Properties

Label 165.2.r.a.74.4
Level $165$
Weight $2$
Character 165.74
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 74.4
Character \(\chi\) \(=\) 165.74
Dual form 165.2.r.a.29.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.26516 - 1.74134i) q^{2} +(0.567188 - 1.63655i) q^{3} +(-0.813603 + 2.50401i) q^{4} +(2.23554 + 0.0487905i) q^{5} +(-3.56737 + 1.08283i) q^{6} +(1.15619 - 3.55838i) q^{7} +(1.29554 - 0.420945i) q^{8} +(-2.35660 - 1.85646i) q^{9} +O(q^{10})\) \(q+(-1.26516 - 1.74134i) q^{2} +(0.567188 - 1.63655i) q^{3} +(-0.813603 + 2.50401i) q^{4} +(2.23554 + 0.0487905i) q^{5} +(-3.56737 + 1.08283i) q^{6} +(1.15619 - 3.55838i) q^{7} +(1.29554 - 0.420945i) q^{8} +(-2.35660 - 1.85646i) 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} +(1.34782 - 3.63089i) q^{15} +(1.88802 + 1.37173i) q^{16} +(-3.60354 + 4.95985i) q^{17} +(-0.251266 + 6.45234i) 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} +(0.0459138 - 2.35897i) q^{24} +(4.99524 + 0.218146i) q^{25} +(5.98268 + 1.94389i) q^{26} +(-4.37483 + 2.80373i) q^{27} +(7.96955 + 5.79021i) q^{28} +(1.73641 - 5.34411i) q^{29} +(-8.02781 + 2.24664i) q^{30} +(-1.15665 + 0.840357i) q^{31} -7.74754i q^{32} +(4.27034 - 3.84243i) q^{33} +13.1958 q^{34} +(2.75831 - 7.89847i) q^{35} +(6.56594 - 4.39053i) q^{36} +(-3.51577 - 1.14234i) q^{37} +(3.10355 + 2.25486i) q^{38} +(1.47027 + 4.84381i) q^{39} +(2.91676 - 0.877829i) q^{40} +(-0.0785467 - 0.241742i) q^{41} +(-0.271438 + 13.9460i) q^{42} +8.64616 q^{43} +(-6.37641 + 5.96605i) q^{44} +(-5.17768 - 4.26517i) q^{45} +(-3.39192 - 4.66857i) q^{46} +(2.93342 + 9.02814i) q^{47} +(3.31576 - 2.31181i) q^{48} +(-5.66216 - 4.11380i) q^{49} +(-5.93989 - 8.97439i) q^{50} +(6.07316 + 8.71054i) 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} +(-0.0600724 + 3.08641i) q^{57} +(-11.5027 + 3.73746i) q^{58} +(-0.0480847 - 0.0156237i) q^{59} +(7.99522 + 6.32906i) q^{60} +(1.70674 - 2.34913i) q^{61} +(2.92669 + 0.950939i) q^{62} +(-9.33066 + 6.23924i) q^{63} +(-9.71504 + 7.05839i) q^{64} +(-5.36953 + 3.72494i) q^{65} +(-12.0936 - 2.57483i) q^{66} +2.45040i q^{67} +(-9.48767 - 13.0587i) q^{68} +(1.52064 - 4.38764i) q^{69} +(-17.2436 + 5.18964i) q^{70} +(0.490070 - 0.674523i) q^{71} +(-3.83453 - 1.41312i) q^{72} +(-1.79580 + 5.52690i) q^{73} +(2.45879 + 7.56739i) q^{74} +(3.19024 - 8.05123i) 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} +(2.10710 + 8.74987i) q^{81} +(-0.321580 + 0.442617i) q^{82} +(0.718410 - 0.988807i) q^{83} +(13.9962 - 9.75843i) 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} +(-0.876527 + 14.4122i) q^{90} +(3.37903 + 10.3996i) q^{91} +(-2.18129 + 6.71333i) q^{92} +(0.719248 + 2.36956i) q^{93} +(12.0098 - 16.5301i) q^{94} +(-3.81621 + 1.14853i) q^{95} +(-12.6792 - 4.39431i) q^{96} +(-4.47759 - 6.16287i) q^{97} +15.0643i q^{98} +(-3.86624 - 9.16800i) 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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(-1\)

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 −0.972159 0.234324i \(-0.924712\pi\)
0.0775584 0.996988i \(-0.475288\pi\)
\(3\) 0.567188 1.63655i 0.327466 0.944863i
\(4\) −0.813603 + 2.50401i −0.406802 + 1.25201i
\(5\) 2.23554 + 0.0487905i 0.999762 + 0.0218198i
\(6\) −3.56737 + 1.08283i −1.45637 + 0.442062i
\(7\) 1.15619 3.55838i 0.436997 1.34494i −0.454028 0.890987i \(-0.650014\pi\)
0.891026 0.453953i \(-0.149986\pi\)
\(8\) 1.29554 0.420945i 0.458041 0.148827i
\(9\) −2.35660 1.85646i −0.785532 0.618821i
\(10\) −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 −0.865231 0.501373i \(-0.832828\pi\)
0.209463 + 0.977817i \(0.432828\pi\)
\(14\) −7.65909 + 2.48859i −2.04698 + 0.665104i
\(15\) 1.34782 3.63089i 0.348005 0.937493i
\(16\) 1.88802 + 1.37173i 0.472004 + 0.342931i
\(17\) −3.60354 + 4.95985i −0.873987 + 1.20294i 0.104064 + 0.994571i \(0.466815\pi\)
−0.978050 + 0.208369i \(0.933185\pi\)
\(18\) −0.251266 + 6.45234i −0.0592239 + 1.52083i
\(19\) −1.69505 + 0.550755i −0.388871 + 0.126352i −0.496926 0.867793i \(-0.665538\pi\)
0.108055 + 0.994145i \(0.465538\pi\)
\(20\) −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 \(-0.409826\pi\)
0.279516 + 0.960141i \(0.409826\pi\)
\(24\) 0.0459138 2.35897i 0.00937211 0.481522i
\(25\) 4.99524 + 0.218146i 0.999048 + 0.0436292i
\(26\) 5.98268 + 1.94389i 1.17330 + 0.381229i
\(27\) −4.37483 + 2.80373i −0.841936 + 0.539578i
\(28\) 7.96955 + 5.79021i 1.50610 + 1.09425i
\(29\) 1.73641 5.34411i 0.322442 0.992376i −0.650139 0.759815i \(-0.725289\pi\)
0.972582 0.232561i \(-0.0747105\pi\)
\(30\) −8.02781 + 2.24664i −1.46567 + 0.410179i
\(31\) −1.15665 + 0.840357i −0.207741 + 0.150933i −0.686791 0.726855i \(-0.740981\pi\)
0.479050 + 0.877788i \(0.340981\pi\)
\(32\) 7.74754i 1.36958i
\(33\) 4.27034 3.84243i 0.743370 0.668880i
\(34\) 13.1958 2.26306
\(35\) 2.75831 7.89847i 0.466240 1.33508i
\(36\) 6.56594 4.39053i 1.09432 0.731754i
\(37\) −3.51577 1.14234i −0.577990 0.187800i 0.00541019 0.999985i \(-0.498278\pi\)
−0.583400 + 0.812185i \(0.698278\pi\)
\(38\) 3.10355 + 2.25486i 0.503462 + 0.365787i
\(39\) 1.47027 + 4.84381i 0.235432 + 0.775630i
\(40\) 2.91676 0.877829i 0.461180 0.138797i
\(41\) −0.0785467 0.241742i −0.0122669 0.0377537i 0.944736 0.327833i \(-0.106318\pi\)
−0.957003 + 0.290079i \(0.906318\pi\)
\(42\) −0.271438 + 13.9460i −0.0418838 + 2.15191i
\(43\) 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
\(45\) −5.17768 4.26517i −0.771843 0.635814i
\(46\) −3.39192 4.66857i −0.500111 0.688343i
\(47\) 2.93342 + 9.02814i 0.427883 + 1.31689i 0.900206 + 0.435464i \(0.143416\pi\)
−0.472323 + 0.881426i \(0.656584\pi\)
\(48\) 3.31576 2.31181i 0.478588 0.333681i
\(49\) −5.66216 4.11380i −0.808880 0.587686i
\(50\) −5.93989 8.97439i −0.840027 1.26917i
\(51\) 6.07316 + 8.71054i 0.850412 + 1.21972i
\(52\) −2.37781 7.31814i −0.329743 1.01484i
\(53\) 4.45543 3.23706i 0.612001 0.444645i −0.238117 0.971236i \(-0.576530\pi\)
0.850118 + 0.526592i \(0.176530\pi\)
\(54\) 10.4171 + 4.07090i 1.41758 + 0.553979i
\(55\) 6.41259 + 3.72541i 0.864674 + 0.502334i
\(56\) 5.09670i 0.681075i
\(57\) −0.0600724 + 3.08641i −0.00795679 + 0.408805i
\(58\) −11.5027 + 3.73746i −1.51038 + 0.490753i
\(59\) −0.0480847 0.0156237i −0.00626009 0.00203403i 0.305885 0.952068i \(-0.401048\pi\)
−0.312145 + 0.950034i \(0.601048\pi\)
\(60\) 7.99522 + 6.32906i 1.03218 + 0.817078i
\(61\) 1.70674 2.34913i 0.218526 0.300776i −0.685653 0.727928i \(-0.740483\pi\)
0.904179 + 0.427153i \(0.140483\pi\)
\(62\) 2.92669 + 0.950939i 0.371690 + 0.120769i
\(63\) −9.33066 + 6.23924i −1.17555 + 0.786071i
\(64\) −9.71504 + 7.05839i −1.21438 + 0.882299i
\(65\) −5.36953 + 3.72494i −0.666008 + 0.462021i
\(66\) −12.0936 2.57483i −1.48862 0.316940i
\(67\) 2.45040i 0.299364i 0.988734 + 0.149682i \(0.0478250\pi\)
−0.988734 + 0.149682i \(0.952175\pi\)
\(68\) −9.48767 13.0587i −1.15055 1.58359i
\(69\) 1.52064 4.38764i 0.183064 0.528209i
