Properties

Label 136.3.q.a.5.5
Level $136$
Weight $3$
Character 136.5
Analytic conductor $3.706$
Analytic rank $0$
Dimension $272$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [136,3,Mod(5,136)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(136, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([0, 8, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("136.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.q (of order \(16\), degree \(8\), 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: \(3.70573159530\)
Analytic rank: \(0\)
Dimension: \(272\)
Relative dimension: \(34\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 136.5
Dual form 136.3.q.a.109.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.83427 - 0.797164i) q^{2} +(-2.62580 + 1.75450i) q^{3} +(2.72906 + 2.92442i) q^{4} +(3.72340 + 0.740630i) q^{5} +(6.21503 - 1.12503i) q^{6} +(-0.824370 - 4.14439i) q^{7} +(-2.67457 - 7.53967i) q^{8} +(0.372384 - 0.899013i) q^{9} +O(q^{10})\) \(q+(-1.83427 - 0.797164i) q^{2} +(-2.62580 + 1.75450i) q^{3} +(2.72906 + 2.92442i) q^{4} +(3.72340 + 0.740630i) q^{5} +(6.21503 - 1.12503i) q^{6} +(-0.824370 - 4.14439i) q^{7} +(-2.67457 - 7.53967i) q^{8} +(0.372384 - 0.899013i) q^{9} +(-6.23929 - 4.32667i) q^{10} +(-5.80130 + 8.68226i) q^{11} +(-12.2969 - 2.89080i) q^{12} +(-4.77706 + 4.77706i) q^{13} +(-1.79165 + 8.25907i) q^{14} +(-11.0763 + 4.58796i) q^{15} +(-1.10448 + 15.9618i) q^{16} +(12.0091 + 12.0325i) q^{17} +(-1.39971 + 1.35218i) q^{18} +(-30.8540 + 12.7801i) q^{19} +(7.99545 + 12.9100i) q^{20} +(9.43597 + 9.43597i) q^{21} +(17.5623 - 11.3010i) q^{22} +(-4.79130 + 7.17069i) q^{23} +(20.2513 + 15.1051i) q^{24} +(-9.78183 - 4.05177i) q^{25} +(12.5705 - 4.95429i) q^{26} +(-4.94537 - 24.8621i) q^{27} +(9.87019 - 13.7211i) q^{28} +(-4.58881 + 23.0695i) q^{29} +(23.9743 + 0.414107i) q^{30} +(-20.8291 + 13.9175i) q^{31} +(14.7501 - 28.3978i) q^{32} -32.9763i q^{33} +(-12.4360 - 31.6440i) q^{34} -16.0418i q^{35} +(3.64535 - 1.36445i) q^{36} +(-7.52786 + 5.02995i) q^{37} +(66.7822 + 1.15353i) q^{38} +(4.16223 - 20.9249i) q^{39} +(-4.37439 - 30.0541i) q^{40} +(-0.560733 - 2.81899i) q^{41} +(-9.78605 - 24.8301i) q^{42} +(-6.97124 - 2.88758i) q^{43} +(-41.2227 + 6.72895i) q^{44} +(2.05237 - 3.07159i) q^{45} +(14.5047 - 9.33349i) q^{46} +(50.6376 + 50.6376i) q^{47} +(-25.1049 - 43.8503i) q^{48} +(28.7737 - 11.9185i) q^{49} +(14.7126 + 15.2297i) q^{50} +(-52.6445 - 10.5249i) q^{51} +(-27.0070 - 0.933262i) q^{52} +(22.9067 - 9.48825i) q^{53} +(-10.7480 + 49.5459i) q^{54} +(-28.0309 + 28.0309i) q^{55} +(-29.0425 + 17.3000i) q^{56} +(58.5935 - 87.6914i) q^{57} +(26.8073 - 38.6576i) q^{58} +(20.7368 - 50.0631i) q^{59} +(-43.6451 - 19.8710i) q^{60} +(2.47345 + 12.4349i) q^{61} +(49.3006 - 8.92426i) q^{62} +(-4.03284 - 0.802183i) q^{63} +(-49.6933 + 40.3308i) q^{64} +(-21.3249 + 14.2489i) q^{65} +(-26.2875 + 60.4872i) q^{66} +54.2042 q^{67} +(-2.41450 + 67.9571i) q^{68} -27.2351i q^{69} +(-12.7879 + 29.4248i) q^{70} +(68.2615 + 102.161i) q^{71} +(-7.77423 - 0.403173i) q^{72} +(14.3495 - 72.1399i) q^{73} +(17.8178 - 3.22533i) q^{74} +(32.7939 - 6.52312i) q^{75} +(-121.577 - 55.3523i) q^{76} +(40.7651 + 16.8855i) q^{77} +(-24.3153 + 35.0639i) q^{78} +(-78.0068 - 52.1225i) q^{79} +(-15.9342 + 58.6142i) q^{80} +(62.7988 + 62.7988i) q^{81} +(-1.21867 + 5.61778i) q^{82} +(5.40373 + 13.0458i) q^{83} +(-1.84344 + 53.3460i) q^{84} +(35.8031 + 53.6961i) q^{85} +(10.4852 + 10.8538i) q^{86} +(-28.4262 - 68.6269i) q^{87} +(80.9774 + 20.5186i) q^{88} +(-114.977 + 114.977i) q^{89} +(-6.21315 + 3.99803i) q^{90} +(23.7361 + 15.8599i) q^{91} +(-34.0458 + 5.55744i) q^{92} +(30.2745 - 73.0892i) q^{93} +(-52.5163 - 133.249i) q^{94} +(-124.347 + 24.7341i) q^{95} +(11.0931 + 100.446i) q^{96} +(-39.8758 - 7.93180i) q^{97} +(-62.2796 - 1.07575i) q^{98} +(5.64516 + 8.44858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 272 q - 8 q^{2} - 8 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 272 q - 8 q^{2} - 8 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 8 q^{12} - 8 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} + 136 q^{24} - 16 q^{25} - 232 q^{26} + 232 q^{28} - 200 q^{30} - 16 q^{31} + 32 q^{32} + 56 q^{34} - 200 q^{36} + 192 q^{38} - 16 q^{39} - 456 q^{40} - 16 q^{41} + 424 q^{42} - 360 q^{44} + 200 q^{46} - 16 q^{47} - 80 q^{48} - 16 q^{49} - 16 q^{52} - 456 q^{54} - 16 q^{55} - 448 q^{56} - 336 q^{57} - 512 q^{58} - 736 q^{60} - 288 q^{62} - 16 q^{63} - 152 q^{64} + 144 q^{65} - 80 q^{66} + 80 q^{68} + 288 q^{70} - 16 q^{71} + 512 q^{72} + 464 q^{73} + 328 q^{74} + 496 q^{76} + 1136 q^{78} - 16 q^{79} + 520 q^{80} - 464 q^{81} + 592 q^{82} + 1184 q^{86} - 16 q^{87} - 840 q^{88} - 16 q^{89} + 1512 q^{90} - 1016 q^{92} + 664 q^{94} - 16 q^{95} - 768 q^{96} - 16 q^{97} + 400 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.83427 0.797164i −0.917133 0.398582i
\(3\) −2.62580 + 1.75450i −0.875266 + 0.584834i −0.910021 0.414562i \(-0.863935\pi\)
0.0347554 + 0.999396i \(0.488935\pi\)
\(4\) 2.72906 + 2.92442i 0.682265 + 0.731105i
\(5\) 3.72340 + 0.740630i 0.744679 + 0.148126i 0.552825 0.833297i \(-0.313550\pi\)
0.191855 + 0.981423i \(0.438550\pi\)
\(6\) 6.21503 1.12503i 1.03584 0.187505i
\(7\) −0.824370 4.14439i −0.117767 0.592056i −0.993928 0.110036i \(-0.964903\pi\)
0.876160 0.482020i \(-0.160097\pi\)
\(8\) −2.67457 7.53967i −0.334322 0.942459i
\(9\) 0.372384 0.899013i 0.0413760 0.0998904i
\(10\) −6.23929 4.32667i −0.623929 0.432667i
\(11\) −5.80130 + 8.68226i −0.527391 + 0.789297i −0.995539 0.0943535i \(-0.969922\pi\)
0.468147 + 0.883650i \(0.344922\pi\)
\(12\) −12.2969 2.89080i −1.02474 0.240900i
\(13\) −4.77706 + 4.77706i −0.367466 + 0.367466i −0.866552 0.499086i \(-0.833669\pi\)
0.499086 + 0.866552i \(0.333669\pi\)
\(14\) −1.79165 + 8.25907i −0.127975 + 0.589933i
\(15\) −11.0763 + 4.58796i −0.738421 + 0.305864i
\(16\) −1.10448 + 15.9618i −0.0690301 + 0.997615i
\(17\) 12.0091 + 12.0325i 0.706419 + 0.707794i
\(18\) −1.39971 + 1.35218i −0.0777618 + 0.0751210i
\(19\) −30.8540 + 12.7801i −1.62389 + 0.672639i −0.994528 0.104471i \(-0.966685\pi\)
−0.629365 + 0.777109i \(0.716685\pi\)
\(20\) 7.99545 + 12.9100i 0.399773 + 0.645500i
\(21\) 9.43597 + 9.43597i 0.449332 + 0.449332i
\(22\) 17.5623 11.3010i 0.798287 0.513681i
\(23\) −4.79130 + 7.17069i −0.208317 + 0.311769i −0.920885 0.389835i \(-0.872532\pi\)
0.712568 + 0.701604i \(0.247532\pi\)
\(24\) 20.2513 + 15.1051i 0.843802 + 0.629379i
\(25\) −9.78183 4.05177i −0.391273 0.162071i
\(26\) 12.5705 4.95429i 0.483481 0.190550i
\(27\) −4.94537 24.8621i −0.183162 0.920818i
\(28\) 9.87019 13.7211i 0.352507 0.490039i
\(29\) −4.58881 + 23.0695i −0.158235 + 0.795501i 0.817395 + 0.576078i \(0.195417\pi\)
−0.975630 + 0.219423i \(0.929583\pi\)
\(30\) 23.9743 + 0.414107i 0.799142 + 0.0138036i
\(31\) −20.8291 + 13.9175i −0.671905 + 0.448952i −0.844154 0.536101i \(-0.819897\pi\)
0.172249 + 0.985053i \(0.444897\pi\)
\(32\) 14.7501 28.3978i 0.460941 0.887431i
\(33\) 32.9763i 0.999281i
\(34\) −12.4360 31.6440i −0.365766 0.930707i
\(35\) 16.0418i 0.458336i
\(36\) 3.64535 1.36445i 0.101260 0.0379015i
\(37\) −7.52786 + 5.02995i −0.203456 + 0.135945i −0.653124 0.757251i \(-0.726542\pi\)
0.449669 + 0.893195i \(0.351542\pi\)
\(38\) 66.7822 + 1.15353i 1.75743 + 0.0303560i
\(39\) 4.16223 20.9249i 0.106724 0.536537i
\(40\) −4.37439 30.0541i −0.109360 0.751352i
\(41\) −0.560733 2.81899i −0.0136764 0.0687560i 0.973344 0.229348i \(-0.0736595\pi\)
−0.987021 + 0.160592i \(0.948660\pi\)
\(42\) −9.78605 24.8301i −0.233001 0.591192i
\(43\) −6.97124 2.88758i −0.162122 0.0671530i 0.300147 0.953893i \(-0.402964\pi\)
−0.462268 + 0.886740i \(0.652964\pi\)
\(44\) −41.2227 + 6.72895i −0.936880 + 0.152931i
\(45\) 2.05237 3.07159i 0.0456082 0.0682575i
\(46\) 14.5047 9.33349i 0.315320 0.202902i
\(47\) 50.6376 + 50.6376i 1.07740 + 1.07740i 0.996742 + 0.0806535i \(0.0257007\pi\)
0.0806535 + 0.996742i \(0.474299\pi\)
\(48\) −25.1049 43.8503i −0.523019 0.913549i
