Properties

Label 920.2.bb.a.11.19
Level $920$
Weight $2$
Character 920.11
Analytic conductor $7.346$
Analytic rank $0$
Dimension $480$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,2,Mod(11,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bb (of order \(22\), degree \(10\), 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: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(48\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 11.19
Character \(\chi\) \(=\) 920.11
Dual form 920.2.bb.a.251.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.412411 - 1.35274i) q^{2} +(-0.429309 + 2.98591i) q^{3} +(-1.65983 + 1.11577i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(4.21623 - 0.650679i) q^{6} +(-1.41433 - 1.63223i) q^{7} +(2.19389 + 1.78517i) q^{8} +(-5.85288 - 1.71856i) q^{9} +(0.776818 + 1.18176i) q^{10} +(0.260861 - 0.405908i) q^{11} +(-2.61902 - 5.43513i) q^{12} +(-0.398969 - 0.345709i) q^{13} +(-1.62470 + 2.58638i) q^{14} +(-0.429309 - 2.98591i) q^{15} +(1.51009 - 3.70400i) q^{16} +(1.00123 - 0.457246i) q^{17} +(0.0890221 + 8.62620i) q^{18} +(-2.30954 - 1.05473i) q^{19} +(1.27825 - 1.53821i) q^{20} +(5.48088 - 3.52235i) q^{21} +(-0.656672 - 0.185477i) q^{22} +(-4.73300 - 0.773739i) q^{23} +(-6.27222 + 5.78438i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.303116 + 0.682277i) q^{26} +(3.88472 - 8.50636i) q^{27} +(4.16876 + 1.13115i) q^{28} +(7.04860 - 3.21899i) q^{29} +(-3.86212 + 1.81217i) q^{30} +(-4.41035 + 0.634113i) q^{31} +(-5.63334 - 0.515200i) q^{32} +(1.10002 + 0.953169i) q^{33} +(-1.03145 - 1.16583i) q^{34} +(1.81690 + 1.16765i) q^{35} +(11.6323 - 3.67797i) q^{36} +(3.42102 + 1.00450i) q^{37} +(-0.474301 + 3.55920i) q^{38} +(1.20354 - 1.04287i) q^{39} +(-2.60796 - 1.09477i) q^{40} +(5.07992 - 1.49160i) q^{41} +(-7.02521 - 5.96157i) q^{42} +(9.40966 + 1.35291i) q^{43} +(0.0199156 + 0.964802i) q^{44} +6.09997 q^{45} +(0.905274 + 6.72164i) q^{46} +1.55715i q^{47} +(10.4115 + 6.09917i) q^{48} +(0.332374 - 2.31171i) q^{49} +(-1.07829 - 0.915034i) q^{50} +(0.935459 + 3.18588i) q^{51} +(1.04796 + 0.128659i) q^{52} +(-0.419139 - 0.483712i) q^{53} +(-13.1090 - 1.74692i) q^{54} +(-0.135937 + 0.462959i) q^{55} +(-0.189087 - 6.10576i) q^{56} +(4.14084 - 6.44327i) q^{57} +(-7.26139 - 8.20741i) q^{58} +(7.29413 - 8.41787i) q^{59} +(4.04419 + 4.47710i) q^{60} +(-1.47679 - 10.2713i) q^{61} +(2.67667 + 5.70456i) q^{62} +(5.47285 + 11.9839i) q^{63} +(1.62632 + 7.83295i) q^{64} +(0.480205 + 0.219302i) q^{65} +(0.835735 - 1.88114i) q^{66} +(-0.346109 - 0.538557i) q^{67} +(-1.15169 + 1.87610i) q^{68} +(4.34224 - 13.8002i) q^{69} +(0.830220 - 2.93935i) q^{70} +(-3.06304 - 4.76619i) q^{71} +(-9.77266 - 14.2187i) q^{72} +(5.17201 - 11.3251i) q^{73} +(-0.0520336 - 5.04204i) q^{74} +(1.25315 + 2.74401i) q^{75} +(5.01029 - 0.826246i) q^{76} +(-1.03148 + 0.148304i) q^{77} +(-1.90709 - 1.19799i) q^{78} +(1.22567 - 1.41450i) q^{79} +(-0.405388 + 3.97940i) q^{80} +(8.33661 + 5.35761i) q^{81} +(-4.11277 - 6.25668i) q^{82} +(-2.13633 + 7.27566i) q^{83} +(-5.16720 + 11.9619i) q^{84} +(-0.831851 + 0.720803i) q^{85} +(-2.05052 - 13.2868i) q^{86} +(6.58558 + 22.4284i) q^{87} +(1.29692 - 0.424836i) q^{88} +(-17.3851 - 2.49959i) q^{89} +(-2.51570 - 8.25170i) q^{90} +1.14016i q^{91} +(8.71932 - 3.99669i) q^{92} -13.4412i q^{93} +(2.10643 - 0.642187i) q^{94} +(2.51314 + 0.361335i) q^{95} +(3.95679 - 16.5995i) q^{96} +(4.34339 + 14.7922i) q^{97} +(-3.26423 + 0.503760i) q^{98} +(-2.22437 + 1.92743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(-1\) \(e\left(\frac{9}{22}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.412411 1.35274i −0.291619 0.956535i
\(3\) −0.429309 + 2.98591i −0.247862 + 1.72392i 0.362664 + 0.931920i \(0.381867\pi\)
−0.610525 + 0.791997i \(0.709042\pi\)
\(4\) −1.65983 + 1.11577i −0.829917 + 0.557887i
\(5\) −0.959493 + 0.281733i −0.429098 + 0.125995i
\(6\) 4.21623 0.650679i 1.72127 0.265638i
\(7\) −1.41433 1.63223i −0.534568 0.616925i 0.422650 0.906293i \(-0.361100\pi\)
−0.957218 + 0.289369i \(0.906555\pi\)
\(8\) 2.19389 + 1.78517i 0.775658 + 0.631154i
\(9\) −5.85288 1.71856i −1.95096 0.572854i
\(10\) 0.776818 + 1.18176i 0.245651 + 0.373705i
\(11\) 0.260861 0.405908i 0.0786526 0.122386i −0.799699 0.600402i \(-0.795007\pi\)
0.878351 + 0.478016i \(0.158644\pi\)
\(12\) −2.61902 5.43513i −0.756046 1.56899i
\(13\) −0.398969 0.345709i −0.110654 0.0958823i 0.597776 0.801663i \(-0.296051\pi\)
−0.708431 + 0.705780i \(0.750596\pi\)
\(14\) −1.62470 + 2.58638i −0.434219 + 0.691240i
\(15\) −0.429309 2.98591i −0.110847 0.770959i
\(16\) 1.51009 3.70400i 0.377524 0.926000i
\(17\) 1.00123 0.457246i 0.242834 0.110898i −0.290281 0.956941i \(-0.593749\pi\)
0.533115 + 0.846043i \(0.321021\pi\)
\(18\) 0.0890221 + 8.62620i 0.0209827 + 2.03322i
\(19\) −2.30954 1.05473i −0.529844 0.241972i 0.132485 0.991185i \(-0.457705\pi\)
−0.662329 + 0.749213i \(0.730432\pi\)
\(20\) 1.27825 1.53821i 0.285825 0.343954i
\(21\) 5.48088 3.52235i 1.19603 0.768639i
\(22\) −0.656672 0.185477i −0.140003 0.0395439i
\(23\) −4.73300 0.773739i −0.986900 0.161336i
\(24\) −6.27222 + 5.78438i −1.28031 + 1.18073i
\(25\) 0.841254 0.540641i 0.168251 0.108128i
\(26\) −0.303116 + 0.682277i −0.0594459 + 0.133806i
\(27\) 3.88472 8.50636i 0.747615 1.63705i
\(28\) 4.16876 + 1.13115i 0.787821 + 0.213767i
\(29\) 7.04860 3.21899i 1.30889 0.597751i 0.365928 0.930643i \(-0.380752\pi\)
0.942965 + 0.332892i \(0.108024\pi\)
\(30\) −3.86212 + 1.81217i −0.705124 + 0.330855i
\(31\) −4.41035 + 0.634113i −0.792123 + 0.113890i −0.526487 0.850183i \(-0.676491\pi\)
−0.265636 + 0.964073i \(0.585582\pi\)
\(32\) −5.63334 0.515200i −0.995844 0.0910753i
\(33\) 1.10002 + 0.953169i 0.191488 + 0.165925i
\(34\) −1.03145 1.16583i −0.176893 0.199939i
\(35\) 1.81690 + 1.16765i 0.307111 + 0.197369i
\(36\) 11.6323 3.67797i 1.93872 0.612995i
\(37\) 3.42102 + 1.00450i 0.562413 + 0.165139i 0.550568 0.834791i \(-0.314411\pi\)
0.0118450 + 0.999930i \(0.496230\pi\)
\(38\) −0.474301 + 3.55920i −0.0769417 + 0.577378i
\(39\) 1.20354 1.04287i 0.192720 0.166993i
\(40\) −2.60796 1.09477i −0.412355 0.173098i
\(41\) 5.07992 1.49160i 0.793351 0.232949i 0.140147 0.990131i \(-0.455243\pi\)
0.653204 + 0.757182i \(0.273424\pi\)
\(42\) −7.02521 5.96157i −1.08401 0.919890i
\(43\) 9.40966 + 1.35291i 1.43496 + 0.206316i 0.815521 0.578728i \(-0.196451\pi\)
0.619440 + 0.785044i \(0.287360\pi\)
\(44\) 0.0199156 + 0.964802i 0.00300238 + 0.145449i
\(45\) 6.09997 0.909330
\(46\) 0.905274 + 6.72164i 0.133475 + 0.991052i
\(47\) 1.55715i 0.227134i 0.993530 + 0.113567i \(0.0362276\pi\)
−0.993530 + 0.113567i \(0.963772\pi\)
\(48\) 10.4115 + 6.09917i 1.50277 + 0.880339i
\(49\) 0.332374 2.31171i 0.0474821 0.330245i
\(50\) −1.07829 0.915034i −0.152493 0.129405i
\(51\) 0.935459 + 3.18588i 0.130990 + 0.446112i
\(52\) 1.04796 + 0.128659i 0.145325 + 0.0178418i
\(53\) −0.419139 0.483712i −0.0575732 0.0664430i 0.726232 0.687449i \(-0.241270\pi\)
−0.783806 + 0.621006i \(0.786724\pi\)
\(54\) −13.1090 1.74692i −1.78391 0.237725i
\(55\) −0.135937 + 0.462959i −0.0183297 + 0.0624254i
\(56\) −0.189087 6.10576i −0.0252679 0.815917i
\(57\) 4.14084 6.44327i 0.548467 0.853432i
\(58\) −7.26139 8.20741i −0.953468 1.07769i
\(59\) 7.29413 8.41787i 0.949615 1.09591i −0.0456737 0.998956i \(-0.514543\pi\)
0.995289 0.0969575i \(-0.0309111\pi\)
\(60\) 4.04419 + 4.47710i 0.522102 + 0.577992i
\(61\) −1.47679 10.2713i −0.189084 1.31511i −0.834386 0.551181i \(-0.814177\pi\)
0.645301 0.763928i \(-0.276732\pi\)
\(62\) 2.67667 + 5.70456i 0.339938 + 0.724480i
\(63\) 5.47285 + 11.9839i 0.689514 + 1.50982i
\(64\) 1.62632 + 7.83295i 0.203290 + 0.979119i
\(65\) 0.480205 + 0.219302i 0.0595622 + 0.0272011i
\(66\) 0.835735 1.88114i 0.102872 0.231552i
\(67\) −0.346109 0.538557i −0.0422840 0.0657952i 0.819468 0.573125i \(-0.194269\pi\)
−0.861752 + 0.507330i \(0.830633\pi\)
\(68\) −1.15169 + 1.87610i −0.139663 + 0.227510i
