Properties

Label 8281.2.a.cz.1.7
Level $8281$
Weight $2$
Character 8281.1
Self dual yes
Analytic conductor $66.124$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8281,2,Mod(1,8281)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8281, 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("8281.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.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: \(66.1241179138\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 8281.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.63103 q^{2} -1.44692 q^{3} +0.660273 q^{4} +0.621753 q^{5} +2.35997 q^{6} +2.18514 q^{8} -0.906425 q^{9} +O(q^{10})\) \(q-1.63103 q^{2} -1.44692 q^{3} +0.660273 q^{4} +0.621753 q^{5} +2.35997 q^{6} +2.18514 q^{8} -0.906425 q^{9} -1.01410 q^{10} -3.06320 q^{11} -0.955361 q^{12} -0.899626 q^{15} -4.88459 q^{16} +0.322567 q^{17} +1.47841 q^{18} -4.08463 q^{19} +0.410526 q^{20} +4.99618 q^{22} -1.64522 q^{23} -3.16172 q^{24} -4.61342 q^{25} +5.65228 q^{27} -4.35648 q^{29} +1.46732 q^{30} -5.12069 q^{31} +3.59664 q^{32} +4.43220 q^{33} -0.526117 q^{34} -0.598487 q^{36} -10.1678 q^{37} +6.66218 q^{38} +1.35862 q^{40} -2.69567 q^{41} +0.0291770 q^{43} -2.02254 q^{44} -0.563572 q^{45} +2.68341 q^{46} +2.63668 q^{47} +7.06760 q^{48} +7.52465 q^{50} -0.466728 q^{51} -5.25376 q^{53} -9.21906 q^{54} -1.90455 q^{55} +5.91013 q^{57} +7.10556 q^{58} -14.6294 q^{59} -0.593999 q^{60} -7.76622 q^{61} +8.35201 q^{62} +3.90292 q^{64} -7.22907 q^{66} +10.7043 q^{67} +0.212982 q^{68} +2.38050 q^{69} +0.706685 q^{71} -1.98067 q^{72} +13.6825 q^{73} +16.5841 q^{74} +6.67525 q^{75} -2.69697 q^{76} -7.49414 q^{79} -3.03701 q^{80} -5.45912 q^{81} +4.39673 q^{82} -15.3279 q^{83} +0.200557 q^{85} -0.0475887 q^{86} +6.30347 q^{87} -6.69352 q^{88} -0.0211515 q^{89} +0.919206 q^{90} -1.08629 q^{92} +7.40922 q^{93} -4.30051 q^{94} -2.53963 q^{95} -5.20405 q^{96} +6.81907 q^{97} +2.77656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 14 q^{2} + 38 q^{4} + 42 q^{8} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 14 q^{2} + 38 q^{4} + 42 q^{8} + 36 q^{9} + 52 q^{11} + 44 q^{15} + 42 q^{16} + 46 q^{18} + 68 q^{22} - 8 q^{23} + 32 q^{25} - 8 q^{29} + 118 q^{32} + 66 q^{36} + 28 q^{37} - 16 q^{43} + 130 q^{44} + 48 q^{46} + 90 q^{50} + 4 q^{51} + 52 q^{57} - 34 q^{58} + 100 q^{60} + 62 q^{64} + 40 q^{67} + 188 q^{71} - 42 q^{72} + 96 q^{74} + 8 q^{79} - 4 q^{81} + 64 q^{85} + 58 q^{86} + 156 q^{88} - 76 q^{92} - 16 q^{93} - 64 q^{95} + 156 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.63103 −1.15332 −0.576658 0.816986i \(-0.695643\pi\)
−0.576658 + 0.816986i \(0.695643\pi\)
\(3\) −1.44692 −0.835379 −0.417690 0.908590i \(-0.637160\pi\)
−0.417690 + 0.908590i \(0.637160\pi\)
\(4\) 0.660273 0.330136
\(5\) 0.621753 0.278056 0.139028 0.990288i \(-0.455602\pi\)
0.139028 + 0.990288i \(0.455602\pi\)
\(6\) 2.35997 0.963456
\(7\) 0 0
\(8\) 2.18514 0.772564
\(9\) −0.906425 −0.302142
\(10\) −1.01410 −0.320687
\(11\) −3.06320 −0.923588 −0.461794 0.886987i \(-0.652794\pi\)
−0.461794 + 0.886987i \(0.652794\pi\)
\(12\) −0.955361 −0.275789
\(13\) 0 0
\(14\) 0 0
\(15\) −0.899626 −0.232283
\(16\) −4.88459 −1.22115
\(17\) 0.322567 0.0782339 0.0391169 0.999235i \(-0.487546\pi\)
0.0391169 + 0.999235i \(0.487546\pi\)
\(18\) 1.47841 0.348465
\(19\) −4.08463 −0.937079 −0.468540 0.883442i \(-0.655220\pi\)
−0.468540 + 0.883442i \(0.655220\pi\)
\(20\) 0.410526 0.0917965
\(21\) 0 0
\(22\) 4.99618 1.06519
\(23\) −1.64522 −0.343052 −0.171526 0.985180i \(-0.554870\pi\)
−0.171526 + 0.985180i \(0.554870\pi\)
\(24\) −3.16172 −0.645384
\(25\) −4.61342 −0.922685
\(26\) 0 0
\(27\) 5.65228 1.08778
\(28\) 0 0
\(29\) −4.35648 −0.808977 −0.404489 0.914543i \(-0.632550\pi\)
−0.404489 + 0.914543i \(0.632550\pi\)
\(30\) 1.46732 0.267895
\(31\) −5.12069 −0.919702 −0.459851 0.887996i \(-0.652097\pi\)
−0.459851 + 0.887996i \(0.652097\pi\)
\(32\) 3.59664 0.635803
\(33\) 4.43220 0.771547
\(34\) −0.526117 −0.0902283
\(35\) 0 0
\(36\) −0.598487 −0.0997479
\(37\) −10.1678 −1.67158 −0.835790 0.549049i \(-0.814990\pi\)
−0.835790 + 0.549049i \(0.814990\pi\)
\(38\) 6.66218 1.08075
\(39\) 0 0
\(40\) 1.35862 0.214816
\(41\) −2.69567 −0.420993 −0.210497 0.977595i \(-0.567508\pi\)
−0.210497 + 0.977595i \(0.567508\pi\)
\(42\) 0 0
\(43\) 0.0291770 0.00444945 0.00222472 0.999998i \(-0.499292\pi\)
0.00222472 + 0.999998i \(0.499292\pi\)
\(44\) −2.02254 −0.304910
\(45\) −0.563572 −0.0840124
\(46\) 2.68341 0.395647
\(47\) 2.63668 0.384599 0.192299 0.981336i \(-0.438406\pi\)
0.192299 + 0.981336i \(0.438406\pi\)
\(48\) 7.06760 1.02012
\(49\) 0 0
\(50\) 7.52465 1.06415
\(51\) −0.466728 −0.0653550
\(52\) 0 0
\(53\) −5.25376 −0.721659 −0.360830 0.932632i \(-0.617506\pi\)
−0.360830 + 0.932632i \(0.617506\pi\)
\(54\) −9.21906 −1.25456
\(55\) −1.90455 −0.256810
