Properties

Label 5.27.c.a.2.9
Level $5$
Weight $27$
Character 5.2
Analytic conductor $21.415$
Analytic rank $0$
Dimension $24$
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] = [5,27,Mod(2,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 27, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.2");
 
S:= CuspForms(chi, 27);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 27 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\), degree \(2\), 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: \(21.4146460365\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2.9
Character \(\chi\) \(=\) 5.2
Dual form 5.27.c.a.3.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(6254.19 + 6254.19i) q^{2} +(-748889. + 748889. i) q^{3} +1.11210e7i q^{4} +(7.43869e8 + 9.67872e8i) q^{5} -9.36739e9 q^{6} +(5.67260e10 + 5.67260e10i) q^{7} +(3.50159e11 - 3.50159e11i) q^{8} +1.42020e12i q^{9} +O(q^{10})\) \(q+(6254.19 + 6254.19i) q^{2} +(-748889. + 748889. i) q^{3} +1.11210e7i q^{4} +(7.43869e8 + 9.67872e8i) q^{5} -9.36739e9 q^{6} +(5.67260e10 + 5.67260e10i) q^{7} +(3.50159e11 - 3.50159e11i) q^{8} +1.42020e12i q^{9} +(-1.40096e12 + 1.07056e13i) q^{10} -7.24796e12 q^{11} +(-8.32836e12 - 8.32836e12i) q^{12} +(-3.18649e14 + 3.18649e14i) q^{13} +7.09550e14i q^{14} +(-1.28190e15 - 1.67754e14i) q^{15} +5.12624e15 q^{16} +(-2.33224e15 - 2.33224e15i) q^{17} +(-8.88217e15 + 8.88217e15i) q^{18} -5.21951e16i q^{19} +(-1.07637e16 + 8.27253e15i) q^{20} -8.49629e16 q^{21} +(-4.53301e16 - 4.53301e16i) q^{22} +(-5.96659e17 + 5.96659e17i) q^{23} +5.24461e17i q^{24} +(-3.83435e17 + 1.43994e18i) q^{25} -3.98579e18 q^{26} +(-2.96715e18 - 2.96715e18i) q^{27} +(-6.30847e17 + 6.30847e17i) q^{28} +5.57295e18i q^{29} +(-6.96811e18 - 9.06644e18i) q^{30} +2.76741e18 q^{31} +(8.56169e18 + 8.56169e18i) q^{32} +(5.42792e18 - 5.42792e18i) q^{33} -2.91725e19i q^{34} +(-1.27068e19 + 9.71001e19i) q^{35} -1.57939e19 q^{36} +(1.45897e20 + 1.45897e20i) q^{37} +(3.26438e20 - 3.26438e20i) q^{38} -4.77266e20i q^{39} +(5.99381e20 + 7.84367e19i) q^{40} +7.08740e20 q^{41} +(-5.31374e20 - 5.31374e20i) q^{42} +(-1.15322e20 + 1.15322e20i) q^{43} -8.06042e19i q^{44} +(-1.37457e21 + 1.05644e21i) q^{45} -7.46324e21 q^{46} +(4.77547e21 + 4.77547e21i) q^{47} +(-3.83899e21 + 3.83899e21i) q^{48} -2.95181e21i q^{49} +(-1.14037e22 + 6.60758e21i) q^{50} +3.49318e21 q^{51} +(-3.54368e21 - 3.54368e21i) q^{52} +(8.79555e21 - 8.79555e21i) q^{53} -3.71142e22i q^{54} +(-5.39153e21 - 7.01510e21i) q^{55} +3.97262e22 q^{56} +(3.90883e22 + 3.90883e22i) q^{57} +(-3.48543e22 + 3.48543e22i) q^{58} -1.00850e22i q^{59} +(1.86558e21 - 1.42560e22i) q^{60} +2.85427e23 q^{61} +(1.73079e22 + 1.73079e22i) q^{62} +(-8.05619e22 + 8.05619e22i) q^{63} -2.36923e23i q^{64} +(-5.45445e23 - 7.13784e22i) q^{65} +6.78945e22 q^{66} +(2.54963e23 + 2.54963e23i) q^{67} +(2.59367e22 - 2.59367e22i) q^{68} -8.93663e23i q^{69} +(-6.86753e23 + 5.27812e23i) q^{70} -3.34850e23 q^{71} +(4.97294e23 + 4.97294e23i) q^{72} +(-2.01383e24 + 2.01383e24i) q^{73} +1.82493e24i q^{74} +(-7.91204e23 - 1.36551e24i) q^{75} +5.80459e23 q^{76} +(-4.11148e23 - 4.11148e23i) q^{77} +(2.98491e24 - 2.98491e24i) q^{78} -6.89052e24i q^{79} +(3.81325e24 + 4.96154e24i) q^{80} +8.34182e23 q^{81} +(4.43260e24 + 4.43260e24i) q^{82} +(8.09054e24 - 8.09054e24i) q^{83} -9.44869e23i q^{84} +(5.22429e23 - 3.99219e24i) q^{85} -1.44249e24 q^{86} +(-4.17352e24 - 4.17352e24i) q^{87} +(-2.53794e24 + 2.53794e24i) q^{88} +3.36606e25i q^{89} +(-1.52040e25 - 1.98963e24i) q^{90} -3.61514e25 q^{91} +(-6.63542e24 - 6.63542e24i) q^{92} +(-2.07248e24 + 2.07248e24i) q^{93} +5.97335e25i q^{94} +(5.05181e25 - 3.88263e25i) q^{95} -1.28235e25 q^{96} +(-5.11251e25 - 5.11251e25i) q^{97} +(1.84612e25 - 1.84612e25i) q^{98} -1.02935e25i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8} - 1486502924970 q^{10} - 60046450487712 q^{11} + 474303804173880 q^{12} - 175933888149240 q^{13} + 81\!\cdots\!60 q^{15}+ \cdots + 37\!\cdots\!90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6254.19 + 6254.19i 0.763451 + 0.763451i 0.976944 0.213493i \(-0.0684842\pi\)
−0.213493 + 0.976944i \(0.568484\pi\)
\(3\) −748889. + 748889.i −0.469723 + 0.469723i −0.901825 0.432102i \(-0.857772\pi\)
0.432102 + 0.901825i \(0.357772\pi\)
\(4\) 1.11210e7i 0.165715i
\(5\) 7.43869e8 + 9.67872e8i 0.609377 + 0.792881i
\(6\) −9.36739e9 −0.717220
\(7\) 5.67260e10 + 5.67260e10i 0.585474 + 0.585474i 0.936402 0.350929i \(-0.114134\pi\)
−0.350929 + 0.936402i \(0.614134\pi\)
\(8\) 3.50159e11 3.50159e11i 0.636936 0.636936i
\(9\) 1.42020e12i 0.558722i
\(10\) −1.40096e12 + 1.07056e13i −0.140096 + 1.07056i
\(11\) −7.24796e12 −0.209948 −0.104974 0.994475i \(-0.533476\pi\)
−0.104974 + 0.994475i \(0.533476\pi\)
\(12\) −8.32836e12 8.32836e12i −0.0778401 0.0778401i
\(13\) −3.18649e14 + 3.18649e14i −1.05208 + 1.05208i −0.0535145 + 0.998567i \(0.517042\pi\)
−0.998567 + 0.0535145i \(0.982958\pi\)
\(14\) 7.09550e14i 0.893961i
\(15\) −1.28190e15 1.67754e14i −0.658672 0.0861957i
\(16\) 5.12624e15 1.13825
\(17\) −2.33224e15 2.33224e15i −0.235471 0.235471i 0.579501 0.814972i \(-0.303248\pi\)
−0.814972 + 0.579501i \(0.803248\pi\)
\(18\) −8.88217e15 + 8.88217e15i −0.426557 + 0.426557i
\(19\) 5.21951e16i 1.24117i −0.784137 0.620587i \(-0.786894\pi\)
0.784137 0.620587i \(-0.213106\pi\)
\(20\) −1.07637e16 + 8.27253e15i −0.131392 + 0.100983i
\(21\) −8.49629e16 −0.550020
\(22\) −4.53301e16 4.53301e16i −0.160285 0.160285i
\(23\) −5.96659e17 + 5.96659e17i −1.18376 + 1.18376i −0.205000 + 0.978762i \(0.565719\pi\)
−0.978762 + 0.205000i \(0.934281\pi\)
\(24\) 5.24461e17i 0.598366i
\(25\) −3.83435e17 + 1.43994e18i −0.257319 + 0.966327i
\(26\) −3.98579e18 −1.60643
\(27\) −2.96715e18 2.96715e18i −0.732167 0.732167i
\(28\) −6.30847e17 + 6.30847e17i −0.0970218 + 0.0970218i
\(29\) 5.57295e18i 0.543139i 0.962419 + 0.271570i \(0.0875427\pi\)
−0.962419 + 0.271570i \(0.912457\pi\)
\(30\) −6.96811e18 9.06644e18i −0.437058 0.568670i
\(31\) 2.76741e18 0.113337 0.0566685 0.998393i \(-0.481952\pi\)
0.0566685 + 0.998393i \(0.481952\pi\)
\(32\) 8.56169e18 + 8.56169e18i 0.232065 + 0.232065i
\(33\) 5.42792e18 5.42792e18i 0.0986171 0.0986171i
\(34\) 2.91725e19i 0.359541i
\(35\) −1.27068e19 + 9.71001e19i −0.107436 + 0.820985i
\(36\) −1.57939e19 −0.0925886
\(37\) 1.45897e20 + 1.45897e20i 0.598994 + 0.598994i 0.940045 0.341051i \(-0.110783\pi\)
−0.341051 + 0.940045i \(0.610783\pi\)
\(38\) 3.26438e20 3.26438e20i 0.947576 0.947576i
\(39\) 4.77266e20i 0.988373i
\(40\) 5.99381e20 + 7.84367e19i 0.893148 + 0.116880i
\(41\) 7.08740e20 0.766120 0.383060 0.923723i \(-0.374870\pi\)
0.383060 + 0.923723i \(0.374870\pi\)
\(42\) −5.31374e20 5.31374e20i −0.419914 0.419914i
\(43\) −1.15322e20 + 1.15322e20i −0.0671155 + 0.0671155i −0.739868 0.672752i \(-0.765112\pi\)
0.672752 + 0.739868i \(0.265112\pi\)
\(44\) 8.06042e19i 0.0347915i
\(45\) −1.37457e21 + 1.05644e21i −0.442999 + 0.340472i
\(46\) −7.46324e21 −1.80749
\(47\) 4.77547e21 + 4.77547e21i 0.874469 + 0.874469i 0.992956 0.118487i \(-0.0378043\pi\)
−0.118487 + 0.992956i \(0.537804\pi\)
\(48\) −3.83899e21 + 3.83899e21i −0.534663 + 0.534663i
\(49\) 2.95181e21i 0.314441i
\(50\) −1.14037e22 + 6.60758e21i −0.934193 + 0.541293i
\(51\) 3.49318e21 0.221212
\(52\) −3.54368e21 3.54368e21i −0.174346 0.174346i
\(53\) 8.79555e21 8.79555e21i 0.337813 0.337813i −0.517731 0.855544i \(-0.673223\pi\)
0.855544 + 0.517731i \(0.173223\pi\)
\(54\) 3.71142e22i 1.11795i
\(55\) −5.39153e21 7.01510e21i −0.127937 0.166463i
\(56\) 3.97262e22 0.745818
\(57\) 3.90883e22 + 3.90883e22i 0.583008 + 0.583008i