\(70\) −17.2436 + 5.18964i −2.06100 + 0.620281i
\(71\) 0.490070 0.674523i 0.0581606 0.0800512i −0.778946 0.627091i \(-0.784245\pi\)
0.837107 + 0.547040i \(0.184245\pi\)
\(72\) −3.83453 1.41312i −0.451903 0.166537i
\(73\) −1.79580 + 5.52690i −0.210182 + 0.646875i 0.789278 + 0.614036i \(0.210455\pi\)
−0.999461 + 0.0328393i \(0.989545\pi\)
\(74\) 2.45879 + 7.56739i 0.285829 + 0.879691i
\(75\) 3.19024 8.05123i 0.368378 0.929676i
\(76\) 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 0.411586 0.911371i \(-0.364975\pi\)
−0.993952 + 0.109813i \(0.964975\pi\)
\(80\) 4.15380 + 3.15866i 0.464409 + 0.353149i
\(81\) 2.10710 + 8.74987i 0.234122 + 0.972207i
\(82\) −0.321580 + 0.442617i −0.0355126 + 0.0488789i
\(83\) 0.718410 0.988807i 0.0788557 0.108536i −0.767767 0.640729i \(-0.778632\pi\)
0.846623 + 0.532194i \(0.178632\pi\)
\(84\) 13.9962 9.75843i 1.52711 1.06473i
\(85\) −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 \(-0.0251695\pi\)
\(90\) −0.876527 + 14.4122i −0.0923940 + 1.51918i
\(91\) 3.37903 + 10.3996i 0.354219 + 1.09017i
\(92\) −2.18129 + 6.71333i −0.227415 + 0.699913i
\(93\) 0.719248 + 2.36956i 0.0745825 + 0.245712i
\(94\) 12.0098 16.5301i 1.23872 1.70495i
\(95\) −3.81621 + 1.14853i −0.391535 + 0.117837i
\(96\) −12.6792 4.39431i −1.29407 0.448492i
\(97\) −4.47759 6.16287i −0.454630 0.625745i 0.518754 0.854924i \(-0.326396\pi\)
−0.973384 + 0.229179i \(0.926396\pi\)
\(98\) 15.0643i 1.52173i
\(99\) −3.86624 9.16800i −0.388572 0.921418i
\(100\) −4.61038 + 12.3307i −0.461038 + 1.23307i
\(101\) −8.50114 + 6.17644i −0.845895 + 0.614579i −0.924011 0.382366i \(-0.875110\pi\)
0.0781161 + 0.996944i \(0.475110\pi\)
\(102\) 7.48450 21.5956i 0.741076 2.13828i
\(103\) −3.92066 1.27390i −0.386314 0.125521i 0.109420 0.993996i \(-0.465101\pi\)
−0.495734 + 0.868475i \(0.665101\pi\)
\(104\) −2.34006 + 3.22081i −0.229462 + 0.315827i
\(105\) −11.3618 8.99403i −1.10879 0.877727i
\(106\) −11.2736 3.66303i −1.09499 0.355785i
\(107\) −2.15093 + 0.698881i −0.207939 + 0.0675634i −0.411134 0.911575i \(-0.634867\pi\)
0.203196 + 0.979138i \(0.434867\pi\)
\(108\) −3.46120 13.2357i −0.333054 1.27361i
\(109\) 13.9966i 1.34063i 0.742076 + 0.670315i \(0.233841\pi\)
−0.742076 + 0.670315i \(0.766159\pi\)
\(110\) −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 \(-0.124335\pi\)
−0.971880 + 0.235477i \(0.924335\pi\)
\(114\) 5.45049 3.80019i 0.510485 0.355920i
\(115\) 5.99353 + 0.130809i 0.558900 + 0.0121980i
\(116\) 11.9690 + 8.69597i 1.11129 + 0.807400i
\(117\) 8.76106 + 0.341171i 0.809960 + 0.0315413i
\(118\) 0.0336285 + 0.103498i 0.00309576 + 0.00952776i
\(119\) 13.4826 + 18.5573i 1.23595 + 1.70114i
\(120\) 0.217737 5.27131i 0.0198766 0.481203i
\(121\) 5.86026 + 9.30899i 0.532751 + 0.846272i
\(122\) −6.24993 −0.565842
\(123\) −0.440174 0.00856732i −0.0396891 0.000772489i
\(124\) −1.16321 3.57999i −0.104459 0.321492i
\(125\) 11.1564 + 0.731393i 0.997858 + 0.0654178i
\(126\) 22.6694 + 8.35421i 2.01955 + 0.744252i
\(127\) 16.3861 + 11.9052i 1.45403 + 1.05641i 0.984869 + 0.173302i \(0.0554438\pi\)
0.469161 + 0.883112i \(0.344556\pi\)
\(128\) 9.84539 + 3.19896i 0.870218 + 0.282751i
\(129\) 4.90400 14.1499i 0.431773 1.24583i
\(130\) 13.2797 + 4.63754i 1.16470 + 0.406739i
\(131\) −11.4641 −1.00163 −0.500813 0.865556i \(-0.666966\pi\)
−0.500813 + 0.865556i \(0.666966\pi\)
\(132\) 6.14712 + 13.8192i 0.535039 + 1.20281i
\(133\) 6.66839i 0.578223i
\(134\) 4.26698 3.10014i 0.368611 0.267811i
\(135\) −9.91688 + 6.05438i −0.853509 + 0.521078i
\(136\) −2.58069 + 7.94256i −0.221293 + 0.681069i
\(137\) −14.9880 10.8894i −1.28051 0.930347i −0.280944 0.959724i \(-0.590648\pi\)
−0.999568 + 0.0293772i \(0.990648\pi\)
\(138\) −9.56421 + 2.90309i −0.814160 + 0.247127i
\(139\) 7.52360 + 2.44457i 0.638143 + 0.207345i 0.610179 0.792264i \(-0.291098\pi\)
0.0279644 + 0.999609i \(0.491098\pi\)
\(140\) 17.5337 + 13.3331i 1.48187 + 1.12685i
\(141\) 16.4388 + 0.319957i 1.38440 + 0.0269452i
\(142\) −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
\(147\) −9.94395 + 6.93311i −0.820163 + 0.571834i
\(148\) 5.72089 7.87413i 0.470254 0.647249i
\(149\) −5.44385 3.95519i −0.445978 0.324022i 0.342028 0.939690i \(-0.388886\pi\)
−0.788006 + 0.615668i \(0.788886\pi\)
\(150\) −18.0561 + 4.63077i −1.47427 + 0.378101i
\(151\) 5.06380 1.64533i 0.412086 0.133895i −0.0956350 0.995416i \(-0.530488\pi\)
0.507721 + 0.861522i \(0.330488\pi\)
\(152\) −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
\(156\) −13.3252 0.259355i −1.06687 0.0207650i
\(157\) −8.71622 + 2.83207i −0.695630 + 0.226024i −0.635426 0.772162i \(-0.719175\pi\)
−0.0602045 + 0.998186i \(0.519175\pi\)
\(158\) −5.85731 + 18.0270i −0.465983 + 1.43415i
\(159\) −2.77055 9.12757i −0.219719 0.723863i
\(160\) 0.378006 17.3199i 0.0298840 1.36926i
\(161\) 3.09977 9.54010i 0.244296 0.751865i
\(162\) 12.5707 14.7391i 0.987645 1.15801i
\(163\) −13.6145 18.7387i −1.06637 1.46773i −0.873700 0.486465i \(-0.838286\pi\)
−0.192668 0.981264i \(-0.561714\pi\)
\(164\) 0.669231 0.0522581
\(165\) 9.73396 8.38153i 0.757788 0.652501i
\(166\) −2.63075 −0.204186
\(167\) 8.67860 + 11.9451i 0.671570 + 0.924337i 0.999795 0.0202628i \(-0.00645029\pi\)
−0.328225 + 0.944600i \(0.606450\pi\)
\(168\) −8.34101 2.89078i −0.643523 0.223029i
\(169\) −1.37779 + 4.24039i −0.105983 + 0.326184i
\(170\) 29.4997 + 0.643830i 2.26252 + 0.0493795i
\(171\) 5.01700 + 1.84889i 0.383660 + 0.141388i
\(172\) −7.03455 + 21.6501i −0.536379 + 1.65081i
\(173\) 0.743915 0.241713i 0.0565588 0.0183771i −0.280601 0.959825i \(-0.590534\pi\)
0.337160 + 0.941447i \(0.390534\pi\)
\(174\) −0.407656 + 20.9446i −0.0309043 + 1.58781i
\(175\) 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 \(-0.828628\pi\)
−0.393189 + 0.919458i \(0.628628\pi\)
\(180\) 14.8926 9.49482i 1.11003 0.707702i
\(181\) −18.7514 13.6237i −1.39378 1.01264i −0.995439 0.0954051i \(-0.969585\pi\)
−0.398343 0.917236i \(-0.630415\pi\)
\(182\) 13.8342 19.0411i 1.02546 1.41142i
\(183\) −2.87643 4.12557i −0.212632 0.304971i
\(184\) 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
\(189\) 4.91860 + 18.8089i 0.357776 + 1.36815i
\(190\) 6.82808 + 5.19224i 0.495361 + 0.376685i
\(191\) −11.7130 3.80577i −0.847519 0.275376i −0.147113 0.989120i \(-0.546998\pi\)
−0.700407 + 0.713744i \(0.746998\pi\)
\(192\) 6.04117 + 19.9026i 0.435984 + 1.43635i
\(193\) −14.3079 10.3953i −1.02991 0.748272i −0.0616173 0.998100i \(-0.519626\pi\)
−0.968290 + 0.249828i \(0.919626\pi\)
\(194\) −5.06679 + 15.5940i −0.363775 + 1.11958i
\(195\) 3.05052 + 10.9002i 0.218452 + 0.780582i
\(196\) 14.9078 10.8311i 1.06484 0.773651i
\(197\) 10.8770i 0.774956i 0.921879 + 0.387478i \(0.126654\pi\)
−0.921879 + 0.387478i \(0.873346\pi\)
\(198\) −11.0732 + 18.3314i −0.786936 + 1.30275i
\(199\) 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
\(201\) 4.01021 + 1.38984i 0.282858 + 0.0980316i
