Properties

Label 804.2.c.b.671.14
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(128\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.14
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36593 + 0.366392i) q^{2} +(-0.973809 + 1.43237i) q^{3} +(1.73151 - 1.00093i) q^{4} -2.42154i q^{5} +(0.805342 - 2.31331i) q^{6} +1.75439i q^{7} +(-1.99839 + 2.00161i) q^{8} +(-1.10339 - 2.78972i) q^{9} +O(q^{10})\) \(q+(-1.36593 + 0.366392i) q^{2} +(-0.973809 + 1.43237i) q^{3} +(1.73151 - 1.00093i) q^{4} -2.42154i q^{5} +(0.805342 - 2.31331i) q^{6} +1.75439i q^{7} +(-1.99839 + 2.00161i) q^{8} +(-1.10339 - 2.78972i) q^{9} +(0.887230 + 3.30764i) q^{10} +0.337759 q^{11} +(-0.252459 + 3.45489i) q^{12} -1.33945 q^{13} +(-0.642794 - 2.39637i) q^{14} +(3.46855 + 2.35811i) q^{15} +(1.99628 - 3.46624i) q^{16} +4.05920i q^{17} +(2.52928 + 3.40628i) q^{18} -1.16371i q^{19} +(-2.42378 - 4.19292i) q^{20} +(-2.51294 - 1.70844i) q^{21} +(-0.461354 + 0.123752i) q^{22} +1.81407 q^{23} +(-0.921002 - 4.81163i) q^{24} -0.863832 q^{25} +(1.82959 - 0.490764i) q^{26} +(5.07041 + 1.13618i) q^{27} +(1.75602 + 3.03775i) q^{28} -8.51104i q^{29} +(-5.60177 - 1.95016i) q^{30} -4.75899i q^{31} +(-1.45677 + 5.46606i) q^{32} +(-0.328913 + 0.483798i) q^{33} +(-1.48726 - 5.54458i) q^{34} +4.24832 q^{35} +(-4.70285 - 3.72602i) q^{36} +6.50846 q^{37} +(0.426373 + 1.58954i) q^{38} +(1.30437 - 1.91860i) q^{39} +(4.84696 + 4.83917i) q^{40} +0.0765846i q^{41} +(4.05846 + 1.41288i) q^{42} -9.26180i q^{43} +(0.584835 - 0.338073i) q^{44} +(-6.75540 + 2.67191i) q^{45} +(-2.47789 + 0.664660i) q^{46} -8.82365 q^{47} +(3.02096 + 6.23488i) q^{48} +3.92212 q^{49} +(1.17993 - 0.316501i) q^{50} +(-5.81430 - 3.95289i) q^{51} +(-2.31928 + 1.34069i) q^{52} +2.03937i q^{53} +(-7.34210 + 0.305820i) q^{54} -0.817896i q^{55} +(-3.51160 - 3.50596i) q^{56} +(1.66686 + 1.13323i) q^{57} +(3.11837 + 11.6255i) q^{58} +14.7468 q^{59} +(8.36614 + 0.611338i) q^{60} +10.1820 q^{61} +(1.74365 + 6.50044i) q^{62} +(4.89425 - 1.93578i) q^{63} +(-0.0128704 - 7.99999i) q^{64} +3.24353i q^{65} +(0.272011 - 0.781343i) q^{66} +1.00000i q^{67} +(4.06297 + 7.02857i) q^{68} +(-1.76656 + 2.59843i) q^{69} +(-5.80289 + 1.55655i) q^{70} +3.10054 q^{71} +(7.78893 + 3.36638i) q^{72} +11.7805 q^{73} +(-8.89008 + 2.38464i) q^{74} +(0.841207 - 1.23733i) q^{75} +(-1.16479 - 2.01498i) q^{76} +0.592561i q^{77} +(-1.07872 + 3.09857i) q^{78} +4.35094i q^{79} +(-8.39363 - 4.83407i) q^{80} +(-6.56505 + 6.15631i) q^{81} +(-0.0280600 - 0.104609i) q^{82} +8.52629 q^{83} +(-6.06122 - 0.442911i) q^{84} +9.82950 q^{85} +(3.39345 + 12.6509i) q^{86} +(12.1910 + 8.28812i) q^{87} +(-0.674975 + 0.676061i) q^{88} +0.230176i q^{89} +(8.24842 - 6.12475i) q^{90} -2.34992i q^{91} +(3.14109 - 1.81575i) q^{92} +(6.81666 + 4.63435i) q^{93} +(12.0525 - 3.23291i) q^{94} -2.81796 q^{95} +(-6.41082 - 7.40954i) q^{96} +0.733942 q^{97} +(-5.35732 + 1.43703i) q^{98} +(-0.372681 - 0.942252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} - 4q^{10} + 4q^{12} - 8q^{13} - 4q^{16} + 18q^{18} - 8q^{21} - 8q^{22} - 24q^{24} - 136q^{25} + 14q^{30} - 32q^{33} + 34q^{36} - 48q^{37} + 16q^{40} - 28q^{42} - 16q^{45} - 28q^{46} - 22q^{48} - 152q^{49} + 8q^{52} - 16q^{54} - 32q^{57} - 20q^{58} - 14q^{60} + 8q^{61} + 16q^{64} + 14q^{66} + 56q^{69} - 4q^{70} - 8q^{72} - 48q^{73} - 36q^{76} + 40q^{78} + 44q^{81} + 60q^{82} + 46q^{84} + 64q^{85} - 28q^{88} - 14q^{90} + 32q^{93} - 8q^{96} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36593 + 0.366392i −0.965856 + 0.259078i
\(3\) −0.973809 + 1.43237i −0.562229 + 0.826982i
\(4\) 1.73151 1.00093i 0.865757 0.500464i
\(5\) 2.42154i 1.08294i −0.840719 0.541472i \(-0.817867\pi\)
0.840719 0.541472i \(-0.182133\pi\)
\(6\) 0.805342 2.31331i 0.328779 0.944407i
\(7\) 1.75439i 0.663097i 0.943438 + 0.331549i \(0.107571\pi\)
−0.943438 + 0.331549i \(0.892429\pi\)
\(8\) −1.99839 + 2.00161i −0.706538 + 0.707675i
\(9\) −1.10339 2.78972i −0.367798 0.929906i
\(10\) 0.887230 + 3.30764i 0.280567 + 1.04597i
\(11\) 0.337759 0.101838 0.0509191 0.998703i \(-0.483785\pi\)
0.0509191 + 0.998703i \(0.483785\pi\)
\(12\) −0.252459 + 3.45489i −0.0728786 + 0.997341i
\(13\) −1.33945 −0.371497 −0.185748 0.982597i \(-0.559471\pi\)
−0.185748 + 0.982597i \(0.559471\pi\)
\(14\) −0.642794 2.39637i −0.171794 0.640457i
\(15\) 3.46855 + 2.35811i 0.895575 + 0.608862i
\(16\) 1.99628 3.46624i 0.499071 0.866561i
\(17\) 4.05920i 0.984501i 0.870453 + 0.492251i \(0.163826\pi\)
−0.870453 + 0.492251i \(0.836174\pi\)
\(18\) 2.52928 + 3.40628i 0.596158 + 0.802867i
\(19\) 1.16371i 0.266973i −0.991051 0.133486i \(-0.957383\pi\)
0.991051 0.133486i \(-0.0426172\pi\)
\(20\) −2.42378 4.19292i −0.541975 0.937566i
\(21\) −2.51294 1.70844i −0.548369 0.372812i
\(22\) −0.461354 + 0.123752i −0.0983611 + 0.0263840i
\(23\) 1.81407 0.378259 0.189130 0.981952i \(-0.439433\pi\)
0.189130 + 0.981952i \(0.439433\pi\)
\(24\) −0.921002 4.81163i −0.187999 0.982169i
\(25\) −0.863832 −0.172766
\(26\) 1.82959 0.490764i 0.358813 0.0962467i
\(27\) 5.07041 + 1.13618i 0.975802 + 0.218658i
\(28\) 1.75602 + 3.03775i 0.331856 + 0.574081i
\(29\) 8.51104i 1.58046i −0.612810 0.790230i \(-0.709961\pi\)
0.612810 0.790230i \(-0.290039\pi\)
\(30\) −5.60177 1.95016i −1.02274 0.356049i
\(31\) 4.75899i 0.854740i −0.904077 0.427370i \(-0.859440\pi\)
0.904077 0.427370i \(-0.140560\pi\)
\(32\) −1.45677 + 5.46606i −0.257524 + 0.966272i
\(33\) −0.328913 + 0.483798i −0.0572564 + 0.0842183i
\(34\) −1.48726 5.54458i −0.255063 0.950887i
\(35\) 4.24832 0.718097
\(36\) −4.70285 3.72602i −0.783808 0.621003i
