Properties

Label 529.2.c.n.501.1
Level $529$
Weight $2$
Character 529.501
Analytic conductor $4.224$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $10$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [529,2,Mod(118,529)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(529, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("529.118");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 529 = 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 529.c (of order \(11\), degree \(10\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.22408626693\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: 20.0.54296067514572573056640625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 2 x^{18} - 3 x^{17} + 5 x^{16} - 8 x^{15} + 13 x^{14} - 21 x^{13} + 34 x^{12} - 55 x^{11} + 89 x^{10} + 55 x^{9} + 34 x^{8} + 21 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 23)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 501.1
Root \(0.256741 - 0.562183i\) of defining polynomial
Character \(\chi\) \(=\) 529.501
Dual form 529.2.c.n.170.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.592999 - 0.174120i) q^{2} +(1.46431 - 1.68991i) q^{3} +(-1.36118 - 0.874775i) q^{4} +(0.175911 - 1.22349i) q^{5} +(-1.16258 + 0.747147i) q^{6} +(-1.34431 - 2.94363i) q^{7} +(1.46431 + 1.68991i) q^{8} +(-0.284630 - 1.97964i) q^{9} +O(q^{10})\) \(q+(-0.592999 - 0.174120i) q^{2} +(1.46431 - 1.68991i) q^{3} +(-1.36118 - 0.874775i) q^{4} +(0.175911 - 1.22349i) q^{5} +(-1.16258 + 0.747147i) q^{6} +(-1.34431 - 2.94363i) q^{7} +(1.46431 + 1.68991i) q^{8} +(-0.284630 - 1.97964i) q^{9} +(-0.317349 + 0.694897i) q^{10} +(-5.02397 + 1.47517i) q^{11} +(-3.47148 + 1.01932i) q^{12} +(1.24625 - 2.72890i) q^{13} +(0.284630 + 1.97964i) q^{14} +(-1.80999 - 2.08884i) q^{15} +(0.770222 + 1.68655i) q^{16} +(-0.642661 + 0.413013i) q^{17} +(-0.175911 + 1.22349i) q^{18} +(1.68251 + 1.08128i) q^{19} +(-1.30972 + 1.51150i) q^{20} +(-6.94296 - 2.03864i) q^{21} +3.23607 q^{22} +5.00000 q^{24} +(3.33149 + 0.978214i) q^{25} +(-1.21418 + 1.40124i) q^{26} +(1.88110 + 1.20891i) q^{27} +(-0.745170 + 5.18277i) q^{28} +(-2.52376 + 1.62192i) q^{29} +(0.709614 + 1.55384i) q^{30} +(-4.39294 - 5.06972i) q^{31} +(-0.799530 - 5.56085i) q^{32} +(-4.86376 + 10.6502i) q^{33} +(0.453011 - 0.133016i) q^{34} +(-3.83797 + 1.12693i) q^{35} +(-1.34431 + 2.94363i) q^{36} +(-0.175911 - 1.22349i) q^{37} +(-0.809452 - 0.934158i) q^{38} +(-2.78669 - 6.10200i) q^{39} +(2.32517 - 1.49429i) q^{40} +(0.494136 - 3.43679i) q^{41} +(3.76220 + 2.41782i) q^{42} +(8.12895 + 2.38688i) q^{44} -2.47214 q^{45} -2.23607 q^{47} +(3.97796 + 1.16803i) q^{48} +(-2.27377 + 2.62407i) q^{49} +(-1.80524 - 1.16016i) q^{50} +(-0.243103 + 1.69082i) q^{51} +(-4.08353 + 2.62433i) q^{52} +(-0.196132 - 0.429470i) q^{53} +(-0.904995 - 1.04442i) q^{54} +(0.921081 + 6.40626i) q^{55} +(3.00597 - 6.58216i) q^{56} +(4.29098 - 1.25995i) q^{57} +(1.77900 - 0.522361i) q^{58} +(2.68862 - 5.88726i) q^{59} +(0.636451 + 4.42662i) q^{60} +(-4.54753 - 5.24813i) q^{61} +(1.72227 + 3.77124i) q^{62} +(-5.44471 + 3.49910i) q^{63} +(0.0335960 - 0.233665i) q^{64} +(-3.11954 - 2.00481i) q^{65} +(4.73862 - 5.46866i) q^{66} +(-2.65197 - 0.778690i) q^{67} +1.23607 q^{68} +2.47214 q^{70} +(-11.7404 - 3.44730i) q^{71} +(2.92863 - 3.37981i) q^{72} +(5.49159 + 3.52923i) q^{73} +(-0.108719 + 0.756156i) q^{74} +(6.53144 - 4.19750i) q^{75} +(-1.34431 - 2.94363i) q^{76} +(11.0961 + 12.8056i) q^{77} +(0.590023 + 4.10370i) q^{78} +(4.54641 - 9.95526i) q^{79} +(2.19896 - 0.645674i) q^{80} +(10.5544 - 3.09906i) q^{81} +(-0.891438 + 1.95198i) q^{82} +(-1.24724 - 8.67473i) q^{83} +(7.66724 + 8.84847i) q^{84} +(0.392265 + 0.858940i) q^{85} +(-0.954677 + 6.63992i) q^{87} +(-9.84957 - 6.32993i) q^{88} +(-6.85779 + 7.91431i) q^{89} +(1.46597 + 0.430449i) q^{90} -9.70820 q^{91} -15.0000 q^{93} +(1.32599 + 0.389345i) q^{94} +(1.61890 - 1.86832i) q^{95} +(-10.5681 - 6.79170i) q^{96} +(2.52014 - 17.5280i) q^{97} +(1.80524 - 1.16016i) q^{98} +(4.35028 + 9.52579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + q^{2} + q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + q^{2} + q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 4 q^{9} + 6 q^{10} - 6 q^{11} - 5 q^{12} - 6 q^{13} + 4 q^{14} - 10 q^{15} + 3 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 4 q^{20} - 10 q^{21} + 20 q^{22} + 100 q^{24} - 2 q^{25} + 3 q^{26} - 6 q^{28} + 6 q^{29} + 10 q^{30} - 9 q^{32} + 10 q^{33} - 8 q^{34} - 8 q^{35} + 2 q^{36} + 2 q^{37} + 2 q^{38} - 10 q^{40} - 2 q^{41} + 8 q^{44} + 40 q^{45} + 15 q^{48} + 2 q^{49} + 11 q^{50} + 10 q^{51} + 3 q^{52} - 8 q^{53} - 5 q^{54} + 4 q^{55} - 10 q^{56} - 3 q^{58} - 4 q^{59} + 4 q^{61} - 15 q^{62} + 4 q^{63} - 4 q^{64} - 6 q^{65} + 10 q^{66} - 10 q^{67} - 20 q^{68} - 40 q^{70} - 20 q^{71} - 22 q^{73} - 6 q^{74} - 20 q^{75} + 2 q^{76} + 16 q^{77} + 15 q^{78} - 4 q^{79} + 18 q^{80} + 22 q^{81} + 11 q^{82} - 22 q^{83} + 10 q^{84} + 16 q^{85} + 10 q^{88} - 12 q^{89} + 12 q^{90} - 60 q^{91} - 300 q^{93} + 5 q^{94} - 4 q^{95} + 5 q^{96} + 22 q^{97} - 11 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/529\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{6}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.592999 0.174120i −0.419314 0.123122i 0.0652676 0.997868i \(-0.479210\pi\)
−0.484581 + 0.874746i \(0.661028\pi\)
\(3\) 1.46431 1.68991i 0.845422 0.975669i −0.154502 0.987992i \(-0.549377\pi\)
0.999924 + 0.0123239i \(0.00392292\pi\)
\(4\) −1.36118 0.874775i −0.680588 0.437388i
\(5\) 0.175911 1.22349i 0.0786697 0.547160i −0.911928 0.410351i \(-0.865406\pi\)
0.990597 0.136809i \(-0.0436847\pi\)
\(6\) −1.16258 + 0.747147i −0.474623 + 0.305022i
\(7\) −1.34431 2.94363i −0.508102 1.11259i −0.973750 0.227618i \(-0.926906\pi\)
0.465649 0.884970i \(-0.345821\pi\)
\(8\) 1.46431 + 1.68991i 0.517713 + 0.597472i
\(9\) −0.284630 1.97964i −0.0948766 0.659881i
\(10\) −0.317349 + 0.694897i −0.100355 + 0.219746i
\(11\) −5.02397 + 1.47517i −1.51478 + 0.444781i −0.930354 0.366663i \(-0.880500\pi\)
−0.584430 + 0.811444i \(0.698682\pi\)
\(12\) −3.47148 + 1.01932i −1.00213 + 0.294252i
\(13\) 1.24625 2.72890i 0.345646 0.756860i −0.654354 0.756189i \(-0.727059\pi\)
1.00000 0.000670851i \(-0.000213539\pi\)
\(14\) 0.284630 + 1.97964i 0.0760705 + 0.529082i
\(15\) −1.80999 2.08884i −0.467338 0.539336i
\(16\) 0.770222 + 1.68655i 0.192555 + 0.421638i
\(17\) −0.642661 + 0.413013i −0.155868 + 0.100170i −0.616250 0.787551i \(-0.711349\pi\)
0.460382 + 0.887721i \(0.347713\pi\)
\(18\) −0.175911 + 1.22349i −0.0414626 + 0.288379i
\(19\) 1.68251 + 1.08128i 0.385994 + 0.248063i 0.719218 0.694785i \(-0.244500\pi\)
−0.333224 + 0.942848i \(0.608137\pi\)
\(20\) −1.30972 + 1.51150i −0.292863 + 0.337981i
\(21\) −6.94296 2.03864i −1.51508 0.444867i
\(22\) 3.23607 0.689932
\(23\) 0 0
\(24\) 5.00000 1.02062
\(25\) 3.33149 + 0.978214i 0.666298 + 0.195643i
\(26\) −1.21418 + 1.40124i −0.238120 + 0.274805i
\(27\) 1.88110 + 1.20891i 0.362018 + 0.232655i
\(28\) −0.745170 + 5.18277i −0.140824 + 0.979452i
\(29\) −2.52376 + 1.62192i −0.468651 + 0.301183i −0.753570 0.657368i \(-0.771670\pi\)
0.284919 + 0.958552i \(0.408033\pi\)
\(30\) 0.709614 + 1.55384i 0.129557 + 0.283691i
\(31\) −4.39294 5.06972i −0.788995 0.910549i 0.208729 0.977973i \(-0.433067\pi\)
−0.997724 + 0.0674245i \(0.978522\pi\)
\(32\) −0.799530 5.56085i −0.141338 0.983029i
\(33\) −4.86376 + 10.6502i −0.846673 + 1.85395i
\(34\) 0.453011 0.133016i 0.0776908 0.0228121i
\(35\) −3.83797 + 1.12693i −0.648736 + 0.190486i
\(36\) −1.34431 + 2.94363i −0.224052 + 0.490605i
\(37\) −0.175911 1.22349i −0.0289196 0.201140i 0.970239 0.242148i \(-0.0778521\pi\)
−0.999159 + 0.0410084i \(0.986943\pi\)
\(38\) −0.809452 0.934158i −0.131311 0.151540i
\(39\) −2.78669 6.10200i −0.446227 0.977102i
\(40\) 2.32517 1.49429i 0.367641 0.236269i
\(41\) 0.494136 3.43679i 0.0771712 0.536737i −0.914160 0.405353i \(-0.867149\pi\)
0.991331 0.131384i \(-0.0419422\pi\)
