Properties

Label 95.5.d.c.94.2
Level $95$
Weight $5$
Character 95.94
Self dual yes
Analytic conductor $9.820$
Analytic rank $0$
Dimension $2$
CM discriminant -95
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,5,Mod(94,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.94");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(9.82014649297\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 94.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 95.94

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+6.70820 q^{2} +4.47214 q^{3} +29.0000 q^{4} +25.0000 q^{5} +30.0000 q^{6} +87.2067 q^{8} -61.0000 q^{9} +O(q^{10})\) \(q+6.70820 q^{2} +4.47214 q^{3} +29.0000 q^{4} +25.0000 q^{5} +30.0000 q^{6} +87.2067 q^{8} -61.0000 q^{9} +167.705 q^{10} -62.0000 q^{11} +129.692 q^{12} -67.0820 q^{13} +111.803 q^{15} +121.000 q^{16} -409.200 q^{18} +361.000 q^{19} +725.000 q^{20} -415.909 q^{22} +390.000 q^{24} +625.000 q^{25} -450.000 q^{26} -635.043 q^{27} +750.000 q^{30} -583.614 q^{32} -277.272 q^{33} -1769.00 q^{36} -2643.03 q^{37} +2421.66 q^{38} -300.000 q^{39} +2180.17 q^{40} -1798.00 q^{44} -1525.00 q^{45} +541.128 q^{48} +2401.00 q^{49} +4192.63 q^{50} -1945.38 q^{52} +791.568 q^{53} -4260.00 q^{54} -1550.00 q^{55} +1614.44 q^{57} +3242.30 q^{60} +7138.00 q^{61} -5851.00 q^{64} -1677.05 q^{65} -1860.00 q^{66} -6077.63 q^{67} -5319.61 q^{72} -17730.0 q^{74} +2795.08 q^{75} +10469.0 q^{76} -2012.46 q^{78} +3025.00 q^{80} +2101.00 q^{81} -5406.81 q^{88} -10230.0 q^{90} +9025.00 q^{95} -2610.00 q^{96} -15415.5 q^{97} +16106.4 q^{98} +3782.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 58 q^{4} + 50 q^{5} + 60 q^{6} - 122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 58 q^{4} + 50 q^{5} + 60 q^{6} - 122 q^{9} - 124 q^{11} + 242 q^{16} + 722 q^{19} + 1450 q^{20} + 780 q^{24} + 1250 q^{25} - 900 q^{26} + 1500 q^{30} - 3538 q^{36} - 600 q^{39} - 3596 q^{44} - 3050 q^{45} + 4802 q^{49} - 8520 q^{54} - 3100 q^{55} + 14276 q^{61} - 11702 q^{64} - 3720 q^{66} - 35460 q^{74} + 20938 q^{76} + 6050 q^{80} + 4202 q^{81} + 18050 q^{95} - 5220 q^{96} + 7564 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.70820 1.67705 0.838525 0.544862i \(-0.183418\pi\)
0.838525 + 0.544862i \(0.183418\pi\)
\(3\) 4.47214 0.496904 0.248452 0.968644i \(-0.420078\pi\)
0.248452 + 0.968644i \(0.420078\pi\)
\(4\) 29.0000 1.81250
\(5\) 25.0000 1.00000
\(6\) 30.0000 0.833333
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 87.2067 1.36260
\(9\) −61.0000 −0.753086
\(10\) 167.705 1.67705
\(11\) −62.0000 −0.512397 −0.256198 0.966624i \(-0.582470\pi\)
−0.256198 + 0.966624i \(0.582470\pi\)
\(12\) 129.692 0.900638
\(13\) −67.0820 −0.396935 −0.198468 0.980107i \(-0.563596\pi\)
−0.198468 + 0.980107i \(0.563596\pi\)
\(14\) 0 0
\(15\) 111.803 0.496904
\(16\) 121.000 0.472656
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −409.200 −1.26296
\(19\) 361.000 1.00000
\(20\) 725.000 1.81250
\(21\) 0 0
\(22\) −415.909 −0.859315
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 390.000 0.677083
\(25\) 625.000 1.00000
\(26\) −450.000 −0.665680
\(27\) −635.043 −0.871116
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 750.000 0.833333
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −583.614 −0.569935
\(33\) −277.272 −0.254612
\(34\) 0 0
\(35\) 0 0
\(36\) −1769.00 −1.36497
\(37\) −2643.03 −1.93063 −0.965315 0.261088i \(-0.915919\pi\)
−0.965315 + 0.261088i \(0.915919\pi\)
\(38\) 2421.66 1.67705
\(39\) −300.000 −0.197239
\(40\) 2180.17 1.36260
