Properties

Label 1575.4.a.i.1.1
Level $1575$
Weight $4$
Character 1575.1
Self dual yes
Analytic conductor $92.928$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1575,4,Mod(1,1575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1575.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.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: \(92.9280082590\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 315)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1575.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{2} +1.00000 q^{4} -7.00000 q^{7} -21.0000 q^{8} -60.0000 q^{11} -38.0000 q^{13} -21.0000 q^{14} -71.0000 q^{16} -84.0000 q^{17} +110.000 q^{19} -180.000 q^{22} +120.000 q^{23} -114.000 q^{26} -7.00000 q^{28} -162.000 q^{29} +236.000 q^{31} -45.0000 q^{32} -252.000 q^{34} +376.000 q^{37} +330.000 q^{38} +126.000 q^{41} +34.0000 q^{43} -60.0000 q^{44} +360.000 q^{46} -6.00000 q^{47} +49.0000 q^{49} -38.0000 q^{52} +582.000 q^{53} +147.000 q^{56} -486.000 q^{58} -492.000 q^{59} -880.000 q^{61} +708.000 q^{62} +433.000 q^{64} +826.000 q^{67} -84.0000 q^{68} +666.000 q^{71} +826.000 q^{73} +1128.00 q^{74} +110.000 q^{76} +420.000 q^{77} -592.000 q^{79} +378.000 q^{82} +792.000 q^{83} +102.000 q^{86} +1260.00 q^{88} -1002.00 q^{89} +266.000 q^{91} +120.000 q^{92} -18.0000 q^{94} -1442.00 q^{97} +147.000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00000 1.06066 0.530330 0.847791i \(-0.322068\pi\)
0.530330 + 0.847791i \(0.322068\pi\)
\(3\) 0 0
\(4\) 1.00000 0.125000
\(5\) 0 0
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) −21.0000 −0.928078
\(9\) 0 0
\(10\) 0 0
\(11\) −60.0000 −1.64461 −0.822304 0.569049i \(-0.807311\pi\)
−0.822304 + 0.569049i \(0.807311\pi\)
\(12\) 0 0
\(13\) −38.0000 −0.810716 −0.405358 0.914158i \(-0.632853\pi\)
−0.405358 + 0.914158i \(0.632853\pi\)
\(14\) −21.0000 −0.400892
\(15\) 0 0
\(16\) −71.0000 −1.10938
\(17\) −84.0000 −1.19841 −0.599206 0.800595i \(-0.704517\pi\)
−0.599206 + 0.800595i \(0.704517\pi\)
\(18\) 0 0
\(19\) 110.000 1.32820 0.664098 0.747645i \(-0.268816\pi\)
0.664098 + 0.747645i \(0.268816\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −180.000 −1.74437
\(23\) 120.000 1.08790 0.543951 0.839117i \(-0.316928\pi\)
0.543951 + 0.839117i \(0.316928\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −114.000 −0.859894
\(27\) 0 0
\(28\) −7.00000 −0.0472456
\(29\) −162.000 −1.03733 −0.518666 0.854977i \(-0.673571\pi\)
−0.518666 + 0.854977i \(0.673571\pi\)
\(30\) 0 0
\(31\) 236.000 1.36732 0.683659 0.729802i \(-0.260388\pi\)
0.683659 + 0.729802i \(0.260388\pi\)
\(32\) −45.0000 −0.248592
\(33\) 0 0
\(34\) −252.000 −1.27111
\(35\) 0 0
\(36\) 0 0
\(37\) 376.000 1.67065 0.835325 0.549757i \(-0.185280\pi\)
0.835325 + 0.549757i \(0.185280\pi\)
\(38\) 330.000 1.40876
\(39\) 0 0
\(40\) 0 0
\(41\) 126.000 0.479949 0.239974 0.970779i \(-0.422861\pi\)
0.239974 + 0.970779i \(0.422861\pi\)
\(42\) 0 0
\(43\) 34.0000 0.120580 0.0602901 0.998181i \(-0.480797\pi\)
0.0602901 + 0.998181i \(0.480797\pi\)
\(44\) −60.0000 −0.205576
\(45\) 0 0
\(46\) 360.000 1.15389
\(47\) −6.00000 −0.0186211 −0.00931053 0.999957i \(-0.502964\pi\)
−0.00931053 + 0.999957i \(0.502964\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −38.0000 −0.101339
\(53\) 582.000 1.50837 0.754187 0.656659i \(-0.228031\pi\)
0.754187 + 0.656659i \(0.228031\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 147.000 0.350780
\(57\) 0 0
\(58\) −486.000 −1.10026
\(59\) −492.000 −1.08564 −0.542822 0.839848i \(-0.682644\pi\)
−0.542822 + 0.839848i \(0.682644\pi\)
\(60\) 0 0
\(61\) −880.000 −1.84709 −0.923545 0.383491i \(-0.874722\pi\)
−0.923545 + 0.383491i \(0.874722\pi\)
\(62\) 708.000 1.45026
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) 0 0
\(66\) 0 0
\(67\) 826.000 1.50615 0.753074 0.657935i \(-0.228570\pi\)
0.753074 + 0.657935i \(0.228570\pi\)
\(68\) −84.0000 −0.149801
\(69\) 0 0
\(70\) 0 0
\(71\) 666.000 1.11323 0.556617 0.830769i \(-0.312099\pi\)
0.556617 + 0.830769i \(0.312099\pi\)
\(72\) 0 0
\(73\) 826.000 1.32433 0.662164 0.749359i \(-0.269638\pi\)
0.662164 + 0.749359i \(0.269638\pi\)
\(74\) 1128.00 1.77199
\(75\) 0 0
\(76\) 110.000 0.166025
\(77\) 420.000 0.621603
\(78\) 0 0
\(79\) −592.000 −0.843104 −0.421552 0.906804i \(-0.638514\pi\)
