Properties

Label 10.26.a.c.1.2
Level $10$
Weight $26$
Character 10.1
Self dual yes
Analytic conductor $39.600$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [10,26,Mod(1,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 26, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.1");
 
S:= CuspForms(chi, 26);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 10.a (trivial)

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: yes
Analytic conductor: \(39.5996779952\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 148387471 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4}\cdot 5 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(12181.4\) of defining polynomial
Character \(\chi\) \(=\) 10.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4096.00 q^{2} +1.24712e6 q^{3} +1.67772e7 q^{4} -2.44141e8 q^{5} -5.10821e9 q^{6} +3.92781e10 q^{7} -6.87195e10 q^{8} +7.08023e11 q^{9} +1.00000e12 q^{10} -1.50696e13 q^{11} +2.09232e13 q^{12} -1.45379e14 q^{13} -1.60883e14 q^{14} -3.04473e14 q^{15} +2.81475e14 q^{16} +1.30302e15 q^{17} -2.90006e15 q^{18} -9.75151e15 q^{19} -4.09600e15 q^{20} +4.89845e16 q^{21} +6.17252e16 q^{22} +1.00704e17 q^{23} -8.57015e16 q^{24} +5.96046e16 q^{25} +5.95471e17 q^{26} -1.73682e17 q^{27} +6.58976e17 q^{28} -1.41726e18 q^{29} +1.24712e18 q^{30} -3.30375e18 q^{31} -1.15292e18 q^{32} -1.87937e19 q^{33} -5.33718e18 q^{34} -9.58937e18 q^{35} +1.18786e19 q^{36} +6.55066e19 q^{37} +3.99422e19 q^{38} -1.81305e20 q^{39} +1.67772e19 q^{40} -9.42027e19 q^{41} -2.00640e20 q^{42} +1.20866e20 q^{43} -2.52827e20 q^{44} -1.72857e20 q^{45} -4.12482e20 q^{46} -8.86966e20 q^{47} +3.51033e20 q^{48} +2.01697e20 q^{49} -2.44141e20 q^{50} +1.62503e21 q^{51} -2.43905e21 q^{52} -6.79454e21 q^{53} +7.11400e20 q^{54} +3.67911e21 q^{55} -2.69917e21 q^{56} -1.21613e22 q^{57} +5.80511e21 q^{58} -1.11112e22 q^{59} -5.10821e21 q^{60} -3.14899e22 q^{61} +1.35322e22 q^{62} +2.78098e22 q^{63} +4.72237e21 q^{64} +3.54928e22 q^{65} +7.69788e22 q^{66} +4.52478e22 q^{67} +2.18611e22 q^{68} +1.25590e23 q^{69} +3.92781e22 q^{70} -3.31126e22 q^{71} -4.86549e22 q^{72} +3.04253e23 q^{73} -2.68315e23 q^{74} +7.43342e22 q^{75} -1.63603e23 q^{76} -5.91906e23 q^{77} +7.42625e23 q^{78} -1.45524e23 q^{79} -6.87195e22 q^{80} -8.16501e23 q^{81} +3.85854e23 q^{82} +8.80567e23 q^{83} +8.21823e23 q^{84} -3.18121e23 q^{85} -4.95068e23 q^{86} -1.76750e24 q^{87} +1.03558e24 q^{88} -1.79771e23 q^{89} +7.08023e23 q^{90} -5.71019e24 q^{91} +1.68953e24 q^{92} -4.12018e24 q^{93} +3.63301e24 q^{94} +2.38074e24 q^{95} -1.43783e24 q^{96} -7.02806e24 q^{97} -8.26151e23 q^{98} -1.06696e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8192 q^{2} + 545212 q^{3} + 33554432 q^{4} - 488281250 q^{5} - 2233188352 q^{6} + 38567856964 q^{7} - 137438953472 q^{8} + 353410472386 q^{9} + 2000000000000 q^{10} - 8379169876416 q^{11} + 9147139489792 q^{12}+ \cdots - 13\!\cdots\!88 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4096.00 −0.707107
\(3\) 1.24712e6 1.35486 0.677428 0.735589i \(-0.263095\pi\)
0.677428 + 0.735589i \(0.263095\pi\)
\(4\) 1.67772e7 0.500000
\(5\) −2.44141e8 −0.447214
\(6\) −5.10821e9 −0.958027
\(7\) 3.92781e10 1.07257 0.536284 0.844038i \(-0.319828\pi\)
0.536284 + 0.844038i \(0.319828\pi\)
\(8\) −6.87195e10 −0.353553
\(9\) 7.08023e11 0.835633
\(10\) 1.00000e12 0.316228
\(11\) −1.50696e13 −1.44775 −0.723876 0.689930i \(-0.757641\pi\)
−0.723876 + 0.689930i \(0.757641\pi\)
\(12\) 2.09232e13 0.677428
\(13\) −1.45379e14 −1.73065 −0.865324 0.501213i \(-0.832887\pi\)
−0.865324 + 0.501213i \(0.832887\pi\)
\(14\) −1.60883e14 −0.758419
\(15\) −3.04473e14 −0.605910
\(16\) 2.81475e14 0.250000
\(17\) 1.30302e15 0.542426 0.271213 0.962519i \(-0.412575\pi\)
0.271213 + 0.962519i \(0.412575\pi\)
\(18\) −2.90006e15 −0.590882
\(19\) −9.75151e15 −1.01077 −0.505385 0.862894i \(-0.668649\pi\)
−0.505385 + 0.862894i \(0.668649\pi\)
\(20\) −4.09600e15 −0.223607
\(21\) 4.89845e16 1.45317
\(22\) 6.17252e16 1.02372
\(23\) 1.00704e17 0.958180 0.479090 0.877766i \(-0.340967\pi\)
0.479090 + 0.877766i \(0.340967\pi\)
\(24\) −8.57015e16 −0.479014
\(25\) 5.96046e16 0.200000
\(26\) 5.95471e17 1.22375
\(27\) −1.73682e17 −0.222693
\(28\) 6.58976e17 0.536284
\(29\) −1.41726e18 −0.743834 −0.371917 0.928266i \(-0.621299\pi\)
−0.371917 + 0.928266i \(0.621299\pi\)
\(30\) 1.24712e18 0.428443
\(31\) −3.30375e18 −0.753332 −0.376666 0.926349i \(-0.622930\pi\)
−0.376666 + 0.926349i \(0.622930\pi\)
\(32\) −1.15292e18 −0.176777
\(33\) −1.87937e19 −1.96149
\(34\) −5.33718e18 −0.383553
\(35\) −9.58937e18 −0.479667
\(36\) 1.18786e19 0.417817
\(37\) 6.55066e19 1.63593 0.817963 0.575271i \(-0.195103\pi\)
0.817963 + 0.575271i \(0.195103\pi\)
\(38\) 3.99422e19 0.714722
\(39\) −1.81305e20 −2.34478
\(40\) 1.67772e19 0.158114
\(41\) −9.42027e19 −0.652026 −0.326013 0.945365i \(-0.605705\pi\)
−0.326013 + 0.945365i \(0.605705\pi\)
\(42\) −2.00640e20 −1.02755
\(43\) 1.20866e20 0.461263 0.230632 0.973041i \(-0.425921\pi\)
0.230632 + 0.973041i \(0.425921\pi\)
\(44\) −2.52827e20 −0.723876
\(45\) −1.72857e20 −0.373707
\(46\) −4.12482e20 −0.677535
\(47\) −8.86966e20 −1.11348 −0.556742 0.830686i \(-0.687949\pi\)
−0.556742 + 0.830686i \(0.687949\pi\)
\(48\) 3.51033e20 0.338714
\(49\) 2.01697e20 0.150400
\(50\) −2.44141e20 −0.141421
\(51\) 1.62503e21 0.734909
\(52\) −2.43905e21 −0.865324
\(53\) −6.79454e21 −1.89982 −0.949908 0.312530i \(-0.898824\pi\)
−0.949908 + 0.312530i \(0.898824\pi\)
\(54\) 7.11400e20 0.157468
\(55\) 3.67911e21 0.647454
\(56\) −2.69917e21 −0.379210
\(57\) −1.21613e22 −1.36945