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −1798.00 −0.928719
\(45\) −1525.00 −0.753086
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 541.128 0.234865
\(49\) 2401.00 1.00000
\(50\) 4192.63 1.67705
\(51\) 0 0
\(52\) −1945.38 −0.719445
\(53\) 791.568 0.281797 0.140899 0.990024i \(-0.455001\pi\)
0.140899 + 0.990024i \(0.455001\pi\)
\(54\) −4260.00 −1.46091
\(55\) −1550.00 −0.512397
\(56\) 0 0
\(57\) 1614.44 0.496904
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 3242.30 0.900638
\(61\) 7138.00 1.91830 0.959151 0.282895i \(-0.0912949\pi\)
0.959151 + 0.282895i \(0.0912949\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −5851.00 −1.42847
\(65\) −1677.05 −0.396935
\(66\) −1860.00 −0.426997
\(67\) −6077.63 −1.35389 −0.676947 0.736031i \(-0.736698\pi\)
−0.676947 + 0.736031i \(0.736698\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −5319.61 −1.02616
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −17730.0 −3.23776
\(75\) 2795.08 0.496904
\(76\) 10469.0 1.81250
\(77\) 0 0
\(78\) −2012.46 −0.330779
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 3025.00 0.472656
\(81\) 2101.00 0.320226
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −5406.81 −0.698194
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −10230.0 −1.26296
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 9025.00 1.00000
\(96\) −2610.00 −0.283203
\(97\) −15415.5 −1.63837 −0.819187 0.573527i \(-0.805575\pi\)
−0.819187 + 0.573527i \(0.805575\pi\)
\(98\) 16106.4 1.67705
\(99\) 3782.00 0.385879
\(100\) 18125.0 1.81250
\(101\) 20098.0 1.97020 0.985100 0.171985i \(-0.0550182\pi\)
0.985100 + 0.171985i \(0.0550182\pi\)
\(102\) 0 0
\(103\) 14637.3 1.37971 0.689853 0.723949i \(-0.257675\pi\)
0.689853 + 0.723949i \(0.257675\pi\)
\(104\) −5850.00 −0.540865
\(105\) 0 0
\(106\) 5310.00 0.472588
\(107\) 17320.6 1.51285 0.756423 0.654082i \(-0.226945\pi\)
0.756423 + 0.654082i \(0.226945\pi\)
\(108\) −18416.3 −1.57890
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −10397.7 −0.859315
\(111\) −11820.0 −0.959338
\(112\) 0 0
\(113\) 23867.8 1.86920 0.934599 0.355703i \(-0.115759\pi\)
0.934599 + 0.355703i \(0.115759\pi\)
\(114\) 10830.0 0.833333
\(115\) 0 0
\(116\) 0 0
\(117\) 4092.00 0.298926
\(118\) 0 0
\(119\) 0 0
\(120\) 9750.00 0.677083
\(121\) −10797.0 −0.737450
\(122\) 47883.2 3.21709
\(123\) 0 0
\(124\) 0 0
\(125\) 15625.0 1.00000
\(126\) 0 0
\(127\) 14208.0 0.880896 0.440448 0.897778i \(-0.354820\pi\)
0.440448 + 0.897778i \(0.354820\pi\)
\(128\) −29911.9 −1.82568
\(129\) 0 0
\(130\) −11250.0 −0.665680
\(131\) −20398.0 −1.18863 −0.594313 0.804234i \(-0.702576\pi\)
−0.594313 + 0.804234i \(0.702576\pi\)
\(132\) −8040.90 −0.461484
\(133\) 0 0
\(134\) −40770.0 −2.27055
\(135\) −15876.1 −0.871116
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 1858.00 0.0961648 0.0480824 0.998843i \(-0.484689\pi\)
0.0480824 + 0.998843i \(0.484689\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4159.09 0.203388
\(144\) −7381.00 −0.355951
\(145\) 0 0
\(146\) 0 0
\(147\) 10737.6 0.496904
\(148\) −76647.9 −3.49927
\(149\) 7618.00 0.343138 0.171569 0.985172i \(-0.445116\pi\)
0.171569 + 0.985172i \(0.445116\pi\)
\(150\) 18750.0 0.833333
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 31481.6 1.36260
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −8700.00 −0.357495
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 3540.00 0.140026
\(160\) −14590.3 −0.569935
\(161\) 0 0
\(162\) 14093.9 0.537035
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) −6931.81 −0.254612
\(166\) 0 0
