Properties

Label 7595.2.a.bf.1.10
Level $7595$
Weight $2$
Character 7595.1
Self dual yes
Analytic conductor $60.646$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7595,2,Mod(1,7595)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7595, 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("7595.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7595.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: \(60.6463803352\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 1085)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 7595.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.628452 q^{2} -1.52512 q^{3} -1.60505 q^{4} +1.00000 q^{5} +0.958466 q^{6} +2.26560 q^{8} -0.674002 q^{9} +O(q^{10})\) \(q-0.628452 q^{2} -1.52512 q^{3} -1.60505 q^{4} +1.00000 q^{5} +0.958466 q^{6} +2.26560 q^{8} -0.674002 q^{9} -0.628452 q^{10} -4.48476 q^{11} +2.44789 q^{12} -3.10381 q^{13} -1.52512 q^{15} +1.78628 q^{16} +0.893389 q^{17} +0.423578 q^{18} -6.74349 q^{19} -1.60505 q^{20} +2.81845 q^{22} +5.95926 q^{23} -3.45532 q^{24} +1.00000 q^{25} +1.95060 q^{26} +5.60330 q^{27} +2.05255 q^{29} +0.958466 q^{30} -1.00000 q^{31} -5.65379 q^{32} +6.83980 q^{33} -0.561452 q^{34} +1.08180 q^{36} -4.09693 q^{37} +4.23796 q^{38} +4.73369 q^{39} +2.26560 q^{40} +7.42574 q^{41} +5.56997 q^{43} +7.19825 q^{44} -0.674002 q^{45} -3.74511 q^{46} +11.0066 q^{47} -2.72429 q^{48} -0.628452 q^{50} -1.36253 q^{51} +4.98177 q^{52} -4.30252 q^{53} -3.52141 q^{54} -4.48476 q^{55} +10.2846 q^{57} -1.28993 q^{58} -9.91053 q^{59} +2.44789 q^{60} +6.58024 q^{61} +0.628452 q^{62} -0.0194157 q^{64} -3.10381 q^{65} -4.29849 q^{66} +10.0098 q^{67} -1.43393 q^{68} -9.08860 q^{69} -13.0016 q^{71} -1.52702 q^{72} +1.93156 q^{73} +2.57473 q^{74} -1.52512 q^{75} +10.8236 q^{76} -2.97490 q^{78} +6.89495 q^{79} +1.78628 q^{80} -6.52372 q^{81} -4.66672 q^{82} -0.685851 q^{83} +0.893389 q^{85} -3.50046 q^{86} -3.13040 q^{87} -10.1607 q^{88} +16.0205 q^{89} +0.423578 q^{90} -9.56489 q^{92} +1.52512 q^{93} -6.91714 q^{94} -6.74349 q^{95} +8.62272 q^{96} +4.21722 q^{97} +3.02273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.628452 −0.444383 −0.222191 0.975003i \(-0.571321\pi\)
−0.222191 + 0.975003i \(0.571321\pi\)
\(3\) −1.52512 −0.880530 −0.440265 0.897868i \(-0.645115\pi\)
−0.440265 + 0.897868i \(0.645115\pi\)
\(4\) −1.60505 −0.802524
\(5\) 1.00000 0.447214
\(6\) 0.958466 0.391292
\(7\) 0 0
\(8\) 2.26560 0.801010
\(9\) −0.674002 −0.224667
\(10\) −0.628452 −0.198734
\(11\) −4.48476 −1.35220 −0.676102 0.736808i \(-0.736332\pi\)
−0.676102 + 0.736808i \(0.736332\pi\)
\(12\) 2.44789 0.706646
\(13\) −3.10381 −0.860842 −0.430421 0.902628i \(-0.641635\pi\)
−0.430421 + 0.902628i \(0.641635\pi\)
\(14\) 0 0
\(15\) −1.52512 −0.393785
\(16\) 1.78628 0.446569
\(17\) 0.893389 0.216679 0.108339 0.994114i \(-0.465447\pi\)
0.108339 + 0.994114i \(0.465447\pi\)
\(18\) 0.423578 0.0998382
\(19\) −6.74349 −1.54706 −0.773531 0.633758i \(-0.781511\pi\)
−0.773531 + 0.633758i \(0.781511\pi\)
\(20\) −1.60505 −0.358900
\(21\) 0 0
\(22\) 2.81845 0.600897
\(23\) 5.95926 1.24259 0.621296 0.783576i \(-0.286607\pi\)
0.621296 + 0.783576i \(0.286607\pi\)
\(24\) −3.45532 −0.705314
\(25\) 1.00000 0.200000
\(26\) 1.95060 0.382543
\(27\) 5.60330 1.07836
\(28\) 0 0
\(29\) 2.05255 0.381150 0.190575 0.981673i \(-0.438965\pi\)
0.190575 + 0.981673i \(0.438965\pi\)
\(30\) 0.958466 0.174991
\(31\) −1.00000 −0.179605
\(32\) −5.65379 −0.999458
\(33\) 6.83980 1.19066
\(34\) −0.561452 −0.0962882
\(35\) 0 0
\(36\) 1.08180 0.180301
\(37\) −4.09693 −0.673532 −0.336766 0.941588i \(-0.609333\pi\)
−0.336766 + 0.941588i \(0.609333\pi\)
\(38\) 4.23796 0.687488
\(39\) 4.73369 0.757997
\(40\) 2.26560 0.358223
\(41\) 7.42574 1.15971 0.579853 0.814721i \(-0.303110\pi\)
0.579853 + 0.814721i \(0.303110\pi\)
\(42\) 0 0
\(43\) 5.56997 0.849413 0.424706 0.905331i \(-0.360377\pi\)
0.424706 + 0.905331i \(0.360377\pi\)
\(44\) 7.19825 1.08518
\(45\) −0.674002 −0.100474
\(46\) −3.74511 −0.552186
\(47\) 11.0066 1.60548 0.802741 0.596328i \(-0.203374\pi\)
0.802741 + 0.596328i \(0.203374\pi\)
\(48\) −2.72429 −0.393217
\(49\) 0 0
\(50\) −0.628452 −0.0888765
\(51\) −1.36253 −0.190792
\(52\) 4.98177 0.690847
\(53\) −4.30252 −0.590997 −0.295498 0.955343i \(-0.595486\pi\)
−0.295498 + 0.955343i \(0.595486\pi\)
\(54\) −3.52141 −0.479203
\(55\) −4.48476 −0.604724
\(56\) 0 0
\(57\) 10.2846 1.36223
\(58\) −1.28993 −0.169376
\(59\) −9.91053 −1.29024 −0.645121 0.764081i \(-0.723193\pi\)
−0.645121 + 0.764081i \(0.723193\pi\)
\(60\) 2.44789 0.316022
\(61\) 6.58024 0.842513 0.421257 0.906942i \(-0.361589\pi\)
0.421257 + 0.906942i \(0.361589\pi\)
\(62\) 0.628452 0.0798135
\(63\) 0 0
\(64\) −0.0194157 −0.00242697
\(65\) −3.10381 −0.384980
\(66\) −4.29849 −0.529107
\(67\) 10.0098 1.22289 0.611444 0.791288i \(-0.290589\pi\)
0.611444 + 0.791288i \(0.290589\pi\)
