Properties

Label 8.9.d.b.3.6
Level $8$
Weight $9$
Character 8.3
Analytic conductor $3.259$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8,9,Mod(3,8)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8.3");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 8.d (of order \(2\), degree \(1\), 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: \(3.25902888049\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 78x^{4} - 514x^{3} + 4237x^{2} - 18333x + 238980 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.6
Root \(-4.53916 + 7.17456i\) of defining polynomial
Character \(\chi\) \(=\) 8.3
Dual form 8.9.d.b.3.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.07833 + 14.3491i) q^{2} -117.615 q^{3} +(-155.795 + 203.136i) q^{4} -306.178i q^{5} +(-832.521 - 1687.68i) q^{6} +4321.70i q^{7} +(-4017.58 - 797.653i) q^{8} +7272.39 q^{9} +O(q^{10})\) \(q+(7.07833 + 14.3491i) q^{2} -117.615 q^{3} +(-155.795 + 203.136i) q^{4} -306.178i q^{5} +(-832.521 - 1687.68i) q^{6} +4321.70i q^{7} +(-4017.58 - 797.653i) q^{8} +7272.39 q^{9} +(4393.38 - 2167.23i) q^{10} +7172.95 q^{11} +(18323.8 - 23891.9i) q^{12} +5492.75i q^{13} +(-62012.5 + 30590.4i) q^{14} +36011.2i q^{15} +(-16992.1 - 63294.8i) q^{16} +6553.97 q^{17} +(51476.3 + 104352. i) q^{18} -162847. q^{19} +(62195.6 + 47700.8i) q^{20} -508298. i q^{21} +(50772.5 + 102926. i) q^{22} +310889. i q^{23} +(472530. + 93816.3i) q^{24} +296880. q^{25} +(-78816.2 + 38879.5i) q^{26} -83670.1 q^{27} +(-877890. - 673297. i) q^{28} +586403. i q^{29} +(-516729. + 254899. i) q^{30} -225390. i q^{31} +(787949. - 691844. i) q^{32} -843649. q^{33} +(46391.1 + 94043.6i) q^{34} +1.32321e6 q^{35} +(-1.13300e6 + 1.47728e6i) q^{36} +1.84804e6i q^{37} +(-1.15269e6 - 2.33671e6i) q^{38} -646033. i q^{39} +(-244224. + 1.23009e6i) q^{40} +2.40081e6 q^{41} +(7.29363e6 - 3.59790e6i) q^{42} -687442. q^{43} +(-1.11751e6 + 1.45708e6i) q^{44} -2.22664e6i q^{45} +(-4.46098e6 + 2.20057e6i) q^{46} -5.71500e6i q^{47} +(1.99854e6 + 7.44445e6i) q^{48} -1.29123e7 q^{49} +(2.10142e6 + 4.25997e6i) q^{50} -770847. q^{51} +(-1.11577e6 - 855741. i) q^{52} +7.20466e6i q^{53} +(-592244. - 1.20059e6i) q^{54} -2.19620e6i q^{55} +(3.44722e6 - 1.73628e7i) q^{56} +1.91533e7 q^{57} +(-8.41437e6 + 4.15075e6i) q^{58} +4.61794e6 q^{59} +(-7.31516e6 - 5.61035e6i) q^{60} -6.84870e6i q^{61} +(3.23415e6 - 1.59538e6i) q^{62} +3.14291e7i q^{63} +(1.55047e7 + 6.40928e6i) q^{64} +1.68176e6 q^{65} +(-5.97163e6 - 1.21056e7i) q^{66} -6.79128e6 q^{67} +(-1.02107e6 + 1.33134e6i) q^{68} -3.65653e7i q^{69} +(9.36610e6 + 1.89869e7i) q^{70} +1.78351e7i q^{71} +(-2.92174e7 - 5.80084e6i) q^{72} +9.60923e6 q^{73} +(-2.65177e7 + 1.30810e7i) q^{74} -3.49177e7 q^{75} +(2.53707e7 - 3.30801e7i) q^{76} +3.09993e7i q^{77} +(9.27000e6 - 4.57283e6i) q^{78} -4.84326e7i q^{79} +(-1.93795e7 + 5.20262e6i) q^{80} -3.78732e7 q^{81} +(1.69937e7 + 3.44495e7i) q^{82} +6.07030e7 q^{83} +(1.03253e8 + 7.91901e7i) q^{84} -2.00668e6i q^{85} +(-4.86594e6 - 9.86419e6i) q^{86} -6.89700e7i q^{87} +(-2.88179e7 - 5.72153e6i) q^{88} -2.61120e7 q^{89} +(3.19504e7 - 1.57609e7i) q^{90} -2.37380e7 q^{91} +(-6.31526e7 - 4.84348e7i) q^{92} +2.65093e7i q^{93} +(8.20053e7 - 4.04527e7i) q^{94} +4.98602e7i q^{95} +(-9.26750e7 + 8.13715e7i) q^{96} +9.48587e7 q^{97} +(-9.13972e7 - 1.85280e8i) q^{98} +5.21645e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 14 q^{2} - 36 q^{3} - 588 q^{4} - 1284 q^{6} - 6824 q^{8} + 16338 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 14 q^{2} - 36 q^{3} - 588 q^{4} - 1284 q^{6} - 6824 q^{8} + 16338 q^{9} - 4080 q^{10} + 46940 q^{11} - 27336 q^{12} - 51744 q^{14} + 20496 q^{16} - 201076 q^{17} + 267990 q^{18} - 95268 q^{19} - 216480 q^{20} + 49404 q^{22} + 1009296 q^{24} - 447930 q^{25} + 1765104 q^{26} + 419256 q^{27} - 2600640 q^{28} - 4325280 q^{30} + 3232096 q^{32} + 1736856 q^{33} + 2378916 q^{34} + 1989120 q^{35} - 7392228 q^{36} - 8088196 q^{38} + 12694080 q^{40} + 3817100 q^{41} + 19064640 q^{42} - 9881508 q^{43} - 9479368 q^{44} - 19226976 q^{46} + 20590944 q^{48} - 12655482 q^{49} + 11106610 q^{50} - 4303176 q^{51} - 17270880 q^{52} - 7366536 q^{54} + 10545024 q^{56} + 7523736 q^{57} + 7354800 q^{58} + 25243484 q^{59} - 5760960 q^{60} - 5304960 q^{62} - 35364288 q^{64} + 27060480 q^{65} - 12683256 q^{66} + 47850204 q^{67} - 9160216 q^{68} + 56582400 q^{70} - 57502200 q^{72} - 55484916 q^{73} - 114255984 q^{74} - 126075300 q^{75} + 151972920 q^{76} + 175397280 q^{78} - 134958720 q^{80} - 79145442 q^{81} - 48197916 q^{82} + 144646364 q^{83} + 216531840 q^{84} + 41826428 q^{86} - 47377776 q^{88} + 142173452 q^{89} - 205943760 q^{90} - 273971712 q^{91} + 97636800 q^{92} + 220009536 q^{94} - 250689984 q^{96} + 125193612 q^{97} - 257093774 q^{98} + 298320276 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.07833 + 14.3491i 0.442396 + 0.896820i
\(3\) −117.615 −1.45204 −0.726021 0.687672i \(-0.758633\pi\)
−0.726021 + 0.687672i \(0.758633\pi\)
\(4\) −155.795 + 203.136i −0.608572 + 0.793498i
\(5\) 306.178i 0.489884i −0.969538 0.244942i \(-0.921231\pi\)
0.969538 0.244942i \(-0.0787690\pi\)
\(6\) −832.521 1687.68i −0.642377 1.30222i
\(7\) 4321.70i 1.79996i 0.435934 + 0.899979i \(0.356418\pi\)
−0.435934 + 0.899979i \(0.643582\pi\)
\(8\) −4017.58 797.653i −0.980855 0.194740i
\(9\) 7272.39 1.10843
\(10\) 4393.38 2167.23i 0.439338 0.216723i
\(11\) 7172.95 0.489922 0.244961 0.969533i \(-0.421225\pi\)
0.244961 + 0.969533i \(0.421225\pi\)
\(12\) 18323.8 23891.9i 0.883673 1.15219i
\(13\) 5492.75i 0.192317i 0.995366 + 0.0961583i \(0.0306555\pi\)
−0.995366 + 0.0961583i \(0.969344\pi\)
\(14\) −62012.5 + 30590.4i −1.61424 + 0.796293i
\(15\) 36011.2i 0.711333i
\(16\) −16992.1 63294.8i −0.259280 0.965802i
\(17\) 6553.97 0.0784709 0.0392354 0.999230i \(-0.487508\pi\)
0.0392354 + 0.999230i \(0.487508\pi\)
\(18\) 51476.3 + 104352.i 0.490363 + 0.994059i
\(19\) −162847. −1.24959 −0.624793 0.780791i \(-0.714817\pi\)
−0.624793 + 0.780791i \(0.714817\pi\)
\(20\) 62195.6 + 47700.8i 0.388722 + 0.298130i
\(21\) 508298.i 2.61361i
\(22\) 50772.5 + 102926.i 0.216739 + 0.439372i
\(23\) 310889.i 1.11095i 0.831534 + 0.555474i \(0.187463\pi\)
−0.831534 + 0.555474i \(0.812537\pi\)
\(24\) 472530. + 93816.3i 1.42424 + 0.282770i
\(25\) 296880. 0.760013
\(26\) −78816.2 + 38879.5i −0.172473 + 0.0850800i
\(27\) −83670.1 −0.157440
\(28\) −877890. 673297.i −1.42826 1.09540i
\(29\) 586403.i 0.829095i 0.910028 + 0.414547i \(0.136060\pi\)
−0.910028 + 0.414547i \(0.863940\pi\)
\(30\) −516729. + 254899.i −0.637937 + 0.314690i
\(31\) 225390.i 0.244055i −0.992527 0.122027i \(-0.961060\pi\)
0.992527 0.122027i \(-0.0389396\pi\)
\(32\) 787949. 691844.i 0.751447 0.659794i
\(33\) −843649. −0.711388
\(34\) 46391.1 + 94043.6i 0.0347152 + 0.0703743i
\(35\) 1.32321e6 0.881771
\(36\) −1.13300e6 + 1.47728e6i −0.674558 + 0.879535i
\(37\) 1.84804e6i 0.986061i 0.870012 + 0.493030i \(0.164111\pi\)
−0.870012 + 0.493030i \(0.835889\pi\)
\(38\) −1.15269e6 2.33671e6i −0.552811 1.12065i
\(39\) 646033.i 0.279252i
\(40\) −244224. + 1.23009e6i −0.0953999 + 0.480505i
\(41\) 2.40081e6 0.849614 0.424807 0.905284i \(-0.360342\pi\)
0.424807 + 0.905284i \(0.360342\pi\)
\(42\) 7.29363e6 3.59790e6i 2.34394 1.15625i
\(43\) −687442. −0.201077 −0.100538 0.994933i \(-0.532057\pi\)
−0.100538 + 0.994933i \(0.532057\pi\)
