Properties

Label 435.4.a.c.1.1
Level $435$
Weight $4$
Character 435.1
Self dual yes
Analytic conductor $25.666$
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] = [435,4,Mod(1,435)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(435, 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("435.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 435.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: \(25.6658308525\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 435.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.00000 q^{2} -3.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} -15.0000 q^{6} +16.0000 q^{7} +45.0000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+5.00000 q^{2} -3.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} -15.0000 q^{6} +16.0000 q^{7} +45.0000 q^{8} +9.00000 q^{9} +25.0000 q^{10} -44.0000 q^{11} -51.0000 q^{12} +78.0000 q^{13} +80.0000 q^{14} -15.0000 q^{15} +89.0000 q^{16} +18.0000 q^{17} +45.0000 q^{18} -28.0000 q^{19} +85.0000 q^{20} -48.0000 q^{21} -220.000 q^{22} +184.000 q^{23} -135.000 q^{24} +25.0000 q^{25} +390.000 q^{26} -27.0000 q^{27} +272.000 q^{28} +29.0000 q^{29} -75.0000 q^{30} -224.000 q^{31} +85.0000 q^{32} +132.000 q^{33} +90.0000 q^{34} +80.0000 q^{35} +153.000 q^{36} +254.000 q^{37} -140.000 q^{38} -234.000 q^{39} +225.000 q^{40} -78.0000 q^{41} -240.000 q^{42} -260.000 q^{43} -748.000 q^{44} +45.0000 q^{45} +920.000 q^{46} +312.000 q^{47} -267.000 q^{48} -87.0000 q^{49} +125.000 q^{50} -54.0000 q^{51} +1326.00 q^{52} +574.000 q^{53} -135.000 q^{54} -220.000 q^{55} +720.000 q^{56} +84.0000 q^{57} +145.000 q^{58} +180.000 q^{59} -255.000 q^{60} -610.000 q^{61} -1120.00 q^{62} +144.000 q^{63} -287.000 q^{64} +390.000 q^{65} +660.000 q^{66} -340.000 q^{67} +306.000 q^{68} -552.000 q^{69} +400.000 q^{70} +296.000 q^{71} +405.000 q^{72} +394.000 q^{73} +1270.00 q^{74} -75.0000 q^{75} -476.000 q^{76} -704.000 q^{77} -1170.00 q^{78} -960.000 q^{79} +445.000 q^{80} +81.0000 q^{81} -390.000 q^{82} -908.000 q^{83} -816.000 q^{84} +90.0000 q^{85} -1300.00 q^{86} -87.0000 q^{87} -1980.00 q^{88} -990.000 q^{89} +225.000 q^{90} +1248.00 q^{91} +3128.00 q^{92} +672.000 q^{93} +1560.00 q^{94} -140.000 q^{95} -255.000 q^{96} +1234.00 q^{97} -435.000 q^{98} -396.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.00000 1.76777 0.883883 0.467707i \(-0.154920\pi\)
0.883883 + 0.467707i \(0.154920\pi\)
\(3\) −3.00000 −0.577350
\(4\) 17.0000 2.12500
\(5\) 5.00000 0.447214
\(6\) −15.0000 −1.02062
\(7\) 16.0000 0.863919 0.431959 0.901893i \(-0.357822\pi\)
0.431959 + 0.901893i \(0.357822\pi\)
\(8\) 45.0000 1.98874
\(9\) 9.00000 0.333333
\(10\) 25.0000 0.790569
\(11\) −44.0000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −51.0000 −1.22687
\(13\) 78.0000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 80.0000 1.52721
\(15\) −15.0000 −0.258199
\(16\) 89.0000 1.39062
\(17\) 18.0000 0.256802 0.128401 0.991722i \(-0.459015\pi\)
0.128401 + 0.991722i \(0.459015\pi\)
\(18\) 45.0000 0.589256
\(19\) −28.0000 −0.338086 −0.169043 0.985609i \(-0.554068\pi\)
−0.169043 + 0.985609i \(0.554068\pi\)
\(20\) 85.0000 0.950329
\(21\) −48.0000 −0.498784
\(22\) −220.000 −2.13201
\(23\) 184.000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) −135.000 −1.14820
\(25\) 25.0000 0.200000
\(26\) 390.000 2.94174
\(27\) −27.0000 −0.192450
\(28\) 272.000 1.83583
\(29\) 29.0000 0.185695
\(30\) −75.0000 −0.456435
\(31\) −224.000 −1.29779 −0.648897 0.760877i \(-0.724769\pi\)
−0.648897 + 0.760877i \(0.724769\pi\)
\(32\) 85.0000 0.469563
\(33\) 132.000 0.696311
\(34\) 90.0000 0.453967
\(35\) 80.0000 0.386356
\(36\) 153.000 0.708333
\(37\) 254.000 1.12858 0.564288 0.825578i \(-0.309151\pi\)
0.564288 + 0.825578i \(0.309151\pi\)
\(38\) −140.000 −0.597658
\(39\) −234.000 −0.960769
\(40\) 225.000 0.889391
\(41\) −78.0000 −0.297111 −0.148556 0.988904i \(-0.547462\pi\)
−0.148556 + 0.988904i \(0.547462\pi\)
\(42\) −240.000 −0.881733
\(43\) −260.000 −0.922084 −0.461042 0.887378i \(-0.652524\pi\)
−0.461042 + 0.887378i \(0.652524\pi\)
\(44\) −748.000 −2.56285
\(45\) 45.0000 0.149071
\(46\) 920.000 2.94884
\(47\) 312.000 0.968295 0.484148 0.874986i \(-0.339130\pi\)
0.484148 + 0.874986i \(0.339130\pi\)
\(48\) −267.000 −0.802878
\(49\) −87.0000 −0.253644
\(50\) 125.000 0.353553
\(51\) −54.0000 −0.148265
\(52\) 1326.00 3.53621
\(53\) 574.000 1.48764 0.743820 0.668380i \(-0.233012\pi\)
0.743820 + 0.668380i \(0.233012\pi\)
\(54\) −135.000 −0.340207
\(55\) −220.000 −0.539360
\(56\) 720.000 1.71811
\(57\) 84.0000 0.195194
\(58\) 145.000 0.328266
\(59\) 180.000 0.397187 0.198593 0.980082i \(-0.436363\pi\)
0.198593 + 0.980082i \(0.436363\pi\)
\(60\) −255.000 −0.548673
\(61\) −610.000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −1120.00 −2.29420
\(63\) 144.000 0.287973
\(64\) −287.000 −0.560547
\(65\) 390.000 0.744208
\(66\) 660.000 1.23091
\(67\) −340.000 −0.619964 −0.309982 0.950742i \(-0.600323\pi\)
−0.309982 + 0.950742i \(0.600323\pi\)
\(68\) 306.000 0.545705
\(69\) −552.000 −0.963087
\(70\) 400.000 0.682988
