Properties

Label 1110.2.u.f.401.2
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 401.2
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.f.191.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.392697 + 1.68695i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.915172 - 1.47053i) q^{6} -0.873718 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.69158 - 1.32492i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.392697 + 1.68695i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.915172 - 1.47053i) 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} +(-1.47053 + 0.915172i) q^{15} -1.00000 q^{16} +(-2.67922 - 2.67922i) q^{17} +(2.84009 - 0.966374i) 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} +(-1.47053 + 0.915172i) 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} +(3.62473 + 5.82434i) q^{39} +1.00000i q^{40} -12.1119 q^{41} +(0.799603 + 1.28483i) q^{42} +(8.06425 - 8.06425i) q^{43} +3.24582i q^{44} +(-0.966374 - 2.84009i) 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} +(5.57183 - 3.46758i) q^{51} +(-2.80064 - 2.80064i) q^{52} -9.17714i q^{53} +(0.514925 + 5.17058i) q^{54} +(-2.29514 - 2.29514i) q^{55} +(-0.617812 - 0.617812i) q^{56} +(2.90596 + 4.66939i) q^{57} -0.0165891i q^{58} +(7.96028 + 7.96028i) q^{59} +(0.915172 + 1.47053i) 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} +(2.97049 + 4.77308i) q^{66} +7.74070i q^{67} +(-2.67922 + 2.67922i) q^{68} +(8.19049 - 5.09728i) q^{69} +0.873718 q^{70} +0.580983i q^{71} +(-0.966374 - 2.84009i) 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} +(-0.0151819 - 0.0243948i) 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} +(-10.8177 + 6.73230i) q^{93} +(2.17042 + 2.17042i) q^{94} +3.17531 q^{95} +(0.915172 + 1.47053i) 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
\(6\) −0.915172 1.47053i −0.373618 0.600341i
\(7\) −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 \(-0.662757\pi\)
−0.489326 + 0.872101i \(0.662757\pi\)
\(12\) 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
\(15\) −1.47053 + 0.915172i −0.379689 + 0.236297i
\(16\) −1.00000 −0.250000
\(17\) −2.67922 2.67922i −0.649807 0.649807i 0.303139 0.952946i \(-0.401965\pi\)
−0.952946 + 0.303139i \(0.901965\pi\)
\(18\) 2.84009 0.966374i 0.669416 0.227777i
\(19\) 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 0.165067 0.986282i \(-0.447216\pi\)
−0.986282 + 0.165067i \(0.947216\pi\)
\(24\) −1.47053 + 0.915172i −0.300171 + 0.186809i
\(25\) 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 −0.708195 0.706017i \(-0.750490\pi\)
0.706017 + 0.708195i \(0.250490\pi\)
\(30\) 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
\(39\) 3.62473 + 5.82434i 0.580421 + 0.932640i
\(40\) 1.00000i 0.158114i
\(41\) −12.1119 −1.89157 −0.945783 0.324799i \(-0.894703\pi\)
−0.945783 + 0.324799i \(0.894703\pi\)
\(42\) 0.799603 + 1.28483i 0.123381 + 0.198253i
\(43\) 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
\(45\) −0.966374 2.84009i −0.144059 0.423376i
\(46\) 5.56975 0.821215
\(47\) 3.06944i 0.447724i −0.974621 0.223862i \(-0.928133\pi\)
