.62473 5.82434i 0.290210 0.466320i
\(157\) −18.4593 −1.47321 −0.736607 0.676321i \(-0.763573\pi\)
−0.736607 + 0.676321i \(0.763573\pi\)
\(158\) 1.07984i 0.0859075i
\(159\) −15.4813 + 3.60384i −1.22775 + 0.285803i
\(160\) 1.00000 0.0790569
\(161\) −3.44106 3.44106i −0.271193 0.271193i
\(162\) −1.16182 8.92469i −0.0912812 0.701190i
\(163\) −7.65805 7.65805i −0.599825 0.599825i 0.340441 0.940266i \(-0.389424\pi\)
−0.940266 + 0.340441i \(0.889424\pi\)
\(164\) 12.1119i 0.945783i
\(165\) 2.97049 4.77308i 0.231252 0.371584i
\(166\) 4.43238 + 4.43238i 0.344019 + 0.344019i
\(167\) −12.4791 12.4791i −0.965665 0.965665i 0.0337648 0.999430i \(-0.489250\pi\)
−0.999430 + 0.0337648i \(0.989250\pi\)
\(168\) −0.799603 + 1.28483i −0.0616907 + 0.0991267i
\(169\) 2.68718i 0.206706i
\(170\) −2.67922 2.67922i −0.205487 0.205487i
\(171\) −3.06854 + 9.01817i −0.234657 + 0.689637i
\(172\) −8.06425 8.06425i −0.614894 0.614894i
\(173\) 9.17456 0.697529 0.348765 0.937210i \(-0.386601\pi\)
0.348765 + 0.937210i \(0.386601\pi\)
\(174\) 0.0279850 0.00651450i 0.00212153 0.000493863i
\(175\) 0.873718i 0.0660469i
\(176\) −3.24582 −0.244663
\(177\) 10.3026 16.5545i 0.774389 1.24432i
\(178\) 9.18420i 0.688385i
\(179\) −10.0110 + 10.0110i −0.748257 + 0.748257i −0.974152 0.225895i \(-0.927470\pi\)
0.225895 + 0.974152i \(0.427470\pi\)
\(180\) 0.966374 2.84009i 0.0720293 0.211688i
\(181\) −22.6754 −1.68545 −0.842724 0.538346i \(-0.819049\pi\)
−0.842724 + 0.538346i \(0.819049\pi\)
\(182\) 3.46054i 0.256512i
\(183\) 8.60203 13.8220i 0.635880 1.02175i
\(184\) 5.56975i 0.410607i
\(185\) −2.58734 + 5.50506i −0.190225 + 0.404740i
\(186\) 2.88881 + 12.4097i 0.211818 + 0.909925i
\(187\) 8.69629 + 8.69629i 0.635936 + 0.635936i
\(188\) 3.06944 0.223862
\(189\) 2.87632 + 3.51257i 0.209221 + 0.255502i
\(190\) −2.24528 + 2.24528i −0.162890 + 0.162890i
\(191\) 6.59688 + 6.59688i 0.477333 + 0.477333i 0.904278 0.426945i \(-0.140410\pi\)
−0.426945 + 0.904278i \(0.640410\pi\)
\(192\) −1.68695 + 0.392697i −0.121745 + 0.0283405i
\(193\) −0.721641 + 0.721641i −0.0519448 + 0.0519448i −0.732602 0.680657i \(-0.761694\pi\)
0.680657 + 0.732602i \(0.261694\pi\)
\(194\) 10.1166i 0.726328i
\(195\) −1.55536 6.68150i −0.111381 0.478472i
\(196\) 6.23662i 0.445473i
\(197\) 14.8081i 1.05504i 0.849544 + 0.527518i \(0.176877\pi\)
−0.849544 + 0.527518i \(0.823123\pi\)
\(198\) −3.13668 + 9.21844i −0.222914 + 0.655126i
\(199\) −15.3316 15.3316i −1.08683 1.08683i −0.995853 0.0909720i \(-0.971003\pi\)
−0.0909720 0.995853i \(-0.528997\pi\)
\(200\) 0.707107 0.707107i 0.0500000 0.0500000i
\(201\) −13.0581 + 3.03975i −0.921050 + 0.214408i
\(202\) −6.97910 + 6.97910i −0.491048 + 0.491048i
\(203\) −0.0102490 + 0.0102490i −0.000719336 + 0.000719336i
\(204\) 5.57183 + 3.46758i 0.390106 + 0.242779i
\(205\) −8.56443 8.56443i −0.598166 0.598166i
\(206\) −6.79409 −0.473367
\(207\) −15.8186 5.38246i −1.09947 0.374107i
\(208\) −2.80064 + 2.80064i −0.194190 + 0.194190i
\(209\) 7.28779 7.28779i 0.504107 0.504107i
\(210\) 0.343107 + 1.47392i 0.0236766 + 0.101710i
\(211\) −14.8756 −1.02408 −0.512039 0.858962i \(-0.671109\pi\)
−0.512039 + 0.858962i \(0.671109\pi\)
\(212\) 9.17714 0.630289
\(213\) 0.980088 0.228151i 0.0671545 0.0156326i
\(214\) −10.4092 10.4092i −0.711558 0.711558i
\(215\) −11.4046 −0.777786
\(216\) −0.514925 + 5.17058i −0.0350362 + 0.351813i
\(217\) −4.54482 4.54482i −0.308523 0.308523i
\(218\) 18.1836i 1.23155i
\(219\) −18.6409 + 4.33935i −1.25964 + 0.293226i
\(220\) −2.29514 + 2.29514i −0.154739 + 0.154739i
\(221\) 15.0071 1.00949
\(222\) 2.20288 10.3028i 0.147847 0.691478i
\(223\) 6.18301 0.414045 0.207022 0.978336i \(-0.433623\pi\)
0.207022 + 0.978336i \(0.433623\pi\)
\(224\) 0.617812 0.617812i 0.0412793 0.0412793i
\(225\) −1.32492 2.69158i −0.0883279 0.179439i
\(226\) 4.38435i 0.291643i
\(227\) 16.9434 + 16.9434i 1.12457 + 1.12457i 0.991045 + 0.133527i \(0.0426304\pi\)
0.133527 + 0.991045i \(0.457370\pi\)
\(228\) 2.90596 4.66939i 0.192452 0.309238i
\(229\) 7.05363 0.466117 0.233058 0.972463i \(-0.425127\pi\)
0.233058 + 0.972463i \(0.425127\pi\)
\(230\) −3.93841 3.93841i −0.259691 0.259691i
\(231\) −1.11366 4.78407i −0.0732737 0.314769i