\(71\) 296.000 0.494771 0.247385 0.968917i \(-0.420429\pi\)
0.247385 + 0.968917i \(0.420429\pi\)
\(72\) 405.000 0.662913
\(73\) 394.000 0.631702 0.315851 0.948809i \(-0.397710\pi\)
0.315851 + 0.948809i \(0.397710\pi\)
\(74\) 1270.00 1.99506
\(75\) −75.0000 −0.115470
\(76\) −476.000 −0.718433
\(77\) −704.000 −1.04193
\(78\) −1170.00 −1.69842
\(79\) −960.000 −1.36720 −0.683598 0.729859i \(-0.739586\pi\)
−0.683598 + 0.729859i \(0.739586\pi\)
\(80\) 445.000 0.621906
\(81\) 81.0000 0.111111
\(82\) −390.000 −0.525223
\(83\) −908.000 −1.20079 −0.600397 0.799702i \(-0.704991\pi\)
−0.600397 + 0.799702i \(0.704991\pi\)
\(84\) −816.000 −1.05992
\(85\) 90.0000 0.114846
\(86\) −1300.00 −1.63003
\(87\) −87.0000 −0.107211
\(88\) −1980.00 −2.39851
\(89\) −990.000 −1.17910 −0.589549 0.807732i \(-0.700695\pi\)
−0.589549 + 0.807732i \(0.700695\pi\)
\(90\) 225.000 0.263523
\(91\) 1248.00 1.43765
\(92\) 3128.00 3.54475
\(93\) 672.000 0.749281
\(94\) 1560.00 1.71172
\(95\) −140.000 −0.151197
\(96\) −255.000 −0.271102
\(97\) 1234.00 1.29169 0.645844 0.763469i \(-0.276506\pi\)
0.645844 + 0.763469i \(0.276506\pi\)
\(98\) −435.000 −0.448384
\(99\) −396.000 −0.402015
\(100\) 425.000 0.425000
\(101\) 1022.00 1.00686 0.503430 0.864036i \(-0.332071\pi\)
0.503430 + 0.864036i \(0.332071\pi\)
\(102\) −270.000 −0.262098
\(103\) −1248.00 −1.19387 −0.596937 0.802288i \(-0.703616\pi\)
−0.596937 + 0.802288i \(0.703616\pi\)
\(104\) 3510.00 3.30946
\(105\) −240.000 −0.223063
\(106\) 2870.00 2.62980
\(107\) −116.000 −0.104805 −0.0524025 0.998626i \(-0.516688\pi\)
−0.0524025 + 0.998626i \(0.516688\pi\)
\(108\) −459.000 −0.408956
\(109\) −826.000 −0.725839 −0.362920 0.931820i \(-0.618220\pi\)
−0.362920 + 0.931820i \(0.618220\pi\)
\(110\) −1100.00 −0.953463
\(111\) −762.000 −0.651584
\(112\) 1424.00 1.20139
\(113\) −2206.00 −1.83649 −0.918243 0.396016i \(-0.870392\pi\)
−0.918243 + 0.396016i \(0.870392\pi\)
\(114\) 420.000 0.345058
\(115\) 920.000 0.746004
\(116\) 493.000 0.394603
\(117\) 702.000 0.554700
\(118\) 900.000 0.702133
\(119\) 288.000 0.221856
\(120\) −675.000 −0.513490
\(121\) 605.000 0.454545
\(122\) −3050.00 −2.26339
\(123\) 234.000 0.171537
\(124\) −3808.00 −2.75781
\(125\) 125.000 0.0894427
\(126\) 720.000 0.509069
\(127\) −2056.00 −1.43654 −0.718270 0.695765i \(-0.755066\pi\)
−0.718270 + 0.695765i \(0.755066\pi\)
\(128\) −2115.00 −1.46048
\(129\) 780.000 0.532366
\(130\) 1950.00 1.31559
\(131\) 12.0000 0.00800340 0.00400170 0.999992i \(-0.498726\pi\)
0.00400170 + 0.999992i \(0.498726\pi\)
\(132\) 2244.00 1.47966
\(133\) −448.000 −0.292079
\(134\) −1700.00 −1.09595
\(135\) −135.000 −0.0860663
\(136\) 810.000 0.510713
\(137\) −2758.00 −1.71994 −0.859970 0.510344i \(-0.829518\pi\)
−0.859970 + 0.510344i \(0.829518\pi\)
\(138\) −2760.00 −1.70251
\(139\) −1436.00 −0.876258 −0.438129 0.898912i \(-0.644359\pi\)
−0.438129 + 0.898912i \(0.644359\pi\)
\(140\) 1360.00 0.821007
\(141\) −936.000 −0.559046
\(142\) 1480.00 0.874640
\(143\) −3432.00 −2.00698
\(144\) 801.000 0.463542
\(145\) 145.000 0.0830455
\(146\) 1970.00 1.11670
\(147\) 261.000 0.146442
\(148\) 4318.00 2.39823
\(149\) −498.000 −0.273810 −0.136905 0.990584i \(-0.543716\pi\)
−0.136905 + 0.990584i \(0.543716\pi\)
\(150\) −375.000 −0.204124
\(151\) −2696.00 −1.45296 −0.726481 0.687186i \(-0.758846\pi\)
−0.726481 + 0.687186i \(0.758846\pi\)
\(152\) −1260.00 −0.672365
\(153\) 162.000 0.0856008
\(154\) −3520.00 −1.84188
\(155\) −1120.00 −0.580391
\(156\) −3978.00 −2.04163
\(157\) 534.000 0.271451 0.135726 0.990746i \(-0.456663\pi\)
0.135726 + 0.990746i \(0.456663\pi\)
\(158\) −4800.00 −2.41688
\(159\) −1722.00 −0.858890
\(160\) 425.000 0.209995
\(161\) 2944.00 1.44112
\(162\) 405.000 0.196419
\(163\) 1380.00 0.663128 0.331564 0.943433i \(-0.392424\pi\)
0.331564 + 0.943433i \(0.392424\pi\)
\(164\) −1326.00 −0.631361
\(165\) 660.000 0.311400
\(166\) −4540.00 −2.12272
\(167\) 2616.00 1.21217 0.606084 0.795400i \(-0.292739\pi\)
0.606084 + 0.795400i \(0.292739\pi\)
\(168\) −2160.00 −0.991950
\(169\) 3887.00 1.76923
\(170\) 450.000 0.203020
\(171\) −252.000 −0.112695
\(172\) −4420.00 −1.95943
\(173\) −330.000 −0.145026 −0.0725128 0.997367i \(-0.523102\pi\)
−0.0725128 + 0.997367i \(0.523102\pi\)
\(174\) −435.000 −0.189525
\(175\) 400.000 0.172784
\(176\) −3916.00 −1.67716
\(177\) −540.000 −0.229316
\(178\) −4950.00 −2.08437
\(179\) −372.000 −0.155333 −0.0776664 0.996979i \(-0.524747\pi\)
−0.0776664 + 0.996979i \(0.524747\pi\)
\(180\) 765.000 0.316776
\(181\) −1010.00 −0.414766 −0.207383 0.978260i \(-0.566495\pi\)
−0.207383 + 0.978260i \(0.566495\pi\)
\(182\) 6240.00 2.54143
\(183\) 1830.00 0.739221
\(184\) 8280.00 3.31744
\(185\) 1270.00 0.504715
\(186\) 3360.00 1.32455
\(187\) −792.000 −0.309715
\(188\) 5304.00 2.05763
\(189\) −432.000 −0.166261
\(190\) −700.000 −0.267281
\(191\) 2008.00 0.760700 0.380350 0.924843i \(-0.375803\pi\)
0.380350 + 0.924843i \(0.375803\pi\)
\(192\) 861.000 0.323632
\(193\) 2578.00 0.961495 0.480747 0.876859i \(-0.340365\pi\)
0.480747 + 0.876859i \(0.340365\pi\)
\(194\) 6170.00 2.28340