\(167\) −54269.4 −1.94591 −0.972953 0.231003i \(-0.925799\pi\)
−0.972953 + 0.231003i \(0.925799\pi\)
\(168\) 0 0
\(169\) −24061.0 −0.842442
\(170\) 0 0
\(171\) −22021.0 −0.753086
\(172\) 0 0
\(173\) −29690.5 −0.992031 −0.496016 0.868314i \(-0.665204\pi\)
−0.496016 + 0.868314i \(0.665204\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −7502.00 −0.242188
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −44225.0 −1.36497
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 31922.1 0.953212
\(184\) 0 0
\(185\) −66075.8 −1.93063
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 60541.5 1.67705
\(191\) 18242.0 0.500041 0.250021 0.968241i \(-0.419563\pi\)
0.250021 + 0.968241i \(0.419563\pi\)
\(192\) −26166.5 −0.709811
\(193\) 70020.2 1.87979 0.939894 0.341466i \(-0.110923\pi\)
0.939894 + 0.341466i \(0.110923\pi\)
\(194\) −103410. −2.74764
\(195\) −7500.00 −0.197239
\(196\) 69629.0 1.81250
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 25370.4 0.647139
\(199\) 24482.0 0.618217 0.309108 0.951027i \(-0.399969\pi\)
0.309108 + 0.951027i \(0.399969\pi\)
\(200\) 54504.2 1.36260
\(201\) −27180.0 −0.672756
\(202\) 134821. 3.30412
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 98190.0 2.31384
\(207\) 0 0
\(208\) −8116.93 −0.187614
\(209\) −22382.0 −0.512397
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 22955.5 0.510757
\(213\) 0 0
\(214\) 116190. 2.53712
\(215\) 0 0
\(216\) −55380.0 −1.18699
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −44950.0 −0.928719
\(221\) 0 0
\(222\) −79291.0 −1.60886
\(223\) −49761.5 −1.00065 −0.500326 0.865837i \(-0.666787\pi\)
−0.500326 + 0.865837i \(0.666787\pi\)
\(224\) 0 0
\(225\) −38125.0 −0.753086
\(226\) 160110. 3.13474
\(227\) −92372.0 −1.79262 −0.896311 0.443427i \(-0.853763\pi\)
−0.896311 + 0.443427i \(0.853763\pi\)
\(228\) 46818.8 0.900638
\(229\) 68098.0 1.29856 0.649282 0.760548i \(-0.275069\pi\)
0.649282 + 0.760548i \(0.275069\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 27450.0 0.501315
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −104638. −1.83187 −0.915933 0.401332i \(-0.868548\pi\)
−0.915933 + 0.401332i \(0.868548\pi\)
\(240\) 13528.2 0.234865
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −72428.5 −1.23674
\(243\) 60834.5 1.03024
\(244\) 207002. 3.47692
\(245\) 60025.0 1.00000
\(246\) 0 0
\(247\) −24216.6 −0.396935
\(248\) 0 0
\(249\) 0 0
\(250\) 104816. 1.67705
\(251\) −92878.0 −1.47423 −0.737115 0.675767i \(-0.763813\pi\)
−0.737115 + 0.675767i \(0.763813\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 95310.0 1.47731
\(255\) 0 0
\(256\) −107039. −1.63329
\(257\) −122317. −1.85192 −0.925959 0.377623i \(-0.876742\pi\)
−0.925959 + 0.377623i \(0.876742\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −48634.5 −0.719445
\(261\) 0 0
\(262\) −136834. −1.99339
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −24180.0 −0.346935
\(265\) 19789.2 0.281797
\(266\) 0 0
\(267\) 0 0
\(268\) −176251. −2.45393
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −106500. −1.46091
\(271\) −145262. −1.97794 −0.988971 0.148111i \(-0.952681\pi\)
−0.988971 + 0.148111i \(0.952681\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −38750.0 −0.512397
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 12463.8 0.161273
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 40361.0 0.496904
\(286\) 27900.0 0.341092
\(287\) 0 0
\(288\) 35600.4 0.429211
\(289\) 83521.0 1.00000
\(290\) 0 0
\(291\) −68940.0 −0.814114
\(292\) 0 0
\(293\) 171663. 1.99959 0.999796 0.0202081i \(-0.00643286\pi\)