\(44\) −1.11751e6 + 1.45708e6i −0.298153 + 0.388752i
\(45\) 2.22664e6i 0.543001i
\(46\) −4.46098e6 + 2.20057e6i −0.996321 + 0.491479i
\(47\) 5.71500e6i 1.17118i −0.810606 0.585592i \(-0.800862\pi\)
0.810606 0.585592i \(-0.199138\pi\)
\(48\) 1.99854e6 + 7.44445e6i 0.376485 + 1.40239i
\(49\) −1.29123e7 −2.23985
\(50\) 2.10142e6 + 4.25997e6i 0.336227 + 0.681595i
\(51\) −770847. −0.113943
\(52\) −1.11577e6 855741.i −0.152603 0.117039i
\(53\) 7.20466e6i 0.913082i 0.889702 + 0.456541i \(0.150912\pi\)
−0.889702 + 0.456541i \(0.849088\pi\)
\(54\) −592244. 1.20059e6i −0.0696508 0.141195i
\(55\) 2.19620e6i 0.240005i
\(56\) 3.44722e6 1.73628e7i 0.350523 1.76550i
\(57\) 1.91533e7 1.81445
\(58\) −8.41437e6 + 4.15075e6i −0.743549 + 0.366788i
\(59\) 4.61794e6 0.381101 0.190551 0.981677i \(-0.438973\pi\)
0.190551 + 0.981677i \(0.438973\pi\)
\(60\) −7.31516e6 5.61035e6i −0.564441 0.432897i
\(61\) 6.84870e6i 0.494640i −0.968934 0.247320i \(-0.920450\pi\)
0.968934 0.247320i \(-0.0795498\pi\)
\(62\) 3.23415e6 1.59538e6i 0.218873 0.107969i
\(63\) 3.14291e7i 1.99512i
\(64\) 1.55047e7 + 6.40928e6i 0.924153 + 0.382023i
\(65\) 1.68176e6 0.0942129
\(66\) −5.97163e6 1.21056e7i −0.314715 0.637987i
\(67\) −6.79128e6 −0.337018 −0.168509 0.985700i \(-0.553895\pi\)
−0.168509 + 0.985700i \(0.553895\pi\)
\(68\) −1.02107e6 + 1.33134e6i −0.0477552 + 0.0622665i
\(69\) 3.65653e7i 1.61314i
\(70\) 9.36610e6 + 1.89869e7i 0.390091 + 0.790790i
\(71\) 1.78351e7i 0.701847i 0.936404 + 0.350924i \(0.114132\pi\)
−0.936404 + 0.350924i \(0.885868\pi\)
\(72\) −2.92174e7 5.80084e6i −1.08721 0.215855i
\(73\) 9.60923e6 0.338374 0.169187 0.985584i \(-0.445886\pi\)
0.169187 + 0.985584i \(0.445886\pi\)
\(74\) −2.65177e7 + 1.30810e7i −0.884319 + 0.436229i
\(75\) −3.49177e7 −1.10357
\(76\) 2.53707e7 3.30801e7i 0.760463 0.991544i
\(77\) 3.09993e7i 0.881839i
\(78\) 9.27000e6 4.57283e6i 0.250439 0.123540i
\(79\) 4.84326e7i 1.24345i −0.783234 0.621727i \(-0.786431\pi\)
0.783234 0.621727i \(-0.213569\pi\)
\(80\) −1.93795e7 + 5.20262e6i −0.473131 + 0.127017i
\(81\) −3.78732e7 −0.879817
\(82\) 1.69937e7 + 3.44495e7i 0.375866 + 0.761951i
\(83\) 6.07030e7 1.27908 0.639540 0.768758i \(-0.279125\pi\)
0.639540 + 0.768758i \(0.279125\pi\)
\(84\) 1.03253e8 + 7.91901e7i 2.07390 + 1.59057i
\(85\) 2.00668e6i 0.0384417i
\(86\) −4.86594e6 9.86419e6i −0.0889556 0.180330i
\(87\) 6.89700e7i 1.20388i
\(88\) −2.88179e7 5.72153e6i −0.480543 0.0954072i
\(89\) −2.61120e7 −0.416179 −0.208090 0.978110i \(-0.566725\pi\)
−0.208090 + 0.978110i \(0.566725\pi\)
\(90\) 3.19504e7 1.57609e7i 0.486974 0.240221i
\(91\) −2.37380e7 −0.346162
\(92\) −6.31526e7 4.84348e7i −0.881536 0.676092i
\(93\) 2.65093e7i 0.354378i
\(94\) 8.20053e7 4.04527e7i 1.05034 0.518127i
\(95\) 4.98602e7i 0.612152i
\(96\) −9.26750e7 + 8.13715e7i −1.09113 + 0.958048i
\(97\) 9.48587e7 1.07150 0.535748 0.844378i \(-0.320030\pi\)
0.535748 + 0.844378i \(0.320030\pi\)
\(98\) −9.13972e7 1.85280e8i −0.990898 2.00874i
\(99\) 5.21645e7 0.543043
\(100\) −4.62523e7 + 6.03069e7i −0.462523 + 0.603069i
\(101\) 1.53591e8i 1.47598i 0.674813 + 0.737989i \(0.264224\pi\)
−0.674813 + 0.737989i \(0.735776\pi\)
\(102\) −5.45631e6 1.10610e7i −0.0504079 0.102186i
\(103\) 9.23743e7i 0.820734i 0.911920 + 0.410367i \(0.134599\pi\)
−0.911920 + 0.410367i \(0.865401\pi\)
\(104\) 4.38131e6 2.20676e7i 0.0374517 0.188635i
\(105\) −1.55630e8 −1.28037
\(106\) −1.03380e8 + 5.09969e7i −0.818870 + 0.403943i
\(107\) −1.90283e7 −0.145166 −0.0725829 0.997362i \(-0.523124\pi\)
−0.0725829 + 0.997362i \(0.523124\pi\)
\(108\) 1.30353e7 1.69964e7i 0.0958136 0.124928i
\(109\) 1.38190e8i 0.978975i −0.872010 0.489487i \(-0.837184\pi\)
0.872010 0.489487i \(-0.162816\pi\)
\(110\) 3.15135e7 1.55454e7i 0.215241 0.106177i
\(111\) 2.17358e8i 1.43180i
\(112\) 2.73541e8 7.34349e7i 1.73840 0.466692i
\(113\) 1.95936e8 1.20171 0.600855 0.799358i \(-0.294827\pi\)
0.600855 + 0.799358i \(0.294827\pi\)
\(114\) 1.35574e8 + 2.74834e8i 0.802705 + 1.62724i
\(115\) 9.51873e7 0.544236
\(116\) −1.19119e8 9.13584e7i −0.657885 0.504564i
\(117\) 3.99454e7i 0.213169i
\(118\) 3.26873e7 + 6.62634e7i 0.168597 + 0.341779i
\(119\) 2.83243e7i 0.141244i
\(120\) 2.87245e7 1.44678e8i 0.138525 0.697714i
\(121\) −1.62908e8 −0.759976
\(122\) 9.82729e7 4.84774e7i 0.443603 0.218826i
\(123\) −2.82372e8 −1.23368
\(124\) 4.57847e7 + 3.51145e7i 0.193657 + 0.148525i
\(125\) 2.10499e8i 0.862203i
\(126\) −4.50979e8 + 2.22465e8i −1.78926 + 0.882632i
\(127\) 4.08192e8i 1.56910i 0.620069 + 0.784548i \(0.287105\pi\)
−0.620069 + 0.784548i \(0.712895\pi\)
\(128\) 1.77800e7 + 2.67846e8i 0.0662356 + 0.997804i
\(129\) 8.08538e7 0.291972
\(130\) 1.19040e7 + 2.41318e7i 0.0416794 + 0.0844920i
\(131\) 6.22874e6 0.0211502 0.0105751 0.999944i \(-0.496634\pi\)
0.0105751 + 0.999944i \(0.496634\pi\)
\(132\) 1.31436e8 1.71375e8i 0.432931 0.564485i
\(133\) 7.03776e8i 2.24920i
\(134\) −4.80709e7 9.74489e7i −0.149095 0.302244i
\(135\) 2.56179e7i 0.0771274i
\(136\) −2.63311e7 5.22779e6i −0.0769685 0.0152814i
\(137\) 1.41077e8 0.400475 0.200237 0.979747i \(-0.435829\pi\)
0.200237 + 0.979747i \(0.435829\pi\)
\(138\) 5.24680e8 2.58821e8i 1.44670 0.713648i
\(139\) −6.47844e8 −1.73545 −0.867723 0.497049i \(-0.834417\pi\)
−0.867723 + 0.497049i \(0.834417\pi\)
\(140\) −2.06148e8 + 2.68790e8i −0.536621 + 0.699684i
\(141\) 6.72173e8i 1.70061i
\(142\) −2.55918e8 + 1.26243e8i −0.629431 + 0.310494i
\(143\) 3.93992e7i 0.0942201i
\(144\) −1.23573e8 4.60304e8i −0.287392 1.07052i
\(145\) 1.79544e8 0.406161
\(146\) 6.80173e7 + 1.37884e8i 0.149695 + 0.303461i
\(147\) 1.51868e9 3.25235
\(148\) −3.75402e8 2.87914e8i −0.782438 0.600089i
\(149\) 5.50744e8i 1.11739i 0.829373 + 0.558695i \(0.188698\pi\)
−0.829373 + 0.558695i \(0.811302\pi\)
\(150\) −2.47159e8 5.01038e8i −0.488215 0.989705i
\(151\) 4.05487e7i 0.0779954i −0.999239 0.0389977i \(-0.987584\pi\)
0.999239 0.0389977i \(-0.0124165\pi\)
\(152\) 6.54252e8 + 1.29896e8i 1.22566 + 0.243344i
\(153\) 4.76630e7 0.0869792
\(154\) −4.44813e8 + 2.19423e8i −0.790851 + 0.390122i
\(155\) −6.90094e7 −0.119559
\(156\) 1.31232e8 + 1.00648e8i 0.221586 + 0.169945i
\(157\) 2.93738e8i 0.483460i 0.970344 + 0.241730i \(0.0777149\pi\)
−0.970344 + 0.241730i \(0.922285\pi\)
\(158\) 6.94965e8 3.42822e8i 1.11515 0.550098i
\(159\) 8.47379e8i 1.32583i
\(160\) −2.11827e8 2.41252e8i −0.323223 0.368122i
\(161\) −1.34357e9 −1.99966
\(162\) −2.68079e8 5.43448e8i −0.389227 0.789038i
\(163\) −4.61580e8 −0.653878 −0.326939 0.945045i \(-0.606017\pi\)
−0.326939 + 0.945045i \(0.606017\pi\)
\(164\) −3.74033e8 + 4.87689e8i −0.517052 + 0.674168i
\(165\) 2.58307e8i 0.348498i
\(166\) 4.29676e8 + 8.71034e8i 0.565859 + 1.14710i
\(167\) 1.08707e9i 1.39762i −0.715306 0.698811i \(-0.753713\pi\)
0.715306 0.698811i \(-0.246287\pi\)
\(168\) −4.05446e8 + 2.04213e9i −0.508974 + 2.56358i
\(169\) 7.85560e8 0.963014
\(170\) 2.87941e7 1.42039e7i 0.0344752 0.0170064i
\(171\) −1.18429e9 −1.38507
\(172\) 1.07100e8 1.39644e8i 0.122370 0.159554i
\(173\) 9.72883e8i 1.08612i −0.839695 0.543058i \(-0.817266\pi\)
0.839695 0.543058i \(-0.182734\pi\)
\(174\) 9.89659e8 4.88193e8i 1.07966 0.532591i
\(175\) 1.28303e9i 1.36799i
\(176\) −1.21884e8 4.54011e8i −0.127027 0.473168i
\(177\) −5.43141e8 −0.553375
\(178\) −1.84829e8 3.74684e8i −0.184116 0.373238i
\(179\) 1.52312e9 1.48362 0.741811 0.670610i \(-0.233967\pi\)
0.741811 + 0.670610i \(0.233967\pi\)
