Properties

Label 490.4.a.e.1.1
Level $490$
Weight $4$
Character 490.1
Self dual yes
Analytic conductor $28.911$
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] = [490,4,Mod(1,490)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(490, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("490.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 490.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: \(28.9109359028\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 490.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -2.00000 q^{6} -8.00000 q^{8} -26.0000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -2.00000 q^{6} -8.00000 q^{8} -26.0000 q^{9} -10.0000 q^{10} -2.00000 q^{11} +4.00000 q^{12} +8.00000 q^{13} +5.00000 q^{15} +16.0000 q^{16} +52.0000 q^{17} +52.0000 q^{18} -26.0000 q^{19} +20.0000 q^{20} +4.00000 q^{22} +67.0000 q^{23} -8.00000 q^{24} +25.0000 q^{25} -16.0000 q^{26} -53.0000 q^{27} +69.0000 q^{29} -10.0000 q^{30} +332.000 q^{31} -32.0000 q^{32} -2.00000 q^{33} -104.000 q^{34} -104.000 q^{36} +196.000 q^{37} +52.0000 q^{38} +8.00000 q^{39} -40.0000 q^{40} -353.000 q^{41} -369.000 q^{43} -8.00000 q^{44} -130.000 q^{45} -134.000 q^{46} -88.0000 q^{47} +16.0000 q^{48} -50.0000 q^{50} +52.0000 q^{51} +32.0000 q^{52} +582.000 q^{53} +106.000 q^{54} -10.0000 q^{55} -26.0000 q^{57} -138.000 q^{58} +350.000 q^{59} +20.0000 q^{60} +467.000 q^{61} -664.000 q^{62} +64.0000 q^{64} +40.0000 q^{65} +4.00000 q^{66} +291.000 q^{67} +208.000 q^{68} +67.0000 q^{69} +770.000 q^{71} +208.000 q^{72} -628.000 q^{73} -392.000 q^{74} +25.0000 q^{75} -104.000 q^{76} -16.0000 q^{78} +1170.00 q^{79} +80.0000 q^{80} +649.000 q^{81} +706.000 q^{82} -525.000 q^{83} +260.000 q^{85} +738.000 q^{86} +69.0000 q^{87} +16.0000 q^{88} -89.0000 q^{89} +260.000 q^{90} +268.000 q^{92} +332.000 q^{93} +176.000 q^{94} -130.000 q^{95} -32.0000 q^{96} +290.000 q^{97} +52.0000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 1.00000 0.192450 0.0962250 0.995360i \(-0.469323\pi\)
0.0962250 + 0.995360i \(0.469323\pi\)
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) −2.00000 −0.136083
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −26.0000 −0.962963
\(10\) −10.0000 −0.316228
\(11\) −2.00000 −0.0548202 −0.0274101 0.999624i \(-0.508726\pi\)
−0.0274101 + 0.999624i \(0.508726\pi\)
\(12\) 4.00000 0.0962250
\(13\) 8.00000 0.170677 0.0853385 0.996352i \(-0.472803\pi\)
0.0853385 + 0.996352i \(0.472803\pi\)
\(14\) 0 0
\(15\) 5.00000 0.0860663
\(16\) 16.0000 0.250000
\(17\) 52.0000 0.741874 0.370937 0.928658i \(-0.379037\pi\)
0.370937 + 0.928658i \(0.379037\pi\)
\(18\) 52.0000 0.680918
\(19\) −26.0000 −0.313937 −0.156969 0.987604i \(-0.550172\pi\)
−0.156969 + 0.987604i \(0.550172\pi\)
\(20\) 20.0000 0.223607
\(21\) 0 0
\(22\) 4.00000 0.0387638
\(23\) 67.0000 0.607412 0.303706 0.952766i \(-0.401776\pi\)
0.303706 + 0.952766i \(0.401776\pi\)
\(24\) −8.00000 −0.0680414
\(25\) 25.0000 0.200000
\(26\) −16.0000 −0.120687
\(27\) −53.0000 −0.377772
\(28\) 0 0
\(29\) 69.0000 0.441827 0.220913 0.975293i \(-0.429096\pi\)
0.220913 + 0.975293i \(0.429096\pi\)
\(30\) −10.0000 −0.0608581
\(31\) 332.000 1.92351 0.961757 0.273903i \(-0.0883146\pi\)
0.961757 + 0.273903i \(0.0883146\pi\)
\(32\) −32.0000 −0.176777
\(33\) −2.00000 −0.0105502
\(34\) −104.000 −0.524584
\(35\) 0 0
\(36\) −104.000 −0.481481
\(37\) 196.000 0.870870 0.435435 0.900220i \(-0.356595\pi\)
0.435435 + 0.900220i \(0.356595\pi\)
\(38\) 52.0000 0.221987
\(39\) 8.00000 0.0328468
\(40\) −40.0000 −0.158114
\(41\) −353.000 −1.34462 −0.672309 0.740271i \(-0.734697\pi\)
−0.672309 + 0.740271i \(0.734697\pi\)
\(42\) 0 0
\(43\) −369.000 −1.30865 −0.654325 0.756213i \(-0.727047\pi\)
−0.654325 + 0.756213i \(0.727047\pi\)
\(44\) −8.00000 −0.0274101
\(45\) −130.000 −0.430650
\(46\) −134.000 −0.429505
\(47\) −88.0000 −0.273109 −0.136554 0.990633i \(-0.543603\pi\)
−0.136554 + 0.990633i \(0.543603\pi\)
\(48\) 16.0000 0.0481125
\(49\) 0 0
\(50\) −50.0000 −0.141421
\(51\) 52.0000 0.142774
\(52\) 32.0000 0.0853385
\(53\) 582.000 1.50837 0.754187 0.656659i \(-0.228031\pi\)
0.754187 + 0.656659i \(0.228031\pi\)
\(54\) 106.000 0.267125
\(55\) −10.0000 −0.0245164
\(56\) 0 0
\(57\) −26.0000 −0.0604173
\(58\) −138.000 −0.312419
\(59\) 350.000 0.772307 0.386154 0.922435i \(-0.373803\pi\)
0.386154 + 0.922435i \(0.373803\pi\)
\(60\) 20.0000 0.0430331
\(61\) 467.000 0.980217 0.490108 0.871662i \(-0.336957\pi\)
0.490108 + 0.871662i \(0.336957\pi\)
\(62\) −664.000 −1.36013
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 40.0000 0.0763291
\(66\) 4.00000 0.00746009
\(67\) 291.000 0.530617 0.265308 0.964164i \(-0.414526\pi\)
0.265308 + 0.964164i \(0.414526\pi\)
\(68\) 208.000 0.370937
\(69\) 67.0000 0.116896
\(70\) 0 0
\(71\) 770.000 1.28707 0.643537 0.765415i \(-0.277466\pi\)
0.643537 + 0.765415i \(0.277466\pi\)
\(72\) 208.000 0.340459
\(73\) −628.000 −1.00687 −0.503437 0.864032i \(-0.667931\pi\)
−0.503437 + 0.864032i \(0.667931\pi\)
