↑

Properties

Label 700.6.a.b.1.1
Level $700$
Weight $6$
Character 700.1
Self dual yes
Analytic conductor $112.269$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,6,Mod(1,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("700.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 700.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: \(112.268673869\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 700.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-26.0000 q^{3} +49.0000 q^{7} +433.000 q^{9} +8.00000 q^{11} -684.000 q^{13} +2218.00 q^{17} -2698.00 q^{19} -1274.00 q^{21} -3344.00 q^{23} -4940.00 q^{27} -3254.00 q^{29} +4788.00 q^{31} -208.000 q^{33} +11470.0 q^{37} +17784.0 q^{39} +13350.0 q^{41} +928.000 q^{43} -1212.00 q^{47} +2401.00 q^{49} -57668.0 q^{51} -13110.0 q^{53} +70148.0 q^{57} +34702.0 q^{59} -1032.00 q^{61} +21217.0 q^{63} -10108.0 q^{67} +86944.0 q^{69} +62720.0 q^{71} +18926.0 q^{73} +392.000 q^{77} +11400.0 q^{79} +23221.0 q^{81} -88958.0 q^{83} +84604.0 q^{87} +19722.0 q^{89} -33516.0 q^{91} -124488. q^{93} -17062.0 q^{97} +3464.00 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −26.0000 −1.66790 −0.833950 − 0.551839i \(-0.813926\pi\)
−0.833950 + 0.551839i \(0.813926\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 433.000 1.78189
\(10\) 0 0
\(11\) 8.00000 0.0199346 0.00996732 − 0.999950i \(-0.496827\pi\)
0.00996732 + 0.999950i \(0.496827\pi\)
\(12\) 0 0
\(13\) −684.000 −1.12253 −0.561265 − 0.827636i \(-0.689685\pi\)
−0.561265 + 0.827636i \(0.689685\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2218.00 1.86140 0.930699 − 0.365786i \(-0.119200\pi\)
0.930699 + 0.365786i \(0.119200\pi\)
\(18\) 0 0
\(19\) −2698.00 −1.71458 −0.857290 − 0.514833i \(-0.827854\pi\)
−0.857290 + 0.514833i \(0.827854\pi\)
\(20\) 0 0
\(21\) −1274.00 −0.630407
\(22\) 0 0
\(23\) −3344.00 −1.31809 −0.659047 − 0.752101i \(-0.729040\pi\)
−0.659047 + 0.752101i \(0.729040\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4940.00 −1.30412
\(28\) 0 0
\(29\) −3254.00 −0.718493 −0.359247 − 0.933243i \(-0.616966\pi\)
−0.359247 + 0.933243i \(0.616966\pi\)
\(30\) 0 0
\(31\) 4788.00 0.894849 0.447425 − 0.894322i \(-0.352341\pi\)
0.447425 + 0.894322i \(0.352341\pi\)
\(32\) 0 0
\(33\) −208.000 −0.0332490
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11470.0 1.37740 0.688698 − 0.725048i \(-0.258182\pi\)
0.688698 + 0.725048i \(0.258182\pi\)
\(38\) 0 0
\(39\) 17784.0 1.87227
\(40\) 0 0
\(41\) 13350.0 1.24029 0.620143 − 0.784489i \(-0.287075\pi\)
0.620143 + 0.784489i \(0.287075\pi\)
\(42\) 0 0
\(43\) 928.000 0.0765380 0.0382690 − 0.999267i \(-0.487816\pi\)
0.0382690 + 0.999267i \(0.487816\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1212.00 −0.0800310 −0.0400155 − 0.999199i \(-0.512741\pi\)
−0.0400155 + 0.999199i \(0.512741\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) −57668.0 −3.10463
\(52\) 0 0
\(53\) −13110.0 −0.641081 −0.320541 − 0.947235i \(-0.603865\pi\)
−0.320541 + 0.947235i \(0.603865\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 70148.0 2.85975
\(58\) 0 0
\(59\) 34702.0 1.29785 0.648925 − 0.760852i \(-0.275219\pi\)
0.648925 + 0.760852i \(0.275219\pi\)
\(60\) 0 0
\(61\) −1032.00 −0.0355104 −0.0177552 − 0.999842i \(-0.505652\pi\)
−0.0177552 + 0.999842i \(0.505652\pi\)
\(62\) 0 0
\(63\) 21217.0 0.673492
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −10108.0 −0.275092 −0.137546 − 0.990495i \(-0.543922\pi\)
−0.137546 + 0.990495i \(0.543922\pi\)
\(68\) 0 0
\(69\) 86944.0 2.19845
\(70\) 0 0
\(71\) 62720.0 1.47659 0.738295 − 0.674477i \(-0.235631\pi\)
0.738295 + 0.674477i \(0.235631\pi\)
\(72\) 0 0
\(73\) 18926.0 0.415673 0.207836 − 0.978164i \(-0.433358\pi\)
0.207836 + 0.978164i \(0.433358\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 392.000 0.00753458
\(78\) 0 0
\(79\) 11400.0 0.205512 0.102756 − 0.994707i \(-0.467234\pi\)
0.102756 + 0.994707i \(0.467234\pi\)
\(80\) 0 0
\(81\) 23221.0 0.393250
\(82\) 0 0
\(83\) −88958.0 −1.41739 −0.708696 − 0.705514i \(-0.750716\pi\)
−0.708696 + 0.705514i \(0.750716\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 84604.0 1.19838
\(88\) 0 0