\(58\) −3.48543e22 + 3.48543e22i −0.414660 + 0.414660i
\(59\) 1.00850e22i 0.0960731i −0.998846 0.0480366i \(-0.984704\pi\)
0.998846 0.0480366i \(-0.0152964\pi\)
\(60\) 1.86558e21 1.42560e22i 0.0142839 0.109152i
\(61\) 2.85427e23 1.76282 0.881408 0.472355i \(-0.156596\pi\)
0.881408 + 0.472355i \(0.156596\pi\)
\(62\) 1.73079e22 + 1.73079e22i 0.0865272 + 0.0865272i
\(63\) −8.05619e22 + 8.05619e22i −0.327117 + 0.327117i
\(64\) 2.36923e23i 0.783913i
\(65\) −5.45445e23 7.13784e22i −1.47529 0.193060i
\(66\) 6.78945e22 0.150579
\(67\) 2.54963e23 + 2.54963e23i 0.465055 + 0.465055i 0.900308 0.435253i \(-0.143341\pi\)
−0.435253 + 0.900308i \(0.643341\pi\)
\(68\) 2.59367e22 2.59367e22i 0.0390210 0.0390210i
\(69\) 8.93663e23i 1.11208i
\(70\) −6.86753e23 + 5.27812e23i −0.708804 + 0.544759i
\(71\) −3.34850e23 −0.287403 −0.143702 0.989621i \(-0.545901\pi\)
−0.143702 + 0.989621i \(0.545901\pi\)
\(72\) 4.97294e23 + 4.97294e23i 0.355870 + 0.355870i
\(73\) −2.01383e24 + 2.01383e24i −1.20455 + 1.20455i −0.231783 + 0.972768i \(0.574456\pi\)
−0.972768 + 0.231783i \(0.925544\pi\)
\(74\) 1.82493e24i 0.914606i
\(75\) −7.91204e23 1.36551e24i −0.333037 0.574774i
\(76\) 5.80459e23 0.205681
\(77\) −4.11148e23 4.11148e23i −0.122919 0.122919i
\(78\) 2.98491e24 2.98491e24i 0.754574 0.754574i
\(79\) 6.89052e24i 1.47605i −0.674775 0.738023i \(-0.735760\pi\)
0.674775 0.738023i \(-0.264240\pi\)
\(80\) 3.81325e24 + 4.96154e24i 0.693626 + 0.902499i
\(81\) 8.34182e23 0.129109
\(82\) 4.43260e24 + 4.43260e24i 0.584895 + 0.584895i
\(83\) 8.09054e24 8.09054e24i 0.911932 0.911932i −0.0844922 0.996424i \(-0.526927\pi\)
0.996424 + 0.0844922i \(0.0269268\pi\)
\(84\) 9.44869e23i 0.0911466i
\(85\) 5.22429e23 3.99219e24i 0.0432097 0.330191i
\(86\) −1.44249e24 −0.102479
\(87\) −4.17352e24 4.17352e24i −0.255125 0.255125i
\(88\) −2.53794e24 + 2.53794e24i −0.133723 + 0.133723i
\(89\) 3.36606e25i 1.53127i 0.643274 + 0.765636i \(0.277576\pi\)
−0.643274 + 0.765636i \(0.722424\pi\)
\(90\) −1.52040e25 1.98963e24i −0.598142 0.0782746i
\(91\) −3.61514e25 −1.23193
\(92\) −6.63542e24 6.63542e24i −0.196167 0.196167i
\(93\) −2.07248e24 + 2.07248e24i −0.0532369 + 0.0532369i
\(94\) 5.97335e25i 1.33523i
\(95\) 5.05181e25 3.88263e25i 0.984103 0.756343i
\(96\) −1.28235e25 −0.218012
\(97\) −5.11251e25 5.11251e25i −0.759630 0.759630i 0.216625 0.976255i \(-0.430495\pi\)
−0.976255 + 0.216625i \(0.930495\pi\)
\(98\) 1.84612e25 1.84612e25i 0.240061 0.240061i
\(99\) 1.02935e25i 0.117302i
\(100\) −1.60135e25 4.26416e24i −0.160135 0.0426416i
\(101\) −1.50967e25 −0.132649 −0.0663245 0.997798i \(-0.521127\pi\)
−0.0663245 + 0.997798i \(0.521127\pi\)
\(102\) 2.18470e25 + 2.18470e25i 0.168884 + 0.168884i
\(103\) 9.25640e25 9.25640e25i 0.630316 0.630316i −0.317831 0.948147i \(-0.602955\pi\)
0.948147 + 0.317831i \(0.102955\pi\)
\(104\) 2.23156e26i 1.34022i
\(105\) −6.32013e25 8.22332e25i −0.335170 0.436100i
\(106\) 1.10018e26 0.515808
\(107\) 1.95019e26 + 1.95019e26i 0.809259 + 0.809259i 0.984522 0.175263i \(-0.0560775\pi\)
−0.175263 + 0.984522i \(0.556077\pi\)
\(108\) 3.29975e25 3.29975e25i 0.121331 0.121331i
\(109\) 2.92708e26i 0.954750i −0.878700 0.477375i \(-0.841588\pi\)
0.878700 0.477375i \(-0.158412\pi\)
\(110\) 1.01541e25 7.75934e25i 0.0294128 0.224760i
\(111\) −2.18521e26 −0.562722
\(112\) 2.90791e26 + 2.90791e26i 0.666417 + 0.666417i
\(113\) 5.51881e26 5.51881e26i 1.12674 1.12674i 0.136041 0.990703i \(-0.456562\pi\)
0.990703 0.136041i \(-0.0434379\pi\)
\(114\) 4.88932e26i 0.890195i
\(115\) −1.02133e27 1.33653e26i −1.65994 0.217224i
\(116\) −6.19765e25 −0.0900064
\(117\) −4.52544e26 4.52544e26i −0.587821 0.587821i
\(118\) 6.30738e25 6.30738e25i 0.0733471 0.0733471i
\(119\) 2.64597e26i 0.275724i
\(120\) −5.07611e26 + 3.90130e26i −0.474433 + 0.364631i
\(121\) −1.13928e27 −0.955922
\(122\) 1.78511e27 + 1.78511e27i 1.34582 + 1.34582i
\(123\) −5.30768e26 + 5.30768e26i −0.359864 + 0.359864i
\(124\) 3.07762e25i 0.0187816i
\(125\) −1.67890e27 + 7.00009e26i −0.922986 + 0.384834i
\(126\) −1.00770e27 −0.499475
\(127\) 1.23338e27 + 1.23338e27i 0.551633 + 0.551633i 0.926912 0.375279i \(-0.122453\pi\)
−0.375279 + 0.926912i \(0.622453\pi\)
\(128\) 2.05633e27 2.05633e27i 0.830544 0.830544i
\(129\) 1.72727e26i 0.0630513i
\(130\) −2.96490e27 3.85773e27i −0.978919 1.27370i
\(131\) 5.33768e27 1.59524 0.797619 0.603162i \(-0.206093\pi\)
0.797619 + 0.603162i \(0.206093\pi\)
\(132\) 6.03636e25 + 6.03636e25i 0.0163423 + 0.0163423i
\(133\) 2.96082e27 2.96082e27i 0.726675 0.726675i
\(134\) 3.18917e27i 0.710094i
\(135\) 6.64650e26 5.07898e27i 0.134355 1.02669i
\(136\) −1.63331e27 −0.299959
\(137\) 2.89434e27 + 2.89434e27i 0.483261 + 0.483261i 0.906172 0.422910i \(-0.138991\pi\)
−0.422910 + 0.906172i \(0.638991\pi\)
\(138\) 5.58914e27 5.58914e27i 0.849018 0.849018i
\(139\) 1.18359e28i 1.63685i 0.574614 + 0.818425i \(0.305152\pi\)
−0.574614 + 0.818425i \(0.694848\pi\)
\(140\) −1.07985e27 1.41312e26i −0.136050 0.0178038i
\(141\) −7.15260e27 −0.821515
\(142\) −2.09422e27 2.09422e27i −0.219418 0.219418i
\(143\) 2.30956e27 2.30956e27i 0.220882 0.220882i
\(144\) 7.28026e27i 0.635967i
\(145\) −5.39390e27 + 4.14554e27i −0.430645 + 0.330977i
\(146\) −2.51897e28 −1.83923
\(147\) 2.21058e27 + 2.21058e27i 0.147700 + 0.147700i
\(148\) −1.62251e27 + 1.62251e27i −0.0992624 + 0.0992624i
\(149\) 1.17062e28i 0.656135i 0.944654 + 0.328067i \(0.106397\pi\)
−0.944654 + 0.328067i \(0.893603\pi\)
\(150\) 3.59179e27 1.34885e28i 0.184554 0.693069i
\(151\) 1.07463e28 0.506477 0.253238 0.967404i \(-0.418504\pi\)
0.253238 + 0.967404i \(0.418504\pi\)
\(152\) −1.82766e28 1.82766e28i −0.790548 0.790548i
\(153\) 3.31223e27 3.31223e27i 0.131563 0.131563i
\(154\) 5.14279e27i 0.187685i
\(155\) 2.05859e27 + 2.67850e27i 0.0690650 + 0.0898627i
\(156\) 5.30765e27 0.163788
\(157\) 2.76978e28 + 2.76978e28i 0.786592 + 0.786592i 0.980934 0.194341i \(-0.0622570\pi\)
−0.194341 + 0.980934i \(0.562257\pi\)
\(158\) 4.30946e28 4.30946e28i 1.12689 1.12689i
\(159\) 1.31738e28i 0.317357i
\(160\) −1.91785e27 + 1.46554e28i −0.0425847 + 0.325415i
\(161\) −6.76921e28 −1.38612
\(162\) 5.21713e27 + 5.21713e27i 0.0985682 + 0.0985682i
\(163\) −3.27062e27 + 3.27062e27i −0.0570415 + 0.0570415i −0.735052 0.678011i \(-0.762842\pi\)
0.678011 + 0.735052i \(0.262842\pi\)
\(164\) 7.88187e27i 0.126958i
\(165\) 9.29119e27 + 1.21587e27i 0.138287 + 0.0180966i
\(166\) 1.01200e29 1.39243
\(167\) 6.03005e27 + 6.03005e27i 0.0767374 + 0.0767374i 0.744434 0.667696i \(-0.232720\pi\)
−0.667696 + 0.744434i \(0.732720\pi\)
\(168\) −2.97505e28 + 2.97505e28i −0.350328 + 0.350328i
\(169\) 1.11341e29i 1.21375i
\(170\) 2.82353e28 2.17005e28i 0.285073 0.219096i
\(171\) 7.41272e28 0.693471
\(172\) −1.28249e27 1.28249e27i −0.0111220 0.0111220i
\(173\) −6.90284e28 + 6.90284e28i −0.555173 + 0.555173i −0.927929 0.372756i \(-0.878413\pi\)
0.372756 + 0.927929i \(0.378413\pi\)
\(174\) 5.22040e28i 0.389550i
\(175\) −1.03433e29 + 5.99312e28i −0.716412 + 0.415105i
\(176\) −3.71548e28 −0.238974
\(177\) 7.55259e27 + 7.55259e27i 0.0451277 + 0.0451277i
\(178\) −2.10520e29 + 2.10520e29i −1.16905 + 1.16905i
\(179\) 3.22901e29i 1.66717i −0.552392 0.833584i \(-0.686285\pi\)
0.552392 0.833584i \(-0.313715\pi\)
\(180\) −1.17486e28 1.52865e28i −0.0564214 0.0734117i
\(181\) 2.64516e29 1.18204 0.591018 0.806658i \(-0.298726\pi\)
0.591018 + 0.806658i \(0.298726\pi\)
\(182\) −2.26098e29 2.26098e29i −0.940520 0.940520i
\(183\) −2.13753e29 + 2.13753e29i −0.828034 + 0.828034i
\(184\) 4.17851e29i 1.50796i
\(185\) −3.26813e28 + 2.49737e29i −0.109917 + 0.839944i
\(186\) −2.59234e28 −0.0812876
\(187\) 1.69040e28 + 1.69040e28i 0.0494365 + 0.0494365i
