Properties

Label 9450.2.a.er.1.1
Level $9450$
Weight $2$
Character 9450.1
Self dual yes
Analytic conductor $75.459$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9450,2,Mod(1,9450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9450, 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("9450.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9450.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: \(75.4586299101\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1890)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 9450.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} -1.73205 q^{11} -1.46410 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +2.26795 q^{19} -1.73205 q^{22} -4.46410 q^{23} -1.46410 q^{26} -1.00000 q^{28} -5.46410 q^{29} -3.73205 q^{31} +1.00000 q^{32} +4.00000 q^{34} +7.19615 q^{37} +2.26795 q^{38} +9.92820 q^{41} -11.4641 q^{43} -1.73205 q^{44} -4.46410 q^{46} +4.53590 q^{47} +1.00000 q^{49} -1.46410 q^{52} +13.8564 q^{53} -1.00000 q^{56} -5.46410 q^{58} -8.92820 q^{59} +13.8564 q^{61} -3.73205 q^{62} +1.00000 q^{64} +8.39230 q^{67} +4.00000 q^{68} +7.73205 q^{71} +3.07180 q^{73} +7.19615 q^{74} +2.26795 q^{76} +1.73205 q^{77} -4.92820 q^{79} +9.92820 q^{82} +2.53590 q^{83} -11.4641 q^{86} -1.73205 q^{88} +1.00000 q^{89} +1.46410 q^{91} -4.46410 q^{92} +4.53590 q^{94} +6.92820 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{7} + 2 q^{8} + 4 q^{13} - 2 q^{14} + 2 q^{16} + 8 q^{17} + 8 q^{19} - 2 q^{23} + 4 q^{26} - 2 q^{28} - 4 q^{29} - 4 q^{31} + 2 q^{32} + 8 q^{34} + 4 q^{37} + 8 q^{38} + 6 q^{41} - 16 q^{43} - 2 q^{46} + 16 q^{47} + 2 q^{49} + 4 q^{52} - 2 q^{56} - 4 q^{58} - 4 q^{59} - 4 q^{62} + 2 q^{64} - 4 q^{67} + 8 q^{68} + 12 q^{71} + 20 q^{73} + 4 q^{74} + 8 q^{76} + 4 q^{79} + 6 q^{82} + 12 q^{83} - 16 q^{86} + 2 q^{89} - 4 q^{91} - 2 q^{92} + 16 q^{94} + 2 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −1.73205 −0.522233 −0.261116 0.965307i \(-0.584091\pi\)
−0.261116 + 0.965307i \(0.584091\pi\)
\(12\) 0 0
\(13\) −1.46410 −0.406069 −0.203034 0.979172i \(-0.565080\pi\)
−0.203034 + 0.979172i \(0.565080\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 2.26795 0.520303 0.260152 0.965568i \(-0.416227\pi\)
0.260152 + 0.965568i \(0.416227\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.73205 −0.369274
\(23\) −4.46410 −0.930830 −0.465415 0.885093i \(-0.654095\pi\)
−0.465415 + 0.885093i \(0.654095\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.46410 −0.287134
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −5.46410 −1.01466 −0.507329 0.861752i \(-0.669367\pi\)
−0.507329 + 0.861752i \(0.669367\pi\)
\(30\) 0 0
\(31\) −3.73205 −0.670296 −0.335148 0.942165i \(-0.608786\pi\)
−0.335148 + 0.942165i \(0.608786\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 0 0
\(37\) 7.19615 1.18304 0.591520 0.806290i \(-0.298528\pi\)
0.591520 + 0.806290i \(0.298528\pi\)
\(38\) 2.26795 0.367910
\(39\) 0 0
\(40\) 0 0
\(41\) 9.92820 1.55052 0.775262 0.631639i \(-0.217618\pi\)
0.775262 + 0.631639i \(0.217618\pi\)
\(42\) 0 0
\(43\) −11.4641 −1.74826 −0.874130 0.485693i \(-0.838567\pi\)
−0.874130 + 0.485693i \(0.838567\pi\)
\(44\) −1.73205 −0.261116
\(45\) 0 0
\(46\) −4.46410 −0.658196
\(47\) 4.53590 0.661629 0.330814 0.943696i \(-0.392677\pi\)
0.330814 + 0.943696i \(0.392677\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −1.46410 −0.203034
\(53\) 13.8564 1.90332 0.951662 0.307148i \(-0.0993745\pi\)
0.951662 + 0.307148i \(0.0993745\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −5.46410 −0.717472
\(59\) −8.92820 −1.16235 −0.581177 0.813778i \(-0.697407\pi\)
−0.581177 + 0.813778i \(0.697407\pi\)
\(60\) 0 0
\(61\) 13.8564 1.77413 0.887066 0.461644i \(-0.152740\pi\)
0.887066 + 0.461644i \(0.152740\pi\)
\(62\) −3.73205 −0.473971
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 8.39230 1.02528 0.512642 0.858603i \(-0.328667\pi\)
0.512642 + 0.858603i \(0.328667\pi\)
\(68\) 4.00000 0.485071
\(69\) 0 0
\(70\) 0 0
\(71\) 7.73205 0.917626 0.458813 0.888533i \(-0.348275\pi\)
0.458813 + 0.888533i \(0.348275\pi\)
\(72\) 0 0
\(73\) 3.07180 0.359527 0.179763 0.983710i \(-0.442467\pi\)
0.179763 + 0.983710i \(0.442467\pi\)
\(74\) 7.19615 0.836536
\(75\) 0 0
\(76\) 2.26795 0.260152
\(77\) 1.73205 0.197386
