Properties

Label 5225.2.a.bc.1.29
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $30$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.29
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.77451 q^{2} -2.74433 q^{3} +5.69792 q^{4} -7.61418 q^{6} -3.20844 q^{7} +10.2599 q^{8} +4.53135 q^{9} +O(q^{10})\) \(q+2.77451 q^{2} -2.74433 q^{3} +5.69792 q^{4} -7.61418 q^{6} -3.20844 q^{7} +10.2599 q^{8} +4.53135 q^{9} +1.00000 q^{11} -15.6370 q^{12} -3.87053 q^{13} -8.90186 q^{14} +17.0705 q^{16} -5.86570 q^{17} +12.5723 q^{18} +1.00000 q^{19} +8.80502 q^{21} +2.77451 q^{22} +6.11891 q^{23} -28.1566 q^{24} -10.7388 q^{26} -4.20253 q^{27} -18.2814 q^{28} +6.40440 q^{29} +1.66215 q^{31} +26.8423 q^{32} -2.74433 q^{33} -16.2745 q^{34} +25.8193 q^{36} -0.251830 q^{37} +2.77451 q^{38} +10.6220 q^{39} +10.7565 q^{41} +24.4296 q^{42} +2.17536 q^{43} +5.69792 q^{44} +16.9770 q^{46} -2.68163 q^{47} -46.8470 q^{48} +3.29408 q^{49} +16.0974 q^{51} -22.0540 q^{52} +8.89909 q^{53} -11.6600 q^{54} -32.9183 q^{56} -2.74433 q^{57} +17.7691 q^{58} -4.09447 q^{59} +4.52319 q^{61} +4.61167 q^{62} -14.5386 q^{63} +40.3335 q^{64} -7.61418 q^{66} -2.61295 q^{67} -33.4223 q^{68} -16.7923 q^{69} -5.51722 q^{71} +46.4913 q^{72} +2.73480 q^{73} -0.698705 q^{74} +5.69792 q^{76} -3.20844 q^{77} +29.4709 q^{78} +8.17104 q^{79} -2.06093 q^{81} +29.8440 q^{82} +12.2337 q^{83} +50.1703 q^{84} +6.03555 q^{86} -17.5758 q^{87} +10.2599 q^{88} -1.84048 q^{89} +12.4184 q^{91} +34.8651 q^{92} -4.56150 q^{93} -7.44022 q^{94} -73.6642 q^{96} +2.65645 q^{97} +9.13947 q^{98} +4.53135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 42 q^{4} + 12 q^{6} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 42 q^{4} + 12 q^{6} + 40 q^{9} + 30 q^{11} - 4 q^{14} + 66 q^{16} + 30 q^{19} + 14 q^{21} + 22 q^{24} + 30 q^{29} + 26 q^{31} + 12 q^{34} + 78 q^{36} + 64 q^{39} + 22 q^{41} + 42 q^{44} + 28 q^{46} + 60 q^{49} + 64 q^{51} + 62 q^{54} - 32 q^{56} - 14 q^{59} + 78 q^{61} + 90 q^{64} + 12 q^{66} - 28 q^{69} + 20 q^{71} + 42 q^{74} + 42 q^{76} + 102 q^{79} + 42 q^{81} + 98 q^{84} - 52 q^{86} - 8 q^{89} + 56 q^{91} + 40 q^{94} - 74 q^{96} + 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.77451 1.96188 0.980938 0.194319i \(-0.0622498\pi\)
0.980938 + 0.194319i \(0.0622498\pi\)
\(3\) −2.74433 −1.58444 −0.792220 0.610236i \(-0.791075\pi\)
−0.792220 + 0.610236i \(0.791075\pi\)
\(4\) 5.69792 2.84896
\(5\) 0 0
\(6\) −7.61418 −3.10848
\(7\) −3.20844 −1.21268 −0.606338 0.795207i \(-0.707362\pi\)
−0.606338 + 0.795207i \(0.707362\pi\)
\(8\) 10.2599 3.62743
\(9\) 4.53135 1.51045
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) −15.6370 −4.51401
\(13\) −3.87053 −1.07349 −0.536746 0.843744i \(-0.680347\pi\)
−0.536746 + 0.843744i \(0.680347\pi\)
\(14\) −8.90186 −2.37912
\(15\) 0 0
\(16\) 17.0705 4.26761
\(17\) −5.86570 −1.42264 −0.711321 0.702867i \(-0.751903\pi\)
−0.711321 + 0.702867i \(0.751903\pi\)
\(18\) 12.5723 2.96332
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 8.80502 1.92141
\(22\) 2.77451 0.591528
\(23\) 6.11891 1.27588 0.637940 0.770086i \(-0.279787\pi\)
0.637940 + 0.770086i \(0.279787\pi\)
\(24\) −28.1566 −5.74745
\(25\) 0 0
\(26\) −10.7388 −2.10606
\(27\) −4.20253 −0.808777
\(28\) −18.2814 −3.45487
\(29\) 6.40440 1.18927 0.594634 0.803997i \(-0.297297\pi\)
0.594634 + 0.803997i \(0.297297\pi\)
\(30\) 0 0
\(31\) 1.66215 0.298532 0.149266 0.988797i \(-0.452309\pi\)
0.149266 + 0.988797i \(0.452309\pi\)
\(32\) 26.8423 4.74510
\(33\) −2.74433 −0.477727
\(34\) −16.2745 −2.79105
\(35\) 0 0
\(36\) 25.8193 4.30321
\(37\) −0.251830 −0.0414006 −0.0207003 0.999786i \(-0.506590\pi\)
−0.0207003 + 0.999786i \(0.506590\pi\)
\(38\) 2.77451 0.450085
\(39\) 10.6220 1.70088
\(40\) 0 0
\(41\) 10.7565 1.67988 0.839941 0.542677i \(-0.182589\pi\)
0.839941 + 0.542677i \(0.182589\pi\)
\(42\) 24.4296 3.76957
\(43\) 2.17536 0.331739 0.165869 0.986148i \(-0.446957\pi\)
0.165869 + 0.986148i \(0.446957\pi\)
\(44\) 5.69792 0.858994
\(45\) 0 0
\(46\) 16.9770 2.50312
\(47\) −2.68163 −0.391156 −0.195578 0.980688i \(-0.562658\pi\)
−0.195578 + 0.980688i \(0.562658\pi\)
\(48\) −46.8470 −6.76178
\(49\) 3.29408 0.470583
\(50\) 0 0
\(51\) 16.0974 2.25409
\(52\) −22.0540 −3.05834
\(53\) 8.89909 1.22238 0.611192 0.791483i \(-0.290690\pi\)
0.611192 + 0.791483i \(0.290690\pi\)
\(54\) −11.6600 −1.58672
\(55\) 0 0
\(56\) −32.9183 −4.39890
\(57\) −2.74433 −0.363495
\(58\) 17.7691 2.33320
\(59\) −4.09447 −0.533054 −0.266527 0.963827i \(-0.585876\pi\)
−0.266527 + 0.963827i \(0.585876\pi\)
\(60\) 0 0
\(61\) 4.52319 0.579135 0.289567 0.957158i \(-0.406489\pi\)
0.289567 + 0.957158i \(0.406489\pi\)
\(62\) 4.61167 0.585682
\(63\) −14.5386 −1.83169
\(64\) 40.3335 5.04169
\(65\) 0 0
