Properties

Label 7605.2.a.bl.1.1
Level $7605$
Weight $2$
Character 7605.1
Self dual yes
Analytic conductor $60.726$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7605,2,Mod(1,7605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7605, 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("7605.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7605.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: \(60.7262307372\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 585)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.30278\) of defining polynomial
Character \(\chi\) \(=\) 7605.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} -3.60555 q^{7} +O(q^{10})\) \(q+2.00000 q^{2} +2.00000 q^{4} -1.00000 q^{5} -3.60555 q^{7} -2.00000 q^{10} +3.00000 q^{11} -7.21110 q^{14} -4.00000 q^{16} -3.60555 q^{17} +7.21110 q^{19} -2.00000 q^{20} +6.00000 q^{22} +3.60555 q^{23} +1.00000 q^{25} -7.21110 q^{28} -7.21110 q^{29} -7.21110 q^{31} -8.00000 q^{32} -7.21110 q^{34} +3.60555 q^{35} -3.60555 q^{37} +14.4222 q^{38} +11.0000 q^{41} +4.00000 q^{43} +6.00000 q^{44} +7.21110 q^{46} -4.00000 q^{47} +6.00000 q^{49} +2.00000 q^{50} +10.8167 q^{53} -3.00000 q^{55} -14.4222 q^{58} +12.0000 q^{59} +13.0000 q^{61} -14.4222 q^{62} -8.00000 q^{64} -7.21110 q^{68} +7.21110 q^{70} -5.00000 q^{71} +7.21110 q^{73} -7.21110 q^{74} +14.4222 q^{76} -10.8167 q^{77} +13.0000 q^{79} +4.00000 q^{80} +22.0000 q^{82} +6.00000 q^{83} +3.60555 q^{85} +8.00000 q^{86} -3.00000 q^{89} +7.21110 q^{92} -8.00000 q^{94} -7.21110 q^{95} +3.60555 q^{97} +12.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} + 4 q^{4} - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{10} + 6 q^{11} - 8 q^{16} - 4 q^{20} + 12 q^{22} + 2 q^{25} - 16 q^{32} + 22 q^{41} + 8 q^{43} + 12 q^{44} - 8 q^{47} + 12 q^{49} + 4 q^{50} - 6 q^{55} + 24 q^{59} + 26 q^{61} - 16 q^{64} - 10 q^{71} + 26 q^{79} + 8 q^{80} + 44 q^{82} + 12 q^{83} + 16 q^{86} - 6 q^{89} - 16 q^{94} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) 0 0
\(4\) 2.00000 1.00000
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −3.60555 −1.36277 −0.681385 0.731925i \(-0.738622\pi\)
−0.681385 + 0.731925i \(0.738622\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) −2.00000 −0.632456
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −7.21110 −1.92725
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) −3.60555 −0.874475 −0.437237 0.899346i \(-0.644043\pi\)
−0.437237 + 0.899346i \(0.644043\pi\)
\(18\) 0 0
\(19\) 7.21110 1.65434 0.827170 0.561951i \(-0.189949\pi\)
0.827170 + 0.561951i \(0.189949\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) 6.00000 1.27920
\(23\) 3.60555 0.751809 0.375905 0.926658i \(-0.377332\pi\)
0.375905 + 0.926658i \(0.377332\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) −7.21110 −1.36277
\(29\) −7.21110 −1.33907 −0.669534 0.742781i \(-0.733506\pi\)
−0.669534 + 0.742781i \(0.733506\pi\)
\(30\) 0 0
\(31\) −7.21110 −1.29515 −0.647576 0.762001i \(-0.724217\pi\)
−0.647576 + 0.762001i \(0.724217\pi\)
\(32\) −8.00000 −1.41421
\(33\) 0 0
\(34\) −7.21110 −1.23669
\(35\) 3.60555 0.609449
\(36\) 0 0
\(37\) −3.60555 −0.592749 −0.296374 0.955072i \(-0.595778\pi\)
−0.296374 + 0.955072i \(0.595778\pi\)
\(38\) 14.4222 2.33959
\(39\) 0 0
\(40\) 0 0
\(41\) 11.0000 1.71791 0.858956 0.512050i \(-0.171114\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) 7.21110 1.06322
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 0 0
\(49\) 6.00000 0.857143
\(50\) 2.00000 0.282843
\(51\) 0 0
\(52\) 0 0
\(53\) 10.8167 1.48578 0.742891 0.669413i \(-0.233454\pi\)
0.742891 + 0.669413i \(0.233454\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) −14.4222 −1.89373
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 13.0000 1.66448 0.832240 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) −14.4222 −1.83162
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) −7.21110 −0.874475
\(69\) 0 0
\(70\) 7.21110 0.861892