\(42\) 3.76220 + 2.41782i 0.580520 + 0.373078i
\(43\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(44\) 8.12895 + 2.38688i 1.22549 + 0.359835i
\(45\) −2.47214 −0.368524
\(46\) 0 0
\(47\) −2.23607 −0.326164 −0.163082 0.986613i \(-0.552144\pi\)
−0.163082 + 0.986613i \(0.552144\pi\)
\(48\) 3.97796 + 1.16803i 0.574169 + 0.168591i
\(49\) −2.27377 + 2.62407i −0.324824 + 0.374866i
\(50\) −1.80524 1.16016i −0.255300 0.164071i
\(51\) −0.243103 + 1.69082i −0.0340412 + 0.236762i
\(52\) −4.08353 + 2.62433i −0.566284 + 0.363928i
\(53\) −0.196132 0.429470i −0.0269409 0.0589922i 0.895683 0.444693i \(-0.146687\pi\)
−0.922624 + 0.385700i \(0.873960\pi\)
\(54\) −0.904995 1.04442i −0.123154 0.142128i
\(55\) 0.921081 + 6.40626i 0.124199 + 0.863820i
\(56\) 3.00597 6.58216i 0.401690 0.879578i
\(57\) 4.29098 1.25995i 0.568355 0.166884i
\(58\) 1.77900 0.522361i 0.233594 0.0685893i
\(59\) 2.68862 5.88726i 0.350029 0.766456i −0.649950 0.759977i \(-0.725210\pi\)
0.999979 0.00647940i \(-0.00206247\pi\)
\(60\) 0.636451 + 4.42662i 0.0821655 + 0.571474i
\(61\) −4.54753 5.24813i −0.582252 0.671954i 0.385836 0.922568i \(-0.373913\pi\)
−0.968087 + 0.250613i \(0.919368\pi\)
\(62\) 1.72227 + 3.77124i 0.218728 + 0.478948i
\(63\) −5.44471 + 3.49910i −0.685969 + 0.440845i
\(64\) 0.0335960 0.233665i 0.00419950 0.0292081i
\(65\) −3.11954 2.00481i −0.386931 0.248666i
\(66\) 4.73862 5.46866i 0.583283 0.673145i
\(67\) −2.65197 0.778690i −0.323990 0.0951321i 0.115693 0.993285i \(-0.463091\pi\)
−0.439683 + 0.898153i \(0.644909\pi\)
\(68\) 1.23607 0.149895
\(69\) 0 0
\(70\) 2.47214 0.295477
\(71\) −11.7404 3.44730i −1.39333 0.409119i −0.502943 0.864320i \(-0.667749\pi\)
−0.890389 + 0.455201i \(0.849568\pi\)
\(72\) 2.92863 3.37981i 0.345142 0.398315i
\(73\) 5.49159 + 3.52923i 0.642742 + 0.413065i 0.821008 0.570917i \(-0.193412\pi\)
−0.178266 + 0.983982i \(0.557049\pi\)
\(74\) −0.108719 + 0.756156i −0.0126383 + 0.0879014i
\(75\) 6.53144 4.19750i 0.754185 0.484685i
\(76\) −1.34431 2.94363i −0.154203 0.337658i
\(77\) 11.0961 + 12.8056i 1.26452 + 1.45934i
\(78\) 0.590023 + 4.10370i 0.0668069 + 0.464652i
\(79\) 4.54641 9.95526i 0.511512 1.12005i −0.461043 0.887378i \(-0.652524\pi\)
0.972554 0.232676i \(-0.0747483\pi\)
\(80\) 2.19896 0.645674i 0.245851 0.0721885i
\(81\) 10.5544 3.09906i 1.17271 0.344340i
\(82\) −0.891438 + 1.95198i −0.0984429 + 0.215560i
\(83\) −1.24724 8.67473i −0.136902 0.952175i −0.936257 0.351316i \(-0.885734\pi\)
0.799355 0.600859i \(-0.205175\pi\)
\(84\) 7.66724 + 8.84847i 0.836565 + 0.965447i
\(85\) 0.392265 + 0.858940i 0.0425471 + 0.0931651i
\(86\) 0 0
\(87\) −0.954677 + 6.63992i −0.102352 + 0.711875i
\(88\) −9.84957 6.32993i −1.04997 0.674773i
\(89\) −6.85779 + 7.91431i −0.726924 + 0.838915i −0.992122 0.125279i \(-0.960017\pi\)
0.265197 + 0.964194i \(0.414563\pi\)
\(90\) 1.46597 + 0.430449i 0.154527 + 0.0453733i
\(91\) −9.70820 −1.01770
\(92\) 0 0
\(93\) −15.0000 −1.55543
\(94\) 1.32599 + 0.389345i 0.136765 + 0.0401579i
\(95\) 1.61890 1.86832i 0.166096 0.191685i
\(96\) −10.5681 6.79170i −1.07860 0.693175i
\(97\) 2.52014 17.5280i 0.255881 1.77969i −0.305555 0.952175i \(-0.598842\pi\)
0.561436 0.827520i \(-0.310249\pi\)
\(98\) 1.80524 1.16016i 0.182357 0.117194i
\(99\) 4.35028 + 9.52579i 0.437220 + 0.957378i
\(100\) −3.67903 4.24583i −0.367903 0.424583i
\(101\) −0.636451 4.42662i −0.0633293 0.440465i −0.996675 0.0814849i \(-0.974034\pi\)
0.933345 0.358980i \(-0.116875\pi\)
\(102\) 0.438565 0.960324i 0.0434244 0.0950862i
\(103\) −4.01101 + 1.17774i −0.395216 + 0.116046i −0.473301 0.880901i \(-0.656938\pi\)
0.0780848 + 0.996947i \(0.475120\pi\)
\(104\) 6.43647 1.88992i 0.631148 0.185322i
\(105\) −3.71558 + 8.13600i −0.362604 + 0.793992i
\(106\) 0.0415269 + 0.288826i 0.00403345 + 0.0280533i
\(107\) 8.78588 + 10.1394i 0.849363 + 0.980217i 0.999965 0.00837738i \(-0.00266663\pi\)
−0.150602 + 0.988594i \(0.548121\pi\)
\(108\) −1.50299 3.29108i −0.144625 0.316684i
\(109\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(110\) 0.569259 3.95929i 0.0542767 0.377503i
\(111\) −2.32517 1.49429i −0.220695 0.141832i
\(112\) 3.92916 4.53450i 0.371271 0.428470i
\(113\) 8.40893 + 2.46908i 0.791046 + 0.232272i 0.652205 0.758043i \(-0.273844\pi\)
0.138841 + 0.990315i \(0.455662\pi\)
\(114\) −2.76393 −0.258866
\(115\) 0 0
\(116\) 4.85410 0.450692
\(117\) −5.75696 1.69040i −0.532231 0.156277i
\(118\) −2.61944 + 3.02300i −0.241139 + 0.278290i
\(119\) 2.07969 + 1.33654i 0.190645 + 0.122520i
\(120\) 0.879554 6.11743i 0.0802919 0.558443i
\(121\) 13.8104 8.87538i 1.25549 0.806853i
\(122\) 1.78288 + 3.90396i 0.161414 + 0.353447i
\(123\) −5.08429 5.86759i −0.458435 0.529063i
\(124\) 1.54470 + 10.7436i 0.138718 + 0.964806i
\(125\) 4.35028 9.52579i 0.389101 0.852013i
\(126\) 3.83797 1.12693i 0.341914 0.100395i
\(127\) 6.99643 2.05434i 0.620833 0.182293i 0.0438350 0.999039i \(-0.486042\pi\)
0.576998 + 0.816746i \(0.304224\pi\)
\(128\) −4.72824 + 10.3534i −0.417921 + 0.915120i
\(129\) 0 0
\(130\) 1.50081 + 1.73202i 0.131630 + 0.151909i
\(131\) 7.77167 + 17.0176i 0.679014 + 1.48683i 0.863685 + 0.504033i \(0.168151\pi\)
−0.184671 + 0.982800i \(0.559122\pi\)
\(132\) 15.9369 10.2420i 1.38713 0.891456i
\(133\) 0.921081 6.40626i 0.0798679 0.555493i
\(134\) 1.43703 + 0.923525i 0.124141 + 0.0797804i
\(135\) 1.80999 2.08884i 0.155779 0.179779i
\(136\) −1.63901 0.481257i −0.140544 0.0412674i
\(137\) 21.8885 1.87006 0.935032 0.354563i \(-0.115370\pi\)
0.935032 + 0.354563i \(0.115370\pi\)
\(138\) 0 0
\(139\) −10.7082 −0.908258 −0.454129 0.890936i \(-0.650049\pi\)
−0.454129 + 0.890936i \(0.650049\pi\)
\(140\) 6.20997 + 1.82341i 0.524838 + 0.154106i
\(141\) −3.27430 + 3.77875i −0.275746 + 0.318228i
\(142\) 6.36182 + 4.08849i 0.533872 + 0.343099i
\(143\) −2.23551 + 15.5483i −0.186943 + 1.30022i
\(144\) 3.11954 2.00481i 0.259962 0.167067i
\(145\) 1.54044 + 3.37310i 0.127927 + 0.280121i
\(146\) −2.64200 3.04903i −0.218653 0.252339i
\(147\) 1.10492 + 7.68491i 0.0911325 + 0.633840i
\(148\) −0.830830 + 1.81926i −0.0682938 + 0.149543i
\(149\) 22.9209 6.73018i 1.87775 0.551358i 0.880787 0.473513i \(-0.157014\pi\)
0.996965 0.0778452i \(-0.0248040\pi\)
\(150\) −4.60401 + 1.35186i −0.375916 + 0.110379i
\(151\) 1.75973 3.85326i 0.143204 0.313574i −0.824416 0.565985i \(-0.808496\pi\)
0.967620 + 0.252411i \(0.0812234\pi\)
\(152\) 0.636451 + 4.42662i 0.0516230 + 0.359046i
\(153\) 1.00054 + 1.15468i 0.0808887 + 0.0933506i
\(154\) −4.35028 9.52579i −0.350556 0.767610i
\(155\) −6.97550 + 4.48288i −0.560286 + 0.360074i
\(156\) −1.54470 + 10.7436i −0.123675 + 0.860178i
\(157\) 9.60409 + 6.17218i 0.766490 + 0.492593i 0.864525 0.502590i \(-0.167619\pi\)
−0.0980350 + 0.995183i \(0.531256\pi\)
\(158\) −4.42943 + 5.11184i −0.352387 + 0.406676i
\(159\) −1.01296 0.297433i −0.0803332 0.0235880i
\(160\) −6.94427 −0.548993
\(161\) 0 0
\(162\) −6.79837 −0.534131
\(163\) 5.53045 + 1.62389i 0.433178 + 0.127193i 0.491050 0.871131i \(-0.336613\pi\)
−0.0578716 + 0.998324i \(0.518431\pi\)
\(164\) −3.67903 + 4.24583i −0.287284 + 0.331543i
\(165\) 12.1747 + 7.82423i 0.947802 + 0.609115i
\(166\) −0.770835 + 5.36128i −0.0598284 + 0.416116i
\(167\) 1.28532 0.826026i 0.0994611 0.0639198i −0.489965 0.871742i \(-0.662990\pi\)
0.589426 + 0.807822i \(0.299354\pi\)
\(168\) −6.72156 14.7182i −0.518579 1.13553i
\(169\) 2.61944 + 3.02300i 0.201496 + 0.232538i
\(170\) −0.0830538 0.577652i −0.00636994 0.0443039i
\(171\) 1.66166 3.63853i 0.127070 0.278245i
\(172\) 0 0
\(173\) −22.0149 + 6.46415i −1.67376 + 0.491460i −0.974684 0.223588i \(-0.928223\pi\)
−0.699076 + 0.715048i \(0.746405\pi\)
\(174\) 1.72227 3.77124i 0.130565 0.285897i
\(175\) −1.59906 11.1217i −0.120878 0.840722i
\(176\) −6.35752 7.33697i −0.479216 0.553045i
\(177\) −6.01194 13.1643i −0.451885 0.989491i
\(178\) 5.44471 3.49910i 0.408098 0.262269i
\(179\) −0.100788 + 0.700995i −0.00753324 + 0.0523949i −0.993241 0.116068i \(-0.962971\pi\)
0.985708 + 0.168462i \(0.0538802\pi\)
\(180\) 3.36501 + 2.16256i 0.250813 + 0.161188i
