Properties

Label 165.2.r.a.29.17
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 29.17
Character \(\chi\) \(=\) 165.29
Dual form 165.2.r.a.74.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26516 - 1.74134i) q^{2} +(-0.567188 - 1.63655i) q^{3} +(-0.813603 - 2.50401i) q^{4} +(-0.737221 + 2.11104i) q^{5} +(-3.56737 - 1.08283i) q^{6} +(-1.15619 - 3.55838i) q^{7} +(-1.29554 - 0.420945i) q^{8} +(-2.35660 + 1.85646i) q^{9} +O(q^{10})\) \(q+(1.26516 - 1.74134i) q^{2} +(-0.567188 - 1.63655i) q^{3} +(-0.813603 - 2.50401i) q^{4} +(-0.737221 + 2.11104i) 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} +(3.87297 + 0.00914202i) 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} +(5.88589 + 0.128459i) q^{20} +(-5.16769 + 3.91042i) q^{21} +(0.881833 - 7.08407i) q^{22} -2.68103 q^{23} +(0.0459138 + 2.35897i) q^{24} +(-3.91301 - 3.11261i) 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} +(4.91583 - 6.73259i) q^{30} +(-1.15665 - 0.840357i) q^{31} -7.74754i q^{32} +(-4.27034 - 3.84243i) q^{33} +13.1958 q^{34} +(8.36425 + 0.182550i) 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} +(1.84373 - 2.42461i) q^{40} +(-0.0785467 + 0.241742i) q^{41} +(0.271438 + 13.9460i) 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} +(-3.31576 - 2.31181i) q^{48} +(-5.66216 + 4.11380i) q^{49} +(-10.3707 + 2.87593i) 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} +(1.24368 + 7.31117i) q^{55} +5.09670i q^{56} +(0.0600724 + 3.08641i) q^{57} +(11.5027 + 3.73746i) q^{58} +(-0.0480847 + 0.0156237i) q^{59} +(-3.12817 - 9.70541i) 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} +(10.9000 - 14.3340i) 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} +(-2.87454 + 8.16927i) q^{75} +4.69252i q^{76} +(-9.06132 - 8.47817i) q^{77} +(-6.57458 - 8.68841i) q^{78} +(-5.17618 + 7.12440i) q^{79} +(1.50389 + 4.99695i) 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} +(-13.1271 + 3.95073i) q^{85} +(-10.9387 + 15.0559i) q^{86} +(7.76104 - 5.87283i) q^{87} +(-4.43636 + 0.854650i) q^{88} +1.49038i q^{89} +(-13.8064 - 4.22637i) 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} +(2.41229 - 3.17229i) 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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

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

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 \(-0.0752876\pi\)
\(3\) −0.567188 1.63655i −0.327466 0.944863i
\(4\) −0.813603 2.50401i −0.406802 1.25201i
\(5\) −0.737221 + 2.11104i −0.329695 + 0.944087i
\(6\) −3.56737 1.08283i −1.45637 0.442062i
\(7\) −1.15619 3.55838i −0.436997 1.34494i −0.891026 0.453953i \(-0.850014\pi\)
0.454028 0.890987i \(-0.349986\pi\)
\(8\) −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 \(-0.167172\pi\)
−0.209463 + 0.977817i \(0.567172\pi\)
\(14\) −7.65909 2.48859i −2.04698 0.665104i
\(15\) 3.87297 + 0.00914202i 0.999997 + 0.00236046i
\(16\) 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 \(0.533185\pi\)
\(18\) 0.251266 + 6.45234i 0.0592239 + 1.52083i
\(19\) −1.69505 0.550755i −0.388871 0.126352i 0.108055 0.994145i \(-0.465538\pi\)
−0.496926 + 0.867793i \(0.665538\pi\)
\(20\) 5.88589 + 0.128459i 1.31612 + 0.0287244i
\(21\) −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 \(0.590174\pi\)
\(24\) 0.0459138 + 2.35897i 0.00937211 + 0.481522i
\(25\) −3.91301 3.11261i −0.782602 0.622522i
\(26\) 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 0.972582 + 0.232561i \(0.0747105\pi\)
−0.650139 + 0.759815i \(0.725289\pi\)
\(30\) 4.91583 6.73259i 0.897504 1.22920i
\(31\) −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
\(33\) −4.27034 3.84243i −0.743370 0.668880i
\(34\) 13.1958 2.26306
\(35\) 8.36425 + 0.182550i 1.41382 + 0.0308565i
\(36\) 6.56594 + 4.39053i 1.09432 + 0.731754i
\(37\) 3.51577 1.14234i 0.577990 0.187800i −0.00541019 0.999985i \(-0.501722\pi\)
0.583400 + 0.812185i \(0.301722\pi\)
\(38\) −3.10355 + 2.25486i −0.503462 + 0.365787i
\(39\) 1.47027 4.84381i 0.235432 0.775630i
\(40\) 1.84373 2.42461i 0.291520 0.383364i
\(41\) −0.0785467 + 0.241742i −0.0122669 + 0.0377537i −0.957003 0.290079i \(-0.906318\pi\)
0.944736 + 0.327833i \(0.106318\pi\)
\(42\) 0.271438 + 13.9460i 0.0418838 + 2.15191i
\(43\) −8.64616 −1.31853 −0.659264 0.751912i \(-0.729132\pi\)
−0.659264 + 0.751912i \(0.729132\pi\)
\(44\) −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 \(0.856584\pi\)
\(48\) −3.31576 2.31181i −0.478588 0.333681i
\(49\) −5.66216 + 4.11380i −0.808880 + 0.587686i
\(50\) −10.3707 + 2.87593i −1.46663 + 0.406718i
\(51\) 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 \(-0.423470\pi\)
−0.850118 + 0.526592i \(0.823470\pi\)
\(54\) 10.4171 4.07090i 1.41758 0.553979i
\(55\) 1.24368 + 7.31117i 0.167697 + 0.985839i
\(56\) 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 −0.312145 0.950034i \(-0.601048\pi\)
0.305885 + 0.952068i \(0.401048\pi\)
\(60\) −3.12817 9.70541i −0.403845 1.25296i
