Properties

Label 9.94.a.b.1.7
Level $9$
Weight $94$
Character 9.1
Self dual yes
Analytic conductor $492.953$
Analytic rank $0$
Dimension $7$
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] = [9,94,Mod(1,9)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 94, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9.1");
 
S:= CuspForms(chi, 94);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 94 \)
Character orbit: \([\chi]\) \(=\) 9.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: \(492.952887545\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} + \cdots - 13\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: multiple of \( 2^{88}\cdot 3^{47}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} \)
Twist minimal: no (minimal twist has level 1)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-3.01170e11\) of defining polynomial
Character \(\chi\) \(=\) 9.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.67226e14 q^{2} +1.80609e28 q^{4} +5.69707e32 q^{5} +3.48367e39 q^{7} +1.36413e42 q^{8} +O(q^{10})\) \(q+1.67226e14 q^{2} +1.80609e28 q^{4} +5.69707e32 q^{5} +3.48367e39 q^{7} +1.36413e42 q^{8} +9.52696e46 q^{10} +4.56983e47 q^{11} -4.65568e49 q^{13} +5.82559e53 q^{14} +4.92506e55 q^{16} +7.16300e56 q^{17} -4.92840e58 q^{19} +1.02894e61 q^{20} +7.64193e61 q^{22} -1.15698e63 q^{23} +2.23592e65 q^{25} -7.78549e63 q^{26} +6.29183e67 q^{28} -1.03850e68 q^{29} -8.93363e67 q^{31} -5.27370e69 q^{32} +1.19784e71 q^{34} +1.98467e72 q^{35} +5.91204e72 q^{37} -8.24156e72 q^{38} +7.77153e74 q^{40} -2.38541e74 q^{41} -1.84207e75 q^{43} +8.25353e75 q^{44} -1.93477e77 q^{46} -5.58584e77 q^{47} +8.20845e78 q^{49} +3.73903e79 q^{50} -8.40858e77 q^{52} +2.41979e80 q^{53} +2.60346e80 q^{55} +4.75217e81 q^{56} -1.73664e82 q^{58} +2.30840e82 q^{59} +1.46410e83 q^{61} -1.49393e82 q^{62} -1.36965e84 q^{64} -2.65237e82 q^{65} +1.40138e84 q^{67} +1.29370e85 q^{68} +3.31888e86 q^{70} +1.74082e86 q^{71} -4.65018e86 q^{73} +9.88645e86 q^{74} -8.90115e86 q^{76} +1.59198e87 q^{77} -1.89450e88 q^{79} +2.80584e88 q^{80} -3.98902e88 q^{82} +2.23742e89 q^{83} +4.08081e89 q^{85} -3.08041e89 q^{86} +6.23383e89 q^{88} +1.44081e90 q^{89} -1.62188e89 q^{91} -2.08962e91 q^{92} -9.34096e91 q^{94} -2.80774e91 q^{95} -8.44825e91 q^{97} +1.37266e93 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots - 62\!\cdots\!60 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 43735426713792 q^{2} + 37\!\cdots\!44 q^{4}+ \cdots + 69\!\cdots\!56 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67226e14 1.68038 0.840192 0.542290i \(-0.182442\pi\)
0.840192 + 0.542290i \(0.182442\pi\)
\(3\) 0 0
\(4\) 1.80609e28 1.82369
\(5\) 5.69707e32 1.79286 0.896429 0.443186i \(-0.146152\pi\)
0.896429 + 0.443186i \(0.146152\pi\)
\(6\) 0 0
\(7\) 3.48367e39 1.75784 0.878918 0.476973i \(-0.158266\pi\)
0.878918 + 0.476973i \(0.158266\pi\)
\(8\) 1.36413e42 1.38411
\(9\) 0 0
\(10\) 9.52696e46 3.01269
\(11\) 4.56983e47 0.171846 0.0859231 0.996302i \(-0.472616\pi\)
0.0859231 + 0.996302i \(0.472616\pi\)
\(12\) 0 0
\(13\) −4.65568e49 −0.00740657 −0.00370328 0.999993i \(-0.501179\pi\)
−0.00370328 + 0.999993i \(0.501179\pi\)
\(14\) 5.82559e53 2.95384
\(15\) 0 0
\(16\) 4.92506e55 0.502149
\(17\) 7.16300e56 0.435733 0.217866 0.975979i \(-0.430090\pi\)
0.217866 + 0.975979i \(0.430090\pi\)
\(18\) 0 0
\(19\) −4.92840e58 −0.170084 −0.0850421 0.996377i \(-0.527102\pi\)
−0.0850421 + 0.996377i \(0.527102\pi\)
\(20\) 1.02894e61 3.26961
\(21\) 0 0
\(22\) 7.64193e61 0.288767
\(23\) −1.15698e63 −0.553328 −0.276664 0.960967i \(-0.589229\pi\)
−0.276664 + 0.960967i \(0.589229\pi\)
\(24\) 0 0
\(25\) 2.23592e65 2.21434
\(26\) −7.78549e63 −0.0124459
\(27\) 0 0
\(28\) 6.29183e67 3.20574
\(29\) −1.03850e68 −1.03490 −0.517452 0.855712i \(-0.673120\pi\)
−0.517452 + 0.855712i \(0.673120\pi\)
\(30\) 0 0
\(31\) −8.93363e67 −0.0400598 −0.0200299 0.999799i \(-0.506376\pi\)
−0.0200299 + 0.999799i \(0.506376\pi\)
\(32\) −5.27370e69 −0.540309
\(33\) 0 0
\(34\) 1.19784e71 0.732198
\(35\) 1.98467e72 3.15155
\(36\) 0 0
\(37\) 5.91204e72 0.708528 0.354264 0.935145i \(-0.384731\pi\)
0.354264 + 0.935145i \(0.384731\pi\)
\(38\) −8.24156e72 −0.285807
\(39\) 0 0
\(40\) 7.77153e74 2.48152
\(41\) −2.38541e74 −0.241609 −0.120805 0.992676i \(-0.538547\pi\)
−0.120805 + 0.992676i \(0.538547\pi\)
\(42\) 0 0
\(43\) −1.84207e75 −0.203715 −0.101857 0.994799i \(-0.532479\pi\)
−0.101857 + 0.994799i \(0.532479\pi\)
\(44\) 8.25353e75 0.313394
\(45\) 0 0
\(46\) −1.93477e77 −0.929803
\(47\) −5.58584e77 −0.987502 −0.493751 0.869603i \(-0.664375\pi\)
−0.493751 + 0.869603i \(0.664375\pi\)
\(48\) 0 0
\(49\) 8.20845e78 2.08999
\(50\) 3.73903e79 3.72095
\(51\) 0 0
\(52\) −8.40858e77 −0.0135073
\(53\) 2.41979e80 1.60306 0.801531 0.597953i \(-0.204019\pi\)
0.801531 + 0.597953i \(0.204019\pi\)
\(54\) 0 0
\(55\) 2.60346e80 0.308096
\(56\) 4.75217e81 2.43304