\(181\) 10.9051 12.5851i 0.810566 0.935443i −0.188345 0.982103i \(-0.560312\pi\)
0.998911 + 0.0466598i \(0.0148577\pi\)
\(182\) 5.75696 + 1.69040i 0.426734 + 0.125300i
\(183\) −15.5279 −1.14785
\(184\) 0 0
\(185\) −1.52786 −0.112331
\(186\) 8.89499 + 2.61180i 0.652212 + 0.191507i
\(187\) 2.61944 3.02300i 0.191553 0.221064i
\(188\) 3.04368 + 1.95606i 0.221983 + 0.142660i
\(189\) 1.02980 7.16242i 0.0749069 0.520989i
\(190\) −1.28532 + 0.826026i −0.0932470 + 0.0599262i
\(191\) 10.8757 + 23.8145i 0.786938 + 1.72315i 0.685213 + 0.728342i \(0.259709\pi\)
0.101725 + 0.994813i \(0.467564\pi\)
\(192\) −0.345677 0.398933i −0.0249471 0.0287905i
\(193\) −1.41522 9.84305i −0.101870 0.708518i −0.975190 0.221371i \(-0.928947\pi\)
0.873320 0.487147i \(-0.161962\pi\)
\(194\) −4.54641 + 9.95526i −0.326414 + 0.714746i
\(195\) −7.95592 + 2.33607i −0.569735 + 0.167289i
\(196\) 5.39046 1.58278i 0.385033 0.113056i
\(197\) −0.611547 + 1.33910i −0.0435709 + 0.0954071i −0.930166 0.367140i \(-0.880337\pi\)
0.886595 + 0.462547i \(0.153064\pi\)
\(198\) −0.921081 6.40626i −0.0654584 0.455273i
\(199\) −8.04941 9.28952i −0.570608 0.658517i 0.394951 0.918702i \(-0.370762\pi\)
−0.965559 + 0.260186i \(0.916216\pi\)
\(200\) 3.22525 + 7.06232i 0.228060 + 0.499382i
\(201\) −5.19923 + 3.34134i −0.366726 + 0.235680i
\(202\) −0.393349 + 2.73580i −0.0276759 + 0.192490i
\(203\) 8.16706 + 5.24865i 0.573215 + 0.368383i
\(204\) 1.80999 2.08884i 0.126725 0.146248i
\(205\) −4.11795 1.20914i −0.287610 0.0844499i
\(206\) 2.58359 0.180007
\(207\) 0 0
\(208\) 5.56231 0.385677
\(209\) −10.0479 2.95034i −0.695031 0.204079i
\(210\) 3.61998 4.17768i 0.249802 0.288287i
\(211\) −19.6991 12.6599i −1.35614 0.871541i −0.358078 0.933692i \(-0.616568\pi\)
−0.998067 + 0.0621507i \(0.980204\pi\)
\(212\) −0.108719 + 0.756156i −0.00746684 + 0.0519330i
\(213\) −23.0173 + 14.7923i −1.57712 + 1.01355i
\(214\) −3.44454 7.54248i −0.235464 0.515594i
\(215\) 0 0
\(216\) 0.711574 + 4.94911i 0.0484165 + 0.336744i
\(217\) −9.01791 + 19.7465i −0.612176 + 1.34048i
\(218\) 0 0
\(219\) 14.0055 4.11238i 0.946402 0.277889i
\(220\) 4.35028 9.52579i 0.293296 0.642229i
\(221\) 0.326157 + 2.26847i 0.0219397 + 0.152594i
\(222\) 1.11864 + 1.29097i 0.0750779 + 0.0866445i
\(223\) 1.66166 + 3.63853i 0.111273 + 0.243654i 0.957073 0.289846i \(-0.0936039\pi\)
−0.845800 + 0.533499i \(0.820877\pi\)
\(224\) −15.2943 + 9.82903i −1.02189 + 0.656730i
\(225\) 0.988273 6.87359i 0.0658849 0.458239i
\(226\) −4.55657 2.92833i −0.303099 0.194790i
\(227\) −7.97643 + 9.20529i −0.529414 + 0.610976i −0.955963 0.293488i \(-0.905184\pi\)
0.426549 + 0.904465i \(0.359729\pi\)
\(228\) −6.94296 2.03864i −0.459809 0.135012i
\(229\) 12.0000 0.792982 0.396491 0.918039i \(-0.370228\pi\)
0.396491 + 0.918039i \(0.370228\pi\)
\(230\) 0 0
\(231\) 37.8885 2.49288
\(232\) −6.43647 1.88992i −0.422575 0.124079i
\(233\) 4.27484 4.93343i 0.280054 0.323200i −0.598243 0.801315i \(-0.704134\pi\)
0.878297 + 0.478115i \(0.158680\pi\)
\(234\) 3.11954 + 2.00481i 0.203931 + 0.131058i
\(235\) −0.393349 + 2.73580i −0.0256592 + 0.178464i
\(236\) −8.80972 + 5.66166i −0.573464 + 0.368543i
\(237\) −10.1661 22.2606i −0.660359 1.44598i
\(238\) −1.00054 1.15468i −0.0648553 0.0748470i
\(239\) −1.95881 13.6238i −0.126705 0.881253i −0.949690 0.313190i \(-0.898602\pi\)
0.822985 0.568062i \(-0.192307\pi\)
\(240\) 2.12884 4.66151i 0.137416 0.300899i
\(241\) −22.1879 + 6.51496i −1.42925 + 0.419665i −0.902623 0.430432i \(-0.858361\pi\)
−0.526626 + 0.850097i \(0.676543\pi\)
\(242\) −9.73492 + 2.85843i −0.625784 + 0.183747i
\(243\) 7.43117 16.2720i 0.476710 1.04385i
\(244\) 1.59906 + 11.1217i 0.102369 + 0.711994i
\(245\) 2.81053 + 3.24352i 0.179558 + 0.207221i
\(246\) 1.99332 + 4.36475i 0.127089 + 0.278287i
\(247\) 5.04752 3.24384i 0.321166 0.206401i
\(248\) 2.13472 14.8473i 0.135555 0.942806i
\(249\) −16.4858 10.5948i −1.04475 0.671418i
\(250\) −4.23835 + 4.89131i −0.268057 + 0.309354i
\(251\) 2.19896 + 0.645674i 0.138797 + 0.0407546i 0.350393 0.936603i \(-0.386048\pi\)
−0.211596 + 0.977357i \(0.567866\pi\)
\(252\) 10.4721 0.659683
\(253\) 0 0
\(254\) −4.50658 −0.282768
\(255\) 2.02593 + 0.594866i 0.126868 + 0.0372520i
\(256\) 4.29740 4.95946i 0.268587 0.309966i
\(257\) −6.28596 4.03974i −0.392107 0.251992i 0.329700 0.944086i \(-0.393052\pi\)
−0.721808 + 0.692093i \(0.756689\pi\)
\(258\) 0 0
\(259\) −3.36501 + 2.16256i −0.209092 + 0.134375i
\(260\) 2.49249 + 5.45779i 0.154578 + 0.338478i
\(261\) 3.92916 + 4.53450i 0.243209 + 0.280678i
\(262\) −1.64549 11.4446i −0.101659 0.707051i
\(263\) −1.22309 + 2.67820i −0.0754193 + 0.165145i −0.943586 0.331127i \(-0.892571\pi\)
0.868167 + 0.496272i \(0.165298\pi\)
\(264\) −25.1199 + 7.37585i −1.54602 + 0.453952i
\(265\) −0.559953 + 0.164417i −0.0343976 + 0.0101001i
\(266\) −1.66166 + 3.63853i −0.101883 + 0.223092i
\(267\) 3.33250 + 23.1781i 0.203946 + 1.41847i
\(268\) 2.92863 + 3.37981i 0.178894 + 0.206455i
\(269\) −3.30017 7.22636i −0.201215 0.440599i 0.781945 0.623348i \(-0.214228\pi\)
−0.983160 + 0.182749i \(0.941501\pi\)
\(270\) −1.43703 + 0.923525i −0.0874550 + 0.0562039i
\(271\) −1.13852 + 7.91857i −0.0691601 + 0.481019i 0.925577 + 0.378559i \(0.123580\pi\)
−0.994737 + 0.102460i \(0.967329\pi\)
\(272\) −1.19156 0.765768i −0.0722488 0.0464315i
\(273\) −14.2159 + 16.4060i −0.860382 + 0.992934i
\(274\) −12.9799 3.81124i −0.784144 0.230245i
\(275\) −18.1803 −1.09632
\(276\) 0 0
\(277\) 15.4721 0.929631 0.464815 0.885408i \(-0.346121\pi\)
0.464815 + 0.885408i \(0.346121\pi\)
\(278\) 6.34996 + 1.86452i 0.380845 + 0.111826i
\(279\) −8.78588 + 10.1394i −0.525997 + 0.607033i
\(280\) −7.52440 4.83564i −0.449669 0.288985i
\(281\) −1.24724 + 8.67473i −0.0744040 + 0.517491i 0.918202 + 0.396112i \(0.129641\pi\)
−0.992606 + 0.121379i \(0.961268\pi\)
\(282\) 2.59962 1.67067i 0.154805 0.0994871i
\(283\) −11.5104 25.2043i −0.684222 1.49824i −0.858106 0.513472i \(-0.828359\pi\)
0.173884 0.984766i \(-0.444368\pi\)
\(284\) 12.9652 + 14.9626i 0.769342 + 0.887868i
\(285\) −0.786697 5.47160i −0.0465999 0.324110i
\(286\) 4.03293 8.83089i 0.238472 0.522182i
\(287\) −10.7809 + 3.16557i −0.636378 + 0.186857i
\(288\) −10.7809 + 3.16557i −0.635272 + 0.186533i
\(289\) −6.81962 + 14.9329i −0.401154 + 0.878405i
\(290\) −0.326157 2.26847i −0.0191526 0.133209i
\(291\) −25.9304 29.9252i −1.52006 1.75425i
\(292\) −4.38774 9.60781i −0.256773 0.562255i
\(293\) 1.28532 0.826026i 0.0750893 0.0482569i −0.502558 0.864544i \(-0.667607\pi\)
0.577647 + 0.816287i \(0.303971\pi\)
\(294\) 0.682880 4.74953i 0.0398264 0.276998i
\(295\) −6.73003 4.32513i −0.391837 0.251819i
\(296\) 1.80999 2.08884i 0.105204 0.121411i
\(297\) −11.2339 3.29858i −0.651859 0.191403i
\(298\) −14.7639 −0.855252
\(299\) 0 0
\(300\) −12.5623 −0.725285
\(301\) 0 0
\(302\) −1.71445 + 1.97858i −0.0986554 + 0.113854i
\(303\) −8.41254 5.40641i −0.483288 0.310590i
\(304\) −0.527732 + 3.67046i −0.0302675 + 0.210515i
\(305\) −7.22098 + 4.64064i −0.413472 + 0.265722i
\(306\) −0.392265 0.858940i −0.0224243 0.0491023i
\(307\) −6.23942 7.20068i −0.356103 0.410964i 0.549227 0.835673i \(-0.314922\pi\)
−0.905330 + 0.424708i \(0.860377\pi\)
\(308\) −3.90176 27.1373i −0.222324 1.54629i
\(309\) −3.88310 + 8.50281i −0.220902 + 0.483708i
\(310\) 4.91703 1.44377i 0.279268 0.0820006i
\(311\) −12.6464 + 3.71333i −0.717114 + 0.210564i −0.619879 0.784698i \(-0.712818\pi\)
−0.0972354 + 0.995261i \(0.531000\pi\)
\(312\) 6.23123 13.6445i 0.352774 0.772467i
\(313\) 3.46689 + 24.1127i 0.195960 + 1.36293i 0.815859 + 0.578250i \(0.196264\pi\)
−0.619899 + 0.784681i \(0.712827\pi\)
\(314\) −4.62052 5.33236i −0.260751 0.300923i
\(315\) 3.32332 + 7.27706i 0.187248 + 0.410016i
\(316\) −14.8971 + 9.57378i −0.838027 + 0.538567i
\(317\) −3.61713 + 25.1577i −0.203158 + 1.41300i 0.591678 + 0.806174i \(0.298466\pi\)
−0.794837 + 0.606823i \(0.792444\pi\)
\(318\) 0.548898 + 0.352755i 0.0307806 + 0.0197815i
\(319\) 10.2867 11.8715i 0.575944 0.664675i
