Properties

Label 7920.2.a.cj.1.3
Level $7920$
Weight $2$
Character 7920.1
Self dual yes
Analytic conductor $63.242$
Analytic rank $0$
Dimension $3$
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] = [7920,2,Mod(1,7920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7920, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("7920.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7920.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: \(63.2415184009\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.311108\) of defining polynomial
Character \(\chi\) \(=\) 7920.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{5} +4.42864 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +4.42864 q^{7} +1.00000 q^{11} -0.622216 q^{13} +5.18421 q^{17} -7.05086 q^{19} +8.85728 q^{23} +1.00000 q^{25} +7.80642 q^{29} -2.75557 q^{31} -4.42864 q^{35} -2.00000 q^{37} +0.193576 q^{41} -5.67307 q^{43} -2.75557 q^{47} +12.6128 q^{49} +10.8573 q^{53} -1.00000 q^{55} -4.85728 q^{59} +6.85728 q^{61} +0.622216 q^{65} +1.24443 q^{67} +2.75557 q^{71} +4.23506 q^{73} +4.42864 q^{77} -8.56199 q^{79} +0.133353 q^{83} -5.18421 q^{85} -5.61285 q^{89} -2.75557 q^{91} +7.05086 q^{95} +7.24443 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{5} + 3 q^{11} - 2 q^{13} + 2 q^{17} - 8 q^{19} + 3 q^{25} + 10 q^{29} - 8 q^{31} - 6 q^{37} + 14 q^{41} - 4 q^{43} - 8 q^{47} + 11 q^{49} + 6 q^{53} - 3 q^{55} + 12 q^{59} - 6 q^{61} + 2 q^{65} + 4 q^{67} + 8 q^{71} - 14 q^{73} - 12 q^{79} - 2 q^{85} + 10 q^{89} - 8 q^{91} + 8 q^{95} + 22 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 4.42864 1.67387 0.836934 0.547304i \(-0.184346\pi\)
0.836934 + 0.547304i \(0.184346\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −0.622216 −0.172572 −0.0862858 0.996270i \(-0.527500\pi\)
−0.0862858 + 0.996270i \(0.527500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.18421 1.25736 0.628678 0.777666i \(-0.283597\pi\)
0.628678 + 0.777666i \(0.283597\pi\)
\(18\) 0 0
\(19\) −7.05086 −1.61758 −0.808789 0.588100i \(-0.799876\pi\)
−0.808789 + 0.588100i \(0.799876\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.85728 1.84687 0.923435 0.383754i \(-0.125369\pi\)
0.923435 + 0.383754i \(0.125369\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.80642 1.44962 0.724808 0.688951i \(-0.241928\pi\)
0.724808 + 0.688951i \(0.241928\pi\)
\(30\) 0 0
\(31\) −2.75557 −0.494915 −0.247457 0.968899i \(-0.579595\pi\)
−0.247457 + 0.968899i \(0.579595\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.42864 −0.748577
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.193576 0.0302315 0.0151158 0.999886i \(-0.495188\pi\)
0.0151158 + 0.999886i \(0.495188\pi\)
\(42\) 0 0
\(43\) −5.67307 −0.865135 −0.432568 0.901602i \(-0.642392\pi\)
−0.432568 + 0.901602i \(0.642392\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.75557 −0.401941 −0.200971 0.979597i \(-0.564410\pi\)
−0.200971 + 0.979597i \(0.564410\pi\)
\(48\) 0 0
\(49\) 12.6128 1.80184
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.8573 1.49136 0.745681 0.666303i \(-0.232124\pi\)
0.745681 + 0.666303i \(0.232124\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.85728 −0.632364 −0.316182 0.948699i \(-0.602401\pi\)
−0.316182 + 0.948699i \(0.602401\pi\)
\(60\) 0 0
\(61\) 6.85728 0.877985 0.438992 0.898491i \(-0.355336\pi\)
0.438992 + 0.898491i \(0.355336\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.622216 0.0771764
\(66\) 0 0
\(67\) 1.24443 0.152031 0.0760157 0.997107i \(-0.475780\pi\)
0.0760157 + 0.997107i \(0.475780\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.75557 0.327026 0.163513 0.986541i \(-0.447717\pi\)
0.163513 + 0.986541i \(0.447717\pi\)
\(72\) 0 0
\(73\) 4.23506 0.495677 0.247838 0.968801i \(-0.420280\pi\)
0.247838 + 0.968801i \(0.420280\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.42864 0.504690
\(78\) 0 0
\(79\) −8.56199 −0.963299 −0.481650 0.876364i \(-0.659962\pi\)