\(180\) 4.52310e8 + 3.46899e8i 0.430870 + 0.330455i
\(181\) 2.73420e8i 0.254751i −0.991855 0.127375i \(-0.959345\pi\)
0.991855 0.127375i \(-0.0406553\pi\)
\(182\) −1.68026e8 3.40620e8i −0.153140 0.310445i
\(183\) 8.05513e8i 0.718238i
\(184\) 2.47982e8 1.24902e9i 0.216346 1.08968i
\(185\) 5.65828e8 0.483056
\(186\) −3.80386e8 + 1.87642e8i −0.317813 + 0.156775i
\(187\) 4.70113e7 0.0384446
\(188\) 1.16092e9 + 8.90366e8i 0.929333 + 0.712750i
\(189\) 3.61597e8i 0.283385i
\(190\) −7.15450e8 + 3.52927e8i −0.548990 + 0.270813i
\(191\) 1.85158e9i 1.39126i −0.718401 0.695630i \(-0.755125\pi\)
0.718401 0.695630i \(-0.244875\pi\)
\(192\) −1.82359e9 7.53830e8i −1.34191 0.554713i
\(193\) 5.49166e8 0.395799 0.197899 0.980222i \(-0.436588\pi\)
0.197899 + 0.980222i \(0.436588\pi\)
\(194\) 6.71441e8 + 1.36114e9i 0.474025 + 0.960939i
\(195\) −1.97801e8 −0.136801
\(196\) 2.01166e9 2.62294e9i 1.36311 1.77731i
\(197\) 1.68731e9i 1.12029i 0.828396 + 0.560143i \(0.189254\pi\)
−0.828396 + 0.560143i \(0.810746\pi\)
\(198\) 3.69237e8 + 7.48514e8i 0.240240 + 0.487012i
\(199\) 1.99216e9i 1.27032i 0.772382 + 0.635158i \(0.219065\pi\)
−0.772382 + 0.635158i \(0.780935\pi\)
\(200\) −1.19274e9 2.36808e8i −0.745463 0.148005i
\(201\) 7.98759e8 0.489364
\(202\) −2.20389e9 + 1.08717e9i −1.32369 + 0.652966i
\(203\) −2.53426e9 −1.49234
\(204\) 1.20094e8 1.56587e8i 0.0693426 0.0904136i
\(205\) 7.35074e8i 0.416213i
\(206\) −1.32549e9 + 6.53856e8i −0.736051 + 0.363089i
\(207\) 2.26090e9i 1.23140i
\(208\) 3.47663e8 9.33337e7i 0.185740 0.0498638i
\(209\) −1.16809e9 −0.612199
\(210\) −1.10160e9 2.23315e9i −0.566429 1.14826i
\(211\) 3.31179e9 1.67083 0.835415 0.549619i \(-0.185227\pi\)
0.835415 + 0.549619i \(0.185227\pi\)
\(212\) −1.46352e9 1.12245e9i −0.724529 0.555676i
\(213\) 2.09769e9i 1.01911i
\(214\) −1.34688e8 2.73039e8i −0.0642207 0.130188i
\(215\) 2.10479e8i 0.0985045i
\(216\) 3.36151e8 + 6.67397e7i 0.154426 + 0.0306598i
\(217\) 9.74067e8 0.439288
\(218\) 1.98291e9 9.78156e8i 0.877964 0.433094i
\(219\) −1.13019e9 −0.491334
\(220\) 4.46126e8 + 3.42155e8i 0.190444 + 0.146060i
\(221\) 3.59993e7i 0.0150913i
\(222\) 3.11889e9 1.53853e9i 1.28407 0.633423i
\(223\) 1.21904e6i 0.000492943i −1.00000 0.000246472i \(-0.999922\pi\)
1.00000 0.000246472i \(-7.84543e-5\pi\)
\(224\) 2.98994e9 + 3.40528e9i 1.18760 + 1.35257i
\(225\) 2.15903e9 0.842419
\(226\) 1.38690e9 + 2.81150e9i 0.531631 + 1.07772i
\(227\) −1.98748e9 −0.748512 −0.374256 0.927326i \(-0.622102\pi\)
−0.374256 + 0.927326i \(0.622102\pi\)
\(228\) −2.98399e9 + 3.89073e9i −1.10422 + 1.43976i
\(229\) 3.87381e9i 1.40863i −0.709889 0.704314i \(-0.751255\pi\)
0.709889 0.704314i \(-0.248745\pi\)
\(230\) 6.73767e8 + 1.36585e9i 0.240768 + 0.488082i
\(231\) 3.64600e9i 1.28047i
\(232\) 4.67746e8 2.35592e9i 0.161458 0.813222i
\(233\) −4.25730e9 −1.44448 −0.722238 0.691645i \(-0.756886\pi\)
−0.722238 + 0.691645i \(0.756886\pi\)
\(234\) −5.73182e8 + 2.82747e8i −0.191174 + 0.0943049i
\(235\) −1.74981e9 −0.573745
\(236\) −7.19450e8 + 9.38068e8i −0.231928 + 0.302403i
\(237\) 5.69642e9i 1.80555i
\(238\) −4.06428e8 + 2.00488e8i −0.126671 + 0.0624858i
\(239\) 3.83381e9i 1.17500i −0.809223 0.587502i \(-0.800111\pi\)
0.809223 0.587502i \(-0.199889\pi\)
\(240\) 2.27932e9 6.11908e8i 0.687007 0.184434i
\(241\) 3.13878e8 0.0930451 0.0465225 0.998917i \(-0.485186\pi\)
0.0465225 + 0.998917i \(0.485186\pi\)
\(242\) −1.15311e9 2.33758e9i −0.336210 0.681562i
\(243\) 5.00344e9 1.43497
\(244\) 1.39122e9 + 1.06699e9i 0.392496 + 0.301024i
\(245\) 3.95345e9i 1.09727i
\(246\) −1.99872e9 4.05179e9i −0.545773 1.10639i
\(247\) 8.94480e8i 0.240316i
\(248\) −1.79783e8 + 9.05522e8i −0.0475272 + 0.239383i
\(249\) −7.13961e9 −1.85728
\(250\) 3.02047e9 1.48998e9i 0.773241 0.381435i
\(251\) 5.87707e9 1.48070 0.740348 0.672224i \(-0.234661\pi\)
0.740348 + 0.672224i \(0.234661\pi\)
\(252\) −6.38436e9 4.89647e9i −1.58312 1.21417i
\(253\) 2.22999e9i 0.544278i
\(254\) −5.85719e9 + 2.88932e9i −1.40720 + 0.694161i
\(255\) 2.36016e8i 0.0558189i
\(256\) −3.71750e9 + 2.15103e9i −0.865548 + 0.500826i
\(257\) 6.42037e9 1.47173 0.735865 0.677129i \(-0.236776\pi\)
0.735865 + 0.677129i \(0.236776\pi\)
\(258\) 5.72310e8 + 1.16018e9i 0.129167 + 0.261847i
\(259\) −7.98665e9 −1.77487
\(260\) −2.62009e8 + 3.41625e8i −0.0573354 + 0.0747578i
\(261\) 4.26455e9i 0.918991i
\(262\) 4.40891e7 + 8.93770e7i 0.00935677 + 0.0189680i
\(263\) 2.77731e9i 0.580499i 0.956951 + 0.290249i \(0.0937382\pi\)
−0.956951 + 0.290249i \(0.906262\pi\)
\(264\) 3.38943e9 + 6.72940e8i 0.697768 + 0.138535i
\(265\) 2.20590e9 0.447305
\(266\) 1.00986e10 4.98156e9i 2.01713 0.995036i
\(267\) 3.07117e9 0.604310
\(268\) 1.05804e9 1.37955e9i 0.205100 0.267423i
\(269\) 8.92780e9i 1.70504i −0.522693 0.852521i \(-0.675072\pi\)
0.522693 0.852521i \(-0.324928\pi\)
\(270\) −3.67594e8 + 1.81332e8i −0.0691694 + 0.0341208i
\(271\) 3.90717e9i 0.724411i 0.932098 + 0.362205i \(0.117976\pi\)
−0.932098 + 0.362205i \(0.882024\pi\)
\(272\) −1.11366e8 4.14832e8i −0.0203459 0.0757874i
\(273\) 2.79196e9 0.502641
\(274\) 9.98592e8 + 2.02434e9i 0.177168 + 0.359154i
\(275\) 2.12951e9 0.372347
\(276\) 7.42772e9 + 5.69668e9i 1.28003 + 0.981715i
\(277\) 2.72513e9i 0.462880i −0.972849 0.231440i \(-0.925656\pi\)
0.972849 0.231440i \(-0.0743437\pi\)
\(278\) −4.58565e9 9.29599e9i −0.767753 1.55638i
\(279\) 1.63912e9i 0.270517i
\(280\) −5.31609e9 1.05546e9i −0.864889 0.171716i
\(281\) 2.69619e9 0.432440 0.216220 0.976345i \(-0.430627\pi\)
0.216220 + 0.976345i \(0.430627\pi\)
\(282\) −9.64509e9 + 4.75786e9i −1.52514 + 0.752342i
\(283\) −1.09816e9 −0.171206 −0.0856031 0.996329i \(-0.527282\pi\)
−0.0856031 + 0.996329i \(0.527282\pi\)
\(284\) −3.62295e9 2.77861e9i −0.556915 0.427125i
\(285\) 5.86433e9i 0.888871i
\(286\) −5.65344e8 + 2.78881e8i −0.0844985 + 0.0416826i
\(287\) 1.03756e10i 1.52927i
\(288\) 5.73027e9 5.03136e9i 0.832924 0.731333i
\(289\) −6.93280e9 −0.993842
\(290\) 1.27087e9 + 2.57629e9i 0.179684 + 0.364253i
\(291\) −1.11569e10 −1.55586
\(292\) −1.49707e9 + 1.95198e9i −0.205925 + 0.268499i
\(293\) 4.39608e9i 0.596479i 0.954491 + 0.298239i \(0.0963994\pi\)
−0.954491 + 0.298239i \(0.903601\pi\)
\(294\) 1.07497e10 + 2.17917e10i 1.43883 + 2.91677i
\(295\) 1.41391e9i 0.186695i
\(296\) 1.47409e9 7.42464e9i 0.192025 0.967182i
\(297\) −6.00161e8 −0.0771333
\(298\) −7.90269e9 + 3.89835e9i −1.00210 + 0.494328i
\(299\) −1.70764e9 −0.213654
\(300\) 5.43998e9 7.09303e9i 0.671603 0.875682i
\(301\) 2.97092e9i 0.361930i
\(302\) 5.81838e8 2.87017e8i 0.0699478 0.0345048i
\(303\) 1.80646e10i 2.14318i
\(304\) 2.76712e9 + 1.03074e10i 0.323992 + 1.20685i
\(305\) −2.09692e9 −0.242316
\(306\) 3.37374e8 + 6.83922e8i 0.0384792 + 0.0780047i
\(307\) 3.80017e8 0.0427808 0.0213904 0.999771i \(-0.493191\pi\)
0.0213904 + 0.999771i \(0.493191\pi\)
\(308\) −6.29706e9 4.82952e9i −0.699738 0.536663i
\(309\) 1.08646e10i 1.19174i
\(310\) −4.88471e8 9.90224e8i −0.0528922 0.107223i
\(311\) 6.94987e9i 0.742908i 0.928451 + 0.371454i \(0.121141\pi\)
−0.928451 + 0.371454i \(0.878859\pi\)
\(312\) −5.15310e8 + 2.59549e9i −0.0543814 + 0.273906i
\(313\) 5.51220e8 0.0574312 0.0287156 0.999588i \(-0.490858\pi\)
0.0287156 + 0.999588i \(0.490858\pi\)
\(314\) −4.21488e9 + 2.07917e9i −0.433577 + 0.213881i
\(315\) 9.62287e9 0.977378
\(316\) 9.83839e9 + 7.54554e9i 0.986678 + 0.756731i
