Properties

Label 608.4.a.k.1.6
Level $608$
Weight $4$
Character 608.1
Self dual yes
Analytic conductor $35.873$
Analytic rank $0$
Dimension $7$
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] = [608,4,Mod(1,608)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(608, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("608.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 608.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: \(35.8731612835\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 3x^{6} - 121x^{5} + 402x^{4} + 4234x^{3} - 14542x^{2} - 40996x + 141664 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(7.37394\) of defining polynomial
Character \(\chi\) \(=\) 608.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+6.88542 q^{3} +4.69330 q^{5} +3.62949 q^{7} +20.4091 q^{9} +O(q^{10})\) \(q+6.88542 q^{3} +4.69330 q^{5} +3.62949 q^{7} +20.4091 q^{9} +43.4975 q^{11} +75.0368 q^{13} +32.3154 q^{15} -13.1508 q^{17} -19.0000 q^{19} +24.9906 q^{21} -96.5591 q^{23} -102.973 q^{25} -45.3813 q^{27} +40.5580 q^{29} +138.828 q^{31} +299.499 q^{33} +17.0343 q^{35} +348.686 q^{37} +516.660 q^{39} -44.3243 q^{41} +214.385 q^{43} +95.7860 q^{45} -334.307 q^{47} -329.827 q^{49} -90.5487 q^{51} +311.122 q^{53} +204.147 q^{55} -130.823 q^{57} +502.875 q^{59} -54.7193 q^{61} +74.0746 q^{63} +352.170 q^{65} +312.959 q^{67} -664.850 q^{69} +642.657 q^{71} -837.348 q^{73} -709.012 q^{75} +157.874 q^{77} +349.595 q^{79} -863.515 q^{81} +521.399 q^{83} -61.7206 q^{85} +279.259 q^{87} +63.4094 q^{89} +272.345 q^{91} +955.887 q^{93} -89.1728 q^{95} -1229.92 q^{97} +887.745 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 3 q^{3} - 17 q^{5} + 42 q^{7} + 86 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 3 q^{3} - 17 q^{5} + 42 q^{7} + 86 q^{9} - 33 q^{11} - 35 q^{13} + 120 q^{15} + 66 q^{17} - 133 q^{19} + 33 q^{21} + 389 q^{23} + 44 q^{25} - 39 q^{27} + 233 q^{29} + 158 q^{31} - 206 q^{33} + 123 q^{35} - 436 q^{37} + 807 q^{39} - 94 q^{41} + 645 q^{43} + 103 q^{45} + 1451 q^{47} + 93 q^{49} + 1741 q^{51} + 3 q^{53} + 1971 q^{55} - 57 q^{57} + 297 q^{59} + 93 q^{61} + 2999 q^{63} - 788 q^{65} + 1641 q^{67} + 945 q^{69} + 2392 q^{71} + 324 q^{73} + 1909 q^{75} - 711 q^{77} + 2492 q^{79} + 143 q^{81} + 310 q^{83} + 2353 q^{85} + 4795 q^{87} - 440 q^{89} - 107 q^{91} + 900 q^{93} + 323 q^{95} - 532 q^{97} - 1591 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 6.88542 1.32510 0.662550 0.749017i \(-0.269474\pi\)
0.662550 + 0.749017i \(0.269474\pi\)
\(4\) 0 0
\(5\) 4.69330 0.419782 0.209891 0.977725i \(-0.432689\pi\)
0.209891 + 0.977725i \(0.432689\pi\)
\(6\) 0 0
\(7\) 3.62949 0.195974 0.0979871 0.995188i \(-0.468760\pi\)
0.0979871 + 0.995188i \(0.468760\pi\)
\(8\) 0 0
\(9\) 20.4091 0.755892
\(10\) 0 0
\(11\) 43.4975 1.19227 0.596137 0.802883i \(-0.296702\pi\)
0.596137 + 0.802883i \(0.296702\pi\)
\(12\) 0 0
\(13\) 75.0368 1.60088 0.800441 0.599412i \(-0.204599\pi\)
0.800441 + 0.599412i \(0.204599\pi\)
\(14\) 0 0
\(15\) 32.3154 0.556253
\(16\) 0 0
\(17\) −13.1508 −0.187620 −0.0938098 0.995590i \(-0.529905\pi\)
−0.0938098 + 0.995590i \(0.529905\pi\)
\(18\) 0 0
\(19\) −19.0000 −0.229416
\(20\) 0 0
\(21\) 24.9906 0.259686
\(22\) 0 0
\(23\) −96.5591 −0.875390 −0.437695 0.899124i \(-0.644205\pi\)
−0.437695 + 0.899124i \(0.644205\pi\)
\(24\) 0 0
\(25\) −102.973 −0.823783
\(26\) 0 0
\(27\) −45.3813 −0.323468
\(28\) 0 0
\(29\) 40.5580 0.259704 0.129852 0.991533i \(-0.458550\pi\)
0.129852 + 0.991533i \(0.458550\pi\)
\(30\) 0 0
\(31\) 138.828 0.804328 0.402164 0.915568i \(-0.368258\pi\)
0.402164 + 0.915568i \(0.368258\pi\)
\(32\) 0 0
\(33\) 299.499 1.57988
\(34\) 0 0
\(35\) 17.0343 0.0822664
\(36\) 0 0
\(37\) 348.686 1.54929 0.774644 0.632398i \(-0.217929\pi\)
0.774644 + 0.632398i \(0.217929\pi\)
\(38\) 0 0
\(39\) 516.660 2.12133
\(40\) 0 0
\(41\) −44.3243 −0.168836 −0.0844182 0.996430i \(-0.526903\pi\)
−0.0844182 + 0.996430i \(0.526903\pi\)
\(42\) 0 0
\(43\) 214.385 0.760313 0.380157 0.924922i \(-0.375870\pi\)
0.380157 + 0.924922i \(0.375870\pi\)
\(44\) 0 0
\(45\) 95.7860 0.317310
\(46\) 0 0
\(47\) −334.307 −1.03752 −0.518762 0.854919i \(-0.673607\pi\)
−0.518762 + 0.854919i \(0.673607\pi\)
\(48\) 0 0
\(49\) −329.827 −0.961594
\(50\) 0 0
