Properties

Label 1900.3.e.f.1101.3
Level $1900$
Weight $3$
Character 1900.1101
Analytic conductor $51.771$
Analytic rank $0$
Dimension $12$
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] = [1900,3,Mod(1101,1900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1900.1101");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.e (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(51.7712502285\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 62x^{10} + 1445x^{8} + 15924x^{6} + 83244x^{4} + 170640x^{2} + 55600 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{12}\cdot 5 \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1101.3
Root \(-3.42504i\) of defining polynomial
Character \(\chi\) \(=\) 1900.1101
Dual form 1900.3.e.f.1101.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.42504i q^{3} -9.18599 q^{7} -2.73093 q^{9} +O(q^{10})\) \(q-3.42504i q^{3} -9.18599 q^{7} -2.73093 q^{9} +11.4382 q^{11} +10.1235i q^{13} +4.19261 q^{17} +(10.8104 - 15.6248i) q^{19} +31.4624i q^{21} +0.952351 q^{23} -21.4719i q^{27} -9.43887i q^{29} +8.52508i q^{31} -39.1762i q^{33} -20.0029i q^{37} +34.6736 q^{39} +61.2499i q^{41} +57.9875 q^{43} +35.3773 q^{47} +35.3824 q^{49} -14.3599i q^{51} -57.6953i q^{53} +(-53.5158 - 37.0260i) q^{57} -16.7603i q^{59} -32.2192 q^{61} +25.0863 q^{63} +6.07252i q^{67} -3.26184i q^{69} -113.671i q^{71} +27.9670 q^{73} -105.071 q^{77} -65.7698i q^{79} -98.1204 q^{81} -60.2358 q^{83} -32.3286 q^{87} -97.9852i q^{89} -92.9948i q^{91} +29.1988 q^{93} -92.0255i q^{97} -31.2368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 12 q^{7} - 16 q^{9} - 32 q^{11} + 12 q^{17} + 24 q^{19} - 4 q^{23} + 124 q^{39} + 176 q^{43} + 72 q^{47} - 24 q^{49} - 140 q^{57} + 152 q^{61} - 48 q^{63} + 148 q^{73} - 376 q^{77} - 468 q^{81} + 208 q^{83} + 84 q^{87} + 184 q^{93} + 392 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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 0
\(3\) 3.42504i 1.14168i −0.821061 0.570841i \(-0.806617\pi\)
0.821061 0.570841i \(-0.193383\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −9.18599 −1.31228 −0.656142 0.754637i \(-0.727813\pi\)
−0.656142 + 0.754637i \(0.727813\pi\)
\(8\) 0 0
\(9\) −2.73093 −0.303436
\(10\) 0 0
\(11\) 11.4382 1.03983 0.519916 0.854217i \(-0.325963\pi\)
0.519916 + 0.854217i \(0.325963\pi\)
\(12\) 0 0
\(13\) 10.1235i 0.778734i 0.921083 + 0.389367i \(0.127306\pi\)
−0.921083 + 0.389367i \(0.872694\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.19261 0.246624 0.123312 0.992368i \(-0.460648\pi\)
0.123312 + 0.992368i \(0.460648\pi\)
\(18\) 0 0
\(19\) 10.8104 15.6248i 0.568967 0.822360i
\(20\) 0 0
\(21\) 31.4624i 1.49821i
\(22\) 0 0
\(23\) 0.952351 0.0414066 0.0207033 0.999786i \(-0.493409\pi\)
0.0207033 + 0.999786i \(0.493409\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 21.4719i 0.795254i
\(28\) 0 0
\(29\) 9.43887i 0.325478i −0.986669 0.162739i \(-0.947967\pi\)
0.986669 0.162739i \(-0.0520329\pi\)
\(30\) 0 0
\(31\) 8.52508i 0.275002i 0.990502 + 0.137501i \(0.0439071\pi\)
−0.990502 + 0.137501i \(0.956093\pi\)
\(32\) 0 0
\(33\) 39.1762i 1.18716i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 20.0029i 0.540618i −0.962774 0.270309i \(-0.912874\pi\)
0.962774 0.270309i \(-0.0871258\pi\)
\(38\) 0 0
\(39\) 34.6736 0.889066
\(40\) 0 0
\(41\) 61.2499i 1.49390i 0.664881 + 0.746950i \(0.268482\pi\)
−0.664881 + 0.746950i \(0.731518\pi\)
\(42\) 0 0
\(43\) 57.9875 1.34855 0.674273 0.738482i \(-0.264457\pi\)
0.674273 + 0.738482i \(0.264457\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 35.3773 0.752709 0.376355 0.926476i \(-0.377177\pi\)
0.376355 + 0.926476i \(0.377177\pi\)
\(48\) 0 0
\(49\) 35.3824 0.722091
\(50\) 0 0
\(51\) 14.3599i 0.281566i
\(52\) 0 0
\(53\) 57.6953i 1.08859i −0.838893 0.544296i \(-0.816797\pi\)
0.838893 0.544296i \(-0.183203\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −53.5158 37.0260i −0.938873 0.649579i
\(58\) 0 0
\(59\) 16.7603i 0.284073i −0.989861 0.142037i \(-0.954635\pi\)
0.989861 0.142037i \(-0.0453651\pi\)
\(60\) 0 0
\(61\) −32.2192 −0.528183 −0.264092 0.964498i \(-0.585072\pi\)
−0.264092 + 0.964498i \(0.585072\pi\)
\(62\) 0 0
\(63\) 25.0863 0.398195
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.07252i 0.0906346i 0.998973 + 0.0453173i \(0.0144299\pi\)