−0.481650 + 0.876364i \(0.659962\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.133353 0.0146374 0.00731870 0.999973i \(-0.497670\pi\)
0.00731870 + 0.999973i \(0.497670\pi\)
\(84\) 0 0
\(85\) −5.18421 −0.562306
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.61285 −0.594961 −0.297480 0.954728i \(-0.596146\pi\)
−0.297480 + 0.954728i \(0.596146\pi\)
\(90\) 0 0
\(91\) −2.75557 −0.288862
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.05086 0.723402
\(96\) 0 0
\(97\) 7.24443 0.735561 0.367780 0.929913i \(-0.380118\pi\)
0.367780 + 0.929913i \(0.380118\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.66370 −0.464056 −0.232028 0.972709i \(-0.574536\pi\)
−0.232028 + 0.972709i \(0.574536\pi\)
\(102\) 0 0
\(103\) 11.6128 1.14425 0.572124 0.820167i \(-0.306120\pi\)
0.572124 + 0.820167i \(0.306120\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.62222 0.253499 0.126750 0.991935i \(-0.459546\pi\)
0.126750 + 0.991935i \(0.459546\pi\)
\(108\) 0 0
\(109\) −19.7146 −1.88831 −0.944156 0.329499i \(-0.893120\pi\)
−0.944156 + 0.329499i \(0.893120\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −8.85728 −0.825946
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 22.9590 2.10465
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 15.1842 1.34738 0.673690 0.739014i \(-0.264708\pi\)
0.673690 + 0.739014i \(0.264708\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.24443 0.108726 0.0543632 0.998521i \(-0.482687\pi\)
0.0543632 + 0.998521i \(0.482687\pi\)
\(132\) 0 0
\(133\) −31.2257 −2.70761
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.488863 0.0417663 0.0208832 0.999782i \(-0.493352\pi\)
0.0208832 + 0.999782i \(0.493352\pi\)
\(138\) 0 0
\(139\) −17.8064 −1.51032 −0.755161 0.655540i \(-0.772441\pi\)
−0.755161 + 0.655540i \(0.772441\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.622216 −0.0520323
\(144\) 0 0
\(145\) −7.80642 −0.648288
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.43801 0.117806 0.0589031 0.998264i \(-0.481240\pi\)
0.0589031 + 0.998264i \(0.481240\pi\)
\(150\) 0 0
\(151\) 12.1748 0.990774 0.495387 0.868672i \(-0.335026\pi\)
0.495387 + 0.868672i \(0.335026\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.75557 0.221333
\(156\) 0 0
\(157\) 18.4701 1.47408 0.737038 0.675851i \(-0.236224\pi\)
0.737038 + 0.675851i \(0.236224\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 39.2257 3.09142
\(162\) 0 0
\(163\) 10.1017 0.791227 0.395614 0.918417i \(-0.370532\pi\)
0.395614 + 0.918417i \(0.370532\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −16.3368 −1.26418 −0.632089 0.774896i \(-0.717802\pi\)
−0.632089 + 0.774896i \(0.717802\pi\)
\(168\) 0 0
\(169\) −12.6128 −0.970219
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 9.18421 0.698262 0.349131 0.937074i \(-0.386477\pi\)
0.349131 + 0.937074i \(0.386477\pi\)
\(174\) 0 0
\(175\) 4.42864 0.334774
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −25.3274 −1.89306 −0.946530 0.322617i \(-0.895437\pi\)
−0.946530 + 0.322617i \(0.895437\pi\)
\(180\) 0 0
\(181\) −13.6128 −1.01184 −0.505918 0.862582i \(-0.668846\pi\)
−0.505918 + 0.862582i \(0.668846\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.00000 0.147043
\(186\) 0 0
\(187\) 5.18421 0.379107
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.10171 0.441504 0.220752 0.975330i \(-0.429149\pi\)
0.220752 + 0.975330i \(0.429149\pi\)
\(192\) 0 0
\(193\) 18.3368 1.31991 0.659955 0.751305i \(-0.270575\pi\)
0.659955 + 0.751305i \(0.270575\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.69535 0.477024 0.238512 0.971140i \(-0.423340\pi\)
0.238512 + 0.971140i \(0.423340\pi\)
\(198\) 0 0
\(199\) −14.1017 −0.999644 −0.499822 0.866128i \(-0.666601\pi\)
−0.499822 + 0.866128i \(0.666601\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 34.5718 2.42647
\(204\) 0 0
\(205\) −0.193576 −0.0135199
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.05086 −0.487718
\(210\) 0 0
