Properties

Label 650.6.a.a.1.1
Level $650$
Weight $6$
Character 650.1
Self dual yes
Analytic conductor $104.249$
Analytic rank $1$
Dimension $1$
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] = [650,6,Mod(1,650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(650, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("650.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 650.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: \(104.249482878\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 650.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} +16.0000 q^{4} +170.000 q^{7} +64.0000 q^{8} -243.000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} +16.0000 q^{4} +170.000 q^{7} +64.0000 q^{8} -243.000 q^{9} -250.000 q^{11} +169.000 q^{13} +680.000 q^{14} +256.000 q^{16} -1062.00 q^{17} -972.000 q^{18} -78.0000 q^{19} -1000.00 q^{22} -1576.00 q^{23} +676.000 q^{26} +2720.00 q^{28} +2578.00 q^{29} -8654.00 q^{31} +1024.00 q^{32} -4248.00 q^{34} -3888.00 q^{36} -10986.0 q^{37} -312.000 q^{38} +1050.00 q^{41} +5900.00 q^{43} -4000.00 q^{44} -6304.00 q^{46} +5962.00 q^{47} +12093.0 q^{49} +2704.00 q^{52} -29046.0 q^{53} +10880.0 q^{56} +10312.0 q^{58} -13922.0 q^{59} -32882.0 q^{61} -34616.0 q^{62} -41310.0 q^{63} +4096.00 q^{64} +69566.0 q^{67} -16992.0 q^{68} -50542.0 q^{71} -15552.0 q^{72} +46750.0 q^{73} -43944.0 q^{74} -1248.00 q^{76} -42500.0 q^{77} -19348.0 q^{79} +59049.0 q^{81} +4200.00 q^{82} +87438.0 q^{83} +23600.0 q^{86} -16000.0 q^{88} +94170.0 q^{89} +28730.0 q^{91} -25216.0 q^{92} +23848.0 q^{94} -182786. q^{97} +48372.0 q^{98} +60750.0 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 16.0000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 170.000 1.31131 0.655653 0.755063i \(-0.272394\pi\)
0.655653 + 0.755063i \(0.272394\pi\)
\(8\) 64.0000 0.353553
\(9\) −243.000 −1.00000
\(10\) 0 0
\(11\) −250.000 −0.622957 −0.311479 0.950253i \(-0.600824\pi\)
−0.311479 + 0.950253i \(0.600824\pi\)
\(12\) 0 0
\(13\) 169.000 0.277350
\(14\) 680.000 0.927233
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) −1062.00 −0.891255 −0.445628 0.895218i \(-0.647019\pi\)
−0.445628 + 0.895218i \(0.647019\pi\)
\(18\) −972.000 −0.707107
\(19\) −78.0000 −0.0495691 −0.0247845 0.999693i \(-0.507890\pi\)
−0.0247845 + 0.999693i \(0.507890\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1000.00 −0.440497
\(23\) −1576.00 −0.621207 −0.310604 0.950539i \(-0.600531\pi\)
−0.310604 + 0.950539i \(0.600531\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 676.000 0.196116
\(27\) 0 0
\(28\) 2720.00 0.655653
\(29\) 2578.00 0.569230 0.284615 0.958642i \(-0.408134\pi\)
0.284615 + 0.958642i \(0.408134\pi\)
\(30\) 0 0
\(31\) −8654.00 −1.61738 −0.808691 0.588234i \(-0.799824\pi\)
−0.808691 + 0.588234i \(0.799824\pi\)
\(32\) 1024.00 0.176777
\(33\) 0 0
\(34\) −4248.00 −0.630213
\(35\) 0 0
\(36\) −3888.00 −0.500000
\(37\) −10986.0 −1.31927 −0.659637 0.751584i \(-0.729290\pi\)
−0.659637 + 0.751584i \(0.729290\pi\)
\(38\) −312.000 −0.0350506
\(39\) 0 0
\(40\) 0 0
\(41\) 1050.00 0.0975505 0.0487753 0.998810i \(-0.484468\pi\)
0.0487753 + 0.998810i \(0.484468\pi\)
\(42\) 0 0
\(43\) 5900.00 0.486610 0.243305 0.969950i \(-0.421768\pi\)
0.243305 + 0.969950i \(0.421768\pi\)
\(44\) −4000.00 −0.311479
\(45\) 0 0
\(46\) −6304.00 −0.439260
\(47\) 5962.00 0.393684 0.196842 0.980435i \(-0.436931\pi\)
0.196842 + 0.980435i \(0.436931\pi\)
\(48\) 0 0
\(49\) 12093.0 0.719522
\(50\) 0 0
\(51\) 0 0
\(52\) 2704.00 0.138675
\(53\) −29046.0 −1.42035 −0.710177 0.704023i \(-0.751385\pi\)
−0.710177 + 0.704023i \(0.751385\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 10880.0 0.463616
\(57\) 0 0
\(58\) 10312.0 0.402507
\(59\) −13922.0 −0.520681 −0.260340 0.965517i \(-0.583835\pi\)
−0.260340 + 0.965517i \(0.583835\pi\)
\(60\) 0 0
\(61\) −32882.0 −1.13145 −0.565723 0.824596i \(-0.691403\pi\)
−0.565723 + 0.824596i \(0.691403\pi\)
\(62\) −34616.0 −1.14366
\(63\) −41310.0 −1.31131
\(64\) 4096.00 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 69566.0 1.89326 0.946629 0.322324i \(-0.104464\pi\)
0.946629 + 0.322324i \(0.104464\pi\)
\(68\) −16992.0 −0.445628
\(69\) 0 0
\(70\) 0 0
\(71\) −50542.0 −1.18989 −0.594945 0.803767i \(-0.702826\pi\)
−0.594945 + 0.803767i \(0.702826\pi\)
\(72\) −15552.0 −0.353553
\(73\) 46750.0 1.02677 0.513387 0.858157i \(-0.328391\pi\)
0.513387 + 0.858157i \(0.328391\pi\)
\(74\) −43944.0 −0.932868
\(75\) 0 0
\(76\) −1248.00 −0.0247845
\(77\) −42500.0 −0.816887
\(78\) 0 0
\(79\) −19348.0 −0.348793 −0.174397 0.984675i \(-0.555798\pi\)
