Properties

Label 252.2.n.b.31.1
Level $252$
Weight $2$
Character 252.31
Analytic conductor $2.012$
Analytic rank $0$
Dimension $84$
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] = [252,2,Mod(31,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.n (of order \(6\), degree \(2\), 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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Character \(\chi\) \(=\) 252.31
Dual form 252.2.n.b.187.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41347 - 0.0457258i) q^{2} +(-0.962720 - 1.43985i) q^{3} +(1.99582 + 0.129265i) q^{4} +0.724862i q^{5} +(1.29494 + 2.07921i) q^{6} +(-1.25991 + 2.32651i) q^{7} +(-2.81513 - 0.273973i) q^{8} +(-1.14634 + 2.77235i) q^{9} +O(q^{10})\) \(q+(-1.41347 - 0.0457258i) q^{2} +(-0.962720 - 1.43985i) q^{3} +(1.99582 + 0.129265i) q^{4} +0.724862i q^{5} +(1.29494 + 2.07921i) q^{6} +(-1.25991 + 2.32651i) q^{7} +(-2.81513 - 0.273973i) q^{8} +(-1.14634 + 2.77235i) q^{9} +(0.0331449 - 1.02457i) q^{10} +0.579473i q^{11} +(-1.73529 - 2.99813i) q^{12} +(3.35535 + 1.93721i) q^{13} +(1.88723 - 3.23085i) q^{14} +(1.04369 - 0.697840i) q^{15} +(3.96658 + 0.515977i) q^{16} +(-3.20279 - 1.84913i) q^{17} +(1.74709 - 3.86622i) q^{18} +(2.04363 + 3.53967i) q^{19} +(-0.0936991 + 1.44669i) q^{20} +(4.56276 - 0.425697i) q^{21} +(0.0264969 - 0.819070i) q^{22} +5.16253i q^{23} +(2.31570 + 4.31712i) q^{24} +4.47457 q^{25} +(-4.65413 - 2.89163i) q^{26} +(5.09537 - 1.01844i) q^{27} +(-2.81528 + 4.48042i) q^{28} +(4.56967 + 7.91490i) q^{29} +(-1.50714 + 0.938655i) q^{30} +(-0.424336 - 0.734971i) q^{31} +(-5.58307 - 0.910696i) q^{32} +(0.834354 - 0.557870i) q^{33} +(4.44251 + 2.76015i) q^{34} +(-1.68640 - 0.913260i) q^{35} +(-2.64625 + 5.38492i) q^{36} +(-1.73892 - 3.01190i) q^{37} +(-2.72676 - 5.09668i) q^{38} +(-0.440968 - 6.69620i) q^{39} +(0.198592 - 2.04058i) q^{40} +(0.854749 + 0.493490i) q^{41} +(-6.46881 + 0.393075i) q^{42} +(-10.9509 + 6.32252i) q^{43} +(-0.0749053 + 1.15652i) q^{44} +(-2.00957 - 0.830938i) q^{45} +(0.236061 - 7.29711i) q^{46} +(5.79030 - 10.0291i) q^{47} +(-3.07578 - 6.20803i) q^{48} +(-3.82527 - 5.86237i) q^{49} +(-6.32470 - 0.204604i) q^{50} +(0.420918 + 6.39174i) q^{51} +(6.44626 + 4.30006i) q^{52} +(-2.70941 + 4.69284i) q^{53} +(-7.24874 + 1.20655i) q^{54} -0.420038 q^{55} +(4.18420 - 6.20423i) q^{56} +(3.12915 - 6.35024i) q^{57} +(-6.09719 - 11.3965i) q^{58} +(-0.193920 - 0.335879i) q^{59} +(2.17323 - 1.25785i) q^{60} +(-0.771976 - 0.445701i) q^{61} +(0.566180 + 1.05827i) q^{62} +(-5.00560 - 6.15987i) q^{63} +(7.84988 + 1.54254i) q^{64} +(-1.40421 + 2.43217i) q^{65} +(-1.20485 + 0.750383i) q^{66} +(-2.73549 + 1.57934i) q^{67} +(-6.15316 - 4.10454i) q^{68} +(7.43328 - 4.97008i) q^{69} +(2.34192 + 1.36798i) q^{70} +7.56506i q^{71} +(3.98664 - 7.49044i) q^{72} +(-10.1955 - 5.88637i) q^{73} +(2.32020 + 4.33675i) q^{74} +(-4.30776 - 6.44272i) q^{75} +(3.62116 + 7.32871i) q^{76} +(-1.34815 - 0.730082i) q^{77} +(0.317108 + 9.48508i) q^{78} +(2.94437 + 1.69993i) q^{79} +(-0.374013 + 2.87523i) q^{80} +(-6.37181 - 6.35610i) q^{81} +(-1.18560 - 0.736619i) q^{82} +(3.46587 + 6.00306i) q^{83} +(9.16147 - 0.259810i) q^{84} +(1.34037 - 2.32158i) q^{85} +(15.7680 - 8.43598i) q^{86} +(6.99696 - 14.1995i) q^{87} +(0.158760 - 1.63129i) q^{88} +(-2.37662 + 1.37214i) q^{89} +(2.80248 + 1.26640i) q^{90} +(-8.73438 + 5.36554i) q^{91} +(-0.667333 + 10.3035i) q^{92} +(-0.649731 + 1.31855i) q^{93} +(-8.64303 + 13.9111i) q^{94} +(-2.56578 + 1.48135i) q^{95} +(4.06367 + 8.91553i) q^{96} +(-9.32750 + 5.38523i) q^{97} +(5.13885 + 8.46122i) q^{98} +(-1.60650 - 0.664272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9} - 18 q^{10} + 9 q^{12} - 18 q^{13} - 25 q^{14} - 7 q^{16} + 6 q^{17} - 13 q^{18} + 24 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{24} - 32 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 14 q^{30} + 9 q^{32} - 6 q^{33} + 24 q^{34} - 38 q^{36} + 2 q^{37} - 6 q^{41} + 7 q^{42} - 13 q^{44} - 18 q^{45} + 10 q^{46} - 9 q^{48} + 2 q^{49} - 17 q^{50} - 2 q^{53} - 42 q^{54} - 32 q^{56} + 6 q^{57} + 26 q^{58} + 8 q^{60} - 24 q^{61} - 8 q^{64} + 50 q^{65} + 27 q^{66} + 18 q^{69} - 4 q^{70} - 7 q^{72} + 30 q^{73} + 46 q^{74} + 46 q^{77} + 15 q^{78} + 3 q^{80} - 26 q^{81} - 18 q^{82} + 29 q^{84} - 50 q^{85} + 18 q^{86} - 2 q^{88} - 102 q^{89} + 39 q^{90} + 28 q^{92} - 24 q^{93} + 3 q^{94} - 30 q^{96} - 6 q^{97} + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41347 0.0457258i −0.999477 0.0323331i
\(3\) −0.962720 1.43985i −0.555827 0.831298i
\(4\) 1.99582 + 0.129265i 0.997909 + 0.0646323i
\(5\) 0.724862i 0.324168i 0.986777 + 0.162084i \(0.0518216\pi\)
−0.986777 + 0.162084i \(0.948178\pi\)
\(6\) 1.29494 + 2.07921i 0.528658 + 0.848835i
\(7\) −1.25991 + 2.32651i −0.476200 + 0.879337i
\(8\) −2.81513 0.273973i −0.995298 0.0968640i
\(9\) −1.14634 + 2.77235i −0.382113 + 0.924116i
\(10\) 0.0331449 1.02457i 0.0104814 0.323999i
\(11\) 0.579473i 0.174718i 0.996177 + 0.0873588i \(0.0278427\pi\)
−0.996177 + 0.0873588i \(0.972157\pi\)
\(12\) −1.73529 2.99813i −0.500936 0.865484i
\(13\) 3.35535 + 1.93721i 0.930608 + 0.537287i 0.887004 0.461762i \(-0.152783\pi\)
0.0436041 + 0.999049i \(0.486116\pi\)
\(14\) 1.88723 3.23085i 0.504383 0.863480i
\(15\) 1.04369 0.697840i 0.269480 0.180181i
\(16\) 3.96658 + 0.515977i 0.991645 + 0.128994i
\(17\) −3.20279 1.84913i −0.776791 0.448480i 0.0585009 0.998287i \(-0.481368\pi\)
−0.835292 + 0.549807i \(0.814701\pi\)
\(18\) 1.74709 3.86622i 0.411793 0.911278i
\(19\) 2.04363 + 3.53967i 0.468841 + 0.812057i 0.999366 0.0356130i \(-0.0113384\pi\)
−0.530525 + 0.847670i \(0.678005\pi\)
\(20\) −0.0936991 + 1.44669i −0.0209517 + 0.323491i
\(21\) 4.56276 0.425697i 0.995676 0.0928946i
\(22\) 0.0264969 0.819070i 0.00564915 0.174626i
\(23\) 5.16253i 1.07646i 0.842797 + 0.538231i \(0.180907\pi\)
−0.842797 + 0.538231i \(0.819093\pi\)
\(24\) 2.31570 + 4.31712i 0.472690 + 0.881229i
\(25\) 4.47457 0.894915
\(26\) −4.65413 2.89163i −0.912749 0.567095i
\(27\) 5.09537 1.01844i 0.980604 0.195999i
\(28\) −2.81528 + 4.48042i −0.532038 + 0.846720i
\(29\) 4.56967 + 7.91490i 0.848566 + 1.46976i 0.882488 + 0.470335i \(0.155867\pi\)
−0.0339219 + 0.999424i \(0.510800\pi\)
\(30\) −1.50714 + 0.938655i −0.275165 + 0.171374i
\(31\) −0.424336 0.734971i −0.0762129 0.132005i 0.825400 0.564548i \(-0.190950\pi\)
−0.901613 + 0.432543i \(0.857616\pi\)
\(32\) −5.58307 0.910696i −0.986956 0.160990i
\(33\) 0.834354 0.557870i 0.145242 0.0971127i
\(34\) 4.44251 + 2.76015i 0.761884 + 0.473362i
\(35\) −1.68640 0.913260i −0.285053 0.154369i
\(36\) −2.64625 + 5.38492i −0.441042 + 0.897487i
\(37\) −1.73892 3.01190i −0.285877 0.495153i 0.686945 0.726710i \(-0.258951\pi\)
−0.972821 + 0.231557i \(0.925618\pi\)
\(38\) −2.72676 5.09668i −0.442340 0.826791i
\(39\) −0.440968 6.69620i −0.0706115 1.07225i
\(40\) 0.198592 2.04058i 0.0314002 0.322644i
\(41\) 0.854749 + 0.493490i 0.133489 + 0.0770701i 0.565258 0.824914i \(-0.308777\pi\)
−0.431768 + 0.901985i \(0.642110\pi\)
\(42\) −6.46881 + 0.393075i −0.998159 + 0.0606528i
\(43\) −10.9509 + 6.32252i −1.67000 + 0.964175i −0.702367 + 0.711815i \(0.747874\pi\)
−0.967633 + 0.252360i \(0.918793\pi\)
\(44\) −0.0749053 + 1.15652i −0.0112924 + 0.174352i
\(45\) −2.00957 0.830938i −0.299569 0.123869i
\(46\) 0.236061 7.29711i 0.0348053 1.07590i
\(47\) 5.79030 10.0291i 0.844603 1.46289i −0.0413633 0.999144i \(-0.513170\pi\)
0.885966 0.463750i \(-0.153497\pi\)
\(48\) −3.07578 6.20803i −0.443950 0.896051i
\(49\) −3.82527 5.86237i −0.546467 0.837481i
\(50\) −6.32470 0.204604i −0.894447 0.0289353i
\(51\) 0.420918 + 6.39174i 0.0589403 + 0.895022i
\(52\) 6.44626 + 4.30006i 0.893936 + 0.596311i
\(53\) −2.70941 + 4.69284i −0.372166 + 0.644611i −0.989899 0.141778i \(-0.954718\pi\)
0.617732 + 0.786388i \(0.288052\pi\)
\(54\) −7.24874 + 1.20655i −0.986429 + 0.164190i
\(55\) −0.420038 −0.0566379
\(56\) 4.18420 6.20423i 0.559137 0.829075i
\(57\) 3.12915 6.35024i 0.414467 0.841110i
\(58\) −6.09719 11.3965i −0.800601 1.49643i