\(202\) 21.5105 + 6.98920i 1.51348 + 0.491758i
\(203\) −17.0087 12.3576i −1.19378 0.867332i
\(204\) −26.7524 + 8.12035i −1.87305 + 0.568538i
\(205\) −0.163799 0.544255i −0.0114402 0.0380124i
\(206\) 2.74196 + 8.43887i 0.191041 + 0.587964i
\(207\) −6.31810 4.97723i −0.439138 0.345941i
\(208\) −6.82045 −0.472913
\(209\) −5.80442 1.11820i −0.401500 0.0773477i
\(210\) −1.28724 + 31.1635i −0.0888281 + 2.15049i
\(211\) 10.0687 + 13.8584i 0.693161 + 0.954055i 0.999997 + 0.00229222i \(0.000729636\pi\)
−0.306836 + 0.951762i \(0.599270\pi\)
\(212\) 4.48069 + 13.7902i 0.307735 + 0.947111i
\(213\) −0.825930 1.18461i −0.0565918 0.0811678i
\(214\) 3.93826 + 2.86131i 0.269214 + 0.195595i
\(215\) 19.3288 + 0.421851i 1.31821 + 0.0287700i
\(216\) −4.48753 + 5.47390i −0.305338 + 0.372451i
\(217\) 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
\(222\) 13.7790 + 0.268188i 0.924787 + 0.0179996i
\(223\) 12.6327 4.10463i 0.845951 0.274866i 0.146202 0.989255i \(-0.453295\pi\)
0.699749 + 0.714389i \(0.253295\pi\)
\(224\) −27.5687 8.95760i −1.84201 0.598505i
\(225\) −11.3668 9.78755i −0.757786 0.652504i
\(226\) −2.05432 + 2.82753i −0.136651 + 0.188085i
\(227\) −2.36556 0.768619i −0.157008 0.0510150i 0.229458 0.973318i \(-0.426305\pi\)
−0.386466 + 0.922303i \(0.626305\pi\)
\(228\) −7.67954 2.66154i −0.508590 0.176265i
\(229\) −9.81334 + 7.12981i −0.648484 + 0.471151i −0.862754 0.505623i \(-0.831263\pi\)
0.214270 + 0.976774i \(0.431263\pi\)
\(230\) −7.35497 10.6023i −0.484972 0.699092i
\(231\) −8.73549 19.6380i −0.574753 1.29209i
\(232\) 7.65442i 0.502537i
\(233\) 3.30584 + 4.55009i 0.216572 + 0.298086i 0.903456 0.428681i \(-0.141022\pi\)
−0.686883 + 0.726768i \(0.741022\pi\)
\(234\) −10.4900 15.6876i −0.685753 1.02553i
\(235\) 6.11728 + 20.3258i 0.399047 + 1.32591i
\(236\) 0.0782437 0.107693i 0.00509323 0.00701023i
\(237\) −14.5953 + 4.43021i −0.948067 + 0.287773i
\(238\) 15.2568 46.9556i 0.988952 3.04368i
\(239\) −4.41810 13.5975i −0.285783 0.879551i −0.986163 0.165780i \(-0.946986\pi\)
0.700379 0.713771i \(-0.253014\pi\)
\(240\) 7.52529 5.00636i 0.485755 0.323159i
\(241\) 12.5806i 0.810390i −0.914230 0.405195i \(-0.867204\pi\)
0.914230 0.405195i \(-0.132796\pi\)
\(242\) 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
\(246\) 0.541969 + 0.777330i 0.0345547 + 0.0495607i
\(247\) 3.06167 4.21403i 0.194810 0.268132i
\(248\) −1.14474 + 1.57560i −0.0726911 + 0.100051i
\(249\) −1.21076 1.73655i −0.0767287 0.110050i
\(250\) −12.8410 20.3524i −0.812134 1.28720i
\(251\) 2.90618 + 4.00001i 0.183436 + 0.252478i 0.890825 0.454346i \(-0.150127\pi\)
−0.707389 + 0.706824i \(0.750127\pi\)
\(252\) −8.03169 28.4404i −0.505949 1.79157i
\(253\) 7.78428 + 4.29791i 0.489393 + 0.270207i
\(254\) 43.5956i 2.73543i
\(255\) 13.1518 + 19.7690i 0.823596 + 1.23798i
\(256\) 0.536150 + 1.65010i 0.0335094 + 0.103131i
\(257\) 2.80157 8.62234i 0.174757 0.537847i −0.824865 0.565329i \(-0.808749\pi\)
0.999622 + 0.0274825i \(0.00874904\pi\)
\(258\) −30.8440 + 9.36230i −1.92027 + 0.582871i
\(259\) −8.12978 + 11.1897i −0.505160 + 0.695293i
\(260\) −4.95862 16.4760i −0.307521 1.02180i
\(261\) −14.0131 + 9.37033i −0.867392 + 0.580009i
\(262\) 14.5039 + 19.9629i 0.896055 + 1.23331i
\(263\) 7.36321i 0.454035i 0.973891 + 0.227017i \(0.0728974\pi\)
−0.973891 + 0.227017i \(0.927103\pi\)
\(264\) 3.91493 6.77558i 0.240947 0.417008i
\(265\) 10.1182 7.01919i 0.621557 0.431185i
\(266\) 11.6119 8.43656i 0.711973 0.517279i
\(267\) −2.43909 0.845326i −0.149270 0.0517331i
\(268\) −6.13584 1.99366i −0.374806 0.121782i
\(269\) −15.0348 + 20.6936i −0.916686 + 1.26171i 0.0481459 + 0.998840i \(0.484669\pi\)
−0.964831 + 0.262869i \(0.915331\pi\)
\(270\) 23.0891 + 9.60889i 1.40516 + 0.584779i
\(271\) −5.91321 1.92132i −0.359202 0.116712i 0.123856 0.992300i \(-0.460474\pi\)
−0.483058 + 0.875588i \(0.660474\pi\)
\(272\) −13.6071 + 4.42121i −0.825051 + 0.268075i
\(273\) 18.9360 + 0.368561i 1.14606 + 0.0223063i
\(274\) 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 −0.207265 0.978285i \(-0.566456\pi\)
0.866356 + 0.499427i \(0.166456\pi\)
\(278\) −5.26171 16.1939i −0.315576 0.971245i
\(279\) 4.28585 + 0.166899i 0.256587 + 0.00999196i
\(280\) 0.248671 11.3939i 0.0148609 0.680913i
\(281\) 9.35985 + 6.80033i 0.558362 + 0.405674i 0.830859 0.556483i \(-0.187850\pi\)
−0.272497 + 0.962157i \(0.587850\pi\)
\(282\) −20.2405 29.0303i −1.20530 1.72873i
\(283\) −2.18516 6.72524i −0.129894 0.399774i 0.864867 0.502002i \(-0.167403\pi\)
−0.994761 + 0.102228i \(0.967403\pi\)
\(284\) 1.29029 + 1.77594i 0.0765648 + 0.105382i
\(285\) −0.284882 + 6.89686i −0.0168749 + 0.408534i
\(286\) 14.2543 + 15.2348i 0.842875 + 0.900850i
\(287\) −0.951023 −0.0561371
\(288\) −14.3830 + 18.2578i −0.847527 + 1.07585i
\(289\) −6.36129 19.5780i −0.374194 1.15165i
\(290\) −25.8971 + 7.79400i −1.52073 + 0.457680i
\(291\) −12.6255 + 3.83230i −0.740119 + 0.224653i
\(292\) −12.3784 8.99341i −0.724389 0.526300i
\(293\) 23.3787 + 7.59620i 1.36580 + 0.443775i 0.897974 0.440048i \(-0.145038\pi\)
0.467823 + 0.883822i \(0.345038\pi\)
\(294\) 24.6535 + 8.54430i 1.43782 + 0.498313i
\(295\) −0.106733 0.0372733i −0.00621422 0.00217014i
\(296\) −5.03568 −0.292693
\(297\) −17.1968 + 1.12733i −0.997858 + 0.0654143i
\(298\) 14.4835i 0.839008i
\(299\) −6.33904 + 4.60558i −0.366596 + 0.266348i
\(300\) 17.5648 + 14.5389i 1.01410 + 0.839405i
\(301\) 9.99658 30.7663i 0.576193 1.77334i
\(302\) −9.27156 6.73618i −0.533518 0.387624i
\(303\) 5.28632 + 17.4157i 0.303691 + 1.00051i
\(304\) −3.95576 1.28531i −0.226879 0.0737173i
\(305\) 3.93010 5.16830i 0.225037 0.295936i
\(306\) −31.0972 24.4975i −1.77771 1.40043i
\(307\) 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 \(-0.402564\pi\)
0.804255 + 0.594284i \(0.202564\pi\)
\(312\) 3.94377 + 5.65643i 0.223272 + 0.320232i
\(313\) −16.5721 + 22.8096i −0.936712 + 1.28927i 0.0204718 + 0.999790i \(0.493483\pi\)
−0.957183 + 0.289482i \(0.906517\pi\)
\(314\) 15.9590 + 11.5949i 0.900617 + 0.654336i
\(315\) −21.1634 + 13.4928i −1.19242 + 0.760233i
\(316\) 22.0510 7.16479i 1.24046 0.403051i
\(317\) 9.41776 6.84240i 0.528954 0.384308i −0.291012 0.956719i \(-0.593992\pi\)
0.819966 + 0.572412i \(0.193992\pi\)
\(318\) −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
\(321\) −0.0762290 + 3.91651i −0.00425469 + 0.218598i
\(322\) −20.5342 + 6.67198i −1.14433 + 0.371815i
\(323\) 3.37651 10.3918i 0.187874 0.578218i
\(324\) −23.6241 1.84272i −1.31245 0.102374i
\(325\) −12.1855 + 8.06524i −0.675931 + 0.447379i
\(326\) −15.4060 + 47.4148i −0.853259 + 2.62606i
\(327\) 22.9061 + 7.93870i 1.26671 + 0.439011i
\(328\) −0.203520 0.280122i −0.0112375 0.0154671i
\(329\) 35.5171 1.95812
\(330\) −26.9100 6.34618i −1.48135 0.349345i
\(331\) −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
\(333\) 6.16454 + 9.21894i 0.337815 + 0.505195i
\(334\) 9.82061 30.2247i 0.537360 1.65382i