\(71\) −5.00000 −0.593391 −0.296695 0.954972i \(-0.595885\pi\)
−0.296695 + 0.954972i \(0.595885\pi\)
\(72\) 0 0
\(73\) 7.21110 0.843996 0.421998 0.906597i \(-0.361329\pi\)
0.421998 + 0.906597i \(0.361329\pi\)
\(74\) −7.21110 −0.838274
\(75\) 0 0
\(76\) 14.4222 1.65434
\(77\) −10.8167 −1.23267
\(78\) 0 0
\(79\) 13.0000 1.46261 0.731307 0.682048i \(-0.238911\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 4.00000 0.447214
\(81\) 0 0
\(82\) 22.0000 2.42949
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 3.60555 0.391077
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 7.21110 0.751809
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) −7.21110 −0.739844
\(96\) 0 0
\(97\) 3.60555 0.366088 0.183044 0.983105i \(-0.441405\pi\)
0.183044 + 0.983105i \(0.441405\pi\)
\(98\) 12.0000 1.21218
\(99\) 0 0
\(100\) 2.00000 0.200000
\(101\) −7.21110 −0.717532 −0.358766 0.933428i \(-0.616802\pi\)
−0.358766 + 0.933428i \(0.616802\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 21.6333 2.10121
\(107\) 3.60555 0.348562 0.174281 0.984696i \(-0.444240\pi\)
0.174281 + 0.984696i \(0.444240\pi\)
\(108\) 0 0
\(109\) 14.4222 1.38140 0.690698 0.723143i \(-0.257303\pi\)
0.690698 + 0.723143i \(0.257303\pi\)
\(110\) −6.00000 −0.572078
\(111\) 0 0
\(112\) 14.4222 1.36277
\(113\) 7.21110 0.678363 0.339182 0.940721i \(-0.389850\pi\)
0.339182 + 0.940721i \(0.389850\pi\)
\(114\) 0 0
\(115\) −3.60555 −0.336219
\(116\) −14.4222 −1.33907
\(117\) 0 0
\(118\) 24.0000 2.20938
\(119\) 13.0000 1.19171
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 26.0000 2.35393
\(123\) 0 0
\(124\) −14.4222 −1.29515
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −21.6333 −1.89011 −0.945055 0.326910i \(-0.893993\pi\)
−0.945055 + 0.326910i \(0.893993\pi\)
\(132\) 0 0
\(133\) −26.0000 −2.25449
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 0 0
\(139\) 7.00000 0.593732 0.296866 0.954919i \(-0.404058\pi\)
0.296866 + 0.954919i \(0.404058\pi\)
\(140\) 7.21110 0.609449
\(141\) 0 0
\(142\) −10.0000 −0.839181
\(143\) 0 0
\(144\) 0 0
\(145\) 7.21110 0.598849
\(146\) 14.4222 1.19359
\(147\) 0 0
\(148\) −7.21110 −0.592749
\(149\) 5.00000 0.409616 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) 0 0
\(151\) −7.21110 −0.586831 −0.293416 0.955985i \(-0.594792\pi\)
−0.293416 + 0.955985i \(0.594792\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −21.6333 −1.74326
\(155\) 7.21110 0.579210
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 26.0000 2.06845
\(159\) 0 0
\(160\) 8.00000 0.632456
\(161\) −13.0000 −1.02454
\(162\) 0 0
\(163\) 10.8167 0.847226 0.423613 0.905843i \(-0.360762\pi\)
0.423613 + 0.905843i \(0.360762\pi\)
\(164\) 22.0000 1.71791
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 10.0000 0.773823 0.386912 0.922117i \(-0.373542\pi\)
0.386912 + 0.922117i \(0.373542\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 7.21110 0.553066
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) −7.21110 −0.548250 −0.274125 0.961694i \(-0.588388\pi\)
−0.274125 + 0.961694i \(0.588388\pi\)
\(174\) 0 0
\(175\) −3.60555 −0.272554
\(176\) −12.0000 −0.904534
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −3.00000 −0.222988 −0.111494 0.993765i \(-0.535564\pi\)
−0.111494 + 0.993765i \(0.535564\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.60555 0.265085
\(186\) 0 0
\(187\) −10.8167 −0.790992
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) −14.4222 −1.04630
\(191\) 7.21110 0.521777 0.260889 0.965369i \(-0.415984\pi\)
0.260889 + 0.965369i \(0.415984\pi\)
\(192\) 0 0
\(193\) −3.60555 −0.259533 −0.129767 0.991545i \(-0.541423\pi\)
−0.129767 + 0.991545i \(0.541423\pi\)
\(194\) 7.21110 0.517727
\(195\) 0 0
\(196\) 12.0000 0.857143
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −14.4222 −1.01474
\(203\) 26.0000 1.82484
\(204\) 0 0
\(205\) −11.0000 −0.768273
\(206\) −20.0000 −1.39347
\(207\) 0 0
\(208\) 0 0
\(209\) 21.6333 1.49641