\(78\) 0 0
\(79\) −4.92820 −0.554466 −0.277233 0.960803i \(-0.589417\pi\)
−0.277233 + 0.960803i \(0.589417\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 9.92820 1.09639
\(83\) 2.53590 0.278351 0.139176 0.990268i \(-0.455555\pi\)
0.139176 + 0.990268i \(0.455555\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −11.4641 −1.23621
\(87\) 0 0
\(88\) −1.73205 −0.184637
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) 0 0
\(91\) 1.46410 0.153480
\(92\) −4.46410 −0.465415
\(93\) 0 0
\(94\) 4.53590 0.467842
\(95\) 0 0
\(96\) 0 0
\(97\) 6.92820 0.703452 0.351726 0.936103i \(-0.385595\pi\)
0.351726 + 0.936103i \(0.385595\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) 0.928203 0.0923597 0.0461798 0.998933i \(-0.485295\pi\)
0.0461798 + 0.998933i \(0.485295\pi\)
\(102\) 0 0
\(103\) −3.53590 −0.348402 −0.174201 0.984710i \(-0.555734\pi\)
−0.174201 + 0.984710i \(0.555734\pi\)
\(104\) −1.46410 −0.143567
\(105\) 0 0
\(106\) 13.8564 1.34585
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) 14.4641 1.38541 0.692705 0.721221i \(-0.256419\pi\)
0.692705 + 0.721221i \(0.256419\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) 11.4641 1.07845 0.539226 0.842161i \(-0.318717\pi\)
0.539226 + 0.842161i \(0.318717\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −5.46410 −0.507329
\(117\) 0 0
\(118\) −8.92820 −0.821908
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) −8.00000 −0.727273
\(122\) 13.8564 1.25450
\(123\) 0 0
\(124\) −3.73205 −0.335148
\(125\) 0 0
\(126\) 0 0
\(127\) −1.46410 −0.129918 −0.0649590 0.997888i \(-0.520692\pi\)
−0.0649590 + 0.997888i \(0.520692\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −7.07180 −0.617866 −0.308933 0.951084i \(-0.599972\pi\)
−0.308933 + 0.951084i \(0.599972\pi\)
\(132\) 0 0
\(133\) −2.26795 −0.196656
\(134\) 8.39230 0.724985
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) 6.53590 0.558399 0.279200 0.960233i \(-0.409931\pi\)
0.279200 + 0.960233i \(0.409931\pi\)
\(138\) 0 0
\(139\) 7.46410 0.633097 0.316548 0.948576i \(-0.397476\pi\)
0.316548 + 0.948576i \(0.397476\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.73205 0.648859
\(143\) 2.53590 0.212062
\(144\) 0 0
\(145\) 0 0
\(146\) 3.07180 0.254224
\(147\) 0 0
\(148\) 7.19615 0.591520
\(149\) 0.928203 0.0760414 0.0380207 0.999277i \(-0.487895\pi\)
0.0380207 + 0.999277i \(0.487895\pi\)
\(150\) 0 0
\(151\) −17.3205 −1.40952 −0.704761 0.709444i \(-0.748946\pi\)
−0.704761 + 0.709444i \(0.748946\pi\)
\(152\) 2.26795 0.183955
\(153\) 0 0
\(154\) 1.73205 0.139573
\(155\) 0 0
\(156\) 0 0
\(157\) 9.46410 0.755318 0.377659 0.925945i \(-0.376729\pi\)
0.377659 + 0.925945i \(0.376729\pi\)
\(158\) −4.92820 −0.392067
\(159\) 0 0
\(160\) 0 0
\(161\) 4.46410 0.351820
\(162\) 0 0
\(163\) 9.46410 0.741286 0.370643 0.928775i \(-0.379137\pi\)
0.370643 + 0.928775i \(0.379137\pi\)
\(164\) 9.92820 0.775262
\(165\) 0 0
\(166\) 2.53590 0.196824
\(167\) −0.928203 −0.0718265 −0.0359133 0.999355i \(-0.511434\pi\)
−0.0359133 + 0.999355i \(0.511434\pi\)
\(168\) 0 0
\(169\) −10.8564 −0.835108
\(170\) 0 0
\(171\) 0 0
\(172\) −11.4641 −0.874130
\(173\) −6.12436 −0.465626 −0.232813 0.972522i \(-0.574793\pi\)
−0.232813 + 0.972522i \(0.574793\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.73205 −0.130558
\(177\) 0 0
\(178\) 1.00000 0.0749532
\(179\) 11.4641 0.856867 0.428434 0.903573i \(-0.359066\pi\)
0.428434 + 0.903573i \(0.359066\pi\)
\(180\) 0 0
\(181\) −23.8564 −1.77323 −0.886616 0.462506i \(-0.846951\pi\)
−0.886616 + 0.462506i \(0.846951\pi\)
\(182\) 1.46410 0.108526
\(183\) 0 0
\(184\) −4.46410 −0.329098
\(185\) 0 0
\(186\) 0 0
\(187\) −6.92820 −0.506640
\(188\) 4.53590 0.330814
\(189\) 0 0
\(190\) 0 0
\(191\) 19.1962 1.38898 0.694492 0.719500i \(-0.255629\pi\)
0.694492 + 0.719500i \(0.255629\pi\)
\(192\) 0 0
\(193\) −9.85641 −0.709480 −0.354740 0.934965i \(-0.615431\pi\)
−0.354740 + 0.934965i \(0.615431\pi\)
\(194\) 6.92820 0.497416
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 12.5359 0.893146 0.446573 0.894747i \(-0.352644\pi\)
0.446573 + 0.894747i \(0.352644\pi\)
\(198\) 0 0
\(199\) 25.0526 1.77593 0.887964 0.459912i \(-0.152119\pi\)
0.887964 + 0.459912i \(0.152119\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0.928203 0.0653082
