Properties

Label 552.2.n.a.91.14
Level $552$
Weight $2$
Character 552.91
Analytic conductor $4.408$
Analytic rank $0$
Dimension $24$
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] = [552,2,Mod(91,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.n (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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.14
Character \(\chi\) \(=\) 552.91
Dual form 552.2.n.a.91.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0902148 - 1.41133i) q^{2} +1.00000 q^{3} +(-1.98372 - 0.254646i) q^{4} +3.06098 q^{5} +(0.0902148 - 1.41133i) q^{6} +0.892124 q^{7} +(-0.538352 + 2.77672i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.0902148 - 1.41133i) q^{2} +1.00000 q^{3} +(-1.98372 - 0.254646i) q^{4} +3.06098 q^{5} +(0.0902148 - 1.41133i) q^{6} +0.892124 q^{7} +(-0.538352 + 2.77672i) q^{8} +1.00000 q^{9} +(0.276146 - 4.32007i) q^{10} -3.95311i q^{11} +(-1.98372 - 0.254646i) q^{12} +4.14787i q^{13} +(0.0804827 - 1.25908i) q^{14} +3.06098 q^{15} +(3.87031 + 1.01029i) q^{16} -1.01396i q^{17} +(0.0902148 - 1.41133i) q^{18} +0.195663i q^{19} +(-6.07214 - 0.779468i) q^{20} +0.892124 q^{21} +(-5.57915 - 0.356629i) q^{22} +(4.42425 - 1.85094i) q^{23} +(-0.538352 + 2.77672i) q^{24} +4.36961 q^{25} +(5.85403 + 0.374200i) q^{26} +1.00000 q^{27} +(-1.76973 - 0.227176i) q^{28} +3.05624i q^{29} +(0.276146 - 4.32007i) q^{30} -2.58909i q^{31} +(1.77502 - 5.37115i) q^{32} -3.95311i q^{33} +(-1.43104 - 0.0914745i) q^{34} +2.73077 q^{35} +(-1.98372 - 0.254646i) q^{36} -6.01692 q^{37} +(0.276146 + 0.0176517i) q^{38} +4.14787i q^{39} +(-1.64789 + 8.49949i) q^{40} -10.2344 q^{41} +(0.0804827 - 1.25908i) q^{42} -10.0034i q^{43} +(-1.00664 + 7.84187i) q^{44} +3.06098 q^{45} +(-2.21316 - 6.41108i) q^{46} +7.33196i q^{47} +(3.87031 + 1.01029i) q^{48} -6.20412 q^{49} +(0.394204 - 6.16698i) q^{50} -1.01396i q^{51} +(1.05624 - 8.22823i) q^{52} +11.2321 q^{53} +(0.0902148 - 1.41133i) q^{54} -12.1004i q^{55} +(-0.480276 + 2.47718i) q^{56} +0.195663i q^{57} +(4.31337 + 0.275718i) q^{58} -4.35054 q^{59} +(-6.07214 - 0.779468i) q^{60} -7.63888 q^{61} +(-3.65407 - 0.233574i) q^{62} +0.892124 q^{63} +(-7.42035 - 2.98971i) q^{64} +12.6966i q^{65} +(-5.57915 - 0.356629i) q^{66} +3.60187i q^{67} +(-0.258202 + 2.01142i) q^{68} +(4.42425 - 1.85094i) q^{69} +(0.246356 - 3.85403i) q^{70} +10.5891i q^{71} +(-0.538352 + 2.77672i) q^{72} +3.24682 q^{73} +(-0.542815 + 8.49188i) q^{74} +4.36961 q^{75} +(0.0498249 - 0.388141i) q^{76} -3.52666i q^{77} +(5.85403 + 0.374200i) q^{78} -1.85136 q^{79} +(11.8470 + 3.09250i) q^{80} +1.00000 q^{81} +(-0.923296 + 14.4442i) q^{82} +3.79082i q^{83} +(-1.76973 - 0.227176i) q^{84} -3.10373i q^{85} +(-14.1181 - 0.902455i) q^{86} +3.05624i q^{87} +(10.9767 + 2.12816i) q^{88} +10.7963i q^{89} +(0.276146 - 4.32007i) q^{90} +3.70042i q^{91} +(-9.24783 + 2.54513i) q^{92} -2.58909i q^{93} +(10.3478 + 0.661451i) q^{94} +0.598921i q^{95} +(1.77502 - 5.37115i) q^{96} +2.49750i q^{97} +(-0.559703 + 8.75607i) q^{98} -3.95311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0902148 1.41133i 0.0637915 0.997963i
\(3\) 1.00000 0.577350
\(4\) −1.98372 0.254646i −0.991861 0.127323i
\(5\) 3.06098 1.36891 0.684457 0.729054i \(-0.260040\pi\)
0.684457 + 0.729054i \(0.260040\pi\)
\(6\) 0.0902148 1.41133i 0.0368300 0.576174i
\(7\) 0.892124 0.337191 0.168596 0.985685i \(-0.446077\pi\)
0.168596 + 0.985685i \(0.446077\pi\)
\(8\) −0.538352 + 2.77672i −0.190336 + 0.981719i
\(9\) 1.00000 0.333333
\(10\) 0.276146 4.32007i 0.0873250 1.36612i
\(11\) 3.95311i 1.19191i −0.803019 0.595953i \(-0.796774\pi\)
0.803019 0.595953i \(-0.203226\pi\)
\(12\) −1.98372 0.254646i −0.572651 0.0735100i
\(13\) 4.14787i 1.15041i 0.818008 + 0.575207i \(0.195078\pi\)
−0.818008 + 0.575207i \(0.804922\pi\)
\(14\) 0.0804827 1.25908i 0.0215099 0.336504i
\(15\) 3.06098 0.790342
\(16\) 3.87031 + 1.01029i 0.967578 + 0.252574i
\(17\) 1.01396i 0.245922i −0.992411 0.122961i \(-0.960761\pi\)
0.992411 0.122961i \(-0.0392391\pi\)
\(18\) 0.0902148 1.41133i 0.0212638 0.332654i
\(19\) 0.195663i 0.0448882i 0.999748 + 0.0224441i \(0.00714478\pi\)
−0.999748 + 0.0224441i \(0.992855\pi\)
\(20\) −6.07214 0.779468i −1.35777 0.174294i
\(21\) 0.892124 0.194677
\(22\) −5.57915 0.356629i −1.18948 0.0760335i
\(23\) 4.42425 1.85094i 0.922521 0.385947i
\(24\) −0.538352 + 2.77672i −0.109891 + 0.566796i
\(25\) 4.36961 0.873923
\(26\) 5.85403 + 0.374200i 1.14807 + 0.0733866i
\(27\) 1.00000 0.192450
\(28\) −1.76973 0.227176i −0.334447 0.0429322i
\(29\) 3.05624i 0.567530i 0.958894 + 0.283765i \(0.0915835\pi\)
−0.958894 + 0.283765i \(0.908416\pi\)
\(30\) 0.276146 4.32007i 0.0504171 0.788733i
\(31\) 2.58909i 0.465015i −0.972595 0.232507i \(-0.925307\pi\)
0.972595 0.232507i \(-0.0746930\pi\)
\(32\) 1.77502 5.37115i 0.313783 0.949495i
\(33\) 3.95311i 0.688147i
\(34\) −1.43104 0.0914745i −0.245421 0.0156878i
\(35\) 2.73077 0.461585
\(36\) −1.98372 0.254646i −0.330620 0.0424410i
\(37\) −6.01692 −0.989176 −0.494588 0.869128i \(-0.664681\pi\)
−0.494588 + 0.869128i \(0.664681\pi\)
\(38\) 0.276146 + 0.0176517i 0.0447968 + 0.00286349i
\(39\) 4.14787i 0.664192i
\(40\) −1.64789 + 8.49949i −0.260554 + 1.34389i
\(41\) −10.2344 −1.59835 −0.799174 0.601099i \(-0.794730\pi\)
−0.799174 + 0.601099i \(0.794730\pi\)
\(42\) 0.0804827 1.25908i 0.0124188 0.194281i
\(43\) 10.0034i 1.52550i −0.646691 0.762752i \(-0.723847\pi\)
0.646691 0.762752i \(-0.276153\pi\)
\(44\) −1.00664 + 7.84187i −0.151757 + 1.18221i
\(45\) 3.06098 0.456304
\(46\) −2.21316 6.41108i −0.326312 0.945262i
\(47\) 7.33196i 1.06948i 0.845018 + 0.534738i \(0.179590\pi\)
−0.845018 + 0.534738i \(0.820410\pi\)
\(48\) 3.87031 + 1.01029i 0.558631 + 0.145824i
\(49\) −6.20412 −0.886302
\(50\) 0.394204 6.16698i 0.0557488 0.872143i
\(51\) 1.01396i 0.141983i
\(52\) 1.05624 8.22823i 0.146474 1.14105i
\(53\) 11.2321 1.54285 0.771425 0.636320i \(-0.219544\pi\)
0.771425 + 0.636320i \(0.219544\pi\)
\(54\) 0.0902148 1.41133i 0.0122767 0.192058i
\(55\) 12.1004i 1.63162i
\(56\) −0.480276 + 2.47718i −0.0641796 + 0.331027i
\(57\) 0.195663i 0.0259162i
\(58\) 4.31337 + 0.275718i 0.566374 + 0.0362036i
\(59\) −4.35054 −0.566393 −0.283196 0.959062i \(-0.591395\pi\)
−0.283196 + 0.959062i \(0.591395\pi\)
\(60\) −6.07214 0.779468i −0.783910 0.100629i
\(61\) −7.63888 −0.978059 −0.489029 0.872267i \(-0.662649\pi\)
−0.489029 + 0.872267i \(0.662649\pi\)
\(62\) −3.65407 0.233574i −0.464068 0.0296640i
\(63\) 0.892124 0.112397
\(64\) −7.42035 2.98971i −0.927544 0.373713i
\(65\) 12.6966i 1.57482i
\(66\) −5.57915 0.356629i −0.686746 0.0438980i
\(67\) 3.60187i 0.440039i 0.975496 + 0.220019i \(0.0706120\pi\)
−0.975496 + 0.220019i \(0.929388\pi\)
\(68\) −0.258202 + 2.01142i −0.0313116 + 0.243921i