\(68\) −1.43393 −0.173890
\(69\) −9.08860 −1.09414
\(70\) 0 0
\(71\) −13.0016 −1.54301 −0.771505 0.636223i \(-0.780496\pi\)
−0.771505 + 0.636223i \(0.780496\pi\)
\(72\) −1.52702 −0.179961
\(73\) 1.93156 0.226072 0.113036 0.993591i \(-0.463942\pi\)
0.113036 + 0.993591i \(0.463942\pi\)
\(74\) 2.57473 0.299306
\(75\) −1.52512 −0.176106
\(76\) 10.8236 1.24155
\(77\) 0 0
\(78\) −2.97490 −0.336841
\(79\) 6.89495 0.775742 0.387871 0.921714i \(-0.373211\pi\)
0.387871 + 0.921714i \(0.373211\pi\)
\(80\) 1.78628 0.199712
\(81\) −6.52372 −0.724857
\(82\) −4.66672 −0.515353
\(83\) −0.685851 −0.0752819 −0.0376409 0.999291i \(-0.511984\pi\)
−0.0376409 + 0.999291i \(0.511984\pi\)
\(84\) 0 0
\(85\) 0.893389 0.0969016
\(86\) −3.50046 −0.377464
\(87\) −3.13040 −0.335614
\(88\) −10.1607 −1.08313
\(89\) 16.0205 1.69817 0.849084 0.528257i \(-0.177154\pi\)
0.849084 + 0.528257i \(0.177154\pi\)
\(90\) 0.423578 0.0446490
\(91\) 0 0
\(92\) −9.56489 −0.997209
\(93\) 1.52512 0.158148
\(94\) −6.91714 −0.713449
\(95\) −6.74349 −0.691867
\(96\) 8.62272 0.880053
\(97\) 4.21722 0.428193 0.214097 0.976812i \(-0.431319\pi\)
0.214097 + 0.976812i \(0.431319\pi\)
\(98\) 0 0
\(99\) 3.02273 0.303796
\(100\) −1.60505 −0.160505
\(101\) −17.8697 −1.77810 −0.889052 0.457806i \(-0.848635\pi\)
−0.889052 + 0.457806i \(0.848635\pi\)
\(102\) 0.856283 0.0847847
\(103\) −3.88759 −0.383055 −0.191528 0.981487i \(-0.561344\pi\)
−0.191528 + 0.981487i \(0.561344\pi\)
\(104\) −7.03199 −0.689544
\(105\) 0 0
\(106\) 2.70393 0.262629
\(107\) −0.402701 −0.0389305 −0.0194653 0.999811i \(-0.506196\pi\)
−0.0194653 + 0.999811i \(0.506196\pi\)
\(108\) −8.99357 −0.865407
\(109\) −8.51377 −0.815472 −0.407736 0.913100i \(-0.633682\pi\)
−0.407736 + 0.913100i \(0.633682\pi\)
\(110\) 2.81845 0.268729
\(111\) 6.24833 0.593065
\(112\) 0 0
\(113\) −12.7872 −1.20292 −0.601461 0.798902i \(-0.705415\pi\)
−0.601461 + 0.798902i \(0.705415\pi\)
\(114\) −6.46341 −0.605354
\(115\) 5.95926 0.555704
\(116\) −3.29445 −0.305882
\(117\) 2.09197 0.193403
\(118\) 6.22830 0.573361
\(119\) 0 0
\(120\) −3.45532 −0.315426
\(121\) 9.11304 0.828458
\(122\) −4.13536 −0.374398
\(123\) −11.3252 −1.02116
\(124\) 1.60505 0.144138
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 21.3099 1.89095 0.945476 0.325691i \(-0.105597\pi\)
0.945476 + 0.325691i \(0.105597\pi\)
\(128\) 11.3198 1.00054
\(129\) −8.49489 −0.747933
\(130\) 1.95060 0.171079
\(131\) −0.227315 −0.0198606 −0.00993030 0.999951i \(-0.503161\pi\)
−0.00993030 + 0.999951i \(0.503161\pi\)
\(132\) −10.9782 −0.955531
\(133\) 0 0
\(134\) −6.29066 −0.543430
\(135\) 5.60330 0.482255
\(136\) 2.02406 0.173562
\(137\) 21.1273 1.80503 0.902514 0.430661i \(-0.141720\pi\)
0.902514 + 0.430661i \(0.141720\pi\)
\(138\) 5.71175 0.486216
\(139\) 7.10186 0.602372 0.301186 0.953565i \(-0.402617\pi\)
0.301186 + 0.953565i \(0.402617\pi\)
\(140\) 0 0
\(141\) −16.7865 −1.41368
\(142\) 8.17090 0.685687
\(143\) 13.9198 1.16404
\(144\) −1.20395 −0.100329
\(145\) 2.05255 0.170455
\(146\) −1.21390 −0.100463
\(147\) 0 0
\(148\) 6.57578 0.540525
\(149\) −16.9951 −1.39229 −0.696145 0.717902i \(-0.745103\pi\)
−0.696145 + 0.717902i \(0.745103\pi\)
\(150\) 0.958466 0.0782584
\(151\) 9.40602 0.765451 0.382725 0.923862i \(-0.374986\pi\)
0.382725 + 0.923862i \(0.374986\pi\)
\(152\) −15.2780 −1.23921
\(153\) −0.602145 −0.0486806
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) −7.59780 −0.608311
\(157\) −5.76050 −0.459738 −0.229869 0.973222i \(-0.573830\pi\)
−0.229869 + 0.973222i \(0.573830\pi\)
\(158\) −4.33314 −0.344726
\(159\) 6.56187 0.520390
\(160\) −5.65379 −0.446971
\(161\) 0 0
\(162\) 4.09984 0.322114
\(163\) 14.7931 1.15869 0.579344 0.815083i \(-0.303309\pi\)
0.579344 + 0.815083i \(0.303309\pi\)
\(164\) −11.9187 −0.930691
\(165\) 6.83980 0.532478
\(166\) 0.431024 0.0334540
\(167\) −13.1759 −1.01958 −0.509792 0.860298i \(-0.670278\pi\)
−0.509792 + 0.860298i \(0.670278\pi\)
\(168\) 0 0
\(169\) −3.36635 −0.258950
\(170\) −0.561452 −0.0430614
\(171\) 4.54512 0.347574
\(172\) −8.94007 −0.681674
\(173\) −13.6830 −1.04030 −0.520150 0.854075i \(-0.674124\pi\)
−0.520150 + 0.854075i \(0.674124\pi\)
\(174\) 1.96730 0.149141
\(175\) 0 0
\(176\) −8.01101 −0.603853
\(177\) 15.1148 1.13610
\(178\) −10.0681 −0.754637
\(179\) 14.2212 1.06295 0.531473 0.847076i \(-0.321639\pi\)
0.531473 + 0.847076i \(0.321639\pi\)
\(180\) 1.08180 0.0806330
\(181\) −14.7671 −1.09763 −0.548816 0.835943i \(-0.684921\pi\)
−0.548816 + 0.835943i \(0.684921\pi\)
\(182\) 0 0
\(183\) −10.0357 −0.741858
\(184\) 13.5013 0.995328
\(185\) −4.09693 −0.301213
\(186\) −0.958466 −0.0702782
\(187\) −4.00663 −0.292994
\(188\) −17.6662 −1.28844
\(189\) 0 0
\(190\) 4.23796 0.307454
\(191\) 22.1209 1.60061 0.800306 0.599591i \(-0.204670\pi\)
0.800306 + 0.599591i \(0.204670\pi\)
\(192\) 0.0296114 0.00213702
\(193\) 21.5583 1.55180 0.775899 0.630858i \(-0.217297\pi\)
