Properties

Label 10.26.a.b.1.1
Level $10$
Weight $26$
Character 10.1
Self dual yes
Analytic conductor $39.600$
Analytic rank $0$
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: \(0\)
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: \( x^{2} - x - 6900880 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3}\cdot 5 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2627.45\) 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)
 
\(f(q)\) \(=\) \(q-4096.00 q^{2} -1.63785e6 q^{3} +1.67772e7 q^{4} +2.44141e8 q^{5} +6.70863e9 q^{6} -2.07876e10 q^{7} -6.87195e10 q^{8} +1.83526e12 q^{9} -1.00000e12 q^{10} +4.14605e12 q^{11} -2.74785e13 q^{12} -1.30955e14 q^{13} +8.51459e13 q^{14} -3.99865e14 q^{15} +2.81475e14 q^{16} -4.62477e15 q^{17} -7.51722e15 q^{18} -5.62727e15 q^{19} +4.09600e15 q^{20} +3.40469e16 q^{21} -1.69822e16 q^{22} -2.45654e16 q^{23} +1.12552e17 q^{24} +5.96046e16 q^{25} +5.36390e17 q^{26} -1.61815e18 q^{27} -3.48758e17 q^{28} -1.86225e18 q^{29} +1.63785e18 q^{30} +7.10276e17 q^{31} -1.15292e18 q^{32} -6.79060e18 q^{33} +1.89431e19 q^{34} -5.07509e18 q^{35} +3.07905e19 q^{36} +5.29105e19 q^{37} +2.30493e19 q^{38} +2.14484e20 q^{39} -1.67772e19 q^{40} -2.57715e20 q^{41} -1.39456e20 q^{42} -1.94678e19 q^{43} +6.95591e19 q^{44} +4.48061e20 q^{45} +1.00620e20 q^{46} +1.05479e21 q^{47} -4.61013e20 q^{48} -9.08945e20 q^{49} -2.44141e20 q^{50} +7.57467e21 q^{51} -2.19705e21 q^{52} +1.71922e21 q^{53} +6.62792e21 q^{54} +1.01222e21 q^{55} +1.42851e21 q^{56} +9.21661e21 q^{57} +7.62780e21 q^{58} -2.29629e22 q^{59} -6.70863e21 q^{60} -9.00207e20 q^{61} -2.90929e21 q^{62} -3.81506e22 q^{63} +4.72237e21 q^{64} -3.19713e22 q^{65} +2.78143e22 q^{66} -1.50272e22 q^{67} -7.75908e22 q^{68} +4.02345e22 q^{69} +2.07876e22 q^{70} +2.23447e23 q^{71} -1.26118e23 q^{72} -3.25252e23 q^{73} -2.16721e23 q^{74} -9.76234e22 q^{75} -9.44099e22 q^{76} -8.61863e22 q^{77} -8.78525e23 q^{78} +6.06979e23 q^{79} +6.87195e22 q^{80} +1.09528e24 q^{81} +1.05560e24 q^{82} -7.26128e23 q^{83} +5.71212e23 q^{84} -1.12909e24 q^{85} +7.97403e22 q^{86} +3.05009e24 q^{87} -2.84914e23 q^{88} +1.91182e24 q^{89} -1.83526e24 q^{90} +2.72223e24 q^{91} -4.12140e23 q^{92} -1.16332e24 q^{93} -4.32043e24 q^{94} -1.37384e24 q^{95} +1.88831e24 q^{96} -1.71656e24 q^{97} +3.72304e24 q^{98} +7.60907e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8192 q^{2} - 438588 q^{3} + 33554432 q^{4} + 488281250 q^{5} + 1796456448 q^{6} - 34008596636 q^{7} - 137438953472 q^{8} + 2426195859786 q^{9} - 2000000000000 q^{10} + 19344682791984 q^{11} - 7358285611008 q^{12}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) \) 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
\(3\) −1.63785e6 −1.77934 −0.889668 0.456608i \(-0.849064\pi\)
−0.889668 + 0.456608i \(0.849064\pi\)
\(4\) 1.67772e7 0.500000
\(5\) 2.44141e8 0.447214
\(6\) 6.70863e9 1.25818
\(7\) −2.07876e10 −0.567647 −0.283824 0.958877i \(-0.591603\pi\)
−0.283824 + 0.958877i \(0.591603\pi\)
\(8\) −6.87195e10 −0.353553
\(9\) 1.83526e12 2.16604
\(10\) −1.00000e12 −0.316228
\(11\) 4.14605e12 0.398314 0.199157 0.979968i \(-0.436180\pi\)
0.199157 + 0.979968i \(0.436180\pi\)
\(12\) −2.74785e13 −0.889668
\(13\) −1.30955e14 −1.55894 −0.779469 0.626441i \(-0.784511\pi\)
−0.779469 + 0.626441i \(0.784511\pi\)
\(14\) 8.51459e13 0.401387
\(15\) −3.99865e14 −0.795743
\(16\) 2.81475e14 0.250000
\(17\) −4.62477e15 −1.92521 −0.962606 0.270904i \(-0.912677\pi\)
−0.962606 + 0.270904i \(0.912677\pi\)
\(18\) −7.51722e15 −1.53162
\(19\) −5.62727e15 −0.583280 −0.291640 0.956528i \(-0.594201\pi\)
−0.291640 + 0.956528i \(0.594201\pi\)
\(20\) 4.09600e15 0.223607
\(21\) 3.40469e16 1.01004
\(22\) −1.69822e16 −0.281651
\(23\) −2.45654e16 −0.233737 −0.116868 0.993147i \(-0.537286\pi\)
−0.116868 + 0.993147i \(0.537286\pi\)
\(24\) 1.12552e17 0.629090
\(25\) 5.96046e16 0.200000
\(26\) 5.36390e17 1.10234
\(27\) −1.61815e18 −2.07477
\(28\) −3.48758e17 −0.283824
\(29\) −1.86225e18 −0.977382 −0.488691 0.872457i \(-0.662525\pi\)
−0.488691 + 0.872457i \(0.662525\pi\)
\(30\) 1.63785e18 0.562676
\(31\) 7.10276e17 0.161959 0.0809796 0.996716i \(-0.474195\pi\)
0.0809796 + 0.996716i \(0.474195\pi\)
\(32\) −1.15292e18 −0.176777
\(33\) −6.79060e18 −0.708735
\(34\) 1.89431e19 1.36133
\(35\) −5.07509e18 −0.253860
\(36\) 3.07905e19 1.08302
\(37\) 5.29105e19 1.32136 0.660679 0.750669i \(-0.270269\pi\)
0.660679 + 0.750669i \(0.270269\pi\)
\(38\) 2.30493e19 0.412442
\(39\) 2.14484e20 2.77387
\(40\) −1.67772e19 −0.158114
\(41\) −2.57715e20 −1.78378 −0.891892 0.452249i \(-0.850622\pi\)
−0.891892 + 0.452249i \(0.850622\pi\)
\(42\) −1.39456e20 −0.714203
\(43\) −1.94678e19 −0.0742954 −0.0371477 0.999310i \(-0.511827\pi\)
−0.0371477 + 0.999310i \(0.511827\pi\)
\(44\) 6.95591e19 0.199157
\(45\) 4.48061e20 0.968681
\(46\) 1.00620e20 0.165277
\(47\) 1.05479e21 1.32417 0.662085 0.749428i \(-0.269672\pi\)
0.662085 + 0.749428i \(0.269672\pi\)
\(48\) −4.61013e20 −0.444834
\(49\) −9.08945e20 −0.677777
\(50\) −2.44141e20 −0.141421
\(51\) 7.57467e21 3.42560
\(52\) −2.19705e21 −0.779469
\(53\) 1.71922e21 0.480709 0.240354 0.970685i \(-0.422736\pi\)
0.240354 + 0.970685i \(0.422736\pi\)
\(54\) 6.62792e21 1.46709
\(55\) 1.01222e21 0.178132
\(56\) 1.42851e21 0.200694
\(57\) 9.21661e21 1.03785
\(58\) 7.62780e21 0.691113
\(59\) −2.29629e22 −1.68026 −0.840130 0.542386i \(-0.817521\pi\)
−0.840130 + 0.542386i \(0.817521\pi\)
\(60\) −6.70863e21 −0.397872
\(61\) −9.00207e20 −0.0434230 −0.0217115 0.999764i \(-0.506912\pi\)
−0.0217115 + 0.999764i \(0.506912\pi\)