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 21.6333 1.48578
\(213\) 0 0
\(214\) 7.21110 0.492941
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) 26.0000 1.76500
\(218\) 28.8444 1.95359
\(219\) 0 0
\(220\) −6.00000 −0.404520
\(221\) 0 0
\(222\) 0 0
\(223\) −14.4222 −0.965782 −0.482891 0.875680i \(-0.660413\pi\)
−0.482891 + 0.875680i \(0.660413\pi\)
\(224\) 28.8444 1.92725
\(225\) 0 0
\(226\) 14.4222 0.959351
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 0 0
\(229\) 14.4222 0.953046 0.476523 0.879162i \(-0.341897\pi\)
0.476523 + 0.879162i \(0.341897\pi\)
\(230\) −7.21110 −0.475486
\(231\) 0 0
\(232\) 0 0
\(233\) −25.2389 −1.65345 −0.826726 0.562604i \(-0.809799\pi\)
−0.826726 + 0.562604i \(0.809799\pi\)
\(234\) 0 0
\(235\) 4.00000 0.260931
\(236\) 24.0000 1.56227
\(237\) 0 0
\(238\) 26.0000 1.68533
\(239\) 7.00000 0.452792 0.226396 0.974035i \(-0.427306\pi\)
0.226396 + 0.974035i \(0.427306\pi\)
\(240\) 0 0
\(241\) 21.6333 1.39352 0.696762 0.717302i \(-0.254623\pi\)
0.696762 + 0.717302i \(0.254623\pi\)
\(242\) −4.00000 −0.257130
\(243\) 0 0
\(244\) 26.0000 1.66448
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −2.00000 −0.126491
\(251\) 21.6333 1.36548 0.682741 0.730660i \(-0.260788\pi\)
0.682741 + 0.730660i \(0.260788\pi\)
\(252\) 0 0
\(253\) 10.8167 0.680037
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 21.6333 1.34945 0.674724 0.738070i \(-0.264263\pi\)
0.674724 + 0.738070i \(0.264263\pi\)
\(258\) 0 0
\(259\) 13.0000 0.807781
\(260\) 0 0
\(261\) 0 0
\(262\) −43.2666 −2.67302
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −10.8167 −0.664462
\(266\) −52.0000 −3.18832
\(267\) 0 0
\(268\) 0 0
\(269\) 7.21110 0.439669 0.219834 0.975537i \(-0.429448\pi\)
0.219834 + 0.975537i \(0.429448\pi\)
\(270\) 0 0
\(271\) 28.8444 1.75217 0.876087 0.482154i \(-0.160145\pi\)
0.876087 + 0.482154i \(0.160145\pi\)
\(272\) 14.4222 0.874475
\(273\) 0 0
\(274\) 24.0000 1.44989
\(275\) 3.00000 0.180907
\(276\) 0 0
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) 14.0000 0.839664
\(279\) 0 0
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) −26.0000 −1.54554 −0.772770 0.634686i \(-0.781129\pi\)
−0.772770 + 0.634686i \(0.781129\pi\)
\(284\) −10.0000 −0.593391
\(285\) 0 0
\(286\) 0 0
\(287\) −39.6611 −2.34112
\(288\) 0 0
\(289\) −4.00000 −0.235294
\(290\) 14.4222 0.846901
\(291\) 0 0
\(292\) 14.4222 0.843996
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 0 0
\(295\) −12.0000 −0.698667
\(296\) 0 0
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) 0 0
\(300\) 0 0
\(301\) −14.4222 −0.831282
\(302\) −14.4222 −0.829905
\(303\) 0 0
\(304\) −28.8444 −1.65434
\(305\) −13.0000 −0.744378
\(306\) 0 0
\(307\) −18.0278 −1.02890 −0.514449 0.857521i \(-0.672004\pi\)
−0.514449 + 0.857521i \(0.672004\pi\)
\(308\) −21.6333 −1.23267
\(309\) 0 0
\(310\) 14.4222 0.819126
\(311\) 14.4222 0.817808 0.408904 0.912577i \(-0.365911\pi\)
0.408904 + 0.912577i \(0.365911\pi\)
\(312\) 0 0
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 26.0000 1.46261
\(317\) 32.0000 1.79730 0.898650 0.438667i \(-0.144549\pi\)
0.898650 + 0.438667i \(0.144549\pi\)
\(318\) 0 0
\(319\) −21.6333 −1.21123
\(320\) 8.00000 0.447214
\(321\) 0 0
\(322\) −26.0000 −1.44892
\(323\) −26.0000 −1.44668
\(324\) 0 0
\(325\) 0 0
\(326\) 21.6333 1.19816
\(327\) 0 0
\(328\) 0 0
\(329\) 14.4222 0.795122
\(330\) 0 0
\(331\) −28.8444 −1.58543 −0.792716 0.609591i \(-0.791334\pi\)
−0.792716 + 0.609591i \(0.791334\pi\)
\(332\) 12.0000 0.658586
\(333\) 0 0
\(334\) 20.0000 1.09435
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 7.21110 0.391077
\(341\) −21.6333 −1.17151
\(342\) 0 0
\(343\) 3.60555 0.194681
\(344\) 0 0
\(345\) 0 0
\(346\) −14.4222 −0.775343
\(347\) −25.2389 −1.35489 −0.677446 0.735572i \(-0.736913\pi\)
−0.677446 + 0.735572i \(0.736913\pi\)
\(348\) 0 0
\(349\) 7.21110 0.386001 0.193001 0.981199i \(-0.438178\pi\)
0.193001 + 0.981199i \(0.438178\pi\)
\(350\) −7.21110 −0.385450
\(351\) 0 0