\(59\) −0.193920 0.335879i −0.0252462 0.0437277i 0.853126 0.521704i \(-0.174704\pi\)
−0.878372 + 0.477977i \(0.841370\pi\)
\(60\) 2.17323 1.25785i 0.280563 0.162388i
\(61\) −0.771976 0.445701i −0.0988414 0.0570661i 0.449765 0.893147i \(-0.351508\pi\)
−0.548606 + 0.836081i \(0.684841\pi\)
\(62\) 0.566180 + 1.05827i 0.0719050 + 0.134400i
\(63\) −5.00560 6.15987i −0.630647 0.776070i
\(64\) 7.84988 + 1.54254i 0.981235 + 0.192817i
\(65\) −1.40421 + 2.43217i −0.174171 + 0.301674i
\(66\) −1.20485 + 0.750383i −0.148306 + 0.0923658i
\(67\) −2.73549 + 1.57934i −0.334193 + 0.192947i −0.657701 0.753279i \(-0.728471\pi\)
0.323508 + 0.946225i \(0.395138\pi\)
\(68\) −6.15316 4.10454i −0.746180 0.497748i
\(69\) 7.43328 4.97008i 0.894862 0.598327i
\(70\) 2.34192 + 1.36798i 0.279913 + 0.163505i
\(71\) 7.56506i 0.897807i 0.893580 + 0.448904i \(0.148185\pi\)
−0.893580 + 0.448904i \(0.851815\pi\)
\(72\) 3.98664 7.49044i 0.469830 0.882757i
\(73\) −10.1955 5.88637i −1.19329 0.688947i −0.234240 0.972179i \(-0.575260\pi\)
−0.959051 + 0.283232i \(0.908593\pi\)
\(74\) 2.32020 + 4.33675i 0.269717 + 0.504137i
\(75\) −4.30776 6.44272i −0.497418 0.743941i
\(76\) 3.62116 + 7.32871i 0.415376 + 0.840661i
\(77\) −1.34815 0.730082i −0.153636 0.0832006i
\(78\) 0.317108 + 9.48508i 0.0359054 + 1.07397i
\(79\) 2.94437 + 1.69993i 0.331268 + 0.191257i 0.656404 0.754410i \(-0.272077\pi\)
−0.325136 + 0.945667i \(0.605410\pi\)
\(80\) −0.374013 + 2.87523i −0.0418159 + 0.321460i
\(81\) −6.37181 6.35610i −0.707979 0.706233i
\(82\) −1.18560 0.736619i −0.130928 0.0813460i
\(83\) 3.46587 + 6.00306i 0.380428 + 0.658921i 0.991123 0.132945i \(-0.0424433\pi\)
−0.610695 + 0.791866i \(0.709110\pi\)
\(84\) 9.16147 0.259810i 0.999598 0.0283476i
\(85\) 1.34037 2.32158i 0.145383 0.251811i
\(86\) 15.7680 8.43598i 1.70030 0.909675i
\(87\) 6.99696 14.1995i 0.750152 1.52234i
\(88\) 0.158760 1.63129i 0.0169238 0.173896i
\(89\) −2.37662 + 1.37214i −0.251921 + 0.145446i −0.620643 0.784093i \(-0.713129\pi\)
0.368723 + 0.929539i \(0.379795\pi\)
\(90\) 2.80248 + 1.26640i 0.295407 + 0.133490i
\(91\) −8.73438 + 5.36554i −0.915612 + 0.562462i
\(92\) −0.667333 + 10.3035i −0.0695743 + 1.07421i
\(93\) −0.649731 + 1.31855i −0.0673740 + 0.136727i
\(94\) −8.64303 + 13.9111i −0.891461 + 1.43482i
\(95\) −2.56578 + 1.48135i −0.263243 + 0.151983i
\(96\) 4.06367 + 8.91553i 0.414746 + 0.909937i
\(97\) −9.32750 + 5.38523i −0.947064 + 0.546788i −0.892168 0.451704i \(-0.850816\pi\)
−0.0548963 + 0.998492i \(0.517483\pi\)
\(98\) 5.13885 + 8.46122i 0.519102 + 0.854712i
\(99\) −1.60650 0.664272i −0.161459 0.0667619i
\(100\) 8.93044 + 0.578404i 0.893044 + 0.0578404i
\(101\) 9.57208i 0.952457i −0.879321 0.476229i \(-0.842003\pi\)
0.879321 0.476229i \(-0.157997\pi\)
\(102\) −0.302689 9.05380i −0.0299707 0.896460i
\(103\) 10.7011 1.05441 0.527206 0.849738i \(-0.323240\pi\)
0.527206 + 0.849738i \(0.323240\pi\)
\(104\) −8.91500 6.37278i −0.874188 0.624903i
\(105\) 0.308572 + 3.30737i 0.0301135 + 0.322767i
\(106\) 4.04427 6.50932i 0.392814 0.632241i
\(107\) 1.37590 0.794374i 0.133013 0.0767950i −0.432017 0.901865i \(-0.642198\pi\)
0.565030 + 0.825070i \(0.308865\pi\)
\(108\) 10.3011 1.37397i 0.991222 0.132210i
\(109\) −4.38392 + 7.59317i −0.419903 + 0.727294i −0.995929 0.0901375i \(-0.971269\pi\)
0.576026 + 0.817431i \(0.304603\pi\)
\(110\) 0.593713 + 0.0192066i 0.0566083 + 0.00183128i
\(111\) −2.66259 + 5.40340i −0.252722 + 0.512868i
\(112\) −6.19795 + 8.57819i −0.585651 + 0.810563i
\(113\) 3.31031 5.73363i 0.311408 0.539375i −0.667259 0.744825i \(-0.732533\pi\)
0.978667 + 0.205451i \(0.0658660\pi\)
\(114\) −4.71335 + 8.83281i −0.441446 + 0.827269i
\(115\) −3.74213 −0.348955
\(116\) 8.09711 + 16.3874i 0.751798 + 1.52153i
\(117\) −9.21700 + 7.08150i −0.852112 + 0.654685i
\(118\) 0.258742 + 0.483623i 0.0238191 + 0.0445211i
\(119\) 8.33724 5.12158i 0.764273 0.469494i
\(120\) −3.12932 + 1.67856i −0.285666 + 0.153231i
\(121\) 10.6642 0.969474
\(122\) 1.07079 + 0.665285i 0.0969446 + 0.0602321i
\(123\) −0.112333 1.70580i −0.0101287 0.153807i
\(124\) −0.751891 1.52172i −0.0675218 0.136654i
\(125\) 6.86776i 0.614271i
\(126\) 6.79362 + 8.93570i 0.605224 + 0.796055i
\(127\) 9.20736i 0.817021i −0.912754 0.408511i \(-0.866048\pi\)
0.912754 0.408511i \(-0.133952\pi\)
\(128\) −11.0251 2.53928i −0.974487 0.224442i
\(129\) 19.6462 + 9.68088i 1.72975 + 0.852354i
\(130\) 2.09603 3.37360i 0.183834 0.295884i
\(131\) 16.1387 1.41005 0.705023 0.709184i \(-0.250937\pi\)
0.705023 + 0.709184i \(0.250937\pi\)
\(132\) 1.73733 1.00555i 0.151215 0.0875223i
\(133\) −10.8099 + 0.294860i −0.937333 + 0.0255676i
\(134\) 3.93876 2.10727i 0.340257 0.182040i
\(135\) 0.738228 + 3.69344i 0.0635365 + 0.317881i
\(136\) 8.50965 + 6.08302i 0.729696 + 0.521615i
\(137\) −2.29753 −0.196291 −0.0981457 0.995172i \(-0.531291\pi\)
−0.0981457 + 0.995172i \(0.531291\pi\)
\(138\) −10.7340 + 6.68518i −0.913739 + 0.569081i
\(139\) 3.40486 5.89740i 0.288797 0.500211i −0.684726 0.728801i \(-0.740078\pi\)
0.973523 + 0.228590i \(0.0734115\pi\)
\(140\) −3.24769 2.04069i −0.274480 0.172470i
\(141\) −20.0148 + 1.31805i −1.68555 + 0.111000i
\(142\) 0.345919 10.6930i 0.0290289 0.897338i
\(143\) −1.12256 + 1.94434i −0.0938734 + 0.162594i
\(144\) −5.97751 + 10.4053i −0.498126 + 0.867105i
\(145\) −5.73721 + 3.31238i −0.476449 + 0.275078i
\(146\) 14.1419 + 8.78642i 1.17039 + 0.727169i
\(147\) −4.75827 + 11.1516i −0.392456 + 0.919771i
\(148\) −3.08124 6.23598i −0.253276 0.512594i
\(149\) −11.8903 −0.974094 −0.487047 0.873376i \(-0.661926\pi\)
−0.487047 + 0.873376i \(0.661926\pi\)
\(150\) 5.79431 + 9.30359i 0.473104 + 0.759635i
\(151\) 13.7417i 1.11828i −0.829073 0.559140i \(-0.811131\pi\)
0.829073 0.559140i \(-0.188869\pi\)
\(152\) −4.78331 10.5245i −0.387977 0.853652i
\(153\) 8.79792 6.75951i 0.711270 0.546474i
\(154\) 1.87219 + 1.09360i 0.150865 + 0.0881246i
\(155\) 0.532753 0.307585i 0.0427917 0.0247058i
\(156\) −0.0145106 13.4214i −0.00116178 1.07457i
\(157\) 10.6702 6.16047i 0.851578 0.491659i −0.00960511 0.999954i \(-0.503057\pi\)
0.861183 + 0.508295i \(0.169724\pi\)
\(158\) −4.08406 2.53745i −0.324910 0.201868i
\(159\) 9.36539 0.616744i 0.742724 0.0489110i
\(160\) 0.660129 4.04695i 0.0521878 0.319940i
\(161\) −12.0107 6.50432i −0.946573 0.512612i
\(162\) 8.71576 + 9.27554i 0.684775 + 0.728755i
\(163\) 4.96214 2.86489i 0.388665 0.224396i −0.292917 0.956138i \(-0.594626\pi\)
0.681582 + 0.731742i \(0.261292\pi\)
\(164\) 1.64213 + 1.09540i 0.128229 + 0.0855367i
\(165\) 0.404379 + 0.604792i 0.0314809 + 0.0470830i
\(166\) −4.62442 8.64364i −0.358924 0.670877i
\(167\) 4.19478 7.26556i 0.324601 0.562226i −0.656830 0.754039i \(-0.728103\pi\)
0.981432 + 0.191812i \(0.0614365\pi\)
\(168\) −12.9614 0.0516813i −0.999992 0.00398730i
\(169\) 1.00560 + 1.74175i 0.0773539 + 0.133981i
\(170\) −2.00073 + 3.22021i −0.153449 + 0.246979i
\(171\) −12.1559 + 1.60799i −0.929584 + 0.122966i
\(172\) −22.6733 + 11.2030i −1.72883 + 0.854223i
\(173\) 15.4748 + 8.93437i 1.17653 + 0.679267i 0.955208 0.295935i \(-0.0956310\pi\)
0.221317 + 0.975202i \(0.428964\pi\)
\(174\) −10.5393 + 19.7506i −0.798982 + 1.49729i
\(175\) −5.63755 + 10.4101i −0.426159 + 0.786932i
\(176\) −0.298995 + 2.29853i −0.0225376 + 0.173258i
\(177\) −0.296925 + 0.602572i −0.0223182 + 0.0452921i
\(178\) 3.42203 1.83081i 0.256492 0.137225i
\(179\) 21.7765 + 12.5727i 1.62765 + 0.939727i 0.984790 + 0.173747i \(0.0555874\pi\)
0.642864 + 0.765980i \(0.277746\pi\)
\(180\) −3.90333 1.91817i −0.290937 0.142972i
\(181\) 21.3865i 1.58965i −0.606841 0.794824i \(-0.707563\pi\)
0.606841 0.794824i \(-0.292437\pi\)
\(182\) 12.5912 7.18467i 0.933319 0.532563i
\(183\) 0.101455 + 1.54061i 0.00749976 + 0.113886i
\(184\) 1.41439 14.5332i 0.104270 1.07140i
\(185\) 2.18321 1.26048i 0.160513 0.0926722i
\(186\) 0.978670 1.83403i 0.0717596 0.134477i
\(187\) 1.07152 1.85593i 0.0783574 0.135719i
\(188\) 12.8528 19.2678i 0.937387 1.40525i
\(189\) −4.05029 + 13.1375i −0.294615 + 0.955616i