0.974621 0.223862i \(-0.0718666\pi\)
\(48\) 0.392697 1.68695i 0.0566810 0.243490i
\(49\) −6.23662 −0.890945
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) 5.57183 3.46758i 0.780213 0.485559i
\(52\) −2.80064 2.80064i −0.388379 0.388379i
\(53\) 9.17714i 1.26058i −0.776361 0.630289i \(-0.782937\pi\)
0.776361 0.630289i \(-0.217063\pi\)
\(54\) 0.514925 + 5.17058i 0.0700724 + 0.703626i
\(55\) −2.29514 2.29514i −0.309477 0.309477i
\(56\) −0.617812 0.617812i −0.0825586 0.0825586i
\(57\) 2.90596 + 4.66939i 0.384903 + 0.618476i
\(58\) 0.0165891i 0.00217826i
\(59\) 7.96028 + 7.96028i 1.03634 + 1.03634i 0.999314 + 0.0370254i \(0.0117882\pi\)
0.0370254 + 0.999314i \(0.488212\pi\)
\(60\) 0.915172 + 1.47053i 0.118148 + 0.189845i
\(61\) −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
\(66\) 2.97049 + 4.77308i 0.365642 + 0.587526i
\(67\) 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
\(69\) 8.19049 5.09728i 0.986019 0.613641i
\(70\) 0.873718 0.104429
\(71\) 0.580983i 0.0689500i 0.999406 + 0.0344750i \(0.0109759\pi\)
−0.999406 + 0.0344750i \(0.989024\pi\)
\(72\) −0.966374 2.84009i −0.113888 0.334708i
\(73\) 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 \(-0.888211\pi\)
0.938963 0.344019i \(-0.111789\pi\)
\(84\) −1.47392 0.343107i −0.160817 0.0374360i
\(85\) 3.78900i 0.410974i
\(86\) 11.4046i 1.22979i
\(87\) −0.0151819 0.0243948i −0.00162767 0.00261540i
\(88\) −2.29514 2.29514i −0.244663 0.244663i
\(89\) 6.49421 6.49421i 0.688385 0.688385i −0.273490 0.961875i \(-0.588178\pi\)
0.961875 + 0.273490i \(0.0881780\pi\)
\(90\) 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
\(93\) −10.8177 + 6.73230i −1.12174 + 0.698107i
\(94\) 2.17042 + 2.17042i 0.223862 + 0.223862i
\(95\) 3.17531 0.325780
\(96\) 0.915172 + 1.47053i 0.0934044 + 0.150085i
\(97\) 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 \(-0.336614\pi\)
0.491048 + 0.871133i \(0.336614\pi\)
\(102\) −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
\(105\) 1.28483 0.799603i 0.125386 0.0780332i
\(106\) 6.48922 + 6.48922i 0.630289 + 0.630289i
\(107\) 14.7208i 1.42312i 0.702628 + 0.711558i \(0.252010\pi\)
−0.702628 + 0.711558i \(0.747990\pi\)
\(108\) −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
\(111\) 10.4632 1.23332i 0.993125 0.117062i
\(112\) 0.873718 0.0825586
\(113\) 3.10020 3.10020i 0.291643 0.291643i −0.546086 0.837729i \(-0.683883\pi\)
0.837729 + 0.546086i \(0.183883\pi\)
\(114\) −5.35658 1.24694i −0.501690 0.116786i
\(115\) 5.56975i 0.519382i
\(116\) 0.0117303 + 0.0117303i 0.00108913 + 0.00108913i
\(117\) −11.2488 + 3.82752i −1.03995 + 0.353854i
\(118\) −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
\(126\) −2.48144 + 0.844338i −0.221064 + 0.0752196i
\(127\) −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
\(129\) 10.4372 + 16.7708i 0.918940 + 1.47658i
\(130\) −2.80064 + 2.80064i −0.245632 + 0.245632i
\(131\) −11.7356 + 11.7356i −1.02535 + 1.02535i −0.0256765 + 0.999670i \(0.508174\pi\)
−0.999670 + 0.0256765i \(0.991826\pi\)
\(132\) −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
\(135\) 5.17058 0.514925i 0.445012 0.0443177i