\(56\) 0 0
\(57\) 5.91013 0.782816
\(58\) 7.10556 0.933006
\(59\) −14.6294 −1.90459 −0.952293 0.305185i \(-0.901282\pi\)
−0.952293 + 0.305185i \(0.901282\pi\)
\(60\) −0.593999 −0.0766849
\(61\) −7.76622 −0.994363 −0.497181 0.867647i \(-0.665632\pi\)
−0.497181 + 0.867647i \(0.665632\pi\)
\(62\) 8.35201 1.06071
\(63\) 0 0
\(64\) 3.90292 0.487865
\(65\) 0 0
\(66\) −7.22907 −0.889836
\(67\) 10.7043 1.30773 0.653867 0.756610i \(-0.273146\pi\)
0.653867 + 0.756610i \(0.273146\pi\)
\(68\) 0.212982 0.0258278
\(69\) 2.38050 0.286579
\(70\) 0 0
\(71\) 0.706685 0.0838681 0.0419340 0.999120i \(-0.486648\pi\)
0.0419340 + 0.999120i \(0.486648\pi\)
\(72\) −1.98067 −0.233424
\(73\) 13.6825 1.60141 0.800705 0.599059i \(-0.204459\pi\)
0.800705 + 0.599059i \(0.204459\pi\)
\(74\) 16.5841 1.92786
\(75\) 6.67525 0.770792
\(76\) −2.69697 −0.309364
\(77\) 0 0
\(78\) 0 0
\(79\) −7.49414 −0.843157 −0.421578 0.906792i \(-0.638524\pi\)
−0.421578 + 0.906792i \(0.638524\pi\)
\(80\) −3.03701 −0.339548
\(81\) −5.45912 −0.606569
\(82\) 4.39673 0.485538
\(83\) −15.3279 −1.68246 −0.841230 0.540677i \(-0.818168\pi\)
−0.841230 + 0.540677i \(0.818168\pi\)
\(84\) 0 0
\(85\) 0.200557 0.0217534
\(86\) −0.0475887 −0.00513162
\(87\) 6.30347 0.675803
\(88\) −6.69352 −0.713531
\(89\) −0.0211515 −0.00224205 −0.00112103 0.999999i \(-0.500357\pi\)
−0.00112103 + 0.999999i \(0.500357\pi\)
\(90\) 0.919206 0.0968928
\(91\) 0 0
\(92\) −1.08629 −0.113254
\(93\) 7.40922 0.768300
\(94\) −4.30051 −0.443563
\(95\) −2.53963 −0.260561
\(96\) −5.20405 −0.531136
\(97\) 6.81907 0.692372 0.346186 0.938166i \(-0.387477\pi\)
0.346186 + 0.938166i \(0.387477\pi\)
\(98\) 0 0
\(99\) 2.77656 0.279054
\(100\) −3.04612 −0.304612
\(101\) −18.6740 −1.85813 −0.929066 0.369915i \(-0.879387\pi\)
−0.929066 + 0.369915i \(0.879387\pi\)
\(102\) 0.761249 0.0753749
\(103\) 16.2419 1.60036 0.800181 0.599758i \(-0.204737\pi\)
0.800181 + 0.599758i \(0.204737\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.56906 0.832301
\(107\) −14.7351 −1.42449 −0.712246 0.701930i \(-0.752322\pi\)
−0.712246 + 0.701930i \(0.752322\pi\)
\(108\) 3.73205 0.359116
\(109\) 3.20868 0.307336 0.153668 0.988123i \(-0.450891\pi\)
0.153668 + 0.988123i \(0.450891\pi\)
\(110\) 3.10639 0.296183
\(111\) 14.7120 1.39640
\(112\) 0 0
\(113\) 13.8675 1.30455 0.652273 0.757985i \(-0.273816\pi\)
0.652273 + 0.757985i \(0.273816\pi\)
\(114\) −9.63963 −0.902834
\(115\) −1.02292 −0.0953879
\(116\) −2.87646 −0.267073
\(117\) 0 0
\(118\) 23.8611 2.19659
\(119\) 0 0
\(120\) −1.96581 −0.179453
\(121\) −1.61683 −0.146985
\(122\) 12.6670 1.14681
\(123\) 3.90042 0.351689
\(124\) −3.38105 −0.303627
\(125\) −5.97718 −0.534615
\(126\) 0 0
\(127\) −1.71753 −0.152406 −0.0762030 0.997092i \(-0.524280\pi\)
−0.0762030 + 0.997092i \(0.524280\pi\)
\(128\) −13.5591 −1.19847
\(129\) −0.0422167 −0.00371698
\(130\) 0 0
\(131\) 11.9464 1.04376 0.521881 0.853018i \(-0.325231\pi\)
0.521881 + 0.853018i \(0.325231\pi\)
\(132\) 2.92646 0.254716
\(133\) 0 0
\(134\) −17.4590 −1.50823
\(135\) 3.51432 0.302465
\(136\) 0.704853 0.0604407
\(137\) 9.25173 0.790428 0.395214 0.918589i \(-0.370670\pi\)
0.395214 + 0.918589i \(0.370670\pi\)
\(138\) −3.88268 −0.330516
\(139\) −7.68373 −0.651725 −0.325863 0.945417i \(-0.605655\pi\)
−0.325863 + 0.945417i \(0.605655\pi\)
\(140\) 0 0
\(141\) −3.81506 −0.321286
\(142\) −1.15263 −0.0967264
\(143\) 0 0
\(144\) 4.42751 0.368959
\(145\) −2.70865 −0.224941
\(146\) −22.3165 −1.84693
\(147\) 0 0
\(148\) −6.71354 −0.551849
\(149\) 11.2644 0.922816 0.461408 0.887188i \(-0.347344\pi\)
0.461408 + 0.887188i \(0.347344\pi\)
\(150\) −10.8876 −0.888966
\(151\) 11.3802 0.926111 0.463056 0.886329i \(-0.346753\pi\)
0.463056 + 0.886329i \(0.346753\pi\)
\(152\) −8.92550 −0.723954
\(153\) −0.292382 −0.0236377
\(154\) 0 0
\(155\) −3.18380 −0.255729
\(156\) 0 0
\(157\) −21.9387 −1.75090 −0.875448 0.483312i \(-0.839434\pi\)
−0.875448 + 0.483312i \(0.839434\pi\)
\(158\) 12.2232 0.972426
\(159\) 7.60176 0.602859
\(160\) 2.23622 0.176789
\(161\) 0 0
\(162\) 8.90401 0.699565
\(163\) −16.5999 −1.30021 −0.650104 0.759846i \(-0.725274\pi\)
−0.650104 + 0.759846i \(0.725274\pi\)
\(164\) −1.77988 −0.138985
\(165\) 2.75573 0.214533
\(166\) 25.0004 1.94041
\(167\) 3.48459 0.269645 0.134823 0.990870i \(-0.456954\pi\)
0.134823 + 0.990870i \(0.456954\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −0.327115 −0.0250886
\(171\) 3.70241 0.283131
\(172\) 0.0192648 0.00146892
\(173\) 1.41713 0.107743 0.0538714 0.998548i \(-0.482844\pi\)
0.0538714 + 0.998548i \(0.482844\pi\)
\(174\) −10.2812 −0.779414
\(175\) 0 0
\(176\) 14.9624 1.12784
\(177\) 21.1676 1.59105
\(178\) 0.0344988 0.00258579
\(179\) −21.0463 −1.57308 −0.786539 0.617541i \(-0.788129\pi\)
−0.786539 + 0.617541i \(0.788129\pi\)
\(180\) −0.372111 −0.0277355
\(181\) −20.7908 −1.54537 −0.772685 0.634789i \(-0.781087\pi\)