\(320\) −0.279976 0.0822085i −0.0156511 0.00459559i
\(321\) 30.0000 1.67444
\(322\) 0 0
\(323\) −1.52786 −0.0850126
\(324\) −17.0774 5.01438i −0.948745 0.278577i
\(325\) 6.82130 7.87220i 0.378377 0.436671i
\(326\) −2.99680 1.92593i −0.165978 0.106667i
\(327\) 0 0
\(328\) 6.53144 4.19750i 0.360638 0.231768i
\(329\) 3.00597 + 6.58216i 0.165725 + 0.362886i
\(330\) −5.85725 6.75963i −0.322431 0.372105i
\(331\) 2.79684 + 19.4524i 0.153728 + 1.06920i 0.909899 + 0.414829i \(0.136159\pi\)
−0.756171 + 0.654374i \(0.772932\pi\)
\(332\) −5.89073 + 12.8989i −0.323296 + 0.707919i
\(333\) −2.37200 + 0.696481i −0.129985 + 0.0381669i
\(334\) −0.906022 + 0.266032i −0.0495753 + 0.0145566i
\(335\) −1.41923 + 3.10767i −0.0775407 + 0.169790i
\(336\) −1.90935 13.2798i −0.104164 0.724475i
\(337\) 15.3345 + 17.6969i 0.835323 + 0.964014i 0.999750 0.0223755i \(-0.00712294\pi\)
−0.164427 + 0.986389i \(0.552577\pi\)
\(338\) −1.02696 2.24873i −0.0558594 0.122315i
\(339\) 16.4858 10.5948i 0.895388 0.575431i
\(340\) 0.217438 1.51231i 0.0117922 0.0820167i
\(341\) 29.5487 + 18.9898i 1.60015 + 1.02836i
\(342\) −1.61890 + 1.86832i −0.0875403 + 0.101027i
\(343\) −10.9540 3.21637i −0.591458 0.173668i
\(344\) 0 0
\(345\) 0 0
\(346\) 14.1803 0.762340
\(347\) 9.48799 + 2.78592i 0.509342 + 0.149556i 0.526298 0.850300i \(-0.323579\pi\)
−0.0169565 + 0.999856i \(0.505398\pi\)
\(348\) 7.10793 8.20298i 0.381025 0.439726i
\(349\) 20.5404 + 13.2005i 1.09950 + 0.706607i 0.958981 0.283471i \(-0.0914859\pi\)
0.140521 + 0.990078i \(0.455122\pi\)
\(350\) −0.988273 + 6.87359i −0.0528254 + 0.367409i
\(351\) 5.64330 3.62673i 0.301217 0.193580i
\(352\) 12.2200 + 26.7581i 0.651329 + 1.42621i
\(353\) −6.12994 7.07433i −0.326264 0.376529i 0.568793 0.822481i \(-0.307411\pi\)
−0.895057 + 0.445952i \(0.852865\pi\)
\(354\) 1.27290 + 8.85323i 0.0676540 + 0.470544i
\(355\) −6.28299 + 13.7578i −0.333467 + 0.730190i
\(356\) 16.2579 4.77375i 0.861667 0.253008i
\(357\) 5.30395 1.55738i 0.280715 0.0824253i
\(358\) 0.181825 0.398141i 0.00960973 0.0210424i
\(359\) −2.83043 19.6861i −0.149385 1.03899i −0.917230 0.398358i \(-0.869580\pi\)
0.767845 0.640635i \(-0.221329\pi\)
\(360\) −3.61998 4.17768i −0.190790 0.220183i
\(361\) −6.23123 13.6445i −0.327959 0.718131i
\(362\) −8.65801 + 5.56417i −0.455055 + 0.292446i
\(363\) 5.22412 36.3346i 0.274195 1.90707i
\(364\) 13.2146 + 8.49250i 0.692632 + 0.445128i
\(365\) 5.28400 6.09806i 0.276577 0.319187i
\(366\) 9.20801 + 2.70372i 0.481310 + 0.141326i
\(367\) 4.18034 0.218212 0.109106 0.994030i \(-0.465201\pi\)
0.109106 + 0.994030i \(0.465201\pi\)
\(368\) 0 0
\(369\) −6.94427 −0.361504
\(370\) 0.906022 + 0.266032i 0.0471019 + 0.0138304i
\(371\) −1.00054 + 1.15468i −0.0519454 + 0.0599481i
\(372\) 20.4177 + 13.1216i 1.05861 + 0.680325i
\(373\) 1.09699 7.62975i 0.0568001 0.395053i −0.941512 0.336979i \(-0.890595\pi\)
0.998312 0.0580743i \(-0.0184960\pi\)
\(374\) −2.07969 + 1.33654i −0.107538 + 0.0691107i
\(375\) −9.72753 21.3003i −0.502327 1.09994i
\(376\) −3.27430 3.77875i −0.168859 0.194874i
\(377\) 1.28083 + 8.90839i 0.0659663 + 0.458806i
\(378\) −1.85779 + 4.06800i −0.0955545 + 0.209235i
\(379\) 23.3739 6.86320i 1.20064 0.352539i 0.380540 0.924764i \(-0.375738\pi\)
0.820096 + 0.572226i \(0.193920\pi\)
\(380\) −3.83797 + 1.12693i −0.196884 + 0.0578103i
\(381\) 6.77332 14.8315i 0.347008 0.759841i
\(382\) −2.30270 16.0156i −0.117817 0.819432i
\(383\) 4.62052 + 5.33236i 0.236098 + 0.272471i 0.861418 0.507897i \(-0.169577\pi\)
−0.625320 + 0.780368i \(0.715032\pi\)
\(384\) 10.5727 + 23.1509i 0.539534 + 1.18141i
\(385\) 17.6194 11.3233i 0.897970 0.577090i
\(386\) −0.874652 + 6.08334i −0.0445186 + 0.309634i
\(387\) 0 0
\(388\) −18.7634 + 21.6541i −0.952566 + 1.09932i
\(389\) 24.4938 + 7.19203i 1.24189 + 0.364650i 0.835723 0.549151i \(-0.185049\pi\)
0.406162 + 0.913801i \(0.366867\pi\)
\(390\) 5.12461 0.259495
\(391\) 0 0
\(392\) −7.76393 −0.392138
\(393\) 40.1383 + 11.7857i 2.02471 + 0.594508i
\(394\) 0.595812 0.687604i 0.0300166 0.0346410i
\(395\) −11.3804 7.31372i −0.572608 0.367993i
\(396\) 2.41142 16.7718i 0.121178 0.842815i
\(397\) −20.5404 + 13.2005i −1.03089 + 0.662514i −0.942718 0.333591i \(-0.891740\pi\)
−0.0881745 + 0.996105i \(0.528103\pi\)
\(398\) 3.15580 + 6.91024i 0.158186 + 0.346379i
\(399\) −9.47723 10.9373i −0.474455 0.547550i
\(400\) 0.916179 + 6.37217i 0.0458090 + 0.318608i
\(401\) 5.89073 12.8989i 0.294169 0.644140i −0.703622 0.710575i \(-0.748435\pi\)
0.997791 + 0.0664346i \(0.0211624\pi\)
\(402\) 3.66494 1.07612i 0.182790 0.0536721i
\(403\) −19.3094 + 5.66976i −0.961871 + 0.282431i
\(404\) −3.00597 + 6.58216i −0.149553 + 0.327475i
\(405\) −1.93502 13.4584i −0.0961519 0.668751i
\(406\) −3.92916 4.53450i −0.195001 0.225043i
\(407\) 2.68862 + 5.88726i 0.133270 + 0.291821i
\(408\) −3.21330 + 2.06506i −0.159082 + 0.102236i
\(409\) −3.03994 + 21.1433i −0.150315 + 1.04547i 0.765376 + 0.643584i \(0.222553\pi\)
−0.915691 + 0.401883i \(0.868356\pi\)
\(410\) 2.23140 + 1.43404i 0.110201 + 0.0708220i
\(411\) 32.0517 36.9896i 1.58099 1.82456i
\(412\) 6.48995 + 1.90562i 0.319737 + 0.0938832i
\(413\) −20.9443 −1.03060
\(414\) 0 0
\(415\) −10.8328 −0.531762
\(416\) −16.1714 4.74835i −0.792868 0.232807i
\(417\) −15.6802 + 18.0959i −0.767861 + 0.886159i
\(418\) 5.44471 + 3.49910i 0.266309 + 0.171147i
\(419\) −0.652313 + 4.53694i −0.0318676 + 0.221644i −0.999532 0.0305981i \(-0.990259\pi\)
0.967664 + 0.252242i \(0.0811679\pi\)
\(420\) 12.1747 7.82423i 0.594066 0.381783i
\(421\) 4.27537 + 9.36175i 0.208369 + 0.456264i 0.984744 0.174007i \(-0.0556714\pi\)
−0.776376 + 0.630270i \(0.782944\pi\)
\(422\) 9.47723 + 10.9373i 0.461345 + 0.532420i
\(423\) 0.636451 + 4.42662i 0.0309453 + 0.215229i
\(424\) 0.438565 0.960324i 0.0212986 0.0466375i
\(425\) −2.54503 + 0.747289i −0.123452 + 0.0362488i
\(426\) 16.2249 4.76405i 0.786097 0.230819i
\(427\) −9.33526 + 20.4414i −0.451765 + 0.989227i
\(428\) −3.08940 21.4872i −0.149332 1.03863i
\(429\) 23.0017 + 26.5454i 1.11053 + 1.28162i
\(430\) 0 0
\(431\) 14.7454 9.47628i 0.710260 0.456456i −0.134977 0.990849i \(-0.543096\pi\)
0.845236 + 0.534392i \(0.179460\pi\)
\(432\) −0.590023 + 4.10370i −0.0283875 + 0.197439i
\(433\) −14.9909 9.63404i −0.720414 0.462982i 0.128367 0.991727i \(-0.459027\pi\)
−0.848781 + 0.528745i \(0.822663\pi\)
\(434\) 8.78588 10.1394i 0.421736 0.486709i
\(435\) 7.95592 + 2.33607i 0.381457 + 0.112006i
\(436\) 0 0
\(437\) 0 0
\(438\) −9.02129 −0.431054
\(439\) 17.9504 + 5.27071i 0.856725 + 0.251557i 0.680460 0.732785i \(-0.261780\pi\)
0.176266 + 0.984343i \(0.443598\pi\)
\(440\) −9.47723 + 10.9373i −0.451809 + 0.521416i
\(441\) 5.84189 + 3.75436i 0.278185 + 0.178779i
\(442\) 0.201576 1.40199i 0.00958799 0.0666859i
\(443\) 32.0725 20.6117i 1.52381 0.979292i 0.532690 0.846310i \(-0.321181\pi\)
0.991118 0.132982i \(-0.0424553\pi\)
\(444\) 1.85779 + 4.06800i 0.0881669 + 0.193059i
\(445\) 8.47670 + 9.78263i 0.401834 + 0.463741i
\(446\) −0.351822 2.44697i −0.0166592 0.115868i
\(447\) 22.1900 48.5893i 1.04955 2.29819i
\(448\) −0.732987 + 0.215225i −0.0346304 + 0.0101684i
\(449\) 14.3389 4.21029i 0.676696 0.198696i 0.0747132 0.997205i \(-0.476196\pi\)
0.601982 + 0.798509i \(0.294378\pi\)
\(450\) −1.78288 + 3.90396i −0.0840456 + 0.184034i
\(451\) 2.58733 + 17.9953i 0.121833 + 0.847365i
\(452\) −9.28615 10.7168i −0.436784 0.504075i
\(453\) −3.93487 8.61616i −0.184876 0.404822i
\(454\) 6.33284 4.06987i 0.297215 0.191008i
\(455\) −1.70778 + 11.8779i −0.0800619 + 0.556843i
\(456\) 8.41254 + 5.40641i 0.393953 + 0.253178i
\(457\) −3.35591 + 3.87292i −0.156983 + 0.181168i −0.828793 0.559556i \(-0.810972\pi\)
0.671810 + 0.740724i \(0.265517\pi\)
\(458\) −7.11599 2.08944i −0.332508 0.0976333i
\(459\) −1.70820 −0.0797321
\(460\) 0 0
\(461\) −1.47214 −0.0685642 −0.0342821 0.999412i \(-0.510914\pi\)
−0.0342821 + 0.999412i \(0.510914\pi\)
\(462\) −22.4679 6.59716i −1.04530 0.306928i
\(463\) 13.0972 15.1150i 0.608679 0.702453i −0.364837 0.931071i \(-0.618875\pi\)