\(69\) 4.42425 1.85094i 0.532618 0.222827i
\(70\) 0.246356 3.85403i 0.0294452 0.460645i
\(71\) 10.5891i 1.25669i 0.777933 + 0.628347i \(0.216268\pi\)
−0.777933 + 0.628347i \(0.783732\pi\)
\(72\) −0.538352 + 2.77672i −0.0634454 + 0.327240i
\(73\) 3.24682 0.380011 0.190006 0.981783i \(-0.439149\pi\)
0.190006 + 0.981783i \(0.439149\pi\)
\(74\) −0.542815 + 8.49188i −0.0631010 + 0.987161i
\(75\) 4.36961 0.504560
\(76\) 0.0498249 0.388141i 0.00571531 0.0445229i
\(77\) 3.52666i 0.401900i
\(78\) 5.85403 + 0.374200i 0.662839 + 0.0423698i
\(79\) −1.85136 −0.208294 −0.104147 0.994562i \(-0.533211\pi\)
−0.104147 + 0.994562i \(0.533211\pi\)
\(80\) 11.8470 + 3.09250i 1.32453 + 0.345751i
\(81\) 1.00000 0.111111
\(82\) −0.923296 + 14.4442i −0.101961 + 1.59509i
\(83\) 3.79082i 0.416097i 0.978119 + 0.208048i \(0.0667111\pi\)
−0.978119 + 0.208048i \(0.933289\pi\)
\(84\) −1.76973 0.227176i −0.193093 0.0247869i
\(85\) 3.10373i 0.336646i
\(86\) −14.1181 0.902455i −1.52240 0.0973142i
\(87\) 3.05624i 0.327663i
\(88\) 10.9767 + 2.12816i 1.17012 + 0.226863i
\(89\) 10.7963i 1.14440i 0.820113 + 0.572202i \(0.193911\pi\)
−0.820113 + 0.572202i \(0.806089\pi\)
\(90\) 0.276146 4.32007i 0.0291083 0.455375i
\(91\) 3.70042i 0.387909i
\(92\) −9.24783 + 2.54513i −0.964153 + 0.265348i
\(93\) 2.58909i 0.268476i
\(94\) 10.3478 + 0.661451i 1.06730 + 0.0682235i
\(95\) 0.598921i 0.0614480i
\(96\) 1.77502 5.37115i 0.181162 0.548191i
\(97\) 2.49750i 0.253583i 0.991929 + 0.126792i \(0.0404679\pi\)
−0.991929 + 0.126792i \(0.959532\pi\)
\(98\) −0.559703 + 8.75607i −0.0565385 + 0.884497i
\(99\) 3.95311i 0.397302i
\(100\) −8.66810 1.11271i −0.866810 0.111271i
\(101\) 3.30462i 0.328822i −0.986392 0.164411i \(-0.947428\pi\)
0.986392 0.164411i \(-0.0525723\pi\)
\(102\) −1.43104 0.0914745i −0.141694 0.00905733i
\(103\) −10.3779 −1.02257 −0.511284 0.859412i \(-0.670830\pi\)
−0.511284 + 0.859412i \(0.670830\pi\)
\(104\) −11.5175 2.23302i −1.12938 0.218965i
\(105\) 2.73077 0.266496
\(106\) 1.01330 15.8523i 0.0984207 1.53971i
\(107\) 18.3222i 1.77127i −0.464381 0.885635i \(-0.653723\pi\)
0.464381 0.885635i \(-0.346277\pi\)
\(108\) −1.98372 0.254646i −0.190884 0.0245033i
\(109\) 12.4462 1.19213 0.596064 0.802937i \(-0.296731\pi\)
0.596064 + 0.802937i \(0.296731\pi\)
\(110\) −17.0777 1.09163i −1.62829 0.104083i
\(111\) −6.01692 −0.571101
\(112\) 3.45280 + 0.901308i 0.326259 + 0.0851656i
\(113\) 16.0203i 1.50707i 0.657410 + 0.753533i \(0.271652\pi\)
−0.657410 + 0.753533i \(0.728348\pi\)
\(114\) 0.276146 + 0.0176517i 0.0258634 + 0.00165323i
\(115\) 13.5426 5.66569i 1.26285 0.528328i
\(116\) 0.778260 6.06273i 0.0722596 0.562911i
\(117\) 4.14787i 0.383471i
\(118\) −0.392483 + 6.14007i −0.0361310 + 0.565239i
\(119\) 0.904581i 0.0829228i
\(120\) −1.64789 + 8.49949i −0.150431 + 0.775894i
\(121\) −4.62705 −0.420641
\(122\) −0.689140 + 10.7810i −0.0623918 + 0.976067i
\(123\) −10.2344 −0.922807
\(124\) −0.659303 + 5.13604i −0.0592071 + 0.461230i
\(125\) −1.92960 −0.172589
\(126\) 0.0804827 1.25908i 0.00716997 0.112168i
\(127\) 0.281251i 0.0249569i 0.999922 + 0.0124785i \(0.00397212\pi\)
−0.999922 + 0.0124785i \(0.996028\pi\)
\(128\) −4.88890 + 10.2029i −0.432121 + 0.901815i
\(129\) 10.0034i 0.880751i
\(130\) 17.9191 + 1.14542i 1.57161 + 0.100460i
\(131\) 21.7964 1.90436 0.952179 0.305542i \(-0.0988377\pi\)
0.952179 + 0.305542i \(0.0988377\pi\)
\(132\) −1.00664 + 7.84187i −0.0876171 + 0.682547i
\(133\) 0.174556i 0.0151359i
\(134\) 5.08344 + 0.324942i 0.439142 + 0.0280707i
\(135\) 3.06098 0.263447
\(136\) 2.81549 + 0.545869i 0.241427 + 0.0468079i
\(137\) 19.1551i 1.63653i 0.574839 + 0.818267i \(0.305065\pi\)
−0.574839 + 0.818267i \(0.694935\pi\)
\(138\) −2.21316 6.41108i −0.188396 0.545747i
\(139\) −13.3472 −1.13210 −0.566048 0.824373i \(-0.691528\pi\)
−0.566048 + 0.824373i \(0.691528\pi\)
\(140\) −5.41710 0.695382i −0.457828 0.0587705i
\(141\) 7.33196i 0.617462i
\(142\) 14.9447 + 0.955293i 1.25413 + 0.0801664i
\(143\) 16.3970 1.37119
\(144\) 3.87031 + 1.01029i 0.322526 + 0.0841912i
\(145\) 9.35510i 0.776899i
\(146\) 0.292911 4.58234i 0.0242415 0.379237i
\(147\) −6.20412 −0.511707
\(148\) 11.9359 + 1.53219i 0.981125 + 0.125945i
\(149\) 1.91404 0.156804 0.0784020 0.996922i \(-0.475018\pi\)
0.0784020 + 0.996922i \(0.475018\pi\)
\(150\) 0.394204 6.16698i 0.0321866 0.503532i
\(151\) 15.4992i 1.26131i 0.776064 + 0.630654i \(0.217213\pi\)
−0.776064 + 0.630654i \(0.782787\pi\)
\(152\) −0.543302 0.105336i −0.0440676 0.00854385i
\(153\) 1.01396i 0.0819741i
\(154\) −4.97729 0.318157i −0.401082 0.0256378i
\(155\) 7.92517i 0.636565i
\(156\) 1.05624 8.22823i 0.0845669 0.658786i
\(157\) −11.0597 −0.882663 −0.441331 0.897344i \(-0.645494\pi\)
−0.441331 + 0.897344i \(0.645494\pi\)
\(158\) −0.167020 + 2.61288i −0.0132874 + 0.207870i
\(159\) 11.2321 0.890765
\(160\) 5.43331 16.4410i 0.429541 1.29978i
\(161\) 3.94698 1.65126i 0.311066 0.130138i
\(162\) 0.0902148 1.41133i 0.00708794 0.110885i
\(163\) 10.0689 0.788659 0.394330 0.918969i \(-0.370977\pi\)
0.394330 + 0.918969i \(0.370977\pi\)
\(164\) 20.3023 + 2.60616i 1.58534 + 0.203507i
\(165\) 12.1004i 0.942014i
\(166\) 5.35011 + 0.341988i 0.415249 + 0.0265434i
\(167\) 11.5383i 0.892858i −0.894819 0.446429i \(-0.852696\pi\)
0.894819 0.446429i \(-0.147304\pi\)
\(168\) −0.480276 + 2.47718i −0.0370541 + 0.191118i
\(169\) −4.20486 −0.323451
\(170\) −4.38039 0.280002i −0.335961 0.0214752i
\(171\) 0.195663i 0.0149627i
\(172\) −2.54733 + 19.8440i −0.194232 + 1.51309i
\(173\) 6.42949i 0.488825i −0.969671 0.244413i \(-0.921405\pi\)
0.969671 0.244413i \(-0.0785951\pi\)
\(174\) 4.31337 + 0.275718i 0.326996 + 0.0209021i
\(175\) 3.89824 0.294679
\(176\) 3.99380 15.2997i 0.301044 1.15326i
\(177\) −4.35054 −0.327007
\(178\) 15.2371 + 0.973984i 1.14207 + 0.0730032i
\(179\) −0.681542 −0.0509408 −0.0254704 0.999676i \(-0.508108\pi\)
−0.0254704 + 0.999676i \(0.508108\pi\)
\(180\) −6.07214 0.779468i −0.452591 0.0580981i
\(181\) 8.75811 0.650985 0.325492 0.945545i \(-0.394470\pi\)
0.325492 + 0.945545i \(0.394470\pi\)
\(182\) 5.22252 + 0.333832i 0.387119 + 0.0247453i
\(183\) −7.63888 −0.564682
\(184\) 2.75773 + 13.2814i 0.203303 + 0.979116i
\(185\) −18.4177 −1.35410
\(186\) −3.65407 0.233574i −0.267930 0.0171265i
\(187\) −4.00831 −0.293116
\(188\) 1.86706 14.5446i 0.136169 1.06077i
\(189\) 0.892124 0.0648924
\(190\) 0.845278 + 0.0540316i 0.0613229 + 0.00391986i
\(191\) −7.03883 −0.509312 −0.254656 0.967032i \(-0.581962\pi\)
−0.254656 + 0.967032i \(0.581962\pi\)
\(192\) −7.42035 2.98971i −0.535518 0.215763i
\(193\) −21.4049 −1.54076 −0.770379 0.637586i \(-0.779933\pi\)
−0.770379 + 0.637586i \(0.779933\pi\)
\(194\) 3.52481 + 0.225312i 0.253067 + 0.0161764i
\(195\) 12.6966i 0.909220i
\(196\) 12.3072 + 1.57985i 0.879089 + 0.112847i