\(195\) −1170.00 −0.429669
\(196\) −1479.00 −0.538994
\(197\) 526.000 0.190233 0.0951166 0.995466i \(-0.469678\pi\)
0.0951166 + 0.995466i \(0.469678\pi\)
\(198\) −1980.00 −0.710669
\(199\) 4440.00 1.58162 0.790812 0.612059i \(-0.209658\pi\)
0.790812 + 0.612059i \(0.209658\pi\)
\(200\) 1125.00 0.397748
\(201\) 1020.00 0.357937
\(202\) 5110.00 1.77989
\(203\) 464.000 0.160426
\(204\) −918.000 −0.315063
\(205\) −390.000 −0.132872
\(206\) −6240.00 −2.11049
\(207\) 1656.00 0.556038
\(208\) 6942.00 2.31414
\(209\) 1232.00 0.407747
\(210\) −1200.00 −0.394323
\(211\) 308.000 0.100491 0.0502455 0.998737i \(-0.484000\pi\)
0.0502455 + 0.998737i \(0.484000\pi\)
\(212\) 9758.00 3.16124
\(213\) −888.000 −0.285656
\(214\) −580.000 −0.185271
\(215\) −1300.00 −0.412369
\(216\) −1215.00 −0.382733
\(217\) −3584.00 −1.12119
\(218\) −4130.00 −1.28311
\(219\) −1182.00 −0.364713
\(220\) −3740.00 −1.14614
\(221\) 1404.00 0.427345
\(222\) −3810.00 −1.15185
\(223\) 4120.00 1.23720 0.618600 0.785706i \(-0.287700\pi\)
0.618600 + 0.785706i \(0.287700\pi\)
\(224\) 1360.00 0.405664
\(225\) 225.000 0.0666667
\(226\) −11030.0 −3.24648
\(227\) 4932.00 1.44206 0.721032 0.692902i \(-0.243668\pi\)
0.721032 + 0.692902i \(0.243668\pi\)
\(228\) 1428.00 0.414788
\(229\) −3050.00 −0.880130 −0.440065 0.897966i \(-0.645045\pi\)
−0.440065 + 0.897966i \(0.645045\pi\)
\(230\) 4600.00 1.31876
\(231\) 2112.00 0.601556
\(232\) 1305.00 0.369299
\(233\) 82.0000 0.0230558 0.0115279 0.999934i \(-0.496330\pi\)
0.0115279 + 0.999934i \(0.496330\pi\)
\(234\) 3510.00 0.980581
\(235\) 1560.00 0.433035
\(236\) 3060.00 0.844021
\(237\) 2880.00 0.789351
\(238\) 1440.00 0.392190
\(239\) −5104.00 −1.38138 −0.690691 0.723150i \(-0.742694\pi\)
−0.690691 + 0.723150i \(0.742694\pi\)
\(240\) −1335.00 −0.359058
\(241\) −2158.00 −0.576801 −0.288400 0.957510i \(-0.593123\pi\)
−0.288400 + 0.957510i \(0.593123\pi\)
\(242\) 3025.00 0.803530
\(243\) −243.000 −0.0641500
\(244\) −10370.0 −2.72078
\(245\) −435.000 −0.113433
\(246\) 1170.00 0.303238
\(247\) −2184.00 −0.562610
\(248\) −10080.0 −2.58097
\(249\) 2724.00 0.693279
\(250\) 625.000 0.158114
\(251\) 6116.00 1.53800 0.769001 0.639248i \(-0.220754\pi\)
0.769001 + 0.639248i \(0.220754\pi\)
\(252\) 2448.00 0.611942
\(253\) −8096.00 −2.01182
\(254\) −10280.0 −2.53947
\(255\) −270.000 −0.0663061
\(256\) −8279.00 −2.02124
\(257\) 3418.00 0.829607 0.414803 0.909911i \(-0.363850\pi\)
0.414803 + 0.909911i \(0.363850\pi\)
\(258\) 3900.00 0.941098
\(259\) 4064.00 0.974999
\(260\) 6630.00 1.58144
\(261\) 261.000 0.0618984
\(262\) 60.0000 0.0141481
\(263\) 7440.00 1.74437 0.872186 0.489174i \(-0.162702\pi\)
0.872186 + 0.489174i \(0.162702\pi\)
\(264\) 5940.00 1.38478
\(265\) 2870.00 0.665293
\(266\) −2240.00 −0.516328
\(267\) 2970.00 0.680753
\(268\) −5780.00 −1.31742
\(269\) 6582.00 1.49186 0.745932 0.666022i \(-0.232004\pi\)
0.745932 + 0.666022i \(0.232004\pi\)
\(270\) −675.000 −0.152145
\(271\) −5504.00 −1.23374 −0.616871 0.787064i \(-0.711600\pi\)
−0.616871 + 0.787064i \(0.711600\pi\)
\(272\) 1602.00 0.357116
\(273\) −3744.00 −0.830026
\(274\) −13790.0 −3.04045
\(275\) −1100.00 −0.241209
\(276\) −9384.00 −2.04656
\(277\) 3718.00 0.806473 0.403236 0.915096i \(-0.367885\pi\)
0.403236 + 0.915096i \(0.367885\pi\)
\(278\) −7180.00 −1.54902
\(279\) −2016.00 −0.432598
\(280\) 3600.00 0.768361
\(281\) 1754.00 0.372366 0.186183 0.982515i \(-0.440388\pi\)
0.186183 + 0.982515i \(0.440388\pi\)
\(282\) −4680.00 −0.988262
\(283\) 3572.00 0.750295 0.375147 0.926965i \(-0.377592\pi\)
0.375147 + 0.926965i \(0.377592\pi\)
\(284\) 5032.00 1.05139
\(285\) 420.000 0.0872935
\(286\) −17160.0 −3.54787
\(287\) −1248.00 −0.256680
\(288\) 765.000 0.156521
\(289\) −4589.00 −0.934053
\(290\) 725.000 0.146805
\(291\) −3702.00 −0.745756
\(292\) 6698.00 1.34237
\(293\) 126.000 0.0251229 0.0125614 0.999921i \(-0.496001\pi\)
0.0125614 + 0.999921i \(0.496001\pi\)
\(294\) 1305.00 0.258875
\(295\) 900.000 0.177627
\(296\) 11430.0 2.24444
\(297\) 1188.00 0.232104
\(298\) −2490.00 −0.484033
\(299\) 14352.0 2.77591
\(300\) −1275.00 −0.245374
\(301\) −4160.00 −0.796606
\(302\) −13480.0 −2.56850
\(303\) −3066.00 −0.581311
\(304\) −2492.00 −0.470151
\(305\) −3050.00 −0.572598
\(306\) 810.000 0.151322
\(307\) −2412.00 −0.448404 −0.224202 0.974543i \(-0.571978\pi\)
−0.224202 + 0.974543i \(0.571978\pi\)
\(308\) −11968.0 −2.21409
\(309\) 3744.00 0.689284
\(310\) −5600.00 −1.02600
\(311\) −2928.00 −0.533864 −0.266932 0.963715i \(-0.586010\pi\)
−0.266932 + 0.963715i \(0.586010\pi\)
\(312\) −10530.0 −1.91072
\(313\) 2874.00 0.519003 0.259502 0.965743i \(-0.416442\pi\)
0.259502 + 0.965743i \(0.416442\pi\)
\(314\) 2670.00 0.479862
\(315\) 720.000 0.128785
\(316\) −16320.0 −2.90529
\(317\) −26.0000 −0.00460664 −0.00230332 0.999997i \(-0.500733\pi\)
−0.00230332 + 0.999997i \(0.500733\pi\)
\(318\) −8610.00 −1.51832
\(319\) −1276.00 −0.223957
\(320\) −1435.00 −0.250684
\(321\) 348.000 0.0605092
\(322\) 14720.0 2.54756
\(323\) −504.000 −0.0868214
\(324\) 1377.00 0.236111
\(325\) 1950.00 0.332820
\(326\) 6900.00 1.17226