0.999796 + 0.0202081i \(0.00643286\pi\)
\(294\) 72030.0 0.833333
\(295\) 0 0
\(296\) −230490. −2.63068
\(297\) 39372.7 0.446357
\(298\) 51103.1 0.575459
\(299\) 0 0
\(300\) 81057.5 0.900638
\(301\) 0 0
\(302\) 0 0
\(303\) 89881.0 0.979000
\(304\) 43681.0 0.472656
\(305\) 178450. 1.91830
\(306\) 0 0
\(307\) 186260. 1.97625 0.988127 0.153638i \(-0.0490991\pi\)
0.988127 + 0.153638i \(0.0490991\pi\)
\(308\) 0 0
\(309\) 65460.0 0.685581
\(310\) 0 0
\(311\) −62222.0 −0.643314 −0.321657 0.946856i \(-0.604240\pi\)
−0.321657 + 0.946856i \(0.604240\pi\)
\(312\) −26162.0 −0.268758
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −65324.5 −0.650066 −0.325033 0.945703i \(-0.605375\pi\)
−0.325033 + 0.945703i \(0.605375\pi\)
\(318\) 23747.0 0.234831
\(319\) 0 0
\(320\) −146275. −1.42847
\(321\) 77460.0 0.751740
\(322\) 0 0
\(323\) 0 0
\(324\) 60929.0 0.580409
\(325\) −41926.3 −0.396935
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) −46500.0 −0.426997
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 161225. 1.45393
\(334\) −364050. −3.26338
\(335\) −151941. −1.35389
\(336\) 0 0
\(337\) 223504. 1.96800 0.984001 0.178165i \(-0.0570160\pi\)
0.984001 + 0.178165i \(0.0570160\pi\)
\(338\) −161406. −1.41282
\(339\) 106740. 0.928812
\(340\) 0 0
\(341\) 0 0
\(342\) −147721. −1.26296
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −199170. −1.66369
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 24722.0 0.202970 0.101485 0.994837i \(-0.467641\pi\)
0.101485 + 0.994837i \(0.467641\pi\)
\(350\) 0 0
\(351\) 42600.0 0.345776
\(352\) 36184.1 0.292033
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −253262. −1.96508 −0.982542 0.186041i \(-0.940434\pi\)
−0.982542 + 0.186041i \(0.940434\pi\)
\(360\) −132990. −1.02616
\(361\) 130321. 1.00000
\(362\) 0 0
\(363\) −48285.7 −0.366442
\(364\) 0 0
\(365\) 0 0
\(366\) 214140. 1.59858
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −443250. −3.23776
\(371\) 0 0
\(372\) 0 0
\(373\) −223316. −1.60510 −0.802551 0.596584i \(-0.796524\pi\)
−0.802551 + 0.596584i \(0.796524\pi\)
\(374\) 0 0
\(375\) 69877.1 0.496904
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 261725. 1.81250
\(381\) 63540.0 0.437721
\(382\) 122371. 0.838594
\(383\) −276660. −1.88603 −0.943015 0.332751i \(-0.892023\pi\)
−0.943015 + 0.332751i \(0.892023\pi\)
\(384\) −133770. −0.907186
\(385\) 0 0
\(386\) 469710. 3.15250
\(387\) 0 0
\(388\) −447048. −2.96955
\(389\) 247922. 1.63838 0.819192 0.573519i \(-0.194422\pi\)
0.819192 + 0.573519i \(0.194422\pi\)
\(390\) −50311.5 −0.330779
\(391\) 0 0
\(392\) 209383. 1.36260
\(393\) −91222.6 −0.590633
\(394\) 0 0
\(395\) 0 0
\(396\) 109678. 0.699406
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 164230. 1.03678
\(399\) 0 0
\(400\) 75625.0 0.472656
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) −182329. −1.12825
\(403\) 0 0
\(404\) 582842. 3.57099
\(405\) 52525.0 0.320226
\(406\) 0 0
\(407\) 163868. 0.989248
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 424482. 2.50072
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 39150.0 0.226227
\(417\) 8309.23 0.0477847
\(418\) −150143. −0.859315
\(419\) −141358. −0.805179 −0.402589 0.915381i \(-0.631890\pi\)
−0.402589 + 0.915381i \(0.631890\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 69030.0 0.383978
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 502297. 2.74203
\(429\) 18600.0 0.101064
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −76840.2 −0.411738
\(433\) −86898.1 −0.463484 −0.231742 0.972777i \(-0.574442\pi\)