\(211\) 10.6637 0.734120 0.367060 0.930197i \(-0.380364\pi\)
0.367060 + 0.930197i \(0.380364\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5.67307 0.386900
\(216\) 0 0
\(217\) −12.2034 −0.828422
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.22570 −0.216984
\(222\) 0 0
\(223\) −8.85728 −0.593127 −0.296564 0.955013i \(-0.595841\pi\)
−0.296564 + 0.955013i \(0.595841\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.3778 0.887915 0.443957 0.896048i \(-0.353574\pi\)
0.443957 + 0.896048i \(0.353574\pi\)
\(228\) 0 0
\(229\) 11.5111 0.760677 0.380339 0.924847i \(-0.375807\pi\)
0.380339 + 0.924847i \(0.375807\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.32693 0.283467 0.141733 0.989905i \(-0.454732\pi\)
0.141733 + 0.989905i \(0.454732\pi\)
\(234\) 0 0
\(235\) 2.75557 0.179753
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3.34614 −0.216444 −0.108222 0.994127i \(-0.534516\pi\)
−0.108222 + 0.994127i \(0.534516\pi\)
\(240\) 0 0
\(241\) −1.34614 −0.0867126 −0.0433563 0.999060i \(-0.513805\pi\)
−0.0433563 + 0.999060i \(0.513805\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −12.6128 −0.805805
\(246\) 0 0
\(247\) 4.38715 0.279148
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 22.7556 1.43632 0.718159 0.695879i \(-0.244985\pi\)
0.718159 + 0.695879i \(0.244985\pi\)
\(252\) 0 0
\(253\) 8.85728 0.556852
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.85728 0.427745 0.213873 0.976862i \(-0.431392\pi\)
0.213873 + 0.976862i \(0.431392\pi\)
\(258\) 0 0
\(259\) −8.85728 −0.550365
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −29.5812 −1.82406 −0.912028 0.410129i \(-0.865484\pi\)
−0.912028 + 0.410129i \(0.865484\pi\)
\(264\) 0 0
\(265\) −10.8573 −0.666957
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −8.48886 −0.517575 −0.258788 0.965934i \(-0.583323\pi\)
−0.258788 + 0.965934i \(0.583323\pi\)
\(270\) 0 0
\(271\) −14.6637 −0.890757 −0.445378 0.895343i \(-0.646931\pi\)
−0.445378 + 0.895343i \(0.646931\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) 14.6035 0.877438 0.438719 0.898624i \(-0.355432\pi\)
0.438719 + 0.898624i \(0.355432\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.193576 0.0115478 0.00577389 0.999983i \(-0.498162\pi\)
0.00577389 + 0.999983i \(0.498162\pi\)
\(282\) 0 0
\(283\) −27.1842 −1.61593 −0.807967 0.589228i \(-0.799432\pi\)
−0.807967 + 0.589228i \(0.799432\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.857279 0.0506036
\(288\) 0 0
\(289\) 9.87601 0.580942
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.81579 0.164500 0.0822502 0.996612i \(-0.473789\pi\)
0.0822502 + 0.996612i \(0.473789\pi\)
\(294\) 0 0
\(295\) 4.85728 0.282802
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.51114 −0.318717
\(300\) 0 0
\(301\) −25.1240 −1.44812
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6.85728 −0.392647
\(306\) 0 0
\(307\) 24.4286 1.39422 0.697108 0.716966i \(-0.254470\pi\)
0.697108 + 0.716966i \(0.254470\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 19.8796 1.12727 0.563633 0.826025i \(-0.309403\pi\)
0.563633 + 0.826025i \(0.309403\pi\)
\(312\) 0 0
\(313\) −15.7146 −0.888239 −0.444120 0.895967i \(-0.646483\pi\)
−0.444120 + 0.895967i \(0.646483\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.4889 −0.926107 −0.463053 0.886330i \(-0.653246\pi\)
−0.463053 + 0.886330i \(0.653246\pi\)
\(318\) 0 0
\(319\) 7.80642 0.437076
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −36.5531 −2.03387
\(324\) 0 0
\(325\) −0.622216 −0.0345143
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −12.2034 −0.672796
\(330\) 0 0
\(331\) −15.3461 −0.843500 −0.421750 0.906712i \(-0.638584\pi\)
−0.421750 + 0.906712i \(0.638584\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.24443 −0.0679905
\(336\) 0 0
\(337\) 28.2351 1.53806 0.769031 0.639212i \(-0.220739\pi\)
0.769031 + 0.639212i \(0.220739\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.75557 −0.149222
\(342\) 0 0
\(343\) 24.8573 1.34217
