Properties

Label 1305.4.a.a.1.1
Level $1305$
Weight $4$
Character 1305.1
Self dual yes
Analytic conductor $76.997$
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] = [1305,4,Mod(1,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, 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("1305.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1305.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: \(76.9974925575\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 435)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1305.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{2} +17.0000 q^{4} -5.00000 q^{5} +16.0000 q^{7} -45.0000 q^{8} +O(q^{10})\) \(q-5.00000 q^{2} +17.0000 q^{4} -5.00000 q^{5} +16.0000 q^{7} -45.0000 q^{8} +25.0000 q^{10} +44.0000 q^{11} +78.0000 q^{13} -80.0000 q^{14} +89.0000 q^{16} -18.0000 q^{17} -28.0000 q^{19} -85.0000 q^{20} -220.000 q^{22} -184.000 q^{23} +25.0000 q^{25} -390.000 q^{26} +272.000 q^{28} -29.0000 q^{29} -224.000 q^{31} -85.0000 q^{32} +90.0000 q^{34} -80.0000 q^{35} +254.000 q^{37} +140.000 q^{38} +225.000 q^{40} +78.0000 q^{41} -260.000 q^{43} +748.000 q^{44} +920.000 q^{46} -312.000 q^{47} -87.0000 q^{49} -125.000 q^{50} +1326.00 q^{52} -574.000 q^{53} -220.000 q^{55} -720.000 q^{56} +145.000 q^{58} -180.000 q^{59} -610.000 q^{61} +1120.00 q^{62} -287.000 q^{64} -390.000 q^{65} -340.000 q^{67} -306.000 q^{68} +400.000 q^{70} -296.000 q^{71} +394.000 q^{73} -1270.00 q^{74} -476.000 q^{76} +704.000 q^{77} -960.000 q^{79} -445.000 q^{80} -390.000 q^{82} +908.000 q^{83} +90.0000 q^{85} +1300.00 q^{86} -1980.00 q^{88} +990.000 q^{89} +1248.00 q^{91} -3128.00 q^{92} +1560.00 q^{94} +140.000 q^{95} +1234.00 q^{97} +435.000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.00000 −1.76777 −0.883883 0.467707i \(-0.845080\pi\)
−0.883883 + 0.467707i \(0.845080\pi\)
\(3\) 0 0
\(4\) 17.0000 2.12500
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 16.0000 0.863919 0.431959 0.901893i \(-0.357822\pi\)
0.431959 + 0.901893i \(0.357822\pi\)
\(8\) −45.0000 −1.98874
\(9\) 0 0
\(10\) 25.0000 0.790569
\(11\) 44.0000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 78.0000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) −80.0000 −1.52721
\(15\) 0 0
\(16\) 89.0000 1.39062
\(17\) −18.0000 −0.256802 −0.128401 0.991722i \(-0.540985\pi\)
−0.128401 + 0.991722i \(0.540985\pi\)
\(18\) 0 0
\(19\) −28.0000 −0.338086 −0.169043 0.985609i \(-0.554068\pi\)
−0.169043 + 0.985609i \(0.554068\pi\)
\(20\) −85.0000 −0.950329
\(21\) 0 0
\(22\) −220.000 −2.13201
\(23\) −184.000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −390.000 −2.94174
\(27\) 0 0
\(28\) 272.000 1.83583
\(29\) −29.0000 −0.185695
\(30\) 0 0
\(31\) −224.000 −1.29779 −0.648897 0.760877i \(-0.724769\pi\)
−0.648897 + 0.760877i \(0.724769\pi\)
\(32\) −85.0000 −0.469563
\(33\) 0 0
\(34\) 90.0000 0.453967
\(35\) −80.0000 −0.386356
\(36\) 0 0
\(37\) 254.000 1.12858 0.564288 0.825578i \(-0.309151\pi\)
0.564288 + 0.825578i \(0.309151\pi\)
\(38\) 140.000 0.597658
\(39\) 0 0
\(40\) 225.000 0.889391
\(41\) 78.0000 0.297111 0.148556 0.988904i \(-0.452538\pi\)
0.148556 + 0.988904i \(0.452538\pi\)
\(42\) 0 0
\(43\) −260.000 −0.922084 −0.461042 0.887378i \(-0.652524\pi\)
−0.461042 + 0.887378i \(0.652524\pi\)
\(44\) 748.000 2.56285
\(45\) 0 0
\(46\) 920.000 2.94884
\(47\) −312.000 −0.968295 −0.484148 0.874986i \(-0.660870\pi\)
−0.484148 + 0.874986i \(0.660870\pi\)
\(48\) 0 0
\(49\) −87.0000 −0.253644
\(50\) −125.000 −0.353553
\(51\) 0 0
\(52\) 1326.00 3.53621
\(53\) −574.000 −1.48764 −0.743820 0.668380i \(-0.766988\pi\)
−0.743820 + 0.668380i \(0.766988\pi\)
\(54\) 0 0
\(55\) −220.000 −0.539360
\(56\) −720.000 −1.71811
\(57\) 0 0
\(58\) 145.000 0.328266
\(59\) −180.000 −0.397187 −0.198593 0.980082i \(-0.563637\pi\)
−0.198593 + 0.980082i \(0.563637\pi\)
\(60\) 0 0
\(61\) −610.000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 1120.00 2.29420
\(63\) 0 0
\(64\) −287.000 −0.560547
\(65\) −390.000 −0.744208
\(66\) 0 0
\(67\) −340.000 −0.619964 −0.309982 0.950742i \(-0.600323\pi\)
−0.309982 + 0.950742i \(0.600323\pi\)
\(68\) −306.000 −0.545705
\(69\) 0 0
\(70\) 400.000 0.682988
\(71\) −296.000 −0.494771 −0.247385 0.968917i \(-0.579571\pi\)
−0.247385 + 0.968917i \(0.579571\pi\)
\(72\) 0 0
\(73\) 394.000 0.631702 0.315851 0.948809i \(-0.397710\pi\)
0.315851 + 0.948809i \(0.397710\pi\)
\(74\) −1270.00 −1.99506