\(190\) 3.69439 1.97653i 0.268019 0.143393i
\(191\) −0.345563 0.199511i −0.0250041 0.0144361i 0.487446 0.873153i \(-0.337929\pi\)
−0.512450 + 0.858717i \(0.671262\pi\)
\(192\) −5.33622 12.7877i −0.385108 0.922871i
\(193\) 8.09770 + 14.0256i 0.582885 + 1.00959i 0.995135 + 0.0985165i \(0.0314097\pi\)
−0.412250 + 0.911071i \(0.635257\pi\)
\(194\) 13.4304 7.18538i 0.964248 0.515880i
\(195\) 4.85383 0.319641i 0.347590 0.0228900i
\(196\) −6.87674 12.1947i −0.491196 0.871049i
\(197\) 23.4117 1.66801 0.834006 0.551756i \(-0.186042\pi\)
0.834006 + 0.551756i \(0.186042\pi\)
\(198\) 2.24037 + 1.01239i 0.159216 + 0.0719474i
\(199\) 6.11333 10.5886i 0.433362 0.750606i −0.563798 0.825913i \(-0.690660\pi\)
0.997160 + 0.0753071i \(0.0239937\pi\)
\(200\) −12.5965 1.22591i −0.890707 0.0866850i
\(201\) 4.90752 + 2.41824i 0.346150 + 0.170569i
\(202\) −0.437691 + 13.5299i −0.0307959 + 0.951959i
\(203\) −24.1714 + 0.659324i −1.69650 + 0.0462754i
\(204\) 0.0138509 + 12.8112i 0.000969754 + 0.896960i
\(205\) −0.357712 + 0.619576i −0.0249837 + 0.0432730i
\(206\) −15.1257 0.489317i −1.05386 0.0340923i
\(207\) −14.3123 5.91801i −0.994776 0.411330i
\(208\) 12.3097 + 9.41541i 0.853526 + 0.652841i
\(209\) −2.05114 + 1.18423i −0.141881 + 0.0819148i
\(210\) −0.284925 4.68900i −0.0196617 0.323571i
\(211\) −11.8107 6.81891i −0.813082 0.469433i 0.0349433 0.999389i \(-0.488875\pi\)
−0.848025 + 0.529956i \(0.822208\pi\)
\(212\) −6.01411 + 9.01582i −0.413051 + 0.619209i
\(213\) 10.8926 7.28304i 0.746346 0.499026i
\(214\) −1.98112 + 1.05991i −0.135426 + 0.0724542i
\(215\) −4.58296 7.93791i −0.312555 0.541361i
\(216\) −14.6231 + 1.47104i −0.994978 + 0.100092i
\(217\) 2.24454 0.0612242i 0.152369 0.00415617i
\(218\) 6.54376 10.5323i 0.443199 0.713337i
\(219\) 1.33991 + 20.3469i 0.0905430 + 1.37492i
\(220\) −0.838319 0.0542960i −0.0565195 0.00366064i
\(221\) −7.16433 12.4090i −0.481925 0.834719i
\(222\) 4.01057 7.51582i 0.269172 0.504429i
\(223\) −8.37599 14.5076i −0.560898 0.971504i −0.997418 0.0718094i \(-0.977123\pi\)
0.436520 0.899694i \(-0.356211\pi\)
\(224\) 9.15289 11.8416i 0.611553 0.791203i
\(225\) −5.12938 + 12.4051i −0.341959 + 0.827005i
\(226\) −4.94122 + 7.95297i −0.328685 + 0.529024i
\(227\) −21.9681 −1.45807 −0.729037 0.684474i \(-0.760032\pi\)
−0.729037 + 0.684474i \(0.760032\pi\)
\(228\) 7.06608 12.2694i 0.467963 0.812563i
\(229\) 3.79488i 0.250773i −0.992108 0.125386i \(-0.959983\pi\)
0.992108 0.125386i \(-0.0400171\pi\)
\(230\) 5.28940 + 0.171112i 0.348773 + 0.0112828i
\(231\) 0.246680 + 2.64399i 0.0162303 + 0.173962i
\(232\) −10.6957 23.5334i −0.702209 1.54504i
\(233\) −10.3989 18.0115i −0.681256 1.17997i −0.974598 0.223963i \(-0.928101\pi\)
0.293341 0.956008i \(-0.405233\pi\)
\(234\) 13.3518 9.58806i 0.872835 0.626791i
\(235\) 7.26972 + 4.19717i 0.474224 + 0.273793i
\(236\) −0.343611 0.695420i −0.0223672 0.0452680i
\(237\) −0.386956 5.87601i −0.0251355 0.381688i
\(238\) −12.0187 + 6.85799i −0.779054 + 0.444538i
\(239\) 0.874254 + 0.504751i 0.0565508 + 0.0326496i 0.528009 0.849239i \(-0.322939\pi\)
−0.471458 + 0.881888i \(0.656272\pi\)
\(240\) 4.49996 2.22952i 0.290471 0.143915i
\(241\) 26.0294i 1.67670i 0.545134 + 0.838349i \(0.316479\pi\)
−0.545134 + 0.838349i \(0.683521\pi\)
\(242\) −15.0736 0.487630i −0.968967 0.0313461i
\(243\) −3.01756 + 15.2936i −0.193576 + 0.981085i
\(244\) −1.48311 0.989326i −0.0949464 0.0633351i
\(245\) 4.24941 2.77279i 0.271485 0.177147i
\(246\) 0.0807806 + 2.41625i 0.00515039 + 0.154054i
\(247\) 15.8358i 1.00761i
\(248\) 0.993196 + 2.18529i 0.0630680 + 0.138766i
\(249\) 5.30684 10.7696i 0.336307 0.682495i
\(250\) 0.314034 9.70740i 0.0198613 0.613950i
\(251\) −18.4201 −1.16266 −0.581332 0.813666i \(-0.697468\pi\)
−0.581332 + 0.813666i \(0.697468\pi\)
\(252\) −9.19402 12.9410i −0.579169 0.815208i
\(253\) −2.99155 −0.188077
\(254\) −0.421014 + 13.0144i −0.0264168 + 0.816594i
\(255\) −4.63313 + 0.305108i −0.290138 + 0.0191066i
\(256\) 15.4675 + 4.09333i 0.966721 + 0.255833i
\(257\) 12.5656i 0.783821i −0.920003 0.391910i \(-0.871814\pi\)
0.920003 0.391910i \(-0.128186\pi\)
\(258\) −27.3267 14.5820i −1.70128 0.907836i
\(259\) 9.19808 0.250896i 0.571541 0.0155899i
\(260\) −3.11695 + 4.67265i −0.193305 + 0.289786i
\(261\) −27.1812 + 3.59555i −1.68248 + 0.222559i
\(262\) −22.8117 0.737956i −1.40931 0.0455911i
\(263\) 9.93943i 0.612892i 0.951888 + 0.306446i \(0.0991398\pi\)
−0.951888 + 0.306446i \(0.900860\pi\)
\(264\) −2.50165 + 1.34189i −0.153966 + 0.0825873i
\(265\) −3.40166 1.96395i −0.208962 0.120645i
\(266\) 15.2929 + 0.0775124i 0.937670 + 0.00475259i
\(267\) 4.26369 + 2.10098i 0.260934 + 0.128578i
\(268\) −5.66369 + 2.79847i −0.345965 + 0.170943i
\(269\) 6.20144 + 3.58040i 0.378108 + 0.218301i 0.676995 0.735988i \(-0.263282\pi\)
−0.298887 + 0.954289i \(0.596615\pi\)
\(270\) −0.874580 5.25434i −0.0532252 0.319769i
\(271\) −3.11123 5.38881i −0.188994 0.327347i 0.755921 0.654663i \(-0.227189\pi\)
−0.944915 + 0.327316i \(0.893856\pi\)
\(272\) −11.7500 8.98730i −0.712450 0.544935i
\(273\) 16.1343 + 7.41068i 0.976495 + 0.448515i
\(274\) 3.24750 + 0.105057i 0.196189 + 0.00634670i
\(275\) 2.59289i 0.156357i
\(276\) 15.4779 8.95851i 0.931662 0.539239i
\(277\) 26.2342 1.57626 0.788130 0.615509i \(-0.211050\pi\)
0.788130 + 0.615509i \(0.211050\pi\)
\(278\) −5.08235 + 8.18013i −0.304819 + 0.490611i
\(279\) 2.52403 0.333880i 0.151109 0.0199889i
\(280\) 4.49721 + 3.03297i 0.268760 + 0.181255i
\(281\) −4.29087 7.43201i −0.255972 0.443357i 0.709187 0.705020i \(-0.249062\pi\)
−0.965159 + 0.261664i \(0.915729\pi\)
\(282\) 28.3507 0.947830i 1.68826 0.0564425i
\(283\) 14.3570 + 24.8670i 0.853435 + 1.47819i 0.878090 + 0.478496i \(0.158818\pi\)
−0.0246550 + 0.999696i \(0.507849\pi\)
\(284\) −0.977895 + 15.0985i −0.0580274 + 0.895930i
\(285\) 4.60305 + 2.26821i 0.272661 + 0.134357i
\(286\) 1.67562 2.69694i 0.0990815 0.159473i
\(287\) −2.22501 + 1.36683i −0.131338 + 0.0806813i
\(288\) 8.92485 14.4342i 0.525902 0.850545i
\(289\) −1.66142 2.87767i −0.0977307 0.169275i
\(290\) 8.26086 4.41963i 0.485094 0.259529i
\(291\) 16.7337 + 8.24573i 0.980947 + 0.483373i
\(292\) −19.5874 13.0660i −1.14627 0.764632i
\(293\) 20.5937 + 11.8898i 1.20310 + 0.694609i 0.961243 0.275704i \(-0.0889109\pi\)
0.241855 + 0.970312i \(0.422244\pi\)
\(294\) 7.23561 15.5450i 0.421989 0.906601i
\(295\) 0.243466 0.140565i 0.0141751 0.00818401i
\(296\) 4.07010 + 8.95529i 0.236570 + 0.520516i
\(297\) 0.590157 + 2.95263i 0.0342444 + 0.171329i
\(298\) 16.8067 + 0.543696i 0.973585 + 0.0314954i
\(299\) −10.0009 + 17.3221i −0.578369 + 1.00176i
\(300\) −7.76470 13.4153i −0.448295 0.774535i
\(301\) −0.912230 33.4432i −0.0525800 1.92763i
\(302\) −0.628349 + 19.4235i −0.0361574 + 1.11770i
\(303\) −13.7824 + 9.21523i −0.791776 + 0.529401i
\(304\) 6.27984 + 15.0949i 0.360173 + 0.865750i
\(305\) 0.323072 0.559576i 0.0184990 0.0320412i
\(306\) −12.7447 + 9.15211i −0.728567 + 0.523191i
\(307\) 12.4459 0.710323 0.355161 0.934805i \(-0.384426\pi\)
0.355161 + 0.934805i \(0.384426\pi\)
\(308\) −2.59628 1.63138i −0.147937 0.0929564i
\(309\) −10.3022 15.4080i −0.586070 0.876530i
\(310\) −0.767097 + 0.410403i −0.0435682 + 0.0233093i
\(311\) −13.8745 24.0314i −0.786752 1.36269i −0.927947 0.372713i \(-0.878428\pi\)
0.141195 0.989982i \(-0.454906\pi\)
\(312\) −0.593195 + 18.9715i −0.0335830 + 1.07405i
\(313\) 21.6896 + 12.5225i 1.22597 + 0.707813i 0.966184 0.257854i \(-0.0830155\pi\)
0.259783 + 0.965667i \(0.416349\pi\)
\(314\) −15.3638 + 8.21975i −0.867029 + 0.463867i
\(315\) 4.46506 3.62837i 0.251577 0.204436i
\(316\) 5.65669 + 3.77336i 0.318214 + 0.212268i
\(317\) −9.58415 + 16.6002i −0.538300 + 0.932362i 0.460696 + 0.887558i \(0.347600\pi\)
−0.998996 + 0.0448044i \(0.985734\pi\)
\(318\) −13.2659 + 0.443511i −0.743917 + 0.0248709i
\(319\) −4.58647 + 2.64800i −0.256793 + 0.148259i
\(320\) −1.11813 + 5.69008i −0.0625051 + 0.318085i
\(321\) −2.46838 1.21632i −0.137772 0.0678886i
\(322\) 16.6794 + 9.74288i 0.929504 + 0.542950i
\(323\) 15.1158i 0.841064i