−0.174397 + 0.984675i \(0.555798\pi\)
\(80\) 0 0
\(81\) 59049.0 1.00000
\(82\) 4200.00 0.0689786
\(83\) 87438.0 1.39317 0.696586 0.717473i \(-0.254701\pi\)
0.696586 + 0.717473i \(0.254701\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 23600.0 0.344085
\(87\) 0 0
\(88\) −16000.0 −0.220249
\(89\) 94170.0 1.26019 0.630097 0.776516i \(-0.283015\pi\)
0.630097 + 0.776516i \(0.283015\pi\)
\(90\) 0 0
\(91\) 28730.0 0.363691
\(92\) −25216.0 −0.310604
\(93\) 0 0
\(94\) 23848.0 0.278376
\(95\) 0 0
\(96\) 0 0
\(97\) −182786. −1.97248 −0.986242 0.165307i \(-0.947139\pi\)
−0.986242 + 0.165307i \(0.947139\pi\)
\(98\) 48372.0 0.508779
\(99\) 60750.0 0.622957
\(100\) 0 0
\(101\) −18514.0 −0.180591 −0.0902957 0.995915i \(-0.528781\pi\)
−0.0902957 + 0.995915i \(0.528781\pi\)
\(102\) 0 0
\(103\) −116056. −1.07789 −0.538945 0.842341i \(-0.681177\pi\)
−0.538945 + 0.842341i \(0.681177\pi\)
\(104\) 10816.0 0.0980581
\(105\) 0 0
\(106\) −116184. −1.00434
\(107\) −153520. −1.29630 −0.648150 0.761513i \(-0.724457\pi\)
−0.648150 + 0.761513i \(0.724457\pi\)
\(108\) 0 0
\(109\) −178622. −1.44002 −0.720010 0.693963i \(-0.755863\pi\)
−0.720010 + 0.693963i \(0.755863\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 43520.0 0.327826
\(113\) 244754. 1.80316 0.901579 0.432615i \(-0.142409\pi\)
0.901579 + 0.432615i \(0.142409\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 41248.0 0.284615
\(117\) −41067.0 −0.277350
\(118\) −55688.0 −0.368177
\(119\) −180540. −1.16871
\(120\) 0 0
\(121\) −98551.0 −0.611924
\(122\) −131528. −0.800053
\(123\) 0 0
\(124\) −138464. −0.808691
\(125\) 0 0
\(126\) −165240. −0.927233
\(127\) −256600. −1.41172 −0.705858 0.708353i \(-0.749438\pi\)
−0.705858 + 0.708353i \(0.749438\pi\)
\(128\) 16384.0 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −262736. −1.33765 −0.668823 0.743421i \(-0.733202\pi\)
−0.668823 + 0.743421i \(0.733202\pi\)
\(132\) 0 0
\(133\) −13260.0 −0.0650002
\(134\) 278264. 1.33874
\(135\) 0 0
\(136\) −67968.0 −0.315106
\(137\) 38286.0 0.174276 0.0871382 0.996196i \(-0.472228\pi\)
0.0871382 + 0.996196i \(0.472228\pi\)
\(138\) 0 0
\(139\) −57776.0 −0.253636 −0.126818 0.991926i \(-0.540476\pi\)
−0.126818 + 0.991926i \(0.540476\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −202168. −0.841379
\(143\) −42250.0 −0.172777
\(144\) −62208.0 −0.250000
\(145\) 0 0
\(146\) 187000. 0.726038
\(147\) 0 0
\(148\) −175776. −0.659637
\(149\) 28866.0 0.106517 0.0532587 0.998581i \(-0.483039\pi\)
0.0532587 + 0.998581i \(0.483039\pi\)
\(150\) 0 0
\(151\) 39870.0 0.142300 0.0711498 0.997466i \(-0.477333\pi\)
0.0711498 + 0.997466i \(0.477333\pi\)
\(152\) −4992.00 −0.0175253
\(153\) 258066. 0.891255
\(154\) −170000. −0.577627
\(155\) 0 0
\(156\) 0 0
\(157\) −161042. −0.521423 −0.260711 0.965417i \(-0.583957\pi\)
−0.260711 + 0.965417i \(0.583957\pi\)
\(158\) −77392.0 −0.246634
\(159\) 0 0
\(160\) 0 0
\(161\) −267920. −0.814593
\(162\) 236196. 0.707107
\(163\) −312830. −0.922230 −0.461115 0.887340i \(-0.652550\pi\)
−0.461115 + 0.887340i \(0.652550\pi\)
\(164\) 16800.0 0.0487753
\(165\) 0 0
\(166\) 349752. 0.985122
\(167\) −532926. −1.47869 −0.739343 0.673329i \(-0.764864\pi\)
−0.739343 + 0.673329i \(0.764864\pi\)
\(168\) 0 0
\(169\) 28561.0 0.0769231
\(170\) 0 0
\(171\) 18954.0 0.0495691
\(172\) 94400.0 0.243305
\(173\) 630458. 1.60155 0.800776 0.598964i \(-0.204421\pi\)
0.800776 + 0.598964i \(0.204421\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −64000.0 −0.155739
\(177\) 0 0
\(178\) 376680. 0.891092
\(179\) −674916. −1.57441 −0.787204 0.616693i \(-0.788472\pi\)
−0.787204 + 0.616693i \(0.788472\pi\)
\(180\) 0 0
\(181\) 186282. 0.422644 0.211322 0.977417i \(-0.432223\pi\)
0.211322 + 0.977417i \(0.432223\pi\)
\(182\) 114920. 0.257168
\(183\) 0 0
\(184\) −100864. −0.219630
\(185\) 0 0
\(186\) 0 0
\(187\) 265500. 0.555214
\(188\) 95392.0 0.196842
\(189\) 0 0
\(190\) 0 0
\(191\) 812180. 1.61090 0.805451 0.592663i \(-0.201923\pi\)
0.805451 + 0.592663i \(0.201923\pi\)
\(192\) 0 0
\(193\) 150142. 0.290141 0.145070 0.989421i \(-0.453659\pi\)
0.145070 + 0.989421i \(0.453659\pi\)
\(194\) −731144. −1.39476
\(195\) 0 0
\(196\) 193488. 0.359761
\(197\) −236394. −0.433981 −0.216991 0.976174i \(-0.569624\pi\)
−0.216991 + 0.976174i \(0.569624\pi\)
\(198\) 243000. 0.440497
\(199\) −39376.0 −0.0704854 −0.0352427 0.999379i \(-0.511220\pi\)
−0.0352427 + 0.999379i \(0.511220\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −74056.0 −0.127697
\(203\) 438260. 0.746435
\(204\) 0 0
