Properties

Label 3610.2.a.bj.1.1
Level $3610$
Weight $2$
Character 3610.1
Self dual yes
Analytic conductor $28.826$
Analytic rank $0$
Dimension $9$
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] = [3610,2,Mod(1,3610)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3610, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("3610.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3610.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(28.8259951297\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 24x^{7} - 6x^{6} + 183x^{5} + 78x^{4} - 455x^{3} - 168x^{2} + 228x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.42897\) of defining polynomial
Character \(\chi\) \(=\) 3610.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.42897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42897 q^{6} +1.86700 q^{7} +1.00000 q^{8} +8.75785 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.42897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42897 q^{6} +1.86700 q^{7} +1.00000 q^{8} +8.75785 q^{9} +1.00000 q^{10} -3.60509 q^{11} -3.42897 q^{12} +2.83690 q^{13} +1.86700 q^{14} -3.42897 q^{15} +1.00000 q^{16} +5.98879 q^{17} +8.75785 q^{18} +1.00000 q^{20} -6.40189 q^{21} -3.60509 q^{22} +5.08775 q^{23} -3.42897 q^{24} +1.00000 q^{25} +2.83690 q^{26} -19.7435 q^{27} +1.86700 q^{28} -1.17848 q^{29} -3.42897 q^{30} +5.19863 q^{31} +1.00000 q^{32} +12.3617 q^{33} +5.98879 q^{34} +1.86700 q^{35} +8.75785 q^{36} -3.35231 q^{37} -9.72766 q^{39} +1.00000 q^{40} +3.72571 q^{41} -6.40189 q^{42} +0.671759 q^{43} -3.60509 q^{44} +8.75785 q^{45} +5.08775 q^{46} -6.32252 q^{47} -3.42897 q^{48} -3.51431 q^{49} +1.00000 q^{50} -20.5354 q^{51} +2.83690 q^{52} -2.56159 q^{53} -19.7435 q^{54} -3.60509 q^{55} +1.86700 q^{56} -1.17848 q^{58} +4.76825 q^{59} -3.42897 q^{60} +8.23638 q^{61} +5.19863 q^{62} +16.3509 q^{63} +1.00000 q^{64} +2.83690 q^{65} +12.3617 q^{66} -7.96385 q^{67} +5.98879 q^{68} -17.4458 q^{69} +1.86700 q^{70} +1.92698 q^{71} +8.75785 q^{72} -5.01201 q^{73} -3.35231 q^{74} -3.42897 q^{75} -6.73070 q^{77} -9.72766 q^{78} +0.601185 q^{79} +1.00000 q^{80} +41.4264 q^{81} +3.72571 q^{82} -1.90282 q^{83} -6.40189 q^{84} +5.98879 q^{85} +0.671759 q^{86} +4.04099 q^{87} -3.60509 q^{88} -0.985918 q^{89} +8.75785 q^{90} +5.29650 q^{91} +5.08775 q^{92} -17.8260 q^{93} -6.32252 q^{94} -3.42897 q^{96} +0.187561 q^{97} -3.51431 q^{98} -31.5728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{8} + 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{8} + 21 q^{9} + 9 q^{10} + 12 q^{11} + 9 q^{13} + 9 q^{16} + 6 q^{17} + 21 q^{18} + 9 q^{20} + 6 q^{21} + 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} - 18 q^{27} - 6 q^{31} + 9 q^{32} + 6 q^{33} + 6 q^{34} + 21 q^{36} + 6 q^{37} + 24 q^{39} + 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} + 18 q^{46} - 3 q^{47} + 39 q^{49} + 9 q^{50} - 48 q^{51} + 9 q^{52} - 18 q^{54} + 12 q^{55} + 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} + 9 q^{65} + 6 q^{66} + 6 q^{68} - 30 q^{69} + 18 q^{71} + 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} + 24 q^{78} - 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} + 6 q^{84} + 6 q^{85} + 18 q^{86} - 24 q^{87} + 12 q^{88} - 18 q^{89} + 21 q^{90} - 60 q^{91} + 18 q^{92} - 3 q^{94} + 18 q^{97} + 39 q^{98} + 54 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.42897 −1.97972 −0.989859 0.142053i \(-0.954630\pi\)
−0.989859 + 0.142053i \(0.954630\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −3.42897 −1.39987
\(7\) 1.86700 0.705660 0.352830 0.935688i \(-0.385219\pi\)
0.352830 + 0.935688i \(0.385219\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.75785 2.91928
\(10\) 1.00000 0.316228
\(11\) −3.60509 −1.08698 −0.543488 0.839417i \(-0.682896\pi\)
−0.543488 + 0.839417i \(0.682896\pi\)
\(12\) −3.42897 −0.989859
\(13\) 2.83690 0.786816 0.393408 0.919364i \(-0.371296\pi\)
0.393408 + 0.919364i \(0.371296\pi\)
\(14\) 1.86700 0.498977
\(15\) −3.42897 −0.885357
\(16\) 1.00000 0.250000
\(17\) 5.98879 1.45249 0.726247 0.687433i \(-0.241263\pi\)
0.726247 + 0.687433i \(0.241263\pi\)
\(18\) 8.75785 2.06425
\(19\) 0 0
\(20\) 1.00000 0.223607
\(21\) −6.40189 −1.39701
\(22\) −3.60509 −0.768607
\(23\) 5.08775 1.06087 0.530435 0.847726i \(-0.322029\pi\)
0.530435 + 0.847726i \(0.322029\pi\)
\(24\) −3.42897 −0.699936
\(25\) 1.00000 0.200000
\(26\) 2.83690 0.556363
\(27\) −19.7435 −3.79964
\(28\) 1.86700 0.352830
\(29\) −1.17848 −0.218839 −0.109419 0.993996i \(-0.534899\pi\)
−0.109419 + 0.993996i \(0.534899\pi\)
\(30\) −3.42897 −0.626042
\(31\) 5.19863 0.933702 0.466851 0.884336i \(-0.345388\pi\)
0.466851 + 0.884336i \(0.345388\pi\)
\(32\) 1.00000 0.176777
\(33\) 12.3617 2.15190
\(34\) 5.98879 1.02707
\(35\) 1.86700 0.315581
\(36\) 8.75785 1.45964
\(37\) −3.35231 −0.551116 −0.275558 0.961285i \(-0.588863\pi\)
−0.275558 + 0.961285i \(0.588863\pi\)
\(38\) 0 0
\(39\) −9.72766 −1.55767
\(40\) 1.00000 0.158114
\(41\) 3.72571 0.581859 0.290929 0.956745i \(-0.406036\pi\)
0.290929 + 0.956745i \(0.406036\pi\)
\(42\) −6.40189 −0.987833
\(43\) 0.671759 0.102442 0.0512211 0.998687i \(-0.483689\pi\)
0.0512211 + 0.998687i \(0.483689\pi\)
\(44\) −3.60509 −0.543488