−0.421552 + 0.906804i \(0.638514\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 378.000 0.509062
\(83\) 792.000 1.04739 0.523695 0.851906i \(-0.324553\pi\)
0.523695 + 0.851906i \(0.324553\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 102.000 0.127895
\(87\) 0 0
\(88\) 1260.00 1.52632
\(89\) −1002.00 −1.19339 −0.596695 0.802468i \(-0.703520\pi\)
−0.596695 + 0.802468i \(0.703520\pi\)
\(90\) 0 0
\(91\) 266.000 0.306422
\(92\) 120.000 0.135988
\(93\) 0 0
\(94\) −18.0000 −0.0197506
\(95\) 0 0
\(96\) 0 0
\(97\) −1442.00 −1.50941 −0.754706 0.656063i \(-0.772220\pi\)
−0.754706 + 0.656063i \(0.772220\pi\)
\(98\) 147.000 0.151523
\(99\) 0 0
\(100\) 0 0
\(101\) 1182.00 1.16449 0.582245 0.813014i \(-0.302175\pi\)
0.582245 + 0.813014i \(0.302175\pi\)
\(102\) 0 0
\(103\) −56.0000 −0.0535713 −0.0267857 0.999641i \(-0.508527\pi\)
−0.0267857 + 0.999641i \(0.508527\pi\)
\(104\) 798.000 0.752407
\(105\) 0 0
\(106\) 1746.00 1.59987
\(107\) −1572.00 −1.42029 −0.710145 0.704056i \(-0.751371\pi\)
−0.710145 + 0.704056i \(0.751371\pi\)
\(108\) 0 0
\(109\) −1402.00 −1.23199 −0.615997 0.787749i \(-0.711246\pi\)
−0.615997 + 0.787749i \(0.711246\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 497.000 0.419304
\(113\) −846.000 −0.704292 −0.352146 0.935945i \(-0.614548\pi\)
−0.352146 + 0.935945i \(0.614548\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −162.000 −0.129667
\(117\) 0 0
\(118\) −1476.00 −1.15150
\(119\) 588.000 0.452957
\(120\) 0 0
\(121\) 2269.00 1.70473
\(122\) −2640.00 −1.95913
\(123\) 0 0
\(124\) 236.000 0.170915
\(125\) 0 0
\(126\) 0 0
\(127\) 1096.00 0.765782 0.382891 0.923794i \(-0.374929\pi\)
0.382891 + 0.923794i \(0.374929\pi\)
\(128\) 1659.00 1.14560
\(129\) 0 0
\(130\) 0 0
\(131\) 492.000 0.328139 0.164070 0.986449i \(-0.447538\pi\)
0.164070 + 0.986449i \(0.447538\pi\)
\(132\) 0 0
\(133\) −770.000 −0.502011
\(134\) 2478.00 1.59751
\(135\) 0 0
\(136\) 1764.00 1.11222
\(137\) −282.000 −0.175860 −0.0879302 0.996127i \(-0.528025\pi\)
−0.0879302 + 0.996127i \(0.528025\pi\)
\(138\) 0 0
\(139\) 2.00000 0.00122042 0.000610208 1.00000i \(-0.499806\pi\)
0.000610208 1.00000i \(0.499806\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1998.00 1.18076
\(143\) 2280.00 1.33331
\(144\) 0 0
\(145\) 0 0
\(146\) 2478.00 1.40466
\(147\) 0 0
\(148\) 376.000 0.208831
\(149\) −606.000 −0.333191 −0.166595 0.986025i \(-0.553277\pi\)
−0.166595 + 0.986025i \(0.553277\pi\)
\(150\) 0 0
\(151\) −2176.00 −1.17272 −0.586359 0.810051i \(-0.699439\pi\)
−0.586359 + 0.810051i \(0.699439\pi\)
\(152\) −2310.00 −1.23267
\(153\) 0 0
\(154\) 1260.00 0.659310
\(155\) 0 0
\(156\) 0 0
\(157\) −146.000 −0.0742170 −0.0371085 0.999311i \(-0.511815\pi\)
−0.0371085 + 0.999311i \(0.511815\pi\)
\(158\) −1776.00 −0.894247
\(159\) 0 0
\(160\) 0 0
\(161\) −840.000 −0.411188
\(162\) 0 0
\(163\) 826.000 0.396916 0.198458 0.980109i \(-0.436407\pi\)
0.198458 + 0.980109i \(0.436407\pi\)
\(164\) 126.000 0.0599936
\(165\) 0 0
\(166\) 2376.00 1.11092
\(167\) 1206.00 0.558821 0.279410 0.960172i \(-0.409861\pi\)
0.279410 + 0.960172i \(0.409861\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) 0 0
\(171\) 0 0
\(172\) 34.0000 0.0150725
\(173\) 1398.00 0.614381 0.307191 0.951648i \(-0.400611\pi\)
0.307191 + 0.951648i \(0.400611\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4260.00 1.82449
\(177\) 0 0
\(178\) −3006.00 −1.26578
\(179\) 2424.00 1.01217 0.506085 0.862484i \(-0.331092\pi\)
0.506085 + 0.862484i \(0.331092\pi\)
\(180\) 0 0
\(181\) 3728.00 1.53094 0.765470 0.643472i \(-0.222507\pi\)
0.765470 + 0.643472i \(0.222507\pi\)
\(182\) 798.000 0.325009
\(183\) 0 0
\(184\) −2520.00 −1.00966
\(185\) 0 0
\(186\) 0 0
\(187\) 5040.00 1.97092
\(188\) −6.00000 −0.00232763
\(189\) 0 0
\(190\) 0 0
\(191\) −2550.00 −0.966029 −0.483014 0.875612i \(-0.660458\pi\)
−0.483014 + 0.875612i \(0.660458\pi\)
\(192\) 0 0
\(193\) 1978.00 0.737718 0.368859 0.929485i \(-0.379749\pi\)
0.368859 + 0.929485i \(0.379749\pi\)
\(194\) −4326.00 −1.60097
\(195\) 0 0
\(196\) 49.0000 0.0178571
\(197\) −1170.00 −0.423142 −0.211571 0.977363i \(-0.567858\pi\)
−0.211571 + 0.977363i \(0.567858\pi\)
\(198\) 0 0
\(199\) 3584.00 1.27670 0.638349 0.769747i \(-0.279618\pi\)
0.638349 + 0.769747i \(0.279618\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3546.00 1.23513