\(197\) 16.5652i 1.18022i 0.807323 + 0.590109i \(0.200915\pi\)
−0.807323 + 0.590109i \(0.799085\pi\)
\(198\) −5.57915 0.356629i −0.396493 0.0253445i
\(199\) −18.7514 −1.32925 −0.664627 0.747175i \(-0.731409\pi\)
−0.664627 + 0.747175i \(0.731409\pi\)
\(200\) −2.35239 + 12.1332i −0.166339 + 0.857947i
\(201\) 3.60187i 0.254056i
\(202\) −4.66392 0.298125i −0.328152 0.0209760i
\(203\) 2.72654i 0.191366i
\(204\) −0.258202 + 2.01142i −0.0180778 + 0.140828i
\(205\) −31.3274 −2.18800
\(206\) −0.936243 + 14.6467i −0.0652311 + 1.02049i
\(207\) 4.42425 1.85094i 0.307507 0.128649i
\(208\) −4.19058 + 16.0536i −0.290564 + 1.11311i
\(209\) 0.773477 0.0535025
\(210\) 0.246356 3.85403i 0.0170002 0.265954i
\(211\) −4.73983 −0.326303 −0.163152 0.986601i \(-0.552166\pi\)
−0.163152 + 0.986601i \(0.552166\pi\)
\(212\) −22.2814 2.86022i −1.53029 0.196441i
\(213\) 10.5891i 0.725553i
\(214\) −25.8587 1.65293i −1.76766 0.112992i
\(215\) 30.6202i 2.08828i
\(216\) −0.538352 + 2.77672i −0.0366302 + 0.188932i
\(217\) 2.30979i 0.156799i
\(218\) 1.12283 17.5657i 0.0760476 1.18970i
\(219\) 3.24682 0.219400
\(220\) −3.08132 + 24.0038i −0.207742 + 1.61834i
\(221\) 4.20580 0.282912
\(222\) −0.542815 + 8.49188i −0.0364314 + 0.569938i
\(223\) 8.79654i 0.589060i −0.955642 0.294530i \(-0.904837\pi\)
0.955642 0.294530i \(-0.0951631\pi\)
\(224\) 1.58354 4.79173i 0.105805 0.320161i
\(225\) 4.36961 0.291308
\(226\) 22.6100 + 1.44527i 1.50400 + 0.0961380i
\(227\) 23.9345i 1.58859i −0.607534 0.794294i \(-0.707841\pi\)
0.607534 0.794294i \(-0.292159\pi\)
\(228\) 0.0498249 0.388141i 0.00329973 0.0257053i
\(229\) 8.58118 0.567060 0.283530 0.958963i \(-0.408494\pi\)
0.283530 + 0.958963i \(0.408494\pi\)
\(230\) −6.77443 19.6242i −0.446693 1.29398i
\(231\) 3.52666i 0.232037i
\(232\) −8.48633 1.64533i −0.557155 0.108021i
\(233\) 6.59907 0.432319 0.216160 0.976358i \(-0.430647\pi\)
0.216160 + 0.976358i \(0.430647\pi\)
\(234\) 5.85403 + 0.374200i 0.382690 + 0.0244622i
\(235\) 22.4430i 1.46402i
\(236\) 8.63027 + 1.10785i 0.561783 + 0.0721149i
\(237\) −1.85136 −0.120258
\(238\) −1.27667 0.0816066i −0.0827539 0.00528977i
\(239\) 14.2318i 0.920576i 0.887770 + 0.460288i \(0.152254\pi\)
−0.887770 + 0.460288i \(0.847746\pi\)
\(240\) 11.8470 + 3.09250i 0.764718 + 0.199620i
\(241\) 18.9358i 1.21976i −0.792492 0.609882i \(-0.791217\pi\)
0.792492 0.609882i \(-0.208783\pi\)
\(242\) −0.417428 + 6.53031i −0.0268333 + 0.419784i
\(243\) 1.00000 0.0641500
\(244\) 15.1534 + 1.94521i 0.970099 + 0.124529i
\(245\) −18.9907 −1.21327
\(246\) −0.923296 + 14.4442i −0.0588672 + 0.920927i
\(247\) −0.811586 −0.0516400
\(248\) 7.18918 + 1.39384i 0.456514 + 0.0885091i
\(249\) 3.79082i 0.240233i
\(250\) −0.174078 + 2.72331i −0.0110097 + 0.172237i
\(251\) 16.7334i 1.05620i −0.849182 0.528100i \(-0.822904\pi\)
0.849182 0.528100i \(-0.177096\pi\)
\(252\) −1.76973 0.227176i −0.111482 0.0143107i
\(253\) −7.31695 17.4895i −0.460013 1.09956i
\(254\) 0.396938 + 0.0253730i 0.0249061 + 0.00159204i
\(255\) 3.10373i 0.194363i
\(256\) 13.9586 + 7.82031i 0.872413 + 0.488769i
\(257\) 10.9984 0.686064 0.343032 0.939324i \(-0.388546\pi\)
0.343032 + 0.939324i \(0.388546\pi\)
\(258\) −14.1181 0.902455i −0.878957 0.0561844i
\(259\) −5.36784 −0.333541
\(260\) 3.23313 25.1865i 0.200510 1.56200i
\(261\) 3.05624i 0.189177i
\(262\) 1.96635 30.7619i 0.121482 1.90048i
\(263\) −32.1667 −1.98348 −0.991742 0.128249i \(-0.959064\pi\)
−0.991742 + 0.128249i \(0.959064\pi\)
\(264\) 10.9767 + 2.12816i 0.675567 + 0.130979i
\(265\) 34.3813 2.11203
\(266\) 0.246356 + 0.0157475i 0.0151051 + 0.000965542i
\(267\) 10.7963i 0.660721i
\(268\) 0.917203 7.14511i 0.0560271 0.436457i
\(269\) 21.2979i 1.29856i 0.760550 + 0.649279i \(0.224929\pi\)
−0.760550 + 0.649279i \(0.775071\pi\)
\(270\) 0.276146 4.32007i 0.0168057 0.262911i
\(271\) 2.36324i 0.143556i −0.997421 0.0717782i \(-0.977133\pi\)
0.997421 0.0717782i \(-0.0228674\pi\)
\(272\) 1.02440 3.92436i 0.0621135 0.237949i
\(273\) 3.70042i 0.223959i
\(274\) 27.0343 + 1.72808i 1.63320 + 0.104397i
\(275\) 17.2736i 1.04163i
\(276\) −9.24783 + 2.54513i −0.556654 + 0.153199i
\(277\) 9.50918i 0.571351i −0.958326 0.285676i \(-0.907782\pi\)
0.958326 0.285676i \(-0.0922180\pi\)
\(278\) −1.20412 + 18.8374i −0.0722180 + 1.12979i
\(279\) 2.58909i 0.155005i
\(280\) −1.47012 + 7.58260i −0.0878563 + 0.453147i
\(281\) 22.7904i 1.35956i −0.733416 0.679780i \(-0.762075\pi\)
0.733416 0.679780i \(-0.237925\pi\)
\(282\) 10.3478 + 0.661451i 0.616205 + 0.0393888i
\(283\) 17.0253i 1.01205i −0.862519 0.506025i \(-0.831114\pi\)
0.862519 0.506025i \(-0.168886\pi\)
\(284\) 2.69647 21.0058i 0.160006 1.24647i
\(285\) 0.598921i 0.0354770i
\(286\) 1.47925 23.1416i 0.0874699 1.36839i
\(287\) −9.13037 −0.538949
\(288\) 1.77502 5.37115i 0.104594 0.316498i
\(289\) 15.9719 0.939522
\(290\) 13.2032 + 0.843968i 0.775316 + 0.0495595i
\(291\) 2.49750i 0.146406i
\(292\) −6.44079 0.826790i −0.376918 0.0483842i
\(293\) −13.2959 −0.776757 −0.388378 0.921500i \(-0.626965\pi\)
−0.388378 + 0.921500i \(0.626965\pi\)
\(294\) −0.559703 + 8.75607i −0.0326425 + 0.510665i
\(295\) −13.3169 −0.775342
\(296\) 3.23922 16.7073i 0.188276 0.971093i
\(297\) 3.95311i 0.229382i
\(298\) 0.172674 2.70134i 0.0100028 0.156485i
\(299\) 7.67746 + 18.3513i 0.443999 + 1.06128i
\(300\) −8.66810 1.11271i −0.500453 0.0642421i
\(301\) 8.92427i 0.514387i
\(302\) 21.8745 + 1.39826i 1.25874 + 0.0804607i
\(303\) 3.30462i 0.189845i
\(304\) −0.197677 + 0.757277i −0.0113376 + 0.0434328i
\(305\) −23.3825 −1.33888
\(306\) −1.43104 0.0914745i −0.0818072 0.00522925i
\(307\) −6.89668 −0.393614 −0.196807 0.980442i \(-0.563057\pi\)
−0.196807 + 0.980442i \(0.563057\pi\)
\(308\) −0.898051 + 6.99591i −0.0511712 + 0.398629i
\(309\) −10.3779 −0.590380
\(310\) −11.1850 0.714967i −0.635268 0.0406074i
\(311\) 20.2868i 1.15036i −0.818026 0.575181i \(-0.804932\pi\)
0.818026 0.575181i \(-0.195068\pi\)
\(312\) −11.5175 2.23302i −0.652049 0.126420i
\(313\) 28.1949i 1.59367i −0.604198 0.796835i \(-0.706506\pi\)
0.604198 0.796835i \(-0.293494\pi\)
\(314\) −0.997751 + 15.6090i −0.0563064 + 0.880865i
\(315\) 2.73077 0.153862
\(316\) 3.67258 + 0.471441i 0.206599 + 0.0265206i
\(317\) 8.49011i 0.476852i −0.971161 0.238426i \(-0.923369\pi\)
0.971161 0.238426i \(-0.0766315\pi\)
\(318\) 1.01330 15.8523i 0.0568232 0.888951i
\(319\) 12.0816 0.676442
\(320\) −22.7136 9.15144i −1.26973 0.511581i
\(321\) 18.3222i 1.02264i
\(322\) −1.97441 5.71948i −0.110029 0.318734i
\(323\) 0.198395 0.0110390
\(324\) −1.98372 0.254646i −0.110207 0.0141470i
\(325\) 18.1246i 1.00537i
\(326\) 0.908366 14.2106i 0.0503097 0.787053i
\(327\) 12.4462 0.688275
\(328\) 5.50972 28.4181i 0.304223 1.56913i
\(329\) 6.54101i 0.360618i
\(330\) −17.0777 1.09163i −0.940095 0.0600925i
