Properties

Label 5225.2.a.t.1.1
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $15$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - x^{14} - 21 x^{13} + 19 x^{12} + 170 x^{11} - 137 x^{10} - 669 x^{9} + 458 x^{8} + 1327 x^{7} + \cdots - 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.77430\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q-2.77430 q^{2} +1.94173 q^{3} +5.69673 q^{4} -5.38694 q^{6} +2.77587 q^{7} -10.2558 q^{8} +0.770318 q^{9} +O(q^{10})\) \(q-2.77430 q^{2} +1.94173 q^{3} +5.69673 q^{4} -5.38694 q^{6} +2.77587 q^{7} -10.2558 q^{8} +0.770318 q^{9} -1.00000 q^{11} +11.0615 q^{12} +5.64562 q^{13} -7.70110 q^{14} +17.0593 q^{16} -5.70735 q^{17} -2.13709 q^{18} -1.00000 q^{19} +5.39000 q^{21} +2.77430 q^{22} +6.18297 q^{23} -19.9141 q^{24} -15.6626 q^{26} -4.32944 q^{27} +15.8134 q^{28} +0.792484 q^{29} -0.751562 q^{31} -26.8158 q^{32} -1.94173 q^{33} +15.8339 q^{34} +4.38829 q^{36} +8.00003 q^{37} +2.77430 q^{38} +10.9623 q^{39} -1.67160 q^{41} -14.9535 q^{42} +7.73402 q^{43} -5.69673 q^{44} -17.1534 q^{46} +1.87396 q^{47} +33.1245 q^{48} +0.705463 q^{49} -11.0821 q^{51} +32.1616 q^{52} +6.61718 q^{53} +12.0112 q^{54} -28.4689 q^{56} -1.94173 q^{57} -2.19859 q^{58} +0.166695 q^{59} +0.201036 q^{61} +2.08506 q^{62} +2.13830 q^{63} +40.2766 q^{64} +5.38694 q^{66} +8.80812 q^{67} -32.5133 q^{68} +12.0057 q^{69} -7.12183 q^{71} -7.90025 q^{72} -9.18192 q^{73} -22.1945 q^{74} -5.69673 q^{76} -2.77587 q^{77} -30.4126 q^{78} -15.8144 q^{79} -10.7176 q^{81} +4.63752 q^{82} +5.55960 q^{83} +30.7053 q^{84} -21.4565 q^{86} +1.53879 q^{87} +10.2558 q^{88} +14.1037 q^{89} +15.6715 q^{91} +35.2227 q^{92} -1.45933 q^{93} -5.19893 q^{94} -52.0692 q^{96} -6.98540 q^{97} -1.95717 q^{98} -0.770318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15 q - q^{2} + 4 q^{3} + 13 q^{4} - q^{6} + 11 q^{7} - 3 q^{8} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 15 q - q^{2} + 4 q^{3} + 13 q^{4} - q^{6} + 11 q^{7} - 3 q^{8} + 19 q^{9} - 15 q^{11} + 11 q^{12} + 3 q^{13} - 11 q^{14} + 13 q^{16} - 5 q^{17} + 12 q^{18} - 15 q^{19} + 10 q^{21} + q^{22} + 26 q^{23} - 11 q^{24} - 5 q^{26} + 19 q^{27} + 18 q^{28} + 7 q^{29} - 10 q^{31} - 12 q^{32} - 4 q^{33} + 17 q^{34} + 24 q^{36} + 31 q^{37} + q^{38} + 4 q^{39} + 2 q^{41} + 22 q^{42} + 26 q^{43} - 13 q^{44} - 23 q^{46} + 26 q^{47} + 46 q^{48} + 12 q^{49} + 12 q^{51} + 16 q^{52} + 21 q^{53} + 5 q^{54} - 10 q^{56} - 4 q^{57} + 34 q^{58} - 11 q^{59} + 20 q^{61} + 25 q^{62} + 27 q^{63} - 3 q^{64} + q^{66} + 41 q^{67} - 6 q^{68} + q^{69} + 25 q^{71} + 54 q^{72} - 6 q^{73} - 9 q^{74} - 13 q^{76} - 11 q^{77} + 28 q^{78} - 6 q^{79} + 43 q^{81} + 18 q^{82} - 20 q^{83} - 14 q^{84} + 35 q^{86} + 29 q^{87} + 3 q^{88} - 3 q^{89} + 30 q^{91} + 54 q^{92} + 2 q^{93} - 28 q^{94} - 61 q^{96} + 28 q^{97} - 2 q^{98} - 19 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77430 −1.96173 −0.980863 0.194702i \(-0.937626\pi\)
−0.980863 + 0.194702i \(0.937626\pi\)
\(3\) 1.94173 1.12106 0.560529 0.828135i \(-0.310598\pi\)
0.560529 + 0.828135i \(0.310598\pi\)
\(4\) 5.69673 2.84837
\(5\) 0 0
\(6\) −5.38694 −2.19921
\(7\) 2.77587 1.04918 0.524590 0.851355i \(-0.324218\pi\)
0.524590 + 0.851355i \(0.324218\pi\)
\(8\) −10.2558 −3.62598
\(9\) 0.770318 0.256773
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 11.0615 3.19318
\(13\) 5.64562 1.56581 0.782907 0.622139i \(-0.213736\pi\)
0.782907 + 0.622139i \(0.213736\pi\)
\(14\) −7.70110 −2.05820
\(15\) 0 0
\(16\) 17.0593 4.26482
\(17\) −5.70735 −1.38424 −0.692118 0.721784i \(-0.743322\pi\)
−0.692118 + 0.721784i \(0.743322\pi\)
\(18\) −2.13709 −0.503717
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 5.39000 1.17619
\(22\) 2.77430 0.591482
\(23\) 6.18297 1.28924 0.644619 0.764504i \(-0.277016\pi\)
0.644619 + 0.764504i \(0.277016\pi\)
\(24\) −19.9141 −4.06494
\(25\) 0 0
\(26\) −15.6626 −3.07170
\(27\) −4.32944 −0.833201
\(28\) 15.8134 2.98845
\(29\) 0.792484 0.147161 0.0735803 0.997289i \(-0.476557\pi\)
0.0735803 + 0.997289i \(0.476557\pi\)
\(30\) 0 0
\(31\) −0.751562 −0.134984 −0.0674922 0.997720i \(-0.521500\pi\)
−0.0674922 + 0.997720i \(0.521500\pi\)
\(32\) −26.8158 −4.74042
\(33\) −1.94173 −0.338012
\(34\) 15.8339 2.71549
\(35\) 0 0
\(36\) 4.38829 0.731382
\(37\) 8.00003 1.31520 0.657598 0.753369i \(-0.271573\pi\)
0.657598 + 0.753369i \(0.271573\pi\)
\(38\) 2.77430 0.450051
\(39\) 10.9623 1.75537
\(40\) 0 0
\(41\) −1.67160 −0.261060 −0.130530 0.991444i \(-0.541668\pi\)
−0.130530 + 0.991444i \(0.541668\pi\)
\(42\) −14.9535 −2.30737
\(43\) 7.73402 1.17943 0.589714 0.807612i \(-0.299241\pi\)
0.589714 + 0.807612i \(0.299241\pi\)
\(44\) −5.69673 −0.858814
\(45\) 0 0
\(46\) −17.1534 −2.52913
\(47\) 1.87396 0.273345 0.136673 0.990616i \(-0.456359\pi\)
0.136673 + 0.990616i \(0.456359\pi\)