\(327\) 2478.00 0.419063
\(328\) −3510.00 −0.590876
\(329\) 4992.00 0.836528
\(330\) 3300.00 0.550482
\(331\) 9340.00 1.55098 0.775488 0.631363i \(-0.217504\pi\)
0.775488 + 0.631363i \(0.217504\pi\)
\(332\) −15436.0 −2.55169
\(333\) 2286.00 0.376192
\(334\) 13080.0 2.14283
\(335\) −1700.00 −0.277256
\(336\) −4272.00 −0.693621
\(337\) −10302.0 −1.66524 −0.832620 0.553845i \(-0.813160\pi\)
−0.832620 + 0.553845i \(0.813160\pi\)
\(338\) 19435.0 3.12759
\(339\) 6618.00 1.06030
\(340\) 1530.00 0.244047
\(341\) 9856.00 1.56520
\(342\) −1260.00 −0.199219
\(343\) −6880.00 −1.08305
\(344\) −11700.0 −1.83378
\(345\) −2760.00 −0.430706
\(346\) −1650.00 −0.256372
\(347\) −8020.00 −1.24074 −0.620369 0.784310i \(-0.713017\pi\)
−0.620369 + 0.784310i \(0.713017\pi\)
\(348\) −1479.00 −0.227824
\(349\) −1306.00 −0.200311 −0.100156 0.994972i \(-0.531934\pi\)
−0.100156 + 0.994972i \(0.531934\pi\)
\(350\) 2000.00 0.305441
\(351\) −2106.00 −0.320256
\(352\) −3740.00 −0.566314
\(353\) 5658.00 0.853102 0.426551 0.904464i \(-0.359728\pi\)
0.426551 + 0.904464i \(0.359728\pi\)
\(354\) −2700.00 −0.405377
\(355\) 1480.00 0.221268
\(356\) −16830.0 −2.50558
\(357\) −864.000 −0.128089
\(358\) −1860.00 −0.274592
\(359\) −12240.0 −1.79945 −0.899725 0.436457i \(-0.856233\pi\)
−0.899725 + 0.436457i \(0.856233\pi\)
\(360\) 2025.00 0.296464
\(361\) −6075.00 −0.885698
\(362\) −5050.00 −0.733210
\(363\) −1815.00 −0.262432
\(364\) 21216.0 3.05500
\(365\) 1970.00 0.282506
\(366\) 9150.00 1.30677
\(367\) 8984.00 1.27782 0.638911 0.769280i \(-0.279385\pi\)
0.638911 + 0.769280i \(0.279385\pi\)
\(368\) 16376.0 2.31972
\(369\) −702.000 −0.0990370
\(370\) 6350.00 0.892218
\(371\) 9184.00 1.28520
\(372\) 11424.0 1.59222
\(373\) −938.000 −0.130209 −0.0651043 0.997878i \(-0.520738\pi\)
−0.0651043 + 0.997878i \(0.520738\pi\)
\(374\) −3960.00 −0.547505
\(375\) −375.000 −0.0516398
\(376\) 14040.0 1.92569
\(377\) 2262.00 0.309016
\(378\) −2160.00 −0.293911
\(379\) −7796.00 −1.05661 −0.528303 0.849056i \(-0.677171\pi\)
−0.528303 + 0.849056i \(0.677171\pi\)
\(380\) −2380.00 −0.321293
\(381\) 6168.00 0.829386
\(382\) 10040.0 1.34474
\(383\) −6944.00 −0.926428 −0.463214 0.886247i \(-0.653304\pi\)
−0.463214 + 0.886247i \(0.653304\pi\)
\(384\) 6345.00 0.843208
\(385\) −3520.00 −0.465963
\(386\) 12890.0 1.69970
\(387\) −2340.00 −0.307361
\(388\) 20978.0 2.74484
\(389\) 2126.00 0.277101 0.138551 0.990355i \(-0.455756\pi\)
0.138551 + 0.990355i \(0.455756\pi\)
\(390\) −5850.00 −0.759555
\(391\) 3312.00 0.428376
\(392\) −3915.00 −0.504432
\(393\) −36.0000 −0.00462076
\(394\) 2630.00 0.336288
\(395\) −4800.00 −0.611428
\(396\) −6732.00 −0.854282
\(397\) −3346.00 −0.423000 −0.211500 0.977378i \(-0.567835\pi\)
−0.211500 + 0.977378i \(0.567835\pi\)
\(398\) 22200.0 2.79594
\(399\) 1344.00 0.168632
\(400\) 2225.00 0.278125
\(401\) 12850.0 1.60025 0.800123 0.599836i \(-0.204768\pi\)
0.800123 + 0.599836i \(0.204768\pi\)
\(402\) 5100.00 0.632748
\(403\) −17472.0 −2.15966
\(404\) 17374.0 2.13958
\(405\) 405.000 0.0496904
\(406\) 2320.00 0.283595
\(407\) −11176.0 −1.36111
\(408\) −2430.00 −0.294860
\(409\) 6122.00 0.740131 0.370065 0.929006i \(-0.379335\pi\)
0.370065 + 0.929006i \(0.379335\pi\)
\(410\) −1950.00 −0.234887
\(411\) 8274.00 0.993008
\(412\) −21216.0 −2.53698
\(413\) 2880.00 0.343137
\(414\) 8280.00 0.982946
\(415\) −4540.00 −0.537012
\(416\) 6630.00 0.781400
\(417\) 4308.00 0.505908
\(418\) 6160.00 0.720803
\(419\) 1372.00 0.159968 0.0799840 0.996796i \(-0.474513\pi\)
0.0799840 + 0.996796i \(0.474513\pi\)
\(420\) −4080.00 −0.474009
\(421\) 12150.0 1.40654 0.703272 0.710921i \(-0.251722\pi\)
0.703272 + 0.710921i \(0.251722\pi\)
\(422\) 1540.00 0.177645
\(423\) 2808.00 0.322765
\(424\) 25830.0 2.95853
\(425\) 450.000 0.0513605
\(426\) −4440.00 −0.504973
\(427\) −9760.00 −1.10613
\(428\) −1972.00 −0.222711
\(429\) 10296.0 1.15873
\(430\) −6500.00 −0.728972
\(431\) 6288.00 0.702743 0.351372 0.936236i \(-0.385715\pi\)
0.351372 + 0.936236i \(0.385715\pi\)
\(432\) −2403.00 −0.267626
\(433\) 15650.0 1.73693 0.868465 0.495750i \(-0.165107\pi\)
0.868465 + 0.495750i \(0.165107\pi\)
\(434\) −17920.0 −1.98200
\(435\) −435.000 −0.0479463
\(436\) −14042.0 −1.54241
\(437\) −5152.00 −0.563967
\(438\) −5910.00 −0.644728
\(439\) −14520.0 −1.57859 −0.789296 0.614013i \(-0.789554\pi\)
−0.789296 + 0.614013i \(0.789554\pi\)
\(440\) −9900.00 −1.07265
\(441\) −783.000 −0.0845481
\(442\) 7020.00 0.755446
\(443\) 7372.00 0.790642 0.395321 0.918543i \(-0.370633\pi\)
0.395321 + 0.918543i \(0.370633\pi\)
\(444\) −12954.0 −1.38462
\(445\) −4950.00 −0.527309
\(446\) 20600.0 2.18708
\(447\) 1494.00 0.158085
\(448\) −4592.00 −0.484267
\(449\) 10666.0 1.12107 0.560534 0.828131i \(-0.310596\pi\)
0.560534 + 0.828131i \(0.310596\pi\)
\(450\) 1125.00 0.117851
\(451\) 3432.00 0.358329
\(452\) −37502.0 −3.90253
\(453\) 8088.00 0.838868
\(454\) 24660.0 2.54923
\(455\) 6240.00 0.642936
\(456\) 3780.00 0.388190
\(457\) −8006.00 −0.819486 −0.409743 0.912201i \(-0.634382\pi\)
−0.409743 + 0.912201i \(0.634382\pi\)
\(458\) −15250.0 −1.55586