\(61\) 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
\(63\) 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
\(70\) 10.9000 14.3340i 1.30279 1.71324i
\(71\) 0.490070 + 0.674523i 0.0581606 + 0.0800512i 0.837107 0.547040i \(-0.184245\pi\)
−0.778946 + 0.627091i \(0.784245\pi\)
\(72\) 3.83453 1.41312i 0.451903 0.166537i
\(73\) 1.79580 + 5.52690i 0.210182 + 0.646875i 0.999461 + 0.0328393i \(0.0104549\pi\)
−0.789278 + 0.614036i \(0.789545\pi\)
\(74\) 2.45879 7.56739i 0.285829 0.879691i
\(75\) −2.87454 + 8.16927i −0.331923 + 0.943307i
\(76\) 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 \(0.364975\pi\)
\(80\) 1.50389 + 4.99695i 0.168139 + 0.558676i
\(81\) 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 \(-0.221368\pi\)
−0.846623 + 0.532194i \(0.821368\pi\)
\(84\) 13.9962 + 9.75843i 1.52711 + 1.06473i
\(85\) −13.1271 + 3.95073i −1.42383 + 0.428516i
\(86\) −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 \(0.0251695\pi\)
−0.996875 + 0.0789901i \(0.974830\pi\)
\(90\) −13.8064 4.22637i −1.45532 0.445499i
\(91\) 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
\(95\) 2.41229 3.17229i 0.247496 0.325470i
\(96\) −12.6792 + 4.39431i −1.29407 + 0.448492i
\(97\) 4.47759 6.16287i 0.454630 0.625745i −0.518754 0.854924i \(-0.673604\pi\)
0.973384 + 0.229179i \(0.0736040\pi\)
\(98\) 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 0.0781161 0.996944i \(-0.475110\pi\)
−0.924011 + 0.382366i \(0.875110\pi\)
\(102\) −7.48450 21.5956i −0.741076 2.13828i
\(103\) 3.92066 1.27390i 0.386314 0.125521i −0.109420 0.993996i \(-0.534899\pi\)
0.495734 + 0.868475i \(0.334899\pi\)
\(104\) −2.34006 3.22081i −0.229462 0.315827i
\(105\) −4.44535 13.7921i −0.433822 1.34597i
\(106\) −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 \(0.565133\pi\)
\(108\) 3.46120 13.2357i 0.333054 1.27361i
\(109\) 13.9966i 1.34063i −0.742076 0.670315i \(-0.766159\pi\)
0.742076 0.670315i \(-0.233841\pi\)
\(110\) 14.3047 + 7.08411i 1.36390 + 0.675444i
\(111\) −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 \(0.0756652\pi\)
\(114\) 5.45049 + 3.80019i 0.510485 + 0.355920i
\(115\) 1.97651 5.65976i 0.184310 0.527776i
\(116\) 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
\(120\) −5.01373 1.64215i −0.457689 0.149907i
\(121\) 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
\(125\) 9.45561 5.96585i 0.845736 0.533602i
\(126\) 22.6694 8.35421i 2.01955 0.744252i
\(127\) −16.3861 + 11.9052i −1.45403 + 1.05641i −0.469161 + 0.883112i \(0.655444\pi\)
−0.984869 + 0.173302i \(0.944556\pi\)
\(128\) −9.84539 + 3.19896i −0.870218 + 0.282751i
\(129\) 4.90400 + 14.1499i 0.431773 + 1.24583i
\(130\) −0.306920 + 14.0628i −0.0269187 + 1.23339i
\(131\) −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
\(135\) −9.14401 + 7.16848i −0.786991 + 0.616965i
\(136\) −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 \(0.00935241\pi\)
\(138\) 9.56421 + 2.90309i 0.814160 + 0.247127i
\(139\) 7.52360 2.44457i 0.638143 0.207345i 0.0279644 0.999609i \(-0.491098\pi\)
0.610179 + 0.792264i \(0.291098\pi\)
\(140\) −6.34808 21.0927i −0.536510 1.78266i
\(141\) 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
\(145\) −12.5618 0.274160i −1.04320 0.0227678i
\(146\) 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 −0.788006 0.615668i \(-0.788886\pi\)
0.342028 + 0.939690i \(0.388886\pi\)
\(150\) 10.5887 + 15.3409i 0.864566 + 1.25258i
\(151\) 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
\(156\) −13.3252 + 0.259355i −1.06687 + 0.0207650i
\(157\) 8.71622 + 2.83207i 0.695630 + 0.226024i 0.635426 0.772162i \(-0.280825\pi\)
0.0602045 + 0.998186i \(0.480825\pi\)
\(158\) 5.85731 + 18.0270i 0.465983 + 1.43415i
\(159\) −2.77055 + 9.12757i −0.219719 + 0.723863i
\(160\) 16.3554 + 5.71165i 1.29301 + 0.451545i
\(161\) 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 0.192668 0.981264i \(-0.438286\pi\)
0.873700 0.486465i \(-0.161714\pi\)
\(164\) 0.669231 0.0522581
\(165\) 11.2597 6.18215i 0.876567 0.481280i
\(166\) −2.63075 −0.204186
\(167\) −8.67860 + 11.9451i −0.671570 + 0.924337i −0.999795 0.0202628i \(-0.993550\pi\)
0.328225 + 0.944600i \(0.393550\pi\)
\(168\) 8.34101 2.89078i 0.643523 0.223029i
\(169\) −1.37779 4.24039i −0.105983 0.326184i
\(170\) −9.72822 + 27.8569i −0.746121 + 2.13653i
\(171\) 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 \(-0.409466\pi\)
−0.337160 + 0.941447i \(0.609466\pi\)
\(174\) −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 −0.393189 0.919458i \(-0.628628\pi\)
−0.858540 + 0.512746i \(0.828628\pi\)
\(180\) −14.1091 + 10.6242i −1.05163 + 0.791881i
\(181\) −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
\(183\) 2.87643 4.12557i 0.212632 0.304971i
\(184\) 3.47337 + 1.12857i 0.256060 + 0.0831990i
\(185\) −0.180364 + 8.26411i −0.0132606 + 0.607589i
\(186\) 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
\(190\) −2.47211 8.21406i −0.179346 0.595910i