\(57\) 0 0
\(58\) −1.73664e82 −1.73904
\(59\) 2.30840e82 1.04398 0.521990 0.852951i \(-0.325190\pi\)
0.521990 + 0.852951i \(0.325190\pi\)
\(60\) 0 0
\(61\) 1.46410e83 1.40518 0.702591 0.711594i \(-0.252027\pi\)
0.702591 + 0.711594i \(0.252027\pi\)
\(62\) −1.49393e82 −0.0673159
\(63\) 0 0
\(64\) −1.36965e84 −1.41007
\(65\) −2.65237e82 −0.0132789
\(66\) 0 0
\(67\) 1.40138e84 0.171426 0.0857131 0.996320i \(-0.472683\pi\)
0.0857131 + 0.996320i \(0.472683\pi\)
\(68\) 1.29370e85 0.794640
\(69\) 0 0
\(70\) 3.31888e86 5.29581
\(71\) 1.74082e86 1.43628 0.718142 0.695897i \(-0.244993\pi\)
0.718142 + 0.695897i \(0.244993\pi\)
\(72\) 0 0
\(73\) −4.65018e86 −1.05428 −0.527141 0.849778i \(-0.676736\pi\)
−0.527141 + 0.849778i \(0.676736\pi\)
\(74\) 9.88645e86 1.19060
\(75\) 0 0
\(76\) −8.90115e86 −0.310180
\(77\) 1.59198e87 0.302077
\(78\) 0 0
\(79\) −1.89450e88 −1.09103 −0.545513 0.838102i \(-0.683665\pi\)
−0.545513 + 0.838102i \(0.683665\pi\)
\(80\) 2.80584e88 0.900282
\(81\) 0 0
\(82\) −3.98902e88 −0.405996
\(83\) 2.23742e89 1.29603 0.648016 0.761627i \(-0.275599\pi\)
0.648016 + 0.761627i \(0.275599\pi\)
\(84\) 0 0
\(85\) 4.08081e89 0.781207
\(86\) −3.08041e89 −0.342319
\(87\) 0 0
\(88\) 6.23383e89 0.237854
\(89\) 1.44081e90 0.325066 0.162533 0.986703i \(-0.448034\pi\)
0.162533 + 0.986703i \(0.448034\pi\)
\(90\) 0 0
\(91\) −1.62188e89 −0.0130195
\(92\) −2.08962e91 −1.00910
\(93\) 0 0
\(94\) −9.34096e91 −1.65938
\(95\) −2.80774e91 −0.304937
\(96\) 0 0
\(97\) −8.44825e91 −0.348242 −0.174121 0.984724i \(-0.555708\pi\)
−0.174121 + 0.984724i \(0.555708\pi\)
\(98\) 1.37266e93 3.51198
\(99\) 0 0
\(100\) 4.03827e93 4.03827
\(101\) −1.31306e93 −0.826683 −0.413342 0.910576i \(-0.635639\pi\)
−0.413342 + 0.910576i \(0.635639\pi\)
\(102\) 0 0
\(103\) −1.21301e93 −0.306854 −0.153427 0.988160i \(-0.549031\pi\)
−0.153427 + 0.988160i \(0.549031\pi\)
\(104\) −6.35094e91 −0.0102515
\(105\) 0 0
\(106\) 4.04652e94 2.69376
\(107\) 1.56019e94 0.671168 0.335584 0.942010i \(-0.391066\pi\)
0.335584 + 0.942010i \(0.391066\pi\)
\(108\) 0 0
\(109\) 2.90925e94 0.528992 0.264496 0.964387i \(-0.414794\pi\)
0.264496 + 0.964387i \(0.414794\pi\)
\(110\) 4.35366e94 0.517719
\(111\) 0 0
\(112\) 1.71573e95 0.882695
\(113\) 5.02384e95 1.70957 0.854787 0.518979i \(-0.173688\pi\)
0.854787 + 0.518979i \(0.173688\pi\)
\(114\) 0 0
\(115\) −6.59141e95 −0.992040
\(116\) −1.87563e96 −1.88734
\(117\) 0 0
\(118\) 3.86024e96 1.75429
\(119\) 2.49535e96 0.765946
\(120\) 0 0
\(121\) −6.86280e96 −0.970469
\(122\) 2.44835e97 2.36124
\(123\) 0 0
\(124\) −1.61350e96 −0.0730566
\(125\) 6.98559e97 2.17715
\(126\) 0 0
\(127\) 5.70958e96 0.0850611 0.0425306 0.999095i \(-0.486458\pi\)
0.0425306 + 0.999095i \(0.486458\pi\)
\(128\) −1.76813e98 −1.82916
\(129\) 0 0
\(130\) −4.43545e96 −0.0223137
\(131\) 6.34511e96 0.0223524 0.0111762 0.999938i \(-0.496442\pi\)
0.0111762 + 0.999938i \(0.496442\pi\)
\(132\) 0 0
\(133\) −1.71689e98 −0.298980
\(134\) 2.34346e98 0.288062
\(135\) 0 0
\(136\) 9.77125e98 0.603102
\(137\) 1.94391e99 0.853436 0.426718 0.904385i \(-0.359670\pi\)
0.426718 + 0.904385i \(0.359670\pi\)
\(138\) 0 0
\(139\) 8.49504e99 1.90098 0.950489 0.310758i \(-0.100583\pi\)
0.950489 + 0.310758i \(0.100583\pi\)
\(140\) 3.58450e100 5.74745
\(141\) 0 0
\(142\) 2.91110e100 2.41351
\(143\) −2.12756e97 −0.00127279
\(144\) 0 0
\(145\) −5.91642e100 −1.85544
\(146\) −7.77630e100 −1.77160
\(147\) 0 0
\(148\) 1.06777e101 1.29213
\(149\) −1.32597e101 −1.17320 −0.586599 0.809878i \(-0.699534\pi\)
−0.586599 + 0.809878i \(0.699534\pi\)
\(150\) 0 0
\(151\) −3.45701e101 −1.64541 −0.822703 0.568472i \(-0.807535\pi\)
−0.822703 + 0.568472i \(0.807535\pi\)
\(152\) −6.72298e100 −0.235415
\(153\) 0 0
\(154\) 2.66220e101 0.507606
\(155\) −5.08955e100 −0.0718216
\(156\) 0 0
\(157\) −1.50836e102 −1.17266 −0.586331 0.810072i \(-0.699428\pi\)
−0.586331 + 0.810072i \(0.699428\pi\)
\(158\) −3.16809e102 −1.83334
\(159\) 0 0
\(160\) −3.00447e102 −0.968697
\(161\) −4.03055e102 −0.972660
\(162\) 0 0
\(163\) −2.68240e102 −0.364586 −0.182293 0.983244i \(-0.558352\pi\)
−0.182293 + 0.983244i \(0.558352\pi\)
\(164\) −4.30827e102 −0.440620
\(165\) 0 0
\(166\) 3.74153e103 2.17783
\(167\) −2.49429e102 −0.109807 −0.0549036 0.998492i \(-0.517485\pi\)
−0.0549036 + 0.998492i \(0.517485\pi\)
\(168\) 0 0
\(169\) −3.95101e103 −0.999945
\(170\) 6.82416e103 1.31273
\(171\) 0 0
\(172\) −3.32695e103 −0.371512
\(173\) −4.59720e103 −0.392057 −0.196029 0.980598i \(-0.562805\pi\)
−0.196029 + 0.980598i \(0.562805\pi\)
\(174\) 0 0
\(175\) 7.78919e104 3.89245
\(176\) 2.25067e103 0.0862923
\(177\) 0 0
\(178\) 2.40941e104 0.546236
\(179\) 3.50256e104 0.611954 0.305977 0.952039i \(-0.401017\pi\)
0.305977 + 0.952039i \(0.401017\pi\)
\(180\) 0 0
\(181\) −1.14588e105 −1.19422 −0.597111 0.802158i \(-0.703685\pi\)
−0.597111 + 0.802158i \(0.703685\pi\)
\(182\) −2.71221e103 −0.0218778