\(75\) 0 0
\(76\) −476.000 −0.718433
\(77\) 704.000 1.04193
\(78\) 0 0
\(79\) −960.000 −1.36720 −0.683598 0.729859i \(-0.739586\pi\)
−0.683598 + 0.729859i \(0.739586\pi\)
\(80\) −445.000 −0.621906
\(81\) 0 0
\(82\) −390.000 −0.525223
\(83\) 908.000 1.20079 0.600397 0.799702i \(-0.295009\pi\)
0.600397 + 0.799702i \(0.295009\pi\)
\(84\) 0 0
\(85\) 90.0000 0.114846
\(86\) 1300.00 1.63003
\(87\) 0 0
\(88\) −1980.00 −2.39851
\(89\) 990.000 1.17910 0.589549 0.807732i \(-0.299305\pi\)
0.589549 + 0.807732i \(0.299305\pi\)
\(90\) 0 0
\(91\) 1248.00 1.43765
\(92\) −3128.00 −3.54475
\(93\) 0 0
\(94\) 1560.00 1.71172
\(95\) 140.000 0.151197
\(96\) 0 0
\(97\) 1234.00 1.29169 0.645844 0.763469i \(-0.276506\pi\)
0.645844 + 0.763469i \(0.276506\pi\)
\(98\) 435.000 0.448384
\(99\) 0 0
\(100\) 425.000 0.425000
\(101\) −1022.00 −1.00686 −0.503430 0.864036i \(-0.667929\pi\)
−0.503430 + 0.864036i \(0.667929\pi\)
\(102\) 0 0
\(103\) −1248.00 −1.19387 −0.596937 0.802288i \(-0.703616\pi\)
−0.596937 + 0.802288i \(0.703616\pi\)
\(104\) −3510.00 −3.30946
\(105\) 0 0
\(106\) 2870.00 2.62980
\(107\) 116.000 0.104805 0.0524025 0.998626i \(-0.483312\pi\)
0.0524025 + 0.998626i \(0.483312\pi\)
\(108\) 0 0
\(109\) −826.000 −0.725839 −0.362920 0.931820i \(-0.618220\pi\)
−0.362920 + 0.931820i \(0.618220\pi\)
\(110\) 1100.00 0.953463
\(111\) 0 0
\(112\) 1424.00 1.20139
\(113\) 2206.00 1.83649 0.918243 0.396016i \(-0.129608\pi\)
0.918243 + 0.396016i \(0.129608\pi\)
\(114\) 0 0
\(115\) 920.000 0.746004
\(116\) −493.000 −0.394603
\(117\) 0 0
\(118\) 900.000 0.702133
\(119\) −288.000 −0.221856
\(120\) 0 0
\(121\) 605.000 0.454545
\(122\) 3050.00 2.26339
\(123\) 0 0
\(124\) −3808.00 −2.75781
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −2056.00 −1.43654 −0.718270 0.695765i \(-0.755066\pi\)
−0.718270 + 0.695765i \(0.755066\pi\)
\(128\) 2115.00 1.46048
\(129\) 0 0
\(130\) 1950.00 1.31559
\(131\) −12.0000 −0.00800340 −0.00400170 0.999992i \(-0.501274\pi\)
−0.00400170 + 0.999992i \(0.501274\pi\)
\(132\) 0 0
\(133\) −448.000 −0.292079
\(134\) 1700.00 1.09595
\(135\) 0 0
\(136\) 810.000 0.510713
\(137\) 2758.00 1.71994 0.859970 0.510344i \(-0.170482\pi\)
0.859970 + 0.510344i \(0.170482\pi\)
\(138\) 0 0
\(139\) −1436.00 −0.876258 −0.438129 0.898912i \(-0.644359\pi\)
−0.438129 + 0.898912i \(0.644359\pi\)
\(140\) −1360.00 −0.821007
\(141\) 0 0
\(142\) 1480.00 0.874640
\(143\) 3432.00 2.00698
\(144\) 0 0
\(145\) 145.000 0.0830455
\(146\) −1970.00 −1.11670
\(147\) 0 0
\(148\) 4318.00 2.39823
\(149\) 498.000 0.273810 0.136905 0.990584i \(-0.456284\pi\)
0.136905 + 0.990584i \(0.456284\pi\)
\(150\) 0 0
\(151\) −2696.00 −1.45296 −0.726481 0.687186i \(-0.758846\pi\)
−0.726481 + 0.687186i \(0.758846\pi\)
\(152\) 1260.00 0.672365
\(153\) 0 0
\(154\) −3520.00 −1.84188
\(155\) 1120.00 0.580391
\(156\) 0 0
\(157\) 534.000 0.271451 0.135726 0.990746i \(-0.456663\pi\)
0.135726 + 0.990746i \(0.456663\pi\)
\(158\) 4800.00 2.41688
\(159\) 0 0
\(160\) 425.000 0.209995
\(161\) −2944.00 −1.44112
\(162\) 0 0
\(163\) 1380.00 0.663128 0.331564 0.943433i \(-0.392424\pi\)
0.331564 + 0.943433i \(0.392424\pi\)
\(164\) 1326.00 0.631361
\(165\) 0 0
\(166\) −4540.00 −2.12272
\(167\) −2616.00 −1.21217 −0.606084 0.795400i \(-0.707261\pi\)
−0.606084 + 0.795400i \(0.707261\pi\)
\(168\) 0 0
\(169\) 3887.00 1.76923
\(170\) −450.000 −0.203020
\(171\) 0 0
\(172\) −4420.00 −1.95943
\(173\) 330.000 0.145026 0.0725128 0.997367i \(-0.476898\pi\)
0.0725128 + 0.997367i \(0.476898\pi\)
\(174\) 0 0
\(175\) 400.000 0.172784
\(176\) 3916.00 1.67716
\(177\) 0 0
\(178\) −4950.00 −2.08437
\(179\) 372.000 0.155333 0.0776664 0.996979i \(-0.475253\pi\)
0.0776664 + 0.996979i \(0.475253\pi\)
\(180\) 0 0
\(181\) −1010.00 −0.414766 −0.207383 0.978260i \(-0.566495\pi\)
−0.207383 + 0.978260i \(0.566495\pi\)
\(182\) −6240.00 −2.54143
\(183\) 0 0
\(184\) 8280.00 3.31744
\(185\) −1270.00 −0.504715
\(186\) 0 0
\(187\) −792.000 −0.309715
\(188\) −5304.00 −2.05763
\(189\) 0 0
\(190\) −700.000 −0.267281
\(191\) −2008.00 −0.760700 −0.380350 0.924843i \(-0.624197\pi\)
−0.380350 + 0.924843i \(0.624197\pi\)
\(192\) 0 0
\(193\) 2578.00 0.961495 0.480747 0.876859i \(-0.340365\pi\)
0.480747 + 0.876859i \(0.340365\pi\)
\(194\) −6170.00 −2.28340
\(195\) 0 0
\(196\) −1479.00 −0.538994
\(197\) −526.000 −0.190233 −0.0951166 0.995466i \(-0.530322\pi\)
−0.0951166 + 0.995466i \(0.530322\pi\)
\(198\) 0 0