\(74\) −392.000 −0.615798
\(75\) 25.0000 0.0384900
\(76\) −104.000 −0.156969
\(77\) 0 0
\(78\) −16.0000 −0.0232262
\(79\) 1170.00 1.66627 0.833135 0.553070i \(-0.186544\pi\)
0.833135 + 0.553070i \(0.186544\pi\)
\(80\) 80.0000 0.111803
\(81\) 649.000 0.890261
\(82\) 706.000 0.950789
\(83\) −525.000 −0.694292 −0.347146 0.937811i \(-0.612849\pi\)
−0.347146 + 0.937811i \(0.612849\pi\)
\(84\) 0 0
\(85\) 260.000 0.331776
\(86\) 738.000 0.925356
\(87\) 69.0000 0.0850296
\(88\) 16.0000 0.0193819
\(89\) −89.0000 −0.106000 −0.0529999 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 260.000 0.304516
\(91\) 0 0
\(92\) 268.000 0.303706
\(93\) 332.000 0.370181
\(94\) 176.000 0.193117
\(95\) −130.000 −0.140397
\(96\) −32.0000 −0.0340207
\(97\) 290.000 0.303557 0.151779 0.988415i \(-0.451500\pi\)
0.151779 + 0.988415i \(0.451500\pi\)
\(98\) 0 0
\(99\) 52.0000 0.0527899
\(100\) 100.000 0.100000
\(101\) 1233.00 1.21473 0.607367 0.794422i \(-0.292226\pi\)
0.607367 + 0.794422i \(0.292226\pi\)
\(102\) −104.000 −0.100956
\(103\) −1553.00 −1.48565 −0.742823 0.669487i \(-0.766514\pi\)
−0.742823 + 0.669487i \(0.766514\pi\)
\(104\) −64.0000 −0.0603434
\(105\) 0 0
\(106\) −1164.00 −1.06658
\(107\) 1831.00 1.65429 0.827147 0.561986i \(-0.189962\pi\)
0.827147 + 0.561986i \(0.189962\pi\)
\(108\) −212.000 −0.188886
\(109\) 811.000 0.712658 0.356329 0.934361i \(-0.384028\pi\)
0.356329 + 0.934361i \(0.384028\pi\)
\(110\) 20.0000 0.0173357
\(111\) 196.000 0.167599
\(112\) 0 0
\(113\) 2170.00 1.80652 0.903259 0.429097i \(-0.141168\pi\)
0.903259 + 0.429097i \(0.141168\pi\)
\(114\) 52.0000 0.0427215
\(115\) 335.000 0.271643
\(116\) 276.000 0.220913
\(117\) −208.000 −0.164356
\(118\) −700.000 −0.546104
\(119\) 0 0
\(120\) −40.0000 −0.0304290
\(121\) −1327.00 −0.996995
\(122\) −934.000 −0.693118
\(123\) −353.000 −0.258772
\(124\) 1328.00 0.961757
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 48.0000 0.0335379 0.0167689 0.999859i \(-0.494662\pi\)
0.0167689 + 0.999859i \(0.494662\pi\)
\(128\) −128.000 −0.0883883
\(129\) −369.000 −0.251850
\(130\) −80.0000 −0.0539728
\(131\) 792.000 0.528224 0.264112 0.964492i \(-0.414921\pi\)
0.264112 + 0.964492i \(0.414921\pi\)
\(132\) −8.00000 −0.00527508
\(133\) 0 0
\(134\) −582.000 −0.375203
\(135\) −265.000 −0.168945
\(136\) −416.000 −0.262292
\(137\) 1084.00 0.676003 0.338001 0.941146i \(-0.390249\pi\)
0.338001 + 0.941146i \(0.390249\pi\)
\(138\) −134.000 −0.0826582
\(139\) 46.0000 0.0280696 0.0140348 0.999902i \(-0.495532\pi\)
0.0140348 + 0.999902i \(0.495532\pi\)
\(140\) 0 0
\(141\) −88.0000 −0.0525598
\(142\) −1540.00 −0.910098
\(143\) −16.0000 −0.00935655
\(144\) −416.000 −0.240741
\(145\) 345.000 0.197591
\(146\) 1256.00 0.711968
\(147\) 0 0
\(148\) 784.000 0.435435
\(149\) −369.000 −0.202884 −0.101442 0.994841i \(-0.532346\pi\)
−0.101442 + 0.994841i \(0.532346\pi\)
\(150\) −50.0000 −0.0272166
\(151\) 2480.00 1.33655 0.668277 0.743913i \(-0.267032\pi\)
0.668277 + 0.743913i \(0.267032\pi\)
\(152\) 208.000 0.110994
\(153\) −1352.00 −0.714397
\(154\) 0 0
\(155\) 1660.00 0.860222
\(156\) 32.0000 0.0164234
\(157\) −1226.00 −0.623219 −0.311610 0.950210i \(-0.600868\pi\)
−0.311610 + 0.950210i \(0.600868\pi\)
\(158\) −2340.00 −1.17823
\(159\) 582.000 0.290287
\(160\) −160.000 −0.0790569
\(161\) 0 0
\(162\) −1298.00 −0.629509
\(163\) −660.000 −0.317148 −0.158574 0.987347i \(-0.550690\pi\)
−0.158574 + 0.987347i \(0.550690\pi\)
\(164\) −1412.00 −0.672309
\(165\) −10.0000 −0.00471818
\(166\) 1050.00 0.490939
\(167\) 949.000 0.439735 0.219868 0.975530i \(-0.429437\pi\)
0.219868 + 0.975530i \(0.429437\pi\)
\(168\) 0 0
\(169\) −2133.00 −0.970869
\(170\) −520.000 −0.234601
\(171\) 676.000 0.302310
\(172\) −1476.00 −0.654325
\(173\) −3392.00 −1.49069 −0.745344 0.666680i \(-0.767715\pi\)
−0.745344 + 0.666680i \(0.767715\pi\)
\(174\) −138.000 −0.0601250
\(175\) 0 0
\(176\) −32.0000 −0.0137051
\(177\) 350.000 0.148631
\(178\) 178.000 0.0749532
\(179\) 268.000 0.111906 0.0559532 0.998433i \(-0.482180\pi\)
0.0559532 + 0.998433i \(0.482180\pi\)
\(180\) −520.000 −0.215325
\(181\) 4093.00 1.68083 0.840415 0.541943i \(-0.182311\pi\)
0.840415 + 0.541943i \(0.182311\pi\)
\(182\) 0 0
\(183\) 467.000 0.188643
\(184\) −536.000 −0.214752
\(185\) 980.000 0.389465
\(186\) −664.000 −0.261757
\(187\) −104.000 −0.0406697
\(188\) −352.000 −0.136554
\(189\) 0 0
\(190\) 260.000 0.0992757
\(191\) −1978.00 −0.749335 −0.374668 0.927159i \(-0.622243\pi\)
−0.374668 + 0.927159i \(0.622243\pi\)
\(192\) 64.0000 0.0240563
\(193\) −3998.00 −1.49110 −0.745550 0.666450i \(-0.767813\pi\)
−0.745550 + 0.666450i \(0.767813\pi\)
\(194\) −580.000 −0.214647
\(195\) 40.0000 0.0146895
\(196\) 0 0
\(197\) −3030.00 −1.09583 −0.547915 0.836534i \(-0.684578\pi\)
−0.547915 + 0.836534i \(0.684578\pi\)
\(198\) −104.000 −0.0373281
\(199\) −356.000 −0.126815 −0.0634075 0.997988i \(-0.520197\pi\)
−0.0634075 + 0.997988i \(0.520197\pi\)
\(200\) −200.000 −0.0707107