\(324\) −11.8954 13.5093i −0.660854 0.750515i
\(325\) 15.0138 + 8.66821i 0.832815 + 0.480826i
\(326\) −7.14486 + 3.82256i −0.395717 + 0.211712i
\(327\) 15.1535 0.997912i 0.837992 0.0551847i
\(328\) −2.27102 1.62341i −0.125396 0.0896380i
\(329\) 16.0375 + 26.1069i 0.884177 + 1.43932i
\(330\) −0.543925 0.873348i −0.0299421 0.0480762i
\(331\) 6.71711 + 3.87813i 0.369206 + 0.213161i 0.673111 0.739541i \(-0.264957\pi\)
−0.303906 + 0.952702i \(0.598291\pi\)
\(332\) 6.14126 + 12.4290i 0.337045 + 0.682131i
\(333\) 10.3434 1.36823i 0.566816 0.0749787i
\(334\) −6.26143 + 10.0779i −0.342610 + 0.551437i
\(335\) −1.14480 1.98285i −0.0625472 0.108335i
\(336\) 18.3182 + 0.665720i 0.999340 + 0.0363180i
\(337\) −16.8555 + 29.1945i −0.918175 + 1.59033i −0.115990 + 0.993250i \(0.537004\pi\)
−0.802185 + 0.597076i \(0.796329\pi\)
\(338\) −1.34175 2.50790i −0.0729815 0.136412i
\(339\) −11.4425 + 0.753527i −0.621470 + 0.0409260i
\(340\) 2.97523 4.46019i 0.161354 0.241888i
\(341\) 0.425895 0.245891i 0.0230635 0.0133157i
\(342\) 17.2556 1.71701i 0.933074 0.0928454i
\(343\) 18.4583 1.51347i 0.996655 0.0817195i
\(344\) 32.5604 14.7984i 1.75554 0.797878i
\(345\) 3.60262 + 5.38810i 0.193959 + 0.290086i
\(346\) −21.4647 13.3361i −1.15395 0.716953i
\(347\) 0.746474 0.430977i 0.0400728 0.0231360i −0.479830 0.877362i \(-0.659302\pi\)
0.519903 + 0.854226i \(0.325968\pi\)
\(348\) 15.8001 27.4351i 0.846977 1.47068i
\(349\) −29.7538 + 17.1783i −1.59268 + 0.919535i −0.599838 + 0.800122i \(0.704768\pi\)
−0.992845 + 0.119414i \(0.961899\pi\)
\(350\) 8.44454 14.4567i 0.451380 0.772741i
\(351\) 19.0697 + 6.45360i 1.01787 + 0.344468i
\(352\) 0.527723 3.23523i 0.0281278 0.172439i
\(353\) 26.4991i 1.41040i −0.709006 0.705202i \(-0.750856\pi\)
0.709006 0.705202i \(-0.249144\pi\)
\(354\) 0.447248 0.838143i 0.0237710 0.0445468i
\(355\) −5.48363 −0.291041
\(356\) −4.92066 + 2.43133i −0.260795 + 0.128860i
\(357\) −15.4007 7.07373i −0.815093 0.374381i
\(358\) −30.2057 18.7669i −1.59642 0.991863i
\(359\) 20.6811 11.9402i 1.09150 0.630181i 0.157528 0.987515i \(-0.449648\pi\)
0.933977 + 0.357334i \(0.116314\pi\)
\(360\) 5.42954 + 2.88976i 0.286162 + 0.152304i
\(361\) 1.14715 1.98692i 0.0603761 0.104574i
\(362\) −0.977916 + 30.2293i −0.0513982 + 1.58882i
\(363\) −10.2667 15.3549i −0.538860 0.805922i
\(364\) −18.1258 + 9.57960i −0.950050 + 0.502108i
\(365\) 4.26680 7.39032i 0.223335 0.386827i
\(366\) −0.0729579 2.18226i −0.00381357 0.114068i
\(367\) 1.54106 0.0804424 0.0402212 0.999191i \(-0.487194\pi\)
0.0402212 + 0.999191i \(0.487194\pi\)
\(368\) −2.66375 + 20.4776i −0.138858 + 1.06747i
\(369\) −2.34796 + 1.80395i −0.122230 + 0.0939101i
\(370\) −3.14355 + 1.68182i −0.163425 + 0.0874338i
\(371\) −7.50431 12.2160i −0.389604 0.634223i
\(372\) −1.46719 + 2.54760i −0.0760702 + 0.132087i
\(373\) 31.5489 1.63354 0.816770 0.576963i \(-0.195762\pi\)
0.816770 + 0.576963i \(0.195762\pi\)
\(374\) −1.59943 + 2.57431i −0.0827046 + 0.133115i
\(375\) 9.88855 6.61174i 0.510643 0.341429i
\(376\) −19.0481 + 26.6468i −0.982333 + 1.37420i
\(377\) 35.4097i 1.82369i
\(378\) 6.32571 18.3844i 0.325359 0.945590i
\(379\) 21.4907i 1.10390i −0.833876 0.551951i \(-0.813883\pi\)
0.833876 0.551951i \(-0.186117\pi\)
\(380\) −5.31231 + 2.62484i −0.272516 + 0.134652i
\(381\) −13.2572 + 8.86412i −0.679188 + 0.454122i
\(382\) 0.479322 + 0.297805i 0.0245242 + 0.0152370i
\(383\) −4.25561 −0.217452 −0.108726 0.994072i \(-0.534677\pi\)
−0.108726 + 0.994072i \(0.534677\pi\)
\(384\) 6.95788 + 18.3191i 0.355068 + 0.934841i
\(385\) 0.529209 0.977221i 0.0269710 0.0498038i
\(386\) −10.8046 20.1951i −0.549938 1.02791i
\(387\) −4.97475 37.6075i −0.252881 1.91170i
\(388\) −19.3121 + 9.54223i −0.980424 + 0.484433i
\(389\) −9.32619 −0.472857 −0.236428 0.971649i \(-0.575977\pi\)
−0.236428 + 0.971649i \(0.575977\pi\)
\(390\) −6.87537 + 0.229860i −0.348148 + 0.0116394i
\(391\) 9.54621 16.5345i 0.482773 0.836187i
\(392\) 9.16248 + 17.5513i 0.462775 + 0.886476i
\(393\) −15.5371 23.2373i −0.783742 1.17217i
\(394\) −33.0918 1.07052i −1.66714 0.0539319i
\(395\) −1.23222 + 2.13426i −0.0619996 + 0.107386i
\(396\) −3.12041 1.53343i −0.156807 0.0770577i
\(397\) −6.08981 + 3.51595i −0.305639 + 0.176461i −0.644973 0.764205i \(-0.723131\pi\)
0.339334 + 0.940666i \(0.389798\pi\)
\(398\) −9.12520 + 14.6872i −0.457405 + 0.736201i
\(399\) 10.8314 + 15.2807i 0.542249 + 0.764992i
\(400\) 17.7488 + 2.30878i 0.887438 + 0.115439i
\(401\) 5.80151 0.289714 0.144857 0.989453i \(-0.453728\pi\)
0.144857 + 0.989453i \(0.453728\pi\)
\(402\) −6.82608 3.64252i −0.340454 0.181672i
\(403\) 3.28812i 0.163793i
\(404\) 1.23733 19.1041i 0.0615595 0.950466i
\(405\) 4.60730 4.61869i 0.228938 0.229504i
\(406\) 34.1958 + 0.173322i 1.69711 + 0.00860182i
\(407\) 1.74531 1.00766i 0.0865119 0.0499477i
\(408\) 0.566223 18.1089i 0.0280322 0.896523i
\(409\) −19.9649 + 11.5268i −0.987202 + 0.569961i −0.904437 0.426608i \(-0.859709\pi\)
−0.0827654 + 0.996569i \(0.526375\pi\)
\(410\) 0.533947 0.859397i 0.0263698 0.0424426i
\(411\) 2.21188 + 3.30810i 0.109104 + 0.163177i
\(412\) 21.3575 + 1.38327i 1.05221 + 0.0681490i
\(413\) 1.02574 0.0279792i 0.0504736 0.00137677i
\(414\) 19.9595 + 9.01940i 0.980957 + 0.443280i
\(415\) −4.35139 + 2.51228i −0.213601 + 0.123323i
\(416\) −16.9690 13.8713i −0.831971 0.680097i
\(417\) −11.7693 + 0.775049i −0.576345 + 0.0379543i
\(418\) 2.95339 1.58009i 0.144455 0.0772845i
\(419\) −7.60902 + 13.1792i −0.371725 + 0.643847i −0.989831 0.142248i \(-0.954567\pi\)
0.618106 + 0.786095i \(0.287900\pi\)
\(420\) 0.188326 + 6.64080i 0.00918939 + 0.324038i
\(421\) −3.47824 6.02448i −0.169519 0.293615i 0.768732 0.639571i \(-0.220888\pi\)
−0.938251 + 0.345956i \(0.887555\pi\)
\(422\) 16.3823 + 10.1784i 0.797478 + 0.495477i
\(423\) 21.1665 + 27.5495i 1.02915 + 1.33950i
\(424\) 8.91305 12.4686i 0.432856 0.605530i
\(425\) −14.3311 8.27408i −0.695162 0.401352i
\(426\) −15.7294 + 9.79631i −0.762090 + 0.474633i
\(427\) 2.00954 1.23447i 0.0972486 0.0597400i
\(428\) 2.84872 1.40757i 0.137698 0.0680375i
\(429\) 3.88027 0.255529i 0.187341 0.0123371i
\(430\) 6.11492 + 11.4296i 0.294888 + 0.551184i
\(431\) −27.3227 15.7748i −1.31609 0.759845i −0.332993 0.942929i \(-0.608059\pi\)
−0.983097 + 0.183084i \(0.941392\pi\)
\(432\) 20.7367 1.41062i 0.997694 0.0678686i
\(433\) 9.13238i 0.438874i −0.975627 0.219437i \(-0.929578\pi\)
0.975627 0.219437i \(-0.0704221\pi\)
\(434\) −3.17540 0.0160945i −0.152424 0.000772562i
\(435\) 10.2927 + 5.07183i 0.493495 + 0.243176i
\(436\) −9.73104 + 14.5879i −0.466032 + 0.698634i
\(437\) −18.2737 + 10.5503i −0.874149 + 0.504690i
\(438\) −0.963555 28.8211i −0.0460404 1.37712i
\(439\) −11.0746 + 19.1817i −0.528560 + 0.915492i 0.470886 + 0.882194i \(0.343934\pi\)
−0.999445 + 0.0332980i \(0.989399\pi\)
\(440\) 1.18246 + 0.115079i 0.0563716 + 0.00548617i
\(441\) 20.6376 3.88470i 0.982741 0.184986i
\(442\) 9.55919 + 17.8674i 0.454684 + 0.849864i
\(443\) −10.8147 6.24389i −0.513824 0.296656i 0.220580 0.975369i \(-0.429205\pi\)
−0.734404 + 0.678713i \(0.762538\pi\)
\(444\) −6.01251 + 10.4400i −0.285341 + 0.495462i
\(445\) −0.994612 1.72272i −0.0471491 0.0816647i
\(446\) 11.1759 + 20.8892i 0.529193 + 0.989131i
\(447\) 11.4471 + 17.1203i 0.541428 + 0.809763i
\(448\) −13.4788 + 16.3193i −0.636815 + 0.771016i
\(449\) 23.2620 1.09780 0.548901 0.835888i \(-0.315047\pi\)
0.548901 + 0.835888i \(0.315047\pi\)
\(450\) 7.81748 17.2997i 0.368519 0.815516i
\(451\) −0.285964 + 0.495304i −0.0134655 + 0.0233229i
\(452\) 7.34794 11.0154i 0.345618 0.518120i
\(453\) −19.7859 + 13.2294i −0.929624 + 0.621570i
\(454\) 31.0514 + 1.00451i 1.45731 + 0.0471440i
\(455\) −3.88928 6.33122i −0.182332 0.296812i
\(456\) −10.5488 + 17.0194i −0.493991 + 0.797007i
\(457\) 2.65987 4.60703i 0.124423 0.215508i −0.797084 0.603868i \(-0.793625\pi\)
0.921507 + 0.388361i \(0.126959\pi\)
\(458\) −0.173524 + 5.36397i −0.00810826 + 0.250642i
\(459\) −18.2026 6.16017i −0.849626 0.287532i
\(460\) −7.46861 0.483725i −0.348226 0.0225538i