\(62\) −2.90929e21 −0.114523
\(63\) −3.81506e22 −1.22955
\(64\) 4.72237e21 0.125000
\(65\) −3.19713e22 −0.697178
\(66\) 2.78143e22 0.501151
\(67\) −1.50272e22 −0.224358 −0.112179 0.993688i \(-0.535783\pi\)
−0.112179 + 0.993688i \(0.535783\pi\)
\(68\) −7.75908e22 −0.962606
\(69\) 4.02345e22 0.415896
\(70\) 2.07876e22 0.179506
\(71\) 2.23447e23 1.61602 0.808008 0.589172i \(-0.200546\pi\)
0.808008 + 0.589172i \(0.200546\pi\)
\(72\) −1.26118e23 −0.765810
\(73\) −3.25252e23 −1.66220 −0.831101 0.556122i \(-0.812289\pi\)
−0.831101 + 0.556122i \(0.812289\pi\)
\(74\) −2.16721e23 −0.934341
\(75\) −9.76234e22 −0.355867
\(76\) −9.44099e22 −0.291640
\(77\) −8.61863e22 −0.226102
\(78\) −8.78525e23 −1.96142
\(79\) 6.06979e23 1.15567 0.577837 0.816152i \(-0.303897\pi\)
0.577837 + 0.816152i \(0.303897\pi\)
\(80\) 6.87195e22 0.111803
\(81\) 1.09528e24 1.52568
\(82\) 1.05560e24 1.26133
\(83\) −7.26128e23 −0.745653 −0.372827 0.927901i \(-0.621611\pi\)
−0.372827 + 0.927901i \(0.621611\pi\)
\(84\) 5.71212e23 0.505018
\(85\) −1.12909e24 −0.860981
\(86\) 7.97403e22 0.0525348
\(87\) 3.05009e24 1.73909
\(88\) −2.84914e23 −0.140825
\(89\) 1.91182e24 0.820488 0.410244 0.911976i \(-0.365444\pi\)
0.410244 + 0.911976i \(0.365444\pi\)
\(90\) −1.83526e24 −0.684961
\(91\) 2.72223e24 0.884926
\(92\) −4.12140e23 −0.116868
\(93\) −1.16332e24 −0.288180
\(94\) −4.32043e24 −0.936330
\(95\) −1.37384e24 −0.260851
\(96\) 1.88831e24 0.314545
\(97\) −1.71656e24 −0.251195 −0.125598 0.992081i \(-0.540085\pi\)
−0.125598 + 0.992081i \(0.540085\pi\)
\(98\) 3.72304e24 0.479260
\(99\) 7.60907e24 0.862763
\(100\) 1.00000e24 0.100000
\(101\) 1.34215e25 1.18518 0.592590 0.805504i \(-0.298105\pi\)
0.592590 + 0.805504i \(0.298105\pi\)
\(102\) −3.10259e25 −2.42227
\(103\) 2.08010e25 1.43754 0.718769 0.695249i \(-0.244706\pi\)
0.718769 + 0.695249i \(0.244706\pi\)
\(104\) 8.99913e24 0.551168
\(105\) 8.31223e24 0.451701
\(106\) −7.04191e24 −0.339912
\(107\) 2.98949e25 1.28322 0.641609 0.767032i \(-0.278267\pi\)
0.641609 + 0.767032i \(0.278267\pi\)
\(108\) −2.71480e25 −1.03739
\(109\) 5.99753e24 0.204240 0.102120 0.994772i \(-0.467437\pi\)
0.102120 + 0.994772i \(0.467437\pi\)
\(110\) −4.14605e24 −0.125958
\(111\) −8.66594e25 −2.35114
\(112\) −5.85118e24 −0.141912
\(113\) −3.21651e25 −0.698080 −0.349040 0.937108i \(-0.613492\pi\)
−0.349040 + 0.937108i \(0.613492\pi\)
\(114\) −3.77512e25 −0.733872
\(115\) −5.99742e24 −0.104530
\(116\) −3.12435e25 −0.488691
\(117\) −2.40335e26 −3.37672
\(118\) 9.40560e25 1.18812
\(119\) 9.61378e25 1.09284
\(120\) 2.74785e25 0.281338
\(121\) −9.11573e25 −0.841346
\(122\) 3.68725e24 0.0307047
\(123\) 4.22099e26 3.17395
\(124\) 1.19165e25 0.0809796
\(125\) 1.45519e25 0.0894427
\(126\) 1.56265e26 0.869420
\(127\) −1.12460e26 −0.566829 −0.283414 0.958998i \(-0.591467\pi\)
−0.283414 + 0.958998i \(0.591467\pi\)
\(128\) −1.93428e25 −0.0883883
\(129\) 3.18854e25 0.132197
\(130\) 1.30955e26 0.492979
\(131\) 2.26749e26 0.775630 0.387815 0.921737i \(-0.373230\pi\)
0.387815 + 0.921737i \(0.373230\pi\)
\(132\) −1.13927e26 −0.354367
\(133\) 1.16977e26 0.331098
\(134\) 6.15513e25 0.158645
\(135\) −3.95055e26 −0.927867
\(136\) 3.17812e26 0.680665
\(137\) 6.81423e26 1.33171 0.665855 0.746081i \(-0.268067\pi\)
0.665855 + 0.746081i \(0.268067\pi\)
\(138\) −1.64800e26 −0.294083
\(139\) 5.03091e26 0.820279 0.410140 0.912023i \(-0.365480\pi\)
0.410140 + 0.912023i \(0.365480\pi\)
\(140\) −8.51459e25 −0.126930
\(141\) −1.72759e27 −2.35614
\(142\) −9.15240e26 −1.14270
\(143\) −5.42944e26 −0.620947
\(144\) 5.16579e26 0.541509
\(145\) −4.54652e26 −0.437098
\(146\) 1.33223e27 1.17535
\(147\) 1.48871e27 1.20599
\(148\) 8.87691e26 0.660679
\(149\) 7.27393e26 0.497669 0.248835 0.968546i \(-0.419952\pi\)
0.248835 + 0.968546i \(0.419952\pi\)
\(150\) 3.99865e26 0.251636
\(151\) 9.92827e25 0.0574992 0.0287496 0.999587i \(-0.490847\pi\)
0.0287496 + 0.999587i \(0.490847\pi\)
\(152\) 3.86703e26 0.206221
\(153\) −8.48765e27 −4.17008
\(154\) 3.53019e26 0.159878
\(155\) 1.73407e26 0.0724304
\(156\) 3.59844e27 1.38694
\(157\) −2.27168e26 −0.0808355 −0.0404177 0.999183i \(-0.512869\pi\)
−0.0404177 + 0.999183i \(0.512869\pi\)
\(158\) −2.48619e27 −0.817184
\(159\) −2.81581e27 −0.855342
\(160\) −2.81475e26 −0.0790569
\(161\) 5.10656e26 0.132680
\(162\) −4.48628e27 −1.07882
\(163\) 5.17654e27 1.15264 0.576322 0.817223i \(-0.304488\pi\)
0.576322 + 0.817223i \(0.304488\pi\)
\(164\) −4.32375e27 −0.891892
\(165\) −1.65786e27 −0.316956
\(166\) 2.97422e27 0.527256
\(167\) 1.02965e27 0.169330 0.0846652 0.996409i \(-0.473018\pi\)
0.0846652 + 0.996409i \(0.473018\pi\)
\(168\) −2.33969e27 −0.357101
\(169\) 1.00927e28 1.43029
\(170\) 4.62477e27 0.608806
\(171\) −1.03275e28 −1.26341
\(172\) −3.26616e26 −0.0371477
\(173\) 1.24548e28 1.31753 0.658766 0.752348i \(-0.271079\pi\)
0.658766 + 0.752348i \(0.271079\pi\)
\(174\) −1.24932e28 −1.22972
\(175\) −1.23904e27 −0.113529
\(176\) 1.16701e27 0.0995785
\(177\) 3.76097e28 2.98975
\(178\) −7.83082e27 −0.580173
\(179\) 4.58615e27 0.316800 0.158400 0.987375i \(-0.449366\pi\)
0.158400 + 0.987375i \(0.449366\pi\)
\(180\) 7.51722e27 0.484341
\(181\) −1.24754e28 −0.750019 −0.375010 0.927021i \(-0.622361\pi\)
−0.375010 + 0.927021i \(0.622361\pi\)
\(182\) −1.11502e28 −0.625737
\(183\) 1.47440e27 0.0772641
\(184\) 1.68812e27 0.0826384
\(185\) 1.29176e28 0.590929
\(186\) 4.76498e27 0.203774
\(187\) −1.91745e28 −0.766839
\(188\) 1.76965e28 0.662085
\(189\) 3.36373e28 1.17774
\(190\) 5.62727e27 0.184449
\(191\) −5.82809e28 −1.78900 −0.894498 0.447072i \(-0.852467\pi\)