\(89\) 19722.0 0.263922 0.131961 − 0.991255i \(-0.457873\pi\)
0.131961 + 0.991255i \(0.457873\pi\)
\(90\) 0 0
\(91\) −33516.0 −0.424276
\(92\) 0 0
\(93\) −124488. −1.49252
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −17062.0 −0.184120 −0.0920599 − 0.995753i \(-0.529345\pi\)
−0.0920599 + 0.995753i \(0.529345\pi\)
\(98\) 0 0
\(99\) 3464.00 0.0355214
\(100\) 0 0
\(101\) 45904.0 0.447762 0.223881 − 0.974617i \(-0.428127\pi\)
0.223881 + 0.974617i \(0.428127\pi\)
\(102\) 0 0
\(103\) 136012. 1.26324 0.631618 − 0.775280i \(-0.282391\pi\)
0.631618 + 0.775280i \(0.282391\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 69156.0 0.583943 0.291971 − 0.956427i \(-0.405689\pi\)
0.291971 + 0.956427i \(0.405689\pi\)
\(108\) 0 0
\(109\) −146414. −1.18037 −0.590183 − 0.807270i \(-0.700944\pi\)
−0.590183 + 0.807270i \(0.700944\pi\)
\(110\) 0 0
\(111\) −298220. −2.29736
\(112\) 0 0
\(113\) 80186.0 0.590748 0.295374 − 0.955382i \(-0.404556\pi\)
0.295374 + 0.955382i \(0.404556\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −296172. −2.00023
\(118\) 0 0
\(119\) 108682. 0.703542
\(120\) 0 0
\(121\) −160987. −0.999603
\(122\) 0 0
\(123\) −347100. −2.06867
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −274800. −1.51185 −0.755923 − 0.654661i \(-0.772811\pi\)
−0.755923 + 0.654661i \(0.772811\pi\)
\(128\) 0 0
\(129\) −24128.0 −0.127658
\(130\) 0 0
\(131\) 180742. 0.920197 0.460099 − 0.887868i \(-0.347814\pi\)
0.460099 + 0.887868i \(0.347814\pi\)
\(132\) 0 0
\(133\) −132202. −0.648051
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 209678. 0.954446 0.477223 − 0.878782i \(-0.341643\pi\)
0.477223 + 0.878782i \(0.341643\pi\)
\(138\) 0 0
\(139\) 17242.0 0.0756921 0.0378461 − 0.999284i \(-0.487950\pi\)
0.0378461 + 0.999284i \(0.487950\pi\)
\(140\) 0 0
\(141\) 31512.0 0.133484
\(142\) 0 0
\(143\) −5472.00 −0.0223772
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −62426.0 −0.238272
\(148\) 0 0
\(149\) 59358.0 0.219035 0.109518 − 0.993985i \(-0.465069\pi\)
0.109518 + 0.993985i \(0.465069\pi\)
\(150\) 0 0
\(151\) −336344. −1.20044 −0.600221 − 0.799834i \(-0.704921\pi\)
−0.600221 + 0.799834i \(0.704921\pi\)
\(152\) 0 0
\(153\) 960394. 3.31681
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −464588. −1.50425 −0.752123 − 0.659023i \(-0.770970\pi\)
−0.752123 + 0.659023i \(0.770970\pi\)
\(158\) 0 0
\(159\) 340860. 1.06926
\(160\) 0 0
\(161\) −163856. −0.498193
\(162\) 0 0
\(163\) −314792. −0.928014 −0.464007 − 0.885831i \(-0.653589\pi\)
−0.464007 + 0.885831i \(0.653589\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −285724. −0.792785 −0.396393 − 0.918081i \(-0.629738\pi\)
−0.396393 + 0.918081i \(0.629738\pi\)
\(168\) 0 0
\(169\) 96563.0 0.260072
\(170\) 0 0
\(171\) −1.16823e6 −3.05520
\(172\) 0 0
\(173\) 709148. 1.80145 0.900724 − 0.434392i \(-0.143037\pi\)
0.900724 + 0.434392i \(0.143037\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −902252. −2.16468
\(178\) 0 0
\(179\) −617148. −1.43965 −0.719825 − 0.694156i \(-0.755778\pi\)
−0.719825 + 0.694156i \(0.755778\pi\)
\(180\) 0 0
\(181\) 237828. 0.539593 0.269797 − 0.962917i \(-0.413044\pi\)
0.269797 + 0.962917i \(0.413044\pi\)
\(182\) 0 0
\(183\) 26832.0 0.0592278
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 17744.0 0.0371063
\(188\) 0 0
\(189\) −242060. −0.492911
\(190\) 0 0
\(191\) −133512. −0.264812 −0.132406 − 0.991196i \(-0.542270\pi\)
−0.132406 + 0.991196i \(0.542270\pi\)
\(192\) 0 0
\(193\) −270446. −0.522622 −0.261311 − 0.965255i \(-0.584155\pi\)
−0.261311 + 0.965255i \(0.584155\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −875102. −1.60655 −0.803273 − 0.595611i \(-0.796910\pi\)
−0.803273 + 0.595611i \(0.796910\pi\)
\(198\) 0 0
\(199\) −347620. −0.622260 −0.311130 − 0.950367i \(-0.600708\pi\)
−0.311130 + 0.950367i \(0.600708\pi\)
\(200\) 0 0
\(201\) 262808. 0.458826
\(202\) 0 0
\(203\) −159446. −0.271565
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.44795e6 −2.34870
\(208\) 0 0
\(209\) −21584.0 −0.0341795
\(210\) 0 0
\(211\) −425380. −0.657765 −0.328883 − 0.944371i \(-0.606672\pi\)
−0.328883 + 0.944371i \(0.606672\pi\)
\(212\) 0 0
\(213\) −1.63072e6 −2.46281
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 234612. 0.338221