\(48\) 33.1245 4.78111
\(49\) 0.705463 0.100780
\(50\) 0 0
\(51\) −11.0821 −1.55181
\(52\) 32.1616 4.46001
\(53\) 6.61718 0.908939 0.454470 0.890762i \(-0.349829\pi\)
0.454470 + 0.890762i \(0.349829\pi\)
\(54\) 12.0112 1.63451
\(55\) 0 0
\(56\) −28.4689 −3.80431
\(57\) −1.94173 −0.257189
\(58\) −2.19859 −0.288689
\(59\) 0.166695 0.0217018 0.0108509 0.999941i \(-0.496546\pi\)
0.0108509 + 0.999941i \(0.496546\pi\)
\(60\) 0 0
\(61\) 0.201036 0.0257400 0.0128700 0.999917i \(-0.495903\pi\)
0.0128700 + 0.999917i \(0.495903\pi\)
\(62\) 2.08506 0.264802
\(63\) 2.13830 0.269401
\(64\) 40.2766 5.03458
\(65\) 0 0
\(66\) 5.38694 0.663086
\(67\) 8.80812 1.07608 0.538041 0.842918i \(-0.319164\pi\)
0.538041 + 0.842918i \(0.319164\pi\)
\(68\) −32.5133 −3.94281
\(69\) 12.0057 1.44531
\(70\) 0 0
\(71\) −7.12183 −0.845206 −0.422603 0.906315i \(-0.638883\pi\)
−0.422603 + 0.906315i \(0.638883\pi\)
\(72\) −7.90025 −0.931054
\(73\) −9.18192 −1.07466 −0.537331 0.843371i \(-0.680567\pi\)
−0.537331 + 0.843371i \(0.680567\pi\)
\(74\) −22.1945 −2.58005
\(75\) 0 0
\(76\) −5.69673 −0.653460
\(77\) −2.77587 −0.316340
\(78\) −30.4126 −3.44355
\(79\) −15.8144 −1.77926 −0.889630 0.456683i \(-0.849037\pi\)
−0.889630 + 0.456683i \(0.849037\pi\)
\(80\) 0 0
\(81\) −10.7176 −1.19084
\(82\) 4.63752 0.512128
\(83\) 5.55960 0.610246 0.305123 0.952313i \(-0.401302\pi\)
0.305123 + 0.952313i \(0.401302\pi\)
\(84\) 30.7053 3.35023
\(85\) 0 0
\(86\) −21.4565 −2.31371
\(87\) 1.53879 0.164976
\(88\) 10.2558 1.09328
\(89\) 14.1037 1.49499 0.747497 0.664265i \(-0.231255\pi\)
0.747497 + 0.664265i \(0.231255\pi\)
\(90\) 0 0
\(91\) 15.6715 1.64282
\(92\) 35.2227 3.67222
\(93\) −1.45933 −0.151326
\(94\) −5.19893 −0.536229
\(95\) 0 0
\(96\) −52.0692 −5.31429
\(97\) −6.98540 −0.709260 −0.354630 0.935007i \(-0.615393\pi\)
−0.354630 + 0.935007i \(0.615393\pi\)
\(98\) −1.95717 −0.197704
\(99\) −0.770318 −0.0774199
\(100\) 0 0
\(101\) 0.910231 0.0905714 0.0452857 0.998974i \(-0.485580\pi\)
0.0452857 + 0.998974i \(0.485580\pi\)
\(102\) 30.7452 3.04423
\(103\) 12.4284 1.22461 0.612304 0.790622i \(-0.290243\pi\)
0.612304 + 0.790622i \(0.290243\pi\)
\(104\) −57.9006 −5.67762
\(105\) 0 0
\(106\) −18.3580 −1.78309
\(107\) 6.28051 0.607159 0.303580 0.952806i \(-0.401818\pi\)
0.303580 + 0.952806i \(0.401818\pi\)
\(108\) −24.6637 −2.37326
\(109\) −3.29802 −0.315893 −0.157947 0.987448i \(-0.550487\pi\)
−0.157947 + 0.987448i \(0.550487\pi\)
\(110\) 0 0
\(111\) 15.5339 1.47441
\(112\) 47.3544 4.47457
\(113\) 20.5504 1.93322 0.966612 0.256246i \(-0.0824856\pi\)
0.966612 + 0.256246i \(0.0824856\pi\)
\(114\) 5.38694 0.504533
\(115\) 0 0
\(116\) 4.51457 0.419167
\(117\) 4.34893 0.402058
\(118\) −0.462462 −0.0425730
\(119\) −15.8429 −1.45231
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −0.557734 −0.0504949
\(123\) −3.24580 −0.292664
\(124\) −4.28144 −0.384485
\(125\) 0 0
\(126\) −5.93229 −0.528491
\(127\) −8.64921 −0.767493 −0.383747 0.923438i \(-0.625366\pi\)
−0.383747 + 0.923438i \(0.625366\pi\)
\(128\) −58.1076 −5.13604
\(129\) 15.0174 1.32221
\(130\) 0 0
\(131\) −9.73817 −0.850828 −0.425414 0.904999i \(-0.639871\pi\)
−0.425414 + 0.904999i \(0.639871\pi\)
\(132\) −11.0615 −0.962781
\(133\) −2.77587 −0.240699
\(134\) −24.4363 −2.11098
\(135\) 0 0
\(136\) 58.5337 5.01922
\(137\) 3.78874 0.323694 0.161847 0.986816i \(-0.448255\pi\)
0.161847 + 0.986816i \(0.448255\pi\)
\(138\) −33.3073 −2.83530
\(139\) 20.9043 1.77308 0.886539 0.462655i \(-0.153103\pi\)
0.886539 + 0.462655i \(0.153103\pi\)
\(140\) 0 0
\(141\) 3.63873 0.306436
\(142\) 19.7581 1.65806
\(143\) −5.64562 −0.472111
\(144\) 13.1411 1.09509
\(145\) 0 0
\(146\) 25.4734 2.10819
\(147\) 1.36982 0.112981
\(148\) 45.5740 3.74616
\(149\) 0.532397 0.0436156 0.0218078 0.999762i \(-0.493058\pi\)
0.0218078 + 0.999762i \(0.493058\pi\)
\(150\) 0 0
\(151\) 4.22734 0.344016 0.172008 0.985096i \(-0.444975\pi\)
0.172008 + 0.985096i \(0.444975\pi\)
\(152\) 10.2558 0.831858
\(153\) −4.39648 −0.355434
\(154\) 7.70110 0.620572
\(155\) 0 0
\(156\) 62.4492 4.99993
\(157\) −7.61939 −0.608093 −0.304047 0.952657i \(-0.598338\pi\)
−0.304047 + 0.952657i \(0.598338\pi\)
\(158\) 43.8739 3.49042
\(159\) 12.8488 1.01897
\(160\) 0 0
\(161\) 17.1631 1.35264
\(162\) 29.7337 2.33610
\(163\) −17.0809 −1.33788 −0.668938 0.743318i \(-0.733251\pi\)
−0.668938 + 0.743318i \(0.733251\pi\)
\(164\) −9.52266 −0.743595
\(165\) 0 0
\(166\) −15.4240 −1.19713
\(167\) 22.4009 1.73343 0.866715 0.498803i \(-0.166227\pi\)
0.866715 + 0.498803i \(0.166227\pi\)
\(168\) −55.2789 −4.26486
\(169\) 18.8731 1.45177
\(170\) 0 0
\(171\) −0.770318 −0.0589077
\(172\) 44.0586 3.35944
\(173\) −12.1596 −0.924476 −0.462238 0.886756i \(-0.652953\pi\)
−0.462238 + 0.886756i \(0.652953\pi\)
\(174\) −4.26907 −0.323637
\(175\) 0 0
\(176\) −17.0593 −1.28589