\(66\) −7.61418 −0.937241
\(67\) −2.61295 −0.319222 −0.159611 0.987180i \(-0.551024\pi\)
−0.159611 + 0.987180i \(0.551024\pi\)
\(68\) −33.4223 −4.05305
\(69\) −16.7923 −2.02156
\(70\) 0 0
\(71\) −5.51722 −0.654774 −0.327387 0.944890i \(-0.606168\pi\)
−0.327387 + 0.944890i \(0.606168\pi\)
\(72\) 46.4913 5.47905
\(73\) 2.73480 0.320084 0.160042 0.987110i \(-0.448837\pi\)
0.160042 + 0.987110i \(0.448837\pi\)
\(74\) −0.698705 −0.0812229
\(75\) 0 0
\(76\) 5.69792 0.653596
\(77\) −3.20844 −0.365636
\(78\) 29.4709 3.33692
\(79\) 8.17104 0.919313 0.459657 0.888097i \(-0.347972\pi\)
0.459657 + 0.888097i \(0.347972\pi\)
\(80\) 0 0
\(81\) −2.06093 −0.228992
\(82\) 29.8440 3.29572
\(83\) 12.2337 1.34283 0.671413 0.741083i \(-0.265688\pi\)
0.671413 + 0.741083i \(0.265688\pi\)
\(84\) 50.1703 5.47403
\(85\) 0 0
\(86\) 6.03555 0.650830
\(87\) −17.5758 −1.88432
\(88\) 10.2599 1.09371
\(89\) −1.84048 −0.195091 −0.0975454 0.995231i \(-0.531099\pi\)
−0.0975454 + 0.995231i \(0.531099\pi\)
\(90\) 0 0
\(91\) 12.4184 1.30180
\(92\) 34.8651 3.63493
\(93\) −4.56150 −0.473005
\(94\) −7.44022 −0.767400
\(95\) 0 0
\(96\) −73.6642 −7.51832
\(97\) 2.65645 0.269722 0.134861 0.990865i \(-0.456941\pi\)
0.134861 + 0.990865i \(0.456941\pi\)
\(98\) 9.13947 0.923226
\(99\) 4.53135 0.455418
\(100\) 0 0
\(101\) 3.36522 0.334852 0.167426 0.985885i \(-0.446454\pi\)
0.167426 + 0.985885i \(0.446454\pi\)
\(102\) 44.6625 4.42225
\(103\) 19.1222 1.88416 0.942082 0.335381i \(-0.108865\pi\)
0.942082 + 0.335381i \(0.108865\pi\)
\(104\) −39.7114 −3.89402
\(105\) 0 0
\(106\) 24.6906 2.39817
\(107\) 19.1096 1.84739 0.923697 0.383125i \(-0.125152\pi\)
0.923697 + 0.383125i \(0.125152\pi\)
\(108\) −23.9457 −2.30417
\(109\) −2.04217 −0.195605 −0.0978023 0.995206i \(-0.531181\pi\)
−0.0978023 + 0.995206i \(0.531181\pi\)
\(110\) 0 0
\(111\) 0.691105 0.0655968
\(112\) −54.7695 −5.17523
\(113\) −2.01233 −0.189305 −0.0946523 0.995510i \(-0.530174\pi\)
−0.0946523 + 0.995510i \(0.530174\pi\)
\(114\) −7.61418 −0.713133
\(115\) 0 0
\(116\) 36.4918 3.38818
\(117\) −17.5387 −1.62146
\(118\) −11.3601 −1.04579
\(119\) 18.8197 1.72520
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 12.5496 1.13619
\(123\) −29.5194 −2.66167
\(124\) 9.47082 0.850505
\(125\) 0 0
\(126\) −40.3374 −3.59354
\(127\) −17.6725 −1.56818 −0.784090 0.620648i \(-0.786870\pi\)
−0.784090 + 0.620648i \(0.786870\pi\)
\(128\) 58.2211 5.14607
\(129\) −5.96990 −0.525620
\(130\) 0 0
\(131\) −4.85389 −0.424086 −0.212043 0.977260i \(-0.568012\pi\)
−0.212043 + 0.977260i \(0.568012\pi\)
\(132\) −15.6370 −1.36102
\(133\) −3.20844 −0.278207
\(134\) −7.24965 −0.626274
\(135\) 0 0
\(136\) −60.1817 −5.16054
\(137\) 0.470694 0.0402141 0.0201071 0.999798i \(-0.493599\pi\)
0.0201071 + 0.999798i \(0.493599\pi\)
\(138\) −46.5905 −3.96604
\(139\) 10.2256 0.867325 0.433663 0.901075i \(-0.357221\pi\)
0.433663 + 0.901075i \(0.357221\pi\)
\(140\) 0 0
\(141\) 7.35929 0.619764
\(142\) −15.3076 −1.28459
\(143\) −3.87053 −0.323670
\(144\) 77.3522 6.44601
\(145\) 0 0
\(146\) 7.58774 0.627965
\(147\) −9.04005 −0.745611
\(148\) −1.43491 −0.117949
\(149\) −19.2747 −1.57905 −0.789523 0.613721i \(-0.789672\pi\)
−0.789523 + 0.613721i \(0.789672\pi\)
\(150\) 0 0
\(151\) −9.24566 −0.752401 −0.376200 0.926538i \(-0.622770\pi\)
−0.376200 + 0.926538i \(0.622770\pi\)
\(152\) 10.2599 0.832190
\(153\) −26.5795 −2.14883
\(154\) −8.90186 −0.717332
\(155\) 0 0
\(156\) 60.5234 4.84575
\(157\) −9.10320 −0.726514 −0.363257 0.931689i \(-0.618335\pi\)
−0.363257 + 0.931689i \(0.618335\pi\)
\(158\) 22.6706 1.80358
\(159\) −24.4220 −1.93679
\(160\) 0 0
\(161\) −19.6321 −1.54723
\(162\) −5.71806 −0.449253
\(163\) −13.1874 −1.03292 −0.516458 0.856313i \(-0.672750\pi\)
−0.516458 + 0.856313i \(0.672750\pi\)
\(164\) 61.2897 4.78592
\(165\) 0 0
\(166\) 33.9426 2.63446
\(167\) 7.56734 0.585578 0.292789 0.956177i \(-0.405417\pi\)
0.292789 + 0.956177i \(0.405417\pi\)
\(168\) 90.3388 6.96979
\(169\) 1.98102 0.152386
\(170\) 0 0
\(171\) 4.53135 0.346521
\(172\) 12.3950 0.945110
\(173\) 12.3483 0.938825 0.469412 0.882979i \(-0.344466\pi\)
0.469412 + 0.882979i \(0.344466\pi\)
\(174\) −48.7643 −3.69681
\(175\) 0 0
\(176\) 17.0705 1.28673
\(177\) 11.2366 0.844592
\(178\) −5.10644 −0.382744
\(179\) 9.75082 0.728810 0.364405 0.931241i \(-0.381272\pi\)
0.364405 + 0.931241i \(0.381272\pi\)
\(180\) 0 0
\(181\) −3.06931 −0.228140 −0.114070 0.993473i \(-0.536389\pi\)
−0.114070 + 0.993473i \(0.536389\pi\)
\(182\) 34.4549 2.55397
\(183\) −12.4131 −0.917604
\(184\) 62.7796 4.62817
\(185\) 0 0
\(186\) −12.6559 −0.927978
\(187\) −5.86570 −0.428943
\(188\) −15.2797 −1.11439
\(189\) 13.4836 0.980784
\(190\) 0 0
\(191\) 11.5267 0.834040 0.417020 0.908897i \(-0.363075\pi\)