0.775899 + 0.630858i \(0.217297\pi\)
\(194\) −2.65032 −0.190282
\(195\) 4.73369 0.338987
\(196\) 0 0
\(197\) 4.87476 0.347312 0.173656 0.984806i \(-0.444442\pi\)
0.173656 + 0.984806i \(0.444442\pi\)
\(198\) −1.89964 −0.135002
\(199\) −13.5023 −0.957150 −0.478575 0.878047i \(-0.658847\pi\)
−0.478575 + 0.878047i \(0.658847\pi\)
\(200\) 2.26560 0.160202
\(201\) −15.2661 −1.07679
\(202\) 11.2303 0.790159
\(203\) 0 0
\(204\) 2.18692 0.153115
\(205\) 7.42574 0.518636
\(206\) 2.44316 0.170223
\(207\) −4.01655 −0.279169
\(208\) −5.54426 −0.384425
\(209\) 30.2429 2.09195
\(210\) 0 0
\(211\) 19.9410 1.37280 0.686398 0.727226i \(-0.259191\pi\)
0.686398 + 0.727226i \(0.259191\pi\)
\(212\) 6.90576 0.474289
\(213\) 19.8291 1.35867
\(214\) 0.253078 0.0173001
\(215\) 5.56997 0.379869
\(216\) 12.6948 0.863774
\(217\) 0 0
\(218\) 5.35050 0.362381
\(219\) −2.94587 −0.199064
\(220\) 7.19825 0.485306
\(221\) −2.77291 −0.186526
\(222\) −3.92677 −0.263548
\(223\) −28.4148 −1.90280 −0.951399 0.307961i \(-0.900353\pi\)
−0.951399 + 0.307961i \(0.900353\pi\)
\(224\) 0 0
\(225\) −0.674002 −0.0449334
\(226\) 8.03617 0.534558
\(227\) −7.83410 −0.519967 −0.259984 0.965613i \(-0.583717\pi\)
−0.259984 + 0.965613i \(0.583717\pi\)
\(228\) −16.5074 −1.09323
\(229\) −15.6446 −1.03382 −0.516911 0.856039i \(-0.672918\pi\)
−0.516911 + 0.856039i \(0.672918\pi\)
\(230\) −3.74511 −0.246945
\(231\) 0 0
\(232\) 4.65027 0.305305
\(233\) 11.4393 0.749414 0.374707 0.927143i \(-0.377743\pi\)
0.374707 + 0.927143i \(0.377743\pi\)
\(234\) −1.31471 −0.0859450
\(235\) 11.0066 0.717993
\(236\) 15.9069 1.03545
\(237\) −10.5156 −0.683064
\(238\) 0 0
\(239\) −3.52378 −0.227934 −0.113967 0.993485i \(-0.536356\pi\)
−0.113967 + 0.993485i \(0.536356\pi\)
\(240\) −2.72429 −0.175852
\(241\) 23.4335 1.50948 0.754741 0.656023i \(-0.227762\pi\)
0.754741 + 0.656023i \(0.227762\pi\)
\(242\) −5.72711 −0.368153
\(243\) −6.86044 −0.440097
\(244\) −10.5616 −0.676137
\(245\) 0 0
\(246\) 7.11732 0.453784
\(247\) 20.9305 1.33178
\(248\) −2.26560 −0.143866
\(249\) 1.04601 0.0662879
\(250\) −0.628452 −0.0397468
\(251\) 17.5688 1.10894 0.554468 0.832205i \(-0.312922\pi\)
0.554468 + 0.832205i \(0.312922\pi\)
\(252\) 0 0
\(253\) −26.7258 −1.68024
\(254\) −13.3923 −0.840306
\(255\) −1.36253 −0.0853248
\(256\) −7.07511 −0.442194
\(257\) −15.6731 −0.977659 −0.488829 0.872379i \(-0.662576\pi\)
−0.488829 + 0.872379i \(0.662576\pi\)
\(258\) 5.33863 0.332369
\(259\) 0 0
\(260\) 4.98177 0.308956
\(261\) −1.38342 −0.0856319
\(262\) 0.142857 0.00882571
\(263\) 3.28965 0.202849 0.101424 0.994843i \(-0.467660\pi\)
0.101424 + 0.994843i \(0.467660\pi\)
\(264\) 15.4963 0.953729
\(265\) −4.30252 −0.264302
\(266\) 0 0
\(267\) −24.4332 −1.49529
\(268\) −16.0662 −0.981397
\(269\) −20.5142 −1.25077 −0.625386 0.780315i \(-0.715059\pi\)
−0.625386 + 0.780315i \(0.715059\pi\)
\(270\) −3.52141 −0.214306
\(271\) −14.1700 −0.860768 −0.430384 0.902646i \(-0.641622\pi\)
−0.430384 + 0.902646i \(0.641622\pi\)
\(272\) 1.59584 0.0967619
\(273\) 0 0
\(274\) −13.2775 −0.802123
\(275\) −4.48476 −0.270441
\(276\) 14.5876 0.878072
\(277\) −15.5823 −0.936250 −0.468125 0.883662i \(-0.655070\pi\)
−0.468125 + 0.883662i \(0.655070\pi\)
\(278\) −4.46318 −0.267684
\(279\) 0.674002 0.0403514
\(280\) 0 0
\(281\) 5.37454 0.320618 0.160309 0.987067i \(-0.448751\pi\)
0.160309 + 0.987067i \(0.448751\pi\)
\(282\) 10.5495 0.628213
\(283\) 22.6902 1.34879 0.674397 0.738368i \(-0.264403\pi\)
0.674397 + 0.738368i \(0.264403\pi\)
\(284\) 20.8682 1.23830
\(285\) 10.2846 0.609210
\(286\) −8.74795 −0.517277
\(287\) 0 0
\(288\) 3.81066 0.224545
\(289\) −16.2019 −0.953050
\(290\) −1.28993 −0.0757474
\(291\) −6.43177 −0.377037
\(292\) −3.10025 −0.181429
\(293\) 11.6084 0.678170 0.339085 0.940756i \(-0.389882\pi\)
0.339085 + 0.940756i \(0.389882\pi\)
\(294\) 0 0
\(295\) −9.91053 −0.577014
\(296\) −9.28201 −0.539506
\(297\) −25.1294 −1.45816
\(298\) 10.6806 0.618709
\(299\) −18.4964 −1.06968
\(300\) 2.44789 0.141329
\(301\) 0 0
\(302\) −5.91123 −0.340153
\(303\) 27.2535 1.56567
\(304\) −12.0457 −0.690870
\(305\) 6.58024 0.376783
\(306\) 0.378420 0.0216328
\(307\) −15.7237 −0.897398 −0.448699 0.893683i \(-0.648112\pi\)
−0.448699 + 0.893683i \(0.648112\pi\)
\(308\) 0 0
\(309\) 5.92904 0.337292
\(310\) 0.628452 0.0356937
\(311\) 25.8444 1.46550 0.732750 0.680498i \(-0.238236\pi\)
0.732750 + 0.680498i \(0.238236\pi\)
\(312\) 10.7247 0.607164
\(313\) −15.4473 −0.873136 −0.436568 0.899671i \(-0.643806\pi\)
−0.436568 + 0.899671i \(0.643806\pi\)
\(314\) 3.62020 0.204300
\(315\) 0 0
\(316\) −11.0667 −0.622552
\(317\) −18.3025 −1.02797 −0.513986 0.857799i \(-0.671832\pi\)
−0.513986 + 0.857799i \(0.671832\pi\)
\(318\) −4.12382 −0.231253
\(319\) −9.20521 −0.515393
\(320\) −0.0194157 −0.00108537
\(321\) 0.614168 0.0342795
\(322\) 0 0
\(323\) −6.02456 −0.335215
\(324\) 10.4709 0.581716