\(191\) −11.7130 + 3.80577i −0.847519 + 0.275376i −0.700407 0.713744i \(-0.746998\pi\)
−0.147113 + 0.989120i \(0.546998\pi\)
\(192\) −6.04117 + 19.9026i −0.435984 + 1.43635i
\(193\) 14.3079 10.3953i 1.02991 0.748272i 0.0616173 0.998100i \(-0.480374\pi\)
0.968290 + 0.249828i \(0.0803742\pi\)
\(194\) −5.06679 15.5940i −0.363775 1.11958i
\(195\) 9.14157 + 6.67477i 0.654642 + 0.477990i
\(196\) 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 \(0.124283\pi\)
\(200\) 3.75921 + 5.67967i 0.265816 + 0.401613i
\(201\) 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
\(205\) −0.452421 0.344033i −0.0315985 0.0240283i
\(206\) 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
\(210\) −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
\(213\) 0.825930 1.18461i 0.0565918 0.0811678i
\(214\) 3.93826 2.86131i 0.269214 0.195595i
\(215\) 6.37413 18.2524i 0.434712 1.24481i
\(216\) −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
\(220\) 17.2954 9.06258i 1.16606 0.610999i
\(221\) 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 \(-0.546705\pi\)
−0.699749 + 0.714389i \(0.746705\pi\)
\(224\) −27.5687 + 8.95760i −1.84201 + 0.598505i
\(225\) 14.9998 + 0.0708136i 0.999989 + 0.00472091i
\(226\) −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 \(0.373695\pi\)
\(228\) 7.67954 2.66154i 0.508590 0.176265i
\(229\) −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
\(231\) −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 \(-0.858978\pi\)
0.686883 + 0.726768i \(0.258978\pi\)
\(234\) −10.4900 + 15.6876i −0.685753 + 1.02553i
\(235\) −16.8962 12.8483i −1.10219 0.838131i
\(236\) 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 0.700379 + 0.713771i \(0.253014\pi\)
−0.986163 + 0.165780i \(0.946986\pi\)
\(240\) 7.32478 5.29539i 0.472813 0.341816i
\(241\) 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
\(245\) −4.51015 14.9858i −0.288143 0.957410i
\(246\) 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
\(250\) 1.57426 24.0131i 0.0995649 1.51872i
\(251\) 2.90618 4.00001i 0.183436 0.252478i −0.707389 0.706824i \(-0.750127\pi\)
0.890825 + 0.454346i \(0.150127\pi\)
\(252\) 8.03169 28.4404i 0.505949 1.79157i
\(253\) −7.78428 + 4.29791i −0.489393 + 0.270207i
\(254\) 43.5956i 2.73543i
\(255\) 13.9111 + 19.2423i 0.871145 + 1.20500i
\(256\) 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 \(0.991251\pi\)
\(258\) 30.8440 + 9.36230i 1.92027 + 0.582871i
\(259\) −8.12978 11.1897i −0.505160 0.695293i
\(260\) 13.6960 + 10.4147i 0.849387 + 0.645895i
\(261\) −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 −0.964831 0.262869i \(-0.915331\pi\)
0.0481459 0.998840i \(-0.484669\pi\)
\(270\) 0.914158 + 24.9920i 0.0556339 + 1.52097i
\(271\) −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
\(273\) −18.9360 + 0.368561i −1.14606 + 0.0223063i
\(274\) 39.8760i 2.40900i
\(275\) −16.3511 2.76449i −0.986007 0.166705i
\(276\) 9.74950 7.37751i 0.586851 0.444074i
\(277\) −10.9695 7.96979i −0.659091 0.478858i 0.207265 0.978285i \(-0.433544\pi\)
−0.866356 + 0.499427i \(0.833544\pi\)
\(278\) 5.26171 16.1939i 0.315576 0.971245i
\(279\) 4.28585 0.166899i 0.256587 0.00999196i
\(280\) −10.7594 3.75739i −0.642995 0.224547i
\(281\) 9.35985 6.80033i 0.558362 0.405674i −0.272497 0.962157i \(-0.587850\pi\)
0.830859 + 0.556483i \(0.187850\pi\)
\(282\) 20.2405 29.0303i 1.20530 1.72873i
\(283\) 2.18516 6.72524i 0.129894 0.399774i −0.864867 0.502002i \(-0.832597\pi\)
0.994761 + 0.102228i \(0.0325970\pi\)
\(284\) 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
\(288\) 14.3830 + 18.2578i 0.847527 + 1.07585i
\(289\) −6.36129 + 19.5780i −0.374194 + 1.15165i
\(290\) −16.3700 + 21.5274i −0.961279 + 1.26413i
\(291\) −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 \(-0.854962\pi\)
−0.467823 + 0.883822i \(0.654962\pi\)
\(294\) 24.6535 8.54430i 1.43782 0.498313i
\(295\) 0.00246681 0.113027i 0.000143623 0.00658068i
\(296\) −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
\(300\) 22.7947 + 0.551328i 1.31605 + 0.0318310i
\(301\) 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
\(305\) −6.21737 + 1.87118i −0.356006 + 0.107144i
\(306\) −31.0972 + 24.4975i −1.77771 + 1.40043i
\(307\) −4.60472 −0.262805 −0.131403 0.991329i \(-0.541948\pi\)
−0.131403 + 0.991329i \(0.541948\pi\)
\(308\) −13.8571 + 29.5875i −0.789584 + 1.68591i
\(309\) −4.30855 5.69382i −0.245105 0.323910i
\(310\) 0.150143 6.87942i 0.00852756 0.390725i
\(311\) 19.4975 + 6.33511i 1.10560 + 0.359231i 0.804255 0.594284i \(-0.202564\pi\)
0.301345 + 0.953515i \(0.402564\pi\)
\(312\) −3.94377 + 5.65643i −0.223272 + 0.320232i
\(313\) 16.5721 + 22.8096i 0.936712 + 1.28927i 0.957183 + 0.289482i \(0.0934832\pi\)
−0.0204718 + 0.999790i \(0.506517\pi\)
\(314\) 15.9590 11.5949i 0.900617 0.654336i
\(315\) −20.0501 + 15.0977i −1.12969 + 0.850660i
\(316\) 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
\(321\) −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