\(45\) 8.75785 1.30554
\(46\) 5.08775 0.750148
\(47\) −6.32252 −0.922234 −0.461117 0.887339i \(-0.652551\pi\)
−0.461117 + 0.887339i \(0.652551\pi\)
\(48\) −3.42897 −0.494930
\(49\) −3.51431 −0.502045
\(50\) 1.00000 0.141421
\(51\) −20.5354 −2.87553
\(52\) 2.83690 0.393408
\(53\) −2.56159 −0.351862 −0.175931 0.984403i \(-0.556294\pi\)
−0.175931 + 0.984403i \(0.556294\pi\)
\(54\) −19.7435 −2.68675
\(55\) −3.60509 −0.486110
\(56\) 1.86700 0.249488
\(57\) 0 0
\(58\) −1.17848 −0.154743
\(59\) 4.76825 0.620774 0.310387 0.950610i \(-0.399541\pi\)
0.310387 + 0.950610i \(0.399541\pi\)
\(60\) −3.42897 −0.442678
\(61\) 8.23638 1.05456 0.527280 0.849692i \(-0.323212\pi\)
0.527280 + 0.849692i \(0.323212\pi\)
\(62\) 5.19863 0.660227
\(63\) 16.3509 2.06002
\(64\) 1.00000 0.125000
\(65\) 2.83690 0.351875
\(66\) 12.3617 1.52163
\(67\) −7.96385 −0.972939 −0.486470 0.873697i \(-0.661716\pi\)
−0.486470 + 0.873697i \(0.661716\pi\)
\(68\) 5.98879 0.726247
\(69\) −17.4458 −2.10022
\(70\) 1.86700 0.223149
\(71\) 1.92698 0.228690 0.114345 0.993441i \(-0.463523\pi\)
0.114345 + 0.993441i \(0.463523\pi\)
\(72\) 8.75785 1.03212
\(73\) −5.01201 −0.586611 −0.293305 0.956019i \(-0.594755\pi\)
−0.293305 + 0.956019i \(0.594755\pi\)
\(74\) −3.35231 −0.389698
\(75\) −3.42897 −0.395944
\(76\) 0 0
\(77\) −6.73070 −0.767034
\(78\) −9.72766 −1.10144
\(79\) 0.601185 0.0676386 0.0338193 0.999428i \(-0.489233\pi\)
0.0338193 + 0.999428i \(0.489233\pi\)
\(80\) 1.00000 0.111803
\(81\) 41.4264 4.60293
\(82\) 3.72571 0.411436
\(83\) −1.90282 −0.208861 −0.104431 0.994532i \(-0.533302\pi\)
−0.104431 + 0.994532i \(0.533302\pi\)
\(84\) −6.40189 −0.698503
\(85\) 5.98879 0.649575
\(86\) 0.671759 0.0724376
\(87\) 4.04099 0.433239
\(88\) −3.60509 −0.384304
\(89\) −0.985918 −0.104507 −0.0522535 0.998634i \(-0.516640\pi\)
−0.0522535 + 0.998634i \(0.516640\pi\)
\(90\) 8.75785 0.923159
\(91\) 5.29650 0.555224
\(92\) 5.08775 0.530435
\(93\) −17.8260 −1.84847
\(94\) −6.32252 −0.652118
\(95\) 0 0
\(96\) −3.42897 −0.349968
\(97\) 0.187561 0.0190440 0.00952199 0.999955i \(-0.496969\pi\)
0.00952199 + 0.999955i \(0.496969\pi\)
\(98\) −3.51431 −0.354999
\(99\) −31.5728 −3.17319
\(100\) 1.00000 0.100000
\(101\) −1.96030 −0.195057 −0.0975287 0.995233i \(-0.531094\pi\)
−0.0975287 + 0.995233i \(0.531094\pi\)
\(102\) −20.5354 −2.03331
\(103\) −17.5040 −1.72472 −0.862359 0.506297i \(-0.831014\pi\)
−0.862359 + 0.506297i \(0.831014\pi\)
\(104\) 2.83690 0.278181
\(105\) −6.40189 −0.624760
\(106\) −2.56159 −0.248804
\(107\) −10.5897 −1.02375 −0.511873 0.859061i \(-0.671048\pi\)
−0.511873 + 0.859061i \(0.671048\pi\)
\(108\) −19.7435 −1.89982
\(109\) 13.8754 1.32902 0.664509 0.747280i \(-0.268641\pi\)
0.664509 + 0.747280i \(0.268641\pi\)
\(110\) −3.60509 −0.343732
\(111\) 11.4950 1.09105
\(112\) 1.86700 0.176415
\(113\) 15.9357 1.49911 0.749553 0.661944i \(-0.230268\pi\)
0.749553 + 0.661944i \(0.230268\pi\)
\(114\) 0 0
\(115\) 5.08775 0.474435
\(116\) −1.17848 −0.109419
\(117\) 24.8452 2.29694
\(118\) 4.76825 0.438953
\(119\) 11.1811 1.02497
\(120\) −3.42897 −0.313021
\(121\) 1.99666 0.181515
\(122\) 8.23638 0.745686
\(123\) −12.7754 −1.15192
\(124\) 5.19863 0.466851
\(125\) 1.00000 0.0894427
\(126\) 16.3509 1.45665
\(127\) 16.8140 1.49200 0.746001 0.665944i \(-0.231971\pi\)
0.746001 + 0.665944i \(0.231971\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.30344 −0.202807
\(130\) 2.83690 0.248813
\(131\) 6.51376 0.569110 0.284555 0.958660i \(-0.408154\pi\)
0.284555 + 0.958660i \(0.408154\pi\)
\(132\) 12.3617 1.07595
\(133\) 0 0
\(134\) −7.96385 −0.687972
\(135\) −19.7435 −1.69925
\(136\) 5.98879 0.513534
\(137\) 20.2461 1.72975 0.864873 0.501991i \(-0.167399\pi\)
0.864873 + 0.501991i \(0.167399\pi\)
\(138\) −17.4458 −1.48508
\(139\) 3.98847 0.338298 0.169149 0.985591i \(-0.445898\pi\)
0.169149 + 0.985591i \(0.445898\pi\)
\(140\) 1.86700 0.157790
\(141\) 21.6797 1.82576
\(142\) 1.92698 0.161708
\(143\) −10.2273 −0.855249
\(144\) 8.75785 0.729821
\(145\) −1.17848 −0.0978678
\(146\) −5.01201 −0.414796
\(147\) 12.0505 0.993907
\(148\) −3.35231 −0.275558
\(149\) 5.63256 0.461437 0.230719 0.973021i \(-0.425892\pi\)
0.230719 + 0.973021i \(0.425892\pi\)
\(150\) −3.42897 −0.279974
\(151\) 1.23848 0.100786 0.0503932 0.998729i \(-0.483953\pi\)
0.0503932 + 0.998729i \(0.483953\pi\)
\(152\) 0 0
\(153\) 52.4489 4.24024
\(154\) −6.73070 −0.542375
\(155\) 5.19863 0.417564
\(156\) −9.72766 −0.778836
\(157\) −21.5073 −1.71647 −0.858235 0.513256i \(-0.828439\pi\)
−0.858235 + 0.513256i \(0.828439\pi\)
\(158\) 0.601185 0.0478277
\(159\) 8.78363 0.696587
\(160\) 1.00000 0.0790569
\(161\) 9.49883 0.748613
\(162\) 41.4264 3.25477
\(163\) 18.0210 1.41151 0.705757 0.708454i \(-0.250607\pi\)
0.705757 + 0.708454i \(0.250607\pi\)
\(164\) 3.72571 0.290929
\(165\) 12.3617 0.962361
\(166\) −1.90282 −0.147687
\(167\) 10.9088 0.844152 0.422076 0.906560i \(-0.361302\pi\)
0.422076 + 0.906560i \(0.361302\pi\)
\(168\) −6.40189 −0.493917
\(169\) −4.95198 −0.380921
\(170\) 5.98879 0.459319
\(171\) 0 0
\(172\) 0.671759 0.0512211
\(173\) −0.145902 −0.0110927 −0.00554637 0.999985i \(-0.501765\pi\)
−0.00554637 + 0.999985i \(0.501765\pi\)
\(174\) 4.04099 0.306347
\(175\) 1.86700 0.141132