\(201\) 291.000 0.102117
\(202\) −2466.00 −0.858946
\(203\) 0 0
\(204\) 208.000 0.0713868
\(205\) −1765.00 −0.601331
\(206\) 3106.00 1.05051
\(207\) −1742.00 −0.584915
\(208\) 128.000 0.0426692
\(209\) 52.0000 0.0172101
\(210\) 0 0
\(211\) −2602.00 −0.848953 −0.424476 0.905439i \(-0.639542\pi\)
−0.424476 + 0.905439i \(0.639542\pi\)
\(212\) 2328.00 0.754187
\(213\) 770.000 0.247697
\(214\) −3662.00 −1.16976
\(215\) −1845.00 −0.585246
\(216\) 424.000 0.133563
\(217\) 0 0
\(218\) −1622.00 −0.503925
\(219\) −628.000 −0.193773
\(220\) −40.0000 −0.0122582
\(221\) 416.000 0.126621
\(222\) −392.000 −0.118510
\(223\) 3156.00 0.947719 0.473860 0.880600i \(-0.342860\pi\)
0.473860 + 0.880600i \(0.342860\pi\)
\(224\) 0 0
\(225\) −650.000 −0.192593
\(226\) −4340.00 −1.27740
\(227\) −4236.00 −1.23856 −0.619280 0.785170i \(-0.712575\pi\)
−0.619280 + 0.785170i \(0.712575\pi\)
\(228\) −104.000 −0.0302086
\(229\) −6334.00 −1.82778 −0.913892 0.405958i \(-0.866938\pi\)
−0.913892 + 0.405958i \(0.866938\pi\)
\(230\) −670.000 −0.192080
\(231\) 0 0
\(232\) −552.000 −0.156209
\(233\) −4688.00 −1.31812 −0.659058 0.752092i \(-0.729045\pi\)
−0.659058 + 0.752092i \(0.729045\pi\)
\(234\) 416.000 0.116217
\(235\) −440.000 −0.122138
\(236\) 1400.00 0.386154
\(237\) 1170.00 0.320674
\(238\) 0 0
\(239\) 1856.00 0.502321 0.251160 0.967945i \(-0.419188\pi\)
0.251160 + 0.967945i \(0.419188\pi\)
\(240\) 80.0000 0.0215166
\(241\) 4806.00 1.28457 0.642286 0.766465i \(-0.277986\pi\)
0.642286 + 0.766465i \(0.277986\pi\)
\(242\) 2654.00 0.704982
\(243\) 2080.00 0.549103
\(244\) 1868.00 0.490108
\(245\) 0 0
\(246\) 706.000 0.182979
\(247\) −208.000 −0.0535819
\(248\) −2656.00 −0.680065
\(249\) −525.000 −0.133617
\(250\) −250.000 −0.0632456
\(251\) 3200.00 0.804710 0.402355 0.915484i \(-0.368192\pi\)
0.402355 + 0.915484i \(0.368192\pi\)
\(252\) 0 0
\(253\) −134.000 −0.0332984
\(254\) −96.0000 −0.0237149
\(255\) 260.000 0.0638503
\(256\) 256.000 0.0625000
\(257\) 1120.00 0.271843 0.135922 0.990720i \(-0.456600\pi\)
0.135922 + 0.990720i \(0.456600\pi\)
\(258\) 738.000 0.178085
\(259\) 0 0
\(260\) 160.000 0.0381645
\(261\) −1794.00 −0.425463
\(262\) −1584.00 −0.373511
\(263\) 6405.00 1.50171 0.750854 0.660468i \(-0.229642\pi\)
0.750854 + 0.660468i \(0.229642\pi\)
\(264\) 16.0000 0.00373005
\(265\) 2910.00 0.674566
\(266\) 0 0
\(267\) −89.0000 −0.0203997
\(268\) 1164.00 0.265308
\(269\) −4935.00 −1.11856 −0.559279 0.828979i \(-0.688922\pi\)
−0.559279 + 0.828979i \(0.688922\pi\)
\(270\) 530.000 0.119462
\(271\) 1446.00 0.324126 0.162063 0.986780i \(-0.448185\pi\)
0.162063 + 0.986780i \(0.448185\pi\)
\(272\) 832.000 0.185468
\(273\) 0 0
\(274\) −2168.00 −0.478006
\(275\) −50.0000 −0.0109640
\(276\) 268.000 0.0584482
\(277\) −8020.00 −1.73962 −0.869811 0.493386i \(-0.835759\pi\)
−0.869811 + 0.493386i \(0.835759\pi\)
\(278\) −92.0000 −0.0198482
\(279\) −8632.00 −1.85227
\(280\) 0 0
\(281\) 4978.00 1.05681 0.528403 0.848994i \(-0.322791\pi\)
0.528403 + 0.848994i \(0.322791\pi\)
\(282\) 176.000 0.0371654
\(283\) −5852.00 −1.22921 −0.614603 0.788837i \(-0.710684\pi\)
−0.614603 + 0.788837i \(0.710684\pi\)
\(284\) 3080.00 0.643537
\(285\) −130.000 −0.0270194
\(286\) 32.0000 0.00661608
\(287\) 0 0
\(288\) 832.000 0.170229
\(289\) −2209.00 −0.449623
\(290\) −690.000 −0.139718
\(291\) 290.000 0.0584196
\(292\) −2512.00 −0.503437
\(293\) 3012.00 0.600556 0.300278 0.953852i \(-0.402921\pi\)
0.300278 + 0.953852i \(0.402921\pi\)
\(294\) 0 0
\(295\) 1750.00 0.345386
\(296\) −1568.00 −0.307899
\(297\) 106.000 0.0207096
\(298\) 738.000 0.143460
\(299\) 536.000 0.103671
\(300\) 100.000 0.0192450
\(301\) 0 0
\(302\) −4960.00 −0.945086
\(303\) 1233.00 0.233776
\(304\) −416.000 −0.0784843
\(305\) 2335.00 0.438366
\(306\) 2704.00 0.505155
\(307\) −9443.00 −1.75551 −0.877753 0.479113i \(-0.840958\pi\)
−0.877753 + 0.479113i \(0.840958\pi\)
\(308\) 0 0
\(309\) −1553.00 −0.285913
\(310\) −3320.00 −0.608269
\(311\) 9994.00 1.82221 0.911106 0.412173i \(-0.135230\pi\)
0.911106 + 0.412173i \(0.135230\pi\)
\(312\) −64.0000 −0.0116131
\(313\) −1456.00 −0.262933 −0.131466 0.991321i \(-0.541969\pi\)
−0.131466 + 0.991321i \(0.541969\pi\)
\(314\) 2452.00 0.440683
\(315\) 0 0
\(316\) 4680.00 0.833135
\(317\) 6872.00 1.21757 0.608785 0.793335i \(-0.291657\pi\)
0.608785 + 0.793335i \(0.291657\pi\)
\(318\) −1164.00 −0.205264
\(319\) −138.000 −0.0242211
\(320\) 320.000 0.0559017
\(321\) 1831.00 0.318369
\(322\) 0 0
\(323\) −1352.00 −0.232902
\(324\) 2596.00 0.445130
\(325\) 200.000 0.0341354
\(326\) 1320.00 0.224258
\(327\) 811.000 0.137151
\(328\) 2824.00 0.475394
\(329\) 0 0
\(330\) 20.0000 0.00333625
\(331\) −392.000 −0.0650945 −0.0325472 0.999470i \(-0.510362\pi\)
−0.0325472 + 0.999470i \(0.510362\pi\)
\(332\) −2100.00 −0.347146
\(333\) −5096.00 −0.838616
\(334\) −1898.00 −0.310940
\(335\) 1455.00 0.237299
\(336\) 0 0
\(337\) 3926.00 0.634608 0.317304 0.948324i \(-0.397222\pi\)
0.317304 + 0.948324i \(0.397222\pi\)
\(338\) 4266.00 0.686508