\(232\) −0.0165891 −0.00108913
\(233\) 4.46090 0.292243 0.146122 0.989267i \(-0.453321\pi\)
0.146122 + 0.989267i \(0.453321\pi\)
\(234\) 5.24761 + 10.6605i 0.343047 + 0.696902i
\(235\) 2.17042 2.17042i 0.141583 0.141583i
\(236\) −7.96028 + 7.96028i −0.518170 + 0.518170i
\(237\) 1.58794 + 0.988240i 0.103148 + 0.0641931i
\(238\) −3.31051 −0.214589
\(239\) −17.0743 17.0743i −1.10444 1.10444i −0.993868 0.110576i \(-0.964730\pi\)
−0.110576 0.993868i \(-0.535270\pi\)
\(240\) −0.915172 + 1.47053i −0.0590741 + 0.0949223i
\(241\) −3.79899 + 3.79899i −0.244715 + 0.244715i −0.818797 0.574083i \(-0.805359\pi\)
0.574083 + 0.818797i \(0.305359\pi\)
\(242\) −0.328543 + 0.328543i −0.0211195 + 0.0211195i
\(243\) 14.1873 + 6.45914i 0.910116 + 0.414354i
\(244\) −6.64635 + 6.64635i −0.425489 + 0.425489i
\(245\) 4.40995 + 4.40995i 0.281742 + 0.281742i
\(246\) 17.8110 + 11.0845i 1.13559 + 0.706722i
\(247\) 12.5765i 0.800221i
\(248\) 7.35632i 0.467127i
\(249\) −10.5743 + 2.46156i −0.670122 + 0.155995i
\(250\) 1.00000i 0.0632456i
\(251\) −2.59871 + 2.59871i −0.164029 + 0.164029i −0.784349 0.620320i \(-0.787003\pi\)
0.620320 + 0.784349i \(0.287003\pi\)
\(252\) −1.15761 2.35168i −0.0729223 0.148142i
\(253\) 12.7834 + 12.7834i 0.803684 + 0.803684i
\(254\) −0.671002 + 0.671002i −0.0421024 + 0.0421024i
\(255\) 6.39183 1.48793i 0.400272 0.0931777i
\(256\) 1.00000 0.0625000
\(257\) 13.1036 + 13.1036i 0.817381 + 0.817381i 0.985728 0.168346i \(-0.0538427\pi\)
−0.168346 + 0.985728i \(0.553843\pi\)
\(258\) 19.2389 4.47855i 1.19776 0.278822i
\(259\) 1.80260 + 4.99958i 0.112008 + 0.310659i
\(260\) 3.96070i 0.245632i
\(261\) −0.0160313 + 0.0471146i −0.000992312 + 0.00291632i
\(262\) 16.5967i 1.02535i
\(263\) 3.79960 0.234293 0.117147 0.993115i \(-0.462625\pi\)
0.117147 + 0.993115i \(0.462625\pi\)
\(264\) 2.97049 4.77308i 0.182821 0.293763i
\(265\) 6.48922 6.48922i 0.398630 0.398630i
\(266\) 2.77433i 0.170105i
\(267\) −13.5056 8.40513i −0.826532 0.514385i
\(268\) 7.74070 0.472838
\(269\) 12.5379i 0.764450i −0.924069 0.382225i \(-0.875158\pi\)
0.924069 0.382225i \(-0.124842\pi\)
\(270\) 3.29204 + 4.02026i 0.200347 + 0.244665i
\(271\) −16.9560 −1.03000 −0.515001 0.857189i \(-0.672209\pi\)
−0.515001 + 0.857189i \(0.672209\pi\)
\(272\) −2.67922 2.67922i −0.162452 0.162452i
\(273\) −5.08883 3.16699i −0.307990 0.191675i
\(274\) 15.0812 + 15.0812i 0.911089 + 0.911089i
\(275\) 3.24582i 0.195731i
\(276\) 8.19049 + 5.09728i 0.493009 + 0.306820i
\(277\) 13.7206 + 13.7206i 0.824392 + 0.824392i 0.986735 0.162342i \(-0.0519048\pi\)
−0.162342 + 0.986735i \(0.551905\pi\)
\(278\) 10.3366 + 10.3366i 0.619951 + 0.619951i
\(279\) −20.8926 7.10896i −1.25081 0.425602i
\(280\) 0.873718i 0.0522146i
\(281\) 16.4710 + 16.4710i 0.982575 + 0.982575i 0.999851 0.0172753i \(-0.00549917\pi\)
−0.0172753 + 0.999851i \(0.505499\pi\)
\(282\) −2.80907 + 4.51371i −0.167278 + 0.268788i
\(283\) −0.457464 0.457464i −0.0271934 0.0271934i 0.693379 0.720573i \(-0.256121\pi\)
−0.720573 + 0.693379i \(0.756121\pi\)
\(284\) −0.580983 −0.0344750
\(285\) −1.24694 5.35658i −0.0738621 0.317296i
\(286\) 12.8557i 0.760176i
\(287\) −10.5824 −0.624660
\(288\) 0.966374 2.84009i 0.0569441 0.167354i
\(289\) 2.64352i 0.155501i
\(290\) −0.0117303 + 0.0117303i −0.000688826 + 0.000688826i
\(291\) 14.8767 + 9.25842i 0.872090 + 0.542738i
\(292\) 11.0501 0.646658
\(293\) 6.48865i 0.379071i 0.981874 + 0.189536i \(0.0606983\pi\)
−0.981874 + 0.189536i \(0.939302\pi\)
\(294\) −9.17113 5.70758i −0.534871 0.332873i
\(295\) 11.2575i 0.655439i
\(296\) −2.58734 + 5.50506i −0.150386 + 0.319975i
\(297\) −10.6854 13.0490i −0.620029 0.757182i
\(298\) −3.02618 3.02618i −0.175302 0.175302i
\(299\) 22.0601 1.27577
\(300\) 0.392697 + 1.68695i 0.0226724 + 0.0973959i
\(301\) −7.04588 + 7.04588i −0.406118 + 0.406118i
\(302\) −11.5029 11.5029i −0.661917 0.661917i
\(303\) −3.87590 16.6501i −0.222664 0.956520i
\(304\) −2.24528 + 2.24528i −0.128776 + 0.128776i
\(305\) 9.39935i 0.538205i
\(306\) −10.1984 + 5.02011i −0.583002 + 0.286981i
\(307\) 4.82152i 0.275178i −0.990489 0.137589i \(-0.956065\pi\)
0.990489 0.137589i \(-0.0439354\pi\)
\(308\) 2.83593i 0.161592i
