Properties

Label 6.31.b.a.5.5
Level $6$
Weight $31$
Character 6.5
Analytic conductor $34.209$
Analytic rank $0$
Dimension $10$
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] = [6,31,Mod(5,6)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 31, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6.5");
 
S:= CuspForms(chi, 31);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 31 \)
Character orbit: \([\chi]\) \(=\) 6.b (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: \(34.2085571416\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + \cdots + 17\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{104}\cdot 3^{53}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.5
Root \(-1.58422e9i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.31.b.a.5.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-23170.5i q^{2} +(1.42278e7 + 1.86071e6i) q^{3} -5.36871e8 q^{4} -3.80214e10i q^{5} +(4.31134e10 - 3.29664e11i) q^{6} +7.78024e12 q^{7} +1.24396e13i q^{8} +(1.98967e14 + 5.29473e13i) q^{9} +O(q^{10})\) \(q-23170.5i q^{2} +(1.42278e7 + 1.86071e6i) q^{3} -5.36871e8 q^{4} -3.80214e10i q^{5} +(4.31134e10 - 3.29664e11i) q^{6} +7.78024e12 q^{7} +1.24396e13i q^{8} +(1.98967e14 + 5.29473e13i) q^{9} -8.80973e14 q^{10} -2.27578e15i q^{11} +(-7.63847e15 - 9.98958e14i) q^{12} +1.13538e16 q^{13} -1.80272e17i q^{14} +(7.07466e16 - 5.40959e17i) q^{15} +2.88230e17 q^{16} +4.86602e18i q^{17} +(1.22681e18 - 4.61015e18i) q^{18} +1.09576e19 q^{19} +2.04126e19i q^{20} +(1.10695e20 + 1.44767e19i) q^{21} -5.27308e19 q^{22} -4.33263e20i q^{23} +(-2.31463e19 + 1.76987e20i) q^{24} -5.14303e20 q^{25} -2.63073e20i q^{26} +(2.73233e21 + 1.12354e21i) q^{27} -4.17698e21 q^{28} -1.37646e21i q^{29} +(-1.25343e22 - 1.63923e21i) q^{30} -7.68233e21 q^{31} -6.67843e21i q^{32} +(4.23455e21 - 3.23792e22i) q^{33} +1.12748e23 q^{34} -2.95815e23i q^{35} +(-1.06819e23 - 2.84259e22i) q^{36} -8.83896e22 q^{37} -2.53892e23i q^{38} +(1.61539e23 + 2.11261e22i) q^{39} +4.72969e23 q^{40} -1.91086e24i q^{41} +(3.35433e23 - 2.56486e24i) q^{42} -5.27890e24 q^{43} +1.22180e24i q^{44} +(2.01313e24 - 7.56499e24i) q^{45} -1.00389e25 q^{46} -1.59051e25i q^{47} +(4.10087e24 + 5.36312e23i) q^{48} +3.79928e25 q^{49} +1.19166e25i q^{50} +(-9.05422e24 + 6.92325e25i) q^{51} -6.09553e24 q^{52} +6.96076e24i q^{53} +(2.60329e25 - 6.33094e25i) q^{54} -8.65282e25 q^{55} +9.67827e25i q^{56} +(1.55901e26 + 2.03888e25i) q^{57} -3.18932e25 q^{58} +5.40161e26i q^{59} +(-3.79818e25 + 2.90425e26i) q^{60} -9.06733e26 q^{61} +1.78003e26i q^{62} +(1.54801e27 + 4.11943e26i) q^{63} -1.54743e26 q^{64} -4.31688e26i q^{65} +(-7.50241e26 - 9.81166e25i) q^{66} +2.89531e27 q^{67} -2.61242e27i q^{68} +(8.06175e26 - 6.16436e27i) q^{69} -6.85418e27 q^{70} -2.12041e27i q^{71} +(-6.58641e26 + 2.47506e27i) q^{72} +5.48943e27 q^{73} +2.04803e27i q^{74} +(-7.31737e27 - 9.56966e26i) q^{75} -5.88280e27 q^{76} -1.77061e28i q^{77} +(4.89502e26 - 3.74294e27i) q^{78} +1.73705e27 q^{79} -1.09589e28i q^{80} +(3.67843e28 + 2.10695e28i) q^{81} -4.42756e28 q^{82} +4.74090e28i q^{83} +(-5.94291e28 - 7.77213e27i) q^{84} +1.85013e29 q^{85} +1.22315e29i q^{86} +(2.56118e27 - 1.95839e28i) q^{87} +2.83097e28 q^{88} +2.15151e29i q^{89} +(-1.75284e29 - 4.66452e28i) q^{90} +8.83354e28 q^{91} +2.32606e29i q^{92} +(-1.09302e29 - 1.42945e28i) q^{93} -3.68530e29 q^{94} -4.16622e29i q^{95} +(1.24266e28 - 9.50191e28i) q^{96} +2.31086e29 q^{97} -8.80310e29i q^{98} +(1.20496e29 - 4.52804e29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} - 11\!\cdots\!60 q^{10}+ \cdots + 27\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23170.5i 0.707107i
\(3\) 1.42278e7 + 1.86071e6i 0.991556 + 0.129676i
\(4\) −5.36871e8 −0.500000
\(5\) 3.80214e10i 1.24588i −0.782268 0.622942i \(-0.785937\pi\)
0.782268 0.622942i \(-0.214063\pi\)
\(6\) 4.31134e10 3.29664e11i 0.0916946 0.701136i
\(7\) 7.78024e12 1.63879 0.819393 0.573232i \(-0.194311\pi\)
0.819393 + 0.573232i \(0.194311\pi\)
\(8\) 1.24396e13i 0.353553i
\(9\) 1.98967e14 + 5.29473e13i 0.966368 + 0.257162i
\(10\) −8.80973e14 −0.880973
\(11\) 2.27578e15i 0.544803i −0.962184 0.272402i \(-0.912182\pi\)
0.962184 0.272402i \(-0.0878179\pi\)
\(12\) −7.63847e15 9.98958e14i −0.495778 0.0648379i
\(13\) 1.13538e16 0.221815 0.110908 0.993831i \(-0.464624\pi\)
0.110908 + 0.993831i \(0.464624\pi\)
\(14\) 1.80272e17i 1.15880i
\(15\) 7.07466e16 5.40959e17i 0.161561 1.23536i
\(16\) 2.88230e17 0.250000
\(17\) 4.86602e18i 1.69996i 0.526811 + 0.849982i \(0.323387\pi\)
−0.526811 + 0.849982i \(0.676613\pi\)
\(18\) 1.22681e18 4.61015e18i 0.181841 0.683326i
\(19\) 1.09576e19 0.721788 0.360894 0.932607i \(-0.382472\pi\)
0.360894 + 0.932607i \(0.382472\pi\)
\(20\) 2.04126e19i 0.622942i
\(21\) 1.10695e20 + 1.44767e19i 1.62495 + 0.212511i
\(22\) −5.27308e19 −0.385234
\(23\) 4.33263e20i 1.62493i −0.583011 0.812464i \(-0.698126\pi\)
0.583011 0.812464i \(-0.301874\pi\)
\(24\) −2.31463e19 + 1.76987e20i −0.0458473 + 0.350568i
\(25\) −5.14303e20 −0.552229
\(26\) 2.63073e20i 0.156847i
\(27\) 2.73233e21 + 1.12354e21i 0.924861 + 0.380305i
\(28\) −4.17698e21 −0.819393
\(29\) 1.37646e21i 0.159512i −0.996814 0.0797559i \(-0.974586\pi\)
0.996814 0.0797559i \(-0.0254141\pi\)
\(30\) −1.25343e22 1.63923e21i −0.873535 0.114241i
\(31\) −7.68233e21 −0.327392 −0.163696 0.986511i \(-0.552342\pi\)
−0.163696 + 0.986511i \(0.552342\pi\)
\(32\) 6.67843e21i 0.176777i
\(33\) 4.23455e21 3.23792e22i 0.0706477 0.540203i
\(34\) 1.12748e23 1.20206
\(35\) 2.95815e23i 2.04174i
\(36\) −1.06819e23 2.84259e22i −0.483184 0.128581i
\(37\) −8.83896e22 −0.265079 −0.132539 0.991178i \(-0.542313\pi\)
−0.132539 + 0.991178i \(0.542313\pi\)
\(38\) 2.53892e23i 0.510382i
\(39\) 1.61539e23 + 2.11261e22i 0.219942 + 0.0287641i
\(40\) 4.72969e23 0.440487
\(41\) 1.91086e24i 1.22877i −0.789005 0.614387i \(-0.789403\pi\)
0.789005 0.614387i \(-0.210597\pi\)
\(42\) 3.35433e23 2.56486e24i 0.150268 1.14901i
\(43\) −5.27890e24 −1.66156 −0.830781 0.556599i \(-0.812106\pi\)
−0.830781 + 0.556599i \(0.812106\pi\)
\(44\) 1.22180e24i 0.272402i
\(45\) 2.01313e24 7.56499e24i 0.320394 1.20398i
\(46\) −1.00389e25 −1.14900
\(47\) 1.59051e25i 1.31847i −0.751938 0.659234i \(-0.770881\pi\)
0.751938 0.659234i \(-0.229119\pi\)
\(48\) 4.10087e24 + 5.36312e23i 0.247889 + 0.0324189i
\(49\) 3.79928e25 1.68562
\(50\) 1.19166e25i 0.390485i
\(51\) −9.05422e24 + 6.92325e25i −0.220444 + 1.68561i
\(52\) −6.09553e24 −0.110908
\(53\) 6.96076e24i 0.0951741i 0.998867 + 0.0475871i \(0.0151532\pi\)
−0.998867 + 0.0475871i \(0.984847\pi\)
\(54\) 2.60329e25 6.33094e25i 0.268916 0.653976i
\(55\) −8.65282e25 −0.678762
\(56\) 9.67827e25i 0.579398i
\(57\) 1.55901e26 + 2.03888e25i 0.715694 + 0.0935985i
\(58\) −3.18932e25 −0.112792