\(58\) 5.80511e21 0.525970
\(59\) −1.11112e22 −0.813039 −0.406520 0.913642i \(-0.633258\pi\)
−0.406520 + 0.913642i \(0.633258\pi\)
\(60\) −5.10821e21 −0.302955
\(61\) −3.14899e22 −1.51897 −0.759483 0.650527i \(-0.774548\pi\)
−0.759483 + 0.650527i \(0.774548\pi\)
\(62\) 1.35322e22 0.532686
\(63\) 2.78098e22 0.896273
\(64\) 4.72237e21 0.125000
\(65\) 3.54928e22 0.773969
\(66\) 7.69788e22 1.38699
\(67\) 4.52478e22 0.675558 0.337779 0.941225i \(-0.390324\pi\)
0.337779 + 0.941225i \(0.390324\pi\)
\(68\) 2.18611e22 0.271213
\(69\) 1.25590e23 1.29819
\(70\) 3.92781e22 0.339176
\(71\) −3.31126e22 −0.239477 −0.119739 0.992805i \(-0.538206\pi\)
−0.119739 + 0.992805i \(0.538206\pi\)
\(72\) −4.86549e22 −0.295441
\(73\) 3.04253e23 1.55489 0.777445 0.628952i \(-0.216516\pi\)
0.777445 + 0.628952i \(0.216516\pi\)
\(74\) −2.68315e23 −1.15677
\(75\) 7.43342e22 0.270971
\(76\) −1.63603e23 −0.505385
\(77\) −5.91906e23 −1.55281
\(78\) 7.42625e23 1.65801
\(79\) −1.45524e23 −0.277075 −0.138537 0.990357i \(-0.544240\pi\)
−0.138537 + 0.990357i \(0.544240\pi\)
\(80\) −6.87195e22 −0.111803
\(81\) −8.16501e23 −1.13735
\(82\) 3.85854e23 0.461052
\(83\) 8.80567e23 0.904245 0.452122 0.891956i \(-0.350667\pi\)
0.452122 + 0.891956i \(0.350667\pi\)
\(84\) 8.21823e23 0.726587
\(85\) −3.18121e23 −0.242580
\(86\) −4.95068e23 −0.326162
\(87\) −1.76750e24 −1.00779
\(88\) 1.03558e24 0.511858
\(89\) −1.79771e23 −0.0771514 −0.0385757 0.999256i \(-0.512282\pi\)
−0.0385757 + 0.999256i \(0.512282\pi\)
\(90\) 7.08023e23 0.264250
\(91\) −5.71019e24 −1.85624
\(92\) 1.68953e24 0.479090
\(93\) −4.12018e24 −1.02066
\(94\) 3.63301e24 0.787352
\(95\) 2.38074e24 0.452030
\(96\) −1.43783e24 −0.239507
\(97\) −7.02806e24 −1.02846 −0.514232 0.857651i \(-0.671923\pi\)
−0.514232 + 0.857651i \(0.671923\pi\)
\(98\) −8.26151e23 −0.106349
\(99\) −1.06696e25 −1.20979
\(100\) 1.00000e24 0.100000
\(101\) −6.59850e24 −0.582677 −0.291339 0.956620i \(-0.594101\pi\)
−0.291339 + 0.956620i \(0.594101\pi\)
\(102\) −6.65611e24 −0.519659
\(103\) 2.14556e25 1.48278 0.741389 0.671075i \(-0.234167\pi\)
0.741389 + 0.671075i \(0.234167\pi\)
\(104\) 9.99035e24 0.611877
\(105\) −1.19591e25 −0.649879
\(106\) 2.78304e25 1.34337
\(107\) 2.29745e24 0.0986164 0.0493082 0.998784i \(-0.484298\pi\)
0.0493082 + 0.998784i \(0.484298\pi\)
\(108\) −2.91389e24 −0.111347
\(109\) 2.46259e25 0.838611 0.419305 0.907845i \(-0.362274\pi\)
0.419305 + 0.907845i \(0.362274\pi\)
\(110\) −1.50696e25 −0.457819
\(111\) 8.16947e25 2.21644
\(112\) 1.10558e25 0.268142
\(113\) −4.71863e25 −1.02408 −0.512042 0.858960i \(-0.671111\pi\)
−0.512042 + 0.858960i \(0.671111\pi\)
\(114\) 4.98128e25 0.968345
\(115\) −2.45858e25 −0.428511
\(116\) −2.37777e25 −0.371917
\(117\) −1.02931e26 −1.44619
\(118\) 4.55116e25 0.574906
\(119\) 5.11802e25 0.581789
\(120\) 2.09232e25 0.214221
\(121\) 1.18747e26 1.09599
\(122\) 1.28982e26 1.07407
\(123\) −1.17482e26 −0.883401
\(124\) −5.54278e25 −0.376666
\(125\) −1.45519e25 −0.0894427
\(126\) −1.13909e26 −0.633761
\(127\) −1.28089e26 −0.645605 −0.322802 0.946466i \(-0.604625\pi\)
−0.322802 + 0.946466i \(0.604625\pi\)
\(128\) −1.93428e25 −0.0883883
\(129\) 1.50735e26 0.624945
\(130\) −1.45379e26 −0.547279
\(131\) 1.65371e26 0.565675 0.282838 0.959168i \(-0.408724\pi\)
0.282838 + 0.959168i \(0.408724\pi\)
\(132\) −3.15305e26 −0.980747
\(133\) −3.83020e26 −1.08412
\(134\) −1.85335e26 −0.477692
\(135\) 4.24027e25 0.0995914
\(136\) −8.95431e25 −0.191777
\(137\) −3.20644e26 −0.626637 −0.313319 0.949648i \(-0.601441\pi\)
−0.313319 + 0.949648i \(0.601441\pi\)
\(138\) −5.14415e26 −0.917962
\(139\) 5.33177e26 0.869333 0.434666 0.900592i \(-0.356866\pi\)
0.434666 + 0.900592i \(0.356866\pi\)
\(140\) −1.60883e26 −0.239833
\(141\) −1.10615e27 −1.50861
\(142\) 1.35629e26 0.169336
\(143\) 2.19080e27 2.50555
\(144\) 1.99291e26 0.208908
\(145\) 3.46012e26 0.332653
\(146\) −1.24622e27 −1.09947
\(147\) 2.51541e26 0.203771
\(148\) 1.09902e27 0.817963
\(149\) 5.79851e26 0.396724 0.198362 0.980129i \(-0.436438\pi\)
0.198362 + 0.980129i \(0.436438\pi\)
\(150\) −3.04473e26 −0.191605
\(151\) 2.88738e27 1.67222 0.836109 0.548564i \(-0.184825\pi\)
0.836109 + 0.548564i \(0.184825\pi\)
\(152\) 6.70119e26 0.357361
\(153\) 9.22570e26 0.453269
\(154\) 2.42445e27 1.09800
\(155\) 8.06580e26 0.336900
\(156\) −3.04179e27 −1.17239
\(157\) −4.99584e27 −1.77772 −0.888859 0.458181i \(-0.848501\pi\)
−0.888859 + 0.458181i \(0.848501\pi\)
\(158\) 5.96067e26 0.195921
\(159\) −8.47361e27 −2.57398
\(160\) 2.81475e26 0.0790569
\(161\) 3.95544e27 1.02771
\(162\) 3.34439e27 0.804228
\(163\) 9.78636e25 0.0217909 0.0108955 0.999941i \(-0.496532\pi\)
0.0108955 + 0.999941i \(0.496532\pi\)
\(164\) −1.58046e27 −0.326013
\(165\) 4.58830e27 0.877207
\(166\) −3.60680e27 −0.639398
\(167\) 8.79974e27 1.44715 0.723576 0.690245i \(-0.242497\pi\)
0.723576 + 0.690245i \(0.242497\pi\)
\(168\) −3.36619e27 −0.513774
\(169\) 1.40786e28 1.99514
\(170\) 1.30302e27 0.171530
\(171\) −6.90429e27 −0.844632
\(172\) 2.02780e27 0.230632
\(173\) −1.48916e28 −1.57530 −0.787651 0.616122i \(-0.788703\pi\)
−0.787651 + 0.616122i \(0.788703\pi\)
\(174\) 7.23968e27 0.712613
\(175\) 2.34115e27 0.214513
\(176\) −4.24173e27 −0.361938
\(177\) −1.38570e28 −1.10155
\(178\) 7.36341e26 0.0545543
\(179\) −1.83964e28 −1.27078 −0.635390 0.772191i \(-0.719161\pi\)
−0.635390 + 0.772191i \(0.719161\pi\)
\(180\) −2.90006e27 −0.186853
\(181\) 1.98192e28 1.19153 0.595764 0.803160i \(-0.296849\pi\)
0.595764 + 0.803160i \(0.296849\pi\)
\(182\) 2.33889e28 1.31256
\(183\) −3.92717e28 −2.05798
\(184\) −6.92030e27 −0.338768