\(205\) 0 0
\(206\) −464224. −0.762183
\(207\) 382968. 0.621207
\(208\) 43264.0 0.0693375
\(209\) 19500.0 0.0308794
\(210\) 0 0
\(211\) −410776. −0.635183 −0.317592 0.948228i \(-0.602874\pi\)
−0.317592 + 0.948228i \(0.602874\pi\)
\(212\) −464736. −0.710177
\(213\) 0 0
\(214\) −614080. −0.916623
\(215\) 0 0
\(216\) 0 0
\(217\) −1.47118e6 −2.12088
\(218\) −714488. −1.01825
\(219\) 0 0
\(220\) 0 0
\(221\) −179478. −0.247190
\(222\) 0 0
\(223\) −1.08688e6 −1.46359 −0.731796 0.681523i \(-0.761318\pi\)
−0.731796 + 0.681523i \(0.761318\pi\)
\(224\) 174080. 0.231808
\(225\) 0 0
\(226\) 979016. 1.27502
\(227\) 256470. 0.330348 0.165174 0.986264i \(-0.447181\pi\)
0.165174 + 0.986264i \(0.447181\pi\)
\(228\) 0 0
\(229\) −298110. −0.375654 −0.187827 0.982202i \(-0.560144\pi\)
−0.187827 + 0.982202i \(0.560144\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 164992. 0.201253
\(233\) 611926. 0.738430 0.369215 0.929344i \(-0.379627\pi\)
0.369215 + 0.929344i \(0.379627\pi\)
\(234\) −164268. −0.196116
\(235\) 0 0
\(236\) −222752. −0.260340
\(237\) 0 0
\(238\) −722160. −0.826401
\(239\) 36570.0 0.0414124 0.0207062 0.999786i \(-0.493409\pi\)
0.0207062 + 0.999786i \(0.493409\pi\)
\(240\) 0 0
\(241\) 380922. 0.422468 0.211234 0.977436i \(-0.432252\pi\)
0.211234 + 0.977436i \(0.432252\pi\)
\(242\) −394204. −0.432696
\(243\) 0 0
\(244\) −526112. −0.565723
\(245\) 0 0
\(246\) 0 0
\(247\) −13182.0 −0.0137480
\(248\) −553856. −0.571831
\(249\) 0 0
\(250\) 0 0
\(251\) −1.22807e6 −1.23038 −0.615188 0.788380i \(-0.710920\pi\)
−0.615188 + 0.788380i \(0.710920\pi\)
\(252\) −660960. −0.655653
\(253\) 394000. 0.386986
\(254\) −1.02640e6 −0.998234
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) 439278. 0.414865 0.207432 0.978249i \(-0.433489\pi\)
0.207432 + 0.978249i \(0.433489\pi\)
\(258\) 0 0
\(259\) −1.86762e6 −1.72997
\(260\) 0 0
\(261\) −626454. −0.569230
\(262\) −1.05094e6 −0.945859
\(263\) 1.67987e6 1.49757 0.748783 0.662816i \(-0.230639\pi\)
0.748783 + 0.662816i \(0.230639\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −53040.0 −0.0459621
\(267\) 0 0
\(268\) 1.11306e6 0.946629
\(269\) 1.93840e6 1.63329 0.816645 0.577141i \(-0.195832\pi\)
0.816645 + 0.577141i \(0.195832\pi\)
\(270\) 0 0
\(271\) −695498. −0.575271 −0.287636 0.957740i \(-0.592869\pi\)
−0.287636 + 0.957740i \(0.592869\pi\)
\(272\) −271872. −0.222814
\(273\) 0 0
\(274\) 153144. 0.123232
\(275\) 0 0
\(276\) 0 0
\(277\) 1.13138e6 0.885948 0.442974 0.896534i \(-0.353923\pi\)
0.442974 + 0.896534i \(0.353923\pi\)
\(278\) −231104. −0.179348
\(279\) 2.10292e6 1.61738
\(280\) 0 0
\(281\) 1.73122e6 1.30793 0.653967 0.756523i \(-0.273103\pi\)
0.653967 + 0.756523i \(0.273103\pi\)
\(282\) 0 0
\(283\) 1.47124e6 1.09199 0.545995 0.837788i \(-0.316152\pi\)
0.545995 + 0.837788i \(0.316152\pi\)
\(284\) −808672. −0.594945
\(285\) 0 0
\(286\) −169000. −0.122172
\(287\) 178500. 0.127919
\(288\) −248832. −0.176777
\(289\) −292013. −0.205664
\(290\) 0 0
\(291\) 0 0
\(292\) 748000. 0.513387
\(293\) −2.88855e6 −1.96567 −0.982834 0.184491i \(-0.940936\pi\)
−0.982834 + 0.184491i \(0.940936\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −703104. −0.466434
\(297\) 0 0
\(298\) 115464. 0.0753192
\(299\) −266344. −0.172292
\(300\) 0 0
\(301\) 1.00300e6 0.638094
\(302\) 159480. 0.100621
\(303\) 0 0
\(304\) −19968.0 −0.0123923
\(305\) 0 0
\(306\) 1.03226e6 0.630213
\(307\) −874118. −0.529327 −0.264664 0.964341i \(-0.585261\pi\)
−0.264664 + 0.964341i \(0.585261\pi\)
\(308\) −680000. −0.408444
\(309\) 0 0
\(310\) 0 0
\(311\) 2.68224e6 1.57252 0.786261 0.617895i \(-0.212014\pi\)
0.786261 + 0.617895i \(0.212014\pi\)
\(312\) 0 0
\(313\) 1.34459e6 0.775761 0.387880 0.921710i \(-0.373207\pi\)
0.387880 + 0.921710i \(0.373207\pi\)
\(314\) −644168. −0.368702
\(315\) 0 0
\(316\) −309568. −0.174397
\(317\) −1.32074e6 −0.738191 −0.369095 0.929392i \(-0.620332\pi\)
−0.369095 + 0.929392i \(0.620332\pi\)
\(318\) 0 0
\(319\) −644500. −0.354606
\(320\) 0 0
\(321\) 0 0
\(322\) −1.07168e6 −0.576004
\(323\) 82836.0 0.0441787
\(324\) 944784. 0.500000
\(325\) 0 0
\(326\) −1.25132e6 −0.652115
\(327\) 0 0
\(328\) 67200.0 0.0344893
\(329\) 1.01354e6 0.516239
\(330\) 0 0
\(331\) −2.05728e6 −1.03210 −0.516051 0.856558i \(-0.672599\pi\)
−0.516051 + 0.856558i \(0.672599\pi\)
\(332\) 1.39901e6 0.696586
\(333\) 2.66960e6 1.31927
\(334\) −2.13170e6 −1.04559
\(335\) 0 0
\(336\) 0 0
\(337\) −453398. −0.217473 −0.108736 0.994071i \(-0.534680\pi\)
−0.108736 + 0.994071i \(0.534680\pi\)
\(338\) 114244. 0.0543928
\(339\) 0 0
\(340\) 0 0