\(183\) 0 0
\(184\) −1.57827e105 −0.765867
\(185\) 3.36813e105 1.27029
\(186\) 0 0
\(187\) 3.27337e104 0.0748790
\(188\) −1.00885e106 −1.80089
\(189\) 0 0
\(190\) −4.69527e105 −0.512411
\(191\) −1.60846e106 −1.37518 −0.687589 0.726100i \(-0.741331\pi\)
−0.687589 + 0.726100i \(0.741331\pi\)
\(192\) 0 0
\(193\) −1.70685e106 −0.899043 −0.449521 0.893270i \(-0.648405\pi\)
−0.449521 + 0.893270i \(0.648405\pi\)
\(194\) −1.41276e106 −0.585180
\(195\) 0 0
\(196\) 1.48252e107 3.81148
\(197\) −3.10588e106 −0.630239 −0.315119 0.949052i \(-0.602045\pi\)
−0.315119 + 0.949052i \(0.602045\pi\)
\(198\) 0 0
\(199\) −6.17602e106 −0.783504 −0.391752 0.920071i \(-0.628131\pi\)
−0.391752 + 0.920071i \(0.628131\pi\)
\(200\) 3.05008e107 3.06490
\(201\) 0 0
\(202\) −2.19577e107 −1.38915
\(203\) −3.61780e107 −1.81919
\(204\) 0 0
\(205\) −1.35898e107 −0.433172
\(206\) −2.02846e107 −0.515633
\(207\) 0 0
\(208\) −2.29295e105 −0.00371920
\(209\) −2.25220e106 −0.0292283
\(210\) 0 0
\(211\) −8.25722e107 −0.688176 −0.344088 0.938937i \(-0.611812\pi\)
−0.344088 + 0.938937i \(0.611812\pi\)
\(212\) 4.37037e108 2.92349
\(213\) 0 0
\(214\) 2.60904e108 1.12782
\(215\) −1.04944e108 −0.365232
\(216\) 0 0
\(217\) −3.11218e107 −0.0704186
\(218\) 4.86502e108 0.888909
\(219\) 0 0
\(220\) 4.70209e108 0.561871
\(221\) −3.33486e106 −0.00322728
\(222\) 0 0
\(223\) −2.48798e109 −1.58369 −0.791846 0.610721i \(-0.790880\pi\)
−0.791846 + 0.610721i \(0.790880\pi\)
\(224\) −1.83719e109 −0.949774
\(225\) 0 0
\(226\) 8.40115e109 2.87274
\(227\) 4.23182e109 1.17849 0.589244 0.807955i \(-0.299426\pi\)
0.589244 + 0.807955i \(0.299426\pi\)
\(228\) 0 0
\(229\) 5.89882e109 1.09248 0.546242 0.837627i \(-0.316058\pi\)
0.546242 + 0.837627i \(0.316058\pi\)
\(230\) −1.10225e110 −1.66701
\(231\) 0 0
\(232\) −1.41665e110 −1.43242
\(233\) −2.13090e110 −1.76406 −0.882031 0.471192i \(-0.843824\pi\)
−0.882031 + 0.471192i \(0.843824\pi\)
\(234\) 0 0
\(235\) −3.18229e110 −1.77045
\(236\) 4.16918e110 1.90389
\(237\) 0 0
\(238\) 4.17287e110 1.28708
\(239\) 8.20500e109 0.208246 0.104123 0.994564i \(-0.466796\pi\)
0.104123 + 0.994564i \(0.466796\pi\)
\(240\) 0 0
\(241\) 3.90307e110 0.672378 0.336189 0.941795i \(-0.390862\pi\)
0.336189 + 0.941795i \(0.390862\pi\)
\(242\) −1.14764e111 −1.63076
\(243\) 0 0
\(244\) 2.64429e111 2.56261
\(245\) 4.67641e111 3.74705
\(246\) 0 0
\(247\) 2.29451e108 0.00125974
\(248\) −1.21866e110 −0.0554472
\(249\) 0 0
\(250\) 1.16817e112 3.65844
\(251\) 1.23935e111 0.322379 0.161190 0.986923i \(-0.448467\pi\)
0.161190 + 0.986923i \(0.448467\pi\)
\(252\) 0 0
\(253\) −5.28721e110 −0.0950873
\(254\) 9.54789e110 0.142935
\(255\) 0 0
\(256\) −1.60033e112 −1.66361
\(257\) 1.72101e112 1.49243 0.746213 0.665707i \(-0.231870\pi\)
0.746213 + 0.665707i \(0.231870\pi\)
\(258\) 0 0
\(259\) 2.05956e112 1.24548
\(260\) −4.79043e110 −0.0242166
\(261\) 0 0
\(262\) 1.06107e111 0.0375606
\(263\) 6.46068e111 0.191574 0.0957869 0.995402i \(-0.469463\pi\)
0.0957869 + 0.995402i \(0.469463\pi\)
\(264\) 0 0
\(265\) 1.37857e113 2.87407
\(266\) −2.87109e112 −0.502401
\(267\) 0 0
\(268\) 2.53102e112 0.312628
\(269\) 7.61241e111 0.0790753 0.0395377 0.999218i \(-0.487411\pi\)
0.0395377 + 0.999218i \(0.487411\pi\)
\(270\) 0 0
\(271\) −8.48308e112 −0.624427 −0.312213 0.950012i \(-0.601070\pi\)
−0.312213 + 0.950012i \(0.601070\pi\)
\(272\) 3.52782e112 0.218802
\(273\) 0 0
\(274\) 3.25073e113 1.43410
\(275\) 1.02177e113 0.380526
\(276\) 0 0
\(277\) 1.01098e113 0.268802 0.134401 0.990927i \(-0.457089\pi\)
0.134401 + 0.990927i \(0.457089\pi\)
\(278\) 1.42059e114 3.19437
\(279\) 0 0
\(280\) 2.70735e114 4.36210
\(281\) −2.93864e113 −0.401146 −0.200573 0.979679i \(-0.564280\pi\)
−0.200573 + 0.979679i \(0.564280\pi\)
\(282\) 0 0
\(283\) 1.44060e114 1.41408 0.707042 0.707172i \(-0.250029\pi\)
0.707042 + 0.707172i \(0.250029\pi\)
\(284\) 3.14408e114 2.61933
\(285\) 0 0
\(286\) −3.55783e111 −0.00213877
\(287\) −8.30999e113 −0.424710
\(288\) 0 0
\(289\) −2.18931e114 −0.810137
\(290\) −9.89377e114 −3.11785
\(291\) 0 0
\(292\) −8.39866e114 −1.92268
\(293\) −2.96400e114 −0.578807 −0.289403 0.957207i \(-0.593457\pi\)
−0.289403 + 0.957207i \(0.593457\pi\)
\(294\) 0 0
\(295\) 1.31511e115 1.87171
\(296\) 8.06478e114 0.980682
\(297\) 0 0
\(298\) −2.21736e115 −1.97142
\(299\) 5.38654e112 0.00409826
\(300\) 0 0
\(301\) −6.41716e114 −0.358097
\(302\) −5.78102e115 −2.76491
\(303\) 0 0
\(304\) −2.42727e114 −0.0854075
\(305\) 8.34105e115 2.51929
\(306\) 0 0
\(307\) 1.05946e115 0.236129 0.118065 0.993006i \(-0.462331\pi\)
0.118065 + 0.993006i \(0.462331\pi\)
\(308\) 2.87526e115 0.550895
\(309\) 0 0
\(310\) −8.51103e114 −0.120688
\(311\) 9.04218e115 1.10386 0.551931 0.833890i \(-0.313891\pi\)
0.551931 + 0.833890i \(0.313891\pi\)
\(312\) 0 0
\(313\) −8.51474e115 −0.771542 −0.385771 0.922595i \(-0.626064\pi\)
−0.385771 + 0.922595i \(0.626064\pi\)
\(314\) −2.52237e116 −1.97052
