Properties

Label 1155.2.k.b.769.14
Level $1155$
Weight $2$
Character 1155.769
Analytic conductor $9.223$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(769,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.769");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.k (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 769.14
Character \(\chi\) \(=\) 1155.769
Dual form 1155.2.k.b.769.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.63529 q^{2} +1.00000 q^{3} +0.674169 q^{4} +(-1.84877 + 1.25780i) q^{5} -1.63529 q^{6} +(1.79271 + 1.94582i) q^{7} +2.16812 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.63529 q^{2} +1.00000 q^{3} +0.674169 q^{4} +(-1.84877 + 1.25780i) q^{5} -1.63529 q^{6} +(1.79271 + 1.94582i) q^{7} +2.16812 q^{8} +1.00000 q^{9} +(3.02327 - 2.05687i) q^{10} +(-3.27552 + 0.520547i) q^{11} +0.674169 q^{12} -4.17087i q^{13} +(-2.93159 - 3.18197i) q^{14} +(-1.84877 + 1.25780i) q^{15} -4.89383 q^{16} -7.58089i q^{17} -1.63529 q^{18} +5.73183 q^{19} +(-1.24638 + 0.847970i) q^{20} +(1.79271 + 1.94582i) q^{21} +(5.35642 - 0.851244i) q^{22} -2.17955i q^{23} +2.16812 q^{24} +(1.83588 - 4.65076i) q^{25} +6.82058i q^{26} +1.00000 q^{27} +(1.20859 + 1.31181i) q^{28} +5.39200i q^{29} +(3.02327 - 2.05687i) q^{30} +0.864081i q^{31} +3.66660 q^{32} +(-3.27552 + 0.520547i) q^{33} +12.3969i q^{34} +(-5.76174 - 1.34250i) q^{35} +0.674169 q^{36} +2.91371i q^{37} -9.37321 q^{38} -4.17087i q^{39} +(-4.00834 + 2.72706i) q^{40} -3.36581 q^{41} +(-2.93159 - 3.18197i) q^{42} +5.31325 q^{43} +(-2.20825 + 0.350936i) q^{44} +(-1.84877 + 1.25780i) q^{45} +3.56419i q^{46} +10.7554 q^{47} -4.89383 q^{48} +(-0.572412 + 6.97656i) q^{49} +(-3.00219 + 7.60533i) q^{50} -7.58089i q^{51} -2.81187i q^{52} +11.1538i q^{53} -1.63529 q^{54} +(5.40093 - 5.08232i) q^{55} +(3.88679 + 4.21876i) q^{56} +5.73183 q^{57} -8.81748i q^{58} -10.8770i q^{59} +(-1.24638 + 0.847970i) q^{60} +15.3838 q^{61} -1.41302i q^{62} +(1.79271 + 1.94582i) q^{63} +3.79172 q^{64} +(5.24612 + 7.71097i) q^{65} +(5.35642 - 0.851244i) q^{66} -10.6944i q^{67} -5.11080i q^{68} -2.17955i q^{69} +(9.42212 + 2.19537i) q^{70} -1.55383 q^{71} +2.16812 q^{72} -2.25681i q^{73} -4.76475i q^{74} +(1.83588 - 4.65076i) q^{75} +3.86423 q^{76} +(-6.88493 - 5.44038i) q^{77} +6.82058i q^{78} +8.24756i q^{79} +(9.04756 - 6.15546i) q^{80} +1.00000 q^{81} +5.50407 q^{82} -5.54564i q^{83} +(1.20859 + 1.31181i) q^{84} +(9.53524 + 14.0153i) q^{85} -8.68870 q^{86} +5.39200i q^{87} +(-7.10171 + 1.12861i) q^{88} -1.62655i q^{89} +(3.02327 - 2.05687i) q^{90} +(8.11575 - 7.47715i) q^{91} -1.46938i q^{92} +0.864081i q^{93} -17.5882 q^{94} +(-10.5968 + 7.20950i) q^{95} +3.66660 q^{96} +8.80400 q^{97} +(0.936058 - 11.4087i) q^{98} +(-3.27552 + 0.520547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.63529 −1.15632 −0.578162 0.815922i \(-0.696230\pi\)
−0.578162 + 0.815922i \(0.696230\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.674169 0.337085
\(5\) −1.84877 + 1.25780i −0.826794 + 0.562505i
\(6\) −1.63529 −0.667604
\(7\) 1.79271 + 1.94582i 0.677579 + 0.735450i
\(8\) 2.16812 0.766545
\(9\) 1.00000 0.333333
\(10\) 3.02327 2.05687i 0.956041 0.650438i
\(11\) −3.27552 + 0.520547i −0.987606 + 0.156951i
\(12\) 0.674169 0.194616
\(13\) 4.17087i 1.15679i −0.815756 0.578396i \(-0.803679\pi\)
0.815756 0.578396i \(-0.196321\pi\)
\(14\) −2.93159 3.18197i −0.783501 0.850418i
\(15\) −1.84877 + 1.25780i −0.477350 + 0.324763i
\(16\) −4.89383 −1.22346
\(17\) 7.58089i 1.83864i −0.393516 0.919318i \(-0.628742\pi\)
0.393516 0.919318i \(-0.371258\pi\)
\(18\) −1.63529 −0.385441
\(19\) 5.73183 1.31497 0.657487 0.753466i \(-0.271620\pi\)
0.657487 + 0.753466i \(0.271620\pi\)
\(20\) −1.24638 + 0.847970i −0.278699 + 0.189612i
\(21\) 1.79271 + 1.94582i 0.391200 + 0.424612i
\(22\) 5.35642 0.851244i 1.14199 0.181486i
\(23\) 2.17955i 0.454467i −0.973840 0.227233i \(-0.927032\pi\)
0.973840 0.227233i \(-0.0729681\pi\)
\(24\) 2.16812 0.442565
\(25\) 1.83588 4.65076i 0.367176 0.930152i
\(26\) 6.82058i 1.33763i
\(27\) 1.00000 0.192450
\(28\) 1.20859 + 1.31181i 0.228402 + 0.247909i
\(29\) 5.39200i 1.00127i 0.865659 + 0.500635i \(0.166900\pi\)
−0.865659 + 0.500635i \(0.833100\pi\)
\(30\) 3.02327 2.05687i 0.551971 0.375531i
\(31\) 0.864081i 0.155194i 0.996985 + 0.0775968i \(0.0247247\pi\)
−0.996985 + 0.0775968i \(0.975275\pi\)
\(32\) 3.66660 0.648169
\(33\) −3.27552 + 0.520547i −0.570195 + 0.0906155i
\(34\) 12.3969i 2.12606i
\(35\) −5.76174 1.34250i −0.973913 0.226924i
\(36\) 0.674169 0.112362
\(37\) 2.91371i 0.479010i 0.970895 + 0.239505i \(0.0769852\pi\)
−0.970895 + 0.239505i \(0.923015\pi\)
\(38\) −9.37321 −1.52053
\(39\) 4.17087i 0.667874i
\(40\) −4.00834 + 2.72706i −0.633774 + 0.431185i
\(41\) −3.36581 −0.525651 −0.262826 0.964843i \(-0.584654\pi\)
−0.262826 + 0.964843i \(0.584654\pi\)
\(42\) −2.93159 3.18197i −0.452354 0.490989i
\(43\) 5.31325 0.810263 0.405132 0.914258i \(-0.367226\pi\)
0.405132 + 0.914258i \(0.367226\pi\)
\(44\) −2.20825 + 0.350936i −0.332907 + 0.0529057i
\(45\) −1.84877 + 1.25780i −0.275598 + 0.187502i
\(46\) 3.56419i 0.525511i
\(47\) 10.7554 1.56884 0.784420 0.620229i \(-0.212961\pi\)
0.784420 + 0.620229i \(0.212961\pi\)
\(48\) −4.89383 −0.706364
\(49\) −0.572412 + 6.97656i −0.0817731 + 0.996651i
\(50\) −3.00219 + 7.60533i −0.424574 + 1.07556i
\(51\) 7.58089i 1.06154i
\(52\) 2.81187i 0.389937i
\(53\) 11.1538i 1.53209i 0.642788 + 0.766044i \(0.277777\pi\)
−0.642788 + 0.766044i \(0.722223\pi\)
\(54\) −1.63529 −0.222535
\(55\) 5.40093 5.08232i 0.728261 0.685300i
\(56\) 3.88679 + 4.21876i 0.519395 + 0.563755i
\(57\) 5.73183 0.759200
\(58\) 8.81748i 1.15779i
\(59\) 10.8770i 1.41606i −0.706180 0.708032i \(-0.749583\pi\)
0.706180 0.708032i \(-0.250417\pi\)
\(60\) −1.24638 + 0.847970i −0.160907 + 0.109472i
\(61\) 15.3838 1.96969 0.984846 0.173430i \(-0.0554851\pi\)
0.984846 + 0.173430i \(0.0554851\pi\)
\(62\) 1.41302i 0.179454i
\(63\) 1.79271 + 1.94582i 0.225860 + 0.245150i
\(64\) 3.79172 0.473965
\(65\) 5.24612 + 7.71097i 0.650701 + 0.956428i
\(66\) 5.35642 0.851244i 0.659330 0.104781i
\(67\) 10.6944i 1.30653i −0.757131 0.653263i \(-0.773400\pi\)
0.757131 0.653263i \(-0.226600\pi\)
\(68\) 5.11080i 0.619776i
\(69\) 2.17955i 0.262387i
\(70\) 9.42212 + 2.19537i 1.12616 + 0.262397i