0.973516 + 0.228618i \(0.0734207\pi\)
\(464\) −4.67931 3.00721i −0.217231 0.139606i
\(465\) −2.63866 + 18.3523i −0.122365 + 0.851067i
\(466\) −3.39399 + 2.18118i −0.157223 + 0.101041i
\(467\) 5.42355 + 11.8759i 0.250972 + 0.549551i 0.992624 0.121233i \(-0.0386848\pi\)
−0.741652 + 0.670784i \(0.765958\pi\)
\(468\) 6.35752 + 7.33697i 0.293877 + 0.339152i
\(469\) 1.27290 + 8.85323i 0.0587772 + 0.408804i
\(470\) 0.709614 1.55384i 0.0327320 0.0716732i
\(471\) 24.4938 7.19203i 1.12862 0.331391i
\(472\) 13.8859 4.07727i 0.639151 0.187672i
\(473\) 0 0
\(474\) 2.15246 + 14.9707i 0.0988656 + 0.687625i
\(475\) 4.54753 + 5.24813i 0.208655 + 0.240801i
\(476\) −1.66166 3.63853i −0.0761621 0.166772i
\(477\) −0.794372 + 0.510512i −0.0363718 + 0.0233747i
\(478\) −1.21061 + 8.41999i −0.0553721 + 0.385122i
\(479\) −26.5809 17.0825i −1.21451 0.780519i −0.233103 0.972452i \(-0.574888\pi\)
−0.981408 + 0.191933i \(0.938524\pi\)
\(480\) −10.1686 + 11.7352i −0.464130 + 0.535635i
\(481\) −3.55800 1.04472i −0.162231 0.0476352i
\(482\) 14.2918 0.650973
\(483\) 0 0
\(484\) −26.5623 −1.20738
\(485\) −21.0019 6.16672i −0.953647 0.280016i
\(486\) −7.23996 + 8.35536i −0.328411 + 0.379007i
\(487\) −12.3733 7.95186i −0.560689 0.360333i 0.229393 0.973334i \(-0.426326\pi\)
−0.790082 + 0.613001i \(0.789962\pi\)
\(488\) 2.20985 15.3698i 0.100035 0.695759i
\(489\) 10.8425 6.96807i 0.490316 0.315107i
\(490\) −1.10188 2.41278i −0.0497778 0.108998i
\(491\) −5.46647 6.30864i −0.246698 0.284705i 0.618873 0.785491i \(-0.287590\pi\)
−0.865571 + 0.500786i \(0.833044\pi\)
\(492\) 1.78780 + 12.4344i 0.0806004 + 0.560588i
\(493\) 0.952046 2.08469i 0.0428780 0.0938898i
\(494\) −3.55800 + 1.04472i −0.160082 + 0.0470043i
\(495\) 12.4199 3.64682i 0.558235 0.163912i
\(496\) 5.16680 11.3137i 0.231996 0.508001i
\(497\) 5.63520 + 39.1937i 0.252773 + 1.75808i
\(498\) 7.93132 + 9.15323i 0.355411 + 0.410166i
\(499\) 8.01410 + 17.5484i 0.358760 + 0.785576i 0.999836 + 0.0180982i \(0.00576116\pi\)
−0.641076 + 0.767478i \(0.721512\pi\)
\(500\) −14.2544 + 9.16077i −0.637477 + 0.409682i
\(501\) 0.486206 3.38163i 0.0217221 0.151080i
\(502\) −1.19156 0.765768i −0.0531818 0.0341779i
\(503\) −17.6447 + 20.3631i −0.786740 + 0.907947i −0.997577 0.0695746i \(-0.977836\pi\)
0.210836 + 0.977521i \(0.432381\pi\)
\(504\) −13.8859 4.07727i −0.618528 0.181616i
\(505\) −5.52786 −0.245987
\(506\) 0 0
\(507\) 8.94427 0.397229
\(508\) −11.3205 3.32399i −0.502264 0.147478i
\(509\) 18.5358 21.3915i 0.821585 0.948160i −0.177770 0.984072i \(-0.556888\pi\)
0.999355 + 0.0359125i \(0.0114338\pi\)
\(510\) −1.09780 0.705510i −0.0486112 0.0312405i
\(511\) 3.00635 20.9096i 0.132993 0.924986i
\(512\) 15.7383 10.1144i 0.695543 0.446998i
\(513\) 1.85779 + 4.06800i 0.0820235 + 0.179606i
\(514\) 3.02417 + 3.49008i 0.133390 + 0.153941i
\(515\) 0.735367 + 5.11459i 0.0324041 + 0.225376i
\(516\) 0 0
\(517\) 11.2339 3.29858i 0.494068 0.145071i
\(518\) 2.37200 0.696481i 0.104220 0.0306016i
\(519\) −21.3128 + 46.6686i −0.935530 + 2.04853i
\(520\) −1.18005 8.20740i −0.0517484 0.359918i
\(521\) 20.5734 + 23.7429i 0.901336 + 1.04020i 0.998988 + 0.0449764i \(0.0143212\pi\)
−0.0976523 + 0.995221i \(0.531133\pi\)
\(522\) −1.54044 3.37310i −0.0674234 0.147637i
\(523\) −34.5962 + 22.2336i −1.51279 + 0.972209i −0.519762 + 0.854311i \(0.673979\pi\)
−0.993026 + 0.117898i \(0.962384\pi\)
\(524\) 4.30794 29.9624i 0.188193 1.30891i
\(525\) −21.1362 13.5834i −0.922458 0.592828i
\(526\) 1.19162 1.37521i 0.0519573 0.0599619i
\(527\) 4.91703 + 1.44377i 0.214189 + 0.0628916i
\(528\) −21.7082 −0.944728
\(529\) 0 0
\(530\) 0.360680 0.0156669
\(531\) −12.4199 3.64682i −0.538979 0.158259i
\(532\) −6.85779 + 7.91431i −0.297323 + 0.343129i
\(533\) −8.76284 5.63154i −0.379561 0.243929i
\(534\) 2.05960 14.3248i 0.0891276 0.619896i
\(535\) 13.9510 8.96577i 0.603155 0.387624i
\(536\) −2.56741 5.62183i −0.110895 0.242826i
\(537\) 1.03703 + 1.19680i 0.0447512 + 0.0516457i
\(538\) 0.698742 + 4.85986i 0.0301249 + 0.209523i
\(539\) 7.55239 16.5374i 0.325304 0.712317i
\(540\) −4.29098 + 1.25995i −0.184655 + 0.0542195i
\(541\) 33.0223 9.69622i 1.41974 0.416873i 0.520325 0.853969i \(-0.325811\pi\)
0.899415 + 0.437095i \(0.143993\pi\)
\(542\) 2.05392 4.49747i 0.0882236 0.193183i
\(543\) −5.29924 36.8571i −0.227412 1.58169i
\(544\) 2.81053 + 3.24352i 0.120500 + 0.139065i
\(545\) 0 0
\(546\) 11.2866 7.25346i 0.483022 0.310419i
\(547\) 4.20413 29.2403i 0.179755 1.25023i −0.677573 0.735456i \(-0.736968\pi\)
0.857328 0.514771i \(-0.172123\pi\)
\(548\) −29.7942 19.1476i −1.27274 0.817943i
\(549\) −9.09506 + 10.4963i −0.388168 + 0.447970i
\(550\) 10.7809 + 3.16557i 0.459700 + 0.134980i
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) −35.4164 −1.50606
\(554\) −9.17497 2.69401i −0.389807 0.114458i
\(555\) −2.23727 + 2.58195i −0.0949669 + 0.109598i
\(556\) 14.5758 + 9.36727i 0.618150 + 0.397261i
\(557\) −1.05546 + 7.34092i −0.0447215 + 0.311045i 0.955166 + 0.296070i \(0.0956760\pi\)
−0.999888 + 0.0149752i \(0.995233\pi\)
\(558\) 6.97550 4.48288i 0.295297 0.189776i
\(559\) 0 0
\(560\) −4.85671 5.60495i −0.205234 0.236852i
\(561\) −1.27290 8.85323i −0.0537420 0.373784i
\(562\) 2.25006 4.92694i 0.0949129 0.207830i
\(563\) −31.6098 + 9.28147i −1.33219 + 0.391167i −0.868878 0.495026i \(-0.835159\pi\)
−0.463316 + 0.886193i \(0.653340\pi\)
\(564\) 7.76246 2.27926i 0.326859 0.0959743i
\(565\) 4.50011 9.85388i 0.189321 0.414556i
\(566\) 2.43709 + 16.9503i 0.102438 + 0.712475i
\(567\) −23.3109 26.9022i −0.978966 1.12979i
\(568\) −11.3660 24.8881i −0.476908 1.04428i
\(569\) 18.6593 11.9916i 0.782238 0.502714i −0.0875376 0.996161i \(-0.527900\pi\)
0.869776 + 0.493447i \(0.164263\pi\)
\(570\) −0.486206 + 3.38163i −0.0203649 + 0.141641i
\(571\) 12.0230 + 7.72673i 0.503148 + 0.323354i 0.767474 0.641080i \(-0.221513\pi\)
−0.264326 + 0.964433i \(0.585150\pi\)
\(572\) 16.6442 19.2084i 0.695929 0.803145i
\(573\) 56.1697 + 16.4929i 2.34652 + 0.689001i
\(574\) 6.94427 0.289848
\(575\) 0 0
\(576\) −0.472136 −0.0196723
\(577\) −21.9614 6.44845i −0.914265 0.268452i −0.209430 0.977824i \(-0.567161\pi\)
−0.704835 + 0.709371i \(0.748979\pi\)
\(578\) 6.64415 7.66776i 0.276360 0.318937i
\(579\) −18.7062 12.0217i −0.777402 0.499606i
\(580\) 0.853889 5.93893i 0.0354558 0.246601i
\(581\) −23.8585 + 15.3329i −0.989818 + 0.636118i
\(582\) 10.1661 + 22.2606i 0.421398 + 0.922733i
\(583\) 1.61890 + 1.86832i 0.0670482 + 0.0773777i
\(584\) 2.07733 + 14.4482i 0.0859607 + 0.597870i
\(585\) −3.08089 + 6.74620i −0.127379 + 0.278921i
\(586\) −0.906022 + 0.266032i −0.0374274 + 0.0109897i
\(587\) 23.7073 6.96111i 0.978507 0.287316i 0.246899 0.969041i \(-0.420588\pi\)
0.731608 + 0.681726i \(0.238770\pi\)
\(588\) 5.21857 11.4271i 0.215210 0.471245i
\(589\) −1.90935 13.2798i −0.0786736 0.547187i
\(590\) 3.23781 + 3.73663i 0.133299 + 0.153835i
\(591\) 1.36746 + 2.99432i 0.0562499 + 0.123170i
\(592\) 1.92798 1.23904i 0.0792396 0.0509242i
\(593\) 0.419014 2.91430i 0.0172068 0.119676i −0.979408 0.201893i \(-0.935291\pi\)
0.996614 + 0.0822165i \(0.0261999\pi\)
\(594\) 6.08737 + 3.91211i 0.249768 + 0.160516i
\(595\) 2.00108 2.30937i 0.0820361 0.0946747i
\(596\) −37.0868 10.8897i −1.51913 0.446058i
\(597\) −27.4853 −1.12490
\(598\) 0 0
\(599\) 33.8885 1.38465 0.692324 0.721587i \(-0.256587\pi\)
0.692324 + 0.721587i \(0.256587\pi\)
\(600\) 16.6575 + 4.89107i 0.680038 + 0.199677i
\(601\) −30.7055 + 35.4360i −1.25250 + 1.44546i −0.405309 + 0.914180i \(0.632836\pi\)
−0.847193 + 0.531285i \(0.821710\pi\)
\(602\) 0 0
\(603\) −0.786697 + 5.47160i −0.0320368 + 0.222821i
\(604\) −5.76604 + 3.70561i −0.234617 + 0.150779i
\(605\) −8.42952 18.4581i −0.342709 0.750427i
\(606\) 4.04726 + 4.67079i 0.164409 + 0.189738i
\(607\) −3.76738 26.2027i −0.152913 1.06353i −0.911304 0.411734i \(-0.864923\pi\)
0.758391 0.651800i \(-0.225986\pi\)
\(608\) 4.66763 10.2207i 0.189297 0.414504i
\(609\) 20.8289 6.11591i 0.844028 0.247829i
\(610\) 5.09006 1.49458i 0.206091 0.0605137i