\(218\) 0 0
\(219\) −492076. −0.693301
\(220\) 0 0
\(221\) −1.51711e6 −2.08947
\(222\) 0 0
\(223\) −481592. −0.648511 −0.324255 − 0.945970i \(-0.605114\pi\)
−0.324255 + 0.945970i \(0.605114\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6042.00 0.00778245 0.00389122 − 0.999992i \(-0.498761\pi\)
0.00389122 + 0.999992i \(0.498761\pi\)
\(228\) 0 0
\(229\) 1804.00 0.00227325 0.00113663 − 0.999999i \(-0.499638\pi\)
0.00113663 + 0.999999i \(0.499638\pi\)
\(230\) 0 0
\(231\) −10192.0 −0.0125669
\(232\) 0 0
\(233\) 1.61153e6 1.94468 0.972339 − 0.233576i \(-0.0750427\pi\)
0.972339 + 0.233576i \(0.0750427\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −296400. −0.342774
\(238\) 0 0
\(239\) −987096. −1.11780 −0.558901 − 0.829235i \(-0.688777\pi\)
−0.558901 + 0.829235i \(0.688777\pi\)
\(240\) 0 0
\(241\) 893510. 0.990962 0.495481 − 0.868619i \(-0.334992\pi\)
0.495481 + 0.868619i \(0.334992\pi\)
\(242\) 0 0
\(243\) 596674. 0.648219
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.84543e6 1.92467
\(248\) 0 0
\(249\) 2.31291e6 2.36407
\(250\) 0 0
\(251\) 365946. 0.366634 0.183317 − 0.983054i \(-0.441317\pi\)
0.183317 + 0.983054i \(0.441317\pi\)
\(252\) 0 0
\(253\) −26752.0 −0.0262757
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.40459e6 −1.32653 −0.663266 − 0.748383i \(-0.730830\pi\)
−0.663266 + 0.748383i \(0.730830\pi\)
\(258\) 0 0
\(259\) 562030. 0.520607
\(260\) 0 0
\(261\) −1.40898e6 −1.28028
\(262\) 0 0
\(263\) −1.09968e6 −0.980341 −0.490170 − 0.871627i \(-0.663065\pi\)
−0.490170 + 0.871627i \(0.663065\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −512772. −0.440196
\(268\) 0 0
\(269\) 814948. 0.686672 0.343336 − 0.939213i \(-0.388443\pi\)
0.343336 + 0.939213i \(0.388443\pi\)
\(270\) 0 0
\(271\) −1.69906e6 −1.40535 −0.702675 − 0.711511i \(-0.748011\pi\)
−0.702675 + 0.711511i \(0.748011\pi\)
\(272\) 0 0
\(273\) 871416. 0.707651
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.36508e6 1.06895 0.534477 − 0.845183i \(-0.320508\pi\)
0.534477 + 0.845183i \(0.320508\pi\)
\(278\) 0 0
\(279\) 2.07320e6 1.59453
\(280\) 0 0
\(281\) −715846. −0.540821 −0.270411 − 0.962745i \(-0.587159\pi\)
−0.270411 + 0.962745i \(0.587159\pi\)
\(282\) 0 0
\(283\) −217726. −0.161601 −0.0808005 − 0.996730i \(-0.525748\pi\)
−0.0808005 + 0.996730i \(0.525748\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 654150. 0.468784
\(288\) 0 0
\(289\) 3.49967e6 2.46480
\(290\) 0 0
\(291\) 443612. 0.307094
\(292\) 0 0
\(293\) −1.50708e6 −1.02557 −0.512787 − 0.858516i \(-0.671387\pi\)
−0.512787 + 0.858516i \(0.671387\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −39520.0 −0.0259972
\(298\) 0 0
\(299\) 2.28730e6 1.47960
\(300\) 0 0
\(301\) 45472.0 0.0289286
\(302\) 0 0
\(303\) −1.19350e6 −0.746822
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −12502.0 −0.00757066 −0.00378533 − 0.999993i \(-0.501205\pi\)
−0.00378533 + 0.999993i \(0.501205\pi\)
\(308\) 0 0
\(309\) −3.53631e6 −2.10695
\(310\) 0 0
\(311\) −647432. −0.379571 −0.189786 − 0.981826i \(-0.560779\pi\)
−0.189786 + 0.981826i \(0.560779\pi\)
\(312\) 0 0
\(313\) 935978. 0.540014 0.270007 − 0.962858i \(-0.412974\pi\)
0.270007 + 0.962858i \(0.412974\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −705942. −0.394567 −0.197284 − 0.980346i \(-0.563212\pi\)
−0.197284 + 0.980346i \(0.563212\pi\)
\(318\) 0 0
\(319\) −26032.0 −0.0143229
\(320\) 0 0
\(321\) −1.79806e6 −0.973959
\(322\) 0 0
\(323\) −5.98416e6 −3.19152
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 3.80676e6 1.96873
\(328\) 0 0
\(329\) −59388.0 −0.0302489
\(330\) 0 0
\(331\) −1.14304e6 −0.573445 −0.286722 − 0.958014i \(-0.592566\pi\)
−0.286722 + 0.958014i \(0.592566\pi\)
\(332\) 0 0
\(333\) 4.96651e6 2.45437
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2.36402e6 1.13390 0.566952 − 0.823751i \(-0.308123\pi\)
0.566952 + 0.823751i \(0.308123\pi\)
\(338\) 0 0
\(339\) −2.08484e6 −0.985309
\(340\) 0 0
\(341\) 38304.0 0.0178385
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −726240. −0.323785 −0.161892 − 0.986808i \(-0.551760\pi\)
−0.161892 + 0.986808i \(0.551760\pi\)
\(348\) 0 0
\(349\) 136180. 0.0598480 0.0299240 − 0.999552i \(-0.490473\pi\)