\(37\) 6.50846 1.06998 0.534992 0.844857i \(-0.320315\pi\)
0.534992 + 0.844857i \(0.320315\pi\)
\(38\) 0.426373 + 1.58954i 0.0691668 + 0.257857i
\(39\) 1.30437 1.91860i 0.208866 0.307221i
\(40\) 4.84696 + 4.83917i 0.766372 + 0.765140i
\(41\) 0.0765846i 0.0119605i 0.999982 + 0.00598026i \(0.00190359\pi\)
−0.999982 + 0.00598026i \(0.998096\pi\)
\(42\) 4.05846 + 1.41288i 0.626233 + 0.218013i
\(43\) 9.26180i 1.41241i −0.708007 0.706206i \(-0.750405\pi\)
0.708007 0.706206i \(-0.249595\pi\)
\(44\) 0.584835 0.338073i 0.0881671 0.0509664i
\(45\) −6.75540 + 2.67191i −1.00704 + 0.398304i
\(46\) −2.47789 + 0.664660i −0.365344 + 0.0979987i
\(47\) −8.82365 −1.28706 −0.643531 0.765420i \(-0.722531\pi\)
−0.643531 + 0.765420i \(0.722531\pi\)
\(48\) 3.02096 + 6.23488i 0.436038 + 0.899928i
\(49\) 3.92212 0.560302
\(50\) 1.17993 0.316501i 0.166868 0.0447600i
\(51\) −5.81430 3.95289i −0.814165 0.553515i
\(52\) −2.31928 + 1.34069i −0.321626 + 0.185921i
\(53\) 2.03937i 0.280130i 0.990142 + 0.140065i \(0.0447311\pi\)
−0.990142 + 0.140065i \(0.955269\pi\)
\(54\) −7.34210 + 0.305820i −0.999134 + 0.0416169i
\(55\) 0.817896i 0.110285i
\(56\) −3.51160 3.50596i −0.469257 0.468503i
\(57\) 1.66686 + 1.13323i 0.220782 + 0.150100i
\(58\) 3.11837 + 11.6255i 0.409463 + 1.52650i
\(59\) 14.7468 1.91987 0.959933 0.280231i \(-0.0904110\pi\)
0.959933 + 0.280231i \(0.0904110\pi\)
\(60\) 8.36614 + 0.611338i 1.08006 + 0.0789234i
\(61\) 10.1820 1.30367 0.651835 0.758361i \(-0.273999\pi\)
0.651835 + 0.758361i \(0.273999\pi\)
\(62\) 1.74365 + 6.50044i 0.221444 + 0.825556i
\(63\) 4.89425 1.93578i 0.616618 0.243886i
\(64\) −0.0128704 7.99999i −0.00160880 0.999999i
\(65\) 3.24353i 0.402310i
\(66\) 0.272011 0.781343i 0.0334823 0.0961767i
\(67\) 1.00000i 0.122169i
\(68\) 4.06297 + 7.02857i 0.492708 + 0.852339i
\(69\) −1.76656 + 2.59843i −0.212668 + 0.312814i
\(70\) −5.80289 + 1.55655i −0.693578 + 0.186043i
\(71\) 3.10054 0.367966 0.183983 0.982929i \(-0.441101\pi\)
0.183983 + 0.982929i \(0.441101\pi\)
\(72\) 7.78893 + 3.36638i 0.917934 + 0.396732i
\(73\) 11.7805 1.37880 0.689401 0.724380i \(-0.257874\pi\)
0.689401 + 0.724380i \(0.257874\pi\)
\(74\) −8.89008 + 2.38464i −1.03345 + 0.277209i
\(75\) 0.841207 1.23733i 0.0971343 0.142875i
\(76\) −1.16479 2.01498i −0.133610 0.231134i
\(77\) 0.592561i 0.0675286i
\(78\) −1.07872 + 3.09857i −0.122140 + 0.350844i
\(79\) 4.35094i 0.489519i 0.969584 + 0.244760i \(0.0787091\pi\)
−0.969584 + 0.244760i \(0.921291\pi\)
\(80\) −8.39363 4.83407i −0.938437 0.540466i
\(81\) −6.56505 + 6.15631i −0.729450 + 0.684035i
\(82\) −0.0280600 0.104609i −0.00309871 0.0115521i
\(83\) 8.52629 0.935882 0.467941 0.883760i \(-0.344996\pi\)
0.467941 + 0.883760i \(0.344996\pi\)
\(84\) −6.06122 0.442911i −0.661334 0.0483256i
\(85\) 9.82950 1.06616
\(86\) 3.39345 + 12.6509i 0.365925 + 1.36419i
\(87\) 12.1910 + 8.28812i 1.30701 + 0.888580i
\(88\) −0.674975 + 0.676061i −0.0719525 + 0.0720684i
\(89\) 0.230176i 0.0243986i 0.999926 + 0.0121993i \(0.00388326\pi\)
−0.999926 + 0.0121993i \(0.996117\pi\)
\(90\) 8.24842 6.12475i 0.869460 0.645605i
\(91\) 2.34992i 0.246338i
\(92\) 3.14109 1.81575i 0.327481 0.189305i
\(93\) 6.81666 + 4.63435i 0.706855 + 0.480559i
\(94\) 12.0525 3.23291i 1.24312 0.333449i
\(95\) −2.81796 −0.289116
\(96\) −6.41082 7.40954i −0.654302 0.756233i
\(97\) 0.733942 0.0745205 0.0372603 0.999306i \(-0.488137\pi\)
0.0372603 + 0.999306i \(0.488137\pi\)
\(98\) −5.35732 + 1.43703i −0.541172 + 0.145162i
\(99\) −0.372681 0.942252i −0.0374559 0.0946999i
\(100\) −1.49574 + 0.864635i −0.149574 + 0.0864635i
\(101\) 7.44649i 0.740953i 0.928842 + 0.370477i \(0.120806\pi\)
−0.928842 + 0.370477i \(0.879194\pi\)
\(102\) 9.39022 + 3.26905i 0.929770 + 0.323684i
\(103\) 5.90797i 0.582130i −0.956703 0.291065i \(-0.905990\pi\)
0.956703 0.291065i \(-0.0940096\pi\)
\(104\) 2.67675 2.68106i 0.262477 0.262899i
\(105\) −4.13705 + 6.08518i −0.403735 + 0.593853i
\(106\) −0.747210 2.78564i −0.0725754 0.270565i
\(107\) −2.90009 −0.280362 −0.140181 0.990126i \(-0.544768\pi\)
−0.140181 + 0.990126i \(0.544768\pi\)
\(108\) 9.91673 3.10781i 0.954238 0.299050i
\(109\) −3.34202 −0.320107 −0.160054 0.987108i \(-0.551167\pi\)
−0.160054 + 0.987108i \(0.551167\pi\)
\(110\) 0.299670 + 1.11719i 0.0285724 + 0.106519i
\(111\) −6.33799 + 9.32255i −0.601575 + 0.884857i
\(112\) 6.08114 + 3.50226i 0.574614 + 0.330932i
\(113\) 6.51949i 0.613302i −0.951822 0.306651i \(-0.900792\pi\)
0.951822 0.306651i \(-0.0992084\pi\)
\(114\) −2.69202 0.937182i −0.252131 0.0877751i
\(115\) 4.39283i 0.409634i
\(116\) −8.51894 14.7370i −0.790964 1.36829i
\(117\) 1.47794 + 3.73669i 0.136636 + 0.345457i
\(118\) −20.1430 + 5.40309i −1.85431 + 0.497395i
\(119\) −7.12143 −0.652820
\(120\) −11.6515 + 2.23024i −1.06363 + 0.203592i
\(121\) −10.8859 −0.989629
\(122\) −13.9079 + 3.73060i −1.25916 + 0.337752i
\(123\) −0.109698 0.0745788i −0.00989113 0.00672454i
\(124\) −4.76341 8.24026i −0.427767 0.739997i
\(125\) 10.0159i 0.895847i
\(126\) −5.97594 + 4.43735i −0.532379 + 0.395311i
\(127\) 13.5743i 1.20452i −0.798299 0.602262i \(-0.794266\pi\)
0.798299 0.602262i \(-0.205734\pi\)
\(128\) 2.94871 + 10.9227i 0.260632 + 0.965438i
\(129\) 13.2664 + 9.01922i 1.16804 + 0.794098i
\(130\) −1.18840 4.43042i −0.104230 0.388574i
\(131\) 18.1110 1.58236 0.791182 0.611580i \(-0.209466\pi\)
0.791182 + 0.611580i \(0.209466\pi\)
\(132\) −0.0852703 + 1.16692i −0.00742183 + 0.101567i
\(133\) 2.04160 0.177029
\(134\) −0.366392 1.36593i −0.0316514 0.117998i
\(135\) 2.75130 12.2782i 0.236794 1.05674i
\(136\) −8.12493 8.11187i −0.696707 0.695587i