\(59\) 5.40161e26i 1.47823i 0.673577 + 0.739117i \(0.264757\pi\)
−0.673577 + 0.739117i \(0.735243\pi\)
\(60\) −3.79818e25 + 2.90425e26i −0.0807805 + 0.617682i
\(61\) −9.06733e26 −1.50498 −0.752492 0.658601i \(-0.771148\pi\)
−0.752492 + 0.658601i \(0.771148\pi\)
\(62\) 1.78003e26i 0.231501i
\(63\) 1.54801e27 + 4.11943e26i 1.58367 + 0.421433i
\(64\) −1.54743e26 −0.125000
\(65\) 4.31688e26i 0.276356i
\(66\) −7.50241e26 9.81166e25i −0.381981 0.0499555i
\(67\) 2.89531e27 1.17645 0.588225 0.808698i \(-0.299827\pi\)
0.588225 + 0.808698i \(0.299827\pi\)
\(68\) 2.61242e27i 0.849982i
\(69\) 8.06175e26 6.16436e27i 0.210714 1.61121i
\(70\) −6.85418e27 −1.44373
\(71\) 2.12041e27i 0.361031i −0.983572 0.180516i \(-0.942223\pi\)
0.983572 0.180516i \(-0.0577767\pi\)
\(72\) −6.58641e26 + 2.47506e27i −0.0909204 + 0.341663i
\(73\) 5.48943e27 0.616147 0.308073 0.951363i \(-0.400316\pi\)
0.308073 + 0.951363i \(0.400316\pi\)
\(74\) 2.04803e27i 0.187439i
\(75\) −7.31737e27 9.56966e26i −0.547566 0.0716106i
\(76\) −5.88280e27 −0.360894
\(77\) 1.77061e28i 0.892816i
\(78\) 4.89502e26 3.74294e27i 0.0203393 0.155523i
\(79\) 1.73705e27 0.0596220 0.0298110 0.999556i \(-0.490509\pi\)
0.0298110 + 0.999556i \(0.490509\pi\)
\(80\) 1.09589e28i 0.311471i
\(81\) 3.67843e28 + 2.10695e28i 0.867736 + 0.497026i
\(82\) −4.42756e28 −0.868874
\(83\) 4.74090e28i 0.775692i 0.921724 + 0.387846i \(0.126781\pi\)
−0.921724 + 0.387846i \(0.873219\pi\)
\(84\) −5.94291e28 7.77213e27i −0.812475 0.106255i
\(85\) 1.85013e29 2.11796
\(86\) 1.22315e29i 1.17490i
\(87\) 2.56118e27 1.95839e28i 0.0206848 0.158165i
\(88\) 2.83097e28 0.192617
\(89\) 2.15151e29i 1.23564i 0.786318 + 0.617822i \(0.211985\pi\)
−0.786318 + 0.617822i \(0.788015\pi\)
\(90\) −1.75284e29 4.66452e28i −0.851345 0.226553i
\(91\) 8.83354e28 0.363508
\(92\) 2.32606e29i 0.812464i
\(93\) −1.09302e29 1.42945e28i −0.324627 0.0424547i
\(94\) −3.68530e29 −0.932298
\(95\) 4.16622e29i 0.899265i
\(96\) 1.24266e28 9.50191e28i 0.0229236 0.175284i
\(97\) 2.31086e29 0.364920 0.182460 0.983213i \(-0.441594\pi\)
0.182460 + 0.983213i \(0.441594\pi\)
\(98\) 8.80310e29i 1.19191i
\(99\) 1.20496e29 4.52804e29i 0.140102 0.526480i
\(100\) 2.76114e29 0.276114
\(101\) 5.36165e29i 0.461825i 0.972975 + 0.230913i \(0.0741711\pi\)
−0.972975 + 0.230913i \(0.925829\pi\)
\(102\) 1.60415e30 + 2.09791e29i 1.19191 + 0.155878i
\(103\) −2.11607e30 −1.35823 −0.679113 0.734033i \(-0.737636\pi\)
−0.679113 + 0.734033i \(0.737636\pi\)
\(104\) 1.41236e29i 0.0784236i
\(105\) 5.50425e29 4.20879e30i 0.264764 2.02450i
\(106\) 1.61284e29 0.0672983
\(107\) 2.33057e30i 0.844705i 0.906432 + 0.422353i \(0.138796\pi\)
−0.906432 + 0.422353i \(0.861204\pi\)
\(108\) −1.46691e30 6.03196e29i −0.462431 0.190152i
\(109\) 1.56872e30 0.430674 0.215337 0.976540i \(-0.430915\pi\)
0.215337 + 0.976540i \(0.430915\pi\)
\(110\) 2.00490e30i 0.479957i
\(111\) −1.25758e30 1.64467e29i −0.262841 0.0343743i
\(112\) 2.24250e30 0.409697
\(113\) 3.55407e30i 0.568263i 0.958785 + 0.284132i \(0.0917053\pi\)
−0.958785 + 0.284132i \(0.908295\pi\)
\(114\) 4.72418e29 3.61231e30i 0.0661841 0.506072i
\(115\) −1.64733e31 −2.02447
\(116\) 7.38980e29i 0.0797559i
\(117\) 2.25903e30 + 6.01154e29i 0.214355 + 0.0570424i
\(118\) 1.25158e31 1.04527
\(119\) 3.78588e31i 2.78588i
\(120\) 6.72929e30 + 8.80056e29i 0.436767 + 0.0571204i
\(121\) 1.22702e31 0.703190
\(122\) 2.10094e31i 1.06418i
\(123\) 3.55556e30 2.71873e31i 0.159342 1.21840i
\(124\) 4.12442e30 0.163696
\(125\) 1.58557e31i 0.557872i
\(126\) 9.54491e30 3.58681e31i 0.297998 1.11982i
\(127\) −1.99255e31 −0.552528 −0.276264 0.961082i \(-0.589096\pi\)
−0.276264 + 0.961082i \(0.589096\pi\)
\(128\) 3.58546e30i 0.0883883i
\(129\) −7.51069e31 9.82248e30i −1.64753 0.215464i
\(130\) −1.00024e31 −0.195413
\(131\) 2.03315e31i 0.354079i −0.984204 0.177040i \(-0.943348\pi\)
0.984204 0.177040i \(-0.0566521\pi\)
\(132\) −2.27341e30 + 1.73834e31i −0.0353239 + 0.270101i
\(133\) 8.52524e31 1.18286
\(134\) 6.70857e31i 0.831875i
\(135\) 4.27185e31 1.03887e32i 0.473816 1.15227i
\(136\) −6.05311e31 −0.601028
\(137\) 1.46014e32i 1.29893i 0.760390 + 0.649467i \(0.225008\pi\)
−0.760390 + 0.649467i \(0.774992\pi\)
\(138\) −1.42831e32 1.86795e31i −1.13930 0.148997i
\(139\) 9.21852e31 0.659841 0.329921 0.944009i \(-0.392978\pi\)
0.329921 + 0.944009i \(0.392978\pi\)
\(140\) 1.58815e32i 1.02087i
\(141\) 2.95948e31 2.26294e32i 0.170973 1.30734i
\(142\) −4.91310e31 −0.255288
\(143\) 2.58388e31i 0.120846i
\(144\) 5.73482e31 + 1.52610e31i 0.241592 + 0.0642904i
\(145\) −5.23348e31 −0.198733
\(146\) 1.27193e32i 0.435682i
\(147\) 5.40552e32 + 7.06933e31i 1.67139 + 0.218584i
\(148\) 4.74538e31 0.132539
\(149\) 4.01131e32i 1.01273i 0.862320 + 0.506363i \(0.169010\pi\)
−0.862320 + 0.506363i \(0.830990\pi\)
\(150\) −2.21734e31 + 1.69547e32i −0.0506364 + 0.387187i
\(151\) −3.75341e32 −0.775840 −0.387920 0.921693i \(-0.626806\pi\)
−0.387920 + 0.921693i \(0.626806\pi\)
\(152\) 1.36307e32i 0.255191i
\(153\) −2.57642e32 + 9.68175e32i −0.437166 + 1.64279i
\(154\) −4.10259e32 −0.631316
\(155\) 2.92093e32i 0.407892i
\(156\) −8.67257e31 1.13420e31i −0.109971 0.0143820i
\(157\) 4.70110e32 0.541633 0.270816 0.962631i \(-0.412706\pi\)
0.270816 + 0.962631i \(0.412706\pi\)
\(158\) 4.02483e31i 0.0421591i
\(159\) −1.29519e31 + 9.90360e31i −0.0123418 + 0.0943705i
\(160\) −2.53923e32 −0.220243
\(161\) 3.37089e33i 2.66291i
\(162\) 4.88190e32 8.52310e32i 0.351450 0.613582i
\(163\) 7.58294e32 0.497764 0.248882 0.968534i \(-0.419937\pi\)
0.248882 + 0.968534i \(0.419937\pi\)
\(164\) 1.02589e33i 0.614387i
\(165\) −1.23110e33 1.61003e32i −0.673031 0.0880189i
\(166\) 1.09849e33 0.548497
\(167\) 3.37257e32i 0.153891i −0.997035 0.0769456i \(-0.975483\pi\)
0.997035 0.0769456i \(-0.0245168\pi\)
\(168\) −1.80084e32 + 1.37700e33i −0.0751339 + 0.574506i
\(169\) −2.49109e33 −0.950798
\(170\) 4.28683e33i 1.49762i
\(171\) 2.18019e33 + 5.80173e32i 0.697514 + 0.185616i
\(172\) 2.83409e33 0.830781
\(173\) 1.70291e33i 0.457616i −0.973472 0.228808i \(-0.926517\pi\)
0.973472 0.228808i \(-0.0734828\pi\)
\(174\) −4.53768e32 5.93438e31i −0.111839 0.0146264i
\(175\) −4.00140e33 −0.904984
\(176\) 6.55948e32i 0.136201i
\(177\) −1.00508e33 + 7.68528e33i −0.191691 + 1.46575i
\(178\) 4.98516e33 0.873733
\(179\) 2.93722e33i 0.473305i −0.971594 0.236652i \(-0.923950\pi\)
0.971594 0.236652i \(-0.0760502\pi\)
\(180\) −1.08079e33 + 4.06142e33i −0.160197 + 0.601992i
\(181\) −5.16473e33 −0.704480 −0.352240 0.935910i \(-0.614580\pi\)
−0.352240 + 0.935910i \(0.614580\pi\)
\(182\) 2.04677e33i 0.257039i
\(183\) −1.29008e34 1.68716e33i −1.49228 0.195160i
\(184\) 5.38960e33 0.574499
\(185\) 3.36069e33i 0.330258i
\(186\) −3.31212e32 + 2.53259e33i −0.0300200 + 0.229546i