\(309\) 6.21776 9.99091i 0.353716 0.568363i
\(310\) −5.20171 5.20171i −0.295437 0.295437i
\(311\) −6.45365 + 6.45365i −0.365953 + 0.365953i −0.865999 0.500046i \(-0.833316\pi\)
0.500046 + 0.865999i \(0.333316\pi\)
\(312\) −1.55536 6.68150i −0.0880548 0.378265i
\(313\) −23.6394 + 23.6394i −1.33618 + 1.33618i −0.436449 + 0.899729i \(0.643764\pi\)
−0.899729 + 0.436449i \(0.856236\pi\)
\(314\) −13.0527 + 13.0527i −0.736607 + 0.736607i
\(315\) −2.48144 0.844338i −0.139813 0.0475731i
\(316\) −0.763562 0.763562i −0.0429537 0.0429537i
\(317\) −2.73418 −0.153567 −0.0767834 0.997048i \(-0.524465\pi\)
−0.0767834 + 0.997048i \(0.524465\pi\)
\(318\) −8.39867 + 13.4953i −0.470974 + 0.756777i
\(319\) 0.0380744 0.0380744i 0.00213176 0.00213176i
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) 24.8332 5.78083i 1.38606 0.322654i
\(322\) −4.86639 −0.271193
\(323\) 12.0312 0.669436
\(324\) −7.13224 5.48918i −0.396236 0.304955i
\(325\) 2.80064 + 2.80064i 0.155352 + 0.155352i
\(326\) −10.8301 −0.599825
\(327\) 26.7396 + 16.6412i 1.47870 + 0.920259i
\(328\) −8.56443 8.56443i −0.472891 0.472891i
\(329\) 2.68183i 0.147854i
\(330\) −1.27463 5.47553i −0.0701659 0.301418i
\(331\) −15.9221 + 15.9221i −0.875158 + 0.875158i −0.993029 0.117871i \(-0.962393\pi\)
0.117871 + 0.993029i \(0.462393\pi\)
\(332\) 6.26833 0.344019
\(333\) 13.1345 + 12.6682i 0.719769 + 0.694214i
\(334\) −17.6482 −0.965665
\(335\) 5.47350 5.47350i 0.299049 0.299049i
\(336\) 0.343107 + 1.47392i 0.0187180 + 0.0804087i
\(337\) 6.36440i 0.346691i −0.984861 0.173346i \(-0.944542\pi\)
0.984861 0.173346i \(-0.0554577\pi\)
\(338\) −1.90012 1.90012i −0.103353 0.103353i
\(339\) −6.44732 4.01244i −0.350170 0.217926i
\(340\) −3.78900 −0.205487
\(341\) 16.8838 + 16.8838i 0.914310 + 0.914310i
\(342\) 4.20703 + 8.54659i 0.227490 + 0.462147i
\(343\) 11.5651 0.624455
\(344\) −11.4046 −0.614894
\(345\) 9.39587 2.18723i 0.505857 0.117756i
\(346\) 6.48740 6.48740i 0.348765 0.348765i
\(347\) −11.1501 + 11.1501i −0.598571 + 0.598571i −0.939932 0.341361i \(-0.889112\pi\)
0.341361 + 0.939932i \(0.389112\pi\)
\(348\) 0.0151819 0.0243948i 0.000813836 0.00130770i
\(349\) −5.32513 −0.285048 −0.142524 0.989791i \(-0.545522\pi\)
−0.142524 + 0.989791i \(0.545522\pi\)
\(350\) −0.617812 0.617812i −0.0330234 0.0330234i
\(351\) −20.4791 2.03946i −1.09309 0.108859i
\(352\) −2.29514 + 2.29514i −0.122332 + 0.122332i
\(353\) 1.76426 1.76426i 0.0939022 0.0939022i −0.658595 0.752497i \(-0.728849\pi\)
0.752497 + 0.658595i \(0.228849\pi\)
\(354\) −4.42080 18.9909i −0.234963 1.00935i
\(355\) −0.410817 + 0.410817i −0.0218039 + 0.0218039i
\(356\) 6.49421 + 6.49421i 0.344192 + 0.344192i
\(357\) 3.02969 4.86821i 0.160348 0.257653i
\(358\) 14.1577i 0.748257i
\(359\) 31.2814i 1.65097i −0.564426 0.825483i \(-0.690903\pi\)
0.564426 0.825483i \(-0.309097\pi\)
\(360\) −1.32492 2.69158i −0.0698293 0.141859i
\(361\) 8.91741i 0.469337i
\(362\) −16.0339 + 16.0339i −0.842724 + 0.842724i
\(363\) −0.182459 0.783806i −0.00957661 0.0411391i
\(364\) 2.44697 + 2.44697i 0.128256 + 0.128256i
\(365\) 7.81360 7.81360i 0.408983 0.408983i
\(366\) −3.69110 15.8562i −0.192937 0.828817i
\(367\) 9.81757 0.512473 0.256237 0.966614i \(-0.417517\pi\)
0.256237 + 0.966614i \(0.417517\pi\)
\(368\) −3.93841 3.93841i −0.205304 0.205304i
\(369\) −32.6002 + 16.0473i −1.69710 + 0.835390i
\(370\) 2.06314 + 5.72219i 0.107258 + 0.297482i
\(371\) 8.01823i 0.416286i
\(372\) 10.8177 + 6.73230i 0.560871 + 0.349054i
\(373\) 22.1399i 1.14636i −0.819429 0.573181i \(-0.805709\pi\)
0.819429 0.573181i \(-0.194291\pi\)
\(374\) 12.2984 0.635936
\(375\) 1.47053 + 0.915172i 0.0759379 + 0.0472593i
\(376\) 2.17042 2.17042i 0.111931 0.111931i
\(377\) 0.0657046i 0.00338396i
\(378\) 4.51762 + 0.449899i 0.232362 + 0.0231403i
\(379\) −5.96113 −0.306203 −0.153101 0.988211i \(-0.548926\pi\)
−0.153101 + 0.988211i \(0.548926\pi\)
\(380\) 3.17531i 0.162890i
\(381\) −0.372646 1.60081i −0.0190912 0.0820121i
\(382\) 9.32939 0.477333
\(383\) 9.16947 + 9.16947i 0.468538 + 0.468538i 0.901441 0.432903i \(-0.142511\pi\)
−0.432903 + 0.901441i \(0.642511\pi\)
\(384\) −0.915172 + 1.47053i −0.0467022 + 0.0750427i