\(137\) 6.99766i 0.597850i −0.954277 0.298925i \(-0.903372\pi\)
0.954277 0.298925i \(-0.0966281\pi\)
\(138\) 1.46095 4.19651i 0.124364 0.357231i
\(139\) 1.25579i 0.106515i 0.998581 + 0.0532574i \(0.0169604\pi\)
−0.998581 + 0.0532574i \(0.983040\pi\)
\(140\) 7.35602 4.25226i 0.621697 0.359382i
\(141\) 8.59255 12.6388i 0.723623 1.06438i
\(142\) −4.23511 + 1.13601i −0.355403 + 0.0953320i
\(143\) −0.452412 −0.0378326
\(144\) −11.8725 1.74444i −0.989377 0.145370i
\(145\) −20.6098 −1.71155
\(146\) −16.0913 + 4.31628i −1.33173 + 0.357218i
\(147\) −3.81939 + 5.61794i −0.315018 + 0.463360i
\(148\) 11.2695 6.51450i 0.926346 0.535489i
\(149\) 8.81368i 0.722045i 0.932557 + 0.361022i \(0.117572\pi\)
−0.932557 + 0.361022i \(0.882428\pi\)
\(150\) −0.695680 + 1.99832i −0.0568021 + 0.163162i
\(151\) 12.8312i 1.04419i −0.852887 0.522095i \(-0.825151\pi\)
0.852887 0.522095i \(-0.174849\pi\)
\(152\) 2.32929 + 2.32554i 0.188930 + 0.188626i
\(153\) 11.3240 4.47890i 0.915494 0.362097i
\(154\) −0.217109 0.809395i −0.0174952 0.0652229i
\(155\) −11.5241 −0.925635
\(156\) 0.338156 4.62766i 0.0270742 0.370509i
\(157\) −18.8027 −1.50062 −0.750308 0.661089i \(-0.770095\pi\)
−0.750308 + 0.661089i \(0.770095\pi\)
\(158\) −1.59415 5.94307i −0.126824 0.472805i
\(159\) −2.92115 1.98596i −0.231662 0.157497i
\(160\) 13.2363 + 3.52763i 1.04642 + 0.278884i
\(161\) 3.18258i 0.250823i
\(162\) 6.71175 10.8145i 0.527325 0.849664i
\(163\) 8.64155i 0.676859i 0.940992 + 0.338429i \(0.109896\pi\)
−0.940992 + 0.338429i \(0.890104\pi\)
\(164\) 0.0766558 + 0.132607i 0.00598581 + 0.0103549i
\(165\) 1.17153 + 0.796474i 0.0912037 + 0.0620054i
\(166\) −11.6463 + 3.12396i −0.903928 + 0.242466i
\(167\) 13.8923 1.07502 0.537509 0.843258i \(-0.319365\pi\)
0.537509 + 0.843258i \(0.319365\pi\)
\(168\) 8.44147 1.61580i 0.651274 0.124661i
\(169\) −11.2059 −0.861990
\(170\) −13.4264 + 3.60145i −1.02976 + 0.276218i
\(171\) −3.24641 + 1.28403i −0.248259 + 0.0981920i
\(172\) −9.27040 16.0369i −0.706861 1.22280i
\(173\) 13.4769i 1.02463i −0.858799 0.512313i \(-0.828789\pi\)
0.858799 0.512313i \(-0.171211\pi\)
\(174\) −19.6887 6.85430i −1.49260 0.519623i
\(175\) 1.51550i 0.114561i
\(176\) 0.674263 1.17076i 0.0508245 0.0882490i
\(177\) −14.3605 + 21.1229i −1.07940 + 1.58769i
\(178\) −0.0843346 0.314404i −0.00632115 0.0235656i
\(179\) −15.6492 −1.16967 −0.584837 0.811151i \(-0.698841\pi\)
−0.584837 + 0.811151i \(0.698841\pi\)
\(180\) −9.02268 + 11.3881i −0.672511 + 0.848820i
\(181\) −1.47999 −0.110007 −0.0550033 0.998486i \(-0.517517\pi\)
−0.0550033 + 0.998486i \(0.517517\pi\)
\(182\) 0.860991 + 3.20982i 0.0638209 + 0.237928i
\(183\) −9.91531 + 14.5844i −0.732961 + 1.07811i
\(184\) −3.62522 + 3.63105i −0.267255 + 0.267685i
\(185\) 15.7605i 1.15873i
\(186\) −11.0090 3.83261i −0.807222 0.281021i
\(187\) 1.37103i 0.100260i
\(188\) −15.2783 + 8.83185i −1.11428 + 0.644129i
\(189\) −1.99330 + 8.89548i −0.144991 + 0.647051i
\(190\) 3.84913 1.03248i 0.279245 0.0749037i
\(191\) −9.98074 −0.722181 −0.361090 0.932531i \(-0.617595\pi\)
−0.361090 + 0.932531i \(0.617595\pi\)
\(192\) 11.4715 + 7.77202i 0.827885 + 0.560898i
\(193\) 10.5987 0.762908 0.381454 0.924388i \(-0.375423\pi\)
0.381454 + 0.924388i \(0.375423\pi\)
\(194\) −1.00251 + 0.268910i −0.0719761 + 0.0193066i
\(195\) −4.64595 3.15858i −0.332703 0.226190i
\(196\) 6.79120 3.92576i 0.485086 0.280411i
\(197\) 0.207828i 0.0148071i −0.999973 0.00740355i \(-0.997643\pi\)
0.999973 0.00740355i \(-0.00235665\pi\)
\(198\) 0.854289 + 1.15050i 0.0607117 + 0.0817625i
\(199\) 5.84910i 0.414632i 0.978274 + 0.207316i \(0.0664728\pi\)
−0.978274 + 0.207316i \(0.933527\pi\)
\(200\) 1.72627 1.72905i 0.122066 0.122263i
\(201\) −1.43237 0.973809i −0.101032 0.0686872i
\(202\) −2.72833 10.1714i −0.191965 0.715655i
\(203\) 14.9317 1.04800
\(204\) −14.0241 1.02478i −0.981884 0.0717491i
\(205\) 0.185452 0.0129526
\(206\) 2.16463 + 8.06986i 0.150817 + 0.562254i
\(207\) −2.00163 5.06074i −0.139123 0.351746i
\(208\) −2.67392 + 4.64286i −0.185403 + 0.321925i
\(209\) 0.393053i 0.0271880i
\(210\) 3.42135 9.82769i 0.236095 0.678175i
\(211\) 4.93959i 0.340055i −0.985439 0.170028i \(-0.945614\pi\)
0.985439 0.170028i \(-0.0543857\pi\)
\(212\) 2.04127 + 3.53121i 0.140195 + 0.242524i
\(213\) −3.01933 + 4.44114i −0.206881 + 0.304302i
\(214\) 3.96131 1.06257i 0.270790 0.0726357i
\(215\) −22.4278 −1.52956
\(216\) −12.4069 + 7.87845i −0.844179 + 0.536061i
\(217\) 8.34913 0.566776
\(218\) 4.56495 1.22449i 0.309177 0.0829327i
\(219\) −11.4719 + 16.8741i −0.775202 + 1.14024i
\(220\) −0.818655 1.41620i −0.0551937 0.0954800i
\(221\) 5.43710i 0.365739i
\(222\) 5.24153 15.0561i 0.351789 1.01050i
\(223\) 11.8399i 0.792860i −0.918065 0.396430i \(-0.870249\pi\)
0.918065 0.396430i \(-0.129751\pi\)
\(224\) −9.58960 2.55575i −0.640732 0.170763i
\(225\) 0.953147 + 2.40985i 0.0635431 + 0.160657i
\(226\) 2.38869 + 8.90515i 0.158893 + 0.592361i
\(227\) 21.9181 1.45475 0.727377 0.686239i \(-0.240739\pi\)
0.727377 + 0.686239i \(0.240739\pi\)
\(228\) 4.02048 + 0.293788i 0.266263 + 0.0194566i
\(229\) −4.54827 −0.300558 −0.150279 0.988644i \(-0.548017\pi\)
−0.150279 + 0.988644i \(0.548017\pi\)
\(230\) 1.60950 + 6.00029i 0.106127 + 0.395647i
\(231\) −0.848770 0.577041i −0.0558449 0.0379665i
\(232\) 17.0358 + 17.0084i 1.11845 + 1.11666i
\(233\) 26.5742i 1.74093i 0.492228 + 0.870466i \(0.336183\pi\)
−0.492228 + 0.870466i \(0.663817\pi\)
\(234\) −3.38785 4.56254i −0.221471 0.298263i
\(235\) 21.3668i 1.39382i
\(236\) 25.5342 14.7605i 1.66214 0.960824i
\(237\) −6.23218 4.23699i −0.404824 0.275222i