\(51\) −90.5487 −0.248615
\(52\) 0 0
\(53\) 311.122 0.806338 0.403169 0.915126i \(-0.367909\pi\)
0.403169 + 0.915126i \(0.367909\pi\)
\(54\) 0 0
\(55\) 204.147 0.500495
\(56\) 0 0
\(57\) −130.823 −0.303999
\(58\) 0 0
\(59\) 502.875 1.10964 0.554820 0.831971i \(-0.312787\pi\)
0.554820 + 0.831971i \(0.312787\pi\)
\(60\) 0 0
\(61\) −54.7193 −0.114854 −0.0574270 0.998350i \(-0.518290\pi\)
−0.0574270 + 0.998350i \(0.518290\pi\)
\(62\) 0 0
\(63\) 74.0746 0.148135
\(64\) 0 0
\(65\) 352.170 0.672021
\(66\) 0 0
\(67\) 312.959 0.570658 0.285329 0.958430i \(-0.407897\pi\)
0.285329 + 0.958430i \(0.407897\pi\)
\(68\) 0 0
\(69\) −664.850 −1.15998
\(70\) 0 0
\(71\) 642.657 1.07422 0.537108 0.843513i \(-0.319517\pi\)
0.537108 + 0.843513i \(0.319517\pi\)
\(72\) 0 0
\(73\) −837.348 −1.34252 −0.671261 0.741221i \(-0.734247\pi\)
−0.671261 + 0.741221i \(0.734247\pi\)
\(74\) 0 0
\(75\) −709.012 −1.09160
\(76\) 0 0
\(77\) 157.874 0.233655
\(78\) 0 0
\(79\) 349.595 0.497880 0.248940 0.968519i \(-0.419918\pi\)
0.248940 + 0.968519i \(0.419918\pi\)
\(80\) 0 0
\(81\) −863.515 −1.18452
\(82\) 0 0
\(83\) 521.399 0.689530 0.344765 0.938689i \(-0.387959\pi\)
0.344765 + 0.938689i \(0.387959\pi\)
\(84\) 0 0
\(85\) −61.7206 −0.0787593
\(86\) 0 0
\(87\) 279.259 0.344135
\(88\) 0 0
\(89\) 63.4094 0.0755211 0.0377606 0.999287i \(-0.487978\pi\)
0.0377606 + 0.999287i \(0.487978\pi\)
\(90\) 0 0
\(91\) 272.345 0.313731
\(92\) 0 0
\(93\) 955.887 1.06582
\(94\) 0 0
\(95\) −89.1728 −0.0963046
\(96\) 0 0
\(97\) −1229.92 −1.28742 −0.643711 0.765269i \(-0.722606\pi\)
−0.643711 + 0.765269i \(0.722606\pi\)
\(98\) 0 0
\(99\) 887.745 0.901229
\(100\) 0 0
\(101\) −1077.89 −1.06192 −0.530962 0.847396i \(-0.678169\pi\)
−0.530962 + 0.847396i \(0.678169\pi\)
\(102\) 0 0
\(103\) 1896.77 1.81451 0.907255 0.420580i \(-0.138174\pi\)
0.907255 + 0.420580i \(0.138174\pi\)
\(104\) 0 0
\(105\) 117.288 0.109011
\(106\) 0 0
\(107\) −480.564 −0.434186 −0.217093 0.976151i \(-0.569657\pi\)
−0.217093 + 0.976151i \(0.569657\pi\)
\(108\) 0 0
\(109\) 124.669 0.109552 0.0547758 0.998499i \(-0.482556\pi\)
0.0547758 + 0.998499i \(0.482556\pi\)
\(110\) 0 0
\(111\) 2400.85 2.05296
\(112\) 0 0
\(113\) −1778.75 −1.48080 −0.740400 0.672166i \(-0.765364\pi\)
−0.740400 + 0.672166i \(0.765364\pi\)
\(114\) 0 0
\(115\) −453.181 −0.367473
\(116\) 0 0
\(117\) 1531.43 1.21009
\(118\) 0 0
\(119\) −47.7307 −0.0367686
\(120\) 0 0
\(121\) 561.036 0.421515
\(122\) 0 0
\(123\) −305.191 −0.223725
\(124\) 0 0
\(125\) −1069.95 −0.765591
\(126\) 0 0
\(127\) 1077.80 0.753068 0.376534 0.926403i \(-0.377116\pi\)
0.376534 + 0.926403i \(0.377116\pi\)
\(128\) 0 0
\(129\) 1476.13 1.00749
\(130\) 0 0
\(131\) −1092.79 −0.728835 −0.364417 0.931236i \(-0.618732\pi\)
−0.364417 + 0.931236i \(0.618732\pi\)
\(132\) 0 0
\(133\) −68.9604 −0.0449596
\(134\) 0 0
\(135\) −212.988 −0.135786
\(136\) 0 0
\(137\) 3052.21 1.90341 0.951706 0.307010i \(-0.0993286\pi\)
0.951706 + 0.307010i \(0.0993286\pi\)
\(138\) 0 0
\(139\) −1428.73 −0.871821 −0.435911 0.899990i \(-0.643574\pi\)
−0.435911 + 0.899990i \(0.643574\pi\)
\(140\) 0 0
\(141\) −2301.84 −1.37482
\(142\) 0 0
\(143\) 3263.92 1.90869
\(144\) 0 0
\(145\) 190.351 0.109019
\(146\) 0 0
\(147\) −2271.00 −1.27421
\(148\) 0 0
\(149\) 571.022 0.313959 0.156980 0.987602i \(-0.449824\pi\)
0.156980 + 0.987602i \(0.449824\pi\)
\(150\) 0 0
\(151\) −997.782 −0.537737 −0.268869 0.963177i \(-0.586650\pi\)
−0.268869 + 0.963177i \(0.586650\pi\)
\(152\) 0 0
\(153\) −268.395 −0.141820
\(154\) 0 0
\(155\) 651.560 0.337642
\(156\) 0 0
\(157\) −2171.23 −1.10371 −0.551857 0.833939i \(-0.686080\pi\)
−0.551857 + 0.833939i \(0.686080\pi\)
\(158\) 0 0
\(159\) 2142.21 1.06848
\(160\) 0 0
\(161\) −350.461 −0.171554
\(162\) 0 0
\(163\) 305.488 0.146795 0.0733977 0.997303i \(-0.476616\pi\)
0.0733977 + 0.997303i \(0.476616\pi\)
\(164\) 0 0
\(165\) 1405.64 0.663206
\(166\) 0 0
\(167\) −136.673 −0.0633300 −0.0316650 0.999499i \(-0.510081\pi\)
−0.0316650 + 0.999499i \(0.510081\pi\)
\(168\) 0 0
\(169\) 3433.52 1.56282
\(170\) 0 0
\(171\) −387.772 −0.173413
\(172\) 0 0
\(173\) −1508.96 −0.663144 −0.331572 0.943430i \(-0.607579\pi\)
−0.331572 + 0.943430i \(0.607579\pi\)
\(174\) 0 0
\(175\) −373.739 −0.161440
\(176\) 0 0
\(177\) 3462.51 1.47038
\(178\) 0 0