\(335\) −0.119556 + 5.47796i −0.00653206 + 0.299293i
\(336\) −4.39266 14.4716i −0.239639 0.789491i
\(337\) −4.52795 + 13.9356i −0.246653 + 0.759121i 0.748707 + 0.662901i \(0.230675\pi\)
−0.995360 + 0.0962195i \(0.969325\pi\)
\(338\) 9.12706 2.96556i 0.496446 0.161305i
\(339\) −2.81192 0.0547298i −0.152722 0.00297251i
\(340\) −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
\(345\) 3.61353 9.73452i 0.194546 0.524089i
\(346\) −1.36207 0.989602i −0.0732254 0.0532014i
\(347\) −5.35219 + 7.36665i −0.287321 + 0.395463i −0.928141 0.372228i \(-0.878594\pi\)
0.640821 + 0.767690i \(0.278594\pi\)
\(348\) 21.0200 14.6556i 1.12679 0.785622i
\(349\) 9.20764 2.99174i 0.492874 0.160144i −0.0520257 0.998646i \(-0.516568\pi\)
0.544900 + 0.838501i \(0.316568\pi\)
\(350\) −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 \(-0.604920\pi\)
−0.323680 + 0.946166i \(0.604920\pi\)
\(354\) 0.188453 + 0.00366796i 0.0100162 + 0.000194950i
\(355\) 1.12848 1.48401i 0.0598935 0.0787631i
\(356\) 3.73194 + 1.21258i 0.197792 + 0.0642666i
\(357\) 38.0171 11.5396i 2.01208 0.610739i
\(358\) 30.6629 + 22.2779i 1.62059 + 1.17742i
\(359\) 3.55028 10.9266i 0.187377 0.576686i −0.812604 0.582816i \(-0.801951\pi\)
0.999981 + 0.00612922i \(0.00195100\pi\)
\(360\) −8.50328 3.34616i −0.448162 0.176358i
\(361\) −12.8015 + 9.30081i −0.673761 + 0.489516i
\(362\) 49.8886i 2.62209i
\(363\) 18.5585 4.31066i 0.974069 0.226251i
\(364\) −28.7899 −1.50900
\(365\) −4.28423 + 12.2680i −0.224247 + 0.642135i
\(366\) −3.54488 + 10.2283i −0.185294 + 0.534643i
\(367\) −0.551086 0.179059i −0.0287665 0.00934679i 0.294598 0.955621i \(-0.404814\pi\)
−0.323365 + 0.946274i \(0.604814\pi\)
\(368\) 5.06183 + 3.67763i 0.263866 + 0.191710i
\(369\) −0.263682 + 0.715507i −0.0137267 + 0.0372478i
\(370\) 5.12751 + 17.0371i 0.266566 + 0.885719i
\(371\) −6.36737 19.5968i −0.330578 1.01741i
\(372\) −6.51859 0.126875i −0.337973 0.00657814i
\(373\) −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
\(375\) 7.52473 17.8432i 0.388575 0.921417i
\(376\) 7.60071 + 10.4615i 0.391977 + 0.539509i
\(377\) 5.07476 + 15.6185i 0.261364 + 0.804394i
\(378\) 26.5299 32.3612i 1.36455 1.66448i
\(379\) 3.28240 + 2.38480i 0.168606 + 0.122499i 0.668888 0.743363i \(-0.266771\pi\)
−0.500283 + 0.865862i \(0.666771\pi\)
\(380\) 0.228950 10.4903i 0.0117449 0.538141i
\(381\) 28.7774 20.0642i 1.47431 1.02792i
\(382\) 8.19158 + 25.2111i 0.419118 + 1.28991i
\(383\) −22.8848 + 16.6268i −1.16936 + 0.849590i −0.990932 0.134363i \(-0.957101\pi\)
−0.178428 + 0.983953i \(0.557101\pi\)
\(384\) 10.8194 14.2981i 0.552128 0.729645i
\(385\) 20.6706 18.5111i 1.05347 0.943416i
\(386\) 38.0666i 1.93754i
\(387\) −20.3755 16.0513i −1.03575 0.815932i
\(388\) 19.0749 6.19781i 0.968381 0.314646i
\(389\) 37.3298 + 12.1292i 1.89270 + 0.614975i 0.977058 + 0.212973i \(0.0683148\pi\)
0.915639 + 0.402001i \(0.131685\pi\)
\(390\) 15.1216 19.1025i 0.765713 0.967292i
\(391\) −9.66119 + 13.2975i −0.488587 + 0.672483i
\(392\) −9.06722 2.94612i −0.457964 0.148801i
\(393\) −6.50231 + 18.7616i −0.327998 + 0.946399i
\(394\) 18.9406 13.7611i 0.954212 0.693276i
\(395\) −11.2239 16.1794i −0.564737 0.814074i
\(396\) 26.1024 2.22201i 1.31169 0.111660i
\(397\) 5.73171i 0.287666i 0.989602 + 0.143833i \(0.0459429\pi\)
−0.989602 + 0.143833i \(0.954057\pi\)
\(398\) −33.0080 45.4317i −1.65454 2.27728i
\(399\) 10.9132 + 3.78223i 0.546342 + 0.189348i
\(400\) 9.13186 + 7.26396i 0.456593 + 0.363198i
\(401\) 14.9545 20.5831i 0.746790 1.02787i −0.251409 0.967881i \(-0.580894\pi\)
0.998199 0.0599878i \(-0.0191062\pi\)
\(402\) −2.65336 8.74149i −0.132338 0.435986i
\(403\) 1.29119 3.97389i 0.0643190 0.197953i
\(404\) −8.54933 26.3121i −0.425345 1.30908i
\(405\) 4.28358 + 19.6634i 0.212853 + 0.977084i
\(406\) 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 0.414171 0.910199i \(-0.364072\pi\)
−0.993637 + 0.112633i \(0.964072\pi\)
\(410\) −0.740500 + 0.973797i −0.0365707 + 0.0480924i
\(411\) −26.3221 + 18.3523i −1.29837 + 0.905252i
\(412\) 6.37972 8.78093i 0.314306 0.432605i
\(413\) −0.111190 + 0.153039i −0.00547129 + 0.00753058i
\(414\) −0.673650 + 17.2989i −0.0331081 + 0.850195i
\(415\) 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 \(0.842179\pi\)
\(420\) 31.7651 21.1324i 1.54998 1.03116i
\(421\) 1.31040 + 4.03300i 0.0638650 + 0.196556i 0.977898 0.209084i \(-0.0670484\pi\)
−0.914033 + 0.405641i \(0.867048\pi\)
\(422\) 11.3937 35.0662i 0.554636 1.70699i
\(423\) 9.84751 26.7215i 0.478802 1.29924i
\(424\) 4.40955 6.06923i 0.214147 0.294748i
\(425\) −19.0825 + 23.9895i −0.925638 + 1.16366i
\(426\) −1.01787 + 2.93693i −0.0493159 + 0.142295i
\(427\) −6.38578 8.78928i −0.309030 0.425343i
\(428\) 5.95458i 0.287826i
\(429\) −3.49613 + 16.4208i −0.168795 + 0.792804i
\(430\) −23.7194 34.1917i −1.14385 1.64887i
\(431\) 20.9898 15.2500i 1.01104 0.734567i 0.0466170 0.998913i \(-0.485156\pi\)
0.964428 + 0.264346i \(0.0851560\pi\)
\(432\) −12.1057 0.707573i −0.582435 0.0340431i
\(433\) −2.14388 0.696587i −0.103028 0.0334758i 0.257049 0.966398i \(-0.417250\pi\)
−0.360077 + 0.932922i \(0.617250\pi\)
\(434\) 6.76760 9.31480i 0.324855 0.447125i
\(435\) −17.0635 13.5076i −0.818134 0.647639i
\(436\) −35.0477 11.3877i −1.67848 0.545371i
\(437\) −4.54447 + 1.47659i −0.217391 + 0.0706348i
\(438\) 0.421600 21.6610i 0.0201448 1.03500i
\(439\) 6.34927i 0.303034i −0.988455 0.151517i \(-0.951584\pi\)
0.988455 0.151517i \(-0.0484159\pi\)
\(440\) 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 \(-0.162158\pi\)
−0.992942 + 0.118604i \(0.962158\pi\)
\(444\) −9.64159 13.8286i −0.457570 0.656278i
\(445\) 0.0727165 3.33180i 0.00344709 0.157943i
\(446\) −23.1299 16.8049i −1.09523 0.795734i
\(447\) −9.56056 + 6.66581i −0.452199 + 0.315282i
\(448\) 13.8840 + 42.7306i 0.655958 + 2.01883i
\(449\) −16.2063 22.3060i −0.764821 1.05269i −0.996798 0.0799647i \(-0.974519\pi\)
0.231976 0.972721i \(-0.425481\pi\)
\(450\) −2.66268 + 32.1762i −0.125520 + 1.51680i
\(451\) 0.159474 0.827807i 0.00750934 0.0389799i
\(452\) 4.27518 0.201088
\(453\) 0.179461 9.22037i 0.00843180 0.433211i
\(454\) 1.65438 + 5.09167i 0.0776441 + 0.238964i
\(455\) 7.04655 + 23.4135i 0.330347 + 1.09764i
\(456\) 1.22139 + 4.02385i 0.0571966 + 0.188434i
\(457\) −13.0649 9.49221i −0.611150 0.444027i 0.238669 0.971101i \(-0.423289\pi\)
−0.849819 + 0.527074i \(0.823289\pi\)
\(458\) 24.8308 + 8.06802i 1.16027 + 0.376994i
\(459\) 1.85880 31.8018i 0.0867615 1.48438i
\(460\) −5.20390 + 14.9015i −0.242633 + 0.694784i
\(461\) −31.9271 −1.48699 −0.743497 0.668739i \(-0.766834\pi\)
−0.743497 + 0.668739i \(0.766834\pi\)
\(462\) −23.1447 + 40.0566i −1.07679 + 1.86360i
\(463\) 37.3488i 1.73575i −0.496786 0.867873i \(-0.665487\pi\)
0.496786 0.867873i \(-0.334513\pi\)
\(464\) 10.6090 7.70790i 0.492511 0.357830i
\(465\) 1.49229 + 5.33233i 0.0692034 + 0.247281i
\(466\) 3.74085 11.5132i 0.173292 0.533336i