\(176\) −3.60509 −0.271744
\(177\) −16.3502 −1.22896
\(178\) −0.985918 −0.0738977
\(179\) −5.69949 −0.426000 −0.213000 0.977052i \(-0.568323\pi\)
−0.213000 + 0.977052i \(0.568323\pi\)
\(180\) 8.75785 0.652772
\(181\) 18.5013 1.37519 0.687594 0.726096i \(-0.258667\pi\)
0.687594 + 0.726096i \(0.258667\pi\)
\(182\) 5.29650 0.392603
\(183\) −28.2423 −2.08773
\(184\) 5.08775 0.375074
\(185\) −3.35231 −0.246466
\(186\) −17.8260 −1.30706
\(187\) −21.5901 −1.57883
\(188\) −6.32252 −0.461117
\(189\) −36.8611 −2.68125
\(190\) 0 0
\(191\) 18.8820 1.36626 0.683128 0.730298i \(-0.260619\pi\)
0.683128 + 0.730298i \(0.260619\pi\)
\(192\) −3.42897 −0.247465
\(193\) −4.88366 −0.351533 −0.175767 0.984432i \(-0.556240\pi\)
−0.175767 + 0.984432i \(0.556240\pi\)
\(194\) 0.187561 0.0134661
\(195\) −9.72766 −0.696613
\(196\) −3.51431 −0.251022
\(197\) −3.51747 −0.250609 −0.125305 0.992118i \(-0.539991\pi\)
−0.125305 + 0.992118i \(0.539991\pi\)
\(198\) −31.5728 −2.24378
\(199\) −0.840516 −0.0595826 −0.0297913 0.999556i \(-0.509484\pi\)
−0.0297913 + 0.999556i \(0.509484\pi\)
\(200\) 1.00000 0.0707107
\(201\) 27.3078 1.92615
\(202\) −1.96030 −0.137926
\(203\) −2.20023 −0.154426
\(204\) −20.5354 −1.43777
\(205\) 3.72571 0.260215
\(206\) −17.5040 −1.21956
\(207\) 44.5578 3.09698
\(208\) 2.83690 0.196704
\(209\) 0 0
\(210\) −6.40189 −0.441772
\(211\) 27.4095 1.88695 0.943474 0.331447i \(-0.107537\pi\)
0.943474 + 0.331447i \(0.107537\pi\)
\(212\) −2.56159 −0.175931
\(213\) −6.60755 −0.452742
\(214\) −10.5897 −0.723898
\(215\) 0.671759 0.0458136
\(216\) −19.7435 −1.34338
\(217\) 9.70585 0.658876
\(218\) 13.8754 0.939757
\(219\) 17.1860 1.16132
\(220\) −3.60509 −0.243055
\(221\) 16.9896 1.14285
\(222\) 11.4950 0.771491
\(223\) 11.4351 0.765754 0.382877 0.923799i \(-0.374933\pi\)
0.382877 + 0.923799i \(0.374933\pi\)
\(224\) 1.86700 0.124744
\(225\) 8.75785 0.583857
\(226\) 15.9357 1.06003
\(227\) −15.6154 −1.03643 −0.518214 0.855251i \(-0.673403\pi\)
−0.518214 + 0.855251i \(0.673403\pi\)
\(228\) 0 0
\(229\) 5.50003 0.363452 0.181726 0.983349i \(-0.441832\pi\)
0.181726 + 0.983349i \(0.441832\pi\)
\(230\) 5.08775 0.335477
\(231\) 23.0794 1.51851
\(232\) −1.17848 −0.0773713
\(233\) −11.3286 −0.742162 −0.371081 0.928601i \(-0.621013\pi\)
−0.371081 + 0.928601i \(0.621013\pi\)
\(234\) 24.8452 1.62418
\(235\) −6.32252 −0.412436
\(236\) 4.76825 0.310387
\(237\) −2.06145 −0.133905
\(238\) 11.1811 0.724761
\(239\) 1.48334 0.0959493 0.0479747 0.998849i \(-0.484723\pi\)
0.0479747 + 0.998849i \(0.484723\pi\)
\(240\) −3.42897 −0.221339
\(241\) 8.41913 0.542324 0.271162 0.962534i \(-0.412592\pi\)
0.271162 + 0.962534i \(0.412592\pi\)
\(242\) 1.99666 0.128350
\(243\) −82.8195 −5.31287
\(244\) 8.23638 0.527280
\(245\) −3.51431 −0.224521
\(246\) −12.7754 −0.814528
\(247\) 0 0
\(248\) 5.19863 0.330114
\(249\) 6.52470 0.413486
\(250\) 1.00000 0.0632456
\(251\) 11.0908 0.700044 0.350022 0.936741i \(-0.386174\pi\)
0.350022 + 0.936741i \(0.386174\pi\)
\(252\) 16.3509 1.03001
\(253\) −18.3418 −1.15314
\(254\) 16.8140 1.05501
\(255\) −20.5354 −1.28598
\(256\) 1.00000 0.0625000
\(257\) −11.4846 −0.716390 −0.358195 0.933647i \(-0.616608\pi\)
−0.358195 + 0.933647i \(0.616608\pi\)
\(258\) −2.30344 −0.143406
\(259\) −6.25875 −0.388900
\(260\) 2.83690 0.175937
\(261\) −10.3210 −0.638853
\(262\) 6.51376 0.402422
\(263\) 31.7383 1.95707 0.978533 0.206092i \(-0.0660746\pi\)
0.978533 + 0.206092i \(0.0660746\pi\)
\(264\) 12.3617 0.760813
\(265\) −2.56159 −0.157357
\(266\) 0 0
\(267\) 3.38069 0.206895
\(268\) −7.96385 −0.486470
\(269\) 23.3579 1.42416 0.712079 0.702100i \(-0.247754\pi\)
0.712079 + 0.702100i \(0.247754\pi\)
\(270\) −19.7435 −1.20155
\(271\) −22.0881 −1.34176 −0.670878 0.741567i \(-0.734083\pi\)
−0.670878 + 0.741567i \(0.734083\pi\)
\(272\) 5.98879 0.363124
\(273\) −18.1615 −1.09919
\(274\) 20.2461 1.22311
\(275\) −3.60509 −0.217395
\(276\) −17.4458 −1.05011
\(277\) −19.8124 −1.19041 −0.595207 0.803572i \(-0.702930\pi\)
−0.595207 + 0.803572i \(0.702930\pi\)
\(278\) 3.98847 0.239213
\(279\) 45.5289 2.72574
\(280\) 1.86700 0.111575
\(281\) 21.1618 1.26241 0.631203 0.775617i \(-0.282561\pi\)
0.631203 + 0.775617i \(0.282561\pi\)
\(282\) 21.6797 1.29101
\(283\) −18.6499 −1.10862 −0.554310 0.832311i \(-0.687018\pi\)
−0.554310 + 0.832311i \(0.687018\pi\)
\(284\) 1.92698 0.114345
\(285\) 0 0
\(286\) −10.2273 −0.604752
\(287\) 6.95591 0.410594
\(288\) 8.75785 0.516061
\(289\) 18.8656 1.10974
\(290\) −1.17848 −0.0692030
\(291\) −0.643143 −0.0377017
\(292\) −5.01201 −0.293305
\(293\) 29.7307 1.73688 0.868442 0.495791i \(-0.165122\pi\)
0.868442 + 0.495791i \(0.165122\pi\)
\(294\) 12.0505 0.702798
\(295\) 4.76825 0.277619
\(296\) −3.35231 −0.194849
\(297\) 71.1771 4.13011
\(298\) 5.63256 0.326285
\(299\) 14.4335 0.834709
\(300\) −3.42897 −0.197972
\(301\) 1.25417 0.0722894
\(302\) 1.23848 0.0712668
\(303\) 6.72182 0.386159
\(304\) 0 0
\(305\) 8.23638 0.471614
\(306\) 52.4489 2.99831
\(307\) 5.16143 0.294578 0.147289 0.989093i \(-0.452945\pi\)
0.147289 + 0.989093i \(0.452945\pi\)
\(308\) −6.73070 −0.383517
\(309\) 60.0207 3.41446
\(310\) 5.19863 0.295263
\(311\) −26.0374 −1.47645 −0.738223 0.674557i \(-0.764335\pi\)
−0.738223 + 0.674557i \(0.764335\pi\)