\(341\) 2.16350e6 1.00756
\(342\) 75816.0 0.0350506
\(343\) −801380. −0.367793
\(344\) 377600. 0.172043
\(345\) 0 0
\(346\) 2.52183e6 1.13247
\(347\) 1.23065e6 0.548669 0.274334 0.961634i \(-0.411543\pi\)
0.274334 + 0.961634i \(0.411543\pi\)
\(348\) 0 0
\(349\) −2.43825e6 −1.07155 −0.535777 0.844360i \(-0.679981\pi\)
−0.535777 + 0.844360i \(0.679981\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −256000. −0.110124
\(353\) 2.68315e6 1.14606 0.573031 0.819534i \(-0.305767\pi\)
0.573031 + 0.819534i \(0.305767\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.50672e6 0.630097
\(357\) 0 0
\(358\) −2.69966e6 −1.11327
\(359\) 1.58693e6 0.649864 0.324932 0.945737i \(-0.394659\pi\)
0.324932 + 0.945737i \(0.394659\pi\)
\(360\) 0 0
\(361\) −2.47002e6 −0.997543
\(362\) 745128. 0.298854
\(363\) 0 0
\(364\) 459680. 0.181845
\(365\) 0 0
\(366\) 0 0
\(367\) 60052.0 0.0232735 0.0116368 0.999932i \(-0.496296\pi\)
0.0116368 + 0.999932i \(0.496296\pi\)
\(368\) −403456. −0.155302
\(369\) −255150. −0.0975505
\(370\) 0 0
\(371\) −4.93782e6 −1.86252
\(372\) 0 0
\(373\) 4.01853e6 1.49553 0.747766 0.663963i \(-0.231127\pi\)
0.747766 + 0.663963i \(0.231127\pi\)
\(374\) 1.06200e6 0.392596
\(375\) 0 0
\(376\) 381568. 0.139188
\(377\) 435682. 0.157876
\(378\) 0 0
\(379\) 1.67581e6 0.599276 0.299638 0.954053i \(-0.403134\pi\)
0.299638 + 0.954053i \(0.403134\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 3.24872e6 1.13908
\(383\) −687258. −0.239399 −0.119700 0.992810i \(-0.538193\pi\)
−0.119700 + 0.992810i \(0.538193\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 600568. 0.205161
\(387\) −1.43370e6 −0.486610
\(388\) −2.92458e6 −0.986242
\(389\) 1.37611e6 0.461082 0.230541 0.973063i \(-0.425950\pi\)
0.230541 + 0.973063i \(0.425950\pi\)
\(390\) 0 0
\(391\) 1.67371e6 0.553655
\(392\) 773952. 0.254389
\(393\) 0 0
\(394\) −945576. −0.306871
\(395\) 0 0
\(396\) 972000. 0.311479
\(397\) 721198. 0.229656 0.114828 0.993385i \(-0.463368\pi\)
0.114828 + 0.993385i \(0.463368\pi\)
\(398\) −157504. −0.0498407
\(399\) 0 0
\(400\) 0 0
\(401\) 2.22681e6 0.691548 0.345774 0.938318i \(-0.387616\pi\)
0.345774 + 0.938318i \(0.387616\pi\)
\(402\) 0 0
\(403\) −1.46253e6 −0.448581
\(404\) −296224. −0.0902957
\(405\) 0 0
\(406\) 1.75304e6 0.527809
\(407\) 2.74650e6 0.821852
\(408\) 0 0
\(409\) 2.00783e6 0.593496 0.296748 0.954956i \(-0.404098\pi\)
0.296748 + 0.954956i \(0.404098\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.85690e6 −0.538945
\(413\) −2.36674e6 −0.682772
\(414\) 1.53187e6 0.439260
\(415\) 0 0
\(416\) 173056. 0.0490290
\(417\) 0 0
\(418\) 78000.0 0.0218350
\(419\) 5.99378e6 1.66788 0.833942 0.551852i \(-0.186079\pi\)
0.833942 + 0.551852i \(0.186079\pi\)
\(420\) 0 0
\(421\) −5.32737e6 −1.46490 −0.732449 0.680822i \(-0.761623\pi\)
−0.732449 + 0.680822i \(0.761623\pi\)
\(422\) −1.64310e6 −0.449142
\(423\) −1.44877e6 −0.393684
\(424\) −1.85894e6 −0.502171
\(425\) 0 0
\(426\) 0 0
\(427\) −5.58994e6 −1.48367
\(428\) −2.45632e6 −0.648150
\(429\) 0 0
\(430\) 0 0
\(431\) −5.42972e6 −1.40794 −0.703970 0.710230i \(-0.748591\pi\)
−0.703970 + 0.710230i \(0.748591\pi\)
\(432\) 0 0
\(433\) −7.43979e6 −1.90696 −0.953479 0.301459i \(-0.902526\pi\)
−0.953479 + 0.301459i \(0.902526\pi\)
\(434\) −5.88472e6 −1.49969
\(435\) 0 0
\(436\) −2.85795e6 −0.720010
\(437\) 122928. 0.0307927
\(438\) 0 0
\(439\) 6.86418e6 1.69991 0.849957 0.526852i \(-0.176628\pi\)
0.849957 + 0.526852i \(0.176628\pi\)
\(440\) 0 0
\(441\) −2.93860e6 −0.719522
\(442\) −717912. −0.174790
\(443\) 3.46630e6 0.839182 0.419591 0.907713i \(-0.362173\pi\)
0.419591 + 0.907713i \(0.362173\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −4.34753e6 −1.03492
\(447\) 0 0
\(448\) 696320. 0.163913
\(449\) −1.40426e6 −0.328725 −0.164362 0.986400i \(-0.552557\pi\)
−0.164362 + 0.986400i \(0.552557\pi\)
\(450\) 0 0
\(451\) −262500. −0.0607698
\(452\) 3.91606e6 0.901579
\(453\) 0 0
\(454\) 1.02588e6 0.233591
\(455\) 0 0
\(456\) 0 0
\(457\) 5.95072e6 1.33284 0.666421 0.745575i \(-0.267825\pi\)
0.666421 + 0.745575i \(0.267825\pi\)
\(458\) −1.19244e6 −0.265627
\(459\) 0 0
\(460\) 0 0
\(461\) −6.25465e6 −1.37073 −0.685363 0.728202i \(-0.740356\pi\)
−0.685363 + 0.728202i \(0.740356\pi\)
\(462\) 0 0
\(463\) 1.55055e6 0.336149 0.168075 0.985774i \(-0.446245\pi\)
0.168075 + 0.985774i \(0.446245\pi\)
\(464\) 659968. 0.142308
\(465\) 0 0
\(466\) 2.44770e6 0.522149
\(467\) 1.80480e6 0.382945 0.191472 0.981498i \(-0.438674\pi\)
0.191472 + 0.981498i \(0.438674\pi\)
\(468\) −657072. −0.138675