\(185\) −1.59928e28 −0.731608
\(186\) 1.68763e28 0.721713
\(187\) −1.96361e28 −0.785299
\(188\) −1.48808e28 −0.556742
\(189\) −6.82188e27 −0.238853
\(190\) −9.75151e27 −0.319633
\(191\) −3.54565e28 −1.08837 −0.544187 0.838964i \(-0.683162\pi\)
−0.544187 + 0.838964i \(0.683162\pi\)
\(192\) 5.88936e27 0.169357
\(193\) −1.29750e28 −0.349657 −0.174829 0.984599i \(-0.555937\pi\)
−0.174829 + 0.984599i \(0.555937\pi\)
\(194\) 2.87869e28 0.727234
\(195\) 4.42639e28 1.04862
\(196\) 3.38392e27 0.0752001
\(197\) 6.04380e28 1.26032 0.630162 0.776463i \(-0.282988\pi\)
0.630162 + 0.776463i \(0.282988\pi\)
\(198\) 4.37029e28 0.855451
\(199\) 5.51931e28 1.01443 0.507215 0.861820i \(-0.330675\pi\)
0.507215 + 0.861820i \(0.330675\pi\)
\(200\) −4.09600e27 −0.0707107
\(201\) 5.64295e28 0.915283
\(202\) 2.70275e28 0.412015
\(203\) −5.56674e28 −0.797812
\(204\) 2.72634e28 0.367455
\(205\) 2.29987e28 0.291595
\(206\) −8.78823e28 −1.04848
\(207\) 7.13004e28 0.800687
\(208\) −4.09205e28 −0.432662
\(209\) 1.46952e29 1.46334
\(210\) 4.89845e28 0.459534
\(211\) −7.38048e28 −0.652460 −0.326230 0.945290i \(-0.605778\pi\)
−0.326230 + 0.945290i \(0.605778\pi\)
\(212\) −1.13993e29 −0.949908
\(213\) −4.12955e28 −0.324457
\(214\) −9.41036e27 −0.0697323
\(215\) −2.95083e28 −0.206283
\(216\) 1.19353e28 0.0787339
\(217\) −1.29765e29 −0.807999
\(218\) −1.00868e29 −0.592987
\(219\) 3.79441e29 2.10665
\(220\) 6.17252e28 0.323727
\(221\) −1.89432e29 −0.938749
\(222\) −3.34621e29 −1.56726
\(223\) 3.22437e29 1.42769 0.713846 0.700303i \(-0.246952\pi\)
0.713846 + 0.700303i \(0.246952\pi\)
\(224\) −4.52845e28 −0.189605
\(225\) 4.22014e28 0.167127
\(226\) 1.93275e29 0.724137
\(227\) −4.50494e29 −1.59722 −0.798611 0.601847i \(-0.794432\pi\)
−0.798611 + 0.601847i \(0.794432\pi\)
\(228\) −2.04033e29 −0.684723
\(229\) −3.03906e28 −0.0965596 −0.0482798 0.998834i \(-0.515374\pi\)
−0.0482798 + 0.998834i \(0.515374\pi\)
\(230\) 1.00704e29 0.303003
\(231\) −7.38178e29 −2.10383
\(232\) 9.73937e28 0.262985
\(233\) −1.03711e29 −0.265386 −0.132693 0.991157i \(-0.542362\pi\)
−0.132693 + 0.991157i \(0.542362\pi\)
\(234\) 4.21607e29 1.02261
\(235\) 2.16544e29 0.497965
\(236\) −1.86415e29 −0.406520
\(237\) −1.81486e29 −0.375396
\(238\) −2.09634e29 −0.411387
\(239\) 8.96475e29 1.66942 0.834708 0.550693i \(-0.185636\pi\)
0.834708 + 0.550693i \(0.185636\pi\)
\(240\) −8.57015e28 −0.151477
\(241\) 1.66839e29 0.279952 0.139976 0.990155i \(-0.455297\pi\)
0.139976 + 0.990155i \(0.455297\pi\)
\(242\) −4.86387e29 −0.774979
\(243\) −8.71118e29 −1.31825
\(244\) −5.28312e29 −0.759483
\(245\) −4.92425e28 −0.0672610
\(246\) 4.81207e29 0.624659
\(247\) 1.41766e30 1.74929
\(248\) 2.27032e29 0.266343
\(249\) 1.09817e30 1.22512
\(250\) 5.96046e28 0.0632456
\(251\) −1.77969e28 −0.0179648 −0.00898241 0.999960i \(-0.502859\pi\)
−0.00898241 + 0.999960i \(0.502859\pi\)
\(252\) 4.66570e29 0.448136
\(253\) −1.51757e30 −1.38721
\(254\) 5.24654e29 0.456512
\(255\) −3.96735e29 −0.328661
\(256\) 7.92282e28 0.0625000
\(257\) 1.02153e30 0.767515 0.383758 0.923434i \(-0.374630\pi\)
0.383758 + 0.923434i \(0.374630\pi\)
\(258\) −6.17409e29 −0.441903
\(259\) 2.57297e30 1.75464
\(260\) 5.95471e29 0.386985
\(261\) −1.00346e30 −0.621572
\(262\) −6.77358e29 −0.399993
\(263\) −2.39313e30 −1.34747 −0.673735 0.738973i \(-0.735311\pi\)
−0.673735 + 0.738973i \(0.735311\pi\)
\(264\) 1.29149e30 0.693493
\(265\) 1.65882e30 0.849624
\(266\) 1.56885e30 0.766587
\(267\) −2.24196e29 −0.104529
\(268\) 7.59132e29 0.337779
\(269\) 7.43966e29 0.315973 0.157986 0.987441i \(-0.449500\pi\)
0.157986 + 0.987441i \(0.449500\pi\)
\(270\) −1.73682e29 −0.0704217
\(271\) −2.89456e30 −1.12064 −0.560319 0.828277i \(-0.689322\pi\)
−0.560319 + 0.828277i \(0.689322\pi\)
\(272\) 3.66768e29 0.135607
\(273\) −7.12130e30 −2.51493
\(274\) 1.31336e30 0.443099
\(275\) −8.98220e29 −0.289550
\(276\) 2.10704e30 0.649097
\(277\) −2.46028e30 −0.724415 −0.362208 0.932097i \(-0.617977\pi\)
−0.362208 + 0.932097i \(0.617977\pi\)
\(278\) −2.18389e30 −0.614711
\(279\) −2.33913e30 −0.629509
\(280\) 6.58976e29 0.169588
\(281\) 5.42013e30 1.33408 0.667038 0.745024i \(-0.267562\pi\)
0.667038 + 0.745024i \(0.267562\pi\)
\(282\) 4.53081e30 1.06675
\(283\) 6.30761e30 1.42080 0.710402 0.703796i \(-0.248513\pi\)
0.710402 + 0.703796i \(0.248513\pi\)
\(284\) −5.55538e29 −0.119739
\(285\) 2.96907e30 0.612435
\(286\) −8.97353e30 −1.77169
\(287\) −3.70010e30 −0.699342
\(288\) −8.16294e29 −0.147720
\(289\) −4.07276e30 −0.705774
\(290\) −1.41726e30 −0.235221
\(291\) −8.76484e30 −1.39342
\(292\) 5.10452e30 0.777445
\(293\) 9.79285e30 1.42910 0.714552 0.699582i \(-0.246631\pi\)
0.714552 + 0.699582i \(0.246631\pi\)
\(294\) −1.03031e30 −0.144088
\(295\) 2.71270e30 0.363602
\(296\) −4.50158e30 −0.578387
\(297\) 2.61732e30 0.322404
\(298\) −2.37507e30 −0.280526
\(299\) −1.46402e31 −1.65827
\(300\) 1.24712e30 0.135486
\(301\) 4.74739e30 0.494736
\(302\) −1.18267e31 −1.18244
\(303\) −8.22913e30 −0.789444
\(304\) −2.74481e30 −0.252692
\(305\) 7.68796e30 0.679302
\(306\) −3.77885e30 −0.320510
\(307\) −5.75594e30 −0.468691 −0.234345 0.972153i \(-0.575295\pi\)
−0.234345 + 0.972153i \(0.575295\pi\)
\(308\) −9.93053e30 −0.776406
\(309\) 2.67578e31 2.00895
\(310\) −3.30375e30 −0.238224
\(311\) 1.84953e31 1.28102 0.640510 0.767950i \(-0.278723\pi\)
0.640510 + 0.767950i \(0.278723\pi\)
\(312\) 1.24592e31 0.829004
\(313\) 2.39300e31 1.52982 0.764908 0.644140i \(-0.222784\pi\)
0.764908 + 0.644140i \(0.222784\pi\)
\(314\) 2.04630e31 1.25704
\(315\) −6.78949e30 −0.400825
\(316\) −2.44149e30 −0.138537