\(461\) −7.88185 + 4.55059i −0.367094 + 0.211942i −0.672188 0.740380i \(-0.734645\pi\)
0.305094 + 0.952322i \(0.401312\pi\)
\(462\) −0.227776 3.74850i −0.0105971 0.174396i
\(463\) −0.490550 0.283219i −0.0227978 0.0131623i 0.488558 0.872532i \(-0.337523\pi\)
−0.511356 + 0.859369i \(0.670856\pi\)
\(464\) 14.0421 + 33.7529i 0.651886 + 1.56694i
\(465\) −0.955768 0.470966i −0.0443227 0.0218405i
\(466\) 13.8750 + 25.9343i 0.642748 + 1.20138i
\(467\) −4.77345 8.26785i −0.220889 0.382591i 0.734189 0.678945i \(-0.237562\pi\)
−0.955078 + 0.296354i \(0.904229\pi\)
\(468\) −19.3109 + 12.9420i −0.892644 + 0.598242i
\(469\) −0.227871 8.35395i −0.0105221 0.385750i
\(470\) −10.0836 6.26501i −0.465124 0.288983i
\(471\) −19.1426 9.43274i −0.882045 0.434638i
\(472\) 0.453887 + 0.998670i 0.0208918 + 0.0459675i
\(473\) −3.66373 6.34576i −0.168458 0.291778i
\(474\) 0.278267 + 8.32329i 0.0127812 + 0.382301i
\(475\) 9.14438 + 15.8385i 0.419573 + 0.726722i
\(476\) 17.3017 9.14403i 0.793020 0.419116i
\(477\) −9.90427 12.8910i −0.453485 0.590239i
\(478\) −1.21266 0.753428i −0.0554655 0.0344610i
\(479\) 23.9234 1.09309 0.546545 0.837430i \(-0.315943\pi\)
0.546545 + 0.837430i \(0.315943\pi\)
\(480\) −6.46253 + 2.94560i −0.294973 + 0.134448i
\(481\) 13.4746i 0.614391i
\(482\) 1.19021 36.7918i 0.0542128 1.67582i
\(483\) 2.19767 + 23.5554i 0.0999976 + 1.07181i
\(484\) 21.2838 + 1.37851i 0.967447 + 0.0626593i
\(485\) −3.90355 6.76115i −0.177251 0.307008i
\(486\) 4.96455 21.4791i 0.225197 0.974313i
\(487\) 13.0207 + 7.51748i 0.590022 + 0.340650i 0.765106 0.643904i \(-0.222686\pi\)
−0.175084 + 0.984553i \(0.556020\pi\)
\(488\) 2.05110 + 1.46620i 0.0928490 + 0.0663719i
\(489\) −8.90217 4.38665i −0.402570 0.198371i
\(490\) −6.13322 + 3.72496i −0.277071 + 0.168277i
\(491\) 13.4272 + 7.75218i 0.605960 + 0.349851i 0.771383 0.636372i \(-0.219566\pi\)
−0.165423 + 0.986223i \(0.552899\pi\)
\(492\) −0.00369647 3.41899i −0.000166650 0.154140i
\(493\) 33.7997i 1.52226i
\(494\) 0.724106 22.3835i 0.0325791 1.00708i
\(495\) 0.481506 1.16449i 0.0216421 0.0523400i
\(496\) −1.30393 3.13427i −0.0585483 0.140733i
\(497\) −17.6002 9.53128i −0.789475 0.427536i
\(498\) −7.99353 + 14.9799i −0.358199 + 0.671264i
\(499\) 0.434299i 0.0194419i −0.999953 0.00972096i \(-0.996906\pi\)
0.999953 0.00972096i \(-0.00309433\pi\)
\(500\) −0.887759 + 13.7068i −0.0397018 + 0.612987i
\(501\) −14.4997 + 0.954857i −0.647800 + 0.0426599i
\(502\) 26.0363 + 0.842273i 1.16206 + 0.0375925i
\(503\) −16.6525 −0.742496 −0.371248 0.928534i \(-0.621070\pi\)
−0.371248 + 0.928534i \(0.621070\pi\)
\(504\) 12.4038 + 18.7122i 0.552508 + 0.833508i
\(505\) 6.93844 0.308756
\(506\) 4.22848 + 0.136791i 0.187979 + 0.00608110i
\(507\) 1.53975 3.12474i 0.0683827 0.138774i
\(508\) 1.19019 18.3762i 0.0528060 0.815313i
\(509\) 11.3583i 0.503446i 0.967799 + 0.251723i \(0.0809972\pi\)
−0.967799 + 0.251723i \(0.919003\pi\)
\(510\) 6.56276 0.219408i 0.290604 0.00971556i
\(511\) 26.5400 16.3036i 1.17406 0.721228i
\(512\) −21.6758 6.49309i −0.957944 0.286957i
\(513\) 14.0180 + 15.9546i 0.618909 + 0.704414i
\(514\) −0.574573 + 17.7612i −0.0253433 + 0.783411i
\(515\) 7.75683i 0.341807i
\(516\) 37.9588 + 21.8608i 1.67104 + 0.962369i
\(517\) 5.81159 + 3.35532i 0.255593 + 0.147567i
\(518\) −13.0127 0.0659551i −0.571746 0.00289790i
\(519\) −2.03373 30.8827i −0.0892709 1.35560i
\(520\) 4.61939 6.46215i 0.202574 0.283384i
\(521\) −30.1497 17.4069i −1.32088 0.762612i −0.337013 0.941500i \(-0.609417\pi\)
−0.983869 + 0.178888i \(0.942750\pi\)
\(522\) 38.5844 3.83933i 1.68879 0.168043i
\(523\) −11.7500 20.3516i −0.513791 0.889912i −0.999872 0.0159982i \(-0.994907\pi\)
0.486081 0.873914i \(-0.338426\pi\)
\(524\) 32.2099 + 2.08616i 1.40710 + 0.0911345i
\(525\) 20.4164 1.90481i 0.891045 0.0831328i
\(526\) 0.454489 14.0491i 0.0198167 0.612571i
\(527\) 3.13861i 0.136720i
\(528\) 3.59738 1.78233i 0.156556 0.0775659i
\(529\) −3.65177 −0.158772
\(530\) 4.71836 + 2.93154i 0.204952 + 0.127338i
\(531\) 1.15347 0.152582i 0.0500563 0.00662148i
\(532\) −21.6126 0.808844i −0.937026 0.0350678i
\(533\) 1.91199 + 3.31167i 0.0828175 + 0.143444i
\(534\) −5.93055 3.16465i −0.256640 0.136948i
\(535\) 0.575812 + 0.997335i 0.0248945 + 0.0431186i
\(536\) 8.13345 3.69658i 0.351311 0.159668i
\(537\) −2.86192 43.4589i −0.123501 1.87539i
\(538\) −8.60185 5.34437i −0.370852 0.230412i
\(539\) 3.39708 2.21664i 0.146323 0.0954773i
\(540\) 0.995937 + 7.46686i 0.0428583 + 0.321323i
\(541\) 3.83947 + 6.65016i 0.165072 + 0.285913i 0.936681 0.350184i \(-0.113881\pi\)
−0.771609 + 0.636097i \(0.780548\pi\)
\(542\) 4.15124 + 7.75921i 0.178311 + 0.333287i
\(543\) −30.7934 + 20.5892i −1.32147 + 0.883569i
\(544\) 16.1974 + 13.2406i 0.694458 + 0.567686i
\(545\) −5.50400 3.17774i −0.235766 0.136119i
\(546\) −22.4666 11.2126i −0.961482 0.479853i
\(547\) 3.76933 2.17622i 0.161165 0.0930485i −0.417248 0.908792i \(-0.637006\pi\)
0.578413 + 0.815744i \(0.303672\pi\)
\(548\) −4.58545 0.296989i −0.195881 0.0126868i
\(549\) 2.12058 1.62926i 0.0905043 0.0695352i
\(550\) 0.118562 3.66499i 0.00505551 0.156276i
\(551\) −18.6774 + 32.3503i −0.795685 + 1.37817i
\(552\) −22.2873 + 11.9549i −0.948610 + 0.508834i
\(553\) −7.66454 + 4.70834i −0.325929 + 0.200219i
\(554\) −37.0813 1.19958i −1.57544 0.0509653i
\(555\) −3.91672 1.93001i −0.166256 0.0819244i
\(556\) 7.55781 11.3300i 0.320523 0.480499i
\(557\) 16.1918 28.0450i 0.686068 1.18830i −0.287032 0.957921i \(-0.592669\pi\)
0.973100 0.230384i \(-0.0739981\pi\)
\(558\) −3.58291 + 0.356517i −0.151677 + 0.0150926i
\(559\) −48.9923 −2.07215
\(560\) −6.21801 4.49266i −0.262759 0.189850i
\(561\) −3.70384 + 0.243911i −0.156376 + 0.0102979i
\(562\) 5.72520 + 10.7012i 0.241503 + 0.451401i
\(563\) 7.52653 + 13.0363i 0.317205 + 0.549416i 0.979904 0.199471i \(-0.0639223\pi\)
−0.662699 + 0.748886i \(0.730589\pi\)
\(564\) −40.1164 + 0.0433721i −1.68920 + 0.00182629i
\(565\) 4.15609 + 2.39952i 0.174848 + 0.100949i
\(566\) −19.1562 35.8054i −0.805194 1.50501i
\(567\) 22.8154 6.81597i 0.958157 0.286244i
\(568\) 2.07262 21.2966i 0.0869652 0.893586i
\(569\) 15.7256 27.2375i 0.659252 1.14186i −0.321558 0.946890i \(-0.604207\pi\)
0.980810 0.194967i \(-0.0624601\pi\)
\(570\) −6.40257 3.41653i −0.268174 0.143103i
\(571\) 0.849545 0.490485i 0.0355523 0.0205262i −0.482118 0.876106i \(-0.660133\pi\)
0.517671 + 0.855580i \(0.326799\pi\)
\(572\) −2.49177 + 3.73543i −0.104186 + 0.156186i
\(573\) 0.0454147 + 0.689633i 0.00189723 + 0.0288098i
\(574\) 3.20750 1.83024i 0.133878 0.0763926i
\(575\) 23.1001i 0.963343i
\(576\) −13.2751 + 19.9943i −0.553128 + 0.833097i
\(577\) −6.71704 3.87808i −0.279634 0.161447i 0.353624 0.935388i \(-0.384949\pi\)
−0.633258 + 0.773941i \(0.718283\pi\)
\(578\) 2.21679 + 4.14348i 0.0922064 + 0.172346i
\(579\) 12.3990 25.1622i 0.515285 1.04571i
\(580\) −11.8786 + 5.86929i −0.493232 + 0.243709i
\(581\) −18.3328 + 0.500064i −0.760573 + 0.0207462i
\(582\) −23.2756 12.4203i −0.964805 0.514837i
\(583\) −2.71937 1.57003i −0.112625 0.0650240i
\(584\) 27.0889 + 19.3641i 1.12095 + 0.801294i
\(585\) −5.13311 6.68106i −0.212228 0.276228i
\(586\) −28.5650 17.7476i −1.18001 0.733145i
\(587\) −9.68642 16.7774i −0.399801 0.692476i 0.593900 0.804539i \(-0.297588\pi\)
−0.993701 + 0.112063i \(0.964254\pi\)
\(588\) −10.9382 + 21.6416i −0.451082 + 0.892483i
\(589\) 1.73437 3.00402i 0.0714635 0.123778i
\(590\) −0.350560 + 0.187552i −0.0144323 + 0.00772141i
\(591\) −22.5389 33.7093i −0.927126 1.38661i
\(592\) −5.34350 12.8442i −0.219616 0.527893i
\(593\) 8.54276 4.93217i 0.350809 0.202540i −0.314232 0.949346i \(-0.601747\pi\)
0.665042 + 0.746806i \(0.268414\pi\)
\(594\) −0.699160 4.20045i −0.0286869 0.172346i
\(595\) 3.71244 + 6.04335i 0.152195 + 0.247753i
\(596\) −23.7309 1.53700i −0.972058 0.0629580i
\(597\) −21.1314 + 1.39158i −0.864851 + 0.0569535i
\(598\) 14.9281 24.0271i 0.610457 0.982541i
\(599\) 26.7752 15.4587i 1.09401 0.631625i 0.159366 0.987220i \(-0.449055\pi\)
0.934640 + 0.355595i \(0.115722\pi\)
\(600\) 10.3618 + 19.3173i 0.423018 + 0.788625i