0.417020 + 0.908897i \(0.363075\pi\)
\(192\) −110.688 −7.98825
\(193\) −6.25518 −0.450258 −0.225129 0.974329i \(-0.572280\pi\)
−0.225129 + 0.974329i \(0.572280\pi\)
\(194\) 7.37036 0.529161
\(195\) 0 0
\(196\) 18.7694 1.34067
\(197\) 6.53160 0.465357 0.232678 0.972554i \(-0.425251\pi\)
0.232678 + 0.972554i \(0.425251\pi\)
\(198\) 12.5723 0.893473
\(199\) 11.4237 0.809808 0.404904 0.914359i \(-0.367305\pi\)
0.404904 + 0.914359i \(0.367305\pi\)
\(200\) 0 0
\(201\) 7.17079 0.505788
\(202\) 9.33686 0.656939
\(203\) −20.5481 −1.44220
\(204\) 91.7218 6.42181
\(205\) 0 0
\(206\) 53.0547 3.69650
\(207\) 27.7269 1.92715
\(208\) −66.0717 −4.58125
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) −0.159122 −0.0109544 −0.00547722 0.999985i \(-0.501743\pi\)
−0.00547722 + 0.999985i \(0.501743\pi\)
\(212\) 50.7063 3.48252
\(213\) 15.1411 1.03745
\(214\) 53.0198 3.62436
\(215\) 0 0
\(216\) −43.1176 −2.93378
\(217\) −5.33292 −0.362022
\(218\) −5.66603 −0.383752
\(219\) −7.50519 −0.507154
\(220\) 0 0
\(221\) 22.7034 1.52720
\(222\) 1.91748 0.128693
\(223\) 0.537456 0.0359907 0.0179954 0.999838i \(-0.494272\pi\)
0.0179954 + 0.999838i \(0.494272\pi\)
\(224\) −86.1220 −5.75427
\(225\) 0 0
\(226\) −5.58325 −0.371392
\(227\) 13.5232 0.897565 0.448783 0.893641i \(-0.351858\pi\)
0.448783 + 0.893641i \(0.351858\pi\)
\(228\) −15.6370 −1.03558
\(229\) −10.6187 −0.701704 −0.350852 0.936431i \(-0.614108\pi\)
−0.350852 + 0.936431i \(0.614108\pi\)
\(230\) 0 0
\(231\) 8.80502 0.579328
\(232\) 65.7087 4.31399
\(233\) 7.83409 0.513228 0.256614 0.966514i \(-0.417393\pi\)
0.256614 + 0.966514i \(0.417393\pi\)
\(234\) −48.6614 −3.18110
\(235\) 0 0
\(236\) −23.3299 −1.51865
\(237\) −22.4240 −1.45660
\(238\) 52.2156 3.38464
\(239\) 25.3402 1.63912 0.819560 0.572994i \(-0.194218\pi\)
0.819560 + 0.572994i \(0.194218\pi\)
\(240\) 0 0
\(241\) −30.0559 −1.93607 −0.968035 0.250814i \(-0.919302\pi\)
−0.968035 + 0.250814i \(0.919302\pi\)
\(242\) 2.77451 0.178352
\(243\) 18.2634 1.17160
\(244\) 25.7728 1.64993
\(245\) 0 0
\(246\) −81.9019 −5.22188
\(247\) −3.87053 −0.246276
\(248\) 17.0536 1.08290
\(249\) −33.5734 −2.12763
\(250\) 0 0
\(251\) 24.0428 1.51757 0.758783 0.651344i \(-0.225794\pi\)
0.758783 + 0.651344i \(0.225794\pi\)
\(252\) −82.8395 −5.21840
\(253\) 6.11891 0.384693
\(254\) −49.0325 −3.07657
\(255\) 0 0
\(256\) 80.8682 5.05426
\(257\) −6.58227 −0.410591 −0.205295 0.978700i \(-0.565815\pi\)
−0.205295 + 0.978700i \(0.565815\pi\)
\(258\) −16.5635 −1.03120
\(259\) 0.807981 0.0502055
\(260\) 0 0
\(261\) 29.0206 1.79633
\(262\) −13.4672 −0.832005
\(263\) −16.0460 −0.989442 −0.494721 0.869052i \(-0.664730\pi\)
−0.494721 + 0.869052i \(0.664730\pi\)
\(264\) −28.1566 −1.73292
\(265\) 0 0
\(266\) −8.90186 −0.545808
\(267\) 5.05089 0.309110
\(268\) −14.8884 −0.909451
\(269\) −17.0574 −1.04001 −0.520005 0.854163i \(-0.674070\pi\)
−0.520005 + 0.854163i \(0.674070\pi\)
\(270\) 0 0
\(271\) 14.8456 0.901807 0.450904 0.892573i \(-0.351102\pi\)
0.450904 + 0.892573i \(0.351102\pi\)
\(272\) −100.130 −6.07128
\(273\) −34.0801 −2.06262
\(274\) 1.30595 0.0788951
\(275\) 0 0
\(276\) −95.6812 −5.75933
\(277\) −8.59398 −0.516362 −0.258181 0.966097i \(-0.583123\pi\)
−0.258181 + 0.966097i \(0.583123\pi\)
\(278\) 28.3711 1.70158
\(279\) 7.53180 0.450917
\(280\) 0 0
\(281\) −13.4669 −0.803368 −0.401684 0.915778i \(-0.631575\pi\)
−0.401684 + 0.915778i \(0.631575\pi\)
\(282\) 20.4184 1.21590
\(283\) −14.2887 −0.849374 −0.424687 0.905340i \(-0.639616\pi\)
−0.424687 + 0.905340i \(0.639616\pi\)
\(284\) −31.4367 −1.86542
\(285\) 0 0
\(286\) −10.7388 −0.635001
\(287\) −34.5116 −2.03715
\(288\) 121.632 7.16723
\(289\) 17.4065 1.02391
\(290\) 0 0
\(291\) −7.29019 −0.427358
\(292\) 15.5827 0.911907
\(293\) 29.5456 1.72607 0.863036 0.505143i \(-0.168560\pi\)
0.863036 + 0.505143i \(0.168560\pi\)
\(294\) −25.0817 −1.46280
\(295\) 0 0
\(296\) −2.58376 −0.150178
\(297\) −4.20253 −0.243855
\(298\) −53.4779 −3.09789
\(299\) −23.6834 −1.36965
\(300\) 0 0
\(301\) −6.97950 −0.402292
\(302\) −25.6522 −1.47612
\(303\) −9.23529 −0.530553
\(304\) 17.0705 0.979058
\(305\) 0 0
\(306\) −73.7453 −4.21574
\(307\) 21.6031 1.23295 0.616477 0.787373i \(-0.288559\pi\)
0.616477 + 0.787373i \(0.288559\pi\)
\(308\) −18.2814 −1.04168
\(309\) −52.4776 −2.98535
\(310\) 0 0
\(311\) 21.4045 1.21374 0.606870 0.794801i \(-0.292425\pi\)
0.606870 + 0.794801i \(0.292425\pi\)
\(312\) 108.981 6.16984
\(313\) 22.7332 1.28496 0.642478 0.766304i \(-0.277906\pi\)
0.642478 + 0.766304i \(0.277906\pi\)
\(314\) −25.2569 −1.42533
\(315\) 0 0
\(316\) 46.5579 2.61909
\(317\) 1.29414 0.0726859 0.0363430 0.999339i \(-0.488429\pi\)
0.0363430 + 0.999339i \(0.488429\pi\)
\(318\) −67.7592 −3.79975
\(319\) 6.40440 0.358578
\(320\) 0 0