\(69\) 4.34224 13.8002i 0.522744 1.66134i
\(70\) 0.830220 2.93935i 0.0992303 0.351319i
\(71\) −3.06304 4.76619i −0.363516 0.565642i 0.610529 0.791994i \(-0.290957\pi\)
−0.974046 + 0.226351i \(0.927320\pi\)
\(72\) −9.77266 14.2187i −1.15172 1.67569i
\(73\) 5.17201 11.3251i 0.605338 1.32551i −0.320379 0.947289i \(-0.603810\pi\)
0.925717 0.378216i \(-0.123463\pi\)
\(74\) −0.0520336 5.04204i −0.00604878 0.586125i
\(75\) 1.25315 + 2.74401i 0.144701 + 0.316851i
\(76\) 5.01029 0.826246i 0.574720 0.0947769i
\(77\) −1.03148 + 0.148304i −0.117548 + 0.0169009i
\(78\) −1.90709 1.19799i −0.215935 0.135645i
\(79\) 1.22567 1.41450i 0.137899 0.159143i −0.682600 0.730793i \(-0.739151\pi\)
0.820498 + 0.571649i \(0.193696\pi\)
\(80\) −0.405388 + 3.97940i −0.0453238 + 0.444911i
\(81\) 8.33661 + 5.35761i 0.926290 + 0.595291i
\(82\) −4.11277 6.25668i −0.454180 0.690935i
\(83\) −2.13633 + 7.27566i −0.234492 + 0.798607i 0.755212 + 0.655480i \(0.227534\pi\)
−0.989704 + 0.143127i \(0.954284\pi\)
\(84\) −5.16720 + 11.9619i −0.563788 + 1.30515i
\(85\) −0.831851 + 0.720803i −0.0902269 + 0.0781820i
\(86\) −2.05052 13.2868i −0.221113 1.43275i
\(87\) 6.58558 + 22.4284i 0.706049 + 2.40458i
\(88\) 1.29692 0.424836i 0.138252 0.0452877i
\(89\) −17.3851 2.49959i −1.84281 0.264956i −0.869415 0.494082i \(-0.835504\pi\)
−0.973397 + 0.229126i \(0.926413\pi\)
\(90\) −2.51570 8.25170i −0.265178 0.869806i
\(91\) 1.14016i 0.119521i
\(92\) 8.71932 3.99669i 0.909052 0.416683i
\(93\) 13.4412i 1.39378i
\(94\) 2.10643 0.642187i 0.217261 0.0662365i
\(95\) 2.51314 + 0.361335i 0.257842 + 0.0370721i
\(96\) 3.95679 16.5995i 0.403838 1.69418i
\(97\) 4.34339 + 14.7922i 0.441005 + 1.50192i 0.817732 + 0.575600i \(0.195231\pi\)
−0.376727 + 0.926324i \(0.622951\pi\)
\(98\) −3.26423 + 0.503760i −0.329737 + 0.0508875i
\(99\) −2.22437 + 1.92743i −0.223557 + 0.193714i
\(100\) −0.793108 + 1.83602i −0.0793108 + 0.183602i
\(101\) 3.40016 11.5799i 0.338329 1.15224i −0.598111 0.801413i \(-0.704082\pi\)
0.936440 0.350828i \(-0.114100\pi\)
\(102\) 3.92389 2.57933i 0.388523 0.255392i
\(103\) −0.0633518 0.0407137i −0.00624224 0.00401164i 0.537516 0.843254i \(-0.319363\pi\)
−0.543758 + 0.839242i \(0.682999\pi\)
\(104\) −0.258146 1.47068i −0.0253133 0.144212i
\(105\) −4.26650 + 4.92381i −0.416368 + 0.480514i
\(106\) −0.481481 + 0.766477i −0.0467656 + 0.0744468i
\(107\) −7.18451 + 1.03298i −0.694552 + 0.0998616i −0.480544 0.876970i \(-0.659561\pi\)
−0.214008 + 0.976832i \(0.568652\pi\)
\(108\) 3.04318 + 18.4536i 0.292830 + 1.77570i
\(109\) 1.79258 + 3.92520i 0.171698 + 0.375966i 0.975845 0.218465i \(-0.0701048\pi\)
−0.804147 + 0.594430i \(0.797378\pi\)
\(110\) 0.682327 0.00704159i 0.0650573 0.000671389i
\(111\) −4.46803 + 9.78363i −0.424087 + 0.928621i
\(112\) −8.18155 + 2.77387i −0.773084 + 0.262106i
\(113\) −6.49012 10.0988i −0.610539 0.950018i −0.999585 0.0287994i \(-0.990832\pi\)
0.389046 0.921218i \(-0.372805\pi\)
\(114\) −10.4238 2.94422i −0.976281 0.275751i
\(115\) 4.75927 0.591044i 0.443804 0.0551151i
\(116\) −8.10784 + 13.2076i −0.752794 + 1.22630i
\(117\) 1.74100 + 2.70904i 0.160955 + 0.250451i
\(118\) −14.3954 6.39546i −1.32521 0.588750i
\(119\) −2.16240 0.987536i −0.198227 0.0905273i
\(120\) 4.38851 7.31716i 0.400614 0.667962i
\(121\) 4.47285 + 9.79418i 0.406623 + 0.890380i
\(122\) −13.2854 + 6.23374i −1.20281 + 0.564376i
\(123\) 2.27293 + 15.8086i 0.204943 + 1.42541i
\(124\) 6.61292 5.97348i 0.593858 0.536434i
\(125\) −0.654861 + 0.755750i −0.0585725 + 0.0675963i
\(126\) 13.9540 12.3456i 1.24312 1.09984i
\(127\) −7.73517 + 12.0362i −0.686385 + 1.06804i 0.306832 + 0.951764i \(0.400731\pi\)
−0.993217 + 0.116272i \(0.962905\pi\)
\(128\) 9.92526 5.43040i 0.877277 0.479984i
\(129\) −8.07931 + 27.5156i −0.711344 + 2.42261i
\(130\) 0.0986179 0.740038i 0.00864936 0.0649056i
\(131\) −4.39184 5.06845i −0.383717 0.442833i 0.530729 0.847542i \(-0.321918\pi\)
−0.914446 + 0.404709i \(0.867373\pi\)
\(132\) −2.88936 0.354732i −0.251487 0.0308755i
\(133\) 1.54490 + 5.26144i 0.133960 + 0.456224i
\(134\) −0.585790 + 0.690304i −0.0506045 + 0.0596332i
\(135\) −1.33085 + 9.25624i −0.114541 + 0.796651i
\(136\) 3.01285 + 0.784217i 0.258350 + 0.0672461i
\(137\) 10.4500i 0.892806i −0.894832 0.446403i \(-0.852705\pi\)
0.894832 0.446403i \(-0.147295\pi\)
\(138\) −20.4589 0.182596i −1.74157 0.0155436i
\(139\) 5.08260 0.431100 0.215550 0.976493i \(-0.430846\pi\)
0.215550 + 0.976493i \(0.430846\pi\)
\(140\) −4.31858 + 0.0891446i −0.364986 + 0.00753409i
\(141\) −4.64952 0.668499i −0.391560 0.0562978i
\(142\) −5.18420 + 6.10914i −0.435048 + 0.512668i
\(143\) −0.244402 + 0.0717628i −0.0204379 + 0.00600110i
\(144\) −15.2040 + 19.0839i −1.26700 + 1.59032i
\(145\) −5.85619 + 5.07442i −0.486330 + 0.421407i
\(146\) −17.4530 2.32580i −1.44442 0.192484i
\(147\) 6.75988 + 1.98488i 0.557546 + 0.163710i
\(148\) −6.79913 + 2.14978i −0.558885 + 0.176711i
\(149\) −16.5149 10.6135i −1.35296 0.869492i −0.355093 0.934831i \(-0.615551\pi\)
−0.997863 + 0.0653390i \(0.979187\pi\)
\(150\) 3.19513 2.82685i 0.260881 0.230811i
\(151\) −12.4236 10.7651i −1.01102 0.876054i −0.0187098 0.999825i \(-0.505956\pi\)
−0.992311 + 0.123771i \(0.960501\pi\)
\(152\) −3.18400 6.43689i −0.258257 0.522100i
\(153\) −6.64588 + 0.955533i −0.537287 + 0.0772502i
\(154\) 0.626012 + 1.33417i 0.0504455 + 0.107510i
\(155\) 4.05305 1.85097i 0.325549 0.148673i
\(156\) −0.834062 + 3.07387i −0.0667784 + 0.246106i
\(157\) 1.97474 4.32408i 0.157601 0.345099i −0.814316 0.580422i \(-0.802888\pi\)
0.971917 + 0.235323i \(0.0756149\pi\)
\(158\) −2.41893 1.07466i −0.192440 0.0854955i
\(159\) 1.62426 1.04385i 0.128812 0.0827827i
\(160\) 5.55030 1.09277i 0.438790 0.0863907i
\(161\) 5.43113 + 8.81967i 0.428033 + 0.695088i
\(162\) 3.80937 13.4868i 0.299292 1.05963i
\(163\) −18.0513 + 11.6009i −1.41389 + 0.908651i −0.999999 0.00167569i \(-0.999467\pi\)
−0.413890 + 0.910327i \(0.635830\pi\)
\(164\) −6.76754 + 8.14386i −0.528456 + 0.635928i
\(165\) −1.32400 0.604649i −0.103073 0.0470718i
\(166\) 10.7231 0.110662i 0.832278 0.00858907i
\(167\) 3.02919 1.38339i 0.234406 0.107050i −0.294749 0.955575i \(-0.595236\pi\)
0.529155 + 0.848525i \(0.322509\pi\)
\(168\) 18.3124 + 2.05666i 1.41284 + 0.158675i
\(169\) −1.81043 12.5918i −0.139264 0.968602i
\(170\) 1.31813 + 0.828014i 0.101096 + 0.0635058i
\(171\) 11.7048 + 10.1423i 0.895091 + 0.775601i
\(172\) −17.1280 + 8.25347i −1.30600 + 0.629321i
\(173\) 1.52566 2.37398i 0.115994 0.180490i −0.778402 0.627766i \(-0.783969\pi\)
0.894396 + 0.447276i \(0.147606\pi\)
\(174\) 27.6240 18.1584i 2.09417 1.37658i
\(175\) −2.07226 0.608471i −0.156648 0.0459961i
\(176\) −1.10956 1.57919i −0.0836361 0.119036i
\(177\) 22.0036 + 25.3935i 1.65389 + 1.90869i
\(178\) 3.78849 + 24.5484i 0.283959 + 1.83998i
\(179\) −5.50605 + 1.61672i −0.411541 + 0.120839i −0.480948 0.876749i \(-0.659707\pi\)
0.0694069 + 0.997588i \(0.477889\pi\)
\(180\) −10.1249 + 6.80619i −0.754668 + 0.507304i
\(181\) −1.55415 + 10.8094i −0.115519 + 0.803455i 0.846874 + 0.531794i \(0.178482\pi\)
−0.962393 + 0.271661i \(0.912427\pi\)
\(182\) 1.54234 0.470214i 0.114326 0.0348546i
\(183\) 31.3033 2.31401
\(184\) −9.00244 10.1467i −0.663669 0.748027i
\(185\) −3.56545 −0.262137
\(186\) −18.1824 + 5.54329i −1.33320 + 0.406453i
\(187\) 0.0755820 0.525685i 0.00552711 0.0384419i
\(188\) −1.73743 2.58461i −0.126715 0.188502i
\(189\) −19.3786 + 5.69008i −1.40959 + 0.413892i
\(190\) −0.547653 3.54865i −0.0397310 0.257446i
\(191\) −7.84295 9.05125i −0.567496 0.654925i 0.397373 0.917657i \(-0.369922\pi\)
−0.964869 + 0.262732i \(0.915376\pi\)
\(192\) −24.0867 + 1.49330i −1.73831 + 0.107769i
\(193\) 13.3549 + 3.92134i 0.961304 + 0.282264i 0.724486 0.689290i \(-0.242077\pi\)
0.236818 + 0.971554i \(0.423895\pi\)
\(194\) 18.2188 11.9760i 1.30804 0.859826i
\(195\) −0.860974 + 1.33970i −0.0616557 + 0.0959381i
\(196\) 2.02767 + 4.20792i 0.144833 + 0.300565i
\(197\) −7.46744 6.47057i −0.532033 0.461009i 0.346936 0.937889i \(-0.387222\pi\)
