Properties

Label 608.4.a.k.1.2
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 1.2
Root \(-6.10834\) 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)
 
\(f(q)\) \(=\) \(q-5.20712 q^{3} +7.79991 q^{5} +26.8592 q^{7} +0.114065 q^{9} +40.7763 q^{11} +24.2099 q^{13} -40.6150 q^{15} +70.2535 q^{17} -19.0000 q^{19} -139.859 q^{21} +37.2905 q^{23} -64.1614 q^{25} +139.998 q^{27} -171.838 q^{29} +64.4716 q^{31} -212.327 q^{33} +209.499 q^{35} -432.867 q^{37} -126.064 q^{39} +270.141 q^{41} +49.8344 q^{43} +0.889699 q^{45} +362.230 q^{47} +378.416 q^{49} -365.818 q^{51} -515.513 q^{53} +318.052 q^{55} +98.9352 q^{57} +71.0451 q^{59} +735.093 q^{61} +3.06370 q^{63} +188.835 q^{65} -224.369 q^{67} -194.176 q^{69} +67.6494 q^{71} -89.3246 q^{73} +334.096 q^{75} +1095.22 q^{77} +1219.09 q^{79} -732.067 q^{81} +948.434 q^{83} +547.970 q^{85} +894.780 q^{87} +877.711 q^{89} +650.258 q^{91} -335.711 q^{93} -148.198 q^{95} +812.241 q^{97} +4.65117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 3 q^{3} - 17 q^{5} + 42 q^{7} + 86 q^{9} - 33 q^{11} - 35 q^{13} + 120 q^{15} + 66 q^{17} - 133 q^{19} + 33 q^{21} + 389 q^{23} + 44 q^{25} - 39 q^{27} + 233 q^{29} + 158 q^{31} - 206 q^{33} + 123 q^{35}+ \cdots - 1591 q^{99}+O(q^{100}) \) 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
\(3\) −5.20712 −1.00211 −0.501055 0.865415i \(-0.667055\pi\)
−0.501055 + 0.865415i \(0.667055\pi\)
\(4\) 0 0
\(5\) 7.79991 0.697645 0.348822 0.937189i \(-0.386582\pi\)
0.348822 + 0.937189i \(0.386582\pi\)
\(6\) 0 0
\(7\) 26.8592 1.45026 0.725130 0.688612i \(-0.241780\pi\)
0.725130 + 0.688612i \(0.241780\pi\)
\(8\) 0 0
\(9\) 0.114065 0.00422464
\(10\) 0 0
\(11\) 40.7763 1.11768 0.558842 0.829274i \(-0.311246\pi\)
0.558842 + 0.829274i \(0.311246\pi\)
\(12\) 0 0
\(13\) 24.2099 0.516508 0.258254 0.966077i \(-0.416853\pi\)
0.258254 + 0.966077i \(0.416853\pi\)
\(14\) 0 0
\(15\) −40.6150 −0.699117
\(16\) 0 0
\(17\) 70.2535 1.00229 0.501146 0.865363i \(-0.332912\pi\)
0.501146 + 0.865363i \(0.332912\pi\)
\(18\) 0 0
\(19\) −19.0000 −0.229416
\(20\) 0 0
\(21\) −139.859 −1.45332
\(22\) 0 0
\(23\) 37.2905 0.338069 0.169035 0.985610i \(-0.445935\pi\)
0.169035 + 0.985610i \(0.445935\pi\)
\(24\) 0 0
\(25\) −64.1614 −0.513292
\(26\) 0 0
\(27\) 139.998 0.997877
\(28\) 0 0
\(29\) −171.838 −1.10033 −0.550164 0.835057i \(-0.685435\pi\)
−0.550164 + 0.835057i \(0.685435\pi\)
\(30\) 0 0
\(31\) 64.4716 0.373530 0.186765 0.982405i \(-0.440200\pi\)
0.186765 + 0.982405i \(0.440200\pi\)
\(32\) 0 0
\(33\) −212.327 −1.12004
\(34\) 0 0
\(35\) 209.499 1.01177
\(36\) 0 0
\(37\) −432.867 −1.92332 −0.961660 0.274245i \(-0.911572\pi\)
−0.961660 + 0.274245i \(0.911572\pi\)
\(38\) 0 0
\(39\) −126.064 −0.517598
\(40\) 0 0
\(41\) 270.141 1.02900 0.514498 0.857491i \(-0.327978\pi\)
0.514498 + 0.857491i \(0.327978\pi\)
\(42\) 0 0
\(43\) 49.8344 0.176736 0.0883682 0.996088i \(-0.471835\pi\)
0.0883682 + 0.996088i \(0.471835\pi\)
\(44\) 0 0
\(45\) 0.889699 0.00294730
\(46\) 0 0
\(47\) 362.230 1.12418 0.562092 0.827074i \(-0.309997\pi\)
0.562092 + 0.827074i \(0.309997\pi\)
\(48\) 0 0
\(49\) 378.416 1.10325
\(50\) 0 0
\(51\) −365.818 −1.00441
\(52\) 0 0
\(53\) −515.513 −1.33606 −0.668029 0.744135i \(-0.732862\pi\)
−0.668029 + 0.744135i \(0.732862\pi\)
\(54\) 0 0
\(55\) 318.052 0.779747
\(56\) 0 0
\(57\) 98.9352 0.229900
\(58\) 0 0
\(59\) 71.0451 0.156768 0.0783838 0.996923i \(-0.475024\pi\)
0.0783838 + 0.996923i \(0.475024\pi\)
\(60\) 0 0
\(61\) 735.093 1.54293 0.771467 0.636269i \(-0.219523\pi\)
0.771467 + 0.636269i \(0.219523\pi\)
\(62\) 0 0
\(63\) 3.06370 0.00612683
\(64\) 0 0
\(65\) 188.835 0.360340
\(66\) 0 0
\(67\) −224.369 −0.409121 −0.204560 0.978854i \(-0.565576\pi\)
−0.204560 + 0.978854i \(0.565576\pi\)
\(68\) 0 0
\(69\) −194.176 −0.338783
\(70\) 0 0
\(71\) 67.6494 0.113078 0.0565388 0.998400i \(-0.481994\pi\)
0.0565388 + 0.998400i \(0.481994\pi\)
\(72\) 0 0
\(73\) −89.3246 −0.143214 −0.0716072 0.997433i \(-0.522813\pi\)
−0.0716072 + 0.997433i \(0.522813\pi\)
\(74\) 0 0
\(75\) 334.096 0.514375
\(76\) 0 0
\(77\) 1095.22 1.62093
\(78\) 0 0
\(79\) 1219.09 1.73619 0.868093 0.496401i \(-0.165346\pi\)
