Properties

Label 4025.2.a.y.1.4
Level $4025$
Weight $2$
Character 4025.1
Self dual yes
Analytic conductor $32.140$
Analytic rank $1$
Dimension $12$
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] = [4025,2,Mod(1,4025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4025, 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("4025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4025.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: \(32.1397868136\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} - 210 x^{3} - 81 x^{2} + 58 x + 17 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 805)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.11343\) of defining polynomial
Character \(\chi\) \(=\) 4025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.11343 q^{2} +2.87976 q^{3} -0.760266 q^{4} -3.20642 q^{6} -1.00000 q^{7} +3.07337 q^{8} +5.29300 q^{9} +O(q^{10})\) \(q-1.11343 q^{2} +2.87976 q^{3} -0.760266 q^{4} -3.20642 q^{6} -1.00000 q^{7} +3.07337 q^{8} +5.29300 q^{9} -1.44843 q^{11} -2.18938 q^{12} -2.99328 q^{13} +1.11343 q^{14} -1.90146 q^{16} -0.663092 q^{17} -5.89340 q^{18} -6.91587 q^{19} -2.87976 q^{21} +1.61273 q^{22} +1.00000 q^{23} +8.85056 q^{24} +3.33282 q^{26} +6.60327 q^{27} +0.760266 q^{28} +2.85250 q^{29} +5.80140 q^{31} -4.02959 q^{32} -4.17113 q^{33} +0.738309 q^{34} -4.02409 q^{36} -1.45671 q^{37} +7.70036 q^{38} -8.61991 q^{39} +1.31097 q^{41} +3.20642 q^{42} +6.04918 q^{43} +1.10119 q^{44} -1.11343 q^{46} -7.26934 q^{47} -5.47575 q^{48} +1.00000 q^{49} -1.90954 q^{51} +2.27569 q^{52} -7.52908 q^{53} -7.35230 q^{54} -3.07337 q^{56} -19.9160 q^{57} -3.17607 q^{58} -1.21914 q^{59} +1.29657 q^{61} -6.45948 q^{62} -5.29300 q^{63} +8.28961 q^{64} +4.64428 q^{66} -6.72336 q^{67} +0.504126 q^{68} +2.87976 q^{69} -15.4619 q^{71} +16.2673 q^{72} -12.0554 q^{73} +1.62195 q^{74} +5.25790 q^{76} +1.44843 q^{77} +9.59770 q^{78} -12.1005 q^{79} +3.13682 q^{81} -1.45968 q^{82} -12.8092 q^{83} +2.18938 q^{84} -6.73536 q^{86} +8.21450 q^{87} -4.45157 q^{88} -17.4986 q^{89} +2.99328 q^{91} -0.760266 q^{92} +16.7066 q^{93} +8.09393 q^{94} -11.6042 q^{96} +2.17861 q^{97} -1.11343 q^{98} -7.66654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 12 q^{12} + 2 q^{13} - 2 q^{14} - 4 q^{16} - 8 q^{17} + 20 q^{18} - 26 q^{19} + 4 q^{22} + 12 q^{23} - 12 q^{24} - 22 q^{26} + 12 q^{27} - 8 q^{28} - 12 q^{29} - 50 q^{31} + 14 q^{32} + 4 q^{33} - 28 q^{34} - 18 q^{36} + 8 q^{37} - 4 q^{38} - 26 q^{39} - 4 q^{41} + 6 q^{42} + 26 q^{43} - 10 q^{44} + 2 q^{46} + 16 q^{47} - 40 q^{48} + 12 q^{49} - 32 q^{51} + 10 q^{52} - 18 q^{53} - 10 q^{54} - 6 q^{56} - 10 q^{57} - 18 q^{58} - 18 q^{59} + 8 q^{61} - 54 q^{62} - 8 q^{63} + 12 q^{64} - 2 q^{66} + 38 q^{67} - 36 q^{68} - 24 q^{71} + 18 q^{72} - 14 q^{73} + 36 q^{74} - 56 q^{76} + 8 q^{77} - 26 q^{78} - 44 q^{79} - 16 q^{81} - 44 q^{82} - 14 q^{83} + 12 q^{84} - 32 q^{86} + 16 q^{87} + 32 q^{88} - 10 q^{89} - 2 q^{91} + 8 q^{92} + 26 q^{93} + 18 q^{94} - 38 q^{96} - 4 q^{97} + 2 q^{98} - 56 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11343 −0.787316 −0.393658 0.919257i \(-0.628791\pi\)
−0.393658 + 0.919257i \(0.628791\pi\)
\(3\) 2.87976 1.66263 0.831314 0.555803i \(-0.187589\pi\)
0.831314 + 0.555803i \(0.187589\pi\)
\(4\) −0.760266 −0.380133
\(5\) 0 0
\(6\) −3.20642 −1.30901
\(7\) −1.00000 −0.377964
\(8\) 3.07337 1.08660
\(9\) 5.29300 1.76433
\(10\) 0 0
\(11\) −1.44843 −0.436719 −0.218359 0.975868i \(-0.570070\pi\)
−0.218359 + 0.975868i \(0.570070\pi\)
\(12\) −2.18938 −0.632020
\(13\) −2.99328 −0.830186 −0.415093 0.909779i \(-0.636251\pi\)
−0.415093 + 0.909779i \(0.636251\pi\)
\(14\) 1.11343 0.297578
\(15\) 0 0
\(16\) −1.90146 −0.475366
\(17\) −0.663092 −0.160823 −0.0804117 0.996762i \(-0.525624\pi\)
−0.0804117 + 0.996762i \(0.525624\pi\)
\(18\) −5.89340 −1.38909
\(19\) −6.91587 −1.58661 −0.793304 0.608825i \(-0.791641\pi\)
−0.793304 + 0.608825i \(0.791641\pi\)
\(20\) 0 0
\(21\) −2.87976 −0.628414
\(22\) 1.61273 0.343836
\(23\) 1.00000 0.208514
\(24\) 8.85056 1.80661
\(25\) 0 0
\(26\) 3.33282 0.653619
\(27\) 6.60327 1.27080
\(28\) 0.760266 0.143677
\(29\) 2.85250 0.529696 0.264848 0.964290i \(-0.414678\pi\)
0.264848 + 0.964290i \(0.414678\pi\)
\(30\) 0 0
\(31\) 5.80140 1.04196 0.520981 0.853568i \(-0.325566\pi\)
0.520981 + 0.853568i \(0.325566\pi\)
\(32\) −4.02959 −0.712338
\(33\) −4.17113 −0.726100
\(34\) 0.738309 0.126619
\(35\) 0 0
\(36\) −4.02409 −0.670681
\(37\) −1.45671 −0.239482 −0.119741 0.992805i \(-0.538206\pi\)
−0.119741 + 0.992805i \(0.538206\pi\)
\(38\) 7.70036 1.24916
\(39\) −8.61991 −1.38029
\(40\) 0 0
\(41\) 1.31097 0.204740 0.102370 0.994746i \(-0.467357\pi\)
0.102370 + 0.994746i \(0.467357\pi\)
\(42\) 3.20642 0.494761
\(43\) 6.04918 0.922491 0.461246 0.887272i \(-0.347403\pi\)
0.461246 + 0.887272i \(0.347403\pi\)
\(44\) 1.10119 0.166011