\(317\) 9.38012e9i 0.928905i 0.885598 + 0.464452i \(0.153749\pi\)
−0.885598 + 0.464452i \(0.846251\pi\)
\(318\) 1.21591e10 5.99802e9i 1.18903 0.586543i
\(319\) 4.20624e9i 0.406192i
\(320\) 1.96238e9 4.74720e9i 0.187147 0.452728i
\(321\) 2.23802e9 0.210787
\(322\) −9.51021e9 1.92790e10i −0.884640 1.79333i
\(323\) −1.06730e9 −0.0980561
\(324\) 5.90044e9 7.69340e9i 0.535432 0.698133i
\(325\) 1.63069e9i 0.146163i
\(326\) −3.26722e9 6.62327e9i −0.289273 0.586411i
\(327\) 1.62533e10i 1.42151i
\(328\) −9.64544e9 1.91501e9i −0.833349 0.165454i
\(329\) 2.46985e10 2.10808
\(330\) −3.70647e9 + 1.82838e9i −0.312540 + 0.154174i
\(331\) 1.45676e10 1.21360 0.606801 0.794854i \(-0.292452\pi\)
0.606801 + 0.794854i \(0.292452\pi\)
\(332\) −9.45719e9 + 1.23309e10i −0.778412 + 1.01495i
\(333\) 1.34396e10i 1.09298i
\(334\) 1.55984e10 7.69460e9i 1.25342 0.618302i
\(335\) 2.07934e9i 0.165100i
\(336\) −3.21726e10 + 8.63708e9i −2.52423 + 0.677656i
\(337\) −1.43980e10 −1.11630 −0.558152 0.829739i \(-0.688489\pi\)
−0.558152 + 0.829739i \(0.688489\pi\)
\(338\) 5.56046e9 + 1.12721e10i 0.426033 + 0.863651i
\(339\) −2.30451e10 −1.74493
\(340\) 4.07628e8 + 3.12629e8i 0.0305034 + 0.0233945i
\(341\) 1.61671e9i 0.119568i
\(342\) −8.38278e9 1.69935e10i −0.612750 1.24216i
\(343\) 3.08892e10i 2.23167i
\(344\) 2.76186e9 + 5.48341e8i 0.197227 + 0.0391577i
\(345\) −1.11955e10 −0.790254
\(346\) 1.39600e10 6.88639e9i 0.974051 0.480493i
\(347\) 1.26794e10 0.874539 0.437270 0.899331i \(-0.355946\pi\)
0.437270 + 0.899331i \(0.355946\pi\)
\(348\) 1.40103e10 + 1.07452e10i 0.955277 + 0.732648i
\(349\) 1.29547e10i 0.873222i 0.899650 + 0.436611i \(0.143821\pi\)
−0.899650 + 0.436611i \(0.856179\pi\)
\(350\) −1.84103e10 + 9.08168e9i −1.22684 + 0.605193i
\(351\) 4.59579e8i 0.0302783i
\(352\) 5.65192e9 4.96256e9i 0.368150 0.323248i
\(353\) −2.77667e10 −1.78824 −0.894120 0.447828i \(-0.852198\pi\)
−0.894120 + 0.447828i \(0.852198\pi\)
\(354\) −3.84453e9 7.79359e9i −0.244811 0.496278i
\(355\) 5.46072e9 0.343824
\(356\) 4.06811e9 5.30428e9i 0.253275 0.330237i
\(357\) 3.33137e9i 0.205093i
\(358\) 1.07812e10 + 2.18555e10i 0.656347 + 1.33054i
\(359\) 1.05991e10i 0.638103i −0.947737 0.319052i \(-0.896636\pi\)
0.947737 0.319052i \(-0.103364\pi\)
\(360\) −1.77609e9 + 8.94572e9i −0.105744 + 0.532605i
\(361\) 9.53565e9 0.561464
\(362\) 3.92333e9 1.93536e9i 0.228466 0.112701i
\(363\) 1.91605e10 1.10352
\(364\) 3.69825e9 4.82204e9i 0.210664 0.274679i
\(365\) 2.94213e9i 0.165764i
\(366\) −1.15584e10 + 5.70169e9i −0.644130 + 0.317745i
\(367\) 1.91289e10i 1.05445i −0.849726 0.527224i \(-0.823233\pi\)
0.849726 0.527224i \(-0.176767\pi\)
\(368\) 1.96777e10 5.28267e9i 1.07296 0.288046i
\(369\) 1.74596e10 0.941735
\(370\) 4.00511e9 + 8.11913e9i 0.213702 + 0.433214i
\(371\) −3.11363e10 −1.64351
\(372\) −5.38499e9 4.13001e9i −0.281198 0.215665i
\(373\) 3.40704e10i 1.76012i 0.474865 + 0.880059i \(0.342497\pi\)
−0.474865 + 0.880059i \(0.657503\pi\)
\(374\) 3.32761e8 + 6.74570e8i 0.0170077 + 0.0344779i
\(375\) 2.47579e10i 1.25196i
\(376\) −4.55859e9 + 2.29605e10i −0.228076 + 1.14876i
\(377\) −3.22097e9 −0.159449
\(378\) 5.18859e9 2.55950e9i 0.254146 0.125368i
\(379\) 4.16311e9 0.201772 0.100886 0.994898i \(-0.467832\pi\)
0.100886 + 0.994898i \(0.467832\pi\)
\(380\) −1.01284e10 7.76794e9i −0.485742 0.372539i
\(381\) 4.80096e10i 2.27839i
\(382\) 2.65685e10 1.31061e10i 1.24771 0.615487i
\(383\) 7.32538e9i 0.340436i −0.985406 0.170218i \(-0.945553\pi\)
0.985406 0.170218i \(-0.0544472\pi\)
\(384\) −2.09120e9 3.15028e10i −0.0961769 1.44885i
\(385\) 9.49130e9 0.431999
\(386\) 3.88718e9 + 7.88004e9i 0.175100 + 0.354960i
\(387\) −4.99935e9 −0.222879
\(388\) −1.47785e10 + 1.92692e10i −0.652083 + 0.850230i
\(389\) 4.02169e10i 1.75635i −0.478341 0.878174i \(-0.658762\pi\)
0.478341 0.878174i \(-0.341238\pi\)
\(390\) −1.40010e9 2.83827e9i −0.0605202 0.122686i
\(391\) 2.03756e9i 0.0871771i
\(392\) 5.18761e10 + 1.02995e10i 2.19696 + 0.436187i
\(393\) −7.32596e8 −0.0307110
\(394\) −2.42114e10 + 1.19433e10i −1.00469 + 0.495610i
\(395\) −1.48290e10 −0.609148
\(396\) −8.12694e9 + 1.05965e10i −0.330481 + 0.430903i
\(397\) 6.79229e9i 0.273435i −0.990610 0.136717i \(-0.956345\pi\)
0.990610 0.136717i \(-0.0436552\pi\)
\(398\) −2.85857e10 + 1.41012e10i −1.13924 + 0.561982i
\(399\) 8.27749e10i 3.26593i
\(400\) −5.04463e9 1.87910e10i −0.197056 0.734023i
\(401\) −5.36689e9 −0.207561 −0.103780 0.994600i \(-0.533094\pi\)
−0.103780 + 0.994600i \(0.533094\pi\)
\(402\) 5.65388e9 + 1.14615e10i 0.216492 + 0.438871i
\(403\) 1.23801e9 0.0469358
\(404\) −3.11998e10 2.39286e10i −1.17119 0.898239i
\(405\) 1.15959e10i 0.431009i
\(406\) −1.79383e10 3.63643e10i −0.660202 1.33836i
\(407\) 1.32559e10i 0.483093i
\(408\) 3.09694e9 + 6.14869e8i 0.111762 + 0.0221892i
\(409\) −1.14532e10 −0.409293 −0.204647 0.978836i \(-0.565605\pi\)
−0.204647 + 0.978836i \(0.565605\pi\)
\(410\) 1.05477e10 5.20309e9i 0.373268 0.184131i
\(411\) −1.65929e10 −0.581506
\(412\) −1.87645e10 1.43914e10i −0.651251 0.499476i
\(413\) 1.99573e10i 0.685966i
\(414\) −3.24420e10 + 1.60034e10i −1.10435 + 0.544768i
\(415\) 1.85859e10i 0.626601i
\(416\) 3.80013e9 + 4.32801e9i 0.126889 + 0.144516i
\(417\) 7.61964e10 2.51994
\(418\) −8.26816e9 1.67611e10i −0.270834 0.549033i
\(419\) 3.53809e10 1.14792 0.573961 0.818883i \(-0.305406\pi\)
0.573961 + 0.818883i \(0.305406\pi\)
\(420\) 2.42462e10 3.16139e10i 0.779197 1.01597i
\(421\) 4.32861e10i 1.37791i 0.724806 + 0.688953i \(0.241929\pi\)
−0.724806 + 0.688953i \(0.758071\pi\)
\(422\) 2.34419e10 + 4.75212e10i 0.739168 + 1.49843i
\(423\) 4.15617e10i 1.29817i
\(424\) 5.74682e9 2.89453e10i 0.177813 0.895601i
\(425\) 1.94574e9 0.0596389
\(426\) 3.00999e10 1.48481e10i 0.913960 0.450851i
\(427\) 2.95980e10 0.890330
\(428\) 2.96450e9 3.86532e9i 0.0883439 0.115189i
\(429\) 4.63396e9i 0.136812i
\(430\) −3.02020e9 + 1.48984e9i −0.0883408 + 0.0435779i
\(431\) 2.06603e10i 0.598724i −0.954140 0.299362i \(-0.903226\pi\)
0.954140 0.299362i \(-0.0967739\pi\)
\(432\) 1.42173e9 + 5.29588e9i 0.0408210 + 0.152056i
\(433\) −3.26720e10 −0.929447 −0.464723 0.885456i \(-0.653846\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(434\) 6.89477e9 + 1.39770e10i 0.194339 + 0.393963i
\(435\) −2.11171e10 −0.589762
\(436\) 2.80714e10 + 2.15293e10i 0.776815 + 0.595777i
\(437\) 5.06274e10i 1.38822i
\(438\) −7.99988e9 1.62173e10i −0.217364 0.440638i
\(439\) 2.83909e10i 0.764401i 0.924079 + 0.382201i \(0.124834\pi\)
−0.924079 + 0.382201i \(0.875166\pi\)
\(440\) −1.75180e9 + 8.82340e9i −0.0467385 + 0.235410i
\(441\) −9.39030e10 −2.48270
\(442\) −5.16559e8 + 2.54815e8i −0.0135341 + 0.00667630i
\(443\) −1.69063e10 −0.438968 −0.219484 0.975616i \(-0.570437\pi\)
−0.219484 + 0.975616i \(0.570437\pi\)
\(444\) 4.41531e10 + 3.38631e10i 1.13613 + 0.871355i
\(445\) 7.99491e9i 0.203880i
\(446\) 1.74921e7 8.62873e6i 0.000442081 0.000218076i
\(447\) 6.47760e10i 1.62250i
\(448\) −2.76990e10 + 6.70067e10i −0.687624 + 1.66344i
\(449\) 2.99952e10 0.738016 0.369008 0.929426i \(-0.379697\pi\)
0.369008 + 0.929426i \(0.379697\pi\)
\(450\) 1.52823e10 + 3.09801e10i 0.372682 + 0.755498i
\(451\) 1.72209e10 0.416245
\(452\) −3.05257e10 + 3.98015e10i −0.731327 + 0.953555i
\(453\) 4.76915e9i 0.113253i
\(454\) −1.40680e10 2.85185e10i −0.331138 0.671280i
\(455\) 7.26805e9i 0.169579i
\(456\) −7.69501e10 1.52777e10i −1.77971 0.353345i