\(331\) −14.3840 −0.790619 −0.395309 0.918548i \(-0.629363\pi\)
−0.395309 + 0.918548i \(0.629363\pi\)
\(332\) 0.965318 7.51994i 0.0529787 0.412710i
\(333\) −6.01692 −0.329725
\(334\) −16.2843 1.04092i −0.891040 0.0569567i
\(335\) 11.0253i 0.602375i
\(336\) 3.45280 + 0.901308i 0.188365 + 0.0491704i
\(337\) 29.2613i 1.59396i 0.604003 + 0.796982i \(0.293571\pi\)
−0.604003 + 0.796982i \(0.706429\pi\)
\(338\) −0.379341 + 5.93447i −0.0206334 + 0.322792i
\(339\) 16.0203i 0.870105i
\(340\) −0.790352 + 6.15693i −0.0428629 + 0.333906i
\(341\) −10.2350 −0.554254
\(342\) 0.276146 + 0.0176517i 0.0149323 + 0.000954495i
\(343\) −11.7797 −0.636044
\(344\) 27.7767 + 5.38535i 1.49762 + 0.290359i
\(345\) 13.5426 5.66569i 0.729107 0.305030i
\(346\) −9.07416 0.580035i −0.487830 0.0311829i
\(347\) 2.16372 0.116155 0.0580774 0.998312i \(-0.481503\pi\)
0.0580774 + 0.998312i \(0.481503\pi\)
\(348\) 0.778260 6.06273i 0.0417191 0.324997i
\(349\) 23.8000i 1.27399i −0.770869 0.636993i \(-0.780178\pi\)
0.770869 0.636993i \(-0.219822\pi\)
\(350\) 0.351679 5.50171i 0.0187980 0.294079i
\(351\) 4.14787i 0.221397i
\(352\) −21.2327 7.01685i −1.13171 0.373999i
\(353\) 20.3453 1.08287 0.541436 0.840742i \(-0.317881\pi\)
0.541436 + 0.840742i \(0.317881\pi\)
\(354\) −0.392483 + 6.14007i −0.0208603 + 0.326341i
\(355\) 32.4130i 1.72030i
\(356\) 2.74923 21.4168i 0.145709 1.13509i
\(357\) 0.904581i 0.0478755i
\(358\) −0.0614852 + 0.961883i −0.00324959 + 0.0508371i
\(359\) 11.3988 0.601608 0.300804 0.953686i \(-0.402745\pi\)
0.300804 + 0.953686i \(0.402745\pi\)
\(360\) −1.64789 + 8.49949i −0.0868512 + 0.447963i
\(361\) 18.9617 0.997985
\(362\) 0.790111 12.3606i 0.0415273 0.649659i
\(363\) −4.62705 −0.242857
\(364\) 0.942297 7.34060i 0.0493898 0.384752i
\(365\) 9.93845 0.520202
\(366\) −0.689140 + 10.7810i −0.0360219 + 0.563532i
\(367\) 1.55485 0.0811626 0.0405813 0.999176i \(-0.487079\pi\)
0.0405813 + 0.999176i \(0.487079\pi\)
\(368\) 18.9932 2.69390i 0.990091 0.140429i
\(369\) −10.2344 −0.532783
\(370\) −1.66155 + 25.9935i −0.0863798 + 1.35134i
\(371\) 10.0204 0.520235
\(372\) −0.659303 + 5.13604i −0.0341832 + 0.266291i
\(373\) −9.25006 −0.478950 −0.239475 0.970903i \(-0.576975\pi\)
−0.239475 + 0.970903i \(0.576975\pi\)
\(374\) −0.361609 + 5.65706i −0.0186983 + 0.292519i
\(375\) −1.92960 −0.0996441
\(376\) −20.3588 3.94717i −1.04993 0.203560i
\(377\) −12.6769 −0.652894
\(378\) 0.0804827 1.25908i 0.00413959 0.0647603i
\(379\) 23.7934i 1.22219i 0.791559 + 0.611093i \(0.209270\pi\)
−0.791559 + 0.611093i \(0.790730\pi\)
\(380\) 0.152513 1.18809i 0.00782376 0.0609479i
\(381\) 0.281251i 0.0144089i
\(382\) −0.635007 + 9.93414i −0.0324898 + 0.508275i
\(383\) 13.8513 0.707766 0.353883 0.935290i \(-0.384861\pi\)
0.353883 + 0.935290i \(0.384861\pi\)
\(384\) −4.88890 + 10.2029i −0.249485 + 0.520663i
\(385\) 10.7950i 0.550166i
\(386\) −1.93104 + 30.2094i −0.0982872 + 1.53762i
\(387\) 10.0034i 0.508502i
\(388\) 0.635980 4.95436i 0.0322870 0.251519i
\(389\) 25.1821 1.27678 0.638392 0.769711i \(-0.279600\pi\)
0.638392 + 0.769711i \(0.279600\pi\)
\(390\) 17.9191 + 1.14542i 0.907369 + 0.0580005i
\(391\) −1.87678 4.48603i −0.0949130 0.226869i
\(392\) 3.34000 17.2271i 0.168695 0.870100i
\(393\) 21.7964 1.09948
\(394\) 23.3790 + 1.49442i 1.17782 + 0.0752879i
\(395\) −5.66697 −0.285136
\(396\) −1.00664 + 7.84187i −0.0505857 + 0.394069i
\(397\) 34.8682i 1.74998i −0.484137 0.874992i \(-0.660866\pi\)
0.484137 0.874992i \(-0.339134\pi\)
\(398\) −1.69166 + 26.4645i −0.0847951 + 1.32655i
\(399\) 0.174556i 0.00873872i
\(400\) 16.9118 + 4.41460i 0.845588 + 0.220730i
\(401\) 26.5370i 1.32520i −0.748976 0.662598i \(-0.769454\pi\)
0.748976 0.662598i \(-0.230546\pi\)
\(402\) 5.08344 + 0.324942i 0.253539 + 0.0162066i
\(403\) 10.7392 0.534959
\(404\) −0.841509 + 6.55545i −0.0418666 + 0.326146i
\(405\) 3.06098 0.152101
\(406\) 3.84806 + 0.245975i 0.190976 + 0.0122075i
\(407\) 23.7855i 1.17900i
\(408\) 2.81549 + 0.545869i 0.139388 + 0.0270246i
\(409\) −24.6444 −1.21859 −0.609294 0.792944i \(-0.708547\pi\)
−0.609294 + 0.792944i \(0.708547\pi\)
\(410\) −2.82619 + 44.2134i −0.139576 + 2.18354i
\(411\) 19.1551i 0.944853i
\(412\) 20.5869 + 2.64270i 1.01425 + 0.130197i
\(413\) −3.88122 −0.190982
\(414\) −2.21316 6.41108i −0.108771 0.315087i
\(415\) 11.6036i 0.569600i
\(416\) 22.2789 + 7.36257i 1.09231 + 0.360980i
\(417\) −13.3472 −0.653616
\(418\) 0.0697791 1.09163i 0.00341301 0.0533936i
\(419\) 12.6674i 0.618843i −0.950925 0.309421i \(-0.899865\pi\)
0.950925 0.309421i \(-0.100135\pi\)
\(420\) −5.41710 0.695382i −0.264327 0.0339311i
\(421\) 28.7090 1.39919 0.699594 0.714540i \(-0.253364\pi\)
0.699594 + 0.714540i \(0.253364\pi\)
\(422\) −0.427603 + 6.68948i −0.0208154 + 0.325639i
\(423\) 7.33196i 0.356492i
\(424\) −6.04683 + 31.1885i −0.293660 + 1.51465i
\(425\) 4.43063i 0.214917i
\(426\) 14.9447 + 0.955293i 0.724075 + 0.0462841i
\(427\) −6.81483 −0.329793
\(428\) −4.66567 + 36.3461i −0.225524 + 1.75685i
\(429\) 16.3970 0.791654
\(430\) −43.2154 2.76240i −2.08403 0.133215i
\(431\) 22.9516 1.10554 0.552770 0.833334i \(-0.313571\pi\)
0.552770 + 0.833334i \(0.313571\pi\)
\(432\) 3.87031 + 1.01029i 0.186210 + 0.0486078i
\(433\) 15.0677i 0.724106i −0.932157 0.362053i \(-0.882076\pi\)
0.932157 0.362053i \(-0.117924\pi\)
\(434\) −3.25988 0.208377i −0.156479 0.0100024i
\(435\) 9.35510i 0.448543i
\(436\) −24.6898 3.16937i −1.18243 0.151785i
\(437\) 0.362160 + 0.865664i 0.0173245 + 0.0414103i
\(438\) 0.292911 4.58234i 0.0139958 0.218953i
\(439\) 22.4462i 1.07130i 0.844441 + 0.535649i \(0.179933\pi\)
−0.844441 + 0.535649i \(0.820067\pi\)
\(440\) 33.5994 + 6.51427i 1.60179 + 0.310555i
\(441\) −6.20412 −0.295434
\(442\) 0.379425 5.93578i 0.0180474 0.282336i
\(443\) −28.7923 −1.36796 −0.683981 0.729500i \(-0.739753\pi\)
−0.683981 + 0.729500i \(0.739753\pi\)
\(444\) 11.9359 + 1.53219i 0.566453 + 0.0727144i
\(445\) 33.0472i 1.56659i
\(446\) −12.4149 0.793578i −0.587860 0.0375770i
\(447\) 1.91404 0.0905308
\(448\) −6.61987 2.66719i −0.312760 0.126013i
\(449\) 10.0261 0.473160 0.236580 0.971612i \(-0.423973\pi\)
0.236580 + 0.971612i \(0.423973\pi\)
\(450\) 0.394204 6.16698i 0.0185829 0.290714i
\(451\) 40.4578i 1.90508i
\(452\) 4.07952 31.7799i 0.191884 1.49480i
\(453\) 15.4992i 0.728216i
\(454\) −33.7795 2.15924i −1.58535 0.101338i
\(455\) 11.3269i 0.531014i
\(456\) −0.543302 0.105336i −0.0254424 0.00493279i
\(457\) 8.91212i 0.416891i 0.978034 + 0.208446i \(0.0668404\pi\)
−0.978034 + 0.208446i \(0.933160\pi\)
\(458\) 0.774149 12.1109i 0.0361736 0.565905i
\(459\) 1.01396i 0.0473278i
\(460\) −28.3074 + 7.79059i −1.31984 + 0.363238i
\(461\) 36.2700i 1.68926i −0.535349 0.844631i \(-0.679820\pi\)
0.535349 0.844631i \(-0.320180\pi\)
\(462\) −4.97729 0.318157i −0.231565 0.0148020i