\(352\) −24.0000 −1.27920
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 0 0
\(355\) 5.00000 0.265372
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 0 0
\(359\) 4.00000 0.211112 0.105556 0.994413i \(-0.466338\pi\)
0.105556 + 0.994413i \(0.466338\pi\)
\(360\) 0 0
\(361\) 33.0000 1.73684
\(362\) −6.00000 −0.315353
\(363\) 0 0
\(364\) 0 0
\(365\) −7.21110 −0.377446
\(366\) 0 0
\(367\) −18.0000 −0.939592 −0.469796 0.882775i \(-0.655673\pi\)
−0.469796 + 0.882775i \(0.655673\pi\)
\(368\) −14.4222 −0.751809
\(369\) 0 0
\(370\) 7.21110 0.374887
\(371\) −39.0000 −2.02478
\(372\) 0 0
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) −21.6333 −1.11863
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 21.6333 1.11123 0.555614 0.831440i \(-0.312483\pi\)
0.555614 + 0.831440i \(0.312483\pi\)
\(380\) −14.4222 −0.739844
\(381\) 0 0
\(382\) 14.4222 0.737904
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 0 0
\(385\) 10.8167 0.551268
\(386\) −7.21110 −0.367035
\(387\) 0 0
\(388\) 7.21110 0.366088
\(389\) −28.8444 −1.46247 −0.731235 0.682126i \(-0.761056\pi\)
−0.731235 + 0.682126i \(0.761056\pi\)
\(390\) 0 0
\(391\) −13.0000 −0.657438
\(392\) 0 0
\(393\) 0 0
\(394\) 4.00000 0.201517
\(395\) −13.0000 −0.654101
\(396\) 0 0
\(397\) −18.0278 −0.904787 −0.452394 0.891818i \(-0.649430\pi\)
−0.452394 + 0.891818i \(0.649430\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −14.4222 −0.717532
\(405\) 0 0
\(406\) 52.0000 2.58072
\(407\) −10.8167 −0.536162
\(408\) 0 0
\(409\) −21.6333 −1.06970 −0.534849 0.844948i \(-0.679632\pi\)
−0.534849 + 0.844948i \(0.679632\pi\)
\(410\) −22.0000 −1.08650
\(411\) 0 0
\(412\) −20.0000 −0.985329
\(413\) −43.2666 −2.12901
\(414\) 0 0
\(415\) −6.00000 −0.294528
\(416\) 0 0
\(417\) 0 0
\(418\) 43.2666 2.11624
\(419\) −21.6333 −1.05686 −0.528428 0.848978i \(-0.677218\pi\)
−0.528428 + 0.848978i \(0.677218\pi\)
\(420\) 0 0
\(421\) 7.21110 0.351448 0.175724 0.984440i \(-0.443773\pi\)
0.175724 + 0.984440i \(0.443773\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.60555 −0.174895
\(426\) 0 0
\(427\) −46.8722 −2.26830
\(428\) 7.21110 0.348562
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 52.0000 2.49608
\(435\) 0 0
\(436\) 28.8444 1.38140
\(437\) 26.0000 1.24375
\(438\) 0 0
\(439\) −25.0000 −1.19318 −0.596592 0.802544i \(-0.703479\pi\)
−0.596592 + 0.802544i \(0.703479\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.8167 −0.513915 −0.256957 0.966423i \(-0.582720\pi\)
−0.256957 + 0.966423i \(0.582720\pi\)
\(444\) 0 0
\(445\) 3.00000 0.142214
\(446\) −28.8444 −1.36582
\(447\) 0 0
\(448\) 28.8444 1.36277
\(449\) 27.0000 1.27421 0.637104 0.770778i \(-0.280132\pi\)
0.637104 + 0.770778i \(0.280132\pi\)
\(450\) 0 0
\(451\) 33.0000 1.55391
\(452\) 14.4222 0.678363
\(453\) 0 0
\(454\) 36.0000 1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) 18.0278 0.843303 0.421651 0.906758i \(-0.361451\pi\)
0.421651 + 0.906758i \(0.361451\pi\)
\(458\) 28.8444 1.34781
\(459\) 0 0
\(460\) −7.21110 −0.336219
\(461\) −5.00000 −0.232873 −0.116437 0.993198i \(-0.537147\pi\)
−0.116437 + 0.993198i \(0.537147\pi\)
\(462\) 0 0
\(463\) −18.0278 −0.837821 −0.418910 0.908028i \(-0.637588\pi\)
−0.418910 + 0.908028i \(0.637588\pi\)
\(464\) 28.8444 1.33907
\(465\) 0 0
\(466\) −50.4777 −2.33834
\(467\) 32.4500 1.50161 0.750803 0.660527i \(-0.229667\pi\)
0.750803 + 0.660527i \(0.229667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8.00000 0.369012
\(471\) 0 0
\(472\) 0 0
\(473\) 12.0000 0.551761
\(474\) 0 0
\(475\) 7.21110 0.330868
\(476\) 26.0000 1.19171
\(477\) 0 0
\(478\) 14.0000 0.640345
\(479\) −3.00000 −0.137073 −0.0685367 0.997649i \(-0.521833\pi\)
−0.0685367 + 0.997649i \(0.521833\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 43.2666 1.97074
\(483\) 0 0
\(484\) −4.00000 −0.181818
\(485\) −3.60555 −0.163720
\(486\) 0 0
\(487\) −10.8167 −0.490149 −0.245075 0.969504i \(-0.578812\pi\)
−0.245075 + 0.969504i \(0.578812\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −12.0000 −0.542105