\(312\) −9.72766 −0.550721
\(313\) −0.277126 −0.0156641 −0.00783204 0.999969i \(-0.502493\pi\)
−0.00783204 + 0.999969i \(0.502493\pi\)
\(314\) −21.5073 −1.21373
\(315\) 16.3509 0.921269
\(316\) 0.601185 0.0338193
\(317\) −24.9278 −1.40009 −0.700043 0.714101i \(-0.746836\pi\)
−0.700043 + 0.714101i \(0.746836\pi\)
\(318\) 8.78363 0.492561
\(319\) 4.24854 0.237872
\(320\) 1.00000 0.0559017
\(321\) 36.3118 2.02673
\(322\) 9.49883 0.529349
\(323\) 0 0
\(324\) 41.4264 2.30147
\(325\) 2.83690 0.157363
\(326\) 18.0210 0.998091
\(327\) −47.5782 −2.63108
\(328\) 3.72571 0.205718
\(329\) −11.8041 −0.650783
\(330\) 12.3617 0.680492
\(331\) 10.6969 0.587956 0.293978 0.955812i \(-0.405021\pi\)
0.293978 + 0.955812i \(0.405021\pi\)
\(332\) −1.90282 −0.104431
\(333\) −29.3590 −1.60886
\(334\) 10.9088 0.596906
\(335\) −7.96385 −0.435112
\(336\) −6.40189 −0.349252
\(337\) 4.55791 0.248285 0.124142 0.992264i \(-0.460382\pi\)
0.124142 + 0.992264i \(0.460382\pi\)
\(338\) −4.95198 −0.269352
\(339\) −54.6431 −2.96781
\(340\) 5.98879 0.324788
\(341\) −18.7415 −1.01491
\(342\) 0 0
\(343\) −19.6302 −1.05993
\(344\) 0.671759 0.0362188
\(345\) −17.4458 −0.939248
\(346\) −0.145902 −0.00784376
\(347\) 20.8929 1.12159 0.560794 0.827956i \(-0.310496\pi\)
0.560794 + 0.827956i \(0.310496\pi\)
\(348\) 4.04099 0.216620
\(349\) −11.2844 −0.604038 −0.302019 0.953302i \(-0.597661\pi\)
−0.302019 + 0.953302i \(0.597661\pi\)
\(350\) 1.86700 0.0997953
\(351\) −56.0104 −2.98962
\(352\) −3.60509 −0.192152
\(353\) −8.21584 −0.437285 −0.218642 0.975805i \(-0.570163\pi\)
−0.218642 + 0.975805i \(0.570163\pi\)
\(354\) −16.3502 −0.869004
\(355\) 1.92698 0.102273
\(356\) −0.985918 −0.0522535
\(357\) −38.3396 −2.02915
\(358\) −5.69949 −0.301227
\(359\) −10.7491 −0.567314 −0.283657 0.958926i \(-0.591548\pi\)
−0.283657 + 0.958926i \(0.591548\pi\)
\(360\) 8.75785 0.461579
\(361\) 0 0
\(362\) 18.5013 0.972405
\(363\) −6.84650 −0.359348
\(364\) 5.29650 0.277612
\(365\) −5.01201 −0.262340
\(366\) −28.2423 −1.47625
\(367\) −14.9478 −0.780268 −0.390134 0.920758i \(-0.627571\pi\)
−0.390134 + 0.920758i \(0.627571\pi\)
\(368\) 5.08775 0.265217
\(369\) 32.6293 1.69861
\(370\) −3.35231 −0.174278
\(371\) −4.78249 −0.248295
\(372\) −17.8260 −0.924234
\(373\) −8.72226 −0.451622 −0.225811 0.974171i \(-0.572503\pi\)
−0.225811 + 0.974171i \(0.572503\pi\)
\(374\) −21.5901 −1.11640
\(375\) −3.42897 −0.177071
\(376\) −6.32252 −0.326059
\(377\) −3.34325 −0.172186
\(378\) −36.8611 −1.89593
\(379\) −15.9169 −0.817597 −0.408799 0.912625i \(-0.634052\pi\)
−0.408799 + 0.912625i \(0.634052\pi\)
\(380\) 0 0
\(381\) −57.6548 −2.95375
\(382\) 18.8820 0.966090
\(383\) 1.74388 0.0891081 0.0445540 0.999007i \(-0.485813\pi\)
0.0445540 + 0.999007i \(0.485813\pi\)
\(384\) −3.42897 −0.174984
\(385\) −6.73070 −0.343028
\(386\) −4.88366 −0.248572
\(387\) 5.88316 0.299058
\(388\) 0.187561 0.00952199
\(389\) 32.4754 1.64657 0.823284 0.567630i \(-0.192139\pi\)
0.823284 + 0.567630i \(0.192139\pi\)
\(390\) −9.72766 −0.492579
\(391\) 30.4695 1.54091
\(392\) −3.51431 −0.177500
\(393\) −22.3355 −1.12668
\(394\) −3.51747 −0.177208
\(395\) 0.601185 0.0302489
\(396\) −31.5728 −1.58659
\(397\) −4.10529 −0.206039 −0.103019 0.994679i \(-0.532850\pi\)
−0.103019 + 0.994679i \(0.532850\pi\)
\(398\) −0.840516 −0.0421313
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −31.1991 −1.55801 −0.779003 0.627020i \(-0.784275\pi\)
−0.779003 + 0.627020i \(0.784275\pi\)
\(402\) 27.3078 1.36199
\(403\) 14.7480 0.734652
\(404\) −1.96030 −0.0975287
\(405\) 41.4264 2.05849
\(406\) −2.20023 −0.109196
\(407\) 12.0854 0.599049
\(408\) −20.5354 −1.01665
\(409\) −8.77338 −0.433816 −0.216908 0.976192i \(-0.569597\pi\)
−0.216908 + 0.976192i \(0.569597\pi\)
\(410\) 3.72571 0.184000
\(411\) −69.4235 −3.42441
\(412\) −17.5040 −0.862359
\(413\) 8.90233 0.438055
\(414\) 44.5578 2.18990
\(415\) −1.90282 −0.0934055
\(416\) 2.83690 0.139091
\(417\) −13.6764 −0.669734
\(418\) 0 0
\(419\) −6.13252 −0.299593 −0.149797 0.988717i \(-0.547862\pi\)
−0.149797 + 0.988717i \(0.547862\pi\)
\(420\) −6.40189 −0.312380
\(421\) 3.83612 0.186961 0.0934805 0.995621i \(-0.470201\pi\)
0.0934805 + 0.995621i \(0.470201\pi\)
\(422\) 27.4095 1.33427
\(423\) −55.3717 −2.69226
\(424\) −2.56159 −0.124402
\(425\) 5.98879 0.290499
\(426\) −6.60755 −0.320137
\(427\) 15.3773 0.744160
\(428\) −10.5897 −0.511873
\(429\) 35.0691 1.69315
\(430\) 0.671759 0.0323951
\(431\) 25.5855 1.23241 0.616205 0.787586i \(-0.288669\pi\)
0.616205 + 0.787586i \(0.288669\pi\)
\(432\) −19.7435 −0.949910
\(433\) −28.4636 −1.36787 −0.683937 0.729541i \(-0.739734\pi\)
−0.683937 + 0.729541i \(0.739734\pi\)
\(434\) 9.70585 0.465896
\(435\) 4.04099 0.193751
\(436\) 13.8754 0.664509
\(437\) 0 0
\(438\) 17.1860 0.821180
\(439\) −38.1049 −1.81865 −0.909324 0.416090i \(-0.863400\pi\)
−0.909324 + 0.416090i \(0.863400\pi\)
\(440\) −3.60509 −0.171866
\(441\) −30.7778 −1.46561
\(442\) 16.9896 0.808114
\(443\) 22.7785 1.08224 0.541119 0.840946i \(-0.318001\pi\)
0.541119 + 0.840946i \(0.318001\pi\)
\(444\) 11.4950 0.545527
\(445\) −0.985918 −0.0467370
\(446\) 11.4351 0.541470
\(447\) −19.3139 −0.913516
\(448\) 1.86700 0.0882074
\(449\) 31.1821 1.47157 0.735787 0.677213i \(-0.236812\pi\)