\(179\) 770.548 0.321751 0.160875 0.986975i \(-0.448568\pi\)
0.160875 + 0.986975i \(0.448568\pi\)
\(180\) 0 0
\(181\) 2292.62 0.941486 0.470743 0.882270i \(-0.343986\pi\)
0.470743 + 0.882270i \(0.343986\pi\)
\(182\) 0 0
\(183\) −376.766 −0.152193
\(184\) 0 0
\(185\) 1636.49 0.650363
\(186\) 0 0
\(187\) −572.027 −0.223694
\(188\) 0 0
\(189\) −164.711 −0.0633914
\(190\) 0 0
\(191\) −1670.39 −0.632803 −0.316402 0.948625i \(-0.602475\pi\)
−0.316402 + 0.948625i \(0.602475\pi\)
\(192\) 0 0
\(193\) −663.849 −0.247590 −0.123795 0.992308i \(-0.539507\pi\)
−0.123795 + 0.992308i \(0.539507\pi\)
\(194\) 0 0
\(195\) 2424.84 0.890495
\(196\) 0 0
\(197\) −2470.86 −0.893611 −0.446806 0.894631i \(-0.647438\pi\)
−0.446806 + 0.894631i \(0.647438\pi\)
\(198\) 0 0
\(199\) −4348.26 −1.54894 −0.774472 0.632608i \(-0.781984\pi\)
−0.774472 + 0.632608i \(0.781984\pi\)
\(200\) 0 0
\(201\) 2154.86 0.756179
\(202\) 0 0
\(203\) 147.205 0.0508954
\(204\) 0 0
\(205\) −208.027 −0.0708744
\(206\) 0 0
\(207\) −1970.68 −0.661700
\(208\) 0 0
\(209\) −826.453 −0.273526
\(210\) 0 0
\(211\) −3910.79 −1.27597 −0.637986 0.770048i \(-0.720232\pi\)
−0.637986 + 0.770048i \(0.720232\pi\)
\(212\) 0 0
\(213\) 4424.97 1.42344
\(214\) 0 0
\(215\) 1006.18 0.319166
\(216\) 0 0
\(217\) 503.874 0.157628
\(218\) 0 0
\(219\) −5765.50 −1.77898
\(220\) 0 0
\(221\) −986.792 −0.300357
\(222\) 0 0
\(223\) −70.6739 −0.0212228 −0.0106114 0.999944i \(-0.503378\pi\)
−0.0106114 + 0.999944i \(0.503378\pi\)
\(224\) 0 0
\(225\) −2101.58 −0.622691
\(226\) 0 0
\(227\) −1132.37 −0.331091 −0.165546 0.986202i \(-0.552939\pi\)
−0.165546 + 0.986202i \(0.552939\pi\)
\(228\) 0 0
\(229\) 2922.00 0.843194 0.421597 0.906783i \(-0.361470\pi\)
0.421597 + 0.906783i \(0.361470\pi\)
\(230\) 0 0
\(231\) 1087.03 0.309616
\(232\) 0 0
\(233\) −926.052 −0.260376 −0.130188 0.991489i \(-0.541558\pi\)
−0.130188 + 0.991489i \(0.541558\pi\)
\(234\) 0 0
\(235\) −1569.00 −0.435534
\(236\) 0 0
\(237\) 2407.11 0.659740
\(238\) 0 0
\(239\) 4376.11 1.18438 0.592190 0.805798i \(-0.298263\pi\)
0.592190 + 0.805798i \(0.298263\pi\)
\(240\) 0 0
\(241\) −3964.69 −1.05970 −0.529850 0.848091i \(-0.677752\pi\)
−0.529850 + 0.848091i \(0.677752\pi\)
\(242\) 0 0
\(243\) −4720.37 −1.24614
\(244\) 0 0
\(245\) −1547.98 −0.403660
\(246\) 0 0
\(247\) −1425.70 −0.367267
\(248\) 0 0
\(249\) 3590.05 0.913697
\(250\) 0 0
\(251\) −219.854 −0.0552870 −0.0276435 0.999618i \(-0.508800\pi\)
−0.0276435 + 0.999618i \(0.508800\pi\)
\(252\) 0 0
\(253\) −4200.08 −1.04370
\(254\) 0 0
\(255\) −424.973 −0.104364
\(256\) 0 0
\(257\) −5582.44 −1.35495 −0.677477 0.735544i \(-0.736926\pi\)
−0.677477 + 0.735544i \(0.736926\pi\)
\(258\) 0 0
\(259\) 1265.55 0.303620
\(260\) 0 0
\(261\) 827.751 0.196308
\(262\) 0 0
\(263\) −2971.76 −0.696755 −0.348378 0.937354i \(-0.613267\pi\)
−0.348378 + 0.937354i \(0.613267\pi\)
\(264\) 0 0
\(265\) 1460.19 0.338486
\(266\) 0 0
\(267\) 436.601 0.100073
\(268\) 0 0
\(269\) −5969.51 −1.35304 −0.676519 0.736425i \(-0.736513\pi\)
−0.676519 + 0.736425i \(0.736513\pi\)
\(270\) 0 0
\(271\) 6355.51 1.42461 0.712306 0.701869i \(-0.247651\pi\)
0.712306 + 0.701869i \(0.247651\pi\)
\(272\) 0 0
\(273\) 1875.21 0.415726
\(274\) 0 0
\(275\) −4479.07 −0.982174
\(276\) 0 0
\(277\) −8038.80 −1.74370 −0.871849 0.489774i \(-0.837079\pi\)
−0.871849 + 0.489774i \(0.837079\pi\)
\(278\) 0 0
\(279\) 2833.34 0.607985
\(280\) 0 0
\(281\) −4478.81 −0.950831 −0.475416 0.879761i \(-0.657702\pi\)
−0.475416 + 0.879761i \(0.657702\pi\)
\(282\) 0 0
\(283\) 8812.45 1.85105 0.925523 0.378691i \(-0.123626\pi\)
0.925523 + 0.378691i \(0.123626\pi\)
\(284\) 0 0
\(285\) −613.992 −0.127613
\(286\) 0 0
\(287\) −160.875 −0.0330876
\(288\) 0 0
\(289\) −4740.06 −0.964799
\(290\) 0 0
\(291\) −8468.55 −1.70596
\(292\) 0 0
\(293\) 942.016 0.187826 0.0939132 0.995580i \(-0.470062\pi\)
0.0939132 + 0.995580i \(0.470062\pi\)
\(294\) 0 0
\(295\) 2360.14 0.465807
\(296\) 0 0
\(297\) −1973.98 −0.385662
\(298\) 0 0
\(299\) −7245.48 −1.40140
\(300\) 0 0
\(301\) 778.110 0.149002
\(302\) 0 0
\(303\) −7421.74 −1.40715
\(304\) 0 0
\(305\) −256.815 −0.0482136
\(306\) 0 0
\(307\) −5371.60 −0.998610 −0.499305 0.866426i \(-0.666411\pi\)
−0.499305 + 0.866426i \(0.666411\pi\)
\(308\) 0 0
\(309\) 13060.1 2.40441
\(310\) 0 0