\(45\) 0 0
\(46\) −1.11343 −0.164167
\(47\) −7.26934 −1.06034 −0.530171 0.847891i \(-0.677872\pi\)
−0.530171 + 0.847891i \(0.677872\pi\)
\(48\) −5.47575 −0.790357
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.90954 −0.267390
\(52\) 2.27569 0.315581
\(53\) −7.52908 −1.03420 −0.517099 0.855925i \(-0.672988\pi\)
−0.517099 + 0.855925i \(0.672988\pi\)
\(54\) −7.35230 −1.00052
\(55\) 0 0
\(56\) −3.07337 −0.410697
\(57\) −19.9160 −2.63794
\(58\) −3.17607 −0.417038
\(59\) −1.21914 −0.158719 −0.0793594 0.996846i \(-0.525287\pi\)
−0.0793594 + 0.996846i \(0.525287\pi\)
\(60\) 0 0
\(61\) 1.29657 0.166009 0.0830045 0.996549i \(-0.473548\pi\)
0.0830045 + 0.996549i \(0.473548\pi\)
\(62\) −6.45948 −0.820354
\(63\) −5.29300 −0.666855
\(64\) 8.28961 1.03620
\(65\) 0 0
\(66\) 4.64428 0.571671
\(67\) −6.72336 −0.821389 −0.410694 0.911773i \(-0.634714\pi\)
−0.410694 + 0.911773i \(0.634714\pi\)
\(68\) 0.504126 0.0611343
\(69\) 2.87976 0.346682
\(70\) 0 0
\(71\) −15.4619 −1.83499 −0.917497 0.397742i \(-0.869794\pi\)
−0.917497 + 0.397742i \(0.869794\pi\)
\(72\) 16.2673 1.91713
\(73\) −12.0554 −1.41098 −0.705491 0.708719i \(-0.749273\pi\)
−0.705491 + 0.708719i \(0.749273\pi\)
\(74\) 1.62195 0.188548
\(75\) 0 0
\(76\) 5.25790 0.603122
\(77\) 1.44843 0.165064
\(78\) 9.59770 1.08673
\(79\) −12.1005 −1.36141 −0.680706 0.732557i \(-0.738327\pi\)
−0.680706 + 0.732557i \(0.738327\pi\)
\(80\) 0 0
\(81\) 3.13682 0.348536
\(82\) −1.45968 −0.161195
\(83\) −12.8092 −1.40599 −0.702995 0.711194i \(-0.748155\pi\)
−0.702995 + 0.711194i \(0.748155\pi\)
\(84\) 2.18938 0.238881
\(85\) 0 0
\(86\) −6.73536 −0.726293
\(87\) 8.21450 0.880687
\(88\) −4.45157 −0.474539
\(89\) −17.4986 −1.85485 −0.927423 0.374013i \(-0.877981\pi\)
−0.927423 + 0.374013i \(0.877981\pi\)
\(90\) 0 0
\(91\) 2.99328 0.313781
\(92\) −0.760266 −0.0792632
\(93\) 16.7066 1.73240
\(94\) 8.09393 0.834825
\(95\) 0 0
\(96\) −11.6042 −1.18435
\(97\) 2.17861 0.221204 0.110602 0.993865i \(-0.464722\pi\)
0.110602 + 0.993865i \(0.464722\pi\)
\(98\) −1.11343 −0.112474
\(99\) −7.66654 −0.770517
\(100\) 0 0
\(101\) −2.86707 −0.285285 −0.142642 0.989774i \(-0.545560\pi\)
−0.142642 + 0.989774i \(0.545560\pi\)
\(102\) 2.12615 0.210520
\(103\) 13.7697 1.35677 0.678386 0.734706i \(-0.262680\pi\)
0.678386 + 0.734706i \(0.262680\pi\)
\(104\) −9.19946 −0.902081
\(105\) 0 0
\(106\) 8.38313 0.814241
\(107\) 7.16382 0.692552 0.346276 0.938133i \(-0.387446\pi\)
0.346276 + 0.938133i \(0.387446\pi\)
\(108\) −5.02024 −0.483073
\(109\) 10.5009 1.00580 0.502902 0.864343i \(-0.332265\pi\)
0.502902 + 0.864343i \(0.332265\pi\)
\(110\) 0 0
\(111\) −4.19498 −0.398170
\(112\) 1.90146 0.179671
\(113\) 13.7108 1.28980 0.644901 0.764266i \(-0.276898\pi\)
0.644901 + 0.764266i \(0.276898\pi\)
\(114\) 22.1751 2.07689
\(115\) 0 0
\(116\) −2.16866 −0.201355
\(117\) −15.8434 −1.46472
\(118\) 1.35743 0.124962
\(119\) 0.663092 0.0607855
\(120\) 0 0
\(121\) −8.90205 −0.809277
\(122\) −1.44365 −0.130702
\(123\) 3.77529 0.340406
\(124\) −4.41061 −0.396084
\(125\) 0 0
\(126\) 5.89340 0.525026
\(127\) 17.5841 1.56033 0.780166 0.625572i \(-0.215134\pi\)
0.780166 + 0.625572i \(0.215134\pi\)
\(128\) −1.17074 −0.103480
\(129\) 17.4202 1.53376
\(130\) 0 0
\(131\) −2.10117 −0.183580 −0.0917901 0.995778i \(-0.529259\pi\)
−0.0917901 + 0.995778i \(0.529259\pi\)
\(132\) 3.17117 0.276015
\(133\) 6.91587 0.599682
\(134\) 7.48601 0.646693
\(135\) 0 0
\(136\) −2.03793 −0.174751
\(137\) −3.72916 −0.318604 −0.159302 0.987230i \(-0.550924\pi\)
−0.159302 + 0.987230i \(0.550924\pi\)
\(138\) −3.20642 −0.272948
\(139\) 7.08538 0.600974 0.300487 0.953786i \(-0.402851\pi\)
0.300487 + 0.953786i \(0.402851\pi\)
\(140\) 0 0
\(141\) −20.9339 −1.76296
\(142\) 17.2158 1.44472
\(143\) 4.33556 0.362558
\(144\) −10.0644 −0.838703
\(145\) 0 0
\(146\) 13.4229 1.11089
\(147\) 2.87976 0.237518
\(148\) 1.10749 0.0910350
\(149\) 1.47690 0.120992 0.0604960 0.998168i \(-0.480732\pi\)
0.0604960 + 0.998168i \(0.480732\pi\)
\(150\) 0 0
\(151\) −7.10228 −0.577975 −0.288988 0.957333i \(-0.593319\pi\)
−0.288988 + 0.957333i \(0.593319\pi\)
\(152\) −21.2550 −1.72401
\(153\) −3.50974 −0.283746
\(154\) −1.61273 −0.129958
\(155\) 0 0
\(156\) 6.55343 0.524694
\(157\) −18.6138 −1.48554 −0.742770 0.669547i \(-0.766488\pi\)
−0.742770 + 0.669547i \(0.766488\pi\)
\(158\) 13.4731 1.07186
\(159\) −21.6819 −1.71949
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) −3.49264 −0.274408
\(163\) 0.205611 0.0161047 0.00805233 0.999968i \(-0.497437\pi\)
0.00805233 + 0.999968i \(0.497437\pi\)
\(164\) −0.996689 −0.0778284
\(165\) 0 0
\(166\) 14.2622 1.10696
\(167\) 1.27677 0.0987995 0.0493997 0.998779i \(-0.484269\pi\)
0.0493997 + 0.998779i \(0.484269\pi\)
\(168\) −8.85056 −0.682836
\(169\) −4.04028 −0.310791
\(170\) 0 0
\(171\) −36.6057 −2.79930
\(172\) −4.59899 −0.350669
\(173\) 18.0714 1.37395 0.686973 0.726683i \(-0.258939\pi\)