−0.894498 + 0.447072i \(0.852467\pi\)
\(192\) −7.73452e27 −0.222417
\(193\) −2.07224e28 −0.558437 −0.279218 0.960228i \(-0.590075\pi\)
−0.279218 + 0.960228i \(0.590075\pi\)
\(194\) 7.03102e27 0.177622
\(195\) 5.23642e28 1.24051
\(196\) −1.52496e28 −0.338888
\(197\) 2.21753e28 0.462425 0.231213 0.972903i \(-0.425731\pi\)
0.231213 + 0.972903i \(0.425731\pi\)
\(198\) −3.11668e28 −0.610066
\(199\) −2.56881e28 −0.472138 −0.236069 0.971736i \(-0.575859\pi\)
−0.236069 + 0.971736i \(0.575859\pi\)
\(200\) −4.09600e27 −0.0707107
\(201\) 2.46122e28 0.399209
\(202\) −5.49745e28 −0.838049
\(203\) 3.87118e28 0.554808
\(204\) 1.27082e29 1.71280
\(205\) −6.29188e28 −0.797732
\(206\) −8.52010e28 −1.01649
\(207\) −4.50839e28 −0.506282
\(208\) −3.68604e28 −0.389734
\(209\) −2.33309e28 −0.232329
\(210\) −3.40469e28 −0.319401
\(211\) −1.69750e29 −1.50065 −0.750323 0.661072i \(-0.770102\pi\)
−0.750323 + 0.661072i \(0.770102\pi\)
\(212\) 2.88437e28 0.240354
\(213\) −3.65973e29 −2.87543
\(214\) −1.22450e29 −0.907372
\(215\) −4.75289e27 −0.0332259
\(216\) 1.11198e29 0.733543
\(217\) −1.47649e28 −0.0919357
\(218\) −2.45659e28 −0.144420
\(219\) 5.32713e29 2.95762
\(220\) 1.69822e28 0.0890658
\(221\) 6.05635e29 3.00129
\(222\) 3.54957e29 1.66251
\(223\) −1.64686e29 −0.729197 −0.364598 0.931165i \(-0.618794\pi\)
−0.364598 + 0.931165i \(0.618794\pi\)
\(224\) 2.39665e28 0.100347
\(225\) 1.09390e29 0.433207
\(226\) 1.31748e29 0.493617
\(227\) −5.10933e29 −1.81151 −0.905754 0.423803i \(-0.860695\pi\)
−0.905754 + 0.423803i \(0.860695\pi\)
\(228\) 1.54629e29 0.518926
\(229\) 1.25023e29 0.397235 0.198617 0.980077i \(-0.436355\pi\)
0.198617 + 0.980077i \(0.436355\pi\)
\(230\) 2.45654e28 0.0739140
\(231\) 1.41160e29 0.402311
\(232\) 1.27973e29 0.345557
\(233\) −5.70548e29 −1.45997 −0.729984 0.683464i \(-0.760472\pi\)
−0.729984 + 0.683464i \(0.760472\pi\)
\(234\) 9.84414e29 2.38770
\(235\) 2.57518e29 0.592187
\(236\) −3.85253e29 −0.840130
\(237\) −9.94140e29 −2.05633
\(238\) −3.93780e29 −0.772756
\(239\) 6.05498e29 1.12756 0.563780 0.825925i \(-0.309347\pi\)
0.563780 + 0.825925i \(0.309347\pi\)
\(240\) −1.12552e29 −0.198936
\(241\) −5.11295e29 −0.857943 −0.428972 0.903318i \(-0.641124\pi\)
−0.428972 + 0.903318i \(0.641124\pi\)
\(242\) 3.73380e29 0.594921
\(243\) −4.22872e29 −0.639927
\(244\) −1.51030e28 −0.0217115
\(245\) −2.21910e29 −0.303111
\(246\) −1.72892e30 −2.24432
\(247\) 7.36916e29 0.909298
\(248\) −4.88098e28 −0.0572613
\(249\) 1.18929e30 1.32677
\(250\) −5.96046e28 −0.0632456
\(251\) 2.51767e29 0.254142 0.127071 0.991894i \(-0.459442\pi\)
0.127071 + 0.991894i \(0.459442\pi\)
\(252\) −6.40061e29 −0.614773
\(253\) −1.01850e29 −0.0931006
\(254\) 4.60636e29 0.400808
\(255\) 1.84929e30 1.53198
\(256\) 7.92282e28 0.0625000
\(257\) 4.32516e29 0.324967 0.162483 0.986711i \(-0.448050\pi\)
0.162483 + 0.986711i \(0.448050\pi\)
\(258\) −1.30603e29 −0.0934771
\(259\) −1.09988e30 −0.750065
\(260\) −5.36390e29 −0.348589
\(261\) −3.41772e30 −2.11705
\(262\) −9.28765e29 −0.548454
\(263\) 3.00951e30 1.69453 0.847265 0.531171i \(-0.178248\pi\)
0.847265 + 0.531171i \(0.178248\pi\)
\(264\) 4.66646e29 0.250576
\(265\) 4.19730e29 0.214979
\(266\) −4.79139e29 −0.234121
\(267\) −3.13127e30 −1.45992
\(268\) −2.52114e29 −0.112179
\(269\) 5.09495e29 0.216390 0.108195 0.994130i \(-0.465493\pi\)
0.108195 + 0.994130i \(0.465493\pi\)
\(270\) 1.61815e30 0.656101
\(271\) 1.05937e30 0.410140 0.205070 0.978747i \(-0.434258\pi\)
0.205070 + 0.978747i \(0.434258\pi\)
\(272\) −1.30176e30 −0.481303
\(273\) −4.45860e30 −1.57458
\(274\) −2.79111e30 −0.941661
\(275\) 2.47124e29 0.0796628
\(276\) 6.75022e29 0.207948
\(277\) 5.67674e30 1.67148 0.835741 0.549124i \(-0.185039\pi\)
0.835741 + 0.549124i \(0.185039\pi\)
\(278\) −2.06066e30 −0.580025
\(279\) 1.30354e30 0.350810
\(280\) 3.48758e29 0.0897529
\(281\) −1.50424e30 −0.370245 −0.185122 0.982715i \(-0.559268\pi\)
−0.185122 + 0.982715i \(0.559268\pi\)
\(282\) 7.07621e30 1.66605
\(283\) −4.46973e30 −1.00682 −0.503409 0.864048i \(-0.667921\pi\)
−0.503409 + 0.864048i \(0.667921\pi\)
\(284\) 3.74882e30 0.808008
\(285\) 2.25015e30 0.464142
\(286\) 2.22390e30 0.439076
\(287\) 5.35728e30 1.01256
\(288\) −2.11591e30 −0.382905
\(289\) 1.56179e31 2.70644
\(290\) 1.86225e30 0.309075
\(291\) 2.81146e30 0.446961
\(292\) −5.45682e30 −0.831101
\(293\) 4.32602e30 0.631311 0.315655 0.948874i \(-0.397776\pi\)
0.315655 + 0.948874i \(0.397776\pi\)
\(294\) −6.09777e30 −0.852766
\(295\) −5.60617e30 −0.751435
\(296\) −3.63598e30 −0.467170
\(297\) −6.70891e30 −0.826411
\(298\) −2.97940e30 −0.351905
\(299\) 3.21696e30 0.364381
\(300\) −1.63785e30 −0.177934
\(301\) 4.04689e29 0.0421736
\(302\) −4.06662e29 −0.0406581
\(303\) −2.19824e31 −2.10883
\(304\) −1.58393e30 −0.145820
\(305\) −2.19777e29 −0.0194193
\(306\) 3.47654e31 2.94869
\(307\) 1.40982e31 1.14798 0.573991 0.818862i \(-0.305395\pi\)
0.573991 + 0.818862i \(0.305395\pi\)
\(308\) −1.44597e30 −0.113051
\(309\) −3.40689e31 −2.55786
\(310\) −7.10276e29 −0.0512160
\(311\) −4.30946e30 −0.298482 −0.149241 0.988801i \(-0.547683\pi\)
−0.149241 + 0.988801i \(0.547683\pi\)
\(312\) −1.47392e31 −0.980712
\(313\) −2.24958e30 −0.143813 −0.0719065 0.997411i \(-0.522908\pi\)
−0.0719065 + 0.997411i \(0.522908\pi\)
\(314\) 9.30481e29 0.0571593
\(315\) −9.31411e30 −0.549869
\(316\) 1.01834e31 0.577837
\(317\) 7.47129e30 0.407525 0.203763 0.979020i \(-0.434683\pi\)
0.203763 + 0.979020i \(0.434683\pi\)
\(318\) 1.15336e31 0.604818
\(319\) −7.72100e30 −0.389305
\(320\) 1.15292e30 0.0559017