0.0299240 + 0.999552i \(0.490473\pi\)
\(350\) 0 0
\(351\) 3.37896e6 1.46391
\(352\) 0 0
\(353\) 1.16907e6 0.499349 0.249674 − 0.968330i \(-0.419676\pi\)
0.249674 + 0.968330i \(0.419676\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.82573e6 −1.17344
\(358\) 0 0
\(359\) −4280.00 −0.00175270 −0.000876350 − 1.00000i \(-0.500279\pi\)
−0.000876350 1.00000i \(0.500279\pi\)
\(360\) 0 0
\(361\) 4.80310e6 1.93979
\(362\) 0 0
\(363\) 4.18566e6 1.66724
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −2.44796e6 −0.948722 −0.474361 − 0.880330i \(-0.657321\pi\)
−0.474361 + 0.880330i \(0.657321\pi\)
\(368\) 0 0
\(369\) 5.78055e6 2.21006
\(370\) 0 0
\(371\) −642390. −0.242306
\(372\) 0 0
\(373\) 904514. 0.336623 0.168311 − 0.985734i \(-0.446169\pi\)
0.168311 + 0.985734i \(0.446169\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.22574e6 0.806530
\(378\) 0 0
\(379\) −4.23034e6 −1.51279 −0.756393 − 0.654117i \(-0.773040\pi\)
−0.756393 + 0.654117i \(0.773040\pi\)
\(380\) 0 0
\(381\) 7.14480e6 2.52161
\(382\) 0 0
\(383\) −4.55400e6 −1.58634 −0.793169 − 0.609002i \(-0.791570\pi\)
−0.793169 + 0.609002i \(0.791570\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 401824. 0.136382
\(388\) 0 0
\(389\) −3.98541e6 −1.33536 −0.667680 − 0.744448i \(-0.732713\pi\)
−0.667680 + 0.744448i \(0.732713\pi\)
\(390\) 0 0
\(391\) −7.41699e6 −2.45350
\(392\) 0 0
\(393\) −4.69929e6 −1.53480
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −552420. −0.175911 −0.0879555 − 0.996124i \(-0.528033\pi\)
−0.0879555 + 0.996124i \(0.528033\pi\)
\(398\) 0 0
\(399\) 3.43725e6 1.08088
\(400\) 0 0
\(401\) 38190.0 0.0118601 0.00593006 − 0.999982i \(-0.498112\pi\)
0.00593006 + 0.999982i \(0.498112\pi\)
\(402\) 0 0
\(403\) −3.27499e6 −1.00449
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 91760.0 0.0274579
\(408\) 0 0
\(409\) −3.92475e6 −1.16012 −0.580062 − 0.814573i \(-0.696972\pi\)
−0.580062 + 0.814573i \(0.696972\pi\)
\(410\) 0 0
\(411\) −5.45163e6 −1.59192
\(412\) 0 0
\(413\) 1.70040e6 0.490541
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −448292. −0.126247
\(418\) 0 0
\(419\) 598386. 0.166512 0.0832562 − 0.996528i \(-0.473468\pi\)
0.0832562 + 0.996528i \(0.473468\pi\)
\(420\) 0 0
\(421\) 4.61597e6 1.26928 0.634641 − 0.772807i \(-0.281148\pi\)
0.634641 + 0.772807i \(0.281148\pi\)
\(422\) 0 0
\(423\) −524796. −0.142607
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −50568.0 −0.0134217
\(428\) 0 0
\(429\) 142272. 0.0373230
\(430\) 0 0
\(431\) −61560.0 −0.0159627 −0.00798133 − 0.999968i \(-0.502541\pi\)
−0.00798133 + 0.999968i \(0.502541\pi\)
\(432\) 0 0
\(433\) 3.79727e6 0.973310 0.486655 − 0.873594i \(-0.338217\pi\)
0.486655 + 0.873594i \(0.338217\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9.02211e6 2.25998
\(438\) 0 0
\(439\) −2.28852e6 −0.566752 −0.283376 − 0.959009i \(-0.591455\pi\)
−0.283376 + 0.959009i \(0.591455\pi\)
\(440\) 0 0
\(441\) 1.03963e6 0.254556
\(442\) 0 0
\(443\) 4.75976e6 1.15233 0.576163 − 0.817335i \(-0.304549\pi\)
0.576163 + 0.817335i \(0.304549\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.54331e6 −0.365329
\(448\) 0 0
\(449\) −4.36715e6 −1.02231 −0.511155 − 0.859489i \(-0.670782\pi\)
−0.511155 + 0.859489i \(0.670782\pi\)
\(450\) 0 0
\(451\) 106800. 0.0247246
\(452\) 0 0
\(453\) 8.74494e6 2.00222
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.44994e6 −1.22068 −0.610339 − 0.792140i \(-0.708967\pi\)
−0.610339 + 0.792140i \(0.708967\pi\)
\(458\) 0 0
\(459\) −1.09569e7 −2.42749
\(460\) 0 0
\(461\) 1.66966e6 0.365911 0.182956 − 0.983121i \(-0.441434\pi\)
0.182956 + 0.983121i \(0.441434\pi\)
\(462\) 0 0
\(463\) −70768.0 −0.0153421 −0.00767104 − 0.999971i \(-0.502442\pi\)
−0.00767104 + 0.999971i \(0.502442\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.66083e6 −1.20112 −0.600562 − 0.799578i \(-0.705056\pi\)
−0.600562 + 0.799578i \(0.705056\pi\)
\(468\) 0 0
\(469\) −495292. −0.103975
\(470\) 0 0
\(471\) 1.20793e7 2.50893
\(472\) 0 0
\(473\) 7424.00 0.00152576
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −5.67663e6 −1.14234
\(478\) 0 0
\(479\) −1.44948e6 −0.288652 −0.144326 − 0.989530i \(-0.546101\pi\)