\(177\) 0.323677 0.0243290
\(178\) −39.1280 −2.93277
\(179\) 24.8004 1.85367 0.926835 0.375468i \(-0.122518\pi\)
0.926835 + 0.375468i \(0.122518\pi\)
\(180\) 0 0
\(181\) 8.89610 0.661242 0.330621 0.943764i \(-0.392742\pi\)
0.330621 + 0.943764i \(0.392742\pi\)
\(182\) −43.4775 −3.22277
\(183\) 0.390358 0.0288561
\(184\) −63.4115 −4.67475
\(185\) 0 0
\(186\) 4.04862 0.296859
\(187\) 5.70735 0.417363
\(188\) 10.6755 0.778588
\(189\) −12.0180 −0.874179
\(190\) 0 0
\(191\) 10.3255 0.747125 0.373563 0.927605i \(-0.378136\pi\)
0.373563 + 0.927605i \(0.378136\pi\)
\(192\) 78.2063 5.64406
\(193\) 21.7903 1.56850 0.784249 0.620446i \(-0.213048\pi\)
0.784249 + 0.620446i \(0.213048\pi\)
\(194\) 19.3796 1.39137
\(195\) 0 0
\(196\) 4.01883 0.287060
\(197\) 22.1100 1.57527 0.787637 0.616139i \(-0.211304\pi\)
0.787637 + 0.616139i \(0.211304\pi\)
\(198\) 2.13709 0.151876
\(199\) −26.9341 −1.90931 −0.954654 0.297718i \(-0.903774\pi\)
−0.954654 + 0.297718i \(0.903774\pi\)
\(200\) 0 0
\(201\) 17.1030 1.20635
\(202\) −2.52525 −0.177676
\(203\) 2.19983 0.154398
\(204\) −63.1320 −4.42012
\(205\) 0 0
\(206\) −34.4801 −2.40235
\(207\) 4.76285 0.331041
\(208\) 96.3102 6.67791
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) 22.3720 1.54015 0.770076 0.637952i \(-0.220218\pi\)
0.770076 + 0.637952i \(0.220218\pi\)
\(212\) 37.6963 2.58899
\(213\) −13.8287 −0.947525
\(214\) −17.4240 −1.19108
\(215\) 0 0
\(216\) 44.4020 3.02118
\(217\) −2.08624 −0.141623
\(218\) 9.14970 0.619696
\(219\) −17.8288 −1.20476
\(220\) 0 0
\(221\) −32.2216 −2.16746
\(222\) −43.0957 −2.89239
\(223\) −20.6722 −1.38431 −0.692156 0.721748i \(-0.743339\pi\)
−0.692156 + 0.721748i \(0.743339\pi\)
\(224\) −74.4374 −4.97356
\(225\) 0 0
\(226\) −57.0131 −3.79245
\(227\) −3.83032 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(228\) −11.0615 −0.732567
\(229\) 23.6716 1.56427 0.782133 0.623112i \(-0.214132\pi\)
0.782133 + 0.623112i \(0.214132\pi\)
\(230\) 0 0
\(231\) −5.39000 −0.354636
\(232\) −8.12759 −0.533602
\(233\) −22.6832 −1.48603 −0.743014 0.669276i \(-0.766605\pi\)
−0.743014 + 0.669276i \(0.766605\pi\)
\(234\) −12.0652 −0.788728
\(235\) 0 0
\(236\) 0.949616 0.0618148
\(237\) −30.7073 −1.99465
\(238\) 43.9529 2.84904
\(239\) 10.6914 0.691568 0.345784 0.938314i \(-0.387613\pi\)
0.345784 + 0.938314i \(0.387613\pi\)
\(240\) 0 0
\(241\) −22.1453 −1.42651 −0.713253 0.700907i \(-0.752779\pi\)
−0.713253 + 0.700907i \(0.752779\pi\)
\(242\) −2.77430 −0.178339
\(243\) −7.82230 −0.501801
\(244\) 1.14525 0.0733170
\(245\) 0 0
\(246\) 9.00481 0.574126
\(247\) −5.64562 −0.359222
\(248\) 7.70789 0.489452
\(249\) 10.7953 0.684121
\(250\) 0 0
\(251\) 3.23296 0.204063 0.102031 0.994781i \(-0.467466\pi\)
0.102031 + 0.994781i \(0.467466\pi\)
\(252\) 12.1813 0.767352
\(253\) −6.18297 −0.388720
\(254\) 23.9955 1.50561
\(255\) 0 0
\(256\) 80.6547 5.04092
\(257\) 17.9652 1.12064 0.560319 0.828277i \(-0.310679\pi\)
0.560319 + 0.828277i \(0.310679\pi\)
\(258\) −41.6627 −2.59381
\(259\) 22.2070 1.37988
\(260\) 0 0
\(261\) 0.610465 0.0377868
\(262\) 27.0166 1.66909
\(263\) −5.55208 −0.342356 −0.171178 0.985240i \(-0.554757\pi\)
−0.171178 + 0.985240i \(0.554757\pi\)
\(264\) 19.9141 1.22563
\(265\) 0 0
\(266\) 7.70110 0.472184
\(267\) 27.3857 1.67598
\(268\) 50.1775 3.06508
\(269\) 22.7264 1.38565 0.692825 0.721106i \(-0.256366\pi\)
0.692825 + 0.721106i \(0.256366\pi\)
\(270\) 0 0
\(271\) −2.63465 −0.160044 −0.0800218 0.996793i \(-0.525499\pi\)
−0.0800218 + 0.996793i \(0.525499\pi\)
\(272\) −97.3633 −5.90352
\(273\) 30.4299 1.84170
\(274\) −10.5111 −0.634998
\(275\) 0 0
\(276\) 68.3930 4.11677
\(277\) −6.51174 −0.391252 −0.195626 0.980679i \(-0.562674\pi\)
−0.195626 + 0.980679i \(0.562674\pi\)
\(278\) −57.9947 −3.47829
\(279\) −0.578941 −0.0346603
\(280\) 0 0
\(281\) −28.6180 −1.70721 −0.853603 0.520924i \(-0.825588\pi\)
−0.853603 + 0.520924i \(0.825588\pi\)
\(282\) −10.0949 −0.601144
\(283\) 4.40932 0.262107 0.131054 0.991375i \(-0.458164\pi\)
0.131054 + 0.991375i \(0.458164\pi\)
\(284\) −40.5711 −2.40745
\(285\) 0 0
\(286\) 15.6626 0.926152
\(287\) −4.64015 −0.273899
\(288\) −20.6567 −1.21721
\(289\) 15.5739 0.916111
\(290\) 0 0
\(291\) −13.5638 −0.795122
\(292\) −52.3069 −3.06103
\(293\) −6.12582 −0.357874 −0.178937 0.983860i \(-0.557266\pi\)
−0.178937 + 0.983860i \(0.557266\pi\)
\(294\) −3.80029 −0.221637
\(295\) 0 0
\(296\) −82.0469 −4.76888
\(297\) 4.32944 0.251220
\(298\) −1.47703 −0.0855619
\(299\) 34.9067 2.01871
\(300\) 0 0
\(301\) 21.4687 1.23743
\(302\) −11.7279 −0.674864
\(303\) 1.76742 0.101536
\(304\) −17.0593 −0.978416
\(305\) 0 0
\(306\) 12.1971 0.697264
\(307\) −18.2599 −1.04215 −0.521073 0.853512i \(-0.674468\pi\)
−0.521073 + 0.853512i \(0.674468\pi\)
\(308\) −15.8134 −0.901052
\(309\) 24.1326 1.37286
\(310\) 0 0
