Properties

Label 165.2.r.a.29.18
Level $165$
Weight $2$
Character 165.29
Analytic conductor $1.318$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,2,Mod(29,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.r (of order \(10\), degree \(4\), 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: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 29.18
Character \(\chi\) \(=\) 165.29
Dual form 165.2.r.a.74.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26516 - 1.74134i) q^{2} +(1.42080 - 0.990613i) q^{3} +(-0.813603 - 2.50401i) q^{4} +(-2.23554 + 0.0487905i) q^{5} +(0.0725479 - 3.72738i) q^{6} +(1.15619 + 3.55838i) q^{7} +(-1.29554 - 0.420945i) q^{8} +(1.03737 - 2.81493i) q^{9} +O(q^{10})\) \(q+(1.26516 - 1.74134i) q^{2} +(1.42080 - 0.990613i) q^{3} +(-0.813603 - 2.50401i) q^{4} +(-2.23554 + 0.0487905i) q^{5} +(0.0725479 - 3.72738i) q^{6} +(1.15619 + 3.55838i) q^{7} +(-1.29554 - 0.420945i) q^{8} +(1.03737 - 2.81493i) q^{9} +(-2.74334 + 3.95455i) q^{10} +(-2.90347 + 1.60308i) q^{11} +(-3.63648 - 2.75175i) q^{12} +(-2.36441 - 1.71784i) q^{13} +(7.65909 + 2.48859i) q^{14} +(-3.12793 + 2.28387i) q^{15} +(1.88802 - 1.37173i) q^{16} +(3.60354 + 4.95985i) q^{17} +(-3.58931 - 5.36775i) q^{18} +(-1.69505 - 0.550755i) q^{19} +(1.94101 + 5.55811i) q^{20} +(5.16769 + 3.91042i) q^{21} +(-0.881833 + 7.08407i) q^{22} -2.68103 q^{23} +(-2.25770 + 0.685294i) q^{24} +(4.99524 - 0.218146i) q^{25} +(-5.98268 + 1.94389i) q^{26} +(-1.31461 - 5.02711i) q^{27} +(7.96955 - 5.79021i) q^{28} +(-1.73641 - 5.34411i) q^{29} +(0.0196774 + 8.33623i) q^{30} +(-1.15665 - 0.840357i) q^{31} -7.74754i q^{32} +(-2.53723 + 5.15388i) q^{33} +13.1958 q^{34} +(-2.75831 - 7.89847i) q^{35} +(-7.89264 - 0.307354i) q^{36} +(-3.51577 + 1.14234i) q^{37} +(-3.10355 + 2.25486i) q^{38} +(-5.06107 - 0.0985063i) q^{39} +(2.91676 + 0.877829i) q^{40} +(0.0785467 - 0.241742i) q^{41} +(13.3473 - 4.05139i) q^{42} +8.64616 q^{43} +(6.37641 + 5.96605i) q^{44} +(-2.18174 + 6.34350i) q^{45} +(-3.39192 + 4.66857i) q^{46} +(-2.93342 + 9.02814i) q^{47} +(1.32366 - 3.81925i) q^{48} +(-5.66216 + 4.11380i) q^{49} +(5.93989 - 8.97439i) q^{50} +(10.0332 + 3.47726i) q^{51} +(-2.37781 + 7.31814i) q^{52} +(-4.45543 - 3.23706i) q^{53} +(-10.4171 - 4.07090i) q^{54} +(6.41259 - 3.72541i) q^{55} -5.09670i q^{56} +(-2.95392 + 0.896622i) q^{57} +(-11.5027 - 3.73746i) q^{58} +(0.0480847 - 0.0156237i) q^{59} +(8.26374 + 5.97421i) q^{60} +(1.70674 + 2.34913i) q^{61} +(-2.92669 + 0.950939i) q^{62} +(11.2160 + 0.436771i) q^{63} +(-9.71504 - 7.05839i) q^{64} +(5.36953 + 3.72494i) q^{65} +(5.76465 + 10.9386i) q^{66} -2.45040i q^{67} +(9.48767 - 13.0587i) q^{68} +(-3.80922 + 2.65586i) q^{69} +(-17.2436 - 5.18964i) q^{70} +(-0.490070 - 0.674523i) q^{71} +(-2.52889 + 3.21018i) q^{72} +(-1.79580 - 5.52690i) q^{73} +(-2.45879 + 7.56739i) q^{74} +(6.88116 - 5.25829i) q^{75} +4.69252i q^{76} +(-9.06132 - 8.47817i) q^{77} +(-6.57458 + 8.68841i) q^{78} +(-5.17618 + 7.12440i) q^{79} +(-4.15380 + 3.15866i) q^{80} +(-6.84772 - 5.84027i) q^{81} +(-0.321580 - 0.442617i) q^{82} +(-0.718410 - 0.988807i) q^{83} +(5.58731 - 16.1215i) q^{84} +(-8.29783 - 10.9121i) q^{85} +(10.9387 - 15.0559i) q^{86} +(-7.76104 - 5.87283i) q^{87} +(4.43636 - 0.854650i) q^{88} -1.49038i q^{89} +(8.28594 + 11.8247i) q^{90} +(3.37903 - 10.3996i) q^{91} +(2.18129 + 6.71333i) q^{92} +(-2.47584 - 0.0481886i) q^{93} +(12.0098 + 16.5301i) q^{94} +(3.81621 + 1.14853i) q^{95} +(-7.67481 - 11.0077i) q^{96} +(-4.47759 + 6.16287i) q^{97} +15.0643i q^{98} +(1.50059 + 9.83607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 4 q^{4} - 10 q^{6} - 10 q^{9} - 2 q^{15} - 60 q^{16} - 20 q^{19} - 30 q^{24} + 6 q^{25} + 10 q^{30} - 20 q^{31} - 56 q^{34} + 2 q^{36} - 50 q^{39} + 60 q^{40} - 92 q^{45} - 40 q^{46} + 72 q^{49} + 30 q^{51} + 4 q^{55} + 54 q^{60} + 96 q^{64} - 42 q^{66} + 30 q^{69} - 86 q^{70} + 2 q^{75} - 66 q^{81} + 140 q^{84} - 30 q^{85} + 120 q^{90} + 48 q^{91} + 60 q^{94} - 70 q^{96} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26516 1.74134i 0.894600 1.23131i −0.0775584 0.996988i \(-0.524712\pi\)
0.972159 0.234324i \(-0.0752876\pi\)
\(3\) 1.42080 0.990613i 0.820302 0.571931i
\(4\) −0.813603 2.50401i −0.406802 1.25201i
\(5\) −2.23554 + 0.0487905i −0.999762 + 0.0218198i
\(6\) 0.0725479 3.72738i 0.0296176 1.52170i
\(7\) 1.15619 + 3.55838i 0.436997 + 1.34494i 0.891026 + 0.453953i \(0.149986\pi\)
−0.454028 + 0.890987i \(0.650014\pi\)
\(8\) −1.29554 0.420945i −0.458041 0.148827i
\(9\) 1.03737 2.81493i 0.345791 0.938312i
\(10\) −2.74334 + 3.95455i −0.867520 + 1.25054i
\(11\) −2.90347 + 1.60308i −0.875429 + 0.483347i
\(12\) −3.63648 2.75175i −1.04976 0.794361i
\(13\) −2.36441 1.71784i −0.655768 0.476443i 0.209463 0.977817i \(-0.432828\pi\)
−0.865231 + 0.501373i \(0.832828\pi\)
\(14\) 7.65909 + 2.48859i 2.04698 + 0.665104i
\(15\) −3.12793 + 2.28387i −0.807627 + 0.589693i
\(16\) 1.88802 1.37173i 0.472004 0.342931i
\(17\) 3.60354 + 4.95985i 0.873987 + 1.20294i 0.978050 + 0.208369i \(0.0668154\pi\)
−0.104064 + 0.994571i \(0.533185\pi\)
\(18\) −3.58931 5.36775i −0.846010 1.26519i
\(19\) −1.69505 0.550755i −0.388871 0.126352i 0.108055 0.994145i \(-0.465538\pi\)
−0.496926 + 0.867793i \(0.665538\pi\)
\(20\) 1.94101 + 5.55811i 0.434023 + 1.24283i
\(21\) 5.16769 + 3.91042i 1.12768 + 0.853325i
\(22\) −0.881833 + 7.08407i −0.188007 + 1.51033i
\(23\) −2.68103 −0.559033 −0.279516 0.960141i \(-0.590174\pi\)
−0.279516 + 0.960141i \(0.590174\pi\)
\(24\) −2.25770 + 0.685294i −0.460851 + 0.139885i
\(25\) 4.99524 0.218146i 0.999048 0.0436292i
\(26\) −5.98268 + 1.94389i −1.17330 + 0.381229i
\(27\) −1.31461 5.02711i −0.252996 0.967467i
\(28\) 7.96955 5.79021i 1.50610 1.09425i
\(29\) −1.73641 5.34411i −0.322442 0.992376i −0.972582 0.232561i \(-0.925289\pi\)
0.650139 0.759815i \(-0.274711\pi\)
\(30\) 0.0196774 + 8.33623i 0.00359258 + 1.52198i
\(31\) −1.15665 0.840357i −0.207741 0.150933i 0.479050 0.877788i \(-0.340981\pi\)
−0.686791 + 0.726855i \(0.740981\pi\)
\(32\) 7.74754i 1.36958i
\(33\) −2.53723 + 5.15388i −0.441675 + 0.897175i
\(34\) 13.1958 2.26306
\(35\) −2.75831 7.89847i −0.466240 1.33508i
\(36\) −7.89264 0.307354i −1.31544 0.0512256i
\(37\) −3.51577 + 1.14234i −0.577990 + 0.187800i −0.583400 0.812185i \(-0.698278\pi\)
0.00541019 + 0.999985i \(0.498278\pi\)
\(38\) −3.10355 + 2.25486i −0.503462 + 0.365787i
\(39\) −5.06107 0.0985063i −0.810421 0.0157736i
\(40\) 2.91676 + 0.877829i 0.461180 + 0.138797i
\(41\) 0.0785467 0.241742i 0.0122669 0.0377537i −0.944736 0.327833i \(-0.893682\pi\)
0.957003 + 0.290079i \(0.0936817\pi\)
\(42\) 13.3473 4.05139i 2.05953 0.625144i
\(43\) 8.64616 1.31853 0.659264 0.751912i \(-0.270868\pi\)
0.659264 + 0.751912i \(0.270868\pi\)
\(44\) 6.37641 + 5.96605i 0.961280 + 0.899416i
\(45\) −2.18174 + 6.34350i −0.325235 + 0.945633i
\(46\) −3.39192 + 4.66857i −0.500111 + 0.688343i
\(47\) −2.93342 + 9.02814i −0.427883 + 1.31689i 0.472323 + 0.881426i \(0.343416\pi\)
−0.900206 + 0.435464i \(0.856584\pi\)
\(48\) 1.32366 3.81925i 0.191053 0.551261i
\(49\) −5.66216 + 4.11380i −0.808880 + 0.587686i
\(50\) 5.93989 8.97439i 0.840027 1.26917i
\(51\) 10.0332 + 3.47726i 1.40493 + 0.486914i
\(52\) −2.37781 + 7.31814i −0.329743 + 1.01484i
\(53\) −4.45543 3.23706i −0.612001 0.444645i 0.238117 0.971236i \(-0.423470\pi\)
−0.850118 + 0.526592i \(0.823470\pi\)
\(54\) −10.4171 4.07090i −1.41758 0.553979i
\(55\) 6.41259 3.72541i 0.864674 0.502334i
\(56\) 5.09670i 0.681075i
\(57\) −2.95392 + 0.896622i −0.391256 + 0.118760i
\(58\) −11.5027 3.73746i −1.51038 0.490753i
\(59\) 0.0480847 0.0156237i 0.00626009 0.00203403i −0.305885 0.952068i \(-0.598952\pi\)
0.312145 + 0.950034i \(0.398952\pi\)
\(60\) 8.26374 + 5.97421i 1.06684 + 0.771267i
\(61\) 1.70674 + 2.34913i 0.218526 + 0.300776i 0.904179 0.427153i \(-0.140483\pi\)
−0.685653 + 0.727928i \(0.740483\pi\)
\(62\) −2.92669 + 0.950939i −0.371690 + 0.120769i