\(49\) 28.7737 11.9185i 0.587219 0.243234i
\(50\) 14.7126 + 15.2297i 0.294251 + 0.304595i
\(51\) −52.6445 10.5249i −1.03225 0.206370i
\(52\) −27.0070 0.933262i −0.519366 0.0179473i
\(53\) 22.9067 9.48825i 0.432201 0.179024i −0.155967 0.987762i \(-0.549849\pi\)
0.588168 + 0.808739i \(0.299849\pi\)
\(54\) −10.7480 + 49.5459i −0.199038 + 0.917517i
\(55\) −28.0309 + 28.0309i −0.509653 + 0.509653i
\(56\) −29.0425 + 17.3000i −0.518616 + 0.308928i
\(57\) 58.5935 87.6914i 1.02796 1.53845i
\(58\) 26.8073 38.6576i 0.462195 0.666510i
\(59\) 20.7368 50.0631i 0.351472 0.848528i −0.644967 0.764210i \(-0.723129\pi\)
0.996439 0.0843175i \(-0.0268710\pi\)
\(60\) −43.6451 19.8710i −0.727418 0.331184i
\(61\) 2.47345 + 12.4349i 0.0405484 + 0.203851i 0.995749 0.0921086i \(-0.0293607\pi\)
−0.955201 + 0.295959i \(0.904361\pi\)
\(62\) 49.3006 8.92426i 0.795170 0.143940i
\(63\) −4.03284 0.802183i −0.0640134 0.0127331i
\(64\) −49.6933 + 40.3308i −0.776458 + 0.630169i
\(65\) −21.3249 + 14.2489i −0.328076 + 0.219213i
\(66\) −26.2875 + 60.4872i −0.398295 + 0.916473i
\(67\) 54.2042 0.809018 0.404509 0.914534i \(-0.367442\pi\)
0.404509 + 0.914534i \(0.367442\pi\)
\(68\) −2.41450 + 67.9571i −0.0355074 + 0.999369i
\(69\) 27.2351i 0.394712i
\(70\) −12.7879 + 29.4248i −0.182685 + 0.420355i
\(71\) 68.2615 + 102.161i 0.961430 + 1.43888i 0.897544 + 0.440924i \(0.145349\pi\)
0.0638857 + 0.997957i \(0.479651\pi\)
\(72\) −7.77423 0.403173i −0.107975 0.00559963i
\(73\) 14.3495 72.1399i 0.196569 0.988218i −0.748944 0.662633i \(-0.769439\pi\)
0.945513 0.325585i \(-0.105561\pi\)
\(74\) 17.8178 3.22533i 0.240781 0.0435855i
\(75\) 32.7939 6.52312i 0.437253 0.0869749i
\(76\) −121.577 55.3523i −1.59969 0.728320i
\(77\) 40.7651 + 16.8855i 0.529417 + 0.219292i
\(78\) −24.3153 + 35.0639i −0.311734 + 0.449538i
\(79\) −78.0068 52.1225i −0.987428 0.659779i −0.0466891 0.998909i \(-0.514867\pi\)
−0.940739 + 0.339131i \(0.889867\pi\)
\(80\) −15.9342 + 58.6142i −0.199178 + 0.732678i
\(81\) 62.7988 + 62.7988i 0.775293 + 0.775293i
\(82\) −1.21867 + 5.61778i −0.0148618 + 0.0685095i
\(83\) 5.40373 + 13.0458i 0.0651052 + 0.157178i 0.953084 0.302707i \(-0.0978905\pi\)
−0.887978 + 0.459885i \(0.847891\pi\)
\(84\) −1.84344 + 53.3460i −0.0219457 + 0.635072i
\(85\) 35.8031 + 53.6961i 0.421213 + 0.631719i
\(86\) 10.4852 + 10.8538i 0.121921 + 0.126207i
\(87\) −28.4262 68.6269i −0.326738 0.788816i
\(88\) 80.9774 + 20.5186i 0.920198 + 0.233166i
\(89\) −114.977 + 114.977i −1.29187 + 1.29187i −0.358246 + 0.933627i \(0.616625\pi\)
−0.933627 + 0.358246i \(0.883375\pi\)
\(90\) −6.21315 + 3.99803i −0.0690350 + 0.0444225i
\(91\) 23.7361 + 15.8599i 0.260836 + 0.174285i
\(92\) −34.0458 + 5.55744i −0.370064 + 0.0604070i
\(93\) 30.2745 73.0892i 0.325533 0.785905i
\(94\) −52.5163 133.249i −0.558684 1.41755i
\(95\) −124.347 + 24.7341i −1.30892 + 0.260359i
\(96\) 11.0931 + 100.446i 0.115554 + 1.04631i
\(97\) −39.8758 7.93180i −0.411091 0.0817711i −0.0147875 0.999891i \(-0.504707\pi\)
−0.396303 + 0.918120i \(0.629707\pi\)
\(98\) −62.2796 1.07575i −0.635506 0.0109771i
\(99\) 5.64516 + 8.44858i 0.0570218 + 0.0853392i
\(100\) −14.8461 39.6637i −0.148461 0.396637i
\(101\) 159.253 1.57676 0.788382 0.615186i \(-0.210919\pi\)
0.788382 + 0.615186i \(0.210919\pi\)
\(102\) 88.1740 + 61.2718i 0.864451 + 0.600704i
\(103\) −25.0301 −0.243010 −0.121505 0.992591i \(-0.538772\pi\)
−0.121505 + 0.992591i \(0.538772\pi\)
\(104\) 48.7941 + 23.2409i 0.469174 + 0.223470i
\(105\) 28.1453 + 42.1224i 0.268050 + 0.401166i
\(106\) −49.5806 0.856404i −0.467741 0.00807929i
\(107\) −22.6694 4.50922i −0.211863 0.0421422i 0.0880174 0.996119i \(-0.471947\pi\)
−0.299881 + 0.953977i \(0.596947\pi\)
\(108\) 59.2110 82.3124i 0.548250 0.762152i
\(109\) −96.2744 + 19.1502i −0.883251 + 0.175690i −0.615820 0.787887i \(-0.711175\pi\)
−0.267432 + 0.963577i \(0.586175\pi\)
\(110\) 73.7613 29.0709i 0.670558 0.264281i
\(111\) 10.9416 26.4153i 0.0985726 0.237975i
\(112\) 67.0626 8.58106i 0.598773 0.0766166i
\(113\) −113.912 76.1138i −1.00807 0.673573i −0.0621848 0.998065i \(-0.519807\pi\)
−0.945889 + 0.324492i \(0.894807\pi\)
\(114\) −177.380 + 114.141i −1.55597 + 1.00123i
\(115\) −23.1507 + 23.1507i −0.201311 + 0.201311i
\(116\) −79.9881 + 49.5384i −0.689553 + 0.427056i
\(117\) 2.51574 + 6.07354i 0.0215021 + 0.0519106i
\(118\) −77.9454 + 75.2984i −0.660554 + 0.638122i
\(119\) 39.9674 59.6897i 0.335860 0.501594i
\(120\) 64.2162 + 71.2410i 0.535135 + 0.593675i
\(121\) 4.57810 + 11.0525i 0.0378355 + 0.0913431i
\(122\) 5.37568 24.7806i 0.0440630 0.203120i
\(123\) 6.41830 + 6.41830i 0.0521813 + 0.0521813i
\(124\) −97.5444 22.9312i −0.786648 0.184929i
\(125\) −112.334 75.0594i −0.898675 0.600475i
\(126\) 6.75783 + 4.68625i 0.0536336 + 0.0371925i
\(127\) 120.311 + 49.8344i 0.947329 + 0.392397i 0.802226 0.597020i \(-0.203649\pi\)
0.145103 + 0.989417i \(0.453649\pi\)
\(128\) 123.301 34.3637i 0.963289 0.268466i
\(129\) 23.3713 4.64884i 0.181173 0.0360376i
\(130\) 50.4743 9.13672i 0.388263 0.0702825i
\(131\) 8.39324 42.1957i 0.0640705 0.322104i −0.935437 0.353494i \(-0.884993\pi\)
0.999507 + 0.0313900i \(0.00999339\pi\)
\(132\) 96.4365 89.9941i 0.730579 0.681774i
\(133\) 78.4010 + 117.335i 0.589481 + 0.882221i
\(134\) −99.4249 43.2096i −0.741977 0.322460i
\(135\) 96.2341i 0.712845i
\(136\) 58.6018 122.727i 0.430896 0.902402i
\(137\) 87.2616 0.636946 0.318473 0.947932i \(-0.396830\pi\)
0.318473 + 0.947932i \(0.396830\pi\)
\(138\) −21.7109 + 49.9564i −0.157325 + 0.362003i
\(139\) 111.605 74.5724i 0.802917 0.536492i −0.0850623 0.996376i \(-0.527109\pi\)
0.887979 + 0.459884i \(0.152109\pi\)
\(140\) 46.9129 43.7789i 0.335092 0.312706i
\(141\) −221.808 44.1203i −1.57310 0.312910i
\(142\) −43.7710 241.805i −0.308246 1.70285i
\(143\) −13.7625 69.1889i −0.0962414 0.483838i
\(144\) 13.9386 + 6.93687i 0.0967959 + 0.0481727i
\(145\) −34.1719 + 82.4984i −0.235669 + 0.568954i
\(146\) −83.8282 + 120.885i −0.574166 + 0.827978i
\(147\) −54.6430 + 81.7790i −0.371721 + 0.556320i
\(148\) −35.2537 8.28759i −0.238200 0.0559972i
\(149\) 202.284 202.284i 1.35761 1.35761i 0.480758 0.876853i \(-0.340361\pi\)
0.876853 0.480758i \(-0.159639\pi\)
\(150\) −65.3528 14.1770i −0.435685 0.0945135i
\(151\) 223.516 92.5834i 1.48024 0.613135i 0.511071 0.859538i \(-0.329249\pi\)
0.969167 + 0.246403i \(0.0792488\pi\)
\(152\) 178.879 + 198.447i 1.17684 + 1.30558i
\(153\) 15.2894 6.31566i 0.0999306 0.0412788i
\(154\) −61.3135 63.4689i −0.398140 0.412136i
\(155\) −87.8626 + 36.3939i −0.566855 + 0.234799i
\(156\) 72.5523 44.9333i 0.465079 0.288034i
\(157\) −61.8626 61.8626i −0.394029 0.394029i 0.482092 0.876121i \(-0.339877\pi\)
−0.876121 + 0.482092i \(0.839877\pi\)
\(158\) 101.535 + 157.791i 0.642627 + 0.998676i
\(159\) −43.5011 + 65.1040i −0.273592 + 0.409459i
\(160\) 75.9528 94.8119i 0.474705 0.592574i
\(161\) 33.6679 + 13.9457i 0.209118 + 0.0866193i
\(162\) −65.1287 165.251i −0.402029 1.02007i
\(163\) 30.5250 + 153.460i 0.187270 + 0.941470i 0.954070 + 0.299584i \(0.0968478\pi\)
−0.766800 + 0.641886i \(0.778152\pi\)
\(164\) 6.71366 9.33302i 0.0409369 0.0569087i
\(165\) 24.4232 122.784i 0.148019 0.744144i
\(166\) 0.487738 28.2371i 0.00293818 0.170103i
\(167\) 205.446 137.275i 1.23022 0.822005i 0.241297 0.970451i \(-0.422427\pi\)
0.988920 + 0.148447i \(0.0474273\pi\)
\(168\) 45.9069 96.3813i 0.273255 0.573698i
\(169\) 123.359i 0.729937i
\(170\) −22.8678 127.034i −0.134516 0.747258i
\(171\) 32.4973i 0.190042i
\(172\) −10.5804 28.2672i −0.0615140 0.164344i
\(173\) −211.088 + 141.045i −1.22016 + 0.815287i −0.987554 0.157283i \(-0.949726\pi\)
−0.232609 + 0.972570i \(0.574726\pi\)
\(174\) −2.56573 + 148.540i −0.0147456 + 0.853680i
\(175\) −8.72825 + 43.8799i −0.0498757 + 0.250742i
\(176\) −132.177 102.189i −0.751008 0.580618i
\(177\) 33.3851 + 167.838i 0.188617 + 0.948240i
\(178\) 302.553 119.242i 1.69974 0.669901i
\(179\) 36.2671 + 15.0223i 0.202610 + 0.0839237i 0.481681 0.876347i \(-0.340026\pi\)
−0.279071 + 0.960270i \(0.590026\pi\)
\(180\) 14.5836 2.38055i 0.0810202 0.0132253i