−0.772685 + 0.634789i \(0.781087\pi\)
\(182\) 0 0
\(183\) 11.2371 0.830670
\(184\) −3.59504 −0.265030
\(185\) −6.32188 −0.464794
\(186\) −12.0847 −0.886093
\(187\) −0.988085 −0.0722559
\(188\) 1.74092 0.126970
\(189\) 0 0
\(190\) 4.14223 0.300509
\(191\) 5.77056 0.417543 0.208772 0.977964i \(-0.433053\pi\)
0.208772 + 0.977964i \(0.433053\pi\)
\(192\) −5.64721 −0.407553
\(193\) −9.09061 −0.654356 −0.327178 0.944963i \(-0.606098\pi\)
−0.327178 + 0.944963i \(0.606098\pi\)
\(194\) −11.1221 −0.798523
\(195\) 0 0
\(196\) 0 0
\(197\) 22.6642 1.61475 0.807377 0.590036i \(-0.200886\pi\)
0.807377 + 0.590036i \(0.200886\pi\)
\(198\) −4.52866 −0.321838
\(199\) 6.32121 0.448099 0.224049 0.974578i \(-0.428072\pi\)
0.224049 + 0.974578i \(0.428072\pi\)
\(200\) −10.0810 −0.712833
\(201\) −15.4882 −1.09245
\(202\) 30.4579 2.14301
\(203\) 0 0
\(204\) −0.308168 −0.0215760
\(205\) −1.67604 −0.117060
\(206\) −26.4911 −1.84572
\(207\) 1.49127 0.103650
\(208\) 0 0
\(209\) 12.5120 0.865475
\(210\) 0 0
\(211\) 13.2077 0.909259 0.454629 0.890681i \(-0.349772\pi\)
0.454629 + 0.890681i \(0.349772\pi\)
\(212\) −3.46891 −0.238246
\(213\) −1.02252 −0.0700617
\(214\) 24.0334 1.64289
\(215\) 0.0181409 0.00123720
\(216\) 12.3510 0.840381
\(217\) 0 0
\(218\) −5.23346 −0.354455
\(219\) −19.7974 −1.33778
\(220\) −1.25752 −0.0847822
\(221\) 0 0
\(222\) −23.9958 −1.61049
\(223\) 14.9324 0.999949 0.499975 0.866040i \(-0.333343\pi\)
0.499975 + 0.866040i \(0.333343\pi\)
\(224\) 0 0
\(225\) 4.18172 0.278781
\(226\) −22.6184 −1.50455
\(227\) 16.6916 1.10786 0.553931 0.832563i \(-0.313127\pi\)
0.553931 + 0.832563i \(0.313127\pi\)
\(228\) 3.90230 0.258436
\(229\) −15.0896 −0.997147 −0.498573 0.866848i \(-0.666143\pi\)
−0.498573 + 0.866848i \(0.666143\pi\)
\(230\) 1.66842 0.110012
\(231\) 0 0
\(232\) −9.51951 −0.624987
\(233\) 10.7315 0.703047 0.351523 0.936179i \(-0.385664\pi\)
0.351523 + 0.936179i \(0.385664\pi\)
\(234\) 0 0
\(235\) 1.63936 0.106940
\(236\) −9.65939 −0.628773
\(237\) 10.8434 0.704356
\(238\) 0 0
\(239\) 2.60488 0.168496 0.0842479 0.996445i \(-0.473151\pi\)
0.0842479 + 0.996445i \(0.473151\pi\)
\(240\) 4.39430 0.283651
\(241\) −22.4531 −1.44633 −0.723165 0.690675i \(-0.757313\pi\)
−0.723165 + 0.690675i \(0.757313\pi\)
\(242\) 2.63710 0.169519
\(243\) −9.05794 −0.581067
\(244\) −5.12782 −0.328275
\(245\) 0 0
\(246\) −6.36172 −0.405608
\(247\) 0 0
\(248\) −11.1894 −0.710529
\(249\) 22.1783 1.40549
\(250\) 9.74898 0.616579
\(251\) −19.8520 −1.25305 −0.626524 0.779402i \(-0.715523\pi\)
−0.626524 + 0.779402i \(0.715523\pi\)
\(252\) 0 0
\(253\) 5.03963 0.316839
\(254\) 2.80135 0.175772
\(255\) −0.290189 −0.0181724
\(256\) 14.3095 0.894343
\(257\) −4.30542 −0.268564 −0.134282 0.990943i \(-0.542873\pi\)
−0.134282 + 0.990943i \(0.542873\pi\)
\(258\) 0.0688569 0.00428685
\(259\) 0 0
\(260\) 0 0
\(261\) 3.94882 0.244426
\(262\) −19.4850 −1.20379
\(263\) −21.2519 −1.31045 −0.655224 0.755434i \(-0.727426\pi\)
−0.655224 + 0.755434i \(0.727426\pi\)
\(264\) 9.68498 0.596069
\(265\) −3.26654 −0.200662
\(266\) 0 0
\(267\) 0.0306045 0.00187296
\(268\) 7.06773 0.431730
\(269\) −30.8114 −1.87860 −0.939302 0.343090i \(-0.888526\pi\)
−0.939302 + 0.343090i \(0.888526\pi\)
\(270\) −5.73198 −0.348837
\(271\) 0.666306 0.0404752 0.0202376 0.999795i \(-0.493558\pi\)
0.0202376 + 0.999795i \(0.493558\pi\)
\(272\) −1.57560 −0.0955350
\(273\) 0 0
\(274\) −15.0899 −0.911613
\(275\) 14.1318 0.852181
\(276\) 1.57178 0.0946100
\(277\) −15.4086 −0.925815 −0.462907 0.886407i \(-0.653194\pi\)
−0.462907 + 0.886407i \(0.653194\pi\)
\(278\) 12.5324 0.751645
\(279\) 4.64152 0.277880
\(280\) 0 0
\(281\) −14.6079 −0.871436 −0.435718 0.900083i \(-0.643505\pi\)
−0.435718 + 0.900083i \(0.643505\pi\)
\(282\) 6.22249 0.370544
\(283\) −1.10196 −0.0655045 −0.0327523 0.999464i \(-0.510427\pi\)
−0.0327523 + 0.999464i \(0.510427\pi\)
\(284\) 0.466605 0.0276879
\(285\) 3.67464 0.217667
\(286\) 0 0
\(287\) 0 0
\(288\) −3.26009 −0.192102
\(289\) −16.8960 −0.993879
\(290\) 4.41790 0.259428
\(291\) −9.86665 −0.578393
\(292\) 9.03415 0.528683
\(293\) 12.1452 0.709529 0.354764 0.934956i \(-0.384561\pi\)
0.354764 + 0.934956i \(0.384561\pi\)
\(294\) 0 0
\(295\) −9.09588 −0.529582
\(296\) −22.2181 −1.29140
\(297\) −17.3140 −1.00466
\(298\) −18.3726 −1.06430
\(299\) 0 0
\(300\) 4.40748 0.254466
\(301\) 0 0
\(302\) −18.5616 −1.06810
\(303\) 27.0198 1.55224
\(304\) 19.9517 1.14431
\(305\) −4.82867 −0.276489
\(306\) 0.476886 0.0272617
\(307\) −21.4221 −1.22262 −0.611312 0.791390i \(-0.709358\pi\)
−0.611312 + 0.791390i \(0.709358\pi\)
\(308\) 0 0
\(309\) −23.5007 −1.33691
\(310\) 5.19289 0.294936
\(311\) −12.6808 −0.719062 −0.359531 0.933133i \(-0.617063\pi\)
−0.359531 + 0.933133i \(0.617063\pi\)
\(312\) 0 0
\(313\) 21.7396 1.22879 0.614397 0.788997i \(-0.289399\pi\)