\(321\) −52.4430 −2.92708
\(322\) −54.4696 −3.03547
\(323\) −5.86570 −0.326376
\(324\) −11.7430 −0.652388
\(325\) 0 0
\(326\) −36.5885 −2.02645
\(327\) 5.60440 0.309924
\(328\) 110.361 6.09366
\(329\) 8.60386 0.474346
\(330\) 0 0
\(331\) −22.3804 −1.23014 −0.615068 0.788474i \(-0.710872\pi\)
−0.615068 + 0.788474i \(0.710872\pi\)
\(332\) 69.7068 3.82566
\(333\) −1.14113 −0.0625335
\(334\) 20.9957 1.14883
\(335\) 0 0
\(336\) 150.306 8.19984
\(337\) 19.7453 1.07560 0.537798 0.843074i \(-0.319256\pi\)
0.537798 + 0.843074i \(0.319256\pi\)
\(338\) 5.49636 0.298962
\(339\) 5.52251 0.299942
\(340\) 0 0
\(341\) 1.66215 0.0900107
\(342\) 12.5723 0.679831
\(343\) 11.8902 0.642011
\(344\) 22.3190 1.20336
\(345\) 0 0
\(346\) 34.2605 1.84186
\(347\) −21.6561 −1.16256 −0.581279 0.813704i \(-0.697448\pi\)
−0.581279 + 0.813704i \(0.697448\pi\)
\(348\) −100.145 −5.36836
\(349\) 4.59915 0.246187 0.123093 0.992395i \(-0.460719\pi\)
0.123093 + 0.992395i \(0.460719\pi\)
\(350\) 0 0
\(351\) 16.2660 0.868216
\(352\) 26.8423 1.43070
\(353\) −0.690423 −0.0367475 −0.0183737 0.999831i \(-0.505849\pi\)
−0.0183737 + 0.999831i \(0.505849\pi\)
\(354\) 31.1760 1.65699
\(355\) 0 0
\(356\) −10.4869 −0.555806
\(357\) −51.6476 −2.73348
\(358\) 27.0538 1.42984
\(359\) 0.484355 0.0255633 0.0127816 0.999918i \(-0.495931\pi\)
0.0127816 + 0.999918i \(0.495931\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −8.51583 −0.447582
\(363\) −2.74433 −0.144040
\(364\) 70.7589 3.70877
\(365\) 0 0
\(366\) −34.4403 −1.80023
\(367\) 10.4333 0.544614 0.272307 0.962210i \(-0.412213\pi\)
0.272307 + 0.962210i \(0.412213\pi\)
\(368\) 104.453 5.44497
\(369\) 48.7414 2.53738
\(370\) 0 0
\(371\) −28.5522 −1.48236
\(372\) −25.9911 −1.34757
\(373\) −12.4034 −0.642226 −0.321113 0.947041i \(-0.604057\pi\)
−0.321113 + 0.947041i \(0.604057\pi\)
\(374\) −16.2745 −0.841533
\(375\) 0 0
\(376\) −27.5134 −1.41889
\(377\) −24.7884 −1.27667
\(378\) 37.4103 1.92418
\(379\) −17.1068 −0.878719 −0.439359 0.898311i \(-0.644795\pi\)
−0.439359 + 0.898311i \(0.644795\pi\)
\(380\) 0 0
\(381\) 48.4991 2.48469
\(382\) 31.9809 1.63628
\(383\) −27.5259 −1.40651 −0.703253 0.710939i \(-0.748270\pi\)
−0.703253 + 0.710939i \(0.748270\pi\)
\(384\) −159.778 −8.15363
\(385\) 0 0
\(386\) −17.3551 −0.883350
\(387\) 9.85730 0.501075
\(388\) 15.1363 0.768427
\(389\) −29.4568 −1.49352 −0.746760 0.665094i \(-0.768391\pi\)
−0.746760 + 0.665094i \(0.768391\pi\)
\(390\) 0 0
\(391\) −35.8917 −1.81512
\(392\) 33.7970 1.70701
\(393\) 13.3207 0.671939
\(394\) 18.1220 0.912973
\(395\) 0 0
\(396\) 25.8193 1.29747
\(397\) −0.725541 −0.0364138 −0.0182069 0.999834i \(-0.505796\pi\)
−0.0182069 + 0.999834i \(0.505796\pi\)
\(398\) 31.6953 1.58874
\(399\) 8.80502 0.440802
\(400\) 0 0
\(401\) 25.0438 1.25063 0.625314 0.780373i \(-0.284971\pi\)
0.625314 + 0.780373i \(0.284971\pi\)
\(402\) 19.8954 0.992294
\(403\) −6.43342 −0.320471
\(404\) 19.1748 0.953981
\(405\) 0 0
\(406\) −57.0111 −2.82941
\(407\) −0.251830 −0.0124827
\(408\) 165.158 8.17656
\(409\) −38.9407 −1.92550 −0.962748 0.270401i \(-0.912844\pi\)
−0.962748 + 0.270401i \(0.912844\pi\)
\(410\) 0 0
\(411\) −1.29174 −0.0637168
\(412\) 108.957 5.36791
\(413\) 13.1368 0.646422
\(414\) 76.9287 3.78084
\(415\) 0 0
\(416\) −103.894 −5.09383
\(417\) −28.0625 −1.37422
\(418\) 2.77451 0.135706
\(419\) 35.0064 1.71018 0.855088 0.518482i \(-0.173503\pi\)
0.855088 + 0.518482i \(0.173503\pi\)
\(420\) 0 0
\(421\) −6.05787 −0.295242 −0.147621 0.989044i \(-0.547162\pi\)
−0.147621 + 0.989044i \(0.547162\pi\)
\(422\) −0.441487 −0.0214913
\(423\) −12.1514 −0.590822
\(424\) 91.3040 4.43411
\(425\) 0 0
\(426\) 42.0091 2.03535
\(427\) −14.5124 −0.702303
\(428\) 108.885 5.26315
\(429\) 10.6220 0.512836
\(430\) 0 0
\(431\) −9.48475 −0.456864 −0.228432 0.973560i \(-0.573360\pi\)
−0.228432 + 0.973560i \(0.573360\pi\)
\(432\) −71.7390 −3.45155
\(433\) 25.8710 1.24328 0.621641 0.783302i \(-0.286466\pi\)
0.621641 + 0.783302i \(0.286466\pi\)
\(434\) −14.7963 −0.710243
\(435\) 0 0
\(436\) −11.6361 −0.557270
\(437\) 6.11891 0.292707
\(438\) −20.8233 −0.994974
\(439\) −1.01956 −0.0486612 −0.0243306 0.999704i \(-0.507745\pi\)
−0.0243306 + 0.999704i \(0.507745\pi\)
\(440\) 0 0
\(441\) 14.9266 0.710792
\(442\) 62.9908 2.99617
\(443\) 17.3007 0.821982 0.410991 0.911639i \(-0.365183\pi\)
0.410991 + 0.911639i \(0.365183\pi\)
\(444\) 3.93786 0.186883
\(445\) 0 0
\(446\) 1.49118 0.0706094
\(447\) 52.8962 2.50190
\(448\) −129.408 −6.11393
\(449\) −30.9651 −1.46133 −0.730667 0.682734i \(-0.760791\pi\)
−0.730667 + 0.682734i \(0.760791\pi\)
\(450\) 0 0
\(451\) 10.7565 0.506504
\(452\) −11.4661 −0.539321
\(453\) 25.3731 1.19213
\(454\) 37.5202 1.76091
\(455\) 0 0
\(456\) −28.1566 −1.31855