\(321\) −4.89634e31 −2.28328
\(322\) −2.09165e30 −0.0938189
\(323\) 2.60248e31 1.12294
\(324\) 1.83758e31 0.762840
\(325\) −7.80550e30 −0.311787
\(326\) −2.12031e31 −0.815042
\(327\) −9.82304e30 −0.363412
\(328\) 1.77101e31 0.630663
\(329\) −2.19266e31 −0.751662
\(330\) 6.79060e30 0.224122
\(331\) −1.01412e31 −0.322286 −0.161143 0.986931i \(-0.551518\pi\)
−0.161143 + 0.986931i \(0.551518\pi\)
\(332\) −1.21824e31 −0.372827
\(333\) 9.71045e31 2.86211
\(334\) −4.21746e30 −0.119735
\(335\) −3.66874e30 −0.100336
\(336\) 9.58335e30 0.252509
\(337\) −4.27054e31 −1.08420 −0.542099 0.840315i \(-0.682370\pi\)
−0.542099 + 0.840315i \(0.682370\pi\)
\(338\) −4.13396e31 −1.01136
\(339\) 5.26816e31 1.24212
\(340\) −1.89431e31 −0.430491
\(341\) 2.94484e30 0.0645107
\(342\) 4.23014e31 0.893364
\(343\) 4.67723e31 0.952385
\(344\) 1.33782e30 0.0262674
\(345\) 9.82287e30 0.185994
\(346\) −5.10149e31 −0.931636
\(347\) 1.42992e30 0.0251880 0.0125940 0.999921i \(-0.495991\pi\)
0.0125940 + 0.999921i \(0.495991\pi\)
\(348\) 5.11720e31 0.869545
\(349\) 3.55571e30 0.0582920 0.0291460 0.999575i \(-0.490721\pi\)
0.0291460 + 0.999575i \(0.490721\pi\)
\(350\) 5.07509e30 0.0802774
\(351\) 2.11903e32 3.23444
\(352\) −4.78007e30 −0.0704127
\(353\) 6.63973e31 0.943988 0.471994 0.881602i \(-0.343534\pi\)
0.471994 + 0.881602i \(0.343534\pi\)
\(354\) −1.54049e32 −2.11407
\(355\) 5.45525e31 0.722704
\(356\) 3.20750e31 0.410244
\(357\) −1.57459e32 −1.94453
\(358\) −1.87849e31 −0.224012
\(359\) −1.86335e31 −0.214593 −0.107296 0.994227i \(-0.534219\pi\)
−0.107296 + 0.994227i \(0.534219\pi\)
\(360\) −3.07905e31 −0.342481
\(361\) −6.14104e31 −0.659784
\(362\) 5.10992e31 0.530344
\(363\) 1.49302e32 1.49704
\(364\) 4.56714e31 0.442463
\(365\) −7.94071e31 −0.743359
\(366\) −6.03915e30 −0.0546339
\(367\) 8.66272e31 0.757406 0.378703 0.925518i \(-0.376370\pi\)
0.378703 + 0.925518i \(0.376370\pi\)
\(368\) −6.91456e30 −0.0584341
\(369\) −4.72975e32 −3.86374
\(370\) −5.29105e31 −0.417850
\(371\) −3.57383e31 −0.272873
\(372\) −1.95173e31 −0.144090
\(373\) −2.52885e32 −1.80536 −0.902678 0.430316i \(-0.858402\pi\)
−0.902678 + 0.430316i \(0.858402\pi\)
\(374\) 7.85388e31 0.542237
\(375\) −2.38338e31 −0.159149
\(376\) −7.24848e31 −0.468165
\(377\) 2.43871e32 1.52368
\(378\) −1.37779e32 −0.832787
\(379\) −7.89983e31 −0.461985 −0.230992 0.972956i \(-0.574197\pi\)
−0.230992 + 0.972956i \(0.574197\pi\)
\(380\) −2.30493e31 −0.130425
\(381\) 1.84192e32 1.00858
\(382\) 2.38719e32 1.26501
\(383\) 2.10109e32 1.07761 0.538803 0.842432i \(-0.318877\pi\)
0.538803 + 0.842432i \(0.318877\pi\)
\(384\) 3.16806e31 0.157273
\(385\) −2.10416e31 −0.101116
\(386\) 8.48790e31 0.394874
\(387\) −3.57285e31 −0.160927
\(388\) −2.87991e31 −0.125598
\(389\) 1.39534e32 0.589264 0.294632 0.955611i \(-0.404803\pi\)
0.294632 + 0.955611i \(0.404803\pi\)
\(390\) −2.14484e32 −0.877176
\(391\) 1.13610e32 0.449993
\(392\) 6.24622e31 0.239630
\(393\) −3.71381e32 −1.38011
\(394\) −9.08300e31 −0.326984
\(395\) 1.48188e32 0.516833
\(396\) 1.27659e32 0.431382
\(397\) −1.58963e32 −0.520494 −0.260247 0.965542i \(-0.583804\pi\)
−0.260247 + 0.965542i \(0.583804\pi\)
\(398\) 1.05219e32 0.333852
\(399\) −1.91591e32 −0.589134
\(400\) 1.67772e31 0.0500000
\(401\) 4.43370e32 1.28074 0.640371 0.768066i \(-0.278781\pi\)
0.640371 + 0.768066i \(0.278781\pi\)
\(402\) −1.00812e32 −0.282283
\(403\) −9.30138e31 −0.252484
\(404\) 2.25176e32 0.592590
\(405\) 2.67403e32 0.682305
\(406\) −1.58563e32 −0.392308
\(407\) 2.19369e32 0.526315
\(408\) −5.20528e32 −1.21113
\(409\) −1.41371e32 −0.319021 −0.159510 0.987196i \(-0.550992\pi\)
−0.159510 + 0.987196i \(0.550992\pi\)
\(410\) 2.57715e32 0.564082
\(411\) −1.11607e33 −2.36956
\(412\) 3.48983e32 0.718769
\(413\) 4.77343e32 0.953795
\(414\) 1.84664e32 0.357996
\(415\) −1.77277e32 −0.333466
\(416\) 1.50980e32 0.275584
\(417\) −8.23987e32 −1.45955
\(418\) 9.55634e31 0.164281
\(419\) 5.65693e32 0.943856 0.471928 0.881637i \(-0.343558\pi\)
0.471928 + 0.881637i \(0.343558\pi\)
\(420\) 1.39456e32 0.225851
\(421\) −9.28896e32 −1.46030 −0.730148 0.683289i \(-0.760549\pi\)
−0.730148 + 0.683289i \(0.760549\pi\)
\(422\) 6.95294e32 1.06112
\(423\) 1.93582e33 2.86820
\(424\) −1.18144e32 −0.169956
\(425\) −2.75658e32 −0.385043
\(426\) 1.49902e33 2.03324
\(427\) 1.87131e31 0.0246489
\(428\) 5.01554e32 0.641609
\(429\) 8.89260e32 1.10487
\(430\) 1.94678e31 0.0234943
\(431\) −1.00278e33 −1.17555 −0.587773 0.809026i \(-0.699995\pi\)
−0.587773 + 0.809026i \(0.699995\pi\)
\(432\) −4.55467e32 −0.518693
\(433\) −5.32205e31 −0.0588817 −0.0294408 0.999567i \(-0.509373\pi\)
−0.0294408 + 0.999567i \(0.509373\pi\)
\(434\) 6.04771e31 0.0650084
\(435\) 7.44651e32 0.777745
\(436\) 1.00622e32 0.102120
\(437\) 1.38236e32 0.136334
\(438\) −2.18199e33 −2.09135
\(439\) −4.95347e32 −0.461427 −0.230714 0.973022i \(-0.574106\pi\)
−0.230714 + 0.973022i \(0.574106\pi\)
\(440\) −6.95591e31 −0.0629790
\(441\) −1.66815e33 −1.46809
\(442\) −2.48068e33 −2.12223
\(443\) −6.00200e32 −0.499171 −0.249585 0.968353i \(-0.580294\pi\)
−0.249585 + 0.968353i \(0.580294\pi\)
\(444\) −1.45390e33 −1.17557
\(445\) 4.66753e32 0.366933
\(446\) 6.74552e32 0.515620
\(447\) −1.19136e33 −0.885521
\(448\) −9.81666e31 −0.0709559
\(449\) 2.44542e31 0.0171899 0.00859497 0.999963i \(-0.497264\pi\)
0.00859497 + 0.999963i \(0.497264\pi\)
\(450\) −4.48061e32 −0.306324
\(451\) −1.06850e33 −0.710506
\(452\) −5.39642e32 −0.349040
\(453\) −1.62610e32 −0.102310
\(454\) 2.09278e33 1.28093
\(455\) 6.64606e32 0.395751
\(456\) −6.33361e32 −0.366936