\(188\) −5.31078e28 + 5.31078e28i −0.144913 + 0.144913i
\(189\) 3.36628e29i 0.857328i
\(190\) 5.58777e29 + 7.31231e28i 1.32875 + 0.173883i
\(191\) 3.07926e28 0.0683932 0.0341966 0.999415i \(-0.489113\pi\)
0.0341966 + 0.999415i \(0.489113\pi\)
\(192\) 1.77429e29 + 1.77429e29i 0.368221 + 0.368221i
\(193\) 4.02979e29 4.02979e29i 0.781696 0.781696i −0.198421 0.980117i \(-0.563581\pi\)
0.980117 + 0.198421i \(0.0635813\pi\)
\(194\) 6.39493e29i 1.15988i
\(195\) 4.61932e29 3.55023e29i 0.783661 0.602292i
\(196\) 3.28269e28 0.0521077
\(197\) −4.70545e29 4.70545e29i −0.699101 0.699101i 0.265115 0.964217i \(-0.414590\pi\)
−0.964217 + 0.265115i \(0.914590\pi\)
\(198\) 6.43776e28 6.43776e28i 0.0895545 0.0895545i
\(199\) 2.75507e29i 0.358958i 0.983762 + 0.179479i \(0.0574411\pi\)
−0.983762 + 0.179479i \(0.942559\pi\)
\(200\) 3.69944e29 + 6.38471e29i 0.451592 + 0.779384i
\(201\) −3.81878e29 −0.436894
\(202\) −9.44177e28 9.44177e28i −0.101271 0.101271i
\(203\) −3.16131e29 + 3.16131e29i −0.317994 + 0.317994i
\(204\) 3.88474e28i 0.0366581i
\(205\) 5.27210e29 + 6.85970e29i 0.466856 + 0.607442i
\(206\) 1.15783e30 0.962431
\(207\) −8.47372e29 8.47372e29i −0.661393 0.661393i
\(208\) −1.63347e30 + 1.63347e30i −1.19754 + 1.19754i
\(209\) 3.78308e29i 0.260582i
\(210\) 1.19030e29 9.09575e29i 0.0770555 0.588827i
\(211\) −2.20208e30 −1.34017 −0.670087 0.742282i \(-0.733743\pi\)
−0.670087 + 0.742282i \(0.733743\pi\)
\(212\) 9.78149e28 + 9.78149e28i 0.0559807 + 0.0559807i
\(213\) 2.50766e29 2.50766e29i 0.135000 0.135000i
\(214\) 2.43937e30i 1.23566i
\(215\) −1.97402e29 2.58325e28i −0.0941132 0.0123159i
\(216\) −2.07795e30 −0.932686
\(217\) 1.56984e29 + 1.56984e29i 0.0663558 + 0.0663558i
\(218\) 1.83065e30 1.83065e30i 0.728905 0.728905i
\(219\) 3.01627e30i 1.13161i
\(220\) 7.80145e28 5.99589e28i 0.0275855 0.0212011i
\(221\) 1.48633e30 0.495469
\(222\) −1.36667e30 1.36667e30i −0.429611 0.429611i
\(223\) 1.15101e30 1.15101e30i 0.341284 0.341284i −0.515566 0.856850i \(-0.672418\pi\)
0.856850 + 0.515566i \(0.172418\pi\)
\(224\) 9.71341e29i 0.271736i
\(225\) −2.04499e30 5.44553e29i −0.539907 0.143770i
\(226\) 6.90313e30 1.72043
\(227\) 4.52492e30 + 4.52492e30i 1.06482 + 1.06482i 0.997748 + 0.0670680i \(0.0213644\pi\)
0.0670680 + 0.997748i \(0.478636\pi\)
\(228\) −4.34700e29 + 4.34700e29i −0.0966131 + 0.0966131i
\(229\) 5.05515e30i 1.06138i 0.847565 + 0.530692i \(0.178068\pi\)
−0.847565 + 0.530692i \(0.821932\pi\)
\(230\) −5.55167e30 7.22346e30i −1.10144 1.43312i
\(231\) 6.15808e29 0.115475
\(232\) 1.95142e30 + 1.95142e30i 0.345945 + 0.345945i
\(233\) 3.06962e29 3.06962e29i 0.0514585 0.0514585i −0.680909 0.732368i \(-0.738415\pi\)
0.732368 + 0.680909i \(0.238415\pi\)
\(234\) 5.66060e30i 0.897545i
\(235\) −1.06972e30 + 8.17437e30i −0.160468 + 1.22623i
\(236\) 1.12155e29 0.0159208
\(237\) 5.16024e30 + 5.16024e30i 0.693332 + 0.693332i
\(238\) 1.65484e30 1.65484e30i 0.210502 0.210502i
\(239\) 6.86868e30i 0.827371i −0.910420 0.413686i \(-0.864241\pi\)
0.910420 0.413686i \(-0.135759\pi\)
\(240\) −6.57135e30 8.59945e29i −0.749736 0.0981125i
\(241\) −8.79465e30 −0.950598 −0.475299 0.879824i \(-0.657660\pi\)
−0.475299 + 0.879824i \(0.657660\pi\)
\(242\) −7.12530e30 7.12530e30i −0.729800 0.729800i
\(243\) 6.91738e30 6.91738e30i 0.671521 0.671521i
\(244\) 3.17422e30i 0.292125i
\(245\) 2.85697e30 2.19576e30i 0.249314 0.191613i
\(246\) −6.63905e30 −0.549477
\(247\) 1.66319e31 + 1.66319e31i 1.30582 + 1.30582i
\(248\) 9.69034e29 9.69034e29i 0.0721884 0.0721884i
\(249\) 1.21178e31i 0.856710i
\(250\) −1.48782e31 6.12218e30i −0.998456 0.410852i
\(251\) −2.09500e31 −1.33483 −0.667413 0.744687i \(-0.732599\pi\)
−0.667413 + 0.744687i \(0.732599\pi\)
\(252\) −8.95925e29 8.95925e29i −0.0542082 0.0542082i
\(253\) 4.32456e30 4.32456e30i 0.248528 0.248528i
\(254\) 1.54276e31i 0.842289i
\(255\) 2.59846e30 + 3.38095e30i 0.134801 + 0.175394i
\(256\) 9.82170e30 0.484247
\(257\) −2.49219e31 2.49219e31i −1.16802 1.16802i −0.982673 0.185346i \(-0.940659\pi\)
−0.185346 0.982673i \(-0.559341\pi\)
\(258\) 1.08027e30 1.08027e30i 0.0481366 0.0481366i
\(259\) 1.65522e31i 0.701391i
\(260\) 7.93796e29 6.06587e30i 0.0319930 0.244478i
\(261\) −7.91468e30 −0.303464
\(262\) 3.33829e31 + 3.33829e31i 1.21789 + 1.21789i
\(263\) 1.85981e31 1.85981e31i 0.645718 0.645718i −0.306237 0.951955i \(-0.599070\pi\)
0.951955 + 0.306237i \(0.0990701\pi\)
\(264\) 3.80127e30i 0.125626i
\(265\) 1.50557e31 + 1.97023e30i 0.473701 + 0.0619899i
\(266\) 3.70350e31 1.10956
\(267\) −2.52081e31 2.52081e31i −0.719273 0.719273i
\(268\) −2.83543e30 + 2.83543e30i −0.0770667 + 0.0770667i
\(269\) 2.38894e31i 0.618623i −0.950961 0.309311i \(-0.899901\pi\)
0.950961 0.309311i \(-0.100099\pi\)
\(270\) 3.59218e31 2.76081e31i 0.886398 0.681251i
\(271\) 9.57627e30 0.225214 0.112607 0.993640i \(-0.464080\pi\)
0.112607 + 0.993640i \(0.464080\pi\)
\(272\) −1.19556e31 1.19556e31i −0.268025 0.268025i
\(273\) 2.70734e31 2.70734e31i 0.578666 0.578666i
\(274\) 3.62035e31i 0.737893i
\(275\) 2.77912e30 1.04366e31i 0.0540235 0.202878i
\(276\) 9.93838e30 0.184288
\(277\) −1.23203e31 1.23203e31i −0.217964 0.217964i 0.589676 0.807640i \(-0.299255\pi\)
−0.807640 + 0.589676i \(0.799255\pi\)
\(278\) −7.40240e31 + 7.40240e31i −1.24965 + 1.24965i
\(279\) 3.93026e30i 0.0633238i
\(280\) 2.95511e31 + 3.84499e31i 0.454485 + 0.591345i
\(281\) −1.02452e32 −1.50431 −0.752156 0.658985i \(-0.770986\pi\)
−0.752156 + 0.658985i \(0.770986\pi\)
\(282\) −4.47337e31 4.47337e31i −0.627187 0.627187i
\(283\) −5.03276e31 + 5.03276e31i −0.673880 + 0.673880i −0.958608 0.284728i \(-0.908097\pi\)
0.284728 + 0.958608i \(0.408097\pi\)
\(284\) 3.72385e30i 0.0476271i
\(285\) −8.75591e30 + 6.69091e31i −0.106984 + 0.817527i
\(286\) 2.88888e31 0.337265
\(287\) 4.02040e31 + 4.02040e31i 0.448543 + 0.448543i
\(288\) −1.21593e31 + 1.21593e31i −0.129660 + 0.129660i
\(289\) 8.72220e31i 0.889107i
\(290\) −5.96615e31 7.80747e30i −0.581460 0.0760915i
\(291\) 7.65741e31 0.713630
\(292\) −2.23957e31 2.23957e31i −0.199612 0.199612i
\(293\) −1.84989e31 + 1.84989e31i −0.157713 + 0.157713i −0.781552 0.623840i \(-0.785572\pi\)
0.623840 + 0.781552i \(0.285572\pi\)
\(294\) 2.76508e31i 0.225524i
\(295\) 9.76103e30 7.50195e30i 0.0761745 0.0585448i
\(296\) 1.02174e32 0.763042
\(297\) 2.15058e31 + 2.15058e31i 0.153717 + 0.153717i
\(298\) −7.32126e31 + 7.32126e31i −0.500927 + 0.500927i
\(299\) 3.80250e32i 2.49083i
\(300\) 1.51857e31 8.79894e30i 0.0952487 0.0551892i
\(301\) −1.30835e31 −0.0785887
\(302\) 6.72095e31 + 6.72095e31i 0.386670 + 0.386670i
\(303\) 1.13058e31 1.13058e31i 0.0623083 0.0623083i
\(304\) 2.67564e32i 1.41277i
\(305\) 2.12320e32 + 2.76257e32i 1.07422 + 1.39770i
\(306\) 4.14307e31 0.200883
\(307\) 1.16178e31 + 1.16178e31i 0.0539912 + 0.0539912i 0.733587 0.679596i \(-0.237845\pi\)
−0.679596 + 0.733587i \(0.737845\pi\)
\(308\) 4.57235e30 4.57235e30i 0.0203695 0.0203695i
\(309\) 1.38640e32i 0.592147i
\(310\) −3.87703e30 + 2.96267e31i −0.0158780 + 0.121333i
\(311\) 2.03862e32 0.800667 0.400333 0.916370i \(-0.368894\pi\)
0.400333 + 0.916370i \(0.368894\pi\)
\(312\) −1.67119e32 1.67119e32i −0.629530 0.629530i
\(313\) −5.36965e31 + 5.36965e31i −0.194030 + 0.194030i −0.797435 0.603405i \(-0.793810\pi\)
0.603405 + 0.797435i \(0.293810\pi\)
\(314\) 3.46455e32i 1.20105i
\(315\) −1.37901e32 1.80461e31i −0.458702 0.0600270i
\(316\) 7.66292e31 0.244603
\(317\) 1.09772e32 + 1.09772e32i 0.336294 + 0.336294i 0.854971 0.518676i \(-0.173575\pi\)
−0.518676 + 0.854971i \(0.673575\pi\)
\(318\) −8.23914e31 + 8.23914e31i −0.242287 + 0.242287i
\(319\) 4.03925e31i 0.114031i