−0.998973 + 0.0453173i \(0.985570\pi\)
\(68\) 0 0
\(69\) 3.26184i 0.0472731i
\(70\) 0 0
\(71\) 113.671i 1.60101i −0.599328 0.800503i \(-0.704566\pi\)
0.599328 0.800503i \(-0.295434\pi\)
\(72\) 0 0
\(73\) 27.9670 0.383109 0.191554 0.981482i \(-0.438647\pi\)
0.191554 + 0.981482i \(0.438647\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −105.071 −1.36456
\(78\) 0 0
\(79\) 65.7698i 0.832529i −0.909244 0.416264i \(-0.863339\pi\)
0.909244 0.416264i \(-0.136661\pi\)
\(80\) 0 0
\(81\) −98.1204 −1.21136
\(82\) 0 0
\(83\) −60.2358 −0.725733 −0.362866 0.931841i \(-0.618202\pi\)
−0.362866 + 0.931841i \(0.618202\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −32.3286 −0.371593
\(88\) 0 0
\(89\) 97.9852i 1.10096i −0.834849 0.550478i \(-0.814445\pi\)
0.834849 0.550478i \(-0.185555\pi\)
\(90\) 0 0
\(91\) 92.9948i 1.02192i
\(92\) 0 0
\(93\) 29.1988 0.313965
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 92.0255i 0.948717i −0.880332 0.474358i \(-0.842680\pi\)
0.880332 0.474358i \(-0.157320\pi\)
\(98\) 0 0
\(99\) −31.2368 −0.315523
\(100\) 0 0
\(101\) 64.7709 0.641296 0.320648 0.947198i \(-0.396099\pi\)
0.320648 + 0.947198i \(0.396099\pi\)
\(102\) 0 0
\(103\) 204.226i 1.98278i 0.130940 + 0.991390i \(0.458200\pi\)
−0.130940 + 0.991390i \(0.541800\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 203.574i 1.90256i −0.308324 0.951281i \(-0.599768\pi\)
0.308324 0.951281i \(-0.400232\pi\)
\(108\) 0 0
\(109\) 63.6932i 0.584341i −0.956366 0.292171i \(-0.905622\pi\)
0.956366 0.292171i \(-0.0943775\pi\)
\(110\) 0 0
\(111\) −68.5107 −0.617213
\(112\) 0 0
\(113\) 2.01143i 0.0178003i −0.999960 0.00890013i \(-0.997167\pi\)
0.999960 0.00890013i \(-0.00283304\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 27.6467i 0.236296i
\(118\) 0 0
\(119\) −38.5133 −0.323641
\(120\) 0 0
\(121\) 9.83149 0.0812520
\(122\) 0 0
\(123\) 209.783 1.70556
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 41.7788i 0.328967i 0.986380 + 0.164484i \(0.0525958\pi\)
−0.986380 + 0.164484i \(0.947404\pi\)
\(128\) 0 0
\(129\) 198.610i 1.53961i
\(130\) 0 0
\(131\) −50.6875 −0.386928 −0.193464 0.981107i \(-0.561972\pi\)
−0.193464 + 0.981107i \(0.561972\pi\)
\(132\) 0 0
\(133\) −99.3041 + 143.530i −0.746647 + 1.07917i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −30.0467 −0.219319 −0.109659 0.993969i \(-0.534976\pi\)
−0.109659 + 0.993969i \(0.534976\pi\)
\(138\) 0 0
\(139\) −210.679 −1.51567 −0.757837 0.652444i \(-0.773744\pi\)
−0.757837 + 0.652444i \(0.773744\pi\)
\(140\) 0 0
\(141\) 121.169i 0.859354i
\(142\) 0 0
\(143\) 115.795i 0.809753i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 121.186i 0.824397i
\(148\) 0 0
\(149\) −263.989 −1.77174 −0.885868 0.463938i \(-0.846436\pi\)
−0.885868 + 0.463938i \(0.846436\pi\)
\(150\) 0 0
\(151\) 90.3173i 0.598128i 0.954233 + 0.299064i \(0.0966743\pi\)
−0.954233 + 0.299064i \(0.903326\pi\)
\(152\) 0 0
\(153\) −11.4497 −0.0748348
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −108.051 −0.688222 −0.344111 0.938929i \(-0.611820\pi\)
−0.344111 + 0.938929i \(0.611820\pi\)
\(158\) 0 0
\(159\) −197.609 −1.24282
\(160\) 0 0
\(161\) −8.74829 −0.0543372
\(162\) 0 0
\(163\) 127.846 0.784333 0.392167 0.919894i \(-0.371726\pi\)
0.392167 + 0.919894i \(0.371726\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 143.920i 0.861798i 0.902400 + 0.430899i \(0.141803\pi\)
−0.902400 + 0.430899i \(0.858197\pi\)
\(168\) 0 0
\(169\) 66.5138 0.393573
\(170\) 0 0
\(171\) −29.5224 + 42.6703i −0.172645 + 0.249534i
\(172\) 0 0
\(173\) 291.098i 1.68265i −0.540532 0.841323i \(-0.681777\pi\)
0.540532 0.841323i \(-0.318223\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −57.4048 −0.324321
\(178\) 0 0
\(179\) 91.3328i 0.510239i −0.966910 0.255120i \(-0.917885\pi\)
0.966910 0.255120i \(-0.0821148\pi\)
\(180\) 0 0
\(181\) 182.671i 1.00923i 0.863344 + 0.504617i \(0.168366\pi\)
−0.863344 + 0.504617i \(0.831634\pi\)
\(182\) 0 0
\(183\) 110.352i 0.603017i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 47.9558 0.256448
\(188\) 0 0
\(189\) 197.240i 1.04360i
\(190\) 0 0
\(191\) 358.406 1.87647 0.938235 0.345998i \(-0.112460\pi\)
0.938235 + 0.345998i \(0.112460\pi\)
\(192\) 0 0
\(193\) 131.778i 0.682786i 0.939921 + 0.341393i \(0.110899\pi\)