\(317\) −2.04161e30 −0.111360 −0.0556802 0.998449i \(-0.517733\pi\)
−0.0556802 + 0.998449i \(0.517733\pi\)
\(318\) 3.47079e31 1.82008
\(319\) 2.13577e31 1.07689
\(320\) −1.15292e30 −0.0559017
\(321\) 2.86520e30 0.133611
\(322\) −1.62015e31 −0.726702
\(323\) −1.27064e31 −0.548268
\(324\) −1.36986e31 −0.568675
\(325\) −8.66525e30 −0.346130
\(326\) −4.00849e29 −0.0154085
\(327\) 3.07114e31 1.13620
\(328\) 6.47356e30 0.230526
\(329\) −3.48383e31 −1.19429
\(330\) −1.87937e31 −0.620279
\(331\) −1.75414e31 −0.557459 −0.278730 0.960370i \(-0.589913\pi\)
−0.278730 + 0.960370i \(0.589913\pi\)
\(332\) 1.47735e31 0.452122
\(333\) 4.63802e31 1.36703
\(334\) −3.60437e31 −1.02329
\(335\) −1.10468e31 −0.302119
\(336\) 1.37879e31 0.363293
\(337\) −7.33154e31 −1.86132 −0.930661 0.365882i \(-0.880768\pi\)
−0.930661 + 0.365882i \(0.880768\pi\)
\(338\) −5.76658e31 −1.41078
\(339\) −5.88471e31 −1.38749
\(340\) −5.33718e30 −0.121290
\(341\) 4.97863e31 1.09064
\(342\) 2.82800e31 0.597245
\(343\) −4.47523e31 −0.911253
\(344\) −8.30586e30 −0.163081
\(345\) −3.06615e31 −0.580570
\(346\) 6.09958e31 1.11391
\(347\) −1.54701e31 −0.272505 −0.136253 0.990674i \(-0.543506\pi\)
−0.136253 + 0.990674i \(0.543506\pi\)
\(348\) −2.96537e31 −0.503894
\(349\) −1.14544e31 −0.187782 −0.0938910 0.995582i \(-0.529931\pi\)
−0.0938910 + 0.995582i \(0.529931\pi\)
\(350\) −9.58937e30 −0.151684
\(351\) 2.52496e31 0.385403
\(352\) 1.73741e31 0.255929
\(353\) 3.77306e31 0.536427 0.268213 0.963360i \(-0.413567\pi\)
0.268213 + 0.963360i \(0.413567\pi\)
\(354\) 5.67584e31 0.778914
\(355\) 8.08414e30 0.107098
\(356\) −3.01605e30 −0.0385757
\(357\) 6.38279e31 0.788239
\(358\) 7.53518e31 0.898578
\(359\) −1.13693e32 −1.30934 −0.654671 0.755914i \(-0.727193\pi\)
−0.654671 + 0.755914i \(0.727193\pi\)
\(360\) 1.18786e31 0.132125
\(361\) 2.01551e30 0.0216544
\(362\) −8.11795e31 −0.842537
\(363\) 1.48092e32 1.48490
\(364\) −9.58011e31 −0.928118
\(365\) −7.42806e31 −0.695368
\(366\) 1.60857e32 1.45521
\(367\) −7.28071e31 −0.636572 −0.318286 0.947995i \(-0.603107\pi\)
−0.318286 + 0.947995i \(0.603107\pi\)
\(368\) 2.83455e31 0.239545
\(369\) −6.66976e31 −0.544855
\(370\) 6.55066e31 0.517325
\(371\) −2.66876e32 −2.03768
\(372\) −6.91251e31 −0.510328
\(373\) 1.71061e32 1.22121 0.610604 0.791936i \(-0.290927\pi\)
0.610604 + 0.791936i \(0.290927\pi\)
\(374\) 8.04294e31 0.555290
\(375\) −1.81480e31 −0.121182
\(376\) 6.09518e31 0.393676
\(377\) 2.06040e32 1.28731
\(378\) 2.79424e31 0.168895
\(379\) 2.81613e31 0.164688 0.0823441 0.996604i \(-0.473759\pi\)
0.0823441 + 0.996604i \(0.473759\pi\)
\(380\) 3.99422e31 0.226015
\(381\) −1.59743e32 −0.874701
\(382\) 1.45230e32 0.769597
\(383\) 9.78501e31 0.501853 0.250926 0.968006i \(-0.419265\pi\)
0.250926 + 0.968006i \(0.419265\pi\)
\(384\) −2.41228e31 −0.119753
\(385\) 1.44508e32 0.694438
\(386\) 5.31458e31 0.247245
\(387\) 8.55760e31 0.385447
\(388\) −1.17911e32 −0.514232
\(389\) −1.33194e32 −0.562489 −0.281244 0.959636i \(-0.590747\pi\)
−0.281244 + 0.959636i \(0.590747\pi\)
\(390\) −1.81305e32 −0.741484
\(391\) 1.31219e32 0.519742
\(392\) −1.38605e31 −0.0531745
\(393\) 2.06237e32 0.766408
\(394\) −2.47554e32 −0.891184
\(395\) 3.55284e31 0.123912
\(396\) −1.79007e32 −0.604895
\(397\) 5.53789e32 1.81327 0.906637 0.421912i \(-0.138641\pi\)
0.906637 + 0.421912i \(0.138641\pi\)
\(398\) −2.26071e32 −0.717310
\(399\) −4.77673e32 −1.46882
\(400\) 1.67772e31 0.0500000
\(401\) −1.52543e32 −0.440643 −0.220321 0.975427i \(-0.570711\pi\)
−0.220321 + 0.975427i \(0.570711\pi\)
\(402\) −2.31135e32 −0.647203
\(403\) 4.80295e32 1.30375
\(404\) −1.10704e32 −0.291339
\(405\) 1.99341e32 0.508639
\(406\) 2.28014e32 0.564138
\(407\) −9.87161e32 −2.36841
\(408\) −1.11671e32 −0.259830
\(409\) 6.35123e32 1.43323 0.716616 0.697468i \(-0.245690\pi\)
0.716616 + 0.697468i \(0.245690\pi\)
\(410\) −9.42027e31 −0.206189
\(411\) −3.99882e32 −0.849003
\(412\) 3.59966e32 0.741389
\(413\) −4.36427e32 −0.872039
\(414\) −2.92046e32 −0.566171
\(415\) −2.14982e32 −0.404391
\(416\) 1.67610e32 0.305938
\(417\) 6.64936e32 1.17782
\(418\) −6.01914e32 −1.03474
\(419\) −7.80832e32 −1.30281 −0.651406 0.758729i \(-0.725821\pi\)
−0.651406 + 0.758729i \(0.725821\pi\)
\(420\) −2.00640e32 −0.324939
\(421\) 3.57315e32 0.561726 0.280863 0.959748i \(-0.409379\pi\)
0.280863 + 0.959748i \(0.409379\pi\)
\(422\) 3.02305e32 0.461359
\(423\) −6.27992e32 −0.930464
\(424\) 4.66917e32 0.671686
\(425\) 7.76662e31 0.108485
\(426\) 1.69146e32 0.229426
\(427\) −1.23686e33 −1.62919
\(428\) 3.85448e31 0.0493082
\(429\) 2.73220e33 3.39466
\(430\) 1.20866e32 0.145864
\(431\) 9.85346e31 0.115511 0.0577554 0.998331i \(-0.481606\pi\)
0.0577554 + 0.998331i \(0.481606\pi\)
\(432\) −4.88870e31 −0.0556733
\(433\) −5.52126e32 −0.610857 −0.305429 0.952215i \(-0.598800\pi\)
−0.305429 + 0.952215i \(0.598800\pi\)
\(434\) 5.31517e32 0.571342
\(435\) 4.31519e32 0.450696
\(436\) 4.13153e32 0.419305
\(437\) −9.82012e32 −0.968498
\(438\) −1.55419e33 −1.48963
\(439\) 1.02785e33 0.957470 0.478735 0.877959i \(-0.341095\pi\)
0.478735 + 0.877959i \(0.341095\pi\)
\(440\) −2.52827e32 −0.228910
\(441\) 1.42806e32 0.125679
\(442\) 7.75913e32 0.663796
\(443\) −8.34580e32 −0.694099 −0.347050 0.937847i \(-0.612816\pi\)
−0.347050 + 0.937847i \(0.612816\pi\)
\(444\) 1.37061e33 1.10822
\(445\) 4.38893e31 0.0345032
\(446\) −1.32070e33 −1.00953
\(447\) 7.23145e32 0.537503
\(448\) 1.85485e32 0.134071
\(449\) −2.21599e33 −1.55772 −0.778859 0.627199i \(-0.784201\pi\)
−0.778859 + 0.627199i \(0.784201\pi\)
\(450\) −1.72857e32 −0.118176
\(451\) 1.41960e33 0.943972
\(452\) −7.91655e32 −0.512042