0.686973 + 0.726683i \(0.258939\pi\)
\(174\) −9.14630 −0.693379
\(175\) 0 0
\(176\) 2.75414 0.207601
\(177\) −3.51083 −0.263890
\(178\) 19.4835 1.46035
\(179\) −8.27553 −0.618542 −0.309271 0.950974i \(-0.600085\pi\)
−0.309271 + 0.950974i \(0.600085\pi\)
\(180\) 0 0
\(181\) −21.5703 −1.60331 −0.801653 0.597790i \(-0.796046\pi\)
−0.801653 + 0.597790i \(0.796046\pi\)
\(182\) −3.33282 −0.247045
\(183\) 3.73381 0.276011
\(184\) 3.07337 0.226572
\(185\) 0 0
\(186\) −18.6017 −1.36394
\(187\) 0.960443 0.0702346
\(188\) 5.52664 0.403071
\(189\) −6.60327 −0.480317
\(190\) 0 0
\(191\) 12.6588 0.915959 0.457980 0.888963i \(-0.348573\pi\)
0.457980 + 0.888963i \(0.348573\pi\)
\(192\) 23.8721 1.72282
\(193\) 14.0594 1.01201 0.506007 0.862529i \(-0.331121\pi\)
0.506007 + 0.862529i \(0.331121\pi\)
\(194\) −2.42574 −0.174158
\(195\) 0 0
\(196\) −0.760266 −0.0543047
\(197\) 4.16293 0.296596 0.148298 0.988943i \(-0.452620\pi\)
0.148298 + 0.988943i \(0.452620\pi\)
\(198\) 8.53618 0.606640
\(199\) −26.7246 −1.89446 −0.947228 0.320561i \(-0.896129\pi\)
−0.947228 + 0.320561i \(0.896129\pi\)
\(200\) 0 0
\(201\) −19.3616 −1.36566
\(202\) 3.19230 0.224609
\(203\) −2.85250 −0.200206
\(204\) 1.45176 0.101644
\(205\) 0 0
\(206\) −15.3317 −1.06821
\(207\) 5.29300 0.367889
\(208\) 5.69161 0.394642
\(209\) 10.0172 0.692901
\(210\) 0 0
\(211\) −5.22635 −0.359796 −0.179898 0.983685i \(-0.557577\pi\)
−0.179898 + 0.983685i \(0.557577\pi\)
\(212\) 5.72410 0.393133
\(213\) −44.5266 −3.05091
\(214\) −7.97643 −0.545258
\(215\) 0 0
\(216\) 20.2943 1.38085
\(217\) −5.80140 −0.393825
\(218\) −11.6921 −0.791887
\(219\) −34.7167 −2.34594
\(220\) 0 0
\(221\) 1.98482 0.133513
\(222\) 4.67083 0.313485
\(223\) 4.66532 0.312413 0.156206 0.987724i \(-0.450073\pi\)
0.156206 + 0.987724i \(0.450073\pi\)
\(224\) 4.02959 0.269238
\(225\) 0 0
\(226\) −15.2661 −1.01548
\(227\) −25.0909 −1.66534 −0.832672 0.553767i \(-0.813190\pi\)
−0.832672 + 0.553767i \(0.813190\pi\)
\(228\) 15.1415 1.00277
\(229\) −18.2807 −1.20802 −0.604011 0.796976i \(-0.706432\pi\)
−0.604011 + 0.796976i \(0.706432\pi\)
\(230\) 0 0
\(231\) 4.17113 0.274440
\(232\) 8.76679 0.575568
\(233\) 18.7459 1.22809 0.614044 0.789272i \(-0.289542\pi\)
0.614044 + 0.789272i \(0.289542\pi\)
\(234\) 17.6406 1.15320
\(235\) 0 0
\(236\) 0.926872 0.0603342
\(237\) −34.8465 −2.26352
\(238\) −0.738309 −0.0478575
\(239\) −18.2568 −1.18094 −0.590468 0.807061i \(-0.701057\pi\)
−0.590468 + 0.807061i \(0.701057\pi\)
\(240\) 0 0
\(241\) 18.4641 1.18937 0.594687 0.803957i \(-0.297276\pi\)
0.594687 + 0.803957i \(0.297276\pi\)
\(242\) 9.91184 0.637157
\(243\) −10.7765 −0.691315
\(244\) −0.985740 −0.0631055
\(245\) 0 0
\(246\) −4.20353 −0.268007
\(247\) 20.7011 1.31718
\(248\) 17.8299 1.13220
\(249\) −36.8873 −2.33764
\(250\) 0 0
\(251\) 14.5229 0.916679 0.458339 0.888777i \(-0.348444\pi\)
0.458339 + 0.888777i \(0.348444\pi\)
\(252\) 4.02409 0.253494
\(253\) −1.44843 −0.0910621
\(254\) −19.5787 −1.22848
\(255\) 0 0
\(256\) −15.2757 −0.954730
\(257\) 12.9024 0.804828 0.402414 0.915458i \(-0.368171\pi\)
0.402414 + 0.915458i \(0.368171\pi\)
\(258\) −19.3962 −1.20755
\(259\) 1.45671 0.0905157
\(260\) 0 0
\(261\) 15.0983 0.934559
\(262\) 2.33951 0.144536
\(263\) −8.31789 −0.512903 −0.256452 0.966557i \(-0.582553\pi\)
−0.256452 + 0.966557i \(0.582553\pi\)
\(264\) −12.8194 −0.788982
\(265\) 0 0
\(266\) −7.70036 −0.472139
\(267\) −50.3917 −3.08392
\(268\) 5.11154 0.312237
\(269\) 12.4137 0.756877 0.378439 0.925626i \(-0.376461\pi\)
0.378439 + 0.925626i \(0.376461\pi\)
\(270\) 0 0
\(271\) −7.28170 −0.442331 −0.221166 0.975236i \(-0.570986\pi\)
−0.221166 + 0.975236i \(0.570986\pi\)
\(272\) 1.26085 0.0764500
\(273\) 8.61991 0.521701
\(274\) 4.15217 0.250842
\(275\) 0 0
\(276\) −2.18938 −0.131785
\(277\) −4.12299 −0.247726 −0.123863 0.992299i \(-0.539528\pi\)
−0.123863 + 0.992299i \(0.539528\pi\)
\(278\) −7.88910 −0.473157
\(279\) 30.7068 1.83837
\(280\) 0 0
\(281\) 13.3317 0.795305 0.397653 0.917536i \(-0.369825\pi\)
0.397653 + 0.917536i \(0.369825\pi\)
\(282\) 23.3085 1.38800
\(283\) −6.86438 −0.408045 −0.204023 0.978966i \(-0.565402\pi\)
−0.204023 + 0.978966i \(0.565402\pi\)
\(284\) 11.7552 0.697542
\(285\) 0 0
\(286\) −4.82736 −0.285448
\(287\) −1.31097 −0.0773844
\(288\) −21.3286 −1.25680
\(289\) −16.5603 −0.974136
\(290\) 0 0
\(291\) 6.27387 0.367781
\(292\) 9.16533 0.536361
\(293\) −31.1708 −1.82102 −0.910508 0.413492i \(-0.864309\pi\)
−0.910508 + 0.413492i \(0.864309\pi\)
\(294\) −3.20642 −0.187002
\(295\) 0 0
\(296\) −4.47702 −0.260221
\(297\) −9.56439 −0.554982
\(298\) −1.64442 −0.0952590
\(299\) −2.99328 −0.173106
\(300\) 0 0
\(301\) −6.04918 −0.348669
\(302\) 7.90792 0.455049
\(303\) −8.25648 −0.474322
\(304\) 13.1503 0.754219
\(305\) 0 0
\(306\) 3.90787 0.223398
\(307\) 30.3088 1.72981 0.864907 0.501933i \(-0.167378\pi\)