\(325\) −3.10381 −0.172168
\(326\) −9.29677 −0.514901
\(327\) 12.9845 0.718047
\(328\) 16.8237 0.928936
\(329\) 0 0
\(330\) −4.29849 −0.236624
\(331\) 3.48343 0.191466 0.0957332 0.995407i \(-0.469480\pi\)
0.0957332 + 0.995407i \(0.469480\pi\)
\(332\) 1.10082 0.0604155
\(333\) 2.76134 0.151320
\(334\) 8.28044 0.453085
\(335\) 10.0098 0.546892
\(336\) 0 0
\(337\) 12.2942 0.669706 0.334853 0.942270i \(-0.391313\pi\)
0.334853 + 0.942270i \(0.391313\pi\)
\(338\) 2.11559 0.115073
\(339\) 19.5021 1.05921
\(340\) −1.43393 −0.0777659
\(341\) 4.48476 0.242863
\(342\) −2.85639 −0.154456
\(343\) 0 0
\(344\) 12.6193 0.680389
\(345\) −9.08860 −0.489314
\(346\) 8.59912 0.462291
\(347\) 8.12139 0.435979 0.217989 0.975951i \(-0.430050\pi\)
0.217989 + 0.975951i \(0.430050\pi\)
\(348\) 5.02444 0.269338
\(349\) 36.4917 1.95335 0.976677 0.214715i \(-0.0688823\pi\)
0.976677 + 0.214715i \(0.0688823\pi\)
\(350\) 0 0
\(351\) −17.3916 −0.928295
\(352\) 25.3559 1.35147
\(353\) −25.0330 −1.33237 −0.666186 0.745785i \(-0.732075\pi\)
−0.666186 + 0.745785i \(0.732075\pi\)
\(354\) −9.49891 −0.504862
\(355\) −13.0016 −0.690055
\(356\) −25.7137 −1.36282
\(357\) 0 0
\(358\) −8.93737 −0.472354
\(359\) 3.09086 0.163129 0.0815646 0.996668i \(-0.474008\pi\)
0.0815646 + 0.996668i \(0.474008\pi\)
\(360\) −1.52702 −0.0804809
\(361\) 26.4746 1.39340
\(362\) 9.28042 0.487768
\(363\) −13.8985 −0.729482
\(364\) 0 0
\(365\) 1.93156 0.101103
\(366\) 6.30694 0.329669
\(367\) −19.9819 −1.04305 −0.521524 0.853236i \(-0.674636\pi\)
−0.521524 + 0.853236i \(0.674636\pi\)
\(368\) 10.6449 0.554902
\(369\) −5.00496 −0.260548
\(370\) 2.57473 0.133854
\(371\) 0 0
\(372\) −2.44789 −0.126917
\(373\) −17.2769 −0.894564 −0.447282 0.894393i \(-0.647608\pi\)
−0.447282 + 0.894393i \(0.647608\pi\)
\(374\) 2.51798 0.130201
\(375\) −1.52512 −0.0787570
\(376\) 24.9366 1.28601
\(377\) −6.37074 −0.328110
\(378\) 0 0
\(379\) −12.4735 −0.640720 −0.320360 0.947296i \(-0.603804\pi\)
−0.320360 + 0.947296i \(0.603804\pi\)
\(380\) 10.8236 0.555240
\(381\) −32.5003 −1.66504
\(382\) −13.9019 −0.711285
\(383\) 9.09317 0.464639 0.232320 0.972640i \(-0.425368\pi\)
0.232320 + 0.972640i \(0.425368\pi\)
\(384\) −17.2640 −0.881002
\(385\) 0 0
\(386\) −13.5483 −0.689592
\(387\) −3.75417 −0.190835
\(388\) −6.76883 −0.343635
\(389\) −26.2233 −1.32958 −0.664788 0.747032i \(-0.731478\pi\)
−0.664788 + 0.747032i \(0.731478\pi\)
\(390\) −2.97490 −0.150640
\(391\) 5.32393 0.269243
\(392\) 0 0
\(393\) 0.346683 0.0174878
\(394\) −3.06355 −0.154339
\(395\) 6.89495 0.346922
\(396\) −4.85163 −0.243804
\(397\) 22.0450 1.10641 0.553204 0.833046i \(-0.313405\pi\)
0.553204 + 0.833046i \(0.313405\pi\)
\(398\) 8.48553 0.425341
\(399\) 0 0
\(400\) 1.78628 0.0893138
\(401\) 4.42019 0.220734 0.110367 0.993891i \(-0.464797\pi\)
0.110367 + 0.993891i \(0.464797\pi\)
\(402\) 9.59403 0.478506
\(403\) 3.10381 0.154612
\(404\) 28.6818 1.42697
\(405\) −6.52372 −0.324166
\(406\) 0 0
\(407\) 18.3737 0.910753
\(408\) −3.08694 −0.152826
\(409\) −16.5367 −0.817689 −0.408844 0.912604i \(-0.634068\pi\)
−0.408844 + 0.912604i \(0.634068\pi\)
\(410\) −4.66672 −0.230473
\(411\) −32.2217 −1.58938
\(412\) 6.23976 0.307411
\(413\) 0 0
\(414\) 2.52421 0.124058
\(415\) −0.685851 −0.0336671
\(416\) 17.5483 0.860376
\(417\) −10.8312 −0.530407
\(418\) −19.0062 −0.929624
\(419\) −21.7783 −1.06394 −0.531970 0.846763i \(-0.678548\pi\)
−0.531970 + 0.846763i \(0.678548\pi\)
\(420\) 0 0
\(421\) 14.5816 0.710666 0.355333 0.934740i \(-0.384368\pi\)
0.355333 + 0.934740i \(0.384368\pi\)
\(422\) −12.5320 −0.610047
\(423\) −7.41849 −0.360699
\(424\) −9.74780 −0.473395
\(425\) 0.893389 0.0433357
\(426\) −12.4616 −0.603768
\(427\) 0 0
\(428\) 0.646354 0.0312427
\(429\) −21.2295 −1.02497
\(430\) −3.50046 −0.168807
\(431\) −21.5009 −1.03566 −0.517830 0.855483i \(-0.673260\pi\)
−0.517830 + 0.855483i \(0.673260\pi\)
\(432\) 10.0090 0.481560
\(433\) −15.8270 −0.760597 −0.380298 0.924864i \(-0.624179\pi\)
−0.380298 + 0.924864i \(0.624179\pi\)
\(434\) 0 0
\(435\) −3.13040 −0.150091
\(436\) 13.6650 0.654435
\(437\) −40.1862 −1.92237
\(438\) 1.85134 0.0884604
\(439\) −22.0465 −1.05222 −0.526112 0.850415i \(-0.676351\pi\)
−0.526112 + 0.850415i \(0.676351\pi\)
\(440\) −10.1607 −0.484391
\(441\) 0 0
\(442\) 1.74264 0.0828890
\(443\) −29.1921 −1.38696 −0.693480 0.720475i \(-0.743924\pi\)
−0.693480 + 0.720475i \(0.743924\pi\)
\(444\) −10.0289 −0.475949
\(445\) 16.0205 0.759444
\(446\) 17.8574 0.845571
\(447\) 25.9195 1.22595
\(448\) 0 0
\(449\) 26.3294 1.24256 0.621280 0.783589i \(-0.286613\pi\)
0.621280 + 0.783589i \(0.286613\pi\)
\(450\) 0.423578 0.0199676
\(451\) −33.3026 −1.56816
\(452\) 20.5241 0.965374
\(453\) −14.3453 −0.674002
\(454\) 4.92336 0.231065
\(455\) 0 0
\(456\) 23.3009 1.09116
\(457\) 14.2530 0.666728 0.333364 0.942798i \(-0.391816\pi\)
0.333364 + 0.942798i \(0.391816\pi\)
\(458\) 9.83187 0.459413