\(459\) −486.000 −0.0494217
\(460\) 15640.0 1.58526
\(461\) 1254.00 0.126691 0.0633456 0.997992i \(-0.479823\pi\)
0.0633456 + 0.997992i \(0.479823\pi\)
\(462\) 10560.0 1.06341
\(463\) −4584.00 −0.460122 −0.230061 0.973176i \(-0.573893\pi\)
−0.230061 + 0.973176i \(0.573893\pi\)
\(464\) 2581.00 0.258233
\(465\) 3360.00 0.335089
\(466\) 410.000 0.0407573
\(467\) 11588.0 1.14824 0.574121 0.818771i \(-0.305344\pi\)
0.574121 + 0.818771i \(0.305344\pi\)
\(468\) 11934.0 1.17874
\(469\) −5440.00 −0.535599
\(470\) 7800.00 0.765505
\(471\) −1602.00 −0.156722
\(472\) 8100.00 0.789900
\(473\) 11440.0 1.11208
\(474\) 14400.0 1.39539
\(475\) −700.000 −0.0676173
\(476\) 4896.00 0.471445
\(477\) 5166.00 0.495880
\(478\) −25520.0 −2.44196
\(479\) −18200.0 −1.73607 −0.868037 0.496500i \(-0.834618\pi\)
−0.868037 + 0.496500i \(0.834618\pi\)
\(480\) −1275.00 −0.121241
\(481\) 19812.0 1.87807
\(482\) −10790.0 −1.01965
\(483\) −8832.00 −0.832029
\(484\) 10285.0 0.965909
\(485\) 6170.00 0.577660
\(486\) −1215.00 −0.113402
\(487\) 3824.00 0.355815 0.177908 0.984047i \(-0.443067\pi\)
0.177908 + 0.984047i \(0.443067\pi\)
\(488\) −27450.0 −2.54632
\(489\) −4140.00 −0.382857
\(490\) −2175.00 −0.200523
\(491\) −3100.00 −0.284931 −0.142465 0.989800i \(-0.545503\pi\)
−0.142465 + 0.989800i \(0.545503\pi\)
\(492\) 3978.00 0.364516
\(493\) 522.000 0.0476870
\(494\) −10920.0 −0.994563
\(495\) −1980.00 −0.179787
\(496\) −19936.0 −1.80474
\(497\) 4736.00 0.427442
\(498\) 13620.0 1.22556
\(499\) 19740.0 1.77091 0.885455 0.464726i \(-0.153847\pi\)
0.885455 + 0.464726i \(0.153847\pi\)
\(500\) 2125.00 0.190066
\(501\) −7848.00 −0.699846
\(502\) 30580.0 2.71883
\(503\) −6720.00 −0.595686 −0.297843 0.954615i \(-0.596267\pi\)
−0.297843 + 0.954615i \(0.596267\pi\)
\(504\) 6480.00 0.572703
\(505\) 5110.00 0.450281
\(506\) −40480.0 −3.55643
\(507\) −11661.0 −1.02147
\(508\) −34952.0 −3.05265
\(509\) 10886.0 0.947964 0.473982 0.880535i \(-0.342816\pi\)
0.473982 + 0.880535i \(0.342816\pi\)
\(510\) −1350.00 −0.117214
\(511\) 6304.00 0.545739
\(512\) −24475.0 −2.11260
\(513\) 756.000 0.0650647
\(514\) 17090.0 1.46655
\(515\) −6240.00 −0.533917
\(516\) 13260.0 1.13128
\(517\) −13728.0 −1.16781
\(518\) 20320.0 1.72357
\(519\) 990.000 0.0837306
\(520\) 17550.0 1.48004
\(521\) 22522.0 1.89387 0.946935 0.321424i \(-0.104161\pi\)
0.946935 + 0.321424i \(0.104161\pi\)
\(522\) 1305.00 0.109422
\(523\) −13212.0 −1.10463 −0.552314 0.833636i \(-0.686255\pi\)
−0.552314 + 0.833636i \(0.686255\pi\)
\(524\) 204.000 0.0170072
\(525\) −1200.00 −0.0997567
\(526\) 37200.0 3.08364
\(527\) −4032.00 −0.333276
\(528\) 11748.0 0.968307
\(529\) 21689.0 1.78261
\(530\) 14350.0 1.17608
\(531\) 1620.00 0.132396
\(532\) −7616.00 −0.620668
\(533\) −6084.00 −0.494423
\(534\) 14850.0 1.20341
\(535\) −580.000 −0.0468703
\(536\) −15300.0 −1.23295
\(537\) 1116.00 0.0896815
\(538\) 32910.0 2.63727
\(539\) 3828.00 0.305907
\(540\) −2295.00 −0.182891
\(541\) −4642.00 −0.368900 −0.184450 0.982842i \(-0.559050\pi\)
−0.184450 + 0.982842i \(0.559050\pi\)
\(542\) −27520.0 −2.18097
\(543\) 3030.00 0.239465
\(544\) 1530.00 0.120585
\(545\) −4130.00 −0.324605
\(546\) −18720.0 −1.46729
\(547\) 4060.00 0.317355 0.158677 0.987330i \(-0.449277\pi\)
0.158677 + 0.987330i \(0.449277\pi\)
\(548\) −46886.0 −3.65487
\(549\) −5490.00 −0.426790
\(550\) −5500.00 −0.426401
\(551\) −812.000 −0.0627811
\(552\) −24840.0 −1.91533
\(553\) −15360.0 −1.18115
\(554\) 18590.0 1.42566
\(555\) −3810.00 −0.291397
\(556\) −24412.0 −1.86205
\(557\) −1386.00 −0.105434 −0.0527170 0.998609i \(-0.516788\pi\)
−0.0527170 + 0.998609i \(0.516788\pi\)
\(558\) −10080.0 −0.764732
\(559\) −20280.0 −1.53444
\(560\) 7120.00 0.537277
\(561\) 2376.00 0.178814
\(562\) 8770.00 0.658256
\(563\) 2452.00 0.183551 0.0917757 0.995780i \(-0.470746\pi\)
0.0917757 + 0.995780i \(0.470746\pi\)
\(564\) −15912.0 −1.18797
\(565\) −11030.0 −0.821302
\(566\) 17860.0 1.32635
\(567\) 1296.00 0.0959910
\(568\) 13320.0 0.983970
\(569\) −20862.0 −1.53705 −0.768524 0.639821i \(-0.779009\pi\)
−0.768524 + 0.639821i \(0.779009\pi\)
\(570\) 2100.00 0.154315
\(571\) −9420.00 −0.690394 −0.345197 0.938530i \(-0.612188\pi\)
−0.345197 + 0.938530i \(0.612188\pi\)
\(572\) −58344.0 −4.26483
\(573\) −6024.00 −0.439191
\(574\) −6240.00 −0.453750
\(575\) 4600.00 0.333623
\(576\) −2583.00 −0.186849
\(577\) 13202.0 0.952524 0.476262 0.879303i \(-0.341991\pi\)
0.476262 + 0.879303i \(0.341991\pi\)
\(578\) −22945.0 −1.65119
\(579\) −7734.00 −0.555119
\(580\) 2465.00 0.176472
\(581\) −14528.0 −1.03739
\(582\) −18510.0 −1.31832
\(583\) −25256.0 −1.79416
\(584\) 17730.0 1.25629
\(585\) 3510.00 0.248069
\(586\) 630.000 0.0444114
\(587\) −8708.00 −0.612296 −0.306148 0.951984i \(-0.599040\pi\)
−0.306148 + 0.951984i \(0.599040\pi\)
\(588\) 4437.00 0.311188
\(589\) 6272.00 0.438766
\(590\) 4500.00 0.314004
\(591\) −1578.00 −0.109831
\(592\) 22606.0 1.56943
\(593\) −4390.00 −0.304006 −0.152003 0.988380i \(-0.548572\pi\)
−0.152003 + 0.988380i \(0.548572\pi\)
\(594\) 5940.00 0.410305
\(595\) 1440.00 0.0992172
\(596\) −8466.00 −0.581847