\(601\) −13.3705 + 7.71949i −0.545396 + 0.314885i −0.747263 0.664528i \(-0.768632\pi\)
0.201867 + 0.979413i \(0.435299\pi\)
\(602\) −0.239805 + 47.3128i −0.00977374 + 1.92833i
\(603\) −1.24267 9.39418i −0.0506054 0.382561i
\(604\) 1.77631 27.4258i 0.0722770 1.11594i
\(605\) 7.73009i 0.314273i
\(606\) 19.9024 12.3953i 0.808479 0.503524i
\(607\) −9.12660 −0.370437 −0.185219 0.982697i \(-0.559299\pi\)
−0.185219 + 0.982697i \(0.559299\pi\)
\(608\) −8.18616 21.6234i −0.331993 0.876943i
\(609\) 24.2196 + 34.1685i 0.981430 + 1.38458i
\(610\) −0.482240 + 0.776174i −0.0195253 + 0.0314264i
\(611\) 38.8570 22.4341i 1.57199 0.907587i
\(612\) 18.4328 12.3535i 0.745102 0.499361i
\(613\) −10.5959 + 18.3526i −0.427963 + 0.741253i −0.996692 0.0812716i \(-0.974102\pi\)
0.568729 + 0.822525i \(0.307435\pi\)
\(614\) −17.5919 0.569097i −0.709951 0.0229669i
\(615\) 1.23647 0.0814261i 0.0498594 0.00328342i
\(616\) 3.59518 + 2.42463i 0.144854 + 0.0976911i
\(617\) −1.36130 + 2.35785i −0.0548040 + 0.0949233i −0.892126 0.451787i \(-0.850787\pi\)
0.837322 + 0.546710i \(0.184120\pi\)
\(618\) 13.8573 + 22.2499i 0.557423 + 0.895021i
\(619\) −19.5491 −0.785746 −0.392873 0.919593i \(-0.628519\pi\)
−0.392873 + 0.919593i \(0.628519\pi\)
\(620\) 1.10304 0.545017i 0.0442990 0.0218884i
\(621\) 5.25772 + 26.3050i 0.210985 + 1.05558i
\(622\) 18.5124 + 34.6022i 0.742281 + 1.38742i
\(623\) −0.197976 7.25798i −0.00793173 0.290785i
\(624\) 1.70595 26.7886i 0.0682928 1.07240i
\(625\) 17.3947 0.695788
\(626\) −30.0851 18.6920i −1.20244 0.747082i
\(627\) 3.67979 + 1.81326i 0.146957 + 0.0724146i
\(628\) 22.0922 10.9159i 0.881574 0.435591i
\(629\) 12.8620i 0.512840i
\(630\) −6.47715 + 4.92444i −0.258056 + 0.196194i
\(631\) 47.6971i 1.89879i 0.314080 + 0.949396i \(0.398304\pi\)
−0.314080 + 0.949396i \(0.601696\pi\)
\(632\) −7.82304 5.59221i −0.311184 0.222446i
\(633\) 1.55219 + 23.5703i 0.0616940 + 0.936837i
\(634\) 14.3060 23.0258i 0.568164 0.914470i
\(635\) 6.67407 0.264852
\(636\) 18.7713 0.0202948i 0.744332 0.000804740i
\(637\) −1.47846 27.0807i −0.0585787 1.07298i
\(638\) 6.60393 3.53316i 0.261452 0.139879i
\(639\) −20.9730 8.67212i −0.829678 0.343064i
\(640\) 1.84063 7.99166i 0.0727571 0.315898i
\(641\) −7.82329 −0.309001 −0.154501 0.987993i \(-0.549377\pi\)
−0.154501 + 0.987993i \(0.549377\pi\)
\(642\) 3.43338 + 1.83211i 0.135505 + 0.0723077i
\(643\) 20.8295 36.0777i 0.821435 1.42277i −0.0831794 0.996535i \(-0.526507\pi\)
0.904614 0.426232i \(-0.140159\pi\)
\(644\) −23.1303 14.5340i −0.911463 0.572719i
\(645\) −7.01730 + 14.2408i −0.276306 + 0.560730i
\(646\) −0.691182 + 21.3658i −0.0271942 + 0.840624i
\(647\) −9.38911 + 16.2624i −0.369124 + 0.639342i −0.989429 0.145019i \(-0.953676\pi\)
0.620305 + 0.784361i \(0.287009\pi\)
\(648\) 16.1961 + 19.6389i 0.636242 + 0.771490i
\(649\) 0.194632 0.112371i 0.00763999 0.00441095i
\(650\) −20.8252 12.9388i −0.816833 0.507502i
\(651\) −2.24902 3.17286i −0.0881459 0.124354i
\(652\) 10.2739 5.07638i 0.402355 0.198806i
\(653\) 0.900784 0.0352504 0.0176252 0.999845i \(-0.494389\pi\)
0.0176252 + 0.999845i \(0.494389\pi\)
\(654\) −21.4647 + 0.717616i −0.839338 + 0.0280610i
\(655\) 11.6983i 0.457092i
\(656\) 3.13580 + 2.39850i 0.122433 + 0.0936456i
\(657\) 28.0065 21.5176i 1.09264 0.839483i
\(658\) −21.4749 37.6348i −0.837177 1.46716i
\(659\) 11.5880 6.69033i 0.451404 0.260618i −0.257019 0.966406i \(-0.582740\pi\)
0.708423 + 0.705788i \(0.249407\pi\)
\(660\) 0.728889 + 1.25933i 0.0283720 + 0.0490192i
\(661\) 1.46411 0.845304i 0.0569473 0.0328785i −0.471256 0.881996i \(-0.656199\pi\)
0.528203 + 0.849118i \(0.322866\pi\)
\(662\) −9.31713 5.78878i −0.362121 0.224987i
\(663\) −10.9698 + 22.2619i −0.426033 + 0.864582i
\(664\) −8.11218 17.8489i −0.314814 0.692672i
\(665\) −0.213733 7.83566i −0.00828822 0.303854i
\(666\) −14.6827 + 1.46100i −0.568944 + 0.0566127i
\(667\) −40.8609 + 23.5911i −1.58214 + 0.913450i
\(668\) 9.31119 13.9585i 0.360261 0.540071i
\(669\) −12.8251 + 26.0270i −0.495847 + 1.00626i
\(670\) 1.52748 + 2.85506i 0.0590117 + 0.110301i
\(671\) 0.258271 0.447339i 0.00997045 0.0172693i
\(672\) −25.8619 1.77859i −0.997644 0.0686108i
\(673\) 12.6580 + 21.9243i 0.487930 + 0.845119i 0.999904 0.0138817i \(-0.00441883\pi\)
−0.511974 + 0.859001i \(0.671085\pi\)
\(674\) 25.1597 40.4949i 0.969115 1.55981i
\(675\) 22.7996 4.55708i 0.877557 0.175402i
\(676\) 1.78185 + 3.60621i 0.0685327 + 0.138700i
\(677\) 28.5659 + 16.4925i 1.09788 + 0.633859i 0.935662 0.352897i \(-0.114803\pi\)
0.162213 + 0.986756i \(0.448137\pi\)
\(678\) 16.2081 0.541874i 0.622469 0.0208106i
\(679\) −0.776996 28.4854i −0.0298184 1.09317i
\(680\) −4.40935 + 6.16833i −0.169091 + 0.236544i
\(681\) 21.1491 + 31.6308i 0.810437 + 1.21209i
\(682\) −0.613236 + 0.328086i −0.0234820 + 0.0125631i
\(683\) −5.67586 3.27696i −0.217181 0.125389i 0.387463 0.921885i \(-0.373351\pi\)
−0.604644 + 0.796496i \(0.706685\pi\)
\(684\) −24.4688 + 1.63793i −0.935588 + 0.0626277i
\(685\) 1.66539i 0.0636314i
\(686\) −26.1596 + 1.29522i −0.998777 + 0.0494518i
\(687\) −5.46407 + 3.65341i −0.208467 + 0.139386i
\(688\) −46.7000 + 19.4284i −1.78042 + 0.740699i
\(689\) −18.1821 + 10.4974i −0.692682 + 0.399920i
\(690\) −4.84584 7.78068i −0.184478 0.296205i
\(691\) 0.205384 0.355736i 0.00781318 0.0135328i −0.862092 0.506751i \(-0.830846\pi\)
0.869906 + 0.493218i \(0.164180\pi\)
\(692\) 29.7299 + 19.8317i 1.13016 + 0.753889i
\(693\) 3.56947 2.90061i 0.135593 0.110185i
\(694\) −1.07483 + 0.575041i −0.0407999 + 0.0218283i
\(695\) 4.27480 + 2.46806i 0.162152 + 0.0936187i
\(696\) −23.5876 + 38.0563i −0.894085 + 1.44252i
\(697\) −1.82506 3.16109i −0.0691289 0.119735i
\(698\) 42.8417 22.9206i 1.62158 0.867558i
\(699\) −15.9226 + 32.3129i −0.602247 + 1.22219i
\(700\) −12.5972 + 20.0480i −0.476129 + 0.757743i
\(701\) 17.5496 0.662841 0.331420 0.943483i \(-0.392472\pi\)
0.331420 + 0.943483i \(0.392472\pi\)
\(702\) −26.6594 9.99398i −1.00620 0.377198i
\(703\) 7.10742 12.3104i 0.268061 0.464296i
\(704\) −0.893857 + 4.54879i −0.0336885 + 0.171439i
\(705\) −0.955403 14.5080i −0.0359826 0.546403i
\(706\) −1.21169 + 37.4558i −0.0456027 + 1.40967i
\(707\) 22.2695 + 12.0599i 0.837531 + 0.453560i
\(708\) −0.670499 + 1.16424i −0.0251989 + 0.0437549i
\(709\) 8.42157 14.5866i 0.316279 0.547811i −0.663430 0.748238i \(-0.730900\pi\)
0.979708 + 0.200428i \(0.0642332\pi\)
\(710\) 7.75097 + 0.250744i 0.290889 + 0.00941024i
\(711\) −8.08805 + 6.21412i −0.303326 + 0.233048i
\(712\) 7.06640 3.21162i 0.264825 0.120361i
\(713\) 3.79431 2.19065i 0.142098 0.0820404i
\(714\) 21.4451 + 10.7027i 0.802562 + 0.400540i
\(715\) −1.40938 0.813704i −0.0527077 0.0304308i
\(716\) 41.8368 + 27.9077i 1.56351 + 1.04296i
\(717\) −0.114896 1.74473i −0.00429089 0.0651581i
\(718\) −29.7781 + 15.9315i −1.11131 + 0.594559i
\(719\) 15.7871 + 27.3440i 0.588759 + 1.01976i 0.994395 + 0.105726i \(0.0337166\pi\)
−0.405636 + 0.914035i \(0.632950\pi\)
\(720\) −7.54238 4.33288i −0.281088 0.161477i
\(721\) −13.4824 + 24.8962i −0.502111 + 0.927182i
\(722\) −1.71231 + 2.75600i −0.0637258 + 0.102568i
\(723\) 37.4784 25.0590i 1.39384 0.931954i
\(724\) 2.76452 42.6836i 0.102743 1.58632i
\(725\) 20.4473 + 35.4158i 0.759394 + 1.31531i
\(726\) 13.8095 + 22.1732i 0.512520 + 0.822923i
\(727\) 14.8377 + 25.6997i 0.550301 + 0.953150i 0.998253 + 0.0590918i \(0.0188205\pi\)
−0.447951 + 0.894058i \(0.647846\pi\)
\(728\) 26.0584 12.7117i 0.965788 0.471127i
\(729\) 24.9256 10.3786i 0.923169 0.384394i
\(730\) −6.36895 + 10.2509i −0.235725 + 0.379404i
\(731\) 46.7647 1.72965
\(732\) 0.00333851 + 3.08790i 0.000123395 + 0.114132i
\(733\) 15.8662i 0.586033i 0.956107 + 0.293016i \(0.0946591\pi\)
−0.956107 + 0.293016i \(0.905341\pi\)
\(734\) −2.17824 0.0704661i −0.0804004 0.00260095i
\(735\) −8.08340 3.44909i −0.298161 0.127222i
\(736\) 4.70150 28.8228i 0.173300 1.06242i
\(737\) −0.915182 1.58514i −0.0337112 0.0583894i
\(738\) 3.40126 2.44248i 0.125202 0.0899090i
\(739\) −0.242332 0.139910i −0.00891432 0.00514668i 0.495536 0.868587i \(-0.334972\pi\)