\(311\) −25.5350 −1.44796 −0.723978 0.689823i \(-0.757688\pi\)
−0.723978 + 0.689823i \(0.757688\pi\)
\(312\) −112.427 −6.36494
\(313\) −9.91636 −0.560506 −0.280253 0.959926i \(-0.590418\pi\)
−0.280253 + 0.959926i \(0.590418\pi\)
\(314\) 21.1385 1.19291
\(315\) 0 0
\(316\) −90.0904 −5.06798
\(317\) −19.1690 −1.07664 −0.538320 0.842741i \(-0.680941\pi\)
−0.538320 + 0.842741i \(0.680941\pi\)
\(318\) −35.6463 −1.99895
\(319\) −0.792484 −0.0443706
\(320\) 0 0
\(321\) 12.1951 0.680661
\(322\) −47.6156 −2.65351
\(323\) 5.70735 0.317566
\(324\) −61.0551 −3.39195
\(325\) 0 0
\(326\) 47.3874 2.62455
\(327\) −6.40387 −0.354135
\(328\) 17.1437 0.946600
\(329\) 5.20188 0.286789
\(330\) 0 0
\(331\) 18.8363 1.03534 0.517668 0.855582i \(-0.326800\pi\)
0.517668 + 0.855582i \(0.326800\pi\)
\(332\) 31.6716 1.73820
\(333\) 6.16256 0.337706
\(334\) −62.1467 −3.40051
\(335\) 0 0
\(336\) 91.9494 5.01625
\(337\) −20.8985 −1.13841 −0.569206 0.822195i \(-0.692749\pi\)
−0.569206 + 0.822195i \(0.692749\pi\)
\(338\) −52.3595 −2.84798
\(339\) 39.9034 2.16726
\(340\) 0 0
\(341\) 0.751562 0.0406993
\(342\) 2.13709 0.115561
\(343\) −17.4728 −0.943444
\(344\) −79.3188 −4.27658
\(345\) 0 0
\(346\) 33.7343 1.81357
\(347\) 21.4054 1.14910 0.574550 0.818469i \(-0.305177\pi\)
0.574550 + 0.818469i \(0.305177\pi\)
\(348\) 8.76608 0.469911
\(349\) −28.7244 −1.53758 −0.768790 0.639501i \(-0.779141\pi\)
−0.768790 + 0.639501i \(0.779141\pi\)
\(350\) 0 0
\(351\) −24.4424 −1.30464
\(352\) 26.8158 1.42929
\(353\) 1.14505 0.0609450 0.0304725 0.999536i \(-0.490299\pi\)
0.0304725 + 0.999536i \(0.490299\pi\)
\(354\) −0.897976 −0.0477269
\(355\) 0 0
\(356\) 80.3452 4.25829
\(357\) −30.7626 −1.62813
\(358\) −68.8038 −3.63639
\(359\) −3.47233 −0.183263 −0.0916314 0.995793i \(-0.529208\pi\)
−0.0916314 + 0.995793i \(0.529208\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −24.6804 −1.29718
\(363\) 1.94173 0.101914
\(364\) 89.2765 4.67936
\(365\) 0 0
\(366\) −1.08297 −0.0566077
\(367\) 36.1011 1.88446 0.942231 0.334964i \(-0.108724\pi\)
0.942231 + 0.334964i \(0.108724\pi\)
\(368\) 105.477 5.49836
\(369\) −1.28766 −0.0670331
\(370\) 0 0
\(371\) 18.3684 0.953642
\(372\) −8.31341 −0.431030
\(373\) 36.2892 1.87898 0.939491 0.342572i \(-0.111298\pi\)
0.939491 + 0.342572i \(0.111298\pi\)
\(374\) −15.8339 −0.818751
\(375\) 0 0
\(376\) −19.2190 −0.991146
\(377\) 4.47407 0.230426
\(378\) 33.3414 1.71490
\(379\) −19.1454 −0.983432 −0.491716 0.870756i \(-0.663630\pi\)
−0.491716 + 0.870756i \(0.663630\pi\)
\(380\) 0 0
\(381\) −16.7944 −0.860405
\(382\) −28.6460 −1.46565
\(383\) −6.21204 −0.317420 −0.158710 0.987325i \(-0.550734\pi\)
−0.158710 + 0.987325i \(0.550734\pi\)
\(384\) −112.829 −5.75780
\(385\) 0 0
\(386\) −60.4527 −3.07696
\(387\) 5.95766 0.302845
\(388\) −39.7940 −2.02023
\(389\) 14.0343 0.711569 0.355784 0.934568i \(-0.384214\pi\)
0.355784 + 0.934568i \(0.384214\pi\)
\(390\) 0 0
\(391\) −35.2884 −1.78461
\(392\) −7.23511 −0.365428
\(393\) −18.9089 −0.953828
\(394\) −61.3398 −3.09026
\(395\) 0 0
\(396\) −4.38829 −0.220520
\(397\) 3.75176 0.188295 0.0941476 0.995558i \(-0.469987\pi\)
0.0941476 + 0.995558i \(0.469987\pi\)
\(398\) 74.7232 3.74554
\(399\) −5.39000 −0.269837
\(400\) 0 0
\(401\) 22.9411 1.14563 0.572813 0.819686i \(-0.305852\pi\)
0.572813 + 0.819686i \(0.305852\pi\)
\(402\) −47.4488 −2.36653
\(403\) −4.24303 −0.211361
\(404\) 5.18534 0.257980
\(405\) 0 0
\(406\) −6.10300 −0.302887
\(407\) −8.00003 −0.396547
\(408\) 113.657 5.62684
\(409\) −2.70169 −0.133590 −0.0667951 0.997767i \(-0.521277\pi\)
−0.0667951 + 0.997767i \(0.521277\pi\)
\(410\) 0 0
\(411\) 7.35671 0.362880
\(412\) 70.8014 3.48813
\(413\) 0.462724 0.0227692
\(414\) −13.2136 −0.649411
\(415\) 0 0
\(416\) −151.392 −7.42261
\(417\) 40.5905 1.98772
\(418\) −2.77430 −0.135695
\(419\) −23.3880 −1.14258 −0.571290 0.820748i \(-0.693557\pi\)
−0.571290 + 0.820748i \(0.693557\pi\)
\(420\) 0 0
\(421\) −4.71276 −0.229686 −0.114843 0.993384i \(-0.536636\pi\)
−0.114843 + 0.993384i \(0.536636\pi\)
\(422\) −62.0666 −3.02136
\(423\) 1.44355 0.0701876
\(424\) −67.8647 −3.29580
\(425\) 0 0
\(426\) 38.3649 1.85878
\(427\) 0.558051 0.0270060
\(428\) 35.7783 1.72941
\(429\) −10.9623 −0.529264
\(430\) 0 0
\(431\) −36.0747 −1.73766 −0.868829 0.495113i \(-0.835127\pi\)
−0.868829 + 0.495113i \(0.835127\pi\)
\(432\) −73.8571 −3.55345
\(433\) −7.25920 −0.348855 −0.174427 0.984670i \(-0.555807\pi\)
−0.174427 + 0.984670i \(0.555807\pi\)
\(434\) 5.78785 0.277826
\(435\) 0 0
\(436\) −18.7879 −0.899779
\(437\) −6.18297 −0.295771
\(438\) 49.4624 2.36341
\(439\) 12.6990 0.606092 0.303046 0.952976i \(-0.401996\pi\)
0.303046 + 0.952976i \(0.401996\pi\)
\(440\) 0 0
\(441\) 0.543431 0.0258777
\(442\) 89.3922 4.25196
\(443\) 31.5571 1.49932 0.749662 0.661821i \(-0.230216\pi\)
0.749662 + 0.661821i \(0.230216\pi\)