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.62222 0.140768 0.0703840 0.997520i \(-0.477578\pi\)
0.0703840 + 0.997520i \(0.477578\pi\)
\(348\) 0 0
\(349\) 5.14272 0.275284 0.137642 0.990482i \(-0.456048\pi\)
0.137642 + 0.990482i \(0.456048\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.34614 0.497445 0.248722 0.968575i \(-0.419989\pi\)
0.248722 + 0.968575i \(0.419989\pi\)
\(354\) 0 0
\(355\) −2.75557 −0.146250
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.7556 0.567657 0.283829 0.958875i \(-0.408395\pi\)
0.283829 + 0.958875i \(0.408395\pi\)
\(360\) 0 0
\(361\) 30.7146 1.61656
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.23506 −0.221673
\(366\) 0 0
\(367\) −33.7975 −1.76422 −0.882108 0.471046i \(-0.843876\pi\)
−0.882108 + 0.471046i \(0.843876\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 48.0830 2.49634
\(372\) 0 0
\(373\) 33.9496 1.75784 0.878922 0.476965i \(-0.158263\pi\)
0.878922 + 0.476965i \(0.158263\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.85728 −0.250163
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.6351 −0.747820 −0.373910 0.927465i \(-0.621983\pi\)
−0.373910 + 0.927465i \(0.621983\pi\)
\(384\) 0 0
\(385\) −4.42864 −0.225704
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.61285 0.284583 0.142291 0.989825i \(-0.454553\pi\)
0.142291 + 0.989825i \(0.454553\pi\)
\(390\) 0 0
\(391\) 45.9180 2.32217
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.56199 0.430801
\(396\) 0 0
\(397\) −12.7556 −0.640184 −0.320092 0.947387i \(-0.603714\pi\)
−0.320092 + 0.947387i \(0.603714\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 1.71456 0.0854082
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.00000 −0.0991363
\(408\) 0 0
\(409\) −7.12399 −0.352258 −0.176129 0.984367i \(-0.556358\pi\)
−0.176129 + 0.984367i \(0.556358\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −21.5111 −1.05849
\(414\) 0 0
\(415\) −0.133353 −0.00654605
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15.6128 0.762738 0.381369 0.924423i \(-0.375453\pi\)
0.381369 + 0.924423i \(0.375453\pi\)
\(420\) 0 0
\(421\) 7.89829 0.384939 0.192470 0.981303i \(-0.438350\pi\)
0.192470 + 0.981303i \(0.438350\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.18421 0.251471
\(426\) 0 0
\(427\) 30.3684 1.46963
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 34.3051 1.65242 0.826210 0.563362i \(-0.190492\pi\)
0.826210 + 0.563362i \(0.190492\pi\)
\(432\) 0 0
\(433\) 14.4701 0.695390 0.347695 0.937608i \(-0.386964\pi\)
0.347695 + 0.937608i \(0.386964\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −62.4514 −2.98746
\(438\) 0 0
\(439\) 19.3176 0.921977 0.460988 0.887406i \(-0.347495\pi\)
0.460988 + 0.887406i \(0.347495\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.1240 −0.623539 −0.311770 0.950158i \(-0.600922\pi\)
−0.311770 + 0.950158i \(0.600922\pi\)
\(444\) 0 0
\(445\) 5.61285 0.266074
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 32.3051 1.52457 0.762287 0.647240i \(-0.224077\pi\)
0.762287 + 0.647240i \(0.224077\pi\)
\(450\) 0 0
\(451\) 0.193576 0.00911514
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.75557 0.129183
\(456\) 0 0
\(457\) −23.4608 −1.09745 −0.548724 0.836004i \(-0.684886\pi\)
−0.548724 + 0.836004i \(0.684886\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 28.8671 1.34448 0.672238 0.740335i \(-0.265333\pi\)
0.672238 + 0.740335i \(0.265333\pi\)
\(462\) 0 0
\(463\) 19.3461 0.899091 0.449546 0.893257i \(-0.351586\pi\)
0.449546 + 0.893257i \(0.351586\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.14272 0.145428 0.0727139 0.997353i \(-0.476834\pi\)
0.0727139 + 0.997353i \(0.476834\pi\)
\(468\) 0 0
\(469\) 5.51114 0.254481
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.67307 −0.260848
\(474\) 0 0
\(475\) −7.05086 −0.323515
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −24.8573 −1.13576 −0.567879 0.823112i \(-0.692236\pi\)