0.864907 + 0.501933i \(0.167378\pi\)
\(308\) −1.10119 −0.0627463
\(309\) 39.6535 2.25581
\(310\) 0 0
\(311\) −11.7717 −0.667514 −0.333757 0.942659i \(-0.608317\pi\)
−0.333757 + 0.942659i \(0.608317\pi\)
\(312\) −26.4922 −1.49983
\(313\) −24.4892 −1.38421 −0.692106 0.721795i \(-0.743317\pi\)
−0.692106 + 0.721795i \(0.743317\pi\)
\(314\) 20.7252 1.16959
\(315\) 0 0
\(316\) 9.19959 0.517517
\(317\) −4.07739 −0.229009 −0.114505 0.993423i \(-0.536528\pi\)
−0.114505 + 0.993423i \(0.536528\pi\)
\(318\) 24.1414 1.35378
\(319\) −4.13165 −0.231328
\(320\) 0 0
\(321\) 20.6301 1.15146
\(322\) 1.11343 0.0620492
\(323\) 4.58586 0.255164
\(324\) −2.38482 −0.132490
\(325\) 0 0
\(326\) −0.228934 −0.0126795
\(327\) 30.2401 1.67228
\(328\) 4.02911 0.222470
\(329\) 7.26934 0.400772
\(330\) 0 0
\(331\) 4.69263 0.257930 0.128965 0.991649i \(-0.458835\pi\)
0.128965 + 0.991649i \(0.458835\pi\)
\(332\) 9.73839 0.534464
\(333\) −7.71037 −0.422526
\(334\) −1.42160 −0.0777864
\(335\) 0 0
\(336\) 5.47575 0.298727
\(337\) 21.4035 1.16592 0.582960 0.812501i \(-0.301894\pi\)
0.582960 + 0.812501i \(0.301894\pi\)
\(338\) 4.49858 0.244691
\(339\) 39.4837 2.14446
\(340\) 0 0
\(341\) −8.40293 −0.455044
\(342\) 40.7580 2.20394
\(343\) −1.00000 −0.0539949
\(344\) 18.5914 1.00238
\(345\) 0 0
\(346\) −20.1214 −1.08173
\(347\) 28.5572 1.53303 0.766515 0.642226i \(-0.221989\pi\)
0.766515 + 0.642226i \(0.221989\pi\)
\(348\) −6.24521 −0.334778
\(349\) 9.75879 0.522376 0.261188 0.965288i \(-0.415886\pi\)
0.261188 + 0.965288i \(0.415886\pi\)
\(350\) 0 0
\(351\) −19.7654 −1.05500
\(352\) 5.83659 0.311091
\(353\) 37.2666 1.98350 0.991750 0.128191i \(-0.0409170\pi\)
0.991750 + 0.128191i \(0.0409170\pi\)
\(354\) 3.90908 0.207765
\(355\) 0 0
\(356\) 13.3036 0.705089
\(357\) 1.90954 0.101064
\(358\) 9.21425 0.486988
\(359\) −5.15223 −0.271924 −0.135962 0.990714i \(-0.543413\pi\)
−0.135962 + 0.990714i \(0.543413\pi\)
\(360\) 0 0
\(361\) 28.8292 1.51733
\(362\) 24.0171 1.26231
\(363\) −25.6357 −1.34553
\(364\) −2.27569 −0.119278
\(365\) 0 0
\(366\) −4.15735 −0.217308
\(367\) −23.3715 −1.21998 −0.609990 0.792409i \(-0.708827\pi\)
−0.609990 + 0.792409i \(0.708827\pi\)
\(368\) −1.90146 −0.0991206
\(369\) 6.93898 0.361229
\(370\) 0 0
\(371\) 7.52908 0.390890
\(372\) −12.7015 −0.658541
\(373\) 31.2466 1.61789 0.808943 0.587888i \(-0.200040\pi\)
0.808943 + 0.587888i \(0.200040\pi\)
\(374\) −1.06939 −0.0552968
\(375\) 0 0
\(376\) −22.3414 −1.15217
\(377\) −8.53833 −0.439746
\(378\) 7.35230 0.378162
\(379\) 20.5672 1.05647 0.528233 0.849099i \(-0.322855\pi\)
0.528233 + 0.849099i \(0.322855\pi\)
\(380\) 0 0
\(381\) 50.6378 2.59425
\(382\) −14.0947 −0.721150
\(383\) −21.5957 −1.10349 −0.551743 0.834014i \(-0.686037\pi\)
−0.551743 + 0.834014i \(0.686037\pi\)
\(384\) −3.37145 −0.172049
\(385\) 0 0
\(386\) −15.6542 −0.796775
\(387\) 32.0183 1.62758
\(388\) −1.65632 −0.0840871
\(389\) −19.3475 −0.980957 −0.490478 0.871453i \(-0.663178\pi\)
−0.490478 + 0.871453i \(0.663178\pi\)
\(390\) 0 0
\(391\) −0.663092 −0.0335340
\(392\) 3.07337 0.155229
\(393\) −6.05086 −0.305226
\(394\) −4.63514 −0.233515
\(395\) 0 0
\(396\) 5.82861 0.292899
\(397\) −32.1676 −1.61445 −0.807223 0.590247i \(-0.799030\pi\)
−0.807223 + 0.590247i \(0.799030\pi\)
\(398\) 29.7560 1.49154
\(399\) 19.9160 0.997048
\(400\) 0 0
\(401\) −23.7719 −1.18711 −0.593556 0.804793i \(-0.702276\pi\)
−0.593556 + 0.804793i \(0.702276\pi\)
\(402\) 21.5579 1.07521
\(403\) −17.3652 −0.865023
\(404\) 2.17974 0.108446
\(405\) 0 0
\(406\) 3.17607 0.157626
\(407\) 2.10995 0.104586
\(408\) −5.86874 −0.290546
\(409\) −9.99727 −0.494333 −0.247166 0.968973i \(-0.579499\pi\)
−0.247166 + 0.968973i \(0.579499\pi\)
\(410\) 0 0
\(411\) −10.7391 −0.529719
\(412\) −10.4687 −0.515754
\(413\) 1.21914 0.0599900
\(414\) −5.89340 −0.289645
\(415\) 0 0
\(416\) 12.0617 0.591373
\(417\) 20.4042 0.999196
\(418\) −11.1534 −0.545532
\(419\) −16.2626 −0.794482 −0.397241 0.917714i \(-0.630032\pi\)
−0.397241 + 0.917714i \(0.630032\pi\)
\(420\) 0 0
\(421\) −6.62211 −0.322742 −0.161371 0.986894i \(-0.551592\pi\)
−0.161371 + 0.986894i \(0.551592\pi\)
\(422\) 5.81919 0.283274
\(423\) −38.4766 −1.87080
\(424\) −23.1397 −1.12376
\(425\) 0 0
\(426\) 49.5774 2.40203
\(427\) −1.29657 −0.0627455
\(428\) −5.44641 −0.263262
\(429\) 12.4854 0.602799
\(430\) 0 0
\(431\) 16.1629 0.778540 0.389270 0.921124i \(-0.372727\pi\)
0.389270 + 0.921124i \(0.372727\pi\)
\(432\) −12.5559 −0.604095
\(433\) 2.34223 0.112561 0.0562803 0.998415i \(-0.482076\pi\)
0.0562803 + 0.998415i \(0.482076\pi\)
\(434\) 6.45948 0.310065
\(435\) 0 0
\(436\) −7.98349 −0.382340
\(437\) −6.91587 −0.330831
\(438\) 38.6547 1.84699
\(439\) −28.8480 −1.37684 −0.688421 0.725311i \(-0.741696\pi\)
−0.688421 + 0.725311i \(0.741696\pi\)
\(440\) 0 0
\(441\) 5.29300 0.252047
\(442\) −2.20996 −0.105117
\(443\) −27.5171 −1.30737 −0.653687 0.756765i \(-0.726779\pi\)