−0.144326 + 0.989530i \(0.546101\pi\)
\(480\) 0 0
\(481\) −7.84548e6 −1.54617
\(482\) 0 0
\(483\) 4.26026e6 0.830937
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −4.07504e6 −0.778591 −0.389296 − 0.921113i \(-0.627282\pi\)
−0.389296 + 0.921113i \(0.627282\pi\)
\(488\) 0 0
\(489\) 8.18459e6 1.54784
\(490\) 0 0
\(491\) 986100. 0.184594 0.0922969 − 0.995732i \(-0.470579\pi\)
0.0922969 + 0.995732i \(0.470579\pi\)
\(492\) 0 0
\(493\) −7.21737e6 −1.33740
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.07328e6 0.558099
\(498\) 0 0
\(499\) 5.98342e6 1.07572 0.537859 − 0.843035i \(-0.319233\pi\)
0.537859 + 0.843035i \(0.319233\pi\)
\(500\) 0 0
\(501\) 7.42882e6 1.32229
\(502\) 0 0
\(503\) 3.49373e6 0.615700 0.307850 − 0.951435i \(-0.400391\pi\)
0.307850 + 0.951435i \(0.400391\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.51064e6 −0.433775
\(508\) 0 0
\(509\) 2.15711e6 0.369043 0.184522 − 0.982828i \(-0.440926\pi\)
0.184522 + 0.982828i \(0.440926\pi\)
\(510\) 0 0
\(511\) 927374. 0.157110
\(512\) 0 0
\(513\) 1.33281e7 2.23602
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −9696.00 −0.00159539
\(518\) 0 0
\(519\) −1.84378e7 −3.00464
\(520\) 0 0
\(521\) −6.65817e6 −1.07463 −0.537317 − 0.843380i \(-0.680562\pi\)
−0.537317 + 0.843380i \(0.680562\pi\)
\(522\) 0 0
\(523\) −5.95223e6 −0.951537 −0.475768 − 0.879571i \(-0.657830\pi\)
−0.475768 + 0.879571i \(0.657830\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.06198e7 1.66567
\(528\) 0 0
\(529\) 4.74599e6 0.737374
\(530\) 0 0
\(531\) 1.50260e7 2.31263
\(532\) 0 0
\(533\) −9.13140e6 −1.39226
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.60458e7 2.40119
\(538\) 0 0
\(539\) 19208.0 0.00284780
\(540\) 0 0
\(541\) −6.39681e6 −0.939659 −0.469830 − 0.882757i \(-0.655685\pi\)
−0.469830 + 0.882757i \(0.655685\pi\)
\(542\) 0 0
\(543\) −6.18353e6 −0.899988
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 5.51851e6 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(548\) 0 0
\(549\) −446856. −0.0632757
\(550\) 0 0
\(551\) 8.77929e6 1.23191
\(552\) 0 0
\(553\) 558600. 0.0776762
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.02159e6 −0.276093 −0.138046 − 0.990426i \(-0.544082\pi\)
−0.138046 + 0.990426i \(0.544082\pi\)
\(558\) 0 0
\(559\) −634752. −0.0859161
\(560\) 0 0
\(561\) −461344. −0.0618896
\(562\) 0 0
\(563\) −8.14678e6 −1.08322 −0.541608 − 0.840631i \(-0.682184\pi\)
−0.541608 + 0.840631i \(0.682184\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.13783e6 0.148634
\(568\) 0 0
\(569\) −1.19824e7 −1.55154 −0.775772 − 0.631013i \(-0.782639\pi\)
−0.775772 + 0.631013i \(0.782639\pi\)
\(570\) 0 0
\(571\) 1.39582e6 0.179159 0.0895793 − 0.995980i \(-0.471448\pi\)
0.0895793 + 0.995980i \(0.471448\pi\)
\(572\) 0 0
\(573\) 3.47131e6 0.441679
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.96784e6 −0.246065 −0.123033 − 0.992403i \(-0.539262\pi\)
−0.123033 + 0.992403i \(0.539262\pi\)
\(578\) 0 0
\(579\) 7.03160e6 0.871681
\(580\) 0 0
\(581\) −4.35894e6 −0.535724
\(582\) 0 0
\(583\) −104880. −0.0127797
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.18897e6 0.381993 0.190997 − 0.981591i \(-0.438828\pi\)
0.190997 + 0.981591i \(0.438828\pi\)
\(588\) 0 0
\(589\) −1.29180e7 −1.53429
\(590\) 0 0
\(591\) 2.27527e7 2.67956
\(592\) 0 0
\(593\) −1.67500e6 −0.195604 −0.0978022 − 0.995206i \(-0.531181\pi\)
−0.0978022 + 0.995206i \(0.531181\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 9.03812e6 1.03787
\(598\) 0 0
\(599\) −1.00635e7 −1.14599 −0.572994 − 0.819559i \(-0.694218\pi\)
−0.572994 + 0.819559i \(0.694218\pi\)
\(600\) 0 0
\(601\) 1.72798e6 0.195143 0.0975713 − 0.995229i \(-0.468893\pi\)
0.0975713 + 0.995229i \(0.468893\pi\)
\(602\) 0 0
\(603\) −4.37676e6 −0.490185
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 1.69523e7 1.86748 0.933740 − 0.357953i \(-0.116525\pi\)
0.933740 + 0.357953i \(0.116525\pi\)
\(608\) 0 0
\(609\) 4.14560e6 0.452943
\(610\) 0 0
\(611\) 829008. 0.0898371
\(612\) 0 0
\(613\) −1.01942e7 −1.09572 −0.547861 − 0.836569i \(-0.684558\pi\)
−0.547861 + 0.836569i \(0.684558\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.57452e7 −1.66508 −0.832540 − 0.553965i \(-0.813114\pi\)