−0.878968 + 0.476880i \(0.841768\pi\)
\(198\) 3.52467 + 2.21411i 0.250487 + 0.157350i
\(199\) −3.50663 24.3892i −0.248579 1.72890i −0.606441 0.795129i \(-0.707403\pi\)
0.357862 0.933774i \(-0.383506\pi\)
\(200\) 2.81076 + 0.315675i 0.198750 + 0.0223216i
\(201\) 1.75667 0.802244i 0.123906 0.0565860i
\(202\) −17.0669 + 0.176130i −1.20082 + 0.0123924i
\(203\) −15.2232 6.95221i −1.06846 0.487949i
\(204\) −5.10743 4.24427i −0.357592 0.297158i
\(205\) −4.45392 + 2.86236i −0.311075 + 0.199916i
\(206\) −0.0289482 + 0.102490i −0.00201692 + 0.00714079i
\(207\) 26.3720 + 12.6626i 1.83298 + 0.880109i
\(208\) −1.88299 + 0.955729i −0.130562 + 0.0662679i
\(209\) −1.03059 + 0.662322i −0.0712876 + 0.0458138i
\(210\) 8.42021 + 3.74085i 0.581050 + 0.258143i
\(211\) −0.576404 + 1.26215i −0.0396813 + 0.0868899i −0.928435 0.371496i \(-0.878845\pi\)
0.888753 + 0.458386i \(0.151572\pi\)
\(212\) 1.23542 + 0.335217i 0.0848487 + 0.0230228i
\(213\) 15.5464 7.09981i 1.06522 0.486471i
\(214\) 4.36032 + 9.29279i 0.298066 + 0.635242i
\(215\) −9.40966 + 1.35291i −0.641734 + 0.0922674i
\(216\) 23.7080 11.7271i 1.61312 0.797930i
\(217\) 7.27273 + 6.30186i 0.493705 + 0.427798i
\(218\) 4.57051 4.04370i 0.309554 0.273874i
\(219\) 31.5954 + 20.3052i 2.13502 + 1.37210i
\(220\) −0.290925 0.920110i −0.0196142 0.0620338i
\(221\) −0.557533 0.163706i −0.0375037 0.0110121i
\(222\) 15.0774 + 2.00922i 1.01193 + 0.134850i
\(223\) 19.6080 16.9905i 1.31305 1.13777i 0.332158 0.943224i \(-0.392223\pi\)
0.980894 0.194542i \(-0.0623221\pi\)
\(224\) 7.12651 + 9.92357i 0.476160 + 0.663047i
\(225\) −5.85288 + 1.71856i −0.390192 + 0.114571i
\(226\) −10.9845 + 12.9443i −0.730680 + 0.861045i
\(227\) 10.4390 + 1.50090i 0.692860 + 0.0996182i 0.479744 0.877409i \(-0.340730\pi\)
0.213116 + 0.977027i \(0.431639\pi\)
\(228\) 0.316134 + 15.3150i 0.0209365 + 1.01426i
\(229\) 4.84212 0.319976 0.159988 0.987119i \(-0.448854\pi\)
0.159988 + 0.987119i \(0.448854\pi\)
\(230\) −2.76231 6.19432i −0.182141 0.408442i
\(231\) 3.14358i 0.206832i
\(232\) 21.2103 + 5.52085i 1.39253 + 0.362462i
\(233\) 3.11432 21.6606i 0.204026 1.41903i −0.588156 0.808748i \(-0.700146\pi\)
0.792182 0.610285i \(-0.208945\pi\)
\(234\) 2.94664 3.47236i 0.192628 0.226996i
\(235\) −0.438700 1.49408i −0.0286176 0.0974627i
\(236\) −2.71459 + 22.1109i −0.176705 + 1.43930i
\(237\) 3.69738 + 4.26700i 0.240170 + 0.277171i
\(238\) −0.444084 + 3.33245i −0.0287857 + 0.216010i
\(239\) −0.419264 + 1.42788i −0.0271199 + 0.0923621i −0.971941 0.235225i \(-0.924417\pi\)
0.944821 + 0.327587i \(0.106235\pi\)
\(240\) −11.7081 2.91885i −0.755755 0.188411i
\(241\) 4.37954 6.81469i 0.282111 0.438973i −0.671061 0.741402i \(-0.734161\pi\)
0.953172 + 0.302429i \(0.0977976\pi\)
\(242\) 11.4044 10.0899i 0.733100 0.648601i
\(243\) −1.20470 + 1.39030i −0.0772814 + 0.0891875i
\(244\) 13.9117 + 15.4009i 0.890607 + 0.985943i
\(245\) 0.332374 + 2.31171i 0.0212346 + 0.147690i
\(246\) 20.4476 9.59432i 1.30369 0.611712i
\(247\) 0.556805 + 1.21923i 0.0354286 + 0.0775779i
\(248\) −10.8078 6.48206i −0.686298 0.411611i
\(249\) −20.8073 9.50238i −1.31861 0.602189i
\(250\) 1.29241 + 0.574179i 0.0817391 + 0.0363143i
\(251\) −3.99664 6.21890i −0.252266 0.392533i 0.691906 0.721988i \(-0.256771\pi\)
−0.944171 + 0.329455i \(0.893135\pi\)
\(252\) −22.4553 13.7848i −1.41455 0.868358i
\(253\) −1.54872 + 1.71933i −0.0973675 + 0.108093i
\(254\) 19.4719 + 5.49985i 1.22178 + 0.345091i
\(255\) −1.79513 2.79328i −0.112416 0.174922i
\(256\) −11.4392 11.1868i −0.714952 0.699174i
\(257\) 10.8442 23.7456i 0.676445 1.48121i −0.189922 0.981799i \(-0.560823\pi\)
0.866367 0.499409i \(-0.166449\pi\)
\(258\) 40.5536 0.418511i 2.52476 0.0260554i
\(259\) −3.19889 7.00459i −0.198769 0.435244i
\(260\) −1.04175 + 0.171795i −0.0646068 + 0.0106543i
\(261\) −46.7867 + 6.72691i −2.89602 + 0.416385i
\(262\) −5.04508 + 8.03133i −0.311686 + 0.496177i
\(263\) −19.2852 + 22.2564i −1.18918 + 1.37239i −0.277893 + 0.960612i \(0.589636\pi\)
−0.911286 + 0.411774i \(0.864909\pi\)
\(264\) 0.711745 + 4.05487i 0.0438049 + 0.249560i
\(265\) 0.538439 + 0.346034i 0.0330760 + 0.0212567i
\(266\) 6.48024 4.25973i 0.397329 0.261181i
\(267\) 14.9271 50.8371i 0.913526 3.11118i
\(268\) 1.17539 + 0.507734i 0.0717985 + 0.0310148i
\(269\) 7.93844 6.87870i 0.484016 0.419402i −0.378370 0.925655i \(-0.623515\pi\)
0.862385 + 0.506253i \(0.168970\pi\)
\(270\) 13.0702 2.01709i 0.795426 0.122756i
\(271\) 7.19233 + 24.4948i 0.436903 + 1.48796i 0.824359 + 0.566067i \(0.191536\pi\)
−0.387456 + 0.921888i \(0.626646\pi\)
\(272\) −0.181688 4.39903i −0.0110165 0.266731i
\(273\) −3.40441 0.489480i −0.206044 0.0296247i
\(274\) −14.1362 + 4.30971i −0.854000 + 0.260359i
\(275\) 0.482504i 0.0290961i
\(276\) 8.19047 + 27.7509i 0.493008 + 1.67041i
\(277\) 13.6362i 0.819319i 0.912238 + 0.409660i \(0.134353\pi\)
−0.912238 + 0.409660i \(0.865647\pi\)
\(278\) −2.09612 6.87545i −0.125717 0.412362i
\(279\) 26.9030 + 3.86807i 1.61064 + 0.231575i
\(280\) 1.90162 + 5.80517i 0.113644 + 0.346925i
\(281\) −6.63895 22.6102i −0.396046 1.34881i −0.880522 0.474005i \(-0.842808\pi\)
0.484476 0.874805i \(-0.339010\pi\)
\(282\) 1.01320 + 6.56530i 0.0603355 + 0.390958i
\(283\) 0.179403 0.155454i 0.0106644 0.00924078i −0.649512 0.760351i \(-0.725027\pi\)
0.660177 + 0.751110i \(0.270481\pi\)
\(284\) 10.4021 + 4.49341i 0.617253 + 0.266635i
\(285\) −2.15783 + 7.34888i −0.127819 + 0.435310i
\(286\) 0.197871 + 0.301017i 0.0117003 + 0.0177995i
\(287\) −9.61934 6.18198i −0.567812 0.364911i
\(288\) 32.0859 + 12.6966i 1.89068 + 0.748157i
\(289\) −10.3392 + 11.9321i −0.608191 + 0.701890i
\(290\) 9.27955 + 5.82918i 0.544914 + 0.342301i
\(291\) −46.0330 + 6.61854i −2.69850 + 0.387986i
\(292\) 4.05161 + 24.5686i 0.237102 + 1.43777i
\(293\) 10.8927 + 23.8516i 0.636356 + 1.39342i 0.903005 + 0.429631i \(0.141356\pi\)
−0.266649 + 0.963794i \(0.585916\pi\)
\(294\) −0.102818 9.96298i −0.00599644 0.581053i
\(295\) −4.62708 + 10.1319i −0.269399 + 0.589901i
\(296\) 5.71214 + 8.31088i 0.332012 + 0.483060i
\(297\) −2.43943 3.79582i −0.141550 0.220256i
\(298\) −7.54641 + 26.7176i −0.437152 + 1.54771i
\(299\) 1.62083 + 1.94494i 0.0937352 + 0.112479i
\(300\) −5.14171 3.15637i −0.296857 0.182233i
\(301\) −11.1002 17.2722i −0.639803 0.995552i
\(302\) −9.43883 + 21.2457i −0.543144 + 1.22255i
\(303\) 33.1168 + 15.1239i 1.90251 + 0.868847i
\(304\) −7.39434 + 6.96178i −0.424095 + 0.399286i
\(305\) 4.31074 + 9.43921i 0.246832 + 0.540488i
\(306\) 4.03343 + 8.59610i 0.230576 + 0.491406i
\(307\) −0.734146 5.10610i −0.0418999 0.291420i −0.999988 0.00494582i \(-0.998426\pi\)
0.958088 0.286475i \(-0.0924834\pi\)
\(308\) 1.54661 1.39706i 0.0881263 0.0796049i
\(309\) 0.148765 0.171684i 0.00846295 0.00976676i
\(310\) −4.17541 4.71938i −0.237147 0.268043i
\(311\) −3.99032 + 6.20906i −0.226270 + 0.352084i −0.935763 0.352629i \(-0.885288\pi\)
0.709493 + 0.704713i \(0.248924\pi\)
\(312\) 4.50213 0.139425i 0.254883 0.00789339i
\(313\) −9.59787 + 32.6874i −0.542504 + 1.84760i −0.0119808 + 0.999928i \(0.503814\pi\)
−0.530523 + 0.847670i \(0.678004\pi\)
\(314\) −6.66377 0.888019i −0.376059 0.0501138i
\(315\) −8.62740 9.95655i −0.486099 0.560988i
\(316\) −0.456147 + 3.71540i −0.0256603 + 0.209008i
\(317\) −2.83066 9.64035i −0.158986 0.541456i −1.00000 0.000442633i \(-0.999859\pi\)
0.841014 0.541013i \(-0.181959\pi\)
\(318\) −2.08193 1.76672i −0.116749 0.0990725i
\(319\) 0.532094 3.70079i 0.0297915 0.207205i
\(320\) −3.76724 7.05747i −0.210595 0.394525i
\(321\) 21.8958i 1.22210i
\(322\) 9.69090 10.9843i 0.540053 0.612129i
\(323\) −2.79465 −0.155498
\(324\) −19.8153 + 0.409029i −1.10085 + 0.0227238i
\(325\) −0.522538 0.0751297i −0.0289852 0.00416744i
\(326\) 23.1376 + 19.6345i 1.28147 + 1.08745i
\(327\) −12.4899 + 3.66735i −0.690691 + 0.202805i
\(328\) 13.8076 + 5.79613i 0.762395 + 0.320038i
\(329\) 2.54163 2.20233i 0.140124 0.121419i