−0.231742 + 0.972777i \(0.574442\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) −135170. −0.698194
\(441\) −146461. −0.753086
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −342780. −1.73880
\(445\) 0 0
\(446\) −333810. −1.67815
\(447\) 34068.7 0.170506
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −255750. −1.26296
\(451\) 0 0
\(452\) 692166. 3.38792
\(453\) 0 0
\(454\) −619650. −3.00632
\(455\) 0 0
\(456\) 140790. 0.677083
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 456815. 2.17776
\(459\) 0 0
\(460\) 0 0
\(461\) −67438.0 −0.317324 −0.158662 0.987333i \(-0.550718\pi\)
−0.158662 + 0.987333i \(0.550718\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 118668. 0.541804
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 225625. 1.00000
\(476\) 0 0
\(477\) −48285.7 −0.212218
\(478\) −701933. −3.07213
\(479\) 349138. 1.52169 0.760845 0.648934i \(-0.224785\pi\)
0.760845 + 0.648934i \(0.224785\pi\)
\(480\) −65250.0 −0.283203
\(481\) 177300. 0.766335
\(482\) 0 0
\(483\) 0 0
\(484\) −313113. −1.33663
\(485\) −385386. −1.63837
\(486\) 408090. 1.72776
\(487\) −470071. −1.98201 −0.991004 0.133835i \(-0.957271\pi\)
−0.991004 + 0.133835i \(0.957271\pi\)
\(488\) 622481. 2.61389
\(489\) 0 0
\(490\) 402660. 1.67705
\(491\) −393358. −1.63164 −0.815821 0.578304i \(-0.803715\pi\)
−0.815821 + 0.578304i \(0.803715\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −162450. −0.665680
\(495\) 94550.0 0.385879
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 461218. 1.85227 0.926137 0.377188i \(-0.123109\pi\)
0.926137 + 0.377188i \(0.123109\pi\)
\(500\) 453125. 1.81250
\(501\) −242700. −0.966928
\(502\) −623045. −2.47236
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 502450. 1.97020
\(506\) 0 0
\(507\) −107604. −0.418613
\(508\) 412031. 1.59662
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −239449. −0.913427
\(513\) −229251. −0.871116
\(514\) −820530. −3.10576
\(515\) 365933. 1.37971
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −132780. −0.492944
\(520\) −146250. −0.540865
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −242636. −0.887057 −0.443528 0.896260i \(-0.646273\pi\)
−0.443528 + 0.896260i \(0.646273\pi\)
\(524\) −591542. −2.15438
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −33550.0 −0.120344
\(529\) 279841. 1.00000
\(530\) 132750. 0.472588
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 433015. 1.51285
\(536\) −530010. −1.84482
\(537\) 0 0
\(538\) 0 0
\(539\) −148862. −0.512397
\(540\) −460406. −1.57890
\(541\) −472862. −1.61562 −0.807811 0.589441i \(-0.799348\pi\)
−0.807811 + 0.589441i \(0.799348\pi\)
\(542\) −974447. −3.31711
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 584030. 1.95191 0.975956 0.217968i \(-0.0699427\pi\)
0.975956 + 0.217968i \(0.0699427\pi\)
\(548\) 0 0
\(549\) −435418. −1.44465
\(550\) −259943. −0.859315
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −295500. −0.959338
\(556\) 53882.0 0.174299
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −545525. −1.72107 −0.860533 0.509395i \(-0.829869\pi\)
−0.860533 + 0.509395i \(0.829869\pi\)
\(564\) 0 0
\(565\) 596695. 1.86920
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 270750. 0.833333
\(571\) −479102. −1.46945 −0.734727 0.678363i \(-0.762690\pi\)
−0.734727 + 0.678363i \(0.762690\pi\)
\(572\) 120614. 0.368641
\(573\) 81580.7 0.248472
\(574\) 0 0
\(575\) 0 0
\(576\) 356911. 1.07576
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 560276. 1.67705
\(579\) 313140. 0.934074
\(580\) 0 0
\(581\) 0 0
\(582\) −462464. −1.36531