\(385\) 2.00531 + 2.00531i 0.102200 + 0.102200i
\(386\) 1.02055i 0.0519448i
\(387\) −11.0211 + 32.3900i −0.560233 + 1.64648i
\(388\) −7.15350 7.15350i −0.363164 0.363164i
\(389\) −6.40269 6.40269i −0.324629 0.324629i 0.525911 0.850540i \(-0.323725\pi\)
−0.850540 + 0.525911i \(0.823725\pi\)
\(390\) −5.82434 3.62473i −0.294927 0.183545i
\(391\) 21.1038i 1.06726i
\(392\) 4.40995 + 4.40995i 0.222736 + 0.222736i
\(393\) 24.4059 + 15.1888i 1.23112 + 0.766175i
\(394\) 10.4709 + 10.4709i 0.527518 + 0.527518i
\(395\) −1.07984 −0.0543327
\(396\) 4.30045 + 8.73639i 0.216106 + 0.439020i
\(397\) 2.29166i 0.115015i −0.998345 0.0575075i \(-0.981685\pi\)
0.998345 0.0575075i \(-0.0183153\pi\)
\(398\) −21.6821 −1.08683
\(399\) −4.07973 2.53899i −0.204242 0.127108i
\(400\) 1.00000i 0.0500000i
\(401\) −17.9575 + 17.9575i −0.896756 + 0.896756i −0.995148 0.0983914i \(-0.968630\pi\)
0.0983914 + 0.995148i \(0.468630\pi\)
\(402\) −7.08407 + 11.3829i −0.353321 + 0.567729i
\(403\) 29.1362 1.45138
\(404\) 9.86993i 0.491048i
\(405\) −8.92469 + 1.16182i −0.443472 + 0.0577313i
\(406\) 0.0144942i 0.000719336i
\(407\) −6.69660 18.5732i −0.331938 0.920640i
\(408\) 6.39183 1.48793i 0.316443 0.0736634i
\(409\) 2.75786 + 2.75786i 0.136367 + 0.136367i 0.771995 0.635628i \(-0.219259\pi\)
−0.635628 + 0.771995i \(0.719259\pi\)
\(410\) −12.1119 −0.598166
\(411\) −35.9793 + 8.37547i −1.77473 + 0.413131i
\(412\) −4.80415 + 4.80415i −0.236683 + 0.236683i
\(413\) 6.95504 + 6.95504i 0.342235 + 0.342235i
\(414\) −14.9914 + 7.37947i −0.736788 + 0.362681i
\(415\) 4.43238 4.43238i 0.217577 0.217577i
\(416\) 3.96070i 0.194190i
\(417\) −24.6602 + 5.74054i −1.20761 + 0.281115i
\(418\) 10.3065i 0.504107i
\(419\) 9.86970i 0.482166i −0.970504 0.241083i \(-0.922497\pi\)
0.970504 0.241083i \(-0.0775027\pi\)
\(420\) 1.28483 + 0.799603i 0.0626932 + 0.0390166i
\(421\) −5.59923 5.59923i −0.272890 0.272890i 0.557373 0.830262i \(-0.311809\pi\)
−0.830262 + 0.557373i \(0.811809\pi\)
\(422\) −10.5186 + 10.5186i −0.512039 + 0.512039i
\(423\) −4.06676 8.26165i −0.197733 0.401695i
\(424\) 6.48922 6.48922i 0.315144 0.315144i
\(425\) −2.67922 + 2.67922i −0.129961 + 0.129961i
\(426\) 0.531700 0.854354i 0.0257609 0.0413936i
\(427\) 5.80703 + 5.80703i 0.281022 + 0.281022i
\(428\) −14.7208 −0.711558
\(429\) 18.9048 + 11.7652i 0.912731 + 0.568030i
\(430\) −8.06425 + 8.06425i −0.388893 + 0.388893i
\(431\) −16.1018 + 16.1018i −0.775598 + 0.775598i −0.979079 0.203481i \(-0.934774\pi\)
0.203481 + 0.979079i \(0.434774\pi\)
\(432\) 3.29204 + 4.02026i 0.158388 + 0.193425i
\(433\) 32.3378 1.55405 0.777027 0.629468i \(-0.216727\pi\)
0.777027 + 0.629468i \(0.216727\pi\)
\(434\) −6.42735 −0.308523
\(435\) −0.00651450 0.0279850i −0.000312347 0.00134178i
\(436\) −12.8578 12.8578i −0.615776 0.615776i
\(437\) 17.6857 0.846021
\(438\) −10.1128 + 16.2495i −0.483206 + 0.776432i
\(439\) 18.7980 + 18.7980i 0.897177 + 0.897177i 0.995186 0.0980082i \(-0.0312472\pi\)
−0.0980082 + 0.995186i \(0.531247\pi\)
\(440\) 3.24582i 0.154739i
\(441\) 16.7863 8.26301i 0.799349 0.393477i
\(442\) 10.6116 10.6116i 0.504743 0.504743i
\(443\) −14.1166 −0.670698 −0.335349 0.942094i \(-0.608854\pi\)
−0.335349 + 0.942094i \(0.608854\pi\)
\(444\) −5.72750 8.84284i −0.271815 0.419662i
\(445\) 9.18420 0.435373
\(446\) 4.37205 4.37205i 0.207022 0.207022i
\(447\) 7.21957 1.68061i 0.341474 0.0794903i
\(448\) 0.873718i 0.0412793i
\(449\) 6.93149 + 6.93149i 0.327117 + 0.327117i 0.851489 0.524372i \(-0.175700\pi\)
−0.524372 + 0.851489i \(0.675700\pi\)
\(450\) −2.84009 0.966374i −0.133883 0.0455553i
\(451\) 39.3132 1.85119
\(452\) 3.10020 + 3.10020i 0.145821 + 0.145821i
\(453\) 27.4425 6.38822i 1.28936 0.300145i
\(454\) 23.9616 1.12457
\(455\) 3.46054 0.162233
\(456\) −1.24694 5.35658i −0.0583931 0.250845i
\(457\) 14.8024 14.8024i 0.692425 0.692425i −0.270340 0.962765i \(-0.587136\pi\)
0.962765 + 0.270340i \(0.0871361\pi\)
\(458\) 4.98767 4.98767i 0.233058 0.233058i
\(459\) 1.95105 19.5913i 0.0910671 0.914443i
\(460\) −5.56975 −0.259691
\(461\) −5.43289 5.43289i −0.253035 0.253035i 0.569179 0.822214i \(-0.307261\pi\)
−0.822214 + 0.569179i \(0.807261\pi\)
\(462\) −4.17033 2.59537i −0.194021 0.120747i