\(181\) −141.280 + 211.440i −0.780552 + 1.16818i 0.201485 + 0.979492i \(0.435423\pi\)
−0.982037 + 0.188687i \(0.939577\pi\)
\(182\) −30.8953 48.0129i −0.169754 0.263807i
\(183\) −28.3118 28.3118i −0.154709 0.154709i
\(184\) 66.8793 + 16.9463i 0.363475 + 0.0920995i
\(185\) −31.7545 + 13.1532i −0.171646 + 0.0710982i
\(186\) −113.796 + 109.931i −0.611804 + 0.591028i
\(187\) −174.138 + 34.4622i −0.931219 + 0.184290i
\(188\) −9.89272 + 286.279i −0.0526209 + 1.52276i
\(189\) −98.9613 + 40.9911i −0.523605 + 0.216884i
\(190\) 247.802 + 53.7560i 1.30422 + 0.282926i
\(191\) −201.130 + 201.130i −1.05304 + 1.05304i −0.0545249 + 0.998512i \(0.517364\pi\)
−0.998512 + 0.0545249i \(0.982636\pi\)
\(192\) 59.7241 193.088i 0.311063 1.00566i
\(193\) −32.7498 + 49.0135i −0.169688 + 0.253956i −0.906561 0.422076i \(-0.861302\pi\)
0.736873 + 0.676031i \(0.236302\pi\)
\(194\) 66.8199 + 46.3366i 0.344433 + 0.238848i
\(195\) 30.9953 74.8292i 0.158950 0.383740i
\(196\) 113.380 + 51.6203i 0.578468 + 0.263369i
\(197\) −24.9355 125.359i −0.126576 0.636342i −0.991031 0.133632i \(-0.957336\pi\)
0.864455 0.502711i \(-0.167664\pi\)
\(198\) −3.61982 19.9971i −0.0182819 0.100995i
\(199\) 97.1901 + 19.3323i 0.488393 + 0.0971473i 0.433143 0.901325i \(-0.357405\pi\)
0.0552497 + 0.998473i \(0.482405\pi\)
\(200\) −4.38678 + 84.5886i −0.0219339 + 0.422943i
\(201\) −142.329 + 95.1013i −0.708106 + 0.473141i
\(202\) −292.113 126.951i −1.44610 0.628470i
\(203\) 99.3920 0.489616
\(204\) −112.891 182.678i −0.553387 0.895480i
\(205\) 10.9115i 0.0532270i
\(206\) 45.9118 + 19.9531i 0.222873 + 0.0968596i
\(207\) 4.66234 + 6.97769i 0.0225234 + 0.0337086i
\(208\) −70.9745 81.5268i −0.341223 0.391956i
\(209\) 68.0328 342.024i 0.325516 1.63648i
\(210\) −18.0475 99.7001i −0.0859403 0.474762i
\(211\) 182.108 36.2236i 0.863072 0.171676i 0.256345 0.966585i \(-0.417482\pi\)
0.606728 + 0.794910i \(0.292482\pi\)
\(212\) 90.2613 + 41.0948i 0.425761 + 0.193843i
\(213\) −358.482 148.488i −1.68301 0.697127i
\(214\) 37.9871 + 26.3423i 0.177510 + 0.123095i
\(215\) −23.8181 15.9147i −0.110782 0.0740219i
\(216\) −174.225 + 103.782i −0.806598 + 0.480472i
\(217\) 74.8505 + 74.8505i 0.344933 + 0.344933i
\(218\) 191.859 + 41.6200i 0.880085 + 0.190918i
\(219\) 88.8907 + 214.601i 0.405893 + 0.979913i
\(220\) −158.472 5.47621i −0.720328 0.0248918i
\(221\) −114.848 0.111669i −0.519675 0.000505290i
\(222\) −41.1270 + 39.7304i −0.185257 + 0.178966i
\(223\) −85.3007 205.934i −0.382514 0.923471i −0.991478 0.130273i \(-0.958415\pi\)
0.608964 0.793198i \(-0.291585\pi\)
\(224\) −129.851 37.7199i −0.579692 0.168393i
\(225\) −7.28519 + 7.28519i −0.0323786 + 0.0323786i
\(226\) 148.270 + 230.420i 0.656063 + 1.01956i
\(227\) −84.1410 56.2212i −0.370665 0.247671i 0.356261 0.934387i \(-0.384052\pi\)
−0.726926 + 0.686716i \(0.759052\pi\)
\(228\) 416.352 67.9628i 1.82610 0.298082i
\(229\) −124.716 + 301.091i −0.544612 + 1.31481i 0.376827 + 0.926284i \(0.377015\pi\)
−0.921438 + 0.388525i \(0.872985\pi\)
\(230\) 60.9195 24.0097i 0.264868 0.104390i
\(231\) −136.666 + 27.1847i −0.591630 + 0.117682i
\(232\) 186.210 27.1030i 0.802628 0.116823i
\(233\) −388.732 77.3236i −1.66838 0.331861i −0.731586 0.681749i \(-0.761220\pi\)
−0.936792 + 0.349888i \(0.886220\pi\)
\(234\) 0.227070 13.1459i 0.000970383 0.0561792i
\(235\) 151.040 + 226.048i 0.642724 + 0.961905i
\(236\) 202.998 75.9820i 0.860160 0.321958i
\(237\) 296.279 1.25012
\(238\) −120.893 + 77.6262i −0.507955 + 0.326160i
\(239\) 40.8028 0.170723 0.0853615 0.996350i \(-0.472795\pi\)
0.0853615 + 0.996350i \(0.472795\pi\)
\(240\) −60.9987 181.866i −0.254161 0.757774i
\(241\) −151.688 227.018i −0.629412 0.941982i −0.999914 0.0131499i \(-0.995814\pi\)
0.370501 0.928832i \(-0.379186\pi\)
\(242\) 0.413217 23.9227i 0.00170751 0.0988543i
\(243\) −51.3187 10.2079i −0.211188 0.0420079i
\(244\) −29.6147 + 41.1690i −0.121372 + 0.168725i
\(245\) 115.963 23.0665i 0.473319 0.0941490i
\(246\) −6.65643 16.8893i −0.0270586 0.0686557i
\(247\) 86.3398 208.443i 0.349554 0.843898i
\(248\) 160.642 + 119.821i 0.647752 + 0.483148i
\(249\) −37.0779 24.7747i −0.148907 0.0994967i
\(250\) 146.216 + 227.228i 0.584865 + 0.908912i
\(251\) −94.1278 + 94.1278i −0.375011 + 0.375011i −0.869299 0.494287i \(-0.835429\pi\)
0.494287 + 0.869299i \(0.335429\pi\)
\(252\) −8.65995 13.9829i −0.0343649 0.0554879i
\(253\) −34.4620 83.1987i −0.136214 0.328848i
\(254\) −180.956 187.317i −0.712424 0.737468i
\(255\) −188.222 78.1784i −0.738124 0.306582i
\(256\) −253.560 35.2591i −0.990470 0.137731i
\(257\) 53.9702 + 130.296i 0.210001 + 0.506987i 0.993423 0.114503i \(-0.0365276\pi\)
−0.783422 + 0.621490i \(0.786528\pi\)
\(258\) −46.5751 10.1036i −0.180524 0.0391611i
\(259\) 27.0518 + 27.0518i 0.104447 + 0.104447i
\(260\) −99.8666 23.4771i −0.384102 0.0902965i
\(261\) 19.0310 + 12.7161i 0.0729157 + 0.0487207i
\(262\) −49.0323 + 70.7072i −0.187146 + 0.269875i
\(263\) 389.000 + 161.129i 1.47909 + 0.612659i 0.968911 0.247410i \(-0.0795795\pi\)
0.510178 + 0.860069i \(0.329580\pi\)
\(264\) −248.630 + 88.1974i −0.941781 + 0.334081i
\(265\) 92.3179 18.3632i 0.348369 0.0692950i
\(266\) −50.2726 277.723i −0.188995 1.04407i
\(267\) 100.179 503.632i 0.375201 1.88626i
\(268\) 147.926 + 158.516i 0.551964 + 0.591477i
\(269\) 273.969 + 410.024i 1.01847 + 1.52425i 0.841660 + 0.540008i \(0.181579\pi\)
0.176813 + 0.984244i \(0.443421\pi\)
\(270\) −76.7144 + 176.519i −0.284127 + 0.653773i
\(271\) 365.500i 1.34871i 0.738408 + 0.674354i \(0.235578\pi\)
−0.738408 + 0.674354i \(0.764422\pi\)
\(272\) −205.325 + 178.398i −0.754870 + 0.655875i
\(273\) −90.1524 −0.330228
\(274\) −160.061 69.5618i −0.584164 0.253875i
\(275\) 91.9259 61.4229i 0.334276 0.223356i
\(276\) 79.6469 74.3262i 0.288576 0.269298i
\(277\) 5.30517 + 1.05526i 0.0191522 + 0.00380962i 0.204657 0.978834i \(-0.434392\pi\)
−0.185505 + 0.982643i \(0.559392\pi\)
\(278\) −264.160 + 47.8176i −0.950217 + 0.172006i
\(279\) 4.75565 + 23.9083i 0.0170453 + 0.0856927i
\(280\) −120.950 + 42.9049i −0.431963 + 0.153232i
\(281\) 86.0831 207.823i 0.306345 0.739583i −0.693472 0.720483i \(-0.743920\pi\)
0.999818 0.0190999i \(-0.00608006\pi\)
\(282\) 371.683 + 257.746i 1.31803 + 0.913992i
\(283\) −287.868 + 430.825i −1.01720 + 1.52235i −0.174007 + 0.984744i \(0.555671\pi\)
−0.843196 + 0.537607i \(0.819329\pi\)
\(284\) −112.471 + 478.428i −0.396024 + 1.68460i
\(285\) 283.114 283.114i 0.993382 0.993382i
\(286\) −29.9108 + 137.882i −0.104583 + 0.482104i
\(287\) −11.2208 + 4.64779i −0.0390967 + 0.0161944i
\(288\) −20.0373 23.8354i −0.0695739 0.0827619i
\(289\) −0.562000 + 288.999i −0.00194464 + 0.999998i
\(290\) 128.445 124.083i 0.442914 0.427873i
\(291\) 118.622 49.1349i 0.407636 0.168849i
\(292\) 250.128 154.910i 0.856603 0.530514i
\(293\) −45.0208 45.0208i −0.153655 0.153655i 0.626093 0.779748i \(-0.284653\pi\)
−0.779748 + 0.626093i \(0.784653\pi\)
\(294\) 165.421 106.445i 0.562656 0.362058i
\(295\) 114.290 171.047i 0.387423 0.579819i
\(296\) 58.0580 + 43.3046i 0.196142 + 0.146299i
\(297\) 244.549 + 101.295i 0.823396 + 0.341062i
\(298\) −532.296 + 209.789i −1.78623 + 0.703990i
\(299\) −11.3665 57.1431i −0.0380150 0.191114i
\(300\) 108.573 + 78.1013i 0.361910 + 0.260338i
\(301\) −6.22038 + 31.2720i −0.0206657 + 0.103894i
\(302\) −483.792 8.35653i −1.60196 0.0276706i
\(303\) −418.167 + 279.410i −1.38009 + 0.922145i
\(304\) −169.917 506.601i −0.558937 1.66645i
\(305\) 48.1320i 0.157810i
\(306\) −33.0794 0.603553i −0.108103 0.00197240i
\(307\) 416.188i 1.35566i −0.735218 0.677831i \(-0.762920\pi\)
0.735218 0.677831i \(-0.237080\pi\)
\(308\) 61.8702 + 165.296i 0.200877 + 0.536675i
\(309\) 65.7239 43.9153i 0.212699 0.142121i
\(310\) 190.175 + 3.28489i 0.613468 + 0.0105964i
\(311\) −45.0469 + 226.466i −0.144845 + 0.728186i 0.838278 + 0.545243i \(0.183562\pi\)
−0.983123 + 0.182943i \(0.941438\pi\)
\(312\) −168.899 + 24.5834i −0.541344 + 0.0787931i
\(313\) 98.2061 + 493.715i 0.313757 + 1.57736i 0.739905 + 0.672711i \(0.234870\pi\)
−0.426148 + 0.904654i \(0.640130\pi\)