\(583\) −49077.2 −0.144392
\(584\) 0 0
\(585\) 102300. 0.298926
\(586\) 1.15155e6 3.35342
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 311390. 0.900638
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −319807. −0.912524
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 264120. 0.748563
\(595\) 0 0
\(596\) 220922. 0.621937
\(597\) 109487. 0.307194
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 243750. 0.677083
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 370736. 1.01960
\(604\) 0 0
\(605\) −269925. −0.737450
\(606\) 602940. 1.64183
\(607\) 309369. 0.839652 0.419826 0.907605i \(-0.362091\pi\)
0.419826 + 0.907605i \(0.362091\pi\)
\(608\) −210685. −0.569935
\(609\) 0 0
\(610\) 1.19708e6 3.21709
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 1.24947e6 3.31428
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 439119. 1.14976
\(619\) −766142. −1.99953 −0.999765 0.0216731i \(-0.993101\pi\)
−0.999765 + 0.0216731i \(0.993101\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −417398. −1.07887
\(623\) 0 0
\(624\) −36300.0 −0.0932261
\(625\) 390625. 1.00000
\(626\) 0 0
\(627\) −100095. −0.254612
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 504178. 1.26627 0.633133 0.774043i \(-0.281768\pi\)
0.633133 + 0.774043i \(0.281768\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −438210. −1.09019
\(635\) 355199. 0.880896
\(636\) 102660. 0.253797
\(637\) −161064. −0.396935
\(638\) 0 0
\(639\) 0 0
\(640\) −747797. −1.82568
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 519617. 1.26071
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 183221. 0.436341
\(649\) 0 0
\(650\) −281250. −0.665680
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) −509950. −1.18863
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −201023. −0.461484
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.08153e6 2.43832
\(667\) 0 0
\(668\) −1.57381e6 −3.52695
\(669\) −222540. −0.497228
\(670\) −1.01925e6 −2.27055
\(671\) −442556. −0.982931
\(672\) 0 0
\(673\) 540775. 1.19395 0.596976 0.802259i \(-0.296369\pi\)
0.596976 + 0.802259i \(0.296369\pi\)
\(674\) 1.49931e6 3.30044
\(675\) −396902. −0.871116
\(676\) −697769. −1.52693
\(677\) −533289. −1.16355 −0.581775 0.813350i \(-0.697642\pi\)
−0.581775 + 0.813350i \(0.697642\pi\)
\(678\) 716034. 1.55767
\(679\) 0 0
\(680\) 0 0
\(681\) −413100. −0.890761
\(682\) 0 0
\(683\) 641774. 1.37575 0.687877 0.725828i \(-0.258543\pi\)
0.687877 + 0.725828i \(0.258543\pi\)
\(684\) −638609. −1.36497
\(685\) 0 0
\(686\) 0 0
\(687\) 304544. 0.645262
\(688\) 0 0
\(689\) −53100.0 −0.111855
\(690\) 0 0
\(691\) 954658. 1.99936 0.999682 0.0252304i \(-0.00803194\pi\)
0.999682 + 0.0252304i \(0.00803194\pi\)
\(692\) −861025. −1.79806
\(693\) 0 0
\(694\) 0 0
\(695\) 46450.0 0.0961648
\(696\) 0 0
\(697\) 0 0
\(698\) 165840. 0.340392
\(699\) 0 0
\(700\) 0 0
\(701\) −75422.0 −0.153484 −0.0767418 0.997051i \(-0.524452\pi\)
−0.0767418 + 0.997051i \(0.524452\pi\)
\(702\) 285769. 0.579885
\(703\) −954135. −1.93063
\(704\) 362762. 0.731942
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −964558. −1.91883 −0.959414 0.282003i \(-0.909001\pi\)
−0.959414 + 0.282003i \(0.909001\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 103977. 0.203388
\(716\) 0 0
\(717\) −467955. −0.910261
\(718\) −1.69893e6 −3.29555
\(719\) 522898. 1.01148 0.505742 0.862685i \(-0.331219\pi\)
0.505742 + 0.862685i \(0.331219\pi\)
\(720\) −184525. −0.355951
\(721\) 0 0
\(722\) 874220. 1.67705
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −323910. −0.614541