\(311\) −8180.21 −1.49150 −0.745751 0.666225i \(-0.767909\pi\)
−0.745751 + 0.666225i \(0.767909\pi\)
\(312\) 0 0
\(313\) −621.565 −0.112246 −0.0561229 0.998424i \(-0.517874\pi\)
−0.0561229 + 0.998424i \(0.517874\pi\)
\(314\) 0 0
\(315\) 347.655 0.0621845
\(316\) 0 0
\(317\) −2641.47 −0.468012 −0.234006 0.972235i \(-0.575184\pi\)
−0.234006 + 0.972235i \(0.575184\pi\)
\(318\) 0 0
\(319\) 1764.17 0.309639
\(320\) 0 0
\(321\) −3308.89 −0.575340
\(322\) 0 0
\(323\) 249.865 0.0430429
\(324\) 0 0
\(325\) −7726.76 −1.31878
\(326\) 0 0
\(327\) 858.398 0.145167
\(328\) 0 0
\(329\) −1213.36 −0.203328
\(330\) 0 0
\(331\) 7450.56 1.23722 0.618610 0.785698i \(-0.287696\pi\)
0.618610 + 0.785698i \(0.287696\pi\)
\(332\) 0 0
\(333\) 7116.36 1.17109
\(334\) 0 0
\(335\) 1468.81 0.239552
\(336\) 0 0
\(337\) 121.084 0.0195722 0.00978612 0.999952i \(-0.496885\pi\)
0.00978612 + 0.999952i \(0.496885\pi\)
\(338\) 0 0
\(339\) −12247.4 −1.96221
\(340\) 0 0
\(341\) 6038.66 0.958978
\(342\) 0 0
\(343\) −2442.02 −0.384422
\(344\) 0 0
\(345\) −3120.35 −0.486938
\(346\) 0 0
\(347\) −9376.43 −1.45059 −0.725293 0.688441i \(-0.758296\pi\)
−0.725293 + 0.688441i \(0.758296\pi\)
\(348\) 0 0
\(349\) −4225.67 −0.648124 −0.324062 0.946036i \(-0.605049\pi\)
−0.324062 + 0.946036i \(0.605049\pi\)
\(350\) 0 0
\(351\) −3405.27 −0.517834
\(352\) 0 0
\(353\) 10833.3 1.63343 0.816714 0.577043i \(-0.195794\pi\)
0.816714 + 0.577043i \(0.195794\pi\)
\(354\) 0 0
\(355\) 3016.19 0.450937
\(356\) 0 0
\(357\) −328.646 −0.0487221
\(358\) 0 0
\(359\) −1002.24 −0.147343 −0.0736715 0.997283i \(-0.523472\pi\)
−0.0736715 + 0.997283i \(0.523472\pi\)
\(360\) 0 0
\(361\) 361.000 0.0526316
\(362\) 0 0
\(363\) 3862.97 0.558550
\(364\) 0 0
\(365\) −3929.93 −0.563567
\(366\) 0 0
\(367\) −4868.42 −0.692451 −0.346225 0.938151i \(-0.612537\pi\)
−0.346225 + 0.938151i \(0.612537\pi\)
\(368\) 0 0
\(369\) −904.617 −0.127622
\(370\) 0 0
\(371\) 1129.22 0.158021
\(372\) 0 0
\(373\) 10466.0 1.45284 0.726421 0.687250i \(-0.241182\pi\)
0.726421 + 0.687250i \(0.241182\pi\)
\(374\) 0 0
\(375\) −7367.03 −1.01449
\(376\) 0 0
\(377\) 3043.34 0.415756
\(378\) 0 0
\(379\) 11355.1 1.53898 0.769490 0.638659i \(-0.220510\pi\)
0.769490 + 0.638659i \(0.220510\pi\)
\(380\) 0 0
\(381\) 7421.14 0.997891
\(382\) 0 0
\(383\) −8723.90 −1.16389 −0.581946 0.813228i \(-0.697708\pi\)
−0.581946 + 0.813228i \(0.697708\pi\)
\(384\) 0 0
\(385\) 740.951 0.0980840
\(386\) 0 0
\(387\) 4375.41 0.574714
\(388\) 0 0
\(389\) 2155.33 0.280924 0.140462 0.990086i \(-0.455141\pi\)
0.140462 + 0.990086i \(0.455141\pi\)
\(390\) 0 0
\(391\) 1269.83 0.164240
\(392\) 0 0
\(393\) −7524.31 −0.965780
\(394\) 0 0
\(395\) 1640.75 0.209001
\(396\) 0 0
\(397\) −4708.96 −0.595305 −0.297652 0.954674i \(-0.596204\pi\)
−0.297652 + 0.954674i \(0.596204\pi\)
\(398\) 0 0
\(399\) −474.821 −0.0595759
\(400\) 0 0
\(401\) −1051.63 −0.130962 −0.0654812 0.997854i \(-0.520858\pi\)
−0.0654812 + 0.997854i \(0.520858\pi\)
\(402\) 0 0
\(403\) 10417.2 1.28763
\(404\) 0 0
\(405\) −4052.74 −0.497240
\(406\) 0 0
\(407\) 15167.0 1.84717
\(408\) 0 0
\(409\) 3346.05 0.404527 0.202263 0.979331i \(-0.435170\pi\)
0.202263 + 0.979331i \(0.435170\pi\)
\(410\) 0 0
\(411\) 21015.7 2.52221
\(412\) 0 0
\(413\) 1825.18 0.217461
\(414\) 0 0
\(415\) 2447.08 0.289452
\(416\) 0 0
\(417\) −9837.40 −1.15525
\(418\) 0 0
\(419\) −15743.9 −1.83565 −0.917827 0.396982i \(-0.870058\pi\)
−0.917827 + 0.396982i \(0.870058\pi\)
\(420\) 0 0
\(421\) 3755.30 0.434732 0.217366 0.976090i \(-0.430254\pi\)
0.217366 + 0.976090i \(0.430254\pi\)
\(422\) 0 0
\(423\) −6822.89 −0.784255
\(424\) 0 0
\(425\) 1354.17 0.154558
\(426\) 0 0
\(427\) −198.603 −0.0225084
\(428\) 0 0
\(429\) 22473.4 2.52920
\(430\) 0 0
\(431\) 9670.09 1.08072 0.540362 0.841433i \(-0.318287\pi\)
0.540362 + 0.841433i \(0.318287\pi\)
\(432\) 0 0
\(433\) −10656.7 −1.18274 −0.591370 0.806401i \(-0.701413\pi\)
−0.591370 + 0.806401i \(0.701413\pi\)
\(434\) 0 0
\(435\) 1310.65 0.144461
\(436\) 0 0
\(437\) 1834.62 0.200828
\(438\) 0 0
\(439\) 5113.47 0.555929 0.277964 0.960591i \(-0.410340\pi\)
0.277964 + 0.960591i \(0.410340\pi\)
\(440\) 0 0
\(441\) −6731.46 −0.726861
\(442\) 0 0
\(443\) 2552.54 0.273758 0.136879 0.990588i \(-0.456293\pi\)
0.136879 + 0.990588i \(0.456293\pi\)
\(444\) 0 0
\(445\) 297.600 0.0317024