\(457\) −38.9037 −1.81984 −0.909920 0.414784i \(-0.863857\pi\)
−0.909920 + 0.414784i \(0.863857\pi\)
\(458\) −29.4618 −1.37666
\(459\) 24.6508 1.15060
\(460\) 0 0
\(461\) −24.5284 −1.14240 −0.571200 0.820811i \(-0.693522\pi\)
−0.571200 + 0.820811i \(0.693522\pi\)
\(462\) 24.4296 1.13657
\(463\) 5.44017 0.252826 0.126413 0.991978i \(-0.459654\pi\)
0.126413 + 0.991978i \(0.459654\pi\)
\(464\) 109.326 5.07533
\(465\) 0 0
\(466\) 21.7358 1.00689
\(467\) −14.4461 −0.668487 −0.334243 0.942487i \(-0.608481\pi\)
−0.334243 + 0.942487i \(0.608481\pi\)
\(468\) −99.9343 −4.61946
\(469\) 8.38348 0.387113
\(470\) 0 0
\(471\) 24.9822 1.15112
\(472\) −42.0089 −1.93362
\(473\) 2.17536 0.100023
\(474\) −62.2157 −2.85766
\(475\) 0 0
\(476\) 107.233 4.91504
\(477\) 40.3249 1.84635
\(478\) 70.3066 3.21575
\(479\) 25.0982 1.14677 0.573383 0.819288i \(-0.305631\pi\)
0.573383 + 0.819288i \(0.305631\pi\)
\(480\) 0 0
\(481\) 0.974716 0.0444432
\(482\) −83.3905 −3.79833
\(483\) 53.8771 2.45149
\(484\) 5.69792 0.258996
\(485\) 0 0
\(486\) 50.6721 2.29854
\(487\) −27.8647 −1.26267 −0.631336 0.775510i \(-0.717493\pi\)
−0.631336 + 0.775510i \(0.717493\pi\)
\(488\) 46.4075 2.10077
\(489\) 36.1905 1.63659
\(490\) 0 0
\(491\) −5.39887 −0.243648 −0.121824 0.992552i \(-0.538874\pi\)
−0.121824 + 0.992552i \(0.538874\pi\)
\(492\) −168.199 −7.58300
\(493\) −37.5663 −1.69190
\(494\) −10.7388 −0.483163
\(495\) 0 0
\(496\) 28.3737 1.27402
\(497\) 17.7017 0.794028
\(498\) −93.1498 −4.17414
\(499\) −40.0954 −1.79492 −0.897458 0.441100i \(-0.854589\pi\)
−0.897458 + 0.441100i \(0.854589\pi\)
\(500\) 0 0
\(501\) −20.7673 −0.927813
\(502\) 66.7069 2.97728
\(503\) −19.3594 −0.863193 −0.431596 0.902067i \(-0.642050\pi\)
−0.431596 + 0.902067i \(0.642050\pi\)
\(504\) −149.165 −6.64432
\(505\) 0 0
\(506\) 16.9770 0.754719
\(507\) −5.43657 −0.241446
\(508\) −100.696 −4.46768
\(509\) −29.1426 −1.29172 −0.645862 0.763454i \(-0.723502\pi\)
−0.645862 + 0.763454i \(0.723502\pi\)
\(510\) 0 0
\(511\) −8.77444 −0.388158
\(512\) 107.928 4.76977
\(513\) −4.20253 −0.185546
\(514\) −18.2626 −0.805528
\(515\) 0 0
\(516\) −34.0160 −1.49747
\(517\) −2.68163 −0.117938
\(518\) 2.24175 0.0984970
\(519\) −33.8878 −1.48751
\(520\) 0 0
\(521\) 36.9334 1.61808 0.809042 0.587751i \(-0.199987\pi\)
0.809042 + 0.587751i \(0.199987\pi\)
\(522\) 80.5180 3.52418
\(523\) −43.8433 −1.91713 −0.958567 0.284867i \(-0.908050\pi\)
−0.958567 + 0.284867i \(0.908050\pi\)
\(524\) −27.6571 −1.20820
\(525\) 0 0
\(526\) −44.5200 −1.94116
\(527\) −9.74970 −0.424704
\(528\) −46.8470 −2.03875
\(529\) 14.4410 0.627872
\(530\) 0 0
\(531\) −18.5535 −0.805151
\(532\) −18.2814 −0.792601
\(533\) −41.6334 −1.80334
\(534\) 14.0138 0.606435
\(535\) 0 0
\(536\) −26.8086 −1.15796
\(537\) −26.7595 −1.15476
\(538\) −47.3260 −2.04037
\(539\) 3.29408 0.141886
\(540\) 0 0
\(541\) 26.3462 1.13271 0.566355 0.824161i \(-0.308353\pi\)
0.566355 + 0.824161i \(0.308353\pi\)
\(542\) 41.1894 1.76923
\(543\) 8.42319 0.361474
\(544\) −157.449 −6.75058
\(545\) 0 0
\(546\) −94.5557 −4.04661
\(547\) 13.6728 0.584609 0.292304 0.956325i \(-0.405578\pi\)
0.292304 + 0.956325i \(0.405578\pi\)
\(548\) 2.68198 0.114568
\(549\) 20.4961 0.874754
\(550\) 0 0
\(551\) 6.40440 0.272837
\(552\) −172.288 −7.33306
\(553\) −26.2163 −1.11483
\(554\) −23.8441 −1.01304
\(555\) 0 0
\(556\) 58.2647 2.47097
\(557\) −13.0278 −0.552007 −0.276004 0.961157i \(-0.589010\pi\)
−0.276004 + 0.961157i \(0.589010\pi\)
\(558\) 20.8971 0.884644
\(559\) −8.41978 −0.356119
\(560\) 0 0
\(561\) 16.0974 0.679634
\(562\) −37.3641 −1.57611
\(563\) −26.1689 −1.10289 −0.551445 0.834211i \(-0.685923\pi\)
−0.551445 + 0.834211i \(0.685923\pi\)
\(564\) 41.9326 1.76568
\(565\) 0 0
\(566\) −39.6441 −1.66637
\(567\) 6.61235 0.277693
\(568\) −56.6063 −2.37515
\(569\) 24.2618 1.01711 0.508554 0.861030i \(-0.330180\pi\)
0.508554 + 0.861030i \(0.330180\pi\)
\(570\) 0 0
\(571\) 6.25197 0.261637 0.130818 0.991406i \(-0.458240\pi\)
0.130818 + 0.991406i \(0.458240\pi\)
\(572\) −22.0540 −0.922123
\(573\) −31.6330 −1.32149
\(574\) −95.7528 −3.99664
\(575\) 0 0
\(576\) 182.765 7.61521
\(577\) 5.41416 0.225395 0.112697 0.993629i \(-0.464051\pi\)
0.112697 + 0.993629i \(0.464051\pi\)
\(578\) 48.2944 2.00878
\(579\) 17.1663 0.713406
\(580\) 0 0
\(581\) −39.2512 −1.62841
\(582\) −20.2267 −0.838424
\(583\) 8.89909 0.368562
\(584\) 28.0588 1.16108
\(585\) 0 0
\(586\) 81.9746 3.38634
\(587\) 29.2069 1.20550 0.602749 0.797931i \(-0.294072\pi\)
0.602749 + 0.797931i \(0.294072\pi\)
\(588\) −51.5095 −2.12422
\(589\) 1.66215 0.0684879
\(590\) 0 0
\(591\) −17.9249 −0.737330
\(592\) −4.29885 −0.176682
\(593\) −13.3606 −0.548653 −0.274326 0.961637i \(-0.588455\pi\)
−0.274326 + 0.961637i \(0.588455\pi\)
\(594\) −11.6600 −0.478414