−0.567879 + 0.823112i \(0.692236\pi\)
\(480\) 0 0
\(481\) 1.24443 0.0567412
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.24443 −0.328953
\(486\) 0 0
\(487\) 11.5299 0.522468 0.261234 0.965275i \(-0.415871\pi\)
0.261234 + 0.965275i \(0.415871\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16.3872 0.739542 0.369771 0.929123i \(-0.379436\pi\)
0.369771 + 0.929123i \(0.379436\pi\)
\(492\) 0 0
\(493\) 40.4701 1.82268
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.2034 0.547398
\(498\) 0 0
\(499\) 25.3274 1.13381 0.566905 0.823783i \(-0.308141\pi\)
0.566905 + 0.823783i \(0.308141\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 19.0923 0.851285 0.425643 0.904891i \(-0.360048\pi\)
0.425643 + 0.904891i \(0.360048\pi\)
\(504\) 0 0
\(505\) 4.66370 0.207532
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 32.4514 1.43838 0.719191 0.694812i \(-0.244512\pi\)
0.719191 + 0.694812i \(0.244512\pi\)
\(510\) 0 0
\(511\) 18.7556 0.829698
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11.6128 −0.511723
\(516\) 0 0
\(517\) −2.75557 −0.121190
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 29.2257 1.28040 0.640200 0.768208i \(-0.278851\pi\)
0.640200 + 0.768208i \(0.278851\pi\)
\(522\) 0 0
\(523\) −6.71408 −0.293586 −0.146793 0.989167i \(-0.546895\pi\)
−0.146793 + 0.989167i \(0.546895\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.2854 −0.622284
\(528\) 0 0
\(529\) 55.4514 2.41093
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.120446 −0.00521710
\(534\) 0 0
\(535\) −2.62222 −0.113368
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 12.6128 0.543274
\(540\) 0 0
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 19.7146 0.844479
\(546\) 0 0
\(547\) −41.3689 −1.76881 −0.884403 0.466724i \(-0.845434\pi\)
−0.884403 + 0.466724i \(0.845434\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −55.0420 −2.34487
\(552\) 0 0
\(553\) −37.9180 −1.61244
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 20.7971 0.881200 0.440600 0.897704i \(-0.354766\pi\)
0.440600 + 0.897704i \(0.354766\pi\)
\(558\) 0 0
\(559\) 3.52987 0.149298
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 37.7275 1.59002 0.795012 0.606594i \(-0.207465\pi\)
0.795012 + 0.606594i \(0.207465\pi\)
\(564\) 0 0
\(565\) −6.00000 −0.252422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.33630 0.307554 0.153777 0.988106i \(-0.450856\pi\)
0.153777 + 0.988106i \(0.450856\pi\)
\(570\) 0 0
\(571\) −36.6450 −1.53354 −0.766772 0.641919i \(-0.778138\pi\)
−0.766772 + 0.641919i \(0.778138\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.85728 0.369374
\(576\) 0 0
\(577\) 4.22216 0.175771 0.0878853 0.996131i \(-0.471989\pi\)
0.0878853 + 0.996131i \(0.471989\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.590573 0.0245011
\(582\) 0 0
\(583\) 10.8573 0.449663
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 34.3684 1.41854 0.709268 0.704939i \(-0.249026\pi\)
0.709268 + 0.704939i \(0.249026\pi\)
\(588\) 0 0
\(589\) 19.4291 0.800563
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −27.9398 −1.14735 −0.573675 0.819083i \(-0.694483\pi\)
−0.573675 + 0.819083i \(0.694483\pi\)
\(594\) 0 0
\(595\) −22.9590 −0.941227
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −31.2257 −1.27585 −0.637924 0.770100i \(-0.720206\pi\)
−0.637924 + 0.770100i \(0.720206\pi\)
\(600\) 0 0
\(601\) −8.75557 −0.357147 −0.178574 0.983927i \(-0.557148\pi\)
−0.178574 + 0.983927i \(0.557148\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.00000 −0.0406558
\(606\) 0 0
\(607\) 15.1842 0.616308 0.308154 0.951336i \(-0.400289\pi\)
0.308154 + 0.951336i \(0.400289\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.71456 0.0693636
\(612\) 0 0
\(613\) 42.7239 1.72560 0.862802 0.505543i \(-0.168708\pi\)
0.862802 + 0.505543i \(0.168708\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.51114 0.141353 0.0706765 0.997499i \(-0.477484\pi\)
0.0706765 + 0.997499i \(0.477484\pi\)
\(618\) 0 0