\(457\) −1.65246e33 −0.931492 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(458\) −5.12095e32 −0.280887
\(459\) 7.48355e33 3.99438
\(460\) −1.00620e32 −0.0522651
\(461\) 1.16768e33 0.590284 0.295142 0.955453i \(-0.404633\pi\)
0.295142 + 0.955453i \(0.404633\pi\)
\(462\) −5.78192e32 −0.284477
\(463\) −2.39229e33 −1.14565 −0.572823 0.819679i \(-0.694152\pi\)
−0.572823 + 0.819679i \(0.694152\pi\)
\(464\) −5.24178e32 −0.244345
\(465\) −2.84015e32 −0.128878
\(466\) 2.33697e33 1.03235
\(467\) 4.47360e33 1.92396 0.961981 0.273116i \(-0.0880544\pi\)
0.961981 + 0.273116i \(0.0880544\pi\)
\(468\) −4.03216e33 −1.68836
\(469\) 3.12379e32 0.127356
\(470\) −1.05479e33 −0.418740
\(471\) 3.72067e32 0.143834
\(472\) 1.57800e33 0.594061
\(473\) −8.07146e31 −0.0295929
\(474\) 4.07200e33 1.45405
\(475\) −3.35411e32 −0.116656
\(476\) 1.61292e33 0.546421
\(477\) 3.15521e33 1.04123
\(478\) −2.48012e33 −0.797305
\(479\) 2.33765e33 0.732127 0.366064 0.930590i \(-0.380705\pi\)
0.366064 + 0.930590i \(0.380705\pi\)
\(480\) 4.61013e32 0.140669
\(481\) −6.92887e33 −2.05991
\(482\) 2.09426e33 0.606657
\(483\) −8.36377e32 −0.236082
\(484\) −1.52937e33 −0.420673
\(485\) −4.19082e32 −0.112338
\(486\) 1.73208e33 0.452496
\(487\) −1.27777e33 −0.325343 −0.162672 0.986680i \(-0.552011\pi\)
−0.162672 + 0.986680i \(0.552011\pi\)
\(488\) 6.18618e31 0.0153523
\(489\) −8.47839e33 −2.05094
\(490\) 9.08945e32 0.214332
\(491\) 5.48118e33 1.25996 0.629978 0.776613i \(-0.283064\pi\)
0.629978 + 0.776613i \(0.283064\pi\)
\(492\) 7.08164e33 1.58698
\(493\) 8.61250e33 1.88167
\(494\) −3.01841e33 −0.642970
\(495\) 1.85768e33 0.385840
\(496\) 1.99925e32 0.0404898
\(497\) −4.64493e33 −0.917327
\(498\) −4.87132e33 −0.938167
\(499\) 3.23941e33 0.608429 0.304214 0.952604i \(-0.401606\pi\)
0.304214 + 0.952604i \(0.401606\pi\)
\(500\) 2.44141e32 0.0447214
\(501\) −1.68642e33 −0.301296
\(502\) −1.03124e33 −0.179706
\(503\) −4.70148e33 −0.799162 −0.399581 0.916698i \(-0.630844\pi\)
−0.399581 + 0.916698i \(0.630844\pi\)
\(504\) 2.62169e33 0.434710
\(505\) 3.27674e33 0.530029
\(506\) 4.17176e32 0.0658321
\(507\) −1.65303e34 −2.54496
\(508\) −1.88677e33 −0.283414
\(509\) −7.74677e32 −0.113540 −0.0567699 0.998387i \(-0.518080\pi\)
−0.0567699 + 0.998387i \(0.518080\pi\)
\(510\) −7.57467e33 −1.08327
\(511\) 6.76120e33 0.943544
\(512\) −3.24519e32 −0.0441942
\(513\) 9.10574e33 1.21017
\(514\) −1.77159e33 −0.229786
\(515\) 5.07837e33 0.642887
\(516\) 5.34948e32 0.0660983
\(517\) 4.37322e33 0.527436
\(518\) 4.50512e33 0.530376
\(519\) −2.03991e34 −2.34433
\(520\) 2.19705e33 0.246490
\(521\) −7.09925e33 −0.777573 −0.388786 0.921328i \(-0.627106\pi\)
−0.388786 + 0.921328i \(0.627106\pi\)
\(522\) 1.39990e34 1.49698
\(523\) −8.65615e33 −0.903761 −0.451880 0.892079i \(-0.649247\pi\)
−0.451880 + 0.892079i \(0.649247\pi\)
\(524\) 3.80422e33 0.387815
\(525\) 2.02935e33 0.202007
\(526\) −1.23270e34 −1.19821
\(527\) −3.28486e33 −0.311806
\(528\) −1.91138e33 −0.177184
\(529\) −1.04423e34 −0.945367
\(530\) −1.71922e33 −0.152013
\(531\) −4.21428e34 −3.63950
\(532\) 1.96255e33 0.165549
\(533\) 3.37490e34 2.78081
\(534\) 1.28257e34 1.03232
\(535\) 7.29857e33 0.573873
\(536\) 1.03266e33 0.0793226
\(537\) −7.51142e33 −0.563694
\(538\) −2.08689e33 −0.153011
\(539\) −3.76853e33 −0.269968
\(540\) −6.62792e33 −0.463933
\(541\) 2.82575e34 1.93272 0.966358 0.257202i \(-0.0828007\pi\)
0.966358 + 0.257202i \(0.0828007\pi\)
\(542\) −4.33918e33 −0.290013
\(543\) 2.04328e34 1.33454
\(544\) 5.33200e33 0.340333
\(545\) 1.46424e33 0.0913389
\(546\) 1.82624e34 1.11340
\(547\) 1.70002e34 1.01300 0.506502 0.862239i \(-0.330938\pi\)
0.506502 + 0.862239i \(0.330938\pi\)
\(548\) 1.14324e34 0.665855
\(549\) −1.65211e33 −0.0940558
\(550\) −1.01222e33 −0.0563301
\(551\) 1.04794e34 0.570088
\(552\) −2.76489e33 −0.147041
\(553\) −1.26176e34 −0.656015
\(554\) −2.32519e34 −1.18192
\(555\) −2.11571e34 −1.05146
\(556\) 8.44047e33 0.410140
\(557\) 1.04504e34 0.496529 0.248264 0.968692i \(-0.420140\pi\)
0.248264 + 0.968692i \(0.420140\pi\)
\(558\) −5.33930e33 −0.248060
\(559\) 2.54940e33 0.115822
\(560\) −1.42851e33 −0.0634649
\(561\) 3.14050e34 1.36447
\(562\) 6.16138e33 0.261803
\(563\) −1.28118e34 −0.532421 −0.266211 0.963915i \(-0.585772\pi\)
−0.266211 + 0.963915i \(0.585772\pi\)
\(564\) −2.89842e34 −1.17807
\(565\) −7.85282e33 −0.312191
\(566\) 1.83080e34 0.711927
\(567\) −2.27683e34 −0.866048
\(568\) −1.53552e34 −0.571348
\(569\) −6.19441e33 −0.225474 −0.112737 0.993625i \(-0.535962\pi\)
−0.112737 + 0.993625i \(0.535962\pi\)
\(570\) −9.21661e33 −0.328198
\(571\) 5.43372e32 0.0189298 0.00946490 0.999955i \(-0.496987\pi\)
0.00946490 + 0.999955i \(0.496987\pi\)
\(572\) −9.10908e33 −0.310473
\(573\) 9.54553e34 3.18322
\(574\) −2.19434e34 −0.715988
\(575\) −1.46421e33 −0.0467473
\(576\) 8.66677e33 0.270755
\(577\) 1.51288e34 0.462495 0.231248 0.972895i \(-0.425719\pi\)
0.231248 + 0.972895i \(0.425719\pi\)
\(578\) −6.39708e34 −1.91374
\(579\) 3.39402e34 0.993646
\(580\) −7.62780e33 −0.218549
\(581\) 1.50944e34 0.423268
\(582\) −1.15157e34 −0.316049
\(583\) 7.12795e33 0.191473
\(584\) 2.23511e34 0.587677
\(585\) −5.86756e34 −1.51011
\(586\) −1.77194e34 −0.446404
\(587\) −3.71765e33 −0.0916837 −0.0458418 0.998949i \(-0.514597\pi\)
−0.0458418 + 0.998949i \(0.514597\pi\)
\(588\) 2.49765e34 0.602996
\(589\) −3.99691e33 −0.0944677
\(590\) 2.29629e34 0.531345
\(591\) −3.63198e34 −0.822810
\(592\) 1.48930e34 0.330339
\(593\) −4.27000e34 −0.927351 −0.463676 0.886005i \(-0.653470\pi\)
−0.463676 + 0.886005i \(0.653470\pi\)