−0.653687 + 0.756765i \(0.726779\pi\)
\(444\) 3.18930 0.151357
\(445\) 0 0
\(446\) −5.19452 −0.245968
\(447\) 4.25310 0.201165
\(448\) −8.28961 −0.391647
\(449\) −0.919843 −0.0434101 −0.0217050 0.999764i \(-0.506909\pi\)
−0.0217050 + 0.999764i \(0.506909\pi\)
\(450\) 0 0
\(451\) −1.89886 −0.0894137
\(452\) −10.4239 −0.490297
\(453\) −20.4528 −0.960958
\(454\) 27.9371 1.31115
\(455\) 0 0
\(456\) −61.2093 −2.86639
\(457\) −1.00887 −0.0471930 −0.0235965 0.999722i \(-0.507512\pi\)
−0.0235965 + 0.999722i \(0.507512\pi\)
\(458\) 20.3543 0.951096
\(459\) −4.37858 −0.204374
\(460\) 0 0
\(461\) 15.4967 0.721754 0.360877 0.932613i \(-0.382477\pi\)
0.360877 + 0.932613i \(0.382477\pi\)
\(462\) −4.64428 −0.216071
\(463\) −41.6691 −1.93653 −0.968265 0.249927i \(-0.919593\pi\)
−0.968265 + 0.249927i \(0.919593\pi\)
\(464\) −5.42392 −0.251799
\(465\) 0 0
\(466\) −20.8724 −0.966894
\(467\) 4.55326 0.210700 0.105350 0.994435i \(-0.466404\pi\)
0.105350 + 0.994435i \(0.466404\pi\)
\(468\) 12.0452 0.556790
\(469\) 6.72336 0.310456
\(470\) 0 0
\(471\) −53.6031 −2.46990
\(472\) −3.74688 −0.172464
\(473\) −8.76182 −0.402869
\(474\) 38.7992 1.78211
\(475\) 0 0
\(476\) −0.504126 −0.0231066
\(477\) −39.8514 −1.82467
\(478\) 20.3278 0.929771
\(479\) 10.1748 0.464899 0.232450 0.972608i \(-0.425326\pi\)
0.232450 + 0.972608i \(0.425326\pi\)
\(480\) 0 0
\(481\) 4.36035 0.198815
\(482\) −20.5585 −0.936414
\(483\) −2.87976 −0.131033
\(484\) 6.76792 0.307633
\(485\) 0 0
\(486\) 11.9989 0.544283
\(487\) 31.1690 1.41240 0.706202 0.708010i \(-0.250407\pi\)
0.706202 + 0.708010i \(0.250407\pi\)
\(488\) 3.98485 0.180386
\(489\) 0.592109 0.0267761
\(490\) 0 0
\(491\) 13.3052 0.600456 0.300228 0.953867i \(-0.402937\pi\)
0.300228 + 0.953867i \(0.402937\pi\)
\(492\) −2.87022 −0.129400
\(493\) −1.89147 −0.0851875
\(494\) −23.0493 −1.03704
\(495\) 0 0
\(496\) −11.0312 −0.495313
\(497\) 15.4619 0.693563
\(498\) 41.0716 1.84046
\(499\) −39.3655 −1.76224 −0.881121 0.472890i \(-0.843211\pi\)
−0.881121 + 0.472890i \(0.843211\pi\)
\(500\) 0 0
\(501\) 3.67679 0.164267
\(502\) −16.1703 −0.721716
\(503\) 6.98352 0.311380 0.155690 0.987806i \(-0.450240\pi\)
0.155690 + 0.987806i \(0.450240\pi\)
\(504\) −16.2673 −0.724605
\(505\) 0 0
\(506\) 1.61273 0.0716947
\(507\) −11.6350 −0.516729
\(508\) −13.3686 −0.593134
\(509\) 30.8880 1.36908 0.684542 0.728973i \(-0.260002\pi\)
0.684542 + 0.728973i \(0.260002\pi\)
\(510\) 0 0
\(511\) 12.0554 0.533301
\(512\) 19.3499 0.855154
\(513\) −45.6673 −2.01626
\(514\) −14.3659 −0.633654
\(515\) 0 0
\(516\) −13.2440 −0.583033
\(517\) 10.5291 0.463071
\(518\) −1.62195 −0.0712645
\(519\) 52.0414 2.28436
\(520\) 0 0
\(521\) 38.1013 1.66925 0.834623 0.550821i \(-0.185685\pi\)
0.834623 + 0.550821i \(0.185685\pi\)
\(522\) −16.8109 −0.735794
\(523\) 13.0908 0.572421 0.286210 0.958167i \(-0.407604\pi\)
0.286210 + 0.958167i \(0.407604\pi\)
\(524\) 1.59745 0.0697849
\(525\) 0 0
\(526\) 9.26142 0.403817
\(527\) −3.84686 −0.167572
\(528\) 7.93125 0.345163
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −6.45291 −0.280033
\(532\) −5.25790 −0.227959
\(533\) −3.92411 −0.169972
\(534\) 56.1078 2.42802
\(535\) 0 0
\(536\) −20.6634 −0.892522
\(537\) −23.8315 −1.02841
\(538\) −13.8218 −0.595902
\(539\) −1.44843 −0.0623884
\(540\) 0 0
\(541\) 19.8575 0.853742 0.426871 0.904312i \(-0.359616\pi\)
0.426871 + 0.904312i \(0.359616\pi\)
\(542\) 8.10768 0.348255
\(543\) −62.1171 −2.66570
\(544\) 2.67199 0.114561
\(545\) 0 0
\(546\) −9.59770 −0.410744
\(547\) −2.33451 −0.0998163 −0.0499081 0.998754i \(-0.515893\pi\)
−0.0499081 + 0.998754i \(0.515893\pi\)
\(548\) 2.83515 0.121112
\(549\) 6.86275 0.292895
\(550\) 0 0
\(551\) −19.7275 −0.840420
\(552\) 8.85056 0.376705
\(553\) 12.1005 0.514565
\(554\) 4.59067 0.195039
\(555\) 0 0
\(556\) −5.38677 −0.228450
\(557\) 3.11889 0.132152 0.0660759 0.997815i \(-0.478952\pi\)
0.0660759 + 0.997815i \(0.478952\pi\)
\(558\) −34.1900 −1.44738
\(559\) −18.1069 −0.765840
\(560\) 0 0
\(561\) 2.76584 0.116774
\(562\) −14.8440 −0.626157
\(563\) 33.1239 1.39601 0.698003 0.716094i \(-0.254072\pi\)
0.698003 + 0.716094i \(0.254072\pi\)
\(564\) 15.9154 0.670158
\(565\) 0 0
\(566\) 7.64304 0.321261
\(567\) −3.13682 −0.131734
\(568\) −47.5203 −1.99391
\(569\) −36.2581 −1.52002 −0.760008 0.649913i \(-0.774805\pi\)
−0.760008 + 0.649913i \(0.774805\pi\)
\(570\) 0 0
\(571\) −24.4478 −1.02311 −0.511554 0.859251i \(-0.670930\pi\)
−0.511554 + 0.859251i \(0.670930\pi\)
\(572\) −3.29618 −0.137820
\(573\) 36.4543 1.52290
\(574\) 1.45968 0.0609260
\(575\) 0 0
\(576\) 43.8769 1.82820
\(577\) 41.1613 1.71357 0.856784 0.515675i \(-0.172459\pi\)
0.856784 + 0.515675i \(0.172459\pi\)
\(578\) 18.4388 0.766953
\(579\) 40.4875 1.68260
\(580\) 0 0
\(581\) 12.8092 0.531415
\(582\) −6.98554 −0.289560
\(583\) 10.9054 0.451654
\(584\) −37.0508 −1.53317
\(585\) 0 0