\(463\) −1.14209 + 1.14209i −0.0530773 + 0.0530773i −0.733147 0.680070i \(-0.761949\pi\)
0.680070 + 0.733147i \(0.261949\pi\)
\(464\) −0.0117303 + 0.0117303i −0.000544565 + 0.000544565i
\(465\) 12.4097 2.88881i 0.575487 0.133965i
\(466\) 3.15433 3.15433i 0.146122 0.146122i
\(467\) 8.44172 + 8.44172i 0.390636 + 0.390636i 0.874914 0.484278i \(-0.160918\pi\)
−0.484278 + 0.874914i \(0.660918\pi\)
\(468\) 11.2488 + 3.82752i 0.519974 + 0.176927i
\(469\) 6.76319i 0.312295i
\(470\) 3.06944i 0.141583i
\(471\) −7.24893 31.1399i −0.334013 1.43485i
\(472\) 11.2575i 0.518170i
\(473\) 26.1751 26.1751i 1.20353 1.20353i
\(474\) 1.82163 0.424050i 0.0836704 0.0194773i
\(475\) 2.24528 + 2.24528i 0.103021 + 0.103021i
\(476\) −2.34089 + 2.34089i −0.107294 + 0.107294i
\(477\) −12.1590 24.7010i −0.556721 1.13098i
\(478\) −24.1467 −1.10444
\(479\) −9.71035 9.71035i −0.443677 0.443677i 0.449569 0.893246i \(-0.351578\pi\)
−0.893246 + 0.449569i \(0.851578\pi\)
\(480\) 0.392697 + 1.68695i 0.0179241 + 0.0769982i
\(481\) −21.8039 10.2477i −0.994173 0.467254i
\(482\) 5.37258i 0.244715i
\(483\) 4.45359 7.15618i 0.202645 0.325617i
\(484\) 0.464630i 0.0211195i
\(485\) −10.1166 −0.459370
\(486\) 14.5992 5.46463i 0.662235 0.247881i
\(487\) −3.87550 + 3.87550i −0.175616 + 0.175616i −0.789442 0.613826i \(-0.789630\pi\)
0.613826 + 0.789442i \(0.289630\pi\)
\(488\) 9.39935i 0.425489i
\(489\) 9.91143 15.9260i 0.448210 0.720199i
\(490\) 6.23662 0.281742
\(491\) 37.5934i 1.69657i −0.529541 0.848284i \(-0.677636\pi\)
0.529541 0.848284i \(-0.322364\pi\)
\(492\) 20.4322 4.75632i 0.921154 0.214432i
\(493\) 0.0628561 0.00283090
\(494\) −8.89290 8.89290i −0.400111 0.400111i
\(495\) 9.21844 + 3.13668i 0.414338 + 0.140983i
\(496\) −5.20171 5.20171i −0.233563 0.233563i
\(497\) 0.507616i 0.0227697i
\(498\) −5.73660 + 9.21777i −0.257063 + 0.413058i
\(499\) −13.8728 13.8728i −0.621031 0.621031i 0.324764 0.945795i \(-0.394715\pi\)
−0.945795 + 0.324764i \(0.894715\pi\)
\(500\) −0.707107 0.707107i −0.0316228 0.0316228i
\(501\) 16.1511 25.9522i 0.721579 1.15946i
\(502\) 3.67514i 0.164029i
\(503\) 11.0121 + 11.0121i 0.491005 + 0.491005i 0.908623 0.417618i \(-0.137135\pi\)
−0.417618 + 0.908623i \(0.637135\pi\)
\(504\) −2.48144 0.844338i −0.110532 0.0376098i
\(505\) 6.97910 + 6.97910i 0.310566 + 0.310566i
\(506\) 18.0784 0.803684
\(507\) 4.53313 1.05525i 0.201323 0.0468652i
\(508\) 0.948940i 0.0421024i
\(509\) 8.43066 0.373683 0.186841 0.982390i \(-0.440175\pi\)
0.186841 + 0.982390i \(0.440175\pi\)
\(510\) 3.46758 5.57183i 0.153547 0.246725i
\(511\) 9.65467i 0.427098i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −16.4182 1.63505i −0.724880 0.0721890i
\(514\) 18.5313 0.817381
\(515\) 6.79409i 0.299383i
\(516\) 10.4372 16.7708i 0.459470 0.738292i
\(517\) 9.96287i 0.438167i
\(518\) 4.80987 + 2.26060i 0.211334 + 0.0993251i
\(519\) 3.60283 + 15.4770i 0.158147 + 0.679365i
\(520\) 2.80064 + 2.80064i 0.122816 + 0.122816i
\(521\) −10.1891 −0.446392 −0.223196 0.974774i \(-0.571649\pi\)
−0.223196 + 0.974774i \(0.571649\pi\)
\(522\) 0.0219792 + 0.0446509i 0.000962005 + 0.00195432i
\(523\) 21.5024 21.5024i 0.940233 0.940233i −0.0580790 0.998312i \(-0.518498\pi\)
0.998312 + 0.0580790i \(0.0184975\pi\)
\(524\) −11.7356 11.7356i −0.512673 0.512673i
\(525\) 1.47392 0.343107i 0.0643269 0.0149744i
\(526\) 2.68672 2.68672i 0.117147 0.117147i
\(527\) 27.8731i 1.21417i
\(528\) −1.27463 5.47553i −0.0554710 0.238292i
\(529\) 8.02212i 0.348788i
\(530\) 9.17714i 0.398630i
\(531\) 31.9724 + 10.8790i 1.38748 + 0.472108i
\(532\) 1.96174 + 1.96174i 0.0850524 + 0.0850524i
\(533\) 33.9212 33.9212i 1.46929 1.46929i
\(534\) −15.4933 + 3.60661i −0.670459 + 0.156073i
\(535\) −10.4092 + 10.4092i −0.450029 + 0.450029i
\(536\) 5.47350 5.47350i 0.236419 0.236419i
\(537\) −20.8193 12.9567i −0.898420 0.559124i
\(538\) −8.86564 8.86564i −0.382225 0.382225i
\(539\) −20.2430 −0.871926
\(540\) 5.17058 + 0.514925i 0.222506 + 0.0221588i
\(541\) −14.4179 + 14.4179i −0.619875 + 0.619875i −0.945499 0.325625i \(-0.894425\pi\)
0.325625 + 0.945499i \(0.394425\pi\)
\(542\) −11.9897 + 11.9897i −0.515001 + 0.515001i
\(543\) −8.90456 38.2522i −0.382131 1.64156i