\(325\) −3.90497 14.0814i −0.216609 0.781096i
\(326\) −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
\(330\) 3.48008 27.4283i 0.191572 1.50988i
\(331\) −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
\(335\) −5.17291 1.80649i −0.282626 0.0986990i
\(336\) −4.39266 + 14.4716i −0.239639 + 0.789491i
\(337\) 4.52795 + 13.9356i 0.246653 + 0.759121i 0.995360 + 0.0962195i \(0.0306751\pi\)
−0.748707 + 0.662901i \(0.769325\pi\)
\(338\) −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
\(345\) −10.3835 0.0245100i −0.559031 0.00131957i
\(346\) −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 \(0.721406\pi\)
\(348\) −21.0200 14.6556i −1.12679 0.785622i
\(349\) 9.20764 + 2.99174i 0.492874 + 0.160144i 0.544900 0.838501i \(-0.316568\pi\)
−0.0520257 + 0.998646i \(0.516568\pi\)
\(350\) 22.2241 + 33.5777i 1.18793 + 1.79480i
\(351\) 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 \(0.395080\pi\)
\(354\) 0.188453 0.00366796i 0.0100162 0.000194950i
\(355\) −1.78524 + 0.537286i −0.0947506 + 0.0285162i
\(356\) 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 0.999981 0.00612922i \(-0.00195100\pi\)
−0.812604 + 0.582816i \(0.801951\pi\)
\(360\) 0.156257 + 9.13663i 0.00823547 + 0.481543i
\(361\) −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
\(365\) −12.9914 0.283538i −0.680003 0.0148410i
\(366\) −3.54488 10.2283i −0.185294 0.534643i
\(367\) 0.551086 0.179059i 0.0287665 0.00934679i −0.294598 0.955621i \(-0.595186\pi\)
0.323365 + 0.946274i \(0.395186\pi\)
\(368\) −5.06183 + 3.67763i −0.263866 + 0.191710i
\(369\) −0.263682 0.715507i −0.0137267 0.0372478i
\(370\) 14.1624 + 10.7695i 0.736269 + 0.559878i
\(371\) −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 \(-0.338504\pi\)
0.485867 + 0.874032i \(0.338504\pi\)
\(374\) 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
\(378\) −26.5299 32.3612i −1.36455 1.66448i
\(379\) 3.28240 2.38480i 0.168606 0.122499i −0.500283 0.865862i \(-0.666771\pi\)
0.668888 + 0.743363i \(0.266771\pi\)
\(380\) −9.90611 3.45942i −0.508173 0.177465i
\(381\) 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 \(-0.0428988\pi\)
0.178428 + 0.983953i \(0.442899\pi\)
\(384\) 10.8194 + 14.2981i 0.552128 + 0.729645i
\(385\) 24.5780 12.8786i 1.25261 0.656352i
\(386\) 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 0.915639 0.402001i \(-0.131685\pi\)
0.977058 0.212973i \(-0.0683148\pi\)
\(390\) 23.1885 7.47395i 1.17420 0.378458i
\(391\) −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
\(400\) −11.6575 0.509091i −0.582874 0.0254545i
\(401\) 14.9545 + 20.5831i 0.746790 + 1.02787i 0.998199 + 0.0599878i \(0.0191062\pi\)
−0.251409 + 0.967881i \(0.580894\pi\)
\(402\) 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
\(405\) 16.9180 + 10.8988i 0.840660 + 0.541563i
\(406\) 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 \(0.364072\pi\)
\(410\) −1.17146 + 0.352563i −0.0578543 + 0.0174119i
\(411\) −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
\(415\) 2.61704 0.787626i 0.128465 0.0386630i
\(416\) 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 \(-0.842179\pi\)
0.879585 0.475742i \(-0.157821\pi\)
\(420\) −30.9188 + 22.3525i −1.50868 + 1.09069i
\(421\) 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
\(423\) −9.84751 26.7215i −0.478802 1.29924i
\(424\) 4.40955 + 6.06923i 0.214147 + 0.294748i
\(425\) 1.33739 30.6243i 0.0648729 1.48550i
\(426\) −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 0.964428 0.264346i \(-0.0851560\pi\)
0.0466170 + 0.998913i \(0.485156\pi\)
\(432\) 12.1057 0.707573i 0.582435 0.0340431i
\(433\) 2.14388 0.696587i 0.103028 0.0334758i −0.257049 0.966398i \(-0.582750\pi\)
0.360077 + 0.932922i \(0.382750\pi\)
\(434\) 6.76760 + 9.31480i 0.324855 + 0.447125i
\(435\) 6.67620 + 20.7135i 0.320099 + 0.993134i
\(436\) −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 \(0.0484159\pi\)
−0.988455 + 0.151517i \(0.951584\pi\)
\(440\) 1.46638 9.99542i 0.0699067 0.476513i
\(441\) 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 \(0.0378417\pi\)
\(444\) −9.64159 + 13.8286i −0.457570 + 0.656278i
\(445\) −3.14626 1.09874i −0.149147 0.0520853i
\(446\) −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 0.231976 + 0.972721i \(0.425481\pi\)
−0.996798 + 0.0799647i \(0.974519\pi\)
\(450\) 19.1004 26.0302i 0.900403 1.22707i
\(451\) 0.159474 + 0.827807i 0.00750934 + 0.0389799i
\(452\) −4.27518 −0.201088
\(453\) −0.179461 9.22037i −0.00843180 0.433211i
\(454\) 1.65438 5.09167i 0.0776441 0.238964i
\(455\) 19.4629 + 14.8001i 0.912435 + 0.693839i
\(456\) 1.22139 4.02385i 0.0571966 0.188434i
\(457\) 13.0649 9.49221i 0.611150 0.444027i −0.238669 0.971101i \(-0.576711\pi\)
0.849819 + 0.527074i \(0.176711\pi\)
\(458\) −24.8308 + 8.06802i −1.16027 + 0.376994i
\(459\) 1.85880 + 31.8018i 0.0867615 + 1.48438i
\(460\) −15.7802 0.344403i −0.735757 0.0160579i