0.735787 + 0.677213i \(0.236812\pi\)
\(450\) 8.75785 0.412849
\(451\) −13.4315 −0.632466
\(452\) 15.9357 0.749553
\(453\) −4.24673 −0.199529
\(454\) −15.6154 −0.732865
\(455\) 5.29650 0.248304
\(456\) 0 0
\(457\) −13.0810 −0.611902 −0.305951 0.952047i \(-0.598974\pi\)
−0.305951 + 0.952047i \(0.598974\pi\)
\(458\) 5.50003 0.257000
\(459\) −118.240 −5.51896
\(460\) 5.08775 0.237218
\(461\) 18.2208 0.848626 0.424313 0.905516i \(-0.360516\pi\)
0.424313 + 0.905516i \(0.360516\pi\)
\(462\) 23.0794 1.07375
\(463\) −23.0080 −1.06927 −0.534636 0.845083i \(-0.679551\pi\)
−0.534636 + 0.845083i \(0.679551\pi\)
\(464\) −1.17848 −0.0547097
\(465\) −17.8260 −0.826660
\(466\) −11.3286 −0.524788
\(467\) −25.0530 −1.15932 −0.579658 0.814860i \(-0.696814\pi\)
−0.579658 + 0.814860i \(0.696814\pi\)
\(468\) 24.8452 1.14847
\(469\) −14.8685 −0.686564
\(470\) −6.32252 −0.291636
\(471\) 73.7480 3.39813
\(472\) 4.76825 0.219477
\(473\) −2.42175 −0.111352
\(474\) −2.06145 −0.0946854
\(475\) 0 0
\(476\) 11.1811 0.512483
\(477\) −22.4340 −1.02718
\(478\) 1.48334 0.0678464
\(479\) 21.6632 0.989815 0.494907 0.868946i \(-0.335202\pi\)
0.494907 + 0.868946i \(0.335202\pi\)
\(480\) −3.42897 −0.156510
\(481\) −9.51017 −0.433626
\(482\) 8.41913 0.383481
\(483\) −32.5712 −1.48204
\(484\) 1.99666 0.0907574
\(485\) 0.187561 0.00851672
\(486\) −82.8195 −3.75677
\(487\) 3.32533 0.150685 0.0753425 0.997158i \(-0.475995\pi\)
0.0753425 + 0.997158i \(0.475995\pi\)
\(488\) 8.23638 0.372843
\(489\) −61.7935 −2.79440
\(490\) −3.51431 −0.158760
\(491\) −5.03905 −0.227409 −0.113705 0.993515i \(-0.536272\pi\)
−0.113705 + 0.993515i \(0.536272\pi\)
\(492\) −12.7754 −0.575958
\(493\) −7.05769 −0.317862
\(494\) 0 0
\(495\) −31.5728 −1.41909
\(496\) 5.19863 0.233426
\(497\) 3.59766 0.161377
\(498\) 6.52470 0.292379
\(499\) −10.2386 −0.458343 −0.229171 0.973386i \(-0.573602\pi\)
−0.229171 + 0.973386i \(0.573602\pi\)
\(500\) 1.00000 0.0447214
\(501\) −37.4061 −1.67118
\(502\) 11.0908 0.495006
\(503\) 6.70316 0.298879 0.149439 0.988771i \(-0.452253\pi\)
0.149439 + 0.988771i \(0.452253\pi\)
\(504\) 16.3509 0.728327
\(505\) −1.96030 −0.0872323
\(506\) −18.3418 −0.815392
\(507\) 16.9802 0.754117
\(508\) 16.8140 0.746001
\(509\) −24.0556 −1.06625 −0.533124 0.846037i \(-0.678982\pi\)
−0.533124 + 0.846037i \(0.678982\pi\)
\(510\) −20.5354 −0.909322
\(511\) −9.35741 −0.413948
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −11.4846 −0.506564
\(515\) −17.5040 −0.771317
\(516\) −2.30344 −0.101403
\(517\) 22.7932 1.00245
\(518\) −6.25875 −0.274994
\(519\) 0.500295 0.0219605
\(520\) 2.83690 0.124406
\(521\) −26.4750 −1.15989 −0.579945 0.814656i \(-0.696926\pi\)
−0.579945 + 0.814656i \(0.696926\pi\)
\(522\) −10.3210 −0.451737
\(523\) 15.6235 0.683166 0.341583 0.939852i \(-0.389037\pi\)
0.341583 + 0.939852i \(0.389037\pi\)
\(524\) 6.51376 0.284555
\(525\) −6.40189 −0.279401
\(526\) 31.7383 1.38385
\(527\) 31.1335 1.35620
\(528\) 12.3617 0.537976
\(529\) 2.88523 0.125445
\(530\) −2.56159 −0.111268
\(531\) 41.7597 1.81222
\(532\) 0 0
\(533\) 10.5695 0.457816
\(534\) 3.38069 0.146297
\(535\) −10.5897 −0.457833
\(536\) −7.96385 −0.343986
\(537\) 19.5434 0.843359
\(538\) 23.3579 1.00703
\(539\) 12.6694 0.545710
\(540\) −19.7435 −0.849626
\(541\) −14.8243 −0.637347 −0.318673 0.947865i \(-0.603237\pi\)
−0.318673 + 0.947865i \(0.603237\pi\)
\(542\) −22.0881 −0.948765
\(543\) −63.4403 −2.72248
\(544\) 5.98879 0.256767
\(545\) 13.8754 0.594355
\(546\) −18.1615 −0.777242
\(547\) 19.3818 0.828707 0.414353 0.910116i \(-0.364008\pi\)
0.414353 + 0.910116i \(0.364008\pi\)
\(548\) 20.2461 0.864873
\(549\) 72.1330 3.07856
\(550\) −3.60509 −0.153721
\(551\) 0 0
\(552\) −17.4458 −0.742541
\(553\) 1.12241 0.0477298
\(554\) −19.8124 −0.841750
\(555\) 11.4950 0.487934
\(556\) 3.98847 0.169149
\(557\) −38.1240 −1.61536 −0.807682 0.589618i \(-0.799278\pi\)
−0.807682 + 0.589618i \(0.799278\pi\)
\(558\) 45.5289 1.92739
\(559\) 1.90572 0.0806032
\(560\) 1.86700 0.0788951
\(561\) 74.0319 3.12563
\(562\) 21.1618 0.892656
\(563\) −12.3292 −0.519613 −0.259806 0.965661i \(-0.583659\pi\)
−0.259806 + 0.965661i \(0.583659\pi\)
\(564\) 21.6797 0.912882
\(565\) 15.9357 0.670421
\(566\) −18.6499 −0.783912
\(567\) 77.3431 3.24810
\(568\) 1.92698 0.0808541
\(569\) 3.18778 0.133639 0.0668194 0.997765i \(-0.478715\pi\)
0.0668194 + 0.997765i \(0.478715\pi\)
\(570\) 0 0
\(571\) 3.67370 0.153740 0.0768698 0.997041i \(-0.475507\pi\)
0.0768698 + 0.997041i \(0.475507\pi\)
\(572\) −10.2273 −0.427624
\(573\) −64.7460 −2.70480
\(574\) 6.95591 0.290334
\(575\) 5.08775 0.212174
\(576\) 8.75785 0.364910
\(577\) −2.15105 −0.0895492 −0.0447746 0.998997i \(-0.514257\pi\)
−0.0447746 + 0.998997i \(0.514257\pi\)
\(578\) 18.8656 0.784705
\(579\) 16.7459 0.695937
\(580\) −1.17848 −0.0489339
\(581\) −3.55256 −0.147385
\(582\) −0.643143 −0.0266591
\(583\) 9.23477 0.382465
\(584\) −5.01201 −0.207398
\(585\) 24.8452 1.02722
\(586\) 29.7307 1.22816
\(587\) −28.5242 −1.17732 −0.588659 0.808381i \(-0.700344\pi\)
−0.588659 + 0.808381i \(0.700344\pi\)
\(588\) 12.0505 0.496953
\(589\) 0 0
\(590\) 4.76825 0.196306
\(591\) 12.0613 0.496136
\(592\) −3.35231 −0.137779
\(593\) 10.0915 0.414410 0.207205 0.978298i \(-0.433563\pi\)