\(491\) 7.21110 0.325433 0.162716 0.986673i \(-0.447974\pi\)
0.162716 + 0.986673i \(0.447974\pi\)
\(492\) 0 0
\(493\) 26.0000 1.17098
\(494\) 0 0
\(495\) 0 0
\(496\) 28.8444 1.29515
\(497\) 18.0278 0.808655
\(498\) 0 0
\(499\) 28.8444 1.29125 0.645627 0.763653i \(-0.276596\pi\)
0.645627 + 0.763653i \(0.276596\pi\)
\(500\) −2.00000 −0.0894427
\(501\) 0 0
\(502\) 43.2666 1.93108
\(503\) 14.4222 0.643054 0.321527 0.946900i \(-0.395804\pi\)
0.321527 + 0.946900i \(0.395804\pi\)
\(504\) 0 0
\(505\) 7.21110 0.320890
\(506\) 21.6333 0.961718
\(507\) 0 0
\(508\) 0 0
\(509\) −15.0000 −0.664863 −0.332432 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 0 0
\(511\) −26.0000 −1.15017
\(512\) 32.0000 1.41421
\(513\) 0 0
\(514\) 43.2666 1.90841
\(515\) 10.0000 0.440653
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 26.0000 1.14237
\(519\) 0 0
\(520\) 0 0
\(521\) 28.8444 1.26370 0.631848 0.775092i \(-0.282297\pi\)
0.631848 + 0.775092i \(0.282297\pi\)
\(522\) 0 0
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) −43.2666 −1.89011
\(525\) 0 0
\(526\) 0 0
\(527\) 26.0000 1.13258
\(528\) 0 0
\(529\) −10.0000 −0.434783
\(530\) −21.6333 −0.939691
\(531\) 0 0
\(532\) −52.0000 −2.25449
\(533\) 0 0
\(534\) 0 0
\(535\) −3.60555 −0.155882
\(536\) 0 0
\(537\) 0 0
\(538\) 14.4222 0.621785
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) 7.21110 0.310030 0.155015 0.987912i \(-0.450457\pi\)
0.155015 + 0.987912i \(0.450457\pi\)
\(542\) 57.6888 2.47795
\(543\) 0 0
\(544\) 28.8444 1.23669
\(545\) −14.4222 −0.617779
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 24.0000 1.02523
\(549\) 0 0
\(550\) 6.00000 0.255841
\(551\) −52.0000 −2.21527
\(552\) 0 0
\(553\) −46.8722 −1.99321
\(554\) −8.00000 −0.339887
\(555\) 0 0
\(556\) 14.0000 0.593732
\(557\) −42.0000 −1.77960 −0.889799 0.456354i \(-0.849155\pi\)
−0.889799 + 0.456354i \(0.849155\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −14.4222 −0.609449
\(561\) 0 0
\(562\) 60.0000 2.53095
\(563\) 32.4500 1.36760 0.683801 0.729668i \(-0.260325\pi\)
0.683801 + 0.729668i \(0.260325\pi\)
\(564\) 0 0
\(565\) −7.21110 −0.303373
\(566\) −52.0000 −2.18572
\(567\) 0 0
\(568\) 0 0
\(569\) 43.2666 1.81383 0.906915 0.421313i \(-0.138431\pi\)
0.906915 + 0.421313i \(0.138431\pi\)
\(570\) 0 0
\(571\) 13.0000 0.544033 0.272017 0.962293i \(-0.412309\pi\)
0.272017 + 0.962293i \(0.412309\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −79.3221 −3.31084
\(575\) 3.60555 0.150362
\(576\) 0 0
\(577\) 3.60555 0.150101 0.0750505 0.997180i \(-0.476088\pi\)
0.0750505 + 0.997180i \(0.476088\pi\)
\(578\) −8.00000 −0.332756
\(579\) 0 0
\(580\) 14.4222 0.598849
\(581\) −21.6333 −0.897501
\(582\) 0 0
\(583\) 32.4500 1.34394
\(584\) 0 0
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) −52.0000 −2.14262
\(590\) −24.0000 −0.988064
\(591\) 0 0
\(592\) 14.4222 0.592749
\(593\) −4.00000 −0.164260 −0.0821302 0.996622i \(-0.526172\pi\)
−0.0821302 + 0.996622i \(0.526172\pi\)
\(594\) 0 0
\(595\) −13.0000 −0.532948
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 0 0
\(599\) 7.21110 0.294638 0.147319 0.989089i \(-0.452936\pi\)
0.147319 + 0.989089i \(0.452936\pi\)
\(600\) 0 0
\(601\) −13.0000 −0.530281 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) −28.8444 −1.17561
\(603\) 0 0
\(604\) −14.4222 −0.586831
\(605\) 2.00000 0.0813116
\(606\) 0 0
\(607\) −20.0000 −0.811775 −0.405887 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) −57.6888 −2.33959
\(609\) 0 0
\(610\) −26.0000 −1.05271
\(611\) 0 0
\(612\) 0 0
\(613\) 3.60555 0.145627 0.0728134 0.997346i \(-0.476802\pi\)
0.0728134 + 0.997346i \(0.476802\pi\)
\(614\) −36.0555 −1.45508
\(615\) 0 0
\(616\) 0 0
\(617\) 34.0000 1.36879 0.684394 0.729112i \(-0.260067\pi\)
0.684394 + 0.729112i \(0.260067\pi\)
\(618\) 0 0
\(619\) 14.4222 0.579677 0.289839 0.957076i \(-0.406398\pi\)
0.289839 + 0.957076i \(0.406398\pi\)
\(620\) 14.4222 0.579210