\(339\) 2170.00 0.347664
\(340\) 1040.00 0.165888
\(341\) −664.000 −0.105448
\(342\) −1352.00 −0.213765
\(343\) 0 0
\(344\) 2952.00 0.462678
\(345\) 335.000 0.0522777
\(346\) 6784.00 1.05408
\(347\) −1785.00 −0.276149 −0.138075 0.990422i \(-0.544091\pi\)
−0.138075 + 0.990422i \(0.544091\pi\)
\(348\) 276.000 0.0425148
\(349\) 1591.00 0.244024 0.122012 0.992529i \(-0.461065\pi\)
0.122012 + 0.992529i \(0.461065\pi\)
\(350\) 0 0
\(351\) −424.000 −0.0644771
\(352\) 64.0000 0.00969094
\(353\) −1686.00 −0.254212 −0.127106 0.991889i \(-0.540569\pi\)
−0.127106 + 0.991889i \(0.540569\pi\)
\(354\) −700.000 −0.105098
\(355\) 3850.00 0.575597
\(356\) −356.000 −0.0529999
\(357\) 0 0
\(358\) −536.000 −0.0791298
\(359\) 7372.00 1.08379 0.541893 0.840447i \(-0.317708\pi\)
0.541893 + 0.840447i \(0.317708\pi\)
\(360\) 1040.00 0.152258
\(361\) −6183.00 −0.901443
\(362\) −8186.00 −1.18853
\(363\) −1327.00 −0.191872
\(364\) 0 0
\(365\) −3140.00 −0.450288
\(366\) −934.000 −0.133391
\(367\) −6637.00 −0.944002 −0.472001 0.881598i \(-0.656468\pi\)
−0.472001 + 0.881598i \(0.656468\pi\)
\(368\) 1072.00 0.151853
\(369\) 9178.00 1.29482
\(370\) −1960.00 −0.275393
\(371\) 0 0
\(372\) 1328.00 0.185090
\(373\) 3476.00 0.482521 0.241261 0.970460i \(-0.422439\pi\)
0.241261 + 0.970460i \(0.422439\pi\)
\(374\) 208.000 0.0287578
\(375\) 125.000 0.0172133
\(376\) 704.000 0.0965586
\(377\) 552.000 0.0754097
\(378\) 0 0
\(379\) −2378.00 −0.322295 −0.161147 0.986930i \(-0.551519\pi\)
−0.161147 + 0.986930i \(0.551519\pi\)
\(380\) −520.000 −0.0701985
\(381\) 48.0000 0.00645437
\(382\) 3956.00 0.529860
\(383\) 2457.00 0.327799 0.163899 0.986477i \(-0.447593\pi\)
0.163899 + 0.986477i \(0.447593\pi\)
\(384\) −128.000 −0.0170103
\(385\) 0 0
\(386\) 7996.00 1.05437
\(387\) 9594.00 1.26018
\(388\) 1160.00 0.151779
\(389\) 8562.00 1.11597 0.557983 0.829853i \(-0.311575\pi\)
0.557983 + 0.829853i \(0.311575\pi\)
\(390\) −80.0000 −0.0103871
\(391\) 3484.00 0.450623
\(392\) 0 0
\(393\) 792.000 0.101657
\(394\) 6060.00 0.774869
\(395\) 5850.00 0.745178
\(396\) 208.000 0.0263949
\(397\) 9842.00 1.24422 0.622111 0.782929i \(-0.286275\pi\)
0.622111 + 0.782929i \(0.286275\pi\)
\(398\) 712.000 0.0896717
\(399\) 0 0
\(400\) 400.000 0.0500000
\(401\) −8097.00 −1.00834 −0.504171 0.863604i \(-0.668202\pi\)
−0.504171 + 0.863604i \(0.668202\pi\)
\(402\) −582.000 −0.0722078
\(403\) 2656.00 0.328300
\(404\) 4932.00 0.607367
\(405\) 3245.00 0.398137
\(406\) 0 0
\(407\) −392.000 −0.0477413
\(408\) −416.000 −0.0504781
\(409\) −15259.0 −1.84477 −0.922383 0.386277i \(-0.873761\pi\)
−0.922383 + 0.386277i \(0.873761\pi\)
\(410\) 3530.00 0.425206
\(411\) 1084.00 0.130097
\(412\) −6212.00 −0.742823
\(413\) 0 0
\(414\) 3484.00 0.413597
\(415\) −2625.00 −0.310497
\(416\) −256.000 −0.0301717
\(417\) 46.0000 0.00540199
\(418\) −104.000 −0.0121694
\(419\) −16224.0 −1.89163 −0.945817 0.324701i \(-0.894736\pi\)
−0.945817 + 0.324701i \(0.894736\pi\)
\(420\) 0 0
\(421\) 2977.00 0.344632 0.172316 0.985042i \(-0.444875\pi\)
0.172316 + 0.985042i \(0.444875\pi\)
\(422\) 5204.00 0.600300
\(423\) 2288.00 0.262994
\(424\) −4656.00 −0.533291
\(425\) 1300.00 0.148375
\(426\) −1540.00 −0.175148
\(427\) 0 0
\(428\) 7324.00 0.827147
\(429\) −16.0000 −0.00180067
\(430\) 3690.00 0.413832
\(431\) 14202.0 1.58721 0.793604 0.608435i \(-0.208202\pi\)
0.793604 + 0.608435i \(0.208202\pi\)
\(432\) −848.000 −0.0944431
\(433\) −14310.0 −1.58821 −0.794105 0.607781i \(-0.792060\pi\)
−0.794105 + 0.607781i \(0.792060\pi\)
\(434\) 0 0
\(435\) 345.000 0.0380264
\(436\) 3244.00 0.356329
\(437\) −1742.00 −0.190689
\(438\) 1256.00 0.137018
\(439\) 2356.00 0.256141 0.128070 0.991765i \(-0.459122\pi\)
0.128070 + 0.991765i \(0.459122\pi\)
\(440\) 80.0000 0.00866784
\(441\) 0 0
\(442\) −832.000 −0.0895344
\(443\) 8291.00 0.889204 0.444602 0.895728i \(-0.353345\pi\)
0.444602 + 0.895728i \(0.353345\pi\)
\(444\) 784.000 0.0837995
\(445\) −445.000 −0.0474045
\(446\) −6312.00 −0.670139
\(447\) −369.000 −0.0390450
\(448\) 0 0
\(449\) −3521.00 −0.370081 −0.185040 0.982731i \(-0.559242\pi\)
−0.185040 + 0.982731i \(0.559242\pi\)
\(450\) 1300.00 0.136184
\(451\) 706.000 0.0737123
\(452\) 8680.00 0.903259
\(453\) 2480.00 0.257220
\(454\) 8472.00 0.875794
\(455\) 0 0
\(456\) 208.000 0.0213607
\(457\) −5432.00 −0.556014 −0.278007 0.960579i \(-0.589674\pi\)
−0.278007 + 0.960579i \(0.589674\pi\)
\(458\) 12668.0 1.29244
\(459\) −2756.00 −0.280259
\(460\) 1340.00 0.135821
\(461\) 5350.00 0.540508 0.270254 0.962789i \(-0.412892\pi\)
0.270254 + 0.962789i \(0.412892\pi\)
\(462\) 0 0
\(463\) −10123.0 −1.01610 −0.508052 0.861327i \(-0.669634\pi\)
−0.508052 + 0.861327i \(0.669634\pi\)
\(464\) 1104.00 0.110457
\(465\) 1660.00 0.165550
\(466\) 9376.00 0.932049
\(467\) −6463.00 −0.640411 −0.320206 0.947348i \(-0.603752\pi\)
−0.320206 + 0.947348i \(0.603752\pi\)
\(468\) −832.000 −0.0821778
\(469\) 0 0
\(470\) 880.000 0.0863646
\(471\) −1226.00 −0.119939
\(472\) −2800.00 −0.273052