−0.939921 + 0.341393i \(0.889101\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −35.9154 −0.182312 −0.0911558 0.995837i \(-0.529056\pi\)
−0.0911558 + 0.995837i \(0.529056\pi\)
\(198\) 0 0
\(199\) 121.742 0.611769 0.305885 0.952069i \(-0.401048\pi\)
0.305885 + 0.952069i \(0.401048\pi\)
\(200\) 0 0
\(201\) 20.7986 0.103476
\(202\) 0 0
\(203\) 86.7054i 0.427120i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2.60080 −0.0125643
\(208\) 0 0
\(209\) 123.651 178.719i 0.591631 0.855117i
\(210\) 0 0
\(211\) 272.967i 1.29368i −0.762626 0.646840i \(-0.776090\pi\)
0.762626 0.646840i \(-0.223910\pi\)
\(212\) 0 0
\(213\) −389.330 −1.82784
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 78.3113i 0.360881i
\(218\) 0 0
\(219\) 95.7881i 0.437388i
\(220\) 0 0
\(221\) 42.4441i 0.192055i
\(222\) 0 0
\(223\) 81.1828i 0.364048i 0.983294 + 0.182024i \(0.0582649\pi\)
−0.983294 + 0.182024i \(0.941735\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 337.268i 1.48576i −0.669423 0.742882i \(-0.733459\pi\)
0.669423 0.742882i \(-0.266541\pi\)
\(228\) 0 0
\(229\) −240.819 −1.05161 −0.525806 0.850605i \(-0.676236\pi\)
−0.525806 + 0.850605i \(0.676236\pi\)
\(230\) 0 0
\(231\) 359.872i 1.55789i
\(232\) 0 0
\(233\) −136.526 −0.585948 −0.292974 0.956120i \(-0.594645\pi\)
−0.292974 + 0.956120i \(0.594645\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −225.264 −0.950483
\(238\) 0 0
\(239\) −320.734 −1.34198 −0.670991 0.741466i \(-0.734131\pi\)
−0.670991 + 0.741466i \(0.734131\pi\)
\(240\) 0 0
\(241\) 359.039i 1.48979i −0.667183 0.744894i \(-0.732500\pi\)
0.667183 0.744894i \(-0.267500\pi\)
\(242\) 0 0
\(243\) 142.820i 0.587736i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 158.179 + 109.439i 0.640400 + 0.443074i
\(248\) 0 0
\(249\) 206.310i 0.828556i
\(250\) 0 0
\(251\) 103.786 0.413490 0.206745 0.978395i \(-0.433713\pi\)
0.206745 + 0.978395i \(0.433713\pi\)
\(252\) 0 0
\(253\) 10.8931 0.0430559
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 56.5607i 0.220080i −0.993927 0.110040i \(-0.964902\pi\)
0.993927 0.110040i \(-0.0350980\pi\)
\(258\) 0 0
\(259\) 183.746i 0.709444i
\(260\) 0 0
\(261\) 25.7769i 0.0987620i
\(262\) 0 0
\(263\) −280.514 −1.06659 −0.533296 0.845929i \(-0.679047\pi\)
−0.533296 + 0.845929i \(0.679047\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −335.603 −1.25694
\(268\) 0 0
\(269\) 102.156i 0.379763i 0.981807 + 0.189881i \(0.0608103\pi\)
−0.981807 + 0.189881i \(0.939190\pi\)
\(270\) 0 0
\(271\) 476.115 1.75688 0.878441 0.477851i \(-0.158584\pi\)
0.878441 + 0.477851i \(0.158584\pi\)
\(272\) 0 0
\(273\) −318.511 −1.16671
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −264.070 −0.953323 −0.476661 0.879087i \(-0.658153\pi\)
−0.476661 + 0.879087i \(0.658153\pi\)
\(278\) 0 0
\(279\) 23.2814i 0.0834457i
\(280\) 0 0
\(281\) 242.447i 0.862800i 0.902161 + 0.431400i \(0.141980\pi\)
−0.902161 + 0.431400i \(0.858020\pi\)
\(282\) 0 0
\(283\) 271.524 0.959450 0.479725 0.877419i \(-0.340736\pi\)
0.479725 + 0.877419i \(0.340736\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 562.641i 1.96042i
\(288\) 0 0
\(289\) −271.422 −0.939176
\(290\) 0 0
\(291\) −315.191 −1.08313
\(292\) 0 0
\(293\) 188.495i 0.643328i −0.946854 0.321664i \(-0.895758\pi\)
0.946854 0.321664i \(-0.104242\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 245.598i 0.826931i
\(298\) 0 0
\(299\) 9.64117i 0.0322447i
\(300\) 0 0
\(301\) −532.672 −1.76968
\(302\) 0 0
\(303\) 221.843i 0.732156i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 262.646i 0.855524i −0.903891 0.427762i \(-0.859302\pi\)
0.903891 0.427762i \(-0.140698\pi\)
\(308\) 0 0
\(309\) 699.484 2.26370
\(310\) 0 0
\(311\) 352.334 1.13291 0.566454 0.824093i \(-0.308315\pi\)
0.566454 + 0.824093i \(0.308315\pi\)
\(312\) 0 0
\(313\) 483.965 1.54621 0.773106 0.634277i \(-0.218702\pi\)
0.773106 + 0.634277i \(0.218702\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 80.3004i 0.253313i −0.991947 0.126657i \(-0.959575\pi\)
0.991947 0.126657i \(-0.0404247\pi\)
\(318\) 0 0
\(319\) 107.963i 0.338443i
\(320\) 0 0
\(321\) −697.251 −2.17212
\(322\) 0 0
\(323\) 45.3238 65.5089i 0.140321 0.202814i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −218.152 −0.667132
\(328\) 0 0