\(63\) 11.2160 + 0.436771i 1.41308 + 0.0550279i
\(64\) −9.71504 7.05839i −1.21438 0.882299i
\(65\) 5.36953 + 3.72494i 0.666008 + 0.462021i
\(66\) 5.76465 + 10.9386i 0.709580 + 1.34645i
\(67\) 2.45040i 0.299364i −0.988734 0.149682i \(-0.952175\pi\)
0.988734 0.149682i \(-0.0478250\pi\)
\(68\) 9.48767 13.0587i 1.15055 1.58359i
\(69\) −3.80922 + 2.65586i −0.458576 + 0.319728i
\(70\) −17.2436 5.18964i −2.06100 0.620281i
\(71\) −0.490070 0.674523i −0.0581606 0.0800512i 0.778946 0.627091i \(-0.215755\pi\)
−0.837107 + 0.547040i \(0.815755\pi\)
\(72\) −2.52889 + 3.21018i −0.298032 + 0.378323i
\(73\) −1.79580 5.52690i −0.210182 0.646875i −0.999461 0.0328393i \(-0.989545\pi\)
0.789278 0.614036i \(-0.210455\pi\)
\(74\) −2.45879 + 7.56739i −0.285829 + 0.879691i
\(75\) 6.88116 5.25829i 0.794568 0.607175i
\(76\) 4.69252i 0.538269i
\(77\) −9.06132 8.47817i −1.03263 0.966177i
\(78\) −6.57458 + 8.68841i −0.744425 + 0.983769i
\(79\) −5.17618 + 7.12440i −0.582366 + 0.801558i −0.993952 0.109813i \(-0.964975\pi\)
0.411586 + 0.911371i \(0.364975\pi\)
\(80\) −4.15380 + 3.15866i −0.464409 + 0.353149i
\(81\) −6.84772 5.84027i −0.760858 0.648919i
\(82\) −0.321580 0.442617i −0.0355126 0.0488789i
\(83\) −0.718410 0.988807i −0.0788557 0.108536i 0.767767 0.640729i \(-0.221368\pi\)
−0.846623 + 0.532194i \(0.821368\pi\)
\(84\) 5.58731 16.1215i 0.609625 1.75900i
\(85\) −8.29783 10.9121i −0.900026 1.18358i
\(86\) 10.9387 15.0559i 1.17956 1.62352i
\(87\) −7.76104 5.87283i −0.832070 0.629633i
\(88\) 4.43636 0.854650i 0.472918 0.0911060i
\(89\) 1.49038i 0.157980i −0.996875 0.0789901i \(-0.974830\pi\)
0.996875 0.0789901i \(-0.0251695\pi\)
\(90\) 8.28594 + 11.8247i 0.873414 + 1.24643i
\(91\) 3.37903 10.3996i 0.354219 1.09017i
\(92\) 2.18129 + 6.71333i 0.227415 + 0.699913i
\(93\) −2.47584 0.0481886i −0.256733 0.00499693i
\(94\) 12.0098 + 16.5301i 1.23872 + 1.70495i
\(95\) 3.81621 + 1.14853i 0.391535 + 0.117837i
\(96\) −7.67481 11.0077i −0.783307 1.12347i
\(97\) −4.47759 + 6.16287i −0.454630 + 0.625745i −0.973384 0.229179i \(-0.926396\pi\)
0.518754 + 0.854924i \(0.326396\pi\)
\(98\) 15.0643i 1.52173i
\(99\) 1.50059 + 9.83607i 0.150815 + 0.988562i
\(100\) −4.61038 12.3307i −0.461038 1.23307i
\(101\) 8.50114 + 6.17644i 0.845895 + 0.614579i 0.924011 0.382366i \(-0.124890\pi\)
−0.0781161 + 0.996944i \(0.524890\pi\)
\(102\) 18.7487 13.0719i 1.85639 1.29431i
\(103\) −3.92066 + 1.27390i −0.386314 + 0.125521i −0.495734 0.868475i \(-0.665101\pi\)
0.109420 + 0.993996i \(0.465101\pi\)
\(104\) 2.34006 + 3.22081i 0.229462 + 0.315827i
\(105\) −11.7433 8.48976i −1.14603 0.828516i
\(106\) −11.2736 + 3.66303i −1.09499 + 0.355785i
\(107\) 2.15093 + 0.698881i 0.207939 + 0.0675634i 0.411134 0.911575i \(-0.365133\pi\)
−0.203196 + 0.979138i \(0.565133\pi\)
\(108\) −11.5184 + 7.38187i −1.10836 + 0.710320i
\(109\) 13.9966i 1.34063i −0.742076 0.670315i \(-0.766159\pi\)
0.742076 0.670315i \(-0.233841\pi\)
\(110\) 1.62573 15.8797i 0.155008 1.51407i
\(111\) −3.86361 + 5.10582i −0.366717 + 0.484623i
\(112\) 7.06402 + 5.13231i 0.667487 + 0.484957i
\(113\) 0.501772 1.54430i 0.0472028 0.145275i −0.924677 0.380752i \(-0.875665\pi\)
0.971880 + 0.235477i \(0.0756652\pi\)
\(114\) −2.17584 + 6.27813i −0.203786 + 0.588001i
\(115\) 5.99353 0.130809i 0.558900 0.0121980i
\(116\) −11.9690 + 8.69597i −1.11129 + 0.807400i
\(117\) −7.28838 + 4.87361i −0.673811 + 0.450565i
\(118\) 0.0336285 0.103498i 0.00309576 0.00952776i
\(119\) −13.4826 + 18.5573i −1.23595 + 1.70114i
\(120\) 5.01373 1.64215i 0.457689 0.149907i
\(121\) 5.86026 9.30899i 0.532751 0.846272i
\(122\) 6.24993 0.565842
\(123\) −0.127873 0.421277i −0.0115299 0.0379853i
\(124\) −1.16321 + 3.57999i −0.104459 + 0.321492i
\(125\) −11.1564 + 0.731393i −0.997858 + 0.0654178i
\(126\) 14.9505 18.9782i 1.33190 1.69072i
\(127\) 16.3861 11.9052i 1.45403 1.05641i 0.469161 0.883112i \(-0.344556\pi\)
0.984869 0.173302i \(-0.0554438\pi\)
\(128\) −9.84539 + 3.19896i −0.870218 + 0.282751i
\(129\) 12.2845 8.56500i 1.08159 0.754106i
\(130\) 13.2797 4.63754i 1.16470 0.406739i
\(131\) 11.4641 1.00163 0.500813 0.865556i \(-0.333034\pi\)
0.500813 + 0.865556i \(0.333034\pi\)
\(132\) 14.9697 + 2.16004i 1.30294 + 0.188007i
\(133\) 6.66839i 0.578223i
\(134\) −4.26698 3.10014i −0.368611 0.267811i
\(135\) 3.18413 + 11.1741i 0.274046 + 0.961717i
\(136\) −2.58069 7.94256i −0.221293 0.681069i
\(137\) 14.9880 10.8894i 1.28051 0.930347i 0.280944 0.959724i \(-0.409352\pi\)
0.999568 + 0.0293772i \(0.00935241\pi\)
\(138\) −0.194503 + 9.99321i −0.0165572 + 0.850678i
\(139\) 7.52360 2.44457i 0.638143 0.207345i 0.0279644 0.999609i \(-0.491098\pi\)
0.610179 + 0.792264i \(0.291098\pi\)
\(140\) −17.5337 + 13.3331i −1.48187 + 1.12685i
\(141\) 4.77557 + 15.7331i 0.402176 + 1.32497i
\(142\) −1.79459 −0.150598
\(143\) 9.61882 + 1.19736i 0.804366 + 0.100128i
\(144\) −1.90274 6.73764i −0.158562 0.561470i
\(145\) 4.14254 + 11.8622i 0.344019 + 0.985104i
\(146\) −11.8962 3.86530i −0.984534 0.319894i
\(147\) −3.96964 + 11.4539i −0.327410 + 0.944703i
\(148\) 5.72089 + 7.87413i 0.470254 + 0.647249i
\(149\) 5.44385 3.95519i 0.445978 0.324022i −0.342028 0.939690i \(-0.611114\pi\)
0.788006 + 0.615668i \(0.211114\pi\)
\(150\) −0.450719 18.6350i −0.0368010 1.52154i
\(151\) 5.06380 + 1.64533i 0.412086 + 0.133895i 0.507721 0.861522i \(-0.330488\pi\)
−0.0956350 + 0.995416i \(0.530488\pi\)
\(152\) 1.96416 + 1.42705i 0.159314 + 0.115749i
\(153\) 17.6999 4.99852i 1.43095 0.404107i
\(154\) −26.2273 + 5.05261i −2.11346 + 0.407151i
\(155\) 2.62674 + 1.82221i 0.210985 + 0.146364i
\(156\) 3.87105 + 12.7531i 0.309932 + 1.02107i
\(157\) −8.71622 2.83207i −0.695630 0.226024i −0.0602045 0.998186i \(-0.519175\pi\)
−0.635426 + 0.772162i \(0.719175\pi\)
\(158\) 5.85731 + 18.0270i 0.465983 + 1.43415i
\(159\) −9.53698 0.185623i −0.756332 0.0147209i
\(160\) 0.378006 + 17.3199i 0.0298840 + 1.36926i
\(161\) −3.09977 9.54010i −0.244296 0.751865i
\(162\) −18.8333 + 4.53534i −1.47968 + 0.356330i
\(163\) −13.6145 + 18.7387i −1.06637 + 1.46773i −0.192668 + 0.981264i \(0.561714\pi\)
−0.873700 + 0.486465i \(0.838286\pi\)
\(164\) −0.669231 −0.0522581
\(165\) 5.42060 11.6455i 0.421993 0.906599i
\(166\) −2.63075 −0.204186
\(167\) −8.67860 + 11.9451i −0.671570 + 0.924337i −0.999795 0.0202628i \(-0.993550\pi\)
0.328225 + 0.944600i \(0.393550\pi\)
\(168\) −5.04886 7.24142i −0.389528 0.558687i
\(169\) −1.37779 4.24039i −0.105983 0.326184i
\(170\) −29.4997 + 0.643830i −2.26252 + 0.0493795i
\(171\) −3.30873 + 4.20011i −0.253025 + 0.321191i
\(172\) −7.03455 21.6501i −0.536379 1.65081i
\(173\) −0.743915 0.241713i −0.0565588 0.0183771i 0.280601 0.959825i \(-0.409466\pi\)
−0.337160 + 0.941447i \(0.609466\pi\)
\(174\) −20.0455 + 6.08454i −1.51964 + 0.461268i
\(175\) 6.55167 + 17.5227i 0.495260 + 1.32459i
\(176\) −3.28281 + 7.00941i −0.247451 + 0.528354i
\(177\) 0.0528419 0.0698314i 0.00397184 0.00524885i
\(178\) −2.59526 1.88557i −0.194523 0.141329i
\(179\) 16.7470 + 5.44143i 1.25173 + 0.406711i 0.858540 0.512746i \(-0.171372\pi\)
0.393189 + 0.919458i \(0.371372\pi\)
\(180\) 17.6593 + 0.302014i 1.31625 + 0.0225108i
\(181\) −18.7514 + 13.6237i −1.39378 + 1.01264i −0.398343 + 0.917236i \(0.630415\pi\)
−0.995439 + 0.0954051i \(0.969585\pi\)
\(182\) −13.8342 19.0411i −1.02546 1.41142i
\(183\) 4.75203 + 1.64694i 0.351280 + 0.121745i
\(184\) 3.47337 + 1.12857i 0.256060 + 0.0831990i
\(185\) 7.80390 2.72529i 0.573754 0.200367i
\(186\) −3.21624 + 4.25031i −0.235826 + 0.311648i
\(187\) −18.4138 8.62399i −1.34655 0.630648i
\(188\) 24.9932 1.82282
\(189\) 16.3684 10.4901i 1.19063 0.763046i
\(190\) 6.82808 5.19224i 0.495361 0.376685i
\(191\) 11.7130 3.80577i 0.847519 0.275376i 0.147113 0.989120i \(-0.453002\pi\)
0.700407 + 0.713744i \(0.253002\pi\)
\(192\) −20.7953 0.404750i −1.50077 0.0292103i
\(193\) −14.3079 + 10.3953i −1.02991 + 0.748272i −0.968290 0.249828i \(-0.919626\pi\)
−0.0616173 + 0.998100i \(0.519626\pi\)