\(444\) 88.4924 4.19966
\(445\) 0 0
\(446\) 57.3508 2.71564
\(447\) 1.03377 0.0488957
\(448\) 111.803 5.28218
\(449\) −26.8725 −1.26819 −0.634095 0.773255i \(-0.718627\pi\)
−0.634095 + 0.773255i \(0.718627\pi\)
\(450\) 0 0
\(451\) 1.67160 0.0787126
\(452\) 117.070 5.50653
\(453\) 8.20835 0.385662
\(454\) 10.6265 0.498724
\(455\) 0 0
\(456\) 19.9141 0.932561
\(457\) −1.39620 −0.0653113 −0.0326557 0.999467i \(-0.510396\pi\)
−0.0326557 + 0.999467i \(0.510396\pi\)
\(458\) −65.6722 −3.06866
\(459\) 24.7097 1.15335
\(460\) 0 0
\(461\) 0.468865 0.0218372 0.0109186 0.999940i \(-0.496524\pi\)
0.0109186 + 0.999940i \(0.496524\pi\)
\(462\) 14.9535 0.695698
\(463\) −14.7332 −0.684709 −0.342355 0.939571i \(-0.611224\pi\)
−0.342355 + 0.939571i \(0.611224\pi\)
\(464\) 13.5192 0.627614
\(465\) 0 0
\(466\) 62.9301 2.91518
\(467\) −25.7658 −1.19230 −0.596150 0.802873i \(-0.703303\pi\)
−0.596150 + 0.802873i \(0.703303\pi\)
\(468\) 24.7747 1.14521
\(469\) 24.4502 1.12901
\(470\) 0 0
\(471\) −14.7948 −0.681708
\(472\) −1.70960 −0.0786905
\(473\) −7.73402 −0.355611
\(474\) 85.1912 3.91296
\(475\) 0 0
\(476\) −90.2526 −4.13672
\(477\) 5.09733 0.233391
\(478\) −29.6611 −1.35667
\(479\) −1.16818 −0.0533757 −0.0266878 0.999644i \(-0.508496\pi\)
−0.0266878 + 0.999644i \(0.508496\pi\)
\(480\) 0 0
\(481\) 45.1651 2.05935
\(482\) 61.4378 2.79841
\(483\) 33.3262 1.51639
\(484\) 5.69673 0.258942
\(485\) 0 0
\(486\) 21.7014 0.984395
\(487\) −9.55493 −0.432975 −0.216488 0.976285i \(-0.569460\pi\)
−0.216488 + 0.976285i \(0.569460\pi\)
\(488\) −2.06179 −0.0933330
\(489\) −33.1664 −1.49984
\(490\) 0 0
\(491\) −13.4103 −0.605200 −0.302600 0.953118i \(-0.597855\pi\)
−0.302600 + 0.953118i \(0.597855\pi\)
\(492\) −18.4904 −0.833613
\(493\) −4.52299 −0.203705
\(494\) 15.6626 0.704696
\(495\) 0 0
\(496\) −12.8211 −0.575684
\(497\) −19.7693 −0.886773
\(498\) −29.9493 −1.34206
\(499\) 23.0956 1.03390 0.516950 0.856015i \(-0.327067\pi\)
0.516950 + 0.856015i \(0.327067\pi\)
\(500\) 0 0
\(501\) 43.4964 1.94328
\(502\) −8.96921 −0.400315
\(503\) −4.38741 −0.195625 −0.0978124 0.995205i \(-0.531185\pi\)
−0.0978124 + 0.995205i \(0.531185\pi\)
\(504\) −21.9301 −0.976844
\(505\) 0 0
\(506\) 17.1534 0.762561
\(507\) 36.6464 1.62752
\(508\) −49.2722 −2.18610
\(509\) 34.2493 1.51807 0.759037 0.651047i \(-0.225670\pi\)
0.759037 + 0.651047i \(0.225670\pi\)
\(510\) 0 0
\(511\) −25.4878 −1.12752
\(512\) −107.545 −4.75286
\(513\) 4.32944 0.191150
\(514\) −49.8408 −2.19838
\(515\) 0 0
\(516\) 85.5500 3.76613
\(517\) −1.87396 −0.0824168
\(518\) −61.6090 −2.70694
\(519\) −23.6106 −1.03639
\(520\) 0 0
\(521\) 26.7269 1.17093 0.585463 0.810699i \(-0.300913\pi\)
0.585463 + 0.810699i \(0.300913\pi\)
\(522\) −1.69361 −0.0741274
\(523\) 6.41346 0.280441 0.140220 0.990120i \(-0.455219\pi\)
0.140220 + 0.990120i \(0.455219\pi\)
\(524\) −55.4757 −2.42347
\(525\) 0 0
\(526\) 15.4031 0.671608
\(527\) 4.28943 0.186850
\(528\) −33.1245 −1.44156
\(529\) 15.2291 0.662133
\(530\) 0 0
\(531\) 0.128408 0.00557244
\(532\) −15.8134 −0.685597
\(533\) −9.43723 −0.408772
\(534\) −75.9760 −3.28780
\(535\) 0 0
\(536\) −90.3346 −3.90186
\(537\) 48.1557 2.07807
\(538\) −63.0497 −2.71826
\(539\) −0.705463 −0.0303865
\(540\) 0 0
\(541\) −10.3586 −0.445351 −0.222675 0.974893i \(-0.571479\pi\)
−0.222675 + 0.974893i \(0.571479\pi\)
\(542\) 7.30931 0.313962
\(543\) 17.2738 0.741291
\(544\) 153.048 6.56186
\(545\) 0 0
\(546\) −84.4216 −3.61291
\(547\) 10.4350 0.446167 0.223083 0.974799i \(-0.428388\pi\)
0.223083 + 0.974799i \(0.428388\pi\)
\(548\) 21.5834 0.921998
\(549\) 0.154862 0.00660934
\(550\) 0 0
\(551\) −0.792484 −0.0337610
\(552\) −123.128 −5.24067
\(553\) −43.8988 −1.86676
\(554\) 18.0655 0.767529
\(555\) 0 0
\(556\) 119.086 5.05037
\(557\) −14.2206 −0.602545 −0.301273 0.953538i \(-0.597411\pi\)
−0.301273 + 0.953538i \(0.597411\pi\)
\(558\) 1.60616 0.0679940
\(559\) 43.6634 1.84676
\(560\) 0 0
\(561\) 11.0821 0.467888
\(562\) 79.3949 3.34907
\(563\) 32.3367 1.36283 0.681414 0.731898i \(-0.261365\pi\)
0.681414 + 0.731898i \(0.261365\pi\)
\(564\) 20.7289 0.872843
\(565\) 0 0
\(566\) −12.2328 −0.514182
\(567\) −29.7506 −1.24941
\(568\) 73.0403 3.06470
\(569\) 21.8662 0.916678 0.458339 0.888777i \(-0.348445\pi\)
0.458339 + 0.888777i \(0.348445\pi\)
\(570\) 0 0
\(571\) −14.3312 −0.599742 −0.299871 0.953980i \(-0.596944\pi\)
−0.299871 + 0.953980i \(0.596944\pi\)
\(572\) −32.1616 −1.34474
\(573\) 20.0493 0.837571
\(574\) 12.8732 0.537315
\(575\) 0 0
\(576\) 31.0258 1.29274
\(577\) −11.8842 −0.494744 −0.247372 0.968921i \(-0.579567\pi\)
−0.247372 + 0.968921i \(0.579567\pi\)
\(578\) −43.2066 −1.79716
\(579\) 42.3109 1.75838
\(580\) 0 0
\(581\) 15.4327 0.640258
\(582\) 37.6299 1.55981
\(583\) −6.61718 −0.274055
\(584\) 94.1682 3.89671
\(585\) 0 0
\(586\) 16.9949 0.702051