\(463\) 29.5920i 1.37525i 0.726064 + 0.687627i \(0.241348\pi\)
−0.726064 + 0.687627i \(0.758652\pi\)
\(464\) −3.08770 + 11.8286i −0.143343 + 0.549129i
\(465\) 7.92517i 0.367521i
\(466\) 0.595334 9.31348i 0.0275783 0.431439i
\(467\) 0.403565i 0.0186747i 0.999956 + 0.00933737i \(0.00297222\pi\)
−0.999956 + 0.00933737i \(0.997028\pi\)
\(468\) 1.05624 8.22823i 0.0488247 0.380350i
\(469\) 3.21331i 0.148377i
\(470\) 31.6745 + 2.02469i 1.46104 + 0.0933920i
\(471\) −11.0597 −0.509606
\(472\) 2.34212 12.0802i 0.107805 0.556038i
\(473\) −39.5445 −1.81826
\(474\) −0.167020 + 2.61288i −0.00767147 + 0.120014i
\(475\) 0.854973i 0.0392288i
\(476\) −0.230348 + 1.79444i −0.0105580 + 0.0822479i
\(477\) 11.2321 0.514284
\(478\) 20.0858 + 1.28391i 0.918701 + 0.0587249i
\(479\) 9.40765 0.429846 0.214923 0.976631i \(-0.431050\pi\)
0.214923 + 0.976631i \(0.431050\pi\)
\(480\) 5.43331 16.4410i 0.247996 0.750426i
\(481\) 24.9574i 1.13796i
\(482\) −26.7248 1.70829i −1.21728 0.0778105i
\(483\) 3.94698 1.65126i 0.179594 0.0751352i
\(484\) 9.17878 + 1.17826i 0.417217 + 0.0535573i
\(485\) 7.64482i 0.347133i
\(486\) 0.0902148 1.41133i 0.00409223 0.0640194i
\(487\) 28.2242i 1.27896i 0.768808 + 0.639480i \(0.220850\pi\)
−0.768808 + 0.639480i \(0.779150\pi\)
\(488\) 4.11241 21.2110i 0.186160 0.960179i
\(489\) 10.0689 0.455333
\(490\) −1.71324 + 26.8022i −0.0773963 + 1.21080i
\(491\) 22.7769 1.02791 0.513953 0.857818i \(-0.328180\pi\)
0.513953 + 0.857818i \(0.328180\pi\)
\(492\) 20.3023 + 2.60616i 0.915297 + 0.117495i
\(493\) 3.09892 0.139568
\(494\) −0.0732171 + 1.14542i −0.00329419 + 0.0515348i
\(495\) 12.1004i 0.543872i
\(496\) 2.61575 10.0206i 0.117450 0.449938i
\(497\) 9.44678i 0.423746i
\(498\) 5.35011 + 0.341988i 0.239744 + 0.0153248i
\(499\) −17.9463 −0.803386 −0.401693 0.915774i \(-0.631578\pi\)
−0.401693 + 0.915774i \(0.631578\pi\)
\(500\) 3.82779 + 0.491365i 0.171184 + 0.0219745i
\(501\) 11.5383i 0.515492i
\(502\) −23.6164 1.50960i −1.05405 0.0673766i
\(503\) −19.7331 −0.879856 −0.439928 0.898033i \(-0.644996\pi\)
−0.439928 + 0.898033i \(0.644996\pi\)
\(504\) −0.480276 + 2.47718i −0.0213932 + 0.110342i
\(505\) 10.1154i 0.450128i
\(506\) −25.3437 + 8.74884i −1.12666 + 0.388933i
\(507\) −4.20486 −0.186745
\(508\) 0.0716194 0.557923i 0.00317760 0.0247538i
\(509\) 18.5397i 0.821756i 0.911690 + 0.410878i \(0.134778\pi\)
−0.911690 + 0.410878i \(0.865222\pi\)
\(510\) −4.38039 0.280002i −0.193967 0.0123987i
\(511\) 2.89656 0.128136
\(512\) 12.2963 18.9947i 0.543426 0.839457i
\(513\) 0.195663i 0.00863874i
\(514\) 0.992222 15.5225i 0.0437650 0.684666i
\(515\) −31.7667 −1.39981
\(516\) −2.54733 + 19.8440i −0.112140 + 0.873583i
\(517\) 28.9840 1.27472
\(518\) −0.484258 + 7.57581i −0.0212771 + 0.332862i
\(519\) 6.42949i 0.282223i
\(520\) −35.2548 6.83522i −1.54603 0.299744i
\(521\) 17.7765i 0.778803i 0.921068 + 0.389401i \(0.127318\pi\)
−0.921068 + 0.389401i \(0.872682\pi\)
\(522\) 4.31337 + 0.275718i 0.188791 + 0.0120679i
\(523\) 23.3129i 1.01940i 0.860352 + 0.509701i \(0.170244\pi\)
−0.860352 + 0.509701i \(0.829756\pi\)
\(524\) −43.2379 5.55036i −1.88886 0.242469i
\(525\) 3.89824 0.170133
\(526\) −2.90191 + 45.3979i −0.126529 + 1.97944i
\(527\) −2.62525 −0.114358
\(528\) 3.99380 15.2997i 0.173808 0.665836i
\(529\) 16.1481 16.3780i 0.702090 0.712089i
\(530\) 3.10170 48.5235i 0.134729 2.10773i
\(531\) −4.35054 −0.188798
\(532\) 0.0444500 0.346270i 0.00192715 0.0150127i
\(533\) 42.4511i 1.83876i
\(534\) 15.2371 + 0.973984i 0.659376 + 0.0421484i
\(535\) 56.0838i 2.42472i
\(536\) −10.0014 1.93907i −0.431994 0.0837552i
\(537\) −0.681542 −0.0294107
\(538\) 30.0585 + 1.92139i 1.29591 + 0.0828370i
\(539\) 24.5255i 1.05639i
\(540\) −6.07214 0.779468i −0.261303 0.0335429i
\(541\) 34.5138i 1.48386i 0.670475 + 0.741932i \(0.266090\pi\)
−0.670475 + 0.741932i \(0.733910\pi\)
\(542\) −3.33531 0.213199i −0.143264 0.00915767i
\(543\) 8.75811 0.375846
\(544\) −5.44616 1.79981i −0.233502 0.0771661i
\(545\) 38.0975 1.63192
\(546\) 5.22252 + 0.333832i 0.223503 + 0.0142867i
\(547\) 7.58510 0.324315 0.162158 0.986765i \(-0.448155\pi\)
0.162158 + 0.986765i \(0.448155\pi\)
\(548\) 4.87778 37.9985i 0.208369 1.62321i
\(549\) −7.63888 −0.326020
\(550\) −24.3787 1.55833i −1.03951 0.0664474i
\(551\) −0.597994 −0.0254754
\(552\) 2.75773 + 13.2814i 0.117377 + 0.565293i
\(553\) −1.65164 −0.0702348
\(554\) −13.4206 0.857869i −0.570188 0.0364474i
\(555\) −18.4177 −0.781788
\(556\) 26.4772 + 3.39882i 1.12288 + 0.144142i
\(557\) 23.6692 1.00290 0.501448 0.865188i \(-0.332801\pi\)
0.501448 + 0.865188i \(0.332801\pi\)
\(558\) −3.65407 0.233574i −0.154689 0.00988799i
\(559\) 41.4929 1.75496
\(560\) 10.5689 + 2.75889i 0.446620 + 0.116584i
\(561\) −4.00831 −0.169231
\(562\) −32.1648 2.05603i −1.35679 0.0867284i
\(563\) 14.4822i 0.610351i 0.952296 + 0.305176i \(0.0987152\pi\)
−0.952296 + 0.305176i \(0.901285\pi\)
\(564\) 1.86706 14.5446i 0.0786172 0.612437i
\(565\) 49.0379i 2.06304i
\(566\) −24.0284 1.53593i −1.00999 0.0645601i
\(567\) 0.892124 0.0374657
\(568\) −29.4029 5.70066i −1.23372 0.239194i
\(569\) 11.4721i 0.480935i −0.970657 0.240467i \(-0.922699\pi\)
0.970657 0.240467i \(-0.0773007\pi\)
\(570\) 0.845278 + 0.0540316i 0.0354048 + 0.00226313i
\(571\) 29.6426i 1.24051i −0.784402 0.620253i \(-0.787030\pi\)
0.784402 0.620253i \(-0.212970\pi\)
\(572\) −32.5271 4.17543i −1.36003 0.174584i
\(573\) −7.03883 −0.294052
\(574\) −0.823695 + 12.8860i −0.0343803 + 0.537851i
\(575\) 19.3323 8.08788i 0.806212 0.337288i
\(576\) −7.42035 2.98971i −0.309181 0.124571i
\(577\) −4.38359 −0.182491 −0.0912456 0.995828i \(-0.529085\pi\)
−0.0912456 + 0.995828i \(0.529085\pi\)
\(578\) 1.44090 22.5416i 0.0599335 0.937609i
\(579\) −21.4049 −0.889557
\(580\) 2.38224 18.5579i 0.0989172 0.770576i
\(581\) 3.38188i 0.140304i
\(582\) 3.52481 + 0.225312i 0.146108 + 0.00933948i
\(583\) 44.4018i 1.83893i
\(584\) −1.74793 + 9.01551i −0.0723299 + 0.373064i
\(585\) 12.6966i 0.524939i
\(586\) −1.19949 + 18.7650i −0.0495505 + 0.775175i
\(587\) 44.8384 1.85068 0.925339 0.379140i \(-0.123780\pi\)
0.925339 + 0.379140i \(0.123780\pi\)
\(588\) 12.3072 + 1.57985i 0.507542 + 0.0651521i
\(589\) 0.506590 0.0208737
\(590\) −1.20138 + 18.7946i −0.0494602 + 0.773763i
\(591\) 16.5652i 0.681400i
\(592\) −23.2874 6.07887i −0.957104 0.249840i
\(593\) 36.8434 1.51298 0.756489 0.654006i \(-0.226913\pi\)
0.756489 + 0.654006i \(0.226913\pi\)
\(594\) −5.57915 0.356629i −0.228915 0.0146327i
\(595\) 2.76891i 0.113514i
\(596\) −3.79692 0.487402i −0.155528 0.0199648i
\(597\) −18.7514 −0.767445
\(598\) 26.5924 9.17989i 1.08744 0.375394i
\(599\) 0.536356i 0.0219149i −0.999940 0.0109575i \(-0.996512\pi\)
0.999940 0.0109575i \(-0.00348794\pi\)
\(600\) −2.35239 + 12.1332i −0.0960359 + 0.495336i