\(469\) 1.18262e7 2.48264
\(470\) 0 0
\(471\) 0 0
\(472\) −891008. −0.184088
\(473\) −1.47500e6 −0.303137
\(474\) 0 0
\(475\) 0 0
\(476\) −2.88864e6 −0.584354
\(477\) 7.05818e6 1.42035
\(478\) 146280. 0.0292830
\(479\) 2.21809e6 0.441712 0.220856 0.975306i \(-0.429115\pi\)
0.220856 + 0.975306i \(0.429115\pi\)
\(480\) 0 0
\(481\) −1.85663e6 −0.365901
\(482\) 1.52369e6 0.298730
\(483\) 0 0
\(484\) −1.57682e6 −0.305962
\(485\) 0 0
\(486\) 0 0
\(487\) 6.14268e6 1.17364 0.586821 0.809717i \(-0.300379\pi\)
0.586821 + 0.809717i \(0.300379\pi\)
\(488\) −2.10445e6 −0.400026
\(489\) 0 0
\(490\) 0 0
\(491\) 6.44486e6 1.20645 0.603226 0.797571i \(-0.293882\pi\)
0.603226 + 0.797571i \(0.293882\pi\)
\(492\) 0 0
\(493\) −2.73784e6 −0.507330
\(494\) −52728.0 −0.00972129
\(495\) 0 0
\(496\) −2.21542e6 −0.404346
\(497\) −8.59214e6 −1.56031
\(498\) 0 0
\(499\) 4.25838e6 0.765584 0.382792 0.923835i \(-0.374963\pi\)
0.382792 + 0.923835i \(0.374963\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −4.91227e6 −0.870008
\(503\) 3.56242e6 0.627806 0.313903 0.949455i \(-0.398363\pi\)
0.313903 + 0.949455i \(0.398363\pi\)
\(504\) −2.64384e6 −0.463616
\(505\) 0 0
\(506\) 1.57600e6 0.273640
\(507\) 0 0
\(508\) −4.10560e6 −0.705858
\(509\) 4.23936e6 0.725281 0.362640 0.931929i \(-0.381875\pi\)
0.362640 + 0.931929i \(0.381875\pi\)
\(510\) 0 0
\(511\) 7.94750e6 1.34641
\(512\) 262144. 0.0441942
\(513\) 0 0
\(514\) 1.75711e6 0.293354
\(515\) 0 0
\(516\) 0 0
\(517\) −1.49050e6 −0.245248
\(518\) −7.47048e6 −1.22328
\(519\) 0 0
\(520\) 0 0
\(521\) 2.38657e6 0.385194 0.192597 0.981278i \(-0.438309\pi\)
0.192597 + 0.981278i \(0.438309\pi\)
\(522\) −2.50582e6 −0.402507
\(523\) 8.84129e6 1.41339 0.706694 0.707519i \(-0.250186\pi\)
0.706694 + 0.707519i \(0.250186\pi\)
\(524\) −4.20378e6 −0.668823
\(525\) 0 0
\(526\) 6.71947e6 1.05894
\(527\) 9.19055e6 1.44150
\(528\) 0 0
\(529\) −3.95257e6 −0.614101
\(530\) 0 0
\(531\) 3.38305e6 0.520681
\(532\) −212160. −0.0325001
\(533\) 177450. 0.0270557
\(534\) 0 0
\(535\) 0 0
\(536\) 4.45222e6 0.669368
\(537\) 0 0
\(538\) 7.75361e6 1.15491
\(539\) −3.02325e6 −0.448231
\(540\) 0 0
\(541\) 70058.0 0.0102912 0.00514558 0.999987i \(-0.498362\pi\)
0.00514558 + 0.999987i \(0.498362\pi\)
\(542\) −2.78199e6 −0.406778
\(543\) 0 0
\(544\) −1.08749e6 −0.157553
\(545\) 0 0
\(546\) 0 0
\(547\) 6.60752e6 0.944213 0.472107 0.881541i \(-0.343494\pi\)
0.472107 + 0.881541i \(0.343494\pi\)
\(548\) 612576. 0.0871382
\(549\) 7.99033e6 1.13145
\(550\) 0 0
\(551\) −201084. −0.0282162
\(552\) 0 0
\(553\) −3.28916e6 −0.457375
\(554\) 4.52551e6 0.626460
\(555\) 0 0
\(556\) −924416. −0.126818
\(557\) 1.10726e7 1.51221 0.756107 0.654448i \(-0.227099\pi\)
0.756107 + 0.654448i \(0.227099\pi\)
\(558\) 8.41169e6 1.14366
\(559\) 997100. 0.134961
\(560\) 0 0
\(561\) 0 0
\(562\) 6.92487e6 0.924849
\(563\) 1.43532e6 0.190843 0.0954216 0.995437i \(-0.469580\pi\)
0.0954216 + 0.995437i \(0.469580\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 5.88498e6 0.772153
\(567\) 1.00383e7 1.31131
\(568\) −3.23469e6 −0.420689
\(569\) −1.17051e7 −1.51564 −0.757818 0.652466i \(-0.773734\pi\)
−0.757818 + 0.652466i \(0.773734\pi\)
\(570\) 0 0
\(571\) 4.81885e6 0.618519 0.309260 0.950978i \(-0.399919\pi\)
0.309260 + 0.950978i \(0.399919\pi\)
\(572\) −676000. −0.0863886
\(573\) 0 0
\(574\) 714000. 0.0904521
\(575\) 0 0
\(576\) −995328. −0.125000
\(577\) 1.35572e6 0.169523 0.0847617 0.996401i \(-0.472987\pi\)
0.0847617 + 0.996401i \(0.472987\pi\)
\(578\) −1.16805e6 −0.145426
\(579\) 0 0
\(580\) 0 0
\(581\) 1.48645e7 1.82687
\(582\) 0 0
\(583\) 7.26150e6 0.884820
\(584\) 2.99200e6 0.363019
\(585\) 0 0
\(586\) −1.15542e7 −1.38994
\(587\) −5.03941e6 −0.603649 −0.301824 0.953364i \(-0.597596\pi\)
−0.301824 + 0.953364i \(0.597596\pi\)
\(588\) 0 0
\(589\) 675012. 0.0801721
\(590\) 0 0
\(591\) 0 0
\(592\) −2.81242e6 −0.329819
\(593\) −9.16124e6 −1.06984 −0.534919 0.844904i \(-0.679658\pi\)
−0.534919 + 0.844904i \(0.679658\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 461856. 0.0532587
\(597\) 0 0
\(598\) −1.06538e6 −0.121829
\(599\) −6.46635e6 −0.736363 −0.368182 0.929754i \(-0.620020\pi\)
−0.368182 + 0.929754i \(0.620020\pi\)
\(600\) 0 0
\(601\) −1.18021e7 −1.33282 −0.666411 0.745585i \(-0.732170\pi\)
−0.666411 + 0.745585i \(0.732170\pi\)
\(602\) 4.01200e6 0.451201
\(603\) −1.69045e7 −1.89326
\(604\) 637920. 0.0711498
\(605\) 0 0
\(606\) 0 0
\(607\) −2.25748e6 −0.248686 −0.124343 0.992239i \(-0.539682\pi\)
−0.124343 + 0.992239i \(0.539682\pi\)
\(608\) −79872.0 −0.00876265