\(203\) 5.46410 0.383505
\(204\) 0 0
\(205\) 0 0
\(206\) −3.53590 −0.246358
\(207\) 0 0
\(208\) −1.46410 −0.101517
\(209\) −3.92820 −0.271719
\(210\) 0 0
\(211\) 10.3923 0.715436 0.357718 0.933830i \(-0.383555\pi\)
0.357718 + 0.933830i \(0.383555\pi\)
\(212\) 13.8564 0.951662
\(213\) 0 0
\(214\) −4.00000 −0.273434
\(215\) 0 0
\(216\) 0 0
\(217\) 3.73205 0.253348
\(218\) 14.4641 0.979633
\(219\) 0 0
\(220\) 0 0
\(221\) −5.85641 −0.393945
\(222\) 0 0
\(223\) 3.39230 0.227166 0.113583 0.993529i \(-0.463767\pi\)
0.113583 + 0.993529i \(0.463767\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 11.4641 0.762581
\(227\) 14.7846 0.981289 0.490645 0.871360i \(-0.336761\pi\)
0.490645 + 0.871360i \(0.336761\pi\)
\(228\) 0 0
\(229\) −2.92820 −0.193501 −0.0967506 0.995309i \(-0.530845\pi\)
−0.0967506 + 0.995309i \(0.530845\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −5.46410 −0.358736
\(233\) 19.4641 1.27514 0.637568 0.770394i \(-0.279941\pi\)
0.637568 + 0.770394i \(0.279941\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −8.92820 −0.581177
\(237\) 0 0
\(238\) −4.00000 −0.259281
\(239\) −4.53590 −0.293403 −0.146701 0.989181i \(-0.546866\pi\)
−0.146701 + 0.989181i \(0.546866\pi\)
\(240\) 0 0
\(241\) 10.3923 0.669427 0.334714 0.942320i \(-0.391360\pi\)
0.334714 + 0.942320i \(0.391360\pi\)
\(242\) −8.00000 −0.514259
\(243\) 0 0
\(244\) 13.8564 0.887066
\(245\) 0 0
\(246\) 0 0
\(247\) −3.32051 −0.211279
\(248\) −3.73205 −0.236985
\(249\) 0 0
\(250\) 0 0
\(251\) −21.8564 −1.37956 −0.689782 0.724017i \(-0.742294\pi\)
−0.689782 + 0.724017i \(0.742294\pi\)
\(252\) 0 0
\(253\) 7.73205 0.486110
\(254\) −1.46410 −0.0918659
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −3.58846 −0.223842 −0.111921 0.993717i \(-0.535700\pi\)
−0.111921 + 0.993717i \(0.535700\pi\)
\(258\) 0 0
\(259\) −7.19615 −0.447147
\(260\) 0 0
\(261\) 0 0
\(262\) −7.07180 −0.436897
\(263\) 24.4641 1.50852 0.754261 0.656575i \(-0.227996\pi\)
0.754261 + 0.656575i \(0.227996\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.26795 −0.139057
\(267\) 0 0
\(268\) 8.39230 0.512642
\(269\) −16.3205 −0.995079 −0.497539 0.867441i \(-0.665763\pi\)
−0.497539 + 0.867441i \(0.665763\pi\)
\(270\) 0 0
\(271\) −10.3923 −0.631288 −0.315644 0.948878i \(-0.602220\pi\)
−0.315644 + 0.948878i \(0.602220\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) 6.53590 0.394848
\(275\) 0 0
\(276\) 0 0
\(277\) −29.0526 −1.74560 −0.872800 0.488079i \(-0.837698\pi\)
−0.872800 + 0.488079i \(0.837698\pi\)
\(278\) 7.46410 0.447667
\(279\) 0 0
\(280\) 0 0
\(281\) 10.3923 0.619953 0.309976 0.950744i \(-0.399679\pi\)
0.309976 + 0.950744i \(0.399679\pi\)
\(282\) 0 0
\(283\) 22.9282 1.36294 0.681470 0.731846i \(-0.261341\pi\)
0.681470 + 0.731846i \(0.261341\pi\)
\(284\) 7.73205 0.458813
\(285\) 0 0
\(286\) 2.53590 0.149951
\(287\) −9.92820 −0.586043
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 3.07180 0.179763
\(293\) 18.9282 1.10580 0.552899 0.833248i \(-0.313522\pi\)
0.552899 + 0.833248i \(0.313522\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 7.19615 0.418268
\(297\) 0 0
\(298\) 0.928203 0.0537694
\(299\) 6.53590 0.377981
\(300\) 0 0
\(301\) 11.4641 0.660780
\(302\) −17.3205 −0.996683
\(303\) 0 0
\(304\) 2.26795 0.130076
\(305\) 0 0
\(306\) 0 0
\(307\) −10.0718 −0.574828 −0.287414 0.957806i \(-0.592796\pi\)
−0.287414 + 0.957806i \(0.592796\pi\)
\(308\) 1.73205 0.0986928
\(309\) 0 0
\(310\) 0 0
\(311\) −16.3923 −0.929522 −0.464761 0.885436i \(-0.653860\pi\)
−0.464761 + 0.885436i \(0.653860\pi\)
\(312\) 0 0
\(313\) 3.32051 0.187686 0.0938431 0.995587i \(-0.470085\pi\)
0.0938431 + 0.995587i \(0.470085\pi\)
\(314\) 9.46410 0.534090
\(315\) 0 0
\(316\) −4.92820 −0.277233
\(317\) 28.9282 1.62477 0.812385 0.583122i \(-0.198169\pi\)
0.812385 + 0.583122i \(0.198169\pi\)
\(318\) 0 0
\(319\) 9.46410 0.529888
\(320\) 0 0
\(321\) 0 0
\(322\) 4.46410 0.248775
\(323\) 9.07180 0.504768
\(324\) 0 0
\(325\) 0 0
\(326\) 9.46410 0.524168
\(327\) 0 0
\(328\) 9.92820 0.548193
\(329\) −4.53590 −0.250072
\(330\) 0 0
\(331\) 28.7846 1.58215 0.791073 0.611722i \(-0.209523\pi\)
0.791073 + 0.611722i \(0.209523\pi\)
\(332\) 2.53590 0.139176
\(333\) 0 0
\(334\) −0.928203 −0.0507890
\(335\) 0 0
\(336\) 0 0