\(467\) 20.3358 + 14.7749i 0.941031 + 0.683699i 0.948669 0.316272i \(-0.102431\pi\)
−0.00763775 + 0.999971i \(0.502431\pi\)
\(468\) −7.98232 + 21.6602i −0.368983 + 1.00124i
\(469\) 8.71945 + 2.83312i 0.402627 + 0.130821i
\(470\) 27.6549 36.3676i 1.27562 1.67751i
\(471\) −0.308902 + 15.8709i −0.0142335 + 0.731290i
\(472\) −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
\(477\) −16.5091 0.642895i −0.755902 0.0294362i
\(478\) −18.0883 + 24.8964i −0.827339 + 1.13873i
\(479\) −10.0657 7.31316i −0.459914 0.334147i 0.333584 0.942720i \(-0.391742\pi\)
−0.793497 + 0.608574i \(0.791742\pi\)
\(480\) −28.1305 10.4423i −1.28398 0.476622i
\(481\) 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
\(486\) −16.9914 28.9324i −0.770744 1.31240i
\(487\) 28.4671 9.24953i 1.28997 0.419136i 0.417888 0.908499i \(-0.362771\pi\)
0.872080 + 0.489363i \(0.162771\pi\)
\(488\) 1.22229 3.76183i 0.0553307 0.170290i
\(489\) −38.3888 + 11.6524i −1.73600 + 0.526940i
\(490\) −0.734996 + 33.6768i −0.0332037 + 1.52136i
\(491\) 4.81815 14.8287i 0.217440 0.669212i −0.781531 0.623866i \(-0.785561\pi\)
0.998971 0.0453457i \(-0.0144389\pi\)
\(492\) 0.379579 1.09523i 0.0171128 0.0493768i
\(493\) 20.2487 + 27.8700i 0.911958 + 1.25520i
\(494\) −11.2115 −0.504431
\(495\) −8.19581 20.6840i −0.368374 0.929678i
\(496\) −3.33652 −0.149814
\(497\) −1.83360 2.52373i −0.0822480 0.113205i
\(498\) −1.49213 + 4.30535i −0.0668638 + 0.192927i
\(499\) 4.37564 13.4668i 0.195881 0.602859i −0.804085 0.594515i \(-0.797344\pi\)
0.999965 0.00834366i \(-0.00265590\pi\)
\(500\) −10.9083 + 27.3407i −0.487834 + 1.22271i
\(501\) 24.4711 7.42787i 1.09329 0.331853i
\(502\) 3.28860 10.1213i 0.146777 0.451734i
\(503\) 25.6404 8.33106i 1.14325 0.371464i 0.324652 0.945834i \(-0.394753\pi\)
0.818596 + 0.574370i \(0.194753\pi\)
\(504\) −9.46183 + 12.0109i −0.421463 + 0.535006i
\(505\) −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 \(-0.591729\pi\)
0.333622 + 0.942707i \(0.391729\pi\)
\(510\) 17.7855 47.9126i 0.787556 2.12160i
\(511\) 17.5905 + 12.7803i 0.778159 + 0.565366i
\(512\) 14.3646 19.7712i 0.634834 0.873773i
\(513\) 5.87138 7.16191i 0.259228 0.316206i
\(514\) −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
\(519\) 0.0263643 1.35455i 0.00115726 0.0594582i
\(520\) −5.38843 + 7.08607i −0.236298 + 0.310745i
\(521\) −6.84744 2.22487i −0.299992 0.0974733i 0.155154 0.987890i \(-0.450413\pi\)
−0.455146 + 0.890417i \(0.650413\pi\)
\(522\) 34.0457 + 12.5467i 1.49014 + 0.549153i
\(523\) −21.1158 15.3415i −0.923328 0.670837i 0.0210218 0.999779i \(-0.493308\pi\)
−0.944350 + 0.328942i \(0.893308\pi\)
\(524\) 9.32725 28.7063i 0.407463 1.25404i
\(525\) −24.9608 20.6608i −1.08938 0.901712i
\(526\) 12.8218 9.31561i 0.559058 0.406180i
\(527\) 8.76507i 0.381813i
\(528\) 13.3332 1.39684i 0.580254 0.0607897i
\(529\) −15.8121 −0.687482
\(530\) −25.0239 8.73887i −1.08697 0.379592i
\(531\) 0.0843114 + 0.126086i 0.00365880 + 0.00547167i
\(532\) −16.6977 5.42543i −0.723939 0.235222i
\(533\) 0.600990 + 0.436645i 0.0260318 + 0.0189132i
\(534\) 1.61383 + 5.31674i 0.0698370 + 0.230078i
\(535\) −4.84259 + 1.45743i −0.209363 + 0.0630101i
\(536\) 1.03149 + 3.17459i 0.0445534 + 0.137121i
\(537\) −0.593513 + 30.4936i −0.0256120 + 1.31590i
\(538\) 55.0558 2.37362
\(539\) −9.84514 21.0212i −0.424060 0.905447i
\(540\) −7.09185 29.7579i −0.305185 1.28057i
\(541\) −0.856788 1.17927i −0.0368362 0.0507007i 0.790202 0.612847i \(-0.209976\pi\)
−0.827038 + 0.562146i \(0.809976\pi\)
\(542\) 4.13547 + 12.7277i 0.177634 + 0.546700i
\(543\) −32.9314 + 22.9604i −1.41322 + 0.985327i
\(544\) 38.4266 + 27.9186i 1.64753 + 1.19700i
\(545\) −0.682901 + 31.2899i −0.0292523 + 1.34031i
\(546\) −23.3152 33.4403i −0.997799 1.43111i
\(547\) −11.1317 34.2598i −0.475956 1.46484i −0.844664 0.535297i \(-0.820200\pi\)
0.368708 0.929545i \(-0.379800\pi\)
\(548\) 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
\(552\) 0.123096 6.32445i 0.00523932 0.269187i
\(553\) −31.3359 + 10.1817i −1.33254 + 0.432968i
\(554\) −27.7562 9.01853i −1.17925 0.383160i
\(555\) −8.88635 + 11.2257i −0.377204 + 0.476506i
\(556\) −12.2424 + 16.8503i −0.519196 + 0.714611i
\(557\) −43.7447 14.2135i −1.85352 0.602246i −0.996162 0.0875319i \(-0.972102\pi\)
−0.857362 0.514714i \(-0.827898\pi\)
\(558\) −5.13164 7.67427i −0.217240 0.324878i
\(559\) −20.4430 + 14.8527i −0.864649 + 0.628204i
\(560\) 16.0423 11.1288i 0.677909 0.470278i
\(561\) 3.66952 + 35.0265i 0.154927 + 1.47882i
\(562\) 24.9021i 1.05043i
\(563\) −10.2627 14.1254i −0.432521 0.595314i 0.536009 0.844213i \(-0.319931\pi\)
−0.968530 + 0.248898i \(0.919931\pi\)
\(564\) −14.1758 + 40.9027i −0.596911 + 1.72231i
\(565\) −1.04638 3.47681i −0.0440217 0.146271i
\(566\) −8.94634 + 12.3136i −0.376043 + 0.517579i
\(567\) 33.5715 + 2.61864i 1.40987 + 0.109973i
\(568\) 0.350966 1.08016i 0.0147262 0.0453226i
\(569\) 11.3275 + 34.8623i 0.474872 + 1.46150i 0.846131 + 0.532975i \(0.178926\pi\)
−0.371259 + 0.928529i \(0.621074\pi\)
\(570\) 12.3702 8.22952i 0.518130 0.344697i
\(571\) 35.7294i 1.49523i −0.664134 0.747614i \(-0.731200\pi\)
0.664134 0.747614i \(-0.268800\pi\)
\(572\) 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
\(576\) 35.9981 + 1.40183i 1.49992 + 0.0584095i
\(577\) 24.0939 33.1623i 1.00304 1.38057i 0.0795990 0.996827i \(-0.474636\pi\)
0.923441 0.383740i \(-0.125364\pi\)
\(578\) −26.0440 + 35.8464i −1.08329 + 1.49101i
\(579\) −25.1277 + 17.5196i −1.04427 + 0.728088i
\(580\) 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
\(585\) 19.5690 + 1.19016i 0.809079 + 0.0492069i
\(586\) −16.3501 50.3206i −0.675418 2.07872i
\(587\) 11.1939 34.4513i 0.462022 1.42196i −0.400667 0.916224i \(-0.631222\pi\)
0.862689 0.505734i \(-0.168778\pi\)
\(588\) −9.27018 30.5406i −0.382296 1.25947i
\(589\) 1.49775 2.06148i 0.0617137 0.0849416i
\(590\) 0.0701280 + 0.233014i 0.00288713 + 0.00959304i
\(591\) 17.8008 + 6.16931i 0.732227 + 0.253772i
\(592\) −5.07086 6.97944i −0.208411 0.286853i
\(593\) 19.0411i 0.781923i 0.920407 + 0.390962i \(0.127857\pi\)
−0.920407 + 0.390962i \(0.872143\pi\)
\(594\) 23.7197 + 28.5191i 0.973229 + 1.17015i
\(595\) 29.2355 + 42.1432i 1.19854 + 1.72770i
\(596\) 14.3330 10.4135i 0.587102 0.426555i
\(597\) 14.7980 42.6978i 0.605641 1.74750i
\(598\) 16.0397 + 5.21163i 0.655914 + 0.213119i
\(599\) 14.7038 20.2381i 0.600783 0.826906i −0.394997 0.918682i \(-0.629254\pi\)
0.995780 + 0.0917761i \(0.0292544\pi\)
\(600\) 0.743949 11.7736i 0.0303716 0.480655i
\(601\) 38.8018 + 12.6075i 1.58276 + 0.514269i 0.962765 0.270338i \(-0.0871355\pi\)
0.619993 + 0.784608i \(0.287136\pi\)
\(602\) −66.2218 + 21.5168i −2.69900 + 0.876957i
\(603\) 4.54908 5.77461i 0.185253 0.235160i
\(604\) 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 −0.853024 0.521872i \(-0.825234\pi\)
0.232731 + 0.972541i \(0.425234\pi\)
\(608\) 4.26699 + 13.1325i 0.173049 + 0.532591i