\(71\) −1.55383 −0.184405 −0.0922027 0.995740i \(-0.529391\pi\)
−0.0922027 + 0.995740i \(0.529391\pi\)
\(72\) 2.16812 0.255515
\(73\) 2.25681i 0.264140i −0.991240 0.132070i \(-0.957838\pi\)
0.991240 0.132070i \(-0.0421623\pi\)
\(74\) 4.76475i 0.553891i
\(75\) 1.83588 4.65076i 0.211989 0.537023i
\(76\) 3.86423 0.443257
\(77\) −6.88493 5.44038i −0.784611 0.619989i
\(78\) 6.82058i 0.772278i
\(79\) 8.24756i 0.927923i 0.885855 + 0.463961i \(0.153572\pi\)
−0.885855 + 0.463961i \(0.846428\pi\)
\(80\) 9.04756 6.15546i 1.01155 0.688202i
\(81\) 1.00000 0.111111
\(82\) 5.50407 0.607823
\(83\) 5.54564i 0.608713i −0.952558 0.304357i \(-0.901559\pi\)
0.952558 0.304357i \(-0.0984415\pi\)
\(84\) 1.20859 + 1.31181i 0.131868 + 0.143130i
\(85\) 9.53524 + 14.0153i 1.03424 + 1.52017i
\(86\) −8.68870 −0.936926
\(87\) 5.39200i 0.578083i
\(88\) −7.10171 + 1.12861i −0.757045 + 0.120310i
\(89\) 1.62655i 0.172414i −0.996277 0.0862069i \(-0.972525\pi\)
0.996277 0.0862069i \(-0.0274746\pi\)
\(90\) 3.02327 2.05687i 0.318680 0.216813i
\(91\) 8.11575 7.47715i 0.850762 0.783818i
\(92\) 1.46938i 0.153194i
\(93\) 0.864081i 0.0896010i
\(94\) −17.5882 −1.81409
\(95\) −10.5968 + 7.20950i −1.08721 + 0.739679i
\(96\) 3.66660 0.374221
\(97\) 8.80400 0.893911 0.446955 0.894556i \(-0.352508\pi\)
0.446955 + 0.894556i \(0.352508\pi\)
\(98\) 0.936058 11.4087i 0.0945562 1.15245i
\(99\) −3.27552 + 0.520547i −0.329202 + 0.0523169i
\(100\) 1.23769 3.13540i 0.123769 0.313540i
\(101\) 0.825476 0.0821379 0.0410690 0.999156i \(-0.486924\pi\)
0.0410690 + 0.999156i \(0.486924\pi\)
\(102\) 12.3969i 1.22748i
\(103\) −11.5317 −1.13625 −0.568127 0.822941i \(-0.692332\pi\)
−0.568127 + 0.822941i \(0.692332\pi\)
\(104\) 9.04293i 0.886733i
\(105\) −5.76174 1.34250i −0.562289 0.131014i
\(106\) 18.2396i 1.77159i
\(107\) 9.69116 0.936880 0.468440 0.883495i \(-0.344816\pi\)
0.468440 + 0.883495i \(0.344816\pi\)
\(108\) 0.674169 0.0648720
\(109\) 10.2781i 0.984462i −0.870465 0.492231i \(-0.836181\pi\)
0.870465 0.492231i \(-0.163819\pi\)
\(110\) −8.83208 + 8.31106i −0.842106 + 0.792428i
\(111\) 2.91371i 0.276557i
\(112\) −8.77321 9.52251i −0.828990 0.899792i
\(113\) 15.0285i 1.41376i 0.707333 + 0.706881i \(0.249898\pi\)
−0.707333 + 0.706881i \(0.750102\pi\)
\(114\) −9.37321 −0.877881
\(115\) 2.74143 + 4.02947i 0.255640 + 0.375750i
\(116\) 3.63512i 0.337513i
\(117\) 4.17087i 0.385597i
\(118\) 17.7870i 1.63743i
\(119\) 14.7510 13.5903i 1.35222 1.24582i
\(120\) −4.00834 + 2.72706i −0.365910 + 0.248945i
\(121\) 10.4581 3.41012i 0.950733 0.310011i
\(122\) −25.1569 −2.27760
\(123\) −3.36581 −0.303485
\(124\) 0.582537i 0.0523134i
\(125\) 2.45561 + 10.9073i 0.219637 + 0.975582i
\(126\) −2.93159 3.18197i −0.261167 0.283473i
\(127\) 7.78569 0.690868 0.345434 0.938443i \(-0.387732\pi\)
0.345434 + 0.938443i \(0.387732\pi\)
\(128\) −13.5338 −1.19623
\(129\) 5.31325 0.467806
\(130\) −8.57892 12.6097i −0.752421 1.10594i
\(131\) 2.89541 0.252973 0.126486 0.991968i \(-0.459630\pi\)
0.126486 + 0.991968i \(0.459630\pi\)
\(132\) −2.20825 + 0.350936i −0.192204 + 0.0305451i
\(133\) 10.2755 + 11.1531i 0.890998 + 0.967097i
\(134\) 17.4884i 1.51077i
\(135\) −1.84877 + 1.25780i −0.159117 + 0.108254i
\(136\) 16.4362i 1.40940i
\(137\) 9.16402i 0.782935i −0.920192 0.391468i \(-0.871967\pi\)
0.920192 0.391468i \(-0.128033\pi\)
\(138\) 3.56419i 0.303404i
\(139\) 7.30048 0.619218 0.309609 0.950864i \(-0.399802\pi\)
0.309609 + 0.950864i \(0.399802\pi\)
\(140\) −3.88439 0.905071i −0.328291 0.0764924i
\(141\) 10.7554 0.905771
\(142\) 2.54096 0.213232
\(143\) 2.17113 + 13.6618i 0.181559 + 1.14245i
\(144\) −4.89383 −0.407820
\(145\) −6.78206 9.96856i −0.563219 0.827844i
\(146\) 3.69054i 0.305431i
\(147\) −0.572412 + 6.97656i −0.0472117 + 0.575417i
\(148\) 1.96433i 0.161467i
\(149\) 16.9556i 1.38905i 0.719467 + 0.694526i \(0.244386\pi\)
−0.719467 + 0.694526i \(0.755614\pi\)
\(150\) −3.00219 + 7.60533i −0.245128 + 0.620973i
\(151\) 16.3343i 1.32927i −0.747170 0.664633i \(-0.768588\pi\)
0.747170 0.664633i \(-0.231412\pi\)
\(152\) 12.4273 1.00799
\(153\) 7.58089i 0.612878i
\(154\) 11.2589 + 8.89659i 0.907264 + 0.716907i
\(155\) −1.08684 1.59748i −0.0872972 0.128313i
\(156\) 2.81187i 0.225130i
\(157\) −0.510450 −0.0407384 −0.0203692 0.999793i \(-0.506484\pi\)
−0.0203692 + 0.999793i \(0.506484\pi\)
\(158\) 13.4871i 1.07298i
\(159\) 11.1538i 0.884551i
\(160\) −6.77869 + 4.61185i −0.535902 + 0.364599i
\(161\) 4.24100 3.90729i 0.334238 0.307937i
\(162\) −1.63529 −0.128480
\(163\) 24.3951i 1.91077i 0.295362 + 0.955385i \(0.404560\pi\)
−0.295362 + 0.955385i \(0.595440\pi\)
\(164\) −2.26912 −0.177189
\(165\) 5.40093 5.08232i 0.420462 0.395658i
\(166\) 9.06873i 0.703870i
\(167\) 14.6558i 1.13410i −0.823682 0.567052i \(-0.808084\pi\)
0.823682 0.567052i \(-0.191916\pi\)
\(168\) 3.88679 + 4.21876i 0.299873 + 0.325484i
\(169\) −4.39617 −0.338167
\(170\) −15.5929 22.9191i −1.19592 1.75781i
\(171\) 5.73183 0.438324
\(172\) 3.58203 0.273127
\(173\) 17.0484i 1.29617i −0.761569 0.648083i \(-0.775571\pi\)
0.761569 0.648083i \(-0.224429\pi\)
\(174\) 8.81748i 0.668452i
\(175\) 12.3407 4.76516i 0.932870 0.360212i
\(176\) 16.0299 2.54747i 1.20830 0.192023i
\(177\) 10.8770i 0.817565i
\(178\) 2.65988i 0.199366i
\(179\) 19.0830 1.42633 0.713166 0.700996i \(-0.247261\pi\)
0.713166 + 0.700996i \(0.247261\pi\)
\(180\) −1.24638 + 0.847970i −0.0928998 + 0.0632040i
\(181\) 7.90098i 0.587275i 0.955917 + 0.293638i \(0.0948659\pi\)
−0.955917 + 0.293638i \(0.905134\pi\)
\(182\) −13.2716 + 12.2273i −0.983757 + 0.906347i
\(183\) 15.3838 1.13720
\(184\) 4.72551i 0.348369i
\(185\) −3.66486 5.38676i −0.269446 0.396043i
\(186\) 1.41302i 0.103608i
\(187\) 3.94620 + 24.8313i 0.288575 + 1.81585i
\(188\) 7.25098 0.528832
\(189\) 1.79271 + 1.94582i 0.130400 + 0.141537i
\(190\) 17.3289 11.7896i 1.25717 0.855309i
\(191\) 0.577417 0.0417804 0.0208902 0.999782i \(-0.493350\pi\)
0.0208902 + 0.999782i \(0.493350\pi\)
\(192\) 3.79172 0.273644
\(193\) −14.2196 −1.02355 −0.511776 0.859119i \(-0.671012\pi\)
−0.511776 + 0.859119i \(0.671012\pi\)
\(194\) −14.3971 −1.03365
\(195\) 5.24612 + 7.71097i 0.375683 + 0.552194i
\(196\) −0.385902 + 4.70338i −0.0275645 + 0.335956i
\(197\) 2.26374 0.161285 0.0806425 0.996743i \(-0.474303\pi\)
0.0806425 + 0.996743i \(0.474303\pi\)