\(199\) 4440.00 1.58162 0.790812 0.612059i \(-0.209658\pi\)
0.790812 + 0.612059i \(0.209658\pi\)
\(200\) −1125.00 −0.397748
\(201\) 0 0
\(202\) 5110.00 1.77989
\(203\) −464.000 −0.160426
\(204\) 0 0
\(205\) −390.000 −0.132872
\(206\) 6240.00 2.11049
\(207\) 0 0
\(208\) 6942.00 2.31414
\(209\) −1232.00 −0.407747
\(210\) 0 0
\(211\) 308.000 0.100491 0.0502455 0.998737i \(-0.484000\pi\)
0.0502455 + 0.998737i \(0.484000\pi\)
\(212\) −9758.00 −3.16124
\(213\) 0 0
\(214\) −580.000 −0.185271
\(215\) 1300.00 0.412369
\(216\) 0 0
\(217\) −3584.00 −1.12119
\(218\) 4130.00 1.28311
\(219\) 0 0
\(220\) −3740.00 −1.14614
\(221\) −1404.00 −0.427345
\(222\) 0 0
\(223\) 4120.00 1.23720 0.618600 0.785706i \(-0.287700\pi\)
0.618600 + 0.785706i \(0.287700\pi\)
\(224\) −1360.00 −0.405664
\(225\) 0 0
\(226\) −11030.0 −3.24648
\(227\) −4932.00 −1.44206 −0.721032 0.692902i \(-0.756332\pi\)
−0.721032 + 0.692902i \(0.756332\pi\)
\(228\) 0 0
\(229\) −3050.00 −0.880130 −0.440065 0.897966i \(-0.645045\pi\)
−0.440065 + 0.897966i \(0.645045\pi\)
\(230\) −4600.00 −1.31876
\(231\) 0 0
\(232\) 1305.00 0.369299
\(233\) −82.0000 −0.0230558 −0.0115279 0.999934i \(-0.503670\pi\)
−0.0115279 + 0.999934i \(0.503670\pi\)
\(234\) 0 0
\(235\) 1560.00 0.433035
\(236\) −3060.00 −0.844021
\(237\) 0 0
\(238\) 1440.00 0.392190
\(239\) 5104.00 1.38138 0.690691 0.723150i \(-0.257306\pi\)
0.690691 + 0.723150i \(0.257306\pi\)
\(240\) 0 0
\(241\) −2158.00 −0.576801 −0.288400 0.957510i \(-0.593123\pi\)
−0.288400 + 0.957510i \(0.593123\pi\)
\(242\) −3025.00 −0.803530
\(243\) 0 0
\(244\) −10370.0 −2.72078
\(245\) 435.000 0.113433
\(246\) 0 0
\(247\) −2184.00 −0.562610
\(248\) 10080.0 2.58097
\(249\) 0 0
\(250\) 625.000 0.158114
\(251\) −6116.00 −1.53800 −0.769001 0.639248i \(-0.779246\pi\)
−0.769001 + 0.639248i \(0.779246\pi\)
\(252\) 0 0
\(253\) −8096.00 −2.01182
\(254\) 10280.0 2.53947
\(255\) 0 0
\(256\) −8279.00 −2.02124
\(257\) −3418.00 −0.829607 −0.414803 0.909911i \(-0.636150\pi\)
−0.414803 + 0.909911i \(0.636150\pi\)
\(258\) 0 0
\(259\) 4064.00 0.974999
\(260\) −6630.00 −1.58144
\(261\) 0 0
\(262\) 60.0000 0.0141481
\(263\) −7440.00 −1.74437 −0.872186 0.489174i \(-0.837298\pi\)
−0.872186 + 0.489174i \(0.837298\pi\)
\(264\) 0 0
\(265\) 2870.00 0.665293
\(266\) 2240.00 0.516328
\(267\) 0 0
\(268\) −5780.00 −1.31742
\(269\) −6582.00 −1.49186 −0.745932 0.666022i \(-0.767996\pi\)
−0.745932 + 0.666022i \(0.767996\pi\)
\(270\) 0 0
\(271\) −5504.00 −1.23374 −0.616871 0.787064i \(-0.711600\pi\)
−0.616871 + 0.787064i \(0.711600\pi\)
\(272\) −1602.00 −0.357116
\(273\) 0 0
\(274\) −13790.0 −3.04045
\(275\) 1100.00 0.241209
\(276\) 0 0
\(277\) 3718.00 0.806473 0.403236 0.915096i \(-0.367885\pi\)
0.403236 + 0.915096i \(0.367885\pi\)
\(278\) 7180.00 1.54902
\(279\) 0 0
\(280\) 3600.00 0.768361
\(281\) −1754.00 −0.372366 −0.186183 0.982515i \(-0.559612\pi\)
−0.186183 + 0.982515i \(0.559612\pi\)
\(282\) 0 0
\(283\) 3572.00 0.750295 0.375147 0.926965i \(-0.377592\pi\)
0.375147 + 0.926965i \(0.377592\pi\)
\(284\) −5032.00 −1.05139
\(285\) 0 0
\(286\) −17160.0 −3.54787
\(287\) 1248.00 0.256680
\(288\) 0 0
\(289\) −4589.00 −0.934053
\(290\) −725.000 −0.146805
\(291\) 0 0
\(292\) 6698.00 1.34237
\(293\) −126.000 −0.0251229 −0.0125614 0.999921i \(-0.503999\pi\)
−0.0125614 + 0.999921i \(0.503999\pi\)
\(294\) 0 0
\(295\) 900.000 0.177627
\(296\) −11430.0 −2.24444
\(297\) 0 0
\(298\) −2490.00 −0.484033
\(299\) −14352.0 −2.77591
\(300\) 0 0
\(301\) −4160.00 −0.796606
\(302\) 13480.0 2.56850
\(303\) 0 0
\(304\) −2492.00 −0.470151
\(305\) 3050.00 0.572598
\(306\) 0 0
\(307\) −2412.00 −0.448404 −0.224202 0.974543i \(-0.571978\pi\)
−0.224202 + 0.974543i \(0.571978\pi\)
\(308\) 11968.0 2.21409
\(309\) 0 0
\(310\) −5600.00 −1.02600
\(311\) 2928.00 0.533864 0.266932 0.963715i \(-0.413990\pi\)
0.266932 + 0.963715i \(0.413990\pi\)
\(312\) 0 0
\(313\) 2874.00 0.519003 0.259502 0.965743i \(-0.416442\pi\)
0.259502 + 0.965743i \(0.416442\pi\)
\(314\) −2670.00 −0.479862
\(315\) 0 0
\(316\) −16320.0 −2.90529
\(317\) 26.0000 0.00460664 0.00230332 0.999997i \(-0.499267\pi\)
0.00230332 + 0.999997i \(0.499267\pi\)
\(318\) 0 0
\(319\) −1276.00 −0.223957
\(320\) 1435.00 0.250684
\(321\) 0 0
\(322\) 14720.0 2.54756
\(323\) 504.000 0.0868214
\(324\) 0 0
\(325\) 1950.00 0.332820
\(326\) −6900.00 −1.17226
\(327\) 0 0
\(328\) −3510.00 −0.590876
\(329\) −4992.00 −0.836528
\(330\) 0 0
\(331\) 9340.00 1.55098 0.775488 0.631363i \(-0.217504\pi\)