\(595\) 0 0
\(596\) −109.826 −4.49864
\(597\) −31.3505 −1.28309
\(598\) −65.7100 −2.68708
\(599\) 7.63307 0.311879 0.155939 0.987767i \(-0.450160\pi\)
0.155939 + 0.987767i \(0.450160\pi\)
\(600\) 0 0
\(601\) −33.4520 −1.36454 −0.682269 0.731102i \(-0.739006\pi\)
−0.682269 + 0.731102i \(0.739006\pi\)
\(602\) −19.3647 −0.789246
\(603\) −11.8402 −0.482169
\(604\) −52.6810 −2.14356
\(605\) 0 0
\(606\) −25.6234 −1.04088
\(607\) −1.87063 −0.0759265 −0.0379633 0.999279i \(-0.512087\pi\)
−0.0379633 + 0.999279i \(0.512087\pi\)
\(608\) 26.8423 1.08860
\(609\) 56.3909 2.28507
\(610\) 0 0
\(611\) 10.3793 0.419903
\(612\) −151.448 −6.12193
\(613\) −30.9265 −1.24911 −0.624556 0.780980i \(-0.714720\pi\)
−0.624556 + 0.780980i \(0.714720\pi\)
\(614\) 59.9381 2.41890
\(615\) 0 0
\(616\) −32.9183 −1.32632
\(617\) 1.25799 0.0506447 0.0253224 0.999679i \(-0.491939\pi\)
0.0253224 + 0.999679i \(0.491939\pi\)
\(618\) −145.600 −5.85688
\(619\) 15.5642 0.625578 0.312789 0.949823i \(-0.398737\pi\)
0.312789 + 0.949823i \(0.398737\pi\)
\(620\) 0 0
\(621\) −25.7149 −1.03190
\(622\) 59.3871 2.38121
\(623\) 5.90508 0.236582
\(624\) 181.323 7.25872
\(625\) 0 0
\(626\) 63.0736 2.52093
\(627\) −2.74433 −0.109598
\(628\) −51.8693 −2.06981
\(629\) 1.47716 0.0588982
\(630\) 0 0
\(631\) −33.5188 −1.33436 −0.667182 0.744895i \(-0.732500\pi\)
−0.667182 + 0.744895i \(0.732500\pi\)
\(632\) 83.8342 3.33475
\(633\) 0.436685 0.0173567
\(634\) 3.59060 0.142601
\(635\) 0 0
\(636\) −139.155 −5.51785
\(637\) −12.7499 −0.505168
\(638\) 17.7691 0.703485
\(639\) −25.0005 −0.989003
\(640\) 0 0
\(641\) 1.89938 0.0750211 0.0375106 0.999296i \(-0.488057\pi\)
0.0375106 + 0.999296i \(0.488057\pi\)
\(642\) −145.504 −5.74258
\(643\) −19.4308 −0.766277 −0.383138 0.923691i \(-0.625157\pi\)
−0.383138 + 0.923691i \(0.625157\pi\)
\(644\) −111.862 −4.40800
\(645\) 0 0
\(646\) −16.2745 −0.640310
\(647\) −7.80761 −0.306949 −0.153474 0.988153i \(-0.549046\pi\)
−0.153474 + 0.988153i \(0.549046\pi\)
\(648\) −21.1449 −0.830652
\(649\) −4.09447 −0.160722
\(650\) 0 0
\(651\) 14.6353 0.573602
\(652\) −75.1406 −2.94273
\(653\) −21.0194 −0.822553 −0.411277 0.911511i \(-0.634917\pi\)
−0.411277 + 0.911511i \(0.634917\pi\)
\(654\) 15.5495 0.608032
\(655\) 0 0
\(656\) 183.618 7.16909
\(657\) 12.3923 0.483471
\(658\) 23.8715 0.930608
\(659\) 32.1192 1.25119 0.625594 0.780149i \(-0.284857\pi\)
0.625594 + 0.780149i \(0.284857\pi\)
\(660\) 0 0
\(661\) −26.8022 −1.04248 −0.521242 0.853409i \(-0.674531\pi\)
−0.521242 + 0.853409i \(0.674531\pi\)
\(662\) −62.0946 −2.41338
\(663\) −62.3056 −2.41975
\(664\) 125.517 4.87101
\(665\) 0 0
\(666\) −3.16608 −0.122683
\(667\) 39.1880 1.51736
\(668\) 43.1181 1.66829
\(669\) −1.47496 −0.0570252
\(670\) 0 0
\(671\) 4.52319 0.174616
\(672\) 236.347 9.11729
\(673\) −13.3416 −0.514281 −0.257140 0.966374i \(-0.582780\pi\)
−0.257140 + 0.966374i \(0.582780\pi\)
\(674\) 54.7837 2.11019
\(675\) 0 0
\(676\) 11.2877 0.434142
\(677\) 35.2641 1.35531 0.677654 0.735381i \(-0.262997\pi\)
0.677654 + 0.735381i \(0.262997\pi\)
\(678\) 15.3223 0.588449
\(679\) −8.52307 −0.327085
\(680\) 0 0
\(681\) −37.1121 −1.42214
\(682\) 4.61167 0.176590
\(683\) 22.6519 0.866753 0.433376 0.901213i \(-0.357322\pi\)
0.433376 + 0.901213i \(0.357322\pi\)
\(684\) 25.8193 0.987224
\(685\) 0 0
\(686\) 32.9895 1.25955
\(687\) 29.1413 1.11181
\(688\) 37.1343 1.41573
\(689\) −34.4442 −1.31222
\(690\) 0 0
\(691\) 13.6411 0.518930 0.259465 0.965752i \(-0.416454\pi\)
0.259465 + 0.965752i \(0.416454\pi\)
\(692\) 70.3597 2.67467
\(693\) −14.5386 −0.552274
\(694\) −60.0850 −2.28080
\(695\) 0 0
\(696\) −180.326 −6.83525
\(697\) −63.0944 −2.38987
\(698\) 12.7604 0.482988
\(699\) −21.4993 −0.813179
\(700\) 0 0
\(701\) 5.88833 0.222399 0.111200 0.993798i \(-0.464531\pi\)
0.111200 + 0.993798i \(0.464531\pi\)
\(702\) 45.1303 1.70333
\(703\) −0.251830 −0.00949795
\(704\) 40.3335 1.52013
\(705\) 0 0
\(706\) −1.91559 −0.0720940
\(707\) −10.7971 −0.406067
\(708\) 64.0251 2.40621
\(709\) −20.0746 −0.753919 −0.376960 0.926230i \(-0.623030\pi\)
−0.376960 + 0.926230i \(0.623030\pi\)
\(710\) 0 0
\(711\) 37.0258 1.38858
\(712\) −18.8832 −0.707678
\(713\) 10.1706 0.380891
\(714\) −143.297 −5.36275
\(715\) 0 0
\(716\) 55.5594 2.07635
\(717\) −69.5418 −2.59709
\(718\) 1.34385 0.0501520
\(719\) −19.9007 −0.742171 −0.371086 0.928599i \(-0.621014\pi\)
−0.371086 + 0.928599i \(0.621014\pi\)
\(720\) 0 0
\(721\) −61.3524 −2.28488
\(722\) 2.77451 0.103257
\(723\) 82.4833 3.06759
\(724\) −17.4887 −0.649961
\(725\) 0 0
\(726\) −7.61418 −0.282589
\(727\) −2.48983 −0.0923426 −0.0461713 0.998934i \(-0.514702\pi\)
−0.0461713 + 0.998934i \(0.514702\pi\)
\(728\) 127.412 4.72219
\(729\) −43.9381 −1.62734
\(730\) 0 0