\(587\) −3.12781 −0.129098 −0.0645492 0.997915i \(-0.520561\pi\)
−0.0645492 + 0.997915i \(0.520561\pi\)
\(588\) 7.80349 0.321811
\(589\) 0.751562 0.0309676
\(590\) 0 0
\(591\) 42.9317 1.76598
\(592\) 136.475 5.60907
\(593\) 10.6248 0.436306 0.218153 0.975915i \(-0.429997\pi\)
0.218153 + 0.975915i \(0.429997\pi\)
\(594\) −12.0112 −0.492824
\(595\) 0 0
\(596\) 3.03292 0.124233
\(597\) −52.2988 −2.14045
\(598\) −96.8416 −3.96015
\(599\) −3.06543 −0.125250 −0.0626250 0.998037i \(-0.519947\pi\)
−0.0626250 + 0.998037i \(0.519947\pi\)
\(600\) 0 0
\(601\) 30.5337 1.24550 0.622748 0.782422i \(-0.286016\pi\)
0.622748 + 0.782422i \(0.286016\pi\)
\(602\) −59.5604 −2.42750
\(603\) 6.78505 0.276309
\(604\) 24.0820 0.979882
\(605\) 0 0
\(606\) −4.90336 −0.199185
\(607\) 3.70830 0.150515 0.0752575 0.997164i \(-0.476022\pi\)
0.0752575 + 0.997164i \(0.476022\pi\)
\(608\) 26.8158 1.08753
\(609\) 4.27149 0.173089
\(610\) 0 0
\(611\) 10.5797 0.428008
\(612\) −25.0455 −1.01241
\(613\) −1.95435 −0.0789353 −0.0394676 0.999221i \(-0.512566\pi\)
−0.0394676 + 0.999221i \(0.512566\pi\)
\(614\) 50.6583 2.04440
\(615\) 0 0
\(616\) 28.4689 1.14704
\(617\) −18.0284 −0.725794 −0.362897 0.931829i \(-0.618212\pi\)
−0.362897 + 0.931829i \(0.618212\pi\)
\(618\) −66.9511 −2.69317
\(619\) −32.2884 −1.29778 −0.648891 0.760882i \(-0.724767\pi\)
−0.648891 + 0.760882i \(0.724767\pi\)
\(620\) 0 0
\(621\) −26.7688 −1.07419
\(622\) 70.8417 2.84049
\(623\) 39.1502 1.56852
\(624\) 187.009 7.48633
\(625\) 0 0
\(626\) 27.5109 1.09956
\(627\) 1.94173 0.0775453
\(628\) −43.4056 −1.73207
\(629\) −45.6590 −1.82054
\(630\) 0 0
\(631\) −29.5491 −1.17633 −0.588166 0.808740i \(-0.700150\pi\)
−0.588166 + 0.808740i \(0.700150\pi\)
\(632\) 162.190 6.45157
\(633\) 43.4404 1.72660
\(634\) 53.1806 2.11207
\(635\) 0 0
\(636\) 73.1960 2.90241
\(637\) 3.98278 0.157804
\(638\) 2.19859 0.0870429
\(639\) −5.48607 −0.217026
\(640\) 0 0
\(641\) −26.2216 −1.03569 −0.517846 0.855474i \(-0.673266\pi\)
−0.517846 + 0.855474i \(0.673266\pi\)
\(642\) −33.8327 −1.33527
\(643\) −2.98936 −0.117889 −0.0589443 0.998261i \(-0.518773\pi\)
−0.0589443 + 0.998261i \(0.518773\pi\)
\(644\) 97.7737 3.85282
\(645\) 0 0
\(646\) −15.8339 −0.622976
\(647\) 7.51779 0.295555 0.147777 0.989021i \(-0.452788\pi\)
0.147777 + 0.989021i \(0.452788\pi\)
\(648\) 109.918 4.31797
\(649\) −0.166695 −0.00654335
\(650\) 0 0
\(651\) −4.05091 −0.158768
\(652\) −97.3050 −3.81076
\(653\) 4.87991 0.190965 0.0954827 0.995431i \(-0.469561\pi\)
0.0954827 + 0.995431i \(0.469561\pi\)
\(654\) 17.7662 0.694715
\(655\) 0 0
\(656\) −28.5163 −1.11337
\(657\) −7.07300 −0.275944
\(658\) −14.4316 −0.562601
\(659\) −2.00729 −0.0781928 −0.0390964 0.999235i \(-0.512448\pi\)
−0.0390964 + 0.999235i \(0.512448\pi\)
\(660\) 0 0
\(661\) 21.8559 0.850097 0.425048 0.905171i \(-0.360257\pi\)
0.425048 + 0.905171i \(0.360257\pi\)
\(662\) −52.2574 −2.03104
\(663\) −62.5656 −2.42985
\(664\) −57.0184 −2.21274
\(665\) 0 0
\(666\) −17.0968 −0.662487
\(667\) 4.89990 0.189725
\(668\) 127.612 4.93744
\(669\) −40.1398 −1.55189
\(670\) 0 0
\(671\) −0.201036 −0.00776091
\(672\) −144.537 −5.57565
\(673\) 3.27215 0.126132 0.0630660 0.998009i \(-0.479912\pi\)
0.0630660 + 0.998009i \(0.479912\pi\)
\(674\) 57.9786 2.23325
\(675\) 0 0
\(676\) 107.515 4.13518
\(677\) 16.7278 0.642902 0.321451 0.946926i \(-0.395830\pi\)
0.321451 + 0.946926i \(0.395830\pi\)
\(678\) −110.704 −4.25156
\(679\) −19.3906 −0.744142
\(680\) 0 0
\(681\) −7.43746 −0.285004
\(682\) −2.08506 −0.0798409
\(683\) 13.4718 0.515486 0.257743 0.966214i \(-0.417021\pi\)
0.257743 + 0.966214i \(0.417021\pi\)
\(684\) −4.38829 −0.167791
\(685\) 0 0
\(686\) 48.4748 1.85078
\(687\) 45.9639 1.75363
\(688\) 131.937 5.03004
\(689\) 37.3581 1.42323
\(690\) 0 0
\(691\) 11.1465 0.424031 0.212016 0.977266i \(-0.431997\pi\)
0.212016 + 0.977266i \(0.431997\pi\)
\(692\) −69.2698 −2.63324
\(693\) −2.13830 −0.0812274
\(694\) −59.3849 −2.25422
\(695\) 0 0
\(696\) −15.7816 −0.598199
\(697\) 9.54042 0.361369
\(698\) 79.6900 3.01631
\(699\) −44.0447 −1.66593
\(700\) 0 0
\(701\) 30.0849 1.13629 0.568145 0.822928i \(-0.307661\pi\)
0.568145 + 0.822928i \(0.307661\pi\)
\(702\) 67.8105 2.55934
\(703\) −8.00003 −0.301727
\(704\) −40.2766 −1.51798
\(705\) 0 0
\(706\) −3.17672 −0.119557
\(707\) 2.52668 0.0950258
\(708\) 1.84390 0.0692980
\(709\) 43.0515 1.61683 0.808416 0.588611i \(-0.200325\pi\)
0.808416 + 0.588611i \(0.200325\pi\)
\(710\) 0 0
\(711\) −12.1821 −0.456865
\(712\) −144.646 −5.42083
\(713\) −4.64688 −0.174027
\(714\) 85.3446 3.19394
\(715\) 0 0
\(716\) 141.281 5.27993
\(717\) 20.7598 0.775289
\(718\) 9.63329 0.359511
\(719\) −38.1215 −1.42169 −0.710845 0.703349i \(-0.751687\pi\)
−0.710845 + 0.703349i \(0.751687\pi\)
\(720\) 0 0
\(721\) 34.4997 1.28484
\(722\) −2.77430 −0.103249