\(136\) 3.78900i 0.324904i
\(137\) 21.3281i 1.82218i −0.412209 0.911089i \(-0.635243\pi\)
0.412209 0.911089i \(-0.364757\pi\)
\(138\) −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 \(0.0560902\pi\)
−0.984515 + 0.175302i \(0.943910\pi\)
\(150\) 1.47053 0.915172i 0.120068 0.0747235i
\(151\) 16.2675i 1.32383i −0.749577 0.661917i \(-0.769743\pi\)
0.749577 0.661917i \(-0.230257\pi\)
\(152\) 3.17531 0.257552
\(153\) 3.66159 + 10.7611i 0.296022 + 0.869983i
\(154\) −2.00531 + 2.00531i −0.161592 + 0.161592i
\(155\) 7.35632i 0.590874i
\(156\) 5.82434 3.62473i 0.466320 0.290210i
\(157\) −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
\(162\) −8.92469 1.16182i −0.701190 0.0912812i
\(163\) −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
\(165\) 4.77308 2.97049i 0.371584 0.231252i
\(166\) 4.43238 + 4.43238i 0.344019 + 0.344019i
\(167\) 12.4791 + 12.4791i 0.965665 + 0.965665i 0.999430 0.0337648i \(-0.0107497\pi\)
−0.0337648 + 0.999430i \(0.510750\pi\)
\(168\) 1.28483 0.799603i 0.0991267 0.0616907i
\(169\) 2.68718i 0.206706i
\(170\) 2.67922 + 2.67922i 0.205487 + 0.205487i
\(171\) −9.01817 + 3.06854i −0.689637 + 0.234657i
\(172\) −8.06425 8.06425i −0.614894 0.614894i
\(173\) −9.17456 −0.697529 −0.348765 0.937210i \(-0.613399\pi\)
−0.348765 + 0.937210i \(0.613399\pi\)
\(174\) 0.0279850 + 0.00651450i 0.00212153 + 0.000493863i
\(175\) 0.873718i 0.0660469i
\(176\) 3.24582 0.244663
\(177\) −16.5545 + 10.3026i −1.24432 + 0.774389i
\(178\) 9.18420i 0.688385i
\(179\) 10.0110 10.0110i 0.748257 0.748257i −0.225895 0.974152i \(-0.572530\pi\)
0.974152 + 0.225895i \(0.0725305\pi\)
\(180\) −2.84009 + 0.966374i −0.211688 + 0.0720293i
\(181\) −22.6754 −1.68545 −0.842724 0.538346i \(-0.819049\pi\)
−0.842724 + 0.538346i \(0.819049\pi\)
\(182\) 3.46054i 0.256512i
\(183\) 13.8220 8.60203i 1.02175 0.635880i
\(184\) 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 0.426945 0.904278i \(-0.359590\pi\)
−0.904278 + 0.426945i \(0.859590\pi\)
\(192\) −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 \(-0.823123\pi\)
0.849544 0.527518i \(-0.176877\pi\)
\(198\) −9.21844 + 3.13668i −0.655126 + 0.222914i
\(199\) −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
\(204\) −3.46758 5.57183i −0.242779 0.390106i
\(205\) −8.56443 8.56443i −0.598166 0.598166i
\(206\) 6.79409 0.473367
\(207\) 5.38246 + 15.8186i 0.374107 + 1.09947i
\(208\) −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
\(216\) 5.17058 0.514925i 0.351813 0.0350362i
\(217\) −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
\(222\) −6.52652 + 8.27070i −0.438031 + 0.555093i
\(223\) 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 \(-0.957370\pi\)
−0.133527 0.991045i \(-0.542630\pi\)
\(228\) 4.66939 2.90596i 0.309238 0.192452i
\(229\) 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 \(-0.546679\pi\)
−0.146122 + 0.989267i \(0.546679\pi\)
\(234\) 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
\(237\) 0.988240 + 1.58794i 0.0641931 + 0.103148i
\(238\) −3.31051 −0.214589
\(239\) 17.0743 + 17.0743i 1.10444 + 1.10444i 0.993868 + 0.110576i \(0.0352697\pi\)