\(315\) 0 0
\(316\) −3.42164e116 −1.98969
\(317\) 2.02778e116 1.01804 0.509021 0.860754i \(-0.330008\pi\)
0.509021 + 0.860754i \(0.330008\pi\)
\(318\) 0 0
\(319\) −4.74577e115 −0.177844
\(320\) −7.80301e116 −2.52806
\(321\) 0 0
\(322\) −6.74012e116 −1.63444
\(323\) −3.53021e115 −0.0741112
\(324\) 0 0
\(325\) −1.04097e115 −0.0164007
\(326\) −4.48566e116 −0.612643
\(327\) 0 0
\(328\) −3.25401e116 −0.334414
\(329\) −1.94592e117 −1.73587
\(330\) 0 0
\(331\) −1.27033e116 −0.0854901 −0.0427450 0.999086i \(-0.513610\pi\)
−0.0427450 + 0.999086i \(0.513610\pi\)
\(332\) 4.04098e117 2.36356
\(333\) 0 0
\(334\) −4.17109e116 −0.184518
\(335\) 7.98374e116 0.307343
\(336\) 0 0
\(337\) −1.73776e117 −0.507225 −0.253612 0.967306i \(-0.581619\pi\)
−0.253612 + 0.967306i \(0.581619\pi\)
\(338\) −6.60710e117 −1.68029
\(339\) 0 0
\(340\) 7.37032e117 1.42468
\(341\) −4.08251e115 −0.00688413
\(342\) 0 0
\(343\) 1.49134e118 1.91602
\(344\) −2.51282e117 −0.281964
\(345\) 0 0
\(346\) −7.68770e117 −0.658806
\(347\) −1.27568e118 −0.955921 −0.477960 0.878381i \(-0.658624\pi\)
−0.477960 + 0.878381i \(0.658624\pi\)
\(348\) 0 0
\(349\) −9.04561e117 −0.518866 −0.259433 0.965761i \(-0.583536\pi\)
−0.259433 + 0.965761i \(0.583536\pi\)
\(350\) 1.30255e119 6.54081
\(351\) 0 0
\(352\) −2.40999e117 −0.0928500
\(353\) −4.00670e118 −1.35289 −0.676447 0.736492i \(-0.736481\pi\)
−0.676447 + 0.736492i \(0.736481\pi\)
\(354\) 0 0
\(355\) 9.91756e118 2.57505
\(356\) 2.60224e118 0.592819
\(357\) 0 0
\(358\) 5.85717e118 1.02832
\(359\) 3.72279e118 0.574085 0.287043 0.957918i \(-0.407328\pi\)
0.287043 + 0.957918i \(0.407328\pi\)
\(360\) 0 0
\(361\) −8.15335e118 −0.971071
\(362\) −1.91621e119 −2.00675
\(363\) 0 0
\(364\) −2.92927e117 −0.0237435
\(365\) −2.64924e119 −1.89018
\(366\) 0 0
\(367\) −1.79087e118 −0.0991043 −0.0495522 0.998772i \(-0.515779\pi\)
−0.0495522 + 0.998772i \(0.515779\pi\)
\(368\) −5.69821e118 −0.277853
\(369\) 0 0
\(370\) 5.63238e119 2.13458
\(371\) 8.42977e119 2.81792
\(372\) 0 0
\(373\) 4.39147e119 1.14327 0.571635 0.820508i \(-0.306309\pi\)
0.571635 + 0.820508i \(0.306309\pi\)
\(374\) 5.47391e118 0.125825
\(375\) 0 0
\(376\) −7.61980e119 −1.36681
\(377\) 4.83493e117 0.00766509
\(378\) 0 0
\(379\) −6.66278e119 −0.825909 −0.412954 0.910752i \(-0.635503\pi\)
−0.412954 + 0.910752i \(0.635503\pi\)
\(380\) −5.07105e119 −0.556110
\(381\) 0 0
\(382\) −2.68976e120 −2.31083
\(383\) −1.79657e120 −1.36679 −0.683395 0.730049i \(-0.739497\pi\)
−0.683395 + 0.730049i \(0.739497\pi\)
\(384\) 0 0
\(385\) 9.06960e119 0.541582
\(386\) −2.85429e120 −1.51074
\(387\) 0 0
\(388\) −1.52583e120 −0.635085
\(389\) 3.75042e120 1.38492 0.692459 0.721458i \(-0.256528\pi\)
0.692459 + 0.721458i \(0.256528\pi\)
\(390\) 0 0
\(391\) −8.28747e119 −0.241103
\(392\) 1.11974e121 2.89277
\(393\) 0 0
\(394\) −5.19383e120 −1.05904
\(395\) −1.07931e121 −1.95606
\(396\) 0 0
\(397\) −6.93819e119 −0.0994232 −0.0497116 0.998764i \(-0.515830\pi\)
−0.0497116 + 0.998764i \(0.515830\pi\)
\(398\) −1.03279e121 −1.31659
\(399\) 0 0
\(400\) 1.10120e121 1.11193
\(401\) 4.38284e120 0.394042 0.197021 0.980399i \(-0.436873\pi\)
0.197021 + 0.980399i \(0.436873\pi\)
\(402\) 0 0
\(403\) 4.15921e117 0.000296706 0
\(404\) −2.37150e121 −1.50761
\(405\) 0 0
\(406\) −6.04989e121 −3.05694
\(407\) 2.70170e120 0.121758
\(408\) 0 0
\(409\) 1.19957e121 0.430421 0.215210 0.976568i \(-0.430956\pi\)
0.215210 + 0.976568i \(0.430956\pi\)
\(410\) −2.27257e121 −0.727894
\(411\) 0 0
\(412\) −2.19080e121 −0.559606
\(413\) 8.04171e121 1.83515
\(414\) 0 0
\(415\) 1.27467e122 2.32360
\(416\) 2.45527e119 0.00400183
\(417\) 0 0
\(418\) −3.76625e120 −0.0491148
\(419\) 1.55294e122 1.81219 0.906095 0.423074i \(-0.139049\pi\)
0.906095 + 0.423074i \(0.139049\pi\)
\(420\) 0 0
\(421\) 1.20749e122 1.12919 0.564595 0.825368i \(-0.309032\pi\)
0.564595 + 0.825368i \(0.309032\pi\)
\(422\) −1.38082e122 −1.15640
\(423\) 0 0
\(424\) 3.30091e122 2.21882
\(425\) 1.60159e122 0.964861
\(426\) 0 0
\(427\) 5.10043e122 2.47008
\(428\) 2.81785e122 1.22400
\(429\) 0 0
\(430\) −1.75493e122 −0.613729
\(431\) −1.44577e122 −0.453842 −0.226921 0.973913i \(-0.572866\pi\)
−0.226921 + 0.973913i \(0.572866\pi\)
\(432\) 0 0
\(433\) −6.73888e122 −1.70569 −0.852846 0.522163i \(-0.825125\pi\)
−0.852846 + 0.522163i \(0.825125\pi\)
\(434\) −5.20437e121 −0.118330
\(435\) 0 0
\(436\) 5.25438e122 0.964716
\(437\) 5.70208e121 0.0941124
\(438\) 0 0
\(439\) −1.23553e123 −1.64912 −0.824560 0.565775i \(-0.808577\pi\)
−0.824560 + 0.565775i \(0.808577\pi\)
\(440\) 3.55145e122 0.426439
\(441\) 0 0
\(442\) −5.57674e120 −0.00542307
\(443\) −2.19056e122 −0.191771 −0.0958854 0.995392i \(-0.530568\pi\)
−0.0958854 + 0.995392i \(0.530568\pi\)
\(444\) 0 0
\(445\) 8.20840e122 0.582798
\(446\) −4.16054e123 −2.66121
\(447\) 0 0
\(448\) −4.77142e123 −2.47868
\(449\) −7.18526e122 −0.336502 −0.168251 0.985744i \(-0.553812\pi\)