\(187\) 1.10740e34 0.926146
\(188\) 8.53901e33i 0.659234i
\(189\) 2.12582e34 + 8.74140e33i 1.51565 + 0.623238i
\(190\) −9.65332e33 −0.635877
\(191\) 1.93599e34i 1.17870i 0.807878 + 0.589350i \(0.200616\pi\)
−0.807878 + 0.589350i \(0.799384\pi\)
\(192\) −2.20164e33 2.87930e32i −0.123945 0.0162095i
\(193\) 2.42851e34 1.26468 0.632339 0.774692i \(-0.282095\pi\)
0.632339 + 0.774692i \(0.282095\pi\)
\(194\) 5.35437e33i 0.258037i
\(195\) 8.03244e32 6.14195e33i 0.0358367 0.274023i
\(196\) −2.03972e34 −0.842810
\(197\) 3.38838e34i 1.29717i −0.761140 0.648587i \(-0.775360\pi\)
0.761140 0.648587i \(-0.224640\pi\)
\(198\) −1.04917e34 2.79196e33i −0.372278 0.0990674i
\(199\) −4.61962e34 −1.51988 −0.759941 0.649992i \(-0.774772\pi\)
−0.759941 + 0.649992i \(0.774772\pi\)
\(200\) 6.39770e33i 0.195242i
\(201\) 4.11938e34 + 5.38732e33i 1.16652 + 0.152557i
\(202\) 1.24232e34 0.326560
\(203\) 1.07092e34i 0.261406i
\(204\) 4.86095e33 3.71689e34i 0.110222 0.842805i
\(205\) −7.26537e34 −1.53091
\(206\) 4.90304e34i 0.960411i
\(207\) 2.29401e34 8.62049e34i 0.417869 1.57028i
\(208\) 3.27251e33 0.0554538
\(209\) 2.49370e34i 0.393233i
\(210\) −9.75196e34 1.27536e34i −1.43154 0.187216i
\(211\) 1.17815e35 1.61051 0.805256 0.592928i \(-0.202028\pi\)
0.805256 + 0.592928i \(0.202028\pi\)
\(212\) 3.73703e33i 0.0475871i
\(213\) 3.94546e33 3.01687e34i 0.0468170 0.357983i
\(214\) 5.40004e34 0.597297
\(215\) 2.00711e35i 2.07012i
\(216\) −1.39763e34 + 3.39890e34i −0.134458 + 0.326988i
\(217\) −5.97704e34 −0.536525
\(218\) 3.63481e34i 0.304533i
\(219\) 7.81022e34 + 1.02142e34i 0.610944 + 0.0798993i
\(220\) 4.64545e34 0.339381
\(221\) 5.52479e34i 0.377078i
\(222\) −3.81078e33 + 2.91388e34i −0.0243063 + 0.185856i
\(223\) 3.92453e34 0.234000 0.117000 0.993132i \(-0.462672\pi\)
0.117000 + 0.993132i \(0.462672\pi\)
\(224\) 5.19598e34i 0.289699i
\(225\) −1.02329e35 2.72309e34i −0.533656 0.142012i
\(226\) 8.23496e34 0.401823
\(227\) 6.36451e34i 0.290655i 0.989384 + 0.145327i \(0.0464235\pi\)
−0.989384 + 0.145327i \(0.953576\pi\)
\(228\) −8.36990e34 1.09461e34i −0.357847 0.0467992i
\(229\) −1.18324e35 −0.473739 −0.236870 0.971541i \(-0.576121\pi\)
−0.236870 + 0.971541i \(0.576121\pi\)
\(230\) 3.81693e35i 1.43152i
\(231\) 3.29458e34 2.51918e35i 0.115777 0.885277i
\(232\) 1.71225e34 0.0563959
\(233\) 5.79194e35i 1.78849i 0.447583 + 0.894243i \(0.352285\pi\)
−0.447583 + 0.894243i \(0.647715\pi\)
\(234\) 1.39290e34 5.23428e34i 0.0403351 0.151572i
\(235\) −6.04736e35 −1.64266
\(236\) 2.89997e35i 0.739117i
\(237\) 2.47143e34 + 3.23214e33i 0.0591186 + 0.00773153i
\(238\) 8.77206e35 1.96991
\(239\) 4.01382e35i 0.846426i −0.906030 0.423213i \(-0.860902\pi\)
0.906030 0.423213i \(-0.139098\pi\)
\(240\) 2.03913e34 1.55921e35i 0.0403903 0.308841i
\(241\) −4.24885e35 −0.790707 −0.395353 0.918529i \(-0.629378\pi\)
−0.395353 + 0.918529i \(0.629378\pi\)
\(242\) 2.84307e35i 0.497230i
\(243\) 4.84154e35 + 3.68216e35i 0.795957 + 0.605353i
\(244\) 4.86799e35 0.752492
\(245\) 1.44454e36i 2.10009i
\(246\) −6.29943e35 8.23839e34i −0.861538 0.112672i
\(247\) 1.24410e35 0.160104
\(248\) 9.55648e34i 0.115750i
\(249\) −8.82142e34 + 6.74524e35i −0.100588 + 0.769143i
\(250\) −3.67383e35 −0.394475
\(251\) 1.65303e36i 1.67176i −0.548911 0.835881i \(-0.684957\pi\)
0.548911 0.835881i \(-0.315043\pi\)
\(252\) −8.31081e35 2.21160e35i −0.791836 0.210716i
\(253\) −9.86011e35 −0.885266
\(254\) 4.61684e35i 0.390696i
\(255\) 2.63231e36 + 3.44254e35i 2.10008 + 0.274648i
\(256\) 8.30767e34 0.0625000
\(257\) 1.80039e36i 1.27752i 0.769405 + 0.638762i \(0.220553\pi\)
−0.769405 + 0.638762i \(0.779447\pi\)
\(258\) −2.27592e35 + 1.74026e36i −0.152356 + 1.16498i
\(259\) −6.87692e35 −0.434408
\(260\) 2.31761e35i 0.138178i
\(261\) 7.28797e34 2.73869e35i 0.0410203 0.154147i
\(262\) −4.71091e35 −0.250372
\(263\) 1.84926e36i 0.928243i 0.885772 + 0.464122i \(0.153630\pi\)
−0.885772 + 0.464122i \(0.846370\pi\)
\(264\) 4.02783e35 + 5.26759e34i 0.190991 + 0.0249777i
\(265\) 2.64658e35 0.118576
\(266\) 1.97534e36i 0.836406i
\(267\) −4.00333e35 + 3.06112e36i −0.160233 + 1.22521i
\(268\) −1.55441e36 −0.588225
\(269\) 3.50145e36i 1.25304i −0.779406 0.626519i \(-0.784479\pi\)
0.779406 0.626519i \(-0.215521\pi\)
\(270\) −2.40711e36 9.89808e35i −0.814778 0.335038i
\(271\) 2.98225e36 0.955004 0.477502 0.878631i \(-0.341542\pi\)
0.477502 + 0.878631i \(0.341542\pi\)
\(272\) 1.40253e36i 0.424991i
\(273\) 1.25681e36 + 1.64366e35i 0.360439 + 0.0471381i
\(274\) 3.38322e36 0.918485
\(275\) 1.17044e36i 0.300856i
\(276\) −4.32812e35 + 3.30947e36i −0.105357 + 0.805604i
\(277\) 3.69874e36 0.852820 0.426410 0.904530i \(-0.359778\pi\)
0.426410 + 0.904530i \(0.359778\pi\)
\(278\) 2.13598e36i 0.466578i
\(279\) −1.52853e36 4.06759e35i −0.316381 0.0841926i
\(280\) 3.67981e36 0.721864
\(281\) 2.72349e36i 0.506443i 0.967408 + 0.253222i \(0.0814902\pi\)
−0.967408 + 0.253222i \(0.918510\pi\)
\(282\) −5.24335e36 6.85725e35i −0.924426 0.120896i
\(283\) −5.44695e36 −0.910660 −0.455330 0.890323i \(-0.650479\pi\)
−0.455330 + 0.890323i \(0.650479\pi\)
\(284\) 1.13839e36i 0.180516i
\(285\) 7.75210e35 5.92759e36i 0.116613 0.891672i
\(286\) −5.98696e35 −0.0854508
\(287\) 1.48670e37i 2.01370i
\(288\) 3.53605e35 1.32879e36i 0.0454602 0.170831i
\(289\) −1.54847e37 −1.88988
\(290\) 1.21262e36i 0.140526i
\(291\) 3.28783e36 + 4.29982e35i 0.361838 + 0.0473212i
\(292\) −2.94711e36 −0.308073
\(293\) 9.85499e36i 0.978682i 0.872092 + 0.489341i \(0.162763\pi\)
−0.872092 + 0.489341i \(0.837237\pi\)
\(294\) 1.63800e36 1.25248e37i 0.154562 1.18185i
\(295\) 2.05377e37 1.84171
\(296\) 1.09953e36i 0.0937196i
\(297\) 2.55693e36 6.21817e36i 0.207191 0.503867i
\(298\) 9.29439e36 0.716106
\(299\) 4.91919e36i 0.360434i
\(300\) 3.92849e36 + 5.13767e35i 0.273783 + 0.0358053i
\(301\) −4.10711e37 −2.72295
\(302\) 8.69683e36i 0.548601i
\(303\) −9.97644e35 + 7.62842e36i −0.0598875 + 0.457926i
\(304\) 3.15830e36 0.180447
\(305\) 3.44752e37i 1.87504i
\(306\) 2.24331e37 + 5.96970e36i 1.16163 + 0.309123i
\(307\) 3.55895e37 1.75487 0.877437 0.479692i \(-0.159251\pi\)
0.877437 + 0.479692i \(0.159251\pi\)
\(308\) 9.50589e36i 0.446408i
\(309\) −3.01070e37 3.93739e36i −1.34676 0.176129i
\(310\) 6.76793e36 0.288423
\(311\) 3.42711e37i 1.39162i 0.718224 + 0.695812i \(0.244955\pi\)
−0.718224 + 0.695812i \(0.755045\pi\)
\(312\) −2.62799e35 + 2.00948e36i −0.0101696 + 0.0777614i
\(313\) −1.06099e37 −0.391332 −0.195666 0.980671i \(-0.562687\pi\)
−0.195666 + 0.980671i \(0.562687\pi\)
\(314\) 1.08927e37i 0.382992i
\(315\) 1.56626e37 5.88574e37i 0.525057 1.97307i
\(316\) −9.32573e35 −0.0298110
\(317\) 6.66930e36i 0.203325i −0.994819 0.101663i \(-0.967584\pi\)
0.994819 0.101663i \(-0.0324162\pi\)
\(318\) 2.29471e36 + 3.00102e35i 0.0667300 + 0.00872695i