0.868093 + 0.496401i \(0.165346\pi\)
\(80\) 0 0
\(81\) −732.067 −1.00421
\(82\) 0 0
\(83\) 948.434 1.25427 0.627133 0.778912i \(-0.284228\pi\)
0.627133 + 0.778912i \(0.284228\pi\)
\(84\) 0 0
\(85\) 547.970 0.699244
\(86\) 0 0
\(87\) 894.780 1.10265
\(88\) 0 0
\(89\) 877.711 1.04536 0.522681 0.852528i \(-0.324932\pi\)
0.522681 + 0.852528i \(0.324932\pi\)
\(90\) 0 0
\(91\) 650.258 0.749072
\(92\) 0 0
\(93\) −335.711 −0.374318
\(94\) 0 0
\(95\) −148.198 −0.160051
\(96\) 0 0
\(97\) 812.241 0.850212 0.425106 0.905143i \(-0.360237\pi\)
0.425106 + 0.905143i \(0.360237\pi\)
\(98\) 0 0
\(99\) 4.65117 0.00472182
\(100\) 0 0
\(101\) −348.563 −0.343400 −0.171700 0.985149i \(-0.554926\pi\)
−0.171700 + 0.985149i \(0.554926\pi\)
\(102\) 0 0
\(103\) −44.7869 −0.0428445 −0.0214223 0.999771i \(-0.506819\pi\)
−0.0214223 + 0.999771i \(0.506819\pi\)
\(104\) 0 0
\(105\) −1090.89 −1.01390
\(106\) 0 0
\(107\) −1433.73 −1.29537 −0.647683 0.761910i \(-0.724262\pi\)
−0.647683 + 0.761910i \(0.724262\pi\)
\(108\) 0 0
\(109\) 1772.92 1.55794 0.778968 0.627063i \(-0.215743\pi\)
0.778968 + 0.627063i \(0.215743\pi\)
\(110\) 0 0
\(111\) 2253.99 1.92738
\(112\) 0 0
\(113\) 305.042 0.253947 0.126973 0.991906i \(-0.459474\pi\)
0.126973 + 0.991906i \(0.459474\pi\)
\(114\) 0 0
\(115\) 290.862 0.235852
\(116\) 0 0
\(117\) 2.76151 0.00218206
\(118\) 0 0
\(119\) 1886.95 1.45358
\(120\) 0 0
\(121\) 331.709 0.249218
\(122\) 0 0
\(123\) −1406.65 −1.03117
\(124\) 0 0
\(125\) −1475.44 −1.05574
\(126\) 0 0
\(127\) 345.706 0.241547 0.120774 0.992680i \(-0.461463\pi\)
0.120774 + 0.992680i \(0.461463\pi\)
\(128\) 0 0
\(129\) −259.493 −0.177109
\(130\) 0 0
\(131\) 2607.14 1.73883 0.869415 0.494083i \(-0.164496\pi\)
0.869415 + 0.494083i \(0.164496\pi\)
\(132\) 0 0
\(133\) −510.325 −0.332713
\(134\) 0 0
\(135\) 1091.97 0.696164
\(136\) 0 0
\(137\) 702.056 0.437815 0.218908 0.975746i \(-0.429751\pi\)
0.218908 + 0.975746i \(0.429751\pi\)
\(138\) 0 0
\(139\) −2535.33 −1.54708 −0.773538 0.633750i \(-0.781515\pi\)
−0.773538 + 0.633750i \(0.781515\pi\)
\(140\) 0 0
\(141\) −1886.17 −1.12656
\(142\) 0 0
\(143\) 987.190 0.577293
\(144\) 0 0
\(145\) −1340.32 −0.767638
\(146\) 0 0
\(147\) −1970.46 −1.10558
\(148\) 0 0
\(149\) −2056.85 −1.13090 −0.565448 0.824784i \(-0.691297\pi\)
−0.565448 + 0.824784i \(0.691297\pi\)
\(150\) 0 0
\(151\) 532.903 0.287199 0.143599 0.989636i \(-0.454132\pi\)
0.143599 + 0.989636i \(0.454132\pi\)
\(152\) 0 0
\(153\) 8.01348 0.00423433
\(154\) 0 0
\(155\) 502.872 0.260591
\(156\) 0 0
\(157\) 2554.89 1.29874 0.649370 0.760472i \(-0.275032\pi\)
0.649370 + 0.760472i \(0.275032\pi\)
\(158\) 0 0
\(159\) 2684.33 1.33888
\(160\) 0 0
\(161\) 1001.59 0.490289
\(162\) 0 0
\(163\) −894.659 −0.429909 −0.214954 0.976624i \(-0.568960\pi\)
−0.214954 + 0.976624i \(0.568960\pi\)
\(164\) 0 0
\(165\) −1656.13 −0.781392
\(166\) 0 0
\(167\) −2895.98 −1.34190 −0.670951 0.741502i \(-0.734114\pi\)
−0.670951 + 0.741502i \(0.734114\pi\)
\(168\) 0 0
\(169\) −1610.88 −0.733219
\(170\) 0 0
\(171\) −2.16724 −0.000969199 0
\(172\) 0 0
\(173\) −927.867 −0.407771 −0.203886 0.978995i \(-0.565357\pi\)
−0.203886 + 0.978995i \(0.565357\pi\)
\(174\) 0 0
\(175\) −1723.32 −0.744406
\(176\) 0 0
\(177\) −369.940 −0.157098
\(178\) 0 0
\(179\) −3219.75 −1.34444 −0.672222 0.740350i \(-0.734660\pi\)
−0.672222 + 0.740350i \(0.734660\pi\)
\(180\) 0 0
\(181\) 823.223 0.338064 0.169032 0.985611i \(-0.445936\pi\)
0.169032 + 0.985611i \(0.445936\pi\)
\(182\) 0 0
\(183\) −3827.71 −1.54619
\(184\) 0 0
\(185\) −3376.32 −1.34179
\(186\) 0 0
\(187\) 2864.68 1.12025
\(188\) 0 0
\(189\) 3760.24 1.44718
\(190\) 0 0
\(191\) 2292.84 0.868607 0.434304 0.900767i \(-0.356995\pi\)
0.434304 + 0.900767i \(0.356995\pi\)
\(192\) 0 0
\(193\) 910.072 0.339422 0.169711 0.985494i \(-0.445717\pi\)
0.169711 + 0.985494i \(0.445717\pi\)
\(194\) 0 0
\(195\) −983.285 −0.361100
\(196\) 0 0
\(197\) 784.134 0.283590 0.141795 0.989896i \(-0.454713\pi\)
0.141795 + 0.989896i \(0.454713\pi\)
\(198\) 0 0
\(199\) 2725.37 0.970837 0.485419 0.874282i \(-0.338667\pi\)
0.485419 + 0.874282i \(0.338667\pi\)
\(200\) 0 0