\(461\) −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
\(465\) −4.47200 3.26525i −0.207384 0.151422i
\(466\) 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 \(0.497569\pi\)
\(468\) 7.98232 + 21.6602i 0.368983 + 1.00124i
\(469\) 8.71945 2.83312i 0.402627 0.130821i
\(470\) −43.7496 + 13.1669i −2.01802 + 0.607344i
\(471\) −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
\(475\) 4.91846 + 7.43113i 0.225674 + 0.340964i
\(476\) −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 −0.793497 0.608574i \(-0.791742\pi\)
0.333584 + 0.942720i \(0.391742\pi\)
\(480\) 0.0708282 30.0060i 0.00323285 1.36958i
\(481\) 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 \(-0.637229\pi\)
−0.872080 + 0.489363i \(0.837229\pi\)
\(488\) −1.22229 3.76183i −0.0553307 0.170290i
\(489\) −38.3888 11.6524i −1.73600 0.526940i
\(490\) −31.8014 11.1057i −1.43664 0.501706i
\(491\) 4.81815 + 14.8287i 0.217440 + 0.669212i 0.998971 + 0.0453457i \(0.0144389\pi\)
−0.781531 + 0.623866i \(0.785561\pi\)
\(492\) −0.379579 1.09523i −0.0171128 0.0493768i
\(493\) −20.2487 + 27.8700i −0.911958 + 1.25520i
\(494\) −11.2115 −0.504431
\(495\) −16.5038 14.9206i −0.741789 0.670633i
\(496\) −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 0.999965 + 0.00834366i \(0.00265590\pi\)
−0.804085 + 0.594515i \(0.797344\pi\)
\(500\) −22.6317 18.8231i −1.01212 0.841796i
\(501\) 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 \(-0.605247\pi\)
−0.818596 + 0.574370i \(0.805247\pi\)
\(504\) −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 0.333622 0.942707i \(-0.391729\pi\)
−0.284203 + 0.958764i \(0.591729\pi\)
\(510\) 51.1070 + 0.120636i 2.26306 + 0.00534187i
\(511\) 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
\(515\) −0.201135 + 9.21583i −0.00886308 + 0.406098i
\(516\) 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
\(520\) 8.52442 2.56551i 0.373820 0.112505i
\(521\) −6.84744 + 2.22487i −0.299992 + 0.0974733i −0.455146 0.890417i \(-0.650413\pi\)
0.155154 + 0.987890i \(0.450413\pi\)
\(522\) −34.0457 + 12.5467i −1.49014 + 0.549153i
\(523\) 21.1158 15.3415i 0.923328 0.670837i −0.0210218 0.999779i \(-0.506692\pi\)
0.944350 + 0.328942i \(0.106692\pi\)
\(524\) 9.32725 + 28.7063i 0.407463 + 1.25404i
\(525\) 32.3929 + 0.783476i 1.41374 + 0.0341937i
\(526\) 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
\(530\) 0.578353 26.4996i 0.0251221 1.15107i
\(531\) 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
\(535\) −3.06108 + 4.02549i −0.132342 + 0.174037i
\(536\) 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
\(540\) 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
\(543\) 32.9314 + 22.9604i 1.41322 + 0.985327i
\(544\) 38.4266 27.9186i 1.64753 1.19700i
\(545\) 29.5474 + 10.3186i 1.26567 + 0.442000i
\(546\) −23.3152 + 33.4403i −0.997799 + 1.43111i
\(547\) 11.1317 34.2598i 0.475956 1.46484i −0.368708 0.929545i \(-0.620200\pi\)
0.844664 0.535297i \(-0.179800\pi\)
\(548\) −39.4616 28.6705i −1.68572 1.22474i
\(549\) −8.38318 2.36745i −0.357786 0.101040i
\(550\) −25.5006 + 24.9752i −1.08735 + 1.06495i
\(551\) 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
\(555\) 13.6269 4.39213i 0.578431 0.186435i
\(556\) −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 \(-0.0278980\pi\)
\(558\) 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 \(-0.680069\pi\)
0.968530 + 0.248898i \(0.0800686\pi\)
\(564\) −14.1758 40.9027i −0.596911 1.72231i
\(565\) 2.89016 + 2.19775i 0.121590 + 0.0924601i
\(566\) −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 −0.371259 0.928529i \(-0.621074\pi\)
0.846131 0.532975i \(-0.178926\pi\)
\(570\) −12.0406 + 8.70464i −0.504324 + 0.364597i
\(571\) 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
\(575\) 10.4909 + 8.34500i 0.437500 + 0.348010i
\(576\) 35.9981 1.40183i 1.49992 0.0584095i
\(577\) −24.0939 33.1623i −1.00304 1.38057i −0.923441 0.383740i \(-0.874636\pi\)
−0.0795990 0.996827i \(-0.525364\pi\)
\(578\) 26.0440 + 35.8464i 1.08329 + 1.49101i
\(579\) −25.1277 17.5196i −1.04427 0.728088i
\(580\) 9.53379 + 31.6779i 0.395869 + 1.31535i
\(581\) −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
\(585\) 5.73861 18.7465i 0.237262 0.775072i
\(586\) −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 \(-0.368778\pi\)
\(588\) 9.27018 30.5406i 0.382296 1.25947i
\(589\) 1.49775 + 2.06148i 0.0617137 + 0.0849416i
\(590\) −0.193697 0.147292i −0.00797438 0.00606392i
\(591\) 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 0.995780 0.0917761i \(-0.0292544\pi\)
−0.394997 + 0.918682i \(0.629254\pi\)
\(600\) 7.16289 9.37357i 0.292424 0.382675i
\(601\) 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
\(603\) −4.54908 5.77461i −0.185253 0.235160i
\(604\) 14.0185i 0.570403i
\(605\) 15.3314 + 19.2340i 0.623310 + 0.781975i
\(606\) 23.6387 + 31.2389i 0.960256 + 1.26899i
\(607\) 15.2824 + 11.1033i 0.620293 + 0.450669i 0.853024 0.521872i \(-0.174766\pi\)
−0.232731 + 0.972541i \(0.574766\pi\)