\(319\) −3.13251e36 −0.0869025
\(320\) 5.88352e36i 0.155736i
\(321\) −4.33650e36 + 3.31587e37i −0.109538 + 0.837573i
\(322\) −7.81051e37 −1.88296
\(323\) 5.33197e37i 1.22701i
\(324\) −1.97484e37 1.13116e37i −0.433868 0.248513i
\(325\) −5.83930e36 −0.122493
\(326\) 1.75700e37i 0.351972i
\(327\) 2.23194e37 + 2.91893e36i 0.427038 + 0.0558480i
\(328\) 2.37703e37 0.434437
\(329\) 1.23746e38i 2.16069i
\(330\) −3.73053e36 + 2.85252e37i −0.0622388 + 0.475904i
\(331\) 1.18046e38 1.88205 0.941026 0.338336i \(-0.109864\pi\)
0.941026 + 0.338336i \(0.109864\pi\)
\(332\) 2.54525e37i 0.387846i
\(333\) −1.75866e37 4.67999e36i −0.256164 0.0681681i
\(334\) −7.81440e36 −0.108817
\(335\) 1.10084e38i 1.46572i
\(336\) 3.19057e37 + 4.17263e36i 0.406237 + 0.0531277i
\(337\) 9.88992e36 0.120433 0.0602163 0.998185i \(-0.480821\pi\)
0.0602163 + 0.998185i \(0.480821\pi\)
\(338\) 5.77197e37i 0.672316i
\(339\) −6.61308e36 + 5.05665e37i −0.0736900 + 0.563465i
\(340\) −9.93279e37 −1.05898
\(341\) 1.74833e37i 0.178364i
\(342\) 1.34429e37 5.05160e37i 0.131251 0.493217i
\(343\) 1.20231e38 1.12358
\(344\) 6.56672e37i 0.587451i
\(345\) −2.34378e38 3.06519e37i −2.00738 0.262525i
\(346\) −3.94573e37 −0.323583
\(347\) 1.26069e37i 0.0990069i −0.998774 0.0495034i \(-0.984236\pi\)
0.998774 0.0495034i \(-0.0157639\pi\)
\(348\) −1.37502e36 + 1.05140e37i −0.0103424 + 0.0790824i
\(349\) 9.26991e37 0.667873 0.333937 0.942596i \(-0.391623\pi\)
0.333937 + 0.942596i \(0.391623\pi\)
\(350\) 9.27143e37i 0.639921i
\(351\) 3.10224e37 + 1.27565e37i 0.205148 + 0.0843574i
\(352\) −1.51986e37 −0.0963085
\(353\) 8.73770e37i 0.530612i 0.964164 + 0.265306i \(0.0854729\pi\)
−0.964164 + 0.265306i \(0.914527\pi\)
\(354\) 1.78072e38 + 2.32882e37i 1.03644 + 0.135546i
\(355\) −8.06210e37 −0.449804
\(356\) 1.15508e38i 0.617822i
\(357\) −7.04440e37 + 5.38645e38i −0.361261 + 2.76236i
\(358\) −6.80567e37 −0.334677
\(359\) 2.48400e37i 0.117148i −0.998283 0.0585739i \(-0.981345\pi\)
0.998283 0.0585739i \(-0.0186553\pi\)
\(360\) 9.41051e37 + 2.50424e37i 0.425672 + 0.113276i
\(361\) −1.10398e38 −0.479021
\(362\) 1.19669e38i 0.498143i
\(363\) 1.74578e38 + 2.28313e37i 0.697252 + 0.0911866i
\(364\) −4.74247e37 −0.181754
\(365\) 2.08716e38i 0.767648i
\(366\) −3.90924e37 + 2.98917e38i −0.137999 + 1.05520i
\(367\) 5.68207e37 0.192538 0.0962688 0.995355i \(-0.469309\pi\)
0.0962688 + 0.995355i \(0.469309\pi\)
\(368\) 1.24880e38i 0.406232i
\(369\) 1.01175e38 3.80198e38i 0.315994 1.18745i
\(370\) 7.78689e37 0.233528
\(371\) 5.41564e37i 0.155970i
\(372\) 5.86812e37 + 7.67433e36i 0.162314 + 0.0212274i
\(373\) −1.02713e38 −0.272893 −0.136446 0.990647i \(-0.543568\pi\)
−0.136446 + 0.990647i \(0.543568\pi\)
\(374\) 2.56589e38i 0.654884i
\(375\) 2.95027e37 2.25590e38i 0.0723424 0.553161i
\(376\) 1.97853e38 0.466149
\(377\) 1.56280e37i 0.0353821i
\(378\) 2.02542e38 4.92562e38i 0.440696 1.07173i
\(379\) −5.04928e38 −1.05594 −0.527972 0.849262i \(-0.677048\pi\)
−0.527972 + 0.849262i \(0.677048\pi\)
\(380\) 2.23672e38i 0.449633i
\(381\) −2.83496e38 3.70755e37i −0.547863 0.0716495i
\(382\) 4.48579e38 0.833467
\(383\) 2.52753e38i 0.451560i 0.974178 + 0.225780i \(0.0724930\pi\)
−0.974178 + 0.225780i \(0.927507\pi\)
\(384\) −6.67148e36 + 5.10130e37i −0.0114618 + 0.0876420i
\(385\) −6.73210e38 −1.11235
\(386\) 5.62697e38i 0.894262i
\(387\) −1.05033e39 2.79504e38i −1.60568 0.427290i
\(388\) −1.24063e38 −0.182460
\(389\) 9.46333e37i 0.133906i 0.997756 + 0.0669530i \(0.0213278\pi\)
−0.997756 + 0.0669530i \(0.978672\pi\)
\(390\) −1.42312e38 1.86115e37i −0.193763 0.0253404i
\(391\) 2.10827e39 2.76232
\(392\) 4.72613e38i 0.595957i
\(393\) 3.78310e37 2.89272e38i 0.0459155 0.351089i
\(394\) −7.85103e38 −0.917241
\(395\) 6.60451e37i 0.0742821i
\(396\) −6.46909e37 + 2.43097e38i −0.0700512 + 0.263240i
\(397\) −2.35941e38 −0.246006 −0.123003 0.992406i \(-0.539252\pi\)
−0.123003 + 0.992406i \(0.539252\pi\)
\(398\) 1.07039e39i 1.07472i
\(399\) 1.21295e39 + 1.58630e38i 1.17287 + 0.153388i
\(400\) −1.48238e38 −0.138057
\(401\) 2.91357e38i 0.261372i 0.991424 + 0.130686i \(0.0417180\pi\)
−0.991424 + 0.130686i \(0.958282\pi\)
\(402\) 1.24827e38 9.54479e38i 0.107874 0.824851i
\(403\) −8.72237e37 −0.0726205
\(404\) 2.87851e38i 0.230913i
\(405\) 8.01091e38 1.39859e39i 0.619237 1.08110i
\(406\) −2.48136e38 −0.184842
\(407\) 2.01155e38i 0.144416i
\(408\) −8.61221e38 1.12631e38i −0.595953 0.0779388i
\(409\) 1.29846e38 0.0866120 0.0433060 0.999062i \(-0.486211\pi\)
0.0433060 + 0.999062i \(0.486211\pi\)
\(410\) 1.68342e39i 1.08252i
\(411\) −2.71690e38 + 2.07745e39i −0.168440 + 1.28797i
\(412\) 1.13606e39 0.679113
\(413\) 4.20258e39i 2.42251i
\(414\) −1.99741e39 5.31533e38i −1.11036 0.295478i
\(415\) 1.80256e39 0.966423
\(416\) 7.58257e37i 0.0392118i
\(417\) 1.31159e39 + 1.71530e38i 0.654270 + 0.0855654i
\(418\) −5.77802e38 −0.278057
\(419\) 9.93091e38i 0.461083i −0.973063 0.230541i \(-0.925950\pi\)
0.973063 0.230541i \(-0.0740497\pi\)
\(420\) −2.95507e38 + 2.25958e39i −0.132382 + 1.01225i
\(421\) −1.22865e39 −0.531125 −0.265562 0.964094i \(-0.585558\pi\)
−0.265562 + 0.964094i \(0.585558\pi\)
\(422\) 2.72983e39i 1.13880i
\(423\) 8.42135e38 3.16459e39i 0.339060 1.27413i
\(424\) −8.65888e37 −0.0336491
\(425\) 2.50261e39i 0.938769i
\(426\) −6.99023e38 9.14182e37i −0.253132 0.0331046i
\(427\) −7.05460e39 −2.46635
\(428\) 1.25121e39i 0.422353i
\(429\) 4.80783e37 3.67627e38i 0.0156707 0.119825i
\(430\) 4.65057e39 1.46379
\(431\) 1.55422e39i 0.472448i −0.971699 0.236224i \(-0.924090\pi\)
0.971699 0.236224i \(-0.0759099\pi\)
\(432\) 7.87540e38 + 3.23838e38i 0.231215 + 0.0950762i
\(433\) 2.46856e39 0.700045 0.350022 0.936741i \(-0.386174\pi\)
0.350022 + 0.936741i \(0.386174\pi\)
\(434\) 1.38491e39i 0.379380i
\(435\) −7.44606e38 9.73796e37i −0.197055 0.0257709i
\(436\) −8.42202e38 −0.215337
\(437\) 4.74751e39i 1.17285i
\(438\) 2.36668e38 1.80967e39i 0.0564973 0.432003i
\(439\) −7.41940e39 −1.71160 −0.855798 0.517310i \(-0.826933\pi\)
−0.855798 + 0.517310i \(0.826933\pi\)
\(440\) 1.07637e39i 0.239979i
\(441\) 7.55929e39 + 2.01161e39i 1.62893 + 0.433477i
\(442\) 1.28012e39 0.266635
\(443\) 1.68756e38i 0.0339784i −0.999856 0.0169892i \(-0.994592\pi\)
0.999856 0.0169892i \(-0.00540810\pi\)
\(444\) 6.75161e38 + 8.82975e37i 0.131420 + 0.0171872i
\(445\) 8.18035e39 1.53947
\(446\) 9.09333e38i 0.165463i
\(447\) −7.46386e38 + 5.70719e39i −0.131326 + 1.00418i
\(448\) −1.20393e39 −0.204848
\(449\) 5.79376e39i 0.953378i 0.879072 + 0.476689i \(0.158163\pi\)
−0.879072 + 0.476689i \(0.841837\pi\)
\(450\) −6.30954e38 + 2.37101e39i −0.100418 + 0.377352i
\(451\) −4.34870e39 −0.669440
\(452\) 1.90808e39i 0.284132i
\(453\) −5.34026e39 6.98399e38i −0.769289 0.100608i