\(201\) 1168.32 0.409984
\(202\) 0 0
\(203\) −4615.43 −1.59576
\(204\) 0 0
\(205\) 2107.07 0.717875
\(206\) 0 0
\(207\) 4.25355 0.00142822
\(208\) 0 0
\(209\) −774.750 −0.256414
\(210\) 0 0
\(211\) 193.856 0.0632493 0.0316247 0.999500i \(-0.489932\pi\)
0.0316247 + 0.999500i \(0.489932\pi\)
\(212\) 0 0
\(213\) −352.258 −0.113316
\(214\) 0 0
\(215\) 388.703 0.123299
\(216\) 0 0
\(217\) 1731.65 0.541716
\(218\) 0 0
\(219\) 465.123 0.143517
\(220\) 0 0
\(221\) 1700.83 0.517692
\(222\) 0 0
\(223\) −271.131 −0.0814184 −0.0407092 0.999171i \(-0.512962\pi\)
−0.0407092 + 0.999171i \(0.512962\pi\)
\(224\) 0 0
\(225\) −7.31860 −0.00216847
\(226\) 0 0
\(227\) −1282.75 −0.375061 −0.187531 0.982259i \(-0.560048\pi\)
−0.187531 + 0.982259i \(0.560048\pi\)
\(228\) 0 0
\(229\) 1038.29 0.299618 0.149809 0.988715i \(-0.452134\pi\)
0.149809 + 0.988715i \(0.452134\pi\)
\(230\) 0 0
\(231\) −5702.94 −1.62435
\(232\) 0 0
\(233\) −4460.70 −1.25421 −0.627103 0.778936i \(-0.715760\pi\)
−0.627103 + 0.778936i \(0.715760\pi\)
\(234\) 0 0
\(235\) 2825.36 0.784282
\(236\) 0 0
\(237\) −6347.96 −1.73985
\(238\) 0 0
\(239\) 2616.79 0.708227 0.354114 0.935202i \(-0.384783\pi\)
0.354114 + 0.935202i \(0.384783\pi\)
\(240\) 0 0
\(241\) −4926.25 −1.31671 −0.658356 0.752707i \(-0.728748\pi\)
−0.658356 + 0.752707i \(0.728748\pi\)
\(242\) 0 0
\(243\) 32.0056 0.00844923
\(244\) 0 0
\(245\) 2951.61 0.769680
\(246\) 0 0
\(247\) −459.988 −0.118495
\(248\) 0 0
\(249\) −4938.60 −1.25691
\(250\) 0 0
\(251\) −2239.77 −0.563239 −0.281620 0.959526i \(-0.590872\pi\)
−0.281620 + 0.959526i \(0.590872\pi\)
\(252\) 0 0
\(253\) 1520.57 0.377855
\(254\) 0 0
\(255\) −2853.35 −0.700719
\(256\) 0 0
\(257\) 8191.14 1.98813 0.994065 0.108790i \(-0.0346975\pi\)
0.994065 + 0.108790i \(0.0346975\pi\)
\(258\) 0 0
\(259\) −11626.4 −2.78931
\(260\) 0 0
\(261\) −19.6007 −0.00464849
\(262\) 0 0
\(263\) 6874.34 1.61175 0.805875 0.592086i \(-0.201696\pi\)
0.805875 + 0.592086i \(0.201696\pi\)
\(264\) 0 0
\(265\) −4020.95 −0.932095
\(266\) 0 0
\(267\) −4570.34 −1.04757
\(268\) 0 0
\(269\) −578.895 −0.131211 −0.0656057 0.997846i \(-0.520898\pi\)
−0.0656057 + 0.997846i \(0.520898\pi\)
\(270\) 0 0
\(271\) −5685.01 −1.27432 −0.637158 0.770733i \(-0.719890\pi\)
−0.637158 + 0.770733i \(0.719890\pi\)
\(272\) 0 0
\(273\) −3385.97 −0.750652
\(274\) 0 0
\(275\) −2616.27 −0.573698
\(276\) 0 0
\(277\) 6612.18 1.43425 0.717125 0.696944i \(-0.245457\pi\)
0.717125 + 0.696944i \(0.245457\pi\)
\(278\) 0 0
\(279\) 7.35397 0.00157803
\(280\) 0 0
\(281\) 2678.07 0.568542 0.284271 0.958744i \(-0.408248\pi\)
0.284271 + 0.958744i \(0.408248\pi\)
\(282\) 0 0
\(283\) 5219.03 1.09625 0.548126 0.836396i \(-0.315341\pi\)
0.548126 + 0.836396i \(0.315341\pi\)
\(284\) 0 0
\(285\) 771.686 0.160388
\(286\) 0 0
\(287\) 7255.76 1.49231
\(288\) 0 0
\(289\) 22.5476 0.00458938
\(290\) 0 0
\(291\) −4229.44 −0.852006
\(292\) 0 0
\(293\) −6337.23 −1.26357 −0.631784 0.775145i \(-0.717677\pi\)
−0.631784 + 0.775145i \(0.717677\pi\)
\(294\) 0 0
\(295\) 554.145 0.109368
\(296\) 0 0
\(297\) 5708.61 1.11531
\(298\) 0 0
\(299\) 902.797 0.174616
\(300\) 0 0
\(301\) 1338.51 0.256314
\(302\) 0 0
\(303\) 1815.01 0.344124
\(304\) 0 0
\(305\) 5733.66 1.07642
\(306\) 0 0
\(307\) 7659.20 1.42389 0.711944 0.702236i \(-0.247815\pi\)
0.711944 + 0.702236i \(0.247815\pi\)
\(308\) 0 0
\(309\) 233.211 0.0429349
\(310\) 0 0
\(311\) −5374.55 −0.979945 −0.489973 0.871738i \(-0.662993\pi\)
−0.489973 + 0.871738i \(0.662993\pi\)
\(312\) 0 0
\(313\) −2164.94 −0.390957 −0.195479 0.980708i \(-0.562626\pi\)
−0.195479 + 0.980708i \(0.562626\pi\)
\(314\) 0 0
\(315\) 23.8966 0.00427435
\(316\) 0 0
\(317\) 4072.50 0.721559 0.360779 0.932651i \(-0.382511\pi\)
0.360779 + 0.932651i \(0.382511\pi\)
\(318\) 0 0
\(319\) −7006.92 −1.22982
\(320\) 0 0
\(321\) 7465.61 1.29810
\(322\) 0 0
\(323\) −1334.82 −0.229942
\(324\) 0 0
\(325\) −1553.34 −0.265119
\(326\) 0 0
\(327\) −9231.81 −1.56122
\(328\) 0 0
\(329\) 9729.21 1.63036
\(330\) 0 0
\(331\) −6388.27 −1.06082 −0.530410 0.847742i \(-0.677962\pi\)
−0.530410 + 0.847742i \(0.677962\pi\)
\(332\) 0 0
\(333\) −49.3751 −0.00812534