\(459\) 5.00593 0.233657
\(460\) −9.56489 −0.445965
\(461\) −1.88451 −0.0877704 −0.0438852 0.999037i \(-0.513974\pi\)
−0.0438852 + 0.999037i \(0.513974\pi\)
\(462\) 0 0
\(463\) −38.3234 −1.78104 −0.890519 0.454945i \(-0.849659\pi\)
−0.890519 + 0.454945i \(0.849659\pi\)
\(464\) 3.66643 0.170210
\(465\) 1.52512 0.0707259
\(466\) −7.18906 −0.333027
\(467\) −5.88209 −0.272191 −0.136095 0.990696i \(-0.543455\pi\)
−0.136095 + 0.990696i \(0.543455\pi\)
\(468\) −3.35772 −0.155211
\(469\) 0 0
\(470\) −6.91714 −0.319064
\(471\) 8.78548 0.404813
\(472\) −22.4533 −1.03350
\(473\) −24.9800 −1.14858
\(474\) 6.60857 0.303542
\(475\) −6.74349 −0.309413
\(476\) 0 0
\(477\) 2.89991 0.132778
\(478\) 2.21453 0.101290
\(479\) 18.8916 0.863180 0.431590 0.902070i \(-0.357953\pi\)
0.431590 + 0.902070i \(0.357953\pi\)
\(480\) 8.62272 0.393571
\(481\) 12.7161 0.579805
\(482\) −14.7268 −0.670788
\(483\) 0 0
\(484\) −14.6269 −0.664858
\(485\) 4.21722 0.191494
\(486\) 4.31146 0.195572
\(487\) −14.1560 −0.641471 −0.320735 0.947169i \(-0.603930\pi\)
−0.320735 + 0.947169i \(0.603930\pi\)
\(488\) 14.9082 0.674862
\(489\) −22.5613 −1.02026
\(490\) 0 0
\(491\) −32.2203 −1.45408 −0.727040 0.686595i \(-0.759104\pi\)
−0.727040 + 0.686595i \(0.759104\pi\)
\(492\) 18.1774 0.819501
\(493\) 1.83373 0.0825870
\(494\) −13.1538 −0.591819
\(495\) 3.02273 0.135862
\(496\) −1.78628 −0.0802061
\(497\) 0 0
\(498\) −0.657365 −0.0294572
\(499\) −1.13745 −0.0509191 −0.0254595 0.999676i \(-0.508105\pi\)
−0.0254595 + 0.999676i \(0.508105\pi\)
\(500\) −1.60505 −0.0717799
\(501\) 20.0949 0.897774
\(502\) −11.0412 −0.492792
\(503\) −29.6040 −1.31998 −0.659990 0.751275i \(-0.729439\pi\)
−0.659990 + 0.751275i \(0.729439\pi\)
\(504\) 0 0
\(505\) −17.8697 −0.795192
\(506\) 16.7959 0.746669
\(507\) 5.13410 0.228013
\(508\) −34.2035 −1.51753
\(509\) −7.51171 −0.332951 −0.166475 0.986046i \(-0.553239\pi\)
−0.166475 + 0.986046i \(0.553239\pi\)
\(510\) 0.856283 0.0379168
\(511\) 0 0
\(512\) −18.1932 −0.804033
\(513\) −37.7858 −1.66828
\(514\) 9.84977 0.434455
\(515\) −3.88759 −0.171308
\(516\) 13.6347 0.600234
\(517\) −49.3621 −2.17094
\(518\) 0 0
\(519\) 20.8683 0.916015
\(520\) −7.03199 −0.308373
\(521\) −21.1550 −0.926817 −0.463409 0.886145i \(-0.653374\pi\)
−0.463409 + 0.886145i \(0.653374\pi\)
\(522\) 0.869416 0.0380533
\(523\) 7.08430 0.309775 0.154887 0.987932i \(-0.450498\pi\)
0.154887 + 0.987932i \(0.450498\pi\)
\(524\) 0.364851 0.0159386
\(525\) 0 0
\(526\) −2.06739 −0.0901424
\(527\) −0.893389 −0.0389166
\(528\) 12.2178 0.531710
\(529\) 12.5127 0.544032
\(530\) 2.70393 0.117451
\(531\) 6.67972 0.289875
\(532\) 0 0
\(533\) −23.0481 −0.998323
\(534\) 15.3551 0.664480
\(535\) −0.402701 −0.0174103
\(536\) 22.6781 0.979546
\(537\) −21.6891 −0.935955
\(538\) 12.8922 0.555822
\(539\) 0 0
\(540\) −8.99357 −0.387022
\(541\) 20.9831 0.902133 0.451066 0.892490i \(-0.351044\pi\)
0.451066 + 0.892490i \(0.351044\pi\)
\(542\) 8.90519 0.382511
\(543\) 22.5217 0.966497
\(544\) −5.05103 −0.216561
\(545\) −8.51377 −0.364690
\(546\) 0 0
\(547\) 7.43394 0.317853 0.158926 0.987290i \(-0.449197\pi\)
0.158926 + 0.987290i \(0.449197\pi\)
\(548\) −33.9103 −1.44858
\(549\) −4.43509 −0.189285
\(550\) 2.81845 0.120179
\(551\) −13.8414 −0.589663
\(552\) −20.5911 −0.876416
\(553\) 0 0
\(554\) 9.79274 0.416053
\(555\) 6.24833 0.265227
\(556\) −11.3988 −0.483418
\(557\) −16.4996 −0.699109 −0.349555 0.936916i \(-0.613667\pi\)
−0.349555 + 0.936916i \(0.613667\pi\)
\(558\) −0.423578 −0.0179315
\(559\) −17.2881 −0.731211
\(560\) 0 0
\(561\) 6.11060 0.257990
\(562\) −3.37764 −0.142477
\(563\) 1.70528 0.0718691 0.0359345 0.999354i \(-0.488559\pi\)
0.0359345 + 0.999354i \(0.488559\pi\)
\(564\) 26.9431 1.13451
\(565\) −12.7872 −0.537963
\(566\) −14.2597 −0.599381
\(567\) 0 0
\(568\) −29.4565 −1.23597
\(569\) 31.9978 1.34142 0.670709 0.741721i \(-0.265990\pi\)
0.670709 + 0.741721i \(0.265990\pi\)
\(570\) −6.46341 −0.270722
\(571\) 4.90648 0.205330 0.102665 0.994716i \(-0.467263\pi\)
0.102665 + 0.994716i \(0.467263\pi\)
\(572\) −22.3420 −0.934166
\(573\) −33.7371 −1.40939
\(574\) 0 0
\(575\) 5.95926 0.248518
\(576\) 0.0130862 0.000545260 0
\(577\) 12.2116 0.508377 0.254189 0.967155i \(-0.418192\pi\)
0.254189 + 0.967155i \(0.418192\pi\)
\(578\) 10.1821 0.423519
\(579\) −32.8790 −1.36640
\(580\) −3.29445 −0.136795
\(581\) 0 0
\(582\) 4.04206 0.167549
\(583\) 19.2958 0.799149
\(584\) 4.37615 0.181086
\(585\) 2.09197 0.0864925
\(586\) −7.29533 −0.301367
\(587\) −6.18296 −0.255198 −0.127599 0.991826i \(-0.540727\pi\)
−0.127599 + 0.991826i \(0.540727\pi\)
\(588\) 0 0
\(589\) 6.74349 0.277861
\(590\) 6.22830 0.256415
\(591\) −7.43460 −0.305819
\(592\) −7.31825 −0.300778
\(593\) −40.2425 −1.65256 −0.826281 0.563258i \(-0.809548\pi\)
−0.826281 + 0.563258i \(0.809548\pi\)
\(594\) 15.7927 0.647980
\(595\) 0 0
\(596\) 27.2779 1.11735