\(611\) −2.78669 + 6.10200i −0.112737 + 0.246860i
\(612\) −0.351822 2.44697i −0.0142215 0.0989130i
\(613\) 3.73808 + 4.31397i 0.150980 + 0.174240i 0.826201 0.563375i \(-0.190497\pi\)
−0.675222 + 0.737615i \(0.735952\pi\)
\(614\) 2.44619 + 5.35641i 0.0987202 + 0.216167i
\(615\) −8.07330 + 5.18839i −0.325547 + 0.209216i
\(616\) −5.39210 + 37.5029i −0.217254 + 1.51103i
\(617\) 6.33284 + 4.06987i 0.254951 + 0.163847i 0.661873 0.749616i \(-0.269762\pi\)
−0.406923 + 0.913463i \(0.633398\pi\)
\(618\) 3.78319 4.36603i 0.152182 0.175628i
\(619\) 18.6299 + 5.47023i 0.748799 + 0.219867i 0.633799 0.773498i \(-0.281495\pi\)
0.115001 + 0.993365i \(0.463313\pi\)
\(620\) 13.4164 0.538816
\(621\) 0 0
\(622\) 8.14590 0.326621
\(623\) 32.5158 + 9.54751i 1.30272 + 0.382513i
\(624\) 8.14496 9.39978i 0.326059 0.376292i
\(625\) 3.71532 + 2.38769i 0.148613 + 0.0955076i
\(626\) 2.14265 14.9025i 0.0856377 0.595623i
\(627\) −19.6991 + 12.6599i −0.786708 + 0.505586i
\(628\) −7.67360 16.8028i −0.306210 0.670507i
\(629\) 0.618367 + 0.713633i 0.0246559 + 0.0284544i
\(630\) −0.703643 4.89395i −0.0280338 0.194979i
\(631\) −5.13481 + 11.2437i −0.204414 + 0.447603i −0.983877 0.178844i \(-0.942764\pi\)
0.779464 + 0.626447i \(0.215492\pi\)
\(632\) 23.4808 6.89460i 0.934018 0.274252i
\(633\) −50.2397 + 14.7517i −1.99685 + 0.586328i
\(634\) 6.52542 14.2887i 0.259158 0.567476i
\(635\) −1.28271 8.92141i −0.0509026 0.354036i
\(636\) 1.11864 + 1.29097i 0.0443568 + 0.0511905i
\(637\) 4.32713 + 9.47510i 0.171447 + 0.375417i
\(638\) −8.16706 + 5.24865i −0.323337 + 0.207796i
\(639\) −3.48275 + 24.2230i −0.137775 + 0.958249i
\(640\) 11.8355 + 7.60621i 0.467839 + 0.300662i
\(641\) −11.3323 + 13.0782i −0.447600 + 0.516558i −0.934046 0.357153i \(-0.883748\pi\)
0.486446 + 0.873711i \(0.338293\pi\)
\(642\) −17.7900 5.22361i −0.702114 0.206159i
\(643\) 29.5967 1.16718 0.583591 0.812048i \(-0.301647\pi\)
0.583591 + 0.812048i \(0.301647\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.906022 + 0.266032i 0.0356470 + 0.0104669i
\(647\) −4.39294 + 5.06972i −0.172704 + 0.199311i −0.835502 0.549487i \(-0.814823\pi\)
0.662798 + 0.748798i \(0.269369\pi\)
\(648\) 20.6921 + 13.2980i 0.812862 + 0.522395i
\(649\) −4.82284 + 33.5436i −0.189313 + 1.31670i
\(650\) −5.41573 + 3.48048i −0.212423 + 0.136516i
\(651\) 20.1647 + 44.1545i 0.790316 + 1.73055i
\(652\) −6.10739 7.04830i −0.239184 0.276033i
\(653\) 5.45136 + 37.9151i 0.213328 + 1.48373i 0.761937 + 0.647652i \(0.224249\pi\)
−0.548608 + 0.836079i \(0.684842\pi\)
\(654\) 0 0
\(655\) 22.1879 6.51496i 0.866953 0.254560i
\(656\) 6.17692 1.81371i 0.241168 0.0708134i
\(657\) 5.42355 11.8759i 0.211593 0.463323i
\(658\) −0.636451 4.42662i −0.0248115 0.172567i
\(659\) −6.97589 8.05060i −0.271742 0.313607i 0.603433 0.797414i \(-0.293799\pi\)
−0.875175 + 0.483807i \(0.839254\pi\)
\(660\) −9.72753 21.3003i −0.378643 0.829114i
\(661\) 19.3019 12.4046i 0.750759 0.482483i −0.108454 0.994101i \(-0.534590\pi\)
0.859213 + 0.511618i \(0.170954\pi\)
\(662\) 1.72854 12.0223i 0.0671817 0.467259i
\(663\) 4.31110 + 2.77057i 0.167429 + 0.107600i
\(664\) 12.8331 14.8102i 0.498022 0.574749i
\(665\) −7.67594 2.25386i −0.297660 0.0874010i
\(666\) 1.52786 0.0592035
\(667\) 0 0
\(668\) −2.47214 −0.0956498
\(669\) 8.58197 + 2.51989i 0.331798 + 0.0974247i
\(670\) 1.38271 1.59573i 0.0534187 0.0616485i
\(671\) 30.5886 + 19.6581i 1.18086 + 0.758891i
\(672\) −5.78545 + 40.2387i −0.223179 + 1.55224i
\(673\) 2.52376 1.62192i 0.0972838 0.0625205i −0.491094 0.871106i \(-0.663403\pi\)
0.588378 + 0.808586i \(0.299767\pi\)
\(674\) −6.01194 13.1643i −0.231571 0.507071i
\(675\) 5.08429 + 5.86759i 0.195695 + 0.225844i
\(676\) −0.921081 6.40626i −0.0354262 0.246395i
\(677\) −7.47747 + 16.3734i −0.287383 + 0.629280i −0.997174 0.0751323i \(-0.976062\pi\)
0.709791 + 0.704412i \(0.248789\pi\)
\(678\) −11.6209 + 3.41219i −0.446296 + 0.131044i
\(679\) −54.9837 + 16.1447i −2.11008 + 0.619576i
\(680\) −0.877131 + 1.92065i −0.0336364 + 0.0736535i
\(681\) 3.87610 + 26.9588i 0.148532 + 1.03307i
\(682\) −14.2159 16.4060i −0.544353 0.628217i
\(683\) 11.0487 + 24.1933i 0.422766 + 0.925729i 0.994446 + 0.105252i \(0.0335649\pi\)
−0.571679 + 0.820477i \(0.693708\pi\)
\(684\) −5.44471 + 3.49910i −0.208184 + 0.133791i
\(685\) 3.85043 26.7803i 0.147117 1.02322i
\(686\) 5.93566 + 3.81461i 0.226624 + 0.145643i
\(687\) 17.5718 20.2789i 0.670404 0.773688i
\(688\) 0 0
\(689\) −1.41641 −0.0539608
\(690\) 0 0
\(691\) 7.05573 0.268413 0.134206 0.990953i \(-0.457152\pi\)
0.134206 + 0.990953i \(0.457152\pi\)
\(692\) 35.6208 + 10.4592i 1.35410 + 0.397600i
\(693\) 22.1923 25.6113i 0.843015 0.972891i
\(694\) −5.14128 3.30410i −0.195160 0.125422i
\(695\) −1.88369 + 13.1013i −0.0714524 + 0.496962i
\(696\) −12.6188 + 8.10961i −0.478314 + 0.307394i
\(697\) 1.10188 + 2.41278i 0.0417366 + 0.0913904i
\(698\) −9.88196 11.4044i −0.374038 0.431663i
\(699\) −2.07733 14.4482i −0.0785720 0.546480i
\(700\) −7.55239 + 16.5374i −0.285453 + 0.625056i
\(701\) −3.66494 + 1.07612i −0.138423 + 0.0406446i −0.350210 0.936671i \(-0.613890\pi\)
0.211787 + 0.977316i \(0.432072\pi\)
\(702\) −3.97796 + 1.16803i −0.150138 + 0.0440846i
\(703\) 1.02696 2.24873i 0.0387326 0.0848126i
\(704\) 0.175911 + 1.22349i 0.00662989 + 0.0461119i
\(705\) 4.04726 + 4.67079i 0.152429 + 0.175912i
\(706\) 2.40327 + 5.26242i 0.0904481 + 0.198054i
\(707\) −12.1747 + 7.82423i −0.457878 + 0.294260i
\(708\) −3.33250 + 23.1781i −0.125243 + 0.871085i
\(709\) 35.3906 + 22.7442i 1.32912 + 0.854175i 0.996056 0.0887288i \(-0.0282805\pi\)
0.333066 + 0.942904i \(0.391917\pi\)
\(710\) 6.12133 7.06439i 0.229729 0.265122i
\(711\) −21.0019 6.16672i −0.787633 0.231270i
\(712\) −23.4164 −0.877567
\(713\) 0 0
\(714\) −3.41641 −0.127856
\(715\) 18.6299 + 5.47023i 0.696719 + 0.204575i
\(716\) 0.750404 0.866012i 0.0280439 0.0323644i
\(717\) −25.8913 16.6393i −0.966930 0.621408i
\(718\) −1.74930 + 12.1667i −0.0652835 + 0.454057i
\(719\) −2.57064 + 1.65205i −0.0958688 + 0.0616111i −0.587697 0.809081i \(-0.699965\pi\)
0.491828 + 0.870692i \(0.336329\pi\)
\(720\) −1.90409 4.16938i −0.0709614 0.155384i
\(721\) 8.85887 + 10.2237i 0.329921 + 0.380750i
\(722\) 1.31933 + 9.17615i 0.0491004 + 0.341501i
\(723\) −21.4804 + 47.0354i −0.798863 + 1.74927i
\(724\) −25.8528 + 7.59108i −0.960813 + 0.282120i
\(725\) −9.99447 + 2.93464i −0.371185 + 0.108990i
\(726\) −9.42449 + 20.6367i −0.349775 + 0.765901i
\(727\) −3.94329 27.4262i −0.146248 1.01718i −0.922290 0.386499i \(-0.873684\pi\)
0.776041 0.630682i \(-0.217225\pi\)
\(728\) −14.2159 16.4060i −0.526874 0.608046i
\(729\) −2.90791 6.36742i −0.107700 0.235831i
\(730\) −4.19520 + 2.69609i −0.155271 + 0.0997868i
\(731\) 0 0
\(732\) 21.1362 + 13.5834i 0.781215 + 0.502057i
\(733\) −20.4553 + 23.6066i −0.755533 + 0.871931i −0.995092 0.0989503i \(-0.968452\pi\)
0.239560 + 0.970882i \(0.422997\pi\)
\(734\) −2.47894 0.727882i −0.0914993 0.0268666i
\(735\) 9.59675 0.353981
\(736\) 0 0
\(737\) 14.4721 0.533088
\(738\) 4.11795 + 1.20914i 0.151584 + 0.0445090i
\(739\) −17.5631 + 20.2689i −0.646071 + 0.745605i −0.980436 0.196838i \(-0.936933\pi\)
0.334365 + 0.942444i \(0.391478\pi\)
\(740\) 2.07969 + 1.33654i 0.0764510 + 0.0491321i
\(741\) 1.90935 13.2798i 0.0701419 0.487847i
\(742\) 0.794372 0.510512i 0.0291623 0.0187415i
\(743\) −17.0838 37.4083i −0.626743 1.37238i −0.910512 0.413483i \(-0.864312\pi\)
0.283769 0.958893i \(-0.408415\pi\)
\(744\) −21.9647 25.3486i −0.805265 0.929325i
\(745\) −4.20225 29.2273i −0.153959 1.07081i
\(746\) −1.97901 + 4.33342i −0.0724567 + 0.158658i
\(747\) −16.8179 + 4.93817i −0.615333 + 0.180678i
\(748\) −6.20997 + 1.82341i −0.227059 + 0.0666705i
\(749\) 18.0358 39.4930i 0.659015 1.44304i
\(750\) 2.05960 + 14.3248i 0.0752059 + 0.523069i
\(751\) 0.236195 + 0.272584i 0.00861888 + 0.00994672i 0.760043 0.649873i \(-0.225178\pi\)
−0.751424 + 0.659820i \(0.770633\pi\)
\(752\) −1.72227 3.77124i −0.0628047 0.137523i
\(753\) 4.31110 2.77057i 0.157105 0.100965i