\(544\) −3.78900 −0.162452
\(545\) −18.1836 −0.778902
\(546\) −5.83774 + 1.35894i −0.249832 + 0.0581574i
\(547\) −16.2982 16.2982i −0.696862 0.696862i 0.266870 0.963732i \(-0.414010\pi\)
−0.963732 + 0.266870i \(0.914010\pi\)
\(548\) 21.3281 0.911089
\(549\) 26.6950 + 9.08329i 1.13932 + 0.387665i
\(550\) 2.29514 + 2.29514i 0.0978653 + 0.0978653i
\(551\) 0.0526756i 0.00224406i
\(552\) 9.39587 2.18723i 0.399915 0.0930945i
\(553\) −0.667138 + 0.667138i −0.0283696 + 0.0283696i
\(554\) 19.4039 0.824392
\(555\) −10.3028 2.20288i −0.437329 0.0935069i
\(556\) 14.6182 0.619951
\(557\) 13.8613 13.8613i 0.587322 0.587322i −0.349583 0.936905i \(-0.613677\pi\)
0.936905 + 0.349583i \(0.113677\pi\)
\(558\) −19.8001 + 9.74653i −0.838206 + 0.412603i
\(559\) 45.1702i 1.91049i
\(560\) −0.617812 0.617812i −0.0261073 0.0261073i
\(561\) −11.2552 + 18.0852i −0.475193 + 0.763557i
\(562\) 23.2935 0.982575
\(563\) −9.05310 9.05310i −0.381543 0.381543i 0.490115 0.871658i \(-0.336955\pi\)
−0.871658 + 0.490115i \(0.836955\pi\)
\(564\) 1.20536 + 5.17799i 0.0507549 + 0.218033i
\(565\) 4.38435 0.184451
\(566\) −0.646951 −0.0271934
\(567\) −4.79600 + 6.23157i −0.201413 + 0.261701i
\(568\) −0.410817 + 0.410817i −0.0172375 + 0.0172375i
\(569\) −22.3048 + 22.3048i −0.935066 + 0.935066i −0.998017 0.0629509i \(-0.979949\pi\)
0.0629509 + 0.998017i \(0.479949\pi\)
\(570\) −4.66939 2.90596i −0.195579 0.121717i
\(571\) −15.8222 −0.662138 −0.331069 0.943607i \(-0.607409\pi\)
−0.331069 + 0.943607i \(0.607409\pi\)
\(572\) −9.09039 9.09039i −0.380088 0.380088i
\(573\) −8.53800 + 13.7192i −0.356680 + 0.573126i
\(574\) −7.48290 + 7.48290i −0.312330 + 0.312330i
\(575\) −3.93841 + 3.93841i −0.164243 + 0.164243i
\(576\) −1.32492 2.69158i −0.0552049 0.112149i
\(577\) −16.3027 + 16.3027i −0.678689 + 0.678689i −0.959704 0.281014i \(-0.909329\pi\)
0.281014 + 0.959704i \(0.409329\pi\)
\(578\) −1.86925 1.86925i −0.0777505 0.0777505i
\(579\) −1.50076 0.933983i −0.0623693 0.0388150i
\(580\) 0.0165891i 0.000688826i
\(581\) 5.47675i 0.227214i
\(582\) 17.0661 3.97275i 0.707414 0.164676i
\(583\) 29.7874i 1.23367i
\(584\) 7.81360 7.81360i 0.323329 0.323329i
\(585\) 10.6605 5.24761i 0.440759 0.216962i
\(586\) 4.58817 + 4.58817i 0.189536 + 0.189536i
\(587\) −12.6200 + 12.6200i −0.520882 + 0.520882i −0.917838 0.396956i \(-0.870067\pi\)
0.396956 + 0.917838i \(0.370067\pi\)
\(588\) −10.5208 + 2.44910i −0.433872 + 0.100999i
\(589\) 23.3586 0.962474
\(590\) 7.96028 + 7.96028i 0.327719 + 0.327719i
\(591\) −24.9805 + 5.81512i −1.02756 + 0.239202i
\(592\) 2.06314 + 5.72219i 0.0847946 + 0.235180i
\(593\) 21.6189i 0.887782i −0.896081 0.443891i \(-0.853598\pi\)
0.896081 0.443891i \(-0.146402\pi\)
\(594\) −16.7828 1.67136i −0.688606 0.0685765i
\(595\) 3.31051i 0.135718i
\(596\) −4.27966 −0.175302
\(597\) 19.8429 31.8842i 0.812114 1.30493i
\(598\) 15.5989 15.5989i 0.637885 0.637885i
\(599\) 0.728152i 0.0297515i 0.999889 + 0.0148757i \(0.00473527\pi\)
−0.999889 + 0.0148757i \(0.995265\pi\)
\(600\) 1.47053 + 0.915172i 0.0600341 + 0.0373618i
\(601\) 39.4004 1.60718 0.803588 0.595186i \(-0.202921\pi\)
0.803588 + 0.595186i \(0.202921\pi\)
\(602\) 9.96438i 0.406118i
\(603\) −10.2558 20.8347i −0.417648 0.848454i
\(604\) −16.2675 −0.661917
\(605\) 0.328543 + 0.328543i 0.0133572 + 0.0133572i
\(606\) −14.5140 9.03269i −0.589592 0.366928i
\(607\) 18.6181 + 18.6181i 0.755684 + 0.755684i 0.975534 0.219850i \(-0.0705567\pi\)
−0.219850 + 0.975534i \(0.570557\pi\)
\(608\) 3.17531i 0.128776i
\(609\) −0.0213142 0.0132647i −0.000863694 0.000537513i
\(610\) 6.64635 + 6.64635i 0.269103 + 0.269103i
\(611\) 8.59641 + 8.59641i 0.347774 + 0.347774i
\(612\) −3.66159 + 10.7611i −0.148011 + 0.434991i
\(613\) 34.7946i 1.40534i −0.711516 0.702670i \(-0.751991\pi\)
0.711516 0.702670i \(-0.248009\pi\)
\(614\) −3.40933 3.40933i −0.137589 0.137589i
\(615\) 11.0845 17.8110i 0.446970 0.718207i
\(616\) 2.00531 + 2.00531i 0.0807962 + 0.0807962i
\(617\) −9.78568 −0.393957 −0.196978 0.980408i \(-0.563113\pi\)
−0.196978 + 0.980408i \(0.563113\pi\)
\(618\) −2.66802 11.4613i −0.107324 0.461040i
\(619\) 36.0295i 1.44815i −0.689723 0.724074i \(-0.742268\pi\)