\(330\) −0.271904 + 2.04039i −0.0149678 + 0.112320i
\(331\) 19.8081 + 5.81617i 1.08875 + 0.319686i 0.776374 0.630273i \(-0.217057\pi\)
0.312376 + 0.949959i \(0.398875\pi\)
\(332\) −4.57205 14.4600i −0.250924 0.793598i
\(333\) −18.2965 11.7585i −1.00264 0.644360i
\(334\) −3.12064 3.52720i −0.170754 0.193000i
\(335\) 0.483818 + 0.419231i 0.0264338 + 0.0229050i
\(336\) −4.77013 25.6202i −0.260232 1.39770i
\(337\) −21.3091 + 3.06379i −1.16078 + 0.166895i −0.695674 0.718358i \(-0.744894\pi\)
−0.465109 + 0.885253i \(0.653985\pi\)
\(338\) −16.2869 + 7.64206i −0.885889 + 0.415673i
\(339\) 32.9405 15.0434i 1.78908 0.817046i
\(340\) 0.576480 2.12457i 0.0312640 0.115221i
\(341\) −0.893099 + 1.95561i −0.0483640 + 0.105902i
\(342\) 8.89272 20.0164i 0.480863 1.08237i
\(343\) −16.9616 + 10.9006i −0.915841 + 0.588575i
\(344\) 18.2286 + 19.7660i 0.982821 + 1.06571i
\(345\) −0.278395 + 14.4645i −0.0149883 + 0.778743i
\(346\) −3.84059 1.08478i −0.206471 0.0583179i
\(347\) 15.2256 9.78488i 0.817352 0.525280i −0.0638838 0.997957i \(-0.520349\pi\)
0.881236 + 0.472677i \(0.156712\pi\)
\(348\) −35.9561 29.8795i −1.92745 1.60171i
\(349\) 19.6330 + 8.96610i 1.05093 + 0.479944i 0.864557 0.502534i \(-0.167599\pi\)
0.186375 + 0.982479i \(0.440326\pi\)
\(350\) 0.0315190 + 3.05418i 0.00168476 + 0.163253i
\(351\) −4.49061 + 2.05079i −0.239691 + 0.109463i
\(352\) −1.67865 + 2.15222i −0.0894721 + 0.114714i
\(353\) −1.38940 9.66346i −0.0739501 0.514334i −0.992805 0.119739i \(-0.961794\pi\)
0.918855 0.394595i \(-0.129115\pi\)
\(354\) 25.2764 40.2378i 1.34342 2.13861i
\(355\) 4.28176 + 3.71016i 0.227252 + 0.196915i
\(356\) 31.6453 15.2489i 1.67720 0.808190i
\(357\) 3.87703 6.03278i 0.205194 0.319289i
\(358\) 4.45777 + 6.78152i 0.235600 + 0.358414i
\(359\) 12.9111 + 3.79103i 0.681419 + 0.200083i 0.604082 0.796922i \(-0.293540\pi\)
0.0773373 + 0.997005i \(0.475358\pi\)
\(360\) 13.3827 + 10.8895i 0.705329 + 0.573927i
\(361\) −8.22085 9.48736i −0.432676 0.499335i
\(362\) 15.2633 2.35554i 0.802220 0.123804i
\(363\) −31.1648 + 9.15081i −1.63573 + 0.480293i
\(364\) −1.27216 1.89247i −0.0666792 0.0991924i
\(365\) −1.77185 + 12.3235i −0.0927430 + 0.645042i
\(366\) −12.9098 42.3453i −0.674808 2.21343i
\(367\) 2.48501 0.129716 0.0648581 0.997894i \(-0.479341\pi\)
0.0648581 + 0.997894i \(0.479341\pi\)
\(368\) −10.0132 + 16.3626i −0.521975 + 0.852961i
\(369\) −32.2956 −1.68124
\(370\) 1.47043 + 4.82314i 0.0764441 + 0.250743i
\(371\) −0.196726 + 1.36826i −0.0102135 + 0.0710366i
\(372\) 14.9973 + 22.3101i 0.777574 + 1.15672i
\(373\) −33.3038 + 9.77889i −1.72441 + 0.506332i −0.985817 0.167824i \(-0.946326\pi\)
−0.738590 + 0.674155i \(0.764508\pi\)
\(374\) −0.742288 + 0.114555i −0.0383828 + 0.00592351i
\(375\) −1.97546 2.27981i −0.102012 0.117729i
\(376\) −2.77978 + 3.41622i −0.143356 + 0.176178i
\(377\) −3.92501 1.15249i −0.202148 0.0593561i
\(378\) 15.6892 + 23.8677i 0.806965 + 1.22762i
\(379\) 17.2970 26.9146i 0.888487 1.38251i −0.0352067 0.999380i \(-0.511209\pi\)
0.923693 0.383132i \(-0.125155\pi\)
\(380\) −4.57456 + 2.20434i −0.234670 + 0.113080i
\(381\) −32.6181 28.2638i −1.67108 1.44800i
\(382\) −9.00950 + 14.3423i −0.460966 + 0.733818i
\(383\) 1.09135 + 7.59048i 0.0557652 + 0.387855i 0.998521 + 0.0543709i \(0.0173153\pi\)
−0.942756 + 0.333484i \(0.891776\pi\)
\(384\) 11.9537 + 31.9673i 0.610008 + 1.63132i
\(385\) 0.947916 0.432899i 0.0483103 0.0220626i
\(386\) −0.203127 19.6829i −0.0103389 1.00183i
\(387\) −52.7486 24.0895i −2.68136 1.22454i
\(388\) −23.7141 19.7064i −1.20390 1.00044i
\(389\) −9.40313 + 6.04302i −0.476757 + 0.306393i −0.756860 0.653577i \(-0.773268\pi\)
0.280103 + 0.959970i \(0.409631\pi\)
\(390\) 2.16735 + 0.612169i 0.109748 + 0.0309984i
\(391\) −5.09261 + 1.38946i −0.257544 + 0.0702678i
\(392\) 4.85600 4.47831i 0.245265 0.226189i
\(393\) 17.0194 10.9377i 0.858516 0.551735i
\(394\) −5.67337 + 12.7701i −0.285820 + 0.643347i
\(395\) −0.777511 + 1.70251i −0.0391208 + 0.0856627i
\(396\) 1.54151 5.68110i 0.0774637 0.285486i
\(397\) 22.0159 10.0543i 1.10495 0.504612i 0.222456 0.974943i \(-0.428593\pi\)
0.882490 + 0.470331i \(0.155866\pi\)
\(398\) −31.5461 + 14.8020i −1.58127 + 0.741955i
\(399\) −16.3734 + 2.35414i −0.819696 + 0.117855i
\(400\) −0.732161 3.93242i −0.0366080 0.196621i
\(401\) −17.1431 14.8545i −0.856083 0.741800i 0.111658 0.993747i \(-0.464384\pi\)
−0.967741 + 0.251946i \(0.918929\pi\)
\(402\) −1.80970 2.04547i −0.0902597 0.102019i
\(403\) 1.97881 + 1.27171i 0.0985717 + 0.0633482i
\(404\) 7.27684 + 23.0145i 0.362036 + 1.14501i
\(405\) −9.50833 2.79190i −0.472473 0.138731i
\(406\) −3.12633 + 23.4603i −0.155157 + 1.16431i
\(407\) 1.30015 1.12658i 0.0644460 0.0558427i
\(408\) −3.63505 + 8.65943i −0.179962 + 0.428706i
\(409\) 28.0301 8.23037i 1.38600 0.406966i 0.498145 0.867094i \(-0.334015\pi\)
0.887853 + 0.460128i \(0.152196\pi\)
\(410\) 5.70889 + 4.84454i 0.281942 + 0.239255i
\(411\) 31.2029 + 4.48629i 1.53912 + 0.221293i
\(412\) 0.150581 0.00310831i 0.00741858 0.000153135i
\(413\) −24.0562 −1.18373
\(414\) 6.25309 40.8967i 0.307323 2.00997i
\(415\) 7.58281i 0.372226i
\(416\) 2.06942 + 2.15305i 0.101462 + 0.105562i
\(417\) −2.18201 + 15.1762i −0.106853 + 0.743181i
\(418\) 1.32098 + 1.12098i 0.0646113 + 0.0548289i
\(419\) 0.562285 + 1.91497i 0.0274694 + 0.0935522i 0.972087 0.234621i \(-0.0753851\pi\)
−0.944617 + 0.328174i \(0.893567\pi\)
\(420\) 1.58783 12.9332i 0.0774780 0.631074i
\(421\) 0.532308 + 0.614316i 0.0259431 + 0.0299399i 0.768573 0.639762i \(-0.220967\pi\)
−0.742630 + 0.669702i \(0.766422\pi\)
\(422\) 1.94508 + 0.259202i 0.0946850 + 0.0126178i
\(423\) 2.67606 9.11382i 0.130114 0.443129i
\(424\) −0.0560362 1.80945i −0.00272136 0.0878746i
\(425\) 0.595081 0.925965i 0.0288657 0.0449159i
\(426\) −16.0157 18.1023i −0.775965 0.877058i
\(427\) −14.6765 + 16.9376i −0.710245 + 0.819666i
\(428\) 10.7725 9.73086i 0.520709 0.470359i
\(429\) −0.109353 0.760570i −0.00527963 0.0367207i
\(430\) 5.71079 + 12.1709i 0.275399 + 0.586934i
\(431\) −5.50933 12.0638i −0.265375 0.581091i 0.729295 0.684199i \(-0.239848\pi\)
−0.994670 + 0.103109i \(0.967121\pi\)
\(432\) −25.6412 27.2344i −1.23367 1.31032i
\(433\) 35.5534 + 16.2367i 1.70859 + 0.780285i 0.996976 + 0.0777109i \(0.0247611\pi\)
0.711610 + 0.702574i \(0.247966\pi\)
\(434\) 5.52544 12.4371i 0.265230 0.597000i
\(435\) −12.6376 19.6646i −0.605929 0.942843i
\(436\) −7.35502 4.51506i −0.352241 0.216232i
\(437\) 10.1150 + 6.77902i 0.483864 + 0.324285i
\(438\) 14.4374 51.1146i 0.689844 2.44235i
\(439\) −3.58757 5.58236i −0.171225 0.266432i 0.745026 0.667035i \(-0.232437\pi\)
−0.916252 + 0.400603i \(0.868801\pi\)
\(440\) −1.12469 + 0.773011i −0.0536176 + 0.0368519i
\(441\) −5.91817 + 12.9590i −0.281818 + 0.617095i
\(442\) 0.00848006 + 0.821714i 0.000403355 + 0.0390850i
\(443\) −8.98524 19.6749i −0.426902 0.934784i −0.993819 0.111010i \(-0.964591\pi\)
0.566918 0.823775i \(-0.308136\pi\)
\(444\) −3.50013 21.2245i −0.166109 1.00727i
\(445\) 17.3851 2.49959i 0.824131 0.118492i
\(446\) −31.0703 19.5176i −1.47122 0.924185i
\(447\) 38.7810 44.7556i 1.83428 2.11687i
\(448\) 10.4850 13.7329i 0.495370 0.648820i
\(449\) −4.30542 2.76693i −0.203185 0.130579i 0.435091 0.900386i \(-0.356716\pi\)
−0.638277 + 0.769807i \(0.720352\pi\)
\(450\) 4.73857 + 7.20870i 0.223378 + 0.339821i
\(451\) 0.719703 2.45108i 0.0338895 0.115417i
\(452\) 22.0405 + 9.52086i 1.03670 + 0.447824i
\(453\) 37.4773 32.4743i 1.76084 1.52577i
\(454\) −2.27482 14.7403i −0.106763 0.691795i
\(455\) −0.321219 1.09397i −0.0150590 0.0512862i
\(456\) 20.5869 6.74373i 0.964070 0.315804i
\(457\) −7.73970 1.11280i −0.362048 0.0520546i −0.0411094 0.999155i \(-0.513089\pi\)
−0.320939 + 0.947100i \(0.603998\pi\)
\(458\) −1.99695 6.55015i −0.0933112 0.306068i
\(459\) 10.2931i 0.480440i
\(460\) −7.24013 + 6.29131i −0.337573 + 0.293334i
\(461\) 10.1583i 0.473120i 0.971617 + 0.236560i \(0.0760200\pi\)
−0.971617 + 0.236560i \(0.923980\pi\)