0.110576 + 0.993868i \(0.464730\pi\)
\(240\) 1.47053 0.915172i 0.0949223 0.0590741i
\(241\) −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
\(246\) 11.0845 + 17.8110i 0.706722 + 1.13559i
\(247\) 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 −0.620320 0.784349i \(-0.712997\pi\)
0.784349 + 0.620320i \(0.212997\pi\)
\(252\) 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 0.168346 0.985728i \(-0.446157\pi\)
−0.985728 + 0.168346i \(0.946157\pi\)
\(258\) −19.2389 4.47855i −1.19776 0.278822i
\(259\) 1.80260 + 4.99958i 0.112008 + 0.310659i
\(260\) 3.96070i 0.245632i
\(261\) 0.0471146 0.0160313i 0.00291632 0.000992312i
\(262\) 16.5967i 1.02535i
\(263\) −3.79960 −0.234293 −0.117147 0.993115i \(-0.537375\pi\)
−0.117147 + 0.993115i \(0.537375\pi\)
\(264\) 4.77308 2.97049i 0.293763 0.182821i
\(265\) 6.48922 6.48922i 0.398630 0.398630i
\(266\) 2.77433i 0.170105i
\(267\) 8.40513 + 13.5056i 0.514385 + 0.826532i
\(268\) 7.74070 0.472838
\(269\) 12.5379i 0.764450i 0.924069 + 0.382225i \(0.124842\pi\)
−0.924069 + 0.382225i \(0.875158\pi\)
\(270\) −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
\(273\) −3.16699 5.08883i −0.191675 0.307990i
\(274\) 15.0812 + 15.0812i 0.911089 + 0.911089i
\(275\) 3.24582i 0.195731i
\(276\) −5.09728 8.19049i −0.306820 0.493009i
\(277\) 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
\(279\) −7.10896 20.8926i −0.425602 1.25081i
\(280\) 0.873718i 0.0522146i
\(281\) −16.4710 16.4710i −0.982575 0.982575i 0.0172753 0.999851i \(-0.494501\pi\)
−0.999851 + 0.0172753i \(0.994501\pi\)
\(282\) −4.51371 + 2.80907i −0.268788 + 0.167278i
\(283\) −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
\(288\) −2.84009 + 0.966374i −0.167354 + 0.0569441i
\(289\) 2.64352i 0.155501i
\(290\) 0.0117303 0.0117303i 0.000688826 0.000688826i
\(291\) 9.25842 + 14.8767i 0.542738 + 0.872090i
\(292\) 11.0501 0.646658
\(293\) 6.48865i 0.379071i −0.981874 0.189536i \(-0.939302\pi\)
0.981874 0.189536i \(-0.0606983\pi\)
\(294\) 5.70758 + 9.17113i 0.332873 + 0.534871i
\(295\) 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
\(309\) 9.99091 6.21776i 0.568363 0.353716i
\(310\) −5.20171 5.20171i −0.295437 0.295437i
\(311\) 6.45365 6.45365i 0.365953 0.365953i −0.500046 0.865999i \(-0.666684\pi\)
0.865999 + 0.500046i \(0.166684\pi\)
\(312\) −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
\(315\) 0.844338 + 2.48144i 0.0475731 + 0.139813i
\(316\) −0.763562 0.763562i −0.0429537 0.0429537i
\(317\) 2.73418 0.153567 0.0767834 0.997048i \(-0.475535\pi\)
0.0767834 + 0.997048i \(0.475535\pi\)
\(318\) −13.4953 + 8.39867i −0.756777 + 0.470974i
\(319\) 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
\(327\) 16.6412 + 26.7396i 0.920259 + 1.47870i
\(328\) −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
\(333\) −2.02833 + 18.1352i −0.111152 + 0.993803i
\(334\) −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
\(339\) 4.01244 + 6.44732i 0.217926 + 0.350170i
\(340\) −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 −0.341361 0.939932i \(-0.610888\pi\)