\(473\) 738.000 0.0717405
\(474\) −2340.00 −0.226751
\(475\) −650.000 −0.0627875
\(476\) 0 0
\(477\) −15132.0 −1.45251
\(478\) −3712.00 −0.355194
\(479\) 17640.0 1.68266 0.841328 0.540525i \(-0.181774\pi\)
0.841328 + 0.540525i \(0.181774\pi\)
\(480\) −160.000 −0.0152145
\(481\) 1568.00 0.148638
\(482\) −9612.00 −0.908329
\(483\) 0 0
\(484\) −5308.00 −0.498497
\(485\) 1450.00 0.135755
\(486\) −4160.00 −0.388275
\(487\) −10032.0 −0.933456 −0.466728 0.884401i \(-0.654567\pi\)
−0.466728 + 0.884401i \(0.654567\pi\)
\(488\) −3736.00 −0.346559
\(489\) −660.000 −0.0610352
\(490\) 0 0
\(491\) 5916.00 0.543758 0.271879 0.962331i \(-0.412355\pi\)
0.271879 + 0.962331i \(0.412355\pi\)
\(492\) −1412.00 −0.129386
\(493\) 3588.00 0.327780
\(494\) 416.000 0.0378881
\(495\) 260.000 0.0236083
\(496\) 5312.00 0.480879
\(497\) 0 0
\(498\) 1050.00 0.0944812
\(499\) 13894.0 1.24645 0.623227 0.782041i \(-0.285821\pi\)
0.623227 + 0.782041i \(0.285821\pi\)
\(500\) 500.000 0.0447214
\(501\) 949.000 0.0846271
\(502\) −6400.00 −0.569016
\(503\) −18427.0 −1.63344 −0.816719 0.577036i \(-0.804209\pi\)
−0.816719 + 0.577036i \(0.804209\pi\)
\(504\) 0 0
\(505\) 6165.00 0.543245
\(506\) 268.000 0.0235456
\(507\) −2133.00 −0.186844
\(508\) 192.000 0.0167689
\(509\) −18557.0 −1.61596 −0.807981 0.589209i \(-0.799440\pi\)
−0.807981 + 0.589209i \(0.799440\pi\)
\(510\) −520.000 −0.0451490
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 1378.00 0.118597
\(514\) −2240.00 −0.192222
\(515\) −7765.00 −0.664402
\(516\) −1476.00 −0.125925
\(517\) 176.000 0.0149719
\(518\) 0 0
\(519\) −3392.00 −0.286883
\(520\) −320.000 −0.0269864
\(521\) 9930.00 0.835012 0.417506 0.908674i \(-0.362904\pi\)
0.417506 + 0.908674i \(0.362904\pi\)
\(522\) 3588.00 0.300848
\(523\) 7924.00 0.662509 0.331255 0.943541i \(-0.392528\pi\)
0.331255 + 0.943541i \(0.392528\pi\)
\(524\) 3168.00 0.264112
\(525\) 0 0
\(526\) −12810.0 −1.06187
\(527\) 17264.0 1.42701
\(528\) −32.0000 −0.00263754
\(529\) −7678.00 −0.631051
\(530\) −5820.00 −0.476990
\(531\) −9100.00 −0.743703
\(532\) 0 0
\(533\) −2824.00 −0.229495
\(534\) 178.000 0.0144247
\(535\) 9155.00 0.739823
\(536\) −2328.00 −0.187601
\(537\) 268.000 0.0215364
\(538\) 9870.00 0.790940
\(539\) 0 0
\(540\) −1060.00 −0.0844725
\(541\) −23497.0 −1.86731 −0.933655 0.358173i \(-0.883400\pi\)
−0.933655 + 0.358173i \(0.883400\pi\)
\(542\) −2892.00 −0.229192
\(543\) 4093.00 0.323476
\(544\) −1664.00 −0.131146
\(545\) 4055.00 0.318710
\(546\) 0 0
\(547\) 11131.0 0.870068 0.435034 0.900414i \(-0.356736\pi\)
0.435034 + 0.900414i \(0.356736\pi\)
\(548\) 4336.00 0.338001
\(549\) −12142.0 −0.943912
\(550\) 100.000 0.00775275
\(551\) −1794.00 −0.138706
\(552\) −536.000 −0.0413291
\(553\) 0 0
\(554\) 16040.0 1.23010
\(555\) 980.000 0.0749526
\(556\) 184.000 0.0140348
\(557\) −11978.0 −0.911174 −0.455587 0.890191i \(-0.650571\pi\)
−0.455587 + 0.890191i \(0.650571\pi\)
\(558\) 17264.0 1.30976
\(559\) −2952.00 −0.223357
\(560\) 0 0
\(561\) −104.000 −0.00782689
\(562\) −9956.00 −0.747275
\(563\) 10059.0 0.752995 0.376498 0.926418i \(-0.377128\pi\)
0.376498 + 0.926418i \(0.377128\pi\)
\(564\) −352.000 −0.0262799
\(565\) 10850.0 0.807899
\(566\) 11704.0 0.869180
\(567\) 0 0
\(568\) −6160.00 −0.455049
\(569\) −15666.0 −1.15422 −0.577111 0.816665i \(-0.695820\pi\)
−0.577111 + 0.816665i \(0.695820\pi\)
\(570\) 260.000 0.0191056
\(571\) 2530.00 0.185424 0.0927121 0.995693i \(-0.470446\pi\)
0.0927121 + 0.995693i \(0.470446\pi\)
\(572\) −64.0000 −0.00467828
\(573\) −1978.00 −0.144210
\(574\) 0 0
\(575\) 1675.00 0.121482
\(576\) −1664.00 −0.120370
\(577\) −12818.0 −0.924819 −0.462409 0.886667i \(-0.653015\pi\)
−0.462409 + 0.886667i \(0.653015\pi\)
\(578\) 4418.00 0.317932
\(579\) −3998.00 −0.286962
\(580\) 1380.00 0.0987955
\(581\) 0 0
\(582\) −580.000 −0.0413089
\(583\) −1164.00 −0.0826895
\(584\) 5024.00 0.355984
\(585\) −1040.00 −0.0735021
\(586\) −6024.00 −0.424657
\(587\) 15228.0 1.07074 0.535372 0.844616i \(-0.320171\pi\)
0.535372 + 0.844616i \(0.320171\pi\)
\(588\) 0 0
\(589\) −8632.00 −0.603863
\(590\) −3500.00 −0.244225
\(591\) −3030.00 −0.210893
\(592\) 3136.00 0.217718
\(593\) 2598.00 0.179911 0.0899554 0.995946i \(-0.471328\pi\)
0.0899554 + 0.995946i \(0.471328\pi\)
\(594\) −212.000 −0.0146439
\(595\) 0 0
\(596\) −1476.00 −0.101442
\(597\) −356.000 −0.0244055
\(598\) −1072.00 −0.0733066
\(599\) −2548.00 −0.173804 −0.0869019 0.996217i \(-0.527697\pi\)
−0.0869019 + 0.996217i \(0.527697\pi\)
\(600\) −200.000 −0.0136083
\(601\) −1706.00 −0.115789 −0.0578945 0.998323i \(-0.518439\pi\)
−0.0578945 + 0.998323i \(0.518439\pi\)
\(602\) 0 0
\(603\) −7566.00 −0.510964
\(604\) 9920.00 0.668277
\(605\) −6635.00 −0.445870
\(606\) −2466.00 −0.165304
\(607\) 12567.0 0.840328 0.420164 0.907448i \(-0.361973\pi\)
0.420164 + 0.907448i \(0.361973\pi\)
\(608\) 832.000 0.0554968
\(609\) 0 0
\(610\) −4670.00 −0.309972
\(611\) −704.000 −0.0466134
\(612\) −5408.00 −0.357198