\(621\) 0 0
\(622\) 28.8444 1.15656
\(623\) 10.8167 0.433360
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 52.0000 2.07834
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) 13.0000 0.518344
\(630\) 0 0
\(631\) −28.8444 −1.14828 −0.574139 0.818758i \(-0.694663\pi\)
−0.574139 + 0.818758i \(0.694663\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 64.0000 2.54176
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −43.2666 −1.71294
\(639\) 0 0
\(640\) 0 0
\(641\) −43.2666 −1.70893 −0.854464 0.519510i \(-0.826114\pi\)
−0.854464 + 0.519510i \(0.826114\pi\)
\(642\) 0 0
\(643\) 25.2389 0.995323 0.497662 0.867371i \(-0.334192\pi\)
0.497662 + 0.867371i \(0.334192\pi\)
\(644\) −26.0000 −1.02454
\(645\) 0 0
\(646\) −52.0000 −2.04591
\(647\) −18.0278 −0.708744 −0.354372 0.935104i \(-0.615305\pi\)
−0.354372 + 0.935104i \(0.615305\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 0 0
\(652\) 21.6333 0.847226
\(653\) 7.21110 0.282192 0.141096 0.989996i \(-0.454937\pi\)
0.141096 + 0.989996i \(0.454937\pi\)
\(654\) 0 0
\(655\) 21.6333 0.845283
\(656\) −44.0000 −1.71791
\(657\) 0 0
\(658\) 28.8444 1.12447
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −7.21110 −0.280479 −0.140240 0.990118i \(-0.544787\pi\)
−0.140240 + 0.990118i \(0.544787\pi\)
\(662\) −57.6888 −2.24214
\(663\) 0 0
\(664\) 0 0
\(665\) 26.0000 1.00824
\(666\) 0 0
\(667\) −26.0000 −1.00672
\(668\) 20.0000 0.773823
\(669\) 0 0
\(670\) 0 0
\(671\) 39.0000 1.50558
\(672\) 0 0
\(673\) −40.0000 −1.54189 −0.770943 0.636904i \(-0.780215\pi\)
−0.770943 + 0.636904i \(0.780215\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.8167 0.415718 0.207859 0.978159i \(-0.433351\pi\)
0.207859 + 0.978159i \(0.433351\pi\)
\(678\) 0 0
\(679\) −13.0000 −0.498894
\(680\) 0 0
\(681\) 0 0
\(682\) −43.2666 −1.65676
\(683\) 38.0000 1.45403 0.727015 0.686622i \(-0.240907\pi\)
0.727015 + 0.686622i \(0.240907\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 7.21110 0.275321
\(687\) 0 0
\(688\) −16.0000 −0.609994
\(689\) 0 0
\(690\) 0 0
\(691\) −14.4222 −0.548647 −0.274323 0.961638i \(-0.588454\pi\)
−0.274323 + 0.961638i \(0.588454\pi\)
\(692\) −14.4222 −0.548250
\(693\) 0 0
\(694\) −50.4777 −1.91611
\(695\) −7.00000 −0.265525
\(696\) 0 0
\(697\) −39.6611 −1.50227
\(698\) 14.4222 0.545889
\(699\) 0 0
\(700\) −7.21110 −0.272554
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −26.0000 −0.980609
\(704\) −24.0000 −0.904534
\(705\) 0 0
\(706\) −48.0000 −1.80650
\(707\) 26.0000 0.977831
\(708\) 0 0
\(709\) 28.8444 1.08327 0.541637 0.840612i \(-0.317805\pi\)
0.541637 + 0.840612i \(0.317805\pi\)
\(710\) 10.0000 0.375293
\(711\) 0 0
\(712\) 0 0
\(713\) −26.0000 −0.973708
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 8.00000 0.298557
\(719\) 21.6333 0.806786 0.403393 0.915027i \(-0.367831\pi\)
0.403393 + 0.915027i \(0.367831\pi\)
\(720\) 0 0
\(721\) 36.0555 1.34278
\(722\) 66.0000 2.45627
\(723\) 0 0
\(724\) −6.00000 −0.222988
\(725\) −7.21110 −0.267814
\(726\) 0 0
\(727\) −26.0000 −0.964287 −0.482143 0.876092i \(-0.660142\pi\)
−0.482143 + 0.876092i \(0.660142\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −14.4222 −0.533790
\(731\) −14.4222 −0.533425
\(732\) 0 0
\(733\) −32.4500 −1.19857 −0.599283 0.800537i \(-0.704548\pi\)
−0.599283 + 0.800537i \(0.704548\pi\)
\(734\) −36.0000 −1.32878
\(735\) 0 0
\(736\) −28.8444 −1.06322
\(737\) 0 0
\(738\) 0 0
\(739\) −21.6333 −0.795794 −0.397897 0.917430i \(-0.630260\pi\)
−0.397897 + 0.917430i \(0.630260\pi\)
\(740\) 7.21110 0.265085
\(741\) 0 0
\(742\) −78.0000 −2.86347
\(743\) 2.00000 0.0733729 0.0366864 0.999327i \(-0.488320\pi\)
0.0366864 + 0.999327i \(0.488320\pi\)
\(744\) 0 0
\(745\) −5.00000 −0.183186
\(746\) −52.0000 −1.90386
\(747\) 0 0
\(748\) −21.6333 −0.790992
\(749\) −13.0000 −0.475010
\(750\) 0 0
\(751\) −25.0000 −0.912263 −0.456131 0.889912i \(-0.650765\pi\)
−0.456131 + 0.889912i \(0.650765\pi\)
\(752\) 16.0000 0.583460
\(753\) 0 0
\(754\) 0 0