\(586\) 34.7066 1.43372
\(587\) 44.9204 1.85406 0.927031 0.374984i \(-0.122352\pi\)
0.927031 + 0.374984i \(0.122352\pi\)
\(588\) −2.18938 −0.0902886
\(589\) −40.1217 −1.65319
\(590\) 0 0
\(591\) 11.9882 0.493130
\(592\) 2.76988 0.113842
\(593\) −32.4937 −1.33436 −0.667178 0.744898i \(-0.732498\pi\)
−0.667178 + 0.744898i \(0.732498\pi\)
\(594\) 10.6493 0.436946
\(595\) 0 0
\(596\) −1.12283 −0.0459931
\(597\) −76.9603 −3.14978
\(598\) 3.33282 0.136289
\(599\) 27.3234 1.11640 0.558201 0.829706i \(-0.311492\pi\)
0.558201 + 0.829706i \(0.311492\pi\)
\(600\) 0 0
\(601\) 5.51397 0.224920 0.112460 0.993656i \(-0.464127\pi\)
0.112460 + 0.993656i \(0.464127\pi\)
\(602\) 6.73536 0.274513
\(603\) −35.5867 −1.44920
\(604\) 5.39962 0.219708
\(605\) 0 0
\(606\) 9.19303 0.373442
\(607\) 7.96719 0.323378 0.161689 0.986842i \(-0.448306\pi\)
0.161689 + 0.986842i \(0.448306\pi\)
\(608\) 27.8681 1.13020
\(609\) −8.21450 −0.332868
\(610\) 0 0
\(611\) 21.7592 0.880282
\(612\) 2.66834 0.107861
\(613\) 6.29976 0.254445 0.127222 0.991874i \(-0.459394\pi\)
0.127222 + 0.991874i \(0.459394\pi\)
\(614\) −33.7468 −1.36191
\(615\) 0 0
\(616\) 4.45157 0.179359
\(617\) 22.2397 0.895336 0.447668 0.894200i \(-0.352255\pi\)
0.447668 + 0.894200i \(0.352255\pi\)
\(618\) −44.1515 −1.77603
\(619\) 6.07253 0.244076 0.122038 0.992525i \(-0.461057\pi\)
0.122038 + 0.992525i \(0.461057\pi\)
\(620\) 0 0
\(621\) 6.60327 0.264980
\(622\) 13.1071 0.525545
\(623\) 17.4986 0.701066
\(624\) 16.3905 0.656143
\(625\) 0 0
\(626\) 27.2671 1.08981
\(627\) 28.8470 1.15204
\(628\) 14.1514 0.564703
\(629\) 0.965934 0.0385143
\(630\) 0 0
\(631\) −48.3297 −1.92398 −0.961988 0.273093i \(-0.911953\pi\)
−0.961988 + 0.273093i \(0.911953\pi\)
\(632\) −37.1893 −1.47931
\(633\) −15.0506 −0.598208
\(634\) 4.53990 0.180303
\(635\) 0 0
\(636\) 16.4840 0.653634
\(637\) −2.99328 −0.118598
\(638\) 4.60032 0.182128
\(639\) −81.8400 −3.23754
\(640\) 0 0
\(641\) 17.7883 0.702595 0.351297 0.936264i \(-0.385741\pi\)
0.351297 + 0.936264i \(0.385741\pi\)
\(642\) −22.9702 −0.906561
\(643\) 29.4888 1.16292 0.581462 0.813573i \(-0.302481\pi\)
0.581462 + 0.813573i \(0.302481\pi\)
\(644\) 0.760266 0.0299587
\(645\) 0 0
\(646\) −5.10604 −0.200895
\(647\) −2.00709 −0.0789067 −0.0394534 0.999221i \(-0.512562\pi\)
−0.0394534 + 0.999221i \(0.512562\pi\)
\(648\) 9.64063 0.378720
\(649\) 1.76584 0.0693154
\(650\) 0 0
\(651\) −16.7066 −0.654784
\(652\) −0.156319 −0.00612192
\(653\) 5.44963 0.213260 0.106630 0.994299i \(-0.465994\pi\)
0.106630 + 0.994299i \(0.465994\pi\)
\(654\) −33.6703 −1.31661
\(655\) 0 0
\(656\) −2.49277 −0.0973263
\(657\) −63.8094 −2.48944
\(658\) −8.09393 −0.315534
\(659\) 5.72411 0.222980 0.111490 0.993766i \(-0.464438\pi\)
0.111490 + 0.993766i \(0.464438\pi\)
\(660\) 0 0
\(661\) −0.634951 −0.0246967 −0.0123484 0.999924i \(-0.503931\pi\)
−0.0123484 + 0.999924i \(0.503931\pi\)
\(662\) −5.22493 −0.203073
\(663\) 5.71580 0.221983
\(664\) −39.3674 −1.52775
\(665\) 0 0
\(666\) 8.58499 0.332661
\(667\) 2.85250 0.110449
\(668\) −0.970685 −0.0375569
\(669\) 13.4350 0.519426
\(670\) 0 0
\(671\) −1.87800 −0.0724992
\(672\) 11.6042 0.447643
\(673\) 27.6288 1.06501 0.532506 0.846426i \(-0.321250\pi\)
0.532506 + 0.846426i \(0.321250\pi\)
\(674\) −23.8313 −0.917948
\(675\) 0 0
\(676\) 3.07169 0.118142
\(677\) −13.9294 −0.535351 −0.267676 0.963509i \(-0.586256\pi\)
−0.267676 + 0.963509i \(0.586256\pi\)
\(678\) −43.9625 −1.68837
\(679\) −2.17861 −0.0836074
\(680\) 0 0
\(681\) −72.2557 −2.76885
\(682\) 9.35611 0.358264
\(683\) 22.8605 0.874732 0.437366 0.899284i \(-0.355911\pi\)
0.437366 + 0.899284i \(0.355911\pi\)
\(684\) 27.8300 1.06411
\(685\) 0 0
\(686\) 1.11343 0.0425111
\(687\) −52.6440 −2.00849
\(688\) −11.5023 −0.438521
\(689\) 22.5366 0.858577
\(690\) 0 0
\(691\) 24.1913 0.920282 0.460141 0.887846i \(-0.347799\pi\)
0.460141 + 0.887846i \(0.347799\pi\)
\(692\) −13.7391 −0.522283
\(693\) 7.66654 0.291228
\(694\) −31.7965 −1.20698
\(695\) 0 0
\(696\) 25.2462 0.956956
\(697\) −0.869297 −0.0329270
\(698\) −10.8658 −0.411275
\(699\) 53.9838 2.04185
\(700\) 0 0
\(701\) 27.5742 1.04146 0.520731 0.853721i \(-0.325659\pi\)
0.520731 + 0.853721i \(0.325659\pi\)
\(702\) 22.0075 0.830619
\(703\) 10.0744 0.379964
\(704\) −12.0069 −0.452528
\(705\) 0 0
\(706\) −41.4938 −1.56164
\(707\) 2.86707 0.107827
\(708\) 2.66917 0.100313
\(709\) 37.7172 1.41650 0.708249 0.705963i \(-0.249485\pi\)
0.708249 + 0.705963i \(0.249485\pi\)
\(710\) 0 0
\(711\) −64.0479 −2.40198
\(712\) −53.7797 −2.01548
\(713\) 5.80140 0.217264
\(714\) −2.12615 −0.0795691
\(715\) 0 0
\(716\) 6.29161 0.235128
\(717\) −52.5752 −1.96346
\(718\) 5.73667 0.214091
\(719\) −28.5538 −1.06488 −0.532438 0.846469i \(-0.678724\pi\)
−0.532438 + 0.846469i \(0.678724\pi\)
\(720\) 0 0
\(721\) −13.7697 −0.512811
\(722\) −32.0994 −1.19462
\(723\) 53.1720 1.97749
\(724\) 16.3991 0.609469