\(337\) 18.2679 0.995119 0.497559 0.867430i \(-0.334230\pi\)
0.497559 + 0.867430i \(0.334230\pi\)
\(338\) −10.8564 −0.590511
\(339\) 0 0
\(340\) 0 0
\(341\) 6.46410 0.350051
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −11.4641 −0.618103
\(345\) 0 0
\(346\) −6.12436 −0.329247
\(347\) −8.07180 −0.433317 −0.216658 0.976247i \(-0.569516\pi\)
−0.216658 + 0.976247i \(0.569516\pi\)
\(348\) 0 0
\(349\) 31.8564 1.70523 0.852617 0.522536i \(-0.175014\pi\)
0.852617 + 0.522536i \(0.175014\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.73205 −0.0923186
\(353\) −8.66025 −0.460939 −0.230469 0.973080i \(-0.574026\pi\)
−0.230469 + 0.973080i \(0.574026\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) 11.4641 0.605897
\(359\) 35.4641 1.87172 0.935862 0.352367i \(-0.114623\pi\)
0.935862 + 0.352367i \(0.114623\pi\)
\(360\) 0 0
\(361\) −13.8564 −0.729285
\(362\) −23.8564 −1.25386
\(363\) 0 0
\(364\) 1.46410 0.0767398
\(365\) 0 0
\(366\) 0 0
\(367\) −2.60770 −0.136121 −0.0680603 0.997681i \(-0.521681\pi\)
−0.0680603 + 0.997681i \(0.521681\pi\)
\(368\) −4.46410 −0.232707
\(369\) 0 0
\(370\) 0 0
\(371\) −13.8564 −0.719389
\(372\) 0 0
\(373\) 3.19615 0.165490 0.0827452 0.996571i \(-0.473631\pi\)
0.0827452 + 0.996571i \(0.473631\pi\)
\(374\) −6.92820 −0.358249
\(375\) 0 0
\(376\) 4.53590 0.233921
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −14.0000 −0.719132 −0.359566 0.933120i \(-0.617075\pi\)
−0.359566 + 0.933120i \(0.617075\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 19.1962 0.982161
\(383\) 24.9282 1.27377 0.636886 0.770958i \(-0.280222\pi\)
0.636886 + 0.770958i \(0.280222\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −9.85641 −0.501678
\(387\) 0 0
\(388\) 6.92820 0.351726
\(389\) −6.92820 −0.351274 −0.175637 0.984455i \(-0.556198\pi\)
−0.175637 + 0.984455i \(0.556198\pi\)
\(390\) 0 0
\(391\) −17.8564 −0.903037
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) 12.5359 0.631549
\(395\) 0 0
\(396\) 0 0
\(397\) −26.3923 −1.32459 −0.662296 0.749242i \(-0.730418\pi\)
−0.662296 + 0.749242i \(0.730418\pi\)
\(398\) 25.0526 1.25577
\(399\) 0 0
\(400\) 0 0
\(401\) 28.3923 1.41784 0.708922 0.705287i \(-0.249182\pi\)
0.708922 + 0.705287i \(0.249182\pi\)
\(402\) 0 0
\(403\) 5.46410 0.272186
\(404\) 0.928203 0.0461798
\(405\) 0 0
\(406\) 5.46410 0.271179
\(407\) −12.4641 −0.617823
\(408\) 0 0
\(409\) −2.67949 −0.132492 −0.0662462 0.997803i \(-0.521102\pi\)
−0.0662462 + 0.997803i \(0.521102\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −3.53590 −0.174201
\(413\) 8.92820 0.439328
\(414\) 0 0
\(415\) 0 0
\(416\) −1.46410 −0.0717835
\(417\) 0 0
\(418\) −3.92820 −0.192135
\(419\) −16.5359 −0.807831 −0.403916 0.914796i \(-0.632351\pi\)
−0.403916 + 0.914796i \(0.632351\pi\)
\(420\) 0 0
\(421\) −2.46410 −0.120093 −0.0600465 0.998196i \(-0.519125\pi\)
−0.0600465 + 0.998196i \(0.519125\pi\)
\(422\) 10.3923 0.505889
\(423\) 0 0
\(424\) 13.8564 0.672927
\(425\) 0 0
\(426\) 0 0
\(427\) −13.8564 −0.670559
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 0 0
\(431\) 20.5167 0.988253 0.494126 0.869390i \(-0.335488\pi\)
0.494126 + 0.869390i \(0.335488\pi\)
\(432\) 0 0
\(433\) −10.2487 −0.492522 −0.246261 0.969204i \(-0.579202\pi\)
−0.246261 + 0.969204i \(0.579202\pi\)
\(434\) 3.73205 0.179144
\(435\) 0 0
\(436\) 14.4641 0.692705
\(437\) −10.1244 −0.484314
\(438\) 0 0
\(439\) −38.3923 −1.83236 −0.916182 0.400762i \(-0.868746\pi\)
−0.916182 + 0.400762i \(0.868746\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −5.85641 −0.278561
\(443\) 16.8564 0.800872 0.400436 0.916325i \(-0.368859\pi\)
0.400436 + 0.916325i \(0.368859\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 3.39230 0.160630
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 0 0
\(451\) −17.1962 −0.809735
\(452\) 11.4641 0.539226
\(453\) 0 0
\(454\) 14.7846 0.693876
\(455\) 0 0
\(456\) 0 0
\(457\) −30.5167 −1.42751 −0.713755 0.700396i \(-0.753007\pi\)
−0.713755 + 0.700396i \(0.753007\pi\)
\(458\) −2.92820 −0.136826
\(459\) 0 0
\(460\) 0 0
\(461\) 15.3923 0.716891 0.358446 0.933551i \(-0.383307\pi\)
0.358446 + 0.933551i \(0.383307\pi\)
\(462\) 0 0
\(463\) 27.8564 1.29460 0.647298 0.762237i \(-0.275899\pi\)
0.647298 + 0.762237i \(0.275899\pi\)
\(464\) −5.46410 −0.253665
\(465\) 0 0
\(466\) 19.4641 0.901657