\(613\) −9628.00 −0.634374 −0.317187 0.948363i \(-0.602738\pi\)
−0.317187 + 0.948363i \(0.602738\pi\)
\(614\) 18886.0 1.24133
\(615\) −1765.00 −0.115726
\(616\) 0 0
\(617\) −4316.00 −0.281614 −0.140807 0.990037i \(-0.544970\pi\)
−0.140807 + 0.990037i \(0.544970\pi\)
\(618\) 3106.00 0.202171
\(619\) −16402.0 −1.06503 −0.532514 0.846421i \(-0.678753\pi\)
−0.532514 + 0.846421i \(0.678753\pi\)
\(620\) 6640.00 0.430111
\(621\) −3551.00 −0.229463
\(622\) −19988.0 −1.28850
\(623\) 0 0
\(624\) 128.000 0.00821170
\(625\) 625.000 0.0400000
\(626\) 2912.00 0.185922
\(627\) 52.0000 0.00331209
\(628\) −4904.00 −0.311610
\(629\) 10192.0 0.646076
\(630\) 0 0
\(631\) 8490.00 0.535628 0.267814 0.963471i \(-0.413699\pi\)
0.267814 + 0.963471i \(0.413699\pi\)
\(632\) −9360.00 −0.589115
\(633\) −2602.00 −0.163381
\(634\) −13744.0 −0.860953
\(635\) 240.000 0.0149986
\(636\) 2328.00 0.145143
\(637\) 0 0
\(638\) 276.000 0.0171269
\(639\) −20020.0 −1.23940
\(640\) −640.000 −0.0395285
\(641\) −123.000 −0.00757911 −0.00378955 0.999993i \(-0.501206\pi\)
−0.00378955 + 0.999993i \(0.501206\pi\)
\(642\) −3662.00 −0.225121
\(643\) 23924.0 1.46729 0.733647 0.679530i \(-0.237816\pi\)
0.733647 + 0.679530i \(0.237816\pi\)
\(644\) 0 0
\(645\) −1845.00 −0.112631
\(646\) 2704.00 0.164686
\(647\) −181.000 −0.0109982 −0.00549911 0.999985i \(-0.501750\pi\)
−0.00549911 + 0.999985i \(0.501750\pi\)
\(648\) −5192.00 −0.314755
\(649\) −700.000 −0.0423381
\(650\) −400.000 −0.0241374
\(651\) 0 0
\(652\) −2640.00 −0.158574
\(653\) −17812.0 −1.06744 −0.533719 0.845662i \(-0.679206\pi\)
−0.533719 + 0.845662i \(0.679206\pi\)
\(654\) −1622.00 −0.0969805
\(655\) 3960.00 0.236229
\(656\) −5648.00 −0.336154
\(657\) 16328.0 0.969583
\(658\) 0 0
\(659\) 15334.0 0.906416 0.453208 0.891405i \(-0.350280\pi\)
0.453208 + 0.891405i \(0.350280\pi\)
\(660\) −40.0000 −0.00235909
\(661\) −1337.00 −0.0786736 −0.0393368 0.999226i \(-0.512525\pi\)
−0.0393368 + 0.999226i \(0.512525\pi\)
\(662\) 784.000 0.0460287
\(663\) 416.000 0.0243682
\(664\) 4200.00 0.245469
\(665\) 0 0
\(666\) 10192.0 0.592991
\(667\) 4623.00 0.268371
\(668\) 3796.00 0.219868
\(669\) 3156.00 0.182389
\(670\) −2910.00 −0.167796
\(671\) −934.000 −0.0537357
\(672\) 0 0
\(673\) −15112.0 −0.865564 −0.432782 0.901499i \(-0.642468\pi\)
−0.432782 + 0.901499i \(0.642468\pi\)
\(674\) −7852.00 −0.448736
\(675\) −1325.00 −0.0755545
\(676\) −8532.00 −0.485435
\(677\) −25392.0 −1.44150 −0.720749 0.693196i \(-0.756202\pi\)
−0.720749 + 0.693196i \(0.756202\pi\)
\(678\) −4340.00 −0.245836
\(679\) 0 0
\(680\) −2080.00 −0.117301
\(681\) −4236.00 −0.238361
\(682\) 1328.00 0.0745627
\(683\) 29231.0 1.63762 0.818809 0.574066i \(-0.194635\pi\)
0.818809 + 0.574066i \(0.194635\pi\)
\(684\) 2704.00 0.151155
\(685\) 5420.00 0.302318
\(686\) 0 0
\(687\) −6334.00 −0.351757
\(688\) −5904.00 −0.327163
\(689\) 4656.00 0.257445
\(690\) −670.000 −0.0369659
\(691\) 7538.00 0.414991 0.207496 0.978236i \(-0.433469\pi\)
0.207496 + 0.978236i \(0.433469\pi\)
\(692\) −13568.0 −0.745344
\(693\) 0 0
\(694\) 3570.00 0.195267
\(695\) 230.000 0.0125531
\(696\) −552.000 −0.0300625
\(697\) −18356.0 −0.997537
\(698\) −3182.00 −0.172551
\(699\) −4688.00 −0.253672
\(700\) 0 0
\(701\) 22125.0 1.19208 0.596041 0.802954i \(-0.296739\pi\)
0.596041 + 0.802954i \(0.296739\pi\)
\(702\) 848.000 0.0455922
\(703\) −5096.00 −0.273399
\(704\) −128.000 −0.00685253
\(705\) −440.000 −0.0235055
\(706\) 3372.00 0.179755
\(707\) 0 0
\(708\) 1400.00 0.0743153
\(709\) −4439.00 −0.235134 −0.117567 0.993065i \(-0.537510\pi\)
−0.117567 + 0.993065i \(0.537510\pi\)
\(710\) −7700.00 −0.407008
\(711\) −30420.0 −1.60456
\(712\) 712.000 0.0374766
\(713\) 22244.0 1.16837
\(714\) 0 0
\(715\) −80.0000 −0.00418438
\(716\) 1072.00 0.0559532
\(717\) 1856.00 0.0966717
\(718\) −14744.0 −0.766353
\(719\) −13650.0 −0.708010 −0.354005 0.935244i \(-0.615180\pi\)
−0.354005 + 0.935244i \(0.615180\pi\)
\(720\) −2080.00 −0.107663
\(721\) 0 0
\(722\) 12366.0 0.637417
\(723\) 4806.00 0.247216
\(724\) 16372.0 0.840415
\(725\) 1725.00 0.0883654
\(726\) 2654.00 0.135674
\(727\) 11397.0 0.581419 0.290709 0.956811i \(-0.406109\pi\)
0.290709 + 0.956811i \(0.406109\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 6280.00 0.318402
\(731\) −19188.0 −0.970853
\(732\) 1868.00 0.0943214
\(733\) −16686.0 −0.840807 −0.420403 0.907337i \(-0.638111\pi\)
−0.420403 + 0.907337i \(0.638111\pi\)
\(734\) 13274.0 0.667510
\(735\) 0 0
\(736\) −2144.00 −0.107376
\(737\) −582.000 −0.0290885
\(738\) −18356.0 −0.915574
\(739\) 22470.0 1.11850 0.559251 0.828999i \(-0.311089\pi\)
0.559251 + 0.828999i \(0.311089\pi\)
\(740\) 3920.00 0.194733
\(741\) −208.000 −0.0103118
\(742\) 0 0
\(743\) 5625.00 0.277741 0.138870 0.990311i \(-0.455653\pi\)
0.138870 + 0.990311i \(0.455653\pi\)
\(744\) −2656.00 −0.130879
\(745\) −1845.00 −0.0907323
\(746\) −6952.00 −0.341194
\(747\) 13650.0 0.668577
\(748\) −416.000 −0.0203348
\(749\) 0 0
\(750\) −250.000 −0.0121716