\(198\) 5.35642 0.851244i 0.380664 0.0604953i
\(199\) 0.287141i 0.0203549i 0.999948 + 0.0101774i \(0.00323964\pi\)
−0.999948 + 0.0101774i \(0.996760\pi\)
\(200\) 3.98040 10.0834i 0.281457 0.713003i
\(201\) 10.6944i 0.754323i
\(202\) −1.34989 −0.0949780
\(203\) −10.4919 + 9.66627i −0.736384 + 0.678439i
\(204\) 5.11080i 0.357828i
\(205\) 6.22260 4.23351i 0.434605 0.295681i
\(206\) 18.8577 1.31388
\(207\) 2.17955i 0.151489i
\(208\) 20.4116i 1.41529i
\(209\) −18.7747 + 2.98369i −1.29868 + 0.206386i
\(210\) 9.42212 + 2.19537i 0.650188 + 0.151495i
\(211\) 15.6678i 1.07861i 0.842109 + 0.539307i \(0.181314\pi\)
−0.842109 + 0.539307i \(0.818686\pi\)
\(212\) 7.51953i 0.516443i
\(213\) −1.55383 −0.106467
\(214\) −15.8478 −1.08334
\(215\) −9.82296 + 6.68301i −0.669920 + 0.455777i
\(216\) 2.16812 0.147522
\(217\) −1.68134 + 1.54904i −0.114137 + 0.105156i
\(218\) 16.8076i 1.13836i
\(219\) 2.25681i 0.152501i
\(220\) 3.64114 3.42634i 0.245486 0.231004i
\(221\) −31.6189 −2.12692
\(222\) 4.76475i 0.319789i
\(223\) −21.1236 −1.41454 −0.707269 0.706945i \(-0.750073\pi\)
−0.707269 + 0.706945i \(0.750073\pi\)
\(224\) 6.57314 + 7.13453i 0.439186 + 0.476696i
\(225\) 1.83588 4.65076i 0.122392 0.310051i
\(226\) 24.5759i 1.63477i
\(227\) 7.65754i 0.508249i 0.967172 + 0.254124i \(0.0817873\pi\)
−0.967172 + 0.254124i \(0.918213\pi\)
\(228\) 3.86423 0.255915
\(229\) 19.9463i 1.31809i −0.752103 0.659045i \(-0.770961\pi\)
0.752103 0.659045i \(-0.229039\pi\)
\(230\) −4.48304 6.58935i −0.295603 0.434489i
\(231\) −6.88493 5.44038i −0.452995 0.357951i
\(232\) 11.6905i 0.767518i
\(233\) 5.69495 0.373088 0.186544 0.982447i \(-0.440271\pi\)
0.186544 + 0.982447i \(0.440271\pi\)
\(234\) 6.82058i 0.445875i
\(235\) −19.8843 + 13.5282i −1.29711 + 0.882481i
\(236\) 7.33293i 0.477333i
\(237\) 8.24756i 0.535736i
\(238\) −24.1222 + 22.2241i −1.56361 + 1.44057i
\(239\) 9.91495i 0.641345i −0.947190 0.320672i \(-0.896091\pi\)
0.947190 0.320672i \(-0.103909\pi\)
\(240\) 9.04756 6.15546i 0.584017 0.397334i
\(241\) 2.07373 0.133581 0.0667903 0.997767i \(-0.478724\pi\)
0.0667903 + 0.997767i \(0.478724\pi\)
\(242\) −17.1020 + 5.57653i −1.09936 + 0.358473i
\(243\) 1.00000 0.0641500
\(244\) 10.3713 0.663953
\(245\) −7.71686 13.6180i −0.493012 0.870023i
\(246\) 5.50407 0.350927
\(247\) 23.9067i 1.52115i
\(248\) 1.87343i 0.118963i
\(249\) 5.54564i 0.351441i
\(250\) −4.01563 17.8366i −0.253971 1.12809i
\(251\) 9.03128i 0.570049i −0.958520 0.285025i \(-0.907998\pi\)
0.958520 0.285025i \(-0.0920018\pi\)
\(252\) 1.20859 + 1.31181i 0.0761338 + 0.0826363i
\(253\) 1.13456 + 7.13915i 0.0713289 + 0.448835i
\(254\) −12.7319 −0.798868
\(255\) 9.53524 + 14.0153i 0.597120 + 0.877672i
\(256\) 14.5482 0.909260
\(257\) 15.2678 0.952376 0.476188 0.879343i \(-0.342018\pi\)
0.476188 + 0.879343i \(0.342018\pi\)
\(258\) −8.68870 −0.540935
\(259\) −5.66954 + 5.22342i −0.352288 + 0.324567i
\(260\) 3.53677 + 5.19850i 0.219341 + 0.322397i
\(261\) 5.39200i 0.333757i
\(262\) −4.73483 −0.292518
\(263\) −6.40729 −0.395090 −0.197545 0.980294i \(-0.563297\pi\)
−0.197545 + 0.980294i \(0.563297\pi\)
\(264\) −7.10171 + 1.12861i −0.437080 + 0.0694609i
\(265\) −14.0292 20.6207i −0.861807 1.26672i
\(266\) −16.8034 18.2385i −1.03028 1.11828i
\(267\) 1.62655i 0.0995432i
\(268\) 7.20982i 0.440410i
\(269\) 13.5541i 0.826410i 0.910638 + 0.413205i \(0.135591\pi\)
−0.910638 + 0.413205i \(0.864409\pi\)
\(270\) 3.02327 2.05687i 0.183990 0.125177i
\(271\) 13.5515 0.823195 0.411598 0.911366i \(-0.364971\pi\)
0.411598 + 0.911366i \(0.364971\pi\)
\(272\) 37.0996i 2.24949i
\(273\) 8.11575 7.47715i 0.491188 0.452537i
\(274\) 14.9858i 0.905327i
\(275\) −3.59252 + 16.1893i −0.216637 + 0.976252i
\(276\) 1.46938i 0.0884465i
\(277\) 10.5948 0.636580 0.318290 0.947993i \(-0.396891\pi\)
0.318290 + 0.947993i \(0.396891\pi\)
\(278\) −11.9384 −0.716017
\(279\) 0.864081i 0.0517312i
\(280\) −12.4921 2.91069i −0.746548 0.173947i
\(281\) 11.4974i 0.685880i −0.939357 0.342940i \(-0.888577\pi\)
0.939357 0.342940i \(-0.111423\pi\)
\(282\) −17.5882 −1.04736
\(283\) 21.6818i 1.28885i −0.764668 0.644424i \(-0.777097\pi\)
0.764668 0.644424i \(-0.222903\pi\)
\(284\) −1.04754 −0.0621602
\(285\) −10.5968 + 7.20950i −0.627702 + 0.427054i
\(286\) −3.55043 22.3409i −0.209941 1.32105i
\(287\) −6.03390 6.54925i −0.356170 0.386590i
\(288\) 3.66660 0.216056
\(289\) −40.4698 −2.38058
\(290\) 11.0906 + 16.3015i 0.651264 + 0.957255i
\(291\) 8.80400 0.516100
\(292\) 1.52147i 0.0890375i
\(293\) 7.13847i 0.417034i 0.978019 + 0.208517i \(0.0668636\pi\)
−0.978019 + 0.208517i \(0.933136\pi\)
\(294\) 0.936058 11.4087i 0.0545920 0.665368i
\(295\) 13.6811 + 20.1090i 0.796543 + 1.17079i
\(296\) 6.31725i 0.367183i
\(297\) −3.27552 + 0.520547i −0.190065 + 0.0302052i
\(298\) 27.7272i 1.60619i
\(299\) −9.09061 −0.525724
\(300\) 1.23769 3.13540i 0.0714582 0.181022i
\(301\) 9.52509 + 10.3386i 0.549017 + 0.595908i
\(302\) 26.7113i 1.53706i
\(303\) 0.825476 0.0474223
\(304\) −28.0507 −1.60882
\(305\) −28.4410 + 19.3497i −1.62853 + 1.10796i
\(306\) 12.3969i 0.708686i
\(307\) 15.4378i 0.881081i −0.897733 0.440540i \(-0.854787\pi\)
0.897733 0.440540i \(-0.145213\pi\)
\(308\) −4.64161 3.66774i −0.264480 0.208989i
\(309\) −11.5317 −0.656016
\(310\) 1.77730 + 2.61235i 0.100944 + 0.148371i
\(311\) 30.4383i 1.72600i 0.505208 + 0.862998i \(0.331416\pi\)
−0.505208 + 0.862998i \(0.668584\pi\)
\(312\) 9.04293i 0.511955i
\(313\) −31.1303 −1.75959 −0.879795 0.475354i \(-0.842320\pi\)
−0.879795 + 0.475354i \(0.842320\pi\)
\(314\) 0.834734 0.0471068
\(315\) −5.76174 1.34250i −0.324638 0.0756412i
\(316\) 5.56025i 0.312789i
\(317\) 28.5646i 1.60435i −0.597089 0.802175i \(-0.703676\pi\)
0.597089 0.802175i \(-0.296324\pi\)
\(318\) 18.2396i 1.02283i
\(319\) −2.80679 17.6616i −0.157150 0.988860i
\(320\) −7.01000 + 4.76922i −0.391871 + 0.266608i
\(321\) 9.69116 0.540908
\(322\) −6.93526 + 6.38954i −0.386487 + 0.356075i
\(323\) 43.4524i 2.41776i
\(324\) 0.674169 0.0374538
\(325\) −19.3977 7.65721i −1.07599 0.424746i
\(326\) 39.8930i 2.20947i
\(327\) 10.2781i 0.568380i
\(328\) −7.29746 −0.402935
\(329\) 19.2813 + 20.9281i 1.06301 + 1.15380i
\(330\) −8.83208 + 8.31106i −0.486190 + 0.457509i
\(331\) −26.6099 −1.46261 −0.731306 0.682050i \(-0.761089\pi\)
−0.731306 + 0.682050i \(0.761089\pi\)