\(203\) 1134.00 0.392075
\(204\) 0 0
\(205\) 0 0
\(206\) −168.000 −0.0568209
\(207\) 0 0
\(208\) 2698.00 0.899388
\(209\) −6600.00 −2.18436
\(210\) 0 0
\(211\) 1640.00 0.535082 0.267541 0.963547i \(-0.413789\pi\)
0.267541 + 0.963547i \(0.413789\pi\)
\(212\) 582.000 0.188547
\(213\) 0 0
\(214\) −4716.00 −1.50644
\(215\) 0 0
\(216\) 0 0
\(217\) −1652.00 −0.516798
\(218\) −4206.00 −1.30673
\(219\) 0 0
\(220\) 0 0
\(221\) 3192.00 0.971571
\(222\) 0 0
\(223\) 1888.00 0.566950 0.283475 0.958980i \(-0.408513\pi\)
0.283475 + 0.958980i \(0.408513\pi\)
\(224\) 315.000 0.0939590
\(225\) 0 0
\(226\) −2538.00 −0.747014
\(227\) −2244.00 −0.656121 −0.328061 0.944657i \(-0.606395\pi\)
−0.328061 + 0.944657i \(0.606395\pi\)
\(228\) 0 0
\(229\) −4084.00 −1.17851 −0.589254 0.807948i \(-0.700578\pi\)
−0.589254 + 0.807948i \(0.700578\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3402.00 0.962725
\(233\) 4026.00 1.13198 0.565991 0.824411i \(-0.308494\pi\)
0.565991 + 0.824411i \(0.308494\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −492.000 −0.135705
\(237\) 0 0
\(238\) 1764.00 0.480433
\(239\) 4590.00 1.24227 0.621135 0.783704i \(-0.286672\pi\)
0.621135 + 0.783704i \(0.286672\pi\)
\(240\) 0 0
\(241\) 1946.00 0.520136 0.260068 0.965590i \(-0.416255\pi\)
0.260068 + 0.965590i \(0.416255\pi\)
\(242\) 6807.00 1.80814
\(243\) 0 0
\(244\) −880.000 −0.230886
\(245\) 0 0
\(246\) 0 0
\(247\) −4180.00 −1.07679
\(248\) −4956.00 −1.26898
\(249\) 0 0
\(250\) 0 0
\(251\) −3636.00 −0.914352 −0.457176 0.889376i \(-0.651139\pi\)
−0.457176 + 0.889376i \(0.651139\pi\)
\(252\) 0 0
\(253\) −7200.00 −1.78917
\(254\) 3288.00 0.812234
\(255\) 0 0
\(256\) 1513.00 0.369385
\(257\) 4152.00 1.00776 0.503881 0.863773i \(-0.331905\pi\)
0.503881 + 0.863773i \(0.331905\pi\)
\(258\) 0 0
\(259\) −2632.00 −0.631446
\(260\) 0 0
\(261\) 0 0
\(262\) 1476.00 0.348044
\(263\) 5388.00 1.26326 0.631632 0.775269i \(-0.282385\pi\)
0.631632 + 0.775269i \(0.282385\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2310.00 −0.532463
\(267\) 0 0
\(268\) 826.000 0.188269
\(269\) −1194.00 −0.270630 −0.135315 0.990803i \(-0.543205\pi\)
−0.135315 + 0.990803i \(0.543205\pi\)
\(270\) 0 0
\(271\) 6788.00 1.52156 0.760778 0.649012i \(-0.224818\pi\)
0.760778 + 0.649012i \(0.224818\pi\)
\(272\) 5964.00 1.32949
\(273\) 0 0
\(274\) −846.000 −0.186528
\(275\) 0 0
\(276\) 0 0
\(277\) 8908.00 1.93224 0.966119 0.258098i \(-0.0830956\pi\)
0.966119 + 0.258098i \(0.0830956\pi\)
\(278\) 6.00000 0.00129445
\(279\) 0 0
\(280\) 0 0
\(281\) −6408.00 −1.36039 −0.680194 0.733032i \(-0.738105\pi\)
−0.680194 + 0.733032i \(0.738105\pi\)
\(282\) 0 0
\(283\) 3652.00 0.767098 0.383549 0.923520i \(-0.374702\pi\)
0.383549 + 0.923520i \(0.374702\pi\)
\(284\) 666.000 0.139154
\(285\) 0 0
\(286\) 6840.00 1.41419
\(287\) −882.000 −0.181404
\(288\) 0 0
\(289\) 2143.00 0.436190
\(290\) 0 0
\(291\) 0 0
\(292\) 826.000 0.165541
\(293\) −2214.00 −0.441445 −0.220722 0.975337i \(-0.570841\pi\)
−0.220722 + 0.975337i \(0.570841\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −7896.00 −1.55049
\(297\) 0 0
\(298\) −1818.00 −0.353402
\(299\) −4560.00 −0.881979
\(300\) 0 0
\(301\) −238.000 −0.0455751
\(302\) −6528.00 −1.24385
\(303\) 0 0
\(304\) −7810.00 −1.47347
\(305\) 0 0
\(306\) 0 0
\(307\) 5452.00 1.01356 0.506779 0.862076i \(-0.330836\pi\)
0.506779 + 0.862076i \(0.330836\pi\)
\(308\) 420.000 0.0777004
\(309\) 0 0
\(310\) 0 0
\(311\) 300.000 0.0546992 0.0273496 0.999626i \(-0.491293\pi\)
0.0273496 + 0.999626i \(0.491293\pi\)
\(312\) 0 0
\(313\) 3994.00 0.721260 0.360630 0.932709i \(-0.382562\pi\)
0.360630 + 0.932709i \(0.382562\pi\)
\(314\) −438.000 −0.0787190
\(315\) 0 0
\(316\) −592.000 −0.105388
\(317\) 2586.00 0.458184 0.229092 0.973405i \(-0.426424\pi\)
0.229092 + 0.973405i \(0.426424\pi\)
\(318\) 0 0
\(319\) 9720.00 1.70600
\(320\) 0 0
\(321\) 0 0
\(322\) −2520.00 −0.436131
\(323\) −9240.00 −1.59173
\(324\) 0 0
\(325\) 0 0
\(326\) 2478.00 0.420993
\(327\) 0 0
\(328\) −2646.00 −0.445430
\(329\) 42.0000 0.00703810
\(330\) 0 0
\(331\) 6248.00 1.03753 0.518763 0.854918i \(-0.326393\pi\)
0.518763 + 0.854918i \(0.326393\pi\)
\(332\) 792.000 0.130924
\(333\) 0 0
\(334\) 3618.00 0.592719
\(335\) 0 0
\(336\) 0 0