\(754\) 0.791599 5.50569i 0.0288283 0.200505i
\(755\) −4.40486 2.83083i −0.160309 0.103025i
\(756\) −7.66724 + 8.84847i −0.278855 + 0.321816i
\(757\) 1.53207 + 0.449856i 0.0556840 + 0.0163503i 0.309456 0.950914i \(-0.399853\pi\)
−0.253772 + 0.967264i \(0.581671\pi\)
\(758\) −15.0557 −0.546849
\(759\) 0 0
\(760\) 5.52786 0.200517
\(761\) −44.4293 13.0456i −1.61056 0.472903i −0.652101 0.758132i \(-0.726112\pi\)
−0.958459 + 0.285229i \(0.907930\pi\)
\(762\) −6.59904 + 7.61570i −0.239058 + 0.275888i
\(763\) 0 0
\(764\) 6.02855 41.9295i 0.218105 1.51696i
\(765\) 1.58874 1.02102i 0.0574412 0.0369152i
\(766\) −1.81149 3.96661i −0.0654519 0.143320i
\(767\) −12.7150 14.6739i −0.459114 0.529845i
\(768\) −2.08829 14.5244i −0.0753548 0.524104i
\(769\) 9.60631 21.0349i 0.346412 0.758537i −0.653586 0.756852i \(-0.726736\pi\)
0.999999 0.00168529i \(-0.000536444\pi\)
\(770\) −12.4199 + 3.64682i −0.447583 + 0.131422i
\(771\) −16.0314 + 4.70725i −0.577357 + 0.169527i
\(772\) −6.68410 + 14.6361i −0.240566 + 0.526766i
\(773\) −0.786697 5.47160i −0.0282955 0.196800i 0.970770 0.240010i \(-0.0771506\pi\)
−0.999066 + 0.0432100i \(0.986242\pi\)
\(774\) 0 0
\(775\) −9.67576 21.1870i −0.347564 0.761058i
\(776\) 33.3109 21.4076i 1.19579 0.768489i
\(777\) −1.27290 + 8.85323i −0.0456651 + 0.317608i
\(778\) −13.2725 8.52974i −0.475843 0.305806i
\(779\) 4.54753 5.24813i 0.162932 0.188034i
\(780\) 12.8729 + 3.77984i 0.460926 + 0.135340i
\(781\) 64.0689 2.29256
\(782\) 0 0
\(783\) −6.70820 −0.239732
\(784\) −6.17692 1.81371i −0.220604 0.0647753i
\(785\) 9.24104 10.6647i 0.329827 0.380640i
\(786\) −21.7499 13.9778i −0.775792 0.498571i
\(787\) 3.49861 24.3334i 0.124712 0.867391i −0.827394 0.561622i \(-0.810177\pi\)
0.952106 0.305769i \(-0.0989134\pi\)
\(788\) 2.00384 1.28779i 0.0713837 0.0458755i
\(789\) 2.73492 + 5.98865i 0.0973658 + 0.213201i
\(790\) 5.47508 + 6.31858i 0.194795 + 0.224805i
\(791\) −4.03615 28.0720i −0.143509 0.998126i
\(792\) −9.72753 + 21.3003i −0.345653 + 0.756874i
\(793\) −19.9889 + 5.86928i −0.709828 + 0.208424i
\(794\) 14.4789 4.25139i 0.513837 0.150876i
\(795\) −0.542097 + 1.18703i −0.0192262 + 0.0420995i
\(796\) 2.83043 + 19.6861i 0.100322 + 0.697756i
\(797\) −22.5015 25.9681i −0.797043 0.919836i 0.201173 0.979556i \(-0.435525\pi\)
−0.998215 + 0.0597196i \(0.980979\pi\)
\(798\) 3.71558 + 8.13600i 0.131530 + 0.288011i
\(799\) 1.43703 0.923525i 0.0508386 0.0326720i
\(800\) 2.77608 19.3080i 0.0981491 0.682642i
\(801\) 17.6194 + 11.3233i 0.622552 + 0.400090i
\(802\) −5.73915 + 6.62334i −0.202657 + 0.233878i
\(803\) −32.7958 9.62971i −1.15734 0.339825i
\(804\) 10.0000 0.352673
\(805\) 0 0
\(806\) 12.4377 0.438099
\(807\) −17.0444 5.00468i −0.599990 0.176173i
\(808\) 6.54861 7.55750i 0.230379 0.265872i
\(809\) 10.1888 + 6.54795i 0.358219 + 0.230214i 0.707355 0.706859i \(-0.249888\pi\)
−0.349135 + 0.937072i \(0.613525\pi\)
\(810\) −1.19591 + 8.31772i −0.0420199 + 0.292255i
\(811\) −20.4824 + 13.1633i −0.719236 + 0.462225i −0.848371 0.529402i \(-0.822416\pi\)
0.129135 + 0.991627i \(0.458780\pi\)
\(812\) −6.52542 14.2887i −0.228997 0.501435i
\(813\) 11.7145 + 13.5193i 0.410846 + 0.474141i
\(814\) −0.569259 3.95929i −0.0199525 0.138773i
\(815\) 2.95967 6.48077i 0.103673 0.227012i
\(816\) −3.03889 + 0.892299i −0.106382 + 0.0312367i
\(817\) 0 0
\(818\) 5.48415 12.0086i 0.191749 0.419872i
\(819\) 2.76324 + 19.2188i 0.0965555 + 0.671558i
\(820\) 4.54753 + 5.24813i 0.158807 + 0.183273i
\(821\) −16.1780 35.4250i −0.564617 1.23634i −0.949614 0.313422i \(-0.898525\pi\)
0.384997 0.922918i \(-0.374203\pi\)
\(822\) −25.4473 + 16.3540i −0.887575 + 0.570410i
\(823\) 5.62727 39.1385i 0.196154 1.36428i −0.619160 0.785265i \(-0.712527\pi\)
0.815314 0.579019i \(-0.196564\pi\)
\(824\) −7.86364 5.05365i −0.273943 0.176052i
\(825\) −26.6217 + 30.7231i −0.926849 + 1.06964i
\(826\) 12.4199 + 3.64682i 0.432145 + 0.126889i
\(827\) −1.52786 −0.0531290 −0.0265645 0.999647i \(-0.508457\pi\)
−0.0265645 + 0.999647i \(0.508457\pi\)
\(828\) 0 0
\(829\) 40.2492 1.39791 0.698957 0.715164i \(-0.253648\pi\)
0.698957 + 0.715164i \(0.253648\pi\)
\(830\) 6.42385 + 1.88621i 0.222975 + 0.0654714i
\(831\) 22.6561 26.1465i 0.785930 0.907011i
\(832\) −0.595779 0.382884i −0.0206549 0.0132741i
\(833\) 0.377487 2.62548i 0.0130791 0.0909674i
\(834\) 12.4492 8.00060i 0.431080 0.277038i
\(835\) −0.784529 1.71788i −0.0271498 0.0594497i
\(836\) 11.0961 + 12.8056i 0.383768 + 0.442892i
\(837\) −2.13472 14.8473i −0.0737868 0.513199i
\(838\) 1.17679 2.57682i 0.0406517 0.0890148i
\(839\) −39.4588 + 11.5861i −1.36227 + 0.399998i −0.879562 0.475784i \(-0.842164\pi\)
−0.482706 + 0.875782i \(0.660346\pi\)
\(840\) −19.1899 + 5.63465i −0.662113 + 0.194414i
\(841\) −8.30830 + 18.1926i −0.286493 + 0.627332i
\(842\) −0.905219 6.29594i −0.0311959 0.216972i
\(843\) 12.8331 + 14.8102i 0.441997 + 0.510092i
\(844\) 15.7395 + 34.4646i 0.541775 + 1.18632i
\(845\) 4.15939 2.67308i 0.143087 0.0919566i
\(846\) 0.393349 2.73580i 0.0135236 0.0940587i
\(847\) −44.6913 28.7213i −1.53561 0.986877i
\(848\) 0.573257 0.661574i 0.0196857 0.0227186i
\(849\) −59.4477 17.4554i −2.04024 0.599069i
\(850\) 1.63932 0.0562282
\(851\) 0 0
\(852\) 44.2705 1.51668
\(853\) 10.1549 + 2.98174i 0.347697 + 0.102093i 0.450918 0.892566i \(-0.351097\pi\)
−0.103221 + 0.994658i \(0.532915\pi\)
\(854\) 9.09506 10.4963i 0.311227 0.359175i
\(855\) −4.15939 2.67308i −0.142248 0.0914172i
\(856\) −4.26945 + 29.6946i −0.145927 + 1.01494i
\(857\) 1.23844 0.795897i 0.0423043 0.0271873i −0.519318 0.854581i \(-0.673814\pi\)
0.561622 + 0.827394i \(0.310178\pi\)
\(858\) −9.01791 19.7465i −0.307867 0.674134i
\(859\) 10.9415 + 12.6272i 0.373321 + 0.430835i 0.911059 0.412277i \(-0.135266\pi\)
−0.537738 + 0.843112i \(0.680721\pi\)
\(860\) 0 0
\(861\) −10.4371 + 22.8542i −0.355697 + 0.778867i
\(862\) −10.3940 + 3.05196i −0.354021 + 0.103950i
\(863\) 20.6685 6.06881i 0.703562 0.206585i 0.0896669 0.995972i \(-0.471420\pi\)
0.613896 + 0.789387i \(0.289602\pi\)
\(864\) 5.21857 11.4271i 0.177539 0.388757i
\(865\) 4.03615 + 28.0720i 0.137233 + 0.954477i
\(866\) 7.21208 + 8.32319i 0.245077 + 0.282833i
\(867\) 15.2491 + 33.3910i 0.517888 + 1.13402i
\(868\) 29.5487 18.9898i 1.00295 0.644556i
\(869\) −8.15534 + 56.7217i −0.276651 + 1.92415i
\(870\) −4.31110 2.77057i −0.146160 0.0939313i
\(871\) −5.42997 + 6.26652i −0.183988 + 0.212333i
\(872\) 0 0
\(873\) −35.4164 −1.19866
\(874\) 0 0
\(875\) −33.8885 −1.14564
\(876\) −22.6613 6.65397i −0.765656 0.224817i
\(877\) 23.8842 27.5638i 0.806511 0.930763i −0.192208 0.981354i \(-0.561565\pi\)
0.998719 + 0.0505907i \(0.0161104\pi\)
\(878\) −9.72683 6.25105i −0.328265 0.210963i
\(879\) 0.486206 3.38163i 0.0163993 0.114060i
\(880\) −10.0950 + 6.48769i −0.340304 + 0.218700i
\(881\) −18.3532 40.1879i −0.618334 1.35396i −0.916725 0.399519i \(-0.869177\pi\)
0.298391 0.954444i \(-0.403550\pi\)
\(882\) −2.81053 3.24352i −0.0946354 0.109215i
\(883\) −0.569259 3.95929i −0.0191571 0.133241i 0.977998 0.208612i \(-0.0668947\pi\)
−0.997155 + 0.0753718i \(0.975986\pi\)
\(884\) 1.54044 3.37310i 0.0518107 0.113450i
\(885\) −17.1639 + 5.03979i −0.576959 + 0.169411i
\(886\) −22.6079 + 6.63827i −0.759526 + 0.223017i
\(887\) 9.58316 20.9842i 0.321771 0.704580i −0.677757 0.735286i \(-0.737048\pi\)
0.999528 + 0.0307053i \(0.00977532\pi\)
\(888\) −0.879554 6.11743i −0.0295159 0.205288i
\(889\) −15.4526 17.8332i −0.518263 0.598107i
\(890\) −3.32332 7.27706i −0.111398 0.243927i
\(891\) −48.4535 + 31.1392i −1.62325 + 1.04320i
\(892\) 0.921081 6.40626i 0.0308401 0.214497i
\(893\) −3.76220 2.41782i −0.125897 0.0809092i
\(894\) −21.6190 + 24.9497i −0.723048 + 0.834442i
\(895\) 0.839929 + 0.246625i 0.0280757 + 0.00824378i
\(896\) 36.8328 1.23050
\(897\) 0 0
\(898\) −9.23607 −0.308212
\(899\) 19.3094 + 5.66976i 0.644005 + 0.189097i
\(900\) −7.35806 + 8.49165i −0.245269 + 0.283055i
\(901\) 0.303423 + 0.194998i 0.0101085 + 0.00649633i
\(902\) 1.59906 11.1217i 0.0532428 0.370312i
\(903\) 0 0