\(320\) 2.29311e32 1.76240e32i 0.621549 0.477699i
\(321\) −2.92095e32 −0.760254
\(322\) −4.23359e32 4.23359e32i −1.05824 1.05824i
\(323\) −1.21731e32 + 1.21731e32i −0.292260 + 0.292260i
\(324\) 9.27689e30i 0.0213953i
\(325\) −3.36654e32 5.81017e32i −0.745934 1.28737i
\(326\) −4.09101e31 −0.0870967
\(327\) 2.19206e32 + 2.19206e32i 0.448467 + 0.448467i
\(328\) 2.48172e32 2.48172e32i 0.487969 0.487969i
\(329\) 5.41787e32i 1.02396i
\(330\) 5.05046e31 + 6.57132e31i 0.0917592 + 0.119391i
\(331\) −3.03702e32 −0.530498 −0.265249 0.964180i \(-0.585454\pi\)
−0.265249 + 0.964180i \(0.585454\pi\)
\(332\) 8.99745e31 + 8.99745e31i 0.151121 + 0.151121i
\(333\) −2.07202e32 + 2.07202e32i −0.334671 + 0.334671i
\(334\) 7.54262e31i 0.117171i
\(335\) −5.71125e31 + 4.36430e32i −0.0853392 + 0.652127i
\(336\) −4.35540e32 −0.626063
\(337\) −1.46102e32 1.46102e32i −0.202054 0.202054i 0.598826 0.800879i \(-0.295634\pi\)
−0.800879 + 0.598826i \(0.795634\pi\)
\(338\) 6.96351e32 6.96351e32i 0.926640 0.926640i
\(339\) 8.26595e32i 1.05851i
\(340\) 4.43969e31 + 5.80990e30i 0.0547176 + 0.00716049i
\(341\) −2.00581e31 −0.0237948
\(342\) 4.63606e32 + 4.63606e32i 0.529431 + 0.529431i
\(343\) 6.99958e32 6.99958e32i 0.769571 0.769571i
\(344\) 8.07622e31i 0.0854965i
\(345\) 8.64951e32 6.64768e32i 0.881746 0.677676i
\(346\) −8.63434e32 −0.847695
\(347\) −3.93314e31 3.93314e31i −0.0371925 0.0371925i 0.688266 0.725458i \(-0.258372\pi\)
−0.725458 + 0.688266i \(0.758372\pi\)
\(348\) 4.64135e31 4.64135e31i 0.0422780 0.0422780i
\(349\) 1.91237e31i 0.0167819i 0.999965 + 0.00839095i \(0.00267095\pi\)
−0.999965 + 0.00839095i \(0.997329\pi\)
\(350\) −1.02171e33 2.72066e32i −0.863858 0.230033i
\(351\) 1.89096e33 1.54060
\(352\) −6.20548e31 6.20548e31i −0.0487215 0.0487215i
\(353\) 2.80382e31 2.80382e31i 0.0212168 0.0212168i −0.696419 0.717636i \(-0.745224\pi\)
0.717636 + 0.696419i \(0.245224\pi\)
\(354\) 9.44706e31i 0.0689056i
\(355\) −2.49084e32 3.24092e32i −0.175137 0.227876i
\(356\) −3.74338e32 −0.253755
\(357\) 1.98154e32 + 1.98154e32i 0.129514 + 0.129514i
\(358\) 2.01948e33 2.01948e33i 1.27280 1.27280i
\(359\) 6.07618e32i 0.369320i −0.982802 0.184660i \(-0.940882\pi\)
0.982802 0.184660i \(-0.0591184\pi\)
\(360\) −1.11395e32 + 8.51239e32i −0.0653033 + 0.499021i
\(361\) −9.55873e32 −0.540514
\(362\) 1.65434e33 + 1.65434e33i 0.902427 + 0.902427i
\(363\) 8.53198e32 8.53198e32i 0.449018 0.449018i
\(364\) 4.02038e32i 0.204150i
\(365\) −3.44715e33 4.51104e32i −1.68909 0.221039i
\(366\) −2.67371e33 −1.26433
\(367\) 1.04708e33 + 1.04708e33i 0.477881 + 0.477881i 0.904453 0.426572i \(-0.140279\pi\)
−0.426572 + 0.904453i \(0.640279\pi\)
\(368\) −3.05862e33 + 3.05862e33i −1.34742 + 1.34742i
\(369\) 1.00655e33i 0.428048i
\(370\) −1.76630e33 + 1.35751e33i −0.725173 + 0.557340i
\(371\) 9.97872e32 0.395561
\(372\) −2.30480e31 2.30480e31i −0.00882216 0.00882216i
\(373\) −3.21980e33 + 3.21980e33i −1.19018 + 1.19018i −0.213168 + 0.977016i \(0.568378\pi\)
−0.977016 + 0.213168i \(0.931622\pi\)
\(374\) 2.11441e32i 0.0754847i
\(375\) 7.33082e32 1.78154e33i 0.252782 0.614312i
\(376\) 3.34435e33 1.11396
\(377\) −1.77582e33 1.77582e33i −0.571427 0.571427i
\(378\) 2.10534e33 2.10534e33i 0.654528 0.654528i
\(379\) 3.87032e33i 1.16262i −0.813683 0.581309i \(-0.802541\pi\)
0.813683 0.581309i \(-0.197459\pi\)
\(380\) 4.31785e32 + 5.61810e32i 0.125337 + 0.163081i
\(381\) −1.84734e33 −0.518228
\(382\) 1.92583e32 + 1.92583e32i 0.0522149 + 0.0522149i
\(383\) 1.77337e33 1.77337e33i 0.464745 0.464745i −0.435462 0.900207i \(-0.643415\pi\)
0.900207 + 0.435462i \(0.143415\pi\)
\(384\) 3.07992e33i 0.780251i
\(385\) 9.20983e31 7.03778e32i 0.0225560 0.172364i
\(386\) 5.04062e33 1.19357
\(387\) −1.63780e32 1.63780e32i −0.0374989 0.0374989i
\(388\) 5.68560e32 5.68560e32i 0.125882 0.125882i
\(389\) 1.05975e33i 0.226912i −0.993543 0.113456i \(-0.963808\pi\)
0.993543 0.113456i \(-0.0361921\pi\)
\(390\) 5.10940e33 + 6.68630e32i 1.05811 + 0.138467i
\(391\) 2.78310e33 0.557482
\(392\) −1.03360e33 1.03360e33i −0.200279 0.200279i
\(393\) −3.99733e33 + 3.99733e33i −0.749319 + 0.749319i
\(394\) 5.88576e33i 1.06746i
\(395\) 6.66914e33 5.12564e33i 1.17033 0.899469i
\(396\) 1.14474e32 0.0194387
\(397\) −1.34395e33 1.34395e33i −0.220855 0.220855i 0.588003 0.808858i \(-0.299914\pi\)
−0.808858 + 0.588003i \(0.799914\pi\)
\(398\) −1.72308e33 + 1.72308e33i −0.274047 + 0.274047i
\(399\) 4.43465e33i 0.682671i
\(400\) −1.96558e33 + 7.38147e33i −0.292894 + 1.09992i
\(401\) −2.91176e33 −0.420029 −0.210014 0.977698i \(-0.567351\pi\)
−0.210014 + 0.977698i \(0.567351\pi\)
\(402\) −2.38834e33 2.38834e33i −0.333547 0.333547i
\(403\) −8.81834e32 + 8.81834e32i −0.119240 + 0.119240i
\(404\) 1.67890e32i 0.0219820i
\(405\) 6.20522e32 + 8.07381e32i 0.0786759 + 0.102368i
\(406\) −3.95429e33 −0.485545
\(407\) −1.05745e33 1.05745e33i −0.125757 0.125757i
\(408\) 1.22317e33 1.22317e33i 0.140898 0.140898i
\(409\) 7.07206e33i 0.789120i 0.918870 + 0.394560i \(0.129103\pi\)
−0.918870 + 0.394560i \(0.870897\pi\)
\(410\) −9.92916e32 + 7.58746e33i −0.107330 + 0.820174i
\(411\) −4.33508e33 −0.453997
\(412\) 1.02940e33 + 1.02940e33i 0.104453 + 0.104453i
\(413\) 5.72084e32 5.72084e32i 0.0562483 0.0562483i
\(414\) 1.05993e34i 1.00988i
\(415\) 1.38489e34 + 1.81231e33i 1.27876 + 0.167343i
\(416\) −5.45636e33 −0.488303
\(417\) −8.86378e33 8.86378e33i −0.768865 0.768865i
\(418\) −2.36601e33 + 2.36601e33i −0.198941 + 0.198941i
\(419\) 1.36015e33i 0.110867i 0.998462 + 0.0554336i \(0.0176541\pi\)
−0.998462 + 0.0554336i \(0.982346\pi\)
\(420\) 9.14512e32 7.02858e32i 0.0722684 0.0555427i
\(421\) −2.23548e33 −0.171279 −0.0856394 0.996326i \(-0.527293\pi\)
−0.0856394 + 0.996326i \(0.527293\pi\)
\(422\) −1.37722e34 1.37722e34i −1.02316 1.02316i
\(423\) −6.78210e33 + 6.78210e33i −0.488585 + 0.488585i
\(424\) 6.15968e33i 0.430331i
\(425\) 4.25254e33 2.46402e33i 0.288133 0.166950i
\(426\) 3.13667e33 0.206131
\(427\) 1.61911e34 + 1.61911e34i 1.03208 + 1.03208i
\(428\) −2.16880e33 + 2.16880e33i −0.134106 + 0.134106i
\(429\) 3.45921e33i 0.207506i
\(430\) −1.07303e33 1.39615e33i −0.0624482 0.0812534i
\(431\) 2.35758e34 1.33126 0.665630 0.746282i \(-0.268163\pi\)
0.665630 + 0.746282i \(0.268163\pi\)
\(432\) −1.52103e34 1.52103e34i −0.833391 0.833391i
\(433\) −2.10238e34 + 2.10238e34i −1.11781 + 1.11781i −0.125752 + 0.992062i \(0.540134\pi\)
−0.992062 + 0.125752i \(0.959866\pi\)
\(434\) 1.96362e33i 0.101319i
\(435\) 9.34882e32 7.14399e33i 0.0468162 0.357751i
\(436\) 3.25519e33 0.158216
\(437\) 3.11427e34 + 3.11427e34i 1.46925 + 1.46925i
\(438\) 1.88643e34 1.88643e34i 0.863928 0.863928i
\(439\) 1.02267e34i 0.454668i −0.973817 0.227334i \(-0.926999\pi\)
0.973817 0.227334i \(-0.0730010\pi\)
\(440\) −4.34429e33 5.68506e32i −0.187514 0.0245386i
\(441\) 4.19215e33 0.175685
\(442\) 9.29580e33 + 9.29580e33i 0.378266 + 0.378266i
\(443\) 1.68073e34 1.68073e34i 0.664125 0.664125i −0.292224 0.956350i \(-0.594395\pi\)
0.956350 + 0.292224i \(0.0943954\pi\)
\(444\) 2.43016e33i 0.0932515i
\(445\) −3.25792e34 + 2.50391e34i −1.21412 + 0.933122i
\(446\) 1.43973e34 0.521107
\(447\) −8.76662e33 8.76662e33i −0.308201 0.308201i
\(448\) 1.34397e34 1.34397e34i 0.458960 0.458960i
\(449\) 5.54257e34i 1.83869i −0.393450 0.919346i \(-0.628719\pi\)
0.393450 0.919346i \(-0.371281\pi\)
\(450\) −9.38405e33 1.61955e34i −0.302432 0.521954i
\(451\) −5.13692e33 −0.160845
\(452\) 6.13744e33 + 6.13744e33i 0.186718 + 0.186718i
\(453\) −8.04780e33 + 8.04780e33i −0.237903 + 0.237903i
\(454\) 5.65994e34i 1.62587i
\(455\) −2.68919e34 3.49899e34i −0.750711 0.976775i
\(456\) 2.73743e34 0.742677