\(594\) 2.74797e34 0.584361
\(595\) 2.34711e34 0.488734
\(596\) 1.22036e34 0.248835
\(597\) 4.20733e34 0.840093
\(598\) −1.31767e34 −0.257656
\(599\) −3.95633e34 −0.757631 −0.378816 0.925472i \(-0.623669\pi\)
−0.378816 + 0.925472i \(0.623669\pi\)
\(600\) 6.70863e33 0.125818
\(601\) −5.03622e33 −0.0925069 −0.0462535 0.998930i \(-0.514728\pi\)
−0.0462535 + 0.998930i \(0.514728\pi\)
\(602\) −1.65761e33 −0.0298212
\(603\) −2.75787e34 −0.485969
\(604\) 1.66569e33 0.0287496
\(605\) −2.22552e34 −0.376261
\(606\) 9.00400e34 1.49117
\(607\) −1.09922e35 −1.78331 −0.891655 0.452716i \(-0.850455\pi\)
−0.891655 + 0.452716i \(0.850455\pi\)
\(608\) 6.48780e33 0.103110
\(609\) −6.34040e34 −0.987190
\(610\) 9.00207e32 0.0137315
\(611\) −1.38130e35 −2.06430
\(612\) −1.42399e35 −2.08504
\(613\) −7.49713e34 −1.07557 −0.537786 0.843082i \(-0.680739\pi\)
−0.537786 + 0.843082i \(0.680739\pi\)
\(614\) −5.77463e34 −0.811745
\(615\) 1.03051e35 1.41943
\(616\) 5.92268e33 0.0799391
\(617\) 9.19873e34 1.21664 0.608321 0.793691i \(-0.291843\pi\)
0.608321 + 0.793691i \(0.291843\pi\)
\(618\) 1.39546e35 1.80868
\(619\) 1.17365e35 1.49075 0.745375 0.666646i \(-0.232271\pi\)
0.745375 + 0.666646i \(0.232271\pi\)
\(620\) 2.90929e33 0.0362152
\(621\) 3.97505e34 0.484950
\(622\) 1.76515e34 0.211058
\(623\) −3.97422e34 −0.465748
\(624\) 6.03718e34 0.693468
\(625\) 3.55271e33 0.0400000
\(626\) 9.21430e33 0.101691
\(627\) 3.82125e34 0.413391
\(628\) −3.81125e33 −0.0404177
\(629\) −2.44699e35 −2.54389
\(630\) 3.81506e34 0.388816
\(631\) −5.93583e34 −0.593082 −0.296541 0.955020i \(-0.595833\pi\)
−0.296541 + 0.955020i \(0.595833\pi\)
\(632\) −4.17113e34 −0.408592
\(633\) 2.78024e35 2.67015
\(634\) −3.06024e34 −0.288164
\(635\) −2.74561e34 −0.253493
\(636\) −4.72415e34 −0.427671
\(637\) 1.19030e35 1.05661
\(638\) 3.16252e34 0.275280
\(639\) 4.10083e35 3.50035
\(640\) −4.72237e33 −0.0395285
\(641\) −6.98225e34 −0.573152 −0.286576 0.958058i \(-0.592517\pi\)
−0.286576 + 0.958058i \(0.592517\pi\)
\(642\) 2.00554e35 1.61452
\(643\) 4.37990e34 0.345802 0.172901 0.984939i \(-0.444686\pi\)
0.172901 + 0.984939i \(0.444686\pi\)
\(644\) 8.56739e33 0.0663400
\(645\) 7.78452e33 0.0591201
\(646\) −1.06598e35 −0.794038
\(647\) 2.19963e35 1.60711 0.803555 0.595231i \(-0.202939\pi\)
0.803555 + 0.595231i \(0.202939\pi\)
\(648\) −7.52673e34 −0.539410
\(649\) −9.52052e34 −0.669271
\(650\) 3.19713e34 0.220467
\(651\) 2.41827e34 0.163585
\(652\) 8.68480e34 0.576322
\(653\) −5.77474e34 −0.375939 −0.187970 0.982175i \(-0.560191\pi\)
−0.187970 + 0.982175i \(0.560191\pi\)
\(654\) 4.02352e34 0.256971
\(655\) 5.53587e34 0.346872
\(656\) −7.25404e34 −0.445946
\(657\) −5.96921e35 −3.60039
\(658\) 8.98113e34 0.531505
\(659\) −2.55494e34 −0.148359 −0.0741793 0.997245i \(-0.523634\pi\)
−0.0741793 + 0.997245i \(0.523634\pi\)
\(660\) −2.78143e34 −0.158478
\(661\) 1.14583e35 0.640623 0.320312 0.947312i \(-0.396212\pi\)
0.320312 + 0.947312i \(0.396212\pi\)
\(662\) 4.15385e34 0.227890
\(663\) −9.91938e35 −5.34030
\(664\) 4.98991e34 0.263628
\(665\) 2.85589e34 0.148071
\(666\) −3.97740e35 −2.02382
\(667\) 4.57471e34 0.228450
\(668\) 1.72747e34 0.0846652
\(669\) 2.69730e35 1.29749
\(670\) 1.50272e34 0.0709483
\(671\) −3.73230e33 −0.0172960
\(672\) −3.92534e34 −0.178551
\(673\) 1.32743e34 0.0592683 0.0296342 0.999561i \(-0.490566\pi\)
0.0296342 + 0.999561i \(0.490566\pi\)
\(674\) 1.74921e35 0.766644
\(675\) −9.64490e34 −0.414955
\(676\) 1.69327e35 0.715143
\(677\) −1.09080e35 −0.452257 −0.226128 0.974098i \(-0.572607\pi\)
−0.226128 + 0.974098i \(0.572607\pi\)
\(678\) −2.15784e35 −0.878310
\(679\) 3.56831e34 0.142590
\(680\) 7.75908e34 0.304403
\(681\) 8.36830e35 3.22328
\(682\) −1.20621e34 −0.0456159
\(683\) −2.56303e35 −0.951690 −0.475845 0.879529i \(-0.657858\pi\)
−0.475845 + 0.879529i \(0.657858\pi\)
\(684\) −1.73267e35 −0.631704
\(685\) 1.66363e35 0.595559
\(686\) −1.91580e35 −0.673438
\(687\) −2.04769e35 −0.706814
\(688\) −5.47971e33 −0.0185739
\(689\) −2.25139e35 −0.749395
\(690\) −4.02345e34 −0.131518
\(691\) 1.27544e35 0.409436 0.204718 0.978821i \(-0.434372\pi\)
0.204718 + 0.978821i \(0.434372\pi\)
\(692\) 2.08957e35 0.658766
\(693\) −1.58174e35 −0.489745
\(694\) −5.85696e33 −0.0178106
\(695\) 1.22825e35 0.366840
\(696\) −2.09601e35 −0.614861
\(697\) 1.19187e36 3.43416
\(698\) −1.45642e34 −0.0412187
\(699\) 9.34471e35 2.59777
\(700\) −2.07876e34 −0.0567647
\(701\) −3.29520e35 −0.883907 −0.441953 0.897038i \(-0.645714\pi\)
−0.441953 + 0.897038i \(0.645714\pi\)
\(702\) −8.67957e35 −2.28709
\(703\) −2.97742e35 −0.770722
\(704\) 1.95792e34 0.0497893
\(705\) −4.21775e35 −1.05370
\(706\) −2.71963e35 −0.667500
\(707\) −2.79001e35 −0.672764
\(708\) 6.30987e35 1.49487
\(709\) −3.54372e35 −0.824863 −0.412432 0.910989i \(-0.635320\pi\)
−0.412432 + 0.910989i \(0.635320\pi\)
\(710\) −2.23447e35 −0.511029
\(711\) 1.11396e36 2.50323
\(712\) −1.31379e35 −0.290086
\(713\) −1.74482e34 −0.0378558
\(714\) 6.44953e35 1.37499
\(715\) −1.32555e35 −0.277696
\(716\) 7.69429e34 0.158400
\(717\) −9.91715e35 −2.00631
\(718\) 7.63230e34 0.151740
\(719\) 8.25549e34 0.161299 0.0806495 0.996743i \(-0.474301\pi\)
0.0806495 + 0.996743i \(0.474301\pi\)
\(720\) 1.26118e35 0.242170
\(721\) −4.32403e35 −0.816014
\(722\) 2.51537e35 0.466538
\(723\) 8.37424e35 1.52657
\(724\) −2.09302e35 −0.375010
\(725\) −1.10999e35 −0.195476
\(726\) −6.11541e35 −1.05857
\(727\) 8.59682e35 1.46271 0.731354 0.681998i \(-0.238889\pi\)
0.731354 + 0.681998i \(0.238889\pi\)
\(728\) −1.87070e35 −0.312869
\(729\) −2.35421e35 −0.387036