\(337\) −3062.00 −0.494949 −0.247474 0.968894i \(-0.579601\pi\)
−0.247474 + 0.968894i \(0.579601\pi\)
\(338\) −2259.00 −0.363531
\(339\) 0 0
\(340\) 0 0
\(341\) −14160.0 −2.24870
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) −714.000 −0.111908
\(345\) 0 0
\(346\) 4194.00 0.651650
\(347\) −5196.00 −0.803850 −0.401925 0.915673i \(-0.631659\pi\)
−0.401925 + 0.915673i \(0.631659\pi\)
\(348\) 0 0
\(349\) 8660.00 1.32825 0.664125 0.747622i \(-0.268804\pi\)
0.664125 + 0.747622i \(0.268804\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2700.00 0.408837
\(353\) −1128.00 −0.170078 −0.0850388 0.996378i \(-0.527101\pi\)
−0.0850388 + 0.996378i \(0.527101\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1002.00 −0.149174
\(357\) 0 0
\(358\) 7272.00 1.07357
\(359\) −6618.00 −0.972938 −0.486469 0.873698i \(-0.661715\pi\)
−0.486469 + 0.873698i \(0.661715\pi\)
\(360\) 0 0
\(361\) 5241.00 0.764106
\(362\) 11184.0 1.62381
\(363\) 0 0
\(364\) 266.000 0.0383027
\(365\) 0 0
\(366\) 0 0
\(367\) −1568.00 −0.223022 −0.111511 0.993763i \(-0.535569\pi\)
−0.111511 + 0.993763i \(0.535569\pi\)
\(368\) −8520.00 −1.20689
\(369\) 0 0
\(370\) 0 0
\(371\) −4074.00 −0.570112
\(372\) 0 0
\(373\) 5200.00 0.721839 0.360919 0.932597i \(-0.382463\pi\)
0.360919 + 0.932597i \(0.382463\pi\)
\(374\) 15120.0 2.09047
\(375\) 0 0
\(376\) 126.000 0.0172818
\(377\) 6156.00 0.840982
\(378\) 0 0
\(379\) −1096.00 −0.148543 −0.0742714 0.997238i \(-0.523663\pi\)
−0.0742714 + 0.997238i \(0.523663\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −7650.00 −1.02463
\(383\) −12318.0 −1.64340 −0.821698 0.569924i \(-0.806973\pi\)
−0.821698 + 0.569924i \(0.806973\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 5934.00 0.782468
\(387\) 0 0
\(388\) −1442.00 −0.188676
\(389\) −6558.00 −0.854766 −0.427383 0.904071i \(-0.640564\pi\)
−0.427383 + 0.904071i \(0.640564\pi\)
\(390\) 0 0
\(391\) −10080.0 −1.30375
\(392\) −1029.00 −0.132583
\(393\) 0 0
\(394\) −3510.00 −0.448810
\(395\) 0 0
\(396\) 0 0
\(397\) 1258.00 0.159036 0.0795179 0.996833i \(-0.474662\pi\)
0.0795179 + 0.996833i \(0.474662\pi\)
\(398\) 10752.0 1.35414
\(399\) 0 0
\(400\) 0 0
\(401\) 2976.00 0.370609 0.185305 0.982681i \(-0.440673\pi\)
0.185305 + 0.982681i \(0.440673\pi\)
\(402\) 0 0
\(403\) −8968.00 −1.10851
\(404\) 1182.00 0.145561
\(405\) 0 0
\(406\) 3402.00 0.415858
\(407\) −22560.0 −2.74756
\(408\) 0 0
\(409\) −9070.00 −1.09653 −0.548267 0.836303i \(-0.684712\pi\)
−0.548267 + 0.836303i \(0.684712\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −56.0000 −0.00669641
\(413\) 3444.00 0.410335
\(414\) 0 0
\(415\) 0 0
\(416\) 1710.00 0.201538
\(417\) 0 0
\(418\) −19800.0 −2.31687
\(419\) −6156.00 −0.717757 −0.358879 0.933384i \(-0.616841\pi\)
−0.358879 + 0.933384i \(0.616841\pi\)
\(420\) 0 0
\(421\) −6874.00 −0.795768 −0.397884 0.917436i \(-0.630255\pi\)
−0.397884 + 0.917436i \(0.630255\pi\)
\(422\) 4920.00 0.567540
\(423\) 0 0
\(424\) −12222.0 −1.39989
\(425\) 0 0
\(426\) 0 0
\(427\) 6160.00 0.698134
\(428\) −1572.00 −0.177536
\(429\) 0 0
\(430\) 0 0
\(431\) 10218.0 1.14196 0.570979 0.820965i \(-0.306564\pi\)
0.570979 + 0.820965i \(0.306564\pi\)
\(432\) 0 0
\(433\) 5830.00 0.647048 0.323524 0.946220i \(-0.395132\pi\)
0.323524 + 0.946220i \(0.395132\pi\)
\(434\) −4956.00 −0.548147
\(435\) 0 0
\(436\) −1402.00 −0.153999
\(437\) 13200.0 1.44495
\(438\) 0 0
\(439\) 8588.00 0.933674 0.466837 0.884343i \(-0.345393\pi\)
0.466837 + 0.884343i \(0.345393\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 9576.00 1.03051
\(443\) −12660.0 −1.35778 −0.678888 0.734242i \(-0.737538\pi\)
−0.678888 + 0.734242i \(0.737538\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 5664.00 0.601341
\(447\) 0 0
\(448\) −3031.00 −0.319646
\(449\) −3636.00 −0.382168 −0.191084 0.981574i \(-0.561200\pi\)
−0.191084 + 0.981574i \(0.561200\pi\)
\(450\) 0 0
\(451\) −7560.00 −0.789327
\(452\) −846.000 −0.0880365
\(453\) 0 0
\(454\) −6732.00 −0.695922
\(455\) 0 0
\(456\) 0 0
\(457\) 3022.00 0.309329 0.154664 0.987967i \(-0.450570\pi\)
0.154664 + 0.987967i \(0.450570\pi\)
\(458\) −12252.0 −1.25000
\(459\) 0 0
\(460\) 0 0
\(461\) 14742.0 1.48938 0.744689 0.667411i \(-0.232598\pi\)
0.744689 + 0.667411i \(0.232598\pi\)
\(462\) 0 0
\(463\) 9268.00 0.930282 0.465141 0.885237i \(-0.346004\pi\)