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 101879. 0.191703
\(730\) 0 0
\(731\) 0 0
\(732\) 925741. 1.72770
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 268440. 0.496904
\(736\) 0 0
\(737\) 376813. 0.693731
\(738\) 0 0
\(739\) 873362. 1.59921 0.799605 0.600527i \(-0.205042\pi\)
0.799605 + 0.600527i \(0.205042\pi\)
\(740\) −1.91620e6 −3.49927
\(741\) −108300. −0.197239
\(742\) 0 0
\(743\) −1.09624e6 −1.98577 −0.992884 0.119085i \(-0.962004\pi\)
−0.992884 + 0.119085i \(0.962004\pi\)
\(744\) 0 0
\(745\) 190450. 0.343138
\(746\) −1.49805e6 −2.69184
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 468750. 0.833333
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) −415363. −0.732551
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 787040. 1.36260
\(761\) 902578. 1.55853 0.779265 0.626694i \(-0.215592\pi\)
0.779265 + 0.626694i \(0.215592\pi\)
\(762\) 426239. 0.734080
\(763\) 0 0
\(764\) 529018. 0.906325
\(765\) 0 0
\(766\) −1.85589e6 −3.16297
\(767\) 0 0
\(768\) −478693. −0.811586
\(769\) −714542. −1.20830 −0.604150 0.796870i \(-0.706487\pi\)
−0.604150 + 0.796870i \(0.706487\pi\)
\(770\) 0 0
\(771\) −547020. −0.920226
\(772\) 2.03059e6 3.40712
\(773\) 697371. 1.16709 0.583546 0.812080i \(-0.301665\pi\)
0.583546 + 0.812080i \(0.301665\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.34433e6 −2.23245
\(777\) 0 0
\(778\) 1.66311e6 2.74765
\(779\) 0 0
\(780\) −217500. −0.357495
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 290521. 0.472656
\(785\) 0 0
\(786\) −611940. −0.990521
\(787\) 404142. 0.652507 0.326253 0.945282i \(-0.394214\pi\)
0.326253 + 0.945282i \(0.394214\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 329816. 0.525800
\(793\) −478832. −0.761441
\(794\) 0 0
\(795\) 88500.0 0.140026
\(796\) 709978. 1.12052
\(797\) 694796. 1.09381 0.546903 0.837196i \(-0.315807\pi\)
0.546903 + 0.837196i \(0.315807\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −364759. −0.569935
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) −788220. −1.21937
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 1.75268e6 2.68460
\(809\) −59038.0 −0.0902058 −0.0451029 0.998982i \(-0.514362\pi\)
−0.0451029 + 0.998982i \(0.514362\pi\)
\(810\) 352348. 0.537035
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) −649631. −0.982847
\(814\) 1.09926e6 1.65902
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.33320e6 −1.97792 −0.988959 0.148189i \(-0.952656\pi\)
−0.988959 + 0.148189i \(0.952656\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 1.27647e6 1.87999
\(825\) −173295. −0.254612
\(826\) 0 0
\(827\) −887053. −1.29700 −0.648498 0.761217i \(-0.724602\pi\)
−0.648498 + 0.761217i \(0.724602\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 392497. 0.567009
\(833\) 0 0
\(834\) 55740.0 0.0801373
\(835\) −1.35673e6 −1.94591
\(836\) −649078. −0.928719
\(837\) 0 0
\(838\) −948258. −1.35033
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 707281. 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −601525. −0.842442
\(846\) 0 0
\(847\) 0 0
\(848\) 95779.7 0.133193
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) −550525. −0.753086
\(856\) 1.51047e6 2.06141
\(857\) −1.12071e6 −1.52592 −0.762962 0.646444i \(-0.776255\pi\)
−0.762962 + 0.646444i \(0.776255\pi\)
\(858\) 124773. 0.169490
\(859\) 1.42104e6 1.92584 0.962921 0.269784i \(-0.0869523\pi\)
0.962921 + 0.269784i \(0.0869523\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.44214e6 1.93636 0.968181 0.250249i \(-0.0805125\pi\)
0.968181 + 0.250249i \(0.0805125\pi\)