0.939932 + 0.341361i \(0.110888\pi\)
\(348\) −0.0243948 + 0.0151819i −0.00130770 + 0.000813836i
\(349\) −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
\(351\) −2.03946 20.4791i −0.108859 1.09309i
\(352\) −2.29514 + 2.29514i −0.122332 + 0.122332i
\(353\) −1.76426 + 1.76426i −0.0939022 + 0.0939022i −0.752497 0.658595i \(-0.771151\pi\)
0.658595 + 0.752497i \(0.271151\pi\)
\(354\) 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
\(357\) −4.86821 + 3.02969i −0.257653 + 0.160348i
\(358\) 14.1577i 0.748257i
\(359\) 31.2814i 1.65097i 0.564426 + 0.825483i \(0.309097\pi\)
−0.564426 + 0.825483i \(0.690903\pi\)
\(360\) 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
\(372\) 6.73230 + 10.8177i 0.349054 + 0.560871i
\(373\) 22.1399i 1.14636i −0.819429 0.573181i \(-0.805709\pi\)
0.819429 0.573181i \(-0.194291\pi\)
\(374\) −12.2984 −0.635936
\(375\) −0.915172 1.47053i −0.0472593 0.0759379i
\(376\) 2.17042 2.17042i 0.111931 0.111931i
\(377\) 0.0657046i 0.00338396i
\(378\) −0.449899 4.51762i −0.0231403 0.232362i
\(379\) −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 0.432903 0.901441i \(-0.357489\pi\)
−0.901441 + 0.432903i \(0.857489\pi\)
\(384\) 1.47053 0.915172i 0.0750427 0.0467022i
\(385\) 2.00531 + 2.00531i 0.102200 + 0.102200i
\(386\) 1.02055i 0.0519448i
\(387\) −32.3900 + 11.0211i −1.64648 + 0.560233i
\(388\) −7.15350 7.15350i −0.363164 0.363164i
\(389\) 6.40269 + 6.40269i 0.324629 + 0.324629i 0.850540 0.525911i \(-0.176275\pi\)
−0.525911 + 0.850540i \(0.676275\pi\)
\(390\) −3.62473 5.82434i −0.183545 0.294927i
\(391\) 21.1038i 1.06726i
\(392\) −4.40995 4.40995i −0.222736 0.222736i
\(393\) −15.1888 24.4059i −0.766175 1.23112i
\(394\) 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
\(399\) −2.53899 4.07973i −0.127108 0.204242i
\(400\) 1.00000i 0.0500000i
\(401\) 17.9575 17.9575i 0.896756 0.896756i −0.0983914 0.995148i \(-0.531370\pi\)
0.995148 + 0.0983914i \(0.0313697\pi\)
\(402\) 11.3829 7.08407i 0.567729 0.353321i
\(403\) 29.1362 1.45138
\(404\) 9.86993i 0.491048i
\(405\) −1.16182 + 8.92469i −0.0577313 + 0.443472i
\(406\) 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 \(0.0775027\pi\)
−0.970504 + 0.241083i \(0.922497\pi\)
\(420\) −0.799603 1.28483i −0.0390166 0.0626932i
\(421\) −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
\(426\) 0.854354 0.531700i 0.0413936 0.0257609i
\(427\) 5.80703 + 5.80703i 0.281022 + 0.281022i
\(428\) 14.7208 0.711558
\(429\) −11.7652 18.9048i −0.568030 0.912731i
\(430\) −8.06425 + 8.06425i −0.388893 + 0.388893i
\(431\) 16.1018 16.1018i 0.775598 0.775598i −0.203481 0.979079i \(-0.565226\pi\)
0.979079 + 0.203481i \(0.0652255\pi\)
\(432\) −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
\(438\) 16.2495 10.1128i 0.776432 0.483206i
\(439\) 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 \(-0.391146\pi\)
0.335349 + 0.942094i \(0.391146\pi\)
\(444\) −1.23332 10.4632i −0.0585310 0.496562i
\(445\) 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 0.524372 0.851489i \(-0.324300\pi\)
−0.851489 + 0.524372i \(0.824300\pi\)
\(450\) 0.966374 + 2.84009i 0.0455553 + 0.133883i