\(194\) 5.06679 + 15.5940i 0.363775 + 1.11958i
\(195\) 11.3190 0.0267182i 0.810572 0.00191333i
\(196\) 14.9078 + 10.8311i 1.06484 + 0.773651i
\(197\) 10.8770i 0.774956i 0.921879 + 0.387478i \(0.126654\pi\)
−0.921879 + 0.387478i \(0.873346\pi\)
\(198\) 19.0264 + 9.83112i 1.35215 + 0.698667i
\(199\) 26.0901 1.84948 0.924739 0.380602i \(-0.124283\pi\)
0.924739 + 0.380602i \(0.124283\pi\)
\(200\) −6.56334 1.82011i −0.464099 0.128701i
\(201\) −2.42740 3.48154i −0.171216 0.245569i
\(202\) 21.5105 6.98920i 1.51348 0.491758i
\(203\) 17.0087 12.3576i 1.19378 0.867332i
\(204\) 0.544052 27.9524i 0.0380913 1.95706i
\(205\) −0.163799 + 0.544255i −0.0114402 + 0.0380124i
\(206\) −2.74196 + 8.43887i −0.191041 + 0.587964i
\(207\) −2.78122 + 7.54692i −0.193308 + 0.524547i
\(208\) −6.82045 −0.472913
\(209\) 5.80442 1.11820i 0.401500 0.0773477i
\(210\) −29.6407 + 9.70826i −2.04540 + 0.669933i
\(211\) 10.0687 13.8584i 0.693161 0.954055i −0.306836 0.951762i \(-0.599270\pi\)
0.999997 0.00229222i \(-0.000729636\pi\)
\(212\) −4.48069 + 13.7902i −0.307735 + 0.947111i
\(213\) −1.36449 0.472896i −0.0934930 0.0324023i
\(214\) 3.93826 2.86131i 0.269214 0.195595i
\(215\) −19.3288 + 0.421851i −1.31821 + 0.0287700i
\(216\) −0.413015 + 7.06618i −0.0281021 + 0.480793i
\(217\) 1.65300 5.08741i 0.112213 0.345356i
\(218\) −24.3728 17.7079i −1.65073 1.19933i
\(219\) −8.02650 6.07371i −0.542381 0.410423i
\(220\) −14.5458 13.0262i −0.980676 0.878227i
\(221\) 17.9174i 1.20525i
\(222\) 4.00289 + 13.1875i 0.268656 + 0.885087i
\(223\) 12.6327 + 4.10463i 0.845951 + 0.274866i 0.699749 0.714389i \(-0.253295\pi\)
0.146202 + 0.989255i \(0.453295\pi\)
\(224\) 27.5687 8.95760i 1.84201 0.598505i
\(225\) 4.56786 14.2876i 0.304524 0.952505i
\(226\) −2.05432 2.82753i −0.136651 0.188085i
\(227\) 2.36556 0.768619i 0.157008 0.0510150i −0.229458 0.973318i \(-0.573695\pi\)
0.386466 + 0.922303i \(0.373695\pi\)
\(228\) 4.64847 + 6.66715i 0.307852 + 0.441543i
\(229\) −9.81334 7.12981i −0.648484 0.471151i 0.214270 0.976774i \(-0.431263\pi\)
−0.862754 + 0.505623i \(0.831263\pi\)
\(230\) 7.35497 10.6023i 0.484972 0.699092i
\(231\) −21.2730 3.06957i −1.39966 0.201963i
\(232\) 7.65442i 0.502537i
\(233\) −3.30584 + 4.55009i −0.216572 + 0.298086i −0.903456 0.428681i \(-0.858978\pi\)
0.686883 + 0.726768i \(0.258978\pi\)
\(234\) −0.734341 + 18.8574i −0.0480054 + 1.23275i
\(235\) 6.11728 20.3258i 0.399047 1.32591i
\(236\) −0.0782437 0.107693i −0.00509323 0.00701023i
\(237\) −0.296818 + 15.2500i −0.0192804 + 0.990592i
\(238\) 15.2568 + 46.9556i 0.988952 + 3.04368i
\(239\) 4.41810 13.5975i 0.285783 0.879551i −0.700379 0.713771i \(-0.746986\pi\)
0.986163 0.165780i \(-0.0530142\pi\)
\(240\) −2.77274 + 8.60265i −0.178979 + 0.555298i
\(241\) 12.5806i 0.810390i 0.914230 + 0.405195i \(0.132796\pi\)
−0.914230 + 0.405195i \(0.867204\pi\)
\(242\) −8.79596 21.9820i −0.565426 1.41306i
\(243\) −15.5147 1.51445i −0.995270 0.0971518i
\(244\) 4.49365 6.18497i 0.287676 0.395952i
\(245\) 12.4572 9.47280i 0.795864 0.605195i
\(246\) −0.895365 0.310311i −0.0570864 0.0197847i
\(247\) 3.06167 + 4.21403i 0.194810 + 0.268132i
\(248\) 1.14474 + 1.57560i 0.0726911 + 0.100051i
\(249\) −2.00024 0.693235i −0.126760 0.0439320i
\(250\) −12.8410 + 20.3524i −0.812134 + 1.28720i
\(251\) −2.90618 + 4.00001i −0.183436 + 0.252478i −0.890825 0.454346i \(-0.849873\pi\)
0.707389 + 0.706824i \(0.249873\pi\)
\(252\) −8.03169 28.4404i −0.505949 1.79157i
\(253\) 7.78428 4.29791i 0.489393 0.270207i
\(254\) 43.5956i 2.73543i
\(255\) −22.5993 7.28401i −1.41522 0.456143i
\(256\) 0.536150 1.65010i 0.0335094 0.103131i
\(257\) −2.80157 8.62234i −0.174757 0.537847i 0.824865 0.565329i \(-0.191251\pi\)
−0.999622 + 0.0274825i \(0.991251\pi\)
\(258\) 0.627261 32.2275i 0.0390516 2.00640i
\(259\) −8.12978 11.1897i −0.505160 0.695293i
\(260\) 4.95862 16.4760i 0.307521 1.02180i
\(261\) −16.8446 0.655959i −1.04266 0.0406029i
\(262\) 14.5039 19.9629i 0.896055 1.23331i
\(263\) 7.36321i 0.454035i 0.973891 + 0.227017i \(0.0728974\pi\)
−0.973891 + 0.227017i \(0.927103\pi\)
\(264\) 5.45657 5.60901i 0.335829 0.345210i
\(265\) 10.1182 + 7.01919i 0.621557 + 0.431185i
\(266\) −11.6119 8.43656i −0.711973 0.517279i
\(267\) −1.47639 2.11754i −0.0903537 0.129591i
\(268\) −6.13584 + 1.99366i −0.374806 + 0.121782i
\(269\) 15.0348 + 20.6936i 0.916686 + 1.26171i 0.964831 + 0.262869i \(0.0846688\pi\)
−0.0481459 + 0.998840i \(0.515331\pi\)
\(270\) 23.4864 + 8.59238i 1.42933 + 0.522916i
\(271\) −5.91321 + 1.92132i −0.359202 + 0.116712i −0.483058 0.875588i \(-0.660474\pi\)
0.123856 + 0.992300i \(0.460474\pi\)
\(272\) 13.6071 + 4.42121i 0.825051 + 0.268075i
\(273\) −5.50102 18.1231i −0.332937 1.09686i
\(274\) 39.8760i 2.40900i
\(275\) −14.1538 + 8.64116i −0.853507 + 0.521081i
\(276\) 9.74950 + 7.37751i 0.586851 + 0.444074i
\(277\) 10.9695 + 7.96979i 0.659091 + 0.478858i 0.866356 0.499427i \(-0.166456\pi\)
−0.207265 + 0.978285i \(0.566456\pi\)
\(278\) 5.26171 16.1939i 0.315576 0.971245i
\(279\) −3.56543 + 2.38414i −0.213457 + 0.142735i
\(280\) 0.248671 + 11.3939i 0.0148609 + 0.680913i
\(281\) −9.35985 + 6.80033i −0.558362 + 0.405674i −0.830859 0.556483i \(-0.812150\pi\)
0.272497 + 0.962157i \(0.412150\pi\)
\(282\) 33.4385 + 11.5889i 1.99123 + 0.690112i
\(283\) −2.18516 + 6.72524i −0.129894 + 0.399774i −0.994761 0.102228i \(-0.967403\pi\)
0.864867 + 0.502002i \(0.167403\pi\)
\(284\) −1.29029 + 1.77594i −0.0765648 + 0.105382i
\(285\) 6.55984 2.14855i 0.388571 0.127269i
\(286\) 14.2543 15.2348i 0.842875 0.900850i
\(287\) 0.951023 0.0561371
\(288\) −21.8088 8.03708i −1.28510 0.473590i
\(289\) −6.36129 + 19.5780i −0.374194 + 1.15165i
\(290\) 25.8971 + 7.79400i 1.52073 + 0.457680i
\(291\) −0.256759 + 13.1918i −0.0150515 + 0.773317i
\(292\) −12.3784 + 8.99341i −0.724389 + 0.526300i
\(293\) −23.3787 + 7.59620i −1.36580 + 0.443775i −0.897974 0.440048i \(-0.854962\pi\)
−0.467823 + 0.883822i \(0.654962\pi\)
\(294\) 14.9229 + 21.4035i 0.870322 + 1.24828i
\(295\) −0.106733 + 0.0372733i −0.00621422 + 0.00217014i
\(296\) 5.03568 0.292693
\(297\) 11.8758 + 12.4886i 0.689103 + 0.724663i
\(298\) 14.4835i 0.839008i
\(299\) 6.33904 + 4.60558i 0.366596 + 0.266348i
\(300\) −18.7654 12.9524i −1.08342 0.747805i
\(301\) 9.99658 + 30.7663i 0.576193 + 1.77334i
\(302\) 9.27156 6.73618i 0.533518 0.387624i
\(303\) 18.1969 + 0.354176i 1.04539 + 0.0203469i
\(304\) −3.95576 + 1.28531i −0.226879 + 0.0737173i
\(305\) −3.93010 5.16830i −0.225037 0.295936i
\(306\) 13.6890 37.1453i 0.782546 2.12346i
\(307\) 4.60472 0.262805 0.131403 0.991329i \(-0.458052\pi\)
0.131403 + 0.991329i \(0.458052\pi\)
\(308\) −13.8571 + 29.5875i −0.789584 + 1.68591i
\(309\) −4.30855 + 5.69382i −0.245105 + 0.323910i
\(310\) 6.49632 2.26865i 0.368966 0.128851i
\(311\) −19.4975 6.33511i −1.10560 0.359231i −0.301345 0.953515i \(-0.597436\pi\)
−0.804255 + 0.594284i \(0.797436\pi\)
\(312\) 6.51534 + 2.25806i 0.368859 + 0.127837i
\(313\) −16.5721 22.8096i −0.936712 1.28927i −0.957183 0.289482i \(-0.906517\pi\)
0.0204718 0.999790i \(-0.493483\pi\)
\(314\) −15.9590 + 11.5949i −0.900617 + 0.654336i
\(315\) −25.0951 0.429182i −1.41395 0.0241817i
\(316\) 22.0510 + 7.16479i 1.24046 + 0.403051i
\(317\) −9.41776 6.84240i −0.528954 0.384308i 0.291012 0.956719i \(-0.406008\pi\)
−0.819966 + 0.572412i \(0.806008\pi\)
\(318\) −12.3890 + 16.3723i −0.694740 + 0.918111i
\(319\) 13.6086 + 12.7328i 0.761938 + 0.712903i
\(320\) 22.0627 + 15.3053i 1.23334 + 0.855591i
\(321\) 3.74838 1.13777i 0.209214 0.0635041i
\(322\) −20.5342 6.67198i −1.14433 0.371815i
\(323\) −3.37651 10.3918i −0.187874 0.578218i
\(324\) −9.05279 + 21.8984i −0.502933 + 1.21658i
\(325\) −12.1855 8.06524i −0.675931 0.447379i
\(326\) 15.4060 + 47.4148i 0.853259 + 2.62606i
\(327\) −13.8652 19.8864i −0.766748 1.09972i
\(328\) −0.203520 + 0.280122i −0.0112375 + 0.0154671i
\(329\) −35.5171 −1.95812
\(330\) −13.4208 24.1724i −0.738790 1.33065i