\(609\) −29.8709 + 20.8266i −1.21043 + 0.843937i
\(610\) −13.9719 0.304937i −0.565707 0.0123466i
\(611\) −22.4447 16.3070i −0.908016 0.659712i
\(612\) −1.88429 + 48.3875i −0.0761681 + 1.95595i
\(613\) 6.20996 + 19.1123i 0.250818 + 0.771938i 0.994625 + 0.103544i \(0.0330181\pi\)
−0.743807 + 0.668394i \(0.766982\pi\)
\(614\) −5.82569 8.01837i −0.235106 0.323595i
\(615\) −0.983606 0.0406288i −0.0396628 0.00163831i
\(616\) 8.17043 14.7981i 0.329196 0.596233i
\(617\) 7.20230 0.289954 0.144977 0.989435i \(-0.453689\pi\)
0.144977 + 0.989435i \(0.453689\pi\)
\(618\) 15.3658 + 0.299073i 0.618105 + 0.0120305i
\(619\) 12.0091 + 36.9603i 0.482688 + 1.48556i 0.835302 + 0.549791i \(0.185293\pi\)
−0.352615 + 0.935769i \(0.614707\pi\)
\(620\) −2.42572 8.05994i −0.0974194 0.323695i
\(621\) −11.7290 + 7.51687i −0.470670 + 0.301642i
\(622\) −35.6989 25.9368i −1.43140 1.03997i
\(623\) −5.30334 1.72316i −0.212474 0.0690369i
\(624\) −3.86847 + 11.1620i −0.154863 + 0.446838i
\(625\) 24.9048 + 2.17938i 0.996193 + 0.0871753i
\(626\) 60.6855 2.42548
\(627\) −5.12219 + 8.86500i −0.204561 + 0.354034i
\(628\) 24.1297i 0.962880i
\(629\) 18.3351 13.3212i 0.731067 0.531152i
\(630\) 50.2706 + 19.7822i 2.00283 + 0.788141i
\(631\) 10.5321 32.4144i 0.419275 1.29040i −0.489096 0.872230i \(-0.662673\pi\)
0.908371 0.418165i \(-0.137327\pi\)
\(632\) −9.70492 7.05104i −0.386041 0.280475i
\(633\) 28.3909 8.61768i 1.12844 0.342522i
\(634\) −23.8299 7.74279i −0.946405 0.307506i
\(635\) 36.0508 + 27.4140i 1.43063 + 1.08789i
\(636\) 25.1097 + 0.488722i 0.995663 + 0.0193791i
\(637\) 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 \(-0.671416\pi\)
0.0896793 + 0.995971i \(0.471416\pi\)
\(642\) 6.91641 4.82226i 0.272969 0.190319i
\(643\) 3.97759 5.47468i 0.156861 0.215900i −0.723352 0.690479i \(-0.757400\pi\)
0.880213 + 0.474579i \(0.157400\pi\)
\(644\) 21.3666 + 15.5237i 0.841961 + 0.611720i
\(645\) 11.6534 31.3933i 0.458854 1.23611i
\(646\) −22.3675 + 7.26765i −0.880038 + 0.285942i
\(647\) 30.2310 21.9641i 1.18850 0.863497i 0.195397 0.980724i \(-0.437401\pi\)
0.993105 + 0.117227i \(0.0374006\pi\)
\(648\) 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
\(651\) 9.26337 + 0.180298i 0.363060 + 0.00706642i
\(652\) 57.9988 18.8449i 2.27141 0.738025i
\(653\) −1.77221 + 5.45432i −0.0693521 + 0.213444i −0.979726 0.200343i \(-0.935794\pi\)
0.910374 + 0.413787i \(0.135794\pi\)
\(654\) −15.1559 49.9310i −0.592642 1.95246i
\(655\) −25.6285 0.559341i −1.00139 0.0218553i
\(656\) 0.183306 0.564157i 0.00715689 0.0220266i
\(657\) 14.4925 9.69085i 0.565405 0.378076i
\(658\) −44.9347 61.8473i −1.75174 2.41106i
\(659\) −37.5865 −1.46416 −0.732081 0.681217i \(-0.761451\pi\)
−0.732081 + 0.681217i \(0.761451\pi\)
\(660\) 13.0679 + 31.1932i 0.508666 + 1.21419i
\(661\) −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
\(663\) −29.3227 10.1625i −1.13880 0.394680i
\(664\) 0.514493 1.58345i 0.0199662 0.0614497i
\(665\) −0.325354 + 14.9074i −0.0126167 + 0.578085i
\(666\) 8.25419 22.3979i 0.319843 0.867903i
\(667\) 4.65535 14.3277i 0.180256 0.554771i
\(668\) −36.9715 + 12.0128i −1.43047 + 0.464788i
\(669\) 0.447704 23.0022i 0.0173092 0.889317i
\(670\) 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 −0.503277 0.864125i \(-0.667872\pi\)
0.666311 + 0.745674i \(0.267872\pi\)
\(674\) 29.9952 9.74602i 1.15537 0.375403i
\(675\) −22.4649 + 13.0509i −0.864675 + 0.502331i
\(676\) −9.49701 6.89998i −0.365270 0.265384i
\(677\) −2.47930 + 3.41247i −0.0952874 + 0.131152i −0.853999 0.520275i \(-0.825829\pi\)
0.758711 + 0.651427i \(0.225829\pi\)
\(678\) 3.46221 + 4.96574i 0.132965 + 0.190708i
\(679\) −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 \(-0.589505\pi\)
−0.277496 + 0.960727i \(0.589505\pi\)
\(684\) −8.71148 + 11.0584i −0.333092 + 0.422827i
\(685\) −32.9749 25.0750i −1.25991 0.958066i
\(686\) −0.00909827 0.00295621i −0.000347374 0.000112869i
\(687\) 6.10229 + 20.1040i 0.232817 + 0.767015i
\(688\) 16.3241 + 11.8602i 0.622351 + 0.452164i
\(689\) −4.97370 + 15.3075i −0.189483 + 0.583168i
\(690\) −21.5228 + 6.02331i −0.819358 + 0.229304i
\(691\) −27.9241 + 20.2881i −1.06228 + 0.771794i −0.974510 0.224346i \(-0.927975\pi\)
−0.0877744 + 0.996140i \(0.527975\pi\)
\(692\) 2.05943i 0.0782878i
\(693\) −37.0933 + 3.15763i −1.40906 + 0.119949i
\(694\) 19.5992 0.743975
\(695\) 16.7000 + 5.83199i 0.633467 + 0.221220i
\(696\) −12.5268 4.34149i −0.474829 0.164564i
\(697\) 1.48205 + 0.481547i 0.0561366 + 0.0182399i
\(698\) −16.8587 12.2486i −0.638113 0.463616i
\(699\) 9.32149 2.82941i 0.352571 0.107018i
\(700\) 38.5467 + 30.6620i 1.45693 + 1.15892i
\(701\) 14.2187 + 43.7608i 0.537034 + 1.65282i 0.739212 + 0.673473i \(0.235198\pi\)
−0.202177 + 0.979349i \(0.564802\pi\)
\(702\) −31.6233 + 8.26962i −1.19355 + 0.312117i
\(703\) 6.58856 0.248492
\(704\) −39.5225 + 4.91981i −1.48956 + 0.185422i
\(705\) 36.7339 + 1.51733i 1.38348 + 0.0571461i
\(706\) 15.3878 + 21.1795i 0.579129 + 0.797103i
\(707\) 12.1492 + 37.3914i 0.456918 + 1.40625i
\(708\) −0.131866 0.189132i −0.00495585 0.00710801i
\(709\) 36.7685 + 26.7139i 1.38087 + 1.00326i 0.996798 + 0.0799582i \(0.0254787\pi\)
0.384072 + 0.923303i \(0.374521\pi\)
\(710\) −4.01187 0.0875589i −0.150563 0.00328603i
\(711\) −1.02801 + 26.3987i −0.0385535 + 0.990030i
\(712\) −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
\(717\) −24.7589 0.481896i −0.924640 0.0179967i
\(718\) −23.5186 + 7.64167i −0.877708 + 0.285185i
\(719\) 10.0623 + 3.26945i 0.375261 + 0.121930i 0.490574 0.871399i \(-0.336787\pi\)
−0.115313 + 0.993329i \(0.536787\pi\)
\(720\) −3.92491 15.1551i −0.146273 0.564796i
\(721\) −9.06603 + 12.4783i −0.337636 + 0.464717i
\(722\) 32.3917 + 10.5247i 1.20549 + 0.391689i
\(723\) −20.5889 7.13558i −0.765708 0.265375i
\(724\) 49.3701 35.8695i 1.83483 1.33308i
\(725\) 9.83956 26.3163i 0.365432 0.977363i
\(726\) −30.9857 26.8630i −1.14999 0.996978i
\(727\) 11.7037i 0.434065i 0.976164 + 0.217032i \(0.0696378\pi\)
−0.976164 + 0.217032i \(0.930362\pi\)
\(728\) 8.75532 + 12.0507i 0.324494 + 0.446627i
\(729\) 11.2782 24.5316i 0.417712 0.908580i
\(730\) 26.7829 8.06059i 0.991280 0.298336i
\(731\) −31.1568 + 42.8836i −1.15238 + 1.58611i
\(732\) 12.6708 3.84604i 0.468325 0.142154i
\(733\) −9.02911 + 27.7888i −0.333498 + 1.02640i 0.633959 + 0.773366i \(0.281429\pi\)
−0.967457 + 0.253035i \(0.918571\pi\)
\(734\) 0.385408 + 1.18616i 0.0142257 + 0.0437821i
\(735\) −22.5683 + 15.0141i −0.832445 + 0.553802i
\(736\) 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 0.925739 0.378163i \(-0.123444\pi\)
−0.645724 + 0.763571i \(0.723444\pi\)
\(740\) 13.1734 17.3238i 0.484265 0.636834i
\(741\) −5.15993 7.40073i −0.189555 0.271873i
\(742\) −26.0689 + 35.8807i −0.957018 + 1.31722i
\(743\) −3.62431 + 4.98843i −0.132963 + 0.183008i −0.870307 0.492510i \(-0.836080\pi\)
0.737344 + 0.675517i \(0.236080\pi\)
\(744\) 1.92927 + 2.76709i 0.0707304 + 0.101446i