\(467\) 28.2487 1.30719 0.653597 0.756843i \(-0.273259\pi\)
0.653597 + 0.756843i \(0.273259\pi\)
\(468\) 0 0
\(469\) −8.39230 −0.387521
\(470\) 0 0
\(471\) 0 0
\(472\) −8.92820 −0.410954
\(473\) 19.8564 0.912999
\(474\) 0 0
\(475\) 0 0
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) −4.53590 −0.207467
\(479\) 20.7846 0.949673 0.474837 0.880074i \(-0.342507\pi\)
0.474837 + 0.880074i \(0.342507\pi\)
\(480\) 0 0
\(481\) −10.5359 −0.480396
\(482\) 10.3923 0.473357
\(483\) 0 0
\(484\) −8.00000 −0.363636
\(485\) 0 0
\(486\) 0 0
\(487\) −5.60770 −0.254109 −0.127054 0.991896i \(-0.540552\pi\)
−0.127054 + 0.991896i \(0.540552\pi\)
\(488\) 13.8564 0.627250
\(489\) 0 0
\(490\) 0 0
\(491\) −17.4449 −0.787276 −0.393638 0.919266i \(-0.628784\pi\)
−0.393638 + 0.919266i \(0.628784\pi\)
\(492\) 0 0
\(493\) −21.8564 −0.984363
\(494\) −3.32051 −0.149397
\(495\) 0 0
\(496\) −3.73205 −0.167574
\(497\) −7.73205 −0.346830
\(498\) 0 0
\(499\) −20.9282 −0.936875 −0.468438 0.883497i \(-0.655183\pi\)
−0.468438 + 0.883497i \(0.655183\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −21.8564 −0.975499
\(503\) −12.3923 −0.552546 −0.276273 0.961079i \(-0.589099\pi\)
−0.276273 + 0.961079i \(0.589099\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 7.73205 0.343732
\(507\) 0 0
\(508\) −1.46410 −0.0649590
\(509\) −41.7128 −1.84889 −0.924444 0.381318i \(-0.875470\pi\)
−0.924444 + 0.381318i \(0.875470\pi\)
\(510\) 0 0
\(511\) −3.07180 −0.135888
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.58846 −0.158280
\(515\) 0 0
\(516\) 0 0
\(517\) −7.85641 −0.345524
\(518\) −7.19615 −0.316181
\(519\) 0 0
\(520\) 0 0
\(521\) −0.215390 −0.00943642 −0.00471821 0.999989i \(-0.501502\pi\)
−0.00471821 + 0.999989i \(0.501502\pi\)
\(522\) 0 0
\(523\) −31.9282 −1.39612 −0.698061 0.716038i \(-0.745954\pi\)
−0.698061 + 0.716038i \(0.745954\pi\)
\(524\) −7.07180 −0.308933
\(525\) 0 0
\(526\) 24.4641 1.06669
\(527\) −14.9282 −0.650283
\(528\) 0 0
\(529\) −3.07180 −0.133556
\(530\) 0 0
\(531\) 0 0
\(532\) −2.26795 −0.0983281
\(533\) −14.5359 −0.629620
\(534\) 0 0
\(535\) 0 0
\(536\) 8.39230 0.362492
\(537\) 0 0
\(538\) −16.3205 −0.703627
\(539\) −1.73205 −0.0746047
\(540\) 0 0
\(541\) 2.46410 0.105940 0.0529700 0.998596i \(-0.483131\pi\)
0.0529700 + 0.998596i \(0.483131\pi\)
\(542\) −10.3923 −0.446388
\(543\) 0 0
\(544\) 4.00000 0.171499
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 6.53590 0.279200
\(549\) 0 0
\(550\) 0 0
\(551\) −12.3923 −0.527930
\(552\) 0 0
\(553\) 4.92820 0.209569
\(554\) −29.0526 −1.23432
\(555\) 0 0
\(556\) 7.46410 0.316548
\(557\) −26.3923 −1.11828 −0.559139 0.829074i \(-0.688868\pi\)
−0.559139 + 0.829074i \(0.688868\pi\)
\(558\) 0 0
\(559\) 16.7846 0.709913
\(560\) 0 0
\(561\) 0 0
\(562\) 10.3923 0.438373
\(563\) 3.60770 0.152046 0.0760231 0.997106i \(-0.475778\pi\)
0.0760231 + 0.997106i \(0.475778\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 22.9282 0.963744
\(567\) 0 0
\(568\) 7.73205 0.324430
\(569\) −21.7128 −0.910248 −0.455124 0.890428i \(-0.650405\pi\)
−0.455124 + 0.890428i \(0.650405\pi\)
\(570\) 0 0
\(571\) −24.5359 −1.02680 −0.513398 0.858151i \(-0.671613\pi\)
−0.513398 + 0.858151i \(0.671613\pi\)
\(572\) 2.53590 0.106031
\(573\) 0 0
\(574\) −9.92820 −0.414395
\(575\) 0 0
\(576\) 0 0
\(577\) −1.32051 −0.0549735 −0.0274867 0.999622i \(-0.508750\pi\)
−0.0274867 + 0.999622i \(0.508750\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 0 0
\(580\) 0 0
\(581\) −2.53590 −0.105207
\(582\) 0 0
\(583\) −24.0000 −0.993978
\(584\) 3.07180 0.127112
\(585\) 0 0
\(586\) 18.9282 0.781917
\(587\) −8.92820 −0.368506 −0.184253 0.982879i \(-0.558987\pi\)
−0.184253 + 0.982879i \(0.558987\pi\)
\(588\) 0 0
\(589\) −8.46410 −0.348757
\(590\) 0 0
\(591\) 0 0
\(592\) 7.19615 0.295760
\(593\) −43.3013 −1.77817 −0.889085 0.457742i \(-0.848658\pi\)
−0.889085 + 0.457742i \(0.848658\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.928203 0.0380207
\(597\) 0 0
\(598\) 6.53590 0.267273
\(599\) −17.8756 −0.730379 −0.365190 0.930933i \(-0.618996\pi\)
−0.365190 + 0.930933i \(0.618996\pi\)
\(600\) 0 0
\(601\) −20.3923 −0.831819 −0.415910 0.909406i \(-0.636537\pi\)
−0.415910 + 0.909406i \(0.636537\pi\)
\(602\) 11.4641 0.467242
\(603\) 0 0
\(604\) −17.3205 −0.704761