\(751\) 17620.0 0.856142 0.428071 0.903745i \(-0.359193\pi\)
0.428071 + 0.903745i \(0.359193\pi\)
\(752\) −1408.00 −0.0682772
\(753\) 3200.00 0.154867
\(754\) −1104.00 −0.0533227
\(755\) 12400.0 0.597725
\(756\) 0 0
\(757\) 39056.0 1.87518 0.937592 0.347737i \(-0.113050\pi\)
0.937592 + 0.347737i \(0.113050\pi\)
\(758\) 4756.00 0.227897
\(759\) −134.000 −0.00640829
\(760\) 1040.00 0.0496378
\(761\) −29738.0 −1.41656 −0.708280 0.705932i \(-0.750528\pi\)
−0.708280 + 0.705932i \(0.750528\pi\)
\(762\) −96.0000 −0.00456393
\(763\) 0 0
\(764\) −7912.00 −0.374668
\(765\) −6760.00 −0.319488
\(766\) −4914.00 −0.231789
\(767\) 2800.00 0.131815
\(768\) 256.000 0.0120281
\(769\) 1118.00 0.0524267 0.0262133 0.999656i \(-0.491655\pi\)
0.0262133 + 0.999656i \(0.491655\pi\)
\(770\) 0 0
\(771\) 1120.00 0.0523162
\(772\) −15992.0 −0.745550
\(773\) −13432.0 −0.624988 −0.312494 0.949920i \(-0.601164\pi\)
−0.312494 + 0.949920i \(0.601164\pi\)
\(774\) −19188.0 −0.891083
\(775\) 8300.00 0.384703
\(776\) −2320.00 −0.107324
\(777\) 0 0
\(778\) −17124.0 −0.789107
\(779\) 9178.00 0.422126
\(780\) 160.000 0.00734477
\(781\) −1540.00 −0.0705577
\(782\) −6968.00 −0.318638
\(783\) −3657.00 −0.166910
\(784\) 0 0
\(785\) −6130.00 −0.278712
\(786\) −1584.00 −0.0718822
\(787\) 9349.00 0.423451 0.211725 0.977329i \(-0.432092\pi\)
0.211725 + 0.977329i \(0.432092\pi\)
\(788\) −12120.0 −0.547915
\(789\) 6405.00 0.289004
\(790\) −11700.0 −0.526921
\(791\) 0 0
\(792\) −416.000 −0.0186640
\(793\) 3736.00 0.167300
\(794\) −19684.0 −0.879797
\(795\) 2910.00 0.129820
\(796\) −1424.00 −0.0634075
\(797\) 28008.0 1.24479 0.622393 0.782705i \(-0.286161\pi\)
0.622393 + 0.782705i \(0.286161\pi\)
\(798\) 0 0
\(799\) −4576.00 −0.202612
\(800\) −800.000 −0.0353553
\(801\) 2314.00 0.102074
\(802\) 16194.0 0.713005
\(803\) 1256.00 0.0551971
\(804\) 1164.00 0.0510586
\(805\) 0 0
\(806\) −5312.00 −0.232143
\(807\) −4935.00 −0.215267
\(808\) −9864.00 −0.429473
\(809\) 19669.0 0.854790 0.427395 0.904065i \(-0.359431\pi\)
0.427395 + 0.904065i \(0.359431\pi\)
\(810\) −6490.00 −0.281525
\(811\) −31860.0 −1.37948 −0.689739 0.724059i \(-0.742275\pi\)
−0.689739 + 0.724059i \(0.742275\pi\)
\(812\) 0 0
\(813\) 1446.00 0.0623781
\(814\) 784.000 0.0337582
\(815\) −3300.00 −0.141833
\(816\) 832.000 0.0356934
\(817\) 9594.00 0.410834
\(818\) 30518.0 1.30445
\(819\) 0 0
\(820\) −7060.00 −0.300666
\(821\) 2230.00 0.0947960 0.0473980 0.998876i \(-0.484907\pi\)
0.0473980 + 0.998876i \(0.484907\pi\)
\(822\) −2168.00 −0.0919923
\(823\) 14803.0 0.626975 0.313487 0.949592i \(-0.398503\pi\)
0.313487 + 0.949592i \(0.398503\pi\)
\(824\) 12424.0 0.525256
\(825\) −50.0000 −0.00211003
\(826\) 0 0
\(827\) 13257.0 0.557426 0.278713 0.960374i \(-0.410092\pi\)
0.278713 + 0.960374i \(0.410092\pi\)
\(828\) −6968.00 −0.292457
\(829\) 21574.0 0.903855 0.451928 0.892055i \(-0.350737\pi\)
0.451928 + 0.892055i \(0.350737\pi\)
\(830\) 5250.00 0.219554
\(831\) −8020.00 −0.334790
\(832\) 512.000 0.0213346
\(833\) 0 0
\(834\) −92.0000 −0.00381978
\(835\) 4745.00 0.196656
\(836\) 208.000 0.00860506
\(837\) −17596.0 −0.726651
\(838\) 32448.0 1.33759
\(839\) −12990.0 −0.534523 −0.267261 0.963624i \(-0.586119\pi\)
−0.267261 + 0.963624i \(0.586119\pi\)
\(840\) 0 0
\(841\) −19628.0 −0.804789
\(842\) −5954.00 −0.243692
\(843\) 4978.00 0.203382
\(844\) −10408.0 −0.424476
\(845\) −10665.0 −0.434186
\(846\) −4576.00 −0.185965
\(847\) 0 0
\(848\) 9312.00 0.377094
\(849\) −5852.00 −0.236561
\(850\) −2600.00 −0.104917
\(851\) 13132.0 0.528977
\(852\) 3080.00 0.123849
\(853\) −24838.0 −0.996995 −0.498498 0.866891i \(-0.666115\pi\)
−0.498498 + 0.866891i \(0.666115\pi\)
\(854\) 0 0
\(855\) 3380.00 0.135197
\(856\) −14648.0 −0.584881
\(857\) 17026.0 0.678643 0.339322 0.940670i \(-0.389803\pi\)
0.339322 + 0.940670i \(0.389803\pi\)
\(858\) 32.0000 0.00127327
\(859\) −6728.00 −0.267237 −0.133618 0.991033i \(-0.542660\pi\)
−0.133618 + 0.991033i \(0.542660\pi\)
\(860\) −7380.00 −0.292623
\(861\) 0 0
\(862\) −28404.0 −1.12232
\(863\) −30099.0 −1.18723 −0.593616 0.804748i \(-0.702300\pi\)
−0.593616 + 0.804748i \(0.702300\pi\)
\(864\) 1696.00 0.0667814
\(865\) −16960.0 −0.666656
\(866\) 28620.0 1.12303
\(867\) −2209.00 −0.0865301
\(868\) 0 0
\(869\) −2340.00 −0.0913453
\(870\) −690.000 −0.0268887
\(871\) 2328.00 0.0905640
\(872\) −6488.00 −0.251963
\(873\) −7540.00 −0.292314
\(874\) 3484.00 0.134838
\(875\) 0 0
\(876\) −2512.00 −0.0968865
\(877\) −5626.00 −0.216621 −0.108310 0.994117i \(-0.534544\pi\)
−0.108310 + 0.994117i \(0.534544\pi\)
\(878\) −4712.00 −0.181119
\(879\) 3012.00 0.115577
\(880\) −160.000 −0.00612909
\(881\) 15927.0 0.609074 0.304537 0.952500i \(-0.401498\pi\)
0.304537 + 0.952500i \(0.401498\pi\)
\(882\) 0 0
\(883\) 39124.0 1.49108 0.745542 0.666458i \(-0.232191\pi\)
0.745542 + 0.666458i \(0.232191\pi\)
\(884\) 1664.00 0.0633104
\(885\) 1750.00 0.0664696
\(886\) −16582.0 −0.628762
\(887\) 25331.0 0.958886 0.479443 0.877573i \(-0.340839\pi\)
0.479443 + 0.877573i \(0.340839\pi\)