\(332\) 3.73870i 0.205188i
\(333\) 2.91371i 0.159670i
\(334\) 23.9665i 1.31139i
\(335\) 13.4514 + 19.7714i 0.734927 + 1.08023i
\(336\) −8.77321 9.52251i −0.478618 0.519495i
\(337\) −19.0036 −1.03519 −0.517597 0.855625i \(-0.673173\pi\)
−0.517597 + 0.855625i \(0.673173\pi\)
\(338\) 7.18900 0.391030
\(339\) 15.0285i 0.816236i
\(340\) 6.42837 + 9.44868i 0.348627 + 0.512427i
\(341\) −0.449794 2.83032i −0.0243577 0.153270i
\(342\) −9.37321 −0.506845
\(343\) −14.6013 + 11.3931i −0.788395 + 0.615170i
\(344\) 11.5197 0.621103
\(345\) 2.74143 + 4.02947i 0.147594 + 0.216940i
\(346\) 27.8791i 1.49879i
\(347\) −7.26940 −0.390242 −0.195121 0.980779i \(-0.562510\pi\)
−0.195121 + 0.980779i \(0.562510\pi\)
\(348\) 3.63512i 0.194863i
\(349\) 0.888707 0.0475714 0.0237857 0.999717i \(-0.492428\pi\)
0.0237857 + 0.999717i \(0.492428\pi\)
\(350\) −20.1806 + 7.79241i −1.07870 + 0.416522i
\(351\) 4.17087i 0.222625i
\(352\) −12.0100 + 1.90864i −0.640136 + 0.101731i
\(353\) 12.9562 0.689589 0.344794 0.938678i \(-0.387949\pi\)
0.344794 + 0.938678i \(0.387949\pi\)
\(354\) 17.7870i 0.945370i
\(355\) 2.87267 1.95440i 0.152465 0.103729i
\(356\) 1.09657i 0.0581181i
\(357\) 14.7510 13.5903i 0.780707 0.719275i
\(358\) −31.2062 −1.64930
\(359\) 8.33660i 0.439989i −0.975501 0.219994i \(-0.929396\pi\)
0.975501 0.219994i \(-0.0706039\pi\)
\(360\) −4.00834 + 2.72706i −0.211258 + 0.143728i
\(361\) 13.8539 0.729154
\(362\) 12.9204i 0.679081i
\(363\) 10.4581 3.41012i 0.548906 0.178985i
\(364\) 5.47139 5.04086i 0.286779 0.264213i
\(365\) 2.83862 + 4.17232i 0.148580 + 0.218389i
\(366\) −25.1569 −1.31497
\(367\) −22.9597 −1.19849 −0.599243 0.800567i \(-0.704532\pi\)
−0.599243 + 0.800567i \(0.704532\pi\)
\(368\) 10.6663i 0.556022i
\(369\) −3.36581 −0.175217
\(370\) 5.99310 + 8.80892i 0.311567 + 0.457954i
\(371\) −21.7032 + 19.9954i −1.12677 + 1.03811i
\(372\) 0.582537i 0.0302031i
\(373\) 35.0778 1.81626 0.908129 0.418691i \(-0.137511\pi\)
0.908129 + 0.418691i \(0.137511\pi\)
\(374\) −6.45318 40.6064i −0.333686 2.09971i
\(375\) 2.45561 + 10.9073i 0.126807 + 0.563252i
\(376\) 23.3190 1.20259
\(377\) 22.4893 1.15826
\(378\) −2.93159 3.18197i −0.150785 0.163663i
\(379\) −5.09918 −0.261928 −0.130964 0.991387i \(-0.541807\pi\)
−0.130964 + 0.991387i \(0.541807\pi\)
\(380\) −7.14406 + 4.86042i −0.366482 + 0.249335i
\(381\) 7.78569 0.398873
\(382\) −0.944243 −0.0483117
\(383\) −2.21160 −0.113008 −0.0565038 0.998402i \(-0.517995\pi\)
−0.0565038 + 0.998402i \(0.517995\pi\)
\(384\) −13.5338 −0.690642
\(385\) 19.5715 + 1.39812i 0.997458 + 0.0712549i
\(386\) 23.2532 1.18356
\(387\) 5.31325 0.270088
\(388\) 5.93539 0.301324
\(389\) 33.7532 1.71135 0.855677 0.517510i \(-0.173141\pi\)
0.855677 + 0.517510i \(0.173141\pi\)
\(390\) −8.57892 12.6097i −0.434411 0.638515i
\(391\) −16.5229 −0.835599
\(392\) −1.24105 + 15.1260i −0.0626827 + 0.763978i
\(393\) 2.89541 0.146054
\(394\) −3.70187 −0.186498
\(395\) −10.3738 15.2478i −0.521961 0.767201i
\(396\) −2.20825 + 0.350936i −0.110969 + 0.0176352i
\(397\) −7.81103 −0.392024 −0.196012 0.980601i \(-0.562799\pi\)
−0.196012 + 0.980601i \(0.562799\pi\)
\(398\) 0.469559i 0.0235368i
\(399\) 10.2755 + 11.1531i 0.514418 + 0.558354i
\(400\) −8.98448 + 22.7600i −0.449224 + 1.13800i
\(401\) −14.3745 −0.717827 −0.358914 0.933371i \(-0.616853\pi\)
−0.358914 + 0.933371i \(0.616853\pi\)
\(402\) 17.4884i 0.872241i
\(403\) 3.60397 0.179527
\(404\) 0.556510 0.0276874
\(405\) −1.84877 + 1.25780i −0.0918660 + 0.0625006i
\(406\) 17.1572 15.8071i 0.851498 0.784496i
\(407\) −1.51672 9.54390i −0.0751810 0.473074i
\(408\) 16.4362i 0.813715i
\(409\) −11.9091 −0.588866 −0.294433 0.955672i \(-0.595131\pi\)
−0.294433 + 0.955672i \(0.595131\pi\)
\(410\) −10.1757 + 6.92302i −0.502544 + 0.341903i
\(411\) 9.16402i 0.452028i
\(412\) −7.77433 −0.383014
\(413\) 21.1646 19.4992i 1.04144 0.959495i
\(414\) 3.56419i 0.175170i
\(415\) 6.97531 + 10.2526i 0.342404 + 0.503280i
\(416\) 15.2929i 0.749797i
\(417\) 7.30048 0.357506
\(418\) 30.7021 4.87919i 1.50169 0.238649i
\(419\) 2.62704i 0.128339i −0.997939 0.0641696i \(-0.979560\pi\)
0.997939 0.0641696i \(-0.0204399\pi\)
\(420\) −3.88439 0.905071i −0.189539 0.0441629i
\(421\) −13.4735 −0.656656 −0.328328 0.944564i \(-0.606485\pi\)
−0.328328 + 0.944564i \(0.606485\pi\)
\(422\) 25.6214i 1.24723i
\(423\) 10.7554 0.522947
\(424\) 24.1827i 1.17441i
\(425\) −35.2569 13.9176i −1.71021 0.675102i
\(426\) 2.54096 0.123110
\(427\) 27.5786 + 29.9340i 1.33462 + 1.44861i
\(428\) 6.53348 0.315808
\(429\) 2.17113 + 13.6618i 0.104823 + 0.659597i
\(430\) 16.0634 10.9286i 0.774645 0.527026i
\(431\) 17.8620i 0.860382i 0.902738 + 0.430191i \(0.141554\pi\)
−0.902738 + 0.430191i \(0.858446\pi\)
\(432\) −4.89383 −0.235455
\(433\) 0.555819 0.0267109 0.0133555 0.999911i \(-0.495749\pi\)
0.0133555 + 0.999911i \(0.495749\pi\)
\(434\) 2.74948 2.53313i 0.131979 0.121594i
\(435\) −6.78206 9.96856i −0.325175 0.477956i
\(436\) 6.92917i 0.331847i
\(437\) 12.4928i 0.597612i
\(438\) 3.69054i 0.176341i
\(439\) 19.6767 0.939117 0.469558 0.882901i \(-0.344413\pi\)
0.469558 + 0.882901i \(0.344413\pi\)
\(440\) 11.7098 11.0191i 0.558245 0.525313i
\(441\) −0.572412 + 6.97656i −0.0272577 + 0.332217i
\(442\) 51.7060 2.45941
\(443\) 40.6848i 1.93299i −0.256677 0.966497i \(-0.582628\pi\)
0.256677 0.966497i \(-0.417372\pi\)
\(444\) 1.96433i 0.0932230i
\(445\) 2.04587 + 3.00711i 0.0969837 + 0.142551i
\(446\) 34.5431 1.63566
\(447\) 16.9556i 0.801970i
\(448\) 6.79744 + 7.37799i 0.321149 + 0.348577i
\(449\) 15.5339 0.733088 0.366544 0.930401i \(-0.380541\pi\)
0.366544 + 0.930401i \(0.380541\pi\)
\(450\) −3.00219 + 7.60533i −0.141525 + 0.358519i
\(451\) 11.0248 1.75206i 0.519136 0.0825013i
\(452\) 10.1317i 0.476557i
\(453\) 16.3343i 0.767453i
\(454\) 12.5223i 0.587700i
\(455\) −5.59939 + 24.0315i −0.262503 + 1.12661i
\(456\) 12.4273 0.581961
\(457\) −28.8051 −1.34745 −0.673724 0.738983i \(-0.735306\pi\)
−0.673724 + 0.738983i \(0.735306\pi\)
\(458\) 32.6180i 1.52414i
\(459\) 7.58089i 0.353846i
\(460\) 1.84819 + 2.71655i 0.0861723 + 0.126660i
\(461\) 19.9251 0.928005 0.464003 0.885834i \(-0.346413\pi\)
0.464003 + 0.885834i \(0.346413\pi\)
\(462\) 11.2589 + 8.89659i 0.523809 + 0.413907i
\(463\) 8.87783i 0.412588i −0.978490 0.206294i \(-0.933860\pi\)
0.978490 0.206294i \(-0.0661403\pi\)