\(314\) 64.1577 + 162.787i 0.204324 + 0.518430i
\(315\) −14.4218 5.97369i −0.0457834 0.0189641i
\(316\) −60.4570 370.370i −0.191320 1.17206i
\(317\) 238.860 357.479i 0.753502 1.12769i −0.234329 0.972157i \(-0.575289\pi\)
0.987830 0.155537i \(-0.0497109\pi\)
\(318\) 131.691 84.7405i 0.414123 0.266479i
\(319\) −173.675 173.675i −0.544434 0.544434i
\(320\) −214.898 + 113.363i −0.671557 + 0.354260i
\(321\) 67.4366 27.9332i 0.210083 0.0870192i
\(322\) −50.6389 52.4190i −0.157264 0.162792i
\(323\) −524.306 217.772i −1.62324 0.674217i
\(324\) −12.2686 + 355.032i −0.0378659 + 1.09578i
\(325\) 66.0840 27.3729i 0.203335 0.0842242i
\(326\) 66.3415 305.819i 0.203502 0.938095i
\(327\) 219.198 219.198i 0.670330 0.670330i
\(328\) −19.7546 + 11.7673i −0.0602274 + 0.0358761i
\(329\) 168.118 251.606i 0.510996 0.764760i
\(330\) −142.677 + 205.749i −0.432356 + 0.623481i
\(331\) 194.722 470.101i 0.588284 1.42024i −0.296858 0.954922i \(-0.595939\pi\)
0.885142 0.465322i \(-0.154061\pi\)
\(332\) −23.4042 + 51.4054i −0.0704946 + 0.154836i
\(333\) 1.71875 + 8.64072i 0.00516140 + 0.0259481i
\(334\) −486.273 + 88.0240i −1.45591 + 0.263545i
\(335\) 201.824 + 40.1452i 0.602459 + 0.119837i
\(336\) −161.037 + 140.193i −0.479277 + 0.417243i
\(337\) 272.567 182.123i 0.808803 0.540425i −0.0810295 0.996712i \(-0.525821\pi\)
0.889833 + 0.456287i \(0.150821\pi\)
\(338\) 98.3377 226.274i 0.290940 0.669449i
\(339\) 432.652 1.27626
\(340\) −59.3212 + 251.243i −0.174474 + 0.738950i
\(341\) 261.583i 0.767106i
\(342\) 25.9056 59.6086i 0.0757475 0.174294i
\(343\) −188.148 281.583i −0.548536 0.820942i
\(344\) −3.12633 + 60.2839i −0.00908818 + 0.175244i
\(345\) 20.1711 101.407i 0.0584671 0.293934i
\(346\) 499.627 90.4413i 1.44401 0.261391i
\(347\) −278.017 + 55.3011i −0.801203 + 0.159369i −0.578676 0.815557i \(-0.696430\pi\)
−0.222527 + 0.974927i \(0.571430\pi\)
\(348\) 123.117 270.417i 0.353785 0.777061i
\(349\) 593.772 + 245.949i 1.70135 + 0.704724i 0.999968 0.00805748i \(-0.00256480\pi\)
0.701386 + 0.712781i \(0.252565\pi\)
\(350\) 50.9894 73.5295i 0.145684 0.210084i
\(351\) 142.392 + 95.1433i 0.405675 + 0.271063i
\(352\) 160.987 + 292.809i 0.457350 + 0.831843i
\(353\) −172.786 172.786i −0.489480 0.489480i 0.418662 0.908142i \(-0.362499\pi\)
−0.908142 + 0.418662i \(0.862499\pi\)
\(354\) 72.5576 334.474i 0.204965 0.944841i
\(355\) 178.502 + 430.941i 0.502821 + 1.21392i
\(356\) −650.018 22.4622i −1.82589 0.0630961i
\(357\) −0.220576 + 226.856i −0.000617861 + 0.635451i
\(358\) −54.5483 56.4658i −0.152370 0.157726i
\(359\) −6.84036 16.5141i −0.0190539 0.0460002i 0.914066 0.405565i \(-0.132925\pi\)
−0.933120 + 0.359565i \(0.882925\pi\)
\(360\) −28.6480 7.25900i −0.0795777 0.0201639i
\(361\) 533.370 533.370i 1.47748 1.47748i
\(362\) 427.698 275.214i 1.18149 0.760261i
\(363\) −31.4128 20.9894i −0.0865366 0.0578219i
\(364\) 18.3960 + 112.697i 0.0505384 + 0.309607i
\(365\) 106.858 257.978i 0.292761 0.706789i
\(366\) 29.3622 + 74.5006i 0.0802247 + 0.203554i
\(367\) −497.173 + 98.8938i −1.35469 + 0.269465i −0.818440 0.574592i \(-0.805161\pi\)
−0.536254 + 0.844057i \(0.680161\pi\)
\(368\) −109.165 84.3978i −0.296645 0.229342i
\(369\) −2.74312 0.545641i −0.00743394 0.00147870i
\(370\) 68.7315 + 1.18720i 0.185761 + 0.00320864i
\(371\) −58.2066 87.1123i −0.156891 0.234804i
\(372\) 296.365 110.929i 0.796679 0.298197i
\(373\) 192.627 0.516427 0.258213 0.966088i \(-0.416866\pi\)
0.258213 + 0.966088i \(0.416866\pi\)
\(374\) 346.887 + 75.6037i 0.927506 + 0.202149i
\(375\) 426.659 1.13776
\(376\) 246.357 517.225i 0.655205 1.37560i
\(377\) −88.2834 132.126i −0.234174 0.350466i
\(378\) 214.198 + 3.69984i 0.566661 + 0.00978793i
\(379\) −235.367 46.8174i −0.621021 0.123529i −0.125455 0.992099i \(-0.540039\pi\)
−0.495566 + 0.868570i \(0.665039\pi\)
\(380\) −411.683 296.142i −1.08338 0.779321i
\(381\) −403.346 + 80.2306i −1.05865 + 0.210579i
\(382\) 529.260 208.592i 1.38550 0.546053i
\(383\) −51.4931 + 124.315i −0.134447 + 0.324583i −0.976737 0.214441i \(-0.931207\pi\)
0.842290 + 0.539024i \(0.181207\pi\)
\(384\) −263.472 + 306.564i −0.686126 + 0.798343i
\(385\) 139.279 + 93.0631i 0.361763 + 0.241722i
\(386\) 99.1435 63.7968i 0.256849 0.165277i
\(387\) −5.19195 + 5.19195i −0.0134159 + 0.0134159i
\(388\) −85.6276 138.260i −0.220690 0.356340i
\(389\) −76.3704 184.374i −0.196325 0.473970i 0.794805 0.606864i \(-0.207573\pi\)
−0.991130 + 0.132894i \(0.957573\pi\)
\(390\) −116.505 + 112.548i −0.298730 + 0.288585i
\(391\) −143.821 + 28.4623i −0.367828 + 0.0727937i
\(392\) −166.819 185.068i −0.425558 0.472111i
\(393\) 51.9934 + 125.523i 0.132299 + 0.319397i
\(394\) −54.1936 + 249.820i −0.137547 + 0.634061i
\(395\) −251.847 251.847i −0.637587 0.637587i
\(396\) −9.30124 + 39.5655i −0.0234880 + 0.0999129i
\(397\) 391.504 + 261.595i 0.986157 + 0.658929i 0.940417 0.340024i \(-0.110435\pi\)
0.0457402 + 0.998953i \(0.485435\pi\)
\(398\) −162.861 112.937i −0.409200 0.283762i
\(399\) −411.730 170.544i −1.03190 0.427429i
\(400\) 75.4775 151.661i 0.188694 0.379152i
\(401\) 363.346 72.2740i 0.906100 0.180235i 0.280021 0.959994i \(-0.409659\pi\)
0.626079 + 0.779759i \(0.284659\pi\)
\(402\) 336.881 60.9813i 0.838012 0.151695i
\(403\) 33.0168 165.986i 0.0819275 0.411877i
\(404\) 434.611 + 465.723i 1.07577 + 1.15278i
\(405\) 187.314 + 280.335i 0.462504 + 0.692186i
\(406\) −182.311 79.2317i −0.449042 0.195152i
\(407\) 94.5391i 0.232283i
\(408\) 61.4476 + 425.072i 0.150607 + 1.04184i
\(409\) −568.749 −1.39059 −0.695293 0.718727i \(-0.744725\pi\)
−0.695293 + 0.718727i \(0.744725\pi\)
\(410\) −8.69828 + 20.0146i −0.0212153 + 0.0488162i
\(411\) −229.131 + 153.101i −0.557497 + 0.372507i
\(412\) −68.3085 73.1985i −0.165797 0.177666i
\(413\) −224.576 44.6709i −0.543767 0.108162i
\(414\) −2.98961 16.5156i −0.00722128 0.0398927i
\(415\) 10.4582 + 52.5767i 0.0252004 + 0.126691i
\(416\) 65.1957 + 206.120i 0.156721 + 0.495481i
\(417\) −162.216 + 391.624i −0.389007 + 0.939146i
\(418\) −397.439 + 573.129i −0.950812 + 1.37112i
\(419\) −290.332 + 434.513i −0.692917 + 1.03702i 0.303532 + 0.952821i \(0.401834\pi\)
−0.996449 + 0.0842018i \(0.973166\pi\)
\(420\) −46.3735 + 197.263i −0.110413 + 0.469674i
\(421\) 12.0004 12.0004i 0.0285044 0.0285044i −0.692711 0.721215i \(-0.743584\pi\)
0.721215 + 0.692711i \(0.243584\pi\)
\(422\) −362.911 78.7265i −0.859979 0.186556i
\(423\) 64.3805 26.6673i 0.152200 0.0630432i
\(424\) −132.804 147.332i −0.313217 0.347480i
\(425\) −68.7183 166.358i −0.161690 0.391431i
\(426\) 539.181 + 558.135i 1.26568 + 1.31018i
\(427\) 49.4960 20.5019i 0.115916 0.0480139i
\(428\) −48.6792 78.6007i −0.113736 0.183647i
\(429\) 157.530 + 157.530i 0.367202 + 0.367202i
\(430\) 31.0020 + 48.1787i 0.0720976 + 0.112044i
\(431\) −372.046 + 556.807i −0.863217 + 1.29190i 0.0919308 + 0.995765i \(0.470696\pi\)
−0.955148 + 0.296130i \(0.904304\pi\)
\(432\) 402.306 51.4775i 0.931265 0.119161i
\(433\) −587.526 243.361i −1.35687 0.562035i −0.418676 0.908136i \(-0.637506\pi\)
−0.938197 + 0.346101i \(0.887506\pi\)
\(434\) −77.6275 196.964i −0.178865 0.453834i
\(435\) −55.0149 276.579i −0.126471 0.635813i
\(436\) −318.742 229.285i −0.731059 0.525883i
\(437\) 56.1883 282.478i 0.128577 0.646402i
\(438\) 8.02322 464.496i 0.0183179 1.06049i
\(439\) −230.592 + 154.076i −0.525266 + 0.350971i −0.789760 0.613416i \(-0.789795\pi\)
0.264494 + 0.964387i \(0.414795\pi\)
\(440\) 286.315 + 136.373i 0.650715 + 0.309939i
\(441\) 30.3062i 0.0687215i
\(442\) 210.573 + 91.7578i 0.476410 + 0.207597i
\(443\) 248.442i 0.560818i 0.959881 + 0.280409i \(0.0904701\pi\)
−0.959881 + 0.280409i \(0.909530\pi\)
\(444\) 107.110 40.0911i 0.241238 0.0902952i
\(445\) −513.259 + 342.949i −1.15339 + 0.770671i
\(446\) −7.69919 + 445.736i −0.0172628 + 0.999409i
\(447\) −176.249 + 886.065i −0.394294 + 1.98225i
\(448\) 208.112 + 172.701i 0.464536 + 0.385493i
\(449\) −11.2679 56.6476i −0.0250956 0.126164i 0.966207 0.257768i \(-0.0829871\pi\)
−0.991302 + 0.131604i \(0.957987\pi\)
\(450\) 19.1705 7.55548i 0.0426010 0.0167899i
\(451\) 27.7282 + 11.4854i 0.0614817 + 0.0254665i