\(334\) 0 0
\(335\) −1750.06 −0.285421
\(336\) 0 0
\(337\) 9593.76 1.55076 0.775379 0.631496i \(-0.217559\pi\)
0.775379 + 0.631496i \(0.217559\pi\)
\(338\) 0 0
\(339\) −1588.39 −0.254482
\(340\) 0 0
\(341\) 2628.91 0.417489
\(342\) 0 0
\(343\) 951.257 0.149746
\(344\) 0 0
\(345\) −1514.55 −0.236350
\(346\) 0 0
\(347\) −8456.74 −1.30830 −0.654152 0.756363i \(-0.726974\pi\)
−0.654152 + 0.756363i \(0.726974\pi\)
\(348\) 0 0
\(349\) −5235.83 −0.803059 −0.401530 0.915846i \(-0.631521\pi\)
−0.401530 + 0.915846i \(0.631521\pi\)
\(350\) 0 0
\(351\) 3389.34 0.515412
\(352\) 0 0
\(353\) 4943.57 0.745381 0.372690 0.927956i \(-0.378435\pi\)
0.372690 + 0.927956i \(0.378435\pi\)
\(354\) 0 0
\(355\) 527.659 0.0788880
\(356\) 0 0
\(357\) −9825.58 −1.45665
\(358\) 0 0
\(359\) −6634.24 −0.975325 −0.487663 0.873032i \(-0.662150\pi\)
−0.487663 + 0.873032i \(0.662150\pi\)
\(360\) 0 0
\(361\) 361.000 0.0526316
\(362\) 0 0
\(363\) −1727.25 −0.249744
\(364\) 0 0
\(365\) −696.723 −0.0999128
\(366\) 0 0
\(367\) 8379.54 1.19185 0.595924 0.803041i \(-0.296786\pi\)
0.595924 + 0.803041i \(0.296786\pi\)
\(368\) 0 0
\(369\) 30.8137 0.00434714
\(370\) 0 0
\(371\) −13846.3 −1.93763
\(372\) 0 0
\(373\) −7995.03 −1.10983 −0.554915 0.831907i \(-0.687249\pi\)
−0.554915 + 0.831907i \(0.687249\pi\)
\(374\) 0 0
\(375\) 7682.80 1.05797
\(376\) 0 0
\(377\) −4160.17 −0.568328
\(378\) 0 0
\(379\) 10776.2 1.46052 0.730258 0.683172i \(-0.239400\pi\)
0.730258 + 0.683172i \(0.239400\pi\)
\(380\) 0 0
\(381\) −1800.13 −0.242057
\(382\) 0 0
\(383\) −5932.82 −0.791522 −0.395761 0.918354i \(-0.629519\pi\)
−0.395761 + 0.918354i \(0.629519\pi\)
\(384\) 0 0
\(385\) 8542.61 1.13084
\(386\) 0 0
\(387\) 5.68437 0.000746648 0
\(388\) 0 0
\(389\) 2543.56 0.331527 0.165763 0.986166i \(-0.446991\pi\)
0.165763 + 0.986166i \(0.446991\pi\)
\(390\) 0 0
\(391\) 2619.78 0.338844
\(392\) 0 0
\(393\) −13575.7 −1.74250
\(394\) 0 0
\(395\) 9508.82 1.21124
\(396\) 0 0
\(397\) −10082.6 −1.27464 −0.637322 0.770598i \(-0.719958\pi\)
−0.637322 + 0.770598i \(0.719958\pi\)
\(398\) 0 0
\(399\) 2657.32 0.333415
\(400\) 0 0
\(401\) −5602.92 −0.697746 −0.348873 0.937170i \(-0.613436\pi\)
−0.348873 + 0.937170i \(0.613436\pi\)
\(402\) 0 0
\(403\) 1560.85 0.192931
\(404\) 0 0
\(405\) −5710.05 −0.700580
\(406\) 0 0
\(407\) −17650.7 −2.14966
\(408\) 0 0
\(409\) −14919.9 −1.80376 −0.901882 0.431983i \(-0.857814\pi\)
−0.901882 + 0.431983i \(0.857814\pi\)
\(410\) 0 0
\(411\) −3655.69 −0.438739
\(412\) 0 0
\(413\) 1908.22 0.227354
\(414\) 0 0
\(415\) 7397.69 0.875033
\(416\) 0 0
\(417\) 13201.7 1.55034
\(418\) 0 0
\(419\) 3609.85 0.420890 0.210445 0.977606i \(-0.432509\pi\)
0.210445 + 0.977606i \(0.432509\pi\)
\(420\) 0 0
\(421\) −1514.54 −0.175331 −0.0876654 0.996150i \(-0.527941\pi\)
−0.0876654 + 0.996150i \(0.527941\pi\)
\(422\) 0 0
\(423\) 41.3179 0.00474928
\(424\) 0 0
\(425\) −4507.56 −0.514468
\(426\) 0 0
\(427\) 19744.0 2.23766
\(428\) 0 0
\(429\) −5140.41 −0.578512
\(430\) 0 0
\(431\) −4215.77 −0.471152 −0.235576 0.971856i \(-0.575698\pi\)
−0.235576 + 0.971856i \(0.575698\pi\)
\(432\) 0 0
\(433\) −10879.5 −1.20747 −0.603737 0.797183i \(-0.706322\pi\)
−0.603737 + 0.797183i \(0.706322\pi\)
\(434\) 0 0
\(435\) 6979.20 0.769257
\(436\) 0 0
\(437\) −708.519 −0.0775584
\(438\) 0 0
\(439\) 4973.00 0.540657 0.270328 0.962768i \(-0.412868\pi\)
0.270328 + 0.962768i \(0.412868\pi\)
\(440\) 0 0
\(441\) 43.1642 0.00466086
\(442\) 0 0
\(443\) 6349.20 0.680947 0.340474 0.940254i \(-0.389413\pi\)
0.340474 + 0.940254i \(0.389413\pi\)
\(444\) 0 0
\(445\) 6846.07 0.729291
\(446\) 0 0
\(447\) 10710.2 1.13328
\(448\) 0 0
\(449\) −12179.4 −1.28014 −0.640070 0.768316i \(-0.721095\pi\)
−0.640070 + 0.768316i \(0.721095\pi\)
\(450\) 0 0
\(451\) 11015.3 1.15009
\(452\) 0 0
\(453\) −2774.89 −0.287805
\(454\) 0 0
\(455\) 5071.95 0.522586
\(456\) 0 0
\(457\) 12539.5 1.28353 0.641767 0.766900i \(-0.278202\pi\)
0.641767 + 0.766900i \(0.278202\pi\)
\(458\) 0 0
\(459\) 9835.36 1.00016
\(460\) 0 0
\(461\) 9809.95 0.991095 0.495548 0.868581i \(-0.334967\pi\)
0.495548 + 0.868581i \(0.334967\pi\)
\(462\) 0 0