\(755\) 7.21110 0.262439
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 43.2666 1.57151
\(759\) 0 0
\(760\) 0 0
\(761\) −38.0000 −1.37750 −0.688749 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 0 0
\(763\) −52.0000 −1.88253
\(764\) 14.4222 0.521777
\(765\) 0 0
\(766\) 16.0000 0.578103
\(767\) 0 0
\(768\) 0 0
\(769\) −7.21110 −0.260039 −0.130020 0.991511i \(-0.541504\pi\)
−0.130020 + 0.991511i \(0.541504\pi\)
\(770\) 21.6333 0.779610
\(771\) 0 0
\(772\) −7.21110 −0.259533
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) −7.21110 −0.259030
\(776\) 0 0
\(777\) 0 0
\(778\) −57.6888 −2.06824
\(779\) 79.3221 2.84201
\(780\) 0 0
\(781\) −15.0000 −0.536742
\(782\) −26.0000 −0.929758
\(783\) 0 0
\(784\) −24.0000 −0.857143
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) 28.8444 1.02819 0.514096 0.857733i \(-0.328127\pi\)
0.514096 + 0.857733i \(0.328127\pi\)
\(788\) 4.00000 0.142494
\(789\) 0 0
\(790\) −26.0000 −0.925038
\(791\) −26.0000 −0.924454
\(792\) 0 0
\(793\) 0 0
\(794\) −36.0555 −1.27956
\(795\) 0 0
\(796\) 0 0
\(797\) −39.6611 −1.40487 −0.702433 0.711749i \(-0.747903\pi\)
−0.702433 + 0.711749i \(0.747903\pi\)
\(798\) 0 0
\(799\) 14.4222 0.510221
\(800\) −8.00000 −0.282843
\(801\) 0 0
\(802\) −20.0000 −0.706225
\(803\) 21.6333 0.763423
\(804\) 0 0
\(805\) 13.0000 0.458190
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 21.6333 0.760587 0.380293 0.924866i \(-0.375823\pi\)
0.380293 + 0.924866i \(0.375823\pi\)
\(810\) 0 0
\(811\) −28.8444 −1.01286 −0.506432 0.862280i \(-0.669036\pi\)
−0.506432 + 0.862280i \(0.669036\pi\)
\(812\) 52.0000 1.82484
\(813\) 0 0
\(814\) −21.6333 −0.758247
\(815\) −10.8167 −0.378891
\(816\) 0 0
\(817\) 28.8444 1.00914
\(818\) −43.2666 −1.51278
\(819\) 0 0
\(820\) −22.0000 −0.768273
\(821\) 15.0000 0.523504 0.261752 0.965135i \(-0.415700\pi\)
0.261752 + 0.965135i \(0.415700\pi\)
\(822\) 0 0
\(823\) −30.0000 −1.04573 −0.522867 0.852414i \(-0.675138\pi\)
−0.522867 + 0.852414i \(0.675138\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −86.5332 −3.01088
\(827\) −4.00000 −0.139094 −0.0695468 0.997579i \(-0.522155\pi\)
−0.0695468 + 0.997579i \(0.522155\pi\)
\(828\) 0 0
\(829\) 26.0000 0.903017 0.451509 0.892267i \(-0.350886\pi\)
0.451509 + 0.892267i \(0.350886\pi\)
\(830\) −12.0000 −0.416526
\(831\) 0 0
\(832\) 0 0
\(833\) −21.6333 −0.749550
\(834\) 0 0
\(835\) −10.0000 −0.346064
\(836\) 43.2666 1.49641
\(837\) 0 0
\(838\) −43.2666 −1.49462
\(839\) 51.0000 1.76072 0.880358 0.474310i \(-0.157302\pi\)
0.880358 + 0.474310i \(0.157302\pi\)
\(840\) 0 0
\(841\) 23.0000 0.793103
\(842\) 14.4222 0.497022
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 7.21110 0.247776
\(848\) −43.2666 −1.48578
\(849\) 0 0
\(850\) −7.21110 −0.247339
\(851\) −13.0000 −0.445634
\(852\) 0 0
\(853\) −54.0833 −1.85178 −0.925888 0.377798i \(-0.876681\pi\)
−0.925888 + 0.377798i \(0.876681\pi\)
\(854\) −93.7443 −3.20787
\(855\) 0 0
\(856\) 0 0
\(857\) 18.0278 0.615816 0.307908 0.951416i \(-0.400371\pi\)
0.307908 + 0.951416i \(0.400371\pi\)
\(858\) 0 0
\(859\) −13.0000 −0.443554 −0.221777 0.975097i \(-0.571186\pi\)
−0.221777 + 0.975097i \(0.571186\pi\)
\(860\) −8.00000 −0.272798
\(861\) 0 0
\(862\) 48.0000 1.63489
\(863\) −6.00000 −0.204242 −0.102121 0.994772i \(-0.532563\pi\)
−0.102121 + 0.994772i \(0.532563\pi\)
\(864\) 0 0
\(865\) 7.21110 0.245185
\(866\) −52.0000 −1.76703
\(867\) 0 0
\(868\) 52.0000 1.76500
\(869\) 39.0000 1.32298
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 52.0000 1.75893
\(875\) 3.60555 0.121890
\(876\) 0 0
\(877\) 50.4777 1.70451 0.852256 0.523125i \(-0.175234\pi\)
0.852256 + 0.523125i \(0.175234\pi\)
\(878\) −50.0000 −1.68742
\(879\) 0 0
\(880\) 12.0000 0.404520
\(881\) 43.2666 1.45769 0.728845 0.684679i \(-0.240058\pi\)
0.728845 + 0.684679i \(0.240058\pi\)
\(882\) 0 0
\(883\) 26.0000 0.874970 0.437485 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −21.6333 −0.726785
\(887\) 25.2389 0.847438 0.423719 0.905794i \(-0.360724\pi\)