\(329\) −324.976 −0.987769
\(330\) 0 0
\(331\) 583.642i 1.76327i −0.471933 0.881634i \(-0.656444\pi\)
0.471933 0.881634i \(-0.343556\pi\)
\(332\) 0 0
\(333\) 54.6263i 0.164043i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 413.317i 1.22646i 0.789904 + 0.613230i \(0.210130\pi\)
−0.789904 + 0.613230i \(0.789870\pi\)
\(338\) 0 0
\(339\) −6.88924 −0.0203222
\(340\) 0 0
\(341\) 97.5112i 0.285957i
\(342\) 0 0
\(343\) 125.091 0.364696
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −207.384 −0.597648 −0.298824 0.954308i \(-0.596594\pi\)
−0.298824 + 0.954308i \(0.596594\pi\)
\(348\) 0 0
\(349\) −176.833 −0.506684 −0.253342 0.967377i \(-0.581530\pi\)
−0.253342 + 0.967377i \(0.581530\pi\)
\(350\) 0 0
\(351\) 217.371 0.619291
\(352\) 0 0
\(353\) 398.294 1.12831 0.564156 0.825668i \(-0.309202\pi\)
0.564156 + 0.825668i \(0.309202\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 131.910i 0.369495i
\(358\) 0 0
\(359\) 89.1125 0.248224 0.124112 0.992268i \(-0.460392\pi\)
0.124112 + 0.992268i \(0.460392\pi\)
\(360\) 0 0
\(361\) −127.271 337.821i −0.352552 0.935792i
\(362\) 0 0
\(363\) 33.6733i 0.0927639i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 450.345 1.22710 0.613550 0.789656i \(-0.289741\pi\)
0.613550 + 0.789656i \(0.289741\pi\)
\(368\) 0 0
\(369\) 167.269i 0.453303i
\(370\) 0 0
\(371\) 529.989i 1.42854i
\(372\) 0 0
\(373\) 442.338i 1.18589i −0.805242 0.592946i \(-0.797965\pi\)
0.805242 0.592946i \(-0.202035\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 95.5549 0.253461
\(378\) 0 0
\(379\) 573.993i 1.51449i −0.653128 0.757247i \(-0.726544\pi\)
0.653128 0.757247i \(-0.273456\pi\)
\(380\) 0 0
\(381\) 143.094 0.375576
\(382\) 0 0
\(383\) 159.706i 0.416987i 0.978024 + 0.208494i \(0.0668560\pi\)
−0.978024 + 0.208494i \(0.933144\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −158.360 −0.409198
\(388\) 0 0
\(389\) 620.531 1.59519 0.797597 0.603190i \(-0.206104\pi\)
0.797597 + 0.603190i \(0.206104\pi\)
\(390\) 0 0
\(391\) 3.99284 0.0102119
\(392\) 0 0
\(393\) 173.607i 0.441748i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 765.284 1.92767 0.963833 0.266506i \(-0.0858694\pi\)
0.963833 + 0.266506i \(0.0858694\pi\)
\(398\) 0 0
\(399\) 491.595 + 340.121i 1.23207 + 0.852433i
\(400\) 0 0
\(401\) 255.996i 0.638393i −0.947688 0.319197i \(-0.896587\pi\)
0.947688 0.319197i \(-0.103413\pi\)
\(402\) 0 0
\(403\) −86.3040 −0.214154
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 228.796i 0.562152i
\(408\) 0 0
\(409\) 225.432i 0.551179i −0.961275 0.275589i \(-0.911127\pi\)
0.961275 0.275589i \(-0.0888730\pi\)
\(410\) 0 0
\(411\) 102.911i 0.250392i
\(412\) 0 0
\(413\) 153.960i 0.372785i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 721.584i 1.73042i
\(418\) 0 0
\(419\) 314.462 0.750506 0.375253 0.926922i \(-0.377556\pi\)
0.375253 + 0.926922i \(0.377556\pi\)
\(420\) 0 0
\(421\) 354.990i 0.843206i −0.906781 0.421603i \(-0.861468\pi\)
0.906781 0.421603i \(-0.138532\pi\)
\(422\) 0 0
\(423\) −96.6129 −0.228399
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 295.965 0.693127
\(428\) 0 0
\(429\) 396.602 0.924480
\(430\) 0 0
\(431\) 178.559i 0.414290i 0.978310 + 0.207145i \(0.0664172\pi\)
−0.978310 + 0.207145i \(0.933583\pi\)
\(432\) 0 0
\(433\) 37.2858i 0.0861104i 0.999073 + 0.0430552i \(0.0137091\pi\)
−0.999073 + 0.0430552i \(0.986291\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.2953 14.8803i 0.0235590 0.0340511i
\(438\) 0 0
\(439\) 365.662i 0.832944i 0.909149 + 0.416472i \(0.136734\pi\)
−0.909149 + 0.416472i \(0.863266\pi\)
\(440\) 0 0
\(441\) −96.6269 −0.219109
\(442\) 0 0
\(443\) 177.806 0.401367 0.200684 0.979656i \(-0.435684\pi\)
0.200684 + 0.979656i \(0.435684\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 904.172i 2.02276i
\(448\) 0 0
\(449\) 204.290i 0.454988i −0.973780 0.227494i \(-0.926947\pi\)
0.973780 0.227494i \(-0.0730532\pi\)
\(450\) 0 0
\(451\) 700.586i 1.55341i
\(452\) 0 0
\(453\) 309.341 0.682871
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 229.796 0.502837 0.251418 0.967879i \(-0.419103\pi\)
0.251418 + 0.967879i \(0.419103\pi\)
\(458\) 0 0
\(459\) 90.0232i 0.196129i
\(460\) 0 0
\(461\) −249.439 −0.541082 −0.270541 0.962708i \(-0.587203\pi\)
−0.270541 + 0.962708i \(0.587203\pi\)