\(453\) 3.60092e33 2.26561
\(454\) 1.84522e33 1.12941
\(455\) 1.39409e33 0.830134
\(456\) 8.35719e32 0.484172
\(457\) −1.41006e33 −0.794847 −0.397424 0.917635i \(-0.630096\pi\)
−0.397424 + 0.917635i \(0.630096\pi\)
\(458\) 1.24480e32 0.0682780
\(459\) −2.26311e32 −0.120795
\(460\) −4.12482e32 −0.214255
\(461\) −1.02806e33 −0.519704 −0.259852 0.965648i \(-0.583674\pi\)
−0.259852 + 0.965648i \(0.583674\pi\)
\(462\) 3.02358e33 1.48764
\(463\) −5.11786e31 −0.0245090 −0.0122545 0.999925i \(-0.503901\pi\)
−0.0122545 + 0.999925i \(0.503901\pi\)
\(464\) −3.98924e32 −0.185958
\(465\) 1.00590e33 0.456451
\(466\) 4.24802e32 0.187656
\(467\) −1.60375e33 −0.689723 −0.344861 0.938654i \(-0.612074\pi\)
−0.344861 + 0.938654i \(0.612074\pi\)
\(468\) −1.72690e33 −0.723094
\(469\) 1.77725e33 0.724581
\(470\) −8.86966e32 −0.352114
\(471\) −6.23042e33 −2.40855
\(472\) 7.63557e32 0.287453
\(473\) −1.82141e33 −0.667795
\(474\) 7.43368e32 0.265445
\(475\) −5.81235e32 −0.202154
\(476\) 8.58662e32 0.290894
\(477\) −4.81069e33 −1.58755
\(478\) −3.67196e33 −1.18046
\(479\) 2.94257e33 0.921580 0.460790 0.887509i \(-0.347566\pi\)
0.460790 + 0.887509i \(0.347566\pi\)
\(480\) 3.51033e32 0.107111
\(481\) −9.52326e33 −2.83121
\(482\) −6.83371e32 −0.197956
\(483\) 4.93291e33 1.39240
\(484\) 1.99224e33 0.547993
\(485\) 1.71584e33 0.459943
\(486\) 3.56810e33 0.932145
\(487\) −7.02175e32 −0.178786 −0.0893929 0.995996i \(-0.528493\pi\)
−0.0893929 + 0.995996i \(0.528493\pi\)
\(488\) 2.16397e33 0.537035
\(489\) 1.22048e32 0.0295236
\(490\) 2.01697e32 0.0475607
\(491\) −5.67432e33 −1.30435 −0.652176 0.758067i \(-0.726144\pi\)
−0.652176 + 0.758067i \(0.726144\pi\)
\(492\) −1.97102e33 −0.441701
\(493\) −1.84673e33 −0.403475
\(494\) −5.80674e33 −1.23693
\(495\) 2.60489e33 0.541034
\(496\) −9.29924e32 −0.188333
\(497\) −1.30060e33 −0.256856
\(498\) −4.49812e33 −0.866291
\(499\) 2.29378e33 0.430818 0.215409 0.976524i \(-0.430891\pi\)
0.215409 + 0.976524i \(0.430891\pi\)
\(500\) −2.44141e32 −0.0447214
\(501\) 1.09743e34 1.96068
\(502\) 7.28961e31 0.0127031
\(503\) 5.06724e32 0.0861334 0.0430667 0.999072i \(-0.486287\pi\)
0.0430667 + 0.999072i \(0.486287\pi\)
\(504\) −1.91107e33 −0.316880
\(505\) 1.61096e33 0.260581
\(506\) 6.21595e33 0.980903
\(507\) 1.75577e34 2.70313
\(508\) −2.14898e33 −0.322802
\(509\) 5.67895e33 0.832330 0.416165 0.909289i \(-0.363374\pi\)
0.416165 + 0.909289i \(0.363374\pi\)
\(510\) 1.62503e33 0.232399
\(511\) 1.19505e34 1.66772
\(512\) −3.24519e32 −0.0441942
\(513\) 1.69366e33 0.225091
\(514\) −4.18419e33 −0.542715
\(515\) −5.23819e33 −0.663119
\(516\) 2.52891e33 0.312473
\(517\) 1.33663e34 1.61205
\(518\) −1.05389e34 −1.24072
\(519\) −1.85716e34 −2.13431
\(520\) −2.43905e33 −0.273640
\(521\) −9.13970e33 −1.00106 −0.500530 0.865719i \(-0.666862\pi\)
−0.500530 + 0.865719i \(0.666862\pi\)
\(522\) 4.11015e33 0.439518
\(523\) 3.76955e33 0.393566 0.196783 0.980447i \(-0.436950\pi\)
0.196783 + 0.980447i \(0.436950\pi\)
\(524\) 2.77446e33 0.282838
\(525\) 2.91970e33 0.290635
\(526\) 9.80226e33 0.952806
\(527\) −4.30487e33 −0.408627
\(528\) −5.28995e33 −0.490374
\(529\) −9.04558e32 −0.0818918
\(530\) −6.79454e33 −0.600775
\(531\) −7.86699e33 −0.679403
\(532\) −6.42602e33 −0.542059
\(533\) 1.36951e34 1.12843
\(534\) 9.18306e32 0.0739132
\(535\) −5.60901e32 −0.0441026
\(536\) −3.10941e33 −0.238846
\(537\) −2.29426e34 −1.72172
\(538\) −3.04729e33 −0.223427
\(539\) −3.03950e33 −0.217742
\(540\) 7.11400e32 0.0497957
\(541\) −1.11229e34 −0.760770 −0.380385 0.924828i \(-0.624209\pi\)
−0.380385 + 0.924828i \(0.624209\pi\)
\(542\) 1.18561e34 0.792411
\(543\) 2.47170e34 1.61435
\(544\) −1.50228e33 −0.0958883
\(545\) −6.01217e33 −0.375038
\(546\) 2.91689e34 1.77833
\(547\) 1.75655e34 1.04669 0.523346 0.852120i \(-0.324683\pi\)
0.523346 + 0.852120i \(0.324683\pi\)
\(548\) −5.37952e33 −0.313319
\(549\) −2.22955e34 −1.26930
\(550\) 3.67911e33 0.204743
\(551\) 1.38205e34 0.751844
\(552\) −8.63045e33 −0.458981
\(553\) −5.71591e33 −0.297181
\(554\) 1.00773e34 0.512239
\(555\) −1.99450e34 −0.991223
\(556\) 8.94522e33 0.434666
\(557\) 3.64954e33 0.173400 0.0866999 0.996234i \(-0.472368\pi\)
0.0866999 + 0.996234i \(0.472368\pi\)
\(558\) 9.58108e33 0.445130
\(559\) −1.75714e34 −0.798285
\(560\) −2.69917e33 −0.119917
\(561\) −2.44886e34 −1.06397
\(562\) −2.22008e34 −0.943334
\(563\) 4.06393e34 1.68885 0.844426 0.535672i \(-0.179942\pi\)
0.844426 + 0.535672i \(0.179942\pi\)
\(564\) −1.85582e34 −0.754305
\(565\) 1.15201e34 0.457984
\(566\) −2.58360e34 −1.00466
\(567\) −3.20706e34 −1.21988
\(568\) 2.27548e33 0.0846680
\(569\) 1.05009e34 0.382228 0.191114 0.981568i \(-0.438790\pi\)
0.191114 + 0.981568i \(0.438790\pi\)
\(570\) −1.21613e34 −0.433057
\(571\) −3.85212e34 −1.34199 −0.670994 0.741463i \(-0.734132\pi\)
−0.670994 + 0.741463i \(0.734132\pi\)
\(572\) 3.67556e34 1.25277
\(573\) −4.42185e34 −1.47459
\(574\) 1.51556e34 0.494509
\(575\) 6.00240e33 0.191636
\(576\) 3.34354e33 0.104454
\(577\) −5.52922e34 −1.69031 −0.845154 0.534522i \(-0.820492\pi\)
−0.845154 + 0.534522i \(0.820492\pi\)
\(578\) 1.66820e34 0.499057
\(579\) −1.61814e34 −0.473735
\(580\) 5.80511e33 0.166326
\(581\) 3.45869e34 0.969863
\(582\) 3.59008e34 0.985296
\(583\) 1.02391e35 2.75046
\(584\) −2.09081e34 −0.549736
\(585\) 2.51297e34 0.646755
\(586\) −4.01115e34 −1.01053
\(587\) −3.59799e34 −0.887326 −0.443663 0.896194i \(-0.646321\pi\)
−0.443663 + 0.896194i \(0.646321\pi\)
\(588\) 4.22015e33 0.101885
\(589\) 3.22166e34 0.761445
\(590\) −1.11112e34 −0.257106
\(591\) 7.53735e34 1.70756
\(592\) 1.84385e34 0.408981