\(725\) 0 0
\(726\) 28.5437 1.05935
\(727\) −2.95773 −0.109696 −0.0548480 0.998495i \(-0.517467\pi\)
−0.0548480 + 0.998495i \(0.517467\pi\)
\(728\) 9.19946 0.340955
\(729\) −40.4442 −1.49793
\(730\) 0 0
\(731\) −4.01116 −0.148358
\(732\) −2.83869 −0.104921
\(733\) −29.3085 −1.08254 −0.541268 0.840850i \(-0.682055\pi\)
−0.541268 + 0.840850i \(0.682055\pi\)
\(734\) 26.0226 0.960510
\(735\) 0 0
\(736\) −4.02959 −0.148533
\(737\) 9.73832 0.358716
\(738\) −7.72609 −0.284401
\(739\) 15.4678 0.568993 0.284497 0.958677i \(-0.408174\pi\)
0.284497 + 0.958677i \(0.408174\pi\)
\(740\) 0 0
\(741\) 59.6142 2.18998
\(742\) −8.38313 −0.307754
\(743\) 7.62875 0.279872 0.139936 0.990161i \(-0.455310\pi\)
0.139936 + 0.990161i \(0.455310\pi\)
\(744\) 51.3457 1.88242
\(745\) 0 0
\(746\) −34.7910 −1.27379
\(747\) −67.7990 −2.48063
\(748\) −0.730193 −0.0266985
\(749\) −7.16382 −0.261760
\(750\) 0 0
\(751\) −4.82336 −0.176007 −0.0880034 0.996120i \(-0.528049\pi\)
−0.0880034 + 0.996120i \(0.528049\pi\)
\(752\) 13.8224 0.504051
\(753\) 41.8225 1.52410
\(754\) 9.50686 0.346219
\(755\) 0 0
\(756\) 5.02024 0.182584
\(757\) −4.81593 −0.175038 −0.0875190 0.996163i \(-0.527894\pi\)
−0.0875190 + 0.996163i \(0.527894\pi\)
\(758\) −22.9002 −0.831773
\(759\) −4.17113 −0.151402
\(760\) 0 0
\(761\) 21.0293 0.762311 0.381156 0.924511i \(-0.375526\pi\)
0.381156 + 0.924511i \(0.375526\pi\)
\(762\) −56.3818 −2.04250
\(763\) −10.5009 −0.380159
\(764\) −9.62406 −0.348186
\(765\) 0 0
\(766\) 24.0453 0.868793
\(767\) 3.64923 0.131766
\(768\) −43.9902 −1.58736
\(769\) −26.7473 −0.964533 −0.482267 0.876024i \(-0.660186\pi\)
−0.482267 + 0.876024i \(0.660186\pi\)
\(770\) 0 0
\(771\) 37.1557 1.33813
\(772\) −10.6888 −0.384700
\(773\) −18.0588 −0.649530 −0.324765 0.945795i \(-0.605285\pi\)
−0.324765 + 0.945795i \(0.605285\pi\)
\(774\) −35.6502 −1.28142
\(775\) 0 0
\(776\) 6.69568 0.240361
\(777\) 4.19498 0.150494
\(778\) 21.5421 0.772323
\(779\) −9.06652 −0.324842
\(780\) 0 0
\(781\) 22.3956 0.801376
\(782\) 0.738309 0.0264019
\(783\) 18.8358 0.673138
\(784\) −1.90146 −0.0679094
\(785\) 0 0
\(786\) 6.73723 0.240309
\(787\) −30.6722 −1.09335 −0.546674 0.837346i \(-0.684106\pi\)
−0.546674 + 0.837346i \(0.684106\pi\)
\(788\) −3.16493 −0.112746
\(789\) −23.9535 −0.852767
\(790\) 0 0
\(791\) −13.7108 −0.487500
\(792\) −23.5621 −0.837244
\(793\) −3.88100 −0.137818
\(794\) 35.8165 1.27108
\(795\) 0 0
\(796\) 20.3178 0.720145
\(797\) −8.87753 −0.314458 −0.157229 0.987562i \(-0.550256\pi\)
−0.157229 + 0.987562i \(0.550256\pi\)
\(798\) −22.1751 −0.784992
\(799\) 4.82024 0.170528
\(800\) 0 0
\(801\) −92.6200 −3.27257
\(802\) 26.4684 0.934633
\(803\) 17.4615 0.616202
\(804\) 14.7200 0.519134
\(805\) 0 0
\(806\) 19.3350 0.681047
\(807\) 35.7485 1.25841
\(808\) −8.81159 −0.309991
\(809\) −45.1721 −1.58817 −0.794083 0.607810i \(-0.792048\pi\)
−0.794083 + 0.607810i \(0.792048\pi\)
\(810\) 0 0
\(811\) 46.7969 1.64326 0.821630 0.570021i \(-0.193065\pi\)
0.821630 + 0.570021i \(0.193065\pi\)
\(812\) 2.16866 0.0761050
\(813\) −20.9695 −0.735433
\(814\) −2.34929 −0.0823424
\(815\) 0 0
\(816\) 3.63093 0.127108
\(817\) −41.8353 −1.46363
\(818\) 11.1313 0.389196
\(819\) 15.8434 0.553614
\(820\) 0 0
\(821\) −37.9685 −1.32511 −0.662555 0.749013i \(-0.730528\pi\)
−0.662555 + 0.749013i \(0.730528\pi\)
\(822\) 11.9572 0.417057
\(823\) −48.8194 −1.70174 −0.850869 0.525378i \(-0.823924\pi\)
−0.850869 + 0.525378i \(0.823924\pi\)
\(824\) 42.3195 1.47427
\(825\) 0 0
\(826\) −1.35743 −0.0472311
\(827\) 30.1297 1.04771 0.523855 0.851807i \(-0.324493\pi\)
0.523855 + 0.851807i \(0.324493\pi\)
\(828\) −4.02409 −0.139847
\(829\) 13.5220 0.469638 0.234819 0.972039i \(-0.424550\pi\)
0.234819 + 0.972039i \(0.424550\pi\)
\(830\) 0 0
\(831\) −11.8732 −0.411877
\(832\) −24.8131 −0.860240
\(833\) −0.663092 −0.0229748
\(834\) −22.7187 −0.786683
\(835\) 0 0
\(836\) −7.61571 −0.263395
\(837\) 38.3082 1.32413
\(838\) 18.1074 0.625508
\(839\) 34.4251 1.18849 0.594243 0.804285i \(-0.297452\pi\)
0.594243 + 0.804285i \(0.297452\pi\)
\(840\) 0 0
\(841\) −20.8632 −0.719422
\(842\) 7.37328 0.254100
\(843\) 38.3922 1.32230
\(844\) 3.97341 0.136771
\(845\) 0 0
\(846\) 42.8411 1.47291
\(847\) 8.90205 0.305878
\(848\) 14.3163 0.491623
\(849\) −19.7678 −0.678428
\(850\) 0 0
\(851\) −1.45671 −0.0499355
\(852\) 33.8521 1.15975
\(853\) 31.0886 1.06445 0.532226 0.846602i \(-0.321356\pi\)
0.532226 + 0.846602i \(0.321356\pi\)
\(854\) 1.44365 0.0494006
\(855\) 0 0
\(856\) 22.0171 0.752528
\(857\) 23.5785 0.805427 0.402714 0.915326i \(-0.368067\pi\)
0.402714 + 0.915326i \(0.368067\pi\)
\(858\) −13.9016 −0.474593
\(859\) −31.9744 −1.09095 −0.545476 0.838126i \(-0.683651\pi\)
−0.545476 + 0.838126i \(0.683651\pi\)
\(860\) 0 0
\(861\) −3.77529 −0.128661
\(862\) −17.9963 −0.612957
\(863\) −27.5084 −0.936397 −0.468198 0.883623i \(-0.655097\pi\)