−0.168251 + 0.985744i \(0.553812\pi\)
\(450\) 0 0
\(451\) −1.09009e122 −0.0415197
\(452\) 9.07351e123 3.11773
\(453\) 0 0
\(454\) 7.07670e123 1.98031
\(455\) −9.23999e121 −0.0233422
\(456\) 0 0
\(457\) 4.72549e123 0.973518 0.486759 0.873536i \(-0.338179\pi\)
0.486759 + 0.873536i \(0.338179\pi\)
\(458\) 9.86434e123 1.83579
\(459\) 0 0
\(460\) −1.19047e124 −1.80917
\(461\) −1.23678e124 −1.69902 −0.849510 0.527573i \(-0.823102\pi\)
−0.849510 + 0.527573i \(0.823102\pi\)
\(462\) 0 0
\(463\) 7.69925e123 0.864833 0.432417 0.901674i \(-0.357661\pi\)
0.432417 + 0.901674i \(0.357661\pi\)
\(464\) −5.11468e123 −0.519676
\(465\) 0 0
\(466\) −3.56342e124 −2.96430
\(467\) 1.64477e124 1.23843 0.619215 0.785222i \(-0.287451\pi\)
0.619215 + 0.785222i \(0.287451\pi\)
\(468\) 0 0
\(469\) 4.88194e123 0.301339
\(470\) −5.32161e124 −2.97504
\(471\) 0 0
\(472\) 3.14895e124 1.44498
\(473\) −8.41793e122 −0.0350076
\(474\) 0 0
\(475\) −1.10195e124 −0.376625
\(476\) 4.50684e124 1.39685
\(477\) 0 0
\(478\) 1.37209e124 0.349933
\(479\) 2.79704e124 0.647287 0.323643 0.946179i \(-0.395092\pi\)
0.323643 + 0.946179i \(0.395092\pi\)
\(480\) 0 0
\(481\) −2.75245e122 −0.00524776
\(482\) 6.52693e124 1.12985
\(483\) 0 0
\(484\) −1.23949e125 −1.76983
\(485\) −4.81302e124 −0.624349
\(486\) 0 0
\(487\) 2.15017e124 0.230343 0.115172 0.993346i \(-0.463258\pi\)
0.115172 + 0.993346i \(0.463258\pi\)
\(488\) 1.99721e125 1.94493
\(489\) 0 0
\(490\) 7.82016e125 6.29648
\(491\) 2.58184e123 0.0189077 0.00945387 0.999955i \(-0.496991\pi\)
0.00945387 + 0.999955i \(0.496991\pi\)
\(492\) 0 0
\(493\) −7.43879e124 −0.450942
\(494\) 3.83700e122 0.00211685
\(495\) 0 0
\(496\) −4.39986e123 −0.0201160
\(497\) 6.06444e125 2.52475
\(498\) 0 0
\(499\) 4.24177e125 1.46511 0.732557 0.680706i \(-0.238327\pi\)
0.732557 + 0.680706i \(0.238327\pi\)
\(500\) 1.26166e126 3.97043
\(501\) 0 0
\(502\) 2.07252e125 0.541721
\(503\) −6.20313e125 −1.47809 −0.739043 0.673658i \(-0.764722\pi\)
−0.739043 + 0.673658i \(0.764722\pi\)
\(504\) 0 0
\(505\) −7.48057e125 −1.48213
\(506\) −8.84158e124 −0.159783
\(507\) 0 0
\(508\) 1.03120e125 0.155125
\(509\) −6.21343e125 −0.853011 −0.426505 0.904485i \(-0.640255\pi\)
−0.426505 + 0.904485i \(0.640255\pi\)
\(510\) 0 0
\(511\) −1.61997e126 −1.85325
\(512\) −9.25092e125 −0.966344
\(513\) 0 0
\(514\) 2.87797e126 2.50785
\(515\) −6.91058e125 −0.550146
\(516\) 0 0
\(517\) −2.55263e125 −0.169698
\(518\) 3.44412e126 2.09288
\(519\) 0 0
\(520\) −3.61817e124 −0.0183795
\(521\) −1.08310e126 −0.503170 −0.251585 0.967835i \(-0.580952\pi\)
−0.251585 + 0.967835i \(0.580952\pi\)
\(522\) 0 0
\(523\) −2.12144e126 −0.824711 −0.412356 0.911023i \(-0.635294\pi\)
−0.412356 + 0.911023i \(0.635294\pi\)
\(524\) 1.14599e125 0.0407638
\(525\) 0 0
\(526\) 1.08039e126 0.321917
\(527\) −6.39916e124 −0.0174554
\(528\) 0 0
\(529\) −3.03348e126 −0.693828
\(530\) 2.30533e127 4.82953
\(531\) 0 0
\(532\) −3.10087e126 −0.545246
\(533\) 1.11057e124 0.00178950
\(534\) 0 0
\(535\) 8.88850e126 1.20331
\(536\) 1.91166e126 0.237273
\(537\) 0 0
\(538\) 1.27299e126 0.132877
\(539\) 3.75112e126 0.359156
\(540\) 0 0
\(541\) 5.54574e126 0.446978 0.223489 0.974706i \(-0.428255\pi\)
0.223489 + 0.974706i \(0.428255\pi\)
\(542\) −1.41859e127 −1.04928
\(543\) 0 0
\(544\) −3.77755e126 −0.235430
\(545\) 1.65742e127 0.948408
\(546\) 0 0
\(547\) 2.32636e127 1.12271 0.561354 0.827576i \(-0.310281\pi\)
0.561354 + 0.827576i \(0.310281\pi\)
\(548\) 3.51089e127 1.55640
\(549\) 0 0
\(550\) 1.70867e127 0.639430
\(551\) 5.11816e126 0.176021
\(552\) 0 0
\(553\) −6.59982e127 −1.91784
\(554\) 1.69061e127 0.451690
\(555\) 0 0
\(556\) 1.53428e128 3.46679
\(557\) −5.86328e127 −1.21864 −0.609318 0.792926i \(-0.708557\pi\)
−0.609318 + 0.792926i \(0.708557\pi\)
\(558\) 0 0
\(559\) 8.57607e124 0.00150883
\(560\) 9.77462e127 1.58255
\(561\) 0 0
\(562\) −4.91416e127 −0.674079
\(563\) 6.83447e127 0.863107 0.431554 0.902087i \(-0.357966\pi\)
0.431554 + 0.902087i \(0.357966\pi\)
\(564\) 0 0
\(565\) 2.86211e128 3.06502
\(566\) 2.40906e128 2.37620
\(567\) 0 0
\(568\) 2.37470e128 1.98797
\(569\) 1.82425e128 1.40722 0.703611 0.710585i \(-0.251570\pi\)
0.703611 + 0.710585i \(0.251570\pi\)
\(570\) 0 0
\(571\) 8.22711e127 0.539099 0.269549 0.962987i \(-0.413125\pi\)
0.269549 + 0.962987i \(0.413125\pi\)
\(572\) −3.84258e125 −0.00232117
\(573\) 0 0
\(574\) −1.38964e128 −0.713675
\(575\) −2.58692e128 −1.22526
\(576\) 0 0
\(577\) −1.15417e128 −0.465150 −0.232575 0.972578i \(-0.574715\pi\)
−0.232575 + 0.972578i \(0.574715\pi\)
\(578\) −3.66110e128 −1.36134
\(579\) 0 0
\(580\) −1.06856e129 −3.38374
\(581\) 7.79442e128 2.27821
\(582\) 0 0
\(583\) 1.10580e128 0.275480
\(584\) −6.34344e128 −1.45924
\(585\) 0 0
\(586\) −4.95657e128 −0.972617
\(587\) −4.28859e128 −0.777397 −0.388699 0.921365i \(-0.627075\pi\)
−0.388699 + 0.921365i \(0.627075\pi\)
\(588\) 0 0
\(589\) 4.40285e126 0.00681354