\(463\) −10361.5 −1.04004 −0.520022 0.854153i \(-0.674076\pi\)
−0.520022 + 0.854153i \(0.674076\pi\)
\(464\) 0 0
\(465\) −2618.51 −0.261141
\(466\) 0 0
\(467\) −14250.6 −1.41208 −0.706038 0.708174i \(-0.749519\pi\)
−0.706038 + 0.708174i \(0.749519\pi\)
\(468\) 0 0
\(469\) −6026.38 −0.593331
\(470\) 0 0
\(471\) −13303.6 −1.30148
\(472\) 0 0
\(473\) 2032.06 0.197536
\(474\) 0 0
\(475\) 1219.07 0.117757
\(476\) 0 0
\(477\) −58.8021 −0.00564437
\(478\) 0 0
\(479\) −9231.75 −0.880604 −0.440302 0.897850i \(-0.645129\pi\)
−0.440302 + 0.897850i \(0.645129\pi\)
\(480\) 0 0
\(481\) −10479.6 −0.993411
\(482\) 0 0
\(483\) −5215.40 −0.491323
\(484\) 0 0
\(485\) 6335.41 0.593146
\(486\) 0 0
\(487\) 12264.5 1.14119 0.570595 0.821231i \(-0.306713\pi\)
0.570595 + 0.821231i \(0.306713\pi\)
\(488\) 0 0
\(489\) 4658.59 0.430816
\(490\) 0 0
\(491\) 7462.60 0.685911 0.342956 0.939352i \(-0.388572\pi\)
0.342956 + 0.939352i \(0.388572\pi\)
\(492\) 0 0
\(493\) −12072.2 −1.10285
\(494\) 0 0
\(495\) 36.2787 0.00329415
\(496\) 0 0
\(497\) 1817.01 0.163992
\(498\) 0 0
\(499\) 6515.51 0.584517 0.292259 0.956339i \(-0.405593\pi\)
0.292259 + 0.956339i \(0.405593\pi\)
\(500\) 0 0
\(501\) 15079.7 1.34473
\(502\) 0 0
\(503\) 19970.3 1.77024 0.885119 0.465365i \(-0.154077\pi\)
0.885119 + 0.465365i \(0.154077\pi\)
\(504\) 0 0
\(505\) −2718.76 −0.239571
\(506\) 0 0
\(507\) 8388.05 0.734766
\(508\) 0 0
\(509\) 12882.7 1.12184 0.560921 0.827869i \(-0.310447\pi\)
0.560921 + 0.827869i \(0.310447\pi\)
\(510\) 0 0
\(511\) −2399.19 −0.207698
\(512\) 0 0
\(513\) −2659.97 −0.228929
\(514\) 0 0
\(515\) −349.334 −0.0298903
\(516\) 0 0
\(517\) 14770.4 1.25648
\(518\) 0 0
\(519\) 4831.51 0.408632
\(520\) 0 0
\(521\) −9248.25 −0.777684 −0.388842 0.921304i \(-0.627125\pi\)
−0.388842 + 0.921304i \(0.627125\pi\)
\(522\) 0 0
\(523\) 12189.8 1.01916 0.509582 0.860422i \(-0.329800\pi\)
0.509582 + 0.860422i \(0.329800\pi\)
\(524\) 0 0
\(525\) 8973.55 0.745977
\(526\) 0 0
\(527\) 4529.35 0.374386
\(528\) 0 0
\(529\) −10776.4 −0.885709
\(530\) 0 0
\(531\) 8.10379 0.000662287 0
\(532\) 0 0
\(533\) 6540.07 0.531486
\(534\) 0 0
\(535\) −11183.0 −0.903705
\(536\) 0 0
\(537\) 16765.6 1.34728
\(538\) 0 0
\(539\) 15430.4 1.23309
\(540\) 0 0
\(541\) 11873.6 0.943597 0.471798 0.881706i \(-0.343605\pi\)
0.471798 + 0.881706i \(0.343605\pi\)
\(542\) 0 0
\(543\) −4286.62 −0.338778
\(544\) 0 0
\(545\) 13828.6 1.08689
\(546\) 0 0
\(547\) 14476.6 1.13158 0.565791 0.824549i \(-0.308571\pi\)
0.565791 + 0.824549i \(0.308571\pi\)
\(548\) 0 0
\(549\) 83.8486 0.00651834
\(550\) 0 0
\(551\) 3264.92 0.252432
\(552\) 0 0
\(553\) 32743.9 2.51792
\(554\) 0 0
\(555\) 17580.9 1.34463
\(556\) 0 0
\(557\) −8641.98 −0.657401 −0.328701 0.944434i \(-0.606611\pi\)
−0.328701 + 0.944434i \(0.606611\pi\)
\(558\) 0 0
\(559\) 1206.48 0.0912859
\(560\) 0 0
\(561\) −14916.7 −1.12261
\(562\) 0 0
\(563\) −10421.6 −0.780136 −0.390068 0.920786i \(-0.627549\pi\)
−0.390068 + 0.920786i \(0.627549\pi\)
\(564\) 0 0
\(565\) 2379.30 0.177164
\(566\) 0 0
\(567\) −19662.7 −1.45636
\(568\) 0 0
\(569\) −19122.4 −1.40888 −0.704440 0.709764i \(-0.748802\pi\)
−0.704440 + 0.709764i \(0.748802\pi\)
\(570\) 0 0
\(571\) 22719.0 1.66508 0.832538 0.553968i \(-0.186887\pi\)
0.832538 + 0.553968i \(0.186887\pi\)
\(572\) 0 0
\(573\) −11939.1 −0.870440
\(574\) 0 0
\(575\) −2392.61 −0.173528
\(576\) 0 0
\(577\) −14566.0 −1.05094 −0.525468 0.850813i \(-0.676110\pi\)
−0.525468 + 0.850813i \(0.676110\pi\)
\(578\) 0 0
\(579\) −4738.85 −0.340138
\(580\) 0 0
\(581\) 25474.2 1.81901
\(582\) 0 0
\(583\) −21020.7 −1.49329
\(584\) 0 0
\(585\) 21.5395 0.00152231
\(586\) 0 0
\(587\) 1884.52 0.132509 0.0662544 0.997803i \(-0.478895\pi\)
0.0662544 + 0.997803i \(0.478895\pi\)
\(588\) 0 0
\(589\) −1224.96 −0.0856937
\(590\) 0 0
\(591\) −4083.08 −0.284189
\(592\) 0 0
\(593\) −16442.1 −1.13861 −0.569305 0.822126i \(-0.692788\pi\)
−0.569305 + 0.822126i \(0.692788\pi\)
\(594\) 0 0
\(595\) 14718.0 1.01409
\(596\) 0 0
\(597\) −14191.3 −0.972886
\(598\) 0 0
\(599\) −22081.2 −1.50620 −0.753101 0.657905i \(-0.771443\pi\)
−0.753101 + 0.657905i \(0.771443\pi\)
\(600\) 0 0