\(238\) 9.72735 2.60923i 0.630530 0.169131i
\(239\) −0.563864 −0.0364733 −0.0182366 0.999834i \(-0.505805\pi\)
−0.0182366 + 0.999834i \(0.505805\pi\)
\(240\) 15.0980 7.31537i 0.974571 0.472205i
\(241\) −20.6935 −1.33299 −0.666494 0.745510i \(-0.732206\pi\)
−0.666494 + 0.745510i \(0.732206\pi\)
\(242\) 14.8694 3.98851i 0.955839 0.256391i
\(243\) −2.42504 15.3987i −0.155567 0.987825i
\(244\) 17.6303 10.1914i 1.12866 0.652441i
\(245\) 9.49754i 0.606776i
\(246\) 0.177164 + 0.0616768i 0.0112956 + 0.00393237i
\(247\) 1.55873i 0.0991795i
\(248\) 9.52564 + 9.51032i 0.604879 + 0.603906i
\(249\) −8.30298 + 12.2128i −0.526180 + 0.773957i
\(250\) 3.66973 + 13.6810i 0.232094 + 0.865260i
\(251\) 6.57418 0.414959 0.207479 0.978239i \(-0.433474\pi\)
0.207479 + 0.978239i \(0.433474\pi\)
\(252\) 6.53689 8.25063i 0.411785 0.519741i
\(253\) 0.612718 0.0385213
\(254\) 4.97351 + 18.5415i 0.312065 + 1.16340i
\(255\) −9.57206 + 14.0795i −0.599425 + 0.881694i
\(256\) −8.02970 13.8392i −0.501857 0.864951i
\(257\) 9.06984i 0.565761i 0.959155 + 0.282881i \(0.0912900\pi\)
−0.959155 + 0.282881i \(0.908710\pi\)
\(258\) −21.4255 7.45891i −1.33389 0.464372i
\(259\) 11.4184i 0.709503i
\(260\) 3.24654 + 5.61621i 0.201342 + 0.348303i
\(261\) −23.7434 + 9.39103i −1.46968 + 0.581290i
\(262\) −24.7383 + 6.63572i −1.52834 + 0.409956i
\(263\) −3.87258 −0.238794 −0.119397 0.992847i \(-0.538096\pi\)
−0.119397 + 0.992847i \(0.538096\pi\)
\(264\) −0.311077 1.62517i −0.0191455 0.100022i
\(265\) 4.93842 0.303365
\(266\) −2.78867 + 0.748024i −0.170984 + 0.0458643i
\(267\) −0.329698 0.224148i −0.0201772 0.0137176i
\(268\) 1.00093 + 1.73151i 0.0611415 + 0.105769i
\(269\) 23.0395i 1.40474i −0.711812 0.702370i \(-0.752125\pi\)
0.711812 0.702370i \(-0.247875\pi\)
\(270\) 0.740555 + 17.7792i 0.0450687 + 1.08201i
\(271\) 0.600063i 0.0364512i 0.999834 + 0.0182256i \(0.00580172\pi\)
−0.999834 + 0.0182256i \(0.994198\pi\)
\(272\) 14.0702 + 8.10332i 0.853131 + 0.491336i
\(273\) 3.36596 + 2.28837i 0.203717 + 0.138499i
\(274\) 2.56388 + 9.55829i 0.154890 + 0.577438i
\(275\) −0.291767 −0.0175942
\(276\) −0.457978 + 6.26741i −0.0275670 + 0.377254i
\(277\) 5.70716 0.342910 0.171455 0.985192i \(-0.445153\pi\)
0.171455 + 0.985192i \(0.445153\pi\)
\(278\) −0.460111 1.71532i −0.0275956 0.102878i
\(279\) −13.2762 + 5.25104i −0.794828 + 0.314372i
\(280\) −8.48980 + 8.50347i −0.507362 + 0.508179i
\(281\) 13.7301i 0.819070i 0.912294 + 0.409535i \(0.134309\pi\)
−0.912294 + 0.409535i \(0.865691\pi\)
\(282\) −7.10605 + 20.4119i −0.423159 + 1.21551i
\(283\) 24.8048i 1.47449i 0.675625 + 0.737245i \(0.263874\pi\)
−0.675625 + 0.737245i \(0.736126\pi\)
\(284\) 5.36863 3.10342i 0.318570 0.184154i
\(285\) 2.74415 4.03637i 0.162550 0.239094i
\(286\) 0.617962 0.165760i 0.0365408 0.00980159i
\(287\) −0.134359 −0.00793098
\(288\) 16.8562 1.96722i 0.993259 0.115920i
\(289\) 0.522866 0.0307568
\(290\) 28.1515 7.55125i 1.65311 0.443425i
\(291\) −0.714719 + 1.05128i −0.0418976 + 0.0616271i
\(292\) 20.3981 11.7914i 1.19371 0.690042i
\(293\) 14.2943i 0.835079i −0.908659 0.417540i \(-0.862892\pi\)
0.908659 0.417540i \(-0.137108\pi\)
\(294\) 3.15864 9.07309i 0.184216 0.529153i
\(295\) 35.7098i 2.07911i
\(296\) −13.0064 + 13.0274i −0.755984 + 0.757201i
\(297\) 1.71258 + 0.383755i 0.0993739 + 0.0222677i
\(298\) −3.22926 12.0388i −0.187066 0.697392i
\(299\) −2.42986 −0.140522
\(300\) 0.218082 2.98445i 0.0125910 0.172307i
\(301\) 16.2488 0.936566
\(302\) 4.70125 + 17.5265i 0.270527 + 1.00854i
\(303\) −10.6662 7.25146i −0.612755 0.416585i
\(304\) −4.03369 2.32309i −0.231348 0.133238i
\(305\) 24.6560i 1.41180i
\(306\) −13.8268 + 10.2669i −0.790424 + 0.586918i
\(307\) 20.1390i 1.14940i 0.818366 + 0.574698i \(0.194880\pi\)
−0.818366 + 0.574698i \(0.805120\pi\)
\(308\) 0.593111 + 1.02603i 0.0337957 + 0.0584634i
\(309\) 8.46243 + 5.75323i 0.481411 + 0.327290i
\(310\) 15.7410 4.22232i 0.894031 0.239812i
\(311\) 16.6924 0.946539 0.473270 0.880918i \(-0.343074\pi\)
0.473270 + 0.880918i \(0.343074\pi\)
\(312\) 1.23364 + 6.44494i 0.0698410 + 0.364873i
\(313\) −28.8533 −1.63089 −0.815443 0.578838i \(-0.803507\pi\)
−0.815443 + 0.578838i \(0.803507\pi\)
\(314\) 25.6831 6.88914i 1.44938 0.388776i
\(315\) −4.68756 11.8516i −0.264114 0.667762i
\(316\) 4.35498 + 7.53372i 0.244987 + 0.423805i
\(317\) 34.8536i 1.95757i −0.204883 0.978786i \(-0.565682\pi\)
0.204883 0.978786i \(-0.434318\pi\)
\(318\) 4.71772 + 1.64239i 0.264556 + 0.0921008i
\(319\) 2.87468i 0.160951i
\(320\) −19.3723 + 0.0311662i −1.08294 + 0.00174224i
\(321\) 2.82413 4.15402i 0.157628 0.231855i
\(322\) −1.16607 4.34718i −0.0649827 0.242259i
\(323\) 4.72372 0.262835
\(324\) −5.20544 + 17.2309i −0.289191 + 0.957271i
\(325\) 1.15706 0.0641822
\(326\) −3.16619 11.8037i −0.175359 0.653748i
\(327\) 3.25448 4.78702i 0.179973 0.264723i
\(328\) −0.153292 0.153046i −0.00846416 0.00845055i
\(329\) 15.4801i 0.853447i
\(330\) −1.89205 0.658685i −0.104154 0.0362594i
\(331\) 23.5479i 1.29431i −0.762360 0.647154i \(-0.775959\pi\)
0.762360 0.647154i \(-0.224041\pi\)
\(332\) 14.7634 8.53421i 0.810246 0.468376i
\(333\) −7.18139 18.1568i −0.393538 0.994984i
\(334\) −18.9759 + 5.09002i −1.03831 + 0.278513i
\(335\) 2.42154 0.132303
\(336\) −10.9384 + 5.29995i −0.596740 + 0.289136i
\(337\) −31.7590 −1.73002 −0.865010 0.501754i \(-0.832688\pi\)
−0.865010 + 0.501754i \(0.832688\pi\)
\(338\) 15.3064 4.10574i 0.832559 0.223323i
\(339\) 9.33835 + 6.34873i 0.507189 + 0.344816i
\(340\) 17.0199 9.83863i 0.923035 0.533575i
\(341\) 1.60739i 0.0870452i
\(342\) 3.96391 2.94335i 0.214344 0.159158i