\(601\) 2.32091 0.0946721 0.0473360 0.998879i \(-0.484927\pi\)
0.0473360 + 0.998879i \(0.484927\pi\)
\(602\) −12.5951 0.805101i −0.513339 0.0328135i
\(603\) 3.60187i 0.146680i
\(604\) 3.94681 30.7461i 0.160594 1.25104i
\(605\) −14.1633 −0.575821
\(606\) −4.66392 0.298125i −0.189459 0.0121105i
\(607\) 4.31945i 0.175321i 0.996150 + 0.0876605i \(0.0279391\pi\)
−0.996150 + 0.0876605i \(0.972061\pi\)
\(608\) 1.05094 + 0.347306i 0.0426211 + 0.0140851i
\(609\) 2.72654i 0.110485i
\(610\) −2.10945 + 33.0005i −0.0854090 + 1.33615i
\(611\) −30.4120 −1.23034
\(612\) −0.258202 + 2.01142i −0.0104372 + 0.0813070i
\(613\) −4.29197 −0.173351 −0.0866756 0.996237i \(-0.527624\pi\)
−0.0866756 + 0.996237i \(0.527624\pi\)
\(614\) −0.622182 + 9.73351i −0.0251092 + 0.392813i
\(615\) −31.3274 −1.26324
\(616\) 9.79255 + 1.89858i 0.394553 + 0.0764961i
\(617\) 36.9423i 1.48724i −0.668602 0.743621i \(-0.733107\pi\)
0.668602 0.743621i \(-0.266893\pi\)
\(618\) −0.936243 + 14.6467i −0.0376612 + 0.589178i
\(619\) 2.34420i 0.0942215i −0.998890 0.0471108i \(-0.984999\pi\)
0.998890 0.0471108i \(-0.0150014\pi\)
\(620\) −2.01811 + 15.7213i −0.0810494 + 0.631384i
\(621\) 4.42425 1.85094i 0.177539 0.0742756i
\(622\) −28.6315 1.83017i −1.14802 0.0733833i
\(623\) 9.63161i 0.385882i
\(624\) −4.19058 + 16.0536i −0.167757 + 0.642657i
\(625\) −27.7545 −1.11018
\(626\) −39.7924 2.54360i −1.59042 0.101663i
\(627\) 0.773477 0.0308897
\(628\) 21.9394 + 2.81632i 0.875479 + 0.112383i
\(629\) 6.10094i 0.243260i
\(630\) 0.246356 3.85403i 0.00981507 0.153548i
\(631\) 42.3515 1.68599 0.842993 0.537925i \(-0.180791\pi\)
0.842993 + 0.537925i \(0.180791\pi\)
\(632\) 0.996681 5.14070i 0.0396458 0.204486i
\(633\) −4.73983 −0.188391
\(634\) −11.9824 0.765934i −0.475881 0.0304191i
\(635\) 0.860903i 0.0341639i
\(636\) −22.2814 2.86022i −0.883516 0.113415i
\(637\) 25.7339i 1.01961i
\(638\) 1.08994 17.0512i 0.0431513 0.675064i
\(639\) 10.5891i 0.418898i
\(640\) −14.9648 + 31.2308i −0.591537 + 1.23451i
\(641\) 35.6357i 1.40753i 0.710435 + 0.703763i \(0.248498\pi\)
−0.710435 + 0.703763i \(0.751502\pi\)
\(642\) −25.8587 1.65293i −1.02056 0.0652360i
\(643\) 17.2554i 0.680486i −0.940338 0.340243i \(-0.889491\pi\)
0.940338 0.340243i \(-0.110509\pi\)
\(644\) −8.25021 + 2.27057i −0.325104 + 0.0894729i
\(645\) 30.6202i 1.20567i
\(646\) 0.0178982 0.280002i 0.000704195 0.0110165i
\(647\) 20.7332i 0.815107i −0.913181 0.407553i \(-0.866382\pi\)
0.913181 0.407553i \(-0.133618\pi\)
\(648\) −0.538352 + 2.77672i −0.0211485 + 0.109080i
\(649\) 17.1982i 0.675087i
\(650\) 25.5799 + 1.63511i 1.00332 + 0.0641342i
\(651\) 2.30979i 0.0905278i
\(652\) −19.9740 2.56401i −0.782240 0.100415i
\(653\) 41.9915i 1.64325i 0.570026 + 0.821626i \(0.306933\pi\)
−0.570026 + 0.821626i \(0.693067\pi\)
\(654\) 1.12283 17.5657i 0.0439061 0.686873i
\(655\) 66.7183 2.60690
\(656\) −39.6104 10.3398i −1.54653 0.403701i
\(657\) 3.24682 0.126670
\(658\) 9.23155 + 0.590096i 0.359883 + 0.0230043i
\(659\) 5.13261i 0.199938i −0.994991 0.0999690i \(-0.968126\pi\)
0.994991 0.0999690i \(-0.0318744\pi\)
\(660\) −3.08132 + 24.0038i −0.119940 + 0.934347i
\(661\) 6.38665 0.248412 0.124206 0.992256i \(-0.460362\pi\)
0.124206 + 0.992256i \(0.460362\pi\)
\(662\) −1.29765 + 20.3007i −0.0504347 + 0.789008i
\(663\) 4.20580 0.163340
\(664\) −10.5260 2.04079i −0.408490 0.0791982i
\(665\) 0.534312i 0.0207197i
\(666\) −0.542815 + 8.49188i −0.0210337 + 0.329054i
\(667\) 5.65691 + 13.5216i 0.219036 + 0.523558i
\(668\) −2.93818 + 22.8887i −0.113681 + 0.885591i
\(669\) 8.79654i 0.340094i
\(670\) 15.5603 + 0.994642i 0.601148 + 0.0384264i
\(671\) 30.1973i 1.16575i
\(672\) 1.58354 4.79173i 0.0610863 0.184845i
\(673\) 6.07738 0.234266 0.117133 0.993116i \(-0.462630\pi\)
0.117133 + 0.993116i \(0.462630\pi\)
\(674\) 41.2974 + 2.63980i 1.59072 + 0.101681i
\(675\) 4.36961 0.168187
\(676\) 8.34129 + 1.07075i 0.320819 + 0.0411828i
\(677\) 7.89600 0.303468 0.151734 0.988421i \(-0.451514\pi\)
0.151734 + 0.988421i \(0.451514\pi\)
\(678\) 22.6100 + 1.44527i 0.868333 + 0.0555053i
\(679\) 2.22808i 0.0855060i
\(680\) 8.61818 + 1.67090i 0.330492 + 0.0640760i
\(681\) 23.9345i 0.917172i
\(682\) −0.923344 + 14.4449i −0.0353567 + 0.553125i
\(683\) 43.6655 1.67082 0.835408 0.549631i \(-0.185232\pi\)
0.835408 + 0.549631i \(0.185232\pi\)
\(684\) 0.0498249 0.388141i 0.00190510 0.0148410i
\(685\) 58.6335i 2.24027i
\(686\) −1.06270 + 16.6251i −0.0405742 + 0.634749i
\(687\) 8.58118 0.327392
\(688\) 10.1064 38.7163i 0.385302 1.47604i
\(689\) 46.5894i 1.77492i
\(690\) −6.77443 19.6242i −0.257898 0.747081i
\(691\) −15.7471 −0.599049 −0.299525 0.954089i \(-0.596828\pi\)
−0.299525 + 0.954089i \(0.596828\pi\)
\(692\) −1.63725 + 12.7543i −0.0622388 + 0.484847i
\(693\) 3.52666i 0.133967i
\(694\) 0.195200 3.05373i 0.00740968 0.115918i
\(695\) −40.8556 −1.54974
\(696\) −8.48633 1.64533i −0.321673 0.0623662i
\(697\) 10.3773i 0.393070i
\(698\) −33.5898 2.14712i −1.27139 0.0812695i
\(699\) 6.59907 0.249600
\(700\) −7.73302 0.992671i −0.292281 0.0375194i
\(701\) −35.7030 −1.34849 −0.674243 0.738510i \(-0.735530\pi\)
−0.674243 + 0.738510i \(0.735530\pi\)
\(702\) 5.85403 + 0.374200i 0.220946 + 0.0141233i
\(703\) 1.17729i 0.0444023i
\(704\) −11.8186 + 29.3335i −0.445431 + 1.10555i
\(705\) 22.4430i 0.845252i
\(706\) 1.83545 28.7140i 0.0690780 1.08067i
\(707\) 2.94813i 0.110876i
\(708\) 8.63027 + 1.10785i 0.324345 + 0.0416355i
\(709\) 25.5486 0.959499 0.479749 0.877406i \(-0.340728\pi\)
0.479749 + 0.877406i \(0.340728\pi\)
\(710\) 45.7456 + 2.92413i 1.71680 + 0.109741i
\(711\) −1.85136 −0.0694313
\(712\) −29.9782 5.81220i −1.12348 0.217821i
\(713\) −4.79225 11.4548i −0.179471 0.428986i
\(714\) −1.27667 0.0816066i −0.0477780 0.00305405i
\(715\) 50.1909 1.87703
\(716\) 1.35199 + 0.173552i 0.0505262 + 0.00648595i
\(717\) 14.2318i 0.531495i
\(718\) 1.02834 16.0876i 0.0383774 0.600382i
\(719\) 12.9790i 0.484036i −0.970272 0.242018i \(-0.922191\pi\)
0.970272 0.242018i \(-0.0778094\pi\)
\(720\) 11.8470 + 3.09250i 0.441510 + 0.115250i
\(721\) −9.25840 −0.344801
\(722\) 1.71063 26.7613i 0.0636630 0.995952i
\(723\) 18.9358i 0.704231i
\(724\) −17.3737 2.23022i −0.645687 0.0828854i
\(725\) 13.3546i 0.495977i
\(726\) −0.417428 + 6.53031i −0.0154922 + 0.242362i
\(727\) −25.5652 −0.948160 −0.474080 0.880482i \(-0.657219\pi\)
−0.474080 + 0.880482i \(0.657219\pi\)
\(728\) −10.2750 1.99213i −0.380818 0.0738331i
\(729\) 1.00000 0.0370370
\(730\) 0.896595 14.0265i 0.0331845 0.519143i
\(731\) −10.1431 −0.375156
\(732\) 15.1534 + 1.94521i 0.560087 + 0.0718971i
\(733\) −35.4883 −1.31079 −0.655395 0.755286i \(-0.727498\pi\)
−0.655395 + 0.755286i \(0.727498\pi\)
\(734\) 0.140271 2.19442i 0.00517749 0.0809973i
\(735\) −18.9907 −0.700482
\(736\) −2.08852 27.0488i −0.0769838 0.997032i
\(737\) 14.2386 0.524485