\(601\) 22054.4 1.49687 0.748434 0.663209i \(-0.230806\pi\)
0.748434 + 0.663209i \(0.230806\pi\)
\(602\) 0 0
\(603\) −25.5928 −0.00172839
\(604\) 0 0
\(605\) 2587.30 0.173866
\(606\) 0 0
\(607\) 26705.7 1.78575 0.892876 0.450302i \(-0.148684\pi\)
0.892876 + 0.450302i \(0.148684\pi\)
\(608\) 0 0
\(609\) 24033.1 1.59913
\(610\) 0 0
\(611\) 8769.54 0.580651
\(612\) 0 0
\(613\) −4759.75 −0.313613 −0.156806 0.987629i \(-0.550120\pi\)
−0.156806 + 0.987629i \(0.550120\pi\)
\(614\) 0 0
\(615\) −10971.8 −0.719389
\(616\) 0 0
\(617\) −360.734 −0.0235375 −0.0117687 0.999931i \(-0.503746\pi\)
−0.0117687 + 0.999931i \(0.503746\pi\)
\(618\) 0 0
\(619\) −14562.1 −0.945560 −0.472780 0.881180i \(-0.656750\pi\)
−0.472780 + 0.881180i \(0.656750\pi\)
\(620\) 0 0
\(621\) 5220.60 0.337352
\(622\) 0 0
\(623\) 23574.6 1.51605
\(624\) 0 0
\(625\) −3488.13 −0.223240
\(626\) 0 0
\(627\) 4034.22 0.256955
\(628\) 0 0
\(629\) −30410.4 −1.92773
\(630\) 0 0
\(631\) 328.881 0.0207489 0.0103744 0.999946i \(-0.496698\pi\)
0.0103744 + 0.999946i \(0.496698\pi\)
\(632\) 0 0
\(633\) −1009.43 −0.0633828
\(634\) 0 0
\(635\) 2696.48 0.168514
\(636\) 0 0
\(637\) 9161.41 0.569840
\(638\) 0 0
\(639\) 7.71646 0.000477712 0
\(640\) 0 0
\(641\) −7278.40 −0.448486 −0.224243 0.974533i \(-0.571991\pi\)
−0.224243 + 0.974533i \(0.571991\pi\)
\(642\) 0 0
\(643\) −6629.96 −0.406625 −0.203313 0.979114i \(-0.565171\pi\)
−0.203313 + 0.979114i \(0.565171\pi\)
\(644\) 0 0
\(645\) −2024.02 −0.123559
\(646\) 0 0
\(647\) −17987.5 −1.09298 −0.546492 0.837464i \(-0.684037\pi\)
−0.546492 + 0.837464i \(0.684037\pi\)
\(648\) 0 0
\(649\) 2896.96 0.175217
\(650\) 0 0
\(651\) −9016.92 −0.542859
\(652\) 0 0
\(653\) −8638.65 −0.517698 −0.258849 0.965918i \(-0.583343\pi\)
−0.258849 + 0.965918i \(0.583343\pi\)
\(654\) 0 0
\(655\) 20335.4 1.21309
\(656\) 0 0
\(657\) −10.1888 −0.000605029 0
\(658\) 0 0
\(659\) −18722.0 −1.10669 −0.553343 0.832953i \(-0.686648\pi\)
−0.553343 + 0.832953i \(0.686648\pi\)
\(660\) 0 0
\(661\) 6277.59 0.369395 0.184697 0.982795i \(-0.440870\pi\)
0.184697 + 0.982795i \(0.440870\pi\)
\(662\) 0 0
\(663\) −8856.41 −0.518785
\(664\) 0 0
\(665\) −3980.49 −0.232115
\(666\) 0 0
\(667\) −6407.91 −0.371987
\(668\) 0 0
\(669\) 1411.81 0.0815902
\(670\) 0 0
\(671\) 29974.4 1.72451
\(672\) 0 0
\(673\) −14862.3 −0.851265 −0.425632 0.904896i \(-0.639948\pi\)
−0.425632 + 0.904896i \(0.639948\pi\)
\(674\) 0 0
\(675\) −8982.49 −0.512202
\(676\) 0 0
\(677\) 5571.65 0.316301 0.158151 0.987415i \(-0.449447\pi\)
0.158151 + 0.987415i \(0.449447\pi\)
\(678\) 0 0
\(679\) 21816.1 1.23303
\(680\) 0 0
\(681\) 6679.41 0.375853
\(682\) 0 0
\(683\) −29053.9 −1.62770 −0.813849 0.581077i \(-0.802632\pi\)
−0.813849 + 0.581077i \(0.802632\pi\)
\(684\) 0 0
\(685\) 5475.97 0.305440
\(686\) 0 0
\(687\) −5406.52 −0.300250
\(688\) 0 0
\(689\) −12480.5 −0.690086
\(690\) 0 0
\(691\) 27785.8 1.52970 0.764849 0.644210i \(-0.222814\pi\)
0.764849 + 0.644210i \(0.222814\pi\)
\(692\) 0 0
\(693\) 124.927 0.00684786
\(694\) 0 0
\(695\) −19775.3 −1.07931
\(696\) 0 0
\(697\) 18978.3 1.03136
\(698\) 0 0
\(699\) 23227.4 1.25685
\(700\) 0 0
\(701\) 6058.01 0.326402 0.163201 0.986593i \(-0.447818\pi\)
0.163201 + 0.986593i \(0.447818\pi\)
\(702\) 0 0
\(703\) 8224.46 0.441240
\(704\) 0 0
\(705\) −14712.0 −0.785937
\(706\) 0 0
\(707\) −9362.14 −0.498019
\(708\) 0 0
\(709\) 30416.6 1.61117 0.805586 0.592479i \(-0.201851\pi\)
0.805586 + 0.592479i \(0.201851\pi\)
\(710\) 0 0
\(711\) 139.056 0.00733477
\(712\) 0 0
\(713\) 2404.17 0.126279
\(714\) 0 0
\(715\) 7699.99 0.402746
\(716\) 0 0
\(717\) −13626.0 −0.709722
\(718\) 0 0
\(719\) −7483.56 −0.388164 −0.194082 0.980985i \(-0.562173\pi\)
−0.194082 + 0.980985i \(0.562173\pi\)
\(720\) 0 0
\(721\) −1202.94 −0.0621357
\(722\) 0 0
\(723\) 25651.5 1.31949
\(724\) 0 0
\(725\) 11025.4 0.564789
\(726\) 0 0
\(727\) 7721.59 0.393918 0.196959 0.980412i \(-0.436893\pi\)
0.196959 + 0.980412i \(0.436893\pi\)
\(728\) 0 0
\(729\) 19599.1 0.995740
\(730\) 0 0
\(731\) 3501.04 0.177142
\(732\) 0 0
\(733\) −4540.36 −0.228788 −0.114394 0.993435i \(-0.536493\pi\)
−0.114394 + 0.993435i \(0.536493\pi\)
\(734\) 0 0