\(619\) −17.5941 −0.707167 −0.353584 0.935403i \(-0.615037\pi\)
−0.353584 + 0.935403i \(0.615037\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −24.8573 −0.995886
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −10.3684 −0.413416
\(630\) 0 0
\(631\) −15.8163 −0.629636 −0.314818 0.949152i \(-0.601943\pi\)
−0.314818 + 0.949152i \(0.601943\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −15.1842 −0.602567
\(636\) 0 0
\(637\) −7.84791 −0.310946
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −25.8163 −1.01968 −0.509841 0.860269i \(-0.670296\pi\)
−0.509841 + 0.860269i \(0.670296\pi\)
\(642\) 0 0
\(643\) −18.1017 −0.713862 −0.356931 0.934131i \(-0.616177\pi\)
−0.356931 + 0.934131i \(0.616177\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −47.0420 −1.84941 −0.924705 0.380684i \(-0.875689\pi\)
−0.924705 + 0.380684i \(0.875689\pi\)
\(648\) 0 0
\(649\) −4.85728 −0.190665
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −30.0830 −1.17724 −0.588619 0.808411i \(-0.700328\pi\)
−0.588619 + 0.808411i \(0.700328\pi\)
\(654\) 0 0
\(655\) −1.24443 −0.0486240
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −10.2854 −0.400664 −0.200332 0.979728i \(-0.564202\pi\)
−0.200332 + 0.979728i \(0.564202\pi\)
\(660\) 0 0
\(661\) −27.7146 −1.07797 −0.538986 0.842315i \(-0.681192\pi\)
−0.538986 + 0.842315i \(0.681192\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 31.2257 1.21088
\(666\) 0 0
\(667\) 69.1437 2.67725
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.85728 0.264722
\(672\) 0 0
\(673\) −9.86665 −0.380331 −0.190166 0.981752i \(-0.560903\pi\)
−0.190166 + 0.981752i \(0.560903\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 5.65433 0.217314 0.108657 0.994079i \(-0.465345\pi\)
0.108657 + 0.994079i \(0.465345\pi\)
\(678\) 0 0
\(679\) 32.0830 1.23123
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34.1847 1.30804 0.654020 0.756477i \(-0.273081\pi\)
0.654020 + 0.756477i \(0.273081\pi\)
\(684\) 0 0
\(685\) −0.488863 −0.0186785
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6.75557 −0.257367
\(690\) 0 0
\(691\) 19.2257 0.731380 0.365690 0.930737i \(-0.380833\pi\)
0.365690 + 0.930737i \(0.380833\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 17.8064 0.675436
\(696\) 0 0
\(697\) 1.00354 0.0380118
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 29.9081 1.12961 0.564807 0.825223i \(-0.308950\pi\)
0.564807 + 0.825223i \(0.308950\pi\)
\(702\) 0 0
\(703\) 14.1017 0.531856
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.6539 −0.776768
\(708\) 0 0
\(709\) −15.3274 −0.575633 −0.287816 0.957686i \(-0.592929\pi\)
−0.287816 + 0.957686i \(0.592929\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −24.4068 −0.914043
\(714\) 0 0
\(715\) 0.622216 0.0232695
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 23.8163 0.888197 0.444098 0.895978i \(-0.353524\pi\)
0.444098 + 0.895978i \(0.353524\pi\)
\(720\) 0 0
\(721\) 51.4291 1.91532
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7.80642 0.289923
\(726\) 0 0
\(727\) 32.9403 1.22169 0.610843 0.791752i \(-0.290831\pi\)
0.610843 + 0.791752i \(0.290831\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −29.4104 −1.08778
\(732\) 0 0
\(733\) −29.8666 −1.10315 −0.551575 0.834125i \(-0.685973\pi\)
−0.551575 + 0.834125i \(0.685973\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.24443 0.0458392
\(738\) 0 0
\(739\) 5.06959 0.186488 0.0932440 0.995643i \(-0.470276\pi\)
0.0932440 + 0.995643i \(0.470276\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 22.4385 0.823188 0.411594 0.911367i \(-0.364972\pi\)
0.411594 + 0.911367i \(0.364972\pi\)
\(744\) 0 0
\(745\) −1.43801 −0.0526845
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 11.6128 0.424324
\(750\) 0 0
\(751\) 6.63512 0.242119 0.121060 0.992645i \(-0.461371\pi\)
0.121060 + 0.992645i \(0.461371\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12.1748 −0.443088
\(756\) 0 0