\(608\) −4.26699 + 13.1325i −0.173049 + 0.532591i
\(609\) −29.8709 20.8266i −1.21043 0.843937i
\(610\) −4.60758 + 13.1939i −0.186555 + 0.534204i
\(611\) −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 0.743807 + 0.668394i \(0.233018\pi\)
−0.994625 + 0.103544i \(0.966982\pi\)
\(614\) −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 \(0.546311\pi\)
\(618\) −15.3658 + 0.299073i −0.618105 + 0.0120305i
\(619\) 12.0091 36.9603i 0.482688 1.48556i −0.352615 0.935769i \(-0.614707\pi\)
0.835302 0.549791i \(-0.185293\pi\)
\(620\) −6.69997 5.09483i −0.269077 0.204613i
\(621\) −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
\(625\) 5.62330 + 24.3594i 0.224932 + 0.974374i
\(626\) 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
\(630\) 0.923777 + 54.0149i 0.0368042 + 2.15201i
\(631\) 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
\(633\) −28.3909 8.61768i −1.12844 0.342522i
\(634\) −23.8299 + 7.74279i −0.946405 + 0.307506i
\(635\) −13.0522 43.3685i −0.517961 1.72103i
\(636\) 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
\(640\) 0.505082 23.1424i 0.0199651 0.914783i
\(641\) −10.7142 3.48126i −0.423186 0.137501i 0.0896793 0.995971i \(-0.471416\pi\)
−0.512865 + 0.858469i \(0.671416\pi\)
\(642\) −6.91641 4.82226i −0.272969 0.190319i
\(643\) −3.97759 5.47468i −0.156861 0.215900i 0.723352 0.690479i \(-0.242600\pi\)
−0.880213 + 0.474579i \(0.842600\pi\)
\(644\) 21.3666 15.5237i 0.841961 0.611720i
\(645\) −33.4864 0.0790434i −1.31852 0.00311233i
\(646\) −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
\(651\) 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 \(-0.0642058\pi\)
−0.910374 + 0.413787i \(0.864206\pi\)
\(654\) −15.1559 + 49.9310i −0.592642 + 1.95246i
\(655\) 8.45160 24.2013i 0.330231 0.945622i
\(656\) 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 \(0.761451\pi\)
\(660\) −24.6411 23.1646i −0.959154 0.901683i
\(661\) −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
\(665\) −14.0773 4.91608i −0.545893 0.190637i
\(666\) 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 \(-0.332128\pi\)
−0.666311 + 0.745674i \(0.732128\pi\)
\(674\) 29.9952 + 9.74602i 1.15537 + 0.375403i
\(675\) −8.39183 24.5882i −0.323002 0.946398i
\(676\) −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 \(0.774171\pi\)
\(678\) −3.46221 + 4.96574i −0.132965 + 0.190708i
\(679\) −27.1068 8.80752i −1.04026 0.338002i
\(680\) 18.6696 + 0.407464i 0.715948 + 0.0156255i
\(681\) −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 \(0.410495\pi\)
\(684\) −8.71148 11.0584i −0.333092 0.422827i
\(685\) 11.9386 + 39.6683i 0.456150 + 1.51565i
\(686\) −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
\(690\) −13.1795 + 18.0502i −0.501734 + 0.687161i
\(691\) −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
\(693\) 37.0933 + 3.15763i 1.40906 + 0.119949i
\(694\) 19.5992 0.743975
\(695\) −0.385971 + 17.6848i −0.0146407 + 0.670824i
\(696\) −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
\(700\) 49.2076 + 2.14893i 1.85987 + 0.0812220i
\(701\) 14.2187 43.7608i 0.537034 1.65282i −0.202177 0.979349i \(-0.564802\pi\)
0.739212 0.673473i \(-0.235198\pi\)
\(702\) 31.6233 + 8.26962i 1.19355 + 0.312117i
\(703\) −6.58856 −0.248492
\(704\) −39.5225 4.91981i −1.48956 0.185422i
\(705\) −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
\(708\) 0.131866 0.189132i 0.00495585 0.00710801i
\(709\) 36.7685 26.7139i 1.38087 1.00326i 0.384072 0.923303i \(-0.374521\pi\)
0.996798 0.0799582i \(-0.0254787\pi\)
\(710\) −1.32301 + 3.78845i −0.0496516 + 0.142178i
\(711\) −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
\(715\) −9.61888 + 19.4230i −0.359726 + 0.726380i
\(716\) 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 −0.115313 0.993329i \(-0.536787\pi\)
0.490574 + 0.871399i \(0.336787\pi\)
\(720\) −12.8207 8.98389i −0.477799 0.334810i
\(721\) −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
\(730\) −16.9299 + 22.2638i −0.626605 + 0.824018i
\(731\) −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 0.967457 + 0.253035i \(0.0814286\pi\)
−0.633959 + 0.773366i \(0.718571\pi\)
\(734\) 0.385408 1.18616i 0.0142257 0.0437821i
\(735\) −21.9670 + 15.8809i −0.810265 + 0.585775i
\(736\) 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 \(0.123444\pi\)
\(740\) 20.8402 6.27207i 0.766100 0.230566i
\(741\) −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 \(-0.163920\pi\)
−0.737344 + 0.675517i \(0.763920\pi\)
\(744\) 1.92927 2.76709i 0.0707304 0.101446i
\(745\) −4.33626 14.4081i −0.158868 0.527870i
\(746\) 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
\(750\) −40.1916 + 11.0436i −1.46759 + 0.403255i
\(751\) 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
\(753\) −8.19456 2.48735i −0.298627 0.0906441i
\(754\) 20.7767 + 28.5967i 0.756644 + 1.04143i
\(755\) −7.20649 + 9.47692i −0.262271 + 0.344901i
\(756\) −51.0996 + 2.98675i −1.85847 + 0.108627i