\(462\) −4.25245 + 1.29645i −0.197842 + 0.0603162i
\(463\) −36.0086 5.17726i −1.67346 0.240608i −0.760701 0.649102i \(-0.775145\pi\)
−0.912761 + 0.408494i \(0.866054\pi\)
\(464\) −1.27908 30.9690i −0.0593796 1.43770i
\(465\) 3.78681 + 12.8967i 0.175609 + 0.598070i
\(466\) −30.5856 + 4.72020i −1.41685 + 0.218659i
\(467\) −1.64133 + 1.42222i −0.0759517 + 0.0658125i −0.692009 0.721889i \(-0.743274\pi\)
0.616058 + 0.787701i \(0.288729\pi\)
\(468\) −5.91245 2.55400i −0.273303 0.118059i
\(469\) −0.389533 + 1.32663i −0.0179870 + 0.0612580i
\(470\) −1.84018 + 1.20962i −0.0848810 + 0.0557957i
\(471\) 12.0635 + 7.75276i 0.555858 + 0.357228i
\(472\) 31.0299 5.44663i 1.42827 0.250701i
\(473\) 3.00377 3.46654i 0.138114 0.159392i
\(474\) 4.24732 6.76136i 0.195086 0.310560i
\(475\) −2.51314 + 0.361335i −0.115311 + 0.0165792i
\(476\) 4.69109 0.773608i 0.215016 0.0354582i
\(477\) 1.62188 + 3.55143i 0.0742609 + 0.162609i
\(478\) 2.10447 0.0217180i 0.0962562 0.000993360i
\(479\) −9.93263 + 21.7494i −0.453834 + 0.993757i 0.535016 + 0.844842i \(0.320305\pi\)
−0.988850 + 0.148915i \(0.952422\pi\)
\(480\) 0.880106 + 17.0418i 0.0401712 + 0.777850i
\(481\) −1.01762 1.58344i −0.0463993 0.0721988i
\(482\) −11.0247 3.11394i −0.502162 0.141836i
\(483\) −28.6664 + 12.4305i −1.30437 + 0.565608i
\(484\) −18.3523 11.2660i −0.834195 0.512092i
\(485\) −8.33491 12.9694i −0.378469 0.588909i
\(486\) 2.37755 + 1.05627i 0.107848 + 0.0479136i
\(487\) −3.00977 1.37452i −0.136386 0.0622852i 0.346053 0.938215i \(-0.387522\pi\)
−0.482439 + 0.875930i \(0.660249\pi\)
\(488\) 15.0962 25.1705i 0.683371 1.13942i
\(489\) −26.8896 58.8800i −1.21599 2.66265i
\(490\) 2.99008 1.40300i 0.135078 0.0633809i
\(491\) −0.389973 2.71232i −0.0175993 0.122405i 0.979128 0.203245i \(-0.0651489\pi\)
−0.996727 + 0.0808398i \(0.974240\pi\)
\(492\) −21.4115 23.7035i −0.965304 1.06864i
\(493\) 5.58539 6.44589i 0.251553 0.290308i
\(494\) 1.41968 1.25604i 0.0638743 0.0565119i
\(495\) 1.59125 2.47603i 0.0715212 0.111289i
\(496\) −4.31130 + 17.2935i −0.193583 + 0.776502i
\(497\) −3.44734 + 11.7406i −0.154634 + 0.526637i
\(498\) −4.27312 + 32.0659i −0.191483 + 1.43691i
\(499\) 6.22175 + 7.18028i 0.278524 + 0.321433i 0.877725 0.479165i \(-0.159060\pi\)
−0.599201 + 0.800599i \(0.704515\pi\)
\(500\) 0.243714 1.98510i 0.0108992 0.0887762i
\(501\) 2.83021 + 9.63880i 0.126444 + 0.430630i
\(502\) −6.76431 + 7.97118i −0.301906 + 0.355771i
\(503\) −0.641039 + 4.45852i −0.0285825 + 0.198796i −0.999109 0.0421976i \(-0.986564\pi\)
0.970527 + 0.240993i \(0.0774732\pi\)
\(504\) −9.38642 + 36.0613i −0.418104 + 1.60630i
\(505\) 12.0688i 0.537052i
\(506\) 2.96452 + 1.38596i 0.131789 + 0.0616134i
\(507\) 38.3753 1.70431
\(508\) −0.590544 28.6087i −0.0262012 1.26931i
\(509\) 34.3259 + 4.93532i 1.52147 + 0.218754i 0.851785 0.523891i \(-0.175520\pi\)
0.669685 + 0.742646i \(0.266429\pi\)
\(510\) −3.03826 + 3.58034i −0.134536 + 0.158540i
\(511\) −25.8002 + 7.57561i −1.14133 + 0.335125i
\(512\) −10.4152 + 20.0879i −0.460290 + 0.887768i
\(513\) −17.9438 + 15.5484i −0.792239 + 0.686479i
\(514\) −36.5940 4.87653i −1.61409 0.215095i
\(515\) 0.0722560 + 0.0212163i 0.00318398 + 0.000934900i
\(516\) −17.2909 54.6860i −0.761189 2.40742i
\(517\) 0.632060 + 0.406200i 0.0277980 + 0.0178647i
\(518\) −8.15616 + 7.21606i −0.358361 + 0.317055i
\(519\) 6.43351 + 5.57467i 0.282400 + 0.244701i
\(520\) 0.662026 + 1.33838i 0.0290318 + 0.0586916i
\(521\) −17.3929 + 2.50073i −0.761998 + 0.109559i −0.512349 0.858777i \(-0.671225\pi\)
−0.249650 + 0.968336i \(0.580315\pi\)
\(522\) 28.3951 + 60.5161i 1.24282 + 2.64872i
\(523\) −4.36905 + 1.99528i −0.191045 + 0.0872474i −0.508641 0.860979i \(-0.669852\pi\)
0.317596 + 0.948226i \(0.397125\pi\)
\(524\) 12.9450 + 3.51249i 0.565504 + 0.153444i
\(525\) 2.70648 5.92637i 0.118121 0.258648i
\(526\) 38.0606 + 16.9092i 1.65952 + 0.737277i
\(527\) −4.12583 + 2.65151i −0.179724 + 0.115501i
\(528\) 5.19166 2.63508i 0.225938 0.114677i
\(529\) 21.8027 + 7.32422i 0.947942 + 0.318445i
\(530\) 0.246037 0.871078i 0.0106871 0.0378372i
\(531\) −57.1583 + 36.7334i −2.48046 + 1.59409i
\(532\) −8.43485 7.00935i −0.365697 0.303894i
\(533\) −2.54239 1.16107i −0.110123 0.0502916i
\(534\) −74.9258 + 0.773231i −3.24235 + 0.0334610i
\(535\) 6.60246 3.01524i 0.285449 0.130360i
\(536\) 0.202090 1.79940i 0.00872895 0.0777222i
\(537\) −2.46359 17.1346i −0.106312 0.739414i
\(538\) −12.5790 7.90183i −0.542320 0.340672i
\(539\) −0.851640 0.737950i −0.0366827 0.0317858i
\(540\) −8.11890 16.8487i −0.349382 0.725055i
\(541\) −6.25994 + 9.74066i −0.269136 + 0.418784i −0.949346 0.314234i \(-0.898252\pi\)
0.680210 + 0.733018i \(0.261889\pi\)
\(542\) 30.1691 19.8313i 1.29587 0.851829i
\(543\) −31.6086 9.28113i −1.35646 0.398291i
\(544\) −5.87584 + 2.05999i −0.251924 + 0.0883213i
\(545\) −2.82582 3.26117i −0.121045 0.139693i
\(546\) 0.741876 + 4.80716i 0.0317493 + 0.205727i
\(547\) −33.9732 + 9.97543i −1.45259 + 0.426519i −0.910397 0.413736i \(-0.864224\pi\)
−0.542192 + 0.840254i \(0.682406\pi\)
\(548\) 11.6599 + 17.3453i 0.498085 + 0.740955i
\(549\) −9.00841 + 62.6548i −0.384469 + 2.67404i
\(550\) −0.652704 + 0.198990i −0.0278314 + 0.00848497i
\(551\) −19.6742 −0.838148
\(552\) 34.1621 22.5244i 1.45403 0.958702i
\(553\) −4.04229 −0.171896
\(554\) 18.4463 5.62372i 0.783707 0.238929i
\(555\) 1.53068 10.6461i 0.0649737 0.451902i
\(556\) −8.43626 + 5.67103i −0.357777 + 0.240505i
\(557\) 10.2551 3.01117i 0.434523 0.127588i −0.0571534 0.998365i \(-0.518202\pi\)
0.491677 + 0.870778i \(0.336384\pi\)
\(558\) −5.86261 37.9882i −0.248184 1.60817i
\(559\) −3.28645 3.79277i −0.139002 0.160417i
\(560\) 7.06865 4.96652i 0.298705 0.209874i
\(561\) 1.53720 + 0.451362i 0.0649006 + 0.0190565i
\(562\) −27.8478 + 18.3055i −1.17469 + 0.772171i
\(563\) −3.30995 + 5.15038i −0.139498 + 0.217063i −0.903972 0.427591i \(-0.859362\pi\)
0.764474 + 0.644654i \(0.222999\pi\)
\(564\) 8.46332 4.07821i 0.356370 0.171724i
\(565\) 9.07240 + 7.86128i 0.381679 + 0.330726i
\(566\) −0.284278 0.178576i −0.0119491 0.00750611i
\(567\) −3.04590 21.1847i −0.127916 0.889674i
\(568\) 1.78848 15.9246i 0.0750429 0.668180i
\(569\) 4.58157 2.09233i 0.192069 0.0877151i −0.317059 0.948406i \(-0.602695\pi\)
0.509128 + 0.860691i \(0.329968\pi\)
\(570\) 10.8311 0.111776i 0.453663 0.00468179i
\(571\) 1.14558 + 0.523169i 0.0479411 + 0.0218939i 0.439241 0.898369i \(-0.355247\pi\)
−0.391300 + 0.920263i \(0.627975\pi\)
\(572\) 0.325595 0.391811i 0.0136138 0.0163825i
\(573\) 30.3933 19.5326i 1.26970 0.815985i
\(574\) −4.39551 + 15.5620i −0.183465 + 0.649547i
\(575\) −4.39997 + 1.90794i −0.183491 + 0.0795668i
\(576\) 3.94273 48.6402i 0.164280 2.02668i
\(577\) 29.1215 18.7152i 1.21234 0.779125i 0.231293 0.972884i \(-0.425704\pi\)
0.981049 + 0.193759i \(0.0620680\pi\)
\(578\) 20.4051 + 9.06541i 0.848742 + 0.377071i
\(579\) −17.4421 + 38.1930i −0.724871 + 1.58725i
\(580\) 4.05840 14.9569i 0.168516 0.621050i
\(581\) 14.8970 6.80324i 0.618032 0.282246i
\(582\) 27.9377 + 59.5413i 1.15806 + 2.46806i
\(583\) −0.305680 + 0.0439501i −0.0126600 + 0.00182023i
\(584\) 31.5641 15.6132i 1.30613 0.646078i
\(585\) −2.43370 2.10881i −0.100621 0.0871887i
\(586\) 27.7728 24.5716i 1.14729 1.01505i
\(587\) −19.2146 12.3484i −0.793070 0.509675i 0.0802778 0.996773i \(-0.474419\pi\)
−0.873348 + 0.487098i \(0.838056\pi\)
\(588\) −13.4350 + 4.24793i −0.554048 + 0.175182i
\(589\) 10.8547 + 3.18723i 0.447260 + 0.131327i
\(590\) 15.6141 + 2.08075i 0.642823 + 0.0856629i
\(591\) 22.5264 19.5192i 0.926612 0.802914i
\(592\) 8.88675 11.1546i 0.365243 0.458450i
\(593\) 2.90921 0.854220i 0.119467 0.0350786i −0.221453 0.975171i \(-0.571080\pi\)
0.340919 + 0.940092i \(0.389262\pi\)
\(594\) −4.12873 + 4.86536i −0.169404 + 0.199628i
\(595\) 2.35303 + 0.338315i 0.0964648 + 0.0138696i
\(596\) 39.2543 0.810292i 1.60792 0.0331909i
\(597\) 74.3294 3.04210
\(598\) 1.96255 2.99469i 0.0802548 0.122462i
\(599\) 16.2467i 0.663823i 0.943311 + 0.331911i \(0.107694\pi\)