\(731\) −12.7600 −0.471945
\(732\) −70.7289 −2.61422
\(733\) 1.67302 0.0617945 0.0308973 0.999523i \(-0.490164\pi\)
0.0308973 + 0.999523i \(0.490164\pi\)
\(734\) 28.9473 1.06847
\(735\) 0 0
\(736\) 164.246 6.05418
\(737\) −2.61295 −0.0962491
\(738\) 135.234 4.97802
\(739\) 12.3807 0.455432 0.227716 0.973728i \(-0.426874\pi\)
0.227716 + 0.973728i \(0.426874\pi\)
\(740\) 0 0
\(741\) 10.6220 0.390210
\(742\) −79.2184 −2.90820
\(743\) −2.41474 −0.0885881 −0.0442940 0.999019i \(-0.514104\pi\)
−0.0442940 + 0.999019i \(0.514104\pi\)
\(744\) −46.8006 −1.71579
\(745\) 0 0
\(746\) −34.4135 −1.25997
\(747\) 55.4353 2.02827
\(748\) −33.4223 −1.22204
\(749\) −61.3119 −2.24029
\(750\) 0 0
\(751\) 7.67280 0.279984 0.139992 0.990153i \(-0.455292\pi\)
0.139992 + 0.990153i \(0.455292\pi\)
\(752\) −45.7767 −1.66930
\(753\) −65.9813 −2.40449
\(754\) −68.7759 −2.50467
\(755\) 0 0
\(756\) 76.8282 2.79421
\(757\) 7.03423 0.255663 0.127832 0.991796i \(-0.459198\pi\)
0.127832 + 0.991796i \(0.459198\pi\)
\(758\) −47.4631 −1.72394
\(759\) −16.7923 −0.609522
\(760\) 0 0
\(761\) 8.98118 0.325567 0.162784 0.986662i \(-0.447953\pi\)
0.162784 + 0.986662i \(0.447953\pi\)
\(762\) 134.561 4.87465
\(763\) 6.55219 0.237205
\(764\) 65.6780 2.37615
\(765\) 0 0
\(766\) −76.3709 −2.75939
\(767\) 15.8478 0.572230
\(768\) −221.929 −8.00817
\(769\) 47.2240 1.70294 0.851470 0.524404i \(-0.175712\pi\)
0.851470 + 0.524404i \(0.175712\pi\)
\(770\) 0 0
\(771\) 18.0639 0.650556
\(772\) −35.6415 −1.28277
\(773\) −30.3348 −1.09107 −0.545533 0.838089i \(-0.683673\pi\)
−0.545533 + 0.838089i \(0.683673\pi\)
\(774\) 27.3492 0.983046
\(775\) 0 0
\(776\) 27.2550 0.978398
\(777\) −2.21737 −0.0795476
\(778\) −81.7283 −2.93010
\(779\) 10.7565 0.385392
\(780\) 0 0
\(781\) −5.51722 −0.197422
\(782\) −99.5820 −3.56104
\(783\) −26.9147 −0.961852
\(784\) 56.2315 2.00827
\(785\) 0 0
\(786\) 36.9584 1.31826
\(787\) −3.82340 −0.136289 −0.0681447 0.997675i \(-0.521708\pi\)
−0.0681447 + 0.997675i \(0.521708\pi\)
\(788\) 37.2165 1.32578
\(789\) 44.0356 1.56771
\(790\) 0 0
\(791\) 6.45645 0.229565
\(792\) 46.4913 1.65200
\(793\) −17.5071 −0.621697
\(794\) −2.01302 −0.0714395
\(795\) 0 0
\(796\) 65.0916 2.30711
\(797\) −32.7856 −1.16133 −0.580663 0.814144i \(-0.697207\pi\)
−0.580663 + 0.814144i \(0.697207\pi\)
\(798\) 24.4296 0.864800
\(799\) 15.7297 0.556475
\(800\) 0 0
\(801\) −8.33987 −0.294675
\(802\) 69.4844 2.45358
\(803\) 2.73480 0.0965090
\(804\) 40.8586 1.44097
\(805\) 0 0
\(806\) −17.8496 −0.628725
\(807\) 46.8112 1.64783
\(808\) 34.5270 1.21465
\(809\) 24.8694 0.874361 0.437181 0.899374i \(-0.355977\pi\)
0.437181 + 0.899374i \(0.355977\pi\)
\(810\) 0 0
\(811\) −20.4421 −0.717821 −0.358910 0.933372i \(-0.616852\pi\)
−0.358910 + 0.933372i \(0.616852\pi\)
\(812\) −117.082 −4.10876
\(813\) −40.7413 −1.42886
\(814\) −0.698705 −0.0244896
\(815\) 0 0
\(816\) 274.790 9.61958
\(817\) 2.17536 0.0761061
\(818\) −108.042 −3.77758
\(819\) 56.2719 1.96630
\(820\) 0 0
\(821\) 53.8539 1.87951 0.939757 0.341843i \(-0.111051\pi\)
0.939757 + 0.341843i \(0.111051\pi\)
\(822\) −3.58395 −0.125005
\(823\) 40.2952 1.40460 0.702301 0.711880i \(-0.252156\pi\)
0.702301 + 0.711880i \(0.252156\pi\)
\(824\) 196.192 6.83468
\(825\) 0 0
\(826\) 36.4484 1.26820
\(827\) −33.1923 −1.15421 −0.577105 0.816670i \(-0.695818\pi\)
−0.577105 + 0.816670i \(0.695818\pi\)
\(828\) 157.986 5.49038
\(829\) 28.6178 0.993937 0.496969 0.867769i \(-0.334446\pi\)
0.496969 + 0.867769i \(0.334446\pi\)
\(830\) 0 0
\(831\) 23.5847 0.818145
\(832\) −156.112 −5.41221
\(833\) −19.3221 −0.669471
\(834\) −77.8596 −2.69606
\(835\) 0 0
\(836\) 5.69792 0.197067
\(837\) −6.98525 −0.241445
\(838\) 97.1258 3.35516
\(839\) −5.00397 −0.172756 −0.0863781 0.996262i \(-0.527529\pi\)
−0.0863781 + 0.996262i \(0.527529\pi\)
\(840\) 0 0
\(841\) 12.0164 0.414358
\(842\) −16.8076 −0.579229
\(843\) 36.9576 1.27289
\(844\) −0.906667 −0.0312088
\(845\) 0 0
\(846\) −33.7142 −1.15912
\(847\) −3.20844 −0.110243
\(848\) 151.911 5.21666
\(849\) 39.2129 1.34578
\(850\) 0 0
\(851\) −1.54092 −0.0528222
\(852\) 86.2726 2.95565
\(853\) 14.8401 0.508117 0.254058 0.967189i \(-0.418234\pi\)
0.254058 + 0.967189i \(0.418234\pi\)
\(854\) −40.2647 −1.37783
\(855\) 0 0
\(856\) 196.063 6.70129
\(857\) −9.89677 −0.338067 −0.169034 0.985610i \(-0.554065\pi\)
−0.169034 + 0.985610i \(0.554065\pi\)
\(858\) 29.4709 1.00612
\(859\) −21.7867 −0.743352 −0.371676 0.928363i \(-0.621217\pi\)
−0.371676 + 0.928363i \(0.621217\pi\)
\(860\) 0 0
\(861\) 94.7112 3.22775
\(862\) −26.3155 −0.896311
\(863\) −24.4284 −0.831553 −0.415776 0.909467i \(-0.636490\pi\)
−0.415776 + 0.909467i \(0.636490\pi\)
\(864\) −112.806 −3.83772
\(865\) 0 0
\(866\) 71.7795 2.43917
\(867\) −47.7691 −1.62232