\(331\) −27.3073 −1.50095 −0.750473 0.660901i \(-0.770174\pi\)
−0.750473 + 0.660901i \(0.770174\pi\)
\(332\) −1.89148 + 2.60340i −0.103809 + 0.142880i
\(333\) −0.431541 + 11.0817i −0.0236483 + 0.607274i
\(334\) 9.82061 + 30.2247i 0.537360 + 1.65382i
\(335\) 0.119556 + 5.47796i 0.00653206 + 0.299293i
\(336\) 15.1207 + 0.294302i 0.824903 + 0.0160555i
\(337\) −4.52795 13.9356i −0.246653 0.759121i −0.995360 0.0962195i \(-0.969325\pi\)
0.748707 0.662901i \(-0.230675\pi\)
\(338\) −9.12706 2.96556i −0.496446 0.161305i
\(339\) −0.816880 2.69121i −0.0443668 0.146166i
\(340\) −20.5729 + 29.6560i −1.11572 + 1.60832i
\(341\) 4.70546 + 0.585742i 0.254815 + 0.0317197i
\(342\) 3.12775 + 11.0754i 0.169129 + 0.598890i
\(343\) 0.00359571 + 0.00261244i 0.000194150 + 0.000141058i
\(344\) −11.2014 3.63956i −0.603940 0.196232i
\(345\) 8.38606 6.12312i 0.451490 0.329658i
\(346\) −1.36207 + 0.989602i −0.0732254 + 0.0532014i
\(347\) 5.35219 + 7.36665i 0.287321 + 0.395463i 0.928141 0.372228i \(-0.121406\pi\)
−0.640821 + 0.767690i \(0.721406\pi\)
\(348\) −8.39123 + 24.2119i −0.449817 + 1.29789i
\(349\) 9.20764 + 2.99174i 0.492874 + 0.160144i 0.544900 0.838501i \(-0.316568\pi\)
−0.0520257 + 0.998646i \(0.516568\pi\)
\(350\) 38.8019 + 10.7603i 2.07405 + 0.575162i
\(351\) −5.52751 + 14.1444i −0.295036 + 0.754973i
\(352\) 12.4199 + 22.4947i 0.661985 + 1.19897i
\(353\) 12.1628 0.647361 0.323680 0.946166i \(-0.395080\pi\)
0.323680 + 0.946166i \(0.395080\pi\)
\(354\) −0.0547468 0.180363i −0.00290976 0.00958620i
\(355\) 1.12848 + 1.48401i 0.0598935 + 0.0787631i
\(356\) −3.73194 + 1.21258i −0.197792 + 0.0642666i
\(357\) −0.773136 + 39.7223i −0.0409187 + 2.10233i
\(358\) 30.6629 22.2779i 1.62059 1.17742i
\(359\) −3.55028 10.9266i −0.187377 0.576686i 0.812604 0.582816i \(-0.198049\pi\)
−0.999981 + 0.00612922i \(0.998049\pi\)
\(360\) 5.49679 7.29985i 0.289706 0.384736i
\(361\) −12.8015 9.30081i −0.673761 0.489516i
\(362\) 49.8886i 2.62209i
\(363\) −0.895329 19.0315i −0.0469926 0.998895i
\(364\) −28.7899 −1.50900
\(365\) 4.28423 + 12.2680i 0.224247 + 0.642135i
\(366\) 8.87993 6.19126i 0.464161 0.323622i
\(367\) −0.551086 + 0.179059i −0.0287665 + 0.00934679i −0.323365 0.946274i \(-0.604814\pi\)
0.294598 + 0.955621i \(0.404814\pi\)
\(368\) −5.06183 + 3.67763i −0.263866 + 0.191710i
\(369\) −0.599005 0.471880i −0.0311830 0.0245651i
\(370\) 5.12751 17.0371i 0.266566 0.885719i
\(371\) 6.36737 19.5968i 0.330578 1.01741i
\(372\) 1.89369 + 6.23875i 0.0981832 + 0.323464i
\(373\) −18.7673 −0.971735 −0.485867 0.874032i \(-0.661496\pi\)
−0.485867 + 0.874032i \(0.661496\pi\)
\(374\) −38.3136 + 21.1540i −1.98115 + 1.09384i
\(375\) −15.1265 + 12.0908i −0.781130 + 0.624368i
\(376\) 7.60071 10.4615i 0.391977 0.539509i
\(377\) −5.07476 + 15.6185i −0.261364 + 0.804394i
\(378\) 2.44171 41.7746i 0.125588 2.14865i
\(379\) 3.28240 2.38480i 0.168606 0.122499i −0.500283 0.865862i \(-0.666771\pi\)
0.668888 + 0.743363i \(0.266771\pi\)
\(380\) −0.228950 10.4903i −0.0117449 0.538141i
\(381\) 11.4880 33.1472i 0.588548 1.69818i
\(382\) 8.19158 25.2111i 0.419118 1.28991i
\(383\) 22.8848 + 16.6268i 1.16936 + 0.849590i 0.990932 0.134363i \(-0.0428988\pi\)
0.178428 + 0.983953i \(0.442899\pi\)
\(384\) −10.8194 + 14.2981i −0.552128 + 0.729645i
\(385\) 20.6706 + 18.5111i 1.05347 + 0.943416i
\(386\) 38.0666i 1.93754i
\(387\) 8.96929 24.3384i 0.455935 1.23719i
\(388\) 19.0749 + 6.19781i 0.968381 + 0.314646i
\(389\) −37.3298 + 12.1292i −1.89270 + 0.614975i −0.915639 + 0.402001i \(0.868315\pi\)
−0.977058 + 0.212973i \(0.931685\pi\)
\(390\) 14.2738 19.7440i 0.722782 0.999778i
\(391\) −9.66119 13.2975i −0.488587 0.672483i
\(392\) 9.06722 2.94612i 0.457964 0.148801i
\(393\) 16.2883 11.3565i 0.821636 0.572860i
\(394\) 18.9406 + 13.7611i 0.954212 + 0.693276i
\(395\) 11.2239 16.1794i 0.564737 0.814074i
\(396\) 23.4088 11.7602i 1.17633 0.590970i
\(397\) 5.73171i 0.287666i −0.989602 0.143833i \(-0.954057\pi\)
0.989602 0.143833i \(-0.0459429\pi\)
\(398\) 33.0080 45.4317i 1.65454 2.27728i
\(399\) −6.60580 9.47449i −0.330704 0.474318i
\(400\) 9.13186 7.26396i 0.456593 0.363198i
\(401\) −14.9545 20.5831i −0.746790 1.02787i −0.998199 0.0599878i \(-0.980894\pi\)
0.251409 0.967881i \(-0.419106\pi\)
\(402\) −9.13358 0.177772i −0.455542 0.00886644i
\(403\) 1.29119 + 3.97389i 0.0643190 + 0.197953i
\(404\) 8.54933 26.3121i 0.425345 1.30908i
\(405\) 15.5933 + 12.7220i 0.774836 + 0.632163i
\(406\) 45.2522i 2.24583i
\(407\) 8.37667 8.95283i 0.415216 0.443775i
\(408\) −11.5347 8.72836i −0.571051 0.432118i
\(409\) −11.7190 + 16.1298i −0.579466 + 0.797566i −0.993637 0.112633i \(-0.964072\pi\)
0.414171 + 0.910199i \(0.364072\pi\)
\(410\) 0.740500 + 0.973797i 0.0365707 + 0.0480924i
\(411\) 10.5078 30.3191i 0.518313 1.49553i
\(412\) 6.37972 + 8.78093i 0.314306 + 0.432605i
\(413\) 0.111190 + 0.153039i 0.00547129 + 0.00753058i
\(414\) 9.62305 + 14.3911i 0.472947 + 0.707283i
\(415\) 1.65428 + 2.17546i 0.0812052 + 0.106789i
\(416\) −13.3090 + 18.3183i −0.652529 + 0.898130i
\(417\) 8.26795 10.9262i 0.404883 0.535060i
\(418\) 5.39633 11.5222i 0.263943 0.563567i
\(419\) 19.4764i 0.951485i 0.879585 + 0.475742i \(0.157821\pi\)
−0.879585 + 0.475742i \(0.842179\pi\)
\(420\) −11.7040 + 36.3128i −0.571099 + 1.77188i
\(421\) 1.31040 4.03300i 0.0638650 0.196556i −0.914033 0.405641i \(-0.867048\pi\)
0.977898 + 0.209084i \(0.0670484\pi\)
\(422\) −11.3937 35.0662i −0.554636 1.70699i
\(423\) 22.3706 + 17.6229i 1.08769 + 0.856856i
\(424\) 4.40955 + 6.06923i 0.214147 + 0.294748i
\(425\) 19.0825 + 23.9895i 0.925638 + 1.16366i
\(426\) −2.54976 + 1.77774i −0.123536 + 0.0861319i
\(427\) −6.38578 + 8.78928i −0.309030 + 0.425343i
\(428\) 5.95458i 0.287826i
\(429\) 14.8526 7.82731i 0.717090 0.377906i
\(430\) −23.7194 + 34.1917i −1.14385 + 1.64887i
\(431\) −20.9898 15.2500i −1.01104 0.734567i −0.0466170 0.998913i \(-0.514844\pi\)
−0.964428 + 0.264346i \(0.914844\pi\)
\(432\) −9.37781 7.68799i −0.451190 0.369888i
\(433\) −2.14388 + 0.696587i −0.103028 + 0.0334758i −0.360077 0.932922i \(-0.617250\pi\)
0.257049 + 0.966398i \(0.417250\pi\)
\(434\) −6.76760 9.31480i −0.324855 0.447125i
\(435\) 17.6366 + 12.7503i 0.845611 + 0.611328i
\(436\) −35.0477 + 11.3877i −1.67848 + 0.545371i
\(437\) 4.54447 + 1.47659i 0.217391 + 0.0706348i
\(438\) −20.7311 + 6.29266i −0.990573 + 0.300675i
\(439\) 6.34927i 0.303034i 0.988455 + 0.151517i \(0.0484159\pi\)
−0.988455 + 0.151517i \(0.951584\pi\)
\(440\) −9.87594 + 2.12705i −0.470817 + 0.101403i
\(441\) 5.70631 + 20.2061i 0.271729 + 0.962197i
\(442\) −31.2002 22.6683i −1.48404 1.07822i
\(443\) 2.52406 7.76825i 0.119922 0.369081i −0.873020 0.487684i \(-0.837842\pi\)
0.992942 + 0.118604i \(0.0378417\pi\)
\(444\) 15.9285 + 5.52041i 0.755932 + 0.261987i
\(445\) 0.0727165 + 3.33180i 0.00344709 + 0.157943i
\(446\) 23.1299 16.8049i 1.09523 0.795734i
\(447\) 3.81659 11.0123i 0.180518 0.520864i
\(448\) 13.8840 42.7306i 0.655958 2.01883i
\(449\) 16.2063 22.3060i 0.764821 1.05269i −0.231976 0.972721i \(-0.574519\pi\)
0.996798 0.0799647i \(-0.0254808\pi\)
\(450\) −19.1004 26.0302i −0.900403 1.22707i
\(451\) 0.159474 + 0.827807i 0.00750934 + 0.0389799i
\(452\) −4.27518 −0.201088
\(453\) 8.82455 2.67857i 0.414613 0.125850i
\(454\) 1.65438 5.09167i 0.0776441 0.238964i
\(455\) −7.04655 + 23.4135i −0.330347 + 1.09764i
\(456\) 4.20434 + 0.0818312i 0.196886 + 0.00383210i
\(457\) −13.0649 + 9.49221i −0.611150 + 0.444027i −0.849819 0.527074i \(-0.823289\pi\)
0.238669 + 0.971101i \(0.423289\pi\)
\(458\) −24.8308 + 8.06802i −1.16027 + 0.376994i
\(459\) 20.1964 24.6356i 0.942689 1.14989i
\(460\) −5.20390 14.9015i −0.242633 0.694784i
\(461\) 31.9271 1.48699 0.743497 0.668739i \(-0.233166\pi\)
0.743497 + 0.668739i \(0.233166\pi\)
\(462\) −32.2588 + 33.1599i −1.50081 + 1.54274i
\(463\) 37.3488i 1.73575i 0.496786 + 0.867873i \(0.334513\pi\)
−0.496786 + 0.867873i \(0.665487\pi\)