\(609\) 0 0
\(610\) 0 0
\(611\) 1.00758e6 0.109188
\(612\) 4.12906e6 0.445628
\(613\) 2.75378e6 0.295991 0.147995 0.988988i \(-0.452718\pi\)
0.147995 + 0.988988i \(0.452718\pi\)
\(614\) −3.49647e6 −0.374291
\(615\) 0 0
\(616\) −2.72000e6 −0.288813
\(617\) −3.41607e6 −0.361255 −0.180627 0.983552i \(-0.557813\pi\)
−0.180627 + 0.983552i \(0.557813\pi\)
\(618\) 0 0
\(619\) 9.43169e6 0.989379 0.494690 0.869070i \(-0.335282\pi\)
0.494690 + 0.869070i \(0.335282\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 1.07290e7 1.11194
\(623\) 1.60089e7 1.65250
\(624\) 0 0
\(625\) 0 0
\(626\) 5.37834e6 0.548546
\(627\) 0 0
\(628\) −2.57667e6 −0.260711
\(629\) 1.16671e7 1.17581
\(630\) 0 0
\(631\) −4.87474e6 −0.487391 −0.243696 0.969852i \(-0.578360\pi\)
−0.243696 + 0.969852i \(0.578360\pi\)
\(632\) −1.23827e6 −0.123317
\(633\) 0 0
\(634\) −5.28295e6 −0.521980
\(635\) 0 0
\(636\) 0 0
\(637\) 2.04372e6 0.199559
\(638\) −2.57800e6 −0.250744
\(639\) 1.22817e7 1.18989
\(640\) 0 0
\(641\) 9.74279e6 0.936566 0.468283 0.883579i \(-0.344873\pi\)
0.468283 + 0.883579i \(0.344873\pi\)
\(642\) 0 0
\(643\) −1.63894e6 −0.156327 −0.0781637 0.996941i \(-0.524906\pi\)
−0.0781637 + 0.996941i \(0.524906\pi\)
\(644\) −4.28672e6 −0.407296
\(645\) 0 0
\(646\) 331344. 0.0312390
\(647\) 1.59069e6 0.149391 0.0746955 0.997206i \(-0.476202\pi\)
0.0746955 + 0.997206i \(0.476202\pi\)
\(648\) 3.77914e6 0.353553
\(649\) 3.48050e6 0.324362
\(650\) 0 0
\(651\) 0 0
\(652\) −5.00528e6 −0.461115
\(653\) −1.59778e7 −1.46634 −0.733170 0.680045i \(-0.761960\pi\)
−0.733170 + 0.680045i \(0.761960\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 268800. 0.0243876
\(657\) −1.13602e7 −1.02677
\(658\) 4.05416e6 0.365036
\(659\) −6.02458e6 −0.540397 −0.270199 0.962805i \(-0.587089\pi\)
−0.270199 + 0.962805i \(0.587089\pi\)
\(660\) 0 0
\(661\) −2.00705e7 −1.78671 −0.893355 0.449352i \(-0.851655\pi\)
−0.893355 + 0.449352i \(0.851655\pi\)
\(662\) −8.22911e6 −0.729807
\(663\) 0 0
\(664\) 5.59603e6 0.492561
\(665\) 0 0
\(666\) 1.06784e7 0.932868
\(667\) −4.06293e6 −0.353610
\(668\) −8.52682e6 −0.739343
\(669\) 0 0
\(670\) 0 0
\(671\) 8.22050e6 0.704842
\(672\) 0 0
\(673\) 5.48575e6 0.466873 0.233436 0.972372i \(-0.425003\pi\)
0.233436 + 0.972372i \(0.425003\pi\)
\(674\) −1.81359e6 −0.153776
\(675\) 0 0
\(676\) 456976. 0.0384615
\(677\) 4.74926e6 0.398248 0.199124 0.979974i \(-0.436190\pi\)
0.199124 + 0.979974i \(0.436190\pi\)
\(678\) 0 0
\(679\) −3.10736e7 −2.58653
\(680\) 0 0
\(681\) 0 0
\(682\) 8.65400e6 0.712453
\(683\) 6.13964e6 0.503606 0.251803 0.967778i \(-0.418976\pi\)
0.251803 + 0.967778i \(0.418976\pi\)
\(684\) 303264. 0.0247845
\(685\) 0 0
\(686\) −3.20552e6 −0.260069
\(687\) 0 0
\(688\) 1.51040e6 0.121652
\(689\) −4.90877e6 −0.393935
\(690\) 0 0
\(691\) 1.57617e7 1.25577 0.627883 0.778308i \(-0.283922\pi\)
0.627883 + 0.778308i \(0.283922\pi\)
\(692\) 1.00873e7 0.800776
\(693\) 1.03275e7 0.816887
\(694\) 4.92259e6 0.387967
\(695\) 0 0
\(696\) 0 0
\(697\) −1.11510e6 −0.0869424
\(698\) −9.75298e6 −0.757703
\(699\) 0 0
\(700\) 0 0
\(701\) −1.42036e7 −1.09170 −0.545851 0.837882i \(-0.683793\pi\)
−0.545851 + 0.837882i \(0.683793\pi\)
\(702\) 0 0
\(703\) 856908. 0.0653952
\(704\) −1.02400e6 −0.0778697
\(705\) 0 0
\(706\) 1.07326e7 0.810388
\(707\) −3.14738e6 −0.236810
\(708\) 0 0
\(709\) 1.60718e7 1.20074 0.600369 0.799723i \(-0.295020\pi\)
0.600369 + 0.799723i \(0.295020\pi\)
\(710\) 0 0
\(711\) 4.70156e6 0.348793
\(712\) 6.02688e6 0.445546
\(713\) 1.36387e7 1.00473
\(714\) 0 0
\(715\) 0 0
\(716\) −1.07987e7 −0.787204
\(717\) 0 0
\(718\) 6.34774e6 0.459524
\(719\) −2.07078e7 −1.49387 −0.746933 0.664900i \(-0.768474\pi\)
−0.746933 + 0.664900i \(0.768474\pi\)
\(720\) 0 0
\(721\) −1.97295e7 −1.41344
\(722\) −9.88006e6 −0.705369
\(723\) 0 0
\(724\) 2.98051e6 0.211322
\(725\) 0 0
\(726\) 0 0
\(727\) −5.04803e6 −0.354231 −0.177115 0.984190i \(-0.556677\pi\)
−0.177115 + 0.984190i \(0.556677\pi\)
\(728\) 1.83872e6 0.128584
\(729\) −1.43489e7 −1.00000
\(730\) 0 0
\(731\) −6.26580e6 −0.433694
\(732\) 0 0
\(733\) 2.10377e7 1.44623 0.723115 0.690728i \(-0.242710\pi\)
0.723115 + 0.690728i \(0.242710\pi\)
\(734\) 240208. 0.0164569
\(735\) 0 0
\(736\) −1.61382e6 −0.109815
\(737\) −1.73915e7 −1.17942
\(738\) −1.02060e6 −0.0689786
\(739\) 1.38992e7 0.936218 0.468109 0.883671i \(-0.344935\pi\)
0.468109 + 0.883671i \(0.344935\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.97513e7 −1.31700
\(743\) −1.23267e6 −0.0819169 −0.0409584 0.999161i \(-0.513041\pi\)