\(597\) −13320.0 −0.913151
\(598\) 71760.0 4.90716
\(599\) −20256.0 −1.38170 −0.690850 0.722999i \(-0.742763\pi\)
−0.690850 + 0.722999i \(0.742763\pi\)
\(600\) −3375.00 −0.229640
\(601\) 9610.00 0.652246 0.326123 0.945327i \(-0.394258\pi\)
0.326123 + 0.945327i \(0.394258\pi\)
\(602\) −20800.0 −1.40821
\(603\) −3060.00 −0.206655
\(604\) −45832.0 −3.08755
\(605\) 3025.00 0.203279
\(606\) −15330.0 −1.02762
\(607\) 10376.0 0.693820 0.346910 0.937898i \(-0.387231\pi\)
0.346910 + 0.937898i \(0.387231\pi\)
\(608\) −2380.00 −0.158753
\(609\) −1392.00 −0.0926218
\(610\) −15250.0 −1.01222
\(611\) 24336.0 1.61134
\(612\) 2754.00 0.181902
\(613\) 6822.00 0.449491 0.224746 0.974417i \(-0.427845\pi\)
0.224746 + 0.974417i \(0.427845\pi\)
\(614\) −12060.0 −0.792674
\(615\) 1170.00 0.0767137
\(616\) −31680.0 −2.07212
\(617\) −20070.0 −1.30954 −0.654771 0.755827i \(-0.727235\pi\)
−0.654771 + 0.755827i \(0.727235\pi\)
\(618\) 18720.0 1.21849
\(619\) 19228.0 1.24853 0.624264 0.781214i \(-0.285399\pi\)
0.624264 + 0.781214i \(0.285399\pi\)
\(620\) −19040.0 −1.23333
\(621\) −4968.00 −0.321029
\(622\) −14640.0 −0.943747
\(623\) −15840.0 −1.01865
\(624\) −20826.0 −1.33607
\(625\) 625.000 0.0400000
\(626\) 14370.0 0.917477
\(627\) −3696.00 −0.235413
\(628\) 9078.00 0.576834
\(629\) 4572.00 0.289821
\(630\) 3600.00 0.227663
\(631\) 6552.00 0.413361 0.206681 0.978408i \(-0.433734\pi\)
0.206681 + 0.978408i \(0.433734\pi\)
\(632\) −43200.0 −2.71899
\(633\) −924.000 −0.0580185
\(634\) −130.000 −0.00814347
\(635\) −10280.0 −0.642440
\(636\) −29274.0 −1.82514
\(637\) −6786.00 −0.422090
\(638\) −6380.00 −0.395904
\(639\) 2664.00 0.164924
\(640\) −10575.0 −0.653146
\(641\) −14422.0 −0.888666 −0.444333 0.895862i \(-0.646559\pi\)
−0.444333 + 0.895862i \(0.646559\pi\)
\(642\) 1740.00 0.106966
\(643\) −6212.00 −0.380991 −0.190496 0.981688i \(-0.561009\pi\)
−0.190496 + 0.981688i \(0.561009\pi\)
\(644\) 50048.0 3.06237
\(645\) 3900.00 0.238081
\(646\) −2520.00 −0.153480
\(647\) 22024.0 1.33826 0.669129 0.743146i \(-0.266667\pi\)
0.669129 + 0.743146i \(0.266667\pi\)
\(648\) 3645.00 0.220971
\(649\) −7920.00 −0.479025
\(650\) 9750.00 0.588348
\(651\) 10752.0 0.647318
\(652\) 23460.0 1.40915
\(653\) 16630.0 0.996604 0.498302 0.867004i \(-0.333957\pi\)
0.498302 + 0.867004i \(0.333957\pi\)
\(654\) 12390.0 0.740806
\(655\) 60.0000 0.00357923
\(656\) −6942.00 −0.413170
\(657\) 3546.00 0.210567
\(658\) 24960.0 1.47879
\(659\) −24468.0 −1.44634 −0.723170 0.690670i \(-0.757316\pi\)
−0.723170 + 0.690670i \(0.757316\pi\)
\(660\) 11220.0 0.661724
\(661\) −10226.0 −0.601733 −0.300866 0.953666i \(-0.597276\pi\)
−0.300866 + 0.953666i \(0.597276\pi\)
\(662\) 46700.0 2.74176
\(663\) −4212.00 −0.246728
\(664\) −40860.0 −2.38807
\(665\) −2240.00 −0.130622
\(666\) 11430.0 0.665020
\(667\) 5336.00 0.309761
\(668\) 44472.0 2.57586
\(669\) −12360.0 −0.714298
\(670\) −8500.00 −0.490125
\(671\) 26840.0 1.54418
\(672\) −4080.00 −0.234210
\(673\) 13458.0 0.770829 0.385414 0.922744i \(-0.374059\pi\)
0.385414 + 0.922744i \(0.374059\pi\)
\(674\) −51510.0 −2.94376
\(675\) −675.000 −0.0384900
\(676\) 66079.0 3.75962
\(677\) 22174.0 1.25881 0.629406 0.777076i \(-0.283298\pi\)
0.629406 + 0.777076i \(0.283298\pi\)
\(678\) 33090.0 1.87436
\(679\) 19744.0 1.11591
\(680\) 4050.00 0.228398
\(681\) −14796.0 −0.832576
\(682\) 49280.0 2.76690
\(683\) −2404.00 −0.134680 −0.0673400 0.997730i \(-0.521451\pi\)
−0.0673400 + 0.997730i \(0.521451\pi\)
\(684\) −4284.00 −0.239478
\(685\) −13790.0 −0.769181
\(686\) −34400.0 −1.91457
\(687\) 9150.00 0.508143
\(688\) −23140.0 −1.28227
\(689\) 44772.0 2.47558
\(690\) −13800.0 −0.761387
\(691\) −5956.00 −0.327897 −0.163949 0.986469i \(-0.552423\pi\)
−0.163949 + 0.986469i \(0.552423\pi\)
\(692\) −5610.00 −0.308179
\(693\) −6336.00 −0.347308
\(694\) −40100.0 −2.19334
\(695\) −7180.00 −0.391875
\(696\) −3915.00 −0.213215
\(697\) −1404.00 −0.0762988
\(698\) −6530.00 −0.354103
\(699\) −246.000 −0.0133113
\(700\) 6800.00 0.367165
\(701\) −14586.0 −0.785885 −0.392943 0.919563i \(-0.628543\pi\)
−0.392943 + 0.919563i \(0.628543\pi\)
\(702\) −10530.0 −0.566139
\(703\) −7112.00 −0.381556
\(704\) 12628.0 0.676045
\(705\) −4680.00 −0.250013
\(706\) 28290.0 1.50809
\(707\) 16352.0 0.869845
\(708\) −9180.00 −0.487296
\(709\) −4370.00 −0.231479 −0.115740 0.993280i \(-0.536924\pi\)
−0.115740 + 0.993280i \(0.536924\pi\)
\(710\) 7400.00 0.391151
\(711\) −8640.00 −0.455732
\(712\) −44550.0 −2.34492
\(713\) −41216.0 −2.16487
\(714\) −4320.00 −0.226431
\(715\) −17160.0 −0.897549
\(716\) −6324.00 −0.330082
\(717\) 15312.0 0.797541
\(718\) −61200.0 −3.18101
\(719\) 144.000 0.00746912 0.00373456 0.999993i \(-0.498811\pi\)
0.00373456 + 0.999993i \(0.498811\pi\)
\(720\) 4005.00 0.207302
\(721\) −19968.0 −1.03141
\(722\) −30375.0 −1.56571
\(723\) 6474.00 0.333016
\(724\) −17170.0 −0.881378
\(725\) 725.000 0.0371391
\(726\) −9075.00 −0.463919
\(727\) −9632.00 −0.491377 −0.245689 0.969349i \(-0.579014\pi\)
−0.245689 + 0.969349i \(0.579014\pi\)
\(728\) 56160.0 2.85910
\(729\) 729.000 0.0370370
\(730\) 9850.00 0.499404