\(451\) 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
\(459\) −19.5913 + 1.95105i −0.914443 + 0.0910671i
\(460\) −5.56975 −0.259691
\(461\) 5.43289 + 5.43289i 0.253035 + 0.253035i 0.822214 0.569179i \(-0.192739\pi\)
−0.569179 + 0.822214i \(0.692739\pi\)
\(462\) −2.59537 4.17033i −0.120747 0.194021i
\(463\) −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 0.484278 0.874914i \(-0.339082\pi\)
−0.874914 + 0.484278i \(0.839082\pi\)
\(468\) 3.82752 + 11.2488i 0.176927 + 0.519974i
\(469\) 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 0.893246 0.449569i \(-0.148422\pi\)
−0.449569 + 0.893246i \(0.648422\pi\)
\(480\) −0.392697 + 1.68695i −0.0179241 + 0.0769982i
\(481\) −21.8039 10.2477i −0.994173 0.467254i
\(482\) 5.37258i 0.244715i
\(483\) −7.15618 + 4.45359i −0.325617 + 0.202645i
\(484\) 0.464630i 0.0211195i
\(485\) 10.1166 0.459370
\(486\) 5.46463 14.5992i 0.247881 0.662235i
\(487\) −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
\(489\) 15.9260 9.91143i 0.720199 0.448210i
\(490\) 6.23662 0.281742
\(491\) 37.5934i 1.69657i 0.529541 + 0.848284i \(0.322364\pi\)
−0.529541 + 0.848284i \(0.677636\pi\)
\(492\) −20.4322 4.75632i −0.921154 0.214432i
\(493\) 0.0628561 0.00283090
\(494\) 8.89290 + 8.89290i 0.400111 + 0.400111i
\(495\) 3.13668 + 9.21844i 0.140983 + 0.414338i
\(496\) −5.20171 5.20171i −0.233563 0.233563i
\(497\) 0.507616i 0.0227697i
\(498\) −9.21777 + 5.73660i −0.413058 + 0.257063i
\(499\) −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
\(501\) −25.9522 + 16.1511i −1.15946 + 0.721579i
\(502\) 3.67514i 0.164029i
\(503\) −11.0121 11.0121i −0.491005 0.491005i 0.417618 0.908623i \(-0.362865\pi\)
−0.908623 + 0.417618i \(0.862865\pi\)
\(504\) 0.844338 + 2.48144i 0.0376098 + 0.110532i
\(505\) 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 \(-0.559825\pi\)
−0.186841 + 0.982390i \(0.559825\pi\)
\(510\) −5.57183 + 3.46758i −0.246725 + 0.153547i
\(511\) 9.65467i 0.427098i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −1.63505 16.4182i −0.0721890 0.724880i
\(514\) 18.5313 0.817381
\(515\) 6.79409i 0.299383i
\(516\) 16.7708 10.4372i 0.738292 0.459470i
\(517\) 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 \(-0.428351\pi\)
0.223196 + 0.974774i \(0.428351\pi\)
\(522\) −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
\(531\) −10.8790 31.9724i −0.472108 1.38748i
\(532\) 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
\(537\) 12.9567 + 20.8193i 0.559124 + 0.898420i
\(538\) −8.86564 8.86564i −0.382225 0.382225i
\(539\) 20.2430 0.871926
\(540\) −0.514925 5.17058i −0.0221588 0.222506i
\(541\) −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
\(549\) 9.08329 + 26.6950i 0.387665 + 1.13932i
\(550\) 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
\(555\) 8.27070 + 6.52652i 0.351072 + 0.277035i
\(556\) 14.6182 0.619951
\(557\) −13.8613 + 13.8613i −0.587322 + 0.587322i −0.936905 0.349583i \(-0.886323\pi\)
0.349583 + 0.936905i \(0.386323\pi\)
\(558\) 19.8001 + 9.74653i 0.838206 + 0.412603i
\(559\) 45.1702i 1.91049i
\(560\) 0.617812 + 0.617812i 0.0261073 + 0.0261073i