−0.832540 + 0.553965i \(0.813114\pi\)
\(618\) 0 0
\(619\) −332690. −0.0348990 −0.0174495 − 0.999848i \(-0.505555\pi\)
−0.0174495 + 0.999848i \(0.505555\pi\)
\(620\) 0 0
\(621\) 1.65194e7 1.71895
\(622\) 0 0
\(623\) 966378. 0.0997532
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 561184. 0.0570081
\(628\) 0 0
\(629\) 2.54405e7 2.56388
\(630\) 0 0
\(631\) 3.59720e6 0.359659 0.179830 − 0.983698i \(-0.442445\pi\)
0.179830 + 0.983698i \(0.442445\pi\)
\(632\) 0 0
\(633\) 1.10599e7 1.09709
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.64228e6 −0.160361
\(638\) 0 0
\(639\) 2.71578e7 2.63113
\(640\) 0 0
\(641\) −1.46389e7 −1.40723 −0.703614 − 0.710583i \(-0.748431\pi\)
−0.703614 + 0.710583i \(0.748431\pi\)
\(642\) 0 0
\(643\) 1.38386e7 1.31997 0.659987 − 0.751277i \(-0.270562\pi\)
0.659987 + 0.751277i \(0.270562\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.40358e7 1.31819 0.659093 − 0.752061i \(-0.270940\pi\)
0.659093 + 0.752061i \(0.270940\pi\)
\(648\) 0 0
\(649\) 277616. 0.0258722
\(650\) 0 0
\(651\) −6.09991e6 −0.564119
\(652\) 0 0
\(653\) −1.61063e7 −1.47813 −0.739064 − 0.673635i \(-0.764732\pi\)
−0.739064 + 0.673635i \(0.764732\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 8.19496e6 0.740685
\(658\) 0 0
\(659\) 4.80075e6 0.430622 0.215311 − 0.976546i \(-0.430924\pi\)
0.215311 + 0.976546i \(0.430924\pi\)
\(660\) 0 0
\(661\) −1.76565e7 −1.57181 −0.785905 − 0.618347i \(-0.787803\pi\)
−0.785905 + 0.618347i \(0.787803\pi\)
\(662\) 0 0
\(663\) 3.94449e7 3.48504
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.08814e7 0.947042
\(668\) 0 0
\(669\) 1.25214e7 1.08165
\(670\) 0 0
\(671\) −8256.00 −0.000707886 0
\(672\) 0 0
\(673\) −6.59225e6 −0.561043 −0.280521 − 0.959848i \(-0.590507\pi\)
−0.280521 + 0.959848i \(0.590507\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.77178e6 −0.819411 −0.409706 − 0.912218i \(-0.634369\pi\)
−0.409706 + 0.912218i \(0.634369\pi\)
\(678\) 0 0
\(679\) −836038. −0.0695908
\(680\) 0 0
\(681\) −157092. −0.0129803
\(682\) 0 0
\(683\) 1.88663e7 1.54752 0.773758 − 0.633481i \(-0.218374\pi\)
0.773758 + 0.633481i \(0.218374\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −46904.0 −0.00379156
\(688\) 0 0
\(689\) 8.96724e6 0.719632
\(690\) 0 0
\(691\) 8.67018e6 0.690769 0.345385 − 0.938461i \(-0.387748\pi\)
0.345385 + 0.938461i \(0.387748\pi\)
\(692\) 0 0
\(693\) 169736. 0.0134258
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 2.96103e7 2.30866
\(698\) 0 0
\(699\) −4.18997e7 −3.24353
\(700\) 0 0
\(701\) 7.93482e6 0.609877 0.304938 − 0.952372i \(-0.401364\pi\)
0.304938 + 0.952372i \(0.401364\pi\)
\(702\) 0 0
\(703\) −3.09461e7 −2.36166
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.24930e6 0.169238
\(708\) 0 0
\(709\) 2.62600e7 1.96191 0.980956 − 0.194228i \(-0.0622202\pi\)
0.980956 + 0.194228i \(0.0622202\pi\)
\(710\) 0 0
\(711\) 4.93620e6 0.366200
\(712\) 0 0
\(713\) −1.60111e7 −1.17950
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2.56645e7 1.86438
\(718\) 0 0
\(719\) 2.20763e7 1.59259 0.796295 − 0.604909i \(-0.206790\pi\)
0.796295 + 0.604909i \(0.206790\pi\)
\(720\) 0 0
\(721\) 6.66459e6 0.477458
\(722\) 0 0
\(723\) −2.32313e7 −1.65283
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −8.49245e6 −0.595933 −0.297966 − 0.954576i \(-0.596308\pi\)
−0.297966 + 0.954576i \(0.596308\pi\)
\(728\) 0 0
\(729\) −2.11562e7 −1.47441
\(730\) 0 0
\(731\) 2.05830e6 0.142468
\(732\) 0 0
\(733\) 1.90713e7 1.31105 0.655526 − 0.755172i \(-0.272447\pi\)
0.655526 + 0.755172i \(0.272447\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −80864.0 −0.00548386
\(738\) 0 0
\(739\) −1.46832e7 −0.989032 −0.494516 − 0.869169i \(-0.664655\pi\)
−0.494516 + 0.869169i \(0.664655\pi\)
\(740\) 0 0
\(741\) −4.79812e7 −3.21015
\(742\) 0 0
\(743\) −1.64265e7 −1.09162 −0.545812 − 0.837908i \(-0.683779\pi\)
−0.545812 + 0.837908i \(0.683779\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −3.85188e7 −2.52564
\(748\) 0 0
\(749\) 3.38864e6 0.220710
\(750\) 0 0
\(751\) −2.44357e7 −1.58097 −0.790486 − 0.612479i \(-0.790172\pi\)
−0.790486 + 0.612479i \(0.790172\pi\)
\(752\) 0 0
\(753\) −9.51460e6 −0.611509