\(446\) 0 0
\(447\) 3931.73 0.416028
\(448\) 0 0
\(449\) 4504.62 0.473466 0.236733 0.971575i \(-0.423923\pi\)
0.236733 + 0.971575i \(0.423923\pi\)
\(450\) 0 0
\(451\) −1928.00 −0.201299
\(452\) 0 0
\(453\) −6870.15 −0.712556
\(454\) 0 0
\(455\) 1278.20 0.131699
\(456\) 0 0
\(457\) 9278.63 0.949751 0.474875 0.880053i \(-0.342493\pi\)
0.474875 + 0.880053i \(0.342493\pi\)
\(458\) 0 0
\(459\) 596.800 0.0606890
\(460\) 0 0
\(461\) 3861.47 0.390123 0.195062 0.980791i \(-0.437509\pi\)
0.195062 + 0.980791i \(0.437509\pi\)
\(462\) 0 0
\(463\) −154.016 −0.0154595 −0.00772975 0.999970i \(-0.502460\pi\)
−0.00772975 + 0.999970i \(0.502460\pi\)
\(464\) 0 0
\(465\) 4486.27 0.447410
\(466\) 0 0
\(467\) 16010.0 1.58641 0.793205 0.608954i \(-0.208411\pi\)
0.793205 + 0.608954i \(0.208411\pi\)
\(468\) 0 0
\(469\) 1135.88 0.111834
\(470\) 0 0
\(471\) −14949.8 −1.46253
\(472\) 0 0
\(473\) 9325.24 0.906501
\(474\) 0 0
\(475\) 1956.49 0.188989
\(476\) 0 0
\(477\) 6349.71 0.609504
\(478\) 0 0
\(479\) 10467.1 0.998441 0.499220 0.866475i \(-0.333620\pi\)
0.499220 + 0.866475i \(0.333620\pi\)
\(480\) 0 0
\(481\) 26164.3 2.48023
\(482\) 0 0
\(483\) −2413.07 −0.227326
\(484\) 0 0
\(485\) −5772.41 −0.540436
\(486\) 0 0
\(487\) 5868.52 0.546054 0.273027 0.962006i \(-0.411975\pi\)
0.273027 + 0.962006i \(0.411975\pi\)
\(488\) 0 0
\(489\) 2103.41 0.194519
\(490\) 0 0
\(491\) −20259.1 −1.86208 −0.931041 0.364915i \(-0.881098\pi\)
−0.931041 + 0.364915i \(0.881098\pi\)
\(492\) 0 0
\(493\) −533.369 −0.0487257
\(494\) 0 0
\(495\) 4166.46 0.378320
\(496\) 0 0
\(497\) 2332.52 0.210519
\(498\) 0 0
\(499\) 6557.19 0.588256 0.294128 0.955766i \(-0.404971\pi\)
0.294128 + 0.955766i \(0.404971\pi\)
\(500\) 0 0
\(501\) −941.054 −0.0839186
\(502\) 0 0
\(503\) −20542.5 −1.82097 −0.910484 0.413545i \(-0.864291\pi\)
−0.910484 + 0.413545i \(0.864291\pi\)
\(504\) 0 0
\(505\) −5058.87 −0.445776
\(506\) 0 0
\(507\) 23641.2 2.07090
\(508\) 0 0
\(509\) −5464.15 −0.475823 −0.237912 0.971287i \(-0.576463\pi\)
−0.237912 + 0.971287i \(0.576463\pi\)
\(510\) 0 0
\(511\) −3039.15 −0.263100
\(512\) 0 0
\(513\) 862.245 0.0742087
\(514\) 0 0
\(515\) 8902.13 0.761699
\(516\) 0 0
\(517\) −14541.5 −1.23701
\(518\) 0 0
\(519\) −10389.8 −0.878733
\(520\) 0 0
\(521\) −12113.9 −1.01865 −0.509327 0.860573i \(-0.670106\pi\)
−0.509327 + 0.860573i \(0.670106\pi\)
\(522\) 0 0
\(523\) 12706.6 1.06237 0.531185 0.847256i \(-0.321747\pi\)
0.531185 + 0.847256i \(0.321747\pi\)
\(524\) 0 0
\(525\) −2573.35 −0.213925
\(526\) 0 0
\(527\) −1825.69 −0.150908
\(528\) 0 0
\(529\) −2843.34 −0.233693
\(530\) 0 0
\(531\) 10263.2 0.838767
\(532\) 0 0
\(533\) −3325.95 −0.270287
\(534\) 0 0
\(535\) −2255.43 −0.182263
\(536\) 0 0
\(537\) 5305.55 0.426352
\(538\) 0 0
\(539\) −14346.7 −1.14648
\(540\) 0 0
\(541\) −20011.9 −1.59035 −0.795173 0.606383i \(-0.792620\pi\)
−0.795173 + 0.606383i \(0.792620\pi\)
\(542\) 0 0
\(543\) 15785.6 1.24756
\(544\) 0 0
\(545\) 585.109 0.0459877
\(546\) 0 0
\(547\) 14732.5 1.15158 0.575790 0.817597i \(-0.304694\pi\)
0.575790 + 0.817597i \(0.304694\pi\)
\(548\) 0 0
\(549\) −1116.77 −0.0868172
\(550\) 0 0
\(551\) −770.602 −0.0595803
\(552\) 0 0
\(553\) 1268.85 0.0975715
\(554\) 0 0
\(555\) 11267.9 0.861796
\(556\) 0 0
\(557\) −2202.91 −0.167577 −0.0837883 0.996484i \(-0.526702\pi\)
−0.0837883 + 0.996484i \(0.526702\pi\)
\(558\) 0 0
\(559\) 16086.8 1.21717
\(560\) 0 0
\(561\) −3938.65 −0.296417
\(562\) 0 0
\(563\) 14661.2 1.09751 0.548755 0.835983i \(-0.315102\pi\)
0.548755 + 0.835983i \(0.315102\pi\)
\(564\) 0 0
\(565\) −8348.20 −0.621613
\(566\) 0 0
\(567\) −3134.12 −0.232135
\(568\) 0 0
\(569\) 2252.50 0.165957 0.0829785 0.996551i \(-0.473557\pi\)
0.0829785 + 0.996551i \(0.473557\pi\)
\(570\) 0 0
\(571\) 13749.4 1.00770 0.503848 0.863793i \(-0.331917\pi\)
0.503848 + 0.863793i \(0.331917\pi\)
\(572\) 0 0
\(573\) −11501.4 −0.838528
\(574\) 0 0
\(575\) 9942.97 0.721131
\(576\) 0 0
\(577\) −16355.8 −1.18007 −0.590037 0.807376i \(-0.700887\pi\)
−0.590037 + 0.807376i \(0.700887\pi\)
\(578\) 0 0
\(579\) −4570.88 −0.328082
\(580\) 0 0
\(581\) 1892.41 0.135130
\(582\) 0 0
\(583\) 13533.0 0.961375
\(584\) 0 0
\(585\) 7187.47 0.507975
\(586\) 0 0
\(587\) 12704.1 0.893279 0.446640 0.894714i \(-0.352621\pi\)
0.446640 + 0.894714i \(0.352621\pi\)