\(464\) −10.6090 7.70790i −0.492511 0.357830i
\(465\) 5.53719 0.0130703i 0.256781 0.000606123i
\(466\) 3.74085 + 11.5132i 0.173292 + 0.533336i
\(467\) −20.3358 + 14.7749i −0.941031 + 0.683699i −0.948669 0.316272i \(-0.897569\pi\)
0.00763775 + 0.999971i \(0.497569\pi\)
\(468\) 18.1334 + 14.2850i 0.838218 + 0.660325i
\(469\) 8.71945 2.83312i 0.402627 0.130821i
\(470\) −27.6549 36.3676i −1.27562 1.67751i
\(471\) −15.1895 + 4.61058i −0.699897 + 0.212444i
\(472\) −0.0688722 −0.00317010
\(473\) −25.1039 + 13.8605i −1.15428 + 0.637307i
\(474\) 26.1798 + 19.8105i 1.20248 + 0.909924i
\(475\) −8.58732 2.38138i −0.394013 0.109265i
\(476\) 57.4371 + 18.6625i 2.63263 + 0.855392i
\(477\) −13.7341 + 9.18372i −0.628840 + 0.420494i
\(478\) −18.0883 24.8964i −0.827339 1.13873i
\(479\) 10.0657 7.31316i 0.459914 0.334147i −0.333584 0.942720i \(-0.608258\pi\)
0.793497 + 0.608574i \(0.208258\pi\)
\(480\) 17.6944 + 24.2337i 0.807635 + 1.10611i
\(481\) 10.2751 + 3.33858i 0.468503 + 0.152226i
\(482\) 21.9071 + 15.9165i 0.997843 + 0.724975i
\(483\) −13.8547 10.4840i −0.630411 0.477036i
\(484\) −28.0778 7.10033i −1.27626 0.322742i
\(485\) 9.70912 13.9958i 0.440869 0.635516i
\(486\) −22.2657 + 25.1003i −1.00999 + 1.13857i
\(487\) 28.4671 + 9.24953i 1.28997 + 0.419136i 0.872080 0.489363i \(-0.162771\pi\)
0.417888 + 0.908499i \(0.362771\pi\)
\(488\) −1.22229 3.76183i −0.0553307 0.170290i
\(489\) −0.780695 + 40.1107i −0.0353043 + 1.81387i
\(490\) −0.734996 33.6768i −0.0332037 1.52136i
\(491\) −4.81815 14.8287i −0.217440 0.669212i −0.998971 0.0453457i \(-0.985561\pi\)
0.781531 0.623866i \(-0.214439\pi\)
\(492\) −0.950846 + 0.662948i −0.0428675 + 0.0298880i
\(493\) 20.2487 27.8700i 0.911958 1.25520i
\(494\) 11.2115 0.504431
\(495\) −3.83454 21.9157i −0.172350 0.985036i
\(496\) −3.33652 −0.149814
\(497\) 1.83360 2.52373i 0.0822480 0.113205i
\(498\) −3.73778 + 2.60605i −0.167494 + 0.116780i
\(499\) 4.37564 + 13.4668i 0.195881 + 0.602859i 0.999965 + 0.00834366i \(0.00265590\pi\)
−0.804085 + 0.594515i \(0.797344\pi\)
\(500\) 10.9083 + 27.3407i 0.487834 + 1.22271i
\(501\) −0.497657 + 25.5687i −0.0222337 + 1.14233i
\(502\) 3.28860 + 10.1213i 0.146777 + 0.451734i
\(503\) −25.6404 8.33106i −1.14325 0.371464i −0.324652 0.945834i \(-0.605247\pi\)
−0.818596 + 0.574370i \(0.805247\pi\)
\(504\) −14.3469 5.28717i −0.639061 0.235509i
\(505\) −19.3060 13.3929i −0.859104 0.595975i
\(506\) 2.36422 18.9926i 0.105102 0.844323i
\(507\) −6.15814 4.65991i −0.273493 0.206954i
\(508\) −43.1425 31.3449i −1.91414 1.39070i
\(509\) −1.11494 0.362267i −0.0494190 0.0160572i 0.284203 0.958764i \(-0.408271\pi\)
−0.333622 + 0.942707i \(0.608271\pi\)
\(510\) −41.2755 + 30.1375i −1.82771 + 1.33451i
\(511\) 17.5905 12.7803i 0.778159 0.565366i
\(512\) −14.3646 19.7712i −0.634834 0.873773i
\(513\) −0.540379 + 9.24521i −0.0238583 + 0.408186i
\(514\) −18.5588 6.03013i −0.818595 0.265978i
\(515\) 8.70262 3.03914i 0.383483 0.133920i
\(516\) −31.4416 23.7921i −1.38414 1.04739i
\(517\) −5.95575 30.9154i −0.261934 1.35966i
\(518\) −29.7705 −1.30804
\(519\) −1.29640 + 0.393505i −0.0569057 + 0.0172730i
\(520\) −5.38843 7.08607i −0.236298 0.310745i
\(521\) 6.84744 2.22487i 0.299992 0.0974733i −0.155154 0.987890i \(-0.549587\pi\)
0.455146 + 0.890417i \(0.349587\pi\)
\(522\) −22.4533 + 28.5023i −0.982755 + 1.24751i
\(523\) −21.1158 + 15.3415i −0.923328 + 0.670837i −0.944350 0.328942i \(-0.893308\pi\)
0.0210218 + 0.999779i \(0.493308\pi\)
\(524\) −9.32725 28.7063i −0.407463 1.25404i
\(525\) 26.6669 + 18.4062i 1.16384 + 0.803312i
\(526\) 12.8218 + 9.31561i 0.559058 + 0.406180i
\(527\) 8.76507i 0.381813i
\(528\) 2.27937 + 13.2110i 0.0991970 + 0.574935i
\(529\) −15.8121 −0.687482
\(530\) 25.0239 8.73887i 1.08697 0.379592i
\(531\) 0.00590212 0.151563i 0.000256130 0.00657726i
\(532\) −16.6977 + 5.42543i −0.723939 + 0.235222i
\(533\) −0.600990 + 0.436645i −0.0260318 + 0.0189132i
\(534\) −5.55522 0.108124i −0.240398 0.00467899i
\(535\) −4.84259 1.45743i −0.209363 0.0630101i
\(536\) −1.03149 + 3.17459i −0.0445534 + 0.137121i
\(537\) 29.1846 8.85858i 1.25941 0.382276i
\(538\) 55.0558 2.37362
\(539\) 9.84514 21.0212i 0.424060 0.905447i
\(540\) 25.3896 17.0644i 1.09259 0.734335i
\(541\) −0.856788 + 1.17927i −0.0368362 + 0.0507007i −0.827038 0.562146i \(-0.809976\pi\)
0.790202 + 0.612847i \(0.209976\pi\)
\(542\) −4.13547 + 12.7277i −0.177634 + 0.546700i
\(543\) −13.1463 + 37.9320i −0.564161 + 1.62782i
\(544\) 38.4266 27.9186i 1.64753 1.19700i
\(545\) 0.682901 + 31.2899i 0.0292523 + 1.34031i
\(546\) −38.5181 13.3494i −1.64842 0.571302i
\(547\) −11.1317 + 34.2598i −0.475956 + 1.46484i 0.368708 + 0.929545i \(0.379800\pi\)
−0.844664 + 0.535297i \(0.820200\pi\)
\(548\) −39.4616 28.6705i −1.68572 1.22474i
\(549\) 8.38318 2.36745i 0.357786 0.101040i
\(550\) −2.85961 + 35.5790i −0.121934 + 1.51709i
\(551\) 10.0149i 0.426647i
\(552\) 6.05295 1.83729i 0.257631 0.0782004i
\(553\) −31.3359 10.1817i −1.33254 0.432968i
\(554\) 27.7562 9.01853i 1.17925 0.383160i
\(555\) 8.38811 11.6027i 0.356056 0.492509i
\(556\) −12.2424 16.8503i −0.519196 0.714611i
\(557\) 43.7447 14.2135i 1.85352 0.602246i 0.857362 0.514714i \(-0.172102\pi\)
0.996162 0.0875319i \(-0.0278980\pi\)
\(558\) −0.359235 + 9.22492i −0.0152076 + 0.390522i
\(559\) −20.4430 14.8527i −0.864649 0.628204i
\(560\) −16.0423 11.1288i −0.677909 0.470278i
\(561\) −34.7055 + 5.98795i −1.46527 + 0.252811i
\(562\) 24.9021i 1.05043i
\(563\) 10.2627 14.1254i 0.432521 0.595314i −0.536009 0.844213i \(-0.680069\pi\)
0.968530 + 0.248898i \(0.0800686\pi\)
\(564\) 35.5105 24.7586i 1.49526 1.04253i
\(565\) −1.04638 + 3.47681i −0.0440217 + 0.146271i
\(566\) 8.94634 + 12.3136i 0.376043 + 0.517579i
\(567\) 12.8646 31.1192i 0.540264 1.30688i
\(568\) 0.350966 + 1.08016i 0.0147262 + 0.0453226i
\(569\) −11.3275 + 34.8623i −0.474872 + 1.46150i 0.371259 + 0.928529i \(0.378926\pi\)
−0.846131 + 0.532975i \(0.821074\pi\)
\(570\) 4.55786 14.1411i 0.190908 0.592308i
\(571\) 35.7294i 1.49523i 0.664134 + 0.747614i \(0.268800\pi\)
−0.664134 + 0.747614i \(0.731200\pi\)
\(572\) −4.82769 25.0598i −0.201856 1.04780i
\(573\) 12.8718 17.0103i 0.537726 0.710614i
\(574\) 1.20319 1.65605i 0.0502203 0.0691223i
\(575\) −13.3924 + 0.584855i −0.558500 + 0.0243901i
\(576\) −29.9470 + 20.0250i −1.24779 + 0.834376i
\(577\) 24.0939 + 33.1623i 1.00304 + 1.38057i 0.923441 + 0.383740i \(0.125364\pi\)
0.0795990 + 0.996827i \(0.474636\pi\)
\(578\) 26.0440 + 35.8464i 1.08329 + 1.49101i
\(579\) −10.0310 + 28.9433i −0.416876 + 1.20284i
\(580\) 26.3328 20.0241i 1.09341 0.831456i
\(581\) 2.68793 3.69962i 0.111514 0.153486i
\(582\) 22.6465 + 17.1368i 0.938729 + 0.710343i
\(583\) 18.1255 + 2.25628i 0.750681 + 0.0934457i
\(584\) 7.91624i 0.327576i
\(585\) 16.0556 11.2507i 0.663819 0.465160i
\(586\) −16.3501 + 50.3206i −0.675418 + 2.07872i
\(587\) −11.1939 34.4513i −0.462022 1.42196i −0.862689 0.505734i \(-0.831222\pi\)
0.400667 0.916224i \(-0.368778\pi\)
\(588\) 31.9105 + 0.621089i 1.31597 + 0.0256133i
\(589\) 1.49775 + 2.06148i 0.0617137 + 0.0849416i
\(590\) −0.0701280 + 0.233014i −0.00288713 + 0.00959304i
\(591\) 10.7749 + 15.4541i 0.443221 + 0.635698i
\(592\) −5.07086 + 6.97944i −0.208411 + 0.286853i
\(593\) 19.0411i 0.781923i 0.920407 + 0.390962i \(0.127857\pi\)
−0.920407 + 0.390962i \(0.872143\pi\)
\(594\) 36.7716 4.87970i 1.50876 0.200216i
\(595\) 29.2355 42.1432i 1.19854 1.72770i
\(596\) −14.3330 10.4135i −0.587102 0.426555i
\(597\) 37.0689 25.8452i 1.51713 1.05777i
\(598\) 16.0397 5.21163i 0.655914 0.213119i
\(599\) −14.7038 20.2381i −0.600783 0.826906i 0.394997 0.918682i \(-0.370746\pi\)
−0.995780 + 0.0917761i \(0.970746\pi\)
\(600\) −11.1283 + 3.91572i −0.454309 + 0.159858i
\(601\) 38.8018 12.6075i 1.58276 0.514269i 0.619993 0.784608i \(-0.287136\pi\)
0.962765 + 0.270338i \(0.0871355\pi\)
\(602\) 66.2218 + 21.5168i 2.69900 + 0.876957i
\(603\) −6.89772 2.54198i −0.280897 0.103517i
\(604\) 14.0185i 0.570403i