0.614397 + 0.788997i \(0.289399\pi\)
\(314\) 35.7827 2.01934
\(315\) 0 0
\(316\) −4.94818 −0.278357
\(317\) 12.3285 0.692436 0.346218 0.938154i \(-0.387466\pi\)
0.346218 + 0.938154i \(0.387466\pi\)
\(318\) −12.3987 −0.695287
\(319\) 13.3447 0.747162
\(320\) 2.42665 0.135654
\(321\) 21.3204 1.18999
\(322\) 0 0
\(323\) −1.31757 −0.0733113
\(324\) −3.60451 −0.200250
\(325\) 0 0
\(326\) 27.0751 1.49955
\(327\) −4.64270 −0.256742
\(328\) −5.89042 −0.325244
\(329\) 0 0
\(330\) −4.49469 −0.247425
\(331\) 13.3730 0.735048 0.367524 0.930014i \(-0.380206\pi\)
0.367524 + 0.930014i \(0.380206\pi\)
\(332\) −10.1206 −0.555441
\(333\) 9.21637 0.505054
\(334\) −5.68348 −0.310986
\(335\) 6.65540 0.363624
\(336\) 0 0
\(337\) −28.7393 −1.56553 −0.782766 0.622316i \(-0.786192\pi\)
−0.782766 + 0.622316i \(0.786192\pi\)
\(338\) 0 0
\(339\) −20.0652 −1.08979
\(340\) 0.132422 0.00718160
\(341\) 15.6857 0.849427
\(342\) −6.03876 −0.326539
\(343\) 0 0
\(344\) 0.0637558 0.00343748
\(345\) 1.48008 0.0796850
\(346\) −2.31140 −0.124261
\(347\) 13.9206 0.747296 0.373648 0.927571i \(-0.378107\pi\)
0.373648 + 0.927571i \(0.378107\pi\)
\(348\) 4.16201 0.223107
\(349\) −2.65542 −0.142141 −0.0710707 0.997471i \(-0.522642\pi\)
−0.0710707 + 0.997471i \(0.522642\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −11.0172 −0.587220
\(353\) 9.17164 0.488157 0.244079 0.969755i \(-0.421514\pi\)
0.244079 + 0.969755i \(0.421514\pi\)
\(354\) −34.5250 −1.83498
\(355\) 0.439384 0.0233201
\(356\) −0.0139657 −0.000740182 0
\(357\) 0 0
\(358\) 34.3273 1.81425
\(359\) −6.08926 −0.321379 −0.160689 0.987005i \(-0.551372\pi\)
−0.160689 + 0.987005i \(0.551372\pi\)
\(360\) −1.23149 −0.0649050
\(361\) −2.31577 −0.121883
\(362\) 33.9106 1.78230
\(363\) 2.33942 0.122788
\(364\) 0 0
\(365\) 8.50711 0.445282
\(366\) −18.3281 −0.958025
\(367\) 2.83281 0.147871 0.0739357 0.997263i \(-0.476444\pi\)
0.0739357 + 0.997263i \(0.476444\pi\)
\(368\) 8.03622 0.418917
\(369\) 2.44342 0.127200
\(370\) 10.3112 0.536054
\(371\) 0 0
\(372\) 4.89210 0.253644
\(373\) 10.2417 0.530296 0.265148 0.964208i \(-0.414579\pi\)
0.265148 + 0.964208i \(0.414579\pi\)
\(374\) 1.61160 0.0833338
\(375\) 8.64849 0.446606
\(376\) 5.76151 0.297127
\(377\) 0 0
\(378\) 0 0
\(379\) 12.5731 0.645834 0.322917 0.946427i \(-0.395336\pi\)
0.322917 + 0.946427i \(0.395336\pi\)
\(380\) −1.67685 −0.0860206
\(381\) 2.48512 0.127317
\(382\) −9.41198 −0.481559
\(383\) −21.2569 −1.08618 −0.543088 0.839676i \(-0.682745\pi\)
−0.543088 + 0.839676i \(0.682745\pi\)
\(384\) 19.6189 1.00117
\(385\) 0 0
\(386\) 14.8271 0.754679
\(387\) −0.0264467 −0.00134436
\(388\) 4.50245 0.228577
\(389\) 14.3161 0.725853 0.362926 0.931818i \(-0.381778\pi\)
0.362926 + 0.931818i \(0.381778\pi\)
\(390\) 0 0
\(391\) −0.530693 −0.0268383
\(392\) 0 0
\(393\) −17.2855 −0.871937
\(394\) −36.9660 −1.86232
\(395\) −4.65951 −0.234445
\(396\) 1.83328 0.0921260
\(397\) −25.9730 −1.30355 −0.651773 0.758414i \(-0.725974\pi\)
−0.651773 + 0.758414i \(0.725974\pi\)
\(398\) −10.3101 −0.516799
\(399\) 0 0
\(400\) 22.5347 1.12673
\(401\) 25.8931 1.29304 0.646519 0.762898i \(-0.276224\pi\)
0.646519 + 0.762898i \(0.276224\pi\)
\(402\) 25.2618 1.25994
\(403\) 0 0
\(404\) −12.3299 −0.613437
\(405\) −3.39422 −0.168660
\(406\) 0 0
\(407\) 31.1461 1.54385
\(408\) −1.01987 −0.0504909
\(409\) −7.88925 −0.390098 −0.195049 0.980793i \(-0.562487\pi\)
−0.195049 + 0.980793i \(0.562487\pi\)
\(410\) 2.73368 0.135007
\(411\) −13.3865 −0.660307
\(412\) 10.7241 0.528338
\(413\) 0 0
\(414\) −2.43231 −0.119542
\(415\) −9.53020 −0.467819
\(416\) 0 0
\(417\) 11.1177 0.544438
\(418\) −20.4076 −0.998166
\(419\) −8.88956 −0.434283 −0.217142 0.976140i \(-0.569673\pi\)
−0.217142 + 0.976140i \(0.569673\pi\)
\(420\) 0 0
\(421\) −18.1179 −0.883014 −0.441507 0.897258i \(-0.645556\pi\)
−0.441507 + 0.897258i \(0.645556\pi\)
\(422\) −21.5423 −1.04866
\(423\) −2.38995 −0.116203
\(424\) −11.4802 −0.557528
\(425\) −1.48814 −0.0721852
\(426\) 1.66776 0.0808032
\(427\) 0 0
\(428\) −9.72916 −0.470277
\(429\) 0 0
\(430\) −0.0295884 −0.00142688
\(431\) 14.0264 0.675627 0.337814 0.941213i \(-0.390313\pi\)
0.337814 + 0.941213i \(0.390313\pi\)
\(432\) −27.6090 −1.32834
\(433\) −18.1108 −0.870349 −0.435174 0.900346i \(-0.643313\pi\)
−0.435174 + 0.900346i \(0.643313\pi\)
\(434\) 0 0
\(435\) 3.91920 0.187911
\(436\) 2.11860 0.101463
\(437\) 6.72012 0.321467
\(438\) 32.2902 1.54289
\(439\) −31.6624 −1.51116 −0.755581 0.655055i \(-0.772645\pi\)
−0.755581 + 0.655055i \(0.772645\pi\)
\(440\) −4.16171 −0.198402
\(441\) 0 0
\(442\) 0 0
\(443\) −3.52503 −0.167479 −0.0837396 0.996488i \(-0.526686\pi\)
−0.0837396 + 0.996488i \(0.526686\pi\)
\(444\) 9.71395 0.461004
\(445\) −0.0131510 −0.000623417 0
\(446\) −24.3553 −1.15326
\(447\) −16.2987 −0.770902
\(448\) 0 0
\(449\) −5.96156 −0.281343 −0.140672 0.990056i \(-0.544926\pi\)