\(738\) −0.923296 + 14.4442i −0.0339870 + 0.531698i
\(739\) −41.9864 −1.54449 −0.772247 0.635322i \(-0.780867\pi\)
−0.772247 + 0.635322i \(0.780867\pi\)
\(740\) 36.5356 + 4.69000i 1.34308 + 0.172408i
\(741\) −0.811586 −0.0298144
\(742\) 0.903992 14.1422i 0.0331866 0.519176i
\(743\) −22.8728 −0.839123 −0.419561 0.907727i \(-0.637816\pi\)
−0.419561 + 0.907727i \(0.637816\pi\)
\(744\) 7.18918 + 1.39384i 0.263568 + 0.0511007i
\(745\) 5.85883 0.214651
\(746\) −0.834492 + 13.0549i −0.0305529 + 0.477974i
\(747\) 3.79082i 0.138699i
\(748\) 7.95137 + 1.02070i 0.290731 + 0.0373205i
\(749\) 16.3456i 0.597257i
\(750\) −0.174078 + 2.72331i −0.00635644 + 0.0994411i
\(751\) 18.3558 0.669812 0.334906 0.942251i \(-0.391295\pi\)
0.334906 + 0.942251i \(0.391295\pi\)
\(752\) −7.40744 + 28.3770i −0.270122 + 1.03480i
\(753\) 16.7334i 0.609798i
\(754\) −1.14364 + 17.8913i −0.0416491 + 0.651564i
\(755\) 47.4428i 1.72662i
\(756\) −1.76973 0.227176i −0.0643643 0.00826231i
\(757\) 13.2658 0.482155 0.241078 0.970506i \(-0.422499\pi\)
0.241078 + 0.970506i \(0.422499\pi\)
\(758\) 33.5805 + 2.14652i 1.21970 + 0.0779651i
\(759\) −7.31695 17.4895i −0.265589 0.634830i
\(760\) −1.66304 0.322430i −0.0603247 0.0116958i
\(761\) 24.5251 0.889034 0.444517 0.895770i \(-0.353375\pi\)
0.444517 + 0.895770i \(0.353375\pi\)
\(762\) 0.396938 + 0.0253730i 0.0143796 + 0.000919165i
\(763\) 11.1035 0.401975
\(764\) 13.9631 + 1.79241i 0.505167 + 0.0648472i
\(765\) 3.10373i 0.112215i
\(766\) 1.24959 19.5487i 0.0451494 0.706324i
\(767\) 18.0455i 0.651586i
\(768\) 13.9586 + 7.82031i 0.503688 + 0.282191i
\(769\) 3.94832i 0.142380i −0.997463 0.0711901i \(-0.977320\pi\)
0.997463 0.0711901i \(-0.0226797\pi\)
\(770\) −15.2354 0.973873i −0.549046 0.0350959i
\(771\) 10.9984 0.396099
\(772\) 42.4614 + 5.45068i 1.52822 + 0.196174i
\(773\) −16.8096 −0.604599 −0.302300 0.953213i \(-0.597754\pi\)
−0.302300 + 0.953213i \(0.597754\pi\)
\(774\) −14.1181 0.902455i −0.507466 0.0324381i
\(775\) 11.3133i 0.406387i
\(776\) −6.93487 1.34454i −0.248947 0.0482660i
\(777\) −5.36784 −0.192570
\(778\) 2.27180 35.5404i 0.0814480 1.27418i
\(779\) 2.00250i 0.0717470i
\(780\) 3.23313 25.1865i 0.115765 0.901821i
\(781\) 41.8598 1.49786
\(782\) −6.50060 + 2.24406i −0.232461 + 0.0802474i
\(783\) 3.05624i 0.109221i
\(784\) −24.0119 6.26799i −0.857566 0.223857i
\(785\) −33.8536 −1.20829
\(786\) 1.96635 30.7619i 0.0701375 1.09724i
\(787\) 41.0427i 1.46302i −0.681833 0.731508i \(-0.738817\pi\)
0.681833 0.731508i \(-0.261183\pi\)
\(788\) 4.21826 32.8607i 0.150269 1.17061i
\(789\) −32.1667 −1.14516
\(790\) −0.511244 + 7.99798i −0.0181893 + 0.284555i
\(791\) 14.2921i 0.508169i
\(792\) 10.9767 + 2.12816i 0.390039 + 0.0756209i
\(793\) 31.6851i 1.12517i
\(794\) −49.2106 3.14563i −1.74642 0.111634i
\(795\) 34.3813 1.21938
\(796\) 37.1976 + 4.77498i 1.31844 + 0.169245i
\(797\) 34.5930 1.22535 0.612674 0.790336i \(-0.290094\pi\)
0.612674 + 0.790336i \(0.290094\pi\)
\(798\) 0.246356 + 0.0157475i 0.00872092 + 0.000557456i
\(799\) 7.43434 0.263008
\(800\) 7.75616 23.4699i 0.274222 0.829785i
\(801\) 10.7963i 0.381468i
\(802\) −37.4526 2.39403i −1.32250 0.0845362i
\(803\) 12.8350i 0.452938i
\(804\) 0.917203 7.14511i 0.0323473 0.251989i
\(805\) 12.0816 5.05449i 0.425822 0.178147i
\(806\) 0.968837 15.1566i 0.0341258 0.533870i
\(807\) 21.2979i 0.749723i
\(808\) 9.17600 + 1.77905i 0.322811 + 0.0625867i
\(809\) −38.0524 −1.33785 −0.668926 0.743329i \(-0.733246\pi\)
−0.668926 + 0.743329i \(0.733246\pi\)
\(810\) 0.276146 4.32007i 0.00970278 0.151792i
\(811\) −28.4205 −0.997978 −0.498989 0.866608i \(-0.666295\pi\)
−0.498989 + 0.866608i \(0.666295\pi\)
\(812\) 0.694304 5.40871i 0.0243653 0.189808i
\(813\) 2.36324i 0.0828823i
\(814\) 33.5693 + 2.14581i 1.17660 + 0.0752105i
\(815\) 30.8208 1.07961
\(816\) 1.02440 3.92436i 0.0358613 0.137380i
\(817\) 1.95730 0.0684772
\(818\) −2.22329 + 34.7815i −0.0777356 + 1.21611i
\(819\) 3.70042i 0.129303i
\(820\) 62.1449 + 7.97740i 2.17019 + 0.278583i
\(821\) 37.1955i 1.29813i −0.760733 0.649065i \(-0.775160\pi\)
0.760733 0.649065i \(-0.224840\pi\)
\(822\) 27.0343 + 1.72808i 0.942929 + 0.0602736i
\(823\) 10.0207i 0.349301i 0.984630 + 0.174651i \(0.0558796\pi\)
−0.984630 + 0.174651i \(0.944120\pi\)
\(824\) 5.58698 28.8166i 0.194632 1.00387i
\(825\) 17.2736i 0.601388i
\(826\) −0.350144 + 5.47770i −0.0121831 + 0.190594i
\(827\) 47.1667i 1.64015i −0.572258 0.820073i \(-0.693933\pi\)
0.572258 0.820073i \(-0.306067\pi\)
\(828\) −9.24783 + 2.54513i −0.321384 + 0.0884493i
\(829\) 26.2155i 0.910503i −0.890363 0.455252i \(-0.849549\pi\)
0.890363 0.455252i \(-0.150451\pi\)
\(830\) 16.3766 + 1.04682i 0.568440 + 0.0363356i
\(831\) 9.50918i 0.329870i
\(832\) 12.4009 30.7787i 0.429925 1.06706i
\(833\) 6.29075i 0.217962i
\(834\) −1.20412 + 18.8374i −0.0416951 + 0.652284i
\(835\) 35.3184i 1.22225i
\(836\) −1.53436 0.196963i −0.0530671 0.00681211i
\(837\) 2.58909i 0.0894921i
\(838\) −17.8779 1.14279i −0.617583 0.0394769i
\(839\) −26.6221 −0.919097 −0.459549 0.888153i \(-0.651989\pi\)
−0.459549 + 0.888153i \(0.651989\pi\)
\(840\) −1.47012 + 7.58260i −0.0507239 + 0.261625i
\(841\) 19.6594 0.677910
\(842\) 2.58997 40.5179i 0.0892563 1.39634i
\(843\) 22.7904i 0.784942i
\(844\) 9.40251 + 1.20698i 0.323648 + 0.0415460i
\(845\) −12.8710 −0.442776
\(846\) 10.3478 + 0.661451i 0.355766 + 0.0227412i
\(847\) −4.12790 −0.141836
\(848\) 43.4718 + 11.3478i 1.49283 + 0.389684i
\(849\) 17.0253i 0.584307i
\(850\) −6.25310 0.399708i −0.214479 0.0137099i
\(851\) −26.6204 + 11.1369i −0.912535 + 0.381770i
\(852\) 2.69647 21.0058i 0.0923796 0.719648i
\(853\) 10.7592i 0.368388i −0.982890 0.184194i \(-0.941032\pi\)
0.982890 0.184194i \(-0.0589675\pi\)
\(854\) −0.614798 + 9.61799i −0.0210380 + 0.329121i
\(855\) 0.598921i 0.0204827i
\(856\) 50.8755 + 9.86377i 1.73889 + 0.337137i
\(857\) −48.2719 −1.64894 −0.824469 0.565907i \(-0.808526\pi\)
−0.824469 + 0.565907i \(0.808526\pi\)
\(858\) 1.47925 23.1416i 0.0505008 0.790042i
\(859\) 41.1208 1.40302 0.701511 0.712659i \(-0.252509\pi\)
0.701511 + 0.712659i \(0.252509\pi\)
\(860\) −7.79733 + 60.7421i −0.265887 + 2.07129i
\(861\) −9.13037 −0.311162
\(862\) 2.07057 32.3924i 0.0705240 1.10329i
\(863\) 26.4666i 0.900934i −0.892793 0.450467i \(-0.851257\pi\)
0.892793 0.450467i \(-0.148743\pi\)
\(864\) 1.77502 5.37115i 0.0603875 0.182730i
\(865\) 19.6806i 0.669159i
\(866\) −21.2655 1.35933i −0.722632 0.0461918i
\(867\) 15.9719 0.542433
\(868\) −0.588179 + 4.58198i −0.0199641 + 0.155523i
\(869\) 7.31861i 0.248267i
\(870\) 13.2032 + 0.843968i 0.447629 + 0.0286132i
\(871\) −14.9401 −0.506226
\(872\) −6.70042 + 34.5596i −0.226905 + 1.17033i
\(873\) 2.49750i 0.0845277i
\(874\) 1.25441 0.433033i 0.0424311 0.0146476i
\(875\) −1.72144 −0.0581953