0.207205 + 0.978298i \(0.433563\pi\)
\(594\) 71.1771 2.92043
\(595\) 11.1811 0.458379
\(596\) 5.63256 0.230719
\(597\) 2.88211 0.117957
\(598\) 14.4335 0.590228
\(599\) −2.76324 −0.112903 −0.0564514 0.998405i \(-0.517979\pi\)
−0.0564514 + 0.998405i \(0.517979\pi\)
\(600\) −3.42897 −0.139987
\(601\) −17.0215 −0.694321 −0.347160 0.937806i \(-0.612854\pi\)
−0.347160 + 0.937806i \(0.612854\pi\)
\(602\) 1.25417 0.0511163
\(603\) −69.7462 −2.84029
\(604\) 1.23848 0.0503932
\(605\) 1.99666 0.0811758
\(606\) 6.72182 0.273055
\(607\) 45.0807 1.82977 0.914884 0.403717i \(-0.132282\pi\)
0.914884 + 0.403717i \(0.132282\pi\)
\(608\) 0 0
\(609\) 7.54452 0.305720
\(610\) 8.23638 0.333481
\(611\) −17.9364 −0.725628
\(612\) 52.4489 2.12012
\(613\) −1.22843 −0.0496158 −0.0248079 0.999692i \(-0.507897\pi\)
−0.0248079 + 0.999692i \(0.507897\pi\)
\(614\) 5.16143 0.208298
\(615\) −12.7754 −0.515153
\(616\) −6.73070 −0.271188
\(617\) 23.7192 0.954899 0.477449 0.878659i \(-0.341561\pi\)
0.477449 + 0.878659i \(0.341561\pi\)
\(618\) 60.0207 2.41439
\(619\) 12.6509 0.508482 0.254241 0.967141i \(-0.418174\pi\)
0.254241 + 0.967141i \(0.418174\pi\)
\(620\) 5.19863 0.208782
\(621\) −100.450 −4.03092
\(622\) −26.0374 −1.04400
\(623\) −1.84071 −0.0737464
\(624\) −9.72766 −0.389418
\(625\) 1.00000 0.0400000
\(626\) −0.277126 −0.0110762
\(627\) 0 0
\(628\) −21.5073 −0.858235
\(629\) −20.0763 −0.800493
\(630\) 16.3509 0.651436
\(631\) 38.2412 1.52236 0.761179 0.648542i \(-0.224621\pi\)
0.761179 + 0.648542i \(0.224621\pi\)
\(632\) 0.601185 0.0239139
\(633\) −93.9864 −3.73562
\(634\) −24.9278 −0.990010
\(635\) 16.8140 0.667244
\(636\) 8.78363 0.348294
\(637\) −9.96977 −0.395017
\(638\) 4.24854 0.168201
\(639\) 16.8762 0.667611
\(640\) 1.00000 0.0395285
\(641\) −10.2621 −0.405327 −0.202663 0.979248i \(-0.564960\pi\)
−0.202663 + 0.979248i \(0.564960\pi\)
\(642\) 36.3118 1.43311
\(643\) −14.5679 −0.574502 −0.287251 0.957855i \(-0.592741\pi\)
−0.287251 + 0.957855i \(0.592741\pi\)
\(644\) 9.49883 0.374306
\(645\) −2.30344 −0.0906980
\(646\) 0 0
\(647\) 4.44223 0.174642 0.0873211 0.996180i \(-0.472169\pi\)
0.0873211 + 0.996180i \(0.472169\pi\)
\(648\) 41.4264 1.62738
\(649\) −17.1900 −0.674766
\(650\) 2.83690 0.111273
\(651\) −33.2811 −1.30439
\(652\) 18.0210 0.705757
\(653\) 19.4483 0.761072 0.380536 0.924766i \(-0.375740\pi\)
0.380536 + 0.924766i \(0.375740\pi\)
\(654\) −47.5782 −1.86045
\(655\) 6.51376 0.254514
\(656\) 3.72571 0.145465
\(657\) −43.8944 −1.71248
\(658\) −11.8041 −0.460173
\(659\) −12.4606 −0.485395 −0.242698 0.970102i \(-0.578032\pi\)
−0.242698 + 0.970102i \(0.578032\pi\)
\(660\) 12.3617 0.481180
\(661\) −8.25110 −0.320931 −0.160465 0.987041i \(-0.551299\pi\)
−0.160465 + 0.987041i \(0.551299\pi\)
\(662\) 10.6969 0.415748
\(663\) −58.2569 −2.26251
\(664\) −1.90282 −0.0738436
\(665\) 0 0
\(666\) −29.3590 −1.13764
\(667\) −5.99584 −0.232160
\(668\) 10.9088 0.422076
\(669\) −39.2108 −1.51598
\(670\) −7.96385 −0.307670
\(671\) −29.6929 −1.14628
\(672\) −6.40189 −0.246958
\(673\) 1.23314 0.0475341 0.0237671 0.999718i \(-0.492434\pi\)
0.0237671 + 0.999718i \(0.492434\pi\)
\(674\) 4.55791 0.175564
\(675\) −19.7435 −0.759928
\(676\) −4.95198 −0.190461
\(677\) 17.8526 0.686131 0.343065 0.939312i \(-0.388535\pi\)
0.343065 + 0.939312i \(0.388535\pi\)
\(678\) −54.6431 −2.09856
\(679\) 0.350177 0.0134386
\(680\) 5.98879 0.229660
\(681\) 53.5446 2.05184
\(682\) −18.7415 −0.717651
\(683\) −27.7712 −1.06264 −0.531318 0.847173i \(-0.678303\pi\)
−0.531318 + 0.847173i \(0.678303\pi\)
\(684\) 0 0
\(685\) 20.2461 0.773566
\(686\) −19.6302 −0.749485
\(687\) −18.8595 −0.719533
\(688\) 0.671759 0.0256106
\(689\) −7.26699 −0.276850
\(690\) −17.4458 −0.664149
\(691\) 42.6796 1.62361 0.811805 0.583929i \(-0.198485\pi\)
0.811805 + 0.583929i \(0.198485\pi\)
\(692\) −0.145902 −0.00554637
\(693\) −58.9465 −2.23919
\(694\) 20.8929 0.793082
\(695\) 3.98847 0.151291
\(696\) 4.04099 0.153173
\(697\) 22.3125 0.845147
\(698\) −11.2844 −0.427120
\(699\) 38.8455 1.46927
\(700\) 1.86700 0.0705660
\(701\) −39.8475 −1.50502 −0.752509 0.658582i \(-0.771157\pi\)
−0.752509 + 0.658582i \(0.771157\pi\)
\(702\) −56.0104 −2.11398
\(703\) 0 0
\(704\) −3.60509 −0.135872
\(705\) 21.6797 0.816506
\(706\) −8.21584 −0.309207
\(707\) −3.65988 −0.137644
\(708\) −16.3502 −0.614479
\(709\) 48.0511 1.80460 0.902298 0.431113i \(-0.141879\pi\)
0.902298 + 0.431113i \(0.141879\pi\)
\(710\) 1.92698 0.0723181
\(711\) 5.26509 0.197456
\(712\) −0.985918 −0.0369488
\(713\) 26.4494 0.990537
\(714\) −38.3396 −1.43482
\(715\) −10.2273 −0.382479
\(716\) −5.69949 −0.213000
\(717\) −5.08633 −0.189953
\(718\) −10.7491 −0.401152
\(719\) −30.3742 −1.13277 −0.566383 0.824142i \(-0.691658\pi\)
−0.566383 + 0.824142i \(0.691658\pi\)
\(720\) 8.75785 0.326386
\(721\) −32.6799 −1.21706
\(722\) 0 0
\(723\) −28.8690 −1.07365
\(724\) 18.5013 0.687594
\(725\) −1.17848 −0.0437678
\(726\) −6.84650 −0.254097
\(727\) −30.5670 −1.13367 −0.566834 0.823832i \(-0.691832\pi\)
−0.566834 + 0.823832i \(0.691832\pi\)
\(728\) 5.29650 0.196301
\(729\) 159.706 5.91505
\(730\) −5.01201 −0.185503
\(731\) 4.02302 0.148797
\(732\) −28.2423 −1.04387