\(730\) 3.25252e35 0.525634
\(731\) 9.00343e34 0.143035
\(732\) 2.47364e34 0.0386320
\(733\) 1.11362e36 1.70977 0.854883 0.518821i \(-0.173629\pi\)
0.854883 + 0.518821i \(0.173629\pi\)
\(734\) −3.54825e35 −0.535567
\(735\) 3.63456e35 0.539336
\(736\) 2.83220e34 0.0413192
\(737\) −6.23034e34 −0.0893651
\(738\) 1.93730e36 2.73208
\(739\) 8.39662e34 0.116426 0.0582129 0.998304i \(-0.481460\pi\)
0.0582129 + 0.998304i \(0.481460\pi\)
\(740\) 2.16721e35 0.295465
\(741\) −1.20696e36 −1.61795
\(742\) 1.46384e35 0.192950
\(743\) −8.61824e35 −1.11701 −0.558506 0.829500i \(-0.688625\pi\)
−0.558506 + 0.829500i \(0.688625\pi\)
\(744\) 7.99430e34 0.101887
\(745\) 1.77586e35 0.222564
\(746\) 1.03582e36 1.27658
\(747\) −1.33263e36 −1.61511
\(748\) −3.21695e35 −0.383420
\(749\) −6.21444e35 −0.728415
\(750\) 9.76234e34 0.112535
\(751\) −8.00202e35 −0.907195 −0.453597 0.891207i \(-0.649860\pi\)
−0.453597 + 0.891207i \(0.649860\pi\)
\(752\) 2.96898e35 0.331043
\(753\) −4.12356e35 −0.452204
\(754\) −9.98894e35 −1.07740
\(755\) 2.42389e34 0.0257144
\(756\) 5.64341e35 0.588869
\(757\) −7.91448e35 −0.812314 −0.406157 0.913803i \(-0.633131\pi\)
−0.406157 + 0.913803i \(0.633131\pi\)
\(758\) 3.23577e35 0.326673
\(759\) 1.66814e35 0.165657
\(760\) 9.44099e34 0.0922247
\(761\) 2.09934e34 0.0201732 0.0100866 0.999949i \(-0.496789\pi\)
0.0100866 + 0.999949i \(0.496789\pi\)
\(762\) −7.54452e35 −0.713173
\(763\) −1.24674e35 −0.115936
\(764\) −9.77792e35 −0.894498
\(765\) −2.07218e36 −1.86492
\(766\) −8.60607e35 −0.761983
\(767\) 3.00709e36 2.61942
\(768\) −1.29764e35 −0.111209
\(769\) −7.23123e35 −0.609723 −0.304862 0.952397i \(-0.598610\pi\)
−0.304862 + 0.952397i \(0.598610\pi\)
\(770\) 8.61863e34 0.0714997
\(771\) −7.08396e35 −0.578225
\(772\) −3.47664e35 −0.279218
\(773\) −1.19333e36 −0.943014 −0.471507 0.881862i \(-0.656290\pi\)
−0.471507 + 0.881862i \(0.656290\pi\)
\(774\) 1.46344e35 0.113792
\(775\) 4.23357e34 0.0323919
\(776\) 1.17961e35 0.0888110
\(777\) 1.80144e36 1.33462
\(778\) −5.71531e35 −0.416672
\(779\) 1.45023e36 1.04045
\(780\) 8.78525e35 0.620257
\(781\) 9.26423e35 0.643682
\(782\) −4.65345e35 −0.318193
\(783\) 3.01340e36 2.02784
\(784\) −2.55845e35 −0.169444
\(785\) −5.54610e34 −0.0361507
\(786\) 1.52118e36 0.975883
\(787\) 4.78974e35 0.302432 0.151216 0.988501i \(-0.451681\pi\)
0.151216 + 0.988501i \(0.451681\pi\)
\(788\) 3.72040e35 0.231213
\(789\) −4.92912e36 −3.01514
\(790\) −6.06979e35 −0.365456
\(791\) 6.68636e35 0.396263
\(792\) −5.22891e35 −0.305033
\(793\) 1.17886e35 0.0676937
\(794\) 6.51114e35 0.368045
\(795\) −6.87455e35 −0.382521
\(796\) −4.30975e35 −0.236069
\(797\) 2.29881e36 1.23958 0.619788 0.784769i \(-0.287218\pi\)
0.619788 + 0.784769i \(0.287218\pi\)
\(798\) 7.84757e35 0.416581
\(799\) −4.87818e36 −2.54931
\(800\) −6.87195e34 −0.0353553
\(801\) 3.50869e36 1.77721
\(802\) −1.81604e36 −0.905621
\(803\) −1.34851e36 −0.662078
\(804\) 4.12925e35 0.199604
\(805\) 1.24672e35 0.0593363
\(806\) 3.80985e35 0.178533
\(807\) −8.34476e35 −0.385030
\(808\) −9.22320e35 −0.419025
\(809\) 1.08839e36 0.486885 0.243442 0.969915i \(-0.421723\pi\)
0.243442 + 0.969915i \(0.421723\pi\)
\(810\) −1.09528e36 −0.482463
\(811\) 4.47699e36 1.94189 0.970946 0.239299i \(-0.0769178\pi\)
0.970946 + 0.239299i \(0.0769178\pi\)
\(812\) 6.49476e35 0.277404
\(813\) −1.73509e36 −0.729776
\(814\) −8.98537e35 −0.372161
\(815\) 1.26380e36 0.515478
\(816\) 2.13208e36 0.856400
\(817\) 1.09551e35 0.0433351
\(818\) 5.79056e35 0.225582
\(819\) 4.99599e36 1.91678
\(820\) −1.05560e36 −0.398866
\(821\) 3.35501e36 1.24855 0.624274 0.781206i \(-0.285395\pi\)
0.624274 + 0.781206i \(0.285395\pi\)
\(822\) 4.57141e36 1.67553
\(823\) −1.04609e36 −0.377636 −0.188818 0.982012i \(-0.560466\pi\)
−0.188818 + 0.982012i \(0.560466\pi\)
\(824\) −1.42944e36 −0.508246
\(825\) −4.04751e35 −0.141747
\(826\) −1.95520e36 −0.674435
\(827\) −1.70274e36 −0.578535 −0.289267 0.957248i \(-0.593412\pi\)
−0.289267 + 0.957248i \(0.593412\pi\)
\(828\) −7.56383e35 −0.253141
\(829\) 3.63214e36 1.19738 0.598688 0.800983i \(-0.295689\pi\)
0.598688 + 0.800983i \(0.295689\pi\)
\(830\) 7.26128e35 0.235796
\(831\) −9.29763e36 −2.97413
\(832\) −6.18415e35 −0.194867
\(833\) 4.20366e36 1.30486
\(834\) 3.37505e36 1.03206
\(835\) 2.51380e35 0.0757269
\(836\) −3.91428e35 −0.116164
\(837\) −1.14933e36 −0.336029
\(838\) −2.31708e36 −0.667407
\(839\) −4.10710e36 −1.16550 −0.582748 0.812653i \(-0.698023\pi\)
−0.582748 + 0.812653i \(0.698023\pi\)
\(840\) −5.71212e35 −0.159701
\(841\) −1.62368e35 −0.0447251
\(842\) 3.80476e36 1.03258
\(843\) 2.46372e36 0.658790
\(844\) −2.84793e36 −0.750323
\(845\) 2.46403e36 0.639643
\(846\) −7.92911e36 −2.02813
\(847\) 1.89494e36 0.477588
\(848\) 4.83916e35 0.120177
\(849\) 7.32074e36 1.79147
\(850\) 1.12909e36 0.272266
\(851\) −1.29977e36 −0.308850
\(852\) −6.14000e36 −1.43772
\(853\) 2.01380e36 0.464680 0.232340 0.972635i \(-0.425362\pi\)
0.232340 + 0.972635i \(0.425362\pi\)
\(854\) −7.66490e34 −0.0174294
\(855\) −2.52136e36 −0.565013
\(856\) −2.05437e36 −0.453686
\(857\) −3.20819e36 −0.698232 −0.349116 0.937080i \(-0.613518\pi\)
−0.349116 + 0.937080i \(0.613518\pi\)
\(858\) −3.64241e36 −0.781263
\(859\) −1.62270e36 −0.343024 −0.171512 0.985182i \(-0.554865\pi\)
−0.171512 + 0.985182i \(0.554865\pi\)
\(860\) −7.97403e34 −0.0166130
\(861\) −8.77441e36 −1.80168
\(862\) 4.10739e36 0.831237
\(863\) 2.34665e36 0.468074 0.234037 0.972228i \(-0.424806\pi\)
0.234037 + 0.972228i \(0.424806\pi\)
\(864\) 1.86559e36 0.366771
\(865\) 3.04073e36 0.589218
\(866\) 2.17991e35 0.0416356