−0.0409584 + 0.999161i \(0.513041\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.60741e7 1.05750
\(747\) −2.12474e7 −1.39317
\(748\) 4.24800e6 0.277607
\(749\) −2.60984e7 −1.69985
\(750\) 0 0
\(751\) −1.62624e6 −0.105217 −0.0526084 0.998615i \(-0.516753\pi\)
−0.0526084 + 0.998615i \(0.516753\pi\)
\(752\) 1.52627e6 0.0984209
\(753\) 0 0
\(754\) 1.74273e6 0.111635
\(755\) 0 0
\(756\) 0 0
\(757\) −3.49882e6 −0.221913 −0.110956 0.993825i \(-0.535391\pi\)
−0.110956 + 0.993825i \(0.535391\pi\)
\(758\) 6.70324e6 0.423752
\(759\) 0 0
\(760\) 0 0
\(761\) 2.21713e7 1.38781 0.693905 0.720067i \(-0.255889\pi\)
0.693905 + 0.720067i \(0.255889\pi\)
\(762\) 0 0
\(763\) −3.03657e7 −1.88831
\(764\) 1.29949e7 0.805451
\(765\) 0 0
\(766\) −2.74903e6 −0.169281
\(767\) −2.35282e6 −0.144411
\(768\) 0 0
\(769\) 1.08955e6 0.0664400 0.0332200 0.999448i \(-0.489424\pi\)
0.0332200 + 0.999448i \(0.489424\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.40227e6 0.145070
\(773\) −1.95219e6 −0.117510 −0.0587549 0.998272i \(-0.518713\pi\)
−0.0587549 + 0.998272i \(0.518713\pi\)
\(774\) −5.73480e6 −0.344085
\(775\) 0 0
\(776\) −1.16983e7 −0.697379
\(777\) 0 0
\(778\) 5.50442e6 0.326034
\(779\) −81900.0 −0.00483549
\(780\) 0 0
\(781\) 1.26355e7 0.741250
\(782\) 6.69485e6 0.391493
\(783\) 0 0
\(784\) 3.09581e6 0.179880
\(785\) 0 0
\(786\) 0 0
\(787\) 1.44531e7 0.831809 0.415904 0.909408i \(-0.363465\pi\)
0.415904 + 0.909408i \(0.363465\pi\)
\(788\) −3.78230e6 −0.216991
\(789\) 0 0
\(790\) 0 0
\(791\) 4.16082e7 2.36449
\(792\) 3.88800e6 0.220249
\(793\) −5.55706e6 −0.313807
\(794\) 2.88479e6 0.162391
\(795\) 0 0
\(796\) −630016. −0.0352427
\(797\) −1.23500e7 −0.688685 −0.344343 0.938844i \(-0.611898\pi\)
−0.344343 + 0.938844i \(0.611898\pi\)
\(798\) 0 0
\(799\) −6.33164e6 −0.350873
\(800\) 0 0
\(801\) −2.28833e7 −1.26019
\(802\) 8.90724e6 0.488998
\(803\) −1.16875e7 −0.639636
\(804\) 0 0
\(805\) 0 0
\(806\) −5.85010e6 −0.317195
\(807\) 0 0
\(808\) −1.18490e6 −0.0638487
\(809\) 1.15968e7 0.622970 0.311485 0.950251i \(-0.399174\pi\)
0.311485 + 0.950251i \(0.399174\pi\)
\(810\) 0 0
\(811\) −2.47534e7 −1.32155 −0.660774 0.750585i \(-0.729772\pi\)
−0.660774 + 0.750585i \(0.729772\pi\)
\(812\) 7.01216e6 0.373217
\(813\) 0 0
\(814\) 1.09860e7 0.581137
\(815\) 0 0
\(816\) 0 0
\(817\) −460200. −0.0241208
\(818\) 8.03130e6 0.419665
\(819\) −6.98139e6 −0.363691
\(820\) 0 0
\(821\) −2.47470e6 −0.128134 −0.0640671 0.997946i \(-0.520407\pi\)
−0.0640671 + 0.997946i \(0.520407\pi\)
\(822\) 0 0
\(823\) 7.84754e6 0.403863 0.201932 0.979400i \(-0.435278\pi\)
0.201932 + 0.979400i \(0.435278\pi\)
\(824\) −7.42758e6 −0.381092
\(825\) 0 0
\(826\) −9.46696e6 −0.482792
\(827\) 2.26192e7 1.15004 0.575020 0.818140i \(-0.304994\pi\)
0.575020 + 0.818140i \(0.304994\pi\)
\(828\) 6.12749e6 0.310604
\(829\) −1.73912e7 −0.878907 −0.439454 0.898265i \(-0.644828\pi\)
−0.439454 + 0.898265i \(0.644828\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 692224. 0.0346688
\(833\) −1.28428e7 −0.641278
\(834\) 0 0
\(835\) 0 0
\(836\) 312000. 0.0154397
\(837\) 0 0
\(838\) 2.39751e7 1.17937
\(839\) −3.43825e7 −1.68629 −0.843147 0.537684i \(-0.819299\pi\)
−0.843147 + 0.537684i \(0.819299\pi\)
\(840\) 0 0
\(841\) −1.38651e7 −0.675977
\(842\) −2.13095e7 −1.03584
\(843\) 0 0
\(844\) −6.57242e6 −0.317592
\(845\) 0 0
\(846\) −5.79506e6 −0.278376
\(847\) −1.67537e7 −0.802419
\(848\) −7.43578e6 −0.355089
\(849\) 0 0
\(850\) 0 0
\(851\) 1.73139e7 0.819543
\(852\) 0 0
\(853\) −2.31007e7 −1.08706 −0.543528 0.839391i \(-0.682912\pi\)
−0.543528 + 0.839391i \(0.682912\pi\)
\(854\) −2.23598e7 −1.04911
\(855\) 0 0
\(856\) −9.82528e6 −0.458311
\(857\) 7.02305e6 0.326643 0.163322 0.986573i \(-0.447779\pi\)
0.163322 + 0.986573i \(0.447779\pi\)
\(858\) 0 0
\(859\) 8.82135e6 0.407899 0.203949 0.978981i \(-0.434622\pi\)
0.203949 + 0.978981i \(0.434622\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −2.17189e7 −0.995564
\(863\) −2.39560e7 −1.09493 −0.547466 0.836828i \(-0.684408\pi\)
−0.547466 + 0.836828i \(0.684408\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −2.97592e7 −1.34842
\(867\) 0 0
\(868\) −2.35389e7 −1.06044
\(869\) 4.83700e6 0.217283
\(870\) 0 0
\(871\) 1.17567e7 0.525096
\(872\) −1.14318e7 −0.509124
\(873\) 4.44170e7 1.97248
\(874\) 491712. 0.0217737
\(875\) 0 0
\(876\) 0 0
\(877\) 5.79805e6 0.254556 0.127278 0.991867i \(-0.459376\pi\)
0.127278 + 0.991867i \(0.459376\pi\)
\(878\) 2.74567e7 1.20202
\(879\) 0 0
\(880\) 0 0
\(881\) −1.30527e7 −0.566580 −0.283290 0.959034i \(-0.591426\pi\)