0.775488 + 0.631363i \(0.217504\pi\)
\(332\) 15436.0 2.55169
\(333\) 0 0
\(334\) 13080.0 2.14283
\(335\) 1700.00 0.277256
\(336\) 0 0
\(337\) −10302.0 −1.66524 −0.832620 0.553845i \(-0.813160\pi\)
−0.832620 + 0.553845i \(0.813160\pi\)
\(338\) −19435.0 −3.12759
\(339\) 0 0
\(340\) 1530.00 0.244047
\(341\) −9856.00 −1.56520
\(342\) 0 0
\(343\) −6880.00 −1.08305
\(344\) 11700.0 1.83378
\(345\) 0 0
\(346\) −1650.00 −0.256372
\(347\) 8020.00 1.24074 0.620369 0.784310i \(-0.286983\pi\)
0.620369 + 0.784310i \(0.286983\pi\)
\(348\) 0 0
\(349\) −1306.00 −0.200311 −0.100156 0.994972i \(-0.531934\pi\)
−0.100156 + 0.994972i \(0.531934\pi\)
\(350\) −2000.00 −0.305441
\(351\) 0 0
\(352\) −3740.00 −0.566314
\(353\) −5658.00 −0.853102 −0.426551 0.904464i \(-0.640272\pi\)
−0.426551 + 0.904464i \(0.640272\pi\)
\(354\) 0 0
\(355\) 1480.00 0.221268
\(356\) 16830.0 2.50558
\(357\) 0 0
\(358\) −1860.00 −0.274592
\(359\) 12240.0 1.79945 0.899725 0.436457i \(-0.143767\pi\)
0.899725 + 0.436457i \(0.143767\pi\)
\(360\) 0 0
\(361\) −6075.00 −0.885698
\(362\) 5050.00 0.733210
\(363\) 0 0
\(364\) 21216.0 3.05500
\(365\) −1970.00 −0.282506
\(366\) 0 0
\(367\) 8984.00 1.27782 0.638911 0.769280i \(-0.279385\pi\)
0.638911 + 0.769280i \(0.279385\pi\)
\(368\) −16376.0 −2.31972
\(369\) 0 0
\(370\) 6350.00 0.892218
\(371\) −9184.00 −1.28520
\(372\) 0 0
\(373\) −938.000 −0.130209 −0.0651043 0.997878i \(-0.520738\pi\)
−0.0651043 + 0.997878i \(0.520738\pi\)
\(374\) 3960.00 0.547505
\(375\) 0 0
\(376\) 14040.0 1.92569
\(377\) −2262.00 −0.309016
\(378\) 0 0
\(379\) −7796.00 −1.05661 −0.528303 0.849056i \(-0.677171\pi\)
−0.528303 + 0.849056i \(0.677171\pi\)
\(380\) 2380.00 0.321293
\(381\) 0 0
\(382\) 10040.0 1.34474
\(383\) 6944.00 0.926428 0.463214 0.886247i \(-0.346696\pi\)
0.463214 + 0.886247i \(0.346696\pi\)
\(384\) 0 0
\(385\) −3520.00 −0.465963
\(386\) −12890.0 −1.69970
\(387\) 0 0
\(388\) 20978.0 2.74484
\(389\) −2126.00 −0.277101 −0.138551 0.990355i \(-0.544244\pi\)
−0.138551 + 0.990355i \(0.544244\pi\)
\(390\) 0 0
\(391\) 3312.00 0.428376
\(392\) 3915.00 0.504432
\(393\) 0 0
\(394\) 2630.00 0.336288
\(395\) 4800.00 0.611428
\(396\) 0 0
\(397\) −3346.00 −0.423000 −0.211500 0.977378i \(-0.567835\pi\)
−0.211500 + 0.977378i \(0.567835\pi\)
\(398\) −22200.0 −2.79594
\(399\) 0 0
\(400\) 2225.00 0.278125
\(401\) −12850.0 −1.60025 −0.800123 0.599836i \(-0.795232\pi\)
−0.800123 + 0.599836i \(0.795232\pi\)
\(402\) 0 0
\(403\) −17472.0 −2.15966
\(404\) −17374.0 −2.13958
\(405\) 0 0
\(406\) 2320.00 0.283595
\(407\) 11176.0 1.36111
\(408\) 0 0
\(409\) 6122.00 0.740131 0.370065 0.929006i \(-0.379335\pi\)
0.370065 + 0.929006i \(0.379335\pi\)
\(410\) 1950.00 0.234887
\(411\) 0 0
\(412\) −21216.0 −2.53698
\(413\) −2880.00 −0.343137
\(414\) 0 0
\(415\) −4540.00 −0.537012
\(416\) −6630.00 −0.781400
\(417\) 0 0
\(418\) 6160.00 0.720803
\(419\) −1372.00 −0.159968 −0.0799840 0.996796i \(-0.525487\pi\)
−0.0799840 + 0.996796i \(0.525487\pi\)
\(420\) 0 0
\(421\) 12150.0 1.40654 0.703272 0.710921i \(-0.251722\pi\)
0.703272 + 0.710921i \(0.251722\pi\)
\(422\) −1540.00 −0.177645
\(423\) 0 0
\(424\) 25830.0 2.95853
\(425\) −450.000 −0.0513605
\(426\) 0 0
\(427\) −9760.00 −1.10613
\(428\) 1972.00 0.222711
\(429\) 0 0
\(430\) −6500.00 −0.728972
\(431\) −6288.00 −0.702743 −0.351372 0.936236i \(-0.614285\pi\)
−0.351372 + 0.936236i \(0.614285\pi\)
\(432\) 0 0
\(433\) 15650.0 1.73693 0.868465 0.495750i \(-0.165107\pi\)
0.868465 + 0.495750i \(0.165107\pi\)
\(434\) 17920.0 1.98200
\(435\) 0 0
\(436\) −14042.0 −1.54241
\(437\) 5152.00 0.563967
\(438\) 0 0
\(439\) −14520.0 −1.57859 −0.789296 0.614013i \(-0.789554\pi\)
−0.789296 + 0.614013i \(0.789554\pi\)
\(440\) 9900.00 1.07265
\(441\) 0 0
\(442\) 7020.00 0.755446
\(443\) −7372.00 −0.790642 −0.395321 0.918543i \(-0.629367\pi\)
−0.395321 + 0.918543i \(0.629367\pi\)
\(444\) 0 0
\(445\) −4950.00 −0.527309
\(446\) −20600.0 −2.18708
\(447\) 0 0
\(448\) −4592.00 −0.484267
\(449\) −10666.0 −1.12107 −0.560534 0.828131i \(-0.689404\pi\)
−0.560534 + 0.828131i \(0.689404\pi\)
\(450\) 0 0
\(451\) 3432.00 0.358329
\(452\) 37502.0 3.90253
\(453\) 0 0
\(454\) 24660.0 2.54923
\(455\) −6240.00 −0.642936
\(456\) 0 0
\(457\) −8006.00 −0.819486 −0.409743 0.912201i \(-0.634382\pi\)
−0.409743 + 0.912201i \(0.634382\pi\)
\(458\) 15250.0 1.55586
\(459\) 0 0
\(460\) 15640.0 1.58526
\(461\) −1254.00 −0.126691 −0.0633456 0.997992i \(-0.520177\pi\)