\(462\) 0 0
\(463\) −907.359 −1.95974 −0.979869 0.199639i \(-0.936023\pi\)
−0.979869 + 0.199639i \(0.936023\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 270.399 0.579013 0.289507 0.957176i \(-0.406509\pi\)
0.289507 + 0.957176i \(0.406509\pi\)
\(468\) 0 0
\(469\) 55.7821i 0.118938i
\(470\) 0 0
\(471\) 370.079i 0.785730i
\(472\) 0 0
\(473\) 663.270 1.40226
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 157.562i 0.330318i
\(478\) 0 0
\(479\) −221.920 −0.463299 −0.231649 0.972799i \(-0.574412\pi\)
−0.231649 + 0.972799i \(0.574412\pi\)
\(480\) 0 0
\(481\) 202.500 0.420997
\(482\) 0 0
\(483\) 29.9633i 0.0620358i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 881.561i 1.81019i 0.425212 + 0.905094i \(0.360199\pi\)
−0.425212 + 0.905094i \(0.639801\pi\)
\(488\) 0 0
\(489\) 437.879i 0.895458i
\(490\) 0 0
\(491\) 91.7890 0.186943 0.0934715 0.995622i \(-0.470204\pi\)
0.0934715 + 0.995622i \(0.470204\pi\)
\(492\) 0 0
\(493\) 39.5736i 0.0802709i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1044.19i 2.10098i
\(498\) 0 0
\(499\) 471.959 0.945809 0.472905 0.881114i \(-0.343205\pi\)
0.472905 + 0.881114i \(0.343205\pi\)
\(500\) 0 0
\(501\) 492.933 0.983899
\(502\) 0 0
\(503\) 888.718 1.76684 0.883418 0.468586i \(-0.155237\pi\)
0.883418 + 0.468586i \(0.155237\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 227.813i 0.449335i
\(508\) 0 0
\(509\) 418.738i 0.822669i 0.911485 + 0.411334i \(0.134937\pi\)
−0.911485 + 0.411334i \(0.865063\pi\)
\(510\) 0 0
\(511\) −256.904 −0.502748
\(512\) 0 0
\(513\) −335.494 232.119i −0.653985 0.452473i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 404.652 0.782692
\(518\) 0 0
\(519\) −997.023 −1.92105
\(520\) 0 0
\(521\) 186.146i 0.357285i −0.983914 0.178643i \(-0.942829\pi\)
0.983914 0.178643i \(-0.0571706\pi\)
\(522\) 0 0
\(523\) 674.426i 1.28953i −0.764380 0.644766i \(-0.776955\pi\)
0.764380 0.644766i \(-0.223045\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 35.7424i 0.0678223i
\(528\) 0 0
\(529\) −528.093 −0.998285
\(530\) 0 0
\(531\) 45.7712i 0.0861981i
\(532\) 0 0
\(533\) −620.066 −1.16335
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −312.819 −0.582531
\(538\) 0 0
\(539\) 404.710 0.750853
\(540\) 0 0
\(541\) −641.545 −1.18585 −0.592925 0.805258i \(-0.702027\pi\)
−0.592925 + 0.805258i \(0.702027\pi\)
\(542\) 0 0
\(543\) 625.657 1.15222
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 183.171i 0.334865i 0.985884 + 0.167432i \(0.0535476\pi\)
−0.985884 + 0.167432i \(0.946452\pi\)
\(548\) 0 0
\(549\) 87.9882 0.160270
\(550\) 0 0
\(551\) −147.481 102.038i −0.267660 0.185187i
\(552\) 0 0
\(553\) 604.161i 1.09251i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 713.778 1.28147 0.640734 0.767763i \(-0.278630\pi\)
0.640734 + 0.767763i \(0.278630\pi\)
\(558\) 0 0
\(559\) 587.039i 1.05016i
\(560\) 0 0
\(561\) 164.251i 0.292782i
\(562\) 0 0
\(563\) 316.069i 0.561401i 0.959795 + 0.280700i \(0.0905667\pi\)
−0.959795 + 0.280700i \(0.909433\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 901.333 1.58965
\(568\) 0 0
\(569\) 883.884i 1.55340i 0.629871 + 0.776699i \(0.283108\pi\)
−0.629871 + 0.776699i \(0.716892\pi\)
\(570\) 0 0
\(571\) 168.849 0.295708 0.147854 0.989009i \(-0.452763\pi\)
0.147854 + 0.989009i \(0.452763\pi\)
\(572\) 0 0
\(573\) 1227.56i 2.14233i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −380.352 −0.659188 −0.329594 0.944123i \(-0.606912\pi\)
−0.329594 + 0.944123i \(0.606912\pi\)
\(578\) 0 0
\(579\) 451.344 0.779524
\(580\) 0 0
\(581\) 553.326 0.952368
\(582\) 0 0
\(583\) 659.929i 1.13195i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −123.630 −0.210613 −0.105306 0.994440i \(-0.533582\pi\)
−0.105306 + 0.994440i \(0.533582\pi\)
\(588\) 0 0
\(589\) 133.203 + 92.1593i 0.226151 + 0.156467i
\(590\) 0 0
\(591\) 123.012i 0.208142i
\(592\) 0 0
\(593\) −191.622 −0.323141 −0.161570 0.986861i \(-0.551656\pi\)
−0.161570 + 0.986861i \(0.551656\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 416.972i 0.698446i
\(598\) 0 0
\(599\) 277.360i 0.463038i −0.972830 0.231519i \(-0.925630\pi\)
0.972830 0.231519i \(-0.0743695\pi\)
\(600\) 0 0
\(601\) 603.631i 1.00438i −0.864758 0.502188i \(-0.832528\pi\)
0.864758 0.502188i \(-0.167472\pi\)
\(602\) 0 0