\(605\) 0 0
\(606\) 0 0
\(607\) 12.7846 0.518911 0.259456 0.965755i \(-0.416457\pi\)
0.259456 + 0.965755i \(0.416457\pi\)
\(608\) 2.26795 0.0919775
\(609\) 0 0
\(610\) 0 0
\(611\) −6.64102 −0.268667
\(612\) 0 0
\(613\) 49.0526 1.98121 0.990607 0.136739i \(-0.0436622\pi\)
0.990607 + 0.136739i \(0.0436622\pi\)
\(614\) −10.0718 −0.406465
\(615\) 0 0
\(616\) 1.73205 0.0697863
\(617\) 8.92820 0.359436 0.179718 0.983718i \(-0.442481\pi\)
0.179718 + 0.983718i \(0.442481\pi\)
\(618\) 0 0
\(619\) −28.6603 −1.15195 −0.575976 0.817466i \(-0.695378\pi\)
−0.575976 + 0.817466i \(0.695378\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −16.3923 −0.657272
\(623\) −1.00000 −0.0400642
\(624\) 0 0
\(625\) 0 0
\(626\) 3.32051 0.132714
\(627\) 0 0
\(628\) 9.46410 0.377659
\(629\) 28.7846 1.14772
\(630\) 0 0
\(631\) 19.8564 0.790471 0.395236 0.918580i \(-0.370663\pi\)
0.395236 + 0.918580i \(0.370663\pi\)
\(632\) −4.92820 −0.196033
\(633\) 0 0
\(634\) 28.9282 1.14889
\(635\) 0 0
\(636\) 0 0
\(637\) −1.46410 −0.0580098
\(638\) 9.46410 0.374687
\(639\) 0 0
\(640\) 0 0
\(641\) −16.9282 −0.668624 −0.334312 0.942462i \(-0.608504\pi\)
−0.334312 + 0.942462i \(0.608504\pi\)
\(642\) 0 0
\(643\) 29.9282 1.18025 0.590127 0.807311i \(-0.299078\pi\)
0.590127 + 0.807311i \(0.299078\pi\)
\(644\) 4.46410 0.175910
\(645\) 0 0
\(646\) 9.07180 0.356925
\(647\) 27.4641 1.07973 0.539863 0.841753i \(-0.318476\pi\)
0.539863 + 0.841753i \(0.318476\pi\)
\(648\) 0 0
\(649\) 15.4641 0.607019
\(650\) 0 0
\(651\) 0 0
\(652\) 9.46410 0.370643
\(653\) 19.8564 0.777041 0.388521 0.921440i \(-0.372986\pi\)
0.388521 + 0.921440i \(0.372986\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 9.92820 0.387631
\(657\) 0 0
\(658\) −4.53590 −0.176828
\(659\) 22.5167 0.877125 0.438562 0.898701i \(-0.355488\pi\)
0.438562 + 0.898701i \(0.355488\pi\)
\(660\) 0 0
\(661\) −26.2487 −1.02096 −0.510478 0.859891i \(-0.670532\pi\)
−0.510478 + 0.859891i \(0.670532\pi\)
\(662\) 28.7846 1.11875
\(663\) 0 0
\(664\) 2.53590 0.0984119
\(665\) 0 0
\(666\) 0 0
\(667\) 24.3923 0.944474
\(668\) −0.928203 −0.0359133
\(669\) 0 0
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 17.8564 0.688314 0.344157 0.938912i \(-0.388165\pi\)
0.344157 + 0.938912i \(0.388165\pi\)
\(674\) 18.2679 0.703655
\(675\) 0 0
\(676\) −10.8564 −0.417554
\(677\) 18.9090 0.726731 0.363365 0.931647i \(-0.381628\pi\)
0.363365 + 0.931647i \(0.381628\pi\)
\(678\) 0 0
\(679\) −6.92820 −0.265880
\(680\) 0 0
\(681\) 0 0
\(682\) 6.46410 0.247523
\(683\) −6.85641 −0.262353 −0.131177 0.991359i \(-0.541875\pi\)
−0.131177 + 0.991359i \(0.541875\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) −11.4641 −0.437065
\(689\) −20.2872 −0.772880
\(690\) 0 0
\(691\) −32.2487 −1.22680 −0.613399 0.789773i \(-0.710198\pi\)
−0.613399 + 0.789773i \(0.710198\pi\)
\(692\) −6.12436 −0.232813
\(693\) 0 0
\(694\) −8.07180 −0.306401
\(695\) 0 0
\(696\) 0 0
\(697\) 39.7128 1.50423
\(698\) 31.8564 1.20578
\(699\) 0 0
\(700\) 0 0
\(701\) 8.39230 0.316973 0.158486 0.987361i \(-0.449339\pi\)
0.158486 + 0.987361i \(0.449339\pi\)
\(702\) 0 0
\(703\) 16.3205 0.615540
\(704\) −1.73205 −0.0652791
\(705\) 0 0
\(706\) −8.66025 −0.325933
\(707\) −0.928203 −0.0349087
\(708\) 0 0
\(709\) −12.4641 −0.468099 −0.234050 0.972225i \(-0.575198\pi\)
−0.234050 + 0.972225i \(0.575198\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.00000 0.0374766
\(713\) 16.6603 0.623931
\(714\) 0 0
\(715\) 0 0
\(716\) 11.4641 0.428434
\(717\) 0 0
\(718\) 35.4641 1.32351
\(719\) 20.1436 0.751229 0.375615 0.926776i \(-0.377432\pi\)
0.375615 + 0.926776i \(0.377432\pi\)
\(720\) 0 0
\(721\) 3.53590 0.131684
\(722\) −13.8564 −0.515682
\(723\) 0 0
\(724\) −23.8564 −0.886616
\(725\) 0 0
\(726\) 0 0
\(727\) −7.21539 −0.267604 −0.133802 0.991008i \(-0.542719\pi\)
−0.133802 + 0.991008i \(0.542719\pi\)
\(728\) 1.46410 0.0542632
\(729\) 0 0
\(730\) 0 0
\(731\) −45.8564 −1.69606
\(732\) 0 0
\(733\) −0.143594 −0.00530375 −0.00265187 0.999996i \(-0.500844\pi\)
−0.00265187 + 0.999996i \(0.500844\pi\)
\(734\) −2.60770 −0.0962518
\(735\) 0 0
\(736\) −4.46410 −0.164549
\(737\) −14.5359 −0.535437
\(738\) 0 0
\(739\) −47.4641 −1.74600 −0.872998 0.487725i \(-0.837827\pi\)
−0.872998 + 0.487725i \(0.837827\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −13.8564 −0.508685