\(723\) −43.0003 −1.59920
\(724\) 50.6787 1.88346
\(725\) 0 0
\(726\) −5.38694 −0.199928
\(727\) −13.4993 −0.500661 −0.250330 0.968160i \(-0.580539\pi\)
−0.250330 + 0.968160i \(0.580539\pi\)
\(728\) −160.725 −5.95685
\(729\) 16.9639 0.628293
\(730\) 0 0
\(731\) −44.1408 −1.63261
\(732\) 2.22376 0.0821927
\(733\) −1.94137 −0.0717060 −0.0358530 0.999357i \(-0.511415\pi\)
−0.0358530 + 0.999357i \(0.511415\pi\)
\(734\) −100.155 −3.69680
\(735\) 0 0
\(736\) −165.801 −6.11152
\(737\) −8.80812 −0.324451
\(738\) 3.57236 0.131501
\(739\) 29.8113 1.09663 0.548314 0.836273i \(-0.315270\pi\)
0.548314 + 0.836273i \(0.315270\pi\)
\(740\) 0 0
\(741\) −10.9623 −0.402709
\(742\) −50.9595 −1.87078
\(743\) 24.6193 0.903193 0.451596 0.892222i \(-0.350855\pi\)
0.451596 + 0.892222i \(0.350855\pi\)
\(744\) 14.9666 0.548704
\(745\) 0 0
\(746\) −100.677 −3.68605
\(747\) 4.28266 0.156694
\(748\) 32.5133 1.18880
\(749\) 17.4339 0.637020
\(750\) 0 0
\(751\) 28.3911 1.03600 0.518002 0.855379i \(-0.326676\pi\)
0.518002 + 0.855379i \(0.326676\pi\)
\(752\) 31.9684 1.16577
\(753\) 6.27755 0.228767
\(754\) −12.4124 −0.452033
\(755\) 0 0
\(756\) −68.4632 −2.48998
\(757\) −43.5814 −1.58399 −0.791996 0.610526i \(-0.790958\pi\)
−0.791996 + 0.610526i \(0.790958\pi\)
\(758\) 53.1150 1.92922
\(759\) −12.0057 −0.435778
\(760\) 0 0
\(761\) 2.33446 0.0846242 0.0423121 0.999104i \(-0.486528\pi\)
0.0423121 + 0.999104i \(0.486528\pi\)
\(762\) 46.5928 1.68788
\(763\) −9.15489 −0.331429
\(764\) 58.8215 2.12809
\(765\) 0 0
\(766\) 17.2340 0.622691
\(767\) 0.941097 0.0339810
\(768\) 156.610 5.65116
\(769\) 28.9612 1.04437 0.522184 0.852833i \(-0.325117\pi\)
0.522184 + 0.852833i \(0.325117\pi\)
\(770\) 0 0
\(771\) 34.8836 1.25630
\(772\) 124.133 4.46766
\(773\) 10.6188 0.381932 0.190966 0.981597i \(-0.438838\pi\)
0.190966 + 0.981597i \(0.438838\pi\)
\(774\) −16.5283 −0.594098
\(775\) 0 0
\(776\) 71.6411 2.57177
\(777\) 43.1201 1.54693
\(778\) −38.9354 −1.39590
\(779\) 1.67160 0.0598913
\(780\) 0 0
\(781\) 7.12183 0.254839
\(782\) 97.9005 3.50091
\(783\) −3.43102 −0.122614
\(784\) 12.0347 0.429810
\(785\) 0 0
\(786\) 52.4589 1.87115
\(787\) 26.5612 0.946804 0.473402 0.880846i \(-0.343026\pi\)
0.473402 + 0.880846i \(0.343026\pi\)
\(788\) 125.955 4.48696
\(789\) −10.7806 −0.383801
\(790\) 0 0
\(791\) 57.0454 2.02830
\(792\) 7.90025 0.280723
\(793\) 1.13497 0.0403041
\(794\) −10.4085 −0.369383
\(795\) 0 0
\(796\) −153.436 −5.43840
\(797\) −36.6847 −1.29944 −0.649720 0.760174i \(-0.725114\pi\)
−0.649720 + 0.760174i \(0.725114\pi\)
\(798\) 14.9535 0.529347
\(799\) −10.6954 −0.378375
\(800\) 0 0
\(801\) 10.8644 0.383874
\(802\) −63.6455 −2.24740
\(803\) 9.18192 0.324023
\(804\) 97.4311 3.43613
\(805\) 0 0
\(806\) 11.7714 0.414631
\(807\) 44.1285 1.55340
\(808\) −9.33518 −0.328410
\(809\) 55.8765 1.96451 0.982256 0.187544i \(-0.0600528\pi\)
0.982256 + 0.187544i \(0.0600528\pi\)
\(810\) 0 0
\(811\) 47.0778 1.65313 0.826563 0.562844i \(-0.190293\pi\)
0.826563 + 0.562844i \(0.190293\pi\)
\(812\) 12.5319 0.439782
\(813\) −5.11578 −0.179418
\(814\) 22.1945 0.777915
\(815\) 0 0
\(816\) −189.053 −6.61819
\(817\) −7.73402 −0.270579
\(818\) 7.49530 0.262067
\(819\) 12.0721 0.421832
\(820\) 0 0
\(821\) −16.8400 −0.587721 −0.293861 0.955848i \(-0.594940\pi\)
−0.293861 + 0.955848i \(0.594940\pi\)
\(822\) −20.4097 −0.711870
\(823\) 17.5992 0.613468 0.306734 0.951795i \(-0.400764\pi\)
0.306734 + 0.951795i \(0.400764\pi\)
\(824\) −127.464 −4.44041
\(825\) 0 0
\(826\) −1.28373 −0.0446668
\(827\) −20.5723 −0.715368 −0.357684 0.933843i \(-0.616433\pi\)
−0.357684 + 0.933843i \(0.616433\pi\)
\(828\) 27.1327 0.942925
\(829\) 6.67707 0.231904 0.115952 0.993255i \(-0.463008\pi\)
0.115952 + 0.993255i \(0.463008\pi\)
\(830\) 0 0
\(831\) −12.6440 −0.438617
\(832\) 227.387 7.88321
\(833\) −4.02633 −0.139504
\(834\) −112.610 −3.89937
\(835\) 0 0
\(836\) 5.69673 0.197026
\(837\) 3.25384 0.112469
\(838\) 64.8854 2.24143
\(839\) −42.5215 −1.46800 −0.734002 0.679148i \(-0.762350\pi\)
−0.734002 + 0.679148i \(0.762350\pi\)
\(840\) 0 0
\(841\) −28.3720 −0.978344
\(842\) 13.0746 0.450580
\(843\) −55.5684 −1.91388
\(844\) 127.447 4.38692
\(845\) 0 0
\(846\) −4.00483 −0.137689
\(847\) 2.77587 0.0953801
\(848\) 112.884 3.87646
\(849\) 8.56172 0.293837
\(850\) 0 0
\(851\) 49.4639 1.69560
\(852\) −78.7782 −2.69890
\(853\) −35.8445 −1.22729 −0.613646 0.789582i \(-0.710298\pi\)
−0.613646 + 0.789582i \(0.710298\pi\)
\(854\) −1.54820 −0.0529783
\(855\) 0 0
\(856\) −64.4118 −2.20155
\(857\) −13.6836 −0.467423 −0.233711 0.972306i \(-0.575087\pi\)
−0.233711 + 0.972306i \(0.575087\pi\)
\(858\) 30.4126 1.03827
\(859\) −33.7516 −1.15159 −0.575795 0.817594i \(-0.695307\pi\)
−0.575795 + 0.817594i \(0.695307\pi\)
\(860\) 0 0
\(861\) −9.00992 −0.307057
\(862\) 100.082 3.40881