\(457\) 6.23791e9 0.143013 0.0715063 0.997440i \(-0.477219\pi\)
0.0715063 + 0.997440i \(0.477219\pi\)
\(458\) 5.55857e10 2.74201e10i 1.26329 0.623171i
\(459\) −5.48371e8 −0.0123545
\(460\) −1.48297e10 + 1.93359e10i −0.331207 + 0.431851i
\(461\) 4.50780e10i 0.998070i 0.866582 + 0.499035i \(0.166312\pi\)
−0.866582 + 0.499035i \(0.833688\pi\)
\(462\) 5.23168e10 2.58076e10i 1.14835 0.566473i
\(463\) 1.05219e10i 0.228965i 0.993425 + 0.114482i \(0.0365210\pi\)
−0.993425 + 0.114482i \(0.963479\pi\)
\(464\) 3.71163e10 9.96424e9i 0.800742 0.214967i
\(465\) 8.11656e9 0.173604
\(466\) −3.01346e10 6.10885e10i −0.639030 1.29544i
\(467\) −5.51764e10 −1.16008 −0.580038 0.814590i \(-0.696962\pi\)
−0.580038 + 0.814590i \(0.696962\pi\)
\(468\) −8.11434e9 6.22328e9i −0.169149 0.129729i
\(469\) 2.93499e10i 0.606617i
\(470\) −1.23857e10 2.51082e10i −0.253822 0.514546i
\(471\) 3.45481e10i 0.702005i
\(472\) −1.85530e10 3.68352e9i −0.373805 0.0742155i
\(473\) −4.93099e9 −0.0985121
\(474\) −8.17386e10 + 4.03212e10i −1.61925 + 0.798766i
\(475\) −4.83461e10 −0.949702
\(476\) −5.75366e9 4.41276e9i −0.112077 0.0859573i
\(477\) 5.23950e10i 1.01208i
\(478\) 5.50118e10 2.71370e10i 1.05377 0.519816i
\(479\) 2.46128e10i 0.467540i 0.972292 + 0.233770i \(0.0751063\pi\)
−0.972292 + 0.233770i \(0.924894\pi\)
\(480\) 2.49141e10 + 2.83750e10i 0.469333 + 0.534529i
\(481\) −1.01508e10 −0.189636
\(482\) 2.22173e9 + 4.50388e9i 0.0411627 + 0.0834447i
\(483\) 1.58024e11 2.90359
\(484\) 2.53801e10 3.30923e10i 0.462501 0.603040i
\(485\) 2.90436e10i 0.524909i
\(486\) 3.54160e10 + 7.17949e10i 0.634825 + 1.28691i
\(487\) 1.03802e10i 0.184539i −0.995734 0.0922695i \(-0.970588\pi\)
0.995734 0.0922695i \(-0.0294121\pi\)
\(488\) −5.46289e9 + 2.75152e10i −0.0963260 + 0.485170i
\(489\) 5.42890e10 0.949459
\(490\) −5.67285e10 + 2.79838e10i −0.984049 + 0.485425i
\(491\) 5.19024e10 0.893020 0.446510 0.894779i \(-0.352667\pi\)
0.446510 + 0.894779i \(0.352667\pi\)
\(492\) 4.39920e10 5.73598e10i 0.750781 0.978920i
\(493\) 3.84327e9i 0.0650598i
\(494\) 1.28350e10 6.33142e9i 0.215520 0.106315i
\(495\) 1.59716e10i 0.266028i
\(496\) −1.42660e10 + 3.82986e9i −0.235709 + 0.0632785i
\(497\) −7.70780e10 −1.26330
\(498\) −5.05365e10 1.02447e11i −0.821651 1.66564i
\(499\) −8.02548e9 −0.129440 −0.0647200 0.997903i \(-0.520615\pi\)
−0.0647200 + 0.997903i \(0.520615\pi\)
\(500\) 4.27598e10 + 3.27946e10i 0.684157 + 0.524713i
\(501\) 1.27856e11i 2.02941i
\(502\) 4.15998e10 + 8.43308e10i 0.655053 + 1.32792i
\(503\) 1.37392e10i 0.214629i 0.994225 + 0.107314i \(0.0342252\pi\)
−0.994225 + 0.107314i \(0.965775\pi\)
\(504\) 2.50695e10 1.26269e11i 0.388529 1.95692i
\(505\) 4.70261e10 0.723058
\(506\) −3.19984e10 + 1.57846e10i −0.488120 + 0.240786i
\(507\) −9.23940e10 −1.39834
\(508\) −8.29183e10 6.35940e10i −1.24507 0.954908i
\(509\) 6.98889e10i 1.04121i −0.853798 0.520604i \(-0.825707\pi\)
0.853798 0.520604i \(-0.174293\pi\)
\(510\) −3.38663e9 + 1.67060e9i −0.0500595 + 0.0246940i
\(511\) 4.15282e10i 0.609059i
\(512\) −5.71791e10 3.81172e10i −0.832065 0.554678i
\(513\) 1.36254e10 0.196735
\(514\) 4.54455e10 + 9.21267e10i 0.651086 + 1.31988i
\(515\) 2.82830e10 0.402065
\(516\) −1.25966e10 + 1.64243e10i −0.177686 + 0.231680i
\(517\) 4.09934e10i 0.573789i
\(518\) −5.65322e10 1.14601e11i −0.785193 1.59174i
\(519\) 1.14426e11i 1.57709i
\(520\) −6.75660e9 1.34146e9i −0.0924092 0.0183470i
\(521\) 1.24271e11 1.68662 0.843312 0.537425i \(-0.180603\pi\)
0.843312 + 0.537425i \(0.180603\pi\)
\(522\) −6.11925e10 + 3.01859e10i −0.824169 + 0.406557i
\(523\) −1.30062e11 −1.73838 −0.869189 0.494480i \(-0.835359\pi\)
−0.869189 + 0.494480i \(0.835359\pi\)
\(524\) −9.70404e8 + 1.26528e9i −0.0128714 + 0.0167827i
\(525\) 1.50904e11i 1.98638i
\(526\) −3.98519e10 + 1.96587e10i −0.520603 + 0.256810i
\(527\) 1.47720e9i 0.0191512i
\(528\) 1.43354e10 + 5.33986e10i 0.184448 + 0.687060i
\(529\) −1.83409e10 −0.234206
\(530\) 1.56141e10 + 3.16528e10i 0.197886 + 0.401152i
\(531\) 3.35834e10 0.422423
\(532\) 1.42962e11 + 1.09644e11i 1.78474 + 1.36880i
\(533\) 1.31870e10i 0.163395i
\(534\) 2.17388e10 + 4.40687e10i 0.267344 + 0.541957i
\(535\) 5.82603e9i 0.0711144i
\(536\) 2.72845e10 + 5.41709e9i 0.330565 + 0.0656307i
\(537\) −1.79143e11 −2.15428
\(538\) 1.28106e11 6.31939e10i 1.52912 0.754303i
\(539\) −9.26190e10 −1.09735
\(540\) −5.20391e9 3.99113e9i −0.0612005 0.0469376i
\(541\) 1.23457e11i 1.44121i −0.693347 0.720604i \(-0.743865\pi\)
0.693347 0.720604i \(-0.256135\pi\)
\(542\) −5.60644e10 + 2.76562e10i −0.649666 + 0.320476i
\(543\) 3.21584e10i 0.369909i
\(544\) 5.16419e9 4.53432e9i 0.0589667 0.0517746i
\(545\) −4.23108e10 −0.479584
\(546\) 1.97624e10 + 4.00621e10i 0.222366 + 0.450779i
\(547\) 6.29196e10 0.702808 0.351404 0.936224i \(-0.385704\pi\)
0.351404 + 0.936224i \(0.385704\pi\)
\(548\) −2.19791e10 + 2.86578e10i −0.243718 + 0.317776i
\(549\) 4.98064e10i 0.548272i
\(550\) 1.50733e10 + 3.05565e10i 0.164725 + 0.333929i
\(551\) 9.54941e10i 1.03602i
\(552\) −2.91665e10 + 1.46904e11i −0.314143 + 1.58226i
\(553\) 2.09311e11 2.23816
\(554\) 3.91033e10 1.92894e10i 0.415120 0.204776i
\(555\) −6.65500e10 −0.701417
\(556\) 1.00930e11 1.31600e11i 1.05614 1.37707i
\(557\) 1.43749e11i 1.49343i 0.665146 + 0.746713i \(0.268369\pi\)
−0.665146 + 0.746713i \(0.731631\pi\)
\(558\) 2.35200e10 1.16022e10i 0.242605 0.119676i
\(559\) 3.77595e9i 0.0386704i
\(560\) −2.24841e10 8.37522e10i −0.228625 0.851616i
\(561\) −5.52925e9 −0.0558232
\(562\) 1.90845e10 + 3.86880e10i 0.191310 + 0.387821i
\(563\) 1.24137e11 1.23557 0.617786 0.786346i \(-0.288030\pi\)
0.617786 + 0.786346i \(0.288030\pi\)
\(564\) −1.36542e11 1.04721e11i −1.34943 1.03494i
\(565\) 5.99911e10i 0.588699i
\(566\) −7.77313e9 1.57576e10i −0.0757409 0.153541i
\(567\) 1.63677e11i 1.58363i
\(568\) 1.42262e10 7.16541e10i 0.136678 0.688411i
\(569\) −6.03923e9 −0.0576146 −0.0288073 0.999585i \(-0.509171\pi\)
−0.0288073 + 0.999585i \(0.509171\pi\)
\(570\) 8.41479e10 4.15096e10i 0.797157 0.393233i
\(571\) 1.39234e11 1.30979 0.654895 0.755720i \(-0.272713\pi\)
0.654895 + 0.755720i \(0.272713\pi\)
\(572\) −8.00339e9 6.13819e9i −0.0747635 0.0573398i
\(573\) 2.17774e11i 2.02017i
\(574\) −1.48880e11 + 7.34416e10i −1.37148 + 0.676542i
\(575\) 9.22968e10i 0.844336i
\(576\) 1.12756e11 + 4.66107e10i 1.02436 + 0.423444i
\(577\) −1.45928e11 −1.31654 −0.658272 0.752780i \(-0.728713\pi\)
−0.658272 + 0.752780i \(0.728713\pi\)
\(578\) −4.90727e10 9.94796e10i −0.439671 0.891298i
\(579\) −6.45904e10 −0.574716
\(580\) −2.79719e10 + 3.64717e10i −0.247178 + 0.322288i
\(581\) 2.62340e11i 2.30229i
\(582\) −7.89719e10 1.60091e11i −0.688304 1.39532i
\(583\) 5.16786e10i 0.447339i
\(584\) −3.86059e10 7.66484e9i −0.331896 0.0658949i
\(585\) 1.22304e10 0.104428
\(586\) −6.30799e10 + 3.11169e10i −0.534934 + 0.263880i
\(587\) 3.80703e10 0.320652 0.160326 0.987064i \(-0.448745\pi\)
0.160326 + 0.987064i \(0.448745\pi\)
\(588\) −2.36602e11 + 3.08498e11i −1.97929 + 2.58073i
\(589\) 3.67041e10i 0.304968i
\(590\) 2.02884e10 1.00081e10i 0.167432 0.0825933i
\(591\) 1.98453e11i 1.62670i
\(592\) 1.16971e11 3.14021e10i 0.952340 0.255665i
\(593\) −7.93163e10 −0.641421 −0.320711 0.947177i \(-0.603922\pi\)
−0.320711 + 0.947177i \(0.603922\pi\)
\(594\) −4.24814e9 8.61178e9i −0.0341234 0.0691747i
\(595\) 8.67225e9 0.0691933
\(596\) −1.11876e11 8.58029e10i −0.886647 0.680012i