−0.283290 + 0.959034i \(0.591426\pi\)
\(882\) −1.17544e7 −0.508779
\(883\) −4.73009e6 −0.204159 −0.102079 0.994776i \(-0.532550\pi\)
−0.102079 + 0.994776i \(0.532550\pi\)
\(884\) −2.87165e6 −0.123595
\(885\) 0 0
\(886\) 1.38652e7 0.593392
\(887\) −2.80737e7 −1.19809 −0.599046 0.800714i \(-0.704453\pi\)
−0.599046 + 0.800714i \(0.704453\pi\)
\(888\) 0 0
\(889\) −4.36220e7 −1.85119
\(890\) 0 0
\(891\) −1.47622e7 −0.622957
\(892\) −1.73901e7 −0.731796
\(893\) −465036. −0.0195145
\(894\) 0 0
\(895\) 0 0
\(896\) 2.78528e6 0.115904
\(897\) 0 0
\(898\) −5.61705e6 −0.232443
\(899\) −2.23100e7 −0.920663
\(900\) 0 0
\(901\) 3.08469e7 1.26590
\(902\) −1.05000e6 −0.0429708
\(903\) 0 0
\(904\) 1.56643e7 0.637512
\(905\) 0 0
\(906\) 0 0
\(907\) −2.28552e7 −0.922500 −0.461250 0.887270i \(-0.652599\pi\)
−0.461250 + 0.887270i \(0.652599\pi\)
\(908\) 4.10352e6 0.165174
\(909\) 4.49890e6 0.180591
\(910\) 0 0
\(911\) −3.27335e7 −1.30676 −0.653381 0.757029i \(-0.726650\pi\)
−0.653381 + 0.757029i \(0.726650\pi\)
\(912\) 0 0
\(913\) −2.18595e7 −0.867887
\(914\) 2.38029e7 0.942462
\(915\) 0 0
\(916\) −4.76976e6 −0.187827
\(917\) −4.46651e7 −1.75406
\(918\) 0 0
\(919\) −1.27717e7 −0.498839 −0.249419 0.968396i \(-0.580240\pi\)
−0.249419 + 0.968396i \(0.580240\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −2.50186e7 −0.969249
\(923\) −8.54160e6 −0.330016
\(924\) 0 0
\(925\) 0 0
\(926\) 6.20218e6 0.237693
\(927\) 2.82016e7 1.07789
\(928\) 2.63987e6 0.100627
\(929\) 3.48297e7 1.32407 0.662034 0.749473i \(-0.269693\pi\)
0.662034 + 0.749473i \(0.269693\pi\)
\(930\) 0 0
\(931\) −943254. −0.0356660
\(932\) 9.79082e6 0.369215
\(933\) 0 0
\(934\) 7.21918e6 0.270783
\(935\) 0 0
\(936\) −2.62829e6 −0.0980581
\(937\) −3.00172e7 −1.11692 −0.558459 0.829532i \(-0.688607\pi\)
−0.558459 + 0.829532i \(0.688607\pi\)
\(938\) 4.73049e7 1.75549
\(939\) 0 0
\(940\) 0 0
\(941\) −4.50649e7 −1.65907 −0.829534 0.558457i \(-0.811394\pi\)
−0.829534 + 0.558457i \(0.811394\pi\)
\(942\) 0 0
\(943\) −1.65480e6 −0.0605991
\(944\) −3.56403e6 −0.130170
\(945\) 0 0
\(946\) −5.90000e6 −0.214350
\(947\) −2.99276e7 −1.08442 −0.542210 0.840243i \(-0.682412\pi\)
−0.542210 + 0.840243i \(0.682412\pi\)
\(948\) 0 0
\(949\) 7.90075e6 0.284776
\(950\) 0 0
\(951\) 0 0
\(952\) −1.15546e7 −0.413201
\(953\) 4.25147e7 1.51638 0.758188 0.652036i \(-0.226085\pi\)
0.758188 + 0.652036i \(0.226085\pi\)
\(954\) 2.82327e7 1.00434
\(955\) 0 0
\(956\) 585120. 0.0207062
\(957\) 0 0
\(958\) 8.87234e6 0.312338
\(959\) 6.50862e6 0.228530
\(960\) 0 0
\(961\) 4.62626e7 1.61593
\(962\) −7.42654e6 −0.258731
\(963\) 3.73054e7 1.29630
\(964\) 6.09475e6 0.211234
\(965\) 0 0
\(966\) 0 0
\(967\) 3.00251e7 1.03257 0.516284 0.856417i \(-0.327315\pi\)
0.516284 + 0.856417i \(0.327315\pi\)
\(968\) −6.30726e6 −0.216348
\(969\) 0 0
\(970\) 0 0
\(971\) −4.00864e7 −1.36442 −0.682211 0.731155i \(-0.738982\pi\)
−0.682211 + 0.731155i \(0.738982\pi\)
\(972\) 0 0
\(973\) −9.82192e6 −0.332594
\(974\) 2.45707e7 0.829890
\(975\) 0 0
\(976\) −8.41779e6 −0.282861
\(977\) −5.12151e7 −1.71657 −0.858284 0.513174i \(-0.828469\pi\)
−0.858284 + 0.513174i \(0.828469\pi\)
\(978\) 0 0
\(979\) −2.35425e7 −0.785047
\(980\) 0 0
\(981\) 4.34051e7 1.44002
\(982\) 2.57794e7 0.853090
\(983\) −1.82382e7 −0.602004 −0.301002 0.953624i \(-0.597321\pi\)
−0.301002 + 0.953624i \(0.597321\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −1.09513e7 −0.358736
\(987\) 0 0
\(988\) −210912. −0.00687399
\(989\) −9.29840e6 −0.302286
\(990\) 0 0
\(991\) −3.24103e7 −1.04833 −0.524166 0.851616i \(-0.675623\pi\)
−0.524166 + 0.851616i \(0.675623\pi\)
\(992\) −8.86170e6 −0.285915
\(993\) 0 0
\(994\) −3.43686e7 −1.10330
\(995\) 0 0
\(996\) 0 0
\(997\) 2.07867e7 0.662289 0.331145 0.943580i \(-0.392565\pi\)
0.331145 + 0.943580i \(0.392565\pi\)
\(998\) 1.70335e7 0.541350
\(999\) 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 650.6.a.a.1.1 1
5.2 odd 4 650.6.b.a.599.2 2
5.3 odd 4 650.6.b.a.599.1 2
5.4 even 2 26.6.a.a.1.1 1
15.14 odd 2 234.6.a.g.1.1 1
20.19 odd 2 208.6.a.b.1.1 1
40.19 odd 2 832.6.a.e.1.1 1
40.29 even 2 832.6.a.d.1.1 1
65.34 odd 4 338.6.b.a.337.1 2
65.44 odd 4 338.6.b.a.337.2 2
65.64 even 2 338.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
26.6.a.a.1.1 1 5.4 even 2
208.6.a.b.1.1 1 20.19 odd 2
234.6.a.g.1.1 1 15.14 odd 2
338.6.a.d.1.1 1 65.64 even 2
338.6.b.a.337.1 2 65.34 odd 4
338.6.b.a.337.2 2 65.44 odd 4
650.6.a.a.1.1 1 1.1 even 1 trivial
650.6.b.a.599.1 2 5.3 odd 4
650.6.b.a.599.2 2 5.2 odd 4
832.6.a.d.1.1 1 40.29 even 2
832.6.a.e.1.1 1 40.19 odd 2