\(343\) 19.1617i 1.03463i
\(344\) 18.5385 + 18.5087i 0.999528 + 0.997922i
\(345\) 6.29218 + 4.27778i 0.338760 + 0.230308i
\(346\) 4.93781 + 18.4084i 0.265458 + 0.989642i
\(347\) −14.0740 −0.755533 −0.377766 0.925901i \(-0.623308\pi\)
−0.377766 + 0.925901i \(0.623308\pi\)
\(348\) 29.4047 + 2.14869i 1.57626 + 0.115182i
\(349\) 6.22850 0.333404 0.166702 0.986007i \(-0.446688\pi\)
0.166702 + 0.986007i \(0.446688\pi\)
\(350\) 0.555266 + 2.07006i 0.0296802 + 0.110649i
\(351\) −6.79157 1.52186i −0.362507 0.0812306i
\(352\) −0.492039 + 1.84621i −0.0262258 + 0.0984034i
\(353\) 14.8595i 0.790892i −0.918489 0.395446i \(-0.870590\pi\)
0.918489 0.395446i \(-0.129410\pi\)
\(354\) 11.8762 34.1139i 0.631212 1.81313i
\(355\) 7.50807i 0.398487i
\(356\) 0.230390 + 0.398553i 0.0122106 + 0.0211233i
\(357\) 6.93491 10.2005i 0.367034 0.539870i
\(358\) 21.3756 5.73372i 1.12974 0.303037i
\(359\) −11.2390 −0.593174 −0.296587 0.955006i \(-0.595848\pi\)
−0.296587 + 0.955006i \(0.595848\pi\)
\(360\) 8.15182 18.8612i 0.429638 0.994071i
\(361\) 17.6458 0.928726
\(362\) 2.02156 0.542255i 0.106251 0.0285003i
\(363\) 10.6008 15.5927i 0.556398 0.818405i
\(364\) −2.35210 4.06892i −0.123284 0.213269i
\(365\) 28.5269i 1.49317i
\(366\) 8.19998 23.5541i 0.428620 1.23120i
\(367\) 30.6588i 1.60038i 0.599749 + 0.800188i \(0.295267\pi\)
−0.599749 + 0.800188i \(0.704733\pi\)
\(368\) 3.62140 6.28801i 0.188778 0.327785i
\(369\) 0.213649 0.0845030i 0.0111221 0.00439905i
\(370\) 5.77450 + 21.5276i 0.300202 + 1.11917i
\(371\) −3.57786 −0.185753
\(372\) 16.4418 + 1.20145i 0.852467 + 0.0622923i
\(373\) 32.8342 1.70009 0.850045 0.526711i \(-0.176575\pi\)
0.850045 + 0.526711i \(0.176575\pi\)
\(374\) −0.502335 1.87273i −0.0259751 0.0968366i
\(375\) 14.3465 + 9.75355i 0.740849 + 0.503671i
\(376\) 17.6331 17.6615i 0.909358 0.910822i
\(377\) 11.4001i 0.587136i
\(378\) −0.536528 12.8809i −0.0275960 0.662523i
\(379\) 20.9941i 1.07840i −0.842179 0.539198i \(-0.818727\pi\)
0.842179 0.539198i \(-0.181273\pi\)
\(380\) −4.87933 + 2.82057i −0.250305 + 0.144692i
\(381\) 19.4435 + 13.2188i 0.996119 + 0.677217i
\(382\) 13.6330 3.65686i 0.697523 0.187101i
\(383\) −29.2172 −1.49293 −0.746464 0.665425i \(-0.768250\pi\)
−0.746464 + 0.665425i \(0.768250\pi\)
\(384\) −18.5169 6.41295i −0.944934 0.327260i
\(385\) 1.43491 0.0731297
\(386\) −14.4770 + 3.88326i −0.736860 + 0.197653i
\(387\) −25.8378 + 10.2194i −1.31341 + 0.519482i
\(388\) 1.27083 0.734623i 0.0645167 0.0372949i
\(389\) 15.0341i 0.762259i 0.924522 + 0.381129i \(0.124465\pi\)
−0.924522 + 0.381129i \(0.875535\pi\)
\(390\) 7.50330 + 2.61215i 0.379944 + 0.132271i
\(391\) 7.36367i 0.372397i
\(392\) −7.83792 + 7.85054i −0.395875 + 0.396512i
\(393\) −17.6366 + 25.9417i −0.889651 + 1.30859i
\(394\) 0.0761463 + 0.283877i 0.00383620 + 0.0143015i
\(395\) 10.5360 0.530122
\(396\) −1.58843 1.25850i −0.0798216 0.0632418i
\(397\) −14.3972 −0.722572 −0.361286 0.932455i \(-0.617662\pi\)
−0.361286 + 0.932455i \(0.617662\pi\)
\(398\) −2.14306 7.98944i −0.107422 0.400475i
\(399\) −1.98812 + 2.92433i −0.0995307 + 0.146400i
\(400\) −1.72445 + 2.99425i −0.0862227 + 0.149713i
\(401\) 8.28541i 0.413754i 0.978367 + 0.206877i \(0.0663300\pi\)
−0.978367 + 0.206877i \(0.933670\pi\)
\(402\) 2.31331 + 0.805342i 0.115378 + 0.0401668i
\(403\) 6.37444i 0.317533i
\(404\) 7.45341 + 12.8937i 0.370821 + 0.641486i
\(405\) 14.9077 + 15.8975i 0.740771 + 0.789953i
\(406\) −20.3956 + 5.47084i −1.01222 + 0.271513i
\(407\) 2.19829 0.108965
\(408\) 19.5314 3.73854i 0.966947 0.185085i
\(409\) 24.0722 1.19030 0.595148 0.803616i \(-0.297093\pi\)
0.595148 + 0.803616i \(0.297093\pi\)
\(410\) −0.253314 + 0.0679482i −0.0125103 + 0.00335572i
\(411\) 10.0233 + 6.81438i 0.494411 + 0.336129i
\(412\) −5.91346 10.2297i −0.291335 0.503983i
\(413\) 25.8716i 1.27306i
\(414\) 4.58830 + 6.17922i 0.225502 + 0.303692i
\(415\) 20.6467i 1.01351i
\(416\) 1.95128 7.32152i 0.0956693 0.358967i
\(417\) −1.79876 1.22290i −0.0880857 0.0598856i
\(418\) 0.144011 + 0.536881i 0.00704382 + 0.0262597i
\(419\) −23.6806 −1.15687 −0.578436 0.815728i \(-0.696337\pi\)
−0.578436 + 0.815728i \(0.696337\pi\)
\(420\) −1.07253 + 14.6775i −0.0523339 + 0.716187i
\(421\) 35.4520 1.72782 0.863912 0.503643i \(-0.168007\pi\)
0.863912 + 0.503643i \(0.168007\pi\)
\(422\) 1.80982 + 6.74712i 0.0881009 + 0.328445i
\(423\) 9.73596 + 24.6155i 0.473379 + 1.19685i
\(424\) −4.08203 4.07547i −0.198241 0.197922i
\(425\) 3.50647i 0.170089i
\(426\) 2.49699 7.17253i 0.120980 0.347510i
\(427\) 17.8632i 0.864460i
\(428\) −5.02155 + 2.90278i −0.242726 + 0.140311i
\(429\) 0.440562 0.648023i 0.0212706 0.0312868i
\(430\) 30.6347 8.21735i 1.47734 0.396276i
\(431\) −29.6967 −1.43044 −0.715221 0.698898i \(-0.753674\pi\)
−0.715221 + 0.698898i \(0.753674\pi\)
\(432\) 14.0603 15.3072i 0.676474 0.736466i
\(433\) −4.86045 −0.233578 −0.116789 0.993157i \(-0.537260\pi\)
−0.116789 + 0.993157i \(0.537260\pi\)
\(434\) −11.4043 + 3.05905i −0.547424 + 0.146839i
\(435\) 20.0700 29.5209i 0.962282 1.41542i
\(436\) −5.78675 + 3.34512i −0.277135 + 0.160202i
\(437\) 2.11104i 0.100985i
\(438\) 9.48732 27.2520i 0.453322 1.30215i
\(439\) 18.1792i 0.867646i 0.900998 + 0.433823i \(0.142836\pi\)
−0.900998 + 0.433823i \(0.857164\pi\)
\(440\) 1.63711 + 1.63447i 0.0780460 + 0.0779205i
\(441\) −4.32764 10.9416i −0.206078 0.521028i
\(442\) 1.99211 + 7.42669i 0.0947550 + 0.353252i
\(443\) 20.6724 0.982177 0.491089 0.871110i \(-0.336599\pi\)
0.491089 + 0.871110i \(0.336599\pi\)
\(444\) −1.64312 + 22.4860i −0.0779789 + 1.06714i
\(445\) 0.557380 0.0264223
\(446\) 4.33805 + 16.1725i 0.205413 + 0.765789i