\(597\) 2.34309e11i 1.84455i
\(598\) −1.20872e10 2.45031e10i −0.0945195 0.191609i
\(599\) 7.53655e10i 0.585417i 0.956202 + 0.292709i \(0.0945566\pi\)
−0.956202 + 0.292709i \(0.905443\pi\)
\(600\) 1.40285e11 + 2.78522e10i 1.08244 + 0.214909i
\(601\) −1.21175e11 −0.928785 −0.464392 0.885630i \(-0.653727\pi\)
−0.464392 + 0.885630i \(0.653727\pi\)
\(602\) 4.26300e10 2.10291e10i 0.324586 0.160116i
\(603\) −4.93888e10 −0.373559
\(604\) 8.23688e9 + 6.31726e9i 0.0618892 + 0.0474658i
\(605\) 4.98787e10i 0.372301i
\(606\) 2.59212e11 1.27868e11i 1.92205 0.948134i
\(607\) 2.19334e10i 0.161566i 0.996732 + 0.0807832i \(0.0257422\pi\)
−0.996732 + 0.0807832i \(0.974258\pi\)
\(608\) −1.28315e11 + 1.12665e11i −0.938997 + 0.824469i
\(609\) 2.98068e11 2.16693
\(610\) −1.48427e10 3.00890e10i −0.107200 0.217314i
\(611\) 3.13911e10 0.225238
\(612\) −7.42563e9 + 9.68205e9i −0.0529331 + 0.0690179i
\(613\) 4.23372e10i 0.299833i −0.988699 0.149917i \(-0.952099\pi\)
0.988699 0.149917i \(-0.0479005\pi\)
\(614\) 2.68988e9 + 5.45291e9i 0.0189261 + 0.0383667i
\(615\) 8.64560e10i 0.604359i
\(616\) 2.47267e10 1.24542e11i 0.171729 0.864956i
\(617\) 1.11249e11 0.767635 0.383817 0.923409i \(-0.374609\pi\)
0.383817 + 0.923409i \(0.374609\pi\)
\(618\) 1.55898e11 7.69035e10i 1.06878 0.527221i
\(619\) −1.10105e11 −0.749972 −0.374986 0.927030i \(-0.622353\pi\)
−0.374986 + 0.927030i \(0.622353\pi\)
\(620\) 1.07513e10 1.40183e10i 0.0727601 0.0948696i
\(621\) 2.60121e10i 0.174908i
\(622\) −9.97245e10 + 4.91934e10i −0.666255 + 0.328659i
\(623\) 1.12848e11i 0.749104i
\(624\) −4.08905e10 + 1.09775e10i −0.269702 + 0.0724043i
\(625\) 5.15188e10 0.337634
\(626\) 3.90172e9 + 7.90952e9i 0.0254073 + 0.0515054i
\(627\) 1.37386e11 0.888939
\(628\) −5.96685e10 4.57627e10i −0.383625 0.294221i
\(629\) 1.21120e10i 0.0773770i
\(630\) 6.81139e10 + 1.38080e11i 0.432388 + 0.876532i
\(631\) 4.27197e10i 0.269470i 0.990882 + 0.134735i \(0.0430184\pi\)
−0.990882 + 0.134735i \(0.956982\pi\)
\(632\) −3.86324e10 + 1.94582e11i −0.242150 + 1.21965i
\(633\) −3.89517e11 −2.42612
\(634\) −1.34596e11 + 6.63956e10i −0.833060 + 0.410943i
\(635\) 1.24979e11 0.768675
\(636\) 1.72133e11 + 1.32017e11i 1.05205 + 0.806866i
\(637\) 7.09239e10i 0.430759i
\(638\) −6.03558e10 + 2.97731e10i −0.364281 + 0.179697i
\(639\) 1.29704e11i 0.777946i
\(640\) 8.20085e10 5.44384e9i 0.488809 0.0324478i
\(641\) 3.95082e10 0.234021 0.117011 0.993131i \(-0.462669\pi\)
0.117011 + 0.993131i \(0.462669\pi\)
\(642\) 1.58414e10 + 3.21136e10i 0.0932511 + 0.189038i
\(643\) −2.31888e11 −1.35655 −0.678273 0.734810i \(-0.737271\pi\)
−0.678273 + 0.734810i \(0.737271\pi\)
\(644\) 2.09320e11 2.72926e11i 1.21694 1.58673i
\(645\) 2.47556e10i 0.143033i
\(646\) −7.55467e9 1.53147e10i −0.0433796 0.0879386i
\(647\) 2.28008e11i 1.30117i −0.759434 0.650584i \(-0.774524\pi\)
0.759434 0.650584i \(-0.225476\pi\)
\(648\) 1.52159e11 + 3.02097e10i 0.862973 + 0.171335i
\(649\) 3.31242e10 0.186710
\(650\) −2.33990e10 + 1.15426e10i −0.131082 + 0.0646619i
\(651\) −1.14565e11 −0.637865
\(652\) 7.19117e10 9.37634e10i 0.397932 0.518851i
\(653\) 2.39319e11i 1.31621i −0.752927 0.658104i \(-0.771359\pi\)
0.752927 0.658104i \(-0.228641\pi\)
\(654\) −2.33221e11 + 1.15046e11i −1.27484 + 0.628871i
\(655\) 1.90710e9i 0.0103612i
\(656\) −4.07949e10 1.51959e11i −0.220288 0.820560i
\(657\) 6.98820e10 0.375063
\(658\) 1.74824e11 + 3.54402e11i 0.932606 + 1.89057i
\(659\) −1.93384e10 −0.102537 −0.0512684 0.998685i \(-0.516326\pi\)
−0.0512684 + 0.998685i \(0.516326\pi\)
\(660\) −5.24713e10 4.02428e10i −0.276532 0.212086i
\(661\) 6.26405e10i 0.328133i 0.986449 + 0.164066i \(0.0524611\pi\)
−0.986449 + 0.164066i \(0.947539\pi\)
\(662\) 1.03114e11 + 2.09032e11i 0.536892 + 1.08838i
\(663\) 4.23408e9i 0.0219131i
\(664\) −2.43879e11 4.84199e10i −1.25459 0.249087i
\(665\) −2.15481e11 −1.10185
\(666\) −1.92847e11 + 9.51302e10i −0.980203 + 0.483528i
\(667\) −1.82306e11 −0.921082
\(668\) 2.20822e11 + 1.69359e11i 1.10901 + 0.850554i
\(669\) 1.43377e8i 0.000715774i
\(670\) −2.98367e10 + 1.47182e10i −0.148065 + 0.0730393i
\(671\) 4.91254e10i 0.242335i
\(672\) −3.51663e11 4.00513e11i −1.72445 1.96399i
\(673\) 2.62188e11 1.27806 0.639031 0.769181i \(-0.279335\pi\)
0.639031 + 0.769181i \(0.279335\pi\)
\(674\) −1.01914e11 2.06598e11i −0.493848 1.00112i
\(675\) −2.48400e10 −0.119656
\(676\) −1.22386e11 + 1.59575e11i −0.586064 + 0.764150i
\(677\) 7.51591e10i 0.357789i 0.983868 + 0.178894i \(0.0572520\pi\)
−0.983868 + 0.178894i \(0.942748\pi\)
\(678\) −1.63120e11 3.30676e11i −0.771951 1.56489i
\(679\) 4.09951e11i 1.92865i
\(680\) −1.60063e9 + 8.06199e9i −0.00748611 + 0.0377057i
\(681\) 2.33758e11 1.08687
\(682\) 2.31984e10 1.14436e10i 0.107231 0.0528963i
\(683\) 2.26925e11 1.04280 0.521399 0.853313i \(-0.325410\pi\)
0.521399 + 0.853313i \(0.325410\pi\)
\(684\) 1.84506e11 2.40571e11i 0.842917 1.09905i
\(685\) 4.31947e10i 0.196186i
\(686\) 4.43232e11 2.18644e11i 2.00140 0.987280i
\(687\) 4.55620e11i 2.04539i
\(688\) 1.16811e10 + 4.35115e10i 0.0521351 + 0.194201i
\(689\) −3.95734e10 −0.175601
\(690\) −7.92454e10 1.60645e11i −0.349605 0.708716i
\(691\) 1.78978e11 0.785034 0.392517 0.919745i \(-0.371604\pi\)
0.392517 + 0.919745i \(0.371604\pi\)
\(692\) 1.97627e11 + 1.51570e11i 0.861832 + 0.660980i
\(693\) 2.25439e11i 0.977453i
\(694\) 8.97486e10 + 1.81938e11i 0.386892 + 0.784304i
\(695\) 1.98355e11i 0.850168i
\(696\) −5.50142e10 + 2.77093e11i −0.234443 + 1.18083i
\(697\) 1.57348e10 0.0666700
\(698\) −1.85888e11 + 9.16974e10i −0.783123 + 0.386309i
\(699\) 5.00724e11 2.09744
\(700\) −2.60628e11 1.99888e11i −1.08550 0.832522i
\(701\) 3.94384e11i 1.63323i −0.577182 0.816615i \(-0.695848\pi\)
0.577182 0.816615i \(-0.304152\pi\)
\(702\) 6.59456e9 3.25305e9i 0.0271542 0.0133950i
\(703\) 3.00948e11i 1.23217i
\(704\) 1.11215e11 + 4.59734e10i 0.452763 + 0.187161i
\(705\) 2.05804e11 0.833101
\(706\) −1.96542e11 3.98428e11i −0.791109 1.60373i
\(707\) −6.63773e11 −2.65670
\(708\) 8.46184e10 1.10331e11i 0.336769 0.439102i
\(709\) 2.95896e11i 1.17099i −0.810675 0.585496i \(-0.800900\pi\)
0.810675 0.585496i \(-0.199100\pi\)
\(710\) 3.86528e10 + 7.83565e10i 0.152106 + 0.308348i
\(711\) 3.52221e11i 1.37828i
\(712\) 1.04907e11 + 2.08283e10i 0.408211 + 0.0810466i
\(713\) 7.00712e10 0.271132
\(714\) 4.78022e10 2.35805e10i 0.183931 0.0907320i
\(715\) 1.20632e10 0.0461570
\(716\) −2.37294e11 + 3.09401e11i −0.902891 + 1.17725i
\(717\) 4.50915e11i 1.70615i
\(718\) 1.52088e11 7.50239e10i 0.572264 0.282294i
\(719\) 5.83303e10i 0.218262i −0.994027 0.109131i \(-0.965193\pi\)
0.994027 0.109131i \(-0.0348068\pi\)
\(720\) −1.40935e11 + 3.78354e10i −0.524431 + 0.140789i
\(721\) −3.99214e11 −1.47729
\(722\) 6.74965e10 + 1.36828e11i 0.248389 + 0.503532i
\(723\) −3.69169e10 −0.135105
\(724\) 5.55413e10 + 4.25973e10i 0.202144 + 0.155034i
\(725\) 1.74091e11i 0.630123i
\(726\) 1.35624e11 + 2.74936e11i 0.488191 + 0.989657i
\(727\) 1.79422e11i 0.642302i −0.947028 0.321151i \(-0.895930\pi\)
0.947028 0.321151i \(-0.104070\pi\)
\(728\) 9.53694e10 + 1.89347e10i 0.339534 + 0.0674114i
\(729\) −3.39995e11 −1.20382
\(730\) 4.22170e10 2.08254e10i 0.148661 0.0733333i
\(731\) −4.50547e9 −0.0157787
\(732\) −1.63628e11 1.25495e11i −0.569921 0.437100i
\(733\) 4.89146e11i 1.69443i 0.531252 + 0.847214i \(0.321722\pi\)
−0.531252 + 0.847214i \(0.678278\pi\)
\(734\) 2.74483e11 1.35401e11i 0.945651 0.466483i