\(454\) 1.47469e39 0.205524
\(455\) 3.35863e39i 0.452889i
\(456\) −2.53627e38 + 1.93934e39i −0.0330921 + 0.253036i
\(457\) −5.48984e39 −0.693134 −0.346567 0.938025i \(-0.612653\pi\)
−0.346567 + 0.938025i \(0.612653\pi\)
\(458\) 2.74162e39i 0.334984i
\(459\) −5.46716e39 + 1.32956e40i −0.646505 + 1.57223i
\(460\) 8.84402e39 1.01224
\(461\) 1.79816e40i 1.99211i −0.0887186 0.996057i \(-0.528277\pi\)
0.0887186 0.996057i \(-0.471723\pi\)
\(462\) −5.83706e39 7.63370e38i −0.625985 0.0818664i
\(463\) −1.00133e40 −1.03959 −0.519794 0.854292i \(-0.673991\pi\)
−0.519794 + 0.854292i \(0.673991\pi\)
\(464\) 3.96737e38i 0.0398779i
\(465\) −5.43499e38 + 4.15582e39i −0.0528937 + 0.404448i
\(466\) 1.34202e40 1.26465
\(467\) 1.11131e40i 1.01410i 0.861916 + 0.507050i \(0.169264\pi\)
−0.861916 + 0.507050i \(0.830736\pi\)
\(468\) −1.21281e39 3.22742e38i −0.107178 0.0285212i
\(469\) 2.25262e40 1.92795
\(470\) 1.40120e40i 1.16154i
\(471\) 6.68861e39 + 8.74737e38i 0.537060 + 0.0702366i
\(472\) −6.71937e39 −0.522635
\(473\) 1.20136e40i 0.905225i
\(474\) 7.48903e37 5.72643e38i 0.00546701 0.0418031i
\(475\) −5.63551e39 −0.398592
\(476\) 2.03253e40i 1.39294i
\(477\) −3.68554e38 + 1.38496e39i −0.0244751 + 0.0919732i
\(478\) −9.30020e39 −0.598514
\(479\) 4.87641e39i 0.304135i 0.988370 + 0.152068i \(0.0485932\pi\)
−0.988370 + 0.152068i \(0.951407\pi\)
\(480\) −3.61276e39 4.72476e38i −0.218384 0.0285602i
\(481\) −1.00356e39 −0.0587986
\(482\) 9.84478e39i 0.559114i
\(483\) 6.27223e39 4.79602e40i 0.345315 2.64043i
\(484\) −6.58753e39 −0.351595
\(485\) 8.78620e39i 0.454648i
\(486\) 8.53175e39 1.12181e40i 0.428049 0.562826i
\(487\) 1.98513e40 0.965729 0.482864 0.875695i \(-0.339596\pi\)
0.482864 + 0.875695i \(0.339596\pi\)
\(488\) 1.12794e40i 0.532092i
\(489\) 1.07888e40 + 1.41096e39i 0.493561 + 0.0645479i
\(490\) −3.34706e40 −1.48499
\(491\) 6.87806e39i 0.295967i −0.988990 0.147983i \(-0.952722\pi\)
0.988990 0.147983i \(-0.0472783\pi\)
\(492\) −1.90887e39 + 1.45961e40i −0.0796711 + 0.609199i
\(493\) 6.69786e39 0.271164
\(494\) 2.88264e39i 0.113210i
\(495\) −1.72162e40 4.58143e39i −0.655934 0.174551i
\(496\) −2.21428e39 −0.0818479
\(497\) 1.64973e40i 0.591653i
\(498\) 1.56290e40 + 2.04396e39i 0.543866 + 0.0711268i
\(499\) −1.42438e40 −0.480969 −0.240484 0.970653i \(-0.577306\pi\)
−0.240484 + 0.970653i \(0.577306\pi\)
\(500\) 8.51245e39i 0.278936i
\(501\) 6.27535e38 4.79841e39i 0.0199559 0.152592i
\(502\) −3.83015e40 −1.18211
\(503\) 8.74553e39i 0.261979i 0.991384 + 0.130989i \(0.0418154\pi\)
−0.991384 + 0.130989i \(0.958185\pi\)
\(504\) −5.12438e39 + 1.92565e40i −0.148999 + 0.559912i
\(505\) 2.03857e40 0.575381
\(506\) 2.28463e40i 0.625978i
\(507\) −3.54426e40 4.63518e39i −0.942770 0.123295i
\(508\) 1.06974e40 0.276264
\(509\) 6.83043e40i 1.71270i 0.516396 + 0.856350i \(0.327273\pi\)
−0.516396 + 0.856350i \(0.672727\pi\)
\(510\) 7.97653e39 6.09920e40i 0.194205 1.48498i
\(511\) 4.27091e40 1.00973
\(512\) 1.92493e39i 0.0441942i
\(513\) 2.99397e40 + 1.23113e40i 0.667554 + 0.274500i
\(514\) 4.17158e40 0.903346
\(515\) 8.04560e40i 1.69219i
\(516\) 4.03227e40 + 5.27340e39i 0.823767 + 0.107732i
\(517\) −3.61966e40 −0.718306
\(518\) 1.59342e40i 0.307173i
\(519\) 3.16862e39 2.42286e40i 0.0593417 0.453752i
\(520\) 5.37000e39 0.0977067
\(521\) 2.60437e40i 0.460401i −0.973143 0.230201i \(-0.926062\pi\)
0.973143 0.230201i \(-0.0739382\pi\)
\(522\) −6.34568e39 1.68866e39i −0.108998 0.0290057i
\(523\) 4.72362e39 0.0788405 0.0394202 0.999223i \(-0.487449\pi\)
0.0394202 + 0.999223i \(0.487449\pi\)
\(524\) 1.09154e40i 0.177040i
\(525\) −5.69309e40 7.44542e39i −0.897343 0.117355i
\(526\) 4.28482e40 0.656367
\(527\) 3.73824e40i 0.556554i
\(528\) 1.22053e39 9.33267e39i 0.0176619 0.135051i
\(529\) −1.16623e41 −1.64039
\(530\) 6.13225e39i 0.0838459i
\(531\) −2.86001e40 + 1.07474e41i −0.380145 + 1.42852i
\(532\) −4.57696e40 −0.591429
\(533\) 2.16956e40i 0.272561i
\(534\) 7.09275e40 + 9.27590e39i 0.866355 + 0.113302i
\(535\) 8.86114e40 1.05241
\(536\) 3.60164e40i 0.415938i
\(537\) 5.46530e39 4.17900e40i 0.0613761 0.469308i
\(538\) −8.11303e40 −0.886032
\(539\) 8.64631e40i 0.918331i
\(540\) −2.29343e40 + 5.57739e40i −0.236908 + 0.576135i
\(541\) 1.34102e41 1.34734 0.673668 0.739034i \(-0.264718\pi\)
0.673668 + 0.739034i \(0.264718\pi\)
\(542\) 6.91002e40i 0.675290i
\(543\) −7.34825e40 9.61004e39i −0.698532 0.0913540i
\(544\) 3.24974e40 0.300514
\(545\) 5.96450e40i 0.536570i
\(546\) 3.80844e39 2.91210e40i 0.0333317 0.254869i
\(547\) −1.55528e40 −0.132433 −0.0662167 0.997805i \(-0.521093\pi\)
−0.0662167 + 0.997805i \(0.521093\pi\)
\(548\) 7.83908e40i 0.649467i
\(549\) −1.80410e41 4.80091e40i −1.45437 0.387024i
\(550\) 2.71196e40 0.212737
\(551\) 1.50826e40i 0.115134i
\(552\) 7.66819e40 + 1.00285e40i 0.569648 + 0.0744986i
\(553\) 1.35147e40 0.0977077
\(554\) 8.57016e40i 0.603035i
\(555\) −6.25326e39 + 4.78151e40i −0.0428264 + 0.327469i
\(556\) −4.94916e40 −0.329921
\(557\) 9.55049e40i 0.619723i 0.950782 + 0.309862i \(0.100283\pi\)
−0.950782 + 0.309862i \(0.899717\pi\)
\(558\) −9.42479e39 + 3.54167e40i −0.0595331 + 0.223715i
\(559\) −5.99357e40 −0.368560
\(560\) 8.52630e40i 0.510435i
\(561\) 1.57558e41 + 2.06054e40i 0.918326 + 0.120099i
\(562\) 6.31045e40 0.358110
\(563\) 3.04520e41i 1.68263i −0.540543 0.841317i \(-0.681781\pi\)
0.540543 0.841317i \(-0.318219\pi\)
\(564\) −1.58886e40 + 1.21491e41i −0.0854867 + 0.653668i
\(565\) 1.35131e41 0.707991
\(566\) 1.26208e41i 0.643934i
\(567\) 2.86191e41 + 1.63926e41i 1.42203 + 0.814519i
\(568\) 2.63770e40 0.127644
\(569\) 8.74730e40i 0.412278i −0.978523 0.206139i \(-0.933910\pi\)
0.978523 0.206139i \(-0.0660899\pi\)
\(570\) −1.37345e41 1.79620e40i −0.630507 0.0824578i
\(571\) −2.67782e40 −0.119740 −0.0598700 0.998206i \(-0.519069\pi\)
−0.0598700 + 0.998206i \(0.519069\pi\)
\(572\) 1.38721e40i 0.0604228i
\(573\) −3.60231e40 + 2.75448e41i −0.152849 + 1.16875i
\(574\) −3.44475e41 −1.42390
\(575\) 2.22829e41i 0.897332i
\(576\) −3.07886e40 8.19320e39i −0.120796 0.0321452i
\(577\) −4.58861e41 −1.75406 −0.877028 0.480439i \(-0.840477\pi\)
−0.877028 + 0.480439i \(0.840477\pi\)
\(578\) 3.58787e41i 1.33635i
\(579\) 3.45522e41 + 4.51873e40i 1.25400 + 0.163998i
\(580\) 2.80970e40 0.0993666
\(581\) 3.68853e41i 1.27119i
\(582\) 9.96290e39 7.61806e40i 0.0334611 0.255858i
\(583\) 1.58411e40 0.0518511
\(584\) 6.82860e40i 0.217841i
\(585\) 2.28567e40 8.58915e40i 0.0710682 0.267062i
\(586\) 2.28345e41 0.692033
\(587\) 1.12440e41i 0.332160i −0.986112 0.166080i \(-0.946889\pi\)
0.986112 0.166080i \(-0.0531110\pi\)
\(588\) −2.90206e41 3.79532e40i −0.835694 0.109292i
\(589\) −8.41796e40 −0.236307
\(590\) 4.75868e41i 1.30229i
\(591\) 6.30477e40 4.82090e41i 0.168212 1.28622i
\(592\) −2.54766e40 −0.0662697