\(447\) −12.6245 8.58284i −0.597118 0.405954i
\(448\) 14.0351 0.0225797i 0.663096 0.00106679i
\(449\) 24.1650i 1.14042i 0.821499 + 0.570209i \(0.193138\pi\)
−0.821499 + 0.570209i \(0.806862\pi\)
\(450\) −2.18488 2.94245i −0.102996 0.138709i
\(451\) 0.0258672i 0.00121804i
\(452\) −6.52554 11.2886i −0.306936 0.530970i
\(453\) 18.3791 + 12.4952i 0.863526 + 0.587074i
\(454\) −29.9385 + 8.03060i −1.40508 + 0.376895i
\(455\) −5.69041 −0.266771
\(456\) −5.59932 + 1.07178i −0.262212 + 0.0501906i
\(457\) −21.5576 −1.00842 −0.504211 0.863581i \(-0.668217\pi\)
−0.504211 + 0.863581i \(0.668217\pi\)
\(458\) 6.21260 1.66645i 0.290296 0.0778679i
\(459\) −4.61198 + 20.5818i −0.215269 + 0.960678i
\(460\) −4.39691 7.60625i −0.205007 0.354643i
\(461\) 18.8531i 0.878077i −0.898468 0.439039i \(-0.855319\pi\)
0.898468 0.439039i \(-0.144681\pi\)
\(462\) 1.37078 + 0.477214i 0.0637745 + 0.0222020i
\(463\) 4.38292i 0.203692i 0.994800 + 0.101846i \(0.0324748\pi\)
−0.994800 + 0.101846i \(0.967525\pi\)
\(464\) −29.5013 16.9904i −1.36957 0.788762i
\(465\) 11.2222 16.5068i 0.520419 0.765484i
\(466\) −9.73656 36.2984i −0.451037 1.68149i
\(467\) −25.0496 −1.15916 −0.579579 0.814916i \(-0.696783\pi\)
−0.579579 + 0.814916i \(0.696783\pi\)
\(468\) 6.29924 + 4.99082i 0.291182 + 0.230701i
\(469\) −1.75439 −0.0810102
\(470\) −7.82861 29.1855i −0.361107 1.34623i
\(471\) 18.3102 26.9324i 0.843689 1.24098i
\(472\) −29.4698 + 29.5172i −1.35646 + 1.35864i
\(473\) 3.12826i 0.143837i
\(474\) 10.0651 + 3.50400i 0.462305 + 0.160944i
\(475\) 1.00525i 0.0461239i
\(476\) −12.3309 + 7.12804i −0.565184 + 0.326713i
\(477\) 5.68928 2.25023i 0.260494 0.103031i
\(478\) 0.770197 0.206595i 0.0352280 0.00944943i
\(479\) 12.3441 0.564016 0.282008 0.959412i \(-0.408999\pi\)
0.282008 + 0.959412i \(0.408999\pi\)
\(480\) −17.9425 + 15.5240i −0.818958 + 0.708572i
\(481\) −8.71776 −0.397496
\(482\) 28.2659 7.58194i 1.28748 0.345348i
\(483\) −4.55865 3.09923i −0.207426 0.141020i
\(484\) −18.8491 + 10.8960i −0.856778 + 0.495274i
\(485\) 1.77727i 0.0807015i
\(486\) 8.95438 + 20.1450i 0.406179 + 0.913794i
\(487\) 33.9623i 1.53898i 0.638659 + 0.769490i \(0.279489\pi\)
−0.638659 + 0.769490i \(0.720511\pi\)
\(488\) −20.3476 + 20.3804i −0.921092 + 0.922575i
\(489\) −12.3779 8.41522i −0.559750 0.380549i
\(490\) 3.47982 + 12.9730i 0.157202 + 0.586058i
\(491\) −4.55227 −0.205441 −0.102721 0.994710i \(-0.532755\pi\)
−0.102721 + 0.994710i \(0.532755\pi\)
\(492\) −0.264592 0.0193345i −0.0119287 0.000871665i
\(493\) 34.5480 1.55597
\(494\) −0.571105 2.12911i −0.0256952 0.0957932i
\(495\) −2.28170 + 0.902461i −0.102555 + 0.0405626i
\(496\) −16.4958 9.50030i −0.740685 0.426576i
\(497\) 5.43956i 0.243997i
\(498\) 6.86658 19.7240i 0.307699 0.883853i
\(499\) 22.9604i 1.02785i 0.857836 + 0.513923i \(0.171808\pi\)
−0.857836 + 0.513923i \(0.828192\pi\)
\(500\) −10.0252 17.3426i −0.448340 0.775586i
\(501\) −13.5284 + 19.8990i −0.604406 + 0.889020i
\(502\) −8.97985 + 2.40873i −0.400790 + 0.107507i
\(503\) 2.01888 0.0900173 0.0450087 0.998987i \(-0.485668\pi\)
0.0450087 + 0.998987i \(0.485668\pi\)
\(504\) −5.90595 + 13.6648i −0.263072 + 0.608680i
\(505\) 18.0319 0.802411
\(506\) −0.836929 + 0.224495i −0.0372060 + 0.00998001i
\(507\) 10.9124 16.0510i 0.484636 0.712850i
\(508\) −13.5869 23.5041i −0.602821 1.04282i
\(509\) 27.2643i 1.20847i −0.796807 0.604234i \(-0.793479\pi\)
0.796807 0.604234i \(-0.206521\pi\)
\(510\) 7.91611 22.7387i 0.350531 1.00689i
\(511\) 20.6676i 0.914280i
\(512\) 16.0386 + 15.9613i 0.708811 + 0.705398i
\(513\) 1.32218 5.90048i 0.0583756 0.260512i
\(514\) −3.32311 12.3887i −0.146576 0.546444i
\(515\) −14.3064 −0.630414
\(516\) 31.9985 + 2.33822i 1.40866 + 0.102935i
\(517\) −2.98027 −0.131072
\(518\) −4.18360 15.5967i −0.183817 0.685278i
\(519\) 19.3039 + 13.1239i 0.847347 + 0.576074i
\(520\) −6.49227 6.48183i −0.284705 0.284247i
\(521\) 19.6443i 0.860631i 0.902679 + 0.430316i \(0.141598\pi\)
−0.902679 + 0.430316i \(0.858402\pi\)
\(522\) 28.9910 21.5268i 1.26890 0.942204i
\(523\) 23.6600i 1.03458i 0.855810 + 0.517291i \(0.173059\pi\)
−0.855810 + 0.517291i \(0.826941\pi\)
\(524\) 31.3594 18.1278i 1.36994 0.791917i
\(525\) 2.17076 + 1.47581i 0.0947398 + 0.0644095i
\(526\) 5.28967 1.41888i 0.230640 0.0618662i
\(527\) 19.3177 0.841493
\(528\) 1.02036 + 2.10589i 0.0444054 + 0.0916471i
\(529\) −19.7092 −0.856920
\(530\) −6.74552 + 1.80939i −0.293007 + 0.0785951i
\(531\) −16.2715 41.1393i −0.706122 1.78529i
\(532\) 3.53505 2.04349i 0.153264 0.0885966i
\(533\) 0.102581i 0.00444329i
\(534\) 0.532470 + 0.185370i 0.0230422 + 0.00802176i
\(535\) 7.02267i 0.303617i
\(536\) −2.00161 1.99839i −0.0864563 0.0863173i
\(537\) 15.2393 22.4155i 0.657624 0.967298i
\(538\) 8.44146 + 31.4702i 0.363937 + 1.35678i
\(539\) 1.32473 0.0570602
\(540\) −7.52568 24.0137i −0.323854 1.03339i
\(541\) 20.6306 0.886978 0.443489 0.896280i \(-0.353741\pi\)
0.443489 + 0.896280i \(0.353741\pi\)
\(542\) −0.219858 0.819642i −0.00944371 0.0352067i
\(543\) 1.44122 2.11990i 0.0618489 0.0909735i
\(544\) −22.1878 5.91335i −0.951296 0.253533i
\(545\) 8.09281i 0.346658i
\(546\) −5.43610 1.89249i −0.232644 0.0809910i
\(547\) 30.6770i 1.31165i 0.754912 + 0.655826i \(0.227680\pi\)
−0.754912 + 0.655826i \(0.772320\pi\)
\(548\) −7.00416 12.1165i −0.299203 0.517593i
\(549\) −11.2347 28.4049i −0.479487 1.21229i
\(550\) 0.398533 0.106901i 0.0169935 0.00455828i
\(551\) −9.90436 −0.421940
\(552\) −1.67076 8.72862i −0.0711123 0.371515i
\(553\) −7.63325 −0.324599
\(554\) −7.79556 + 2.09106i −0.331202 + 0.0888404i