−0.943311 + 0.331911i \(0.892306\pi\)
\(600\) −2.14926 + 8.25715i −0.0877432 + 0.337097i
\(601\) −4.84423 + 33.6924i −0.197600 + 1.37434i 0.613621 + 0.789601i \(0.289712\pi\)
−0.811221 + 0.584740i \(0.801197\pi\)
\(602\) −18.7870 + 22.1389i −0.765702 + 0.902315i
\(603\) 1.10019 + 3.74692i 0.0448034 + 0.152586i
\(604\) 32.6326 + 4.00637i 1.32780 + 0.163017i
\(605\) −7.05101 8.13730i −0.286664 0.330828i
\(606\) 6.80106 51.0358i 0.276274 2.07319i
\(607\) 6.33804 21.5854i 0.257253 0.876123i −0.725030 0.688718i \(-0.758174\pi\)
0.982283 0.187405i \(-0.0600078\pi\)
\(608\) 12.4670 + 7.13153i 0.505605 + 0.289222i
\(609\) 27.2941 42.4705i 1.10601 1.72099i
\(610\) 10.9910 9.72417i 0.445014 0.393720i
\(611\) 0.538321 0.621255i 0.0217781 0.0251333i
\(612\) 9.96489 9.00132i 0.402807 0.363857i
\(613\) 5.45865 + 37.9657i 0.220473 + 1.53342i 0.736256 + 0.676703i \(0.236592\pi\)
−0.515783 + 0.856719i \(0.672499\pi\)
\(614\) −6.60447 + 3.09893i −0.266535 + 0.125062i
\(615\) −6.63464 14.5278i −0.267535 0.585819i
\(616\) −2.52770 1.51601i −0.101844 0.0610816i
\(617\) 28.7781 + 13.1425i 1.15856 + 0.529098i 0.899568 0.436780i \(-0.143881\pi\)
0.258995 + 0.965879i \(0.416609\pi\)
\(618\) −0.293597 0.130437i −0.0118102 0.00524693i
\(619\) 16.2315 + 25.2568i 0.652401 + 1.01516i 0.997075 + 0.0764327i \(0.0243530\pi\)
−0.344674 + 0.938722i \(0.612011\pi\)
\(620\) −4.66213 + 7.59459i −0.187236 + 0.305006i
\(621\) −24.9681 + 37.2549i −1.00194 + 1.49499i
\(622\) 10.0449 + 2.83720i 0.402765 + 0.113761i
\(623\) 20.5084 + 31.9117i 0.821651 + 1.27851i
\(624\) −2.04534 6.03273i −0.0818790 0.241503i
\(625\) 0.415415 0.909632i 0.0166166 0.0363853i
\(626\) 48.1759 0.497173i 1.92550 0.0198710i
\(627\) −1.53519 3.36160i −0.0613096 0.134249i
\(628\) 1.54696 + 9.38061i 0.0617302 + 0.374327i
\(629\) 3.88453 0.558511i 0.154886 0.0222693i
\(630\) −9.91063 + 15.7769i −0.394849 + 0.628565i
\(631\) 25.8865 29.8746i 1.03052 1.18929i 0.0488334 0.998807i \(-0.484450\pi\)
0.981691 0.190481i \(-0.0610049\pi\)
\(632\) 5.21411 0.915225i 0.207406 0.0364057i
\(633\) −3.52121 2.26294i −0.139955 0.0899439i
\(634\) −11.8735 + 7.80495i −0.471558 + 0.309974i
\(635\) 4.03086 13.7279i 0.159960 0.544773i
\(636\) −1.53130 + 3.54493i −0.0607202 + 0.140566i
\(637\) −0.931787 + 0.807398i −0.0369187 + 0.0319903i
\(638\) −5.22567 + 0.806463i −0.206886 + 0.0319282i
\(639\) 9.73664 + 33.1600i 0.385176 + 1.31179i
\(640\) −7.99330 + 8.00670i −0.315963 + 0.316492i
\(641\) −28.7879 4.13908i −1.13705 0.163484i −0.452029 0.892003i \(-0.649300\pi\)
−0.685025 + 0.728520i \(0.740209\pi\)
\(642\) −29.6194 + 9.03006i −1.16898 + 0.356388i
\(643\) 27.9770i 1.10330i −0.834075 0.551652i \(-0.813998\pi\)
0.834075 0.551652i \(-0.186002\pi\)
\(644\) −18.8555 8.57927i −0.743012 0.338071i
\(645\) 28.6772i 1.12917i
\(646\) 1.15254 + 3.78044i 0.0453462 + 0.148739i
\(647\) −32.3132 4.64594i −1.27036 0.182651i −0.526034 0.850464i \(-0.676322\pi\)
−0.744329 + 0.667813i \(0.767231\pi\)
\(648\) 8.72536 + 26.6363i 0.342764 + 1.04637i
\(649\) −1.51413 5.15664i −0.0594347 0.202416i
\(650\) 0.113870 + 0.737845i 0.00446633 + 0.0289407i
\(651\) −21.9390 + 19.0103i −0.859859 + 0.745072i
\(652\) 17.0182 39.3967i 0.666485 1.54290i
\(653\) −13.4885 + 45.9377i −0.527847 + 1.79768i 0.0718044 + 0.997419i \(0.477124\pi\)
−0.599651 + 0.800262i \(0.704694\pi\)
\(654\) 10.1120 + 15.3831i 0.395409 + 0.601528i
\(655\) 5.64189 + 3.62582i 0.220447 + 0.141673i
\(656\) 2.14628 21.0685i 0.0837981 0.822586i
\(657\) −49.7341 + 57.3962i −1.94031 + 2.23924i
\(658\) −4.02739 2.52990i −0.157004 0.0986259i
\(659\) 1.37730 0.198026i 0.0536522 0.00771402i −0.115436 0.993315i \(-0.536827\pi\)
0.169089 + 0.985601i \(0.445918\pi\)
\(660\) 2.87226 0.473665i 0.111803 0.0184374i
\(661\) 2.23170 + 4.88675i 0.0868032 + 0.190072i 0.948055 0.318105i \(-0.103047\pi\)
−0.861252 + 0.508178i \(0.830319\pi\)
\(662\) −0.301280 29.1939i −0.0117096 1.13465i
\(663\) 0.728167 1.59446i 0.0282797 0.0619238i
\(664\) −17.6752 + 12.1483i −0.685929 + 0.471445i
\(665\) −2.96464 4.61306i −0.114964 0.178887i
\(666\) −8.36050 + 29.5999i −0.323963 + 1.14697i
\(667\) −35.8517 + 9.78171i −1.38818 + 0.378749i
\(668\) −3.48441 + 5.67608i −0.134816 + 0.219614i
\(669\) 42.3141 + 65.8421i 1.63596 + 2.54560i
\(670\) 0.367580 0.827378i 0.0142009 0.0319644i
\(671\) −4.55446 2.07995i −0.175823 0.0802956i
\(672\) −32.6904 + 17.0188i −1.26106 + 0.656516i
\(673\) −18.8281 41.2279i −0.725772 1.58922i −0.805635 0.592412i \(-0.798176\pi\)
0.0798633 0.996806i \(-0.474552\pi\)
\(674\) 12.9327 + 27.5623i 0.498147 + 1.06166i
\(675\) −1.33085 9.25624i −0.0512243 0.356273i
\(676\) 17.0547 + 18.8803i 0.655948 + 0.726165i
\(677\) 22.1074 25.5134i 0.849658 0.980558i −0.150309 0.988639i \(-0.548027\pi\)
0.999967 + 0.00808129i \(0.00257238\pi\)
\(678\) −33.9349 38.3560i −1.30326 1.47305i
\(679\) 18.0013 28.0106i 0.690827 1.07495i
\(680\) −3.11175 + 0.0963667i −0.119330 + 0.00369549i
\(681\) −8.96311 + 30.5255i −0.343467 + 1.16974i
\(682\) 3.01377 + 0.401617i 0.115403 + 0.0153787i
\(683\) 15.2167 + 17.5610i 0.582252 + 0.671954i 0.968087 0.250613i \(-0.0806323\pi\)
−0.385836 + 0.922568i \(0.626087\pi\)
\(684\) −30.7446 3.77457i −1.17555 0.144324i
\(685\) 2.94411 + 10.0267i 0.112489 + 0.383102i
\(686\) 21.7408 + 18.4492i 0.830069 + 0.704394i
\(687\) −2.07877 + 14.4581i −0.0793099 + 0.551612i
\(688\) 19.2206 32.8104i 0.732780 1.25088i
\(689\) 0.337886i 0.0128724i
\(690\) 19.6816 5.58873i 0.749265 0.212759i
\(691\) 19.9812 0.760121 0.380061 0.924962i \(-0.375903\pi\)
0.380061 + 0.924962i \(0.375903\pi\)
\(692\) 0.116477 + 5.64270i 0.00442781 + 0.214503i
\(693\) 6.29200 + 0.904653i 0.239013 + 0.0343649i
\(694\) −19.5156 16.5609i −0.740804 0.628644i
\(695\) −4.87672 + 1.43193i −0.184984 + 0.0543163i
\(696\) −25.5906 + 60.9620i −0.970008 + 2.31076i
\(697\) 4.40414 3.81621i 0.166819 0.144549i
\(698\) 4.03196 30.2562i 0.152612 1.14521i
\(699\) 63.3396 + 18.5982i 2.39572 + 0.703448i
\(700\) 4.11853 1.30222i 0.155666 0.0492192i
\(701\) 31.8196 + 20.4492i 1.20181 + 0.772357i 0.979269 0.202566i \(-0.0649281\pi\)
0.222542 + 0.974923i \(0.428564\pi\)
\(702\) 4.62617 + 5.22887i 0.174604 + 0.197351i
\(703\) −6.84150 5.92819i −0.258032 0.223586i
\(704\) 3.60370 + 1.38318i 0.135820 + 0.0521304i
\(705\) 4.64952 0.668499i 0.175111 0.0251771i
\(706\) −12.4992 + 5.86482i −0.470413 + 0.220725i
\(707\) −23.7100 + 10.8280i −0.891706 + 0.407228i
\(708\) −64.8557 17.5979i −2.43743 0.661371i
\(709\) −3.51131 + 7.68869i −0.131870 + 0.288755i −0.964036 0.265772i \(-0.914373\pi\)
0.832166 + 0.554526i \(0.187101\pi\)
\(710\) 3.25306 7.32224i 0.122085 0.274799i
\(711\) −9.60460 + 6.17250i −0.360201 + 0.231487i
\(712\) −33.6787 36.5192i −1.26216 1.36861i
\(713\) 21.3649 + 0.411204i 0.800120 + 0.0153997i
\(714\) −9.75974 2.75665i −0.365249 0.103165i
\(715\) 0.214284 0.137712i 0.00801376 0.00515013i
\(716\) 7.33522 8.82699i 0.274130 0.329880i
\(717\) −4.08354 1.86489i −0.152503 0.0696456i
\(718\) −0.196377 19.0288i −0.00732871 0.710149i
\(719\) 14.8438 6.77892i 0.553579 0.252811i −0.118927 0.992903i \(-0.537945\pi\)
0.672506 + 0.740092i \(0.265218\pi\)
\(720\) 9.21154 22.5943i 0.343294 0.842040i
\(721\) 0.0231465 + 0.160987i 0.000862021 + 0.00599548i
\(722\) −9.44360 + 15.0334i −0.351454 + 0.559485i
\(723\) 18.4679 + 16.0025i 0.686828 + 0.595140i
\(724\) −9.48119 19.6758i −0.352366 0.731247i
\(725\) 4.18934 6.51875i 0.155588 0.242100i
\(726\) 25.2314 + 38.3841i 0.936426 + 1.42457i
\(727\) −46.3222 13.6014i −1.71799 0.504449i −0.733474 0.679718i \(-0.762102\pi\)
−0.984521 + 0.175269i \(0.943921\pi\)
\(728\) −2.03538 + 2.50138i −0.0754360 + 0.0927073i
\(729\) 15.8344 + 18.2739i 0.586459 + 0.676810i
\(730\) 17.4013 2.68549i 0.644050 0.0993945i
\(731\) 10.0398 2.94796i 0.371337 0.109034i
\(732\) −51.9582 + 34.9274i −1.92043 + 1.29095i
\(733\) 3.43211 23.8708i 0.126768 0.881689i −0.822846 0.568265i \(-0.807615\pi\)