\(743\) 43.3923 1.59191 0.795955 0.605356i \(-0.206969\pi\)
0.795955 + 0.605356i \(0.206969\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 3.19615 0.117019
\(747\) 0 0
\(748\) −6.92820 −0.253320
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) 11.8564 0.432646 0.216323 0.976322i \(-0.430594\pi\)
0.216323 + 0.976322i \(0.430594\pi\)
\(752\) 4.53590 0.165407
\(753\) 0 0
\(754\) 8.00000 0.291343
\(755\) 0 0
\(756\) 0 0
\(757\) 13.8564 0.503620 0.251810 0.967777i \(-0.418974\pi\)
0.251810 + 0.967777i \(0.418974\pi\)
\(758\) −14.0000 −0.508503
\(759\) 0 0
\(760\) 0 0
\(761\) 5.71281 0.207089 0.103545 0.994625i \(-0.466982\pi\)
0.103545 + 0.994625i \(0.466982\pi\)
\(762\) 0 0
\(763\) −14.4641 −0.523636
\(764\) 19.1962 0.694492
\(765\) 0 0
\(766\) 24.9282 0.900693
\(767\) 13.0718 0.471995
\(768\) 0 0
\(769\) 49.9615 1.80166 0.900829 0.434173i \(-0.142959\pi\)
0.900829 + 0.434173i \(0.142959\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −9.85641 −0.354740
\(773\) 42.3731 1.52405 0.762027 0.647546i \(-0.224205\pi\)
0.762027 + 0.647546i \(0.224205\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 6.92820 0.248708
\(777\) 0 0
\(778\) −6.92820 −0.248388
\(779\) 22.5167 0.806743
\(780\) 0 0
\(781\) −13.3923 −0.479214
\(782\) −17.8564 −0.638544
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) −13.8564 −0.493928 −0.246964 0.969025i \(-0.579433\pi\)
−0.246964 + 0.969025i \(0.579433\pi\)
\(788\) 12.5359 0.446573
\(789\) 0 0
\(790\) 0 0
\(791\) −11.4641 −0.407617
\(792\) 0 0
\(793\) −20.2872 −0.720419
\(794\) −26.3923 −0.936628
\(795\) 0 0
\(796\) 25.0526 0.887964
\(797\) −24.5167 −0.868425 −0.434212 0.900811i \(-0.642973\pi\)
−0.434212 + 0.900811i \(0.642973\pi\)
\(798\) 0 0
\(799\) 18.1436 0.641874
\(800\) 0 0
\(801\) 0 0
\(802\) 28.3923 1.00257
\(803\) −5.32051 −0.187757
\(804\) 0 0
\(805\) 0 0
\(806\) 5.46410 0.192465
\(807\) 0 0
\(808\) 0.928203 0.0326541
\(809\) 22.5359 0.792320 0.396160 0.918181i \(-0.370343\pi\)
0.396160 + 0.918181i \(0.370343\pi\)
\(810\) 0 0
\(811\) −37.7321 −1.32495 −0.662476 0.749083i \(-0.730494\pi\)
−0.662476 + 0.749083i \(0.730494\pi\)
\(812\) 5.46410 0.191752
\(813\) 0 0
\(814\) −12.4641 −0.436867
\(815\) 0 0
\(816\) 0 0
\(817\) −26.0000 −0.909625
\(818\) −2.67949 −0.0936862
\(819\) 0 0
\(820\) 0 0
\(821\) 53.3205 1.86090 0.930449 0.366421i \(-0.119417\pi\)
0.930449 + 0.366421i \(0.119417\pi\)
\(822\) 0 0
\(823\) −54.4974 −1.89966 −0.949830 0.312766i \(-0.898745\pi\)
−0.949830 + 0.312766i \(0.898745\pi\)
\(824\) −3.53590 −0.123179
\(825\) 0 0
\(826\) 8.92820 0.310652
\(827\) 6.85641 0.238421 0.119210 0.992869i \(-0.461964\pi\)
0.119210 + 0.992869i \(0.461964\pi\)
\(828\) 0 0
\(829\) 36.5359 1.26894 0.634472 0.772946i \(-0.281218\pi\)
0.634472 + 0.772946i \(0.281218\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.46410 −0.0507586
\(833\) 4.00000 0.138592
\(834\) 0 0
\(835\) 0 0
\(836\) −3.92820 −0.135860
\(837\) 0 0
\(838\) −16.5359 −0.571223
\(839\) −17.4641 −0.602928 −0.301464 0.953478i \(-0.597475\pi\)
−0.301464 + 0.953478i \(0.597475\pi\)
\(840\) 0 0
\(841\) 0.856406 0.0295313
\(842\) −2.46410 −0.0849185
\(843\) 0 0
\(844\) 10.3923 0.357718
\(845\) 0 0
\(846\) 0 0
\(847\) 8.00000 0.274883
\(848\) 13.8564 0.475831
\(849\) 0 0
\(850\) 0 0
\(851\) −32.1244 −1.10121
\(852\) 0 0
\(853\) −56.4974 −1.93443 −0.967217 0.253950i \(-0.918270\pi\)
−0.967217 + 0.253950i \(0.918270\pi\)
\(854\) −13.8564 −0.474156
\(855\) 0 0
\(856\) −4.00000 −0.136717
\(857\) −2.26795 −0.0774717 −0.0387358 0.999249i \(-0.512333\pi\)
−0.0387358 + 0.999249i \(0.512333\pi\)
\(858\) 0 0
\(859\) −24.1244 −0.823112 −0.411556 0.911384i \(-0.635015\pi\)
−0.411556 + 0.911384i \(0.635015\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 20.5167 0.698800
\(863\) 7.21539 0.245615 0.122807 0.992431i \(-0.460810\pi\)
0.122807 + 0.992431i \(0.460810\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −10.2487 −0.348265
\(867\) 0 0
\(868\) 3.73205 0.126674
\(869\) 8.53590 0.289561
\(870\) 0 0
\(871\) −12.2872 −0.416335
\(872\) 14.4641 0.489816
\(873\) 0 0
\(874\) −10.1244 −0.342461
\(875\) 0 0
\(876\) 0 0
\(877\) 40.7846 1.37720 0.688599 0.725142i \(-0.258226\pi\)
0.688599 + 0.725142i \(0.258226\pi\)