\(561\) −18.0852 + 11.2552i −0.763557 + 0.475193i
\(562\) 23.2935 0.982575
\(563\) 9.05310 + 9.05310i 0.381543 + 0.381543i 0.871658 0.490115i \(-0.163045\pi\)
−0.490115 + 0.871658i \(0.663045\pi\)
\(564\) 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 −0.0629509 0.998017i \(-0.520051\pi\)
0.998017 + 0.0629509i \(0.0200512\pi\)
\(570\) −2.90596 4.66939i −0.121717 0.195579i
\(571\) −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
\(573\) 13.7192 8.53800i 0.573126 0.356680i
\(574\) −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
\(579\) −0.933983 1.50076i −0.0388150 0.0623693i
\(580\) 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 −0.396956 0.917838i \(-0.629933\pi\)
0.917838 + 0.396956i \(0.129933\pi\)
\(588\) −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 \(0.146402\pi\)
−0.896081 + 0.443891i \(0.853598\pi\)
\(594\) −1.67136 16.7828i −0.0685765 0.688606i
\(595\) 3.31051i 0.135718i
\(596\) 4.27966 0.175302
\(597\) 31.8842 19.8429i 1.30493 0.812114i
\(598\) 15.5989 15.5989i 0.637885 0.637885i
\(599\) 0.728152i 0.0297515i −0.999889 0.0148757i \(-0.995265\pi\)
0.999889 0.0148757i \(-0.00473527\pi\)
\(600\) −0.915172 1.47053i −0.0373618 0.0600341i
\(601\) 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
\(606\) −9.03269 14.5140i −0.366928 0.589592i
\(607\) 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
\(609\) 0.0132647 + 0.0213142i 0.000537513 + 0.000863694i
\(610\) 6.64635 + 6.64635i 0.269103 + 0.269103i
\(611\) −8.59641 8.59641i −0.347774 0.347774i
\(612\) 10.7611 3.66159i 0.434991 0.148011i
\(613\) 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
\(615\) 17.8110 11.0845i 0.718207 0.446970i
\(616\) 2.00531 + 2.00531i 0.0807962 + 0.0807962i
\(617\) 9.78568 0.393957 0.196978 0.980408i \(-0.436887\pi\)
0.196978 + 0.980408i \(0.436887\pi\)
\(618\) −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
\(621\) −28.7988 + 2.86800i −1.15566 + 0.115089i
\(622\) 9.12683i 0.365953i
\(623\) −5.67411 + 5.67411i −0.227328 + 0.227328i
\(624\) −3.62473 5.82434i −0.145105 0.233160i
\(625\) −1.00000 −0.0400000
\(626\) 33.4312i 1.33618i
\(627\) −9.43222 15.1560i −0.376687 0.605273i
\(628\) 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 \(-0.998048\pi\)
0.999981 0.00613317i \(-0.00195226\pi\)
\(642\) 21.6474 13.4721i 0.854355 0.531701i
\(643\) 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 −0.620833 0.783943i \(-0.713205\pi\)
0.783943 + 0.620833i \(0.213205\pi\)
\(648\) −1.16182 + 8.92469i −0.0456406 + 0.350595i
\(649\) −25.8377 25.8377i −1.01422 1.01422i
\(650\) −3.96070 −0.155352
\(651\) 9.45161 5.88213i 0.370438 0.230539i
\(652\) −7.65805 + 7.65805i −0.299912 + 0.299912i
\(653\) −6.38197 + 6.38197i −0.249746 + 0.249746i −0.820866 0.571120i \(-0.806509\pi\)
0.571120 + 0.820866i \(0.306509\pi\)
\(654\) −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 \(-0.790419\pi\)
−0.790960 + 0.611867i \(0.790419\pi\)
\(660\) −2.97049 4.77308i −0.115626 0.185792i
\(661\) 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
\(666\) −11.3893 14.2578i −0.441326 0.552478i