0.949613 0.313424i \(-0.101476\pi\)
\(734\) −1.02484 3.36158i −0.0378277 0.124078i
\(735\) −7.04527 −0.259869
\(736\) 26.2640 + 6.79718i 0.968104 + 0.250548i
\(737\) −0.308891 −0.0113781
\(738\) 13.3191 + 43.6877i 0.490282 + 1.60817i
\(739\) −2.53589 + 17.6375i −0.0932841 + 0.648805i 0.888510 + 0.458857i \(0.151741\pi\)
−0.981794 + 0.189948i \(0.939168\pi\)
\(740\) 5.91805 3.97824i 0.217552 0.146243i
\(741\) −3.87956 + 1.13914i −0.142519 + 0.0418474i
\(742\) 1.93204 0.298167i 0.0709275 0.0109460i
\(743\) −9.61820 11.1000i −0.352858 0.407220i 0.551376 0.834257i \(-0.314103\pi\)
−0.904234 + 0.427037i \(0.859557\pi\)
\(744\) 23.9948 29.4884i 0.879691 1.08110i
\(745\) 18.8361 + 5.53079i 0.690102 + 0.202632i
\(746\) 26.9632 + 41.0186i 0.987193 + 1.50180i
\(747\) 25.0073 38.9121i 0.914970 1.42372i
\(748\) 0.461092 + 0.956881i 0.0168592 + 0.0349870i
\(749\) 11.8473 + 10.2658i 0.432893 + 0.375104i
\(750\) −2.26929 + 3.61251i −0.0828628 + 0.131910i
\(751\) −3.93244 27.3507i −0.143497 0.998042i −0.926573 0.376116i \(-0.877259\pi\)
0.783076 0.621926i \(-0.213650\pi\)
\(752\) 5.76769 + 2.35145i 0.210326 + 0.0857484i
\(753\) 20.2849 9.26379i 0.739222 0.337591i
\(754\) 0.0596992 + 5.78483i 0.00217412 + 0.210671i
\(755\) 14.9533 + 6.82893i 0.544205 + 0.248530i
\(756\) 25.8164 31.0668i 0.938935 1.12989i
\(757\) −15.5677 + 10.0047i −0.565817 + 0.363629i −0.792061 0.610442i \(-0.790992\pi\)
0.226244 + 0.974071i \(0.427355\pi\)
\(758\) −43.5421 12.2985i −1.58152 0.446701i
\(759\) −4.46887 5.36248i −0.162210 0.194646i
\(760\) 4.86851 + 5.27911i 0.176599 + 0.191493i
\(761\) 11.1789 7.18426i 0.405236 0.260429i −0.322107 0.946703i \(-0.604391\pi\)
0.727343 + 0.686274i \(0.240755\pi\)
\(762\) −24.7815 + 55.7802i −0.897741 + 2.02071i
\(763\) 3.87152 8.47744i 0.140158 0.306904i
\(764\) 23.1171 + 6.27260i 0.836349 + 0.226935i
\(765\) 6.10747 2.78919i 0.220816 0.100843i
\(766\) 9.81789 4.60671i 0.354735 0.166447i
\(767\) −5.82026 + 0.836828i −0.210158 + 0.0302161i
\(768\) 38.3137 29.3539i 1.38253 1.05922i
\(769\) −20.0940 17.4116i −0.724610 0.627878i 0.212399 0.977183i \(-0.431872\pi\)
−0.937009 + 0.349305i \(0.886418\pi\)
\(770\) −0.976532 1.10376i −0.0351918 0.0397766i
\(771\) 66.2466 + 42.5741i 2.38581 + 1.53327i
\(772\) −26.5422 + 8.39224i −0.955274 + 0.302043i
\(773\) 31.0683 + 9.12246i 1.11745 + 0.328112i 0.787763 0.615979i \(-0.211239\pi\)
0.329685 + 0.944091i \(0.393058\pi\)
\(774\) −10.8328 + 81.2901i −0.389376 + 2.92191i
\(775\) −3.36740 + 2.91787i −0.120960 + 0.104813i
\(776\) −16.8778 + 40.2063i −0.605876 + 1.44332i
\(777\) 22.2884 6.54447i 0.799592 0.234781i
\(778\) 12.0526 + 10.2278i 0.432107 + 0.366685i
\(779\) −13.3055 1.91304i −0.476719 0.0685419i
\(780\) −0.0657314 3.18434i −0.00235356 0.114018i
\(781\) −2.73366 −0.0978182
\(782\) 3.97983 + 6.31597i 0.142318 + 0.225859i
\(783\) 72.4628i 2.58961i
\(784\) −8.06067 4.72202i −0.287881 0.168644i
\(785\) −0.676516 + 4.70527i −0.0241459 + 0.167938i
\(786\) −21.8149 18.5121i −0.778113 0.660304i
\(787\) 4.99819 + 17.0223i 0.178166 + 0.606778i 0.999348 + 0.0361113i \(0.0114971\pi\)
−0.821182 + 0.570667i \(0.806685\pi\)
\(788\) 19.6144 + 2.40810i 0.698734 + 0.0857848i
\(789\) −58.1762 67.1389i −2.07113 2.39021i
\(790\) 2.62372 + 0.349638i 0.0933477 + 0.0124396i
\(791\) −7.30440 + 24.8765i −0.259714 + 0.884506i
\(792\) −8.32081 + 0.257684i −0.295667 + 0.00915642i
\(793\) −2.96169 + 4.60848i −0.105173 + 0.163652i
\(794\) −22.6805 25.6353i −0.804902 0.909764i
\(795\) −1.26438 + 1.45917i −0.0448430 + 0.0517516i
\(796\) 33.0333 + 36.5694i 1.17083 + 1.29617i
\(797\) −7.31696 50.8906i −0.259180 1.80264i −0.538700 0.842498i \(-0.681084\pi\)
0.279520 0.960140i \(-0.409825\pi\)
\(798\) 9.93714 + 21.1782i 0.351771 + 0.749699i
\(799\) 0.712001 + 1.55906i 0.0251888 + 0.0551557i
\(800\) −5.01761 + 2.61220i −0.177399 + 0.0923553i
\(801\) 97.4570 + 44.5071i 3.44347 + 1.57258i
\(802\) −13.0244 + 29.3164i −0.459908 + 1.03520i
\(803\) −3.24778 5.05365i −0.114612 0.178339i
\(804\) −2.02066 + 3.29164i −0.0712630 + 0.116087i
\(805\) −7.69592 6.93229i −0.271246 0.244331i
\(806\) 0.904208 3.20129i 0.0318494 0.112761i
\(807\) 17.1311 + 26.6566i 0.603045 + 0.938356i
\(808\) 28.1317 19.3351i 0.989669 0.680208i
\(809\) −2.89540 + 6.34003i −0.101797 + 0.222904i −0.953677 0.300833i \(-0.902735\pi\)
0.851880 + 0.523737i \(0.175463\pi\)
\(810\) 0.144621 + 14.0138i 0.00508148 + 0.492393i
\(811\) 12.3249 + 26.9877i 0.432784 + 0.947665i 0.992867 + 0.119229i \(0.0380421\pi\)
−0.560083 + 0.828437i \(0.689231\pi\)
\(812\) 33.0251 5.44616i 1.15895 0.191123i
\(813\) −76.2272 + 10.9598i −2.67340 + 0.384377i
\(814\) −2.06018 1.29415i −0.0722092 0.0453600i
\(815\) 14.0518 16.2166i 0.492212 0.568043i
\(816\) 13.2131 + 1.34604i 0.462552 + 0.0471209i
\(817\) −20.3050 13.0492i −0.710383 0.456535i
\(818\) −22.6935 34.5232i −0.793460 1.20708i
\(819\) 1.95943 6.67320i 0.0684680 0.233181i
\(820\) 4.19902 9.72061i 0.146636 0.339458i
\(821\) 19.8523 17.2021i 0.692851 0.600359i −0.235584 0.971854i \(-0.575700\pi\)
0.928435 + 0.371495i \(0.121155\pi\)
\(822\) −6.79961 44.0597i −0.237164 1.53676i
\(823\) −9.50782 32.3806i −0.331422 1.12872i −0.941678 0.336515i \(-0.890752\pi\)
0.610257 0.792204i \(-0.291066\pi\)
\(824\) −0.0663060 0.202415i −0.00230988 0.00705147i
\(825\) 1.44071 + 0.207143i 0.0501592 + 0.00721181i
\(826\) 9.92107 + 32.5419i 0.345198 + 1.13228i
\(827\) 5.58209i 0.194108i −0.995279 0.0970541i \(-0.969058\pi\)
0.995279 0.0970541i \(-0.0309420\pi\)
\(828\) −57.9017 + 8.40745i −2.01222 + 0.292179i
\(829\) 3.72702i 0.129445i −0.997903 0.0647224i \(-0.979384\pi\)
0.997903 0.0647224i \(-0.0206162\pi\)
\(830\) −10.2576 + 3.12724i −0.356047 + 0.108548i
\(831\) −40.7164 5.85414i −1.41244 0.203078i
\(832\) 2.05907 3.68734i 0.0713853 0.127835i
\(833\) −0.724239 2.46653i −0.0250934 0.0854603i
\(834\) 21.4294 3.30714i 0.742039 0.114517i
\(835\) −2.51674 + 2.18077i −0.0870955 + 0.0754687i
\(836\) 0.971611 2.24925i 0.0336039 0.0777920i
\(837\) −11.7390 + 39.9794i −0.405760 + 1.38189i
\(838\) 2.35857 1.55038i 0.0814753 0.0535570i
\(839\) 28.2402 + 18.1489i 0.974960 + 0.626569i 0.928099 0.372333i \(-0.121442\pi\)
0.0468605 + 0.998901i \(0.485078\pi\)
\(840\) −18.1501 + 3.18586i −0.626238 + 0.109923i
\(841\) 20.3299 23.4620i 0.701033 0.809035i
\(842\) 0.611483 0.973428i 0.0210731 0.0335465i
\(843\) 70.3622 10.1166i 2.42340 0.348433i
\(844\) −0.451538 2.73809i −0.0155426 0.0942490i
\(845\) 5.28462 + 11.5717i 0.181797 + 0.398079i
\(846\) −13.4323 + 0.138621i −0.461812 + 0.00476588i
\(847\) 9.66024 21.1530i 0.331930 0.726825i
\(848\) −2.42461 + 0.822040i −0.0832615 + 0.0282290i
\(849\) 0.387152 + 0.602421i 0.0132870 + 0.0206750i
\(850\) −1.49801 0.423114i −0.0513814 0.0145127i
\(851\) −15.4145 7.40130i −0.528402 0.253713i
\(852\) −17.8827 + 29.1308i −0.612650 + 0.998004i
\(853\) 13.9572 + 21.7178i 0.477885 + 0.743603i 0.993575 0.113172i \(-0.0361010\pi\)
−0.515691 + 0.856775i \(0.672465\pi\)
\(854\) 28.9649 + 12.8683i 0.991160 + 0.440343i
\(855\) −14.0881 6.43383i −0.481803 0.220032i
\(856\) −17.6061 10.5593i −0.601763 0.360911i
\(857\) 2.45977 + 5.38615i 0.0840243 + 0.183988i 0.946980 0.321291i \(-0.104117\pi\)
−0.862956 + 0.505279i \(0.831390\pi\)
\(858\) −0.983758 + 0.461595i −0.0335849 + 0.0157586i
\(859\) 7.36933 + 51.2548i 0.251438 + 1.74879i 0.589592 + 0.807701i \(0.299289\pi\)
−0.338154 + 0.941091i \(0.609802\pi\)
\(860\) 14.1089 12.7447i 0.481111 0.434589i
\(861\) 22.5885 26.0685i 0.769814 0.888413i
\(862\) −14.0471 + 12.4279i −0.478445 + 0.423298i
\(863\) −25.8137 + 40.1668i −0.878707 + 1.36730i 0.0508847 + 0.998705i \(0.483796\pi\)
−0.929592 + 0.368590i \(0.879840\pi\)
\(864\) −26.2665 + 45.9178i −0.893603 + 1.56216i
\(865\) −0.795036 + 2.70764i −0.0270320 + 0.0920627i
\(866\) 7.30146 54.7908i 0.248114 1.86187i
\(867\) −31.1895 35.9946i −1.05925 1.22244i
\(868\) −19.1030 2.34531i −0.648397 0.0796049i