\(867\) −2.55797e37 −4.81567
\(868\) −2.47714e35 −0.0459679
\(869\) 2.51656e36 0.460321
\(870\) −3.05009e36 −0.549949
\(871\) 1.96788e36 0.349761
\(872\) −4.12147e35 −0.0722098
\(873\) −3.15033e36 −0.544099
\(874\) −5.66216e35 −0.0964027
\(875\) −3.02499e35 −0.0507719
\(876\) 8.93744e36 1.47881
\(877\) −1.82745e36 −0.298092 −0.149046 0.988830i \(-0.547620\pi\)
−0.149046 + 0.988830i \(0.547620\pi\)
\(878\) 2.02894e36 0.326278
\(879\) −7.08537e36 −1.12331
\(880\) 2.84914e35 0.0445329
\(881\) 1.92548e36 0.296715 0.148358 0.988934i \(-0.452601\pi\)
0.148358 + 0.988934i \(0.452601\pi\)
\(882\) 6.83274e36 1.03810
\(883\) 5.88853e36 0.882060 0.441030 0.897492i \(-0.354613\pi\)
0.441030 + 0.897492i \(0.354613\pi\)
\(884\) 1.01609e37 1.50064
\(885\) 9.18206e36 1.33706
\(886\) 2.45842e36 0.352967
\(887\) 1.17351e37 1.66128 0.830640 0.556809i \(-0.187975\pi\)
0.830640 + 0.556809i \(0.187975\pi\)
\(888\) 5.95519e36 0.831253
\(889\) 2.33777e36 0.321759
\(890\) −1.91182e36 −0.259461
\(891\) 4.54110e36 0.607700
\(892\) −2.76296e36 −0.364598
\(893\) −5.93560e36 −0.772363
\(894\) 4.87981e36 0.626158
\(895\) 1.11967e36 0.141677
\(896\) 4.02090e35 0.0501734
\(897\) −5.26889e36 −0.648356
\(898\) −1.00164e35 −0.0121551
\(899\) −1.32271e36 −0.158296
\(900\) 1.83526e36 0.216604
\(901\) −7.95098e36 −0.925467
\(902\) 4.37658e36 0.502404
\(903\) −6.62820e35 −0.0750410
\(904\) 2.21037e36 0.246808
\(905\) −3.04575e36 −0.335419
\(906\) 6.66051e35 0.0723444
\(907\) 9.60913e36 1.02942 0.514711 0.857364i \(-0.327899\pi\)
0.514711 + 0.857364i \(0.327899\pi\)
\(908\) −8.57203e36 −0.905754
\(909\) 2.46320e37 2.56715
\(910\) −2.72223e36 −0.279838
\(911\) 3.31132e36 0.335754 0.167877 0.985808i \(-0.446309\pi\)
0.167877 + 0.985808i \(0.446309\pi\)
\(912\) 2.59424e36 0.259463
\(913\) −3.01056e36 −0.297004
\(914\) 6.76849e36 0.658665
\(915\) 3.59962e35 0.0345535
\(916\) 2.09754e36 0.198617
\(917\) −4.71357e36 −0.440284
\(918\) −3.06526e37 −2.82445
\(919\) −6.37787e36 −0.579738 −0.289869 0.957066i \(-0.593612\pi\)
−0.289869 + 0.957066i \(0.593612\pi\)
\(920\) 4.12140e35 0.0369570
\(921\) −2.30908e37 −2.04264
\(922\) −4.78281e36 −0.417394
\(923\) −2.92614e37 −2.51927
\(924\) 2.36827e36 0.201156
\(925\) 3.15371e36 0.264272
\(926\) 9.79880e36 0.810094
\(927\) 3.81753e37 3.11376
\(928\) 2.14703e36 0.172778
\(929\) −1.01760e37 −0.807940 −0.403970 0.914772i \(-0.632370\pi\)
−0.403970 + 0.914772i \(0.632370\pi\)
\(930\) 1.16332e36 0.0911305
\(931\) 5.11488e36 0.395334
\(932\) −9.57221e36 −0.729984
\(933\) 7.05824e36 0.531099
\(934\) −1.83239e37 −1.36045
\(935\) −4.68128e36 −0.342941
\(936\) 1.65157e37 1.19385
\(937\) 5.01714e36 0.357859 0.178929 0.983862i \(-0.442737\pi\)
0.178929 + 0.983862i \(0.442737\pi\)
\(938\) −1.27950e36 −0.0900546
\(939\) 3.68448e36 0.255892
\(940\) 4.32043e36 0.296094
\(941\) 1.04889e37 0.709348 0.354674 0.934990i \(-0.384592\pi\)
0.354674 + 0.934990i \(0.384592\pi\)
\(942\) −1.52399e36 −0.101706
\(943\) 6.33089e36 0.416936
\(944\) −6.46348e36 −0.420065
\(945\) 8.21224e36 0.526701
\(946\) 3.30607e35 0.0209254
\(947\) −3.09440e37 −1.93286 −0.966432 0.256923i \(-0.917291\pi\)
−0.966432 + 0.256923i \(0.917291\pi\)
\(948\) −1.66789e37 −1.02817
\(949\) 4.25932e37 2.59127
\(950\) 1.37384e36 0.0824883
\(951\) −1.22368e37 −0.725125
\(952\) −6.60654e36 −0.386378
\(953\) −2.63074e34 −0.00151851 −0.000759254 1.00000i \(-0.500242\pi\)
−0.000759254 1.00000i \(0.500242\pi\)
\(954\) −1.29237e37 −0.736263
\(955\) −1.42287e37 −0.800063
\(956\) 1.01586e37 0.563780
\(957\) 1.26458e37 0.692704
\(958\) −9.57503e36 −0.517692
\(959\) −1.41651e37 −0.755941
\(960\) −1.88831e36 −0.0994679
\(961\) −1.87283e37 −0.973769
\(962\) 2.83807e37 1.45658
\(963\) 5.48650e37 2.77950
\(964\) −8.57811e36 −0.428972
\(965\) −5.05918e36 −0.249740
\(966\) 3.42580e36 0.166935
\(967\) −1.63641e37 −0.787158 −0.393579 0.919291i \(-0.628763\pi\)
−0.393579 + 0.919291i \(0.628763\pi\)
\(968\) 6.26429e36 0.297461
\(969\) −4.26247e37 −1.99809
\(970\) 1.71656e36 0.0794350
\(971\) −3.01907e37 −1.37922 −0.689610 0.724181i \(-0.742218\pi\)
−0.689610 + 0.724181i \(0.742218\pi\)
\(972\) −7.09461e36 −0.319963
\(973\) −1.04581e37 −0.465629
\(974\) 5.23376e36 0.230053
\(975\) 1.27842e37 0.554775
\(976\) −2.53386e35 −0.0108557
\(977\) −3.79611e36 −0.160567 −0.0802837 0.996772i \(-0.525583\pi\)
−0.0802837 + 0.996772i \(0.525583\pi\)
\(978\) 3.47275e37 1.45023
\(979\) 7.92650e36 0.326812
\(980\) −3.72304e36 −0.151555
\(981\) 1.10070e37 0.442392
\(982\) −2.24509e37 −0.890923
\(983\) −6.46957e36 −0.253487 −0.126744 0.991936i \(-0.540453\pi\)
−0.126744 + 0.991936i \(0.540453\pi\)
\(984\) −2.90064e37 −1.12216
\(985\) 5.41389e36 0.206803
\(986\) −3.52768e37 −1.33054
\(987\) 3.59124e37 1.33746
\(988\) 1.23634e37 0.454649
\(989\) 4.78236e35 0.0173656
\(990\) −7.60907e36 −0.272830
\(991\) −3.19318e37 −1.13058 −0.565291 0.824891i \(-0.691236\pi\)
−0.565291 + 0.824891i \(0.691236\pi\)
\(992\) −8.18892e35 −0.0286306
\(993\) 1.66098e37 0.573455
\(994\) 1.90256e37 0.648648
\(995\) −6.27152e36 −0.211147
\(996\) 1.99529e37 0.663384
\(997\) 3.10721e37 1.02019 0.510095 0.860118i \(-0.329610\pi\)
0.510095 + 0.860118i \(0.329610\pi\)
\(998\) −1.32686e37 −0.430224
\(999\) −8.56169e37 −2.74152
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.b.1.1 2
5.2 odd 4 50.26.b.f.49.2 4
5.3 odd 4 50.26.b.f.49.3 4
5.4 even 2 50.26.a.f.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.26.a.b.1.1 2 1.1 even 1 trivial
50.26.a.f.1.2 2 5.4 even 2
50.26.b.f.49.2 4 5.2 odd 4
50.26.b.f.49.3 4 5.3 odd 4