\(735\) −15369.4 −0.771304
\(736\) 0 0
\(737\) −9148.96 −0.457268
\(738\) 0 0
\(739\) −36117.7 −1.79785 −0.898925 0.438103i \(-0.855651\pi\)
−0.898925 + 0.438103i \(0.855651\pi\)
\(740\) 0 0
\(741\) 2395.21 0.118745
\(742\) 0 0
\(743\) −14158.2 −0.699079 −0.349539 0.936922i \(-0.613662\pi\)
−0.349539 + 0.936922i \(0.613662\pi\)
\(744\) 0 0
\(745\) −16043.2 −0.788964
\(746\) 0 0
\(747\) 108.183 0.00529883
\(748\) 0 0
\(749\) −38508.9 −1.87862
\(750\) 0 0
\(751\) −8166.40 −0.396799 −0.198400 0.980121i \(-0.563574\pi\)
−0.198400 + 0.980121i \(0.563574\pi\)
\(752\) 0 0
\(753\) 11662.7 0.564428
\(754\) 0 0
\(755\) 4156.60 0.200363
\(756\) 0 0
\(757\) −25616.1 −1.22990 −0.614948 0.788567i \(-0.710823\pi\)
−0.614948 + 0.788567i \(0.710823\pi\)
\(758\) 0 0
\(759\) −7917.77 −0.378652
\(760\) 0 0
\(761\) −30062.7 −1.43203 −0.716013 0.698087i \(-0.754035\pi\)
−0.716013 + 0.698087i \(0.754035\pi\)
\(762\) 0 0
\(763\) 47619.3 2.25941
\(764\) 0 0
\(765\) 62.5044 0.00295406
\(766\) 0 0
\(767\) 1719.99 0.0809718
\(768\) 0 0
\(769\) −21116.2 −0.990209 −0.495105 0.868833i \(-0.664870\pi\)
−0.495105 + 0.868833i \(0.664870\pi\)
\(770\) 0 0
\(771\) −42652.2 −1.99232
\(772\) 0 0
\(773\) −5086.88 −0.236691 −0.118346 0.992972i \(-0.537759\pi\)
−0.118346 + 0.992972i \(0.537759\pi\)
\(774\) 0 0
\(775\) −4136.59 −0.191730
\(776\) 0 0
\(777\) 60540.3 2.79520
\(778\) 0 0
\(779\) −5132.67 −0.236068
\(780\) 0 0
\(781\) 2758.50 0.126385
\(782\) 0 0
\(783\) −24057.0 −1.09799
\(784\) 0 0
\(785\) 19927.9 0.906060
\(786\) 0 0
\(787\) −12350.0 −0.559377 −0.279688 0.960091i \(-0.590231\pi\)
−0.279688 + 0.960091i \(0.590231\pi\)
\(788\) 0 0
\(789\) −35795.5 −1.61515
\(790\) 0 0
\(791\) 8193.19 0.368289
\(792\) 0 0
\(793\) 17796.5 0.796939
\(794\) 0 0
\(795\) 20937.6 0.934061
\(796\) 0 0
\(797\) −10263.6 −0.456155 −0.228078 0.973643i \(-0.573244\pi\)
−0.228078 + 0.973643i \(0.573244\pi\)
\(798\) 0 0
\(799\) 25447.9 1.12676
\(800\) 0 0
\(801\) 100.116 0.00441628
\(802\) 0 0
\(803\) −3642.33 −0.160068
\(804\) 0 0
\(805\) 7812.32 0.342047
\(806\) 0 0
\(807\) 3014.37 0.131488
\(808\) 0 0
\(809\) −42090.0 −1.82918 −0.914590 0.404383i \(-0.867486\pi\)
−0.914590 + 0.404383i \(0.867486\pi\)
\(810\) 0 0
\(811\) −33315.6 −1.44250 −0.721250 0.692674i \(-0.756432\pi\)
−0.721250 + 0.692674i \(0.756432\pi\)
\(812\) 0 0
\(813\) 29602.5 1.27701
\(814\) 0 0
\(815\) −6978.26 −0.299924
\(816\) 0 0
\(817\) −946.853 −0.0405461
\(818\) 0 0
\(819\) 74.1719 0.00316456
\(820\) 0 0
\(821\) −32210.1 −1.36923 −0.684616 0.728903i \(-0.740030\pi\)
−0.684616 + 0.728903i \(0.740030\pi\)
\(822\) 0 0
\(823\) −15834.7 −0.670672 −0.335336 0.942099i \(-0.608850\pi\)
−0.335336 + 0.942099i \(0.608850\pi\)
\(824\) 0 0
\(825\) 13623.2 0.574908
\(826\) 0 0
\(827\) −9712.04 −0.408369 −0.204184 0.978932i \(-0.565454\pi\)
−0.204184 + 0.978932i \(0.565454\pi\)
\(828\) 0 0
\(829\) 8471.30 0.354910 0.177455 0.984129i \(-0.443214\pi\)
0.177455 + 0.984129i \(0.443214\pi\)
\(830\) 0 0
\(831\) −34430.4 −1.43728
\(832\) 0 0
\(833\) 26585.1 1.10578
\(834\) 0 0
\(835\) −22588.4 −0.936171
\(836\) 0 0
\(837\) 9025.90 0.372737
\(838\) 0 0
\(839\) −332.139 −0.0136671 −0.00683356 0.999977i \(-0.502175\pi\)
−0.00683356 + 0.999977i \(0.502175\pi\)
\(840\) 0 0
\(841\) 5139.25 0.210720
\(842\) 0 0
\(843\) −13945.0 −0.569741
\(844\) 0 0
\(845\) −12564.7 −0.511527
\(846\) 0 0
\(847\) 8909.45 0.361431
\(848\) 0 0
\(849\) −27176.1 −1.09857
\(850\) 0 0
\(851\) −16141.8 −0.650216
\(852\) 0 0
\(853\) 15669.4 0.628970 0.314485 0.949262i \(-0.398168\pi\)
0.314485 + 0.949262i \(0.398168\pi\)
\(854\) 0 0
\(855\) −16.9043 −0.000676157 0
\(856\) 0 0
\(857\) −16464.7 −0.656270 −0.328135 0.944631i \(-0.606420\pi\)
−0.328135 + 0.944631i \(0.606420\pi\)
\(858\) 0 0
\(859\) 7766.89 0.308502 0.154251 0.988032i \(-0.450704\pi\)
0.154251 + 0.988032i \(0.450704\pi\)
\(860\) 0 0
\(861\) −37781.6 −1.49546
\(862\) 0 0
\(863\) 7812.54 0.308160 0.154080 0.988058i \(-0.450759\pi\)
0.154080 + 0.988058i \(0.450759\pi\)
\(864\) 0 0
\(865\) −7237.28 −0.284479
\(866\) 0 0
\(867\) −117.408 −0.00459906
\(868\) 0 0
\(869\) 49710.2 1.94051
\(870\) 0 0
\(871\) −5431.95 −0.211314