\(757\) 8.75557 0.318227 0.159113 0.987260i \(-0.449136\pi\)
0.159113 + 0.987260i \(0.449136\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.15257 −0.114280 −0.0571402 0.998366i \(-0.518198\pi\)
−0.0571402 + 0.998366i \(0.518198\pi\)
\(762\) 0 0
\(763\) −87.3087 −3.16079
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.02227 0.109128
\(768\) 0 0
\(769\) −28.9590 −1.04429 −0.522144 0.852857i \(-0.674868\pi\)
−0.522144 + 0.852857i \(0.674868\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −29.1427 −1.04819 −0.524095 0.851660i \(-0.675596\pi\)
−0.524095 + 0.851660i \(0.675596\pi\)
\(774\) 0 0
\(775\) −2.75557 −0.0989830
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.36488 −0.0489018
\(780\) 0 0
\(781\) 2.75557 0.0986020
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −18.4701 −0.659227
\(786\) 0 0
\(787\) 11.2672 0.401632 0.200816 0.979629i \(-0.435641\pi\)
0.200816 + 0.979629i \(0.435641\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 26.5718 0.944786
\(792\) 0 0
\(793\) −4.26671 −0.151515
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −41.9625 −1.48639 −0.743195 0.669075i \(-0.766690\pi\)
−0.743195 + 0.669075i \(0.766690\pi\)
\(798\) 0 0
\(799\) −14.2854 −0.505383
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.23506 0.149452
\(804\) 0 0
\(805\) −39.2257 −1.38252
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27.8064 0.977622 0.488811 0.872390i \(-0.337431\pi\)
0.488811 + 0.872390i \(0.337431\pi\)
\(810\) 0 0
\(811\) −6.78415 −0.238224 −0.119112 0.992881i \(-0.538005\pi\)
−0.119112 + 0.992881i \(0.538005\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −10.1017 −0.353847
\(816\) 0 0
\(817\) 40.0000 1.39942
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.62269 −0.126433 −0.0632164 0.998000i \(-0.520136\pi\)
−0.0632164 + 0.998000i \(0.520136\pi\)
\(822\) 0 0
\(823\) −42.0642 −1.46627 −0.733134 0.680085i \(-0.761943\pi\)
−0.733134 + 0.680085i \(0.761943\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 30.8256 1.07191 0.535956 0.844246i \(-0.319951\pi\)
0.535956 + 0.844246i \(0.319951\pi\)
\(828\) 0 0
\(829\) 7.12399 0.247426 0.123713 0.992318i \(-0.460520\pi\)
0.123713 + 0.992318i \(0.460520\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 65.3876 2.26555
\(834\) 0 0
\(835\) 16.3368 0.565357
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 3.34614 0.115522 0.0577608 0.998330i \(-0.481604\pi\)
0.0577608 + 0.998330i \(0.481604\pi\)
\(840\) 0 0
\(841\) 31.9403 1.10139
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 12.6128 0.433895
\(846\) 0 0
\(847\) 4.42864 0.152170
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −17.7146 −0.607247
\(852\) 0 0
\(853\) −26.4197 −0.904595 −0.452297 0.891867i \(-0.649395\pi\)
−0.452297 + 0.891867i \(0.649395\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −38.7783 −1.32464 −0.662321 0.749220i \(-0.730429\pi\)
−0.662321 + 0.749220i \(0.730429\pi\)
\(858\) 0 0
\(859\) 27.3087 0.931760 0.465880 0.884848i \(-0.345738\pi\)
0.465880 + 0.884848i \(0.345738\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −49.5308 −1.68605 −0.843024 0.537875i \(-0.819227\pi\)
−0.843024 + 0.537875i \(0.819227\pi\)
\(864\) 0 0
\(865\) −9.18421 −0.312272
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −8.56199 −0.290446
\(870\) 0 0
\(871\) −0.774305 −0.0262363
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.42864 −0.149715
\(876\) 0 0
\(877\) −4.50177 −0.152014 −0.0760070 0.997107i \(-0.524217\pi\)
−0.0760070 + 0.997107i \(0.524217\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 15.1240 0.509540 0.254770 0.967002i \(-0.418000\pi\)
0.254770 + 0.967002i \(0.418000\pi\)
\(882\) 0 0
\(883\) 30.2480 1.01793 0.508963 0.860789i \(-0.330029\pi\)
0.508963 + 0.860789i \(0.330029\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 57.1941 1.92039 0.960194 0.279333i \(-0.0901135\pi\)
0.960194 + 0.279333i \(0.0901135\pi\)
\(888\) 0 0
\(889\) 67.2454 2.25534