\(588\) 0 0
\(589\) −2637.72 −0.184525
\(590\) 0 0
\(591\) −17012.9 −1.18412
\(592\) 0 0
\(593\) 7442.67 0.515403 0.257701 0.966225i \(-0.417035\pi\)
0.257701 + 0.966225i \(0.417035\pi\)
\(594\) 0 0
\(595\) −224.015 −0.0154348
\(596\) 0 0
\(597\) −29939.6 −2.05251
\(598\) 0 0
\(599\) −17522.7 −1.19525 −0.597627 0.801774i \(-0.703890\pi\)
−0.597627 + 0.801774i \(0.703890\pi\)
\(600\) 0 0
\(601\) 14983.9 1.01698 0.508490 0.861068i \(-0.330204\pi\)
0.508490 + 0.861068i \(0.330204\pi\)
\(602\) 0 0
\(603\) 6387.21 0.431355
\(604\) 0 0
\(605\) 2633.11 0.176944
\(606\) 0 0
\(607\) −18937.9 −1.26634 −0.633169 0.774013i \(-0.718246\pi\)
−0.633169 + 0.774013i \(0.718246\pi\)
\(608\) 0 0
\(609\) 1013.57 0.0674415
\(610\) 0 0
\(611\) −25085.3 −1.66095
\(612\) 0 0
\(613\) 7209.14 0.474999 0.237500 0.971388i \(-0.423672\pi\)
0.237500 + 0.971388i \(0.423672\pi\)
\(614\) 0 0
\(615\) −1432.36 −0.0939158
\(616\) 0 0
\(617\) −25907.8 −1.69045 −0.845226 0.534408i \(-0.820534\pi\)
−0.845226 + 0.534408i \(0.820534\pi\)
\(618\) 0 0
\(619\) 26596.0 1.72695 0.863475 0.504391i \(-0.168283\pi\)
0.863475 + 0.504391i \(0.168283\pi\)
\(620\) 0 0
\(621\) 4381.98 0.283161
\(622\) 0 0
\(623\) 230.144 0.0148002
\(624\) 0 0
\(625\) 7850.03 0.502402
\(626\) 0 0
\(627\) −5690.48 −0.362450
\(628\) 0 0
\(629\) −4585.50 −0.290677
\(630\) 0 0
\(631\) −231.639 −0.0146140 −0.00730699 0.999973i \(-0.502326\pi\)
−0.00730699 + 0.999973i \(0.502326\pi\)
\(632\) 0 0
\(633\) −26927.5 −1.69079
\(634\) 0 0
\(635\) 5058.46 0.316124
\(636\) 0 0
\(637\) −24749.1 −1.53940
\(638\) 0 0
\(639\) 13116.0 0.811991
\(640\) 0 0
\(641\) 9194.84 0.566574 0.283287 0.959035i \(-0.408575\pi\)
0.283287 + 0.959035i \(0.408575\pi\)
\(642\) 0 0
\(643\) −12339.1 −0.756775 −0.378387 0.925647i \(-0.623521\pi\)
−0.378387 + 0.925647i \(0.623521\pi\)
\(644\) 0 0
\(645\) 6927.95 0.422927
\(646\) 0 0
\(647\) −10852.4 −0.659428 −0.329714 0.944081i \(-0.606952\pi\)
−0.329714 + 0.944081i \(0.606952\pi\)
\(648\) 0 0
\(649\) 21873.8 1.32299
\(650\) 0 0
\(651\) 3469.38 0.208872
\(652\) 0 0
\(653\) 23310.7 1.39696 0.698482 0.715627i \(-0.253859\pi\)
0.698482 + 0.715627i \(0.253859\pi\)
\(654\) 0 0
\(655\) −5128.79 −0.305952
\(656\) 0 0
\(657\) −17089.5 −1.01480
\(658\) 0 0
\(659\) 21318.0 1.26014 0.630069 0.776539i \(-0.283027\pi\)
0.630069 + 0.776539i \(0.283027\pi\)
\(660\) 0 0
\(661\) 26645.4 1.56791 0.783954 0.620818i \(-0.213200\pi\)
0.783954 + 0.620818i \(0.213200\pi\)
\(662\) 0 0
\(663\) −6794.49 −0.398003
\(664\) 0 0
\(665\) −323.652 −0.0188732
\(666\) 0 0
\(667\) −3916.24 −0.227343
\(668\) 0 0
\(669\) −486.620 −0.0281223
\(670\) 0 0
\(671\) −2380.16 −0.136937
\(672\) 0 0
\(673\) 12426.1 0.711728 0.355864 0.934538i \(-0.384187\pi\)
0.355864 + 0.934538i \(0.384187\pi\)
\(674\) 0 0
\(675\) 4673.05 0.266468
\(676\) 0 0
\(677\) −28485.7 −1.61712 −0.808562 0.588411i \(-0.799754\pi\)
−0.808562 + 0.588411i \(0.799754\pi\)
\(678\) 0 0
\(679\) −4464.00 −0.252301
\(680\) 0 0
\(681\) −7796.81 −0.438729
\(682\) 0 0
\(683\) −1899.14 −0.106396 −0.0531981 0.998584i \(-0.516941\pi\)
−0.0531981 + 0.998584i \(0.516941\pi\)
\(684\) 0 0
\(685\) 14324.9 0.799018
\(686\) 0 0
\(687\) 20119.2 1.11732
\(688\) 0 0
\(689\) 23345.6 1.29085
\(690\) 0 0
\(691\) −29568.6 −1.62785 −0.813923 0.580973i \(-0.802672\pi\)
−0.813923 + 0.580973i \(0.802672\pi\)
\(692\) 0 0
\(693\) 3222.06 0.176618
\(694\) 0 0
\(695\) −6705.46 −0.365975
\(696\) 0 0
\(697\) 582.899 0.0316770
\(698\) 0 0
\(699\) −6376.26 −0.345025
\(700\) 0 0
\(701\) −6906.35 −0.372110 −0.186055 0.982539i \(-0.559570\pi\)
−0.186055 + 0.982539i \(0.559570\pi\)
\(702\) 0 0
\(703\) −6625.04 −0.355431
\(704\) 0 0
\(705\) −10803.2 −0.577126
\(706\) 0 0
\(707\) −3912.20 −0.208110
\(708\) 0 0
\(709\) 14410.0 0.763301 0.381650 0.924307i \(-0.375356\pi\)
0.381650 + 0.924307i \(0.375356\pi\)
\(710\) 0 0
\(711\) 7134.90 0.376343
\(712\) 0 0
\(713\) −13405.1 −0.704100
\(714\) 0 0
\(715\) 15318.6 0.801233
\(716\) 0 0
\(717\) 30131.4 1.56942
\(718\) 0 0
\(719\) −11170.9 −0.579419 −0.289710 0.957115i \(-0.593559\pi\)
−0.289710 + 0.957115i \(0.593559\pi\)
\(720\) 0 0
\(721\) 6884.32 0.355597
\(722\) 0 0
\(723\) −27298.6 −1.40421
\(724\) 0 0
\(725\) −4176.37 −0.213940
\(726\) 0 0
\(727\) 29676.9 1.51397 0.756985 0.653433i \(-0.226672\pi\)