0.689723 0.724074i \(-0.257732\pi\)
\(620\) −7.35632 −0.295437
\(621\) 2.86800 28.7988i 0.115089 1.15566i
\(622\) 9.12683i 0.365953i
\(623\) 5.67411 5.67411i 0.227328 0.227328i
\(624\) −5.82434 3.62473i −0.233160 0.145105i
\(625\) −1.00000 −0.0400000
\(626\) 33.4312i 1.33618i
\(627\) 15.1560 + 9.43222i 0.605273 + 0.376687i
\(628\) 18.4593i 0.736607i
\(629\) 9.80340 20.8586i 0.390887 0.831689i
\(630\) −2.35168 + 1.15761i −0.0936932 + 0.0461201i
\(631\) −0.797835 0.797835i −0.0317613 0.0317613i 0.691048 0.722809i \(-0.257149\pi\)
−0.722809 + 0.691048i \(0.757149\pi\)
\(632\) −1.07984 −0.0429537
\(633\) −5.84160 25.0943i −0.232183 0.997409i
\(634\) −1.93336 + 1.93336i −0.0767834 + 0.0767834i
\(635\) 0.671002 + 0.671002i 0.0266279 + 0.0266279i
\(636\) 3.60384 + 15.4813i 0.142902 + 0.613875i
\(637\) −17.4665 + 17.4665i −0.692049 + 0.692049i
\(638\) 0.0538454i 0.00213176i
\(639\) 0.769756 + 1.56376i 0.0304511 + 0.0618615i
\(640\) 1.00000i 0.0395285i
\(641\) 0.310559i 0.0122663i 0.999981 + 0.00613317i \(0.00195226\pi\)
−0.999981 + 0.00613317i \(0.998048\pi\)
\(642\) 13.4721 21.6474i 0.531701 0.854355i
\(643\) 24.4682 + 24.4682i 0.964931 + 0.964931i 0.999406 0.0344744i \(-0.0109757\pi\)
−0.0344744 + 0.999406i \(0.510976\pi\)
\(644\) −3.44106 + 3.44106i −0.135597 + 0.135597i
\(645\) −4.47855 19.2389i −0.176343 0.757531i
\(646\) 8.50737 8.50737i 0.334718 0.334718i
\(647\) −4.14891 + 4.14891i −0.163111 + 0.163111i −0.783943 0.620833i \(-0.786795\pi\)
0.620833 + 0.783943i \(0.286795\pi\)
\(648\) −8.92469 + 1.16182i −0.350595 + 0.0456406i
\(649\) −25.8377 25.8377i −1.01422 1.01422i
\(650\) 3.96070 0.155352
\(651\) 5.88213 9.45161i 0.230539 0.370438i
\(652\) −7.65805 + 7.65805i −0.299912 + 0.299912i
\(653\) 6.38197 6.38197i 0.249746 0.249746i −0.571120 0.820866i \(-0.693491\pi\)
0.820866 + 0.571120i \(0.193491\pi\)
\(654\) 30.6748 7.14067i 1.19948 0.279222i
\(655\) −16.5967 −0.648486
\(656\) −12.1119 −0.472891
\(657\) −14.6405 29.7422i −0.571180 1.16035i
\(658\) −1.89634 1.89634i −0.0739270 0.0739270i
\(659\) 40.6095 1.58192 0.790960 0.611867i \(-0.209581\pi\)
0.790960 + 0.611867i \(0.209581\pi\)
\(660\) −4.77308 2.97049i −0.185792 0.115626i
\(661\) 18.2484 + 18.2484i 0.709782 + 0.709782i 0.966489 0.256707i \(-0.0826375\pi\)
−0.256707 + 0.966489i \(0.582637\pi\)
\(662\) 22.5172i 0.875158i
\(663\) 5.89324 + 25.3162i 0.228875 + 0.983198i
\(664\) 4.43238 4.43238i 0.172010 0.172010i
\(665\) 2.77433 0.107584
\(666\) 18.2453 0.329742i 0.706991 0.0127772i
\(667\) 0.0923973 0.00357764
\(668\) −12.4791 + 12.4791i −0.482833 + 0.482833i
\(669\) 2.42805 + 10.4304i 0.0938738 + 0.403263i
\(670\) 7.74070i 0.299049i
\(671\) −21.5729 21.5729i −0.832811 0.832811i
\(672\) 1.28483 + 0.799603i 0.0495633 + 0.0308453i
\(673\) 43.2033 1.66536 0.832682 0.553752i \(-0.186804\pi\)
0.832682 + 0.553752i \(0.186804\pi\)
\(674\) −4.50031 4.50031i −0.173346 0.173346i
\(675\) 4.02026 3.29204i 0.154740 0.126711i
\(676\) −2.68718 −0.103353
\(677\) −20.8361 −0.800797 −0.400399 0.916341i \(-0.631128\pi\)
−0.400399 + 0.916341i \(0.631128\pi\)
\(678\) −7.39616 + 1.72172i −0.284048 + 0.0661223i
\(679\) −6.25014 + 6.25014i −0.239859 + 0.239859i
\(680\) −2.67922 + 2.67922i −0.102744 + 0.102744i
\(681\) −21.9290 + 35.2362i −0.840320 + 1.35025i
\(682\) 23.8773 0.914310
\(683\) −28.5744 28.5744i −1.09337 1.09337i −0.995166 0.0982022i \(-0.968691\pi\)
−0.0982022 0.995166i \(-0.531309\pi\)
\(684\) 9.01817 + 3.06854i 0.344818 + 0.117328i
\(685\) 15.0812 15.0812i 0.576223 0.576223i
\(686\) 8.17774 8.17774i 0.312228 0.312228i
\(687\) 2.76994 + 11.8991i 0.105680 + 0.453979i
\(688\) −8.06425 + 8.06425i −0.307447 + 0.307447i
\(689\) 25.7019 + 25.7019i 0.979164 + 0.979164i
\(690\) 5.09728 8.19049i 0.194050 0.311807i
\(691\) 34.9094i 1.32802i 0.747725 + 0.664008i \(0.231146\pi\)
−0.747725 + 0.664008i \(0.768854\pi\)
\(692\) 9.17456i 0.348765i
\(693\) 7.63314 3.75738i 0.289959 0.142731i
\(694\) 15.7687i 0.598571i
\(695\) 10.3366 10.3366i 0.392091 0.392091i
\(696\) −0.00651450 0.0279850i −0.000246932 0.00106077i
\(697\) 32.4506 + 32.4506i 1.22915 + 1.22915i
\(698\) −3.76544 + 3.76544i −0.142524 + 0.142524i