\(593\) 1.84371e40i 0.0467598i −0.999727 0.0233799i \(-0.992557\pi\)
0.999727 0.0233799i \(-0.00744272\pi\)
\(594\) −1.44078e41 5.92452e40i −0.356288 0.146506i
\(595\) 1.43944e42 3.47088
\(596\) 2.15356e41i 0.506363i
\(597\) −6.57267e41 8.59574e40i −1.50705 0.197092i
\(598\) −1.13980e41 −0.254865
\(599\) 7.70925e40i 0.168116i −0.996461 0.0840582i \(-0.973212\pi\)
0.996461 0.0840582i \(-0.0267882\pi\)
\(600\) 1.19042e40 9.10249e40i 0.0253182 0.193594i
\(601\) −7.35174e41 −1.52501 −0.762505 0.646982i \(-0.776031\pi\)
−0.762505 + 0.646982i \(0.776031\pi\)
\(602\) 9.51637e41i 1.92541i
\(603\) 5.76071e41 + 1.53299e41i 1.13688 + 0.302538i
\(604\) 2.01510e41 0.387920
\(605\) 4.66531e41i 0.876093i
\(606\) 1.76754e41 + 2.31159e40i 0.323802 + 0.0423469i
\(607\) −8.50614e41 −1.52020 −0.760102 0.649804i \(-0.774851\pi\)
−0.760102 + 0.649804i \(0.774851\pi\)
\(608\) 7.31794e40i 0.127595i
\(609\) 1.99266e40 1.52367e41i 0.0338980 0.259198i
\(610\) 7.98808e41 1.32585
\(611\) 1.80584e41i 0.292457i
\(612\) 1.38321e41 5.19785e41i 0.218583 0.821396i
\(613\) −1.68060e40 −0.0259154 −0.0129577 0.999916i \(-0.504125\pi\)
−0.0129577 + 0.999916i \(0.504125\pi\)
\(614\) 8.24625e41i 1.24088i
\(615\) −1.03370e42 1.35187e41i −1.51798 0.198522i
\(616\) 2.20256e41 0.315658
\(617\) 6.31789e41i 0.883679i 0.897094 + 0.441840i \(0.145674\pi\)
−0.897094 + 0.441840i \(0.854326\pi\)
\(618\) −9.12312e40 + 6.97593e41i −0.124542 + 0.952302i
\(619\) −3.35846e41 −0.447487 −0.223744 0.974648i \(-0.571828\pi\)
−0.223744 + 0.974648i \(0.571828\pi\)
\(620\) 1.56816e41i 0.203946i
\(621\) 4.86788e41 1.18382e42i 0.617968 1.50283i
\(622\) 7.94077e41 0.984027
\(623\) 1.67393e42i 2.02496i
\(624\) 4.65605e40 + 6.08918e39i 0.0549856 + 0.00719102i
\(625\) −1.08184e42 −1.24727
\(626\) 2.45836e41i 0.276714i
\(627\) 4.64004e40 3.54797e41i 0.0509927 0.389912i
\(628\) −2.52389e41 −0.270816
\(629\) 4.30105e41i 0.450625i
\(630\) −1.36375e42 3.62911e41i −1.39517 0.371271i
\(631\) −4.78635e41 −0.478150 −0.239075 0.971001i \(-0.576844\pi\)
−0.239075 + 0.971001i \(0.576844\pi\)
\(632\) 2.16082e40i 0.0210796i
\(633\) 1.67624e42 + 2.19219e41i 1.59691 + 0.208844i
\(634\) −1.54531e41 −0.143773
\(635\) 7.57596e41i 0.688386i
\(636\) 6.95351e39 5.31695e40i 0.00617089 0.0471852i
\(637\) 4.31363e41 0.373896
\(638\) 7.25817e40i 0.0614493i
\(639\) 1.12270e41 4.21891e41i 0.0928434 0.348889i
\(640\) 1.36324e41 0.110122
\(641\) 2.07742e42i 1.63928i 0.572879 + 0.819640i \(0.305827\pi\)
−0.572879 + 0.819640i \(0.694173\pi\)
\(642\) 7.68304e41 + 1.00479e41i 0.592253 + 0.0774549i
\(643\) 9.51151e41 0.716283 0.358142 0.933667i \(-0.383411\pi\)
0.358142 + 0.933667i \(0.383411\pi\)
\(644\) 1.80973e42i 1.33146i
\(645\) −3.73464e41 + 2.85567e42i −0.268444 + 2.05264i
\(646\) 1.23544e42 0.867631
\(647\) 1.62594e42i 1.11568i −0.829948 0.557841i \(-0.811630\pi\)
0.829948 0.557841i \(-0.188370\pi\)
\(648\) −2.62095e41 + 4.57581e41i −0.175725 + 0.306791i
\(649\) 1.22929e42 0.805347
\(650\) 1.35299e41i 0.0866154i
\(651\) −8.50398e41 1.11215e41i −0.531995 0.0695743i
\(652\) −4.07106e41 −0.248882
\(653\) 2.70001e42i 1.61312i −0.591150 0.806562i \(-0.701326\pi\)
0.591150 0.806562i \(-0.298674\pi\)
\(654\) 6.76330e40 5.17151e41i 0.0394905 0.301961i
\(655\) −7.73032e41 −0.441142
\(656\) 5.50769e41i 0.307194i
\(657\) 1.09221e42 + 2.90650e41i 0.595425 + 0.158449i
\(658\) −2.86725e42 −1.52784
\(659\) 1.32042e42i 0.687749i −0.939016 0.343875i \(-0.888261\pi\)
0.939016 0.343875i \(-0.111739\pi\)
\(660\) 6.60943e41 + 8.64381e40i 0.336515 + 0.0440095i
\(661\) −1.08335e42 −0.539195 −0.269598 0.962973i \(-0.586891\pi\)
−0.269598 + 0.962973i \(0.586891\pi\)
\(662\) 2.73518e42i 1.33081i
\(663\) −1.02800e41 + 7.86053e41i −0.0488979 + 0.373894i
\(664\) −5.89747e41 −0.274249
\(665\) 3.24142e42i 1.47370i
\(666\) −1.08438e41 + 4.07489e41i −0.0482021 + 0.181135i
\(667\) −5.96368e41 −0.259195
\(668\) 1.81063e41i 0.0769456i
\(669\) 5.58373e41 + 7.30240e40i 0.232024 + 0.0303441i
\(670\) −2.55069e42 −1.03642
\(671\) 2.06352e42i 0.819920i
\(672\) 9.66819e40 7.39271e41i 0.0375670 0.287253i
\(673\) 1.69638e42 0.644610 0.322305 0.946636i \(-0.395542\pi\)
0.322305 + 0.946636i \(0.395542\pi\)
\(674\) 2.29154e41i 0.0851587i
\(675\) −1.40524e42 5.77840e41i −0.510735 0.210015i
\(676\) 1.33739e42 0.475399
\(677\) 1.13146e42i 0.393379i −0.980466 0.196689i \(-0.936981\pi\)
0.980466 0.196689i \(-0.0630190\pi\)
\(678\) 1.17165e42 + 1.53228e41i 0.398430 + 0.0521067i
\(679\) 1.79790e42 0.598025
\(680\) 2.30148e42i 0.748812i
\(681\) −1.18425e41 + 9.05527e41i −0.0376908 + 0.288200i
\(682\) 4.05096e41 0.126122
\(683\) 9.51949e41i 0.289937i −0.989436 0.144968i \(-0.953692\pi\)
0.989436 0.144968i \(-0.0463080\pi\)
\(684\) −1.17048e42 3.11478e41i −0.348757 0.0928082i
\(685\) 5.55166e42 1.61832
\(686\) 2.78582e42i 0.794495i
\(687\) −1.68348e42 2.20165e41i −0.469739 0.0614325i
\(688\) −1.52154e42 −0.415391
\(689\) 7.90312e40i 0.0211111i
\(690\) −7.10219e41 + 5.43064e42i −0.185633 + 1.41943i
\(691\) −5.40021e42 −1.38115 −0.690574 0.723262i \(-0.742642\pi\)
−0.690574 + 0.723262i \(0.742642\pi\)
\(692\) 9.14245e41i 0.228808i
\(693\) 9.37490e41 3.52292e42i 0.229598 0.862789i
\(694\) −2.92107e41 −0.0700084
\(695\) 3.50501e42i 0.822086i
\(696\) 2.43615e41 + 3.18599e40i 0.0559197 + 0.00731318i
\(697\) 9.29830e42 2.08887
\(698\) 2.14788e42i 0.472258i
\(699\) −1.07771e42 + 8.24063e42i −0.231923 + 1.77338i
\(700\) 2.14823e42 0.452492
\(701\) 6.67700e42i 1.37661i 0.725421 + 0.688306i \(0.241645\pi\)
−0.725421 + 0.688306i \(0.758355\pi\)
\(702\) 2.95573e41 7.18803e41i 0.0596497 0.145062i
\(703\) −9.68534e41 −0.191331
\(704\) 3.52160e41i 0.0681004i
\(705\) −8.60403e42 1.12523e42i −1.62879 0.213013i
\(706\) 2.02457e42 0.375199
\(707\) 4.17149e42i 0.756833i
\(708\) 5.39599e41 4.12600e42i 0.0958456 0.732876i
\(709\) −4.33459e42 −0.753797 −0.376899 0.926255i \(-0.623009\pi\)
−0.376899 + 0.926255i \(0.623009\pi\)
\(710\) 1.86803e42i 0.318059i
\(711\) 3.45616e41 + 9.19722e40i 0.0576168 + 0.0153325i
\(712\) −2.67638e42 −0.436866
\(713\) 3.32847e42i 0.531988i
\(714\) 1.24807e43 + 1.63222e42i 1.95328 + 0.255450i
\(715\) −9.82425e41 −0.150560
\(716\) 1.57691e42i 0.236652i
\(717\) 7.46853e41 5.71076e42i 0.109761 0.839279i
\(718\) −5.75554e41 −0.0828361
\(719\) 9.64399e42i 1.35933i 0.733525 + 0.679663i \(0.237874\pi\)
−0.733525 + 0.679663i \(0.762126\pi\)
\(720\) 5.80245e41 2.18046e42i 0.0800984 0.300996i
\(721\) −1.64636e43 −2.22584
\(722\) 2.55798e42i 0.338719i
\(723\) −6.04516e42 7.90585e41i −0.784031 0.102536i
\(724\) 2.77279e42 0.352240
\(725\) 7.07916e41i 0.0880869i
\(726\) 5.29012e41 4.04505e42i 0.0644787 0.493032i
\(727\) 8.03630e42 0.959489 0.479744 0.877408i \(-0.340729\pi\)
0.479744 + 0.877408i \(0.340729\pi\)