\(597\) 20.5926 0.842800
\(598\) 11.6241 0.475345
\(599\) 36.3748 1.48623 0.743117 0.669161i \(-0.233346\pi\)
0.743117 + 0.669161i \(0.233346\pi\)
\(600\) −3.45532 −0.141063
\(601\) −24.2045 −0.987321 −0.493661 0.869655i \(-0.664341\pi\)
−0.493661 + 0.869655i \(0.664341\pi\)
\(602\) 0 0
\(603\) −6.74660 −0.274743
\(604\) −15.0971 −0.614293
\(605\) 9.11304 0.370498
\(606\) −17.1275 −0.695758
\(607\) −23.1734 −0.940579 −0.470290 0.882512i \(-0.655851\pi\)
−0.470290 + 0.882512i \(0.655851\pi\)
\(608\) 38.1263 1.54622
\(609\) 0 0
\(610\) −4.13536 −0.167436
\(611\) −34.1625 −1.38207
\(612\) 0.966472 0.0390673
\(613\) −44.7988 −1.80941 −0.904703 0.426043i \(-0.859907\pi\)
−0.904703 + 0.426043i \(0.859907\pi\)
\(614\) 9.88158 0.398788
\(615\) −11.3252 −0.456674
\(616\) 0 0
\(617\) 3.36822 0.135600 0.0677998 0.997699i \(-0.478402\pi\)
0.0677998 + 0.997699i \(0.478402\pi\)
\(618\) −3.72612 −0.149887
\(619\) 13.6575 0.548943 0.274472 0.961595i \(-0.411497\pi\)
0.274472 + 0.961595i \(0.411497\pi\)
\(620\) 1.60505 0.0644603
\(621\) 33.3915 1.33996
\(622\) −16.2420 −0.651243
\(623\) 0 0
\(624\) 8.45568 0.338498
\(625\) 1.00000 0.0400000
\(626\) 9.70792 0.388006
\(627\) −46.1241 −1.84202
\(628\) 9.24589 0.368951
\(629\) −3.66015 −0.145940
\(630\) 0 0
\(631\) −29.2207 −1.16326 −0.581628 0.813455i \(-0.697584\pi\)
−0.581628 + 0.813455i \(0.697584\pi\)
\(632\) 15.6212 0.621378
\(633\) −30.4125 −1.20879
\(634\) 11.5022 0.456813
\(635\) 21.3099 0.845660
\(636\) −10.5321 −0.417626
\(637\) 0 0
\(638\) 5.78503 0.229032
\(639\) 8.76312 0.346664
\(640\) 11.3198 0.447454
\(641\) −18.9049 −0.746700 −0.373350 0.927690i \(-0.621791\pi\)
−0.373350 + 0.927690i \(0.621791\pi\)
\(642\) −0.385975 −0.0152332
\(643\) −6.81626 −0.268807 −0.134403 0.990927i \(-0.542912\pi\)
−0.134403 + 0.990927i \(0.542912\pi\)
\(644\) 0 0
\(645\) −8.49489 −0.334486
\(646\) 3.78615 0.148964
\(647\) 1.83008 0.0719479 0.0359740 0.999353i \(-0.488547\pi\)
0.0359740 + 0.999353i \(0.488547\pi\)
\(648\) −14.7801 −0.580618
\(649\) 44.4463 1.74467
\(650\) 1.95060 0.0765087
\(651\) 0 0
\(652\) −23.7437 −0.929875
\(653\) −30.7795 −1.20450 −0.602248 0.798309i \(-0.705728\pi\)
−0.602248 + 0.798309i \(0.705728\pi\)
\(654\) −8.16016 −0.319088
\(655\) −0.227315 −0.00888193
\(656\) 13.2644 0.517888
\(657\) −1.30188 −0.0507911
\(658\) 0 0
\(659\) 24.1721 0.941610 0.470805 0.882237i \(-0.343964\pi\)
0.470805 + 0.882237i \(0.343964\pi\)
\(660\) −10.9782 −0.427326
\(661\) −20.9786 −0.815972 −0.407986 0.912988i \(-0.633769\pi\)
−0.407986 + 0.912988i \(0.633769\pi\)
\(662\) −2.18917 −0.0850844
\(663\) 4.22903 0.164242
\(664\) −1.55386 −0.0603016
\(665\) 0 0
\(666\) −1.73537 −0.0672442
\(667\) 12.2317 0.473613
\(668\) 21.1480 0.818240
\(669\) 43.3361 1.67547
\(670\) −6.29066 −0.243029
\(671\) −29.5108 −1.13925
\(672\) 0 0
\(673\) −10.3613 −0.399397 −0.199699 0.979857i \(-0.563996\pi\)
−0.199699 + 0.979857i \(0.563996\pi\)
\(674\) −7.72630 −0.297606
\(675\) 5.60330 0.215671
\(676\) 5.40316 0.207814
\(677\) 25.1326 0.965924 0.482962 0.875641i \(-0.339561\pi\)
0.482962 + 0.875641i \(0.339561\pi\)
\(678\) −12.2561 −0.470694
\(679\) 0 0
\(680\) 2.02406 0.0776192
\(681\) 11.9480 0.457847
\(682\) −2.81845 −0.107924
\(683\) −0.460467 −0.0176193 −0.00880964 0.999961i \(-0.502804\pi\)
−0.00880964 + 0.999961i \(0.502804\pi\)
\(684\) −7.29514 −0.278937
\(685\) 21.1273 0.807233
\(686\) 0 0
\(687\) 23.8599 0.910312
\(688\) 9.94950 0.379321
\(689\) 13.3542 0.508755
\(690\) 5.71175 0.217443
\(691\) 11.9224 0.453550 0.226775 0.973947i \(-0.427182\pi\)
0.226775 + 0.973947i \(0.427182\pi\)
\(692\) 21.9619 0.834866
\(693\) 0 0
\(694\) −5.10390 −0.193741
\(695\) 7.10186 0.269389
\(696\) −7.09223 −0.268830
\(697\) 6.63407 0.251283
\(698\) −22.9333 −0.868037
\(699\) −17.4463 −0.659881
\(700\) 0 0
\(701\) 11.5297 0.435472 0.217736 0.976008i \(-0.430133\pi\)
0.217736 + 0.976008i \(0.430133\pi\)
\(702\) 10.9298 0.412518
\(703\) 27.6276 1.04200
\(704\) 0.0870749 0.00328176
\(705\) −16.7865 −0.632215
\(706\) 15.7320 0.592083
\(707\) 0 0
\(708\) −24.2599 −0.911745
\(709\) −46.2350 −1.73639 −0.868196 0.496221i \(-0.834720\pi\)
−0.868196 + 0.496221i \(0.834720\pi\)
\(710\) 8.17090 0.306649
\(711\) −4.64720 −0.174284
\(712\) 36.2960 1.36025
\(713\) −5.95926 −0.223176
\(714\) 0 0
\(715\) 13.9198 0.520572
\(716\) −22.8258 −0.853039
\(717\) 5.37420 0.200703
\(718\) −1.94246 −0.0724918
\(719\) −21.8789 −0.815945 −0.407973 0.912994i \(-0.633764\pi\)
−0.407973 + 0.912994i \(0.633764\pi\)
\(720\) −1.20395 −0.0448687
\(721\) 0 0
\(722\) −16.6380 −0.619204
\(723\) −35.7389 −1.32914
\(724\) 23.7019 0.880875
\(725\) 2.05255 0.0762300
\(726\) 8.73454 0.324169
\(727\) −5.93195 −0.220004 −0.110002 0.993931i \(-0.535086\pi\)
−0.110002 + 0.993931i \(0.535086\pi\)
\(728\) 0 0
\(729\) 30.0342 1.11238
\(730\) −1.21390 −0.0449283
\(731\) 4.97615 0.184050
\(732\) 16.1077 0.595359