\(590\) 2.19920e129 3.14519
\(591\) 0 0
\(592\) 2.91172e128 0.355787
\(593\) −8.20747e128 −0.927184 −0.463592 0.886049i \(-0.653440\pi\)
−0.463592 + 0.886049i \(0.653440\pi\)
\(594\) 0 0
\(595\) 1.42162e129 1.37323
\(596\) −2.39482e129 −2.13955
\(597\) 0 0
\(598\) 9.00768e126 0.00688665
\(599\) −4.54499e128 −0.321504 −0.160752 0.986995i \(-0.551392\pi\)
−0.160752 + 0.986995i \(0.551392\pi\)
\(600\) 0 0
\(601\) −2.06533e129 −1.25120 −0.625599 0.780145i \(-0.715145\pi\)
−0.625599 + 0.780145i \(0.715145\pi\)
\(602\) −1.07311e129 −0.601740
\(603\) 0 0
\(604\) −6.24369e129 −3.00071
\(605\) −3.90978e129 −1.73991
\(606\) 0 0
\(607\) −3.80973e129 −1.45419 −0.727094 0.686538i \(-0.759130\pi\)
−0.727094 + 0.686538i \(0.759130\pi\)
\(608\) 2.59909e128 0.0918979
\(609\) 0 0
\(610\) 1.39484e130 4.23338
\(611\) 2.60058e127 0.00731400
\(612\) 0 0
\(613\) −4.21082e129 −1.01731 −0.508656 0.860970i \(-0.669857\pi\)
−0.508656 + 0.860970i \(0.669857\pi\)
\(614\) 1.77169e129 0.396787
\(615\) 0 0
\(616\) 2.17166e129 0.418108
\(617\) 4.88112e129 0.871484 0.435742 0.900072i \(-0.356486\pi\)
0.435742 + 0.900072i \(0.356486\pi\)
\(618\) 0 0
\(619\) −7.62026e129 −1.17045 −0.585227 0.810869i \(-0.698995\pi\)
−0.585227 + 0.810869i \(0.698995\pi\)
\(620\) −9.19219e128 −0.130980
\(621\) 0 0
\(622\) 1.51208e130 1.85491
\(623\) 5.01931e129 0.571413
\(624\) 0 0
\(625\) 1.72204e130 1.68897
\(626\) −1.42388e130 −1.29649
\(627\) 0 0
\(628\) −2.72425e130 −2.13857
\(629\) 4.23479e129 0.308729
\(630\) 0 0
\(631\) −4.44127e129 −0.279346 −0.139673 0.990198i \(-0.544605\pi\)
−0.139673 + 0.990198i \(0.544605\pi\)
\(632\) −2.58434e130 −1.51010
\(633\) 0 0
\(634\) 3.39097e130 1.71070
\(635\) 3.25279e129 0.152503
\(636\) 0 0
\(637\) −3.82159e128 −0.0154796
\(638\) −7.93615e129 −0.298847
\(639\) 0 0
\(640\) −1.00732e131 −3.27942
\(641\) −5.07224e130 −1.53568 −0.767841 0.640640i \(-0.778669\pi\)
−0.767841 + 0.640640i \(0.778669\pi\)
\(642\) 0 0
\(643\) 5.10656e130 1.33757 0.668787 0.743454i \(-0.266814\pi\)
0.668787 + 0.743454i \(0.266814\pi\)
\(644\) −7.27955e130 −1.77383
\(645\) 0 0
\(646\) −5.90343e129 −0.124535
\(647\) 1.41954e130 0.278675 0.139337 0.990245i \(-0.455503\pi\)
0.139337 + 0.990245i \(0.455503\pi\)
\(648\) 0 0
\(649\) 1.05490e130 0.179404
\(650\) −1.74077e129 −0.0275594
\(651\) 0 0
\(652\) −4.84466e130 −0.664890
\(653\) 1.15140e131 1.47150 0.735752 0.677251i \(-0.236829\pi\)
0.735752 + 0.677251i \(0.236829\pi\)
\(654\) 0 0
\(655\) 3.61485e129 0.0400747
\(656\) −1.17483e130 −0.121324
\(657\) 0 0
\(658\) −3.25408e131 −2.91692
\(659\) −1.96031e131 −1.63740 −0.818698 0.574224i \(-0.805304\pi\)
−0.818698 + 0.574224i \(0.805304\pi\)
\(660\) 0 0
\(661\) −2.17070e131 −1.57482 −0.787410 0.616429i \(-0.788579\pi\)
−0.787410 + 0.616429i \(0.788579\pi\)
\(662\) −2.12432e130 −0.143656
\(663\) 0 0
\(664\) 3.05212e131 1.79385
\(665\) −9.78126e130 −0.536029
\(666\) 0 0
\(667\) 1.20153e131 0.572642
\(668\) −4.50492e130 −0.200254
\(669\) 0 0
\(670\) 1.33509e131 0.516454
\(671\) 6.69067e130 0.241475
\(672\) 0 0
\(673\) 2.57783e131 0.810127 0.405063 0.914289i \(-0.367249\pi\)
0.405063 + 0.914289i \(0.367249\pi\)
\(674\) −2.90599e131 −0.852332
\(675\) 0 0
\(676\) −7.13589e131 −1.82359
\(677\) −3.80729e131 −0.908328 −0.454164 0.890918i \(-0.650062\pi\)
−0.454164 + 0.890918i \(0.650062\pi\)
\(678\) 0 0
\(679\) −2.94309e131 −0.612152
\(680\) 5.56675e131 1.08128
\(681\) 0 0
\(682\) −6.82701e129 −0.0115680
\(683\) −6.39876e131 −1.01282 −0.506411 0.862292i \(-0.669028\pi\)
−0.506411 + 0.862292i \(0.669028\pi\)
\(684\) 0 0
\(685\) 1.10746e132 1.53009
\(686\) 2.49390e132 3.21964
\(687\) 0 0
\(688\) −9.07229e130 −0.102295
\(689\) −1.12658e130 −0.0118732
\(690\) 0 0
\(691\) 1.56983e131 0.144585 0.0722925 0.997383i \(-0.476968\pi\)
0.0722925 + 0.997383i \(0.476968\pi\)
\(692\) −8.30297e131 −0.714990
\(693\) 0 0
\(694\) −2.13327e132 −1.60631
\(695\) 4.83968e132 3.40819
\(696\) 0 0
\(697\) −1.70867e131 −0.105277
\(698\) −1.51266e132 −0.871894
\(699\) 0 0
\(700\) 1.40680e133 7.09862
\(701\) 1.73944e132 0.821335 0.410668 0.911785i \(-0.365296\pi\)
0.410668 + 0.911785i \(0.365296\pi\)
\(702\) 0 0
\(703\) −2.91369e131 −0.120509
\(704\) −6.25908e131 −0.242316
\(705\) 0 0
\(706\) −6.70024e132 −2.27338
\(707\) −4.57425e132 −1.45317
\(708\) 0 0
\(709\) 5.69886e132 1.58759 0.793794 0.608186i \(-0.208103\pi\)
0.793794 + 0.608186i \(0.208103\pi\)
\(710\) 1.65847e133 4.32708
\(711\) 0 0
\(712\) 1.96545e132 0.449928
\(713\) 1.03361e131 0.0221662
\(714\) 0 0
\(715\) −1.21209e130 −0.00228193
\(716\) 6.32594e132 1.11601
\(717\) 0 0
\(718\) 6.22546e132 0.964683
\(719\) 5.60725e131 0.0814435 0.0407218 0.999171i \(-0.487034\pi\)
0.0407218 + 0.999171i \(0.487034\pi\)
\(720\) 0 0
\(721\) −4.22572e132 −0.539399
\(722\) −1.36345e133 −1.63177
\(723\) 0 0
\(724\) −2.06956e133 −2.17789
\(725\) −2.32200e133 −2.29163
\(726\) 0 0