\(464\) 26.3876i 1.22501i
\(465\) −1.08684 1.59748i −0.0504011 0.0740816i
\(466\) −9.31288 −0.431411
\(467\) −31.9600 −1.47893 −0.739465 0.673195i \(-0.764922\pi\)
−0.739465 + 0.673195i \(0.764922\pi\)
\(468\) 2.81187i 0.129979i
\(469\) 20.8093 19.1719i 0.960884 0.885274i
\(470\) 32.5165 22.1225i 1.49988 1.02043i
\(471\) −0.510450 −0.0235203
\(472\) 23.5826i 1.08548i
\(473\) −17.4037 + 2.76579i −0.800221 + 0.127171i
\(474\) 13.4871i 0.619485i
\(475\) 10.5230 26.6574i 0.482826 1.22312i
\(476\) 9.94469 9.16216i 0.455814 0.419947i
\(477\) 11.1538i 0.510696i
\(478\) 16.2138i 0.741602i
\(479\) 9.36547 0.427919 0.213960 0.976842i \(-0.431364\pi\)
0.213960 + 0.976842i \(0.431364\pi\)
\(480\) −6.77869 + 4.61185i −0.309403 + 0.210501i
\(481\) 12.1527 0.554115
\(482\) −3.39115 −0.154462
\(483\) 4.24100 3.90729i 0.192972 0.177788i
\(484\) 7.05050 2.29900i 0.320477 0.104500i
\(485\) −16.2765 + 11.0737i −0.739080 + 0.502830i
\(486\) −1.63529 −0.0741782
\(487\) 15.8582i 0.718602i 0.933222 + 0.359301i \(0.116985\pi\)
−0.933222 + 0.359301i \(0.883015\pi\)
\(488\) 33.3538 1.50986
\(489\) 24.3951i 1.10318i
\(490\) 12.6193 + 22.2694i 0.570081 + 1.00603i
\(491\) 26.6209i 1.20139i 0.799480 + 0.600693i \(0.205108\pi\)
−0.799480 + 0.600693i \(0.794892\pi\)
\(492\) −2.26912 −0.102300
\(493\) 40.8762 1.84097
\(494\) 39.0944i 1.75894i
\(495\) 5.40093 5.08232i 0.242754 0.228433i
\(496\) 4.22867i 0.189873i
\(497\) −2.78556 3.02347i −0.124949 0.135621i
\(498\) 9.06873i 0.406379i
\(499\) −12.2258 −0.547301 −0.273651 0.961829i \(-0.588231\pi\)
−0.273651 + 0.961829i \(0.588231\pi\)
\(500\) 1.65550 + 7.35339i 0.0740361 + 0.328854i
\(501\) 14.6558i 0.654775i
\(502\) 14.7687i 0.659161i
\(503\) 0.335068i 0.0149400i −0.999972 0.00746998i \(-0.997622\pi\)
0.999972 0.00746998i \(-0.00237779\pi\)
\(504\) 3.88679 + 4.21876i 0.173132 + 0.187918i
\(505\) −1.52611 + 1.03828i −0.0679111 + 0.0462030i
\(506\) −1.85533 11.6746i −0.0824793 0.518998i
\(507\) −4.39617 −0.195241
\(508\) 5.24887 0.232881
\(509\) 21.9958i 0.974948i −0.873138 0.487474i \(-0.837918\pi\)
0.873138 0.487474i \(-0.162082\pi\)
\(510\) −15.5929 22.9191i −0.690464 1.01487i
\(511\) 4.39134 4.04580i 0.194262 0.178976i
\(512\) 3.27707 0.144827
\(513\) 5.73183 0.253067
\(514\) −24.9672 −1.10126
\(515\) 21.3195 14.5046i 0.939447 0.639149i
\(516\) 3.58203 0.157690
\(517\) −35.2296 + 5.59870i −1.54940 + 0.246231i
\(518\) 9.27134 8.54180i 0.407359 0.375305i
\(519\) 17.0484i 0.748342i
\(520\) 11.3742 + 16.7183i 0.498792 + 0.733145i
\(521\) 6.25907i 0.274215i 0.990556 + 0.137107i \(0.0437806\pi\)
−0.990556 + 0.137107i \(0.956219\pi\)
\(522\) 8.81748i 0.385931i
\(523\) 36.1671i 1.58148i 0.612155 + 0.790738i \(0.290303\pi\)
−0.612155 + 0.790738i \(0.709697\pi\)
\(524\) 1.95199 0.0852732
\(525\) 12.3407 4.76516i 0.538593 0.207968i
\(526\) 10.4778 0.456852
\(527\) 6.55050 0.285344
\(528\) 16.0299 2.54747i 0.697610 0.110864i
\(529\) 18.2496 0.793460
\(530\) 22.9418 + 33.7208i 0.996528 + 1.46474i
\(531\) 10.8770i 0.472021i
\(532\) 6.92742 + 7.51908i 0.300342 + 0.325993i
\(533\) 14.0384i 0.608069i
\(534\) 2.65988i 0.115104i
\(535\) −17.9167 + 12.1895i −0.774606 + 0.527000i
\(536\) 23.1866i 1.00151i
\(537\) 19.0830 0.823493
\(538\) 22.1649i 0.955598i
\(539\) −1.75668 23.1498i −0.0756654 0.997133i
\(540\) −1.24638 + 0.847970i −0.0536357 + 0.0364908i
\(541\) 0.696188i 0.0299315i 0.999888 + 0.0149657i \(0.00476392\pi\)
−0.999888 + 0.0149657i \(0.995236\pi\)
\(542\) −22.1606 −0.951880
\(543\) 7.90098i 0.339064i
\(544\) 27.7961i 1.19175i
\(545\) 12.9278 + 19.0018i 0.553765 + 0.813947i
\(546\) −13.2716 + 12.2273i −0.567972 + 0.523280i
\(547\) −27.6211 −1.18099 −0.590496 0.807041i \(-0.701068\pi\)
−0.590496 + 0.807041i \(0.701068\pi\)
\(548\) 6.17810i 0.263915i
\(549\) 15.3838 0.656564
\(550\) 5.87481 26.4742i 0.250503 1.12886i
\(551\) 30.9061i 1.31664i
\(552\) 4.72551i 0.201131i
\(553\) −16.0482 + 14.7854i −0.682441 + 0.628741i
\(554\) −17.3256 −0.736093
\(555\) −3.66486 5.38676i −0.155565 0.228655i
\(556\) 4.92176 0.208729
\(557\) 36.7731 1.55813 0.779063 0.626946i \(-0.215695\pi\)
0.779063 + 0.626946i \(0.215695\pi\)
\(558\) 1.41302i 0.0598180i
\(559\) 22.1609i 0.937305i
\(560\) 28.1970 + 6.56996i 1.19154 + 0.277632i
\(561\) 3.94620 + 24.8313i 0.166609 + 1.04838i
\(562\) 18.8016i 0.793099i
\(563\) 3.23737i 0.136439i −0.997670 0.0682195i \(-0.978268\pi\)
0.997670 0.0682195i \(-0.0217318\pi\)
\(564\) 7.25098 0.305321
\(565\) −18.9028 27.7842i −0.795248 1.16889i
\(566\) 35.4560i 1.49033i
\(567\) 1.79271 + 1.94582i 0.0752866 + 0.0817167i
\(568\) −3.36888 −0.141355
\(569\) 9.36538i 0.392617i −0.980542 0.196309i \(-0.937105\pi\)
0.980542 0.196309i \(-0.0628954\pi\)
\(570\) 17.3289 11.7896i 0.725827 0.493813i
\(571\) 12.0341i 0.503611i −0.967778 0.251805i \(-0.918976\pi\)
0.967778 0.251805i \(-0.0810243\pi\)
\(572\) 1.46371 + 9.21035i 0.0612008 + 0.385104i
\(573\) 0.577417 0.0241219
\(574\) 9.86718 + 10.7099i 0.411848 + 0.447023i
\(575\) −10.1365 4.00138i −0.422723 0.166869i
\(576\) 3.79172 0.157988
\(577\) 2.09996 0.0874223 0.0437111 0.999044i \(-0.486082\pi\)
0.0437111 + 0.999044i \(0.486082\pi\)
\(578\) 66.1799 2.75272
\(579\) −14.2196 −0.590948
\(580\) −4.57226 6.72049i −0.189853 0.279053i
\(581\) 10.7908 9.94171i 0.447678 0.412451i
\(582\) −14.3971 −0.596778
\(583\) −5.80605 36.5344i −0.240462 1.51310i
\(584\) 4.89303i 0.202475i
\(585\) 5.24612 + 7.71097i 0.216900 + 0.318809i
\(586\) 11.6735i 0.482226i
\(587\) 41.4514 1.71088 0.855441 0.517901i \(-0.173286\pi\)
0.855441 + 0.517901i \(0.173286\pi\)
\(588\) −0.385902 + 4.70338i −0.0159143 + 0.193964i
\(589\) 4.95277i 0.204075i
\(590\) −22.3725 32.8841i −0.921062 1.35382i
\(591\) 2.26374 0.0931179
\(592\) 14.2592i 0.586049i
\(593\) 35.3731i 1.45260i −0.687377 0.726300i \(-0.741238\pi\)
0.687377 0.726300i \(-0.258762\pi\)
\(594\) 5.35642 0.851244i 0.219777 0.0349270i
\(595\) −10.1773 + 43.6791i −0.417230 + 1.79067i
\(596\) 11.4309i 0.468228i
\(597\) 0.287141i 0.0117519i
\(598\) 14.8658 0.607907
\(599\) −29.7933 −1.21732 −0.608662 0.793430i \(-0.708293\pi\)
−0.608662 + 0.793430i \(0.708293\pi\)
\(600\) 3.98040 10.0834i 0.162499 0.411652i
\(601\) −39.9860 −1.63106 −0.815531 0.578713i \(-0.803555\pi\)
−0.815531 + 0.578713i \(0.803555\pi\)