\(555\) 22.5749 + 15.3477i 0.958250 + 0.651472i
\(556\) 1.25696 + 2.17442i 0.0533068 + 0.0922159i
\(557\) 41.7157i 1.76755i 0.467910 + 0.883776i \(0.345007\pi\)
−0.467910 + 0.883776i \(0.654993\pi\)
\(558\) 16.2104 12.0368i 0.686243 0.509560i
\(559\) 12.4057i 0.524706i
\(560\) 8.48084 14.7257i 0.358381 0.622275i
\(561\) −1.96383 1.33512i −0.0829131 0.0563690i
\(562\) −5.03060 18.7543i −0.212203 0.791104i
\(563\) 37.7631 1.59152 0.795762 0.605610i \(-0.207071\pi\)
0.795762 + 0.605610i \(0.207071\pi\)
\(564\) 2.22761 30.4847i 0.0937993 1.28364i
\(565\) −15.7872 −0.664171
\(566\) −9.08826 33.8815i −0.382008 1.42415i
\(567\) −10.8006 11.5177i −0.453581 0.483696i
\(568\) −6.19609 + 6.20607i −0.259982 + 0.260401i
\(569\) 3.56714i 0.149542i 0.997201 + 0.0747712i \(0.0238226\pi\)
−0.997201 + 0.0747712i \(0.976177\pi\)
\(570\) −2.26942 + 6.51882i −0.0950555 + 0.273043i
\(571\) 7.04923i 0.295001i 0.989062 + 0.147501i \(0.0471228\pi\)
−0.989062 + 0.147501i \(0.952877\pi\)
\(572\) −0.783357 + 0.452832i −0.0327538 + 0.0189339i
\(573\) 9.71933 14.2962i 0.406031 0.597230i
\(574\) 0.183525 0.0492281i 0.00766019 0.00205474i
\(575\) −1.56705 −0.0653506
\(576\) −22.3035 + 8.86304i −0.929313 + 0.369293i
\(577\) −31.1050 −1.29492 −0.647459 0.762100i \(-0.724168\pi\)
−0.647459 + 0.762100i \(0.724168\pi\)
\(578\) −0.714197 + 0.191574i −0.0297067 + 0.00796842i
\(579\) −10.3211 + 15.1813i −0.428929 + 0.630911i
\(580\) −35.6861 + 20.6289i −1.48179 + 0.856569i
\(581\) 14.9584i 0.620581i
\(582\) 0.591074 1.69784i 0.0245008 0.0703777i
\(583\) 0.688817i 0.0285279i
\(584\) −23.5420 + 23.5799i −0.974176 + 0.975745i
\(585\) 9.04853 3.57889i 0.374110 0.147969i
\(586\) 5.23730 + 19.5249i 0.216351 + 0.806567i
\(587\) 21.9550 0.906178 0.453089 0.891465i \(-0.350322\pi\)
0.453089 + 0.891465i \(0.350322\pi\)
\(588\) −0.990173 + 13.5505i −0.0408340 + 0.558812i
\(589\) −5.53807 −0.228192
\(590\) 13.0838 + 48.7770i 0.538651 + 2.00812i
\(591\) 0.297687 + 0.202384i 0.0122452 + 0.00832498i
\(592\) 12.9927 22.5599i 0.533998 0.927206i
\(593\) 16.2319i 0.666564i −0.942827 0.333282i \(-0.891844\pi\)
0.942827 0.333282i \(-0.108156\pi\)
\(594\) −2.47986 + 0.103294i −0.101750 + 0.00423819i
\(595\) 17.2448i 0.706967i
\(596\) 8.82186 + 15.2610i 0.361358 + 0.625115i
\(597\) −8.37810 5.69590i −0.342893 0.233118i
\(598\) 3.31901 0.890279i 0.135724 0.0364062i
\(599\) 14.6050 0.596743 0.298371 0.954450i \(-0.403557\pi\)
0.298371 + 0.954450i \(0.403557\pi\)
\(600\) 0.795592 + 4.15644i 0.0324799 + 0.169686i
\(601\) 31.2179 1.27341 0.636703 0.771109i \(-0.280298\pi\)
0.636703 + 0.771109i \(0.280298\pi\)
\(602\) −22.1947 + 5.95343i −0.904588 + 0.242644i
\(603\) 2.78972 1.10339i 0.113606 0.0449337i
\(604\) −12.8431 22.2174i −0.522580 0.904015i
\(605\) 26.3606i 1.07171i
\(606\) 17.2261 + 5.99697i 0.699761 + 0.243610i
\(607\) 34.1317i 1.38536i −0.721244 0.692681i \(-0.756429\pi\)
0.721244 0.692681i \(-0.243571\pi\)
\(608\) 6.36089 + 1.69526i 0.257968 + 0.0687518i
\(609\) −14.5406 + 21.3878i −0.589215 + 0.866676i
\(610\) 9.03377 + 33.6784i 0.365767 + 1.36360i
\(611\) 11.8188 0.478139
\(612\) 15.1247 19.0898i 0.611378 0.771660i
\(613\) 38.0864 1.53829 0.769147 0.639072i \(-0.220681\pi\)
0.769147 + 0.639072i \(0.220681\pi\)
\(614\) −7.37878 27.5085i −0.297783 1.11015i
\(615\) −0.180595 + 0.265637i −0.00728230 + 0.0107115i
\(616\) −1.18608 1.18417i −0.0477883 0.0477115i
\(617\) 31.6358i 1.27361i −0.771025 0.636805i \(-0.780256\pi\)
0.771025 0.636805i \(-0.219744\pi\)
\(618\) −13.6670 4.75794i −0.549767 0.191392i
\(619\) 7.59864i 0.305415i −0.988271 0.152708i \(-0.951201\pi\)
0.988271 0.152708i \(-0.0487993\pi\)
\(620\) −19.9541 + 11.5348i −0.801375 + 0.463247i
\(621\) 9.19808 + 2.06111i 0.369106 + 0.0827093i
\(622\) −22.8006 + 6.11596i −0.914221 + 0.245228i
\(623\) −0.403819 −0.0161787
\(624\) −4.04643 8.35132i −0.161987 0.334320i
\(625\) −28.5730 −1.14292
\(626\) 39.4115 10.5716i 1.57520 0.422527i
\(627\) 0.562999 + 0.382758i 0.0224840 + 0.0152859i
\(628\) −32.5571 + 18.8201i −1.29917 + 0.751004i
\(629\) 26.4191i 1.05340i
\(630\) 10.7452 + 14.4709i 0.428099 + 0.576536i
\(631\) 24.2502i 0.965384i −0.875790 0.482692i \(-0.839659\pi\)
0.875790 0.482692i \(-0.160341\pi\)
\(632\) −8.70889 8.69489i −0.346421 0.345864i
\(633\) 7.07534 + 4.81021i 0.281220 + 0.191189i
\(634\) 12.7701 + 47.6075i 0.507164 + 1.89073i
\(635\) −32.8706 −1.30443
\(636\) −7.04581 0.514858i −0.279385 0.0204155i
\(637\) −5.25348 −0.208151
\(638\) 1.05326 + 3.92661i 0.0416989 + 0.155456i
\(639\) −3.42112 8.64963i −0.135337 0.342174i
\(640\) 26.4497 7.14040i 1.04552 0.282249i
\(641\) 3.70656i 0.146400i 0.997317 + 0.0732001i \(0.0233212\pi\)
−0.997317 + 0.0732001i \(0.976679\pi\)
\(642\) −2.33556 + 6.70882i −0.0921773 + 0.264776i
\(643\) 3.33117i 0.131368i −0.997840 0.0656842i \(-0.979077\pi\)
0.997840 0.0656842i \(-0.0209230\pi\)
\(644\) 3.18554 + 5.51069i 0.125528 + 0.217152i
\(645\) 21.8404 32.1250i 0.859963 1.26492i
\(646\) −6.45226 + 1.73073i −0.253861 + 0.0680948i
\(647\) −5.05294 −0.198652 −0.0993258 0.995055i \(-0.531669\pi\)
−0.0993258 + 0.995055i \(0.531669\pi\)
\(648\) 0.797003 25.4434i 0.0313092 0.999510i
\(649\) 4.98085 0.195516
\(650\) −1.58046 + 0.423938i −0.0619908 + 0.0166282i
\(651\) −8.13045 + 11.9591i −0.318658 + 0.468713i
\(652\) 8.64958 + 14.9630i 0.338744 + 0.585995i
\(653\) 25.1373i 0.983700i −0.870680 0.491850i \(-0.836321\pi\)
0.870680 0.491850i \(-0.163679\pi\)
\(654\) −2.69147 + 7.73114i −0.105245 + 0.302311i
\(655\) 43.8564i 1.71361i
\(656\) 0.265461 + 0.152885i 0.0103645 + 0.00596914i