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 295566. 0.0187463 0.00937313 − 0.999956i \(-0.497016\pi\)
0.00937313 + 0.999956i \(0.497016\pi\)
\(758\) 0 0
\(759\) 695552. 0.0438253
\(760\) 0 0
\(761\) −473842. −0.0296601 −0.0148300 − 0.999890i \(-0.504721\pi\)
−0.0148300 + 0.999890i \(0.504721\pi\)
\(762\) 0 0
\(763\) −7.17429e6 −0.446136
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.37362e7 −1.45687
\(768\) 0 0
\(769\) 2.33241e7 1.42229 0.711145 − 0.703045i \(-0.248177\pi\)
0.711145 + 0.703045i \(0.248177\pi\)
\(770\) 0 0
\(771\) 3.65194e7 2.21253
\(772\) 0 0
\(773\) −1.55583e7 −0.936511 −0.468255 − 0.883593i \(-0.655117\pi\)
−0.468255 + 0.883593i \(0.655117\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.46128e7 −0.868321
\(778\) 0 0
\(779\) −3.60183e7 −2.12657
\(780\) 0 0
\(781\) 501760. 0.0294353
\(782\) 0 0
\(783\) 1.60748e7 0.937001
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −6.66843e6 −0.383784 −0.191892 − 0.981416i \(-0.561462\pi\)
−0.191892 + 0.981416i \(0.561462\pi\)
\(788\) 0 0
\(789\) 2.85917e7 1.63511
\(790\) 0 0
\(791\) 3.92911e6 0.223282
\(792\) 0 0
\(793\) 705888. 0.0398614
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.22461e7 0.682892 0.341446 − 0.939901i \(-0.389083\pi\)
0.341446 + 0.939901i \(0.389083\pi\)
\(798\) 0 0
\(799\) −2.68822e6 −0.148969
\(800\) 0 0
\(801\) 8.53963e6 0.470281
\(802\) 0 0
\(803\) 151408. 0.00828629
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −2.11886e7 −1.14530
\(808\) 0 0
\(809\) −2.91495e7 −1.56588 −0.782941 − 0.622095i \(-0.786282\pi\)
−0.782941 + 0.622095i \(0.786282\pi\)
\(810\) 0 0
\(811\) 7.58849e6 0.405138 0.202569 − 0.979268i \(-0.435071\pi\)
0.202569 + 0.979268i \(0.435071\pi\)
\(812\) 0 0
\(813\) 4.41755e7 2.34398
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −2.50374e6 −0.131230
\(818\) 0 0
\(819\) −1.45124e7 −0.756015
\(820\) 0 0
\(821\) −5.98849e6 −0.310070 −0.155035 − 0.987909i \(-0.549549\pi\)
−0.155035 + 0.987909i \(0.549549\pi\)
\(822\) 0 0
\(823\) −817960. −0.0420952 −0.0210476 − 0.999778i \(-0.506700\pi\)
−0.0210476 + 0.999778i \(0.506700\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.51963e6 −0.128107 −0.0640535 − 0.997946i \(-0.520403\pi\)
−0.0640535 + 0.997946i \(0.520403\pi\)
\(828\) 0 0
\(829\) −1.61006e7 −0.813684 −0.406842 − 0.913499i \(-0.633370\pi\)
−0.406842 + 0.913499i \(0.633370\pi\)
\(830\) 0 0
\(831\) −3.54921e7 −1.78291
\(832\) 0 0
\(833\) 5.32542e6 0.265914
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −2.36527e7 −1.16699
\(838\) 0 0
\(839\) −2.58167e7 −1.26618 −0.633091 − 0.774077i \(-0.718214\pi\)
−0.633091 + 0.774077i \(0.718214\pi\)
\(840\) 0 0
\(841\) −9.92263e6 −0.483768
\(842\) 0 0
\(843\) 1.86120e7 0.902036
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −7.88836e6 −0.377814
\(848\) 0 0
\(849\) 5.66088e6 0.269535
\(850\) 0 0
\(851\) −3.83557e7 −1.81554
\(852\) 0 0
\(853\) 1.54270e7 0.725954 0.362977 − 0.931798i \(-0.381760\pi\)
0.362977 + 0.931798i \(0.381760\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.60517e6 −0.167677 −0.0838384 − 0.996479i \(-0.526718\pi\)
−0.0838384 + 0.996479i \(0.526718\pi\)
\(858\) 0 0
\(859\) 4.06995e6 0.188194 0.0940970 − 0.995563i \(-0.470004\pi\)
0.0940970 + 0.995563i \(0.470004\pi\)
\(860\) 0 0
\(861\) −1.70079e7 −0.781885
\(862\) 0 0
\(863\) −7.25111e6 −0.331419 −0.165710 − 0.986175i \(-0.552991\pi\)
−0.165710 + 0.986175i \(0.552991\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −9.09913e7 −4.11105
\(868\) 0 0
\(869\) 91200.0 0.00409681
\(870\) 0 0
\(871\) 6.91387e6 0.308799
\(872\) 0 0
\(873\) −7.38785e6 −0.328082
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.37414e6 −0.104233 −0.0521167 − 0.998641i \(-0.516597\pi\)
−0.0521167 + 0.998641i \(0.516597\pi\)
\(878\) 0 0
\(879\) 3.91841e7 1.71056
\(880\) 0 0
\(881\) 3.03558e7 1.31766 0.658828 − 0.752293i \(-0.271052\pi\)
0.658828 + 0.752293i \(0.271052\pi\)
\(882\) 0 0
\(883\) −1.53338e6 −0.0661832 −0.0330916 − 0.999452i \(-0.510535\pi\)
−0.0330916 + 0.999452i \(0.510535\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.92379e7 1.24778 0.623888 − 0.781514i \(-0.285552\pi\)
0.623888 + 0.781514i \(0.285552\pi\)
\(888\) 0 0