−0.504451 + 0.863441i \(0.668305\pi\)
\(740\) 4.52023 2.23347i 0.166167 0.0821041i
\(741\) 22.8012 15.2455i 0.837623 0.560056i
\(742\) 10.0486 + 17.6101i 0.368894 + 0.646489i
\(743\) 8.28791 + 4.78503i 0.304054 + 0.175546i 0.644263 0.764804i \(-0.277164\pi\)
−0.340209 + 0.940350i \(0.610498\pi\)
\(744\) 2.19032 3.53388i 0.0803012 0.129558i
\(745\) 8.61886i 0.315770i
\(746\) −44.5936 1.44260i −1.63269 0.0528173i
\(747\) −20.6156 + 2.72705i −0.754286 + 0.0997774i
\(748\) 2.37847 3.56559i 0.0869654 0.130371i
\(749\) 0.114614 + 4.20187i 0.00418792 + 0.153533i
\(750\) −14.2795 + 8.89335i −0.521415 + 0.324739i
\(751\) 29.4817i 1.07580i −0.843007 0.537902i \(-0.819217\pi\)
0.843007 0.537902i \(-0.180783\pi\)
\(752\) 28.1425 36.7936i 1.02625 1.34172i
\(753\) 17.7334 + 26.5221i 0.646240 + 0.966521i
\(754\) 1.61914 50.0507i 0.0589656 1.82274i
\(755\) 9.96081 0.362511
\(756\) −9.78186 + 25.6966i −0.355763 + 0.934576i
\(757\) 27.0636 0.983643 0.491821 0.870696i \(-0.336331\pi\)
0.491821 + 0.870696i \(0.336331\pi\)
\(758\) −0.982680 + 30.3765i −0.0356926 + 1.10333i
\(759\) 2.88002 + 4.30738i 0.104538 + 0.156348i
\(760\) 7.62883 3.46724i 0.276727 0.125770i
\(761\) 34.7896i 1.26112i −0.776140 0.630561i \(-0.782825\pi\)
0.776140 0.630561i \(-0.217175\pi\)
\(762\) 19.1441 11.9230i 0.693516 0.431925i
\(763\) −12.1422 19.7659i −0.439578 0.715574i
\(764\) −0.663892 0.442857i −0.0240188 0.0160220i
\(765\) 4.89972 + 6.37728i 0.177150 + 0.230571i
\(766\) 6.01520 + 0.194591i 0.217338 + 0.00703087i
\(767\) 1.50266i 0.0542578i
\(768\) −8.99712 26.2117i −0.324656 0.945832i
\(769\) −40.8103 23.5618i −1.47166 0.849661i −0.472164 0.881511i \(-0.656527\pi\)
−0.999493 + 0.0318496i \(0.989860\pi\)
\(770\) −0.792707 + 1.35708i −0.0285672 + 0.0489057i
\(771\) −18.0926 + 12.0972i −0.651589 + 0.435669i
\(772\) 14.3485 + 29.0394i 0.516415 + 1.04515i
\(773\) 34.1954 + 19.7427i 1.22992 + 0.710096i 0.967014 0.254724i \(-0.0819848\pi\)
0.262909 + 0.964821i \(0.415318\pi\)
\(774\) 5.31204 + 53.3847i 0.190937 + 1.91887i
\(775\) −1.89872 3.28868i −0.0682041 0.118133i
\(776\) 27.7335 12.6046i 0.995575 0.452480i
\(777\) −9.21643 13.0023i −0.330638 0.466455i
\(778\) 13.1823 + 0.426448i 0.472609 + 0.0152889i
\(779\) 4.03404i 0.144535i
\(780\) 9.72867 0.0105182i 0.348342 0.000376613i
\(781\) −4.38375 −0.156863
\(782\) −14.2494 + 22.9346i −0.509557 + 0.820140i
\(783\) 31.3450 + 35.6754i 1.12018 + 1.27493i
\(784\) −12.1484 25.2273i −0.433871 0.900975i
\(785\) 4.46549 + 7.73445i 0.159380 + 0.276055i
\(786\) 20.8987 + 33.5558i 0.745432 + 1.19690i
\(787\) 15.5076 + 26.8600i 0.552788 + 0.957456i 0.998072 + 0.0620671i \(0.0197693\pi\)
−0.445284 + 0.895389i \(0.646897\pi\)
\(788\) 46.7254 + 3.02630i 1.66452 + 0.107807i
\(789\) 14.3113 9.56889i 0.509496 0.340662i
\(790\) 1.83930 2.96038i 0.0654393 0.105326i
\(791\) 9.16864 + 14.9253i 0.325999 + 0.530683i
\(792\) 4.34051 + 2.31015i 0.154233 + 0.0820875i
\(793\) −1.72684 2.99097i −0.0613217 0.106212i
\(794\) 8.76856 4.69125i 0.311184 0.166486i
\(795\) 0.447054 + 6.78862i 0.0158554 + 0.240768i
\(796\) 13.5698 20.3427i 0.480970 0.721027i
\(797\) −8.30567 4.79528i −0.294202 0.169857i 0.345633 0.938370i \(-0.387664\pi\)
−0.639835 + 0.768512i \(0.720997\pi\)
\(798\) −14.6112 22.0942i −0.517231 0.782125i
\(799\) −37.0903 + 21.4141i −1.31216 + 0.757575i
\(800\) −24.9818 4.07498i −0.883242 0.144072i
\(801\) −1.07964 8.16174i −0.0381472 0.288381i
\(802\) −8.20029 0.265279i −0.289562 0.00936733i
\(803\) 3.41099 5.90800i 0.120371 0.208489i
\(804\) 9.48192 + 5.46073i 0.334402 + 0.192585i
\(805\) 4.71473 8.70608i 0.166173 0.306849i
\(806\) −0.150352 + 4.64767i −0.00529592 + 0.163707i
\(807\) −0.815007 12.3761i −0.0286896 0.435658i
\(808\) −2.62249 + 26.9466i −0.0922588 + 0.947979i
\(809\) −7.65189 + 13.2535i −0.269026 + 0.465967i −0.968611 0.248583i \(-0.920035\pi\)
0.699584 + 0.714550i \(0.253368\pi\)
\(810\) −6.72349 + 6.31772i −0.236239 + 0.221982i
\(811\) 7.91368 0.277887 0.138943 0.990300i \(-0.455629\pi\)
0.138943 + 0.990300i \(0.455629\pi\)
\(812\) −48.3270 1.80862i −1.69594 0.0634701i
\(813\) −4.76384 + 9.66763i −0.167075 + 0.339059i
\(814\) −2.51303 + 1.34449i −0.0880816 + 0.0471244i
\(815\) 2.07665 + 3.59687i 0.0727420 + 0.125993i
\(816\) −1.62839 + 25.5705i −0.0570049 + 0.895148i
\(817\) −44.7593 25.8418i −1.56593 0.904090i
\(818\) 28.7470 15.3799i 1.00511 0.537744i
\(819\) −4.86259 30.3655i −0.169912 1.06105i
\(820\) −0.794018 + 1.19032i −0.0277283 + 0.0415678i
\(821\) −12.5292 + 21.7011i −0.437271 + 0.757375i −0.997478 0.0709774i \(-0.977388\pi\)
0.560207 + 0.828352i \(0.310721\pi\)
\(822\) −2.97517 4.77706i −0.103771 0.166619i
\(823\) −29.8939 + 17.2592i −1.04204 + 0.601619i −0.920409 0.390957i \(-0.872144\pi\)
−0.121626 + 0.992576i \(0.538811\pi\)
\(824\) −30.1250 2.93181i −1.04945 0.102134i
\(825\) 3.73338 2.49623i 0.129980 0.0869076i
\(826\) −1.45114 0.00735513i −0.0504917 0.000255918i
\(827\) 22.6614i 0.788016i 0.919107 + 0.394008i \(0.128912\pi\)
−0.919107 + 0.394008i \(0.871088\pi\)
\(828\) −27.7998 13.6614i −0.966111 0.474765i
\(829\) 7.67197 + 4.42941i 0.266458 + 0.153840i 0.627277 0.778796i \(-0.284169\pi\)
−0.360819 + 0.932636i \(0.617503\pi\)
\(830\) 6.26545 3.35207i 0.217477 0.116352i
\(831\) −25.2562 37.7733i −0.876127 1.31034i
\(832\) 23.3509 + 20.3827i 0.809547 + 0.706641i
\(833\) 1.41124 + 25.8494i 0.0488964 + 0.895627i
\(834\) 16.6710 0.557351i 0.577271 0.0192995i
\(835\) 5.26653 + 3.04063i 0.182256 + 0.105225i
\(836\) −4.24679 + 2.09836i −0.146878 + 0.0725734i
\(837\) −2.91067 3.31279i −0.100607 0.114507i
\(838\) 11.3578 18.2805i 0.392348 0.631491i
\(839\) 15.4881 + 26.8261i 0.534707 + 0.926140i 0.999177 + 0.0405511i \(0.0129114\pi\)
−0.464470 + 0.885589i \(0.653755\pi\)
\(840\) 0.0374618 9.39522i 0.00129256 0.324166i
\(841\) −27.2637 + 47.2222i −0.940129 + 1.62835i
\(842\) 4.64092 + 8.67449i 0.159937 + 0.298943i
\(843\) −6.57007 + 13.3332i −0.226285 + 0.459219i
\(844\) −22.6906 15.1360i −0.781041 0.521003i
\(845\) −1.26253 + 0.728922i −0.0434324 + 0.0250757i
\(846\) −28.6586 39.9083i −0.985302 1.37208i
\(847\) −13.4359 + 24.8104i −0.461664 + 0.852494i
\(848\) −13.1685 + 17.2165i −0.452208 + 0.591218i
\(849\) 21.9831 44.6119i 0.754456 1.53108i
\(850\) 19.8783 + 12.3505i 0.681821 + 0.423619i
\(851\) 15.5490 8.97723i 0.533014 0.307736i
\(852\) 22.6810 13.1276i 0.777038 0.449744i
\(853\) 7.55084 4.35948i 0.258536 0.149266i −0.365131 0.930956i \(-0.618976\pi\)
0.623666 + 0.781691i \(0.285642\pi\)
\(854\) −2.89688 + 1.65300i −0.0991294 + 0.0565644i
\(855\) −1.16557 8.81135i −0.0398617 0.301342i
\(856\) −4.09096 + 1.85931i −0.139826 + 0.0635498i
\(857\) 46.1822i 1.57755i 0.614681 + 0.788776i \(0.289285\pi\)
−0.614681 + 0.788776i \(0.710715\pi\)
\(858\) −5.49634 + 0.183755i −0.187642 + 0.00627330i
\(859\) −30.8054 −1.05107 −0.525534 0.850773i \(-0.676134\pi\)
−0.525534 + 0.850773i \(0.676134\pi\)
\(860\) −8.12066 16.4350i −0.276912 0.560430i
\(861\) 4.11009 + 1.88781i 0.140072 + 0.0643364i
\(862\) 37.8987 + 23.5466i 1.29083 + 0.802001i
\(863\) −12.2843 + 7.09233i −0.418161 + 0.241426i −0.694290 0.719695i \(-0.744282\pi\)
0.276129 + 0.961121i \(0.410948\pi\)
\(864\) −29.3753 + 1.04568i −0.999367 + 0.0355747i
\(865\) −6.47619 + 11.2171i −0.220197 + 0.381392i
\(866\) −0.417586 + 12.9084i −0.0141901 + 0.438645i
\(867\) −2.54393 + 5.16259i −0.0863962 + 0.175331i
\(868\) 4.48760 + 0.167947i 0.152319 + 0.00570049i
\(869\) −0.985065 + 1.70618i −0.0334160 + 0.0578783i
\(870\) −14.3165 7.63954i −0.485375 0.259005i
\(871\) −12.2381 −0.414671
\(872\) 14.4216 20.1747i 0.488377 0.683200i
\(873\) −4.23726 32.0324i −0.143410 1.08413i
\(874\) 26.3118 14.0770i 0.890010 0.476162i
\(875\) −15.9779 8.65275i −0.540151 0.292516i
\(876\) 0.0440916 + 40.7819i 0.00148972 + 1.37789i
\(877\) −34.8503 −1.17681 −0.588405 0.808566i \(-0.700244\pi\)
−0.588405 + 0.808566i \(0.700244\pi\)
\(878\) 16.5307 26.6064i 0.557884 0.897924i
\(879\) −2.70647 41.0984i −0.0912871 1.38621i
\(880\) −1.66611 0.216730i −0.0561647 0.00730597i