\(757\) 3.58874 4.93948i 0.130435 0.179528i −0.738804 0.673920i \(-0.764609\pi\)
0.869239 + 0.494392i \(0.164609\pi\)
\(758\) 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 0.0944811 0.995527i \(-0.469881\pi\)
−0.917606 + 0.397492i \(0.869881\pi\)
\(762\) 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
\(765\) 23.6008 33.6802i 0.853289 1.21771i
\(766\) 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 \(0.136519\pi\)
−0.909429 + 0.415859i \(0.863481\pi\)
\(770\) 8.66907 59.0919i 0.312412 2.12953i
\(771\) −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 \(-0.0792409\pi\)
\(774\) −2.17248 55.7880i −0.0780883 2.00526i
\(775\) 1.91029 + 6.88853i 0.0686195 + 0.247443i
\(776\) −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
\(780\) 9.27609 28.3212i 0.332137 1.01406i
\(781\) 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
\(785\) −12.4044 + 16.3125i −0.442732 + 0.582217i
\(786\) 40.8968 + 12.4137i 1.45874 + 0.442781i
\(787\) 2.48490 1.80539i 0.0885772 0.0643551i −0.542615 0.839981i \(-0.682566\pi\)
0.631192 + 0.775626i \(0.282566\pi\)
\(788\) 27.2362 8.84958i 0.970250 0.315253i
\(789\) 12.0503 4.17632i 0.429001 0.148681i
\(790\) −42.3738 0.924808i −1.50759 0.0329032i
\(791\) −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
\(795\) −17.2262 12.5778i −0.610950 0.446088i
\(796\) −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 \(-0.0100104\pi\)
\(798\) 7.22072 23.7886i 0.255611 0.842108i
\(799\) −55.3489 + 17.9839i −1.95810 + 0.636226i
\(800\) −24.1151 + 30.3162i −0.852597 + 1.07184i
\(801\) −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
\(805\) −22.4248 0.489421i −0.790370 0.0172498i
\(806\) −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 −0.206134 0.978524i \(-0.566088\pi\)
0.866932 + 0.498426i \(0.166088\pi\)
\(810\) 40.3823 15.6712i 1.41889 0.550631i
\(811\) 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
\(816\) −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
\(820\) −0.493371 + 1.41278i −0.0172293 + 0.0493362i
\(821\) 14.0019 + 43.0935i 0.488670 + 1.50397i 0.826594 + 0.562799i \(0.190275\pi\)
−0.337924 + 0.941174i \(0.609725\pi\)
\(822\) −65.2591 + 22.6172i −2.27617 + 0.788865i
\(823\) 16.0956 22.1537i 0.561057 0.772229i −0.430403 0.902637i \(-0.641629\pi\)
0.991460 + 0.130408i \(0.0416287\pi\)
\(824\) −5.61560 −0.195629
\(825\) 4.74989 + 28.3273i 0.165370 + 0.986232i
\(826\) 0.407166 0.0141671
\(827\) −0.625494 + 0.860919i −0.0217506 + 0.0299371i −0.819754 0.572716i \(-0.805890\pi\)
0.798003 + 0.602653i \(0.205890\pi\)
\(828\) −17.6035 11.7711i −0.611763 0.409075i
\(829\) −6.99269 21.5213i −0.242866 0.747466i −0.995980 0.0895753i \(-0.971449\pi\)
0.753114 0.657890i \(-0.228551\pi\)
\(830\) 1.93944 5.55362i 0.0673190 0.192769i
\(831\) −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 0.500304 0.865850i \(-0.333222\pi\)
−0.104179 + 0.994559i \(0.533222\pi\)
\(840\) −0.0465941 + 19.7394i −0.00160765 + 0.681073i
\(841\) −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
\(845\) 9.96737 + 0.217538i 0.342888 + 0.00748352i
\(846\) −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
\(850\) −51.6353 41.0734i −1.77108 1.40881i
\(851\) −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 \(-0.684367\pi\)
0.626793 + 0.779186i \(0.284367\pi\)
\(854\) −7.22609 22.2396i −0.247272 0.761024i
\(855\) 0.204443 + 11.9541i 0.00699180 + 0.408823i
\(856\) −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 \(0.651719\pi\)
\(860\) −50.8903 1.11068i −1.73535 0.0378739i
\(861\) −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 \(-0.855227\pi\)
0.140197 + 0.990124i \(0.455227\pi\)
\(864\) 21.7220 33.8941i 0.738997 1.15310i
\(865\) 1.05870 1.39224i 0.0359967 0.0473376i
\(866\) 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
\(870\) 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
\(873\) 0.889270 + 22.8359i 0.0300972 + 0.772878i
\(874\) 8.32070 6.04534i 0.281452 0.204487i
\(875\) −32.1612 26.7490i −1.08725 0.904281i
\(876\) −21.7390 15.1569i −0.734494 0.512103i
\(877\) 1.44357 4.44286i 0.0487460 0.150025i −0.923721 0.383067i \(-0.874868\pi\)
0.972467 + 0.233042i \(0.0748679\pi\)
\(878\) 11.0562 + 8.03282i 0.373130 + 0.271094i
\(879\) 25.6917 + 33.9519i 0.866558 + 1.14517i
\(880\) 12.3770 + 12.0976i 0.417229 + 0.407811i
\(881\) 0.351265i 0.0118344i 0.999982 + 0.00591720i \(0.00188352\pi\)
−0.999982 + 0.00591720i \(0.998116\pi\)
\(882\) −27.9663 35.5005i −0.941676 1.19537i
\(883\) 1.22742 + 0.398811i 0.0413058 + 0.0134211i 0.329597 0.944122i \(-0.393087\pi\)
−0.288291 + 0.957543i \(0.593087\pi\)
\(884\) 44.8654 14.5777i 1.50899 0.490300i
\(885\) −0.186373 + 0.0600704i −0.00626487 + 0.00201924i
\(886\) −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 \(0.354219\pi\)
\(888\) 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
\(895\) 23.8333 31.3421i 0.796660 1.04765i