−0.140672 + 0.990056i \(0.544926\pi\)
\(450\) −6.82053 −0.321523
\(451\) 8.25737 0.388824
\(452\) 9.15633 0.430678
\(453\) −16.4663 −0.773654
\(454\) −27.2246 −1.27771
\(455\) 0 0
\(456\) 12.9145 0.604776
\(457\) 27.0351 1.26465 0.632325 0.774703i \(-0.282101\pi\)
0.632325 + 0.774703i \(0.282101\pi\)
\(458\) 24.6116 1.15002
\(459\) 1.82324 0.0851014
\(460\) −0.675407 −0.0314910
\(461\) 27.0280 1.25882 0.629409 0.777074i \(-0.283297\pi\)
0.629409 + 0.777074i \(0.283297\pi\)
\(462\) 0 0
\(463\) −19.1949 −0.892063 −0.446032 0.895017i \(-0.647163\pi\)
−0.446032 + 0.895017i \(0.647163\pi\)
\(464\) 21.2796 0.987880
\(465\) 4.60670 0.213631
\(466\) −17.5035 −0.810835
\(467\) −18.7331 −0.866863 −0.433432 0.901186i \(-0.642697\pi\)
−0.433432 + 0.901186i \(0.642697\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.67385 −0.123336
\(471\) 31.7435 1.46266
\(472\) −31.9673 −1.47141
\(473\) −0.0893748 −0.00410946
\(474\) −17.6860 −0.812344
\(475\) 18.8441 0.864629
\(476\) 0 0
\(477\) 4.76214 0.218043
\(478\) −4.24865 −0.194329
\(479\) 34.7686 1.58862 0.794308 0.607515i \(-0.207833\pi\)
0.794308 + 0.607515i \(0.207833\pi\)
\(480\) −3.23564 −0.147686
\(481\) 0 0
\(482\) 36.6217 1.66807
\(483\) 0 0
\(484\) −1.06755 −0.0485249
\(485\) 4.23978 0.192518
\(486\) 14.7738 0.670153
\(487\) 25.0825 1.13660 0.568299 0.822822i \(-0.307602\pi\)
0.568299 + 0.822822i \(0.307602\pi\)
\(488\) −16.9703 −0.768209
\(489\) 24.0188 1.08617
\(490\) 0 0
\(491\) −12.6116 −0.569156 −0.284578 0.958653i \(-0.591853\pi\)
−0.284578 + 0.958653i \(0.591853\pi\)
\(492\) 2.57534 0.116105
\(493\) −1.40525 −0.0632894
\(494\) 0 0
\(495\) 1.72633 0.0775929
\(496\) 25.0124 1.12309
\(497\) 0 0
\(498\) −36.1736 −1.62098
\(499\) 21.8571 0.978457 0.489229 0.872156i \(-0.337278\pi\)
0.489229 + 0.872156i \(0.337278\pi\)
\(500\) −3.94656 −0.176496
\(501\) −5.04191 −0.225256
\(502\) 32.3793 1.44516
\(503\) 37.0022 1.64985 0.824923 0.565246i \(-0.191219\pi\)
0.824923 + 0.565246i \(0.191219\pi\)
\(504\) 0 0
\(505\) −11.6106 −0.516665
\(506\) −8.21981 −0.365415
\(507\) 0 0
\(508\) −1.13404 −0.0503147
\(509\) 1.79789 0.0796901 0.0398450 0.999206i \(-0.487314\pi\)
0.0398450 + 0.999206i \(0.487314\pi\)
\(510\) 0.473309 0.0209585
\(511\) 0 0
\(512\) 3.77891 0.167006
\(513\) −23.0875 −1.01934
\(514\) 7.02228 0.309739
\(515\) 10.0985 0.444991
\(516\) −0.0278746 −0.00122711
\(517\) −8.07665 −0.355211
\(518\) 0 0
\(519\) −2.05048 −0.0900061
\(520\) 0 0
\(521\) −8.06094 −0.353156 −0.176578 0.984287i \(-0.556503\pi\)
−0.176578 + 0.984287i \(0.556503\pi\)
\(522\) −6.44066 −0.281900
\(523\) 10.4616 0.457455 0.228727 0.973490i \(-0.426544\pi\)
0.228727 + 0.973490i \(0.426544\pi\)
\(524\) 7.88788 0.344584
\(525\) 0 0
\(526\) 34.6626 1.51136
\(527\) −1.65176 −0.0719519
\(528\) −21.6494 −0.942171
\(529\) −20.2932 −0.882315
\(530\) 5.32784 0.231427
\(531\) 13.2605 0.575455
\(532\) 0 0
\(533\) 0 0
\(534\) −0.0499169 −0.00216012
\(535\) −9.16157 −0.396089
\(536\) 23.3903 1.01031
\(537\) 30.4524 1.31412
\(538\) 50.2545 2.16662
\(539\) 0 0
\(540\) 2.32041 0.0998546
\(541\) −16.9634 −0.729314 −0.364657 0.931142i \(-0.618814\pi\)
−0.364657 + 0.931142i \(0.618814\pi\)
\(542\) −1.08677 −0.0466806
\(543\) 30.0827 1.29097
\(544\) 1.16016 0.0497413
\(545\) 1.99500 0.0854566
\(546\) 0 0
\(547\) 45.3373 1.93848 0.969242 0.246110i \(-0.0791525\pi\)
0.969242 + 0.246110i \(0.0791525\pi\)
\(548\) 6.10866 0.260949
\(549\) 7.03950 0.300438
\(550\) −23.0495 −0.982833
\(551\) 17.7946 0.758076
\(552\) 5.20173 0.221400
\(553\) 0 0
\(554\) 25.1320 1.06776
\(555\) 9.14725 0.388279
\(556\) −5.07335 −0.215158
\(557\) 25.1006 1.06355 0.531774 0.846886i \(-0.321526\pi\)
0.531774 + 0.846886i \(0.321526\pi\)
\(558\) −7.57047 −0.320484
\(559\) 0 0
\(560\) 0 0
\(561\) 1.42968 0.0603611
\(562\) 23.8260 1.00504
\(563\) 22.9222 0.966054 0.483027 0.875605i \(-0.339537\pi\)
0.483027 + 0.875605i \(0.339537\pi\)
\(564\) −2.51898 −0.106068
\(565\) 8.62216 0.362737
\(566\) 1.79733 0.0755474
\(567\) 0 0
\(568\) 1.54421 0.0647935
\(569\) 8.46758 0.354979 0.177490 0.984123i \(-0.443202\pi\)
0.177490 + 0.984123i \(0.443202\pi\)
\(570\) −5.99347 −0.251039
\(571\) −37.4312 −1.56645 −0.783224 0.621739i \(-0.786426\pi\)
−0.783224 + 0.621739i \(0.786426\pi\)
\(572\) 0 0
\(573\) −8.34953 −0.348807
\(574\) 0 0
\(575\) 7.59010 0.316529
\(576\) −3.53771 −0.147404
\(577\) −16.9867 −0.707165 −0.353582 0.935403i \(-0.615037\pi\)
−0.353582 + 0.935403i \(0.615037\pi\)
\(578\) 27.5579 1.14626
\(579\) 13.1534 0.546636
\(580\) −1.78845 −0.0742613
\(581\) 0 0
\(582\) 16.0928 0.667070
\(583\) 16.0933 0.666516
\(584\) 29.8981 1.23719
\(585\) 0 0
\(586\) −19.8092 −0.818310
\(587\) −20.3458 −0.839761 −0.419881 0.907579i \(-0.637928\pi\)
−0.419881 + 0.907579i \(0.637928\pi\)
\(588\) 0 0
\(589\) 20.9161 0.861834
\(590\) 14.8357 0.610775
\(591\) −32.7932 −1.34893