\(889\) −1.34652e7 −0.571424
\(890\) 0 0
\(891\) 185768. 0.00783929
\(892\) 0 0
\(893\) 3.26998e6 0.137220
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −5.94697e7 −2.46783
\(898\) 0 0
\(899\) −1.55802e7 −0.642943
\(900\) 0 0
\(901\) −2.90780e7 −1.19331
\(902\) 0 0
\(903\) −1.18227e6 −0.0482501
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −4.48227e7 −1.80917 −0.904587 − 0.426289i \(-0.859821\pi\)
−0.904587 + 0.426289i \(0.859821\pi\)
\(908\) 0 0
\(909\) 1.98764e7 0.797864
\(910\) 0 0
\(911\) −3.62906e7 −1.44877 −0.724384 − 0.689397i \(-0.757876\pi\)
−0.724384 + 0.689397i \(0.757876\pi\)
\(912\) 0 0
\(913\) −711664. −0.0282552
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.85636e6 0.347802
\(918\) 0 0
\(919\) 3.25350e7 1.27076 0.635378 − 0.772201i \(-0.280844\pi\)
0.635378 + 0.772201i \(0.280844\pi\)
\(920\) 0 0
\(921\) 325052. 0.0126271
\(922\) 0 0
\(923\) −4.29005e7 −1.65752
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 5.88932e7 2.25095
\(928\) 0 0
\(929\) −4.46676e7 −1.69806 −0.849030 − 0.528344i \(-0.822813\pi\)
−0.849030 + 0.528344i \(0.822813\pi\)
\(930\) 0 0
\(931\) −6.47790e6 −0.244940
\(932\) 0 0
\(933\) 1.68332e7 0.633087
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.56680e7 −0.582995 −0.291498 − 0.956572i \(-0.594154\pi\)
−0.291498 + 0.956572i \(0.594154\pi\)
\(938\) 0 0
\(939\) −2.43354e7 −0.900689
\(940\) 0 0
\(941\) −2.01175e7 −0.740627 −0.370313 − 0.928907i \(-0.620750\pi\)
−0.370313 + 0.928907i \(0.620750\pi\)
\(942\) 0 0
\(943\) −4.46424e7 −1.63481
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.84518e6 0.320503 0.160251 − 0.987076i \(-0.448769\pi\)
0.160251 + 0.987076i \(0.448769\pi\)
\(948\) 0 0
\(949\) −1.29454e7 −0.466605
\(950\) 0 0
\(951\) 1.83545e7 0.658099
\(952\) 0 0
\(953\) 3.14364e7 1.12124 0.560622 − 0.828072i \(-0.310562\pi\)
0.560622 + 0.828072i \(0.310562\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 676832. 0.0238892
\(958\) 0 0
\(959\) 1.02742e7 0.360747
\(960\) 0 0
\(961\) −5.70421e6 −0.199245
\(962\) 0 0
\(963\) 2.99445e7 1.04052
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 9.52158e6 0.327449 0.163724 − 0.986506i \(-0.447649\pi\)
0.163724 + 0.986506i \(0.447649\pi\)
\(968\) 0 0
\(969\) 1.55588e8 5.32313
\(970\) 0 0
\(971\) 1.06520e7 0.362564 0.181282 − 0.983431i \(-0.441975\pi\)
0.181282 + 0.983431i \(0.441975\pi\)
\(972\) 0 0
\(973\) 844858. 0.0286089
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.72931e7 −0.914779 −0.457389 − 0.889266i \(-0.651215\pi\)
−0.457389 + 0.889266i \(0.651215\pi\)
\(978\) 0 0
\(979\) 157776. 0.00526119
\(980\) 0 0
\(981\) −6.33973e7 −2.10328
\(982\) 0 0
\(983\) −1.04764e7 −0.345802 −0.172901 − 0.984939i \(-0.555314\pi\)
−0.172901 + 0.984939i \(0.555314\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.54409e6 0.0504521
\(988\) 0 0
\(989\) −3.10323e6 −0.100884
\(990\) 0 0
\(991\) 1.88230e6 0.0608843 0.0304422 − 0.999537i \(-0.490308\pi\)
0.0304422 + 0.999537i \(0.490308\pi\)
\(992\) 0 0
\(993\) 2.97190e7 0.956449
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −2.71518e7 −0.865090 −0.432545 − 0.901612i \(-0.642384\pi\)
−0.432545 + 0.901612i \(0.642384\pi\)
\(998\) 0 0
\(999\) −5.66618e7 −1.79629
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 700.6.a.b.1.1 1
5.2 odd 4 700.6.e.b.449.2 2
5.3 odd 4 700.6.e.b.449.1 2
5.4 even 2 28.6.a.b.1.1 ✓ 1
15.14 odd 2 252.6.a.a.1.1 1
20.19 odd 2 112.6.a.b.1.1 1
35.4 even 6 196.6.e.a.177.1 2
35.9 even 6 196.6.e.a.165.1 2
35.19 odd 6 196.6.e.i.165.1 2
35.24 odd 6 196.6.e.i.177.1 2
35.34 odd 2 196.6.a.a.1.1 1
40.19 odd 2 448.6.a.o.1.1 1
40.29 even 2 448.6.a.b.1.1 1
60.59 even 2 1008.6.a.l.1.1 1
140.139 even 2 784.6.a.m.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.6.a.b.1.1 ✓ 1 5.4 even 2
112.6.a.b.1.1 1 20.19 odd 2
196.6.a.a.1.1 1 35.34 odd 2
196.6.e.a.165.1 2 35.9 even 6
196.6.e.a.177.1 2 35.4 even 6
196.6.e.i.165.1 2 35.19 odd 6
196.6.e.i.177.1 2 35.24 odd 6
252.6.a.a.1.1 1 15.14 odd 2
448.6.a.b.1.1 1 40.29 even 2
448.6.a.o.1.1 1 40.19 odd 2
700.6.a.b.1.1 1 1.1 even 1 trivial
700.6.e.b.449.1 2 5.3 odd 4
700.6.e.b.449.2 2 5.2 odd 4
784.6.a.m.1.1 1 140.139 even 2
1008.6.a.l.1.1 1 60.59 even 2