\(896\) 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
\(900\) −12.0266 37.6174i −0.400886 1.25391i
\(901\) 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
\(905\) −14.9363 49.6287i −0.496499 1.64971i
\(906\) −16.2828 11.3527i −0.540960 0.377168i
\(907\) 27.1646 + 37.3889i 0.901986 + 1.24148i 0.969830 + 0.243782i \(0.0783881\pi\)
−0.0678437 + 0.997696i \(0.521612\pi\)
\(908\) −3.84926 5.29805i −0.127742 0.175822i
\(909\) 31.5001 1.22667i 1.04479 0.0406860i
\(910\) 50.3955 15.1671i 1.67060 0.502783i
\(911\) 9.37828 12.9081i 0.310716 0.427664i −0.624888 0.780714i \(-0.714855\pi\)
0.935604 + 0.353050i \(0.114855\pi\)
\(912\) 4.34713 + 5.74480i 0.143948 + 0.190229i
\(913\) −3.67102 1.71930i −0.121493 0.0569005i
\(914\) 34.7595i 1.14974i
\(915\) 6.58870 + 9.11373i 0.217816 + 0.301291i
\(916\) −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 0.960218 0.279253i \(-0.0900869\pi\)
−0.562309 + 0.826927i \(0.690087\pi\)
\(920\) −4.94309 + 6.50043i −0.162969 + 0.214313i
\(921\) 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 0.997112 + 0.0759474i \(0.0241981\pi\)
−0.235894 + 0.971779i \(0.575802\pi\)
\(930\) −11.3437 + 3.65620i −0.371974 + 0.119892i
\(931\) 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
\(935\) −31.7807 + 32.5146i −1.03934 + 1.06334i
\(936\) 11.4939 + 3.24593i 0.375690 + 0.106096i
\(937\) −41.5896 30.2166i −1.35867 0.987133i −0.998528 0.0542367i \(-0.982727\pi\)
−0.360144 0.932897i \(-0.617273\pi\)
\(938\) 6.09805 18.7679i 0.199108 0.612792i
\(939\) 27.9295 40.0584i 0.911445 1.30726i
\(940\) −18.4255 + 52.7618i −0.600974 + 1.72090i
\(941\) −9.79828 + 7.11887i −0.319415 + 0.232068i −0.735926 0.677062i \(-0.763253\pi\)
0.416511 + 0.909131i \(0.363253\pi\)
\(942\) −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
\(945\) 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 \(0.374506\pi\)
\(948\) −0.781485 40.1513i −0.0253814 1.30405i
\(949\) −5.24834 + 16.1527i −0.170368 + 0.524340i
\(950\) 19.1627 + 0.836851i 0.621721 + 0.0271510i
\(951\) −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 \(-0.608066\pi\)
0.284820 + 0.958581i \(0.408066\pi\)
\(954\) 19.7671 29.5614i 0.639985 0.957084i
\(955\) 0.600891 27.5322i 0.0194444 0.890922i
\(956\) 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
\(960\) −37.5616 27.4258i −1.21229 0.885163i
\(961\) −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
\(965\) 11.3969 + 37.8683i 0.366878 + 1.21902i
\(966\) −0.727732 37.3896i −0.0234144 1.20299i
\(967\) 13.4682 0.433109 0.216555 0.976270i \(-0.430518\pi\)
0.216555 + 0.976270i \(0.430518\pi\)
\(968\) −11.5108 + 9.59330i −0.369970 + 0.308340i
\(969\) −15.0917 + 11.4200i −0.484814 + 0.366862i
\(970\) 36.6549 + 0.799993i 1.17692 + 0.0256862i
\(971\) 23.4682 + 7.62527i 0.753129 + 0.244707i 0.660327 0.750978i \(-0.270418\pi\)
0.0928021 + 0.995685i \(0.470418\pi\)
\(972\) 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
\(975\) −20.8301 + 14.3775i −0.667097 + 0.460448i
\(976\) 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
\(981\) 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 −0.987196 0.159512i \(-0.949008\pi\)
0.704899 0.709307i \(-0.250992\pi\)
\(984\) −0.573867 0.174190i −0.0182942 0.00555297i
\(985\) −22.9619 8.01877i −0.731626 0.255499i
\(986\) 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
\(990\) −46.8617 + 9.86168i −1.48936 + 0.313425i
\(991\) 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
\(995\) −19.2342 + 55.0773i −0.609764 + 1.74607i
\(996\) 5.33343 + 1.61889i 0.168996 + 0.0512965i
\(997\) 2.41532 + 7.43359i 0.0764939 + 0.235424i 0.981991 0.188929i \(-0.0605016\pi\)
−0.905497 + 0.424353i \(0.860502\pi\)
\(998\) 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.29.17 yes 80
3.2 odd 2 inner 165.2.r.a.29.3 80
5.2 odd 4 825.2.bi.h.326.17 80
5.3 odd 4 825.2.bi.h.326.4 80
5.4 even 2 inner 165.2.r.a.29.4 yes 80
11.8 odd 10 inner 165.2.r.a.74.18 yes 80
15.2 even 4 825.2.bi.h.326.3 80
15.8 even 4 825.2.bi.h.326.18 80
15.14 odd 2 inner 165.2.r.a.29.18 yes 80
33.8 even 10 inner 165.2.r.a.74.4 yes 80
55.8 even 20 825.2.bi.h.701.18 80
55.19 odd 10 inner 165.2.r.a.74.3 yes 80
55.52 even 20 825.2.bi.h.701.3 80
165.8 odd 20 825.2.bi.h.701.4 80
165.74 even 10 inner 165.2.r.a.74.17 yes 80
165.107 odd 20 825.2.bi.h.701.17 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.r.a.29.3 80 3.2 odd 2 inner
165.2.r.a.29.4 yes 80 5.4 even 2 inner
165.2.r.a.29.17 yes 80 1.1 even 1 trivial
165.2.r.a.29.18 yes 80 15.14 odd 2 inner
165.2.r.a.74.3 yes 80 55.19 odd 10 inner
165.2.r.a.74.4 yes 80 33.8 even 10 inner
165.2.r.a.74.17 yes 80 165.74 even 10 inner
165.2.r.a.74.18 yes 80 11.8 odd 10 inner
825.2.bi.h.326.3 80 15.2 even 4
825.2.bi.h.326.4 80 5.3 odd 4
825.2.bi.h.326.17 80 5.2 odd 4
825.2.bi.h.326.18 80 15.8 even 4
825.2.bi.h.701.3 80 55.52 even 20
825.2.bi.h.701.4 80 165.8 odd 20
825.2.bi.h.701.17 80 165.107 odd 20
825.2.bi.h.701.18 80 55.8 even 20