−0.0633456 + 0.997992i \(0.520177\pi\)
\(462\) 0 0
\(463\) −4584.00 −0.460122 −0.230061 0.973176i \(-0.573893\pi\)
−0.230061 + 0.973176i \(0.573893\pi\)
\(464\) −2581.00 −0.258233
\(465\) 0 0
\(466\) 410.000 0.0407573
\(467\) −11588.0 −1.14824 −0.574121 0.818771i \(-0.694656\pi\)
−0.574121 + 0.818771i \(0.694656\pi\)
\(468\) 0 0
\(469\) −5440.00 −0.535599
\(470\) −7800.00 −0.765505
\(471\) 0 0
\(472\) 8100.00 0.789900
\(473\) −11440.0 −1.11208
\(474\) 0 0
\(475\) −700.000 −0.0676173
\(476\) −4896.00 −0.471445
\(477\) 0 0
\(478\) −25520.0 −2.44196
\(479\) 18200.0 1.73607 0.868037 0.496500i \(-0.165382\pi\)
0.868037 + 0.496500i \(0.165382\pi\)
\(480\) 0 0
\(481\) 19812.0 1.87807
\(482\) 10790.0 1.01965
\(483\) 0 0
\(484\) 10285.0 0.965909
\(485\) −6170.00 −0.577660
\(486\) 0 0
\(487\) 3824.00 0.355815 0.177908 0.984047i \(-0.443067\pi\)
0.177908 + 0.984047i \(0.443067\pi\)
\(488\) 27450.0 2.54632
\(489\) 0 0
\(490\) −2175.00 −0.200523
\(491\) 3100.00 0.284931 0.142465 0.989800i \(-0.454497\pi\)
0.142465 + 0.989800i \(0.454497\pi\)
\(492\) 0 0
\(493\) 522.000 0.0476870
\(494\) 10920.0 0.994563
\(495\) 0 0
\(496\) −19936.0 −1.80474
\(497\) −4736.00 −0.427442
\(498\) 0 0
\(499\) 19740.0 1.77091 0.885455 0.464726i \(-0.153847\pi\)
0.885455 + 0.464726i \(0.153847\pi\)
\(500\) −2125.00 −0.190066
\(501\) 0 0
\(502\) 30580.0 2.71883
\(503\) 6720.00 0.595686 0.297843 0.954615i \(-0.403733\pi\)
0.297843 + 0.954615i \(0.403733\pi\)
\(504\) 0 0
\(505\) 5110.00 0.450281
\(506\) 40480.0 3.55643
\(507\) 0 0
\(508\) −34952.0 −3.05265
\(509\) −10886.0 −0.947964 −0.473982 0.880535i \(-0.657184\pi\)
−0.473982 + 0.880535i \(0.657184\pi\)
\(510\) 0 0
\(511\) 6304.00 0.545739
\(512\) 24475.0 2.11260
\(513\) 0 0
\(514\) 17090.0 1.46655
\(515\) 6240.00 0.533917
\(516\) 0 0
\(517\) −13728.0 −1.16781
\(518\) −20320.0 −1.72357
\(519\) 0 0
\(520\) 17550.0 1.48004
\(521\) −22522.0 −1.89387 −0.946935 0.321424i \(-0.895839\pi\)
−0.946935 + 0.321424i \(0.895839\pi\)
\(522\) 0 0
\(523\) −13212.0 −1.10463 −0.552314 0.833636i \(-0.686255\pi\)
−0.552314 + 0.833636i \(0.686255\pi\)
\(524\) −204.000 −0.0170072
\(525\) 0 0
\(526\) 37200.0 3.08364
\(527\) 4032.00 0.333276
\(528\) 0 0
\(529\) 21689.0 1.78261
\(530\) −14350.0 −1.17608
\(531\) 0 0
\(532\) −7616.00 −0.620668
\(533\) 6084.00 0.494423
\(534\) 0 0
\(535\) −580.000 −0.0468703
\(536\) 15300.0 1.23295
\(537\) 0 0
\(538\) 32910.0 2.63727
\(539\) −3828.00 −0.305907
\(540\) 0 0
\(541\) −4642.00 −0.368900 −0.184450 0.982842i \(-0.559050\pi\)
−0.184450 + 0.982842i \(0.559050\pi\)
\(542\) 27520.0 2.18097
\(543\) 0 0
\(544\) 1530.00 0.120585
\(545\) 4130.00 0.324605
\(546\) 0 0
\(547\) 4060.00 0.317355 0.158677 0.987330i \(-0.449277\pi\)
0.158677 + 0.987330i \(0.449277\pi\)
\(548\) 46886.0 3.65487
\(549\) 0 0
\(550\) −5500.00 −0.426401
\(551\) 812.000 0.0627811
\(552\) 0 0
\(553\) −15360.0 −1.18115
\(554\) −18590.0 −1.42566
\(555\) 0 0
\(556\) −24412.0 −1.86205
\(557\) 1386.00 0.105434 0.0527170 0.998609i \(-0.483212\pi\)
0.0527170 + 0.998609i \(0.483212\pi\)
\(558\) 0 0
\(559\) −20280.0 −1.53444
\(560\) −7120.00 −0.537277
\(561\) 0 0
\(562\) 8770.00 0.658256
\(563\) −2452.00 −0.183551 −0.0917757 0.995780i \(-0.529254\pi\)
−0.0917757 + 0.995780i \(0.529254\pi\)
\(564\) 0 0
\(565\) −11030.0 −0.821302
\(566\) −17860.0 −1.32635
\(567\) 0 0
\(568\) 13320.0 0.983970
\(569\) 20862.0 1.53705 0.768524 0.639821i \(-0.220991\pi\)
0.768524 + 0.639821i \(0.220991\pi\)
\(570\) 0 0
\(571\) −9420.00 −0.690394 −0.345197 0.938530i \(-0.612188\pi\)
−0.345197 + 0.938530i \(0.612188\pi\)
\(572\) 58344.0 4.26483
\(573\) 0 0
\(574\) −6240.00 −0.453750
\(575\) −4600.00 −0.333623
\(576\) 0 0
\(577\) 13202.0 0.952524 0.476262 0.879303i \(-0.341991\pi\)
0.476262 + 0.879303i \(0.341991\pi\)
\(578\) 22945.0 1.65119
\(579\) 0 0
\(580\) 2465.00 0.176472
\(581\) 14528.0 1.03739
\(582\) 0 0
\(583\) −25256.0 −1.79416
\(584\) −17730.0 −1.25629
\(585\) 0 0
\(586\) 630.000 0.0444114
\(587\) 8708.00 0.612296 0.306148 0.951984i \(-0.400960\pi\)
0.306148 + 0.951984i \(0.400960\pi\)
\(588\) 0 0
\(589\) 6272.00 0.438766
\(590\) −4500.00 −0.314004
\(591\) 0 0
\(592\) 22606.0 1.56943
\(593\) 4390.00 0.304006 0.152003 0.988380i \(-0.451428\pi\)
0.152003 + 0.988380i \(0.451428\pi\)
\(594\) 0 0
\(595\) 1440.00 0.0992172
\(596\) 8466.00 0.581847
\(597\) 0 0
\(598\) 71760.0 4.90716
\(599\) 20256.0 1.38170 0.690850 0.722999i \(-0.257237\pi\)