\(592\) 49.6656 2.04124
\(593\) −24.0395 −0.987183 −0.493591 0.869694i \(-0.664316\pi\)
−0.493591 + 0.869694i \(0.664316\pi\)
\(594\) 28.2398 1.15869
\(595\) 0 0
\(596\) 7.43758 0.304655
\(597\) −9.14628 −0.374332
\(598\) 0 0
\(599\) 34.8604 1.42436 0.712178 0.701999i \(-0.247709\pi\)
0.712178 + 0.701999i \(0.247709\pi\)
\(600\) 14.5864 0.595486
\(601\) 1.10866 0.0452230 0.0226115 0.999744i \(-0.492802\pi\)
0.0226115 + 0.999744i \(0.492802\pi\)
\(602\) 0 0
\(603\) −9.70260 −0.395121
\(604\) 7.51406 0.305743
\(605\) −1.00527 −0.0408700
\(606\) −44.0701 −1.79023
\(607\) −2.68151 −0.108839 −0.0544196 0.998518i \(-0.517331\pi\)
−0.0544196 + 0.998518i \(0.517331\pi\)
\(608\) −14.6910 −0.595797
\(609\) 0 0
\(610\) 7.87573 0.318879
\(611\) 0 0
\(612\) −0.193052 −0.00780366
\(613\) 11.9915 0.484332 0.242166 0.970235i \(-0.422142\pi\)
0.242166 + 0.970235i \(0.422142\pi\)
\(614\) 34.9402 1.41007
\(615\) 2.42510 0.0977893
\(616\) 0 0
\(617\) −23.9660 −0.964834 −0.482417 0.875942i \(-0.660241\pi\)
−0.482417 + 0.875942i \(0.660241\pi\)
\(618\) 38.3305 1.54188
\(619\) 8.67800 0.348798 0.174399 0.984675i \(-0.444202\pi\)
0.174399 + 0.984675i \(0.444202\pi\)
\(620\) −2.10218 −0.0844255
\(621\) −9.29925 −0.373166
\(622\) 20.6828 0.829305
\(623\) 0 0
\(624\) 0 0
\(625\) 19.3508 0.774032
\(626\) −35.4580 −1.41719
\(627\) −18.1039 −0.723000
\(628\) −14.4855 −0.578034
\(629\) −3.27980 −0.130774
\(630\) 0 0
\(631\) −21.2789 −0.847098 −0.423549 0.905873i \(-0.639216\pi\)
−0.423549 + 0.905873i \(0.639216\pi\)
\(632\) −16.3758 −0.651393
\(633\) −19.1105 −0.759576
\(634\) −20.1082 −0.798597
\(635\) −1.06788 −0.0423775
\(636\) 5.01924 0.199026
\(637\) 0 0
\(638\) −21.7657 −0.861713
\(639\) −0.640557 −0.0253400
\(640\) −8.43040 −0.333241
\(641\) 23.7425 0.937772 0.468886 0.883259i \(-0.344656\pi\)
0.468886 + 0.883259i \(0.344656\pi\)
\(642\) −34.7744 −1.37244
\(643\) 0.0581552 0.00229342 0.00114671 0.999999i \(-0.499635\pi\)
0.00114671 + 0.999999i \(0.499635\pi\)
\(644\) 0 0
\(645\) −0.0262484 −0.00103353
\(646\) 2.14900 0.0845511
\(647\) 37.9906 1.49356 0.746782 0.665069i \(-0.231598\pi\)
0.746782 + 0.665069i \(0.231598\pi\)
\(648\) −11.9289 −0.468613
\(649\) 44.8127 1.75905
\(650\) 0 0
\(651\) 0 0
\(652\) −10.9605 −0.429246
\(653\) 6.02234 0.235672 0.117836 0.993033i \(-0.462404\pi\)
0.117836 + 0.993033i \(0.462404\pi\)
\(654\) 7.57240 0.296104
\(655\) 7.42771 0.290225
\(656\) 13.1672 0.514094
\(657\) −12.4021 −0.483852
\(658\) 0 0
\(659\) 30.5808 1.19126 0.595630 0.803259i \(-0.296902\pi\)
0.595630 + 0.803259i \(0.296902\pi\)
\(660\) 1.81953 0.0708253
\(661\) 50.2882 1.95598 0.977992 0.208640i \(-0.0669038\pi\)
0.977992 + 0.208640i \(0.0669038\pi\)
\(662\) −21.8119 −0.847743
\(663\) 0 0
\(664\) −33.4937 −1.29981
\(665\) 0 0
\(666\) −15.0322 −0.582487
\(667\) 7.16736 0.277521
\(668\) 2.30078 0.0890197
\(669\) −21.6060 −0.835337
\(670\) −10.8552 −0.419373
\(671\) 23.7895 0.918382
\(672\) 0 0
\(673\) 10.0095 0.385837 0.192918 0.981215i \(-0.438205\pi\)
0.192918 + 0.981215i \(0.438205\pi\)
\(674\) 46.8749 1.80555
\(675\) −26.0764 −1.00368
\(676\) 0 0
\(677\) −40.9889 −1.57533 −0.787665 0.616104i \(-0.788710\pi\)
−0.787665 + 0.616104i \(0.788710\pi\)
\(678\) 32.7270 1.25687
\(679\) 0 0
\(680\) 0.438245 0.0168059
\(681\) −24.1514 −0.925485
\(682\) −25.5839 −0.979657
\(683\) 26.1325 0.999932 0.499966 0.866045i \(-0.333346\pi\)
0.499966 + 0.866045i \(0.333346\pi\)
\(684\) 2.44460 0.0934717
\(685\) 5.75229 0.219784
\(686\) 0 0
\(687\) 21.8334 0.832996
\(688\) −0.142517 −0.00543343
\(689\) 0 0
\(690\) −2.41407 −0.0919020
\(691\) 34.7107 1.32046 0.660229 0.751064i \(-0.270459\pi\)
0.660229 + 0.751064i \(0.270459\pi\)
\(692\) 0.935695 0.0355698
\(693\) 0 0
\(694\) −22.7049 −0.861867
\(695\) −4.77738 −0.181216
\(696\) 13.7740 0.522101
\(697\) −0.869533 −0.0329359
\(698\) 4.33108 0.163934
\(699\) −15.5277 −0.587311
\(700\) 0 0
\(701\) 48.3337 1.82554 0.912769 0.408475i \(-0.133939\pi\)
0.912769 + 0.408475i \(0.133939\pi\)
\(702\) 0 0
\(703\) 41.5319 1.56640
\(704\) −11.9554 −0.450587
\(705\) −2.37202 −0.0893355
\(706\) −14.9593 −0.562999
\(707\) 0 0
\(708\) 13.9764 0.525264
\(709\) 11.5080 0.432191 0.216095 0.976372i \(-0.430668\pi\)
0.216095 + 0.976372i \(0.430668\pi\)
\(710\) −0.716650 −0.0268954
\(711\) 6.79288 0.254753
\(712\) −0.0462189 −0.00173213
\(713\) 8.42466 0.315506
\(714\) 0 0
\(715\) 0 0
\(716\) −13.8963 −0.519330
\(717\) −3.76905 −0.140758
\(718\) 9.93179 0.370651
\(719\) −0.0753591 −0.00281042 −0.00140521 0.999999i \(-0.500447\pi\)
−0.00140521 + 0.999999i \(0.500447\pi\)
\(720\) 2.75282 0.102591
\(721\) 0 0
\(722\) 3.77710 0.140569
\(723\) 32.4878 1.20823
\(724\) −13.7276 −0.510183
\(725\) 20.0983 0.746431
\(726\) −3.81568 −0.141613
\(727\) −13.0961 −0.485708 −0.242854 0.970063i \(-0.578084\pi\)