\(735\) 4.64986e11i 1.59328i
\(736\) 2.15087e11 + 2.44965e11i 0.732997 + 0.834819i
\(737\) −4.87135e10 −0.165112
\(738\) 1.23585e11 + 2.50530e11i 0.416620 + 0.844567i
\(739\) −7.93815e10 −0.266159 −0.133080 0.991105i \(-0.542487\pi\)
−0.133080 + 0.991105i \(0.542487\pi\)
\(740\) −8.81528e10 + 1.14940e11i −0.293974 + 0.383304i
\(741\) 1.05205e11i 0.348949i
\(742\) −2.20393e11 4.46779e11i −0.727081 1.47393i
\(743\) 3.46525e11i 1.13705i −0.822666 0.568525i \(-0.807514\pi\)
0.822666 0.568525i \(-0.192486\pi\)
\(744\) 2.11453e10 1.06503e11i 0.0690115 0.347594i
\(745\) 1.68625e11 0.547392
\(746\) −4.88880e11 + 2.41161e11i −1.57851 + 0.778668i
\(747\) 4.41455e11 1.41777
\(748\) −7.32410e9 + 9.54966e9i −0.0233963 + 0.0305057i
\(749\) 8.22344e10i 0.261292i
\(750\) −3.55254e11 + 1.75245e11i −1.12278 + 0.553859i
\(751\) 4.95183e11i 1.55670i 0.627828 + 0.778352i \(0.283944\pi\)
−0.627828 + 0.778352i \(0.716056\pi\)
\(752\) −3.61730e11 + 9.71102e10i −1.13113 + 0.303664i
\(753\) −6.91234e11 −2.15003
\(754\) −2.27991e10 4.62180e10i −0.0705394 0.142997i
\(755\) −1.24151e10 −0.0382087
\(756\) 7.34532e10 + 5.63348e10i 0.224866 + 0.172460i
\(757\) 2.26936e11i 0.691066i −0.938407 0.345533i \(-0.887698\pi\)
0.938407 0.345533i \(-0.112302\pi\)
\(758\) 2.94678e10 + 5.97369e10i 0.0892630 + 0.180953i
\(759\) 2.62281e11i 0.790315i
\(760\) 3.97712e10 2.00317e11i 0.119210 0.600433i
\(761\) 2.72409e10 0.0812236 0.0406118 0.999175i \(-0.487069\pi\)
0.0406118 + 0.999175i \(0.487069\pi\)
\(762\) 6.88896e11 3.39828e11i 2.04331 1.00795i
\(763\) 5.97217e11 1.76211
\(764\) 3.76121e11 + 2.88465e11i 1.10396 + 0.846682i
\(765\) 1.45933e10i 0.0426097i
\(766\) 1.05113e11 5.18515e10i 0.305310 0.150607i
\(767\) 2.53652e10i 0.0732921i
\(768\) 4.37235e11 2.52994e11i 1.25681 0.727220i
\(769\) 1.27241e11 0.363849 0.181925 0.983312i \(-0.441767\pi\)
0.181925 + 0.983312i \(0.441767\pi\)
\(770\) 6.71825e10 + 1.36192e11i 0.191114 + 0.387425i
\(771\) −7.55135e11 −2.13701
\(772\) −8.55570e10 + 1.11555e11i −0.240872 + 0.314065i
\(773\) 2.59208e11i 0.725991i −0.931791 0.362995i \(-0.881754\pi\)
0.931791 0.362995i \(-0.118246\pi\)
\(774\) −3.53870e10 7.17362e10i −0.0986007 0.199882i
\(775\) 6.69138e10i 0.185485i
\(776\) −3.81103e11 7.56644e10i −1.05098 0.208663i
\(777\) 9.39354e11 2.57718
\(778\) 5.77078e11 2.84669e11i 1.57513 0.777001i
\(779\) −3.90965e11 −1.06167
\(780\) 3.08163e10 4.01804e10i 0.0832533 0.108551i
\(781\) 1.27930e11i 0.343851i
\(782\) −2.92371e10 + 1.44225e10i −0.0781822 + 0.0385668i
\(783\) 4.90644e10i 0.130533i
\(784\) 2.19407e11 + 8.17279e11i 0.580746 + 2.16325i
\(785\) 8.99359e10 0.236840
\(786\) −5.18556e9 1.05121e10i −0.0135864 0.0275423i
\(787\) 4.49274e11 1.17115 0.585575 0.810618i \(-0.300869\pi\)
0.585575 + 0.810618i \(0.300869\pi\)
\(788\) −3.42752e11 2.62873e11i −0.888945 0.681775i
\(789\) 3.26654e11i 0.842908i
\(790\) −1.04964e11 2.12783e11i −0.269485 0.546296i
\(791\) 8.46775e11i 2.16303i
\(792\) −2.09575e11 4.16092e10i −0.532646 0.105752i
\(793\) 3.76182e10 0.0951274
\(794\) 9.74633e10 4.80780e10i 0.245222 0.120966i
\(795\) −2.59448e11 −0.649505
\(796\) −4.04678e11 3.10367e11i −1.00799 0.773079i
\(797\) 6.66061e10i 0.165075i 0.996588 + 0.0825374i \(0.0263024\pi\)
−0.996588 + 0.0825374i \(0.973698\pi\)
\(798\) −1.18775e12 + 5.85908e11i −2.92895 + 1.44483i
\(799\) 3.74559e10i 0.0919038i
\(800\) 2.33926e11 2.05395e11i 0.571110 0.501452i
\(801\) −1.89897e11 −0.461304
\(802\) −3.79886e10 7.70102e10i −0.0918240 0.186145i
\(803\) 6.89265e10 0.165777
\(804\) −1.24442e11 + 1.62256e11i −0.297813 + 0.388309i
\(805\) 4.11370e11i 0.979602i
\(806\) 8.76305e9 + 1.77644e10i 0.0207642 + 0.0420930i
\(807\) 1.05005e12i 2.47579i
\(808\) 1.22512e11 6.17064e11i 0.287431 1.44772i
\(809\) −1.25912e9 −0.00293949 −0.00146974 0.999999i \(-0.500468\pi\)
−0.00146974 + 0.999999i \(0.500468\pi\)
\(810\) −1.66392e11 + 8.20799e10i −0.386537 + 0.190676i
\(811\) 6.64956e10 0.153713 0.0768563 0.997042i \(-0.475512\pi\)
0.0768563 + 0.997042i \(0.475512\pi\)
\(812\) 3.94823e11 5.14798e11i 0.908194 1.18417i
\(813\) 4.59543e11i 1.05188i
\(814\) −1.90210e11 + 9.38294e10i −0.433247 + 0.213718i
\(815\) 1.41326e11i 0.320325i
\(816\) 1.30983e10 + 4.87907e10i 0.0295431 + 0.110046i
\(817\) 1.11948e11 0.251263
\(818\) −8.10697e10 1.64344e11i −0.181070 0.367063i
\(819\) −1.72632e11 −0.383695
\(820\) 1.49320e11 + 1.14520e11i 0.330264 + 0.253296i
\(821\) 3.44376e10i 0.0757984i −0.999282 0.0378992i \(-0.987933\pi\)
0.999282 0.0378992i \(-0.0120666\pi\)
\(822\) −1.17450e11 2.38093e11i −0.257256 0.521506i
\(823\) 6.67198e11i 1.45430i −0.686476 0.727152i \(-0.740843\pi\)
0.686476 0.727152i \(-0.259157\pi\)
\(824\) 7.36827e10 3.71121e11i 0.159829 0.805021i
\(825\) −2.50463e11 −0.540664
\(826\) −2.86370e11 + 1.41265e11i −0.615188 + 0.303468i
\(827\) 6.65965e11 1.42374 0.711868 0.702313i \(-0.247849\pi\)
0.711868 + 0.702313i \(0.247849\pi\)
\(828\) −4.59270e11 3.52236e11i −0.977118 0.749399i
\(829\) 4.92924e10i 0.104367i −0.998638 0.0521834i \(-0.983382\pi\)
0.998638 0.0521834i \(-0.0166180\pi\)
\(830\) 2.66691e11 1.31557e11i 0.561948 0.277206i
\(831\) 3.20518e11i 0.672121i
\(832\) −3.52046e10 + 8.51636e10i −0.0734693 + 0.177730i
\(833\) −8.46265e10 −0.175763
\(834\) 5.39343e11 + 1.09335e12i 1.11481 + 2.25993i
\(835\) −3.32835e11 −0.684673
\(836\) 1.81983e11 2.37282e11i 0.372568 0.485779i
\(837\) 1.88584e10i 0.0384240i
\(838\) 2.50437e11 + 5.07684e11i 0.507836 + 1.02948i
\(839\) 8.54314e11i 1.72413i −0.506799 0.862064i \(-0.669172\pi\)
0.506799 0.862064i \(-0.330828\pi\)
\(840\) 6.25255e11 + 1.24138e11i 1.25586 + 0.249338i
\(841\) 1.56378e11 0.312602
\(842\) −6.21117e11 + 3.06393e11i −1.23573 + 0.609580i
\(843\) −3.17114e11 −0.627921
\(844\) −5.15958e11 + 6.72742e11i −1.01682 + 1.32580i
\(845\) 2.40521e11i 0.471766i
\(846\) 5.96374e11 2.94188e11i 1.16423 0.574305i
\(847\) 7.04038e11i 1.36792i
\(848\) 4.56017e11 1.22423e11i 0.881857 0.236743i
\(849\) 1.29160e11 0.248599
\(850\) 1.37726e10 + 2.79197e10i 0.0263840 + 0.0534854i
\(851\) −5.74534e11 −1.09546
\(852\) 4.26115e11 + 3.26808e11i 0.808664 + 0.620203i
\(853\) 7.82406e11i 1.47787i 0.673778 + 0.738934i \(0.264671\pi\)
−0.673778 + 0.738934i \(0.735329\pi\)
\(854\) 2.09505e11 + 4.24706e11i 0.393878 + 0.798466i
\(855\) 3.62603e11i 0.678526i
\(856\) 7.64476e10 + 1.51780e10i 0.142387 + 0.0282695i
\(857\) −1.52126e11 −0.282020 −0.141010 0.990008i \(-0.545035\pi\)
−0.141010 + 0.990008i \(0.545035\pi\)
\(858\) 6.64932e10 3.28007e10i 0.122695 0.0605249i
\(859\) −4.22089e11 −0.775231 −0.387616 0.921821i \(-0.626701\pi\)
−0.387616 + 0.921821i \(0.626701\pi\)
\(860\) −4.27559e10 3.27915e10i −0.0781631 0.0599471i
\(861\) 1.22033e12i 2.22056i
\(862\) 2.96457e11 1.46240e11i 0.536948 0.264873i
\(863\) 6.63648e11i 1.19645i 0.801328 + 0.598225i \(0.204127\pi\)
−0.801328 + 0.598225i \(0.795873\pi\)
\(864\) −6.59277e10 + 5.78866e10i −0.118308 + 0.103878i
\(865\) −2.97875e11 −0.532071
\(866\) −2.31263e11 4.68815e11i −0.411183 0.833546i
\(867\) 8.15405e11 1.44310
\(868\) −1.51754e11 + 1.97868e11i −0.267339 + 0.348575i
\(869\) 3.47405e11i 0.609195i
\(870\) −1.49474e11 3.03012e11i −0.260908 0.528911i
\(871\) 3.73028e10i 0.0648141i
\(872\) −1.10228e11 + 5.55191e11i −0.190645 + 0.960232i
\(873\) 6.89849e11 1.18767
\(874\) 7.26459e11 3.58357e11i 1.24499 0.614145i
\(875\) 9.09712e11 1.55193