\(452\) −88.2846 540.846i −0.195320 1.19656i
\(453\) −424.470 + 635.264i −0.937020 + 1.40235i
\(454\) 109.519 + 170.199i 0.241232 + 0.374887i
\(455\) 76.6325 + 76.6325i 0.168423 + 0.168423i
\(456\) −817.877 207.239i −1.79359 0.454471i
\(457\) −331.768 + 137.423i −0.725968 + 0.300706i −0.714894 0.699233i \(-0.753525\pi\)
−0.0110743 + 0.999939i \(0.503525\pi\)
\(458\) 468.781 452.862i 1.02354 0.988781i
\(459\) 239.763 358.077i 0.522360 0.780124i
\(460\) −130.882 4.52280i −0.284527 0.00983218i
\(461\) −397.028 + 164.454i −0.861232 + 0.356734i −0.769189 0.639021i \(-0.779340\pi\)
−0.0920429 + 0.995755i \(0.529340\pi\)
\(462\) 272.353 + 59.0818i 0.589509 + 0.127883i
\(463\) 218.280 218.280i 0.471447 0.471447i −0.430935 0.902383i \(-0.641816\pi\)
0.902383 + 0.430935i \(0.141816\pi\)
\(464\) −363.164 98.7257i −0.782680 0.212771i
\(465\) 166.856 249.718i 0.358830 0.537028i
\(466\) 651.398 + 451.715i 1.39785 + 0.969346i
\(467\) −55.7544 + 134.603i −0.119388 + 0.288229i −0.972264 0.233884i \(-0.924856\pi\)
0.852876 + 0.522113i \(0.174856\pi\)
\(468\) −10.8960 + 23.9321i −0.0232820 + 0.0511370i
\(469\) −44.6843 224.643i −0.0952758 0.478984i
\(470\) −96.8507 535.035i −0.206065 1.13837i
\(471\) 270.977 + 53.9006i 0.575322 + 0.114439i
\(472\) −432.922 22.4514i −0.917207 0.0475665i
\(473\) 65.5130 43.7744i 0.138505 0.0925463i
\(474\) −543.455 236.183i −1.14653 0.498277i
\(475\) 353.591 0.744401
\(476\) 283.631 46.0152i 0.595864 0.0966706i
\(477\) 24.1267i 0.0505800i
\(478\) −74.8432 32.5265i −0.156576 0.0680472i
\(479\) 112.422 + 168.251i 0.234701 + 0.351254i 0.930060 0.367408i \(-0.119755\pi\)
−0.695359 + 0.718662i \(0.744755\pi\)
\(480\) −33.0890 + 382.216i −0.0689355 + 0.796283i
\(481\) 11.9326 59.9894i 0.0248080 0.124718i
\(482\) 97.2663 + 537.331i 0.201797 + 1.11479i
\(483\) −112.873 + 22.4518i −0.233691 + 0.0464841i
\(484\) −19.8283 + 43.5512i −0.0409676 + 0.0899819i
\(485\) −142.599 59.0665i −0.294019 0.121787i
\(486\) 85.9947 + 59.6335i 0.176944 + 0.122703i
\(487\) 506.815 + 338.643i 1.04069 + 0.695365i 0.953674 0.300842i \(-0.0972676\pi\)
0.0870138 + 0.996207i \(0.472268\pi\)
\(488\) 87.1396 51.9071i 0.178565 0.106367i
\(489\) −349.398 349.398i −0.714514 0.714514i
\(490\) −231.095 50.1316i −0.471622 0.102309i
\(491\) 304.348 + 734.761i 0.619854 + 1.49646i 0.851873 + 0.523748i \(0.175467\pi\)
−0.232020 + 0.972711i \(0.574533\pi\)
\(492\) −1.25390 + 36.2857i −0.00254858 + 0.0737515i
\(493\) −332.692 + 221.830i −0.674831 + 0.449959i
\(494\) −324.533 + 313.512i −0.656950 + 0.634640i
\(495\) 14.7619 + 35.6384i 0.0298220 + 0.0719968i
\(496\) −199.144 347.841i −0.401500 0.701293i
\(497\) 367.121 367.121i 0.738673 0.738673i
\(498\) 48.2613 + 75.0005i 0.0969102 + 0.150603i
\(499\) 85.7659 + 57.3069i 0.171875 + 0.114844i 0.638533 0.769595i \(-0.279542\pi\)
−0.466657 + 0.884438i \(0.654542\pi\)
\(500\) −87.0617 533.355i −0.174123 1.06671i
\(501\) −298.611 + 720.911i −0.596031 + 1.43895i
\(502\) 247.691 97.6200i 0.493408 0.194462i
\(503\) 574.448 114.265i 1.14204 0.227167i 0.412406 0.911000i \(-0.364688\pi\)
0.729638 + 0.683833i \(0.239688\pi\)
\(504\) 4.73794 + 32.5518i 0.00940068 + 0.0645869i
\(505\) 592.963 + 117.948i 1.17418 + 0.233560i
\(506\) −3.11052 + 180.080i −0.00614728 + 0.355890i
\(507\) −216.434 323.917i −0.426892 0.638889i
\(508\) 182.599 + 487.841i 0.359446 + 0.960316i
\(509\) 931.166 1.82940 0.914701 0.404131i \(-0.132426\pi\)
0.914701 + 0.404131i \(0.132426\pi\)
\(510\) 282.927 + 293.443i 0.554759 + 0.575379i
\(511\) −310.805 −0.608229
\(512\) 436.989 + 266.804i 0.853495 + 0.521101i
\(513\) 470.325 + 703.891i 0.916813 + 1.37211i
\(514\) 4.87133 282.020i 0.00947729 0.548677i
\(515\) −93.1969 18.5380i −0.180965 0.0359961i
\(516\) 77.3769 + 55.6606i 0.149955 + 0.107869i
\(517\) −733.413 + 145.885i −1.41859 + 0.282176i
\(518\) −28.0555 71.1850i −0.0541612 0.137423i
\(519\) 306.812 740.709i 0.591159 1.42719i
\(520\) 164.467 + 122.673i 0.316282 + 0.235910i
\(521\) −409.884 273.876i −0.786726 0.525673i 0.0961014 0.995372i \(-0.469363\pi\)
−0.882827 + 0.469698i \(0.844363\pi\)
\(522\) −24.7711 38.4956i −0.0474542 0.0737463i
\(523\) −80.4991 + 80.4991i −0.153918 + 0.153918i −0.779865 0.625947i \(-0.784712\pi\)
0.625947 + 0.779865i \(0.284712\pi\)
\(524\) 146.304 90.6090i 0.279205 0.172918i
\(525\) −54.0687 130.533i −0.102988 0.248635i
\(526\) −585.083 605.651i −1.11233 1.15143i
\(527\) −417.601 83.4882i −0.792412 0.158422i
\(528\) 526.362 + 36.4217i 0.996897 + 0.0689804i
\(529\) 173.977 + 420.018i 0.328880 + 0.793986i
\(530\) −183.974 39.9096i −0.347121 0.0753011i
\(531\) −37.2854 37.2854i −0.0702173 0.0702173i
\(532\) −129.177 + 549.492i −0.242814 + 1.03288i
\(533\) 16.1452 + 10.7879i 0.0302911 + 0.0202399i
\(534\) −585.232 + 843.936i −1.09594 + 1.58040i
\(535\) −81.0674 33.5792i −0.151528 0.0627649i
\(536\) −144.973 408.682i −0.270472 0.762466i
\(537\) −121.587 + 24.1851i −0.226419 + 0.0450375i
\(538\) −175.676 970.491i −0.326535 1.80389i
\(539\) −63.4458 + 318.964i −0.117710 + 0.591769i
\(540\) 281.429 262.628i 0.521165 0.486349i
\(541\) −65.6048 98.1846i −0.121266 0.181487i 0.765870 0.642995i \(-0.222309\pi\)
−0.887136 + 0.461508i \(0.847309\pi\)
\(542\) 291.363 670.424i 0.537571 1.23694i
\(543\) 803.075i 1.47896i
\(544\) 518.832 163.552i 0.953736 0.300647i
\(545\) −372.651 −0.683763
\(546\) 165.363 + 71.8662i 0.302863 + 0.131623i
\(547\) −194.652 + 130.062i −0.355853 + 0.237773i −0.720627 0.693323i \(-0.756146\pi\)
0.364774 + 0.931096i \(0.381146\pi\)
\(548\) 238.142 + 255.190i 0.434565 + 0.465674i
\(549\) 12.1002 + 2.40688i 0.0220405 + 0.00438412i
\(550\) −217.581 + 39.3859i −0.395601 + 0.0716107i
\(551\) −153.248 770.432i −0.278128 1.39824i
\(552\) −205.344 + 72.8423i −0.372000 + 0.131961i
\(553\) −151.709 + 366.259i −0.274339 + 0.662313i
\(554\) −8.88987 6.16473i −0.0160467 0.0111277i
\(555\) 60.3037 90.2509i 0.108655 0.162614i
\(556\) 522.659 + 122.869i 0.940034 + 0.220987i
\(557\) 254.316 254.316i 0.456581 0.456581i −0.440951 0.897531i \(-0.645359\pi\)
0.897531 + 0.440951i \(0.145359\pi\)
\(558\) 10.3357 47.6451i 0.0185227 0.0853855i
\(559\) 47.0962 19.5079i 0.0842507 0.0348978i
\(560\) 256.056 + 17.7178i 0.457243 + 0.0316390i
\(561\) 396.787 396.016i 0.707285 0.705911i
\(562\) −323.568 + 312.580i −0.575744 + 0.556192i
\(563\) −438.189 + 181.504i −0.778310 + 0.322387i −0.736233 0.676728i \(-0.763397\pi\)
−0.0420767 + 0.999114i \(0.513397\pi\)
\(564\) −476.300 769.066i −0.844504 1.36359i
\(565\) −367.769 367.769i −0.650918 0.650918i
\(566\) 871.465 560.770i 1.53969 0.990759i
\(567\) 208.493 312.032i 0.367713 0.550321i
\(568\) 587.687 787.906i 1.03466 1.38716i
\(569\) 470.318 + 194.812i 0.826570 + 0.342377i 0.755544 0.655098i \(-0.227373\pi\)
0.0710262 + 0.997474i \(0.477373\pi\)
\(570\) −744.994 + 293.618i −1.30701 + 0.515119i
\(571\) −95.2326 478.766i −0.166782 0.838470i −0.970060 0.242866i \(-0.921913\pi\)
0.803278 0.595604i \(-0.203087\pi\)
\(572\) 164.779 229.068i 0.288075 0.400468i
\(573\) 175.244 881.010i 0.305836 1.53754i
\(574\) 24.2869 + 0.419507i 0.0423117 + 0.000730849i
\(575\) 75.9217 50.7292i 0.132038 0.0882248i
\(576\) 17.7530 + 59.6935i 0.0308211 + 0.103635i
\(577\) 350.744i 0.607875i 0.952692 + 0.303938i \(0.0983014\pi\)
−0.952692 + 0.303938i \(0.901699\pi\)
\(578\) 231.411 529.654i 0.400365 0.916356i
\(579\) 186.159i 0.321518i
\(580\) −334.517 + 125.210i −0.576754 + 0.215879i
\(581\) 49.6121 33.1497i 0.0853908 0.0570563i
\(582\) −256.753 4.43489i −0.441157 0.00762009i
\(583\) −50.5090 + 253.926i −0.0866364 + 0.435551i
\(584\) −582.290 + 84.7528i −0.997072 + 0.145125i
\(585\) 4.86886 + 24.4774i 0.00832285 + 0.0418418i
\(586\) 46.6911 + 118.469i 0.0796777 + 0.202166i
\(587\) 337.083 + 139.624i 0.574247 + 0.237861i 0.650857 0.759200i \(-0.274410\pi\)
−0.0766099 + 0.997061i \(0.524410\pi\)
\(588\) −388.280 + 63.3806i −0.660340 + 0.107790i
\(589\) 464.791 695.609i 0.789119 1.18100i
\(590\) −345.990 + 222.637i −0.586424 + 0.377351i