\(603\) 16.5836i 0.0275018i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 1035.05i 1.70519i −0.522568 0.852597i \(-0.675026\pi\)
0.522568 0.852597i \(-0.324974\pi\)
\(608\) 0 0
\(609\) 296.970 0.487635
\(610\) 0 0
\(611\) 358.144i 0.586160i
\(612\) 0 0
\(613\) −965.052 −1.57431 −0.787155 0.616756i \(-0.788447\pi\)
−0.787155 + 0.616756i \(0.788447\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 967.261 1.56768 0.783842 0.620960i \(-0.213257\pi\)
0.783842 + 0.620960i \(0.213257\pi\)
\(618\) 0 0
\(619\) 995.539 1.60830 0.804151 0.594425i \(-0.202620\pi\)
0.804151 + 0.594425i \(0.202620\pi\)
\(620\) 0 0
\(621\) 20.4487i 0.0329287i
\(622\) 0 0
\(623\) 900.091i 1.44477i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −612.122 423.510i −0.976271 0.675454i
\(628\) 0 0
\(629\) 83.8643i 0.133330i
\(630\) 0 0
\(631\) 689.387 1.09253 0.546266 0.837612i \(-0.316049\pi\)
0.546266 + 0.837612i \(0.316049\pi\)
\(632\) 0 0
\(633\) −934.922 −1.47697
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 358.196i 0.562317i
\(638\) 0 0
\(639\) 310.429i 0.485804i
\(640\) 0 0
\(641\) 732.715i 1.14308i 0.820574 + 0.571540i \(0.193654\pi\)
−0.820574 + 0.571540i \(0.806346\pi\)
\(642\) 0 0
\(643\) 509.087 0.791738 0.395869 0.918307i \(-0.370443\pi\)
0.395869 + 0.918307i \(0.370443\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1046.09 −1.61683 −0.808416 0.588611i \(-0.799675\pi\)
−0.808416 + 0.588611i \(0.799675\pi\)
\(648\) 0 0
\(649\) 191.707i 0.295389i
\(650\) 0 0
\(651\) −268.220 −0.412012
\(652\) 0 0
\(653\) −351.804 −0.538750 −0.269375 0.963035i \(-0.586817\pi\)
−0.269375 + 0.963035i \(0.586817\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −76.3757 −0.116249
\(658\) 0 0
\(659\) 1238.23i 1.87895i 0.342621 + 0.939474i \(0.388685\pi\)
−0.342621 + 0.939474i \(0.611315\pi\)
\(660\) 0 0
\(661\) 414.630i 0.627277i 0.949542 + 0.313638i \(0.101548\pi\)
−0.949542 + 0.313638i \(0.898452\pi\)
\(662\) 0 0
\(663\) 145.373 0.219265
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.98912i 0.0134769i
\(668\) 0 0
\(669\) 278.055 0.415627
\(670\) 0 0
\(671\) −368.528 −0.549222
\(672\) 0 0
\(673\) 1163.57i 1.72892i −0.502698 0.864462i \(-0.667659\pi\)
0.502698 0.864462i \(-0.332341\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 71.7621i 0.106000i 0.998595 + 0.0530001i \(0.0168784\pi\)
−0.998595 + 0.0530001i \(0.983122\pi\)
\(678\) 0 0
\(679\) 845.345i 1.24499i
\(680\) 0 0
\(681\) −1155.16 −1.69627
\(682\) 0 0
\(683\) 558.227i 0.817316i 0.912688 + 0.408658i \(0.134003\pi\)
−0.912688 + 0.408658i \(0.865997\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 824.816i 1.20061i
\(688\) 0 0
\(689\) 584.081 0.847723
\(690\) 0 0
\(691\) 310.776 0.449748 0.224874 0.974388i \(-0.427803\pi\)
0.224874 + 0.974388i \(0.427803\pi\)
\(692\) 0 0
\(693\) 286.941 0.414056
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 256.797i 0.368432i
\(698\) 0 0
\(699\) 467.607i 0.668965i
\(700\) 0 0
\(701\) 940.642 1.34186 0.670929 0.741522i \(-0.265896\pi\)
0.670929 + 0.741522i \(0.265896\pi\)
\(702\) 0 0
\(703\) −312.541 216.238i −0.444582 0.307594i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −594.985 −0.841563
\(708\) 0 0
\(709\) −780.564 −1.10094 −0.550468 0.834856i \(-0.685551\pi\)
−0.550468 + 0.834856i \(0.685551\pi\)
\(710\) 0 0
\(711\) 179.612i 0.252620i
\(712\) 0 0
\(713\) 8.11886i 0.0113869i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1098.53i 1.53212i
\(718\) 0 0
\(719\) −606.339 −0.843308 −0.421654 0.906757i \(-0.638550\pi\)
−0.421654 + 0.906757i \(0.638550\pi\)
\(720\) 0 0
\(721\) 1876.02i 2.60197i
\(722\) 0 0
\(723\) −1229.72 −1.70086
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −266.418 −0.366463 −0.183231 0.983070i \(-0.558656\pi\)
−0.183231 + 0.983070i \(0.558656\pi\)
\(728\) 0 0
\(729\) −393.919 −0.540355
\(730\) 0 0
\(731\) 243.119 0.332584
\(732\) 0 0
\(733\) −951.526 −1.29813 −0.649063 0.760735i \(-0.724839\pi\)
−0.649063 + 0.760735i \(0.724839\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 69.4584i 0.0942448i
\(738\) 0 0
\(739\) 504.613 0.682832 0.341416 0.939912i \(-0.389094\pi\)
0.341416 + 0.939912i \(0.389094\pi\)
\(740\) 0 0
\(741\) 374.835 541.769i 0.505850 0.731133i
\(742\) 0 0
\(743\) 1081.91i 1.45613i 0.685506 + 0.728067i \(0.259581\pi\)