\(727\) −3.95282e132 −0.343207 −0.171604 0.985166i \(-0.554895\pi\)
−0.171604 + 0.985166i \(0.554895\pi\)
\(728\) −2.21246e131 −0.0180205
\(729\) 0 0
\(730\) −4.43021e133 −3.17623
\(731\) −1.31947e132 −0.0887652
\(732\) 0 0
\(733\) −1.21179e133 −0.717950 −0.358975 0.933347i \(-0.616874\pi\)
−0.358975 + 0.933347i \(0.616874\pi\)
\(734\) −2.99480e132 −0.166533
\(735\) 0 0
\(736\) 6.10159e132 0.298968
\(737\) 6.40405e131 0.0294589
\(738\) 0 0
\(739\) 2.87595e133 1.16631 0.583157 0.812360i \(-0.301817\pi\)
0.583157 + 0.812360i \(0.301817\pi\)
\(740\) 6.08315e133 2.31661
\(741\) 0 0
\(742\) 1.40967e134 4.73519
\(743\) 9.00234e132 0.284037 0.142019 0.989864i \(-0.454641\pi\)
0.142019 + 0.989864i \(0.454641\pi\)
\(744\) 0 0
\(745\) −7.55412e133 −2.10338
\(746\) 7.34366e133 1.92113
\(747\) 0 0
\(748\) 5.91200e132 0.136556
\(749\) 5.43518e133 1.17980
\(750\) 0 0
\(751\) −7.48940e133 −1.43612 −0.718059 0.695982i \(-0.754969\pi\)
−0.718059 + 0.695982i \(0.754969\pi\)
\(752\) −2.75106e133 −0.495873
\(753\) 0 0
\(754\) 8.08525e131 0.0128803
\(755\) −1.96948e134 −2.94998
\(756\) 0 0
\(757\) 1.10318e134 1.46113 0.730565 0.682843i \(-0.239257\pi\)
0.730565 + 0.682843i \(0.239257\pi\)
\(758\) −1.11419e134 −1.38784
\(759\) 0 0
\(760\) −3.83012e133 −0.422066
\(761\) 1.06465e134 1.10362 0.551811 0.833969i \(-0.313937\pi\)
0.551811 + 0.833969i \(0.313937\pi\)
\(762\) 0 0
\(763\) 1.01349e134 0.929881
\(764\) −2.90503e134 −2.50790
\(765\) 0 0
\(766\) −3.00433e134 −2.29673
\(767\) −1.07472e132 −0.00773231
\(768\) 0 0
\(769\) 2.64666e134 1.68703 0.843515 0.537105i \(-0.180482\pi\)
0.843515 + 0.537105i \(0.180482\pi\)
\(770\) 1.51667e134 0.910065
\(771\) 0 0
\(772\) −3.08273e134 −1.63957
\(773\) 1.28102e134 0.641518 0.320759 0.947161i \(-0.396062\pi\)
0.320759 + 0.947161i \(0.396062\pi\)
\(774\) 0 0
\(775\) −1.99748e133 −0.0887062
\(776\) −1.15245e134 −0.482005
\(777\) 0 0
\(778\) 6.27167e134 2.32719
\(779\) 1.17563e133 0.0410939
\(780\) 0 0
\(781\) 7.95523e133 0.246820
\(782\) −1.38588e134 −0.405146
\(783\) 0 0
\(784\) 4.04271e134 1.04948
\(785\) −8.59326e134 −2.10242
\(786\) 0 0
\(787\) 2.01831e133 0.0438696 0.0219348 0.999759i \(-0.493017\pi\)
0.0219348 + 0.999759i \(0.493017\pi\)
\(788\) −5.60951e134 −1.14936
\(789\) 0 0
\(790\) −1.80488e135 −3.28692
\(791\) 1.75014e135 3.00515
\(792\) 0 0
\(793\) −6.81636e132 −0.0104076
\(794\) −1.16024e134 −0.167069
\(795\) 0 0
\(796\) −1.11545e135 −1.42887
\(797\) −1.38083e134 −0.166850 −0.0834252 0.996514i \(-0.526586\pi\)
−0.0834252 + 0.996514i \(0.526586\pi\)
\(798\) 0 0
\(799\) −4.00113e134 −0.430287
\(800\) −1.17916e135 −1.19643
\(801\) 0 0
\(802\) 7.32924e134 0.662141
\(803\) −2.12505e134 −0.181174
\(804\) 0 0
\(805\) −2.29623e135 −1.74384
\(806\) 6.95527e131 0.000498579 0
\(807\) 0 0
\(808\) −1.79118e135 −1.14422
\(809\) −6.20202e134 −0.374047 −0.187024 0.982355i \(-0.559884\pi\)
−0.187024 + 0.982355i \(0.559884\pi\)
\(810\) 0 0
\(811\) 1.84479e135 0.991922 0.495961 0.868345i \(-0.334816\pi\)
0.495961 + 0.868345i \(0.334816\pi\)
\(812\) −6.53408e135 −3.31764
\(813\) 0 0
\(814\) 4.51794e134 0.204600
\(815\) −1.52818e135 −0.653650
\(816\) 0 0
\(817\) 9.07846e133 0.0346487
\(818\) 2.00600e135 0.723272
\(819\) 0 0
\(820\) −2.45445e135 −0.789970
\(821\) 2.15187e135 0.654425 0.327213 0.944951i \(-0.393891\pi\)
0.327213 + 0.944951i \(0.393891\pi\)
\(822\) 0 0
\(823\) −5.23448e135 −1.42161 −0.710806 0.703388i \(-0.751670\pi\)
−0.710806 + 0.703388i \(0.751670\pi\)
\(824\) −1.65470e135 −0.424720
\(825\) 0 0
\(826\) 1.34478e136 3.08375
\(827\) 4.54736e135 0.985719 0.492860 0.870109i \(-0.335952\pi\)
0.492860 + 0.870109i \(0.335952\pi\)
\(828\) 0 0
\(829\) 9.79485e135 1.89763 0.948816 0.315828i \(-0.102282\pi\)
0.948816 + 0.315828i \(0.102282\pi\)
\(830\) 2.13158e136 3.90454
\(831\) 0 0
\(832\) 6.37666e133 0.0104438
\(833\) 5.87971e135 0.910675
\(834\) 0 0
\(835\) −1.42101e135 −0.196869
\(836\) −4.06767e134 −0.0533033
\(837\) 0 0
\(838\) 2.59692e136 3.04517
\(839\) −7.42245e135 −0.823409 −0.411705 0.911317i \(-0.635066\pi\)
−0.411705 + 0.911317i \(0.635066\pi\)
\(840\) 0 0
\(841\) 7.15226e134 0.0710280
\(842\) 2.01924e136 1.89747
\(843\) 0 0
\(844\) −1.49133e136 −1.25502
\(845\) −2.25092e136 −1.79276
\(846\) 0 0
\(847\) −2.39077e136 −1.70592
\(848\) 1.19176e136 0.804976
\(849\) 0 0
\(850\) 2.67826e136 1.62134
\(851\) −6.84013e135 −0.392049
\(852\) 0 0
\(853\) 2.84936e135 0.146426 0.0732128 0.997316i \(-0.476675\pi\)
0.0732128 + 0.997316i \(0.476675\pi\)
\(854\) 8.52923e136 4.15068
\(855\) 0 0
\(856\) 2.12830e136 0.928971
\(857\) −1.21549e136 −0.502507 −0.251254 0.967921i \(-0.580843\pi\)
−0.251254 + 0.967921i \(0.580843\pi\)
\(858\) 0 0
\(859\) −7.04217e135 −0.261231 −0.130615 0.991433i \(-0.541695\pi\)
−0.130615 + 0.991433i \(0.541695\pi\)
\(860\) −1.89538e136 −0.666069
\(861\) 0 0
\(862\) −2.41769e136 −0.762629