0.690850 + 0.722999i \(0.257237\pi\)
\(600\) 0 0
\(601\) 9610.00 0.652246 0.326123 0.945327i \(-0.394258\pi\)
0.326123 + 0.945327i \(0.394258\pi\)
\(602\) 20800.0 1.40821
\(603\) 0 0
\(604\) −45832.0 −3.08755
\(605\) −3025.00 −0.203279
\(606\) 0 0
\(607\) 10376.0 0.693820 0.346910 0.937898i \(-0.387231\pi\)
0.346910 + 0.937898i \(0.387231\pi\)
\(608\) 2380.00 0.158753
\(609\) 0 0
\(610\) −15250.0 −1.01222
\(611\) −24336.0 −1.61134
\(612\) 0 0
\(613\) 6822.00 0.449491 0.224746 0.974417i \(-0.427845\pi\)
0.224746 + 0.974417i \(0.427845\pi\)
\(614\) 12060.0 0.792674
\(615\) 0 0
\(616\) −31680.0 −2.07212
\(617\) 20070.0 1.30954 0.654771 0.755827i \(-0.272765\pi\)
0.654771 + 0.755827i \(0.272765\pi\)
\(618\) 0 0
\(619\) 19228.0 1.24853 0.624264 0.781214i \(-0.285399\pi\)
0.624264 + 0.781214i \(0.285399\pi\)
\(620\) 19040.0 1.23333
\(621\) 0 0
\(622\) −14640.0 −0.943747
\(623\) 15840.0 1.01865
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) −14370.0 −0.917477
\(627\) 0 0
\(628\) 9078.00 0.576834
\(629\) −4572.00 −0.289821
\(630\) 0 0
\(631\) 6552.00 0.413361 0.206681 0.978408i \(-0.433734\pi\)
0.206681 + 0.978408i \(0.433734\pi\)
\(632\) 43200.0 2.71899
\(633\) 0 0
\(634\) −130.000 −0.00814347
\(635\) 10280.0 0.642440
\(636\) 0 0
\(637\) −6786.00 −0.422090
\(638\) 6380.00 0.395904
\(639\) 0 0
\(640\) −10575.0 −0.653146
\(641\) 14422.0 0.888666 0.444333 0.895862i \(-0.353441\pi\)
0.444333 + 0.895862i \(0.353441\pi\)
\(642\) 0 0
\(643\) −6212.00 −0.380991 −0.190496 0.981688i \(-0.561009\pi\)
−0.190496 + 0.981688i \(0.561009\pi\)
\(644\) −50048.0 −3.06237
\(645\) 0 0
\(646\) −2520.00 −0.153480
\(647\) −22024.0 −1.33826 −0.669129 0.743146i \(-0.733333\pi\)
−0.669129 + 0.743146i \(0.733333\pi\)
\(648\) 0 0
\(649\) −7920.00 −0.479025
\(650\) −9750.00 −0.588348
\(651\) 0 0
\(652\) 23460.0 1.40915
\(653\) −16630.0 −0.996604 −0.498302 0.867004i \(-0.666043\pi\)
−0.498302 + 0.867004i \(0.666043\pi\)
\(654\) 0 0
\(655\) 60.0000 0.00357923
\(656\) 6942.00 0.413170
\(657\) 0 0
\(658\) 24960.0 1.47879
\(659\) 24468.0 1.44634 0.723170 0.690670i \(-0.242684\pi\)
0.723170 + 0.690670i \(0.242684\pi\)
\(660\) 0 0
\(661\) −10226.0 −0.601733 −0.300866 0.953666i \(-0.597276\pi\)
−0.300866 + 0.953666i \(0.597276\pi\)
\(662\) −46700.0 −2.74176
\(663\) 0 0
\(664\) −40860.0 −2.38807
\(665\) 2240.00 0.130622
\(666\) 0 0
\(667\) 5336.00 0.309761
\(668\) −44472.0 −2.57586
\(669\) 0 0
\(670\) −8500.00 −0.490125
\(671\) −26840.0 −1.54418
\(672\) 0 0
\(673\) 13458.0 0.770829 0.385414 0.922744i \(-0.374059\pi\)
0.385414 + 0.922744i \(0.374059\pi\)
\(674\) 51510.0 2.94376
\(675\) 0 0
\(676\) 66079.0 3.75962
\(677\) −22174.0 −1.25881 −0.629406 0.777076i \(-0.716702\pi\)
−0.629406 + 0.777076i \(0.716702\pi\)
\(678\) 0 0
\(679\) 19744.0 1.11591
\(680\) −4050.00 −0.228398
\(681\) 0 0
\(682\) 49280.0 2.76690
\(683\) 2404.00 0.134680 0.0673400 0.997730i \(-0.478549\pi\)
0.0673400 + 0.997730i \(0.478549\pi\)
\(684\) 0 0
\(685\) −13790.0 −0.769181
\(686\) 34400.0 1.91457
\(687\) 0 0
\(688\) −23140.0 −1.28227
\(689\) −44772.0 −2.47558
\(690\) 0 0
\(691\) −5956.00 −0.327897 −0.163949 0.986469i \(-0.552423\pi\)
−0.163949 + 0.986469i \(0.552423\pi\)
\(692\) 5610.00 0.308179
\(693\) 0 0
\(694\) −40100.0 −2.19334
\(695\) 7180.00 0.391875
\(696\) 0 0
\(697\) −1404.00 −0.0762988
\(698\) 6530.00 0.354103
\(699\) 0 0
\(700\) 6800.00 0.367165
\(701\) 14586.0 0.785885 0.392943 0.919563i \(-0.371457\pi\)
0.392943 + 0.919563i \(0.371457\pi\)
\(702\) 0 0
\(703\) −7112.00 −0.381556
\(704\) −12628.0 −0.676045
\(705\) 0 0
\(706\) 28290.0 1.50809
\(707\) −16352.0 −0.869845
\(708\) 0 0
\(709\) −4370.00 −0.231479 −0.115740 0.993280i \(-0.536924\pi\)
−0.115740 + 0.993280i \(0.536924\pi\)
\(710\) −7400.00 −0.391151
\(711\) 0 0
\(712\) −44550.0 −2.34492
\(713\) 41216.0 2.16487
\(714\) 0 0
\(715\) −17160.0 −0.897549
\(716\) 6324.00 0.330082
\(717\) 0 0
\(718\) −61200.0 −3.18101
\(719\) −144.000 −0.00746912 −0.00373456 0.999993i \(-0.501189\pi\)
−0.00373456 + 0.999993i \(0.501189\pi\)
\(720\) 0 0
\(721\) −19968.0 −1.03141
\(722\) 30375.0 1.56571
\(723\) 0 0
\(724\) −17170.0 −0.881378
\(725\) −725.000 −0.0371391
\(726\) 0 0
\(727\) −9632.00 −0.491377 −0.245689 0.969349i \(-0.579014\pi\)
−0.245689 + 0.969349i \(0.579014\pi\)
\(728\) −56160.0 −2.85910
\(729\) 0 0
\(730\) 9850.00 0.499404
\(731\) 4680.00 0.236794
\(732\) 0 0