\(657\) −12.9985 32.8643i −0.507121 1.28216i
\(658\) 5.67179 + 21.1447i 0.221109 + 0.824307i
\(659\) −28.1599 −1.09695 −0.548477 0.836166i \(-0.684792\pi\)
−0.548477 + 0.836166i \(0.684792\pi\)
\(660\) 2.82574 + 0.206485i 0.109992 + 0.00803742i
\(661\) −45.2959 −1.76181 −0.880904 0.473295i \(-0.843064\pi\)
−0.880904 + 0.473295i \(0.843064\pi\)
\(662\) 8.62774 + 32.1647i 0.335327 + 1.25011i
\(663\) 7.78797 + 5.29470i 0.302460 + 0.205629i
\(664\) −17.0389 + 17.0663i −0.661236 + 0.662301i
\(665\) 4.94380i 0.191712i
\(666\) 16.4617 + 22.1696i 0.637879 + 0.859055i
\(667\) 15.4396i 0.597824i
\(668\) 24.0547 13.9052i 0.930704 0.538008i
\(669\) 16.9592 + 11.5298i 0.655681 + 0.445769i
\(670\) −3.30764 + 0.887230i −0.127785 + 0.0342767i
\(671\) 3.43906 0.132763
\(672\) 12.9992 11.2471i 0.501456 0.433866i
\(673\) −29.2754 −1.12848 −0.564242 0.825609i \(-0.690832\pi\)
−0.564242 + 0.825609i \(0.690832\pi\)
\(674\) 43.3804 11.6362i 1.67095 0.448210i
\(675\) −4.37999 0.981468i −0.168586 0.0377767i
\(676\) −19.4031 + 11.2163i −0.746274 + 0.431395i
\(677\) 21.5652i 0.828818i 0.910091 + 0.414409i \(0.136012\pi\)
−0.910091 + 0.414409i \(0.863988\pi\)
\(678\) −15.0816 5.25041i −0.579206 0.201641i
\(679\) 1.28762i 0.0494143i
\(680\) −19.6432 + 19.6748i −0.753282 + 0.754495i
\(681\) −21.3440 + 31.3949i −0.817904 + 1.20305i
\(682\) 0.588935 + 2.19558i 0.0225515 + 0.0840732i
\(683\) 5.80503 0.222123 0.111062 0.993814i \(-0.464575\pi\)
0.111062 + 0.993814i \(0.464575\pi\)
\(684\) −4.33599 + 5.47274i −0.165791 + 0.209255i
\(685\) −16.9451 −0.647438
\(686\) −7.02067 26.1734i −0.268050 0.999306i
\(687\) 4.42914 6.51482i 0.168982 0.248556i
\(688\) −32.1037 18.4892i −1.22394 0.704893i
\(689\) 2.73164i 0.104067i
\(690\) −10.1620 3.53773i −0.386861 0.134679i
\(691\) 39.6635i 1.50887i −0.656374 0.754436i \(-0.727911\pi\)
0.656374 0.754436i \(-0.272089\pi\)
\(692\) −13.4894 23.3354i −0.512789 0.887077i
\(693\) 1.65308 0.653828i 0.0627952 0.0248369i
\(694\) 19.2241 5.15660i 0.729736 0.195742i
\(695\) 3.04094 0.115349
\(696\) −40.9520 + 7.83869i −1.55228 + 0.297125i
\(697\) −0.310873 −0.0117751
\(698\) −8.50768 + 2.28207i −0.322020 + 0.0863777i
\(699\) −38.0642 25.8782i −1.43972 0.978802i
\(700\) −1.51691 2.62411i −0.0573337 0.0991820i
\(701\) 43.4754i 1.64204i 0.570896 + 0.821022i \(0.306596\pi\)
−0.570896 + 0.821022i \(0.693404\pi\)
\(702\) 9.83439 0.409632i 0.371175 0.0154605i
\(703\) 7.57394i 0.285656i
\(704\) −0.00434710 2.70207i −0.000163838 0.101838i
\(705\) −30.6052 20.8072i −1.15266 0.783643i
\(706\) 5.44440 + 20.2970i 0.204903 + 0.763888i
\(707\) −13.0640 −0.491324
\(708\) −3.72295 + 50.9484i −0.139917 + 1.91476i
\(709\) −17.2998 −0.649706 −0.324853 0.945765i \(-0.605315\pi\)
−0.324853 + 0.945765i \(0.605315\pi\)
\(710\) 2.75089 + 10.2555i 0.103239 + 0.384881i
\(711\) 12.1379 4.80080i 0.455207 0.180044i
\(712\) −0.460722 0.459982i −0.0172663 0.0172385i
\(713\) 8.63314i 0.323314i
\(714\) −5.73518 + 16.4741i −0.214634 + 0.616528i
\(715\) 1.09553i 0.0409705i
\(716\) −27.0967 + 15.6637i −1.01265 + 0.585380i
\(717\) 0.549095 0.807664i 0.0205063 0.0301628i
\(718\) 15.3517 4.11789i 0.572921 0.153678i
\(719\) 15.7041 0.585662 0.292831 0.956164i \(-0.405403\pi\)
0.292831 + 0.956164i \(0.405403\pi\)
\(720\) −4.22421 + 28.7497i −0.157427 + 1.07144i
\(721\) 10.3649 0.386009
\(722\) −24.1029 + 6.46527i −0.897016 + 0.240612i
\(723\) 20.1515 29.6409i 0.749444 1.10236i
\(724\) −2.56262 + 1.48136i −0.0952390 + 0.0550544i
\(725\) 7.35211i 0.273051i
\(726\) −8.76688 + 25.1826i −0.325370 + 0.934612i
\(727\) 18.6188i 0.690534i −0.938505 0.345267i \(-0.887788\pi\)
0.938505 0.345267i \(-0.112212\pi\)
\(728\) 4.70362 + 4.69606i 0.174328 + 0.174047i
\(729\) 24.4182 + 11.5218i 0.904378 + 0.426733i
\(730\) 10.4520 + 38.9656i 0.386846 + 1.44218i
\(731\) 37.5955 1.39052
\(732\) −2.57053 + 35.1777i −0.0950097 + 1.30020i
\(733\) 37.1929 1.37375 0.686875 0.726776i \(-0.258982\pi\)
0.686875 + 0.726776i \(0.258982\pi\)
\(734\) −11.2331 41.8777i −0.414622 1.54573i
\(735\) 13.6040 + 9.24879i 0.501792 + 0.341147i
\(736\) −2.64269 + 9.91581i −0.0974108 + 0.365502i
\(737\) 0.337759i 0.0124415i
\(738\) −0.260868 + 0.193704i −0.00960270 + 0.00713035i
\(739\) 47.8820i 1.76137i 0.473703 + 0.880685i \(0.342917\pi\)
−0.473703 + 0.880685i \(0.657083\pi\)
\(740\) −15.7751 27.2895i −0.579904 1.00318i
\(741\) −2.23268 1.51790i −0.0820197 0.0557616i
\(742\) 4.88709 1.31090i 0.179411 0.0481246i
\(743\) 9.47111 0.347461 0.173731 0.984793i \(-0.444418\pi\)
0.173731 + 0.984793i \(0.444418\pi\)
\(744\) −22.8985 + 4.38304i −0.839500 + 0.160690i
\(745\) 21.3426 0.781934
\(746\) −44.8491 + 12.0302i −1.64204 + 0.440456i
\(747\) −9.40785 23.7859i −0.344215 0.870282i
\(748\) 1.37231 + 2.37396i 0.0501765 + 0.0868007i
\(749\) 5.08789i 0.185907i
\(750\) −23.1699 8.06620i −0.846044 0.294536i
\(751\) 14.4388i 0.526880i −0.964676 0.263440i \(-0.915143\pi\)
0.964676 0.263440i \(-0.0848570\pi\)
\(752\) −17.6145 + 30.5849i −0.642335 + 1.11532i
\(753\) −6.40199 + 9.41669i −0.233302 + 0.343163i
\(754\) −4.17691 15.5717i −0.152114 0.567089i
\(755\) −31.0713 −1.13080
\(756\) 5.45232 + 17.3978i 0.198299 + 0.632752i
\(757\) −44.9004 −1.63193 −0.815966 0.578100i \(-0.803794\pi\)
−0.815966 + 0.578100i \(0.803794\pi\)
\(758\) 7.69208 + 28.6765i 0.279389 + 1.04158i
\(759\) −0.596670 + 0.877642i −0.0216578 + 0.0318564i
\(760\) 5.63138 5.64045i 0.204272 0.204601i
\(761\) 2.80263i 0.101595i 0.998709 + 0.0507976i \(0.0161763\pi\)
−0.998709 + 0.0507976i \(0.983824\pi\)
\(762\) −31.4016 10.9319i −1.13756 0.396022i
\(763\) 5.86320i 0.212262i