\(602\) −15.5763 16.9066i −0.634842 0.689062i
\(603\) 10.6944i 0.435508i
\(604\) 11.0121i 0.448075i
\(605\) −15.0453 + 19.4587i −0.611677 + 0.791107i
\(606\) −1.34989 −0.0548356
\(607\) 0.361266i 0.0146634i 0.999973 + 0.00733168i \(0.00233377\pi\)
−0.999973 + 0.00733168i \(0.997666\pi\)
\(608\) 21.0163 0.852325
\(609\) −10.4919 + 9.66627i −0.425151 + 0.391697i
\(610\) 46.5093 31.6424i 1.88311 1.28116i
\(611\) 44.8595i 1.81482i
\(612\) 5.11080i 0.206592i
\(613\) −26.4191 −1.06706 −0.533528 0.845782i \(-0.679134\pi\)
−0.533528 + 0.845782i \(0.679134\pi\)
\(614\) 25.2452i 1.01881i
\(615\) 6.22260 4.23351i 0.250919 0.170712i
\(616\) −14.9273 11.7954i −0.601439 0.475249i
\(617\) 23.7919i 0.957825i 0.877863 + 0.478912i \(0.158969\pi\)
−0.877863 + 0.478912i \(0.841031\pi\)
\(618\) 18.8577 0.758567
\(619\) 20.1966i 0.811770i 0.913924 + 0.405885i \(0.133037\pi\)
−0.913924 + 0.405885i \(0.866963\pi\)
\(620\) −0.732715 1.07698i −0.0294265 0.0432524i
\(621\) 2.17955i 0.0874622i
\(622\) 49.7753i 1.99581i
\(623\) 3.16497 2.91592i 0.126802 0.116824i
\(624\) 20.4116i 0.817116i
\(625\) −18.2591 17.0765i −0.730364 0.683058i
\(626\) 50.9070 2.03465
\(627\) −18.7747 + 2.98369i −0.749791 + 0.119157i
\(628\) −0.344130 −0.0137323
\(629\) 22.0885 0.880725
\(630\) 9.42212 + 2.19537i 0.375386 + 0.0874657i
\(631\) −21.8127 −0.868351 −0.434175 0.900828i \(-0.642960\pi\)
−0.434175 + 0.900828i \(0.642960\pi\)
\(632\) 17.8817i 0.711294i
\(633\) 15.6678i 0.622739i
\(634\) 46.7114i 1.85515i
\(635\) −14.3939 + 9.79284i −0.571206 + 0.388617i
\(636\) 7.51953i 0.298169i
\(637\) 29.0983 + 2.38746i 1.15292 + 0.0945944i
\(638\) 4.58991 + 28.8818i 0.181716 + 1.14344i
\(639\) −1.55383 −0.0614685
\(640\) 25.0208 17.0228i 0.989032 0.672884i
\(641\) 16.3512 0.645834 0.322917 0.946427i \(-0.395337\pi\)
0.322917 + 0.946427i \(0.395337\pi\)
\(642\) −15.8478 −0.625465
\(643\) 18.3877 0.725141 0.362571 0.931956i \(-0.381899\pi\)
0.362571 + 0.931956i \(0.381899\pi\)
\(644\) 2.85915 2.63417i 0.112666 0.103801i
\(645\) −9.82296 + 6.68301i −0.386779 + 0.263143i
\(646\) 71.0572i 2.79571i
\(647\) 2.00293 0.0787434 0.0393717 0.999225i \(-0.487464\pi\)
0.0393717 + 0.999225i \(0.487464\pi\)
\(648\) 2.16812 0.0851716
\(649\) 5.66198 + 35.6278i 0.222252 + 1.39851i
\(650\) 31.7209 + 12.5218i 1.24419 + 0.491144i
\(651\) −1.68134 + 1.54904i −0.0658971 + 0.0607118i
\(652\) 16.4464i 0.644091i
\(653\) 4.94844i 0.193647i 0.995302 + 0.0968236i \(0.0308683\pi\)
−0.995302 + 0.0968236i \(0.969132\pi\)
\(654\) 16.8076i 0.657231i
\(655\) −5.35293 + 3.64184i −0.209156 + 0.142299i
\(656\) 16.4717 0.643112
\(657\) 2.25681i 0.0880466i
\(658\) −31.5305 34.2235i −1.22919 1.33417i
\(659\) 4.46793i 0.174046i −0.996206 0.0870228i \(-0.972265\pi\)
0.996206 0.0870228i \(-0.0277353\pi\)
\(660\) 3.64114 3.42634i 0.141731 0.133370i
\(661\) 0.732284i 0.0284826i −0.999899 0.0142413i \(-0.995467\pi\)
0.999899 0.0142413i \(-0.00453329\pi\)
\(662\) 43.5149 1.69125
\(663\) −31.6189 −1.22798
\(664\) 12.0236i 0.466606i
\(665\) −33.0254 7.69498i −1.28067 0.298398i
\(666\) 4.76475i 0.184630i
\(667\) 11.7521 0.455044
\(668\) 9.88052i 0.382289i
\(669\) −21.1236 −0.816684
\(670\) −21.9969 32.3319i −0.849814 1.24909i
\(671\) −50.3899 + 8.00798i −1.94528 + 0.309145i
\(672\) 6.57314 + 7.13453i 0.253564 + 0.275221i
\(673\) 27.7263 1.06877 0.534386 0.845241i \(-0.320543\pi\)
0.534386 + 0.845241i \(0.320543\pi\)
\(674\) 31.0764 1.19702
\(675\) 1.83588 4.65076i 0.0706630 0.179008i
\(676\) −2.96376 −0.113991
\(677\) 20.7844i 0.798809i 0.916775 + 0.399405i \(0.130783\pi\)
−0.916775 + 0.399405i \(0.869217\pi\)
\(678\) 24.5759i 0.943833i
\(679\) 15.7830 + 17.1310i 0.605695 + 0.657427i
\(680\) 20.6735 + 30.3868i 0.792793 + 1.16528i
\(681\) 7.65754i 0.293438i
\(682\) 0.735544 + 4.62838i 0.0281654 + 0.177230i
\(683\) 20.6169i 0.788882i −0.918921 0.394441i \(-0.870938\pi\)
0.918921 0.394441i \(-0.129062\pi\)
\(684\) 3.86423 0.147752
\(685\) 11.5265 + 16.9421i 0.440405 + 0.647326i
\(686\) 23.8773 18.6310i 0.911639 0.711336i
\(687\) 19.9463i 0.761000i
\(688\) −26.0022 −0.991323
\(689\) 46.5209 1.77231
\(690\) −4.48304 6.58935i −0.170666 0.250852i
\(691\) 2.23979i 0.0852056i 0.999092 + 0.0426028i \(0.0135650\pi\)
−0.999092 + 0.0426028i \(0.986435\pi\)
\(692\) 11.4935i 0.436918i
\(693\) −6.88493 5.44038i −0.261537 0.206663i
\(694\) 11.8876 0.451246
\(695\) −13.4969 + 9.18254i −0.511966 + 0.348314i
\(696\) 11.6905i 0.443127i
\(697\) 25.5158i 0.966480i
\(698\) −1.45329 −0.0550080
\(699\) 5.69495 0.215403
\(700\) 8.31973 3.21252i 0.314456 0.121422i
\(701\) 12.8382i 0.484891i −0.970165 0.242446i \(-0.922050\pi\)
0.970165 0.242446i \(-0.0779496\pi\)
\(702\) 6.82058i 0.257426i
\(703\) 16.7009i 0.629886i
\(704\) −12.4199 + 1.97377i −0.468091 + 0.0743891i
\(705\) −19.8843 + 13.5282i −0.748885 + 0.509501i
\(706\) −21.1871 −0.797388
\(707\) 1.47984 + 1.60623i 0.0556549 + 0.0604083i
\(708\) 7.33293i 0.275589i
\(709\) 5.22136 0.196092 0.0980462 0.995182i \(-0.468741\pi\)
0.0980462 + 0.995182i \(0.468741\pi\)
\(710\) −4.69764 + 3.19602i −0.176299 + 0.119944i
\(711\) 8.24756i 0.309308i
\(712\) 3.52655i 0.132163i
\(713\) 1.88331 0.0705304
\(714\) −24.1222 + 22.2241i −0.902750 + 0.831715i
\(715\) −21.1977 22.5266i −0.792749 0.842446i
\(716\) 12.8652 0.480794
\(717\) 9.91495i 0.370281i
\(718\) 13.6327i 0.508769i
\(719\) 13.5036i 0.503599i −0.967779 0.251800i \(-0.918978\pi\)
0.967779 0.251800i \(-0.0810224\pi\)
\(720\) 9.04756 6.15546i 0.337183 0.229401i
\(721\) −20.6730 22.4386i −0.769902 0.835658i
\(722\) −22.6552 −0.843138
\(723\) 2.07373 0.0771228
\(724\) 5.32660i 0.197962i
\(725\) 25.0769 + 9.89906i 0.931333 + 0.367642i
\(726\) −17.1020 + 5.57653i −0.634713 + 0.206965i
\(727\) −1.97850 −0.0733786 −0.0366893 0.999327i \(-0.511681\pi\)
−0.0366893 + 0.999327i \(0.511681\pi\)
\(728\) 17.5959 16.2113i 0.652147 0.600831i
\(729\) 1.00000 0.0370370
\(730\) −4.64196 6.82295i −0.171807 0.252529i
\(731\) 40.2791i 1.48978i
\(732\) 10.3713 0.383333
\(733\) 3.81876i 0.141049i −0.997510 0.0705245i \(-0.977533\pi\)
0.997510 0.0705245i \(-0.0224673\pi\)
\(734\) 37.5457 1.38584
\(735\) −7.71686 13.6180i −0.284641 0.502308i
\(736\) 7.99153i 0.294572i
\(737\) 5.56692 + 35.0296i 0.205060 + 1.29033i
\(738\) 5.50407 0.202608
\(739\) 12.4867i 0.459332i −0.973270 0.229666i \(-0.926237\pi\)