\(593\) 6.31486e33 0.137145 0.0685725 0.997646i \(-0.478156\pi\)
0.0685725 + 0.997646i \(0.478156\pi\)
\(594\) −1.07205e34 −0.227974
\(595\) −1.24952e34 −0.260184
\(596\) 9.72829e33 0.198362
\(597\) 6.88325e34 1.37440
\(598\) 5.99661e34 1.17258
\(599\) −5.02848e34 −0.962945 −0.481472 0.876461i \(-0.659898\pi\)
−0.481472 + 0.876461i \(0.659898\pi\)
\(600\) −5.10821e33 −0.0958027
\(601\) −4.57441e34 −0.840241 −0.420120 0.907468i \(-0.638012\pi\)
−0.420120 + 0.907468i \(0.638012\pi\)
\(602\) −1.94453e34 −0.349831
\(603\) 3.20365e34 0.564519
\(604\) 4.84423e34 0.836109
\(605\) −2.89909e34 −0.490140
\(606\) 3.37065e34 0.558221
\(607\) −2.94626e34 −0.477983 −0.238991 0.971022i \(-0.576817\pi\)
−0.238991 + 0.971022i \(0.576817\pi\)
\(608\) 1.12427e34 0.178680
\(609\) −6.94240e34 −1.08092
\(610\) −3.14899e34 −0.480339
\(611\) 1.28946e35 1.92705
\(612\) 1.54782e34 0.226635
\(613\) −1.15985e35 −1.66398 −0.831989 0.554792i \(-0.812798\pi\)
−0.831989 + 0.554792i \(0.812798\pi\)
\(614\) 2.35763e34 0.331414
\(615\) 2.86822e34 0.395069
\(616\) 4.06755e34 0.549002
\(617\) −5.88912e34 −0.778907 −0.389454 0.921046i \(-0.627336\pi\)
−0.389454 + 0.921046i \(0.627336\pi\)
\(618\) −1.09600e35 −1.42054
\(619\) 6.29583e34 0.799687 0.399844 0.916583i \(-0.369064\pi\)
0.399844 + 0.916583i \(0.369064\pi\)
\(620\) 1.35322e34 0.168450
\(621\) −1.74904e34 −0.213380
\(622\) −7.57566e34 −0.905817
\(623\) −7.06104e33 −0.0827501
\(624\) −5.10328e34 −0.586195
\(625\) 3.55271e33 0.0400000
\(626\) −9.80174e34 −1.08174
\(627\) 1.83267e35 1.98262
\(628\) −8.38163e34 −0.888859
\(629\) 8.53566e34 0.887369
\(630\) 2.78098e34 0.283426
\(631\) −5.00486e33 −0.0500063 −0.0250032 0.999687i \(-0.507960\pi\)
−0.0250032 + 0.999687i \(0.507960\pi\)
\(632\) 1.00003e34 0.0979607
\(633\) −9.20436e34 −0.883989
\(634\) 8.36242e33 0.0787438
\(635\) 3.12718e34 0.288723
\(636\) −1.42164e35 −1.28699
\(637\) −2.93225e34 −0.260290
\(638\) −8.74810e34 −0.761474
\(639\) −2.34445e34 −0.200115
\(640\) 4.72237e33 0.0395285
\(641\) 2.47946e34 0.203532 0.101766 0.994808i \(-0.467551\pi\)
0.101766 + 0.994808i \(0.467551\pi\)
\(642\) −1.17359e34 −0.0944772
\(643\) −1.87298e35 −1.47875 −0.739376 0.673293i \(-0.764879\pi\)
−0.739376 + 0.673293i \(0.764879\pi\)
\(644\) 6.63613e34 0.513856
\(645\) −3.68005e34 −0.279484
\(646\) 5.20456e34 0.387684
\(647\) 1.37605e35 1.00538 0.502692 0.864465i \(-0.332343\pi\)
0.502692 + 0.864465i \(0.332343\pi\)
\(648\) 5.61096e34 0.402114
\(649\) 1.67442e35 1.17708
\(650\) 3.54928e34 0.244751
\(651\) −1.61833e35 −1.09472
\(652\) 1.64188e33 0.0108955
\(653\) −1.43663e35 −0.935256 −0.467628 0.883925i \(-0.654891\pi\)
−0.467628 + 0.883925i \(0.654891\pi\)
\(654\) −1.25794e35 −0.803412
\(655\) −4.03737e34 −0.252978
\(656\) −2.65157e34 −0.163007
\(657\) 2.15418e35 1.29932
\(658\) 1.42698e35 0.844488
\(659\) −1.67433e35 −0.972238 −0.486119 0.873893i \(-0.661588\pi\)
−0.486119 + 0.873893i \(0.661588\pi\)
\(660\) 7.69788e34 0.438604
\(661\) −8.14435e34 −0.455342 −0.227671 0.973738i \(-0.573111\pi\)
−0.227671 + 0.973738i \(0.573111\pi\)
\(662\) 7.18494e34 0.394183
\(663\) −2.36244e35 −1.27187
\(664\) −6.05121e34 −0.319699
\(665\) 9.35109e34 0.484832
\(666\) −1.89973e35 −0.966639
\(667\) −1.42724e35 −0.712726
\(668\) 1.47635e35 0.723576
\(669\) 4.02118e35 1.93432
\(670\) 4.52478e34 0.213630
\(671\) 4.74541e35 2.19909
\(672\) −5.64753e34 −0.256887
\(673\) 2.14831e35 0.959198 0.479599 0.877488i \(-0.340782\pi\)
0.479599 + 0.877488i \(0.340782\pi\)
\(674\) 3.00300e35 1.31615
\(675\) −1.03522e34 −0.0445386
\(676\) 2.36199e35 0.997572
\(677\) −1.65762e35 −0.687268 −0.343634 0.939104i \(-0.611658\pi\)
−0.343634 + 0.939104i \(0.611658\pi\)
\(678\) 2.41038e35 0.981100
\(679\) −2.76049e35 −1.10310
\(680\) 2.18611e34 0.0857651
\(681\) −5.61820e35 −2.16401
\(682\) −2.03925e35 −0.771197
\(683\) 4.25978e35 1.58172 0.790858 0.612000i \(-0.209635\pi\)
0.790858 + 0.612000i \(0.209635\pi\)
\(684\) −1.15835e35 −0.422316
\(685\) 7.82823e34 0.280241
\(686\) 1.83305e35 0.644353
\(687\) −3.79007e34 −0.130824
\(688\) 3.40208e34 0.115316
\(689\) 9.87781e35 3.28791
\(690\) 1.25590e35 0.410525
\(691\) −3.56127e35 −1.14322 −0.571609 0.820526i \(-0.693681\pi\)
−0.571609 + 0.820526i \(0.693681\pi\)
\(692\) −2.49839e35 −0.787651
\(693\) −4.19083e35 −1.29758
\(694\) 6.33656e34 0.192690
\(695\) −1.30170e35 −0.388777
\(696\) 1.21462e35 0.356307
\(697\) −1.22748e35 −0.353676
\(698\) 4.69172e34 0.132782
\(699\) −1.29341e35 −0.359559
\(700\) 3.92781e34 0.107257
\(701\) −6.93164e34 −0.185935 −0.0929674 0.995669i \(-0.529635\pi\)
−0.0929674 + 0.995669i \(0.529635\pi\)
\(702\) −1.03422e35 −0.272521
\(703\) −6.38788e35 −1.65354
\(704\) −7.11643e34 −0.180969
\(705\) 2.70057e35 0.674671
\(706\) −1.54545e35 −0.379311
\(707\) −2.59176e35 −0.624961
\(708\) −2.32482e35 −0.550775
\(709\) −1.75968e34 −0.0409596 −0.0204798 0.999790i \(-0.506519\pi\)
−0.0204798 + 0.999790i \(0.506519\pi\)
\(710\) −3.31126e34 −0.0757294
\(711\) −1.03034e35 −0.231533
\(712\) 1.23538e34 0.0272771
\(713\) −3.32700e35 −0.721827
\(714\) −2.61439e35 −0.557369
\(715\) −5.34864e35 −1.12052
\(716\) −3.08641e35 −0.635390
\(717\) 1.11801e36 2.26182
\(718\) 4.65687e35 0.925845
\(719\) −3.47246e35 −0.678462 −0.339231 0.940703i \(-0.610167\pi\)
−0.339231 + 0.940703i \(0.610167\pi\)
\(720\) −4.86549e34 −0.0934266
\(721\) 8.42736e35 1.59038
\(722\) −8.25554e33 −0.0153120
\(723\) 2.08068e35 0.379294
\(724\) 3.32511e35 0.595764
\(725\) −8.44755e34 −0.148767
\(726\) −6.06584e35 −1.04998
\(727\) −4.86443e35 −0.827660 −0.413830 0.910354i \(-0.635809\pi\)
−0.413830 + 0.910354i \(0.635809\pi\)