\(591\) 285.419 + 285.419i 0.482942 + 0.482942i
\(592\) −71.9729 125.714i −0.121576 0.212355i
\(593\) −644.772 + 267.073i −1.08731 + 0.450377i −0.853067 0.521802i \(-0.825260\pi\)
−0.234239 + 0.972179i \(0.575260\pi\)
\(594\) −367.818 380.748i −0.619223 0.640990i
\(595\) 193.022 192.647i 0.324408 0.323777i
\(596\) 1143.61 + 39.5189i 1.91881 + 0.0663068i
\(597\) −289.120 + 119.757i −0.484288 + 0.200599i
\(598\) −24.7033 + 113.877i −0.0413099 + 0.190429i
\(599\) −174.872 + 174.872i −0.291939 + 0.291939i −0.837846 0.545907i \(-0.816185\pi\)
0.545907 + 0.837846i \(0.316185\pi\)
\(600\) −136.892 229.809i −0.228153 0.383015i
\(601\) −43.4738 + 65.0631i −0.0723357 + 0.108258i −0.865874 0.500263i \(-0.833237\pi\)
0.793538 + 0.608521i \(0.208237\pi\)
\(602\) 36.3387 52.4024i 0.0603633 0.0870472i
\(603\) 20.1848 48.7303i 0.0334739 0.0808131i
\(604\) 880.741 + 400.990i 1.45818 + 0.663890i
\(605\) 8.86026 + 44.5436i 0.0146451 + 0.0736257i
\(606\) 989.764 179.165i 1.63327 0.295651i
\(607\) −645.316 128.361i −1.06312 0.211468i −0.367609 0.929981i \(-0.619823\pi\)
−0.695514 + 0.718512i \(0.744823\pi\)
\(608\) −92.1722 + 1064.69i −0.151599 + 1.75114i
\(609\) −260.983 + 174.383i −0.428544 + 0.286344i
\(610\) 38.3691 88.2868i 0.0629001 0.144732i
\(611\) −483.798 −0.791813
\(612\) 60.1952 + 27.4768i 0.0983582 + 0.0448967i
\(613\) 972.446i 1.58637i −0.608980 0.793186i \(-0.708421\pi\)
0.608980 0.793186i \(-0.291579\pi\)
\(614\) −331.770 + 763.400i −0.540343 + 1.24332i
\(615\) 19.1443 + 28.6515i 0.0311289 + 0.0465878i
\(616\) 18.2816 352.517i 0.0296779 0.572268i
\(617\) −60.2938 + 303.118i −0.0977210 + 0.491276i 0.900667 + 0.434511i \(0.143079\pi\)
−0.998388 + 0.0567655i \(0.981921\pi\)
\(618\) −155.563 + 28.1596i −0.251720 + 0.0455656i
\(619\) 587.478 116.857i 0.949076 0.188783i 0.303803 0.952735i \(-0.401744\pi\)
0.645273 + 0.763952i \(0.276744\pi\)
\(620\) −346.213 157.626i −0.558408 0.254236i
\(621\) 201.973 + 83.6599i 0.325238 + 0.134718i
\(622\) 263.158 379.489i 0.423084 0.610110i
\(623\) 571.292 + 381.725i 0.917001 + 0.612720i
\(624\) 329.403 + 89.5481i 0.527890 + 0.143507i
\(625\) −175.507 175.507i −0.280811 0.280811i
\(626\) 213.436 983.891i 0.340952 1.57171i
\(627\) 421.441 + 1017.45i 0.672155 + 1.62273i
\(628\) 12.0857 349.739i 0.0192447 0.556909i
\(629\) −150.926 30.1736i −0.239946 0.0479707i
\(630\) 21.6913 + 22.4538i 0.0344307 + 0.0356410i
\(631\) −183.224 442.341i −0.290370 0.701015i 0.709624 0.704581i \(-0.248865\pi\)
−0.999994 + 0.00356556i \(0.998865\pi\)
\(632\) −184.352 + 727.551i −0.291696 + 1.15119i
\(633\) −414.625 + 414.625i −0.655016 + 0.655016i
\(634\) −723.102 + 465.301i −1.14054 + 0.733913i
\(635\) 411.056 + 274.659i 0.647333 + 0.432534i
\(636\) −309.109 + 50.4571i −0.486020 + 0.0793350i
\(637\) −80.5186 + 194.389i −0.126403 + 0.305163i
\(638\) 180.118 + 457.012i 0.282317 + 0.716320i
\(639\) 117.263 23.3251i 0.183511 0.0365025i
\(640\) 484.549 36.6291i 0.757108 0.0572330i
\(641\) −522.573 103.946i −0.815247 0.162163i −0.230180 0.973148i \(-0.573932\pi\)
−0.585067 + 0.810985i \(0.698932\pi\)
\(642\) −145.964 2.52123i −0.227358 0.00392715i
\(643\) 248.267 + 371.558i 0.386107 + 0.577851i 0.972710 0.232024i \(-0.0745349\pi\)
−0.586603 + 0.809875i \(0.699535\pi\)
\(644\) 51.0986 + 136.518i 0.0793456 + 0.211984i
\(645\) 90.4638 0.140254
\(646\) 788.116 + 817.410i 1.21999 + 1.26534i
\(647\) −122.892 −0.189942 −0.0949709 0.995480i \(-0.530276\pi\)
−0.0949709 + 0.995480i \(0.530276\pi\)
\(648\) 305.522 641.442i 0.471485 0.989880i
\(649\) 314.361 + 470.474i 0.484377 + 0.724922i
\(650\) −143.036 2.47066i −0.220056 0.00380102i
\(651\) −327.868 65.2169i −0.503637 0.100180i
\(652\) −365.476 + 508.068i −0.560546 + 0.779246i
\(653\) −108.830 + 21.6477i −0.166662 + 0.0331512i −0.277716 0.960663i \(-0.589577\pi\)
0.111054 + 0.993814i \(0.464577\pi\)
\(654\) −576.804 + 227.331i −0.881964 + 0.347600i
\(655\) 62.5027 150.895i 0.0954240 0.230374i
\(656\) 45.6156 5.83680i 0.0695360 0.00889756i
\(657\) −59.5112 39.7641i −0.0905803 0.0605238i
\(658\) −508.944 + 327.495i −0.773471 + 0.497712i
\(659\) 166.662 166.662i 0.252902 0.252902i −0.569257 0.822159i \(-0.692769\pi\)
0.822159 + 0.569257i \(0.192769\pi\)
\(660\) 425.724 263.660i 0.645036 0.399485i
\(661\) −214.194 517.110i −0.324045 0.782315i −0.999011 0.0444655i \(-0.985842\pi\)
0.674966 0.737849i \(-0.264158\pi\)
\(662\) −731.919 + 707.064i −1.10562 + 1.06807i
\(663\) 301.764 201.208i 0.455150 0.303481i
\(664\) 83.9081 75.6342i 0.126368 0.113907i
\(665\) 205.016 + 494.952i 0.308295 + 0.744289i
\(666\) 3.73544 17.2195i 0.00560876 0.0258551i
\(667\) −143.438 143.438i −0.215049 0.215049i
\(668\) 962.124 + 226.180i 1.44031 + 0.338594i
\(669\) 585.294 + 391.081i 0.874879 + 0.584575i
\(670\) −338.196 234.524i −0.504770 0.350035i
\(671\) −122.312 50.6634i −0.182284 0.0755044i
\(672\) 407.142 128.779i 0.605866 0.191635i
\(673\) 892.388 177.507i 1.32598 0.263755i 0.519227 0.854637i \(-0.326220\pi\)
0.806758 + 0.590882i \(0.201220\pi\)
\(674\) −645.142 + 116.782i −0.957184 + 0.173267i
\(675\) −52.3605 + 263.234i −0.0775712 + 0.389977i
\(676\) −360.755 + 336.655i −0.533661 + 0.498010i
\(677\) 181.077 + 271.000i 0.267469 + 0.400296i 0.940755 0.339086i \(-0.110118\pi\)
−0.673286 + 0.739382i \(0.735118\pi\)
\(678\) −793.599 344.895i −1.17050 0.508695i
\(679\) 171.800i 0.253019i
\(680\) 309.093 413.558i 0.454548 0.608173i
\(681\) 319.577 0.469277
\(682\) −208.525 + 479.813i −0.305755 + 0.703538i
\(683\) 81.4199 54.4030i 0.119209 0.0796530i −0.494536 0.869157i \(-0.664662\pi\)
0.613745 + 0.789504i \(0.289662\pi\)
\(684\) −95.0357 + 88.6869i −0.138941 + 0.129659i
\(685\) 324.909 + 64.6285i 0.474320 + 0.0943482i
\(686\) 120.645 + 666.483i 0.175867 + 0.971549i
\(687\) −200.786 1009.42i −0.292265 1.46931i
\(688\) 53.7907 108.084i 0.0781841 0.157099i
\(689\) −64.1006 + 154.752i −0.0930342 + 0.224604i
\(690\) −117.837 + 169.928i −0.170779 + 0.246272i
\(691\) 245.682 367.689i 0.355545 0.532111i −0.609981 0.792416i \(-0.708823\pi\)
0.965527 + 0.260305i \(0.0838230\pi\)
\(692\) −988.546 232.392i −1.42853 0.335826i
\(693\) 30.3605 30.3605i 0.0438103 0.0438103i
\(694\) 554.042 + 120.189i 0.798331 + 0.173183i
\(695\) 470.782 195.004i 0.677384 0.280582i
\(696\) −441.397 + 397.872i −0.634191 + 0.571655i
\(697\) 27.1856 40.6007i 0.0390038 0.0582506i
\(698\) −893.075 924.469i −1.27948 1.32445i
\(699\) 1156.40 478.995i 1.65436 0.685257i
\(700\) −152.143 + 94.2257i −0.217347 + 0.134608i
\(701\) 172.221 + 172.221i 0.245679 + 0.245679i 0.819195 0.573515i \(-0.194421\pi\)
−0.573515 + 0.819195i \(0.694421\pi\)
\(702\) −185.340 288.028i −0.264017 0.410296i
\(703\) 167.981 251.401i 0.238949 0.357612i
\(704\) −61.8767 665.422i −0.0878930 0.945201i
\(705\) −793.202 328.555i −1.12511 0.466035i
\(706\) 179.197 + 454.675i 0.253820 + 0.644016i
\(707\) −131.284 660.007i −0.185691 0.933532i
\(708\) −399.720 + 555.673i −0.564577 + 0.784849i
\(709\) 236.025 1186.58i 0.332899 1.67360i −0.345126 0.938556i \(-0.612164\pi\)
0.678025 0.735039i \(-0.262836\pi\)
\(710\) 16.1115 932.755i 0.0226922 1.31374i
\(711\) −75.9073 + 50.7196i −0.106761 + 0.0713356i
\(712\) 1174.40 + 559.373i 1.64944 + 0.785636i
\(713\) 216.042i 0.303004i
\(714\) 181.246 415.938i 0.253846 0.582546i
\(715\) 267.811i 0.374560i
\(716\) 55.0435 + 147.057i 0.0768764 + 0.205387i
\(717\) −107.140 + 71.5886i −0.149428 + 0.0998446i
\(718\) −0.617407 + 35.7441i −0.000859898 + 0.0497829i
\(719\) 23.1602 116.434i 0.0322117 0.161939i −0.961331 0.275394i \(-0.911192\pi\)
0.993543 + 0.113455i \(0.0361917\pi\)
\(720\) 46.7613 + 36.1521i 0.0649463 + 0.0502112i
\(721\) 20.6340 + 103.734i 0.0286187 + 0.143876i
\(722\) −1403.53 + 553.159i −1.94394 + 0.766148i
\(723\) 796.605 + 329.965i 1.10181 + 0.456383i
\(724\) −1003.90 + 163.871i −1.38660 + 0.226341i
\(725\) 138.359 207.069i 0.190840 0.285613i
\(726\) 40.8874 + 63.5412i 0.0563188 + 0.0875223i
\(727\) 762.761 + 762.761i 1.04919 + 1.04919i 0.998726 + 0.0504639i \(0.0160700\pi\)
0.0504639 + 0.998726i \(0.483930\pi\)