−0.685506 + 0.728067i \(0.740419\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 164.500 0.220214
\(748\) 0 0
\(749\) 1870.03i 2.49670i
\(750\) 0 0
\(751\) 873.565i 1.16320i 0.813474 + 0.581601i \(0.197574\pi\)
−0.813474 + 0.581601i \(0.802426\pi\)
\(752\) 0 0
\(753\) 355.472i 0.472074i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 264.661 0.349619 0.174809 0.984602i \(-0.444069\pi\)
0.174809 + 0.984602i \(0.444069\pi\)
\(758\) 0 0
\(759\) 37.3095i 0.0491561i
\(760\) 0 0
\(761\) 681.093 0.894998 0.447499 0.894284i \(-0.352315\pi\)
0.447499 + 0.894284i \(0.352315\pi\)
\(762\) 0 0
\(763\) 585.085i 0.766822i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 169.674 0.221218
\(768\) 0 0
\(769\) −962.529 −1.25166 −0.625832 0.779958i \(-0.715240\pi\)
−0.625832 + 0.779958i \(0.715240\pi\)
\(770\) 0 0
\(771\) −193.723 −0.251262
\(772\) 0 0
\(773\) 27.0726i 0.0350227i −0.999847 0.0175114i \(-0.994426\pi\)
0.999847 0.0175114i \(-0.00557433\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 629.338 0.809959
\(778\) 0 0
\(779\) 957.019 + 662.134i 1.22852 + 0.849980i
\(780\) 0 0
\(781\) 1300.19i 1.66478i
\(782\) 0 0
\(783\) −202.670 −0.258838
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 49.7504i 0.0632152i 0.999500 + 0.0316076i \(0.0100627\pi\)
−0.999500 + 0.0316076i \(0.989937\pi\)
\(788\) 0 0
\(789\) 960.771i 1.21771i
\(790\) 0 0
\(791\) 18.4770i 0.0233590i
\(792\) 0 0
\(793\) 326.172i 0.411314i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 221.385i 0.277773i −0.990308 0.138886i \(-0.955648\pi\)
0.990308 0.138886i \(-0.0443523\pi\)
\(798\) 0 0
\(799\) 148.324 0.185636
\(800\) 0 0
\(801\) 267.590i 0.334070i
\(802\) 0 0
\(803\) 319.890 0.398369
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 349.889 0.433568
\(808\) 0 0
\(809\) −933.918 −1.15441 −0.577205 0.816599i \(-0.695857\pi\)
−0.577205 + 0.816599i \(0.695857\pi\)
\(810\) 0 0
\(811\) 1390.98i 1.71514i 0.514364 + 0.857572i \(0.328028\pi\)
−0.514364 + 0.857572i \(0.671972\pi\)
\(812\) 0 0
\(813\) 1630.71i 2.00580i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 626.867 906.045i 0.767279 1.10899i
\(818\) 0 0
\(819\) 253.962i 0.310088i
\(820\) 0 0
\(821\) 1066.11 1.29855 0.649275 0.760553i \(-0.275072\pi\)
0.649275 + 0.760553i \(0.275072\pi\)
\(822\) 0 0
\(823\) −495.548 −0.602124 −0.301062 0.953605i \(-0.597341\pi\)
−0.301062 + 0.953605i \(0.597341\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1036.35i 1.25314i 0.779365 + 0.626571i \(0.215542\pi\)
−0.779365 + 0.626571i \(0.784458\pi\)
\(828\) 0 0
\(829\) 355.400i 0.428710i −0.976756 0.214355i \(-0.931235\pi\)
0.976756 0.214355i \(-0.0687649\pi\)
\(830\) 0 0
\(831\) 904.453i 1.08839i
\(832\) 0 0
\(833\) 148.345 0.178085
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 183.049 0.218697
\(838\) 0 0
\(839\) 429.992i 0.512505i −0.966610 0.256253i \(-0.917512\pi\)
0.966610 0.256253i \(-0.0824879\pi\)
\(840\) 0 0
\(841\) 751.908 0.894064
\(842\) 0 0
\(843\) 830.391 0.985043
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −90.3120 −0.106626
\(848\) 0 0
\(849\) 929.983i 1.09539i
\(850\) 0 0
\(851\) 19.0497i 0.0223851i
\(852\) 0 0
\(853\) −557.873 −0.654013 −0.327007 0.945022i \(-0.606040\pi\)
−0.327007 + 0.945022i \(0.606040\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 813.712i 0.949489i −0.880124 0.474745i \(-0.842540\pi\)
0.880124 0.474745i \(-0.157460\pi\)
\(858\) 0 0
\(859\) −368.216 −0.428657 −0.214328 0.976762i \(-0.568756\pi\)
−0.214328 + 0.976762i \(0.568756\pi\)
\(860\) 0 0
\(861\) −1927.07 −2.23818
\(862\) 0 0
\(863\) 963.303i 1.11623i 0.829765 + 0.558113i \(0.188474\pi\)
−0.829765 + 0.558113i \(0.811526\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 929.632i 1.07224i
\(868\) 0 0
\(869\) 752.285i 0.865691i
\(870\) 0 0
\(871\) −61.4754 −0.0705802
\(872\) 0 0
\(873\) 251.315i 0.287875i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 938.800i 1.07047i 0.844704 + 0.535234i \(0.179777\pi\)
−0.844704 + 0.535234i \(0.820223\pi\)
\(878\) 0 0
\(879\) −645.604 −0.734476
\(880\) 0 0
\(881\) 417.023 0.473352 0.236676 0.971589i \(-0.423942\pi\)
0.236676 + 0.971589i \(0.423942\pi\)
\(882\) 0 0
\(883\) 326.997 0.370325 0.185163 0.982708i \(-0.440719\pi\)