\(731\) −4680.00 −0.236794
\(732\) 31110.0 1.57085
\(733\) −19306.0 −0.972829 −0.486414 0.873728i \(-0.661695\pi\)
−0.486414 + 0.873728i \(0.661695\pi\)
\(734\) 44920.0 2.25889
\(735\) 1305.00 0.0654907
\(736\) 15640.0 0.783285
\(737\) 14960.0 0.747705
\(738\) −3510.00 −0.175074
\(739\) −36540.0 −1.81887 −0.909435 0.415845i \(-0.863486\pi\)
−0.909435 + 0.415845i \(0.863486\pi\)
\(740\) 21590.0 1.07252
\(741\) 6552.00 0.324823
\(742\) 45920.0 2.27194
\(743\) 5408.00 0.267026 0.133513 0.991047i \(-0.457374\pi\)
0.133513 + 0.991047i \(0.457374\pi\)
\(744\) 30240.0 1.49012
\(745\) −2490.00 −0.122452
\(746\) −4690.00 −0.230178
\(747\) −8172.00 −0.400265
\(748\) −13464.0 −0.658145
\(749\) −1856.00 −0.0905431
\(750\) −1875.00 −0.0912871
\(751\) −13952.0 −0.677917 −0.338959 0.940801i \(-0.610075\pi\)
−0.338959 + 0.940801i \(0.610075\pi\)
\(752\) 27768.0 1.34654
\(753\) −18348.0 −0.887966
\(754\) 11310.0 0.546268
\(755\) −13480.0 −0.649785
\(756\) −7344.00 −0.353305
\(757\) −4274.00 −0.205206 −0.102603 0.994722i \(-0.532717\pi\)
−0.102603 + 0.994722i \(0.532717\pi\)
\(758\) −38980.0 −1.86783
\(759\) 24288.0 1.16153
\(760\) −6300.00 −0.300691
\(761\) −230.000 −0.0109560 −0.00547799 0.999985i \(-0.501744\pi\)
−0.00547799 + 0.999985i \(0.501744\pi\)
\(762\) 30840.0 1.46616
\(763\) −13216.0 −0.627066
\(764\) 34136.0 1.61649
\(765\) 810.000 0.0382818
\(766\) −34720.0 −1.63771
\(767\) 14040.0 0.660958
\(768\) 24837.0 1.16696
\(769\) −7854.00 −0.368300 −0.184150 0.982898i \(-0.558953\pi\)
−0.184150 + 0.982898i \(0.558953\pi\)
\(770\) −17600.0 −0.823714
\(771\) −10254.0 −0.478974
\(772\) 43826.0 2.04318
\(773\) 19550.0 0.909657 0.454828 0.890579i \(-0.349701\pi\)
0.454828 + 0.890579i \(0.349701\pi\)
\(774\) −11700.0 −0.543343
\(775\) −5600.00 −0.259559
\(776\) 55530.0 2.56883
\(777\) −12192.0 −0.562916
\(778\) 10630.0 0.489851
\(779\) 2184.00 0.100449
\(780\) −19890.0 −0.913046
\(781\) −13024.0 −0.596716
\(782\) 16560.0 0.757269
\(783\) −783.000 −0.0357371
\(784\) −7743.00 −0.352724
\(785\) 2670.00 0.121397
\(786\) −180.000 −0.00816843
\(787\) 27228.0 1.23326 0.616629 0.787254i \(-0.288498\pi\)
0.616629 + 0.787254i \(0.288498\pi\)
\(788\) 8942.00 0.404246
\(789\) −22320.0 −1.00711
\(790\) −24000.0 −1.08086
\(791\) −35296.0 −1.58658
\(792\) −17820.0 −0.799503
\(793\) −47580.0 −2.13066
\(794\) −16730.0 −0.747765
\(795\) −8610.00 −0.384107
\(796\) 75480.0 3.36095
\(797\) −3386.00 −0.150487 −0.0752436 0.997165i \(-0.523973\pi\)
−0.0752436 + 0.997165i \(0.523973\pi\)
\(798\) 6720.00 0.298102
\(799\) 5616.00 0.248661
\(800\) 2125.00 0.0939126
\(801\) −8910.00 −0.393033
\(802\) 64250.0 2.82886
\(803\) −17336.0 −0.761861
\(804\) 17340.0 0.760615
\(805\) 14720.0 0.644487
\(806\) −87360.0 −3.81777
\(807\) −19746.0 −0.861329
\(808\) 45990.0 2.00238
\(809\) 26994.0 1.17313 0.586563 0.809904i \(-0.300481\pi\)
0.586563 + 0.809904i \(0.300481\pi\)
\(810\) 2025.00 0.0878410
\(811\) 8356.00 0.361799 0.180899 0.983502i \(-0.442099\pi\)
0.180899 + 0.983502i \(0.442099\pi\)
\(812\) 7888.00 0.340905
\(813\) 16512.0 0.712302
\(814\) −55880.0 −2.40613
\(815\) 6900.00 0.296560
\(816\) −4806.00 −0.206181
\(817\) 7280.00 0.311744
\(818\) 30610.0 1.30838
\(819\) 11232.0 0.479216
\(820\) −6630.00 −0.282353
\(821\) 9838.00 0.418208 0.209104 0.977893i \(-0.432945\pi\)
0.209104 + 0.977893i \(0.432945\pi\)
\(822\) 41370.0 1.75541
\(823\) −29552.0 −1.25166 −0.625831 0.779959i \(-0.715240\pi\)
−0.625831 + 0.779959i \(0.715240\pi\)
\(824\) −56160.0 −2.37430
\(825\) 3300.00 0.139262
\(826\) 14400.0 0.606586
\(827\) 18556.0 0.780236 0.390118 0.920765i \(-0.372434\pi\)
0.390118 + 0.920765i \(0.372434\pi\)
\(828\) 28152.0 1.18158
\(829\) 7966.00 0.333740 0.166870 0.985979i \(-0.446634\pi\)
0.166870 + 0.985979i \(0.446634\pi\)
\(830\) −22700.0 −0.949311
\(831\) −11154.0 −0.465617
\(832\) −22386.0 −0.932806
\(833\) −1566.00 −0.0651365
\(834\) 21540.0 0.894328
\(835\) 13080.0 0.542098
\(836\) 20944.0 0.866463
\(837\) 6048.00 0.249760
\(838\) 6860.00 0.282786
\(839\) −42048.0 −1.73022 −0.865112 0.501578i \(-0.832753\pi\)
−0.865112 + 0.501578i \(0.832753\pi\)
\(840\) −10800.0 −0.443614
\(841\) 841.000 0.0344828
\(842\) 60750.0 2.48644
\(843\) −5262.00 −0.214986
\(844\) 5236.00 0.213543
\(845\) 19435.0 0.791224
\(846\) 14040.0 0.570573
\(847\) 9680.00 0.392690
\(848\) 51086.0 2.06875
\(849\) −10716.0 −0.433183
\(850\) 2250.00 0.0907934
\(851\) 46736.0 1.88260
\(852\) −15096.0 −0.607019
\(853\) 29950.0 1.20219 0.601095 0.799177i \(-0.294731\pi\)
0.601095 + 0.799177i \(0.294731\pi\)
\(854\) −48800.0 −1.95539
\(855\) −1260.00 −0.0503989
\(856\) −5220.00 −0.208430
\(857\) −31454.0 −1.25373 −0.626866 0.779127i \(-0.715663\pi\)
−0.626866 + 0.779127i \(0.715663\pi\)
\(858\) 51480.0 2.04837
\(859\) −22036.0 −0.875272 −0.437636 0.899152i \(-0.644184\pi\)
−0.437636 + 0.899152i \(0.644184\pi\)
\(860\) −22100.0 −0.876283
\(861\) 3744.00 0.148194
\(862\) 31440.0 1.24229
\(863\) 14048.0 0.554113 0.277056 0.960854i \(-0.410641\pi\)
0.277056 + 0.960854i \(0.410641\pi\)
\(864\) −2295.00 −0.0903675