\(878\) −38.3923 −1.29568
\(879\) 0 0
\(880\) 0 0
\(881\) 25.1436 0.847109 0.423555 0.905871i \(-0.360782\pi\)
0.423555 + 0.905871i \(0.360782\pi\)
\(882\) 0 0
\(883\) 37.0718 1.24757 0.623783 0.781598i \(-0.285595\pi\)
0.623783 + 0.781598i \(0.285595\pi\)
\(884\) −5.85641 −0.196972
\(885\) 0 0
\(886\) 16.8564 0.566302
\(887\) 37.1769 1.24828 0.624139 0.781313i \(-0.285450\pi\)
0.624139 + 0.781313i \(0.285450\pi\)
\(888\) 0 0
\(889\) 1.46410 0.0491044
\(890\) 0 0
\(891\) 0 0
\(892\) 3.39230 0.113583
\(893\) 10.2872 0.344248
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 10.0000 0.333704
\(899\) 20.3923 0.680121
\(900\) 0 0
\(901\) 55.4256 1.84650
\(902\) −17.1962 −0.572569
\(903\) 0 0
\(904\) 11.4641 0.381290
\(905\) 0 0
\(906\) 0 0
\(907\) −44.9282 −1.49182 −0.745908 0.666049i \(-0.767984\pi\)
−0.745908 + 0.666049i \(0.767984\pi\)
\(908\) 14.7846 0.490645
\(909\) 0 0
\(910\) 0 0
\(911\) 16.2487 0.538344 0.269172 0.963092i \(-0.413250\pi\)
0.269172 + 0.963092i \(0.413250\pi\)
\(912\) 0 0
\(913\) −4.39230 −0.145364
\(914\) −30.5167 −1.00940
\(915\) 0 0
\(916\) −2.92820 −0.0967506
\(917\) 7.07180 0.233531
\(918\) 0 0
\(919\) −41.8564 −1.38072 −0.690358 0.723468i \(-0.742547\pi\)
−0.690358 + 0.723468i \(0.742547\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 15.3923 0.506919
\(923\) −11.3205 −0.372619
\(924\) 0 0
\(925\) 0 0
\(926\) 27.8564 0.915418
\(927\) 0 0
\(928\) −5.46410 −0.179368
\(929\) 43.8564 1.43888 0.719441 0.694554i \(-0.244398\pi\)
0.719441 + 0.694554i \(0.244398\pi\)
\(930\) 0 0
\(931\) 2.26795 0.0743290
\(932\) 19.4641 0.637568
\(933\) 0 0
\(934\) 28.2487 0.924326
\(935\) 0 0
\(936\) 0 0
\(937\) 42.6410 1.39302 0.696511 0.717546i \(-0.254735\pi\)
0.696511 + 0.717546i \(0.254735\pi\)
\(938\) −8.39230 −0.274018
\(939\) 0 0
\(940\) 0 0
\(941\) −55.1051 −1.79638 −0.898188 0.439612i \(-0.855116\pi\)
−0.898188 + 0.439612i \(0.855116\pi\)
\(942\) 0 0
\(943\) −44.3205 −1.44327
\(944\) −8.92820 −0.290588
\(945\) 0 0
\(946\) 19.8564 0.645587
\(947\) −50.5692 −1.64328 −0.821639 0.570008i \(-0.806940\pi\)
−0.821639 + 0.570008i \(0.806940\pi\)
\(948\) 0 0
\(949\) −4.49742 −0.145993
\(950\) 0 0
\(951\) 0 0
\(952\) −4.00000 −0.129641
\(953\) −9.46410 −0.306572 −0.153286 0.988182i \(-0.548986\pi\)
−0.153286 + 0.988182i \(0.548986\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −4.53590 −0.146701
\(957\) 0 0
\(958\) 20.7846 0.671520
\(959\) −6.53590 −0.211055
\(960\) 0 0
\(961\) −17.0718 −0.550703
\(962\) −10.5359 −0.339691
\(963\) 0 0
\(964\) 10.3923 0.334714
\(965\) 0 0
\(966\) 0 0
\(967\) 8.14359 0.261880 0.130940 0.991390i \(-0.458200\pi\)
0.130940 + 0.991390i \(0.458200\pi\)
\(968\) −8.00000 −0.257130
\(969\) 0 0
\(970\) 0 0
\(971\) −35.3205 −1.13349 −0.566745 0.823894i \(-0.691797\pi\)
−0.566745 + 0.823894i \(0.691797\pi\)
\(972\) 0 0
\(973\) −7.46410 −0.239288
\(974\) −5.60770 −0.179682
\(975\) 0 0
\(976\) 13.8564 0.443533
\(977\) −41.5692 −1.32992 −0.664959 0.746880i \(-0.731551\pi\)
−0.664959 + 0.746880i \(0.731551\pi\)
\(978\) 0 0
\(979\) −1.73205 −0.0553566
\(980\) 0 0
\(981\) 0 0
\(982\) −17.4449 −0.556688
\(983\) 38.3923 1.22452 0.612262 0.790655i \(-0.290260\pi\)
0.612262 + 0.790655i \(0.290260\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −21.8564 −0.696050
\(987\) 0 0
\(988\) −3.32051 −0.105639
\(989\) 51.1769 1.62733
\(990\) 0 0
\(991\) −15.6077 −0.495795 −0.247897 0.968786i \(-0.579740\pi\)
−0.247897 + 0.968786i \(0.579740\pi\)
\(992\) −3.73205 −0.118493
\(993\) 0 0
\(994\) −7.73205 −0.245246
\(995\) 0 0
\(996\) 0 0
\(997\) 47.9615 1.51896 0.759478 0.650533i \(-0.225454\pi\)
0.759478 + 0.650533i \(0.225454\pi\)
\(998\) −20.9282 −0.662471
\(999\) 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 9450.2.a.er.1.1 2
3.2 odd 2 9450.2.a.eb.1.2 2
5.2 odd 4 1890.2.g.q.379.4 yes 4
5.3 odd 4 1890.2.g.q.379.2 yes 4
5.4 even 2 9450.2.a.ei.1.1 2
15.2 even 4 1890.2.g.n.379.1 4
15.8 even 4 1890.2.g.n.379.3 yes 4
15.14 odd 2 9450.2.a.eu.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1890.2.g.n.379.1 4 15.2 even 4
1890.2.g.n.379.3 yes 4 15.8 even 4
1890.2.g.q.379.2 yes 4 5.3 odd 4
1890.2.g.q.379.4 yes 4 5.2 odd 4
9450.2.a.eb.1.2 2 3.2 odd 2
9450.2.a.ei.1.1 2 5.4 even 2
9450.2.a.er.1.1 2 1.1 even 1 trivial
9450.2.a.eu.1.2 2 15.14 odd 2