\(863\) −2.08063e136 −0.621859 −0.310930 0.950433i \(-0.600640\pi\)
−0.310930 + 0.950433i \(0.600640\pi\)
\(864\) 0 0
\(865\) −2.61906e136 −0.702903
\(866\) −1.12691e137 −2.86621
\(867\) 0 0
\(868\) −5.62089e135 −0.128422
\(869\) −8.65754e135 −0.187489
\(870\) 0 0
\(871\) −6.52436e133 −0.00126968
\(872\) 3.96859e136 0.732183
\(873\) 0 0
\(874\) 9.53535e135 0.158145
\(875\) 2.43355e137 3.82707
\(876\) 0 0
\(877\) 3.05763e136 0.432418 0.216209 0.976347i \(-0.430631\pi\)
0.216209 + 0.976347i \(0.430631\pi\)
\(878\) −2.06612e137 −2.77115
\(879\) 0 0
\(880\) 1.28222e136 0.154710
\(881\) 7.50481e136 0.858935 0.429467 0.903082i \(-0.358701\pi\)
0.429467 + 0.903082i \(0.358701\pi\)
\(882\) 0 0
\(883\) −5.64375e136 −0.581293 −0.290647 0.956830i \(-0.593870\pi\)
−0.290647 + 0.956830i \(0.593870\pi\)
\(884\) −6.02307e134 −0.00588555
\(885\) 0 0
\(886\) −3.66318e136 −0.322248
\(887\) −1.61696e136 −0.134974 −0.0674872 0.997720i \(-0.521498\pi\)
−0.0674872 + 0.997720i \(0.521498\pi\)
\(888\) 0 0
\(889\) 1.98903e136 0.149523
\(890\) 1.37266e137 0.979324
\(891\) 0 0
\(892\) −4.49352e137 −2.88816
\(893\) 2.75293e136 0.167958
\(894\) 0 0
\(895\) 1.99543e137 1.09715
\(896\) −6.15959e137 −3.21536
\(897\) 0 0
\(898\) −1.20156e137 −0.565452
\(899\) 9.27759e135 0.0414581
\(900\) 0 0
\(901\) 1.73330e137 0.698507
\(902\) −1.82291e136 −0.0697689
\(903\) 0 0
\(904\) 6.85316e137 2.36624
\(905\) −6.52815e137 −2.14107
\(906\) 0 0
\(907\) −5.22741e137 −1.54721 −0.773603 0.633671i \(-0.781547\pi\)
−0.773603 + 0.633671i \(0.781547\pi\)
\(908\) 7.64306e137 2.14919
\(909\) 0 0
\(910\) −1.54516e136 −0.0392238
\(911\) −2.17562e137 −0.524781 −0.262391 0.964962i \(-0.584511\pi\)
−0.262391 + 0.964962i \(0.584511\pi\)
\(912\) 0 0
\(913\) 1.02246e137 0.222718
\(914\) 7.90224e137 1.63588
\(915\) 0 0
\(916\) 1.06538e138 1.99235
\(917\) 2.21043e136 0.0392918
\(918\) 0 0
\(919\) −2.13720e137 −0.343301 −0.171650 0.985158i \(-0.554910\pi\)
−0.171650 + 0.985158i \(0.554910\pi\)
\(920\) −8.99153e137 −1.37309
\(921\) 0 0
\(922\) −2.06821e138 −2.85500
\(923\) −8.10468e135 −0.0106379
\(924\) 0 0
\(925\) 1.32188e138 1.56893
\(926\) 1.28751e138 1.45325
\(927\) 0 0
\(928\) 5.47675e137 0.559168
\(929\) −1.80381e138 −1.75171 −0.875853 0.482578i \(-0.839700\pi\)
−0.875853 + 0.482578i \(0.839700\pi\)
\(930\) 0 0
\(931\) −4.04546e137 −0.355474
\(932\) −3.84861e138 −3.21710
\(933\) 0 0
\(934\) 2.75048e138 2.08104
\(935\) 1.86486e137 0.134247
\(936\) 0 0
\(937\) −1.75823e138 −1.14600 −0.573001 0.819555i \(-0.694221\pi\)
−0.573001 + 0.819555i \(0.694221\pi\)
\(938\) 8.16386e137 0.506365
\(939\) 0 0
\(940\) −5.74751e138 −3.22875
\(941\) 2.47445e138 1.32301 0.661503 0.749943i \(-0.269919\pi\)
0.661503 + 0.749943i \(0.269919\pi\)
\(942\) 0 0
\(943\) 2.75988e137 0.133689
\(944\) 1.13690e138 0.524233
\(945\) 0 0
\(946\) −1.40769e137 −0.0588262
\(947\) −5.09791e137 −0.202823 −0.101412 0.994845i \(-0.532336\pi\)
−0.101412 + 0.994845i \(0.532336\pi\)
\(948\) 0 0
\(949\) 2.16497e136 0.00780861
\(950\) −1.84274e138 −0.632874
\(951\) 0 0
\(952\) 3.40398e138 1.06015
\(953\) −4.08950e138 −1.21297 −0.606485 0.795095i \(-0.707421\pi\)
−0.606485 + 0.795095i \(0.707421\pi\)
\(954\) 0 0
\(955\) −9.16351e138 −2.46550
\(956\) 1.48190e138 0.379775
\(957\) 0 0
\(958\) 4.67736e138 1.08769
\(959\) 6.77196e138 1.50020
\(960\) 0 0
\(961\) −4.96524e138 −0.998395
\(962\) −4.60281e136 −0.00881825
\(963\) 0 0
\(964\) 7.04930e138 1.22621
\(965\) −9.72403e138 −1.61186
\(966\) 0 0
\(967\) −8.90772e138 −1.34102 −0.670511 0.741900i \(-0.733925\pi\)
−0.670511 + 0.741900i \(0.733925\pi\)
\(968\) −9.36174e138 −1.34324
\(969\) 0 0
\(970\) −8.04862e138 −1.04915
\(971\) 9.30395e138 1.15604 0.578021 0.816022i \(-0.303825\pi\)
0.578021 + 0.816022i \(0.303825\pi\)
\(972\) 0 0
\(973\) 2.95939e139 3.34161
\(974\) 3.59563e138 0.387065
\(975\) 0 0
\(976\) 7.21076e138 0.705610
\(977\) −1.24550e139 −1.16210 −0.581052 0.813867i \(-0.697359\pi\)
−0.581052 + 0.813867i \(0.697359\pi\)
\(978\) 0 0
\(979\) 6.58426e137 0.0558614
\(980\) 8.44603e139 6.83345
\(981\) 0 0
\(982\) 4.31750e137 0.0317723
\(983\) 4.90628e138 0.344361 0.172181 0.985065i \(-0.444919\pi\)
0.172181 + 0.985065i \(0.444919\pi\)
\(984\) 0 0
\(985\) −1.76944e139 −1.12993
\(986\) −1.24396e139 −0.757755
\(987\) 0 0
\(988\) 4.14409e136 0.00229737
\(989\) 2.13124e138 0.112721
\(990\) 0 0
\(991\) −4.86403e138 −0.234192 −0.117096 0.993121i \(-0.537358\pi\)
−0.117096 + 0.993121i \(0.537358\pi\)
\(992\) 4.71133e137 0.0216447
\(993\) 0 0
\(994\) 1.01413e140 4.24255
\(995\) −3.51852e139 −1.40471
\(996\) 0 0
\(997\) 1.15939e139 0.421602 0.210801 0.977529i \(-0.432393\pi\)
0.210801 + 0.977529i \(0.432393\pi\)
\(998\) 7.09332e139 2.46195
\(999\) 0 0
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 9.94.a.b.1.7 7
3.2 odd 2 1.94.a.a.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.94.a.a.1.1 7 3.2 odd 2
9.94.a.b.1.7 7 1.1 even 1 trivial