\(745\) −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
\(750\) −40.5909 + 9.47129i −1.48217 + 0.345843i
\(751\) 6.97116 + 21.4550i 0.254381 + 0.782905i 0.993951 + 0.109825i \(0.0350290\pi\)
−0.739570 + 0.673080i \(0.764971\pi\)
\(752\) −6.84578 + 21.0691i −0.249640 + 0.768312i
\(753\) 8.19456 2.48735i 0.298627 0.0906441i
\(754\) 20.7767 28.5967i 0.756644 1.04143i
\(755\) 11.4006 3.43112i 0.414909 0.124871i
\(756\) −51.0996 2.98675i −1.85847 0.108627i
\(757\) −3.58874 4.93948i −0.130435 0.179528i 0.738804 0.673920i \(-0.235391\pi\)
−0.869239 + 0.494392i \(0.835391\pi\)
\(758\) 8.73291i 0.317194i
\(759\) 11.4489 10.3016i 0.415568 0.373926i
\(760\) −4.46058 + 3.09438i −0.161802 + 0.112245i
\(761\) −22.7069 + 16.4975i −0.823125 + 0.598035i −0.917606 0.397492i \(-0.869881\pi\)
0.0944811 + 0.995527i \(0.469881\pi\)
\(762\) −71.3465 24.7269i −2.58461 0.895761i
\(763\) 49.8052 + 16.1827i 1.80307 + 0.585852i
\(764\) 19.0594 26.2330i 0.689544 0.949077i
\(765\) 39.8125 10.3108i 1.43943 0.372787i
\(766\) 57.9058 + 18.8147i 2.09222 + 0.679803i
\(767\) 0.140531 0.0456612i 0.00507427 0.00164873i
\(768\) 3.00457 + 0.0584795i 0.108418 + 0.00211020i
\(769\) 23.0642i 0.831717i −0.909429 0.415859i \(-0.863481\pi\)
0.909429 0.415859i \(-0.136519\pi\)
\(770\) −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 −0.969173 0.246379i \(-0.920759\pi\)
0.639260 0.768991i \(-0.279241\pi\)
\(774\) −2.17248 + 55.7880i −0.0780883 + 2.00526i
\(775\) −5.96107 + 3.94546i −0.214128 + 0.141725i
\(776\) −8.39512 6.09941i −0.301367 0.218956i
\(777\) 13.7014 + 19.6514i 0.491534 + 0.704992i
\(778\) −26.1070 80.3491i −0.935982 2.88066i
\(779\) 0.266281 + 0.366504i 0.00954050 + 0.0131314i
\(780\) −29.7763 1.22994i −1.06616 0.0440389i
\(781\) 2.50422 1.17284i 0.0896080 0.0419673i
\(782\) 35.3783 1.26513
\(783\) 7.38695 + 28.2480i 0.263988 + 1.00950i
\(784\) −5.04725 15.5338i −0.180259 0.554780i
\(785\) −19.6236 + 5.90593i −0.700396 + 0.210792i
\(786\) 40.8968 12.4137i 1.45874 0.442781i
\(787\) −2.48490 1.80539i −0.0885772 0.0643551i 0.542615 0.839981i \(-0.317434\pi\)
−0.631192 + 0.775626i \(0.717434\pi\)
\(788\) −27.2362 8.84958i −0.970250 0.315253i
\(789\) 12.0503 + 4.17632i 0.429001 + 0.148681i
\(790\) −13.9738 + 40.0141i −0.497165 + 1.42364i
\(791\) −6.07533 −0.216014
\(792\) −8.86809 10.2500i −0.315114 0.364218i
\(793\) 8.48622i 0.301354i
\(794\) 9.98084 7.25151i 0.354207 0.257346i
\(795\) −5.74833 20.5402i −0.203872 0.728485i
\(796\) −21.2270 + 65.3299i −0.752371 + 2.31556i
\(797\) −37.7811 27.4496i −1.33827 0.972313i −0.999506 0.0314434i \(-0.989990\pi\)
−0.338769 0.940870i \(-0.610010\pi\)
\(798\) −7.22072 23.7886i −0.255611 0.842108i
\(799\) −55.3489 17.9839i −1.95810 0.636226i
\(800\) 1.69009 38.7008i 0.0597538 1.36828i
\(801\) −2.76684 + 3.51223i −0.0977614 + 0.124099i
\(802\) −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
\(807\) 25.3386 + 36.3423i 0.891959 + 1.27931i
\(808\) −8.41360 + 11.5803i −0.295989 + 0.407394i
\(809\) 18.7950 + 13.6554i 0.660798 + 0.480098i 0.866932 0.498426i \(-0.166088\pi\)
−0.206134 + 0.978524i \(0.566088\pi\)
\(810\) 28.8213 32.3365i 1.01268 1.13619i
\(811\) 28.9165 9.39553i 1.01539 0.329922i 0.246394 0.969170i \(-0.420754\pi\)
0.769000 + 0.639248i \(0.220754\pi\)
\(812\) 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
\(816\) −0.482235 + 24.7764i −0.0168816 + 0.867346i
\(817\) −14.6557 + 4.76191i −0.512737 + 0.166598i
\(818\) −13.2611 + 40.8134i −0.463662 + 1.42701i
\(819\) 11.3434 30.7807i 0.396372 1.07556i
\(820\) 1.49609 + 0.0326521i 0.0522457 + 0.00114026i
\(821\) 14.0019 43.0935i 0.488670 1.50397i −0.337924 0.941174i \(-0.609725\pi\)
0.826594 0.562799i \(-0.190275\pi\)
\(822\) 65.2591 + 22.6172i 2.27617 + 0.788865i
\(823\) −16.0956 22.1537i −0.561057 0.772229i 0.430403 0.902637i \(-0.358371\pi\)
−0.991460 + 0.130408i \(0.958371\pi\)
\(824\) −5.61560 −0.195629
\(825\) 22.1696 18.2623i 0.771845 0.635811i
\(826\) 0.407166 0.0141671
\(827\) 0.625494 + 0.860919i 0.0217506 + 0.0299371i 0.819754 0.572716i \(-0.194110\pi\)
−0.798003 + 0.602653i \(0.794110\pi\)
\(828\) 17.6035 11.7711i 0.611763 0.409075i
\(829\) −6.99269 + 21.5213i −0.242866 + 0.747466i 0.753114 + 0.657890i \(0.228551\pi\)
−0.995980 + 0.0895753i \(0.971449\pi\)
\(830\) −5.88113 0.128355i −0.204137 0.00445528i
\(831\) −6.82121 22.4725i −0.236625 0.779561i
\(832\) 10.8451 33.3778i 0.375986 1.15717i
\(833\) 40.8076 13.2592i 1.41390 0.459404i
\(834\) −29.4865 0.573911i −1.02103 0.0198729i
\(835\) 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 \(-0.533222\pi\)
0.500304 + 0.865850i \(0.333222\pi\)
\(840\) −18.5056 6.86941i −0.638503 0.237017i
\(841\) −2.08289 1.51331i −0.0718238 0.0521830i
\(842\) 5.36495 7.38422i 0.184888 0.254477i
\(843\) 16.4379 11.4608i 0.566150 0.394731i
\(844\) −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
\(849\) −12.2456 0.238342i −0.420268 0.00817989i
\(850\) 65.9162 + 2.87861i 2.26091 + 0.0987355i
\(851\) −9.42588 3.06265i −0.323115 0.104986i
\(852\) 3.63825 1.10434i 0.124644 0.0378341i
\(853\) −2.31993 1.68553i −0.0794328 0.0577113i 0.547360 0.836897i \(-0.315633\pi\)
−0.626793 + 0.779186i \(0.715633\pi\)
\(854\) −7.22609 + 22.2396i −0.247272 + 0.761024i
\(855\) 11.1255 + 4.37803i 0.380483 + 0.149726i
\(856\) −2.49242 + 1.81085i −0.0851893 + 0.0618937i
\(857\) 35.7793i 1.22220i −0.791554 0.611099i \(-0.790728\pi\)
0.791554 0.611099i \(-0.209272\pi\)
\(858\) 33.0173 14.6869i 1.12719 0.501404i
\(859\) −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
\(861\) −0.539408 + 1.55640i −0.0183830 + 0.0530419i
\(862\) −53.1108 17.2568i −1.80896 0.587767i
\(863\) 22.2719 + 16.1815i 0.758144 + 0.550824i 0.898340 0.439300i \(-0.144773\pi\)
−0.140197 + 0.990124i \(0.544773\pi\)
\(864\) 21.7220 + 33.8941i 0.738997 + 1.15310i
\(865\) 1.67484 0.504061i 0.0569463 0.0171386i
\(866\) 1.49934 + 4.61450i 0.0509497 + 0.156807i
\(867\) −35.6485 0.693845i −1.21069 0.0235642i
\(868\) −14.0838 −0.478036
\(869\) −3.60788 28.9833i −0.122389 0.983192i
\(870\) −1.93323 + 46.8026i −0.0655426 + 1.58676i
\(871\) −4.20940 5.79375i −0.142630 0.196314i
\(872\) 5.89180 + 18.1331i 0.199522 + 0.614065i
\(873\) −0.889270 + 22.8359i −0.0300972 + 0.772878i
\(874\) 8.32070 + 6.04534i 0.281452 + 0.204487i
\(875\) 15.5014 38.8530i 0.524044 1.31347i
\(876\) −21.7390 + 15.1569i −0.734494 + 0.512103i
\(877\) −1.44357 4.44286i −0.0487460 0.150025i 0.923721 0.383067i \(-0.125132\pi\)
−0.972467 + 0.233042i \(0.925132\pi\)
\(878\) −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 \(-0.00188352\pi\)
\(882\) 27.9663 35.5005i 0.941676 1.19537i
\(883\) −1.22742 + 0.398811i −0.0413058 + 0.0134211i −0.329597 0.944122i \(-0.606913\pi\)
0.288291 + 0.957543i \(0.406913\pi\)
\(884\) 44.8654 + 14.5777i 1.50899 + 0.490300i
\(885\) −0.121537 + 0.153532i −0.00408542 + 0.00516094i