\(733\) −20.1307 −0.743544 −0.371772 0.928324i \(-0.621250\pi\)
−0.371772 + 0.928324i \(0.621250\pi\)
\(734\) 12.5577 0.463513
\(735\) 0 0
\(736\) −33.6924 −1.24192
\(737\) −44.8914 −1.65359
\(738\) 3.14538 0.115783
\(739\) −40.7240 −1.49806 −0.749028 0.662538i \(-0.769479\pi\)
−0.749028 + 0.662538i \(0.769479\pi\)
\(740\) 6.57578 0.241730
\(741\) −31.9216 −1.17267
\(742\) 0 0
\(743\) 18.1651 0.666414 0.333207 0.942854i \(-0.391869\pi\)
0.333207 + 0.942854i \(0.391869\pi\)
\(744\) 3.45532 0.126678
\(745\) −16.9951 −0.622651
\(746\) 10.8577 0.397529
\(747\) 0.462264 0.0169134
\(748\) 6.43083 0.235135
\(749\) 0 0
\(750\) 0.958466 0.0349982
\(751\) 26.0999 0.952400 0.476200 0.879337i \(-0.342014\pi\)
0.476200 + 0.879337i \(0.342014\pi\)
\(752\) 19.6609 0.716958
\(753\) −26.7946 −0.976451
\(754\) 4.00371 0.145806
\(755\) 9.40602 0.342320
\(756\) 0 0
\(757\) 34.2988 1.24661 0.623305 0.781979i \(-0.285789\pi\)
0.623305 + 0.781979i \(0.285789\pi\)
\(758\) 7.83899 0.284725
\(759\) 40.7601 1.47950
\(760\) −15.2780 −0.554193
\(761\) −12.6136 −0.457242 −0.228621 0.973516i \(-0.573422\pi\)
−0.228621 + 0.973516i \(0.573422\pi\)
\(762\) 20.4249 0.739915
\(763\) 0 0
\(764\) −35.5051 −1.28453
\(765\) −0.602145 −0.0217706
\(766\) −5.71462 −0.206478
\(767\) 30.7604 1.11069
\(768\) 10.7904 0.389365
\(769\) 35.4076 1.27683 0.638416 0.769691i \(-0.279590\pi\)
0.638416 + 0.769691i \(0.279590\pi\)
\(770\) 0 0
\(771\) 23.9033 0.860858
\(772\) −34.6020 −1.24535
\(773\) −51.8408 −1.86458 −0.932291 0.361709i \(-0.882194\pi\)
−0.932291 + 0.361709i \(0.882194\pi\)
\(774\) 2.35932 0.0848039
\(775\) −1.00000 −0.0359211
\(776\) 9.55452 0.342987
\(777\) 0 0
\(778\) 16.4801 0.590840
\(779\) −50.0754 −1.79414
\(780\) −7.59780 −0.272045
\(781\) 58.3092 2.08647
\(782\) −3.34584 −0.119647
\(783\) 11.5011 0.411015
\(784\) 0 0
\(785\) −5.76050 −0.205601
\(786\) −0.217874 −0.00777130
\(787\) 6.72042 0.239557 0.119779 0.992801i \(-0.461782\pi\)
0.119779 + 0.992801i \(0.461782\pi\)
\(788\) −7.82422 −0.278726
\(789\) −5.01712 −0.178614
\(790\) −4.33314 −0.154166
\(791\) 0 0
\(792\) 6.84830 0.243344
\(793\) −20.4238 −0.725271
\(794\) −13.8542 −0.491669
\(795\) 6.56187 0.232726
\(796\) 21.6718 0.768136
\(797\) 5.36374 0.189994 0.0949968 0.995478i \(-0.469716\pi\)
0.0949968 + 0.995478i \(0.469716\pi\)
\(798\) 0 0
\(799\) 9.83320 0.347874
\(800\) −5.65379 −0.199892
\(801\) −10.7978 −0.381523
\(802\) −2.77788 −0.0980903
\(803\) −8.66259 −0.305696
\(804\) 24.5029 0.864149
\(805\) 0 0
\(806\) −1.95060 −0.0687068
\(807\) 31.2867 1.10134
\(808\) −40.4856 −1.42428
\(809\) −10.8740 −0.382311 −0.191155 0.981560i \(-0.561223\pi\)
−0.191155 + 0.981560i \(0.561223\pi\)
\(810\) 4.09984 0.144054
\(811\) 44.2555 1.55402 0.777010 0.629489i \(-0.216736\pi\)
0.777010 + 0.629489i \(0.216736\pi\)
\(812\) 0 0
\(813\) 21.6110 0.757932
\(814\) −11.5470 −0.404723
\(815\) 14.7931 0.518181
\(816\) −2.43385 −0.0852017
\(817\) −37.5610 −1.31409
\(818\) 10.3925 0.363367
\(819\) 0 0
\(820\) −11.9187 −0.416218
\(821\) 7.87797 0.274943 0.137471 0.990506i \(-0.456102\pi\)
0.137471 + 0.990506i \(0.456102\pi\)
\(822\) 20.2498 0.706293
\(823\) −16.5354 −0.576389 −0.288194 0.957572i \(-0.593055\pi\)
−0.288194 + 0.957572i \(0.593055\pi\)
\(824\) −8.80771 −0.306831
\(825\) 6.83980 0.238131
\(826\) 0 0
\(827\) 9.58315 0.333239 0.166619 0.986021i \(-0.446715\pi\)
0.166619 + 0.986021i \(0.446715\pi\)
\(828\) 6.44675 0.224040
\(829\) −6.49447 −0.225562 −0.112781 0.993620i \(-0.535976\pi\)
−0.112781 + 0.993620i \(0.535976\pi\)
\(830\) 0.431024 0.0149611
\(831\) 23.7649 0.824396
\(832\) 0.0602628 0.00208924
\(833\) 0 0
\(834\) 6.80690 0.235704
\(835\) −13.1759 −0.455972
\(836\) −48.5413 −1.67884
\(837\) −5.60330 −0.193678
\(838\) 13.6866 0.472796
\(839\) −5.38547 −0.185927 −0.0929636 0.995670i \(-0.529634\pi\)
−0.0929636 + 0.995670i \(0.529634\pi\)
\(840\) 0 0
\(841\) −24.7870 −0.854725
\(842\) −9.16386 −0.315807
\(843\) −8.19682 −0.282314
\(844\) −32.0063 −1.10170
\(845\) −3.36635 −0.115806
\(846\) 4.66216 0.160288
\(847\) 0 0
\(848\) −7.68549 −0.263921
\(849\) −34.6054 −1.18765
\(850\) −0.561452 −0.0192576
\(851\) −24.4147 −0.836924
\(852\) −31.8266 −1.09036
\(853\) −46.7475 −1.60060 −0.800302 0.599597i \(-0.795328\pi\)
−0.800302 + 0.599597i \(0.795328\pi\)
\(854\) 0 0
\(855\) 4.54512 0.155440
\(856\) −0.912358 −0.0311838
\(857\) −5.95898 −0.203555 −0.101777 0.994807i \(-0.532453\pi\)
−0.101777 + 0.994807i \(0.532453\pi\)
\(858\) 13.3417 0.455478
\(859\) −24.0132 −0.819320 −0.409660 0.912238i \(-0.634353\pi\)
−0.409660 + 0.912238i \(0.634353\pi\)
\(860\) −8.94007 −0.304854
\(861\) 0 0
\(862\) 13.5123 0.460230
\(863\) 33.6969 1.14706 0.573528 0.819186i \(-0.305574\pi\)
0.573528 + 0.819186i \(0.305574\pi\)
\(864\) −31.6799 −1.07777
\(865\) −13.6830 −0.465236
\(866\) 9.94651 0.337996
\(867\) 24.7098 0.839189
\(868\) 0 0