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 19.4291 0.650171
\(894\) 0 0
\(895\) 25.3274 0.846602
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −21.5111 −0.717437
\(900\) 0 0
\(901\) 56.2864 1.87517
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 13.6128 0.452506
\(906\) 0 0
\(907\) 53.2641 1.76861 0.884303 0.466913i \(-0.154634\pi\)
0.884303 + 0.466913i \(0.154634\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.590573 −0.0195665 −0.00978327 0.999952i \(-0.503114\pi\)
−0.00978327 + 0.999952i \(0.503114\pi\)
\(912\) 0 0
\(913\) 0.133353 0.00441334
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5.51114 0.181994
\(918\) 0 0
\(919\) −55.8707 −1.84300 −0.921502 0.388375i \(-0.873037\pi\)
−0.921502 + 0.388375i \(0.873037\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.71456 −0.0564354
\(924\) 0 0
\(925\) −2.00000 −0.0657596
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −15.3274 −0.502876 −0.251438 0.967873i \(-0.580903\pi\)
−0.251438 + 0.967873i \(0.580903\pi\)
\(930\) 0 0
\(931\) −88.9314 −2.91461
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −5.18421 −0.169542
\(936\) 0 0
\(937\) −27.8479 −0.909752 −0.454876 0.890555i \(-0.650316\pi\)
−0.454876 + 0.890555i \(0.650316\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −10.4157 −0.339543 −0.169772 0.985483i \(-0.554303\pi\)
−0.169772 + 0.985483i \(0.554303\pi\)
\(942\) 0 0
\(943\) 1.71456 0.0558337
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.47013 0.275242 0.137621 0.990485i \(-0.456054\pi\)
0.137621 + 0.990485i \(0.456054\pi\)
\(948\) 0 0
\(949\) −2.63512 −0.0855397
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 8.71408 0.282277 0.141138 0.989990i \(-0.454924\pi\)
0.141138 + 0.989990i \(0.454924\pi\)
\(954\) 0 0
\(955\) −6.10171 −0.197447
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.16500 0.0699114
\(960\) 0 0
\(961\) −23.4068 −0.755059
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −18.3368 −0.590282
\(966\) 0 0
\(967\) −44.2449 −1.42282 −0.711410 0.702777i \(-0.751943\pi\)
−0.711410 + 0.702777i \(0.751943\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −57.1437 −1.83383 −0.916914 0.399085i \(-0.869328\pi\)
−0.916914 + 0.399085i \(0.869328\pi\)
\(972\) 0 0
\(973\) −78.8582 −2.52808
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 16.2480 0.519819 0.259909 0.965633i \(-0.416307\pi\)
0.259909 + 0.965633i \(0.416307\pi\)
\(978\) 0 0
\(979\) −5.61285 −0.179387
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.12399 0.0358496 0.0179248 0.999839i \(-0.494294\pi\)
0.0179248 + 0.999839i \(0.494294\pi\)
\(984\) 0 0
\(985\) −6.69535 −0.213331
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −50.2480 −1.59779
\(990\) 0 0
\(991\) 53.6513 1.70429 0.852144 0.523307i \(-0.175302\pi\)
0.852144 + 0.523307i \(0.175302\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 14.1017 0.447054
\(996\) 0 0
\(997\) −35.7275 −1.13150 −0.565750 0.824577i \(-0.691413\pi\)
−0.565750 + 0.824577i \(0.691413\pi\)
\(998\) 0 0
\(999\) 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 7920.2.a.cj.1.3 3
3.2 odd 2 2640.2.a.be.1.3 3
4.3 odd 2 495.2.a.e.1.1 3
12.11 even 2 165.2.a.c.1.3 3
20.3 even 4 2475.2.c.r.199.5 6
20.7 even 4 2475.2.c.r.199.2 6
20.19 odd 2 2475.2.a.bb.1.3 3
44.43 even 2 5445.2.a.z.1.3 3
60.23 odd 4 825.2.c.g.199.2 6
60.47 odd 4 825.2.c.g.199.5 6
60.59 even 2 825.2.a.k.1.1 3
84.83 odd 2 8085.2.a.bk.1.3 3
132.131 odd 2 1815.2.a.m.1.1 3
660.659 odd 2 9075.2.a.cf.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.a.c.1.3 3 12.11 even 2
495.2.a.e.1.1 3 4.3 odd 2
825.2.a.k.1.1 3 60.59 even 2
825.2.c.g.199.2 6 60.23 odd 4
825.2.c.g.199.5 6 60.47 odd 4
1815.2.a.m.1.1 3 132.131 odd 2
2475.2.a.bb.1.3 3 20.19 odd 2
2475.2.c.r.199.2 6 20.7 even 4
2475.2.c.r.199.5 6 20.3 even 4
2640.2.a.be.1.3 3 3.2 odd 2
5445.2.a.z.1.3 3 44.43 even 2
7920.2.a.cj.1.3 3 1.1 even 1 trivial
8085.2.a.bk.1.3 3 84.83 odd 2
9075.2.a.cf.1.3 3 660.659 odd 2