0.423719 + 0.905794i \(0.360724\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 6.00000 0.201120
\(891\) 0 0
\(892\) −28.8444 −0.965782
\(893\) −28.8444 −0.965241
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 54.0000 1.80200
\(899\) 52.0000 1.73430
\(900\) 0 0
\(901\) −39.0000 −1.29928
\(902\) 66.0000 2.19756
\(903\) 0 0
\(904\) 0 0
\(905\) 3.00000 0.0997234
\(906\) 0 0
\(907\) −52.0000 −1.72663 −0.863316 0.504664i \(-0.831616\pi\)
−0.863316 + 0.504664i \(0.831616\pi\)
\(908\) 36.0000 1.19470
\(909\) 0 0
\(910\) 0 0
\(911\) 36.0555 1.19457 0.597286 0.802028i \(-0.296246\pi\)
0.597286 + 0.802028i \(0.296246\pi\)
\(912\) 0 0
\(913\) 18.0000 0.595713
\(914\) 36.0555 1.19261
\(915\) 0 0
\(916\) 28.8444 0.953046
\(917\) 78.0000 2.57579
\(918\) 0 0
\(919\) 13.0000 0.428830 0.214415 0.976743i \(-0.431215\pi\)
0.214415 + 0.976743i \(0.431215\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −10.0000 −0.329332
\(923\) 0 0
\(924\) 0 0
\(925\) −3.60555 −0.118550
\(926\) −36.0555 −1.18486
\(927\) 0 0
\(928\) 57.6888 1.89373
\(929\) 5.00000 0.164045 0.0820223 0.996630i \(-0.473862\pi\)
0.0820223 + 0.996630i \(0.473862\pi\)
\(930\) 0 0
\(931\) 43.2666 1.41801
\(932\) −50.4777 −1.65345
\(933\) 0 0
\(934\) 64.8999 2.12359
\(935\) 10.8167 0.353742
\(936\) 0 0
\(937\) −52.0000 −1.69877 −0.849383 0.527777i \(-0.823026\pi\)
−0.849383 + 0.527777i \(0.823026\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 8.00000 0.260931
\(941\) −59.0000 −1.92335 −0.961673 0.274201i \(-0.911587\pi\)
−0.961673 + 0.274201i \(0.911587\pi\)
\(942\) 0 0
\(943\) 39.6611 1.29154
\(944\) −48.0000 −1.56227
\(945\) 0 0
\(946\) 24.0000 0.780307
\(947\) 42.0000 1.36482 0.682408 0.730971i \(-0.260933\pi\)
0.682408 + 0.730971i \(0.260933\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 14.4222 0.467918
\(951\) 0 0
\(952\) 0 0
\(953\) 10.8167 0.350386 0.175193 0.984534i \(-0.443945\pi\)
0.175193 + 0.984534i \(0.443945\pi\)
\(954\) 0 0
\(955\) −7.21110 −0.233346
\(956\) 14.0000 0.452792
\(957\) 0 0
\(958\) −6.00000 −0.193851
\(959\) −43.2666 −1.39715
\(960\) 0 0
\(961\) 21.0000 0.677419
\(962\) 0 0
\(963\) 0 0
\(964\) 43.2666 1.39352
\(965\) 3.60555 0.116067
\(966\) 0 0
\(967\) 14.4222 0.463787 0.231893 0.972741i \(-0.425508\pi\)
0.231893 + 0.972741i \(0.425508\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −7.21110 −0.231535
\(971\) 21.6333 0.694246 0.347123 0.937820i \(-0.387159\pi\)
0.347123 + 0.937820i \(0.387159\pi\)
\(972\) 0 0
\(973\) −25.2389 −0.809121
\(974\) −21.6333 −0.693176
\(975\) 0 0
\(976\) −52.0000 −1.66448
\(977\) 2.00000 0.0639857 0.0319928 0.999488i \(-0.489815\pi\)
0.0319928 + 0.999488i \(0.489815\pi\)
\(978\) 0 0
\(979\) −9.00000 −0.287641
\(980\) −12.0000 −0.383326
\(981\) 0 0
\(982\) 14.4222 0.460231
\(983\) −4.00000 −0.127580 −0.0637901 0.997963i \(-0.520319\pi\)
−0.0637901 + 0.997963i \(0.520319\pi\)
\(984\) 0 0
\(985\) −2.00000 −0.0637253
\(986\) 52.0000 1.65602
\(987\) 0 0
\(988\) 0 0
\(989\) 14.4222 0.458599
\(990\) 0 0
\(991\) −5.00000 −0.158830 −0.0794151 0.996842i \(-0.525305\pi\)
−0.0794151 + 0.996842i \(0.525305\pi\)
\(992\) 57.6888 1.83162
\(993\) 0 0
\(994\) 36.0555 1.14361
\(995\) 0 0
\(996\) 0 0
\(997\) −6.00000 −0.190022 −0.0950110 0.995476i \(-0.530289\pi\)
−0.0950110 + 0.995476i \(0.530289\pi\)
\(998\) 57.6888 1.82611
\(999\) 0 0
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 7605.2.a.bl.1.1 2
3.2 odd 2 7605.2.a.w.1.1 2
13.5 odd 4 585.2.b.f.181.1 4
13.8 odd 4 585.2.b.f.181.4 yes 4
13.12 even 2 7605.2.a.w.1.2 2
39.5 even 4 585.2.b.f.181.3 yes 4
39.8 even 4 585.2.b.f.181.2 yes 4
39.38 odd 2 inner 7605.2.a.bl.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.b.f.181.1 4 13.5 odd 4
585.2.b.f.181.2 yes 4 39.8 even 4
585.2.b.f.181.3 yes 4 39.5 even 4
585.2.b.f.181.4 yes 4 13.8 odd 4
7605.2.a.w.1.1 2 3.2 odd 2
7605.2.a.w.1.2 2 13.12 even 2
7605.2.a.bl.1.1 2 1.1 even 1 trivial
7605.2.a.bl.1.2 2 39.38 odd 2 inner