0.465141 + 0.885237i \(0.346004\pi\)
\(464\) 11502.0 1.15079
\(465\) 0 0
\(466\) 12078.0 1.20065
\(467\) −13920.0 −1.37932 −0.689658 0.724135i \(-0.742239\pi\)
−0.689658 + 0.724135i \(0.742239\pi\)
\(468\) 0 0
\(469\) −5782.00 −0.569271
\(470\) 0 0
\(471\) 0 0
\(472\) 10332.0 1.00756
\(473\) −2040.00 −0.198307
\(474\) 0 0
\(475\) 0 0
\(476\) 588.000 0.0566196
\(477\) 0 0
\(478\) 13770.0 1.31763
\(479\) 8220.00 0.784095 0.392047 0.919945i \(-0.371767\pi\)
0.392047 + 0.919945i \(0.371767\pi\)
\(480\) 0 0
\(481\) −14288.0 −1.35442
\(482\) 5838.00 0.551688
\(483\) 0 0
\(484\) 2269.00 0.213092
\(485\) 0 0
\(486\) 0 0
\(487\) −15752.0 −1.46569 −0.732845 0.680395i \(-0.761808\pi\)
−0.732845 + 0.680395i \(0.761808\pi\)
\(488\) 18480.0 1.71424
\(489\) 0 0
\(490\) 0 0
\(491\) −6552.00 −0.602215 −0.301108 0.953590i \(-0.597356\pi\)
−0.301108 + 0.953590i \(0.597356\pi\)
\(492\) 0 0
\(493\) 13608.0 1.24315
\(494\) −12540.0 −1.14211
\(495\) 0 0
\(496\) −16756.0 −1.51687
\(497\) −4662.00 −0.420763
\(498\) 0 0
\(499\) 4160.00 0.373201 0.186600 0.982436i \(-0.440253\pi\)
0.186600 + 0.982436i \(0.440253\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −10908.0 −0.969816
\(503\) 5166.00 0.457934 0.228967 0.973434i \(-0.426465\pi\)
0.228967 + 0.973434i \(0.426465\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −21600.0 −1.89770
\(507\) 0 0
\(508\) 1096.00 0.0957227
\(509\) 12066.0 1.05072 0.525360 0.850880i \(-0.323931\pi\)
0.525360 + 0.850880i \(0.323931\pi\)
\(510\) 0 0
\(511\) −5782.00 −0.500549
\(512\) −8733.00 −0.753804
\(513\) 0 0
\(514\) 12456.0 1.06889
\(515\) 0 0
\(516\) 0 0
\(517\) 360.000 0.0306243
\(518\) −7896.00 −0.669750
\(519\) 0 0
\(520\) 0 0
\(521\) 17886.0 1.50403 0.752015 0.659146i \(-0.229082\pi\)
0.752015 + 0.659146i \(0.229082\pi\)
\(522\) 0 0
\(523\) −5168.00 −0.432086 −0.216043 0.976384i \(-0.569315\pi\)
−0.216043 + 0.976384i \(0.569315\pi\)
\(524\) 492.000 0.0410174
\(525\) 0 0
\(526\) 16164.0 1.33989
\(527\) −19824.0 −1.63861
\(528\) 0 0
\(529\) 2233.00 0.183529
\(530\) 0 0
\(531\) 0 0
\(532\) −770.000 −0.0627514
\(533\) −4788.00 −0.389102
\(534\) 0 0
\(535\) 0 0
\(536\) −17346.0 −1.39782
\(537\) 0 0
\(538\) −3582.00 −0.287046
\(539\) −2940.00 −0.234944
\(540\) 0 0
\(541\) 7850.00 0.623841 0.311920 0.950108i \(-0.399028\pi\)
0.311920 + 0.950108i \(0.399028\pi\)
\(542\) 20364.0 1.61385
\(543\) 0 0
\(544\) 3780.00 0.297916
\(545\) 0 0
\(546\) 0 0
\(547\) −2990.00 −0.233717 −0.116858 0.993149i \(-0.537282\pi\)
−0.116858 + 0.993149i \(0.537282\pi\)
\(548\) −282.000 −0.0219826
\(549\) 0 0
\(550\) 0 0
\(551\) −17820.0 −1.37778
\(552\) 0 0
\(553\) 4144.00 0.318663
\(554\) 26724.0 2.04945
\(555\) 0 0
\(556\) 2.00000 0.000152552 0
\(557\) −12486.0 −0.949818 −0.474909 0.880035i \(-0.657519\pi\)
−0.474909 + 0.880035i \(0.657519\pi\)
\(558\) 0 0
\(559\) −1292.00 −0.0977563
\(560\) 0 0
\(561\) 0 0
\(562\) −19224.0 −1.44291
\(563\) −732.000 −0.0547960 −0.0273980 0.999625i \(-0.508722\pi\)
−0.0273980 + 0.999625i \(0.508722\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 10956.0 0.813631
\(567\) 0 0
\(568\) −13986.0 −1.03317
\(569\) 456.000 0.0335967 0.0167983 0.999859i \(-0.494653\pi\)
0.0167983 + 0.999859i \(0.494653\pi\)
\(570\) 0 0
\(571\) −14092.0 −1.03281 −0.516403 0.856346i \(-0.672729\pi\)
−0.516403 + 0.856346i \(0.672729\pi\)
\(572\) 2280.00 0.166664
\(573\) 0 0
\(574\) −2646.00 −0.192408
\(575\) 0 0
\(576\) 0 0
\(577\) −10190.0 −0.735208 −0.367604 0.929982i \(-0.619822\pi\)
−0.367604 + 0.929982i \(0.619822\pi\)
\(578\) 6429.00 0.462649
\(579\) 0 0
\(580\) 0 0
\(581\) −5544.00 −0.395876
\(582\) 0 0
\(583\) −34920.0 −2.48068
\(584\) −17346.0 −1.22908
\(585\) 0 0
\(586\) −6642.00 −0.468223
\(587\) 23220.0 1.63270 0.816348 0.577561i \(-0.195995\pi\)
0.816348 + 0.577561i \(0.195995\pi\)
\(588\) 0 0
\(589\) 25960.0 1.81607
\(590\) 0 0
\(591\) 0 0
\(592\) −26696.0 −1.85338
\(593\) 14916.0 1.03293 0.516464 0.856309i \(-0.327248\pi\)
0.516464 + 0.856309i \(0.327248\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −606.000 −0.0416489
\(597\) 0 0
\(598\) −13680.0 −0.935480
\(599\) 16914.0 1.15374 0.576868 0.816838i \(-0.304275\pi\)
0.576868 + 0.816838i \(0.304275\pi\)
\(600\) 0 0
\(601\) 5762.00 0.391076 0.195538 0.980696i \(-0.437355\pi\)