\(728\) 3.92401e35 0.656279
\(729\) −3.94577e35 −0.648691
\(730\) 3.04253e35 0.491699
\(731\) 1.57491e35 0.250201
\(732\) −6.58869e35 −1.02899
\(733\) −1.02677e36 −1.57643 −0.788216 0.615398i \(-0.788995\pi\)
−0.788216 + 0.615398i \(0.788995\pi\)
\(734\) 2.98218e35 0.450125
\(735\) −6.14113e34 −0.0911290
\(736\) −1.16103e35 −0.169384
\(737\) −6.81868e35 −0.978040
\(738\) 2.73194e35 0.385271
\(739\) 5.26186e35 0.729599 0.364799 0.931086i \(-0.381138\pi\)
0.364799 + 0.931086i \(0.381138\pi\)
\(740\) −2.68315e35 −0.365804
\(741\) 1.76800e36 2.37003
\(742\) 1.09313e36 1.44086
\(743\) 6.09530e35 0.790014 0.395007 0.918678i \(-0.370742\pi\)
0.395007 + 0.918678i \(0.370742\pi\)
\(744\) 2.83137e35 0.360856
\(745\) −1.41565e35 −0.177420
\(746\) −7.00664e35 −0.863525
\(747\) 6.23461e35 0.755617
\(748\) −3.29439e35 −0.392649
\(749\) 9.02394e34 0.105773
\(750\) 7.43342e34 0.0856886
\(751\) 1.00495e36 1.13932 0.569660 0.821881i \(-0.307075\pi\)
0.569660 + 0.821881i \(0.307075\pi\)
\(752\) −2.49659e35 −0.278371
\(753\) −2.21949e34 −0.0243397
\(754\) −8.43940e35 −0.910269
\(755\) −7.04928e35 −0.747838
\(756\) −1.14452e35 −0.119427
\(757\) −8.28193e35 −0.850028 −0.425014 0.905187i \(-0.639731\pi\)
−0.425014 + 0.905187i \(0.639731\pi\)
\(758\) −1.15349e35 −0.116452
\(759\) −1.89259e36 −1.87946
\(760\) −1.63603e35 −0.159817
\(761\) −1.30553e35 −0.125452 −0.0627261 0.998031i \(-0.519979\pi\)
−0.0627261 + 0.998031i \(0.519979\pi\)
\(762\) 6.54308e35 0.618507
\(763\) 9.67256e35 0.899466
\(764\) −5.94861e35 −0.544187
\(765\) −2.25237e35 −0.202708
\(766\) −4.00794e35 −0.354864
\(767\) 1.61533e36 1.40709
\(768\) 9.88071e34 0.0846785
\(769\) −7.86348e34 −0.0663033 −0.0331517 0.999450i \(-0.510554\pi\)
−0.0331517 + 0.999450i \(0.510554\pi\)
\(770\) −5.91906e35 −0.491042
\(771\) 1.27397e36 1.03987
\(772\) −2.17685e35 −0.174829
\(773\) 3.60085e35 0.284552 0.142276 0.989827i \(-0.454558\pi\)
0.142276 + 0.989827i \(0.454558\pi\)
\(774\) −3.50519e35 −0.272552
\(775\) −1.96919e35 −0.150666
\(776\) 4.82965e35 0.363617
\(777\) 3.20881e36 2.37728
\(778\) 5.45562e35 0.397740
\(779\) 9.18619e35 0.659048
\(780\) 7.42625e35 0.524308
\(781\) 4.98996e35 0.346704
\(782\) −5.37473e35 −0.367513
\(783\) 2.46153e35 0.165647
\(784\) 5.67727e34 0.0376001
\(785\) 1.21969e36 0.795020
\(786\) −8.44747e35 −0.541932
\(787\) −1.70122e36 −1.07418 −0.537089 0.843526i \(-0.680476\pi\)
−0.537089 + 0.843526i \(0.680476\pi\)
\(788\) 1.01398e36 0.630162
\(789\) −2.98452e36 −1.82563
\(790\) −1.45524e35 −0.0876187
\(791\) −1.85339e36 −1.09840
\(792\) 7.33212e35 0.427725
\(793\) 4.57796e36 2.62880
\(794\) −2.26832e36 −1.28218
\(795\) 2.06875e36 1.15112
\(796\) 9.25987e35 0.507215
\(797\) −3.28276e36 −1.77015 −0.885075 0.465449i \(-0.845893\pi\)
−0.885075 + 0.465449i \(0.845893\pi\)
\(798\) 1.95655e36 1.03861
\(799\) −1.15574e36 −0.603983
\(800\) −6.87195e34 −0.0353553
\(801\) −1.27282e35 −0.0644703
\(802\) 6.24815e35 0.311581
\(803\) −4.58498e36 −2.25109
\(804\) 9.46730e35 0.457642
\(805\) −9.65684e35 −0.459607
\(806\) −1.96729e36 −0.921892
\(807\) 9.27816e35 0.428098
\(808\) 4.53446e35 0.206008
\(809\) −1.22121e36 −0.546303 −0.273152 0.961971i \(-0.588066\pi\)
−0.273152 + 0.961971i \(0.588066\pi\)
\(810\) −8.16501e35 −0.359662
\(811\) −2.29432e36 −0.995160 −0.497580 0.867418i \(-0.665778\pi\)
−0.497580 + 0.867418i \(0.665778\pi\)
\(812\) −9.33944e35 −0.398906
\(813\) −3.60986e36 −1.51830
\(814\) 4.04341e36 1.67472
\(815\) −2.38925e34 −0.00974521
\(816\) 4.57405e35 0.183727
\(817\) −1.17863e36 −0.466231
\(818\) −2.60147e36 −1.01345
\(819\) −4.04295e36 −1.55113
\(820\) 3.85854e35 0.145798
\(821\) 1.68233e36 0.626067 0.313033 0.949742i \(-0.398655\pi\)
0.313033 + 0.949742i \(0.398655\pi\)
\(822\) 1.63792e36 0.600336
\(823\) 3.28620e36 1.18630 0.593152 0.805091i \(-0.297883\pi\)
0.593152 + 0.805091i \(0.297883\pi\)
\(824\) −1.47442e36 −0.524241
\(825\) −1.12019e36 −0.392299
\(826\) 1.78761e36 0.616625
\(827\) −1.84899e36 −0.628225 −0.314112 0.949386i \(-0.601707\pi\)
−0.314112 + 0.949386i \(0.601707\pi\)
\(828\) 1.19622e36 0.400343
\(829\) 6.47231e35 0.213367 0.106684 0.994293i \(-0.465977\pi\)
0.106684 + 0.994293i \(0.465977\pi\)
\(830\) 8.80567e35 0.285947
\(831\) −3.06827e36 −0.981478
\(832\) −6.86531e35 −0.216331
\(833\) 2.62816e35 0.0815811
\(834\) −2.72358e36 −0.832845
\(835\) −2.14837e36 −0.647186
\(836\) 2.46544e36 0.731672
\(837\) 5.73801e35 0.167762
\(838\) 3.19829e36 0.921228
\(839\) 3.82378e36 1.08510 0.542549 0.840024i \(-0.317459\pi\)
0.542549 + 0.840024i \(0.317459\pi\)
\(840\) 8.21823e35 0.229767
\(841\) −1.62172e36 −0.446711
\(842\) −1.46356e36 −0.397200
\(843\) 6.75956e36 1.80748
\(844\) −1.23824e36 −0.326230
\(845\) −3.43715e36 −0.892255
\(846\) 2.57226e36 0.657937
\(847\) 4.66415e36 1.17552
\(848\) −1.91249e36 −0.474954
\(849\) 7.86635e36 1.92499
\(850\) −3.18121e35 −0.0767107
\(851\) 6.59675e36 1.56751
\(852\) −6.92823e35 −0.162229
\(853\) 2.67006e36 0.616110 0.308055 0.951369i \(-0.400322\pi\)
0.308055 + 0.951369i \(0.400322\pi\)
\(854\) 5.06618e36 1.15201
\(855\) 1.68562e36 0.377731
\(856\) −1.57880e35 −0.0348661
\(857\) 5.29681e36 1.15280 0.576400 0.817167i \(-0.304457\pi\)
0.576400 + 0.817167i \(0.304457\pi\)
\(858\) −1.11911e37 −2.40039
\(859\) 9.48590e35 0.200523 0.100261 0.994961i \(-0.468032\pi\)
0.100261 + 0.994961i \(0.468032\pi\)
\(860\) −4.95068e35 −0.103142
\(861\) −4.61447e36 −0.947507
\(862\) −4.03598e35 −0.0816785
\(863\) −6.15179e36 −1.22706 −0.613532 0.789670i \(-0.710252\pi\)
−0.613532 + 0.789670i \(0.710252\pi\)
\(864\) 2.00241e35 0.0393669
\(865\) 3.63563e36 0.704496