\(457\) 4.18717e33 + 4.18717e33i 0.110410 + 0.110410i 0.760154 0.649743i \(-0.225124\pi\)
−0.649743 + 0.760154i \(0.725124\pi\)
\(458\) −3.16159e34 + 3.16159e34i −0.810315 + 0.810315i
\(459\) 1.38402e34i 0.344808i
\(460\) 1.48635e33 1.13581e34i 0.0359973 0.275077i
\(461\) −8.17431e34 −1.92459 −0.962297 0.272002i \(-0.912314\pi\)
−0.962297 + 0.272002i \(0.912314\pi\)
\(462\) 3.85138e33 + 3.85138e33i 0.0881598 + 0.0881598i
\(463\) 3.24302e34 3.24302e34i 0.721767 0.721767i −0.247198 0.968965i \(-0.579510\pi\)
0.968965 + 0.247198i \(0.0795097\pi\)
\(464\) 2.85683e34i 0.618230i
\(465\) −3.54756e33 4.64243e32i −0.0746519 0.00976916i
\(466\) 3.83960e33 0.0785721
\(467\) 1.00991e34 + 1.00991e34i 0.200984 + 0.200984i 0.800422 0.599437i \(-0.204609\pi\)
−0.599437 + 0.800422i \(0.704609\pi\)
\(468\) 5.03272e33 5.03272e33i 0.0974107 0.0974107i
\(469\) 2.89260e34i 0.544555i
\(470\) −5.78143e34 + 4.44338e34i −1.05868 + 0.813658i
\(471\) −4.14852e34 −0.738960
\(472\) −3.53137e33 3.53137e33i −0.0611924 0.0611924i
\(473\) 8.35850e32 8.35850e32i 0.0140907 0.0140907i
\(474\) 6.45462e34i 1.05865i
\(475\) 7.51577e34 + 2.00134e34i 1.19938 + 0.319378i
\(476\) 2.94257e33 0.0456916
\(477\) 1.24914e34 + 1.24914e34i 0.188744 + 0.188744i
\(478\) 4.29580e34 4.29580e34i 0.631657 0.631657i
\(479\) 8.73265e34i 1.24964i −0.780769 0.624819i \(-0.785173\pi\)
0.780769 0.624819i \(-0.214827\pi\)
\(480\) −9.53902e33 1.24115e34i −0.132852 0.172858i
\(481\) −9.29797e34 −1.26038
\(482\) −5.50034e34 5.50034e34i −0.725735 0.725735i
\(483\) 5.06939e34 5.06939e34i 0.651093 0.651093i
\(484\) 1.26699e34i 0.158411i
\(485\) 1.14522e34 8.75130e34i 0.139395 1.06520i
\(486\) 8.65252e34 1.02535
\(487\) 1.04084e35 + 1.04084e35i 1.20090 + 1.20090i 0.973893 + 0.227009i \(0.0728946\pi\)
0.227009 + 0.973893i \(0.427105\pi\)
\(488\) 9.99448e34 9.99448e34i 1.12280 1.12280i
\(489\) 4.89866e33i 0.0535873i
\(490\) 3.16008e34 + 4.13536e33i 0.336627 + 0.0440519i
\(491\) 5.18891e33 0.0538290 0.0269145 0.999638i \(-0.491432\pi\)
0.0269145 + 0.999638i \(0.491432\pi\)
\(492\) −5.90265e33 5.90265e33i −0.0596349 0.0596349i
\(493\) 1.29974e34 1.29974e34i 0.127893 0.127893i
\(494\) 2.08039e35i 1.99385i
\(495\) 9.96281e33 7.65702e33i 0.0930067 0.0714813i
\(496\) 1.41864e34 0.129006
\(497\) −1.89947e34 1.89947e34i −0.168267 0.168267i
\(498\) −7.57873e34 + 7.57873e34i −0.654056 + 0.654056i
\(499\) 6.24363e34i 0.524964i −0.964937 0.262482i \(-0.915459\pi\)
0.964937 0.262482i \(-0.0845411\pi\)
\(500\) −7.78477e33 1.86710e34i −0.0637728 0.152953i
\(501\) −9.03169e33 −0.0720906
\(502\) −1.31025e35 1.31025e35i −1.01908 1.01908i
\(503\) −7.75841e34 + 7.75841e34i −0.588016 + 0.588016i −0.937094 0.349078i \(-0.886495\pi\)
0.349078 + 0.937094i \(0.386495\pi\)
\(504\) 5.64190e34i 0.416705i
\(505\) −1.12300e34 1.46117e34i −0.0808333 0.105175i
\(506\) 5.40933e34 0.379478
\(507\) 8.33824e34 + 8.33824e34i 0.570126 + 0.570126i
\(508\) −1.37164e34 + 1.37164e34i −0.0914138 + 0.0914138i
\(509\) 1.41568e35i 0.919672i 0.888004 + 0.459836i \(0.152092\pi\)
−0.888004 + 0.459836i \(0.847908\pi\)
\(510\) −4.89379e33 + 3.73964e34i −0.0309908 + 0.236819i
\(511\) −2.28473e35 −1.41047
\(512\) −7.65711e34 7.65711e34i −0.460845 0.460845i
\(513\) −1.54870e35 + 1.54870e35i −0.908746 + 0.908746i
\(514\) 3.11732e35i 1.78345i
\(515\) 1.58446e35 + 2.07346e34i 0.883866 + 0.115665i
\(516\) 1.92089e33 0.0104486
\(517\) −3.46124e34 3.46124e34i −0.183593 0.183593i
\(518\) −1.03521e35 + 1.03521e35i −0.535477 + 0.535477i
\(519\) 1.03389e35i 0.521555i
\(520\) −2.15986e35 + 1.65999e35i −1.06263 + 0.816697i
\(521\) 3.71768e35 1.78395 0.891973 0.452089i \(-0.149321\pi\)
0.891973 + 0.452089i \(0.149321\pi\)
\(522\) −4.94999e34 4.94999e34i −0.231680 0.231680i
\(523\) 2.40331e34 2.40331e34i 0.109720 0.109720i −0.650115 0.759836i \(-0.725279\pi\)
0.759836 + 0.650115i \(0.225279\pi\)
\(524\) 5.93601e34i 0.264355i
\(525\) 3.25778e34 1.22341e35i 0.141531 0.531499i
\(526\) 2.32632e35 0.985948
\(527\) −6.45426e33 6.45426e33i −0.0266875 0.0266875i
\(528\) 2.78248e34 2.78248e34i 0.112251 0.112251i
\(529\) 4.57951e35i 1.80258i
\(530\) 8.18390e34 + 1.06483e35i 0.314321 + 0.408974i
\(531\) 1.43227e34 0.0536781
\(532\) 3.29271e34 + 3.29271e34i 0.120421 + 0.120421i
\(533\) −2.25840e35 + 2.25840e35i −0.806021 + 0.806021i
\(534\) 3.15313e35i 1.09826i
\(535\) −4.36848e34 + 3.33822e35i −0.148502 + 1.13479i
\(536\) 1.78555e35 0.592421
\(537\) 2.41817e35 + 2.41817e35i 0.783107 + 0.783107i
\(538\) 1.49409e35 1.49409e35i 0.472288 0.472288i
\(539\) 2.13946e34i 0.0660162i
\(540\) 5.64831e34 + 7.39154e33i 0.170137 + 0.0222647i
\(541\) −5.97797e35 −1.75788 −0.878940 0.476933i \(-0.841749\pi\)
−0.878940 + 0.476933i \(0.841749\pi\)
\(542\) 5.98918e34 + 5.98918e34i 0.171940 + 0.171940i
\(543\) −1.98093e35 + 1.98093e35i −0.555229 + 0.555229i
\(544\) 3.99358e34i 0.109289i
\(545\) 2.83303e35 2.17736e35i 0.757002 0.581803i
\(546\) 3.38644e35 0.883567
\(547\) −9.83000e33 9.83000e33i −0.0250448 0.0250448i 0.694473 0.719518i \(-0.255637\pi\)
−0.719518 + 0.694473i \(0.755637\pi\)
\(548\) −3.21878e34 + 3.21878e34i −0.0800837 + 0.0800837i
\(549\) 4.05362e35i 0.984923i
\(550\) 8.26538e34 4.78914e34i 0.196132 0.113643i
\(551\) 2.90881e35 0.674131
\(552\) −3.12924e35 3.12924e35i −0.708323 0.708323i
\(553\) 3.90871e35 3.90871e35i 0.864186 0.864186i
\(554\) 1.54107e35i 0.332809i
\(555\) −1.62551e35 2.11500e35i −0.342910 0.446171i
\(556\) −1.31626e35 −0.271251
\(557\) 1.31923e35 + 1.31923e35i 0.265585 + 0.265585i 0.827318 0.561734i \(-0.189865\pi\)
−0.561734 + 0.827318i \(0.689865\pi\)
\(558\) −2.45806e34 + 2.45806e34i −0.0483446 + 0.0483446i
\(559\) 7.34946e34i 0.141222i
\(560\) −6.51380e34 + 4.97758e35i −0.122290 + 0.934489i
\(561\) −2.53184e34 −0.0464429
\(562\) −6.40754e35 6.40754e35i −1.14847 1.14847i
\(563\) −3.83699e35 + 3.83699e35i −0.672020 + 0.672020i −0.958181 0.286162i \(-0.907621\pi\)
0.286162 + 0.958181i \(0.407621\pi\)
\(564\) 7.95437e34i 0.136137i
\(565\) 9.44676e35 + 1.23623e35i 1.57999 + 0.206761i
\(566\) −6.29517e35 −1.02895
\(567\) 4.73198e34 + 4.73198e34i 0.0755897 + 0.0755897i
\(568\) −1.17251e35 + 1.17251e35i −0.183057 + 0.183057i
\(569\) 3.21963e35i 0.491300i 0.969359 + 0.245650i \(0.0790013\pi\)
−0.969359 + 0.245650i \(0.920999\pi\)
\(570\) −4.73223e35 + 3.63701e35i −0.705819 + 0.542465i
\(571\) −1.04599e36 −1.52496 −0.762482 0.647009i \(-0.776019\pi\)
−0.762482 + 0.647009i \(0.776019\pi\)
\(572\) 2.56845e34 + 2.56845e34i 0.0366035 + 0.0366035i
\(573\) −2.30603e34 + 2.30603e34i −0.0321258 + 0.0321258i
\(574\) 5.02887e35i 0.684882i
\(575\) −6.30372e35 1.08793e36i −0.839296 1.44850i
\(576\) 3.36477e35 0.437989
\(577\) 1.77056e35 + 1.77056e35i 0.225333 + 0.225333i 0.810740 0.585407i \(-0.199065\pi\)
−0.585407 + 0.810740i \(0.699065\pi\)
\(578\) 5.45503e35 5.45503e35i 0.678790 0.678790i
\(579\) 6.03574e35i 0.734360i
\(580\) −4.61024e34 5.99853e34i −0.0548478 0.0713643i
\(581\) 9.17888e35 1.06782
\(582\) 4.78909e35 + 4.78909e35i 0.544822 + 0.544822i
\(583\) −6.37498e34 + 6.37498e34i −0.0709231 + 0.0709231i
\(584\) 1.41032e36i 1.53444i
\(585\) 1.01371e35 7.74638e35i 0.107867 0.824276i
\(586\) −2.31391e35 −0.240812
\(587\) −6.90189e35 6.90189e35i −0.702542 0.702542i 0.262413 0.964956i \(-0.415482\pi\)
−0.964956 + 0.262413i \(0.915482\pi\)
\(588\) −2.45837e34 + 2.45837e34i −0.0244761 + 0.0244761i
\(589\) 1.44445e35i 0.140671i
\(590\) 1.07966e35 + 1.41287e34i 0.102852 + 0.0134594i
\(591\) 7.04772e35 0.656767
\(592\) 7.47901e35 + 7.47901e35i 0.681807 + 0.681807i
\(593\) 7.31719e35 7.31719e35i 0.652579 0.652579i −0.301034 0.953613i \(-0.597332\pi\)
0.953613 + 0.301034i \(0.0973319\pi\)