\(733\) −43.9998 −1.62517 −0.812586 0.582842i \(-0.801941\pi\)
−0.812586 + 0.582842i \(0.801941\pi\)
\(734\) −14.9478 −0.551733
\(735\) 12.0505 0.444489
\(736\) 5.08775 0.187537
\(737\) 28.7104 1.05756
\(738\) 32.6293 1.20110
\(739\) 29.3015 1.07787 0.538936 0.842347i \(-0.318826\pi\)
0.538936 + 0.842347i \(0.318826\pi\)
\(740\) −3.35231 −0.123233
\(741\) 0 0
\(742\) −4.78249 −0.175571
\(743\) −13.1228 −0.481430 −0.240715 0.970596i \(-0.577382\pi\)
−0.240715 + 0.970596i \(0.577382\pi\)
\(744\) −17.8260 −0.653532
\(745\) 5.63256 0.206361
\(746\) −8.72226 −0.319345
\(747\) −16.6646 −0.609725
\(748\) −21.5901 −0.789413
\(749\) −19.7710 −0.722416
\(750\) −3.42897 −0.125208
\(751\) −20.0098 −0.730167 −0.365084 0.930975i \(-0.618960\pi\)
−0.365084 + 0.930975i \(0.618960\pi\)
\(752\) −6.32252 −0.230559
\(753\) −38.0300 −1.38589
\(754\) −3.34325 −0.121754
\(755\) 1.23848 0.0450731
\(756\) −36.8611 −1.34063
\(757\) −36.4883 −1.32619 −0.663095 0.748536i \(-0.730757\pi\)
−0.663095 + 0.748536i \(0.730757\pi\)
\(758\) −15.9169 −0.578128
\(759\) 62.8935 2.28289
\(760\) 0 0
\(761\) 3.91470 0.141908 0.0709540 0.997480i \(-0.477396\pi\)
0.0709540 + 0.997480i \(0.477396\pi\)
\(762\) −57.6548 −2.08861
\(763\) 25.9053 0.937834
\(764\) 18.8820 0.683128
\(765\) 52.4489 1.89629
\(766\) 1.74388 0.0630089
\(767\) 13.5271 0.488435
\(768\) −3.42897 −0.123732
\(769\) −22.7389 −0.819987 −0.409993 0.912088i \(-0.634469\pi\)
−0.409993 + 0.912088i \(0.634469\pi\)
\(770\) −6.73070 −0.242558
\(771\) 39.3804 1.41825
\(772\) −4.88366 −0.175767
\(773\) −21.8627 −0.786347 −0.393174 0.919464i \(-0.628623\pi\)
−0.393174 + 0.919464i \(0.628623\pi\)
\(774\) 5.88316 0.211466
\(775\) 5.19863 0.186740
\(776\) 0.187561 0.00673306
\(777\) 21.4611 0.769912
\(778\) 32.4754 1.16430
\(779\) 0 0
\(780\) −9.72766 −0.348306
\(781\) −6.94692 −0.248580
\(782\) 30.4695 1.08959
\(783\) 23.2674 0.831510
\(784\) −3.51431 −0.125511
\(785\) −21.5073 −0.767629
\(786\) −22.3355 −0.796681
\(787\) 30.1350 1.07420 0.537098 0.843520i \(-0.319520\pi\)
0.537098 + 0.843520i \(0.319520\pi\)
\(788\) −3.51747 −0.125305
\(789\) −108.830 −3.87444
\(790\) 0.601185 0.0213892
\(791\) 29.7520 1.05786
\(792\) −31.5728 −1.12189
\(793\) 23.3658 0.829744
\(794\) −4.10529 −0.145691
\(795\) 8.78363 0.311523
\(796\) −0.840516 −0.0297913
\(797\) 19.4641 0.689456 0.344728 0.938703i \(-0.387971\pi\)
0.344728 + 0.938703i \(0.387971\pi\)
\(798\) 0 0
\(799\) −37.8642 −1.33954
\(800\) 1.00000 0.0353553
\(801\) −8.63452 −0.305086
\(802\) −31.1991 −1.10168
\(803\) 18.0687 0.637631
\(804\) 27.3078 0.963073
\(805\) 9.49883 0.334790
\(806\) 14.7480 0.519477
\(807\) −80.0937 −2.81943
\(808\) −1.96030 −0.0689632
\(809\) −40.3232 −1.41769 −0.708844 0.705365i \(-0.750783\pi\)
−0.708844 + 0.705365i \(0.750783\pi\)
\(810\) 41.4264 1.45558
\(811\) 19.2857 0.677212 0.338606 0.940928i \(-0.390045\pi\)
0.338606 + 0.940928i \(0.390045\pi\)
\(812\) −2.20023 −0.0772129
\(813\) 75.7395 2.65630
\(814\) 12.0854 0.423592
\(815\) 18.0210 0.631248
\(816\) −20.5354 −0.718883
\(817\) 0 0
\(818\) −8.77338 −0.306754
\(819\) 46.3859 1.62086
\(820\) 3.72571 0.130108
\(821\) 41.9192 1.46299 0.731495 0.681847i \(-0.238823\pi\)
0.731495 + 0.681847i \(0.238823\pi\)
\(822\) −69.4235 −2.42142
\(823\) 23.9246 0.833960 0.416980 0.908916i \(-0.363088\pi\)
0.416980 + 0.908916i \(0.363088\pi\)
\(824\) −17.5040 −0.609780
\(825\) 12.3617 0.430381
\(826\) 8.90233 0.309752
\(827\) −24.6024 −0.855508 −0.427754 0.903895i \(-0.640695\pi\)
−0.427754 + 0.903895i \(0.640695\pi\)
\(828\) 44.5578 1.54849
\(829\) 35.1963 1.22242 0.611209 0.791469i \(-0.290683\pi\)
0.611209 + 0.791469i \(0.290683\pi\)
\(830\) −1.90282 −0.0660477
\(831\) 67.9363 2.35669
\(832\) 2.83690 0.0983519
\(833\) −21.0465 −0.729217
\(834\) −13.6764 −0.473573
\(835\) 10.9088 0.377516
\(836\) 0 0
\(837\) −102.639 −3.54773
\(838\) −6.13252 −0.211844
\(839\) 23.8974 0.825030 0.412515 0.910951i \(-0.364650\pi\)
0.412515 + 0.910951i \(0.364650\pi\)
\(840\) −6.40189 −0.220886
\(841\) −27.6112 −0.952110
\(842\) 3.83612 0.132201
\(843\) −72.5632 −2.49921
\(844\) 27.4095 0.943474
\(845\) −4.95198 −0.170353
\(846\) −55.3717 −1.90372
\(847\) 3.72777 0.128088
\(848\) −2.56159 −0.0879654
\(849\) 63.9499 2.19475
\(850\) 5.98879 0.205414
\(851\) −17.0557 −0.584662
\(852\) −6.60755 −0.226371
\(853\) 26.1190 0.894297 0.447148 0.894460i \(-0.352440\pi\)
0.447148 + 0.894460i \(0.352440\pi\)
\(854\) 15.3773 0.526201
\(855\) 0 0
\(856\) −10.5897 −0.361949
\(857\) 49.1708 1.67964 0.839821 0.542863i \(-0.182660\pi\)
0.839821 + 0.542863i \(0.182660\pi\)
\(858\) 35.0691 1.19724
\(859\) −14.5141 −0.495213 −0.247607 0.968861i \(-0.579644\pi\)
−0.247607 + 0.968861i \(0.579644\pi\)
\(860\) 0.671759 0.0229068
\(861\) −23.8516 −0.812861
\(862\) 25.5855 0.871445
\(863\) 10.9036 0.371161 0.185581 0.982629i \(-0.440583\pi\)
0.185581 + 0.982629i \(0.440583\pi\)
\(864\) −19.7435 −0.671688
\(865\) −0.145902 −0.00496083
\(866\) −28.4636 −0.967233
\(867\) −64.6896 −2.19697
\(868\) 9.70585 0.329438
\(869\) −2.16733 −0.0735215
\(870\) 4.04099 0.137002
\(871\) −22.5927 −0.765524
\(872\) 13.8754 0.469879
\(873\) 1.64263 0.0555948
\(874\) 0 0
\(875\) 1.86700 0.0631161
\(876\) 17.1860 0.580662