\(733\) −19306.0 −0.972829 −0.486414 0.873728i \(-0.661695\pi\)
−0.486414 + 0.873728i \(0.661695\pi\)
\(734\) −44920.0 −2.25889
\(735\) 0 0
\(736\) 15640.0 0.783285
\(737\) −14960.0 −0.747705
\(738\) 0 0
\(739\) −36540.0 −1.81887 −0.909435 0.415845i \(-0.863486\pi\)
−0.909435 + 0.415845i \(0.863486\pi\)
\(740\) −21590.0 −1.07252
\(741\) 0 0
\(742\) 45920.0 2.27194
\(743\) −5408.00 −0.267026 −0.133513 0.991047i \(-0.542626\pi\)
−0.133513 + 0.991047i \(0.542626\pi\)
\(744\) 0 0
\(745\) −2490.00 −0.122452
\(746\) 4690.00 0.230178
\(747\) 0 0
\(748\) −13464.0 −0.658145
\(749\) 1856.00 0.0905431
\(750\) 0 0
\(751\) −13952.0 −0.677917 −0.338959 0.940801i \(-0.610075\pi\)
−0.338959 + 0.940801i \(0.610075\pi\)
\(752\) −27768.0 −1.34654
\(753\) 0 0
\(754\) 11310.0 0.546268
\(755\) 13480.0 0.649785
\(756\) 0 0
\(757\) −4274.00 −0.205206 −0.102603 0.994722i \(-0.532717\pi\)
−0.102603 + 0.994722i \(0.532717\pi\)
\(758\) 38980.0 1.86783
\(759\) 0 0
\(760\) −6300.00 −0.300691
\(761\) 230.000 0.0109560 0.00547799 0.999985i \(-0.498256\pi\)
0.00547799 + 0.999985i \(0.498256\pi\)
\(762\) 0 0
\(763\) −13216.0 −0.627066
\(764\) −34136.0 −1.61649
\(765\) 0 0
\(766\) −34720.0 −1.63771
\(767\) −14040.0 −0.660958
\(768\) 0 0
\(769\) −7854.00 −0.368300 −0.184150 0.982898i \(-0.558953\pi\)
−0.184150 + 0.982898i \(0.558953\pi\)
\(770\) 17600.0 0.823714
\(771\) 0 0
\(772\) 43826.0 2.04318
\(773\) −19550.0 −0.909657 −0.454828 0.890579i \(-0.650299\pi\)
−0.454828 + 0.890579i \(0.650299\pi\)
\(774\) 0 0
\(775\) −5600.00 −0.259559
\(776\) −55530.0 −2.56883
\(777\) 0 0
\(778\) 10630.0 0.489851
\(779\) −2184.00 −0.100449
\(780\) 0 0
\(781\) −13024.0 −0.596716
\(782\) −16560.0 −0.757269
\(783\) 0 0
\(784\) −7743.00 −0.352724
\(785\) −2670.00 −0.121397
\(786\) 0 0
\(787\) 27228.0 1.23326 0.616629 0.787254i \(-0.288498\pi\)
0.616629 + 0.787254i \(0.288498\pi\)
\(788\) −8942.00 −0.404246
\(789\) 0 0
\(790\) −24000.0 −1.08086
\(791\) 35296.0 1.58658
\(792\) 0 0
\(793\) −47580.0 −2.13066
\(794\) 16730.0 0.747765
\(795\) 0 0
\(796\) 75480.0 3.36095
\(797\) 3386.00 0.150487 0.0752436 0.997165i \(-0.476027\pi\)
0.0752436 + 0.997165i \(0.476027\pi\)
\(798\) 0 0
\(799\) 5616.00 0.248661
\(800\) −2125.00 −0.0939126
\(801\) 0 0
\(802\) 64250.0 2.82886
\(803\) 17336.0 0.761861
\(804\) 0 0
\(805\) 14720.0 0.644487
\(806\) 87360.0 3.81777
\(807\) 0 0
\(808\) 45990.0 2.00238
\(809\) −26994.0 −1.17313 −0.586563 0.809904i \(-0.699519\pi\)
−0.586563 + 0.809904i \(0.699519\pi\)
\(810\) 0 0
\(811\) 8356.00 0.361799 0.180899 0.983502i \(-0.442099\pi\)
0.180899 + 0.983502i \(0.442099\pi\)
\(812\) −7888.00 −0.340905
\(813\) 0 0
\(814\) −55880.0 −2.40613
\(815\) −6900.00 −0.296560
\(816\) 0 0
\(817\) 7280.00 0.311744
\(818\) −30610.0 −1.30838
\(819\) 0 0
\(820\) −6630.00 −0.282353
\(821\) −9838.00 −0.418208 −0.209104 0.977893i \(-0.567055\pi\)
−0.209104 + 0.977893i \(0.567055\pi\)
\(822\) 0 0
\(823\) −29552.0 −1.25166 −0.625831 0.779959i \(-0.715240\pi\)
−0.625831 + 0.779959i \(0.715240\pi\)
\(824\) 56160.0 2.37430
\(825\) 0 0
\(826\) 14400.0 0.606586
\(827\) −18556.0 −0.780236 −0.390118 0.920765i \(-0.627566\pi\)
−0.390118 + 0.920765i \(0.627566\pi\)
\(828\) 0 0
\(829\) 7966.00 0.333740 0.166870 0.985979i \(-0.446634\pi\)
0.166870 + 0.985979i \(0.446634\pi\)
\(830\) 22700.0 0.949311
\(831\) 0 0
\(832\) −22386.0 −0.932806
\(833\) 1566.00 0.0651365
\(834\) 0 0
\(835\) 13080.0 0.542098
\(836\) −20944.0 −0.866463
\(837\) 0 0
\(838\) 6860.00 0.282786
\(839\) 42048.0 1.73022 0.865112 0.501578i \(-0.167247\pi\)
0.865112 + 0.501578i \(0.167247\pi\)
\(840\) 0 0
\(841\) 841.000 0.0344828
\(842\) −60750.0 −2.48644
\(843\) 0 0
\(844\) 5236.00 0.213543
\(845\) −19435.0 −0.791224
\(846\) 0 0
\(847\) 9680.00 0.392690
\(848\) −51086.0 −2.06875
\(849\) 0 0
\(850\) 2250.00 0.0907934
\(851\) −46736.0 −1.88260
\(852\) 0 0
\(853\) 29950.0 1.20219 0.601095 0.799177i \(-0.294731\pi\)
0.601095 + 0.799177i \(0.294731\pi\)
\(854\) 48800.0 1.95539
\(855\) 0 0
\(856\) −5220.00 −0.208430
\(857\) 31454.0 1.25373 0.626866 0.779127i \(-0.284337\pi\)
0.626866 + 0.779127i \(0.284337\pi\)
\(858\) 0 0
\(859\) −22036.0 −0.875272 −0.437636 0.899152i \(-0.644184\pi\)
−0.437636 + 0.899152i \(0.644184\pi\)
\(860\) 22100.0 0.876283
\(861\) 0 0
\(862\) 31440.0 1.24229
\(863\) −14048.0 −0.554113 −0.277056 0.960854i \(-0.589359\pi\)
−0.277056 + 0.960854i \(0.589359\pi\)
\(864\) 0 0
\(865\) −1650.00 −0.0648574