\(594\) 2.69002e35i 0.234710i
\(595\) 2.56096e35 1.96825e35i 0.218616 0.168020i
\(596\) −1.30184e35 −0.108731
\(597\) −2.06325e35 2.06325e35i −0.168610 0.168610i
\(598\) 2.37816e36 2.37816e36i 1.90163 1.90163i
\(599\) 1.29851e36i 1.01601i −0.861355 0.508003i \(-0.830384\pi\)
0.861355 0.508003i \(-0.169616\pi\)
\(600\) −7.55192e35 2.01097e35i −0.578217 0.153971i
\(601\) −4.40252e35 −0.329863 −0.164931 0.986305i \(-0.552740\pi\)
−0.164931 + 0.986305i \(0.552740\pi\)
\(602\) −8.18268e34 8.18268e34i −0.0599986 0.0599986i
\(603\) −3.62097e35 + 3.62097e35i −0.259836 + 0.259836i
\(604\) 1.19509e35i 0.0839308i
\(605\) −8.47478e35 1.10268e36i −0.582517 0.757932i
\(606\) 1.41417e35 0.0951386
\(607\) 1.86886e36 + 1.86886e36i 1.23062 + 1.23062i 0.963726 + 0.266893i \(0.0859970\pi\)
0.266893 + 0.963726i \(0.414003\pi\)
\(608\) 4.46878e35 4.46878e35i 0.288033 0.288033i
\(609\) 4.73494e35i 0.298738i
\(610\) −3.99871e35 + 3.05565e36i −0.246963 + 1.88719i
\(611\) −3.04340e36 −1.84002
\(612\) 3.68352e34 + 3.68352e34i 0.0218019 + 0.0218019i
\(613\) −1.14582e36 + 1.14582e36i −0.663942 + 0.663942i −0.956307 0.292365i \(-0.905558\pi\)
0.292365 + 0.956307i \(0.405558\pi\)
\(614\) 1.45319e35i 0.0824393i
\(615\) −9.08537e35 1.18894e35i −0.504622 0.0660363i
\(616\) −2.87934e35 −0.156583
\(617\) 2.45170e35 + 2.45170e35i 0.130545 + 0.130545i 0.769360 0.638815i \(-0.220575\pi\)
−0.638815 + 0.769360i \(0.720575\pi\)
\(618\) −8.67084e35 + 8.67084e35i −0.452076 + 0.452076i
\(619\) 7.48289e35i 0.382024i 0.981588 + 0.191012i \(0.0611770\pi\)
−0.981588 + 0.191012i \(0.938823\pi\)
\(620\) −2.97875e34 + 2.28935e34i −0.0148916 + 0.0114451i
\(621\) 3.54075e36 1.73342
\(622\) 1.27499e36 + 1.27499e36i 0.611270 + 0.611270i
\(623\) −1.90943e36 + 1.90943e36i −0.896519 + 0.896519i
\(624\) 2.44658e36i 1.12502i
\(625\) −1.92640e36 1.10425e36i −0.867574 0.497308i
\(626\) −6.71656e35 −0.296265
\(627\) −2.83311e35 2.83311e35i −0.122401 0.122401i
\(628\) −3.08026e35 + 3.08026e35i −0.130350 + 0.130350i
\(629\) 6.80531e35i 0.282091i
\(630\) −7.49596e35 9.75324e35i −0.304369 0.396024i
\(631\) −1.97667e36 −0.786237 −0.393118 0.919488i \(-0.628604\pi\)
−0.393118 + 0.919488i \(0.628604\pi\)
\(632\) −2.41278e36 2.41278e36i −0.940147 0.940147i
\(633\) 1.64912e36 1.64912e36i 0.629510 0.629510i
\(634\) 1.37306e36i 0.513488i
\(635\) −2.76282e35 + 2.11123e36i −0.101226 + 0.773531i
\(636\) −1.46505e35 −0.0525908
\(637\) 9.40593e35 + 9.40593e35i 0.330818 + 0.330818i
\(638\) 2.52623e35 2.52623e35i 0.0870569 0.0870569i
\(639\) 4.75552e35i 0.160578i
\(640\) 3.51990e36 + 4.60624e35i 1.16464 + 0.152408i
\(641\) 5.06578e36 1.64245 0.821224 0.570606i \(-0.193292\pi\)
0.821224 + 0.570606i \(0.193292\pi\)
\(642\) −1.82682e36 1.82682e36i −0.580417 0.580417i
\(643\) 2.22275e36 2.22275e36i 0.692067 0.692067i −0.270619 0.962686i \(-0.587228\pi\)
0.962686 + 0.270619i \(0.0872285\pi\)
\(644\) 7.52801e35i 0.229701i
\(645\) 1.67178e35 1.28486e35i 0.0499922 0.0384220i
\(646\) −1.52266e36 −0.446253
\(647\) 2.15344e36 + 2.15344e36i 0.618552 + 0.618552i 0.945160 0.326608i \(-0.105906\pi\)
−0.326608 + 0.945160i \(0.605906\pi\)
\(648\) 2.92096e35 2.92096e35i 0.0822339 0.0822339i
\(649\) 7.30960e34i 0.0201703i
\(650\) 1.52829e36 5.73929e36i 0.413364 1.55233i
\(651\) −2.35127e35 −0.0623376
\(652\) −3.63724e34 3.63724e34i −0.00945263 0.00945263i
\(653\) −2.03862e36 + 2.03862e36i −0.519355 + 0.519355i −0.917376 0.398021i \(-0.869697\pi\)
0.398021 + 0.917376i \(0.369697\pi\)
\(654\) 2.74191e36i 0.684766i
\(655\) 3.97053e36 + 5.16619e36i 0.972102 + 1.26483i
\(656\) 3.63317e36 0.872039
\(657\) −2.86003e36 2.86003e36i −0.673008 0.673008i
\(658\) −3.38844e36 + 3.38844e36i −0.781741 + 0.781741i
\(659\) 3.21300e36i 0.726775i 0.931638 + 0.363388i \(0.118380\pi\)
−0.931638 + 0.363388i \(0.881620\pi\)
\(660\) −1.35216e34 + 1.03327e35i −0.00299887 + 0.0229162i
\(661\) 1.30866e36 0.284582 0.142291 0.989825i \(-0.454553\pi\)
0.142291 + 0.989825i \(0.454553\pi\)
\(662\) −1.89941e36 1.89941e36i −0.405009 0.405009i
\(663\) −1.11310e36 + 1.11310e36i −0.232733 + 0.232733i
\(664\) 5.66595e36i 1.16168i
\(665\) 5.06815e36 + 6.63232e35i 1.01899 + 0.133347i
\(666\) −2.59176e36 −0.511010
\(667\) −3.32515e36 3.32515e36i −0.642948 0.642948i
\(668\) −6.70599e34 + 6.70599e34i −0.0127165 + 0.0127165i
\(669\) 1.72396e36i 0.320617i
\(670\) −3.08671e36 + 2.37233e36i −0.563019 + 0.432715i
\(671\) −2.06876e36 −0.370099
\(672\) −7.27427e35 7.27427e35i −0.127641 0.127641i
\(673\) −1.65247e36 + 1.65247e36i −0.284406 + 0.284406i −0.834863 0.550458i \(-0.814453\pi\)
0.550458 + 0.834863i \(0.314453\pi\)
\(674\) 1.82750e36i 0.308516i
\(675\) 5.41022e36 3.13480e36i 0.895912 0.519112i
\(676\) 1.23822e36 0.201137
\(677\) 1.23936e36 + 1.23936e36i 0.197489 + 0.197489i 0.798923 0.601433i \(-0.205403\pi\)
−0.601433 + 0.798923i \(0.705403\pi\)
\(678\) −5.16968e36 + 5.16968e36i −0.808124 + 0.808124i
\(679\) 5.80025e36i 0.889486i
\(680\) −1.21497e36 1.58083e36i −0.182788 0.237832i
\(681\) −6.77733e36 −1.00034
\(682\) −1.25447e35 1.25447e35i −0.0181662 0.0181662i
\(683\) 2.28158e36 2.28158e36i 0.324165 0.324165i −0.526197 0.850363i \(-0.676383\pi\)
0.850363 + 0.526197i \(0.176383\pi\)
\(684\) 8.24365e35i 0.114919i
\(685\) −6.48341e35 + 4.95436e36i −0.0886801 + 0.677657i
\(686\) 8.75534e36 1.17506
\(687\) −3.78575e36 3.78575e36i −0.498556 0.498556i
\(688\) −5.91169e35 + 5.91169e35i −0.0763945 + 0.0763945i
\(689\) 5.60539e36i 0.710814i
\(690\) 9.56716e36 + 1.25198e36i 1.19054 + 0.155798i
\(691\) −8.96721e36 −1.09507 −0.547536 0.836782i \(-0.684434\pi\)
−0.547536 + 0.836782i \(0.684434\pi\)
\(692\) −7.67661e35 7.67661e35i −0.0920006 0.0920006i
\(693\) 5.83910e35 5.83910e35i 0.0686774 0.0686774i
\(694\) 4.91972e35i 0.0567894i
\(695\) −1.14556e37 + 8.80435e36i −1.29783 + 0.997459i
\(696\) −2.92279e36 −0.324996
\(697\) −1.65295e36 1.65295e36i −0.180399 0.180399i
\(698\) −1.19603e35 + 1.19603e35i −0.0128122 + 0.0128122i
\(699\) 4.59761e35i 0.0483425i
\(700\) −6.66492e35 1.15027e36i −0.0687892 0.118720i
\(701\) 3.67140e36 0.371961 0.185980 0.982553i \(-0.440454\pi\)
0.185980 + 0.982553i \(0.440454\pi\)
\(702\) 1.18264e37 + 1.18264e37i 1.17617 + 1.17617i
\(703\) 7.61508e36 7.61508e36i 0.743456 0.743456i
\(704\) 1.71721e36i 0.164581i
\(705\) −5.32060e36 6.92280e36i −0.500613 0.651363i
\(706\) 3.50713e35 0.0323959
\(707\) −8.56375e35 8.56375e35i −0.0776625 0.0776625i
\(708\) −8.39919e34 + 8.39919e34i −0.00747834 + 0.00747834i
\(709\) 1.93132e37i 1.68832i −0.536093 0.844159i \(-0.680100\pi\)
0.536093 0.844159i \(-0.319900\pi\)
\(710\) 4.69111e35 3.58475e36i 0.0402640 0.307681i
\(711\) 9.78589e36 0.824699
\(712\) 1.17866e37 + 1.17866e37i 0.975322 + 0.975322i
\(713\) −1.65120e36 + 1.65120e36i −0.134164 + 0.134164i
\(714\) 2.47858e36i 0.197755i
\(715\) 3.95336e36 + 5.17348e35i 0.309733 + 0.0405326i
\(716\) 3.59096e36 0.276275
\(717\) 5.14388e36 + 5.14388e36i 0.388635 + 0.388635i
\(718\) 3.80016e36 3.80016e36i 0.281958 0.281958i
\(719\) 1.43743e37i 1.04739i −0.851905 0.523697i \(-0.824553\pi\)
0.851905 0.523697i \(-0.175447\pi\)
\(720\) −7.04636e36 + 5.41556e36i −0.504246 + 0.387544i
\(721\) 1.05016e37 0.738067
\(722\) −5.97821e36 5.97821e36i −0.412656 0.412656i
\(723\) 6.58622e36 6.58622e36i 0.446517 0.446517i
\(724\) 2.94167e36i 0.195881i
\(725\) −8.02471e36 2.13687e36i −0.524850 0.139760i
\(726\) 1.06721e37 0.685607
\(727\) −5.89050e36 5.89050e36i −0.371710 0.371710i 0.496390 0.868100i \(-0.334659\pi\)
−0.868100 + 0.496390i \(0.834659\pi\)
\(728\) −1.26587e37 + 1.26587e37i −0.784662 + 0.784662i
\(729\) 1.24811e37i 0.759966i