\(904\) 8.14078 + 17.8258i 0.270758 + 0.592878i
\(905\) −13.4794 15.5560i −0.448070 0.517100i
\(906\) 0.833126 + 5.79452i 0.0276787 + 0.192510i
\(907\) 16.7201 36.6120i 0.555183 1.21568i −0.399136 0.916892i \(-0.630690\pi\)
0.954319 0.298789i \(-0.0965828\pi\)
\(908\) 18.9099 5.55244i 0.627547 0.184264i
\(909\) −8.58197 + 2.51989i −0.284646 + 0.0835796i
\(910\) 3.08089 6.74620i 0.102130 0.223634i
\(911\) 4.45516 + 30.9863i 0.147606 + 1.02662i 0.920123 + 0.391629i \(0.128088\pi\)
−0.772517 + 0.634994i \(0.781003\pi\)
\(912\) 5.42997 + 6.26652i 0.179804 + 0.207505i
\(913\) 19.0628 + 41.7417i 0.630886 + 1.38145i
\(914\) 2.66440 1.71231i 0.0881307 0.0566382i
\(915\) −2.73152 + 18.9981i −0.0903012 + 0.628059i
\(916\) −16.3341 10.4973i −0.539695 0.346841i
\(917\) 39.6459 45.7538i 1.30922 1.51093i
\(918\) 1.01296 + 0.297433i 0.0334328 + 0.00981675i
\(919\) −41.1246 −1.35658 −0.678288 0.734796i \(-0.737278\pi\)
−0.678288 + 0.734796i \(0.737278\pi\)
\(920\) 0 0
\(921\) −21.3050 −0.702022
\(922\) 0.872976 + 0.256329i 0.0287499 + 0.00844174i
\(923\) −24.0388 + 27.7422i −0.791245 + 0.913146i
\(924\) −51.5730 33.1440i −1.69663 1.09036i
\(925\) 0.610786 4.24811i 0.0200825 0.139677i
\(926\) −10.3985 + 6.68269i −0.341715 + 0.219607i
\(927\) 3.47315 + 7.60514i 0.114073 + 0.249786i
\(928\) 11.0371 + 12.7375i 0.362310 + 0.418128i
\(929\) 3.42349 + 23.8109i 0.112321 + 0.781209i 0.965652 + 0.259840i \(0.0836697\pi\)
−0.853331 + 0.521370i \(0.825421\pi\)
\(930\) 4.76023 10.4235i 0.156094 0.341799i
\(931\) −6.66298 + 1.95643i −0.218370 + 0.0641193i
\(932\) −10.1345 + 2.97575i −0.331965 + 0.0974738i
\(933\) −12.2432 + 26.8088i −0.400823 + 0.877681i
\(934\) −1.14832 7.98675i −0.0375742 0.261335i
\(935\) −3.23781 3.73663i −0.105888 0.122201i
\(936\) −5.57338 12.2040i −0.182172 0.398900i
\(937\) −28.7543 + 18.4793i −0.939363 + 0.603692i −0.918214 0.396084i \(-0.870369\pi\)
−0.0211489 + 0.999776i \(0.506732\pi\)
\(938\) 0.786697 5.47160i 0.0256866 0.178654i
\(939\) 45.8249 + 29.4499i 1.49544 + 0.961060i
\(940\) 2.92863 3.37981i 0.0955213 0.110237i
\(941\) 6.38300 + 1.87422i 0.208080 + 0.0610978i 0.384111 0.923287i \(-0.374508\pi\)
−0.176031 + 0.984385i \(0.556326\pi\)
\(942\) −15.7771 −0.514045
\(943\) 0 0
\(944\) 12.0000 0.390567
\(945\) −8.58197 2.51989i −0.279171 0.0819721i
\(946\) 0 0
\(947\) −9.10208 5.84955i −0.295778 0.190085i 0.384332 0.923195i \(-0.374432\pi\)
−0.680110 + 0.733110i \(0.738068\pi\)
\(948\) −5.63520 + 39.1937i −0.183023 + 1.27295i
\(949\) 16.4748 10.5877i 0.534794 0.343691i
\(950\) −1.78288 3.90396i −0.0578442 0.126661i
\(951\) 37.2176 + 42.9514i 1.20686 + 1.39279i
\(952\) 0.786697 + 5.47160i 0.0254970 + 0.177336i
\(953\) −8.50443 + 18.6221i −0.275486 + 0.603229i −0.995915 0.0902993i \(-0.971218\pi\)
0.720429 + 0.693529i \(0.243945\pi\)
\(954\) 0.559953 0.164417i 0.0181291 0.00532319i
\(955\) 31.0498 9.11706i 1.00475 0.295021i
\(956\) −9.25150 + 20.2580i −0.299215 + 0.655190i
\(957\) −4.99875 34.7671i −0.161587 1.12386i
\(958\) 12.7880 + 14.7582i 0.413163 + 0.476815i
\(959\) −29.4250 64.4318i −0.950183 2.08061i
\(960\) −0.548898 + 0.352755i −0.0177156 + 0.0113851i
\(961\) −1.99241 + 13.8575i −0.0642712 + 0.447016i
\(962\) 1.92798 + 1.23904i 0.0621606 + 0.0399482i
\(963\) 17.5718 20.2789i 0.566242 0.653478i
\(964\) 35.9008 + 10.5414i 1.15629 + 0.339516i
\(965\) −12.2918 −0.395687
\(966\) 0 0
\(967\) 27.5410 0.885659 0.442830 0.896606i \(-0.353975\pi\)
0.442830 + 0.896606i \(0.353975\pi\)
\(968\) 35.2213 + 10.3419i 1.13205 + 0.332401i
\(969\) −2.23727 + 2.58195i −0.0718715 + 0.0829441i
\(970\) 11.3804 + 7.31372i 0.365401 + 0.234829i
\(971\) 2.34423 16.3045i 0.0752299 0.523235i −0.917007 0.398872i \(-0.869402\pi\)
0.992237 0.124364i \(-0.0396890\pi\)
\(972\) −24.3495 + 15.6485i −0.781010 + 0.501924i
\(973\) 14.3952 + 31.5210i 0.461488 + 1.01052i
\(974\) 5.95280 + 6.86989i 0.190740 + 0.220126i
\(975\) −3.31477 23.0547i −0.106158 0.738342i
\(976\) 5.34863 11.7119i 0.171205 0.374888i
\(977\) −22.4018 + 6.57776i −0.716697 + 0.210441i −0.619695 0.784843i \(-0.712744\pi\)
−0.0970020 + 0.995284i \(0.530925\pi\)
\(978\) −7.64290 + 2.24416i −0.244393 + 0.0717602i
\(979\) 22.7784 49.8777i 0.728000 1.59410i
\(980\) −0.988273 6.87359i −0.0315692 0.219569i
\(981\) 0 0
\(982\) 2.14315 + 4.69284i 0.0683906 + 0.149755i
\(983\) 34.0473 21.8809i 1.08594 0.697892i 0.130019 0.991512i \(-0.458496\pi\)
0.955922 + 0.293620i \(0.0948599\pi\)
\(984\) 2.47068 17.1840i 0.0787625 0.547805i
\(985\) 1.53080 + 0.983783i 0.0487752 + 0.0313459i
\(986\) −0.927550 + 1.07045i −0.0295392 + 0.0340901i
\(987\) 15.5249 + 4.55853i 0.494164 + 0.145100i
\(988\) −9.70820 −0.308859
\(989\) 0 0
\(990\) −8.00000 −0.254257
\(991\) −23.0278 6.76158i −0.731503 0.214789i −0.105291 0.994441i \(-0.533577\pi\)
−0.626212 + 0.779653i \(0.715396\pi\)
\(992\) −24.6797 + 28.4819i −0.783581 + 0.904300i
\(993\) 36.9683 + 23.7581i 1.17315 + 0.753939i
\(994\) 3.48275 24.2230i 0.110466 0.768308i
\(995\) −12.7816 + 8.21422i −0.405203 + 0.260408i
\(996\) 13.1721 + 28.8428i 0.417373 + 0.913919i
\(997\) −11.0232 12.7214i −0.349107 0.402891i 0.553854 0.832614i \(-0.313157\pi\)
−0.902961 + 0.429723i \(0.858611\pi\)
\(998\) −1.69682 11.8016i −0.0537118 0.373574i
\(999\) 1.14818 2.51416i 0.0363268 0.0795445i
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 529.2.c.n.501.1 20
23.2 even 11 inner 529.2.c.n.118.1 20
23.3 even 11 529.2.a.a.1.2 2
23.4 even 11 inner 529.2.c.n.334.2 20
23.5 odd 22 529.2.c.o.266.1 20
23.6 even 11 inner 529.2.c.n.487.2 20
23.7 odd 22 529.2.c.o.399.1 20
23.8 even 11 inner 529.2.c.n.255.2 20
23.9 even 11 inner 529.2.c.n.170.1 20
23.10 odd 22 529.2.c.o.466.2 20
23.11 odd 22 529.2.c.o.177.1 20
23.12 even 11 inner 529.2.c.n.177.1 20
23.13 even 11 inner 529.2.c.n.466.2 20
23.14 odd 22 529.2.c.o.170.1 20
23.15 odd 22 529.2.c.o.255.2 20
23.16 even 11 inner 529.2.c.n.399.1 20
23.17 odd 22 529.2.c.o.487.2 20
23.18 even 11 inner 529.2.c.n.266.1 20
23.19 odd 22 529.2.c.o.334.2 20
23.20 odd 22 23.2.a.a.1.2 2
23.21 odd 22 529.2.c.o.118.1 20
23.22 odd 2 529.2.c.o.501.1 20
69.20 even 22 207.2.a.d.1.1 2
69.26 odd 22 4761.2.a.w.1.1 2
92.3 odd 22 8464.2.a.bb.1.2 2
92.43 even 22 368.2.a.h.1.2 2
115.43 even 44 575.2.b.d.24.2 4
115.89 odd 22 575.2.a.f.1.1 2
115.112 even 44 575.2.b.d.24.3 4
161.20 even 22 1127.2.a.c.1.2 2
184.43 even 22 1472.2.a.s.1.1 2
184.181 odd 22 1472.2.a.t.1.2 2
253.43 even 22 2783.2.a.c.1.1 2
276.227 odd 22 3312.2.a.ba.1.1 2
299.181 odd 22 3887.2.a.i.1.1 2
345.89 even 22 5175.2.a.be.1.2 2
391.135 odd 22 6647.2.a.b.1.2 2
437.227 even 22 8303.2.a.e.1.1 2
460.319 even 22 9200.2.a.bt.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.2.a.a.1.2 2 23.20 odd 22
207.2.a.d.1.1 2 69.20 even 22
368.2.a.h.1.2 2 92.43 even 22
529.2.a.a.1.2 2 23.3 even 11
529.2.c.n.118.1 20 23.2 even 11 inner
529.2.c.n.170.1 20 23.9 even 11 inner
529.2.c.n.177.1 20 23.12 even 11 inner
529.2.c.n.255.2 20 23.8 even 11 inner
529.2.c.n.266.1 20 23.18 even 11 inner
529.2.c.n.334.2 20 23.4 even 11 inner
529.2.c.n.399.1 20 23.16 even 11 inner
529.2.c.n.466.2 20 23.13 even 11 inner
529.2.c.n.487.2 20 23.6 even 11 inner
529.2.c.n.501.1 20 1.1 even 1 trivial
529.2.c.o.118.1 20 23.21 odd 22
529.2.c.o.170.1 20 23.14 odd 22
529.2.c.o.177.1 20 23.11 odd 22
529.2.c.o.255.2 20 23.15 odd 22
529.2.c.o.266.1 20 23.5 odd 22
529.2.c.o.334.2 20 23.19 odd 22
529.2.c.o.399.1 20 23.7 odd 22
529.2.c.o.466.2 20 23.10 odd 22
529.2.c.o.487.2 20 23.17 odd 22
529.2.c.o.501.1 20 23.22 odd 2
575.2.a.f.1.1 2 115.89 odd 22
575.2.b.d.24.2 4 115.43 even 44
575.2.b.d.24.3 4 115.112 even 44
1127.2.a.c.1.2 2 161.20 even 22
1472.2.a.s.1.1 2 184.43 even 22
1472.2.a.t.1.2 2 184.181 odd 22
2783.2.a.c.1.1 2 253.43 even 22
3312.2.a.ba.1.1 2 276.227 odd 22
3887.2.a.i.1.1 2 299.181 odd 22
4761.2.a.w.1.1 2 69.26 odd 22
5175.2.a.be.1.2 2 345.89 even 22
6647.2.a.b.1.2 2 391.135 odd 22
8303.2.a.e.1.1 2 437.227 even 22
8464.2.a.bb.1.2 2 92.3 odd 22
9200.2.a.bt.1.1 2 460.319 even 22