\(869\) −0.254427 0.866497i −0.00863083 0.0293939i
\(870\) −21.3892 + 25.2054i −0.725162 + 0.854543i
\(871\) −0.0480968 + 0.334520i −0.00162970 + 0.0113348i
\(872\) −3.07443 + 11.8115i −0.104113 + 0.399989i
\(873\) 94.0416i 3.18283i
\(874\) 4.99876 16.4787i 0.169086 0.557401i
\(875\) 2.15975 0.0730128
\(876\) −75.0991 + 1.55021i −2.53736 + 0.0523766i
\(877\) −29.2485 4.20530i −0.987652 0.142003i −0.370488 0.928837i \(-0.620810\pi\)
−0.617164 + 0.786834i \(0.711719\pi\)
\(878\) −6.07195 + 7.15529i −0.204919 + 0.241479i
\(879\) −75.8950 + 22.2848i −2.55988 + 0.751647i
\(880\) 1.50952 + 1.20262i 0.0508860 + 0.0405404i
\(881\) −39.5717 + 34.2891i −1.33321 + 1.15523i −0.358052 + 0.933702i \(0.616559\pi\)
−0.975154 + 0.221528i \(0.928896\pi\)
\(882\) 19.9709 + 2.66134i 0.672456 + 0.0896118i
\(883\) 40.2636 + 11.8225i 1.35498 + 0.397858i 0.876990 0.480508i \(-0.159548\pi\)
0.477989 + 0.878366i \(0.341366\pi\)
\(884\) 1.10807 0.350356i 0.0372685 0.0117837i
\(885\) −28.2665 18.1658i −0.950167 0.610635i
\(886\) −22.9095 + 20.2689i −0.769661 + 0.680947i
\(887\) −8.68381 7.52457i −0.291574 0.252650i 0.496774 0.867880i \(-0.334518\pi\)
−0.788348 + 0.615230i \(0.789063\pi\)
\(888\) −27.2678 + 13.4880i −0.915049 + 0.452628i
\(889\) 30.5859 4.39758i 1.02582 0.147490i
\(890\) −10.5511 22.4867i −0.353674 0.753755i
\(891\) 4.34940 1.98630i 0.145710 0.0665437i
\(892\) −13.5886 + 50.0795i −0.454979 + 1.67679i
\(893\) 1.64237 3.59630i 0.0549600 0.120346i
\(894\) −76.5367 34.0030i −2.55977 1.13723i
\(895\) 4.82753 3.10247i 0.161367 0.103704i
\(896\) −22.9013 8.51990i −0.765078 0.284630i
\(897\) −6.50325 + 4.00469i −0.217137 + 0.133713i
\(898\) −1.96734 + 6.96525i −0.0656509 + 0.232433i
\(899\) −29.0456 + 18.6665i −0.968726 + 0.622562i
\(900\) 7.79728 9.38302i 0.259909 0.312767i
\(901\) −0.640830 0.292657i −0.0213491 0.00974982i
\(902\) −3.61250 + 0.0372809i −0.120283 + 0.00124132i
\(903\) 56.3386 25.7290i 1.87483 0.856207i
\(904\) 3.78952 33.7417i 0.126037 1.12223i
\(905\) −1.55415 10.8094i −0.0516618 0.359316i
\(906\) −59.3855 37.3045i −1.97295 1.23936i
\(907\) −31.9429 27.6787i −1.06065 0.919055i −0.0637648 0.997965i \(-0.520311\pi\)
−0.996882 + 0.0789095i \(0.974856\pi\)
\(908\) −19.0016 + 9.15631i −0.630592 + 0.303863i
\(909\) −39.8015 + 61.9323i −1.32013 + 2.05416i
\(910\) −1.34739 + 0.885694i −0.0446655 + 0.0293605i
\(911\) 45.0086 + 13.2157i 1.49120 + 0.437856i 0.922925 0.384981i \(-0.125792\pi\)
0.568277 + 0.822837i \(0.307610\pi\)
\(912\) −17.6128 25.0676i −0.583218 0.830071i
\(913\) 2.39596 + 2.76509i 0.0792948 + 0.0915111i
\(914\) 1.68661 + 10.9288i 0.0557880 + 0.361492i
\(915\) −30.0353 + 8.81915i −0.992936 + 0.291552i
\(916\) −8.03711 + 5.40271i −0.265554 + 0.178511i
\(917\) −2.06135 + 14.3370i −0.0680717 + 0.473449i
\(918\) −13.9239 + 4.24499i −0.459557 + 0.140105i
\(919\) 36.6864 1.21017 0.605086 0.796160i \(-0.293139\pi\)
0.605086 + 0.796160i \(0.293139\pi\)
\(920\) 11.4964 + 7.19943i 0.379026 + 0.237358i
\(921\) 15.5615 0.512770
\(922\) 13.7416 4.18941i 0.452556 0.137971i
\(923\) −0.425653 + 2.96048i −0.0140105 + 0.0974455i
\(924\) 3.50752 + 5.21781i 0.115389 + 0.171653i
\(925\) 3.42102 1.00450i 0.112483 0.0330278i
\(926\) 7.84686 + 50.8456i 0.257864 + 1.67089i
\(927\) 0.300821 + 0.347166i 0.00988027 + 0.0114024i
\(928\) −41.3656 + 14.5022i −1.35789 + 0.476059i
\(929\) 11.4060 + 3.34911i 0.374220 + 0.109881i 0.463434 0.886132i \(-0.346617\pi\)
−0.0892137 + 0.996013i \(0.528435\pi\)
\(930\) 15.8842 10.4413i 0.520863 0.342385i
\(931\) −3.20587 + 4.98843i −0.105068 + 0.163489i
\(932\) 18.9991 + 39.4279i 0.622336 + 1.29150i
\(933\) −16.8266 14.5804i −0.550879 0.477339i
\(934\) 2.60080 + 1.63376i 0.0851009 + 0.0534583i
\(935\) 0.0755820 + 0.525685i 0.00247180 + 0.0171917i
\(936\) −1.01655 + 9.05133i −0.0332270 + 0.295852i
\(937\) −26.6807 + 12.1846i −0.871619 + 0.398055i −0.800443 0.599409i \(-0.795402\pi\)
−0.0711760 + 0.997464i \(0.522675\pi\)
\(938\) 1.95524 0.0201780i 0.0638408 0.000658834i
\(939\) −93.4811 42.6914i −3.05064 1.39318i
\(940\) 2.39522 + 1.99043i 0.0781235 + 0.0649205i
\(941\) 22.9173 14.7281i 0.747083 0.480121i −0.110879 0.993834i \(-0.535367\pi\)
0.857962 + 0.513713i \(0.171730\pi\)
\(942\) 5.51236 19.5162i 0.179603 0.635872i
\(943\) −25.1974 + 3.12921i −0.820541 + 0.101901i
\(944\) −20.1650 39.7292i −0.656314 1.29308i
\(945\) 16.9906 10.9192i 0.552703 0.355201i
\(946\) −5.92813 2.63370i −0.192740 0.0856288i
\(947\) 25.2679 55.3290i 0.821097 1.79795i 0.271723 0.962375i \(-0.412406\pi\)
0.549374 0.835577i \(-0.314866\pi\)
\(948\) −10.8980 2.95707i −0.353952 0.0960412i
\(949\) −5.97867 + 2.73037i −0.194076 + 0.0886314i
\(950\) 1.52524 + 3.25061i 0.0494853 + 0.105464i
\(951\) 30.0004 4.31341i 0.972831 0.139872i
\(952\) −2.98115 6.02681i −0.0966198 0.195330i
\(953\) −31.7643 27.5239i −1.02895 0.891588i −0.0347756 0.999395i \(-0.511072\pi\)
−0.994172 + 0.107807i \(0.965617\pi\)
\(954\) 4.13529 3.65864i 0.133885 0.118453i
\(955\) 10.0753 + 6.47499i 0.326029 + 0.209526i
\(956\) −0.897286 2.83785i −0.0290203 0.0917827i
\(957\) 10.8218 + 3.17757i 0.349819 + 0.102716i
\(958\) 33.5177 + 4.46659i 1.08291 + 0.144309i
\(959\) −17.0568 + 14.7798i −0.550794 + 0.477266i
\(960\) 22.6903 8.21881i 0.732326 0.265261i
\(961\) −10.6952 + 3.14038i −0.345005 + 0.101303i
\(962\) −1.72232 + 2.02961i −0.0555297 + 0.0654371i
\(963\) 43.8253 + 6.30113i 1.41225 + 0.203051i
\(964\) 0.334358 + 16.1978i 0.0107689 + 0.521697i
\(965\) −13.9187 −0.448058
\(966\) 28.6376 + 33.6518i 0.921401 + 1.08273i
\(967\) 21.6758i 0.697046i 0.937300 + 0.348523i \(0.113317\pi\)
−0.937300 + 0.348523i \(0.886683\pi\)
\(968\) −7.67134 + 29.4722i −0.246566 + 0.947272i
\(969\) 1.19977 8.34457i 0.0385421 0.268066i
\(970\) −14.1068 + 16.6237i −0.452943 + 0.533755i
\(971\) −2.40507 8.19093i −0.0771825 0.262859i 0.911858 0.410507i \(-0.134648\pi\)
−0.989040 + 0.147647i \(0.952830\pi\)
\(972\) 0.448342 3.65183i 0.0143806 0.117133i
\(973\) −7.18849 8.29596i −0.230452 0.265956i
\(974\) −0.618105 + 4.63831i −0.0198053 + 0.148621i
\(975\) 0.448661 1.52800i 0.0143687 0.0489351i
\(976\) −40.2751 10.0406i −1.28917 0.321393i
\(977\) 11.5671 17.9987i 0.370063 0.575829i −0.605420 0.795907i \(-0.706995\pi\)
0.975482 + 0.220077i \(0.0706310\pi\)
\(978\) −68.5600 + 60.6575i −2.19231 + 1.93961i
\(979\) −5.54969 + 6.40469i −0.177369 + 0.204695i
\(980\) −3.13104 3.46621i −0.100017 0.110724i
\(981\) −3.74605 26.0544i −0.119602 0.831852i
\(982\) −3.50825 + 1.64613i −0.111953 + 0.0525301i
\(983\) −11.4282 25.0243i −0.364503 0.798150i −0.999668 0.0257736i \(-0.991795\pi\)
0.635165 0.772377i \(-0.280932\pi\)
\(984\) −23.2344 + 38.7398i −0.740687 + 1.23498i
\(985\) 8.98792 + 4.10465i 0.286379 + 0.130785i
\(986\) −11.0231 4.89725i −0.351048 0.155960i
\(987\) 5.48483 + 8.53456i 0.174584 + 0.271658i
\(988\) −2.28459 1.40245i −0.0726825 0.0446180i
\(989\) −43.4892 13.6839i −1.38288 0.435124i
\(990\) −4.00568 1.13141i −0.127309 0.0359585i
\(991\) 6.78346 + 10.5553i 0.215484 + 0.335299i 0.932121 0.362147i \(-0.117956\pi\)
−0.716637 + 0.697446i \(0.754320\pi\)
\(992\) 25.1717 1.29996i 0.799203 0.0412739i
\(993\) −25.8704 + 56.6482i −0.820971 + 1.79768i
\(994\) 17.3037 0.178574i 0.548840 0.00566401i
\(995\) 10.2358 + 22.4133i 0.324497 + 0.710550i
\(996\) 45.1392 7.44390i 1.43029 0.235869i
\(997\) 5.90824 0.849477i 0.187116 0.0269032i −0.0481198 0.998842i \(-0.515323\pi\)
0.235236 + 0.971938i \(0.424414\pi\)
\(998\) 7.14716 11.3777i 0.226239 0.360154i
\(999\) 21.8344 25.1982i 0.690809 0.797236i
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 920.2.bb.a.11.19 480
8.3 odd 2 920.2.bb.b.11.37 yes 480
23.21 odd 22 920.2.bb.b.251.37 yes 480
184.67 even 22 inner 920.2.bb.a.251.19 yes 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.bb.a.11.19 480 1.1 even 1 trivial
920.2.bb.a.251.19 yes 480 184.67 even 22 inner
920.2.bb.b.11.37 yes 480 8.3 odd 2
920.2.bb.b.251.37 yes 480 23.21 odd 22