\(605\) −12.6466 + 21.0965i −0.514158 + 0.857695i
\(606\) 23.6387 31.2389i 0.960256 1.26899i
\(607\) −15.2824 11.1033i −0.620293 0.450669i 0.232731 0.972541i \(-0.425234\pi\)
−0.853024 + 0.521872i \(0.825234\pi\)
\(608\) −4.26699 + 13.1325i −0.173049 + 0.532591i
\(609\) 11.9245 34.4068i 0.483206 1.39423i
\(610\) −13.9719 + 0.304937i −0.565707 + 0.0123466i
\(611\) 22.4447 16.3070i 0.908016 0.659712i
\(612\) −26.9170 40.2539i −1.08806 1.62717i
\(613\) 6.20996 19.1123i 0.250818 0.771938i −0.743807 0.668394i \(-0.766982\pi\)
0.994625 0.103544i \(-0.0330181\pi\)
\(614\) 5.82569 8.01837i 0.235106 0.323595i
\(615\) 0.306419 + 0.935541i 0.0123560 + 0.0377247i
\(616\) 8.17043 + 14.7981i 0.329196 + 0.596233i
\(617\) −7.20230 −0.289954 −0.144977 0.989435i \(-0.546311\pi\)
−0.144977 + 0.989435i \(0.546311\pi\)
\(618\) 4.46387 + 14.7062i 0.179563 + 0.591570i
\(619\) 12.0091 36.9603i 0.482688 1.48556i −0.352615 0.935769i \(-0.614707\pi\)
0.835302 0.549791i \(-0.185293\pi\)
\(620\) 2.42572 8.05994i 0.0974194 0.323695i
\(621\) 3.52450 + 13.4778i 0.141433 + 0.540846i
\(622\) −35.6989 + 25.9368i −1.43140 + 1.03997i
\(623\) 5.30334 1.72316i 0.212474 0.0690369i
\(624\) −9.69052 + 6.75642i −0.387931 + 0.270473i
\(625\) 24.9048 2.17938i 0.996193 0.0871753i
\(626\) −60.6855 −2.42548
\(627\) 7.13925 7.33868i 0.285114 0.293079i
\(628\) 24.1297i 0.962880i
\(629\) −18.3351 13.3212i −0.731067 0.531152i
\(630\) −32.4965 + 43.1560i −1.29469 + 1.71938i
\(631\) 10.5321 + 32.4144i 0.419275 + 1.29040i 0.908371 + 0.418165i \(0.137327\pi\)
−0.489096 + 0.872230i \(0.662673\pi\)
\(632\) 9.70492 7.05104i 0.386041 0.280475i
\(633\) 0.577373 29.6644i 0.0229485 1.17905i
\(634\) −23.8299 + 7.74279i −0.946405 + 0.307506i
\(635\) −36.0508 + 27.4140i −1.43063 + 1.08789i
\(636\) 7.29451 + 24.0317i 0.289246 + 0.952921i
\(637\) 20.4545 0.810437
\(638\) 39.3892 7.58820i 1.55943 0.300420i
\(639\) −2.40712 + 0.679783i −0.0952244 + 0.0268918i
\(640\) 21.8536 7.63176i 0.863841 0.301672i
\(641\) 10.7142 + 3.48126i 0.423186 + 0.137501i 0.512865 0.858469i \(-0.328584\pi\)
−0.0896793 + 0.995971i \(0.528584\pi\)
\(642\) 2.76104 7.96665i 0.108970 0.314419i
\(643\) 3.97759 + 5.47468i 0.156861 + 0.215900i 0.880213 0.474579i \(-0.157400\pi\)
−0.723352 + 0.690479i \(0.757400\pi\)
\(644\) −21.3666 + 15.5237i −0.841961 + 0.611720i
\(645\) −27.0446 + 19.7467i −1.06488 + 0.777527i
\(646\) −22.3675 7.26765i −0.880038 0.285942i
\(647\) −30.2310 21.9641i −1.18850 0.863497i −0.195397 0.980724i \(-0.562599\pi\)
−0.993105 + 0.117227i \(0.962599\pi\)
\(648\) 6.41304 + 10.4488i 0.251928 + 0.410468i
\(649\) −0.114566 + 0.122446i −0.00449712 + 0.00480644i
\(650\) −29.4609 + 11.0153i −1.15555 + 0.432056i
\(651\) −2.69106 8.86570i −0.105471 0.347474i
\(652\) 57.9988 + 18.8449i 2.27141 + 0.738025i
\(653\) 1.77221 + 5.45432i 0.0693521 + 0.213444i 0.979726 0.200343i \(-0.0642058\pi\)
−0.910374 + 0.413787i \(0.864206\pi\)
\(654\) −52.1706 1.01542i −2.04003 0.0397062i
\(655\) −25.6285 + 0.559341i −1.00139 + 0.0218553i
\(656\) −0.183306 0.564157i −0.00715689 0.0220266i
\(657\) −17.4208 0.678396i −0.679650 0.0264668i
\(658\) −44.9347 + 61.8473i −1.75174 + 2.41106i
\(659\) 37.5865 1.46416 0.732081 0.681217i \(-0.238549\pi\)
0.732081 + 0.681217i \(0.238549\pi\)
\(660\) −33.5706 4.09847i −1.30674 0.159533i
\(661\) −16.3807 −0.637135 −0.318567 0.947900i \(-0.603202\pi\)
−0.318567 + 0.947900i \(0.603202\pi\)
\(662\) −34.5480 + 47.5512i −1.34275 + 1.84813i
\(663\) −17.7492 25.4571i −0.689322 0.988673i
\(664\) 0.514493 + 1.58345i 0.0199662 + 0.0614497i
\(665\) 0.325354 + 14.9074i 0.0126167 + 0.578085i
\(666\) 18.7510 + 14.7715i 0.726588 + 0.572386i
\(667\) 4.65535 + 14.3277i 0.180256 + 0.554771i
\(668\) 36.9715 + 12.0128i 1.43047 + 0.464788i
\(669\) 22.0148 6.68228i 0.851140 0.258352i
\(670\) 9.69024 + 6.72229i 0.374367 + 0.259705i
\(671\) −8.72133 4.08458i −0.336683 0.157683i
\(672\) 30.2962 40.0369i 1.16870 1.54446i
\(673\) 4.22946 + 3.07288i 0.163034 + 0.118451i 0.666311 0.745674i \(-0.267872\pi\)
−0.503277 + 0.864125i \(0.667872\pi\)
\(674\) −29.9952 9.74602i −1.15537 0.375403i
\(675\) −7.66342 24.8248i −0.294965 0.955508i
\(676\) −9.49701 + 6.89998i −0.365270 + 0.265384i
\(677\) 2.47930 + 3.41247i 0.0952874 + 0.131152i 0.853999 0.520275i \(-0.174171\pi\)
−0.758711 + 0.651427i \(0.774171\pi\)
\(678\) −5.71978 1.98233i −0.219667 0.0761310i
\(679\) −27.1068 8.80752i −1.04026 0.338002i
\(680\) 6.15675 + 17.6300i 0.236101 + 0.676078i
\(681\) 2.59960 3.43542i 0.0996170 0.131645i
\(682\) 6.97312 7.45274i 0.267014 0.285380i
\(683\) 14.5043 0.554993 0.277496 0.960727i \(-0.410495\pi\)
0.277496 + 0.960727i \(0.410495\pi\)
\(684\) 13.2091 + 4.86789i 0.505064 + 0.186128i
\(685\) −32.9749 + 25.0750i −1.25991 + 0.958066i
\(686\) 0.00909827 0.00295621i 0.000347374 0.000112869i
\(687\) −21.0057 0.408845i −0.801419 0.0155984i
\(688\) 16.3241 11.8602i 0.622351 0.452164i
\(689\) 4.97370 + 15.3075i 0.189483 + 0.583168i
\(690\) −0.0527556 22.3497i −0.00200837 0.850837i
\(691\) −27.9241 20.2881i −1.06228 0.771794i −0.0877744 0.996140i \(-0.527975\pi\)
−0.974510 + 0.224346i \(0.927975\pi\)
\(692\) 2.05943i 0.0782878i
\(693\) −33.2655 + 16.7120i −1.26365 + 0.634837i
\(694\) 19.5992 0.743975
\(695\) −16.7000 + 5.83199i −0.633467 + 0.221220i
\(696\) 7.58257 + 10.8754i 0.287417 + 0.412232i
\(697\) 1.48205 0.481547i 0.0561366 0.0182399i
\(698\) 16.8587 12.2486i 0.638113 0.463616i
\(699\) −0.189567 + 9.73960i −0.00717007 + 0.368385i
\(700\) 38.5467 30.6620i 1.45693 1.15892i
\(701\) −14.2187 + 43.7608i −0.537034 + 1.65282i 0.202177 + 0.979349i \(0.435198\pi\)
−0.739212 + 0.673473i \(0.764802\pi\)
\(702\) 17.6370 + 27.5201i 0.665667 + 1.03868i
\(703\) 6.58856 0.248492
\(704\) 39.5225 + 4.91981i 1.48956 + 0.185422i
\(705\) −11.4436 34.9389i −0.430991 1.31588i
\(706\) 15.3878 21.1795i 0.579129 0.797103i
\(707\) −12.1492 + 37.3914i −0.456918 + 1.40625i
\(708\) −0.217851 0.0755018i −0.00818735 0.00283753i
\(709\) 36.7685 26.7139i 1.38087 1.00326i 0.384072 0.923303i \(-0.374521\pi\)
0.996798 0.0799582i \(-0.0254787\pi\)
\(710\) 4.01187 0.0875589i 0.150563 0.00328603i
\(711\) 14.6851 + 21.9613i 0.550734 + 0.823612i
\(712\) −0.627369 + 1.93084i −0.0235117 + 0.0723615i
\(713\) 3.10101 + 2.25302i 0.116134 + 0.0843762i
\(714\) 68.1918 + 51.6012i 2.55201 + 1.93113i
\(715\) −21.5616 2.20744i −0.806359 0.0825535i
\(716\) 46.3619i 1.73262i
\(717\) −7.19262 23.6961i −0.268613 0.884946i
\(718\) −23.5186 7.64167i −0.877708 0.285185i
\(719\) −10.0623 + 3.26945i −0.375261 + 0.121930i −0.490574 0.871399i \(-0.663213\pi\)
0.115313 + 0.993329i \(0.463213\pi\)
\(720\) 4.58238 + 14.9694i 0.170775 + 0.557876i
\(721\) −9.06603 12.4783i −0.337636 0.464717i
\(722\) −32.3917 + 10.5247i −1.20549 + 0.391689i
\(723\) 12.4625 + 17.8746i 0.463487 + 0.664765i
\(724\) 49.3701 + 35.8695i 1.83483 + 1.33308i
\(725\) −9.83956 26.3163i −0.365432 0.977363i
\(726\) −34.2730 22.5188i −1.27199 0.835749i
\(727\) 11.7037i 0.434065i −0.976164 0.217032i \(-0.930362\pi\)
0.976164 0.217032i \(-0.0696378\pi\)
\(728\) −8.75532 + 12.0507i −0.324494 + 0.446627i
\(729\) −23.5436 + 13.2173i −0.871986 + 0.489531i
\(730\) 26.7829 + 8.06059i 0.991280 + 0.298336i
\(731\) 31.1568 + 42.8836i 1.15238 + 1.58611i
\(732\) 0.257679 13.2391i 0.00952410 0.489331i
\(733\) −9.02911 27.7888i −0.333498 1.02640i −0.967457 0.253035i \(-0.918571\pi\)
0.633959 0.773366i \(-0.281429\pi\)
\(734\) −0.385408 + 1.18616i −0.0142257 + 0.0437821i
\(735\) 8.31543 25.7993i 0.306719 0.951622i
\(736\) 20.7714i 0.765642i
\(737\) 3.92820 + 7.11467i 0.144697 + 0.262072i
\(738\) −1.57954 + 0.446069i −0.0581436 + 0.0164200i
\(739\) 7.61210 10.4772i 0.280015 0.385408i −0.645724 0.763571i \(-0.723444\pi\)
0.925739 + 0.378163i \(0.123444\pi\)
\(740\) −13.1734 17.3238i −0.484265 0.636834i
\(741\) 8.52451 + 2.95438i 0.313156 + 0.108532i
\(742\) −26.0689 35.8807i −0.957018 1.31722i