\(881\) 23.0498i 0.776567i −0.921540 0.388283i \(-0.873068\pi\)
0.921540 0.388283i \(-0.126932\pi\)
\(882\) −29.3483 + 4.54726i −0.988209 + 0.153114i
\(883\) 1.28738i 0.0433239i 0.999765 + 0.0216620i \(0.00689576\pi\)
−0.999765 + 0.0216620i \(0.993104\pi\)
\(884\) −12.6947 25.6922i −0.426968 0.864121i
\(885\) −0.436782 0.215230i −0.0146823 0.00723486i
\(886\) 15.0008 + 9.32009i 0.503963 + 0.313115i
\(887\) −5.02232 −0.168633 −0.0843165 0.996439i \(-0.526871\pi\)
−0.0843165 + 0.996439i \(0.526871\pi\)
\(888\) 8.97591 14.4818i 0.301212 0.485977i
\(889\) 21.4210 + 11.6004i 0.718437 + 0.389066i
\(890\) 1.32709 + 2.48050i 0.0444840 + 0.0831465i
\(891\) 3.68319 3.69229i 0.123391 0.123696i
\(892\) −14.8416 30.0373i −0.496935 1.00572i
\(893\) 47.3330 1.58394
\(894\) −15.3973 24.7225i −0.514963 0.826845i
\(895\) −9.11347 + 15.7850i −0.304630 + 0.527634i
\(896\) 19.7982 22.4506i 0.661412 0.750023i
\(897\) 34.5694 2.27651i 1.15424 0.0760106i
\(898\) −32.8802 1.06367i −1.09723 0.0354953i
\(899\) 3.87815 6.71714i 0.129343 0.224029i
\(900\) −11.8408 + 24.0952i −0.394695 + 0.803174i
\(901\) 17.3554 10.0201i 0.578191 0.333819i
\(902\) 0.426851 0.687023i 0.0142126 0.0228754i
\(903\) −47.2750 + 33.5099i −1.57321 + 1.11514i
\(904\) −10.8898 + 15.2340i −0.362190 + 0.506674i
\(905\) 15.5023 0.515313
\(906\) 28.5718 17.7946i 0.949235 0.591188i
\(907\) 27.6614i 0.918483i −0.888311 0.459242i \(-0.848121\pi\)
0.888311 0.459242i \(-0.151879\pi\)
\(908\) −43.8443 2.83970i −1.45503 0.0942387i
\(909\) 26.5371 + 10.9728i 0.880181 + 0.363946i
\(910\) 5.20790 + 9.12686i 0.172640 + 0.302552i
\(911\) −9.94522 + 5.74187i −0.329500 + 0.190237i −0.655619 0.755092i \(-0.727592\pi\)
0.326119 + 0.945329i \(0.394259\pi\)
\(912\) 15.6886 23.5742i 0.519502 0.780618i
\(913\) −3.47861 + 2.00837i −0.115125 + 0.0664675i
\(914\) −3.97032 + 6.39029i −0.131326 + 0.211372i
\(915\) −1.11673 + 0.0735408i −0.0369181 + 0.00243118i
\(916\) 0.490544 7.57390i 0.0162080 0.250249i
\(917\) −20.3333 + 37.5468i −0.671464 + 1.23991i
\(918\) 25.4473 + 9.53956i 0.839885 + 0.314853i
\(919\) 23.5746 13.6108i 0.777656 0.448980i −0.0579432 0.998320i \(-0.518454\pi\)
0.835599 + 0.549340i \(0.185121\pi\)
\(920\) 10.5346 + 1.02524i 0.347314 + 0.0338012i
\(921\) −11.9819 17.9202i −0.394816 0.590490i
\(922\) 11.3489 6.07174i 0.373755 0.199962i
\(923\) −14.6551 + 25.3835i −0.482380 + 0.835507i
\(924\) 0.150553 + 5.30882i 0.00495282 + 0.174647i
\(925\) −7.78093 13.4770i −0.255835 0.443120i
\(926\) 0.680430 + 0.422754i 0.0223603 + 0.0138926i
\(927\) −12.2671 + 29.6672i −0.402904 + 0.974398i
\(928\) −18.3047 48.3510i −0.600881 1.58720i
\(929\) −24.2654 14.0097i −0.796123 0.459642i 0.0459904 0.998942i \(-0.485356\pi\)
−0.842114 + 0.539300i \(0.818689\pi\)
\(930\) 1.32942 + 0.709401i 0.0435933 + 0.0232622i
\(931\) 12.9334 25.5207i 0.423876 0.836407i
\(932\) −18.4261 37.2918i −0.603568 1.22153i
\(933\) −21.2443 + 43.1127i −0.695507 + 1.41145i
\(934\) 6.36909 + 11.9047i 0.208403 + 0.389533i
\(935\) 1.34529 + 0.776706i 0.0439958 + 0.0254010i
\(936\) 27.8872 17.4101i 0.911521 0.569067i
\(937\) 7.31723i 0.239043i −0.992832 0.119522i \(-0.961864\pi\)
0.992832 0.119522i \(-0.0381361\pi\)
\(938\) −0.0599023 + 11.8185i −0.00195588 + 0.385888i
\(939\) −2.85049 43.2854i −0.0930224 1.41257i
\(940\) 13.9665 + 9.31651i 0.455537 + 0.303871i
\(941\) 15.0434 8.68531i 0.490401 0.283133i −0.234340 0.972155i \(-0.575293\pi\)
0.724741 + 0.689022i \(0.241960\pi\)
\(942\) 26.6263 + 14.2083i 0.867530 + 0.462930i
\(943\) −2.54766 + 4.41267i −0.0829631 + 0.143696i
\(944\) −0.595892 1.43235i −0.0193946 0.0466190i
\(945\) −9.52291 2.93590i −0.309780 0.0955049i
\(946\) 4.88842 + 9.13710i 0.158936 + 0.297073i
\(947\) −34.0518 19.6598i −1.10654 0.638858i −0.168605 0.985684i \(-0.553926\pi\)
−0.937930 + 0.346825i \(0.887260\pi\)
\(948\) −0.0127333 11.7775i −0.000413558 0.382515i
\(949\) −22.8063 39.5017i −0.740324 1.28228i
\(950\) −12.2011 22.8055i −0.395856 0.739908i
\(951\) 33.1287 2.18164i 1.07427 0.0707446i
\(952\) −24.8736 + 12.1337i −0.806157 + 0.393256i
\(953\) −33.5157 −1.08568 −0.542840 0.839836i \(-0.682651\pi\)
−0.542840 + 0.839836i \(0.682651\pi\)
\(954\) 13.4100 + 18.6740i 0.434164 + 0.604593i
\(955\) 0.144618 0.250486i 0.00467973 0.00810553i
\(956\) 1.67961 + 1.12040i 0.0543223 + 0.0362363i
\(957\) 8.22821 + 4.05454i 0.265980 + 0.131065i
\(958\) −33.8152 1.09392i −1.09252 0.0353430i
\(959\) 2.89468 5.34522i 0.0934740 0.172606i
\(960\) 9.26931 3.86802i 0.299166 0.124840i
\(961\) 15.1399 26.2230i 0.488383 0.845904i
\(962\) −0.616140 + 19.0461i −0.0198651 + 0.614070i
\(963\) 0.625037 + 4.72508i 0.0201415 + 0.152264i
\(964\) −3.36467 + 51.9499i −0.108369 + 1.67319i
\(965\) −10.1667 + 5.86972i −0.327276 + 0.188953i
\(966\) −2.02926 33.3955i −0.0652905 1.07448i
\(967\) 17.2860 + 9.98006i 0.555879 + 0.320937i 0.751490 0.659745i \(-0.229336\pi\)
−0.195611 + 0.980682i \(0.562669\pi\)
\(968\) −30.0211 2.92170i −0.964915 0.0939071i
\(969\) −21.7645 + 14.5523i −0.699175 + 0.467486i
\(970\) 5.20841 + 9.73521i 0.167232 + 0.312579i
\(971\) −26.7791 46.3827i −0.859381 1.48849i −0.872520 0.488578i \(-0.837516\pi\)
0.0131389 0.999914i \(-0.495818\pi\)
\(972\) −7.99941 + 30.1332i −0.256581 + 0.966523i
\(973\) 9.43052 + 15.3516i 0.302329 + 0.492150i
\(974\) −18.0606 11.2211i −0.578700 0.359549i
\(975\) −1.97315 29.9627i −0.0631913 0.959573i
\(976\) −2.83213 2.16623i −0.0906544 0.0693393i
\(977\) −23.0750 39.9671i −0.738236 1.27866i −0.953289 0.302059i \(-0.902326\pi\)
0.215054 0.976602i \(-0.431007\pi\)
\(978\) 12.3824 + 6.60748i 0.395946 + 0.211284i
\(979\) −0.795117 1.37718i −0.0254121 0.0440150i
\(980\) 8.83947 4.98469i 0.282367 0.159230i
\(981\) −16.0254 20.8581i −0.511653 0.665948i
\(982\) −18.6245 11.5715i −0.594331 0.369261i
\(983\) 29.8119 0.950852 0.475426 0.879756i \(-0.342294\pi\)
0.475426 + 0.879756i \(0.342294\pi\)
\(984\) −0.151112 + 4.83283i −0.00481726 + 0.154065i
\(985\) 16.9702i 0.540716i
\(986\) −1.54552 + 47.7750i −0.0492193 + 1.52147i
\(987\) 22.1504 48.2253i 0.705055 1.53503i
\(988\) −2.04701 + 31.6054i −0.0651240 + 1.00550i
\(989\) −32.6402 56.5345i −1.03790 1.79769i
\(990\) −0.733843 + 1.62396i −0.0233231 + 0.0516129i
\(991\) 34.7638 + 20.0709i 1.10431 + 0.637574i 0.937350 0.348390i \(-0.113271\pi\)
0.166960 + 0.985964i \(0.446605\pi\)
\(992\) 1.69976 + 4.48983i 0.0539674 + 0.142552i
\(993\) −0.882778 13.4052i −0.0280141 0.425401i
\(994\) 24.4415 + 14.2770i 0.775239 + 0.452839i
\(995\) 7.67527 + 4.43132i 0.243323 + 0.140482i
\(996\) 11.9836 20.8082i 0.379716 0.659332i
\(997\) 45.5952i 1.44401i −0.691886 0.722007i \(-0.743220\pi\)
0.691886 0.722007i \(-0.256780\pi\)
\(998\) −0.0198587 + 0.613871i −0.000628616 + 0.0194317i
\(999\) −11.9279 13.5757i −0.377381 0.429518i
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 252.2.n.b.31.1 84
3.2 odd 2 756.2.n.b.199.42 84
4.3 odd 2 inner 252.2.n.b.31.30 yes 84
7.5 odd 6 252.2.bj.b.103.28 yes 84
9.2 odd 6 756.2.bj.b.451.15 84
9.7 even 3 252.2.bj.b.115.28 yes 84
12.11 even 2 756.2.n.b.199.13 84
21.5 even 6 756.2.bj.b.523.15 84
28.19 even 6 252.2.bj.b.103.27 yes 84
36.7 odd 6 252.2.bj.b.115.27 yes 84
36.11 even 6 756.2.bj.b.451.16 84
63.47 even 6 756.2.n.b.19.13 84
63.61 odd 6 inner 252.2.n.b.187.30 yes 84
84.47 odd 6 756.2.bj.b.523.16 84
252.47 odd 6 756.2.n.b.19.42 84
252.187 even 6 inner 252.2.n.b.187.1 yes 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.n.b.31.1 84 1.1 even 1 trivial
252.2.n.b.31.30 yes 84 4.3 odd 2 inner
252.2.n.b.187.1 yes 84 252.187 even 6 inner
252.2.n.b.187.30 yes 84 63.61 odd 6 inner
252.2.bj.b.103.27 yes 84 28.19 even 6
252.2.bj.b.103.28 yes 84 7.5 odd 6
252.2.bj.b.115.27 yes 84 36.7 odd 6
252.2.bj.b.115.28 yes 84 9.7 even 3
756.2.n.b.19.13 84 63.47 even 6
756.2.n.b.19.42 84 252.47 odd 6
756.2.n.b.199.13 84 12.11 even 2
756.2.n.b.199.42 84 3.2 odd 2
756.2.bj.b.451.15 84 9.2 odd 6
756.2.bj.b.451.16 84 36.11 even 6
756.2.bj.b.523.15 84 21.5 even 6
756.2.bj.b.523.16 84 84.47 odd 6