−0.468198 + 0.883623i \(0.655097\pi\)
\(864\) −26.6085 −0.905239
\(865\) 0 0
\(866\) −2.60792 −0.0886208
\(867\) −47.6897 −1.61963
\(868\) 4.41061 0.149706
\(869\) 17.5267 0.594554
\(870\) 0 0
\(871\) 20.1249 0.681906
\(872\) 32.2732 1.09291
\(873\) 11.5314 0.390278
\(874\) 7.70036 0.260468
\(875\) 0 0
\(876\) 26.3939 0.891768
\(877\) −36.4417 −1.23055 −0.615274 0.788314i \(-0.710955\pi\)
−0.615274 + 0.788314i \(0.710955\pi\)
\(878\) 32.1204 1.08401
\(879\) −89.7642 −3.02767
\(880\) 0 0
\(881\) −39.9049 −1.34443 −0.672216 0.740355i \(-0.734657\pi\)
−0.672216 + 0.740355i \(0.734657\pi\)
\(882\) −5.89340 −0.198441
\(883\) 52.5102 1.76711 0.883555 0.468327i \(-0.155143\pi\)
0.883555 + 0.468327i \(0.155143\pi\)
\(884\) −1.50899 −0.0507529
\(885\) 0 0
\(886\) 30.6384 1.02932
\(887\) 2.24783 0.0754748 0.0377374 0.999288i \(-0.487985\pi\)
0.0377374 + 0.999288i \(0.487985\pi\)
\(888\) −12.8927 −0.432651
\(889\) −17.5841 −0.589750
\(890\) 0 0
\(891\) −4.54347 −0.152212
\(892\) −3.54688 −0.118758
\(893\) 50.2738 1.68235
\(894\) −4.73554 −0.158380
\(895\) 0 0
\(896\) 1.17074 0.0391118
\(897\) −8.61991 −0.287811
\(898\) 1.02418 0.0341774
\(899\) 16.5485 0.551923
\(900\) 0 0
\(901\) 4.99247 0.166323
\(902\) 2.11425 0.0703968
\(903\) −17.4202 −0.579707
\(904\) 42.1384 1.40150
\(905\) 0 0
\(906\) 22.7729 0.756578
\(907\) 19.1127 0.634625 0.317313 0.948321i \(-0.397220\pi\)
0.317313 + 0.948321i \(0.397220\pi\)
\(908\) 19.0758 0.633052
\(909\) −15.1754 −0.503337
\(910\) 0 0
\(911\) 40.7484 1.35006 0.675028 0.737792i \(-0.264131\pi\)
0.675028 + 0.737792i \(0.264131\pi\)
\(912\) 37.8696 1.25399
\(913\) 18.5532 0.614022
\(914\) 1.12331 0.0371558
\(915\) 0 0
\(916\) 13.8982 0.459209
\(917\) 2.10117 0.0693868
\(918\) 4.87525 0.160907
\(919\) 38.7070 1.27683 0.638414 0.769693i \(-0.279591\pi\)
0.638414 + 0.769693i \(0.279591\pi\)
\(920\) 0 0
\(921\) 87.2819 2.87604
\(922\) −17.2546 −0.568249
\(923\) 46.2819 1.52339
\(924\) −3.17117 −0.104324
\(925\) 0 0
\(926\) 46.3958 1.52466
\(927\) 72.8831 2.39380
\(928\) −11.4944 −0.377322
\(929\) 49.9855 1.63997 0.819986 0.572384i \(-0.193981\pi\)
0.819986 + 0.572384i \(0.193981\pi\)
\(930\) 0 0
\(931\) −6.91587 −0.226658
\(932\) −14.2519 −0.466837
\(933\) −33.8998 −1.10983
\(934\) −5.06975 −0.165887
\(935\) 0 0
\(936\) −48.6927 −1.59157
\(937\) −12.5826 −0.411056 −0.205528 0.978651i \(-0.565891\pi\)
−0.205528 + 0.978651i \(0.565891\pi\)
\(938\) −7.48601 −0.244427
\(939\) −70.5230 −2.30143
\(940\) 0 0
\(941\) 0.761460 0.0248229 0.0124114 0.999923i \(-0.496049\pi\)
0.0124114 + 0.999923i \(0.496049\pi\)
\(942\) 59.6835 1.94459
\(943\) 1.31097 0.0426912
\(944\) 2.31815 0.0754495
\(945\) 0 0
\(946\) 9.75571 0.317185
\(947\) −50.8324 −1.65183 −0.825915 0.563795i \(-0.809341\pi\)
−0.825915 + 0.563795i \(0.809341\pi\)
\(948\) 26.4926 0.860439
\(949\) 36.0853 1.17138
\(950\) 0 0
\(951\) −11.7419 −0.380757
\(952\) 2.03793 0.0660496
\(953\) −10.3471 −0.335174 −0.167587 0.985857i \(-0.553597\pi\)
−0.167587 + 0.985857i \(0.553597\pi\)
\(954\) 44.3719 1.43659
\(955\) 0 0
\(956\) 13.8801 0.448913
\(957\) −11.8981 −0.384612
\(958\) −11.3290 −0.366023
\(959\) 3.72916 0.120421
\(960\) 0 0
\(961\) 2.65627 0.0856861
\(962\) −4.85496 −0.156530
\(963\) 37.9181 1.22189
\(964\) −14.0376 −0.452121
\(965\) 0 0
\(966\) 3.20642 0.103165
\(967\) 15.7145 0.505345 0.252673 0.967552i \(-0.418690\pi\)
0.252673 + 0.967552i \(0.418690\pi\)
\(968\) −27.3593 −0.879361
\(969\) 13.2061 0.424243
\(970\) 0 0
\(971\) −21.1348 −0.678248 −0.339124 0.940742i \(-0.610131\pi\)
−0.339124 + 0.940742i \(0.610131\pi\)
\(972\) 8.19303 0.262792
\(973\) −7.08538 −0.227147
\(974\) −34.7046 −1.11201
\(975\) 0 0
\(976\) −2.46538 −0.0789150
\(977\) 42.8162 1.36981 0.684906 0.728632i \(-0.259843\pi\)
0.684906 + 0.728632i \(0.259843\pi\)
\(978\) −0.659273 −0.0210812
\(979\) 25.3455 0.810046
\(980\) 0 0
\(981\) 55.5813 1.77457
\(982\) −14.8145 −0.472749
\(983\) 17.9746 0.573300 0.286650 0.958035i \(-0.407458\pi\)
0.286650 + 0.958035i \(0.407458\pi\)
\(984\) 11.6029 0.369886
\(985\) 0 0
\(986\) 2.10603 0.0670695
\(987\) 20.9339 0.666335
\(988\) −15.7384 −0.500704
\(989\) 6.04918 0.192353
\(990\) 0 0
\(991\) −23.0706 −0.732862 −0.366431 0.930445i \(-0.619420\pi\)
−0.366431 + 0.930445i \(0.619420\pi\)
\(992\) −23.3773 −0.742230
\(993\) 13.5136 0.428842
\(994\) −17.2158 −0.546053
\(995\) 0 0
\(996\) 28.0442 0.888614
\(997\) 33.9230 1.07435 0.537176 0.843470i \(-0.319491\pi\)
0.537176 + 0.843470i \(0.319491\pi\)
\(998\) 43.8309 1.38744
\(999\) −9.61907 −0.304334
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 4025.2.a.y.1.4 12
5.2 odd 4 805.2.c.b.484.9 24
5.3 odd 4 805.2.c.b.484.16 yes 24
5.4 even 2 4025.2.a.x.1.9 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
805.2.c.b.484.9 24 5.2 odd 4
805.2.c.b.484.16 yes 24 5.3 odd 4
4025.2.a.x.1.9 12 5.4 even 2
4025.2.a.y.1.4 12 1.1 even 1 trivial