\(743\) 3.62431 + 4.98843i 0.132963 + 0.183008i 0.870307 0.492510i \(-0.163920\pi\)
−0.737344 + 0.675517i \(0.763920\pi\)
\(744\) 3.18726 + 1.10463i 0.116851 + 0.0404975i
\(745\) −11.9770 + 9.10758i −0.438802 + 0.333676i
\(746\) −23.7436 + 32.6802i −0.869314 + 1.19651i
\(747\) −3.52868 + 0.996517i −0.129108 + 0.0364607i
\(748\) −6.61305 + 53.1249i −0.241797 + 1.94244i
\(749\) 8.46187i 0.309190i
\(750\) 1.91681 + 41.6372i 0.0699919 + 1.52037i
\(751\) 6.97116 21.4550i 0.254381 0.782905i −0.739570 0.673080i \(-0.764971\pi\)
0.993951 0.109825i \(-0.0350290\pi\)
\(752\) 6.84578 + 21.0691i 0.249640 + 0.768312i
\(753\) −0.166649 + 8.56213i −0.00607303 + 0.312021i
\(754\) 20.7767 + 28.5967i 0.756644 + 1.04143i
\(755\) −11.4006 3.43112i −0.414909 0.124871i
\(756\) −39.5848 32.4519i −1.43969 1.18026i
\(757\) −3.58874 + 4.93948i −0.130435 + 0.179528i −0.869239 0.494392i \(-0.835391\pi\)
0.738804 + 0.673920i \(0.235391\pi\)
\(758\) 8.73291i 0.317194i
\(759\) 6.80238 13.8177i 0.246911 0.501550i
\(760\) −4.46058 3.09438i −0.161802 0.112245i
\(761\) 22.7069 + 16.4975i 0.823125 + 0.598035i 0.917606 0.397492i \(-0.130119\pi\)
−0.0944811 + 0.995527i \(0.530119\pi\)
\(762\) −43.1864 61.9409i −1.56448 2.24388i
\(763\) 49.8052 16.1827i 1.80307 0.585852i
\(764\) −19.0594 26.2330i −0.689544 0.949077i
\(765\) −39.3248 + 12.0380i −1.42179 + 0.435233i
\(766\) 57.9058 18.8147i 2.09222 0.679803i
\(767\) −0.140531 0.0456612i −0.00507427 0.00164873i
\(768\) −0.872846 2.87559i −0.0314961 0.103764i
\(769\) 23.0642i 0.831717i 0.909429 + 0.415859i \(0.136519\pi\)
−0.909429 + 0.415859i \(0.863481\pi\)
\(770\) 58.3856 12.5749i 2.10407 0.453169i
\(771\) −12.5219 9.47540i −0.450965 0.341248i
\(772\) 37.6710 + 27.3696i 1.35581 + 0.985053i
\(773\) 9.17255 28.2302i 0.329914 1.01537i −0.639260 0.768991i \(-0.720759\pi\)
0.969173 0.246379i \(-0.0792409\pi\)
\(774\) −31.0338 46.4104i −1.11549 1.66819i
\(775\) −5.96107 3.94546i −0.214128 0.141725i
\(776\) 8.39512 6.09941i 0.301367 0.218956i
\(777\) −22.6355 7.84489i −0.812043 0.281434i
\(778\) −26.1070 + 80.3491i −0.935982 + 2.88066i
\(779\) −0.266281 + 0.366504i −0.00954050 + 0.0131314i
\(780\) −9.27609 28.3212i −0.332137 1.01406i
\(781\) 2.50422 + 1.17284i 0.0896080 + 0.0419673i
\(782\) −35.3783 −1.26513
\(783\) −24.5827 + 15.7545i −0.878514 + 0.563020i
\(784\) −5.04725 + 15.5338i −0.180259 + 0.554780i
\(785\) 19.6236 + 5.90593i 0.700396 + 0.210792i
\(786\) 0.831699 42.7312i 0.0296657 1.52417i
\(787\) −2.48490 + 1.80539i −0.0885772 + 0.0643551i −0.631192 0.775626i \(-0.717434\pi\)
0.542615 + 0.839981i \(0.317434\pi\)
\(788\) 27.2362 8.84958i 0.970250 0.315253i
\(789\) 7.29409 + 10.4617i 0.259676 + 0.372446i
\(790\) −13.9738 40.0141i −0.497165 1.42364i
\(791\) 6.07533 0.216014
\(792\) 2.19637 13.3747i 0.0780447 0.475248i
\(793\) 8.48622i 0.301354i
\(794\) −9.98084 7.25151i −0.354207 0.257346i
\(795\) 21.3293 0.0503471i 0.756473 0.00178563i
\(796\) −21.2270 65.3299i −0.752371 2.31556i
\(797\) 37.7811 27.4496i 1.33827 0.972313i 0.338769 0.940870i \(-0.389990\pi\)
0.999506 0.0314434i \(-0.0100104\pi\)
\(798\) −24.8556 0.483778i −0.879880 0.0171256i
\(799\) −55.3489 + 17.9839i −1.95810 + 0.636226i
\(800\) −1.69009 38.7008i −0.0597538 1.36828i
\(801\) −4.19533 1.54608i −0.148235 0.0546281i
\(802\) −54.7618 −1.93371
\(803\) 14.0741 + 13.1684i 0.496665 + 0.464702i
\(804\) −6.74289 + 8.91084i −0.237803 + 0.314261i
\(805\) 7.39511 + 21.1760i 0.260643 + 0.746356i
\(806\) 8.55344 + 2.77918i 0.301282 + 0.0978925i
\(807\) 41.8608 + 14.5079i 1.47357 + 0.510702i
\(808\) −8.41360 11.5803i −0.295989 0.407394i
\(809\) −18.7950 + 13.6554i −0.660798 + 0.480098i −0.866932 0.498426i \(-0.833912\pi\)
0.206134 + 0.978524i \(0.433912\pi\)
\(810\) 41.8813 11.0578i 1.47156 0.388531i
\(811\) 28.9165 + 9.39553i 1.01539 + 0.329922i 0.769000 0.639248i \(-0.220754\pi\)
0.246394 + 0.969170i \(0.420754\pi\)
\(812\) −44.7819 32.5359i −1.57154 1.14179i
\(813\) −6.49824 + 8.58753i −0.227903 + 0.301178i
\(814\) −4.99211 25.9133i −0.174974 0.908262i
\(815\) 29.5214 42.5553i 1.03409 1.49065i
\(816\) 23.7127 7.19768i 0.830112 0.251969i
\(817\) −14.6557 4.76191i −0.512737 0.166598i
\(818\) 13.2611 + 40.8134i 0.463662 + 1.42701i
\(819\) −25.7689 20.3000i −0.900437 0.709340i
\(820\) 1.49609 0.0326521i 0.0522457 0.00114026i
\(821\) −14.0019 43.0935i −0.488670 1.50397i −0.826594 0.562799i \(-0.809725\pi\)
0.337924 0.941174i \(-0.390275\pi\)
\(822\) −39.5017 56.6560i −1.37778 1.97611i
\(823\) −16.0956 + 22.1537i −0.561057 + 0.772229i −0.991460 0.130408i \(-0.958371\pi\)
0.430403 + 0.902637i \(0.358371\pi\)
\(824\) 5.61560 0.195629
\(825\) −11.5498 + 26.2983i −0.402111 + 0.915591i
\(826\) 0.407166 0.0141671
\(827\) −0.625494 + 0.860919i −0.0217506 + 0.0299371i −0.819754 0.572716i \(-0.805890\pi\)
0.798003 + 0.602653i \(0.205890\pi\)
\(828\) 21.1604 + 0.824023i 0.735374 + 0.0286368i
\(829\) −6.99269 21.5213i −0.242866 0.747466i −0.995980 0.0895753i \(-0.971449\pi\)
0.753114 0.657890i \(-0.228551\pi\)
\(830\) 5.88113 0.128355i 0.204137 0.00445528i
\(831\) 23.4804 + 0.457012i 0.814528 + 0.0158536i
\(832\) 10.8451 + 33.3778i 0.375986 + 1.15717i
\(833\) −40.8076 13.2592i −1.41390 0.459404i
\(834\) −8.56600 28.2207i −0.296616 0.977202i
\(835\) 18.8185 27.1271i 0.651241 0.938770i
\(836\) −7.52249 13.6246i −0.260171 0.471216i
\(837\) −2.70402 + 6.91935i −0.0934646 + 0.239168i
\(838\) 33.9150 + 24.6407i 1.17157 + 0.851198i
\(839\) −11.4740 3.72811i −0.396125 0.128709i 0.104179 0.994559i \(-0.466778\pi\)
−0.500304 + 0.865850i \(0.666778\pi\)
\(840\) 11.6402 + 15.9421i 0.401625 + 0.550055i
\(841\) −2.08289 + 1.51331i −0.0718238 + 0.0521830i
\(842\) −5.36495 7.38422i −0.184888 0.254477i
\(843\) −6.56202 + 18.9339i −0.226008 + 0.652119i
\(844\) −42.8937 13.9370i −1.47646 0.479732i
\(845\) 3.28698 + 9.41231i 0.113075 + 0.323793i
\(846\) 58.9897 16.6590i 2.02811 0.572747i
\(847\) 39.9005 + 10.0901i 1.37100 + 0.346699i
\(848\) −12.8523 −0.441350
\(849\) 3.55742 + 11.7199i 0.122090 + 0.402226i
\(850\) 65.9162 2.87861i 2.26091 0.0987355i
\(851\) 9.42588 3.06265i 0.323115 0.104986i
\(852\) −0.0739894 + 3.80144i −0.00253483 + 0.130235i
\(853\) −2.31993 + 1.68553i −0.0794328 + 0.0577113i −0.626793 0.779186i \(-0.715633\pi\)
0.547360 + 0.836897i \(0.315633\pi\)
\(854\) 7.22609 + 22.2396i 0.247272 + 0.761024i
\(855\) 7.19187 9.55094i 0.245957 0.326635i
\(856\) −2.49242 1.81085i −0.0851893 0.0618937i
\(857\) 35.7793i 1.22220i −0.791554 0.611099i \(-0.790728\pi\)
0.791554 0.611099i \(-0.209272\pi\)
\(858\) 5.16085 35.7661i 0.176188 1.22104i
\(859\) −26.8935 −0.917593 −0.458797 0.888541i \(-0.651719\pi\)
−0.458797 + 0.888541i \(0.651719\pi\)
\(860\) 16.7823 + 48.0564i 0.572272 + 1.63871i
\(861\) 1.35122 0.942096i 0.0460494 0.0321065i
\(862\) −53.1108 + 17.2568i −1.80896 + 0.587767i
\(863\) −22.2719 + 16.1815i −0.758144 + 0.550824i −0.898340 0.439300i \(-0.855227\pi\)
0.140197 + 0.990124i \(0.455227\pi\)
\(864\) −38.9477 + 10.1850i −1.32503 + 0.346500i
\(865\) 1.67484 + 0.504061i 0.0569463 + 0.0171386i
\(866\) −1.49934 + 4.61450i −0.0509497 + 0.156807i
\(867\) 10.3561 + 34.1181i 0.351712 + 1.15871i
\(868\) −14.0838 −0.478036
\(869\) 3.60788 28.9833i 0.122389 0.983192i
\(870\) 44.5155 14.5802i 1.50922 0.494316i
\(871\) −4.20940 + 5.79375i −0.142630 + 0.196314i
\(872\) −5.89180 + 18.1331i −0.199522 + 0.614065i
\(873\) 12.7032 + 18.9973i 0.429937 + 0.642962i
\(874\) 8.32070 6.04534i 0.281452 0.204487i
\(875\) −15.5014 38.8530i −0.524044 1.31347i
\(876\) −8.67826 + 25.0401i −0.293211 + 0.846025i
\(877\) −1.44357 + 4.44286i −0.0487460 + 0.150025i −0.972467 0.233042i \(-0.925132\pi\)
0.923721 + 0.383067i \(0.125132\pi\)
\(878\) 11.0562 + 8.03282i 0.373130 + 0.271094i
\(879\) −25.6917 + 33.9519i −0.866558 + 1.14517i
\(880\) 6.99685 15.8299i 0.235864 0.533627i
\(881\) 0.351265i 0.0118344i −0.999982 0.00591720i \(-0.998116\pi\)