\(876\) 1.76078e11 2.29583e11i 0.299012 0.389872i
\(877\) 1.83107e11i 0.309533i 0.987951 + 0.154767i \(0.0494626\pi\)
−0.987951 + 0.154767i \(0.950537\pi\)
\(878\) −4.07385e11 + 2.00960e11i −0.685531 + 0.338168i
\(879\) 5.17047e11i 0.866112i
\(880\) −1.39008e11 + 3.73181e10i −0.231798 + 0.0622284i
\(881\) 3.83245e11 0.636170 0.318085 0.948062i \(-0.396960\pi\)
0.318085 + 0.948062i \(0.396960\pi\)
\(882\) −6.64676e11 1.34742e12i −1.09834 2.22654i
\(883\) −5.57963e11 −0.917831 −0.458916 0.888480i \(-0.651762\pi\)
−0.458916 + 0.888480i \(0.651762\pi\)
\(884\) −7.31274e9 5.60850e9i −0.0119749 0.00918412i
\(885\) 1.66298e11i 0.271090i
\(886\) −1.19668e11 2.42590e11i −0.194197 0.393675i
\(887\) 5.00815e11i 0.809064i 0.914524 + 0.404532i \(0.132566\pi\)
−0.914524 + 0.404532i \(0.867434\pi\)
\(888\) −1.73376e11 + 8.73252e11i −0.278829 + 1.40439i
\(889\) −1.76408e12 −2.82430
\(890\) −1.14720e11 + 5.65906e10i −0.182843 + 0.0901954i
\(891\) −2.71663e11 −0.431042
\(892\) 2.47629e8 + 1.89919e8i 0.000391150 + 0.000299992i
\(893\) 9.30673e11i 1.46349i
\(894\) 9.29478e11 4.58506e11i 1.45509 0.717785i
\(895\) 4.66346e11i 0.726803i
\(896\) −1.15755e12 + 7.68397e10i −1.79600 + 0.119221i
\(897\) 2.00844e11 0.310234
\(898\) 2.12316e11 + 4.30404e11i 0.326495 + 0.661868i
\(899\) 1.32169e11 0.202345
\(900\) −3.36365e11 + 4.38575e11i −0.512673 + 0.668458i
\(901\) 4.72191e10i 0.0716503i
\(902\) 1.21895e11 + 2.47104e11i 0.184145 + 0.373297i
\(903\) 3.49426e11i 0.525538i
\(904\) −7.87188e11 1.56289e11i −1.17870 0.234021i
\(905\) −8.37150e10 −0.124798
\(906\) −6.84331e10 + 3.37576e10i −0.101567 + 0.0501024i
\(907\) −2.38926e11 −0.353048 −0.176524 0.984296i \(-0.556485\pi\)
−0.176524 + 0.984296i \(0.556485\pi\)
\(908\) 3.09638e11 4.03727e11i 0.455523 0.593943i
\(909\) 1.11697e12i 1.63601i
\(910\) −1.04290e11 + 5.14457e10i −0.152082 + 0.0750211i
\(911\) 5.49254e11i 0.797443i −0.917072 0.398721i \(-0.869454\pi\)
0.917072 0.398721i \(-0.130546\pi\)
\(912\) −3.25456e11 1.21231e12i −0.470450 1.75240i
\(913\) 4.35419e11 0.626649
\(914\) 4.41540e10 + 8.95085e10i 0.0632681 + 0.128256i
\(915\) 2.46630e11 0.351853
\(916\) 7.86908e11 + 6.03518e11i 1.11774 + 0.857252i
\(917\) 2.69187e10i 0.0380695i
\(918\) −3.88155e9 7.86864e9i −0.00546556 0.0110797i
\(919\) 1.35358e12i 1.89768i −0.315756 0.948840i \(-0.602258\pi\)
0.315756 0.948840i \(-0.397742\pi\)
\(920\) −3.82423e11 7.59264e10i −0.533817 0.105984i
\(921\) −4.46958e10 −0.0621196
\(922\) −6.46829e11 + 3.19077e11i −0.895089 + 0.441542i
\(923\) −9.79639e10 −0.134977
\(924\) 7.40632e11 + 5.68026e11i 1.01605 + 0.779257i
\(925\) 5.48645e11i 0.749419i
\(926\) −1.50980e11 + 7.44773e10i −0.205340 + 0.101293i
\(927\) 6.71782e11i 0.909723i
\(928\) 4.05699e11 + 4.62056e11i 0.547032 + 0.623021i
\(929\) 1.05298e12 1.41370 0.706850 0.707363i \(-0.250116\pi\)
0.706850 + 0.707363i \(0.250116\pi\)
\(930\) 5.74517e10 + 1.16466e11i 0.0768018 + 0.155692i
\(931\) 2.10273e12 2.79888
\(932\) 6.63264e11 8.64809e11i 0.879068 1.14619i
\(933\) 8.17412e11i 1.07873i
\(934\) −3.90557e11 7.91733e11i −0.513212 1.04038i
\(935\) 1.43938e10i 0.0188334i
\(936\) 3.18626e10 1.60484e11i 0.0415124 0.209088i
\(937\) −1.25357e12 −1.62626 −0.813131 0.582080i \(-0.802239\pi\)
−0.813131 + 0.582080i \(0.802239\pi\)
\(938\) 4.21145e11 2.07748e11i 0.544026 0.268365i
\(939\) −6.48320e10 −0.0833925
\(940\) 2.72610e11 3.55448e11i 0.349165 0.455265i
\(941\) 1.06766e12i 1.36168i 0.732431 + 0.680841i \(0.238386\pi\)
−0.732431 + 0.680841i \(0.761614\pi\)
\(942\) 4.95734e11 2.44543e11i 0.629572 0.310564i
\(943\) 7.46384e11i 0.943878i
\(944\) −7.84687e10 2.92292e11i −0.0988117 0.368068i
\(945\) −1.10713e11 −0.138826
\(946\) −3.49032e10 7.07553e10i −0.0435813 0.0883476i
\(947\) −1.86163e11 −0.231470 −0.115735 0.993280i \(-0.536922\pi\)
−0.115735 + 0.993280i \(0.536922\pi\)
\(948\) −1.15715e12 8.87471e11i −1.43270 1.09881i
\(949\) 5.27811e10i 0.0650750i
\(950\) −3.42210e11 6.93724e11i −0.420144 0.851711i
\(951\) 1.10325e12i 1.34881i
\(952\) 2.25929e10 1.13795e11i 0.0275058 0.138540i
\(953\) 3.12215e11 0.378514 0.189257 0.981928i \(-0.439392\pi\)
0.189257 + 0.981928i \(0.439392\pi\)
\(954\) −7.51823e11 + 3.70869e11i −0.907657 + 0.447742i
\(955\) −5.66911e11 −0.681556
\(956\) 7.78784e11 + 5.97287e11i 0.932364 + 0.715075i
\(957\) 4.94719e11i 0.589808i
\(958\) −3.53172e11 + 1.74217e11i −0.419299 + 0.206838i
\(959\) 6.09694e11i 0.720837i
\(960\) −2.30806e11 + 5.58344e11i −0.271745 + 0.657380i
\(961\) 8.02090e11 0.940437
\(962\) −7.18508e10 1.45655e11i −0.0838940 0.170069i
\(963\) −1.38381e11 −0.160906
\(964\) −4.89005e10 + 6.37599e10i −0.0566246 + 0.0738311i
\(965\) 1.68142e11i 0.193895i
\(966\) 1.11855e12 + 2.26751e12i 1.28454 + 2.60400i
\(967\) 8.68168e11i 0.992883i 0.868070 + 0.496441i \(0.165360\pi\)
−0.868070 + 0.496441i \(0.834640\pi\)
\(968\) 6.54495e11 + 1.29944e11i 0.745427 + 0.147998i
\(969\) 1.25530e11 0.142382
\(970\) 4.16751e11 2.05580e11i 0.470749 0.232217i
\(971\) −1.09375e12 −1.23039 −0.615194 0.788376i \(-0.710922\pi\)
−0.615194 + 0.788376i \(0.710922\pi\)
\(972\) −7.79508e11 + 1.01638e12i −0.873284 + 1.13865i
\(973\) 2.79978e12i 3.12373i
\(974\) 1.48946e11 7.34742e10i 0.165498 0.0816393i
\(975\) 1.91794e11i 0.212235i
\(976\) −4.33487e11 + 1.16374e11i −0.477724 + 0.128250i
\(977\) −3.26541e11 −0.358392 −0.179196 0.983813i \(-0.557350\pi\)
−0.179196 + 0.983813i \(0.557350\pi\)
\(978\) 3.84275e11 + 7.78999e11i 0.420036 + 0.851494i
\(979\) −1.87300e11 −0.203895
\(980\) −8.03086e11 6.15925e11i −0.870678 0.667765i
\(981\) 1.00497e12i 1.08512i
\(982\) 3.67382e11 + 7.44753e11i 0.395068 + 0.800878i
\(983\) 1.39780e12i 1.49704i 0.663115 + 0.748518i \(0.269234\pi\)
−0.663115 + 0.748518i \(0.730766\pi\)
\(984\) 1.13445e12 + 2.25235e11i 1.21006 + 0.240246i
\(985\) 5.16615e11 0.548811
\(986\) −5.51475e10 + 2.72039e10i −0.0583469 + 0.0287822i
\(987\) −2.90493e12 −3.06102
\(988\) 1.81701e11 + 1.39355e11i 0.190690 + 0.146250i
\(989\) 2.13718e11i 0.223386i
\(990\) 2.29178e11 1.13052e11i 0.238579 0.117690i
\(991\) 1.15200e11i 0.119442i 0.998215 + 0.0597211i \(0.0190211\pi\)
−0.998215 + 0.0597211i \(0.980979\pi\)
\(992\) −1.55935e11 1.77596e11i −0.161026 0.183394i
\(993\) −1.71338e12 −1.76220
\(994\) −5.45583e11 1.10600e12i −0.558876 1.13295i
\(995\) 6.09955e11 0.622308
\(996\) 1.11231e12 1.45031e12i 1.13029 1.47375i
\(997\) 6.83531e11i 0.691796i 0.938272 + 0.345898i \(0.112426\pi\)
−0.938272 + 0.345898i \(0.887574\pi\)
\(998\) −5.68070e10 1.15159e11i −0.0572637 0.116084i
\(999\) 1.54625e11i 0.155245i
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 8.9.d.b.3.6 yes 6
3.2 odd 2 72.9.b.b.19.1 6
4.3 odd 2 32.9.d.b.15.5 6
8.3 odd 2 inner 8.9.d.b.3.5 6
8.5 even 2 32.9.d.b.15.6 6
12.11 even 2 288.9.b.b.271.4 6
16.3 odd 4 256.9.c.n.255.11 12
16.5 even 4 256.9.c.n.255.12 12
16.11 odd 4 256.9.c.n.255.2 12
16.13 even 4 256.9.c.n.255.1 12
24.5 odd 2 288.9.b.b.271.3 6
24.11 even 2 72.9.b.b.19.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.9.d.b.3.5 6 8.3 odd 2 inner
8.9.d.b.3.6 yes 6 1.1 even 1 trivial
32.9.d.b.15.5 6 4.3 odd 2
32.9.d.b.15.6 6 8.5 even 2
72.9.b.b.19.1 6 3.2 odd 2
72.9.b.b.19.2 6 24.11 even 2
256.9.c.n.255.1 12 16.13 even 4
256.9.c.n.255.2 12 16.11 odd 4
256.9.c.n.255.11 12 16.3 odd 4
256.9.c.n.255.12 12 16.5 even 4
288.9.b.b.271.3 6 24.5 odd 2
288.9.b.b.271.4 6 12.11 even 2