\(728\) 1.09885e42i 0.128519i
\(729\) 6.20328e42 + 6.13976e42i 0.710737 + 0.703458i
\(730\) −4.83604e42 −0.542809
\(731\) 2.56872e43i 2.82460i
\(732\) 6.92605e42 + 9.05788e41i 0.746138 + 0.0975799i
\(733\) 7.56873e42 0.798847 0.399424 0.916767i \(-0.369210\pi\)
0.399424 + 0.916767i \(0.369210\pi\)
\(734\) 1.31656e42i 0.136145i
\(735\) 2.68786e42 2.05525e43i 0.272330 2.08236i
\(736\) −2.89352e42 −0.287249
\(737\) 6.58909e42i 0.640933i
\(738\) −8.80938e42 2.34428e42i −0.839653 0.223441i
\(739\) −2.67662e42 −0.249988 −0.124994 0.992157i \(-0.539891\pi\)
−0.124994 + 0.992157i \(0.539891\pi\)
\(740\) 1.80426e42i 0.165129i
\(741\) 1.77008e42 + 2.31491e41i 0.158752 + 0.0207616i
\(742\) 1.25483e42 0.110287
\(743\) 7.85552e42i 0.676617i 0.941035 + 0.338309i \(0.109855\pi\)
−0.941035 + 0.338309i \(0.890145\pi\)
\(744\) 1.77818e41 1.35967e42i 0.0150100 0.114773i
\(745\) 1.52516e43 1.26174
\(746\) 2.37990e42i 0.192964i
\(747\) −2.51018e42 + 9.43281e42i −0.199478 + 0.749604i
\(748\) −5.94529e42 −0.463073
\(749\) 1.81324e43i 1.38429i
\(750\) −5.22704e42 6.83592e41i −0.391144 0.0511538i
\(751\) −4.73876e42 −0.347589 −0.173794 0.984782i \(-0.555603\pi\)
−0.173794 + 0.984782i \(0.555603\pi\)
\(752\) 4.58435e42i 0.329617i
\(753\) 3.07580e42 2.35189e43i 0.216787 1.65765i
\(754\) −3.62109e41 −0.0250190
\(755\) 1.42710e43i 0.966607i
\(756\) −1.14129e43 4.69301e42i −0.757825 0.311619i
\(757\) −1.48938e43 −0.969544 −0.484772 0.874641i \(-0.661097\pi\)
−0.484772 + 0.874641i \(0.661097\pi\)
\(758\) 1.16994e43i 0.746666i
\(759\) −1.40287e43 1.83468e42i −0.877791 0.114798i
\(760\) 5.18259e42 0.317938
\(761\) 2.11532e42i 0.127235i −0.997974 0.0636173i \(-0.979736\pi\)
0.997974 0.0636173i \(-0.0202637\pi\)
\(762\) −8.59058e41 + 6.56873e42i −0.0506638 + 0.387397i
\(763\) 1.22050e43 0.705783
\(764\) 1.03938e43i 0.589350i
\(765\) 3.68114e43 + 9.79592e42i 2.04673 + 0.544658i
\(766\) 5.85641e42 0.319301
\(767\) 6.13289e42i 0.327895i
\(768\) 1.18200e42 + 1.54581e41i 0.0619723 + 0.00810473i
\(769\) −2.36246e42 −0.121470 −0.0607350 0.998154i \(-0.519344\pi\)
−0.0607350 + 0.998154i \(0.519344\pi\)
\(770\) 1.55986e43i 0.786547i
\(771\) −3.34999e42 + 2.56155e43i −0.165664 + 1.26674i
\(772\) −1.30379e43 −0.632339
\(773\) 3.16955e41i 0.0150767i 0.999972 + 0.00753834i \(0.00239955\pi\)
−0.999972 + 0.00753834i \(0.997600\pi\)
\(774\) −6.47623e42 + 2.43365e43i −0.302140 + 1.13539i
\(775\) 3.95104e42 0.180795
\(776\) 2.87460e42i 0.129019i
\(777\) −9.78431e42 1.27959e42i −0.430740 0.0563321i
\(778\) 2.19270e42 0.0946859
\(779\) 2.09384e43i 0.886915i
\(780\) −4.31238e41 + 3.29743e42i −0.0179184 + 0.137011i
\(781\) −4.82559e42 −0.196691
\(782\) 4.88495e43i 1.95326i
\(783\) 1.54650e42 3.76093e42i 0.0606631 0.147526i
\(784\) 1.09507e43 0.421405
\(785\) 1.78742e43i 0.674812i
\(786\) −6.70256e42 8.76561e41i −0.248258 0.0324671i
\(787\) 1.83268e43 0.665987 0.332993 0.942929i \(-0.391941\pi\)
0.332993 + 0.942929i \(0.391941\pi\)
\(788\) 1.81912e43i 0.648587i
\(789\) −3.44093e42 + 2.63108e43i −0.120371 + 0.920405i
\(790\) −1.53030e42 −0.0525254
\(791\) 2.76515e43i 0.931262i
\(792\) 5.63268e42 + 1.49892e42i 0.186139 + 0.0495337i
\(793\) −1.02949e43 −0.333828
\(794\) 5.46686e42i 0.173953i
\(795\) 3.76549e42 + 4.92450e41i 0.117575 + 0.0153764i
\(796\) 2.48014e43 0.759941
\(797\) 4.40895e43i 1.32575i −0.748732 0.662873i \(-0.769337\pi\)
0.748732 0.662873i \(-0.230663\pi\)
\(798\) 3.67552e42 2.81046e43i 0.108462 0.829344i
\(799\) 7.73947e43 2.24135
\(800\) 3.43474e42i 0.0976211i
\(801\) −1.13917e43 + 4.28079e43i −0.317760 + 1.19409i
\(802\) 6.75087e42 0.184818
\(803\) 1.24927e43i 0.335679i
\(804\) −2.21157e43 2.89230e42i −0.583258 0.0762785i
\(805\) −1.28166e44 −3.31768
\(806\) 2.02102e42i 0.0513504i
\(807\) 6.51517e42 4.98178e43i 0.162489 1.24246i
\(808\) −6.66965e42 −0.163280
\(809\) 3.94451e43i 0.947905i −0.880550 0.473953i \(-0.842827\pi\)
0.880550 0.473953i \(-0.157173\pi\)
\(810\) −3.24060e43 1.85617e43i −0.764452 0.437867i
\(811\) −3.74911e43 −0.868192 −0.434096 0.900867i \(-0.642932\pi\)
−0.434096 + 0.900867i \(0.642932\pi\)
\(812\) 5.74944e42i 0.130703i
\(813\) 4.24308e43 + 5.54909e42i 0.946940 + 0.123841i
\(814\) 4.66086e42 0.102117
\(815\) 2.88314e43i 0.620156i
\(816\) −2.60970e42 + 1.99549e43i −0.0551110 + 0.421403i
\(817\) −5.78439e43 −1.19930
\(818\) 3.00859e42i 0.0612439i
\(819\) 1.75758e43 + 4.67712e42i 0.351283 + 0.0934803i
\(820\) 3.90057e43 0.765455
\(821\) 3.35570e43i 0.646600i −0.946296 0.323300i \(-0.895208\pi\)
0.946296 0.323300i \(-0.104792\pi\)
\(822\) 4.81356e43 + 6.29518e42i 0.910729 + 0.119105i
\(823\) −1.15500e43 −0.214578 −0.107289 0.994228i \(-0.534217\pi\)
−0.107289 + 0.994228i \(0.534217\pi\)
\(824\) 2.63230e43i 0.480206i
\(825\) −2.17784e42 + 1.66527e43i −0.0390137 + 0.298315i
\(826\) 9.73759e43 1.71297
\(827\) 1.92570e43i 0.332664i −0.986070 0.166332i \(-0.946808\pi\)
0.986070 0.166332i \(-0.0531923\pi\)
\(828\) −1.23159e43 + 4.62809e43i −0.208935 + 0.785140i
\(829\) −4.49296e43 −0.748539 −0.374270 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(830\) 4.17661e43i 0.683364i
\(831\) 5.26248e43 + 6.88227e42i 0.845619 + 0.110590i
\(832\) −1.75692e42 −0.0277269
\(833\) 1.84873e44i 2.86549i
\(834\) 3.97442e42 3.03901e43i 0.0605039 0.462639i
\(835\) −1.28230e43 −0.191731
\(836\) 1.33879e43i 0.196616i
\(837\) −2.09907e43 8.63140e42i −0.302792 0.124509i
\(838\) −2.30104e43 −0.326035
\(839\) 1.29960e43i 0.180876i 0.995902 + 0.0904381i \(0.0288267\pi\)
−0.995902 + 0.0904381i \(0.971173\pi\)
\(840\) 5.23554e43 + 6.84704e42i 0.715768 + 0.0936082i
\(841\) 7.25683e43 0.974556
\(842\) 2.84684e43i 0.375562i
\(843\) −5.06761e42 + 3.87491e43i −0.0656734 + 0.502167i
\(844\) −6.32514e43 −0.805256
\(845\) 9.47146e43i 1.18458i
\(846\) −7.33252e43 1.95127e43i −0.900943 0.239751i
\(847\) 9.54654e43 1.15238
\(848\) 2.00630e42i 0.0237935i
\(849\) −7.74978e43 1.01352e43i −0.902971 0.118091i
\(850\) −5.79866e43 −0.663810
\(851\) 3.82960e43i 0.430734i
\(852\) −2.11820e42 + 1.61967e43i −0.0234085 + 0.178992i
\(853\) 4.50119e43 0.488756 0.244378 0.969680i \(-0.421416\pi\)
0.244378 + 0.969680i \(0.421416\pi\)
\(854\) 1.63458e44i 1.74397i
\(855\) 2.20590e43 8.28938e43i 0.231257 0.869021i
\(856\) −2.89912e43 −0.298648
\(857\) 1.11384e44i 1.12749i −0.825949 0.563744i \(-0.809360\pi\)
0.825949 0.563744i \(-0.190640\pi\)
\(858\) −8.51810e42 1.11400e42i −0.0847293 0.0110809i
\(859\) 1.25632e44 1.22802 0.614008 0.789300i \(-0.289556\pi\)
0.614008 + 0.789300i \(0.289556\pi\)
\(860\) 1.07756e44i 1.03506i
\(861\) 2.76631e43 2.11524e44i 0.261128 1.99670i
\(862\) −3.60121e43 −0.334071
\(863\) 1.24301e44i 1.13321i 0.823988 + 0.566607i \(0.191744\pi\)
−0.823988 + 0.566607i \(0.808256\pi\)