−0.242854 + 0.970063i \(0.578084\pi\)
\(728\) 0 0
\(729\) 29.4835 1.09198
\(730\) −13.8754 −0.513551
\(731\) 0.00941152 0.000348098 0
\(732\) 7.41955 0.274234
\(733\) 21.9965 0.812459 0.406230 0.913771i \(-0.366843\pi\)
0.406230 + 0.913771i \(0.366843\pi\)
\(734\) −4.62041 −0.170542
\(735\) 0 0
\(736\) −5.91727 −0.218113
\(737\) −32.7892 −1.20781
\(738\) −3.98531 −0.146701
\(739\) −40.4642 −1.48850 −0.744249 0.667902i \(-0.767193\pi\)
−0.744249 + 0.667902i \(0.767193\pi\)
\(740\) −4.17416 −0.153445
\(741\) 0 0
\(742\) 0 0
\(743\) −13.3064 −0.488165 −0.244083 0.969754i \(-0.578487\pi\)
−0.244083 + 0.969754i \(0.578487\pi\)
\(744\) 16.1902 0.593561
\(745\) 7.00368 0.256595
\(746\) −16.7046 −0.611599
\(747\) 13.8936 0.508341
\(748\) −0.652405 −0.0238543
\(749\) 0 0
\(750\) −14.1060 −0.515078
\(751\) 49.9077 1.82116 0.910580 0.413334i \(-0.135636\pi\)
0.910580 + 0.413334i \(0.135636\pi\)
\(752\) −12.8791 −0.469651
\(753\) 28.7243 1.04677
\(754\) 0 0
\(755\) 7.07570 0.257511
\(756\) 0 0
\(757\) −10.0788 −0.366319 −0.183160 0.983083i \(-0.558632\pi\)
−0.183160 + 0.983083i \(0.558632\pi\)
\(758\) −20.5071 −0.744851
\(759\) −7.29194 −0.264681
\(760\) −5.54946 −0.201300
\(761\) −28.2853 −1.02534 −0.512671 0.858585i \(-0.671344\pi\)
−0.512671 + 0.858585i \(0.671344\pi\)
\(762\) −4.05332 −0.146836
\(763\) 0 0
\(764\) 3.81014 0.137846
\(765\) −0.181790 −0.00657262
\(766\) 34.6707 1.25270
\(767\) 0 0
\(768\) −20.7047 −0.747116
\(769\) 21.7382 0.783901 0.391950 0.919986i \(-0.371800\pi\)
0.391950 + 0.919986i \(0.371800\pi\)
\(770\) 0 0
\(771\) 6.22959 0.224353
\(772\) −6.00228 −0.216027
\(773\) 6.34043 0.228050 0.114025 0.993478i \(-0.463626\pi\)
0.114025 + 0.993478i \(0.463626\pi\)
\(774\) 0.0431355 0.00155047
\(775\) 23.6239 0.848595
\(776\) 14.9006 0.534902
\(777\) 0 0
\(778\) −23.3500 −0.837137
\(779\) 11.0108 0.394504
\(780\) 0 0
\(781\) −2.16471 −0.0774596
\(782\) 0.865579 0.0309530
\(783\) −24.6240 −0.879991
\(784\) 0 0
\(785\) −13.6404 −0.486848
\(786\) 28.1932 1.00562
\(787\) −7.69793 −0.274402 −0.137201 0.990543i \(-0.543811\pi\)
−0.137201 + 0.990543i \(0.543811\pi\)
\(788\) 14.9645 0.533089
\(789\) 30.7498 1.09472
\(790\) 7.59981 0.270389
\(791\) 0 0
\(792\) 6.06717 0.215587
\(793\) 0 0
\(794\) 42.3628 1.50340
\(795\) 4.72642 0.167629
\(796\) 4.17372 0.147934
\(797\) −27.1989 −0.963433 −0.481716 0.876327i \(-0.659986\pi\)
−0.481716 + 0.876327i \(0.659986\pi\)
\(798\) 0 0
\(799\) 0.850503 0.0300886
\(800\) −16.5928 −0.586645
\(801\) 0.0191722 0.000677417 0
\(802\) −42.2325 −1.49128
\(803\) −41.9120 −1.47904
\(804\) −10.2264 −0.360658
\(805\) 0 0
\(806\) 0 0
\(807\) 44.5816 1.56935
\(808\) −40.8053 −1.43553
\(809\) 6.55072 0.230311 0.115156 0.993347i \(-0.463263\pi\)
0.115156 + 0.993347i \(0.463263\pi\)
\(810\) 5.53610 0.194519
\(811\) −6.35691 −0.223221 −0.111611 0.993752i \(-0.535601\pi\)
−0.111611 + 0.993752i \(0.535601\pi\)
\(812\) 0 0
\(813\) −0.964090 −0.0338121
\(814\) −50.8003 −1.78055
\(815\) −10.3211 −0.361531
\(816\) 2.27977 0.0798080
\(817\) −0.119177 −0.00416948
\(818\) 12.8676 0.449906
\(819\) 0 0
\(820\) −1.10664 −0.0386457
\(821\) 42.3383 1.47762 0.738809 0.673915i \(-0.235388\pi\)
0.738809 + 0.673915i \(0.235388\pi\)
\(822\) 21.8338 0.761543
\(823\) 30.0749 1.04835 0.524173 0.851612i \(-0.324375\pi\)
0.524173 + 0.851612i \(0.324375\pi\)
\(824\) 35.4908 1.23638
\(825\) −20.4476 −0.711894
\(826\) 0 0
\(827\) 24.4926 0.851693 0.425846 0.904795i \(-0.359976\pi\)
0.425846 + 0.904795i \(0.359976\pi\)
\(828\) 0.984644 0.0342187
\(829\) 56.7272 1.97022 0.985109 0.171929i \(-0.0550001\pi\)
0.985109 + 0.171929i \(0.0550001\pi\)
\(830\) 15.5441 0.539543
\(831\) 22.2950 0.773406
\(832\) 0 0
\(833\) 0 0
\(834\) −18.1334 −0.627908
\(835\) 2.16655 0.0749766
\(836\) 8.26135 0.285725
\(837\) −28.9436 −1.00044
\(838\) 14.4992 0.500866
\(839\) −30.0186 −1.03636 −0.518179 0.855272i \(-0.673390\pi\)
−0.518179 + 0.855272i \(0.673390\pi\)
\(840\) 0 0
\(841\) −10.0211 −0.345556
\(842\) 29.5510 1.01839
\(843\) 21.1365 0.727979
\(844\) 8.72071 0.300179
\(845\) 0 0
\(846\) 3.89809 0.134019
\(847\) 0 0
\(848\) 25.6624 0.881252
\(849\) 1.59444 0.0547211
\(850\) 2.42720 0.0832523
\(851\) 16.7283 0.573439
\(852\) −0.675139 −0.0231299
\(853\) −30.2869 −1.03700 −0.518501 0.855077i \(-0.673510\pi\)
−0.518501 + 0.855077i \(0.673510\pi\)
\(854\) 0 0
\(855\) 2.30199 0.0787263
\(856\) −32.1982 −1.10051
\(857\) −28.4632 −0.972283 −0.486142 0.873880i \(-0.661596\pi\)
−0.486142 + 0.873880i \(0.661596\pi\)
\(858\) 0 0
\(859\) 48.9603 1.67050 0.835251 0.549868i \(-0.185322\pi\)
0.835251 + 0.549868i \(0.185322\pi\)
\(860\) 0.0119779 0.000408444 0
\(861\) 0 0
\(862\) −22.8775 −0.779212
\(863\) 24.5352 0.835187 0.417594 0.908634i \(-0.362874\pi\)
0.417594 + 0.908634i \(0.362874\pi\)
\(864\) 20.3292 0.691615
\(865\) 0.881108 0.0299586
\(866\) 29.5393 1.00379