\(730\) −1.87378e37 2.43804e37i −1.12079 1.45829i
\(731\) 5.37917e35 0.0316075
\(732\) −2.37714e36 2.37714e36i −0.137218 0.137218i
\(733\) 3.48486e36 3.48486e36i 0.197621 0.197621i −0.601358 0.798980i \(-0.705373\pi\)
0.798980 + 0.601358i \(0.205373\pi\)
\(734\) 1.30972e37i 0.729677i
\(735\) −4.95177e35 + 3.78394e36i −0.0271035 + 0.207114i
\(736\) −1.02168e37 −0.549420
\(737\) −1.84796e36 1.84796e36i −0.0976372 0.0976372i
\(738\) −6.29515e36 + 6.29515e36i −0.326794 + 0.326794i
\(739\) 2.97621e37i 1.51805i 0.651062 + 0.759025i \(0.274324\pi\)
−0.651062 + 0.759025i \(0.725676\pi\)
\(740\) −2.77731e36 3.63447e35i −0.139191 0.0182150i
\(741\) −2.49109e37 −1.22674
\(742\) 6.24088e36 + 6.24088e36i 0.301992 + 0.301992i
\(743\) 9.12879e36 9.12879e36i 0.434069 0.434069i −0.455941 0.890010i \(-0.650697\pi\)
0.890010 + 0.455941i \(0.150697\pi\)
\(744\) 1.45140e36i 0.0678170i
\(745\) −1.13301e37 + 8.70785e36i −0.520237 + 0.399834i
\(746\) −4.02745e37 −1.81729
\(747\) 1.14901e37 + 1.14901e37i 0.509516 + 0.509516i
\(748\) −1.87988e35 + 1.87988e35i −0.00819237 + 0.00819237i
\(749\) 2.21253e37i 0.947600i
\(750\) 1.57269e37 6.55726e36i 0.661984 0.276011i
\(751\) −1.42103e37 −0.587875 −0.293938 0.955825i \(-0.594966\pi\)
−0.293938 + 0.955825i \(0.594966\pi\)
\(752\) 2.44802e37 + 2.44802e37i 0.995367 + 0.995367i
\(753\) 1.56892e37 1.56892e37i 0.626998 0.626998i
\(754\) 2.22126e37i 0.872513i
\(755\) 7.99385e36 + 1.04011e37i 0.308635 + 0.401575i
\(756\) 3.74363e36 0.142072
\(757\) −3.00112e37 3.00112e37i −1.11953 1.11953i −0.991810 0.127722i \(-0.959234\pi\)
−0.127722 0.991810i \(-0.540766\pi\)
\(758\) 2.42057e37 2.42057e37i 0.887602 0.887602i
\(759\) 6.47724e36i 0.233478i
\(760\) 4.09401e36 3.12848e37i 0.145068 1.10855i
\(761\) 1.34961e37 0.470120 0.235060 0.971981i \(-0.424471\pi\)
0.235060 + 0.971981i \(0.424471\pi\)
\(762\) −1.15536e37 1.15536e37i −0.395642 0.395642i
\(763\) 1.66041e37 1.66041e37i 0.558981 0.558981i
\(764\) 3.42443e35i 0.0113338i
\(765\) 5.66968e36 + 7.41950e35i 0.184485 + 0.0241422i
\(766\) 2.21820e37 0.709621
\(767\) 3.21359e36 + 3.21359e36i 0.101077 + 0.101077i
\(768\) −7.35536e36 + 7.35536e36i −0.227462 + 0.227462i
\(769\) 3.01328e37i 0.916214i 0.888897 + 0.458107i \(0.151472\pi\)
−0.888897 + 0.458107i \(0.848528\pi\)
\(770\) 4.97756e36 3.82556e36i 0.148812 0.114371i
\(771\) 3.73274e37 1.09729
\(772\) 4.48151e36 + 4.48151e36i 0.129539 + 0.129539i
\(773\) −6.65204e36 + 6.65204e36i −0.189070 + 0.189070i −0.795294 0.606224i \(-0.792683\pi\)
0.606224 + 0.795294i \(0.292683\pi\)
\(774\) 2.04862e36i 0.0572571i
\(775\) −1.06112e36 + 3.98490e36i −0.0291638 + 0.109521i
\(776\) −3.58039e37 −0.967671
\(777\) −1.23958e37 1.23958e37i −0.329459 0.329459i
\(778\) 6.62786e36 6.62786e36i 0.173236 0.173236i
\(779\) 3.69928e37i 0.950889i
\(780\) 3.94820e36 + 5.13713e36i 0.0998088 + 0.129865i
\(781\) 2.42698e36 0.0603396
\(782\) 1.74060e37 + 1.74060e37i 0.425611 + 0.425611i
\(783\) 1.65358e37 1.65358e37i 0.397668 0.397668i
\(784\) 1.51317e37i 0.357914i
\(785\) −6.20439e36 + 4.74114e37i −0.144342 + 1.10301i
\(786\) −5.00001e37 −1.14414
\(787\) 2.09349e36 + 2.09349e36i 0.0471194 + 0.0471194i 0.730274 0.683155i \(-0.239392\pi\)
−0.683155 + 0.730274i \(0.739392\pi\)
\(788\) 5.23291e36 5.23291e36i 0.115852 0.115852i
\(789\) 2.78558e37i 0.606616i
\(790\) 7.37668e37 + 9.65333e36i 1.58019 + 0.206788i
\(791\) 6.26119e37 1.31936
\(792\) −3.60437e36 3.60437e36i −0.0747140 0.0747140i
\(793\) −9.09511e37 + 9.09511e37i −1.85463 + 1.85463i
\(794\) 1.68107e37i 0.337224i
\(795\) −1.27505e37 + 9.79957e36i −0.251626 + 0.193390i
\(796\) −3.06390e36 −0.0594847
\(797\) −3.27285e37 3.27285e37i −0.625127 0.625127i 0.321711 0.946838i \(-0.395742\pi\)
−0.946838 + 0.321711i \(0.895742\pi\)
\(798\) −2.77351e37 + 2.77351e37i −0.521186 + 0.521186i
\(799\) 2.22751e37i 0.411824i
\(800\) −1.56112e37 + 9.04546e36i −0.283966 + 0.164536i
\(801\) −4.78047e37 −0.855555
\(802\) −1.82107e37 1.82107e37i −0.320671 0.320671i
\(803\) 1.45961e37 1.45961e37i 0.252892 0.252892i
\(804\) 4.24685e36i 0.0723999i
\(805\) −5.03540e37 6.55173e37i −0.844672 1.09903i
\(806\) −1.10303e37 −0.182067
\(807\) 1.78905e37 + 1.78905e37i 0.290581 + 0.290581i
\(808\) −5.28625e36 + 5.28625e36i −0.0844889 + 0.0844889i
\(809\) 3.80070e37i 0.597769i −0.954289 0.298884i \(-0.903386\pi\)
0.954289 0.298884i \(-0.0966145\pi\)
\(810\) −1.16865e36 + 8.93038e36i −0.0180876 + 0.138218i
\(811\) 7.84596e37 1.19502 0.597510 0.801861i \(-0.296157\pi\)
0.597510 + 0.801861i \(0.296157\pi\)
\(812\) −3.51568e36 3.51568e36i −0.0526964 0.0526964i
\(813\) −7.17157e36 + 7.17157e36i −0.105788 + 0.105788i
\(814\) 1.32270e37i 0.192019i
\(815\) −5.59844e36 7.32628e35i −0.0799868 0.0104673i
\(816\) 1.79069e37 0.251795
\(817\) 6.01925e36 + 6.01925e36i 0.0833020 + 0.0833020i
\(818\) −4.42300e37 + 4.42300e37i −0.602455 + 0.602455i
\(819\) 5.13420e37i 0.688307i
\(820\) −7.62864e36 + 5.86307e36i −0.100662 + 0.0773651i
\(821\) 1.21357e38 1.57617 0.788087 0.615563i \(-0.211072\pi\)
0.788087 + 0.615563i \(0.211072\pi\)
\(822\) −2.71124e37 2.71124e37i −0.346605 0.346605i
\(823\) −7.77777e37 + 7.77777e37i −0.978717 + 0.978717i −0.999778 0.0210608i \(-0.993296\pi\)
0.0210608 + 0.999778i \(0.493296\pi\)
\(824\) 6.48243e37i 0.802942i
\(825\) 5.73462e36 + 9.89713e36i 0.0699203 + 0.120672i
\(826\) 7.15585e36 0.0858856
\(827\) 3.09291e36 + 3.09291e36i 0.0365423 + 0.0365423i 0.725142 0.688600i \(-0.241774\pi\)
−0.688600 + 0.725142i \(0.741774\pi\)
\(828\) 9.42359e36 9.42359e36i 0.109603 0.109603i
\(829\) 8.86406e37i 1.01490i 0.861681 + 0.507451i \(0.169412\pi\)
−0.861681 + 0.507451i \(0.830588\pi\)
\(830\) 7.52792e37 + 9.79482e37i 0.848516 + 1.10403i
\(831\) 1.84531e37 0.204765
\(832\) 7.54954e37 + 7.54954e37i 0.824740 + 0.824740i
\(833\) −6.88433e36 + 6.88433e36i −0.0740417 + 0.0740417i
\(834\) 1.10872e38i 1.17398i
\(835\) −1.35075e36 + 1.03219e37i −0.0140816 + 0.107606i
\(836\) −4.20714e36 −0.0431823
\(837\) −8.21131e36 8.21131e36i −0.0829816 0.0829816i
\(838\) −8.50661e36 + 8.50661e36i −0.0846417 + 0.0846417i
\(839\) 1.48941e37i 0.145918i −0.997335 0.0729589i \(-0.976756\pi\)
0.997335 0.0729589i \(-0.0232442\pi\)
\(840\) −5.09252e37 6.66422e36i −0.491250 0.0642863i
\(841\) 7.42227e37 0.705000
\(842\) −1.39811e37 1.39811e37i −0.130763 0.130763i
\(843\) 7.67252e37 7.67252e37i 0.706609 0.706609i
\(844\) 2.44892e37i 0.222087i
\(845\) 1.07764e38 8.28234e37i 0.962360 0.739632i
\(846\) −8.48332e37 −0.746021
\(847\) −6.46270e37 6.46270e37i −0.559667 0.559667i
\(848\) 4.50881e37 4.50881e37i 0.384517 0.384517i
\(849\) 7.53797e37i 0.633074i
\(850\) 4.20066e37 + 1.11858e37i 0.347434 + 0.0925166i
\(851\) −1.74101e38 −1.41813
\(852\) 2.78875e36 + 2.78875e36i 0.0223715 + 0.0223715i
\(853\) 2.75777e37 2.75777e37i 0.217882 0.217882i −0.589724 0.807605i \(-0.700763\pi\)
0.807605 + 0.589724i \(0.200763\pi\)
\(854\) 2.02525e38i 1.57589i
\(855\) 5.51409e37 + 7.17456e37i 0.422585 + 0.549840i
\(856\) 1.36575e38 1.03089
\(857\) −1.41705e38 1.41705e38i −1.05350 1.05350i −0.998486 0.0550120i \(-0.982480\pi\)
−0.0550120 0.998486i \(-0.517520\pi\)
\(858\) −2.16345e37 + 2.16345e37i −0.158421 + 0.158421i
\(859\) 7.78529e37i 0.561518i 0.959778 + 0.280759i \(0.0905861\pi\)
−0.959778 + 0.280759i \(0.909414\pi\)
\(860\) 2.87282e35 2.19529e36i 0.00204093 0.0155960i
\(861\) −6.02167e37 −0.421382
\(862\) 1.47448e38 + 1.47448e38i 1.01635 + 1.01635i
\(863\) 6.25060e37 6.25060e37i 0.424406 0.424406i −0.462312 0.886717i \(-0.652980\pi\)
0.886717 + 0.462312i \(0.152980\pi\)
\(864\) 5.08076e37i 0.339821i
\(865\) −1.18159e38 1.54626e37i −0.778496 0.101876i
\(866\) −2.62974e38 −1.70679