0.185163 + 0.982708i \(0.440719\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 366.885i 0.413624i −0.978381 0.206812i \(-0.933691\pi\)
0.978381 0.206812i \(-0.0663089\pi\)
\(888\) 0 0
\(889\) 383.780i 0.431699i
\(890\) 0 0
\(891\) −1122.32 −1.25961
\(892\) 0 0
\(893\) 382.442 552.765i 0.428267 0.618998i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 33.0214 0.0368132
\(898\) 0 0
\(899\) 80.4671 0.0895073
\(900\) 0 0
\(901\) 241.894i 0.268473i
\(902\) 0 0
\(903\) 1824.43i 2.02041i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 948.571i 1.04583i 0.852384 + 0.522917i \(0.175156\pi\)
−0.852384 + 0.522917i \(0.824844\pi\)
\(908\) 0 0
\(909\) −176.885 −0.194592
\(910\) 0 0
\(911\) 1288.33i 1.41419i −0.707118 0.707096i \(-0.750005\pi\)
0.707118 0.707096i \(-0.249995\pi\)
\(912\) 0 0
\(913\) −688.987 −0.754641
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 465.615 0.507759
\(918\) 0 0
\(919\) −20.3298 −0.0221216 −0.0110608 0.999939i \(-0.503521\pi\)
−0.0110608 + 0.999939i \(0.503521\pi\)
\(920\) 0 0
\(921\) −899.573 −0.976735
\(922\) 0 0
\(923\) 1150.76 1.24676
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 557.727i 0.601648i
\(928\) 0 0
\(929\) −356.003 −0.383210 −0.191605 0.981472i \(-0.561369\pi\)
−0.191605 + 0.981472i \(0.561369\pi\)
\(930\) 0 0
\(931\) 382.498 552.845i 0.410846 0.593819i
\(932\) 0 0
\(933\) 1206.76i 1.29342i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 822.306 0.877595 0.438797 0.898586i \(-0.355405\pi\)
0.438797 + 0.898586i \(0.355405\pi\)
\(938\) 0 0
\(939\) 1657.60i 1.76528i
\(940\) 0 0
\(941\) 1734.01i 1.84273i 0.388699 + 0.921365i \(0.372925\pi\)
−0.388699 + 0.921365i \(0.627075\pi\)
\(942\) 0 0
\(943\) 58.3314i 0.0618572i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1226.54 1.29518 0.647591 0.761988i \(-0.275777\pi\)
0.647591 + 0.761988i \(0.275777\pi\)
\(948\) 0 0
\(949\) 283.125i 0.298340i
\(950\) 0 0
\(951\) −275.032 −0.289203
\(952\) 0 0
\(953\) 1329.78i 1.39537i 0.716406 + 0.697683i \(0.245786\pi\)
−0.716406 + 0.697683i \(0.754214\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −369.779 −0.386394
\(958\) 0 0
\(959\) 276.009 0.287809
\(960\) 0 0
\(961\) 888.323 0.924374
\(962\) 0 0
\(963\) 555.946i 0.577307i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −1006.28 −1.04062 −0.520309 0.853978i \(-0.674183\pi\)
−0.520309 + 0.853978i \(0.674183\pi\)
\(968\) 0 0
\(969\) −224.371 155.236i −0.231549 0.160202i
\(970\) 0 0
\(971\) 1521.07i 1.56650i −0.621710 0.783248i \(-0.713562\pi\)
0.621710 0.783248i \(-0.286438\pi\)
\(972\) 0 0
\(973\) 1935.29 1.98900
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 750.278i 0.767940i −0.923346 0.383970i \(-0.874557\pi\)
0.923346 0.383970i \(-0.125443\pi\)
\(978\) 0 0
\(979\) 1120.77i 1.14481i
\(980\) 0 0
\(981\) 173.941i 0.177310i
\(982\) 0 0
\(983\) 603.980i 0.614425i 0.951641 + 0.307213i \(0.0993963\pi\)
−0.951641 + 0.307213i \(0.900604\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1113.06i 1.12772i
\(988\) 0 0
\(989\) 55.2244 0.0558386
\(990\) 0 0
\(991\) 1522.67i 1.53650i 0.640152 + 0.768248i \(0.278871\pi\)
−0.640152 + 0.768248i \(0.721129\pi\)
\(992\) 0 0
\(993\) −1999.00 −2.01309
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1616.79 −1.62165 −0.810827 0.585285i \(-0.800982\pi\)
−0.810827 + 0.585285i \(0.800982\pi\)
\(998\) 0 0
\(999\) −429.498 −0.429928
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 1900.3.e.f.1101.3 12
5.2 odd 4 1900.3.g.c.949.6 24
5.3 odd 4 1900.3.g.c.949.19 24
5.4 even 2 380.3.e.a.341.10 yes 12
15.14 odd 2 3420.3.o.a.721.5 12
19.18 odd 2 inner 1900.3.e.f.1101.10 12
20.19 odd 2 1520.3.h.b.721.3 12
95.18 even 4 1900.3.g.c.949.5 24
95.37 even 4 1900.3.g.c.949.20 24
95.94 odd 2 380.3.e.a.341.3 12
285.284 even 2 3420.3.o.a.721.6 12
380.379 even 2 1520.3.h.b.721.10 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.3.e.a.341.3 12 95.94 odd 2
380.3.e.a.341.10 yes 12 5.4 even 2
1520.3.h.b.721.3 12 20.19 odd 2
1520.3.h.b.721.10 12 380.379 even 2
1900.3.e.f.1101.3 12 1.1 even 1 trivial
1900.3.e.f.1101.10 12 19.18 odd 2 inner
1900.3.g.c.949.5 24 95.18 even 4
1900.3.g.c.949.6 24 5.2 odd 4
1900.3.g.c.949.19 24 5.3 odd 4
1900.3.g.c.949.20 24 95.37 even 4
3420.3.o.a.721.5 12 15.14 odd 2
3420.3.o.a.721.6 12 285.284 even 2