\(667\) 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
\(672\) −0.799603 1.28483i −0.0308453 0.0495633i
\(673\) 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 \(-0.368872\pi\)
0.400399 + 0.916341i \(0.368872\pi\)
\(678\) −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
\(681\) 35.2362 21.9290i 1.35025 0.840320i
\(682\) 23.8773 0.914310
\(683\) 28.5744 + 28.5744i 1.09337 + 1.09337i 0.995166 + 0.0982022i \(0.0313092\pi\)
0.0982022 + 0.995166i \(0.468691\pi\)
\(684\) 3.06854 + 9.01817i 0.117328 + 0.344818i
\(685\) 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
\(690\) −8.19049 + 5.09728i −0.311807 + 0.194050i
\(691\) 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 0.807111 0.590400i \(-0.201030\pi\)
−0.590400 + 0.807111i \(0.701030\pi\)
\(702\) 15.9230 + 13.0388i 0.600977 + 0.492118i
\(703\) −17.4803 8.21559i −0.659281 0.309857i
\(704\) 3.24582i 0.122332i
\(705\) 2.80907 + 4.51371i 0.105796 + 0.169996i
\(706\) 2.49504i 0.0939022i
\(707\) −8.62354 −0.324322
\(708\) 10.3026 + 16.5545i 0.387195 + 0.622158i
\(709\) −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
\(711\) −3.06685 + 1.04353i −0.115016 + 0.0391354i
\(712\) 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
\(717\) −35.5084 + 22.0984i −1.32609 + 0.825279i
\(718\) −22.1193 22.1193i −0.825483 0.825483i
\(719\) 18.6694i 0.696252i −0.937448 0.348126i \(-0.886818\pi\)
0.937448 0.348126i \(-0.113182\pi\)
\(720\) 0.966374 + 2.84009i 0.0360146 + 0.105844i
\(721\) 4.19747 + 4.19747i 0.156322 + 0.156322i
\(722\) −6.30556 6.30556i −0.234669 0.234669i
\(723\) −4.91684 7.90055i −0.182859 0.293825i
\(724\) 22.6754i 0.842724i
\(725\) −0.0117303 0.0117303i −0.000435652 0.000435652i
\(726\) 0.425216 + 0.683252i 0.0157813 + 0.0253579i
\(727\) 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
\(732\) −8.60203 13.8220i −0.317940 0.510877i
\(733\) 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
\(735\) 9.17113 5.70758i 0.338282 0.210527i
\(736\) −5.56975 −0.205304
\(737\) 25.1249i 0.925489i
\(738\) −34.3990 + 11.7047i −1.26624 + 0.430854i
\(739\) 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 \(-0.467797\pi\)
0.100995 + 0.994887i \(0.467797\pi\)
\(744\) −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
\(753\) 3.36339 + 5.40440i 0.122569 + 0.196947i
\(754\) −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
\(759\) −26.5849 + 16.5449i −0.964970 + 0.600541i
\(760\) 2.24528 + 2.24528i 0.0814450 + 0.0814450i
\(761\) 0.980959 0.0355597 0.0177799 0.999842i \(-0.494340\pi\)
0.0177799 + 0.999842i \(0.494340\pi\)
\(762\) 0.868444 + 1.39545i 0.0314604 + 0.0505517i
\(763\) −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
\(771\) 27.2509 16.9594i 0.981416 0.610776i
\(772\) 0.721641 + 0.721641i 0.0259724 + 0.0259724i
\(773\) 19.8914i 0.715444i −0.933828 0.357722i \(-0.883554\pi\)
0.933828 0.357722i \(-0.116446\pi\)
\(774\) 15.1101 30.6963i 0.543123 1.10336i
\(775\) −5.20171 + 5.20171i −0.186851 + 0.186851i
\(776\) 10.1166 0.363164
\(777\) −9.14190 + 1.07758i −0.327964 + 0.0386579i
\(778\) −9.05477 −0.324629
\(779\) −27.1947