0.195538 + 0.980696i \(0.437355\pi\)
\(602\) −714.000 −0.0483396
\(603\) 0 0
\(604\) −2176.00 −0.146590
\(605\) 0 0
\(606\) 0 0
\(607\) 28528.0 1.90760 0.953802 0.300435i \(-0.0971320\pi\)
0.953802 + 0.300435i \(0.0971320\pi\)
\(608\) −4950.00 −0.330179
\(609\) 0 0
\(610\) 0 0
\(611\) 228.000 0.0150964
\(612\) 0 0
\(613\) 12976.0 0.854969 0.427484 0.904023i \(-0.359400\pi\)
0.427484 + 0.904023i \(0.359400\pi\)
\(614\) 16356.0 1.07504
\(615\) 0 0
\(616\) −8820.00 −0.576896
\(617\) 8874.00 0.579017 0.289509 0.957175i \(-0.406508\pi\)
0.289509 + 0.957175i \(0.406508\pi\)
\(618\) 0 0
\(619\) −17170.0 −1.11490 −0.557448 0.830212i \(-0.688219\pi\)
−0.557448 + 0.830212i \(0.688219\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 900.000 0.0580172
\(623\) 7014.00 0.451059
\(624\) 0 0
\(625\) 0 0
\(626\) 11982.0 0.765011
\(627\) 0 0
\(628\) −146.000 −0.00927712
\(629\) −31584.0 −2.00212
\(630\) 0 0
\(631\) −26728.0 −1.68625 −0.843126 0.537716i \(-0.819287\pi\)
−0.843126 + 0.537716i \(0.819287\pi\)
\(632\) 12432.0 0.782466
\(633\) 0 0
\(634\) 7758.00 0.485977
\(635\) 0 0
\(636\) 0 0
\(637\) −1862.00 −0.115817
\(638\) 29160.0 1.80949
\(639\) 0 0
\(640\) 0 0
\(641\) 24492.0 1.50917 0.754583 0.656204i \(-0.227839\pi\)
0.754583 + 0.656204i \(0.227839\pi\)
\(642\) 0 0
\(643\) 1888.00 0.115794 0.0578969 0.998323i \(-0.481561\pi\)
0.0578969 + 0.998323i \(0.481561\pi\)
\(644\) −840.000 −0.0513985
\(645\) 0 0
\(646\) −27720.0 −1.68828
\(647\) −13134.0 −0.798069 −0.399035 0.916936i \(-0.630655\pi\)
−0.399035 + 0.916936i \(0.630655\pi\)
\(648\) 0 0
\(649\) 29520.0 1.78546
\(650\) 0 0
\(651\) 0 0
\(652\) 826.000 0.0496145
\(653\) 12882.0 0.771993 0.385997 0.922500i \(-0.373858\pi\)
0.385997 + 0.922500i \(0.373858\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −8946.00 −0.532443
\(657\) 0 0
\(658\) 126.000 0.00746503
\(659\) −7380.00 −0.436243 −0.218121 0.975922i \(-0.569993\pi\)
−0.218121 + 0.975922i \(0.569993\pi\)
\(660\) 0 0
\(661\) 560.000 0.0329523 0.0164762 0.999864i \(-0.494755\pi\)
0.0164762 + 0.999864i \(0.494755\pi\)
\(662\) 18744.0 1.10046
\(663\) 0 0
\(664\) −16632.0 −0.972058
\(665\) 0 0
\(666\) 0 0
\(667\) −19440.0 −1.12852
\(668\) 1206.00 0.0698526
\(669\) 0 0
\(670\) 0 0
\(671\) 52800.0 3.03774
\(672\) 0 0
\(673\) 5722.00 0.327737 0.163868 0.986482i \(-0.447603\pi\)
0.163868 + 0.986482i \(0.447603\pi\)
\(674\) −9186.00 −0.524973
\(675\) 0 0
\(676\) −753.000 −0.0428425
\(677\) −13650.0 −0.774907 −0.387454 0.921889i \(-0.626645\pi\)
−0.387454 + 0.921889i \(0.626645\pi\)
\(678\) 0 0
\(679\) 10094.0 0.570504
\(680\) 0 0
\(681\) 0 0
\(682\) −42480.0 −2.38511
\(683\) 1140.00 0.0638666 0.0319333 0.999490i \(-0.489834\pi\)
0.0319333 + 0.999490i \(0.489834\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1029.00 −0.0572703
\(687\) 0 0
\(688\) −2414.00 −0.133769
\(689\) −22116.0 −1.22286
\(690\) 0 0
\(691\) 32510.0 1.78978 0.894891 0.446286i \(-0.147254\pi\)
0.894891 + 0.446286i \(0.147254\pi\)
\(692\) 1398.00 0.0767977
\(693\) 0 0
\(694\) −15588.0 −0.852612
\(695\) 0 0
\(696\) 0 0
\(697\) −10584.0 −0.575176
\(698\) 25980.0 1.40882
\(699\) 0 0
\(700\) 0 0
\(701\) −21402.0 −1.15313 −0.576564 0.817052i \(-0.695607\pi\)
−0.576564 + 0.817052i \(0.695607\pi\)
\(702\) 0 0
\(703\) 41360.0 2.21895
\(704\) −25980.0 −1.39085
\(705\) 0 0
\(706\) −3384.00 −0.180395
\(707\) −8274.00 −0.440135
\(708\) 0 0
\(709\) 12170.0 0.644646 0.322323 0.946630i \(-0.395536\pi\)
0.322323 + 0.946630i \(0.395536\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 21042.0 1.10756
\(713\) 28320.0 1.48751
\(714\) 0 0
\(715\) 0 0
\(716\) 2424.00 0.126521
\(717\) 0 0
\(718\) −19854.0 −1.03196
\(719\) 12012.0 0.623049 0.311524 0.950238i \(-0.399160\pi\)
0.311524 + 0.950238i \(0.399160\pi\)
\(720\) 0 0
\(721\) 392.000 0.0202480
\(722\) 15723.0 0.810456
\(723\) 0 0
\(724\) 3728.00 0.191367
\(725\) 0 0
\(726\) 0 0
\(727\) −8480.00 −0.432608 −0.216304 0.976326i \(-0.569400\pi\)
−0.216304 + 0.976326i \(0.569400\pi\)
\(728\) −5586.00 −0.284383
\(729\) 0 0
\(730\) 0 0
\(731\) −2856.00 −0.144505
\(732\) 0 0
\(733\) 10906.0 0.549553 0.274776 0.961508i \(-0.411396\pi\)
0.274776 + 0.961508i \(0.411396\pi\)
\(734\) −4704.00 −0.236550
\(735\) 0 0
\(736\) −5400.00 −0.270444
\(737\) −49560.0 −2.47702