\(728\) 56.0949 221.381i 0.0770534 0.304094i
\(729\) −585.793 + 242.643i −0.803556 + 0.332844i
\(730\) −401.657 + 388.017i −0.550214 + 0.531530i
\(731\) −48.9736 118.559i −0.0669954 0.162187i
\(732\) 5.53109 160.060i 0.00755613 0.218662i
\(733\) −881.674 + 365.201i −1.20283 + 0.498228i −0.891912 0.452208i \(-0.850636\pi\)
−0.310918 + 0.950437i \(0.600636\pi\)
\(734\) 990.781 + 214.931i 1.34984 + 0.292821i
\(735\) −264.025 + 264.025i −0.359218 + 0.359218i
\(736\) 132.959 + 241.831i 0.180651 + 0.328574i
\(737\) −314.455 + 470.615i −0.426669 + 0.638555i
\(738\) 4.59665 + 3.18757i 0.00622852 + 0.00431920i
\(739\) −255.484 + 616.792i −0.345715 + 0.834631i 0.651400 + 0.758734i \(0.274182\pi\)
−0.997116 + 0.0758965i \(0.975818\pi\)
\(740\) −125.125 56.9679i −0.169088 0.0769836i
\(741\) 139.002 + 698.812i 0.187587 + 0.943066i
\(742\) 37.3235 + 206.187i 0.0503012 + 0.277880i
\(743\) 267.347 + 53.1786i 0.359821 + 0.0715728i 0.371690 0.928357i \(-0.378778\pi\)
−0.0118697 + 0.999930i \(0.503778\pi\)
\(744\) −632.040 32.7777i −0.849516 0.0440561i
\(745\) 903.002 603.366i 1.21208 0.809888i
\(746\) −353.329 153.556i −0.473632 0.205838i
\(747\) 13.7406 0.0183943
\(748\) −576.014 415.203i −0.770073 0.555085i
\(749\) 97.6680i 0.130398i
\(750\) −782.606 340.117i −1.04347 0.453490i
\(751\) −492.879 737.645i −0.656297 0.982218i −0.999083 0.0428043i \(-0.986371\pi\)
0.342787 0.939413i \(-0.388629\pi\)
\(752\) −864.197 + 752.341i −1.14920 + 1.00045i
\(753\) 82.0131 412.308i 0.108915 0.547554i
\(754\) 56.6095 + 312.730i 0.0750789 + 0.414761i
\(755\) 900.809 179.182i 1.19312 0.237327i
\(756\) −389.946 177.537i −0.515802 0.234838i
\(757\) 283.533 + 117.443i 0.374548 + 0.155143i 0.562013 0.827128i \(-0.310027\pi\)
−0.187465 + 0.982271i \(0.560027\pi\)
\(758\) 394.404 + 273.502i 0.520322 + 0.360820i
\(759\) 236.462 + 157.999i 0.311545 + 0.208168i
\(760\) 519.062 + 871.382i 0.682977 + 1.14656i
\(761\) −627.838 627.838i −0.825017 0.825017i 0.161805 0.986823i \(-0.448268\pi\)
−0.986823 + 0.161805i \(0.948268\pi\)
\(762\) 803.801 + 174.369i 1.05486 + 0.228831i
\(763\) 158.732 + 383.212i 0.208036 + 0.502244i
\(764\) −1137.09 39.2934i −1.48833 0.0514312i
\(765\) 61.6060 12.1919i 0.0805307 0.0159372i
\(766\) 193.552 186.979i 0.252678 0.244098i
\(767\) 140.094 + 338.216i 0.182651 + 0.440959i
\(768\) 727.660 352.289i 0.947474 0.458709i
\(769\) −298.940 + 298.940i −0.388738 + 0.388738i −0.874237 0.485499i \(-0.838638\pi\)
0.485499 + 0.874237i \(0.338638\pi\)
\(770\) −181.288 281.731i −0.235439 0.365884i
\(771\) −370.319 247.439i −0.480310 0.320933i
\(772\) −232.712 + 37.9865i −0.301441 + 0.0492054i
\(773\) −144.444 + 348.719i −0.186862 + 0.451124i −0.989352 0.145541i \(-0.953508\pi\)
0.802491 + 0.596665i \(0.203508\pi\)
\(774\) 13.6622 5.38457i 0.0176515 0.00695681i
\(775\) 260.137 51.7444i 0.335661 0.0667670i
\(776\) 46.8477 + 321.865i 0.0603707 + 0.414774i
\(777\) −118.495 23.5701i −0.152503 0.0303348i
\(778\) −6.89315 + 399.071i −0.00886009 + 0.512945i
\(779\) 53.3280 + 79.8110i 0.0684570 + 0.102453i
\(780\) 303.420 113.570i 0.389000 0.145603i
\(781\) −1282.99 −1.64275
\(782\) 286.494 + 62.4411i 0.366361 + 0.0798480i
\(783\) 596.249 0.761494
\(784\) 158.460 + 472.445i 0.202118 + 0.602608i
\(785\) −184.522 276.156i −0.235059 0.351791i
\(786\) 4.69290 271.690i 0.00597061 0.345662i
\(787\) −1058.90 210.628i −1.34549 0.267635i −0.530783 0.847508i \(-0.678102\pi\)
−0.814707 + 0.579873i \(0.803102\pi\)
\(788\) 298.553 415.035i 0.378875 0.526694i
\(789\) −1304.14 + 259.409i −1.65290 + 0.328782i
\(790\) 261.191 + 662.718i 0.330621 + 0.838883i
\(791\) −221.539 + 534.843i −0.280075 + 0.676160i
\(792\) 48.6012 65.1590i 0.0613651 0.0822715i
\(793\) −71.2181 47.5864i −0.0898084 0.0600081i
\(794\) −509.589 791.927i −0.641799 0.997390i
\(795\) −210.190 + 210.190i −0.264390 + 0.264390i
\(796\) 208.702 + 336.984i 0.262188 + 0.423347i
\(797\) 224.222 + 541.319i 0.281332 + 0.679196i 0.999867 0.0162946i \(-0.00518695\pi\)
−0.718535 + 0.695491i \(0.755187\pi\)
\(798\) 619.270 + 641.040i 0.776028 + 0.803308i
\(799\) −1.18371 + 1217.41i −0.00148149 + 1.52367i
\(800\) −259.344 + 218.018i −0.324181 + 0.272523i
\(801\) 60.5502 + 146.181i 0.0755932 + 0.182498i
\(802\) −724.088 157.077i −0.902852 0.195856i
\(803\) 543.092 + 543.092i 0.676329 + 0.676329i
\(804\) −666.541 156.694i −0.829031 0.194892i
\(805\) 115.030 + 76.8609i 0.142895 + 0.0954794i
\(806\) −192.880 + 278.143i −0.239305 + 0.345091i
\(807\) −1438.78 595.960i −1.78287 0.738488i
\(808\) −425.934 1200.72i −0.527146 1.48604i
\(809\) −17.1007 + 3.40154i −0.0211381 + 0.00420463i −0.205648 0.978626i \(-0.565930\pi\)
0.184510 + 0.982831i \(0.440930\pi\)
\(810\) −120.110 663.530i −0.148284 0.819172i
\(811\) 212.309 1067.35i 0.261787 1.31609i −0.596372 0.802708i \(-0.703392\pi\)
0.858159 0.513384i \(-0.171608\pi\)
\(812\) 271.246 + 290.664i 0.334047 + 0.357961i
\(813\) −641.270 959.728i −0.788770 1.18048i
\(814\) −75.3632 + 173.410i −0.0925838 + 0.213034i
\(815\) 593.999i 0.728833i
\(816\) 226.141 828.679i 0.277134 1.01554i
\(817\) 251.994 0.308438
\(818\) 1043.24 + 453.387i 1.27535 + 0.554262i
\(819\) 23.0972 15.4331i 0.0282017 0.0188438i
\(820\) 31.9099 29.7782i 0.0389145 0.0363149i
\(821\) 1448.47 + 288.118i 1.76427 + 0.350936i 0.967409 0.253220i \(-0.0814897\pi\)
0.796866 + 0.604156i \(0.206490\pi\)
\(822\) 542.334 98.1718i 0.659773 0.119430i
\(823\) −176.886 889.265i −0.214928 1.08052i −0.926037 0.377434i \(-0.876807\pi\)
0.711109 0.703082i \(-0.248193\pi\)
\(824\) 66.9447 + 188.719i 0.0812436 + 0.229027i
\(825\) −133.612 + 322.568i −0.161954 + 0.390992i
\(826\) 376.322 + 260.962i 0.455595 + 0.315935i
\(827\) −559.101 + 836.754i −0.676060 + 1.01179i 0.321826 + 0.946799i \(0.395703\pi\)
−0.997886 + 0.0649960i \(0.979297\pi\)
\(828\) −7.68190 + 32.6772i −0.00927765 + 0.0394652i
\(829\) 35.2358 35.2358i 0.0425040 0.0425040i −0.685535 0.728039i \(-0.740432\pi\)
0.728039 + 0.685535i \(0.240432\pi\)
\(830\) 22.7292 104.777i 0.0273846 0.126237i
\(831\) −15.7818 + 6.53702i −0.0189913 + 0.00786645i
\(832\) 44.7253 430.051i 0.0537564 0.516888i
\(833\) 488.956 + 203.089i 0.586982 + 0.243805i
\(834\) 609.735 589.029i 0.731098 0.706270i
\(835\) 866.628 358.969i 1.03788 0.429903i
\(836\) 1185.89 734.446i 1.41853 0.878524i
\(837\) 449.026 + 449.026i 0.536471 + 0.536471i
\(838\) 878.924 565.569i 1.04884 0.674903i
\(839\) −505.556 + 756.618i −0.602570 + 0.901810i −0.999874 0.0158774i \(-0.994946\pi\)
0.397304 + 0.917687i \(0.369946\pi\)
\(840\) 242.313 324.866i 0.288467 0.386745i
\(841\) 265.837 + 110.113i 0.316097 + 0.130931i
\(842\) −31.5781 + 12.4456i −0.0375037 + 0.0147810i
\(843\) 138.589 + 696.734i 0.164400 + 0.826493i
\(844\) 602.917 + 433.705i 0.714357 + 0.513868i
\(845\) −91.3636 + 459.316i −0.108123 + 0.543569i
\(846\) −139.349 2.40697i −0.164715 0.00284512i
\(847\) 42.0319 28.0848i 0.0496244 0.0331580i
\(848\) 126.150 + 376.112i 0.148762 + 0.443528i
\(849\) 1636.33i 1.92736i
\(850\) −6.56704 + 359.925i −0.00772593 + 0.423441i
\(851\) 78.0799i 0.0917508i
\(852\) −544.076 1453.58i −0.638587 1.70609i
\(853\) 329.151 219.932i 0.385875 0.257833i −0.347469 0.937692i \(-0.612959\pi\)
0.733344 + 0.679858i \(0.237959\pi\)
\(854\) −107.132 1.85049i −0.125448 0.00216685i
\(855\) −24.0684 + 121.000i −0.0281502 + 0.141521i
\(856\) 26.6329 + 182.980i 0.0311131 + 0.213762i
\(857\) −12.1047 60.8546i −0.0141246 0.0710089i 0.973080 0.230467i \(-0.0740253\pi\)
−0.987205 + 0.159458i \(0.949025\pi\)
\(858\) −163.374 414.528i −0.190413 0.483133i
\(859\) −111.924 46.3602i −0.130295 0.0539700i 0.316583 0.948565i \(-0.397464\pi\)
−0.446878 + 0.894595i \(0.647464\pi\)
\(860\) −18.4595 113.086i −0.0214646 0.131496i
\(861\) 21.3089 31.8910i 0.0247490 0.0370395i
\(862\) 1126.30 724.749i 1.30661 0.840777i
\(863\) 557.663 + 557.663i 0.646191 + 0.646191i 0.952070 0.305879i \(-0.0989504\pi\)
−0.305879 + 0.952070i \(0.598950\pi\)
\(864\) −778.973 226.281i −0.901589 0.261899i
\(865\) −890.427 + 368.827i −1.02940 + 0.426390i