\(699\) 1.75178 + 7.52530i 0.0662585 + 0.284633i
\(700\) −0.873718 −0.0330234
\(701\) −5.73772 5.73772i −0.216711 0.216711i 0.590400 0.807111i \(-0.298970\pi\)
−0.807111 + 0.590400i \(0.798970\pi\)
\(702\) −15.9230 + 13.0388i −0.600977 + 0.492118i
\(703\) −17.4803 8.21559i −0.659281 0.309857i
\(704\) 3.24582i 0.122332i
\(705\) 4.51371 + 2.80907i 0.169996 + 0.105796i
\(706\) 2.49504i 0.0939022i
\(707\) 8.62354 0.324322
\(708\) −16.5545 10.3026i −0.622158 0.387195i
\(709\) −18.6081 + 18.6081i −0.698842 + 0.698842i −0.964161 0.265319i \(-0.914523\pi\)
0.265319 + 0.964161i \(0.414523\pi\)
\(710\) 0.580983i 0.0218039i
\(711\) −1.04353 + 3.06685i −0.0391354 + 0.115016i
\(712\) 9.18420 0.344192
\(713\) 40.9729i 1.53445i
\(714\) −1.30003 5.58466i −0.0486524 0.209001i
\(715\) −12.8557 −0.480778
\(716\) 10.0110 + 10.0110i 0.374129 + 0.374129i
\(717\) 22.0984 35.5084i 0.825279 1.32609i
\(718\) −22.1193 22.1193i −0.825483 0.825483i
\(719\) 18.6694i 0.696252i 0.937448 + 0.348126i \(0.113182\pi\)
−0.937448 + 0.348126i \(0.886818\pi\)
\(720\) −2.84009 0.966374i −0.105844 0.0360146i
\(721\) 4.19747 + 4.19747i 0.156322 + 0.156322i
\(722\) 6.30556 + 6.30556i 0.234669 + 0.234669i
\(723\) −7.90055 4.91684i −0.293825 0.182859i
\(724\) 22.6754i 0.842724i
\(725\) 0.0117303 + 0.0117303i 0.000435652 + 0.000435652i
\(726\) −0.683252 0.425216i −0.0253579 0.0157813i
\(727\) 20.9335 + 20.9335i 0.776381 + 0.776381i 0.979213 0.202833i \(-0.0650147\pi\)
−0.202833 + 0.979213i \(0.565015\pi\)
\(728\) 3.46054 0.128256
\(729\) −5.32492 + 26.4697i −0.197219 + 0.980359i
\(730\) 11.0501i 0.408983i
\(731\) 43.2119 1.59825
\(732\) −13.8220 8.60203i −0.510877 0.317940i
\(733\) 45.5805i 1.68355i 0.539825 + 0.841777i \(0.318490\pi\)
−0.539825 + 0.841777i \(0.681510\pi\)
\(734\) 6.94207 6.94207i 0.256237 0.256237i
\(735\) −5.70758 + 9.17113i −0.210527 + 0.338282i
\(736\) −5.56975 −0.205304
\(737\) 25.1249i 0.925489i
\(738\) −11.7047 + 34.3990i −0.430854 + 1.26624i
\(739\) 30.7839i 1.13240i −0.824267 0.566202i \(-0.808412\pi\)
0.824267 0.566202i \(-0.191588\pi\)
\(740\) 5.50506 + 2.58734i 0.202370 + 0.0951124i
\(741\) 21.2158 4.93874i 0.779383 0.181429i
\(742\) −5.66975 5.66975i −0.208143 0.208143i
\(743\) −5.50584 −0.201990 −0.100995 0.994887i \(-0.532203\pi\)
−0.100995 + 0.994887i \(0.532203\pi\)
\(744\) 12.4097 2.88881i 0.454963 0.105909i
\(745\) −3.02618 + 3.02618i −0.110871 + 0.110871i
\(746\) −15.6553 15.6553i −0.573181 0.573181i
\(747\) −8.30503 16.8717i −0.303865 0.617303i
\(748\) 8.69629 8.69629i 0.317968 0.317968i
\(749\) 12.8618i 0.469962i
\(750\) 1.68695 0.392697i 0.0615986 0.0143393i
\(751\) 45.1238i 1.64659i −0.567613 0.823295i \(-0.692133\pi\)
0.567613 0.823295i \(-0.307867\pi\)
\(752\) 3.06944i 0.111931i
\(753\) −5.40440 3.36339i −0.196947 0.122569i
\(754\) −0.0464602 0.0464602i −0.00169198 0.00169198i
\(755\) −11.5029 + 11.5029i −0.418633 + 0.418633i
\(756\) 3.51257 2.87632i 0.127751 0.104611i
\(757\) 14.1289 14.1289i 0.513524 0.513524i −0.402080 0.915605i \(-0.631713\pi\)
0.915605 + 0.402080i \(0.131713\pi\)
\(758\) −4.21515 + 4.21515i −0.153101 + 0.153101i
\(759\) −16.5449 + 26.5849i −0.600541 + 0.964970i
\(760\) 2.24528 + 2.24528i 0.0814450 + 0.0814450i
\(761\) −0.980959 −0.0355597 −0.0177799 0.999842i \(-0.505660\pi\)
−0.0177799 + 0.999842i \(0.505660\pi\)
\(762\) −1.39545 0.868444i −0.0505517 0.0314604i
\(763\) −11.2341 + 11.2341i −0.406701 + 0.406701i
\(764\) 6.59688 6.59688i 0.238667 0.238667i
\(765\) 5.02011 + 10.1984i 0.181502 + 0.368723i
\(766\) 12.9676 0.468538
\(767\) −44.5878 −1.60997
\(768\) 0.392697 + 1.68695i 0.0141702 + 0.0608724i
\(769\) −5.20667 5.20667i −0.187757 0.187757i 0.606968 0.794726i \(-0.292385\pi\)
−0.794726 + 0.606968i \(0.792385\pi\)
\(770\) 2.83593 0.102200
\(771\) −16.9594 + 27.2509i −0.610776 + 0.981416i
\(772\) 0.721641 + 0.721641i 0.0259724 + 0.0259724i
\(773\) 19.8914i 0.715444i 0.933828 + 0.357722i \(0.116446\pi\)
−0.933828 + 0.357722i \(0.883554\pi\)
\(774\) 15.1101 + 30.6963i 0.543123 + 1.10336i
\(775\) −5.20171 + 5.20171i −0.186851 + 0.186851i
\(776\) −10.1166 −0.363164
\(777\) −7.72614 + 5.00422i −0.277174 + 0.179525i
\(778\) −9.05477 −0.324629