0.756985 + 0.653433i \(0.226672\pi\)
\(728\) 0 0
\(729\) −9186.85 −0.466740
\(730\) 0 0
\(731\) −2819.34 −0.142650
\(732\) 0 0
\(733\) −252.315 −0.0127142 −0.00635708 0.999980i \(-0.502024\pi\)
−0.00635708 + 0.999980i \(0.502024\pi\)
\(734\) 0 0
\(735\) −10658.5 −0.534890
\(736\) 0 0
\(737\) 13613.0 0.680380
\(738\) 0 0
\(739\) 1702.08 0.0847252 0.0423626 0.999102i \(-0.486512\pi\)
0.0423626 + 0.999102i \(0.486512\pi\)
\(740\) 0 0
\(741\) −9816.54 −0.486666
\(742\) 0 0
\(743\) −11210.7 −0.553539 −0.276769 0.960936i \(-0.589264\pi\)
−0.276769 + 0.960936i \(0.589264\pi\)
\(744\) 0 0
\(745\) 2679.98 0.131794
\(746\) 0 0
\(747\) 10641.3 0.521210
\(748\) 0 0
\(749\) −1744.20 −0.0850892
\(750\) 0 0
\(751\) 37318.2 1.81326 0.906631 0.421925i \(-0.138646\pi\)
0.906631 + 0.421925i \(0.138646\pi\)
\(752\) 0 0
\(753\) −1513.79 −0.0732609
\(754\) 0 0
\(755\) −4682.90 −0.225732
\(756\) 0 0
\(757\) −13356.3 −0.641274 −0.320637 0.947202i \(-0.603897\pi\)
−0.320637 + 0.947202i \(0.603897\pi\)
\(758\) 0 0
\(759\) −28919.4 −1.38301
\(760\) 0 0
\(761\) 37538.5 1.78814 0.894068 0.447932i \(-0.147839\pi\)
0.894068 + 0.447932i \(0.147839\pi\)
\(762\) 0 0
\(763\) 452.485 0.0214693
\(764\) 0 0
\(765\) −1259.66 −0.0595335
\(766\) 0 0
\(767\) 37734.1 1.77640
\(768\) 0 0
\(769\) 422.829 0.0198278 0.00991391 0.999951i \(-0.496844\pi\)
0.00991391 + 0.999951i \(0.496844\pi\)
\(770\) 0 0
\(771\) −38437.5 −1.79545
\(772\) 0 0
\(773\) 23033.6 1.07175 0.535873 0.844298i \(-0.319982\pi\)
0.535873 + 0.844298i \(0.319982\pi\)
\(774\) 0 0
\(775\) −14295.5 −0.662592
\(776\) 0 0
\(777\) 8713.88 0.402328
\(778\) 0 0
\(779\) 842.161 0.0387337
\(780\) 0 0
\(781\) 27954.0 1.28076
\(782\) 0 0
\(783\) −1840.58 −0.0840061
\(784\) 0 0
\(785\) −10190.2 −0.463319
\(786\) 0 0
\(787\) 37994.2 1.72090 0.860448 0.509538i \(-0.170184\pi\)
0.860448 + 0.509538i \(0.170184\pi\)
\(788\) 0 0
\(789\) −20461.8 −0.923271
\(790\) 0 0
\(791\) −6455.95 −0.290199
\(792\) 0 0
\(793\) −4105.96 −0.183868
\(794\) 0 0
\(795\) 10054.0 0.448528
\(796\) 0 0
\(797\) −23765.7 −1.05624 −0.528122 0.849169i \(-0.677103\pi\)
−0.528122 + 0.849169i \(0.677103\pi\)
\(798\) 0 0
\(799\) 4396.39 0.194660
\(800\) 0 0
\(801\) 1294.13 0.0570858
\(802\) 0 0
\(803\) −36422.6 −1.60065
\(804\) 0 0
\(805\) −1644.82 −0.0720152
\(806\) 0 0
\(807\) −41102.6 −1.79291
\(808\) 0 0
\(809\) −7019.58 −0.305062 −0.152531 0.988299i \(-0.548742\pi\)
−0.152531 + 0.988299i \(0.548742\pi\)
\(810\) 0 0
\(811\) 35061.1 1.51808 0.759039 0.651045i \(-0.225669\pi\)
0.759039 + 0.651045i \(0.225669\pi\)
\(812\) 0 0
\(813\) 43760.4 1.88775
\(814\) 0 0
\(815\) 1433.75 0.0616220
\(816\) 0 0
\(817\) −4073.32 −0.174428
\(818\) 0 0
\(819\) 5558.32 0.237147
\(820\) 0 0
\(821\) −306.783 −0.0130412 −0.00652059 0.999979i \(-0.502076\pi\)
−0.00652059 + 0.999979i \(0.502076\pi\)
\(822\) 0 0
\(823\) −23239.1 −0.984281 −0.492140 0.870516i \(-0.663785\pi\)
−0.492140 + 0.870516i \(0.663785\pi\)
\(824\) 0 0
\(825\) −30840.3 −1.30148
\(826\) 0 0
\(827\) −24374.9 −1.02491 −0.512455 0.858714i \(-0.671264\pi\)
−0.512455 + 0.858714i \(0.671264\pi\)
\(828\) 0 0
\(829\) 27129.6 1.13661 0.568306 0.822817i \(-0.307599\pi\)
0.568306 + 0.822817i \(0.307599\pi\)
\(830\) 0 0
\(831\) −55350.5 −2.31058
\(832\) 0 0
\(833\) 4337.48 0.180414
\(834\) 0 0
\(835\) −641.450 −0.0265848
\(836\) 0 0
\(837\) −6300.18 −0.260174
\(838\) 0 0
\(839\) −4376.25 −0.180077 −0.0900386 0.995938i \(-0.528699\pi\)
−0.0900386 + 0.995938i \(0.528699\pi\)
\(840\) 0 0
\(841\) −22744.0 −0.932554
\(842\) 0 0
\(843\) −30838.5 −1.25995
\(844\) 0 0
\(845\) 16114.6 0.656044
\(846\) 0 0
\(847\) 2036.28 0.0826061
\(848\) 0 0
\(849\) 60677.5 2.45282
\(850\) 0 0
\(851\) −33668.8 −1.35623
\(852\) 0 0
\(853\) 46278.7 1.85762 0.928812 0.370550i \(-0.120831\pi\)
0.928812 + 0.370550i \(0.120831\pi\)
\(854\) 0 0
\(855\) −1819.93 −0.0727958
\(856\) 0 0
\(857\) −5108.69 −0.203628 −0.101814 0.994803i \(-0.532465\pi\)
−0.101814 + 0.994803i \(0.532465\pi\)
\(858\) 0 0
\(859\) 12440.5 0.494137 0.247069 0.968998i \(-0.420533\pi\)
0.247069 + 0.968998i \(0.420533\pi\)
\(860\) 0 0
\(861\) −1107.69 −0.0438444
\(862\) 0 0
\(863\) 33694.7 1.32906 0.664531 0.747260i \(-0.268631\pi\)
0.664531 + 0.747260i \(0.268631\pi\)
\(864\) 0 0