\(869\) −30.9222 −1.04896
\(870\) 1.96730 0.0666979
\(871\) −31.0684 −1.05271
\(872\) −19.2888 −0.653201
\(873\) −2.84241 −0.0962010
\(874\) 25.2551 0.854266
\(875\) 0 0
\(876\) 4.72826 0.159753
\(877\) −41.2781 −1.39386 −0.696931 0.717138i \(-0.745452\pi\)
−0.696931 + 0.717138i \(0.745452\pi\)
\(878\) 13.8552 0.467590
\(879\) −17.7042 −0.597149
\(880\) −8.01101 −0.270051
\(881\) 17.8003 0.599708 0.299854 0.953985i \(-0.403062\pi\)
0.299854 + 0.953985i \(0.403062\pi\)
\(882\) 0 0
\(883\) 47.7816 1.60798 0.803989 0.594644i \(-0.202707\pi\)
0.803989 + 0.594644i \(0.202707\pi\)
\(884\) 4.45065 0.149692
\(885\) 15.1148 0.508078
\(886\) 18.3459 0.616341
\(887\) 23.5587 0.791025 0.395512 0.918461i \(-0.370567\pi\)
0.395512 + 0.918461i \(0.370567\pi\)
\(888\) 14.1562 0.475051
\(889\) 0 0
\(890\) −10.0681 −0.337484
\(891\) 29.2573 0.980156
\(892\) 45.6072 1.52704
\(893\) −74.2231 −2.48378
\(894\) −16.2892 −0.544792
\(895\) 14.2212 0.475364
\(896\) 0 0
\(897\) 28.2093 0.941881
\(898\) −16.5468 −0.552172
\(899\) −2.05255 −0.0684565
\(900\) 1.08180 0.0360602
\(901\) −3.84383 −0.128056
\(902\) 20.9291 0.696863
\(903\) 0 0
\(904\) −28.9708 −0.963554
\(905\) −14.7671 −0.490876
\(906\) 9.01535 0.299515
\(907\) 52.2289 1.73423 0.867116 0.498107i \(-0.165971\pi\)
0.867116 + 0.498107i \(0.165971\pi\)
\(908\) 12.5741 0.417286
\(909\) 12.0442 0.399482
\(910\) 0 0
\(911\) 18.8910 0.625886 0.312943 0.949772i \(-0.398685\pi\)
0.312943 + 0.949772i \(0.398685\pi\)
\(912\) 18.3712 0.608332
\(913\) 3.07587 0.101797
\(914\) −8.95734 −0.296282
\(915\) −10.0357 −0.331769
\(916\) 25.1103 0.829668
\(917\) 0 0
\(918\) −3.14599 −0.103833
\(919\) 24.9938 0.824468 0.412234 0.911078i \(-0.364749\pi\)
0.412234 + 0.911078i \(0.364749\pi\)
\(920\) 13.5013 0.445124
\(921\) 23.9805 0.790186
\(922\) 1.18432 0.0390036
\(923\) 40.3546 1.32829
\(924\) 0 0
\(925\) −4.09693 −0.134706
\(926\) 24.0844 0.791463
\(927\) 2.62024 0.0860599
\(928\) −11.6047 −0.380943
\(929\) −57.1220 −1.87411 −0.937057 0.349177i \(-0.886461\pi\)
−0.937057 + 0.349177i \(0.886461\pi\)
\(930\) −0.958466 −0.0314293
\(931\) 0 0
\(932\) −18.3606 −0.601423
\(933\) −39.4158 −1.29042
\(934\) 3.69661 0.120957
\(935\) −4.00663 −0.131031
\(936\) 4.73958 0.154918
\(937\) −5.48542 −0.179201 −0.0896004 0.995978i \(-0.528559\pi\)
−0.0896004 + 0.995978i \(0.528559\pi\)
\(938\) 0 0
\(939\) 23.5591 0.768822
\(940\) −17.6662 −0.576207
\(941\) −19.8486 −0.647045 −0.323523 0.946220i \(-0.604867\pi\)
−0.323523 + 0.946220i \(0.604867\pi\)
\(942\) −5.52125 −0.179892
\(943\) 44.2519 1.44104
\(944\) −17.7029 −0.576182
\(945\) 0 0
\(946\) 15.6987 0.510409
\(947\) 33.2459 1.08035 0.540173 0.841554i \(-0.318359\pi\)
0.540173 + 0.841554i \(0.318359\pi\)
\(948\) 16.8781 0.548175
\(949\) −5.99521 −0.194613
\(950\) 4.23796 0.137498
\(951\) 27.9136 0.905159
\(952\) 0 0
\(953\) −18.8889 −0.611871 −0.305936 0.952052i \(-0.598969\pi\)
−0.305936 + 0.952052i \(0.598969\pi\)
\(954\) −1.82245 −0.0590041
\(955\) 22.1209 0.715816
\(956\) 5.65584 0.182923
\(957\) 14.0391 0.453819
\(958\) −11.8725 −0.383582
\(959\) 0 0
\(960\) 0.0296114 0.000955703 0
\(961\) 1.00000 0.0322581
\(962\) −7.99147 −0.257655
\(963\) 0.271421 0.00874641
\(964\) −37.6118 −1.21140
\(965\) 21.5583 0.693985
\(966\) 0 0
\(967\) −17.2574 −0.554960 −0.277480 0.960731i \(-0.589499\pi\)
−0.277480 + 0.960731i \(0.589499\pi\)
\(968\) 20.6465 0.663604
\(969\) 9.18819 0.295167
\(970\) −2.65032 −0.0850966
\(971\) −23.9709 −0.769262 −0.384631 0.923070i \(-0.625671\pi\)
−0.384631 + 0.923070i \(0.625671\pi\)
\(972\) 11.0113 0.353189
\(973\) 0 0
\(974\) 8.89639 0.285059
\(975\) 4.73369 0.151599
\(976\) 11.7541 0.376240
\(977\) 12.5674 0.402067 0.201034 0.979584i \(-0.435570\pi\)
0.201034 + 0.979584i \(0.435570\pi\)
\(978\) 14.1787 0.453385
\(979\) −71.8480 −2.29627
\(980\) 0 0
\(981\) 5.73830 0.183210
\(982\) 20.2489 0.646168
\(983\) −21.6759 −0.691355 −0.345677 0.938353i \(-0.612351\pi\)
−0.345677 + 0.938353i \(0.612351\pi\)
\(984\) −25.6583 −0.817956
\(985\) 4.87476 0.155323
\(986\) −1.15241 −0.0367002
\(987\) 0 0
\(988\) −33.5945 −1.06878
\(989\) 33.1929 1.05547
\(990\) −1.89964 −0.0603746
\(991\) −39.7085 −1.26138 −0.630691 0.776034i \(-0.717228\pi\)
−0.630691 + 0.776034i \(0.717228\pi\)
\(992\) 5.65379 0.179508
\(993\) −5.31265 −0.168592
\(994\) 0 0
\(995\) −13.5023 −0.428051
\(996\) −1.67889 −0.0531977
\(997\) 9.53611 0.302012 0.151006 0.988533i \(-0.451749\pi\)
0.151006 + 0.988533i \(0.451749\pi\)
\(998\) 0.714830 0.0226276
\(999\) −22.9564 −0.726307
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 7595.2.a.bf.1.10 21
7.3 odd 6 1085.2.j.d.156.12 42
7.5 odd 6 1085.2.j.d.466.12 yes 42
7.6 odd 2 7595.2.a.bg.1.10 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1085.2.j.d.156.12 42 7.3 odd 6
1085.2.j.d.466.12 yes 42 7.5 odd 6
7595.2.a.bf.1.10 21 1.1 even 1 trivial
7595.2.a.bg.1.10 21 7.6 odd 2