\(877\) −11.2484 −0.379831 −0.189915 0.981800i \(-0.560821\pi\)
−0.189915 + 0.981800i \(0.560821\pi\)
\(878\) −38.1049 −1.28598
\(879\) −101.946 −3.43854
\(880\) −3.60509 −0.121528
\(881\) −9.81993 −0.330842 −0.165421 0.986223i \(-0.552898\pi\)
−0.165421 + 0.986223i \(0.552898\pi\)
\(882\) −30.7778 −1.03634
\(883\) 30.4524 1.02481 0.512403 0.858745i \(-0.328755\pi\)
0.512403 + 0.858745i \(0.328755\pi\)
\(884\) 16.9896 0.571423
\(885\) −16.3502 −0.549606
\(886\) 22.7785 0.765258
\(887\) −12.3099 −0.413327 −0.206663 0.978412i \(-0.566260\pi\)
−0.206663 + 0.978412i \(0.566260\pi\)
\(888\) 11.4950 0.385746
\(889\) 31.3918 1.05285
\(890\) −0.985918 −0.0330480
\(891\) −149.346 −5.00327
\(892\) 11.4351 0.382877
\(893\) 0 0
\(894\) −19.3139 −0.645953
\(895\) −5.69949 −0.190513
\(896\) 1.86700 0.0623721
\(897\) −49.4920 −1.65249
\(898\) 31.1821 1.04056
\(899\) −6.12651 −0.204330
\(900\) 8.75785 0.291928
\(901\) −15.3408 −0.511077
\(902\) −13.4315 −0.447221
\(903\) −4.30053 −0.143113
\(904\) 15.9357 0.530014
\(905\) 18.5013 0.615003
\(906\) −4.24673 −0.141088
\(907\) 40.8180 1.35534 0.677670 0.735366i \(-0.262990\pi\)
0.677670 + 0.735366i \(0.262990\pi\)
\(908\) −15.6154 −0.518214
\(909\) −17.1680 −0.569428
\(910\) 5.29650 0.175577
\(911\) −1.58058 −0.0523671 −0.0261836 0.999657i \(-0.508335\pi\)
−0.0261836 + 0.999657i \(0.508335\pi\)
\(912\) 0 0
\(913\) 6.85982 0.227027
\(914\) −13.0810 −0.432680
\(915\) −28.2423 −0.933662
\(916\) 5.50003 0.181726
\(917\) 12.1612 0.401598
\(918\) −118.240 −3.90249
\(919\) −47.7782 −1.57606 −0.788029 0.615638i \(-0.788899\pi\)
−0.788029 + 0.615638i \(0.788899\pi\)
\(920\) 5.08775 0.167738
\(921\) −17.6984 −0.583182
\(922\) 18.2208 0.600069
\(923\) 5.46665 0.179937
\(924\) 23.0794 0.759256
\(925\) −3.35231 −0.110223
\(926\) −23.0080 −0.756089
\(927\) −153.297 −5.03494
\(928\) −1.17848 −0.0386856
\(929\) −47.9567 −1.57341 −0.786705 0.617330i \(-0.788214\pi\)
−0.786705 + 0.617330i \(0.788214\pi\)
\(930\) −17.8260 −0.584537
\(931\) 0 0
\(932\) −11.3286 −0.371081
\(933\) 89.2815 2.92295
\(934\) −25.0530 −0.819761
\(935\) −21.5901 −0.706072
\(936\) 24.8452 0.812090
\(937\) 38.0767 1.24391 0.621955 0.783053i \(-0.286339\pi\)
0.621955 + 0.783053i \(0.286339\pi\)
\(938\) −14.8685 −0.485474
\(939\) 0.950257 0.0310105
\(940\) −6.32252 −0.206218
\(941\) 39.2730 1.28026 0.640132 0.768265i \(-0.278880\pi\)
0.640132 + 0.768265i \(0.278880\pi\)
\(942\) 73.7480 2.40284
\(943\) 18.9555 0.617276
\(944\) 4.76825 0.155193
\(945\) −36.8611 −1.19909
\(946\) −2.42175 −0.0787379
\(947\) −7.16095 −0.232700 −0.116350 0.993208i \(-0.537119\pi\)
−0.116350 + 0.993208i \(0.537119\pi\)
\(948\) −2.06145 −0.0669527
\(949\) −14.2186 −0.461555
\(950\) 0 0
\(951\) 85.4768 2.77178
\(952\) 11.1811 0.362380
\(953\) 33.2331 1.07653 0.538263 0.842777i \(-0.319081\pi\)
0.538263 + 0.842777i \(0.319081\pi\)
\(954\) −22.4340 −0.726329
\(955\) 18.8820 0.611009
\(956\) 1.48334 0.0479747
\(957\) −14.5681 −0.470920
\(958\) 21.6632 0.699905
\(959\) 37.7996 1.22061
\(960\) −3.42897 −0.110670
\(961\) −3.97420 −0.128200
\(962\) −9.51017 −0.306620
\(963\) −92.7431 −2.98860
\(964\) 8.41913 0.271162
\(965\) −4.88366 −0.157211
\(966\) −32.5712 −1.04796
\(967\) −25.2252 −0.811188 −0.405594 0.914053i \(-0.632935\pi\)
−0.405594 + 0.914053i \(0.632935\pi\)
\(968\) 1.99666 0.0641751
\(969\) 0 0
\(970\) 0.187561 0.00602223
\(971\) −43.7283 −1.40331 −0.701654 0.712518i \(-0.747555\pi\)
−0.701654 + 0.712518i \(0.747555\pi\)
\(972\) −82.8195 −2.65644
\(973\) 7.44647 0.238723
\(974\) 3.32533 0.106550
\(975\) −9.72766 −0.311535
\(976\) 8.23638 0.263640
\(977\) 0.00478368 0.000153043 0 7.65217e−5 1.00000i \(-0.499976\pi\)
7.65217e−5 1.00000i \(0.499976\pi\)
\(978\) −61.7935 −1.97594
\(979\) 3.55432 0.113597
\(980\) −3.51431 −0.112261
\(981\) 121.518 3.87978
\(982\) −5.03905 −0.160803
\(983\) −36.9839 −1.17960 −0.589801 0.807548i \(-0.700794\pi\)
−0.589801 + 0.807548i \(0.700794\pi\)
\(984\) −12.7754 −0.407264
\(985\) −3.51747 −0.112076
\(986\) −7.05769 −0.224763
\(987\) 40.4761 1.28837
\(988\) 0 0
\(989\) 3.41774 0.108678
\(990\) −31.5728 −1.00345
\(991\) 5.84928 0.185809 0.0929043 0.995675i \(-0.470385\pi\)
0.0929043 + 0.995675i \(0.470385\pi\)
\(992\) 5.19863 0.165057
\(993\) −36.6795 −1.16399
\(994\) 3.59766 0.114111
\(995\) −0.840516 −0.0266462
\(996\) 6.52470 0.206743
\(997\) −57.9390 −1.83495 −0.917473 0.397798i \(-0.869775\pi\)
−0.917473 + 0.397798i \(0.869775\pi\)
\(998\) −10.2386 −0.324097
\(999\) 66.1863 2.09404
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 3610.2.a.bj.1.1 9
19.3 odd 18 190.2.k.d.161.3 yes 18
19.13 odd 18 190.2.k.d.131.3 18
19.18 odd 2 3610.2.a.bi.1.9 9
95.3 even 36 950.2.u.g.199.3 36
95.13 even 36 950.2.u.g.549.4 36
95.22 even 36 950.2.u.g.199.4 36
95.32 even 36 950.2.u.g.549.3 36
95.79 odd 18 950.2.l.i.351.1 18
95.89 odd 18 950.2.l.i.701.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.k.d.131.3 18 19.13 odd 18
190.2.k.d.161.3 yes 18 19.3 odd 18
950.2.l.i.351.1 18 95.79 odd 18
950.2.l.i.701.1 18 95.89 odd 18
950.2.u.g.199.3 36 95.3 even 36
950.2.u.g.199.4 36 95.22 even 36
950.2.u.g.549.3 36 95.32 even 36
950.2.u.g.549.4 36 95.13 even 36
3610.2.a.bi.1.9 9 19.18 odd 2
3610.2.a.bj.1.1 9 1.1 even 1 trivial