\(866\) 883.680 + 914.744i 1.02042 + 1.05629i
\(867\) −505.574 759.840i −0.583131 0.876401i
\(868\) −14.6230 + 423.166i −0.0168468 + 0.487518i
\(869\) 905.083 374.898i 1.04152 0.431413i
\(870\) −119.567 + 551.175i −0.137433 + 0.633534i
\(871\) −258.937 + 258.937i −0.297287 + 0.297287i
\(872\) 401.879 + 674.659i 0.460870 + 0.773691i
\(873\) −21.9799 + 32.8952i −0.0251774 + 0.0376807i
\(874\) −328.245 + 473.348i −0.375567 + 0.541588i
\(875\) −218.470 + 527.434i −0.249680 + 0.602782i
\(876\) −384.996 + 845.613i −0.439493 + 0.965311i
\(877\) 2.66166 + 13.3810i 0.00303496 + 0.0152578i 0.982273 0.187456i \(-0.0600241\pi\)
−0.979238 + 0.202713i \(0.935024\pi\)
\(878\) 545.791 98.7976i 0.621629 0.112526i
\(879\) 197.204 + 39.2264i 0.224351 + 0.0446262i
\(880\) −416.465 478.384i −0.473256 0.543618i
\(881\) 1402.61 937.193i 1.59206 1.06378i 0.635565 0.772048i \(-0.280767\pi\)
0.956499 0.291735i \(-0.0942326\pi\)
\(882\) −24.1590 + 55.5896i −0.0273912 + 0.0630268i
\(883\) −513.504 −0.581545 −0.290772 0.956792i \(-0.593912\pi\)
−0.290772 + 0.956792i \(0.593912\pi\)
\(884\) −313.101 336.169i −0.354187 0.380282i
\(885\) 649.655i 0.734074i
\(886\) 198.049 455.709i 0.223532 0.514345i
\(887\) −450.484 674.197i −0.507874 0.760087i 0.485596 0.874183i \(-0.338603\pi\)
−0.993470 + 0.114097i \(0.963603\pi\)
\(888\) −228.426 11.8462i −0.257237 0.0133404i
\(889\) 107.352 539.697i 0.120756 0.607083i
\(890\) 1214.84 219.907i 1.36499 0.247087i
\(891\) −909.550 + 180.921i −1.02082 + 0.203054i
\(892\) 369.447 811.461i 0.414179 0.909710i
\(893\) −2209.53 915.216i −2.47427 1.02488i
\(894\) 1029.63 1484.78i 1.15171 1.66083i
\(895\) 123.911 + 82.7947i 0.138448 + 0.0925080i
\(896\) −244.062 482.679i −0.272391 0.538704i
\(897\) 130.104 + 130.104i 0.145043 + 0.145043i
\(898\) −24.4891 + 112.889i −0.0272707 + 0.125712i
\(899\) −225.490 544.381i −0.250823 0.605541i
\(900\) −41.1867 1.42326i −0.0457630 0.00158140i
\(901\) 389.256 + 161.679i 0.432027 + 0.179444i
\(902\) −41.7052 43.1713i −0.0462364 0.0478617i
\(903\) −38.5332 93.0275i −0.0426725 0.103020i
\(904\) −269.206 + 1062.43i −0.297794 + 1.17526i
\(905\) −682.640 + 682.640i −0.754299 + 0.754299i
\(906\) 1285.00 826.871i 1.41832 0.912661i
\(907\) −321.062 214.527i −0.353983 0.236524i 0.365846 0.930675i \(-0.380780\pi\)
−0.719829 + 0.694152i \(0.755780\pi\)
\(908\) −65.2112 399.495i −0.0718185 0.439972i
\(909\) 59.3033 143.171i 0.0652401 0.157504i
\(910\) −79.4756 201.653i −0.0873358 0.221597i
\(911\) −579.899 + 115.349i −0.636553 + 0.126618i −0.502809 0.864398i \(-0.667700\pi\)
−0.133744 + 0.991016i \(0.542700\pi\)
\(912\) 1335.00 + 1032.11i 1.46382 + 1.13170i
\(913\) −144.615 28.7658i −0.158396 0.0315069i
\(914\) 718.098 + 12.4037i 0.785665 + 0.0135708i
\(915\) −84.4476 126.385i −0.0922925 0.138125i
\(916\) −1220.87 + 456.973i −1.33283 + 0.498879i
\(917\) −181.794 −0.198249
\(918\) −725.235 + 465.677i −0.790017 + 0.507274i
\(919\) 94.7825 0.103137 0.0515683 0.998669i \(-0.483578\pi\)
0.0515683 + 0.998669i \(0.483578\pi\)
\(920\) 236.467 + 112.631i 0.257030 + 0.122425i
\(921\) 730.203 + 1092.83i 0.792837 + 1.18656i
\(922\) 859.352 + 14.8436i 0.932052 + 0.0160993i
\(923\) −814.117 161.938i −0.882033 0.175447i
\(924\) −452.470 325.482i −0.489686 0.352253i
\(925\) 94.0165 18.7010i 0.101639 0.0202173i
\(926\) −574.389 + 226.379i −0.620290 + 0.244469i
\(927\) −9.32079 + 22.5024i −0.0100548 + 0.0242744i
\(928\) 587.438 + 470.590i 0.633015 + 0.507101i
\(929\) 439.872 + 293.913i 0.473490 + 0.316376i 0.769319 0.638865i \(-0.220596\pi\)
−0.295829 + 0.955241i \(0.595596\pi\)
\(930\) −505.125 + 325.037i −0.543145 + 0.349502i
\(931\) −735.464 + 735.464i −0.789972 + 0.789972i
\(932\) −834.745 1347.84i −0.895650 1.44618i
\(933\) −279.051 673.688i −0.299090 0.722066i
\(934\) 209.569 202.452i 0.224378 0.216758i
\(935\) −673.908 0.655254i −0.720758 0.000700807i
\(936\) 39.0640 35.2120i 0.0417350 0.0376197i
\(937\) −587.413 1418.14i −0.626908 1.51349i −0.843445 0.537216i \(-0.819476\pi\)
0.216537 0.976274i \(-0.430524\pi\)
\(938\) −97.1147 + 447.676i −0.103534 + 0.477267i
\(939\) −1124.09 1124.09i −1.19712 1.19712i
\(940\) −248.861 + 1058.60i −0.264746 + 1.12617i
\(941\) 1220.60 + 815.576i 1.29713 + 0.866712i 0.996214 0.0869391i \(-0.0277086\pi\)
0.300913 + 0.953652i \(0.402709\pi\)
\(942\) −454.075 314.881i −0.482033 0.334268i
\(943\) 22.9008 + 9.48581i 0.0242850 + 0.0100592i
\(944\) 776.196 + 386.292i 0.822241 + 0.409207i
\(945\) −398.831 + 79.3325i −0.422044 + 0.0839498i
\(946\) −155.064 + 28.0692i −0.163915 + 0.0296715i
\(947\) −79.8060 + 401.212i −0.0842725 + 0.423666i 0.915500 + 0.402319i \(0.131796\pi\)
−0.999772 + 0.0213475i \(0.993204\pi\)
\(948\) 808.563 + 866.445i 0.852915 + 0.913972i
\(949\) 276.068 + 413.165i 0.290904 + 0.435369i
\(950\) −648.579 281.870i −0.682715 0.296705i
\(951\) 1357.75i 1.42771i
\(952\) −556.937 141.697i −0.585017 0.148841i
\(953\) 776.560 0.814858 0.407429 0.913237i \(-0.366425\pi\)
0.407429 + 0.913237i \(0.366425\pi\)
\(954\) −19.2329 + 44.2547i −0.0201603 + 0.0463886i
\(955\) −897.850 + 599.924i −0.940157 + 0.628193i
\(956\) 111.353 + 119.325i 0.116478 + 0.124817i
\(957\) 760.746 + 151.322i 0.794928 + 0.158121i
\(958\) −72.0875 398.235i −0.0752479 0.415694i
\(959\) −71.9358 361.646i −0.0750113 0.377107i
\(960\) 365.383 674.708i 0.380607 0.702821i
\(961\) −127.607 + 308.071i −0.132786 + 0.320573i
\(962\) −69.7090 + 100.524i −0.0724626 + 0.104495i
\(963\) −12.4956 + 18.7009i −0.0129756 + 0.0194194i
\(964\) 249.929 1063.14i 0.259262 1.10285i
\(965\) −158.241 + 158.241i −0.163981 + 0.163981i
\(966\) 224.937 + 48.7957i 0.232854 + 0.0505131i
\(967\) 1032.68 427.751i 1.06792 0.442348i 0.221666 0.975123i \(-0.428851\pi\)
0.846257 + 0.532774i \(0.178851\pi\)
\(968\) 71.0878 64.0781i 0.0734379 0.0661964i
\(969\) 1758.80 348.070i 1.81507 0.359206i
\(970\) 214.479 + 222.018i 0.221112 + 0.228885i
\(971\) −145.404 + 60.2285i −0.149747 + 0.0620273i −0.456298 0.889827i \(-0.650825\pi\)
0.306551 + 0.951854i \(0.400825\pi\)
\(972\) −110.199 177.935i −0.113374 0.183061i
\(973\) −401.061 401.061i −0.412190 0.412190i
\(974\) −659.679 1025.18i −0.677289 1.05254i
\(975\) −125.497 + 187.820i −0.128715 + 0.192636i
\(976\) −201.216 + 25.7468i −0.206164 + 0.0263799i
\(977\) 827.978 + 342.960i 0.847470 + 0.351034i 0.763795 0.645459i \(-0.223334\pi\)
0.0836755 + 0.996493i \(0.473334\pi\)
\(978\) 362.361 + 919.415i 0.370512 + 0.940097i
\(979\) −331.243 1665.27i −0.338349 1.70099i
\(980\) 383.926 + 276.175i 0.391762 + 0.281812i
\(981\) −18.6347 + 93.6832i −0.0189957 + 0.0954976i
\(982\) 27.4703 1590.36i 0.0279738 1.61951i
\(983\) 451.123 301.431i 0.458925 0.306644i −0.304532 0.952502i \(-0.598500\pi\)
0.763458 + 0.645858i \(0.223500\pi\)
\(984\) 31.2257 65.5581i 0.0317334 0.0666241i
\(985\) 485.231i 0.492620i
\(986\) 787.079 141.685i 0.798255 0.143697i
\(987\) 955.629i 0.968216i
\(988\) 845.201 316.358i 0.855467 0.320201i
\(989\) 54.1072 36.1533i 0.0547090 0.0365554i
\(990\) 1.33240 77.1380i 0.00134586 0.0779171i
\(991\) 354.945 1784.43i 0.358168 1.80063i −0.209979 0.977706i \(-0.567340\pi\)
0.568147 0.822927i \(-0.307660\pi\)
\(992\) 87.9960 + 796.784i 0.0887057 + 0.803210i
\(993\) 313.492 + 1576.03i 0.315702 + 1.58714i
\(994\) −966.052 + 380.741i −0.971883 + 0.383039i
\(995\) 347.559 + 143.964i 0.349306 + 0.144687i
\(996\) −28.7362 176.043i −0.0288516 0.176750i
\(997\) 205.212 307.121i 0.205829 0.308045i −0.714165 0.699978i \(-0.753193\pi\)
0.919994 + 0.391932i \(0.128193\pi\)
\(998\) −111.634 173.486i −0.111858 0.173833i
\(999\) 162.283 + 162.283i 0.162446 + 0.162446i
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 136.3.q.a.5.5 272
8.5 even 2 inner 136.3.q.a.5.21 yes 272
17.7 odd 16 inner 136.3.q.a.109.21 yes 272
136.109 odd 16 inner 136.3.q.a.109.5 yes 272
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
136.3.q.a.5.5 272 1.1 even 1 trivial
136.3.q.a.5.21 yes 272 8.5 even 2 inner
136.3.q.a.109.5 yes 272 136.109 odd 16 inner
136.3.q.a.109.21 yes 272 17.7 odd 16 inner