\(738\) 0 0
\(739\) −11104.0 −0.552730 −0.276365 0.961053i \(-0.589130\pi\)
−0.276365 + 0.961053i \(0.589130\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −12222.0 −0.604695
\(743\) 25416.0 1.25494 0.627471 0.778640i \(-0.284090\pi\)
0.627471 + 0.778640i \(0.284090\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 15600.0 0.765625
\(747\) 0 0
\(748\) 5040.00 0.246365
\(749\) 11004.0 0.536819
\(750\) 0 0
\(751\) −30904.0 −1.50160 −0.750801 0.660529i \(-0.770332\pi\)
−0.750801 + 0.660529i \(0.770332\pi\)
\(752\) 426.000 0.0206577
\(753\) 0 0
\(754\) 18468.0 0.891996
\(755\) 0 0
\(756\) 0 0
\(757\) 16216.0 0.778574 0.389287 0.921117i \(-0.372721\pi\)
0.389287 + 0.921117i \(0.372721\pi\)
\(758\) −3288.00 −0.157553
\(759\) 0 0
\(760\) 0 0
\(761\) −7230.00 −0.344399 −0.172199 0.985062i \(-0.555087\pi\)
−0.172199 + 0.985062i \(0.555087\pi\)
\(762\) 0 0
\(763\) 9814.00 0.465650
\(764\) −2550.00 −0.120754
\(765\) 0 0
\(766\) −36954.0 −1.74308
\(767\) 18696.0 0.880148
\(768\) 0 0
\(769\) 4790.00 0.224619 0.112309 0.993673i \(-0.464175\pi\)
0.112309 + 0.993673i \(0.464175\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1978.00 0.0922147
\(773\) 36114.0 1.68038 0.840188 0.542296i \(-0.182445\pi\)
0.840188 + 0.542296i \(0.182445\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 30282.0 1.40085
\(777\) 0 0
\(778\) −19674.0 −0.906616
\(779\) 13860.0 0.637466
\(780\) 0 0
\(781\) −39960.0 −1.83083
\(782\) −30240.0 −1.38284
\(783\) 0 0
\(784\) −3479.00 −0.158482
\(785\) 0 0
\(786\) 0 0
\(787\) −13556.0 −0.614002 −0.307001 0.951709i \(-0.599325\pi\)
−0.307001 + 0.951709i \(0.599325\pi\)
\(788\) −1170.00 −0.0528928
\(789\) 0 0
\(790\) 0 0
\(791\) 5922.00 0.266197
\(792\) 0 0
\(793\) 33440.0 1.49746
\(794\) 3774.00 0.168683
\(795\) 0 0
\(796\) 3584.00 0.159587
\(797\) 39006.0 1.73358 0.866790 0.498673i \(-0.166179\pi\)
0.866790 + 0.498673i \(0.166179\pi\)
\(798\) 0 0
\(799\) 504.000 0.0223157
\(800\) 0 0
\(801\) 0 0
\(802\) 8928.00 0.393091
\(803\) −49560.0 −2.17800
\(804\) 0 0
\(805\) 0 0
\(806\) −26904.0 −1.17575
\(807\) 0 0
\(808\) −24822.0 −1.08074
\(809\) −21480.0 −0.933494 −0.466747 0.884391i \(-0.654574\pi\)
−0.466747 + 0.884391i \(0.654574\pi\)
\(810\) 0 0
\(811\) 146.000 0.00632152 0.00316076 0.999995i \(-0.498994\pi\)
0.00316076 + 0.999995i \(0.498994\pi\)
\(812\) 1134.00 0.0490094
\(813\) 0 0
\(814\) −67680.0 −2.91423
\(815\) 0 0
\(816\) 0 0
\(817\) 3740.00 0.160154
\(818\) −27210.0 −1.16305
\(819\) 0 0
\(820\) 0 0
\(821\) −35562.0 −1.51172 −0.755860 0.654733i \(-0.772781\pi\)
−0.755860 + 0.654733i \(0.772781\pi\)
\(822\) 0 0
\(823\) 33964.0 1.43853 0.719265 0.694736i \(-0.244479\pi\)
0.719265 + 0.694736i \(0.244479\pi\)
\(824\) 1176.00 0.0497183
\(825\) 0 0
\(826\) 10332.0 0.435225
\(827\) −23292.0 −0.979374 −0.489687 0.871898i \(-0.662889\pi\)
−0.489687 + 0.871898i \(0.662889\pi\)
\(828\) 0 0
\(829\) 33716.0 1.41255 0.706276 0.707937i \(-0.250374\pi\)
0.706276 + 0.707937i \(0.250374\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −16454.0 −0.685625
\(833\) −4116.00 −0.171202
\(834\) 0 0
\(835\) 0 0
\(836\) −6600.00 −0.273045
\(837\) 0 0
\(838\) −18468.0 −0.761297
\(839\) 35280.0 1.45173 0.725865 0.687838i \(-0.241440\pi\)
0.725865 + 0.687838i \(0.241440\pi\)
\(840\) 0 0
\(841\) 1855.00 0.0760589
\(842\) −20622.0 −0.844039
\(843\) 0 0
\(844\) 1640.00 0.0668852
\(845\) 0 0
\(846\) 0 0
\(847\) −15883.0 −0.644329
\(848\) −41322.0 −1.67335
\(849\) 0 0
\(850\) 0 0
\(851\) 45120.0 1.81750
\(852\) 0 0
\(853\) −36902.0 −1.48124 −0.740622 0.671922i \(-0.765469\pi\)
−0.740622 + 0.671922i \(0.765469\pi\)
\(854\) 18480.0 0.740483
\(855\) 0 0
\(856\) 33012.0 1.31814
\(857\) −30648.0 −1.22161 −0.610803 0.791783i \(-0.709153\pi\)
−0.610803 + 0.791783i \(0.709153\pi\)
\(858\) 0 0
\(859\) 20918.0 0.830865 0.415432 0.909624i \(-0.363630\pi\)
0.415432 + 0.909624i \(0.363630\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 30654.0 1.21123
\(863\) 19812.0 0.781470 0.390735 0.920503i \(-0.372221\pi\)
0.390735 + 0.920503i \(0.372221\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 17490.0 0.686298
\(867\) 0 0
\(868\) −1652.00 −0.0645997
\(869\) 35520.0 1.38657
\(870\) 0 0
\(871\) −31388.0 −1.22106
\(872\) 29442.0 1.14339
\(873\) 0 0
\(874\) 39600.0 1.53260