\(876\) −6.44079 0.826790i −0.217614 0.0279346i
\(877\) 28.8502i 0.974202i 0.873346 + 0.487101i \(0.161946\pi\)
−0.873346 + 0.487101i \(0.838054\pi\)
\(878\) 31.6790 + 2.02498i 1.06912 + 0.0683397i
\(879\) −13.2959 −0.448461
\(880\) 12.2250 46.8323i 0.412103 1.57872i
\(881\) 17.0655i 0.574953i −0.957788 0.287476i \(-0.907184\pi\)
0.957788 0.287476i \(-0.0928163\pi\)
\(882\) −0.559703 + 8.75607i −0.0188462 + 0.294832i
\(883\) 2.35287 0.0791805 0.0395902 0.999216i \(-0.487395\pi\)
0.0395902 + 0.999216i \(0.487395\pi\)
\(884\) −8.34313 1.07099i −0.280610 0.0360213i
\(885\) −13.3169 −0.447644
\(886\) −2.59749 + 40.6355i −0.0872644 + 1.36518i
\(887\) 5.60160i 0.188083i −0.995568 0.0940417i \(-0.970021\pi\)
0.995568 0.0940417i \(-0.0299787\pi\)
\(888\) 3.23922 16.7073i 0.108701 0.560661i
\(889\) 0.250910i 0.00841526i
\(890\) 46.6406 + 2.98135i 1.56340 + 0.0999350i
\(891\) 3.95311i 0.132434i
\(892\) −2.24001 + 17.4499i −0.0750010 + 0.584266i
\(893\) −1.43459 −0.0480069
\(894\) 0.172674 2.70134i 0.00577509 0.0903464i
\(895\) −2.08619 −0.0697336
\(896\) −4.36150 + 9.10223i −0.145707 + 0.304084i
\(897\) 7.67746 + 18.3513i 0.256343 + 0.612731i
\(898\) 0.904500 14.1501i 0.0301836 0.472196i
\(899\) 7.91289 0.263910
\(900\) −8.66810 1.11271i −0.288937 0.0370902i
\(901\) 11.3890i 0.379422i
\(902\) 57.0994 + 3.64989i 1.90120 + 0.121528i
\(903\) 8.92427i 0.296981i
\(904\) −44.4840 8.62457i −1.47951 0.286849i
\(905\) 26.8084 0.891142
\(906\) 21.8745 + 1.39826i 0.726733 + 0.0464540i
\(907\) 53.9169i 1.79028i −0.445783 0.895141i \(-0.647075\pi\)
0.445783 0.895141i \(-0.352925\pi\)
\(908\) −6.09483 + 47.4794i −0.202264 + 1.57566i
\(909\) 3.30462i 0.109607i
\(910\) 15.9860 + 1.02185i 0.529932 + 0.0338742i
\(911\) −27.6108 −0.914785 −0.457393 0.889265i \(-0.651217\pi\)
−0.457393 + 0.889265i \(0.651217\pi\)
\(912\) −0.197677 + 0.757277i −0.00654576 + 0.0250760i
\(913\) 14.9855 0.495948
\(914\) 12.5780 + 0.804005i 0.416042 + 0.0265941i
\(915\) −23.3825 −0.773001
\(916\) −17.0227 2.18517i −0.562445 0.0721999i
\(917\) 19.4451 0.642132
\(918\) −1.43104 0.0914745i −0.0472314 0.00301911i
\(919\) 19.0333 0.627850 0.313925 0.949448i \(-0.398356\pi\)
0.313925 + 0.949448i \(0.398356\pi\)
\(920\) 8.44136 + 40.6541i 0.278304 + 1.34032i
\(921\) −6.89668 −0.227253
\(922\) −51.1890 3.27209i −1.68582 0.107761i
\(923\) −43.9222 −1.44572
\(924\) −0.898051 + 6.99591i −0.0295437 + 0.230149i
\(925\) −26.2916 −0.864463
\(926\) 41.7641 + 2.66963i 1.37245 + 0.0877295i
\(927\) −10.3779 −0.340856
\(928\) 16.4155 + 5.42489i 0.538866 + 0.178081i
\(929\) −21.7196 −0.712596 −0.356298 0.934372i \(-0.615961\pi\)
−0.356298 + 0.934372i \(0.615961\pi\)
\(930\) −11.1850 0.714967i −0.366772 0.0234447i
\(931\) 1.21392i 0.0397845i
\(932\) −13.0907 1.68043i −0.428801 0.0550442i
\(933\) 20.2868i 0.664161i
\(934\) 0.569564 + 0.0364075i 0.0186367 + 0.00119129i
\(935\) −12.2694 −0.401251
\(936\) −11.5175 2.23302i −0.376461 0.0729884i
\(937\) 16.7401i 0.546875i 0.961890 + 0.273437i \(0.0881606\pi\)
−0.961890 + 0.273437i \(0.911839\pi\)
\(938\) 4.53506 + 0.289888i 0.148075 + 0.00946519i
\(939\) 28.1949i 0.920105i
\(940\) 5.71503 44.5207i 0.186404 1.45210i
\(941\) 38.9995 1.27135 0.635674 0.771958i \(-0.280722\pi\)
0.635674 + 0.771958i \(0.280722\pi\)
\(942\) −0.997751 + 15.6090i −0.0325085 + 0.508568i
\(943\) −45.2797 + 18.9433i −1.47451 + 0.616878i
\(944\) −16.8380 4.39533i −0.548029 0.143056i
\(945\) 2.73077 0.0888321
\(946\) −3.56750 + 55.8105i −0.115989 + 1.81456i
\(947\) 35.7861 1.16289 0.581446 0.813585i \(-0.302487\pi\)
0.581446 + 0.813585i \(0.302487\pi\)
\(948\) 3.67258 + 0.471441i 0.119280 + 0.0153117i
\(949\) 13.4674i 0.437170i
\(950\) 1.20665 + 0.0771312i 0.0391489 + 0.00250247i
\(951\) 8.49011i 0.275311i
\(952\) 2.51177 + 0.486983i 0.0814069 + 0.0157832i
\(953\) 4.44958i 0.144136i −0.997400 0.0720681i \(-0.977040\pi\)
0.997400 0.0720681i \(-0.0229599\pi\)
\(954\) 1.01330 15.8523i 0.0328069 0.513236i
\(955\) −21.5457 −0.697204
\(956\) 3.62406 28.2319i 0.117211 0.913084i
\(957\) 12.0816 0.390544
\(958\) 0.848709 13.2773i 0.0274205 0.428971i
\(959\) 17.0887i 0.551824i
\(960\) −22.7136 9.15144i −0.733078 0.295361i
\(961\) 24.2966 0.783761
\(962\) −35.2233 2.25153i −1.13564 0.0725922i
\(963\) 18.3222i 0.590424i
\(964\) −4.82194 + 37.5634i −0.155304 + 1.20984i
\(965\) −65.5200 −2.10916
\(966\) −1.97441 5.71948i −0.0635256 0.184021i
\(967\) 19.1093i 0.614514i 0.951627 + 0.307257i \(0.0994110\pi\)
−0.951627 + 0.307257i \(0.900589\pi\)
\(968\) 2.49098 12.8480i 0.0800631 0.412951i
\(969\) 0.198395 0.00637338
\(970\) 10.7894 + 0.689676i 0.346426 + 0.0221441i
\(971\) 52.6143i 1.68847i 0.535972 + 0.844236i \(0.319945\pi\)
−0.535972 + 0.844236i \(0.680055\pi\)
\(972\) −1.98372 0.254646i −0.0636279 0.00816778i
\(973\) −11.9074 −0.381732
\(974\) 39.8337 + 2.54624i 1.27635 + 0.0815867i
\(975\) 18.1246i 0.580452i
\(976\) −29.5648 7.71752i −0.946348 0.247032i
\(977\) 4.07699i 0.130435i −0.997871 0.0652173i \(-0.979226\pi\)
0.997871 0.0652173i \(-0.0207741\pi\)
\(978\) 0.908366 14.2106i 0.0290463 0.454405i
\(979\) 42.6788 1.36402
\(980\) 37.6723 + 4.83591i 1.20340 + 0.154477i
\(981\) 12.4462 0.397376
\(982\) 2.05481 32.1458i 0.0655717 1.02581i
\(983\) −3.92937 −0.125327 −0.0626637 0.998035i \(-0.519960\pi\)
−0.0626637 + 0.998035i \(0.519960\pi\)
\(984\) 5.50972 28.4181i 0.175643 0.905937i
\(985\) 50.7057i 1.61562i
\(986\) 0.279568 4.37361i 0.00890327 0.139284i
\(987\) 6.54101i 0.208203i
\(988\) 1.60996 + 0.206667i 0.0512197 + 0.00657497i
\(989\) −18.5157 44.2576i −0.588764 1.40731i
\(990\) −17.0777 1.09163i −0.542764 0.0346944i
\(991\) 40.8198i 1.29668i 0.761350 + 0.648341i \(0.224537\pi\)
−0.761350 + 0.648341i \(0.775463\pi\)
\(992\) −13.9064 4.59570i −0.441529 0.145913i
\(993\) −14.3840 −0.456464
\(994\) 13.3326 + 0.852239i 0.422883 + 0.0270314i
\(995\) −57.3978 −1.81963
\(996\) 0.965318 7.51994i 0.0305873 0.238278i
\(997\) 16.7467i 0.530374i 0.964197 + 0.265187i \(0.0854337\pi\)
−0.964197 + 0.265187i \(0.914566\pi\)
\(998\) −1.61902 + 25.3282i −0.0512492 + 0.801749i
\(999\) −6.01692 −0.190367
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 552.2.n.a.91.14 yes 24
4.3 odd 2 2208.2.n.a.367.22 24
8.3 odd 2 inner 552.2.n.a.91.15 yes 24
8.5 even 2 2208.2.n.a.367.4 24
23.22 odd 2 inner 552.2.n.a.91.13 24
92.91 even 2 2208.2.n.a.367.3 24
184.45 odd 2 2208.2.n.a.367.21 24
184.91 even 2 inner 552.2.n.a.91.16 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.n.a.91.13 24 23.22 odd 2 inner
552.2.n.a.91.14 yes 24 1.1 even 1 trivial
552.2.n.a.91.15 yes 24 8.3 odd 2 inner
552.2.n.a.91.16 yes 24 184.91 even 2 inner
2208.2.n.a.367.3 24 92.91 even 2
2208.2.n.a.367.4 24 8.5 even 2
2208.2.n.a.367.21 24 184.45 odd 2
2208.2.n.a.367.22 24 4.3 odd 2