0.973270 0.229666i \(-0.0737633\pi\)
\(740\) −2.47074 3.63159i −0.0908261 0.133500i
\(741\) 23.9067i 0.878236i
\(742\) 35.4910 32.6983i 1.30292 1.20039i
\(743\) −37.0586 −1.35955 −0.679775 0.733421i \(-0.737922\pi\)
−0.679775 + 0.733421i \(0.737922\pi\)
\(744\) 1.87343i 0.0686832i
\(745\) −21.3267 31.3469i −0.781350 1.14846i
\(746\) −57.3623 −2.10018
\(747\) 5.54564i 0.202904i
\(748\) 2.66041 + 16.7405i 0.0972742 + 0.612094i
\(749\) 17.3734 + 18.8572i 0.634810 + 0.689028i
\(750\) −4.01563 17.8366i −0.146630 0.651302i
\(751\) 3.95633 0.144369 0.0721843 0.997391i \(-0.477003\pi\)
0.0721843 + 0.997391i \(0.477003\pi\)
\(752\) −52.6353 −1.91941
\(753\) 9.03128i 0.329118i
\(754\) −36.7766 −1.33932
\(755\) 20.5453 + 30.1983i 0.747720 + 1.09903i
\(756\) 1.20859 + 1.31181i 0.0439559 + 0.0477101i
\(757\) 20.8523i 0.757888i −0.925420 0.378944i \(-0.876287\pi\)
0.925420 0.378944i \(-0.123713\pi\)
\(758\) 8.33864 0.302873
\(759\) 1.13456 + 7.13915i 0.0411818 + 0.259135i
\(760\) −22.9752 + 15.6310i −0.833396 + 0.566997i
\(761\) 37.0384 1.34264 0.671320 0.741167i \(-0.265727\pi\)
0.671320 + 0.741167i \(0.265727\pi\)
\(762\) −12.7319 −0.461226
\(763\) 19.9993 18.4256i 0.724023 0.667051i
\(764\) 0.389276 0.0140835
\(765\) 9.53524 + 14.0153i 0.344747 + 0.506724i
\(766\) 3.61661 0.130673
\(767\) −45.3665 −1.63809
\(768\) 14.5482 0.524962
\(769\) −20.7036 −0.746590 −0.373295 0.927713i \(-0.621772\pi\)
−0.373295 + 0.927713i \(0.621772\pi\)
\(770\) −32.0051 2.28633i −1.15338 0.0823937i
\(771\) 15.2678 0.549855
\(772\) −9.58645 −0.345024
\(773\) 9.70891 0.349205 0.174603 0.984639i \(-0.444136\pi\)
0.174603 + 0.984639i \(0.444136\pi\)
\(774\) −8.68870 −0.312309
\(775\) 4.01863 + 1.58635i 0.144354 + 0.0569833i
\(776\) 19.0881 0.685223
\(777\) −5.66954 + 5.22342i −0.203394 + 0.187389i
\(778\) −55.1962 −1.97888
\(779\) −19.2923 −0.691217
\(780\) 3.53677 + 5.19850i 0.126637 + 0.186136i
\(781\) 5.08959 0.808840i 0.182120 0.0289426i
\(782\) 27.0197 0.966223
\(783\) 5.39200i 0.192694i
\(784\) 2.80129 34.1421i 0.100046 1.21936i
\(785\) 0.943704 0.642045i 0.0336822 0.0229156i
\(786\) −4.73483 −0.168886
\(787\) 7.13561i 0.254357i −0.991880 0.127178i \(-0.959408\pi\)
0.991880 0.127178i \(-0.0405921\pi\)
\(788\) 1.52614 0.0543667
\(789\) −6.40729 −0.228106
\(790\) 16.9641 + 24.9346i 0.603556 + 0.887132i
\(791\) −29.2427 + 26.9417i −1.03975 + 0.957935i
\(792\) −7.10171 + 1.12861i −0.252348 + 0.0401032i
\(793\) 64.1638i 2.27852i
\(794\) 12.7733 0.453307
\(795\) −14.0292 20.6207i −0.497565 0.731341i
\(796\) 0.193582i 0.00686132i
\(797\) −18.5441 −0.656866 −0.328433 0.944527i \(-0.606520\pi\)
−0.328433 + 0.944527i \(0.606520\pi\)
\(798\) −16.8034 18.2385i −0.594834 0.645638i
\(799\) 81.5357i 2.88453i
\(800\) 6.73143 17.0525i 0.237992 0.602896i
\(801\) 1.62655i 0.0574713i
\(802\) 23.5064 0.830041
\(803\) 1.17478 + 7.39223i 0.0414569 + 0.260866i
\(804\) 7.20982i 0.254271i
\(805\) −2.92604 + 12.5580i −0.103129 + 0.442611i
\(806\) −5.89353 −0.207591
\(807\) 13.5541i 0.477128i
\(808\) 1.78973 0.0629624
\(809\) 25.3382i 0.890845i −0.895320 0.445422i \(-0.853053\pi\)
0.895320 0.445422i \(-0.146947\pi\)
\(810\) 3.02327 2.05687i 0.106227 0.0722709i
\(811\) −14.9314 −0.524311 −0.262155 0.965026i \(-0.584433\pi\)
−0.262155 + 0.965026i \(0.584433\pi\)
\(812\) −7.07329 + 6.51671i −0.248224 + 0.228692i
\(813\) 13.5515 0.475272
\(814\) 2.48027 + 15.6070i 0.0869336 + 0.547026i
\(815\) −30.6841 45.1008i −1.07482 1.57981i
\(816\) 37.0996i 1.29875i
\(817\) 30.4547 1.06547
\(818\) 19.4748 0.680920
\(819\) 8.11575 7.47715i 0.283587 0.261273i
\(820\) 4.19508 2.85411i 0.146499 0.0996697i
\(821\) 31.8707i 1.11230i 0.831083 + 0.556148i \(0.187721\pi\)
−0.831083 + 0.556148i \(0.812279\pi\)
\(822\) 14.9858i 0.522691i
\(823\) 5.84104i 0.203606i −0.994805 0.101803i \(-0.967539\pi\)
0.994805 0.101803i \(-0.0324611\pi\)
\(824\) −25.0021 −0.870989
\(825\) −3.59252 + 16.1893i −0.125076 + 0.563639i
\(826\) −34.6103 + 31.8869i −1.20425 + 1.10949i
\(827\) −12.8645 −0.447341 −0.223671 0.974665i \(-0.571804\pi\)
−0.223671 + 0.974665i \(0.571804\pi\)
\(828\) 1.46938i 0.0510646i
\(829\) 4.31992i 0.150037i −0.997182 0.0750185i \(-0.976098\pi\)
0.997182 0.0750185i \(-0.0239016\pi\)
\(830\) −11.4066 16.7660i −0.395930 0.581955i
\(831\) 10.5948 0.367530
\(832\) 15.8148i 0.548279i
\(833\) 52.8885 + 4.33939i 1.83248 + 0.150351i
\(834\) −11.9384 −0.413393
\(835\) 18.4341 + 27.0952i 0.637939 + 0.937669i
\(836\) −12.6574 + 2.01151i −0.437764 + 0.0695695i
\(837\) 0.864081i 0.0298670i
\(838\) 4.29597i 0.148402i
\(839\) 46.0836i 1.59098i 0.605965 + 0.795491i \(0.292787\pi\)
−0.605965 + 0.795491i \(0.707213\pi\)
\(840\) −12.4921 2.91069i −0.431019 0.100428i
\(841\) −0.0736920 −0.00254110
\(842\) 22.0330 0.759307
\(843\) 11.4974i 0.395993i
\(844\) 10.5627i 0.363584i
\(845\) 8.12749 5.52950i 0.279594 0.190221i
\(846\) −17.5882 −0.604696
\(847\) 25.3837 + 14.2361i 0.872194 + 0.489159i
\(848\) 54.5847i 1.87445i
\(849\) 21.6818i 0.744117i
\(850\) 57.6552 + 22.7593i 1.97756 + 0.780637i
\(851\) 6.35056 0.217694
\(852\) −1.04754 −0.0358882
\(853\) 32.2381i 1.10381i 0.833907 + 0.551906i \(0.186099\pi\)
−0.833907 + 0.551906i \(0.813901\pi\)
\(854\) −45.0990 48.9508i −1.54326 1.67506i
\(855\) −10.5968 + 7.20950i −0.362404 + 0.246560i
\(856\) 21.0116 0.718160
\(857\) 29.0750i 0.993182i 0.867985 + 0.496591i \(0.165415\pi\)
−0.867985 + 0.496591i \(0.834585\pi\)
\(858\) −3.55043 22.3409i −0.121210 0.762707i
\(859\) 27.8898i 0.951588i 0.879557 + 0.475794i \(0.157839\pi\)
−0.879557 + 0.475794i \(0.842161\pi\)
\(860\) −6.62234 + 4.50548i −0.225820 + 0.153635i
\(861\) −6.03390 6.54925i −0.205635 0.223198i
\(862\) 29.2095i 0.994880i
\(863\) 53.7247i 1.82881i 0.404799 + 0.914406i \(0.367342\pi\)
−0.404799 + 0.914406i \(0.632658\pi\)
\(864\) 3.66660 0.124740
\(865\) 21.4435 + 31.5185i 0.729100 + 1.07166i
\(866\) −0.908924 −0.0308865
\(867\) −40.4698 −1.37443
\(868\) −1.13351 + 1.04432i −0.0384739 + 0.0354464i
\(869\) −4.29324 27.0150i −0.145638 0.916423i
\(870\) 11.0906 + 16.3015i 0.376007 + 0.552672i
\(871\) −44.6048 −1.51138
\(872\) 22.2841i 0.754634i
\(873\) 8.80400 0.297970
\(874\) 20.4293i 0.691033i
\(875\) −16.8215 + 24.3318i −0.568670 + 0.822566i
\(876\) 1.52147i 0.0514058i