\(875\) 0 0
\(876\) 0 0
\(877\) −38900.0 −1.49779 −0.748894 0.662690i \(-0.769415\pi\)
−0.748894 + 0.662690i \(0.769415\pi\)
\(878\) 25764.0 0.990311
\(879\) 0 0
\(880\) 0 0
\(881\) −16398.0 −0.627086 −0.313543 0.949574i \(-0.601516\pi\)
−0.313543 + 0.949574i \(0.601516\pi\)
\(882\) 0 0
\(883\) −30422.0 −1.15944 −0.579718 0.814817i \(-0.696837\pi\)
−0.579718 + 0.814817i \(0.696837\pi\)
\(884\) 3192.00 0.121446
\(885\) 0 0
\(886\) −37980.0 −1.44014
\(887\) 6222.00 0.235529 0.117765 0.993042i \(-0.462427\pi\)
0.117765 + 0.993042i \(0.462427\pi\)
\(888\) 0 0
\(889\) −7672.00 −0.289438
\(890\) 0 0
\(891\) 0 0
\(892\) 1888.00 0.0708687
\(893\) −660.000 −0.0247324
\(894\) 0 0
\(895\) 0 0
\(896\) −11613.0 −0.432995
\(897\) 0 0
\(898\) −10908.0 −0.405350
\(899\) −38232.0 −1.41836
\(900\) 0 0
\(901\) −48888.0 −1.80765
\(902\) −22680.0 −0.837208
\(903\) 0 0
\(904\) 17766.0 0.653638
\(905\) 0 0
\(906\) 0 0
\(907\) −21926.0 −0.802691 −0.401346 0.915927i \(-0.631457\pi\)
−0.401346 + 0.915927i \(0.631457\pi\)
\(908\) −2244.00 −0.0820151
\(909\) 0 0
\(910\) 0 0
\(911\) −40662.0 −1.47881 −0.739403 0.673263i \(-0.764892\pi\)
−0.739403 + 0.673263i \(0.764892\pi\)
\(912\) 0 0
\(913\) −47520.0 −1.72254
\(914\) 9066.00 0.328093
\(915\) 0 0
\(916\) −4084.00 −0.147313
\(917\) −3444.00 −0.124025
\(918\) 0 0
\(919\) 25688.0 0.922055 0.461028 0.887386i \(-0.347481\pi\)
0.461028 + 0.887386i \(0.347481\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 44226.0 1.57972
\(923\) −25308.0 −0.902517
\(924\) 0 0
\(925\) 0 0
\(926\) 27804.0 0.986713
\(927\) 0 0
\(928\) 7290.00 0.257873
\(929\) 16026.0 0.565981 0.282990 0.959123i \(-0.408674\pi\)
0.282990 + 0.959123i \(0.408674\pi\)
\(930\) 0 0
\(931\) 5390.00 0.189742
\(932\) 4026.00 0.141498
\(933\) 0 0
\(934\) −41760.0 −1.46299
\(935\) 0 0
\(936\) 0 0
\(937\) −18362.0 −0.640193 −0.320096 0.947385i \(-0.603715\pi\)
−0.320096 + 0.947385i \(0.603715\pi\)
\(938\) −17346.0 −0.603803
\(939\) 0 0
\(940\) 0 0
\(941\) −8034.00 −0.278322 −0.139161 0.990270i \(-0.544441\pi\)
−0.139161 + 0.990270i \(0.544441\pi\)
\(942\) 0 0
\(943\) 15120.0 0.522137
\(944\) 34932.0 1.20439
\(945\) 0 0
\(946\) −6120.00 −0.210337
\(947\) −30732.0 −1.05455 −0.527273 0.849696i \(-0.676786\pi\)
−0.527273 + 0.849696i \(0.676786\pi\)
\(948\) 0 0
\(949\) −31388.0 −1.07365
\(950\) 0 0
\(951\) 0 0
\(952\) −12348.0 −0.420379
\(953\) 28242.0 0.959967 0.479983 0.877278i \(-0.340643\pi\)
0.479983 + 0.877278i \(0.340643\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 4590.00 0.155284
\(957\) 0 0
\(958\) 24660.0 0.831658
\(959\) 1974.00 0.0664690
\(960\) 0 0
\(961\) 25905.0 0.869558
\(962\) −42864.0 −1.43658
\(963\) 0 0
\(964\) 1946.00 0.0650171
\(965\) 0 0
\(966\) 0 0
\(967\) −37496.0 −1.24694 −0.623470 0.781848i \(-0.714277\pi\)
−0.623470 + 0.781848i \(0.714277\pi\)
\(968\) −47649.0 −1.58212
\(969\) 0 0
\(970\) 0 0
\(971\) 27204.0 0.899092 0.449546 0.893257i \(-0.351586\pi\)
0.449546 + 0.893257i \(0.351586\pi\)
\(972\) 0 0
\(973\) −14.0000 −0.000461274 0
\(974\) −47256.0 −1.55460
\(975\) 0 0
\(976\) 62480.0 2.04911
\(977\) 42954.0 1.40657 0.703286 0.710907i \(-0.251715\pi\)
0.703286 + 0.710907i \(0.251715\pi\)
\(978\) 0 0
\(979\) 60120.0 1.96266
\(980\) 0 0
\(981\) 0 0
\(982\) −19656.0 −0.638746
\(983\) −10182.0 −0.330372 −0.165186 0.986262i \(-0.552822\pi\)
−0.165186 + 0.986262i \(0.552822\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 40824.0 1.31856
\(987\) 0 0
\(988\) −4180.00 −0.134599
\(989\) 4080.00 0.131179
\(990\) 0 0
\(991\) 30008.0 0.961893 0.480946 0.876750i \(-0.340293\pi\)
0.480946 + 0.876750i \(0.340293\pi\)
\(992\) −10620.0 −0.339905
\(993\) 0 0
\(994\) −13986.0 −0.446287
\(995\) 0 0
\(996\) 0 0
\(997\) 47554.0 1.51058 0.755291 0.655390i \(-0.227496\pi\)
0.755291 + 0.655390i \(0.227496\pi\)
\(998\) 12480.0 0.395839
\(999\) 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 1575.4.a.i.1.1 1
3.2 odd 2 1575.4.a.c.1.1 1
5.4 even 2 315.4.a.b.1.1 1
15.14 odd 2 315.4.a.e.1.1 yes 1
35.34 odd 2 2205.4.a.f.1.1 1
105.104 even 2 2205.4.a.p.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.4.a.b.1.1 1 5.4 even 2
315.4.a.e.1.1 yes 1 15.14 odd 2
1575.4.a.c.1.1 1 3.2 odd 2
1575.4.a.i.1.1 1 1.1 even 1 trivial
2205.4.a.f.1.1 1 35.34 odd 2
2205.4.a.p.1.1 1 105.104 even 2