\(867\) 24.4471 0.830266
\(868\) 0 0
\(869\) 22.9560 0.778730
\(870\) −6.39235 −0.216721
\(871\) 0 0
\(872\) 7.01141 0.237436
\(873\) −6.18098 −0.209194
\(874\) −10.9607 −0.370753
\(875\) 0 0
\(876\) −13.0717 −0.441651
\(877\) −45.6733 −1.54228 −0.771139 0.636666i \(-0.780313\pi\)
−0.771139 + 0.636666i \(0.780313\pi\)
\(878\) 51.6424 1.74285
\(879\) −17.5731 −0.592726
\(880\) 9.30294 0.313602
\(881\) −37.0156 −1.24709 −0.623543 0.781789i \(-0.714308\pi\)
−0.623543 + 0.781789i \(0.714308\pi\)
\(882\) 0 0
\(883\) 14.5124 0.488381 0.244190 0.969727i \(-0.421478\pi\)
0.244190 + 0.969727i \(0.421478\pi\)
\(884\) 0 0
\(885\) 13.1610 0.442402
\(886\) 5.74944 0.193156
\(887\) −2.47725 −0.0831779 −0.0415890 0.999135i \(-0.513242\pi\)
−0.0415890 + 0.999135i \(0.513242\pi\)
\(888\) 32.1479 1.07881
\(889\) 0 0
\(890\) 0.0214497 0.000718996 0
\(891\) 16.7224 0.560220
\(892\) 9.85947 0.330120
\(893\) −10.7699 −0.360399
\(894\) 26.5837 0.889093
\(895\) −13.0856 −0.437404
\(896\) 0 0
\(897\) 0 0
\(898\) 9.72351 0.324478
\(899\) 22.3081 0.744018
\(900\) 2.76108 0.0920358
\(901\) −1.69469 −0.0564582
\(902\) −13.4681 −0.448437
\(903\) 0 0
\(904\) 30.3025 1.00784
\(905\) −12.9268 −0.429700
\(906\) 26.8571 0.892267
\(907\) 48.5987 1.61369 0.806847 0.590760i \(-0.201172\pi\)
0.806847 + 0.590760i \(0.201172\pi\)
\(908\) 11.0210 0.365745
\(909\) 16.9266 0.561419
\(910\) 0 0
\(911\) 2.13289 0.0706658 0.0353329 0.999376i \(-0.488751\pi\)
0.0353329 + 0.999376i \(0.488751\pi\)
\(912\) −28.8686 −0.955933
\(913\) 46.9525 1.55390
\(914\) −44.0952 −1.45854
\(915\) 6.98670 0.230973
\(916\) −9.96323 −0.329194
\(917\) 0 0
\(918\) −2.97376 −0.0981488
\(919\) −57.8351 −1.90780 −0.953902 0.300118i \(-0.902974\pi\)
−0.953902 + 0.300118i \(0.902974\pi\)
\(920\) −2.23523 −0.0736932
\(921\) 30.9960 1.02135
\(922\) −44.0836 −1.45182
\(923\) 0 0
\(924\) 0 0
\(925\) 46.9085 1.54234
\(926\) 31.3076 1.02883
\(927\) −14.7221 −0.483536
\(928\) −15.6687 −0.514350
\(929\) −40.3415 −1.32356 −0.661781 0.749697i \(-0.730199\pi\)
−0.661781 + 0.749697i \(0.730199\pi\)
\(930\) −7.51369 −0.246384
\(931\) 0 0
\(932\) 7.08575 0.232101
\(933\) 18.3481 0.600689
\(934\) 30.5543 0.999767
\(935\) −0.614345 −0.0200912
\(936\) 0 0
\(937\) −38.6687 −1.26325 −0.631625 0.775274i \(-0.717612\pi\)
−0.631625 + 0.775274i \(0.717612\pi\)
\(938\) 0 0
\(939\) −31.4554 −1.02651
\(940\) 1.08242 0.0353048
\(941\) −24.9826 −0.814410 −0.407205 0.913337i \(-0.633497\pi\)
−0.407205 + 0.913337i \(0.633497\pi\)
\(942\) −51.7747 −1.68691
\(943\) 4.43497 0.144423
\(944\) 71.4586 2.32578
\(945\) 0 0
\(946\) 0.145773 0.00473950
\(947\) 47.3287 1.53798 0.768988 0.639264i \(-0.220761\pi\)
0.768988 + 0.639264i \(0.220761\pi\)
\(948\) 7.15961 0.232533
\(949\) 0 0
\(950\) −30.7354 −0.997189
\(951\) −17.8383 −0.578446
\(952\) 0 0
\(953\) −15.7277 −0.509469 −0.254735 0.967011i \(-0.581988\pi\)
−0.254735 + 0.967011i \(0.581988\pi\)
\(954\) −7.76721 −0.251473
\(955\) 3.58786 0.116101
\(956\) 1.71993 0.0556265
\(957\) −19.3088 −0.624164
\(958\) −56.7087 −1.83218
\(959\) 0 0
\(960\) −3.51117 −0.113323
\(961\) −4.77857 −0.154147
\(962\) 0 0
\(963\) 13.3562 0.430398
\(964\) −14.8251 −0.477486
\(965\) −5.65211 −0.181948
\(966\) 0 0
\(967\) 32.3906 1.04161 0.520806 0.853675i \(-0.325632\pi\)
0.520806 + 0.853675i \(0.325632\pi\)
\(968\) −3.53300 −0.113555
\(969\) 1.90641 0.0612428
\(970\) −6.91522 −0.222034
\(971\) 34.5508 1.10879 0.554395 0.832254i \(-0.312950\pi\)
0.554395 + 0.832254i \(0.312950\pi\)
\(972\) −5.98071 −0.191831
\(973\) 0 0
\(974\) −40.9105 −1.31086
\(975\) 0 0
\(976\) 37.9348 1.21426
\(977\) −53.0833 −1.69828 −0.849142 0.528165i \(-0.822880\pi\)
−0.849142 + 0.528165i \(0.822880\pi\)
\(978\) −39.1754 −1.25269
\(979\) 0.0647911 0.00207073
\(980\) 0 0
\(981\) −2.90842 −0.0928588
\(982\) 20.5700 0.656416
\(983\) −18.1042 −0.577434 −0.288717 0.957414i \(-0.593229\pi\)
−0.288717 + 0.957414i \(0.593229\pi\)
\(984\) 8.52297 0.271702
\(985\) 14.0915 0.448993
\(986\) 2.29202 0.0729927
\(987\) 0 0
\(988\) 0 0
\(989\) −0.0480026 −0.00152639
\(990\) −2.81571 −0.0894891
\(991\) 28.2373 0.896986 0.448493 0.893786i \(-0.351961\pi\)
0.448493 + 0.893786i \(0.351961\pi\)
\(992\) −18.4173 −0.584749
\(993\) −19.3497 −0.614044
\(994\) 0 0
\(995\) 3.93023 0.124597
\(996\) 14.6437 0.464004
\(997\) 13.2773 0.420496 0.210248 0.977648i \(-0.432573\pi\)
0.210248 + 0.977648i \(0.432573\pi\)
\(998\) −35.6496 −1.12847
\(999\) −57.4714 −1.81832
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 8281.2.a.cz.1.7 yes 36
7.6 odd 2 inner 8281.2.a.cz.1.8 yes 36
13.12 even 2 8281.2.a.cy.1.29 36
91.90 odd 2 8281.2.a.cy.1.30 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8281.2.a.cy.1.29 36 13.12 even 2
8281.2.a.cy.1.30 yes 36 91.90 odd 2
8281.2.a.cz.1.7 yes 36 1.1 even 1 trivial
8281.2.a.cz.1.8 yes 36 7.6 odd 2 inner