\(865\) −1650.00 −0.0648574
\(866\) 78250.0 3.07049
\(867\) 13767.0 0.539275
\(868\) −60928.0 −2.38252
\(869\) 42240.0 1.64890
\(870\) −2175.00 −0.0847579
\(871\) −26520.0 −1.03168
\(872\) −37170.0 −1.44350
\(873\) 11106.0 0.430563
\(874\) −25760.0 −0.996962
\(875\) 2000.00 0.0772712
\(876\) −20094.0 −0.775015
\(877\) −39922.0 −1.53714 −0.768569 0.639767i \(-0.779031\pi\)
−0.768569 + 0.639767i \(0.779031\pi\)
\(878\) −72600.0 −2.79058
\(879\) −378.000 −0.0145047
\(880\) −19580.0 −0.750047
\(881\) 38730.0 1.48110 0.740549 0.672003i \(-0.234566\pi\)
0.740549 + 0.672003i \(0.234566\pi\)
\(882\) −3915.00 −0.149461
\(883\) −32948.0 −1.25571 −0.627853 0.778332i \(-0.716066\pi\)
−0.627853 + 0.778332i \(0.716066\pi\)
\(884\) 23868.0 0.908108
\(885\) −2700.00 −0.102553
\(886\) 36860.0 1.39767
\(887\) −21680.0 −0.820680 −0.410340 0.911933i \(-0.634590\pi\)
−0.410340 + 0.911933i \(0.634590\pi\)
\(888\) −34290.0 −1.29583
\(889\) −32896.0 −1.24105
\(890\) −24750.0 −0.932159
\(891\) −3564.00 −0.134005
\(892\) 70040.0 2.62905
\(893\) −8736.00 −0.327367
\(894\) 7470.00 0.279457
\(895\) −1860.00 −0.0694670
\(896\) −33840.0 −1.26174
\(897\) −43056.0 −1.60267
\(898\) 53330.0 1.98179
\(899\) −6496.00 −0.240994
\(900\) 3825.00 0.141667
\(901\) 10332.0 0.382030
\(902\) 17160.0 0.633443
\(903\) 12480.0 0.459921
\(904\) −99270.0 −3.65229
\(905\) −5050.00 −0.185489
\(906\) 40440.0 1.48292
\(907\) 2236.00 0.0818580 0.0409290 0.999162i \(-0.486968\pi\)
0.0409290 + 0.999162i \(0.486968\pi\)
\(908\) 83844.0 3.06438
\(909\) 9198.00 0.335620
\(910\) 31200.0 1.13656
\(911\) 35816.0 1.30257 0.651283 0.758835i \(-0.274231\pi\)
0.651283 + 0.758835i \(0.274231\pi\)
\(912\) 7476.00 0.271442
\(913\) 39952.0 1.44821
\(914\) −40030.0 −1.44866
\(915\) 9150.00 0.330590
\(916\) −51850.0 −1.87028
\(917\) 192.000 0.00691428
\(918\) −2430.00 −0.0873660
\(919\) 39704.0 1.42515 0.712576 0.701595i \(-0.247529\pi\)
0.712576 + 0.701595i \(0.247529\pi\)
\(920\) 41400.0 1.48361
\(921\) 7236.00 0.258886
\(922\) 6270.00 0.223960
\(923\) 23088.0 0.823349
\(924\) 35904.0 1.27831
\(925\) 6350.00 0.225715
\(926\) −22920.0 −0.813389
\(927\) −11232.0 −0.397958
\(928\) 2465.00 0.0871957
\(929\) −19534.0 −0.689871 −0.344935 0.938626i \(-0.612099\pi\)
−0.344935 + 0.938626i \(0.612099\pi\)
\(930\) 16800.0 0.592359
\(931\) 2436.00 0.0857537
\(932\) 1394.00 0.0489935
\(933\) 8784.00 0.308226
\(934\) 57940.0 2.02982
\(935\) −3960.00 −0.138509
\(936\) 31590.0 1.10315
\(937\) −8678.00 −0.302559 −0.151280 0.988491i \(-0.548339\pi\)
−0.151280 + 0.988491i \(0.548339\pi\)
\(938\) −27200.0 −0.946814
\(939\) −8622.00 −0.299647
\(940\) 26520.0 0.920199
\(941\) −7050.00 −0.244233 −0.122117 0.992516i \(-0.538968\pi\)
−0.122117 + 0.992516i \(0.538968\pi\)
\(942\) −8010.00 −0.277049
\(943\) −14352.0 −0.495616
\(944\) 16020.0 0.552337
\(945\) −2160.00 −0.0743543
\(946\) 57200.0 1.96589
\(947\) 23396.0 0.802817 0.401409 0.915899i \(-0.368521\pi\)
0.401409 + 0.915899i \(0.368521\pi\)
\(948\) 48960.0 1.67737
\(949\) 30732.0 1.05121
\(950\) −3500.00 −0.119532
\(951\) 78.0000 0.00265965
\(952\) 12960.0 0.441214
\(953\) −36126.0 −1.22795 −0.613975 0.789326i \(-0.710430\pi\)
−0.613975 + 0.789326i \(0.710430\pi\)
\(954\) 25830.0 0.876601
\(955\) 10040.0 0.340196
\(956\) −86768.0 −2.93544
\(957\) 3828.00 0.129302
\(958\) −91000.0 −3.06897
\(959\) −44128.0 −1.48589
\(960\) 4305.00 0.144733
\(961\) 20385.0 0.684267
\(962\) 99060.0 3.31998
\(963\) −1044.00 −0.0349350
\(964\) −36686.0 −1.22570
\(965\) 12890.0 0.429994
\(966\) −44160.0 −1.47083
\(967\) 38624.0 1.28445 0.642225 0.766516i \(-0.278011\pi\)
0.642225 + 0.766516i \(0.278011\pi\)
\(968\) 27225.0 0.903972
\(969\) 1512.00 0.0501264
\(970\) 30850.0 1.02117
\(971\) −7292.00 −0.241000 −0.120500 0.992713i \(-0.538450\pi\)
−0.120500 + 0.992713i \(0.538450\pi\)
\(972\) −4131.00 −0.136319
\(973\) −22976.0 −0.757016
\(974\) 19120.0 0.628998
\(975\) −5850.00 −0.192154
\(976\) −54290.0 −1.78051
\(977\) −26838.0 −0.878837 −0.439418 0.898282i \(-0.644815\pi\)
−0.439418 + 0.898282i \(0.644815\pi\)
\(978\) −20700.0 −0.676803
\(979\) 43560.0 1.42205
\(980\) −7395.00 −0.241046
\(981\) −7434.00 −0.241946
\(982\) −15500.0 −0.503691
\(983\) 20192.0 0.655163 0.327581 0.944823i \(-0.393766\pi\)
0.327581 + 0.944823i \(0.393766\pi\)
\(984\) 10530.0 0.341142
\(985\) 2630.00 0.0850749
\(986\) 2610.00 0.0842995
\(987\) −14976.0 −0.482970
\(988\) −37128.0 −1.19555
\(989\) −47840.0 −1.53814
\(990\) −9900.00 −0.317821
\(991\) 34400.0 1.10268 0.551338 0.834282i \(-0.314117\pi\)
0.551338 + 0.834282i \(0.314117\pi\)
\(992\) −19040.0 −0.609396
\(993\) −28020.0 −0.895456
\(994\) 23680.0 0.755618
\(995\) 22200.0 0.707324
\(996\) 46308.0 1.47322
\(997\) 58430.0 1.85606 0.928032 0.372499i \(-0.121499\pi\)
0.928032 + 0.372499i \(0.121499\pi\)
\(998\) 98700.0 3.13056
\(999\) −6858.00 −0.217195
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 435.4.a.c.1.1 1
3.2 odd 2 1305.4.a.a.1.1 1
5.4 even 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 1.1 even 1 trivial
1305.4.a.a.1.1 1 3.2 odd 2
2175.4.a.a.1.1 1 5.4 even 2