\(866\) 2.26151e36 0.431941
\(867\) −5.07922e36 −0.956221
\(868\) −2.17709e36 −0.403999
\(869\) 2.19300e36 0.401135
\(870\) −1.76750e36 −0.318690
\(871\) −6.57807e36 −1.16915
\(872\) −1.69228e36 −0.296494
\(873\) −4.97603e36 −0.859418
\(874\) 4.02232e36 0.684832
\(875\) −5.71571e35 −0.0959333
\(876\) 6.36596e36 1.05332
\(877\) 7.20268e35 0.117490 0.0587448 0.998273i \(-0.481290\pi\)
0.0587448 + 0.998273i \(0.481290\pi\)
\(878\) −4.21009e36 −0.677034
\(879\) 1.22129e37 1.93623
\(880\) 1.03558e36 0.161864
\(881\) −6.22632e36 −0.959472 −0.479736 0.877413i \(-0.659268\pi\)
−0.479736 + 0.877413i \(0.659268\pi\)
\(882\) −5.84934e35 −0.0888688
\(883\) −7.42861e36 −1.11275 −0.556376 0.830930i \(-0.687809\pi\)
−0.556376 + 0.830930i \(0.687809\pi\)
\(884\) −3.17814e36 −0.469375
\(885\) 3.38307e36 0.492628
\(886\) 3.41844e36 0.490802
\(887\) 2.96498e36 0.419736 0.209868 0.977730i \(-0.432697\pi\)
0.209868 + 0.977730i \(0.432697\pi\)
\(888\) −5.61401e36 −0.783631
\(889\) −5.03110e36 −0.692455
\(890\) −1.79771e35 −0.0243974
\(891\) 1.23044e37 1.64660
\(892\) 5.40960e36 0.713846
\(893\) 8.64926e36 1.12547
\(894\) −2.96200e36 −0.380072
\(895\) 4.49132e36 0.568310
\(896\) −7.59748e35 −0.0948024
\(897\) −1.82580e37 −2.24672
\(898\) 9.07670e36 1.10147
\(899\) 4.68229e36 0.560354
\(900\) 7.08023e35 0.0835633
\(901\) −8.85344e36 −1.03051
\(902\) −5.81468e36 −0.667489
\(903\) 5.92057e36 0.670296
\(904\) 3.24262e36 0.362068
\(905\) −4.83868e36 −0.532867
\(906\) −1.47494e37 −1.60203
\(907\) −7.50976e36 −0.804516 −0.402258 0.915526i \(-0.631775\pi\)
−0.402258 + 0.915526i \(0.631775\pi\)
\(908\) −7.55803e36 −0.798611
\(909\) −4.67189e36 −0.486905
\(910\) −5.71019e36 −0.586994
\(911\) −9.29828e36 −0.942807 −0.471404 0.881918i \(-0.656252\pi\)
−0.471404 + 0.881918i \(0.656252\pi\)
\(912\) −3.42311e36 −0.342362
\(913\) −1.32698e37 −1.30912
\(914\) 5.77559e36 0.562042
\(915\) 9.58781e36 0.920356
\(916\) −5.09869e35 −0.0482798
\(917\) 6.49544e36 0.606725
\(918\) 9.26971e35 0.0854147
\(919\) 7.54098e36 0.685463 0.342731 0.939433i \(-0.388648\pi\)
0.342731 + 0.939433i \(0.388648\pi\)
\(920\) 1.68953e36 0.151502
\(921\) −7.17835e36 −0.635008
\(922\) 4.21093e36 0.367486
\(923\) 4.81387e36 0.414451
\(924\) −1.23846e37 −1.05192
\(925\) 3.90450e36 0.327185
\(926\) 2.09627e35 0.0173305
\(927\) 1.51911e37 1.23906
\(928\) 1.63399e36 0.131492
\(929\) −7.02005e36 −0.557370 −0.278685 0.960383i \(-0.589899\pi\)
−0.278685 + 0.960383i \(0.589899\pi\)
\(930\) −4.12018e36 −0.322760
\(931\) −1.96685e36 −0.152020
\(932\) −1.73999e36 −0.132693
\(933\) 2.30658e37 1.73560
\(934\) 6.56894e36 0.487708
\(935\) 4.79397e36 0.351196
\(936\) 7.07339e36 0.511304
\(937\) −1.69888e37 −1.21176 −0.605881 0.795555i \(-0.707179\pi\)
−0.605881 + 0.795555i \(0.707179\pi\)
\(938\) −7.27960e36 −0.512356
\(939\) 2.98437e37 2.07268
\(940\) 3.63301e36 0.248982
\(941\) −1.18390e36 −0.0800651 −0.0400325 0.999198i \(-0.512746\pi\)
−0.0400325 + 0.999198i \(0.512746\pi\)
\(942\) 2.55198e37 1.70310
\(943\) −9.48655e36 −0.624758
\(944\) −3.12753e36 −0.203260
\(945\) 1.66550e36 0.106818
\(946\) 7.46049e36 0.472202
\(947\) −3.22631e36 −0.201526 −0.100763 0.994910i \(-0.532128\pi\)
−0.100763 + 0.994910i \(0.532128\pi\)
\(948\) −3.04484e36 −0.187698
\(949\) −4.42319e37 −2.69097
\(950\) 2.38074e36 0.142944
\(951\) −2.54613e36 −0.150877
\(952\) −3.51708e36 −0.205693
\(953\) 1.29808e37 0.749271 0.374635 0.927172i \(-0.377768\pi\)
0.374635 + 0.927172i \(0.377768\pi\)
\(954\) 1.97046e37 1.12257
\(955\) 8.65636e36 0.486736
\(956\) 1.50404e37 0.834708
\(957\) 2.66356e37 1.45903
\(958\) −1.20528e37 −0.651656
\(959\) −1.25943e37 −0.672110
\(960\) −1.43783e36 −0.0757387
\(961\) −8.31801e36 −0.432491
\(962\) 3.90073e37 2.00197
\(963\) 1.62665e36 0.0824071
\(964\) 2.79909e36 0.139976
\(965\) 3.16773e36 0.156371
\(966\) −2.02052e37 −0.984576
\(967\) −2.88610e37 −1.38829 −0.694146 0.719834i \(-0.744218\pi\)
−0.694146 + 0.719834i \(0.744218\pi\)
\(968\) −8.16022e36 −0.387490
\(969\) −1.58465e37 −0.742824
\(970\) −7.02806e36 −0.325229
\(971\) 1.13134e36 0.0516836 0.0258418 0.999666i \(-0.491773\pi\)
0.0258418 + 0.999666i \(0.491773\pi\)
\(972\) −1.46149e37 −0.659126
\(973\) 2.09421e37 0.932418
\(974\) 2.87611e36 0.126421
\(975\) −1.08066e37 −0.468956
\(976\) −8.86361e36 −0.379741
\(977\) 1.01024e37 0.427311 0.213655 0.976909i \(-0.431463\pi\)
0.213655 + 0.976909i \(0.431463\pi\)
\(978\) −4.99908e35 −0.0208763
\(979\) 2.70908e36 0.111696
\(980\) −8.26151e35 −0.0336305
\(981\) 1.74357e37 0.700771
\(982\) 2.32420e37 0.922316
\(983\) −3.32494e37 −1.30276 −0.651380 0.758752i \(-0.725810\pi\)
−0.651380 + 0.758752i \(0.725810\pi\)
\(984\) 8.07331e36 0.312330
\(985\) −1.47554e37 −0.563634
\(986\) 7.56420e36 0.285300
\(987\) −4.34476e37 −1.61808
\(988\) 2.37844e37 0.874643
\(989\) 1.21717e37 0.441973
\(990\) −1.06696e37 −0.382569
\(991\) 2.31893e37 0.821044 0.410522 0.911851i \(-0.365347\pi\)
0.410522 + 0.911851i \(0.365347\pi\)
\(992\) 3.80897e36 0.133172
\(993\) −2.18762e37 −0.755277
\(994\) 5.32726e36 0.181624
\(995\) −1.34749e37 −0.453666
\(996\) 1.84243e37 0.612561
\(997\) 6.52365e36 0.214191 0.107096 0.994249i \(-0.465845\pi\)
0.107096 + 0.994249i \(0.465845\pi\)
\(998\) −9.39530e36 −0.304634
\(999\) −1.13773e37 −0.364309
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 10.26.a.c.1.2 2
5.2 odd 4 50.26.b.c.49.1 4
5.3 odd 4 50.26.b.c.49.4 4
5.4 even 2 50.26.a.e.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.26.a.c.1.2 2 1.1 even 1 trivial
50.26.a.e.1.1 2 5.4 even 2
50.26.b.c.49.1 4 5.2 odd 4
50.26.b.c.49.4 4 5.3 odd 4