\(864\) 7.50348e42 1.82477e43i 0.0672290 0.163494i
\(865\) −6.47472e43 −0.570137
\(866\) 5.71978e43i 0.495007i
\(867\) −2.20312e44 2.88124e43i −1.87392 0.245072i
\(868\) 3.20890e43 0.268262
\(869\) 3.95314e42i 0.0324822i
\(870\) −2.25633e42 + 1.72529e43i −0.0182228 + 0.139339i
\(871\) 3.28728e43 0.260954
\(872\) 1.95142e43i 0.152266i
\(873\) 4.59784e43 + 1.22354e43i 0.352647 + 0.0938433i
\(874\) −1.10002e44 −0.829333
\(875\) 1.23361e44i 0.914232i
\(876\) −4.19308e43 5.48371e42i −0.305472 0.0399497i
\(877\) 7.81734e43 0.559841 0.279921 0.960023i \(-0.409692\pi\)
0.279921 + 0.960023i \(0.409692\pi\)
\(878\) 1.71911e44i 1.21028i
\(879\) −1.83372e43 + 1.40214e44i −0.126911 + 0.970419i
\(880\) −2.49401e43 −0.169690
\(881\) 2.12352e43i 0.142043i 0.997475 + 0.0710213i \(0.0226258\pi\)
−0.997475 + 0.0710213i \(0.977374\pi\)
\(882\) 4.66101e43 1.75152e44i 0.306514 1.15183i
\(883\) 1.34653e44 0.870571 0.435286 0.900292i \(-0.356647\pi\)
0.435286 + 0.900292i \(0.356647\pi\)
\(884\) 2.96610e43i 0.188539i
\(885\) 2.92205e44 + 3.82146e43i 1.82616 + 0.238825i
\(886\) −3.91016e42 −0.0240264
\(887\) 4.81971e43i 0.291183i −0.989345 0.145592i \(-0.953491\pi\)
0.989345 0.145592i \(-0.0465086\pi\)
\(888\) 2.04590e42 1.56438e43i 0.0121532 0.0929282i
\(889\) −1.55025e44 −0.905475
\(890\) 1.89542e44i 1.08857i
\(891\) 4.79495e43 8.37129e43i 0.270781 0.472745i
\(892\) −2.10697e43 −0.117000
\(893\) 1.74282e44i 0.951655i
\(894\) 1.32238e44 + 1.72941e43i 0.710059 + 0.0928615i
\(895\) −1.11677e44 −0.589683
\(896\) 2.78957e43i 0.144850i
\(897\) 9.15316e42 6.99890e43i 0.0467395 0.357391i
\(898\) 1.34244e44 0.674140
\(899\) 1.05744e43i 0.0522228i
\(900\) 5.49375e43 + 1.46195e43i 0.266828 + 0.0710060i
\(901\) −3.38712e43 −0.161793
\(902\) 1.00762e44i 0.473365i
\(903\) −5.84350e44 7.64212e43i −2.69995 0.353100i
\(904\) −4.42111e43 −0.200911
\(905\) 1.96370e44i 0.877701i
\(906\) −1.61822e43 + 1.23736e44i −0.0711403 + 0.543969i
\(907\) −2.08693e43 −0.0902397 −0.0451199 0.998982i \(-0.514367\pi\)
−0.0451199 + 0.998982i \(0.514367\pi\)
\(908\) 3.41692e43i 0.145327i
\(909\) −2.83885e43 + 1.06679e44i −0.118764 + 0.446293i
\(910\) −7.78211e43 −0.320241
\(911\) 1.23452e44i 0.499717i 0.968282 + 0.249858i \(0.0803840\pi\)
−0.968282 + 0.249858i \(0.919616\pi\)
\(912\) 4.49355e43 + 5.87667e42i 0.178924 + 0.0233996i
\(913\) 1.07892e44 0.422599
\(914\) 1.27202e44i 0.490120i
\(915\) −6.41482e43 + 4.90505e44i −0.243147 + 1.85920i
\(916\) 6.35245e43 0.236870
\(917\) 1.58184e44i 0.580260i
\(918\) 3.08064e44 + 1.26677e44i 1.11174 + 0.457148i
\(919\) 5.23347e43 0.185805 0.0929024 0.995675i \(-0.470386\pi\)
0.0929024 + 0.995675i \(0.470386\pi\)
\(920\) 2.04920e44i 0.715759i
\(921\) 5.06358e44 + 6.62215e43i 1.74006 + 0.227565i
\(922\) −4.16642e44 −1.40864
\(923\) 2.40748e43i 0.0800823i
\(924\) −1.76876e43 + 1.35247e44i −0.0578883 + 0.442639i
\(925\) 4.54590e43 0.146384
\(926\) 2.32012e44i 0.735099i
\(927\) −4.21028e44 1.12040e44i −1.31255 0.349284i
\(928\) −9.19258e42 −0.0281980
\(929\) 2.89626e44i 0.874181i 0.899418 + 0.437091i \(0.143991\pi\)
−0.899418 + 0.437091i \(0.856009\pi\)
\(930\) 9.62924e43 + 1.25931e43i 0.285988 + 0.0374015i
\(931\) 4.16308e44 1.21666
\(932\) 3.10952e44i 0.894243i
\(933\) −6.37684e43 + 4.87600e44i −0.180460 + 1.37987i
\(934\) 2.57495e44 0.717078
\(935\) 4.21048e44i 1.15387i
\(936\) −7.47809e42 + 2.81013e43i −0.0201675 + 0.0757860i
\(937\) −2.91104e44 −0.772599 −0.386300 0.922373i \(-0.626247\pi\)
−0.386300 + 0.922373i \(0.626247\pi\)
\(938\) 5.21943e44i 1.36327i
\(939\) −1.50955e44 1.97419e43i −0.388028 0.0507463i
\(940\) 3.24665e44 0.821330
\(941\) 4.64351e44i 1.15612i 0.815995 + 0.578059i \(0.196190\pi\)
−0.815995 + 0.578059i \(0.803810\pi\)
\(942\) 2.02681e43 1.54978e44i 0.0496648 0.379758i
\(943\) −8.27907e44 −1.99667
\(944\) 1.55691e44i 0.369559i
\(945\) 3.32360e44 8.08265e44i 0.776483 1.88832i
\(946\) 2.78361e44 0.640090
\(947\) 8.24458e44i 1.86603i −0.359835 0.933016i \(-0.617167\pi\)
0.359835 0.933016i \(-0.382833\pi\)
\(948\) −1.32684e43 1.73524e42i −0.0295593 0.00386576i
\(949\) 6.23260e43 0.136671
\(950\) 1.30577e44i 0.281847i
\(951\) 1.24096e43 9.48891e43i 0.0263663 0.201608i
\(952\) −4.70946e44 −0.984957
\(953\) 8.05488e44i 1.65831i −0.559020 0.829154i \(-0.688822\pi\)
0.559020 0.829154i \(-0.311178\pi\)
\(954\) 3.20902e43 + 8.53956e42i 0.0650349 + 0.0173065i
\(955\) 7.36092e44 1.46853
\(956\) 2.15490e44i 0.423213i
\(957\) −4.45686e43 5.82868e42i −0.0861687 0.0112691i
\(958\) 1.12989e44 0.215056
\(959\) 1.13603e45i 2.12867i
\(960\) −1.09475e43 + 8.37093e43i −0.0201951 + 0.154421i
\(961\) −4.91600e44 −0.892815
\(962\) 2.32529e43i 0.0415769i
\(963\) −1.23397e44 + 4.63705e44i −0.217226 + 0.816296i
\(964\) 2.28108e44 0.395353
\(965\) 9.23352e44i 1.57564i
\(966\) −1.11126e45 1.45331e44i −1.86706 0.244174i
\(967\) 3.14393e44 0.520086 0.260043 0.965597i \(-0.416263\pi\)
0.260043 + 0.965597i \(0.416263\pi\)
\(968\) 1.52636e44i 0.248615i
\(969\) −9.92122e43 + 7.58619e44i −0.159114 + 1.21665i
\(970\) −2.03580e44 −0.321484
\(971\) 1.87489e43i 0.0291532i −0.999894 0.0145766i \(-0.995360\pi\)
0.999894 0.0145766i \(-0.00464004\pi\)
\(972\) −2.59928e44 1.97685e44i −0.397978 0.302677i
\(973\) 7.17223e44 1.08134
\(974\) 4.59965e44i 0.682873i
\(975\) −8.30801e43 1.08652e43i −0.121458 0.0158843i
\(976\) −2.61348e44 −0.376246
\(977\) 8.73809e44i 1.23879i −0.785079 0.619396i \(-0.787378\pi\)
0.785079 0.619396i \(-0.212622\pi\)
\(978\) 3.26926e43 2.49982e44i 0.0456422 0.349000i
\(979\) 4.89636e44 0.673183
\(980\) 7.75530e44i 1.05004i
\(981\) 3.12124e44 + 8.30597e43i 0.416190 + 0.110753i
\(982\) −1.59368e44 −0.209280
\(983\) 3.87923e44i 0.501698i 0.968026 + 0.250849i \(0.0807098\pi\)
−0.968026 + 0.250849i \(0.919290\pi\)
\(984\) 3.38198e44 + 4.42295e43i 0.430769 + 0.0563360i
\(985\) −1.28831e45 −1.61613
\(986\) 1.55193e44i 0.191742i
\(987\) 2.30254e44 1.76062e45i 0.280189 2.14244i
\(988\) −6.67922e43 −0.0800519
\(989\) 2.28715e45i 2.69992i
\(990\) −1.06154e44 + 3.98908e44i −0.123427 + 0.463815i
\(991\) 7.70247e44 0.882115 0.441058 0.897479i \(-0.354603\pi\)
0.441058 + 0.897479i \(0.354603\pi\)
\(992\) 5.13059e43i 0.0578752i
\(993\) 1.67953e45 + 2.19649e44i 1.86616 + 0.244056i
\(994\) −3.82251e44 −0.418362
\(995\) 1.75644e45i 1.89360i
\(996\) 4.73596e43 3.62132e44i 0.0502942 0.384571i
\(997\) 1.59872e45 1.67242 0.836209 0.548411i \(-0.184767\pi\)
0.836209 + 0.548411i \(0.184767\pi\)
\(998\) 3.30035e44i 0.340096i
\(999\) −2.41509e44 9.93092e43i −0.245161 0.100811i
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 6.31.b.a.5.5 10
3.2 odd 2 inner 6.31.b.a.5.10 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.31.b.a.5.5 10 1.1 even 1 trivial
6.31.b.a.5.10 yes 10 3.2 odd 2 inner