\(872\) 0 0
\(873\) 92.6486 0.00359184
\(874\) 0 0
\(875\) −39629.2 −1.53110
\(876\) 0 0
\(877\) −31616.2 −1.21734 −0.608668 0.793425i \(-0.708296\pi\)
−0.608668 + 0.793425i \(0.708296\pi\)
\(878\) 0 0
\(879\) 32998.7 1.26623
\(880\) 0 0
\(881\) −7258.59 −0.277580 −0.138790 0.990322i \(-0.544321\pi\)
−0.138790 + 0.990322i \(0.544321\pi\)
\(882\) 0 0
\(883\) −26858.2 −1.02361 −0.511806 0.859101i \(-0.671023\pi\)
−0.511806 + 0.859101i \(0.671023\pi\)
\(884\) 0 0
\(885\) −2885.50 −0.109599
\(886\) 0 0
\(887\) −26005.8 −0.984431 −0.492215 0.870473i \(-0.663813\pi\)
−0.492215 + 0.870473i \(0.663813\pi\)
\(888\) 0 0
\(889\) 9285.39 0.350306
\(890\) 0 0
\(891\) −29851.0 −1.12239
\(892\) 0 0
\(893\) −6882.37 −0.257906
\(894\) 0 0
\(895\) −25113.7 −0.937944
\(896\) 0 0
\(897\) −4700.97 −0.174984
\(898\) 0 0
\(899\) −11078.7 −0.411005
\(900\) 0 0
\(901\) −36216.5 −1.33912
\(902\) 0 0
\(903\) −6969.78 −0.256855
\(904\) 0 0
\(905\) 6421.06 0.235849
\(906\) 0 0
\(907\) 41499.6 1.51926 0.759631 0.650354i \(-0.225380\pi\)
0.759631 + 0.650354i \(0.225380\pi\)
\(908\) 0 0
\(909\) −39.7590 −0.00145074
\(910\) 0 0
\(911\) −11858.0 −0.431254 −0.215627 0.976476i \(-0.569179\pi\)
−0.215627 + 0.976476i \(0.569179\pi\)
\(912\) 0 0
\(913\) 38673.6 1.40187
\(914\) 0 0
\(915\) −29855.8 −1.07869
\(916\) 0 0
\(917\) 70025.6 2.52175
\(918\) 0 0
\(919\) −20359.3 −0.730784 −0.365392 0.930854i \(-0.619065\pi\)
−0.365392 + 0.930854i \(0.619065\pi\)
\(920\) 0 0
\(921\) −39882.4 −1.42689
\(922\) 0 0
\(923\) 1637.78 0.0584055
\(924\) 0 0
\(925\) 27773.3 0.987224
\(926\) 0 0
\(927\) −5.10864 −0.000181003 0
\(928\) 0 0
\(929\) 11453.8 0.404508 0.202254 0.979333i \(-0.435173\pi\)
0.202254 + 0.979333i \(0.435173\pi\)
\(930\) 0 0
\(931\) −7189.91 −0.253104
\(932\) 0 0
\(933\) 27985.9 0.982013
\(934\) 0 0
\(935\) 22344.2 0.781534
\(936\) 0 0
\(937\) −26514.3 −0.924422 −0.462211 0.886770i \(-0.652944\pi\)
−0.462211 + 0.886770i \(0.652944\pi\)
\(938\) 0 0
\(939\) 11273.1 0.391782
\(940\) 0 0
\(941\) −32948.7 −1.14144 −0.570721 0.821144i \(-0.693336\pi\)
−0.570721 + 0.821144i \(0.693336\pi\)
\(942\) 0 0
\(943\) 10073.7 0.347872
\(944\) 0 0
\(945\) 29329.5 1.00962
\(946\) 0 0
\(947\) 22527.0 0.772998 0.386499 0.922290i \(-0.373684\pi\)
0.386499 + 0.922290i \(0.373684\pi\)
\(948\) 0 0
\(949\) −2162.54 −0.0739714
\(950\) 0 0
\(951\) −21206.0 −0.723081
\(952\) 0 0
\(953\) −20808.5 −0.707297 −0.353648 0.935378i \(-0.615059\pi\)
−0.353648 + 0.935378i \(0.615059\pi\)
\(954\) 0 0
\(955\) 17883.9 0.605979
\(956\) 0 0
\(957\) 36485.8 1.23241
\(958\) 0 0
\(959\) 18856.7 0.634946
\(960\) 0 0
\(961\) −25634.4 −0.860475
\(962\) 0 0
\(963\) −163.539 −0.00547245
\(964\) 0 0
\(965\) 7098.48 0.236796
\(966\) 0 0
\(967\) 19794.4 0.658269 0.329135 0.944283i \(-0.393243\pi\)
0.329135 + 0.944283i \(0.393243\pi\)
\(968\) 0 0
\(969\) 6950.54 0.230427
\(970\) 0 0
\(971\) −50395.8 −1.66558 −0.832789 0.553590i \(-0.813257\pi\)
−0.832789 + 0.553590i \(0.813257\pi\)
\(972\) 0 0
\(973\) −68096.8 −2.24366
\(974\) 0 0
\(975\) 8088.42 0.265679
\(976\) 0 0
\(977\) 45621.3 1.49391 0.746957 0.664872i \(-0.231514\pi\)
0.746957 + 0.664872i \(0.231514\pi\)
\(978\) 0 0
\(979\) 35789.8 1.16838
\(980\) 0 0
\(981\) 202.229 0.00658173
\(982\) 0 0
\(983\) 29123.9 0.944972 0.472486 0.881338i \(-0.343357\pi\)
0.472486 + 0.881338i \(0.343357\pi\)
\(984\) 0 0
\(985\) 6116.18 0.197845
\(986\) 0 0
\(987\) −50661.1 −1.63380
\(988\) 0 0
\(989\) 1858.35 0.0597492
\(990\) 0 0
\(991\) 28418.2 0.910933 0.455466 0.890253i \(-0.349473\pi\)
0.455466 + 0.890253i \(0.349473\pi\)
\(992\) 0 0
\(993\) 33264.5 1.06306
\(994\) 0 0
\(995\) 21257.7 0.677300
\(996\) 0 0
\(997\) −38478.3 −1.22229 −0.611143 0.791520i \(-0.709290\pi\)
−0.611143 + 0.791520i \(0.709290\pi\)
\(998\) 0 0
\(999\) −60600.5 −1.91924
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.1.2 yes 7
4.3 odd 2 608.4.a.j.1.6 7
8.3 odd 2 1216.4.a.bg.1.2 7
8.5 even 2 1216.4.a.bf.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
608.4.a.j.1.6 7 4.3 odd 2
608.4.a.k.1.2 yes 7 1.1 even 1 trivial
1216.4.a.bf.1.6 7 8.5 even 2
1216.4.a.bg.1.2 7 8.3 odd 2