\(867\) 6.53196e37 + 6.53196e37i 0.417634 + 0.417634i
\(868\) −1.74581e36 + 1.74581e36i −0.0109962 + 0.0109962i
\(869\) 4.99422e37i 0.309892i
\(870\) 5.05268e37 3.88329e37i 0.308867 0.237383i
\(871\) −1.62487e38 −0.978552
\(872\) −1.02494e38 1.02494e38i −0.608114 0.608114i
\(873\) 7.26077e37 7.26077e37i 0.424421 0.424421i
\(874\) 3.89544e38i 2.24341i
\(875\) −1.34946e38 5.55286e37i −0.765694 0.315074i
\(876\) 3.35438e37 0.187525
\(877\) 2.23939e37 + 2.23939e37i 0.123349 + 0.123349i 0.766087 0.642737i \(-0.222201\pi\)
−0.642737 + 0.766087i \(0.722201\pi\)
\(878\) 6.39594e37 6.39594e37i 0.347117 0.347117i
\(879\) 2.77073e37i 0.148163i
\(880\) −2.76383e37 3.59611e37i −0.145625 0.189478i
\(881\) −7.06238e37 −0.366661 −0.183330 0.983051i \(-0.558688\pi\)
−0.183330 + 0.983051i \(0.558688\pi\)
\(882\) 2.62185e37 + 2.62185e37i 0.134127 + 0.134127i
\(883\) −2.10427e38 + 2.10427e38i −1.06075 + 1.06075i −0.0627171 + 0.998031i \(0.519977\pi\)
−0.998031 + 0.0627171i \(0.980023\pi\)
\(884\) 1.65294e37i 0.0821066i
\(885\) −1.69180e36 + 1.29281e37i −0.00828108 + 0.0632807i
\(886\) 2.10232e38 1.01405
\(887\) −6.34328e37 6.34328e37i −0.301513 0.301513i 0.540092 0.841606i \(-0.318389\pi\)
−0.841606 + 0.540092i \(0.818389\pi\)
\(888\) −7.65170e37 + 7.65170e37i −0.358418 + 0.358418i
\(889\) 1.39930e38i 0.645933i
\(890\) −3.60356e38 4.71572e37i −1.63931 0.214525i
\(891\) −6.04612e36 −0.0271061
\(892\) 1.28003e37 + 1.28003e37i 0.0565559 + 0.0565559i
\(893\) 2.49256e38 2.49256e38i 1.08537 1.08537i
\(894\) 1.09656e38i 0.470593i
\(895\) 3.12526e38 2.40196e38i 1.32187 1.01593i
\(896\) 2.33294e38 0.972523
\(897\) 2.84765e38 + 2.84765e38i 1.17000 + 1.17000i
\(898\) 3.46643e38 3.46643e38i 1.40375 1.40375i
\(899\) 1.54226e37i 0.0615578i
\(900\) 6.05594e36 2.27423e37i 0.0238248 0.0894708i
\(901\) −4.10266e37 −0.159090
\(902\) −3.21273e37 3.21273e37i −0.122797 0.122797i
\(903\) 9.79811e36 9.79811e36i 0.0369149 0.0369149i
\(904\) 3.86492e38i 1.43533i
\(905\) 1.96765e38 + 2.56018e38i 0.720306 + 0.937214i
\(906\) −1.00665e38 −0.363255
\(907\) −9.17296e37 9.17296e37i −0.326298 0.326298i 0.524879 0.851177i \(-0.324111\pi\)
−0.851177 + 0.524879i \(0.824111\pi\)
\(908\) −5.03214e37 + 5.03214e37i −0.176456 + 0.176456i
\(909\) 2.14403e37i 0.0741139i
\(910\) 5.06466e37 3.87020e38i 0.172589 1.31885i
\(911\) 1.33399e38 0.448138 0.224069 0.974573i \(-0.428066\pi\)
0.224069 + 0.974573i \(0.428066\pi\)
\(912\) 2.00376e38 + 2.00376e38i 0.663610 + 0.663610i
\(913\) −5.86399e37 + 5.86399e37i −0.191458 + 0.191458i
\(914\) 5.23747e37i 0.168586i
\(915\) −3.65890e38 4.78814e37i −1.16112 0.151947i
\(916\) −5.62181e37 −0.175887
\(917\) 3.02785e38 + 3.02785e38i 0.933970 + 0.933970i
\(918\) −8.65591e37 + 8.65591e37i −0.263244 + 0.263244i
\(919\) 4.57388e38i 1.37146i 0.727855 + 0.685731i \(0.240517\pi\)
−0.727855 + 0.685731i \(0.759483\pi\)
\(920\) −4.04426e38 + 3.10826e38i −1.19563 + 0.918917i
\(921\) −1.74008e37 −0.0507218
\(922\) −5.11237e38 5.11237e38i −1.46933 1.46933i
\(923\) 1.06700e38 1.06700e38i 0.302372 0.302372i
\(924\) 6.84837e36i 0.0191360i
\(925\) −2.66024e38 + 1.54140e38i −0.732957 + 0.424691i
\(926\) 4.05650e38 1.10207
\(927\) 1.31459e38 + 1.31459e38i 0.352171 + 0.352171i
\(928\) −4.77139e37 + 4.77139e37i −0.126044 + 0.126044i
\(929\) 3.44484e38i 0.897357i −0.893693 0.448678i \(-0.851895\pi\)
0.893693 0.448678i \(-0.148105\pi\)
\(930\) −1.92836e37 2.50906e37i −0.0495348 0.0644513i
\(931\) −1.54070e38 −0.390276
\(932\) 3.41371e36 + 3.41371e36i 0.00852745 + 0.00852745i
\(933\) −1.52670e38 + 1.52670e38i −0.376091 + 0.376091i
\(934\) 1.26323e38i 0.306883i
\(935\) −3.78654e36 + 2.89352e37i −0.00907176 + 0.0693227i
\(936\) −3.16925e38 −0.748808
\(937\) 2.78324e38 + 2.78324e38i 0.648539 + 0.648539i 0.952640 0.304101i \(-0.0983559\pi\)
−0.304101 + 0.952640i \(0.598356\pi\)
\(938\) −1.80909e38 + 1.80909e38i −0.415741 + 0.415741i
\(939\) 8.04255e37i 0.182281i
\(940\) −9.09068e37 1.18963e37i −0.203205 0.0265920i
\(941\) −6.49529e37 −0.143197 −0.0715984 0.997434i \(-0.522810\pi\)
−0.0715984 + 0.997434i \(0.522810\pi\)
\(942\) −2.59456e38 2.59456e38i −0.564160 0.564160i
\(943\) −4.22876e38 + 4.22876e38i −0.906904 + 0.906904i
\(944\) 5.16984e37i 0.109356i
\(945\) 3.25813e38 2.50407e38i 0.679759 0.522436i
\(946\) 1.04551e37 0.0215152
\(947\) 2.99649e38 + 2.99649e38i 0.608224 + 0.608224i 0.942482 0.334258i \(-0.108486\pi\)
−0.334258 + 0.942482i \(0.608486\pi\)
\(948\) −5.73868e37 + 5.73868e37i −0.114896 + 0.114896i
\(949\) 1.28341e39i 2.53457i
\(950\) 3.44883e38 + 5.95219e38i 0.671838 + 1.15950i
\(951\) −1.64413e38 −0.315930
\(952\) −9.26510e37 9.26510e37i −0.175618 0.175618i
\(953\) 5.31170e38 5.31170e38i 0.993175 0.993175i −0.00680194 0.999977i \(-0.502165\pi\)
0.999977 + 0.00680194i \(0.00216514\pi\)
\(954\) 1.56247e38i 0.288193i
\(955\) 2.29057e37 + 2.98033e37i 0.0416772 + 0.0542276i
\(956\) 7.63862e37 0.137108
\(957\) 3.02495e37 + 3.02495e37i 0.0535628 + 0.0535628i
\(958\) 5.46157e38 5.46157e38i 0.954038 0.954038i
\(959\) 3.28368e38i 0.565874i
\(960\) −3.97447e37 + 3.03713e38i −0.0675699 + 0.516341i
\(961\) −5.88558e38 −0.987155
\(962\) −5.81513e38 5.81513e38i −0.962240 0.962240i
\(963\) −2.76965e38 + 2.76965e38i −0.452150 + 0.452150i
\(964\) 9.78048e37i 0.157528i
\(965\) 6.89796e38 + 9.02687e37i 1.09614 + 0.143444i
\(966\) 6.34099e38 0.994155
\(967\) −3.92428e38 3.92428e38i −0.607038 0.607038i 0.335133 0.942171i \(-0.391219\pi\)
−0.942171 + 0.335133i \(0.891219\pi\)
\(968\) −3.98931e38 + 3.98931e38i −0.608861 + 0.608861i
\(969\) 1.82327e38i 0.274562i
\(970\) 6.18947e38 4.75699e38i 0.919646 0.706805i
\(971\) −1.64250e38 −0.240799 −0.120399 0.992726i \(-0.538418\pi\)
−0.120399 + 0.992726i \(0.538418\pi\)
\(972\) 7.69278e37 + 7.69278e37i 0.111281 + 0.111281i
\(973\) −6.71403e38 + 6.71403e38i −0.958332 + 0.958332i
\(974\) 1.30192e39i 1.83366i
\(975\) 6.87234e38 + 1.83001e38i 0.955091 + 0.254327i
\(976\) 1.46317e39 2.00653
\(977\) −2.49862e38 2.49862e38i −0.338120 0.338120i 0.517539 0.855659i \(-0.326848\pi\)
−0.855659 + 0.517539i \(0.826848\pi\)
\(978\) 3.06371e37 3.06371e37i 0.0409113 0.0409113i
\(979\) 2.43971e38i 0.321487i
\(980\) 2.44189e37 + 3.17723e37i 0.0317532 + 0.0413151i
\(981\) 4.15702e38 0.533439
\(982\) 3.24524e37 + 3.24524e37i 0.0410958 + 0.0410958i
\(983\) −2.89219e37 + 2.89219e37i −0.0361435 + 0.0361435i −0.724948 0.688804i \(-0.758136\pi\)
0.688804 + 0.724948i \(0.258136\pi\)
\(984\) 3.71707e38i 0.458420i
\(985\) 1.05404e38 8.05451e38i 0.128287 0.980320i
\(986\) 1.62577e38 0.195281
\(987\) −4.05738e38 4.05738e38i −0.480976 0.480976i
\(988\) −1.84963e38 + 1.84963e38i −0.216393 + 0.216393i
\(989\) 1.37616e38i 0.158898i
\(990\) 1.10198e38 + 1.44208e37i 0.125579 + 0.0164336i
\(991\) −1.36818e39 −1.53881 −0.769407 0.638758i \(-0.779448\pi\)
−0.769407 + 0.638758i \(0.779448\pi\)
\(992\) 2.36937e37 + 2.36937e37i 0.0263016 + 0.0263016i
\(993\) 2.27439e38 2.27439e38i 0.249187 0.249187i
\(994\) 2.37593e38i 0.256927i
\(995\) −2.66656e38 + 2.04941e38i −0.284610 + 0.218741i
\(996\) −1.34762e38 −0.141970
\(997\) 1.31247e38 + 1.31247e38i 0.136475 + 0.136475i 0.772044 0.635569i \(-0.219234\pi\)
−0.635569 + 0.772044i \(0.719234\pi\)
\(998\) 3.90488e38 3.90488e38i 0.400785 0.400785i
\(999\) 8.65793e38i 0.877127i
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 5.27.c.a.2.9 24
5.2 odd 4 25.27.c.b.18.4 24
5.3 odd 4 inner 5.27.c.a.3.9 yes 24
5.4 even 2 25.27.c.b.7.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.27.c.a.2.9 24 1.1 even 1 trivial
5.27.c.a.3.9 yes 24 5.3 odd 4 inner
25.27.c.b.7.4 24 5.4 even 2
25.27.c.b.18.4 24 5.2 odd 4