\(888\) −1568.00 −0.0592552
\(889\) 0 0
\(890\) 890.000 0.0335201
\(891\) −1298.00 −0.0488043
\(892\) 12624.0 0.473860
\(893\) 2288.00 0.0857391
\(894\) 738.000 0.0276090
\(895\) 1340.00 0.0500461
\(896\) 0 0
\(897\) 536.000 0.0199515
\(898\) 7042.00 0.261687
\(899\) 22908.0 0.849860
\(900\) −2600.00 −0.0962963
\(901\) 30264.0 1.11902
\(902\) −1412.00 −0.0521225
\(903\) 0 0
\(904\) −17360.0 −0.638700
\(905\) 20465.0 0.751690
\(906\) −4960.00 −0.181882
\(907\) 26385.0 0.965931 0.482966 0.875639i \(-0.339560\pi\)
0.482966 + 0.875639i \(0.339560\pi\)
\(908\) −16944.0 −0.619280
\(909\) −32058.0 −1.16974
\(910\) 0 0
\(911\) −40770.0 −1.48273 −0.741367 0.671100i \(-0.765822\pi\)
−0.741367 + 0.671100i \(0.765822\pi\)
\(912\) −416.000 −0.0151043
\(913\) 1050.00 0.0380613
\(914\) 10864.0 0.393161
\(915\) 2335.00 0.0843636
\(916\) −25336.0 −0.913892
\(917\) 0 0
\(918\) 5512.00 0.198173
\(919\) −14618.0 −0.524704 −0.262352 0.964972i \(-0.584498\pi\)
−0.262352 + 0.964972i \(0.584498\pi\)
\(920\) −2680.00 −0.0960402
\(921\) −9443.00 −0.337847
\(922\) −10700.0 −0.382197
\(923\) 6160.00 0.219674
\(924\) 0 0
\(925\) 4900.00 0.174174
\(926\) 20246.0 0.718493
\(927\) 40378.0 1.43062
\(928\) −2208.00 −0.0781047
\(929\) −41323.0 −1.45938 −0.729690 0.683778i \(-0.760336\pi\)
−0.729690 + 0.683778i \(0.760336\pi\)
\(930\) −3320.00 −0.117061
\(931\) 0 0
\(932\) −18752.0 −0.659058
\(933\) 9994.00 0.350685
\(934\) 12926.0 0.452839
\(935\) −520.000 −0.0181880
\(936\) 1664.00 0.0581085
\(937\) 22620.0 0.788648 0.394324 0.918971i \(-0.370979\pi\)
0.394324 + 0.918971i \(0.370979\pi\)
\(938\) 0 0
\(939\) −1456.00 −0.0506015
\(940\) −1760.00 −0.0610690
\(941\) −51978.0 −1.80067 −0.900337 0.435193i \(-0.856680\pi\)
−0.900337 + 0.435193i \(0.856680\pi\)
\(942\) 2452.00 0.0848094
\(943\) −23651.0 −0.816737
\(944\) 5600.00 0.193077
\(945\) 0 0
\(946\) −1476.00 −0.0507282
\(947\) 9987.00 0.342697 0.171348 0.985210i \(-0.445188\pi\)
0.171348 + 0.985210i \(0.445188\pi\)
\(948\) 4680.00 0.160337
\(949\) −5024.00 −0.171850
\(950\) 1300.00 0.0443974
\(951\) 6872.00 0.234322
\(952\) 0 0
\(953\) 6588.00 0.223931 0.111966 0.993712i \(-0.464285\pi\)
0.111966 + 0.993712i \(0.464285\pi\)
\(954\) 30264.0 1.02708
\(955\) −9890.00 −0.335113
\(956\) 7424.00 0.251160
\(957\) −138.000 −0.00466134
\(958\) −35280.0 −1.18982
\(959\) 0 0
\(960\) 320.000 0.0107583
\(961\) 80433.0 2.69991
\(962\) −3136.00 −0.105103
\(963\) −47606.0 −1.59302
\(964\) 19224.0 0.642286
\(965\) −19990.0 −0.666840
\(966\) 0 0
\(967\) −4091.00 −0.136047 −0.0680236 0.997684i \(-0.521669\pi\)
−0.0680236 + 0.997684i \(0.521669\pi\)
\(968\) 10616.0 0.352491
\(969\) −1352.00 −0.0448220
\(970\) −2900.00 −0.0959932
\(971\) −23640.0 −0.781301 −0.390651 0.920539i \(-0.627750\pi\)
−0.390651 + 0.920539i \(0.627750\pi\)
\(972\) 8320.00 0.274552
\(973\) 0 0
\(974\) 20064.0 0.660053
\(975\) 200.000 0.00656936
\(976\) 7472.00 0.245054
\(977\) 36666.0 1.20066 0.600332 0.799751i \(-0.295035\pi\)
0.600332 + 0.799751i \(0.295035\pi\)
\(978\) 1320.00 0.0431584
\(979\) 178.000 0.00581093
\(980\) 0 0
\(981\) −21086.0 −0.686263
\(982\) −11832.0 −0.384495
\(983\) 41071.0 1.33262 0.666308 0.745677i \(-0.267874\pi\)
0.666308 + 0.745677i \(0.267874\pi\)
\(984\) 2824.00 0.0914897
\(985\) −15150.0 −0.490070
\(986\) −7176.00 −0.231775
\(987\) 0 0
\(988\) −832.000 −0.0267909
\(989\) −24723.0 −0.794889
\(990\) −520.000 −0.0166936
\(991\) 31984.0 1.02523 0.512616 0.858618i \(-0.328676\pi\)
0.512616 + 0.858618i \(0.328676\pi\)
\(992\) −10624.0 −0.340033
\(993\) −392.000 −0.0125274
\(994\) 0 0
\(995\) −1780.00 −0.0567134
\(996\) −2100.00 −0.0668083
\(997\) 43894.0 1.39432 0.697160 0.716916i \(-0.254447\pi\)
0.697160 + 0.716916i \(0.254447\pi\)
\(998\) −27788.0 −0.881377
\(999\) −10388.0 −0.328991
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 490.4.a.e.1.1 1
5.4 even 2 2450.4.a.be.1.1 1
7.2 even 3 490.4.e.m.361.1 2
7.3 odd 6 70.4.e.c.51.1 yes 2
7.4 even 3 490.4.e.m.471.1 2
7.5 odd 6 70.4.e.c.11.1 2
7.6 odd 2 490.4.a.c.1.1 1
21.5 even 6 630.4.k.b.361.1 2
21.17 even 6 630.4.k.b.541.1 2
28.3 even 6 560.4.q.d.401.1 2
28.19 even 6 560.4.q.d.81.1 2
35.3 even 12 350.4.j.e.149.1 4
35.12 even 12 350.4.j.e.249.1 4
35.17 even 12 350.4.j.e.149.2 4
35.19 odd 6 350.4.e.a.151.1 2
35.24 odd 6 350.4.e.a.51.1 2
35.33 even 12 350.4.j.e.249.2 4
35.34 odd 2 2450.4.a.bg.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.4.e.c.11.1 2 7.5 odd 6
70.4.e.c.51.1 yes 2 7.3 odd 6
350.4.e.a.51.1 2 35.24 odd 6
350.4.e.a.151.1 2 35.19 odd 6
350.4.j.e.149.1 4 35.3 even 12
350.4.j.e.149.2 4 35.17 even 12
350.4.j.e.249.1 4 35.12 even 12
350.4.j.e.249.2 4 35.33 even 12
490.4.a.c.1.1 1 7.6 odd 2
490.4.a.e.1.1 1 1.1 even 1 trivial
490.4.e.m.361.1 2 7.2 even 3
490.4.e.m.471.1 2 7.4 even 3
560.4.q.d.81.1 2 28.19 even 6
560.4.q.d.401.1 2 28.3 even 6
630.4.k.b.361.1 2 21.5 even 6
630.4.k.b.541.1 2 21.17 even 6
2450.4.a.be.1.1 1 5.4 even 2
2450.4.a.bg.1.1 1 35.34 odd 2