\(864\) 370620. 0.496480
\(865\) −742263. −0.992031
\(866\) −582930. −0.777286
\(867\) 373517. 0.496904
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 407700. 0.537408
\(872\) 0 0
\(873\) 940343. 1.23384
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.53627e6 1.99742 0.998709 0.0507905i \(-0.0161741\pi\)
0.998709 + 0.0507905i \(0.0161741\pi\)
\(878\) 0 0
\(879\) 767700. 0.993605
\(880\) −187550. −0.242188
\(881\) 1.26018e6 1.62360 0.811802 0.583933i \(-0.198487\pi\)
0.811802 + 0.583933i \(0.198487\pi\)
\(882\) −982490. −1.26296
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −646523. −0.821745 −0.410872 0.911693i \(-0.634776\pi\)
−0.410872 + 0.911693i \(0.634776\pi\)
\(888\) −1.03078e6 −1.30720
\(889\) 0 0
\(890\) 0 0
\(891\) −130262. −0.164083
\(892\) −1.44308e6 −1.81368
\(893\) 0 0
\(894\) 228540. 0.285948
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −1.10562e6 −1.36497
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 2.08143e6 2.54698
\(905\) 0 0
\(906\) 0 0
\(907\) −671746. −0.816565 −0.408282 0.912856i \(-0.633872\pi\)
−0.408282 + 0.912856i \(0.633872\pi\)
\(908\) −2.67879e6 −3.24913
\(909\) −1.22598e6 −1.48373
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 195347. 0.234865
\(913\) 0 0
\(914\) 0 0
\(915\) 798053. 0.953212
\(916\) 1.97484e6 2.35365
\(917\) 0 0
\(918\) 0 0
\(919\) 813602. 0.963343 0.481672 0.876352i \(-0.340030\pi\)
0.481672 + 0.876352i \(0.340030\pi\)
\(920\) 0 0
\(921\) 832980. 0.982009
\(922\) −452388. −0.532168
\(923\) 0 0
\(924\) 0 0
\(925\) −1.65190e6 −1.93063
\(926\) 0 0
\(927\) −892875. −1.03904
\(928\) 0 0
\(929\) −955198. −1.10678 −0.553391 0.832922i \(-0.686666\pi\)
−0.553391 + 0.832922i \(0.686666\pi\)
\(930\) 0 0
\(931\) 866761. 1.00000
\(932\) 0 0
\(933\) −278265. −0.319665
\(934\) 0 0
\(935\) 0 0
\(936\) 356850. 0.407318
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 1.51354e6 1.67705
\(951\) −292140. −0.323020
\(952\) 0 0
\(953\) 1.68922e6 1.85995 0.929973 0.367628i \(-0.119830\pi\)
0.929973 + 0.367628i \(0.119830\pi\)
\(954\) −323910. −0.355900
\(955\) 456050. 0.500041
\(956\) −3.03450e6 −3.32026
\(957\) 0 0
\(958\) 2.34209e6 2.55195
\(959\) 0 0
\(960\) −654162. −0.709811
\(961\) 923521. 1.00000
\(962\) 1.18936e6 1.28518
\(963\) −1.05656e6 −1.13930
\(964\) 0 0
\(965\) 1.75051e6 1.87979
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −941570. −1.00485
\(969\) 0 0
\(970\) −2.58525e6 −2.74764
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 1.76420e6 1.86730
\(973\) 0 0
\(974\) −3.15333e6 −3.32393
\(975\) −187500. −0.197239
\(976\) 863698. 0.906697
\(977\) 907848. 0.951095 0.475548 0.879690i \(-0.342250\pi\)
0.475548 + 0.879690i \(0.342250\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.74072e6 1.81250
\(981\) 0 0
\(982\) −2.63873e6 −2.73635
\(983\) 1.93243e6 1.99985 0.999925 0.0122789i \(-0.00390858\pi\)
0.999925 + 0.0122789i \(0.00390858\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −702282. −0.719445
\(989\) 0 0
\(990\) 634261. 0.647139
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 612050. 0.618217
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 3.09394e6 3.10636
\(999\) 1.67844e6 1.68180
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 95.5.d.c.94.2 yes 2
5.4 even 2 inner 95.5.d.c.94.1 2
19.18 odd 2 inner 95.5.d.c.94.1 2
95.94 odd 2 CM 95.5.d.c.94.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.5.d.c.94.1 2 5.4 even 2 inner
95.5.d.c.94.1 2 19.18 odd 2 inner
95.5.d.c.94.2 yes 2 1.1 even 1 trivial
95.5.d.c.94.2 yes 2 95.94 odd 2 CM