0.999982 0.00591720i \(-0.00188352\pi\)
\(882\) 42.4051 + 15.6273i 1.42785 + 0.526199i
\(883\) −1.22742 0.398811i −0.0413058 0.0134211i 0.288291 0.957543i \(-0.406913\pi\)
−0.329597 + 0.944122i \(0.606913\pi\)
\(884\) −44.8654 + 14.5777i −1.50899 + 0.490300i
\(885\) −0.114723 + 0.158689i −0.00385637 + 0.00533427i
\(886\) −10.3338 14.2233i −0.347171 0.477841i
\(887\) 8.11955 2.63820i 0.272628 0.0885822i −0.169512 0.985528i \(-0.554219\pi\)
0.442140 + 0.896946i \(0.354219\pi\)
\(888\) 7.15472 4.98841i 0.240097 0.167400i
\(889\) 61.3085 + 44.5432i 2.05622 + 1.49393i
\(890\) 5.89379 + 4.08862i 0.197560 + 0.137051i
\(891\) 29.2446 + 5.97959i 0.979730 + 0.200324i
\(892\) 34.9721i 1.17095i
\(893\) 9.94458 13.6875i 0.332783 0.458036i
\(894\) −14.3476 20.5782i −0.479854 0.688240i
\(895\) −37.7040 11.3474i −1.26031 0.379302i
\(896\) −22.7662 31.3350i −0.760566 1.04683i
\(897\) 13.5689 + 0.264098i 0.453052 + 0.00881797i
\(898\) −18.3388 56.4412i −0.611975 1.88347i
\(899\) −2.48254 + 7.64047i −0.0827973 + 0.254824i
\(900\) −39.4927 + 0.186443i −1.31642 + 0.00621478i
\(901\) 33.7632i 1.12481i
\(902\) 1.64325 + 0.769606i 0.0547142 + 0.0256251i
\(903\) 44.6807 + 33.8102i 1.48688 + 1.12513i
\(904\) −1.30013 + 1.78947i −0.0432417 + 0.0595170i
\(905\) 41.2547 31.3712i 1.37135 1.04281i
\(906\) 6.50013 18.7553i 0.215952 0.623104i
\(907\) −27.1646 37.3889i −0.901986 1.24148i −0.969830 0.243782i \(-0.921612\pi\)
0.0678437 0.997696i \(-0.478388\pi\)
\(908\) −3.84926 5.29805i −0.127742 0.175822i
\(909\) 26.2051 17.5229i 0.869169 0.581198i
\(910\) 31.8559 + 41.8922i 1.05601 + 1.38871i
\(911\) −9.37828 + 12.9081i −0.310716 + 0.427664i −0.935604 0.353050i \(-0.885145\pi\)
0.624888 + 0.780714i \(0.285145\pi\)
\(912\) −4.34713 + 5.74480i −0.143948 + 0.190229i
\(913\) 3.67102 + 1.71930i 0.121493 + 0.0569005i
\(914\) 34.7595i 1.14974i
\(915\) −10.7037 3.44993i −0.353853 0.114051i
\(916\) −9.86897 + 30.3736i −0.326080 + 1.00357i
\(917\) 13.2547 + 40.7937i 0.437708 + 1.34713i
\(918\) −17.3473 66.3367i −0.572546 2.18944i
\(919\) 12.0626 + 16.6027i 0.397908 + 0.547674i 0.960218 0.279253i \(-0.0900869\pi\)
−0.562309 + 0.826927i \(0.690087\pi\)
\(920\) −7.81990 2.35348i −0.257815 0.0775920i
\(921\) 6.54240 4.56149i 0.215580 0.150306i
\(922\) 40.3928 55.5959i 1.33027 1.83095i
\(923\) 2.43671i 0.0802053i
\(924\) 9.62151 + 55.7652i 0.316524 + 1.83454i
\(925\) −17.3129 + 6.47323i −0.569246 + 0.212839i
\(926\) 65.0369 + 47.2520i 2.13724 + 1.55280i
\(927\) −0.481239 + 12.3579i −0.0158060 + 0.405887i
\(928\) −41.4037 + 13.4529i −1.35914 + 0.441612i
\(929\) −23.2015 31.9342i −0.761218 1.04773i −0.997112 0.0759474i \(-0.975802\pi\)
0.235894 0.971779i \(-0.424198\pi\)
\(930\) 6.98265 9.65865i 0.228970 0.316720i
\(931\) 11.8633 3.85463i 0.388805 0.126330i
\(932\) 14.0831 + 4.57589i 0.461308 + 0.149888i
\(933\) −33.9777 + 10.3135i −1.11238 + 0.337648i
\(934\) 54.1041i 1.77034i
\(935\) 41.5855 + 18.3808i 1.35999 + 0.601117i
\(936\) 11.4939 3.24593i 0.375690 0.106096i
\(937\) 41.5896 + 30.2166i 1.35867 + 0.987133i 0.998528 + 0.0542367i \(0.0172725\pi\)
0.360144 + 0.932897i \(0.382727\pi\)
\(938\) 6.09805 18.7679i 0.199108 0.612792i
\(939\) −46.1412 15.9914i −1.50576 0.521859i
\(940\) −55.8732 + 1.21943i −1.82238 + 0.0397735i
\(941\) 9.79828 7.11887i 0.319415 0.232068i −0.416511 0.909131i \(-0.636747\pi\)
0.735926 + 0.677062i \(0.236747\pi\)
\(942\) −11.1886 + 32.2832i −0.364543 + 1.05184i
\(943\) −0.210586 + 0.648116i −0.00685762 + 0.0211056i
\(944\) 0.0693533 0.0954567i 0.00225726 0.00310685i
\(945\) −36.0803 + 24.2497i −1.17369 + 0.788843i
\(946\) −7.62448 + 61.2500i −0.247893 + 1.99141i
\(947\) 23.6412 0.768235 0.384118 0.923284i \(-0.374506\pi\)
0.384118 + 0.923284i \(0.374506\pi\)
\(948\) 38.4276 11.6642i 1.24807 0.378835i
\(949\) −5.24834 + 16.1527i −0.170368 + 0.524340i
\(950\) −15.0111 + 11.9406i −0.487024 + 0.387404i
\(951\) −20.1590 0.392364i −0.653699 0.0127233i
\(952\) 25.2788 18.3662i 0.819292 0.595251i
\(953\) −1.48786 + 0.483434i −0.0481964 + 0.0156600i −0.333016 0.942921i \(-0.608066\pi\)
0.284820 + 0.958581i \(0.408066\pi\)
\(954\) −1.38378 + 35.5345i −0.0448014 + 1.15047i
\(955\) −25.9990 + 9.07941i −0.841309 + 0.293803i
\(956\) −37.6430 −1.21746
\(957\) 31.9485 + 4.60999i 1.03275 + 0.149020i
\(958\) 26.7801i 0.865225i
\(959\) 56.0776 + 40.7428i 1.81084 + 1.31565i
\(960\) 46.5084 0.109782i 1.50105 0.00354318i
\(961\) −8.94788 27.5388i −0.288641 0.888347i
\(962\) 18.8132 13.6686i 0.606561 0.440692i
\(963\) 4.19862 5.32974i 0.135299 0.171749i
\(964\) 31.5021 10.2356i 1.01461 0.329668i
\(965\) 31.4787 23.9372i 1.01334 0.770566i
\(966\) −35.7845 + 10.8619i −1.15135 + 0.349476i
\(967\) −13.4682 −0.433109 −0.216555 0.976270i \(-0.569482\pi\)
−0.216555 + 0.976270i \(0.569482\pi\)
\(968\) −11.5108 + 9.59330i −0.369970 + 0.308340i
\(969\) −15.0917 11.4200i −0.484814 0.366862i
\(970\) −12.0878 34.6137i −0.388117 1.11138i
\(971\) −23.4682 7.62527i −0.753129 0.244707i −0.0928021 0.995685i \(-0.529582\pi\)
−0.660327 + 0.750978i \(0.729582\pi\)
\(972\) 8.83063 + 40.0812i 0.283243 + 1.28561i
\(973\) 17.3974 + 23.9454i 0.557734 + 0.767655i
\(974\) 52.1219 37.8688i 1.67009 1.21339i
\(975\) −25.3028 + 0.611990i −0.810337 + 0.0195994i
\(976\) 6.44473 + 2.09402i 0.206291 + 0.0670279i
\(977\) −16.9336 12.3030i −0.541753 0.393607i 0.282983 0.959125i \(-0.408676\pi\)
−0.824736 + 0.565518i \(0.808676\pi\)
\(978\) 68.8586 + 52.1058i 2.20186 + 1.66616i
\(979\) 2.38920 + 4.32728i 0.0763593 + 0.138300i
\(980\) −33.8553 23.4860i −1.08147 0.750233i
\(981\) −39.3995 14.5197i −1.25793 0.463578i
\(982\) −31.9176 10.3706i −1.01853 0.330940i
\(983\) −8.85080 27.2400i −0.282297 0.868820i −0.987196 0.159512i \(-0.949008\pi\)
0.704899 0.709307i \(-0.250992\pi\)
\(984\) −0.0116705 + 0.599608i −0.000372041 + 0.0191148i
\(985\) −0.530696 24.3160i −0.0169094 0.774772i
\(986\) −22.9133 70.5198i −0.729707 2.24581i
\(987\) −50.4629 + 35.1837i −1.60625 + 1.11991i
\(988\) 8.06100 11.0950i 0.256455 0.352980i
\(989\) −23.1806 −0.737100
\(990\) −43.0139 21.0495i −1.36707 0.668997i
\(991\) 51.7038 1.64243 0.821213 0.570622i \(-0.193298\pi\)
0.821213 + 0.570622i \(0.193298\pi\)
\(992\) −6.51069 + 8.96120i −0.206715 + 0.284518i
\(993\) −38.7984 + 27.0510i −1.23123 + 0.858437i
\(994\) −2.07488 6.38582i −0.0658112 0.202546i
\(995\) −58.3253 + 1.27295i −1.84904 + 0.0403552i
\(996\) −0.108463 + 5.57266i −0.00343680 + 0.176576i
\(997\) −2.41532 7.43359i −0.0764939 0.235424i 0.905497 0.424353i \(-0.139498\pi\)
−0.981991 + 0.188929i \(0.939498\pi\)
\(998\) 28.9862 + 9.41818i 0.917542 + 0.298127i
\(999\) 10.3645 + 16.1724i 0.327920 + 0.511673i
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 165.2.r.a.29.18 yes 80
3.2 odd 2 inner 165.2.r.a.29.4 yes 80
5.2 odd 4 825.2.bi.h.326.18 80
5.3 odd 4 825.2.bi.h.326.3 80
5.4 even 2 inner 165.2.r.a.29.3 80
11.8 odd 10 inner 165.2.r.a.74.17 yes 80
15.2 even 4 825.2.bi.h.326.4 80
15.8 even 4 825.2.bi.h.326.17 80
15.14 odd 2 inner 165.2.r.a.29.17 yes 80
33.8 even 10 inner 165.2.r.a.74.3 yes 80
55.8 even 20 825.2.bi.h.701.17 80
55.19 odd 10 inner 165.2.r.a.74.4 yes 80
55.52 even 20 825.2.bi.h.701.4 80
165.8 odd 20 825.2.bi.h.701.3 80
165.74 even 10 inner 165.2.r.a.74.18 yes 80
165.107 odd 20 825.2.bi.h.701.18 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.r.a.29.3 80 5.4 even 2 inner
165.2.r.a.29.4 yes 80 3.2 odd 2 inner
165.2.r.a.29.17 yes 80 15.14 odd 2 inner
165.2.r.a.29.18 yes 80 1.1 even 1 trivial
165.2.r.a.74.3 yes 80 33.8 even 10 inner
165.2.r.a.74.4 yes 80 55.19 odd 10 inner
165.2.r.a.74.17 yes 80 11.8 odd 10 inner
165.2.r.a.74.18 yes 80 165.74 even 10 inner
825.2.bi.h.326.3 80 5.3 odd 4
825.2.bi.h.326.4 80 15.2 even 4
825.2.bi.h.326.17 80 15.8 even 4
825.2.bi.h.326.18 80 5.2 odd 4
825.2.bi.h.701.3 80 165.8 odd 20
825.2.bi.h.701.4 80 55.52 even 20
825.2.bi.h.701.17 80 55.8 even 20
825.2.bi.h.701.18 80 165.107 odd 20