\(868\) −30.3865 −1.03139
\(869\) 8.17104 0.277183
\(870\) 0 0
\(871\) 10.1135 0.342682
\(872\) −20.9525 −0.709542
\(873\) 12.0373 0.407401
\(874\) 16.9770 0.574255
\(875\) 0 0
\(876\) −42.7640 −1.44486
\(877\) 24.9962 0.844062 0.422031 0.906581i \(-0.361317\pi\)
0.422031 + 0.906581i \(0.361317\pi\)
\(878\) −2.82879 −0.0954672
\(879\) −81.0828 −2.73486
\(880\) 0 0
\(881\) −25.3991 −0.855719 −0.427859 0.903845i \(-0.640732\pi\)
−0.427859 + 0.903845i \(0.640732\pi\)
\(882\) 41.4141 1.39449
\(883\) 48.3559 1.62731 0.813653 0.581351i \(-0.197476\pi\)
0.813653 + 0.581351i \(0.197476\pi\)
\(884\) 129.362 4.35092
\(885\) 0 0
\(886\) 48.0010 1.61263
\(887\) −22.8073 −0.765793 −0.382897 0.923791i \(-0.625073\pi\)
−0.382897 + 0.923791i \(0.625073\pi\)
\(888\) 7.09068 0.237948
\(889\) 56.7011 1.90169
\(890\) 0 0
\(891\) −2.06093 −0.0690436
\(892\) 3.06238 0.102536
\(893\) −2.68163 −0.0897374
\(894\) 146.761 4.90843
\(895\) 0 0
\(896\) −186.799 −6.24051
\(897\) 64.9952 2.17013
\(898\) −85.9131 −2.86696
\(899\) 10.6451 0.355034
\(900\) 0 0
\(901\) −52.1994 −1.73901
\(902\) 29.8440 0.993698
\(903\) 19.1540 0.637407
\(904\) −20.6464 −0.686689
\(905\) 0 0
\(906\) 70.3981 2.33882
\(907\) −4.89927 −0.162678 −0.0813388 0.996687i \(-0.525920\pi\)
−0.0813388 + 0.996687i \(0.525920\pi\)
\(908\) 77.0540 2.55713
\(909\) 15.2490 0.505778
\(910\) 0 0
\(911\) 14.2078 0.470727 0.235364 0.971907i \(-0.424372\pi\)
0.235364 + 0.971907i \(0.424372\pi\)
\(912\) −46.8470 −1.55126
\(913\) 12.2337 0.404877
\(914\) −107.939 −3.57030
\(915\) 0 0
\(916\) −60.5046 −1.99913
\(917\) 15.5734 0.514279
\(918\) 68.3939 2.25733
\(919\) 37.3984 1.23366 0.616830 0.787096i \(-0.288417\pi\)
0.616830 + 0.787096i \(0.288417\pi\)
\(920\) 0 0
\(921\) −59.2861 −1.95354
\(922\) −68.0542 −2.24125
\(923\) 21.3546 0.702895
\(924\) 50.1703 1.65048
\(925\) 0 0
\(926\) 15.0938 0.496013
\(927\) 86.6493 2.84594
\(928\) 171.909 5.64319
\(929\) 18.4186 0.604294 0.302147 0.953261i \(-0.402297\pi\)
0.302147 + 0.953261i \(0.402297\pi\)
\(930\) 0 0
\(931\) 3.29408 0.107959
\(932\) 44.6380 1.46217
\(933\) −58.7411 −1.92310
\(934\) −40.0810 −1.31149
\(935\) 0 0
\(936\) −179.946 −5.88172
\(937\) 59.8435 1.95500 0.977501 0.210930i \(-0.0676493\pi\)
0.977501 + 0.210930i \(0.0676493\pi\)
\(938\) 23.2601 0.759468
\(939\) −62.3874 −2.03594
\(940\) 0 0
\(941\) 14.5570 0.474545 0.237272 0.971443i \(-0.423747\pi\)
0.237272 + 0.971443i \(0.423747\pi\)
\(942\) 69.3134 2.25835
\(943\) 65.8180 2.14333
\(944\) −69.8944 −2.27487
\(945\) 0 0
\(946\) 6.03555 0.196233
\(947\) 15.6623 0.508955 0.254478 0.967079i \(-0.418097\pi\)
0.254478 + 0.967079i \(0.418097\pi\)
\(948\) −127.770 −4.14979
\(949\) −10.5851 −0.343608
\(950\) 0 0
\(951\) −3.55154 −0.115166
\(952\) 193.089 6.25806
\(953\) −27.6656 −0.896176 −0.448088 0.893990i \(-0.647895\pi\)
−0.448088 + 0.893990i \(0.647895\pi\)
\(954\) 111.882 3.62231
\(955\) 0 0
\(956\) 144.386 4.66979
\(957\) −17.5758 −0.568145
\(958\) 69.6352 2.24981
\(959\) −1.51019 −0.0487667
\(960\) 0 0
\(961\) −28.2372 −0.910879
\(962\) 2.70436 0.0871921
\(963\) 86.5922 2.79039
\(964\) −171.256 −5.51579
\(965\) 0 0
\(966\) 149.483 4.80953
\(967\) −2.39400 −0.0769857 −0.0384929 0.999259i \(-0.512256\pi\)
−0.0384929 + 0.999259i \(0.512256\pi\)
\(968\) 10.2599 0.329766
\(969\) 16.0974 0.517124
\(970\) 0 0
\(971\) 9.52917 0.305806 0.152903 0.988241i \(-0.451138\pi\)
0.152903 + 0.988241i \(0.451138\pi\)
\(972\) 104.064 3.33784
\(973\) −32.8083 −1.05178
\(974\) −77.3111 −2.47721
\(975\) 0 0
\(976\) 77.2128 2.47152
\(977\) 17.6663 0.565194 0.282597 0.959239i \(-0.408804\pi\)
0.282597 + 0.959239i \(0.408804\pi\)
\(978\) 100.411 3.21079
\(979\) −1.84048 −0.0588221
\(980\) 0 0
\(981\) −9.25380 −0.295451
\(982\) −14.9792 −0.478007
\(983\) 3.24817 0.103601 0.0518003 0.998657i \(-0.483504\pi\)
0.0518003 + 0.998657i \(0.483504\pi\)
\(984\) −302.867 −9.65504
\(985\) 0 0
\(986\) −104.228 −3.31930
\(987\) −23.6118 −0.751573
\(988\) −22.0540 −0.701631
\(989\) 13.3108 0.423259
\(990\) 0 0
\(991\) −15.8274 −0.502774 −0.251387 0.967887i \(-0.580887\pi\)
−0.251387 + 0.967887i \(0.580887\pi\)
\(992\) 44.6161 1.41656
\(993\) 61.4191 1.94908
\(994\) 49.1135 1.55779
\(995\) 0 0
\(996\) −191.298 −6.06152
\(997\) −47.5564 −1.50613 −0.753063 0.657948i \(-0.771425\pi\)
−0.753063 + 0.657948i \(0.771425\pi\)
\(998\) −111.245 −3.52140
\(999\) 1.05832 0.0334838
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 5225.2.a.bc.1.29 30
5.2 odd 4 1045.2.b.e.419.29 yes 30
5.3 odd 4 1045.2.b.e.419.2 30
5.4 even 2 inner 5225.2.a.bc.1.2 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.b.e.419.2 30 5.3 odd 4
1045.2.b.e.419.29 yes 30 5.2 odd 4
5225.2.a.bc.1.2 30 5.4 even 2 inner
5225.2.a.bc.1.29 30 1.1 even 1 trivial