\(866\) −78250.0 −3.07049
\(867\) 0 0
\(868\) −60928.0 −2.38252
\(869\) −42240.0 −1.64890
\(870\) 0 0
\(871\) −26520.0 −1.03168
\(872\) 37170.0 1.44350
\(873\) 0 0
\(874\) −25760.0 −0.996962
\(875\) −2000.00 −0.0772712
\(876\) 0 0
\(877\) −39922.0 −1.53714 −0.768569 0.639767i \(-0.779031\pi\)
−0.768569 + 0.639767i \(0.779031\pi\)
\(878\) 72600.0 2.79058
\(879\) 0 0
\(880\) −19580.0 −0.750047
\(881\) −38730.0 −1.48110 −0.740549 0.672003i \(-0.765434\pi\)
−0.740549 + 0.672003i \(0.765434\pi\)
\(882\) 0 0
\(883\) −32948.0 −1.25571 −0.627853 0.778332i \(-0.716066\pi\)
−0.627853 + 0.778332i \(0.716066\pi\)
\(884\) −23868.0 −0.908108
\(885\) 0 0
\(886\) 36860.0 1.39767
\(887\) 21680.0 0.820680 0.410340 0.911933i \(-0.365410\pi\)
0.410340 + 0.911933i \(0.365410\pi\)
\(888\) 0 0
\(889\) −32896.0 −1.24105
\(890\) 24750.0 0.932159
\(891\) 0 0
\(892\) 70040.0 2.62905
\(893\) 8736.00 0.327367
\(894\) 0 0
\(895\) −1860.00 −0.0694670
\(896\) 33840.0 1.26174
\(897\) 0 0
\(898\) 53330.0 1.98179
\(899\) 6496.00 0.240994
\(900\) 0 0
\(901\) 10332.0 0.382030
\(902\) −17160.0 −0.633443
\(903\) 0 0
\(904\) −99270.0 −3.65229
\(905\) 5050.00 0.185489
\(906\) 0 0
\(907\) 2236.00 0.0818580 0.0409290 0.999162i \(-0.486968\pi\)
0.0409290 + 0.999162i \(0.486968\pi\)
\(908\) −83844.0 −3.06438
\(909\) 0 0
\(910\) 31200.0 1.13656
\(911\) −35816.0 −1.30257 −0.651283 0.758835i \(-0.725769\pi\)
−0.651283 + 0.758835i \(0.725769\pi\)
\(912\) 0 0
\(913\) 39952.0 1.44821
\(914\) 40030.0 1.44866
\(915\) 0 0
\(916\) −51850.0 −1.87028
\(917\) −192.000 −0.00691428
\(918\) 0 0
\(919\) 39704.0 1.42515 0.712576 0.701595i \(-0.247529\pi\)
0.712576 + 0.701595i \(0.247529\pi\)
\(920\) −41400.0 −1.48361
\(921\) 0 0
\(922\) 6270.00 0.223960
\(923\) −23088.0 −0.823349
\(924\) 0 0
\(925\) 6350.00 0.225715
\(926\) 22920.0 0.813389
\(927\) 0 0
\(928\) 2465.00 0.0871957
\(929\) 19534.0 0.689871 0.344935 0.938626i \(-0.387901\pi\)
0.344935 + 0.938626i \(0.387901\pi\)
\(930\) 0 0
\(931\) 2436.00 0.0857537
\(932\) −1394.00 −0.0489935
\(933\) 0 0
\(934\) 57940.0 2.02982
\(935\) 3960.00 0.138509
\(936\) 0 0
\(937\) −8678.00 −0.302559 −0.151280 0.988491i \(-0.548339\pi\)
−0.151280 + 0.988491i \(0.548339\pi\)
\(938\) 27200.0 0.946814
\(939\) 0 0
\(940\) 26520.0 0.920199
\(941\) 7050.00 0.244233 0.122117 0.992516i \(-0.461032\pi\)
0.122117 + 0.992516i \(0.461032\pi\)
\(942\) 0 0
\(943\) −14352.0 −0.495616
\(944\) −16020.0 −0.552337
\(945\) 0 0
\(946\) 57200.0 1.96589
\(947\) −23396.0 −0.802817 −0.401409 0.915899i \(-0.631479\pi\)
−0.401409 + 0.915899i \(0.631479\pi\)
\(948\) 0 0
\(949\) 30732.0 1.05121
\(950\) 3500.00 0.119532
\(951\) 0 0
\(952\) 12960.0 0.441214
\(953\) 36126.0 1.22795 0.613975 0.789326i \(-0.289570\pi\)
0.613975 + 0.789326i \(0.289570\pi\)
\(954\) 0 0
\(955\) 10040.0 0.340196
\(956\) 86768.0 2.93544
\(957\) 0 0
\(958\) −91000.0 −3.06897
\(959\) 44128.0 1.48589
\(960\) 0 0
\(961\) 20385.0 0.684267
\(962\) −99060.0 −3.31998
\(963\) 0 0
\(964\) −36686.0 −1.22570
\(965\) −12890.0 −0.429994
\(966\) 0 0
\(967\) 38624.0 1.28445 0.642225 0.766516i \(-0.278011\pi\)
0.642225 + 0.766516i \(0.278011\pi\)
\(968\) −27225.0 −0.903972
\(969\) 0 0
\(970\) 30850.0 1.02117
\(971\) 7292.00 0.241000 0.120500 0.992713i \(-0.461550\pi\)
0.120500 + 0.992713i \(0.461550\pi\)
\(972\) 0 0
\(973\) −22976.0 −0.757016
\(974\) −19120.0 −0.628998
\(975\) 0 0
\(976\) −54290.0 −1.78051
\(977\) 26838.0 0.878837 0.439418 0.898282i \(-0.355185\pi\)
0.439418 + 0.898282i \(0.355185\pi\)
\(978\) 0 0
\(979\) 43560.0 1.42205
\(980\) 7395.00 0.241046
\(981\) 0 0
\(982\) −15500.0 −0.503691
\(983\) −20192.0 −0.655163 −0.327581 0.944823i \(-0.606234\pi\)
−0.327581 + 0.944823i \(0.606234\pi\)
\(984\) 0 0
\(985\) 2630.00 0.0850749
\(986\) −2610.00 −0.0842995
\(987\) 0 0
\(988\) −37128.0 −1.19555
\(989\) 47840.0 1.53814
\(990\) 0 0
\(991\) 34400.0 1.10268 0.551338 0.834282i \(-0.314117\pi\)
0.551338 + 0.834282i \(0.314117\pi\)
\(992\) 19040.0 0.609396
\(993\) 0 0
\(994\) 23680.0 0.755618
\(995\) −22200.0 −0.707324
\(996\) 0 0
\(997\) 58430.0 1.85606 0.928032 0.372499i \(-0.121499\pi\)
0.928032 + 0.372499i \(0.121499\pi\)
\(998\) −98700.0 −3.13056
\(999\) 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 1305.4.a.a.1.1 1
3.2 odd 2 435.4.a.c.1.1 1
15.14 odd 2 2175.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.4.a.c.1.1 1 3.2 odd 2
1305.4.a.a.1.1 1 1.1 even 1 trivial
2175.4.a.a.1.1 1 15.14 odd 2