\(886\) −10.3338 + 14.2233i −0.347171 + 0.477841i
\(887\) −8.11955 2.63820i −0.272628 0.0885822i 0.169512 0.985528i \(-0.445781\pi\)
−0.442140 + 0.896946i \(0.645781\pi\)
\(888\) −2.85617 + 8.24114i −0.0958469 + 0.276555i
\(889\) 61.3085 44.5432i 2.05622 1.49393i
\(890\) −5.89379 + 4.08862i −0.197560 + 0.137051i
\(891\) −7.90887 + 28.7828i −0.264957 + 0.964260i
\(892\) 34.9721i 1.17095i
\(893\) −9.94458 13.6875i −0.332783 0.458036i
\(894\) 23.7030 + 8.21487i 0.792747 + 0.274746i
\(895\) −37.7040 + 11.3474i −1.26031 + 0.379302i
\(896\) 22.7662 31.3350i 0.760566 1.04683i
\(897\) 3.94184 + 12.9864i 0.131614 + 0.433603i
\(898\) −18.3388 + 56.4412i −0.611975 + 1.88347i
\(899\) 2.48254 + 7.64047i 0.0827973 + 0.254824i
\(900\) 33.7562 20.4994i 1.12521 0.683313i
\(901\) 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
\(906\) −16.2828 + 11.3527i −0.540960 + 0.377168i
\(907\) −27.1646 + 37.3889i −0.901986 + 1.24148i 0.0678437 + 0.997696i \(0.478388\pi\)
−0.969830 + 0.243782i \(0.921612\pi\)
\(908\) 3.84926 5.29805i 0.127742 0.175822i
\(909\) 31.5001 + 1.22667i 1.04479 + 0.0406860i
\(910\) 31.8559 41.8922i 1.05601 1.38871i
\(911\) 9.37828 + 12.9081i 0.310716 + 0.427664i 0.935604 0.353050i \(-0.114855\pi\)
−0.624888 + 0.780714i \(0.714855\pi\)
\(912\) −4.34713 + 5.74480i −0.143948 + 0.190229i
\(913\) 3.67102 1.71930i 0.121493 0.0569005i
\(914\) 34.7595i 1.14974i
\(915\) −6.22907 9.36321i −0.205927 0.309538i
\(916\) −9.86897 30.3736i −0.326080 1.00357i
\(917\) −13.2547 + 40.7937i −0.437708 + 1.34713i
\(918\) −57.7294 + 36.9974i −1.90535 + 1.22110i
\(919\) 12.0626 16.6027i 0.397908 0.547674i −0.562309 0.826927i \(-0.690087\pi\)
0.960218 + 0.279253i \(0.0900869\pi\)
\(920\) 7.81990 2.35348i 0.257815 0.0775920i
\(921\) 2.61174 7.53585i 0.0860597 0.248315i
\(922\) 40.3928 + 55.5959i 1.33027 + 1.83095i
\(923\) 2.43671i 0.0802053i
\(924\) 56.2811 5.89623i 1.85151 0.193972i
\(925\) −17.3129 6.47323i −0.569246 0.212839i
\(926\) −65.0369 + 47.2520i −2.13724 + 1.55280i
\(927\) 6.87446 + 10.2806i 0.225787 + 0.337660i
\(928\) −41.4037 13.4529i −1.35914 0.441612i
\(929\) 23.2015 31.9342i 0.761218 1.04773i −0.235894 0.971779i \(-0.575802\pi\)
0.997112 0.0759474i \(-0.0241981\pi\)
\(930\) 7.39740 9.34481i 0.242570 0.306428i
\(931\) 11.8633 + 3.85463i 0.388805 + 0.126330i
\(932\) −14.0831 + 4.57589i −0.461308 + 0.149888i
\(933\) 0.690990 35.5018i 0.0226220 1.16228i
\(934\) 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 0.360144 0.932897i \(-0.382727\pi\)
0.998528 0.0542367i \(-0.0172725\pi\)
\(938\) −6.09805 18.7679i −0.199108 0.612792i
\(939\) 27.9295 + 40.0584i 0.911445 + 1.30726i
\(940\) −55.8732 1.21943i −1.82238 0.0397735i
\(941\) −9.79828 7.11887i −0.319415 0.232068i 0.416511 0.909131i \(-0.363253\pi\)
−0.735926 + 0.677062i \(0.763253\pi\)
\(942\) 28.0273 19.5412i 0.913179 0.636687i
\(943\) −0.210586 0.648116i −0.00685762 0.0211056i
\(944\) −0.0693533 0.0954567i −0.00225726 0.00310685i
\(945\) 10.0780 + 42.2880i 0.327838 + 1.37563i
\(946\) −7.62448 61.2500i −0.247893 1.99141i
\(947\) −23.6412 −0.768235 −0.384118 0.923284i \(-0.625494\pi\)
−0.384118 + 0.923284i \(0.625494\pi\)
\(948\) 0.781485 40.1513i 0.0253814 1.30405i
\(949\) −5.24834 16.1527i −0.170368 0.524340i
\(950\) 15.0111 + 11.9406i 0.487024 + 0.387404i
\(951\) −5.85630 19.2936i −0.189904 0.625637i
\(952\) 25.2788 + 18.3662i 0.819292 + 0.595251i
\(953\) 1.48786 + 0.483434i 0.0481964 + 0.0156600i 0.333016 0.942921i \(-0.391934\pi\)
−0.284820 + 0.958581i \(0.591934\pi\)
\(954\) 19.7671 + 29.5614i 0.639985 + 0.957084i
\(955\) −25.9990 9.07941i −0.841309 0.293803i
\(956\) 37.6430 1.21746
\(957\) −13.1193 29.4931i −0.424087 0.953378i
\(958\) 26.7801i 0.865225i
\(959\) −56.0776 + 40.7428i −1.81084 + 1.31565i
\(960\) 12.5342 + 44.7877i 0.404539 + 1.44552i
\(961\) −8.94788 + 27.5388i −0.288641 + 0.888347i
\(962\) −18.8132 13.6686i −0.606561 0.440692i
\(963\) 6.36633 + 2.34615i 0.205152 + 0.0756036i
\(964\) 31.5021 + 10.2356i 1.01461 + 0.329668i
\(965\) −31.4787 23.9372i −1.01334 0.770566i
\(966\) −0.727732 + 37.3896i −0.0234144 + 1.20299i
\(967\) −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 \(-0.470418\pi\)
0.660327 + 0.750978i \(0.270418\pi\)
\(972\) −16.4150 + 37.6169i −0.526512 + 1.20656i
\(973\) 17.3974 23.9454i 0.557734 0.767655i
\(974\) −52.1219 37.8688i −1.67009 1.21339i
\(975\) 6.28771 + 24.5167i 0.201368 + 0.785163i
\(976\) 6.44473 2.09402i 0.206291 0.0670279i
\(977\) 16.9336 12.3030i 0.541753 0.393607i −0.282983 0.959125i \(-0.591324\pi\)
0.824736 + 0.565518i \(0.191324\pi\)
\(978\) 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
\(981\) 25.9842 32.9843i 0.829610 1.05311i
\(982\) −31.9176 + 10.3706i −1.01853 + 0.330940i
\(983\) 8.85080 27.2400i 0.282297 0.868820i −0.704899 0.709307i \(-0.749008\pi\)
0.987196 0.159512i \(-0.0509921\pi\)
\(984\) −0.573867 + 0.174190i −0.0182942 + 0.00555297i
\(985\) −0.530696 + 24.3160i −0.0169094 + 0.774772i
\(986\) 22.9133 70.5198i 0.729707 2.24581i
\(987\) 20.1449 58.1255i 0.641218 1.85016i
\(988\) 8.06100 + 11.0950i 0.256455 + 0.352980i
\(989\) 23.1806 0.737100
\(990\) −25.6489 + 40.4402i −0.815175 + 1.28527i
\(991\) 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
\(993\) −15.4884 + 44.6898i −0.491508 + 1.41819i
\(994\) −2.07488 + 6.38582i −0.0658112 + 0.202546i
\(995\) 58.3253 + 1.27295i 1.84904 + 0.0403552i
\(996\) 5.33343 1.61889i 0.168996 0.0512965i
\(997\) −2.41532 + 7.43359i −0.0764939 + 0.235424i −0.981991 0.188929i \(-0.939498\pi\)
0.905497 + 0.424353i \(0.139498\pi\)
\(998\) −28.9862 + 9.41818i −0.917542 + 0.298127i
\(999\) 18.5837 4.85971i 0.587963 0.153755i
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.74.4 yes 80
3.2 odd 2 inner 165.2.r.a.74.18 yes 80
5.2 odd 4 825.2.bi.h.701.17 80
5.3 odd 4 825.2.bi.h.701.4 80
5.4 even 2 inner 165.2.r.a.74.17 yes 80
11.7 odd 10 inner 165.2.r.a.29.3 80
15.2 even 4 825.2.bi.h.701.3 80
15.8 even 4 825.2.bi.h.701.18 80
15.14 odd 2 inner 165.2.r.a.74.3 yes 80
33.29 even 10 inner 165.2.r.a.29.17 yes 80
55.7 even 20 825.2.bi.h.326.3 80
55.18 even 20 825.2.bi.h.326.18 80
55.29 odd 10 inner 165.2.r.a.29.18 yes 80
165.29 even 10 inner 165.2.r.a.29.4 yes 80
165.62 odd 20 825.2.bi.h.326.17 80
165.128 odd 20 825.2.bi.h.326.4 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.r.a.29.3 80 11.7 odd 10 inner
165.2.r.a.29.4 yes 80 165.29 even 10 inner
165.2.r.a.29.17 yes 80 33.29 even 10 inner
165.2.r.a.29.18 yes 80 55.29 odd 10 inner
165.2.r.a.74.3 yes 80 15.14 odd 2 inner
165.2.r.a.74.4 yes 80 1.1 even 1 trivial
165.2.r.a.74.17 yes 80 5.4 even 2 inner
165.2.r.a.74.18 yes 80 3.2 odd 2 inner
825.2.bi.h.326.3 80 55.7 even 20
825.2.bi.h.326.4 80 165.128 odd 20
825.2.bi.h.326.17 80 165.62 odd 20
825.2.bi.h.326.18 80 55.18 even 20
825.2.bi.h.701.3 80 15.2 even 4
825.2.bi.h.701.4 80 5.3 odd 4
825.2.bi.h.701.17 80 5.2 odd 4
825.2.bi.h.701.18 80 15.8 even 4