\(863\) 31.2057 1.06225 0.531127 0.847292i \(-0.321769\pi\)
0.531127 + 0.847292i \(0.321769\pi\)
\(864\) 116.098 3.94972
\(865\) 0 0
\(866\) 20.1392 0.684357
\(867\) 30.2403 1.02701
\(868\) −11.8847 −0.403394
\(869\) 15.8144 0.536467
\(870\) 0 0
\(871\) 49.7273 1.68495
\(872\) 33.8240 1.14542
\(873\) −5.38098 −0.182119
\(874\) 17.1534 0.580222
\(875\) 0 0
\(876\) −101.566 −3.43160
\(877\) 16.3439 0.551894 0.275947 0.961173i \(-0.411009\pi\)
0.275947 + 0.961173i \(0.411009\pi\)
\(878\) −35.2309 −1.18899
\(879\) −11.8947 −0.401198
\(880\) 0 0
\(881\) −16.2582 −0.547752 −0.273876 0.961765i \(-0.588306\pi\)
−0.273876 + 0.961765i \(0.588306\pi\)
\(882\) −1.50764 −0.0507649
\(883\) −3.26796 −0.109976 −0.0549878 0.998487i \(-0.517512\pi\)
−0.0549878 + 0.998487i \(0.517512\pi\)
\(884\) −183.558 −6.17371
\(885\) 0 0
\(886\) −87.5489 −2.94126
\(887\) 20.1909 0.677943 0.338971 0.940797i \(-0.389921\pi\)
0.338971 + 0.940797i \(0.389921\pi\)
\(888\) −159.313 −5.34620
\(889\) −24.0091 −0.805239
\(890\) 0 0
\(891\) 10.7176 0.359052
\(892\) −117.764 −3.94303
\(893\) −1.87396 −0.0627098
\(894\) −2.86799 −0.0959199
\(895\) 0 0
\(896\) −161.299 −5.38863
\(897\) 67.7794 2.26309
\(898\) 74.5523 2.48784
\(899\) −0.595601 −0.0198644
\(900\) 0 0
\(901\) −37.7666 −1.25819
\(902\) −4.63752 −0.154412
\(903\) 41.6863 1.38723
\(904\) −210.762 −7.00984
\(905\) 0 0
\(906\) −22.7724 −0.756562
\(907\) 43.1793 1.43375 0.716873 0.697204i \(-0.245573\pi\)
0.716873 + 0.697204i \(0.245573\pi\)
\(908\) −21.8203 −0.724133
\(909\) 0.701167 0.0232563
\(910\) 0 0
\(911\) 4.27846 0.141752 0.0708758 0.997485i \(-0.477421\pi\)
0.0708758 + 0.997485i \(0.477421\pi\)
\(912\) −33.1245 −1.09686
\(913\) −5.55960 −0.183996
\(914\) 3.87347 0.128123
\(915\) 0 0
\(916\) 134.851 4.45560
\(917\) −27.0319 −0.892672
\(918\) −68.5520 −2.26255
\(919\) 9.63461 0.317817 0.158908 0.987293i \(-0.449203\pi\)
0.158908 + 0.987293i \(0.449203\pi\)
\(920\) 0 0
\(921\) −35.4557 −1.16831
\(922\) −1.30077 −0.0428386
\(923\) −40.2072 −1.32343
\(924\) −30.7053 −1.01013
\(925\) 0 0
\(926\) 40.8742 1.34321
\(927\) 9.57383 0.314446
\(928\) −21.2511 −0.697603
\(929\) −35.3500 −1.15980 −0.579898 0.814689i \(-0.696908\pi\)
−0.579898 + 0.814689i \(0.696908\pi\)
\(930\) 0 0
\(931\) −0.705463 −0.0231206
\(932\) −129.220 −4.23275
\(933\) −49.5821 −1.62324
\(934\) 71.4820 2.33896
\(935\) 0 0
\(936\) −44.6018 −1.45786
\(937\) 4.08039 0.133300 0.0666502 0.997776i \(-0.478769\pi\)
0.0666502 + 0.997776i \(0.478769\pi\)
\(938\) −67.8322 −2.21480
\(939\) −19.2549 −0.628360
\(940\) 0 0
\(941\) 0.772654 0.0251878 0.0125939 0.999921i \(-0.495991\pi\)
0.0125939 + 0.999921i \(0.495991\pi\)
\(942\) 41.0452 1.33732
\(943\) −10.3355 −0.336569
\(944\) 2.84370 0.0925544
\(945\) 0 0
\(946\) 21.4565 0.697610
\(947\) −30.1943 −0.981184 −0.490592 0.871389i \(-0.663219\pi\)
−0.490592 + 0.871389i \(0.663219\pi\)
\(948\) −174.931 −5.68150
\(949\) −51.8377 −1.68272
\(950\) 0 0
\(951\) −37.2211 −1.20698
\(952\) 162.482 5.26607
\(953\) −28.3008 −0.916753 −0.458376 0.888758i \(-0.651569\pi\)
−0.458376 + 0.888758i \(0.651569\pi\)
\(954\) −14.1415 −0.457848
\(955\) 0 0
\(956\) 60.9059 1.96984
\(957\) −1.53879 −0.0497421
\(958\) 3.24089 0.104708
\(959\) 10.5171 0.339613
\(960\) 0 0
\(961\) −30.4352 −0.981779
\(962\) −125.302 −4.03988
\(963\) 4.83799 0.155902
\(964\) −126.156 −4.06321
\(965\) 0 0
\(966\) −92.4567 −2.97475
\(967\) −49.9762 −1.60713 −0.803564 0.595219i \(-0.797065\pi\)
−0.803564 + 0.595219i \(0.797065\pi\)
\(968\) −10.2558 −0.329635
\(969\) 11.0821 0.356010
\(970\) 0 0
\(971\) 3.41933 0.109732 0.0548658 0.998494i \(-0.482527\pi\)
0.0548658 + 0.998494i \(0.482527\pi\)
\(972\) −44.5615 −1.42931
\(973\) 58.0276 1.86028
\(974\) 26.5082 0.849378
\(975\) 0 0
\(976\) 3.42953 0.109777
\(977\) 50.4820 1.61506 0.807531 0.589825i \(-0.200803\pi\)
0.807531 + 0.589825i \(0.200803\pi\)
\(978\) 92.0136 2.94227
\(979\) −14.1037 −0.450758
\(980\) 0 0
\(981\) −2.54053 −0.0811127
\(982\) 37.2043 1.18724
\(983\) −38.0327 −1.21305 −0.606527 0.795063i \(-0.707438\pi\)
−0.606527 + 0.795063i \(0.707438\pi\)
\(984\) 33.2884 1.06119
\(985\) 0 0
\(986\) 12.5481 0.399614
\(987\) 10.1006 0.321507
\(988\) −32.1616 −1.02320
\(989\) 47.8192 1.52056
\(990\) 0 0
\(991\) −46.4663 −1.47605 −0.738025 0.674773i \(-0.764241\pi\)
−0.738025 + 0.674773i \(0.764241\pi\)
\(992\) 20.1538 0.639883
\(993\) 36.5750 1.16067
\(994\) 54.8459 1.73961
\(995\) 0 0
\(996\) 61.4977 1.94863
\(997\) 10.8649 0.344094 0.172047 0.985089i \(-0.444962\pi\)
0.172047 + 0.985089i \(0.444962\pi\)
\(998\) −64.0740 −2.02823
\(999\) −34.6356 −1.09582
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.t.1.1 15
5.4 even 2 5225.2.a.w.1.15 yes 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5225.2.a.t.1.1 15 1.1 even 1 trivial
5225.2.a.w.1.15 yes 15 5.4 even 2