\(865\) −7082.00 −0.278376
\(866\) 0 0
\(867\) −32637.3 −1.27846
\(868\) 0 0
\(869\) 15206.5 0.593608
\(870\) 0 0
\(871\) 23483.5 0.913555
\(872\) 0 0
\(873\) −25101.6 −0.973151
\(874\) 0 0
\(875\) −3883.36 −0.150036
\(876\) 0 0
\(877\) 6266.75 0.241292 0.120646 0.992696i \(-0.461503\pi\)
0.120646 + 0.992696i \(0.461503\pi\)
\(878\) 0 0
\(879\) 6486.18 0.248889
\(880\) 0 0
\(881\) −18875.2 −0.721818 −0.360909 0.932601i \(-0.617534\pi\)
−0.360909 + 0.932601i \(0.617534\pi\)
\(882\) 0 0
\(883\) −24369.5 −0.928765 −0.464383 0.885635i \(-0.653724\pi\)
−0.464383 + 0.885635i \(0.653724\pi\)
\(884\) 0 0
\(885\) 16250.6 0.617241
\(886\) 0 0
\(887\) −46836.8 −1.77297 −0.886486 0.462754i \(-0.846861\pi\)
−0.886486 + 0.462754i \(0.846861\pi\)
\(888\) 0 0
\(889\) 3911.88 0.147582
\(890\) 0 0
\(891\) −37560.8 −1.41227
\(892\) 0 0
\(893\) 6351.82 0.238024
\(894\) 0 0
\(895\) 3616.41 0.135065
\(896\) 0 0
\(897\) −49888.2 −1.85699
\(898\) 0 0
\(899\) 5630.57 0.208888
\(900\) 0 0
\(901\) −4091.50 −0.151285
\(902\) 0 0
\(903\) 5357.62 0.197442
\(904\) 0 0
\(905\) 10760.0 0.395219
\(906\) 0 0
\(907\) −19015.8 −0.696150 −0.348075 0.937467i \(-0.613164\pi\)
−0.348075 + 0.937467i \(0.613164\pi\)
\(908\) 0 0
\(909\) −21998.8 −0.802699
\(910\) 0 0
\(911\) −30625.3 −1.11379 −0.556894 0.830583i \(-0.688007\pi\)
−0.556894 + 0.830583i \(0.688007\pi\)
\(912\) 0 0
\(913\) 22679.6 0.822108
\(914\) 0 0
\(915\) −1768.28 −0.0638879
\(916\) 0 0
\(917\) −3966.27 −0.142833
\(918\) 0 0
\(919\) 48642.7 1.74600 0.873001 0.487719i \(-0.162171\pi\)
0.873001 + 0.487719i \(0.162171\pi\)
\(920\) 0 0
\(921\) −36985.7 −1.32326
\(922\) 0 0
\(923\) 48222.9 1.71969
\(924\) 0 0
\(925\) −35905.2 −1.27628
\(926\) 0 0
\(927\) 38711.4 1.37157
\(928\) 0 0
\(929\) 42194.6 1.49016 0.745080 0.666975i \(-0.232411\pi\)
0.745080 + 0.666975i \(0.232411\pi\)
\(930\) 0 0
\(931\) 6266.71 0.220605
\(932\) 0 0
\(933\) −56324.2 −1.97639
\(934\) 0 0
\(935\) −2684.70 −0.0939026
\(936\) 0 0
\(937\) −28438.1 −0.991498 −0.495749 0.868466i \(-0.665106\pi\)
−0.495749 + 0.868466i \(0.665106\pi\)
\(938\) 0 0
\(939\) −4279.74 −0.148737
\(940\) 0 0
\(941\) 29883.2 1.03524 0.517622 0.855610i \(-0.326818\pi\)
0.517622 + 0.855610i \(0.326818\pi\)
\(942\) 0 0
\(943\) 4279.91 0.147798
\(944\) 0 0
\(945\) −773.040 −0.0266106
\(946\) 0 0
\(947\) −46897.4 −1.60925 −0.804626 0.593782i \(-0.797634\pi\)
−0.804626 + 0.593782i \(0.797634\pi\)
\(948\) 0 0
\(949\) −62831.9 −2.14922
\(950\) 0 0
\(951\) −18187.7 −0.620163
\(952\) 0 0
\(953\) −20401.1 −0.693449 −0.346724 0.937967i \(-0.612706\pi\)
−0.346724 + 0.937967i \(0.612706\pi\)
\(954\) 0 0
\(955\) −7839.66 −0.265639
\(956\) 0 0
\(957\) 12147.1 0.410302
\(958\) 0 0
\(959\) 11078.0 0.373020
\(960\) 0 0
\(961\) −10517.9 −0.353057
\(962\) 0 0
\(963\) −9807.87 −0.328197
\(964\) 0 0
\(965\) −3115.65 −0.103934
\(966\) 0 0
\(967\) −23598.5 −0.784775 −0.392388 0.919800i \(-0.628351\pi\)
−0.392388 + 0.919800i \(0.628351\pi\)
\(968\) 0 0
\(969\) 1720.43 0.0570362
\(970\) 0 0
\(971\) −17149.1 −0.566776 −0.283388 0.959005i \(-0.591458\pi\)
−0.283388 + 0.959005i \(0.591458\pi\)
\(972\) 0 0
\(973\) −5185.56 −0.170854
\(974\) 0 0
\(975\) −53202.0 −1.74752
\(976\) 0 0
\(977\) −56653.2 −1.85517 −0.927583 0.373618i \(-0.878117\pi\)
−0.927583 + 0.373618i \(0.878117\pi\)
\(978\) 0 0
\(979\) 2758.15 0.0900418
\(980\) 0 0
\(981\) 2544.38 0.0828091
\(982\) 0 0
\(983\) −7895.00 −0.256166 −0.128083 0.991763i \(-0.540882\pi\)
−0.128083 + 0.991763i \(0.540882\pi\)
\(984\) 0 0
\(985\) −11596.5 −0.375122
\(986\) 0 0
\(987\) −8354.52 −0.269430
\(988\) 0 0
\(989\) −20700.9 −0.665570
\(990\) 0 0
\(991\) 48458.9 1.55333 0.776664 0.629915i \(-0.216910\pi\)
0.776664 + 0.629915i \(0.216910\pi\)
\(992\) 0 0
\(993\) 51300.3 1.63944
\(994\) 0 0
\(995\) −20407.7 −0.650219
\(996\) 0 0
\(997\) 40325.2 1.28095 0.640477 0.767977i \(-0.278737\pi\)
0.640477 + 0.767977i \(0.278737\pi\)
\(998\) 0 0
\(999\) −15823.8 −0.501145
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 608.4.a.k.1.6 yes 7
4.3 odd 2 608.4.a.j.1.2 7
8.3 odd 2 1216.4.a.bg.1.6 7
8.5 even 2 1216.4.a.bf.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
608.4.a.j.1.2 7 4.3 odd 2
608.4.a.k.1.6 yes 7 1.1 even 1 trivial
1216.4.a.bf.1.2 7 8.5 even 2
1216.4.a.bg.1.6 7 8.3 odd 2