\(877\) 31.4715 1.06272 0.531358 0.847147i \(-0.321682\pi\)
0.531358 + 0.847147i \(0.321682\pi\)
\(878\) −32.1770 −1.08592
\(879\) 7.13847i 0.240774i
\(880\) −26.4313 + 24.8720i −0.890997 + 0.838436i
\(881\) 31.4582i 1.05985i 0.848044 + 0.529926i \(0.177780\pi\)
−0.848044 + 0.529926i \(0.822220\pi\)
\(882\) 0.936058 11.4087i 0.0315187 0.384150i
\(883\) 33.5011i 1.12740i 0.825980 + 0.563700i \(0.190623\pi\)
−0.825980 + 0.563700i \(0.809377\pi\)
\(884\) −21.3165 −0.716951
\(885\) 13.6811 + 20.1090i 0.459885 + 0.675958i
\(886\) 66.5314i 2.23517i
\(887\) 48.3621i 1.62384i −0.583768 0.811920i \(-0.698422\pi\)
0.583768 0.811920i \(-0.301578\pi\)
\(888\) 6.31725i 0.211993i
\(889\) 13.9575 + 15.1495i 0.468118 + 0.508099i
\(890\) −3.34559 4.91749i −0.112145 0.164835i
\(891\) −3.27552 + 0.520547i −0.109734 + 0.0174390i
\(892\) −14.2408 −0.476819
\(893\) 61.6484 2.06298
\(894\) 27.7272i 0.927337i
\(895\) −35.2800 + 24.0026i −1.17928 + 0.802319i
\(896\) −24.2620 26.3342i −0.810538 0.879764i
\(897\) −9.09061 −0.303527
\(898\) −25.4024 −0.847687
\(899\) −4.65913 −0.155391
\(900\) 1.23769 3.13540i 0.0412564 0.104513i
\(901\) 84.5554 2.81695
\(902\) −18.0287 + 2.86512i −0.600290 + 0.0953982i
\(903\) 9.52509 + 10.3386i 0.316975 + 0.344048i
\(904\) 32.5835i 1.08371i
\(905\) −9.93786 14.6071i −0.330346 0.485556i
\(906\) 26.7113i 0.887424i
\(907\) 36.1121i 1.19908i −0.800344 0.599541i \(-0.795350\pi\)
0.800344 0.599541i \(-0.204650\pi\)
\(908\) 5.16248i 0.171323i
\(909\) 0.825476 0.0273793
\(910\) 9.15661 39.2984i 0.303539 1.30273i
\(911\) −24.7742 −0.820804 −0.410402 0.911905i \(-0.634612\pi\)
−0.410402 + 0.911905i \(0.634612\pi\)
\(912\) −28.0507 −0.928850
\(913\) 2.88677 + 18.1649i 0.0955380 + 0.601169i
\(914\) 47.1047 1.55809
\(915\) −28.4410 + 19.3497i −0.940232 + 0.639682i
\(916\) 13.4472i 0.444308i
\(917\) 5.19061 + 5.63393i 0.171409 + 0.186049i
\(918\) 12.3969i 0.409160i
\(919\) 25.4495i 0.839501i −0.907639 0.419751i \(-0.862118\pi\)
0.907639 0.419751i \(-0.137882\pi\)
\(920\) 5.94375 + 8.73637i 0.195960 + 0.288030i
\(921\) 15.4378i 0.508692i
\(922\) −32.5833 −1.07307
\(923\) 6.48082i 0.213319i
\(924\) −4.64161 3.66774i −0.152698 0.120660i
\(925\) 13.5509 + 5.34921i 0.445552 + 0.175881i
\(926\) 14.5178i 0.477085i
\(927\) −11.5317 −0.378751
\(928\) 19.7703i 0.648992i
\(929\) 40.7403i 1.33665i −0.743871 0.668324i \(-0.767012\pi\)
0.743871 0.668324i \(-0.232988\pi\)
\(930\) 1.77730 + 2.61235i 0.0582799 + 0.0856623i
\(931\) −3.28097 + 39.9885i −0.107529 + 1.31057i
\(932\) 3.83936 0.125762
\(933\) 30.4383i 0.996504i
\(934\) 52.2637 1.71012
\(935\) −38.5285 40.9438i −1.26002 1.33901i
\(936\) 9.04293i 0.295578i
\(937\) 7.83618i 0.255997i −0.991774 0.127998i \(-0.959145\pi\)
0.991774 0.127998i \(-0.0408552\pi\)
\(938\) −34.0292 + 31.3515i −1.11109 + 1.02366i
\(939\) −31.1303 −1.01590
\(940\) −13.4054 + 9.12028i −0.437235 + 0.297471i
\(941\) −4.89025 −0.159418 −0.0797089 0.996818i \(-0.525399\pi\)
−0.0797089 + 0.996818i \(0.525399\pi\)
\(942\) 0.834734 0.0271971
\(943\) 7.33594i 0.238891i
\(944\) 53.2302i 1.73250i
\(945\) −5.76174 1.34250i −0.187430 0.0436715i
\(946\) 28.4600 4.52287i 0.925315 0.147051i
\(947\) 16.5945i 0.539248i 0.962966 + 0.269624i \(0.0868995\pi\)
−0.962966 + 0.269624i \(0.913101\pi\)
\(948\) 5.56025i 0.180589i
\(949\) −9.41287 −0.305555
\(950\) −17.2081 + 43.5925i −0.558303 + 1.41433i
\(951\) 28.5646i 0.926272i
\(952\) 31.9819 29.4653i 1.03654 0.954977i
\(953\) −38.7567 −1.25545 −0.627726 0.778434i \(-0.716014\pi\)
−0.627726 + 0.778434i \(0.716014\pi\)
\(954\) 18.2396i 0.590530i
\(955\) −1.06751 + 0.726275i −0.0345438 + 0.0235017i
\(956\) 6.68436i 0.216188i
\(957\) −2.80679 17.6616i −0.0907306 0.570919i
\(958\) −15.3153 −0.494813
\(959\) 17.8315 16.4284i 0.575810 0.530501i
\(960\) −7.01000 + 4.76922i −0.226247 + 0.153926i
\(961\) 30.2534 0.975915
\(962\) −19.8732 −0.640737
\(963\) 9.69116 0.312293
\(964\) 1.39804 0.0450280
\(965\) 26.2888 17.8855i 0.846267 0.575754i
\(966\) −6.93526 + 6.38954i −0.223138 + 0.205580i
\(967\) −9.16393 −0.294692 −0.147346 0.989085i \(-0.547073\pi\)
−0.147346 + 0.989085i \(0.547073\pi\)
\(968\) 22.6743 7.39354i 0.728779 0.237637i
\(969\) 43.4524i 1.39589i
\(970\) 26.6169 18.1087i 0.854616 0.581434i
\(971\) 23.3469i 0.749237i 0.927179 + 0.374619i \(0.122226\pi\)
−0.927179 + 0.374619i \(0.877774\pi\)
\(972\) 0.674169 0.0216240
\(973\) 13.0876 + 14.2054i 0.419570 + 0.455404i
\(974\) 25.9327i 0.830936i
\(975\) −19.3977 7.65721i −0.621224 0.245227i
\(976\) −75.2857 −2.40984
\(977\) 29.9628i 0.958596i 0.877652 + 0.479298i \(0.159109\pi\)
−0.877652 + 0.479298i \(0.840891\pi\)
\(978\) 39.8930i 1.27564i
\(979\) 0.846694 + 5.32779i 0.0270605 + 0.170277i
\(980\) −5.20247 9.18084i −0.166187 0.293271i
\(981\) 10.2781i 0.328154i
\(982\) 43.5329i 1.38919i
\(983\) 24.6226 0.785338 0.392669 0.919680i \(-0.371552\pi\)
0.392669 + 0.919680i \(0.371552\pi\)
\(984\) −7.29746 −0.232635
\(985\) −4.18513 + 2.84733i −0.133349 + 0.0907236i
\(986\) −66.8443 −2.12876
\(987\) 19.2813 + 20.9281i 0.613731 + 0.666149i
\(988\) 16.1172i 0.512756i
\(989\) 11.5805i 0.368238i
\(990\) −8.83208 + 8.31106i −0.280702 + 0.264143i
\(991\) 12.5327 0.398115 0.199058 0.979988i \(-0.436212\pi\)
0.199058 + 0.979988i \(0.436212\pi\)
\(992\) 3.16824i 0.100592i
\(993\) −26.6099 −0.844439
\(994\) 4.55519 + 4.94424i 0.144482 + 0.156822i
\(995\) −0.361166 0.530857i −0.0114497 0.0168293i
\(996\) 3.73870i 0.118465i
\(997\) 17.7248i 0.561349i −0.959803 0.280675i \(-0.909442\pi\)
0.959803 0.280675i \(-0.0905582\pi\)
\(998\) 19.9927 0.632857
\(999\) 2.91371i 0.0921856i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1155.2.k.b.769.14 yes 48
5.4 even 2 1155.2.k.a.769.35 yes 48
7.6 odd 2 1155.2.k.a.769.13 48
11.10 odd 2 inner 1155.2.k.b.769.35 yes 48
35.34 odd 2 inner 1155.2.k.b.769.36 yes 48
55.54 odd 2 1155.2.k.a.769.14 yes 48
77.76 even 2 1155.2.k.a.769.36 yes 48
385.384 even 2 inner 1155.2.k.b.769.13 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.k.a.769.13 48 7.6 odd 2
1155.2.k.a.769.14 yes 48 55.54 odd 2
1155.2.k.a.769.35 yes 48 5.4 even 2
1155.2.k.a.769.36 yes 48 77.76 even 2
1155.2.k.b.769.13 yes 48 385.384 even 2 inner
1155.2.k.b.769.14 yes 48 1.1 even 1 trivial
1155.2.k.b.769.35 yes 48 11.10 odd 2 inner
1155.2.k.b.769.36 yes 48 35.34 odd 2 inner