Properties

Label 1150.4.a.s.1.4
Level $1150$
Weight $4$
Character 1150.1
Self dual yes
Analytic conductor $67.852$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1150,4,Mod(1,1150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1150.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1150.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [5,-10,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(67.8521965066\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 38x^{3} + 38x^{2} + 202x + 101 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.50693\) of defining polynomial
Character \(\chi\) \(=\) 1150.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +5.31348 q^{3} +4.00000 q^{4} -10.6270 q^{6} -34.1697 q^{7} -8.00000 q^{8} +1.23302 q^{9} -58.9953 q^{11} +21.2539 q^{12} -57.0300 q^{13} +68.3394 q^{14} +16.0000 q^{16} +116.881 q^{17} -2.46604 q^{18} -35.0292 q^{19} -181.560 q^{21} +117.991 q^{22} -23.0000 q^{23} -42.5078 q^{24} +114.060 q^{26} -136.912 q^{27} -136.679 q^{28} -171.371 q^{29} +131.300 q^{31} -32.0000 q^{32} -313.470 q^{33} -233.761 q^{34} +4.93208 q^{36} +325.843 q^{37} +70.0584 q^{38} -303.028 q^{39} -72.3772 q^{41} +363.120 q^{42} +59.4075 q^{43} -235.981 q^{44} +46.0000 q^{46} +479.286 q^{47} +85.0156 q^{48} +824.568 q^{49} +621.043 q^{51} -228.120 q^{52} -230.887 q^{53} +273.824 q^{54} +273.358 q^{56} -186.127 q^{57} +342.743 q^{58} +495.740 q^{59} +267.995 q^{61} -262.601 q^{62} -42.1319 q^{63} +64.0000 q^{64} +626.940 q^{66} +11.1110 q^{67} +467.523 q^{68} -122.210 q^{69} -353.044 q^{71} -9.86416 q^{72} +466.427 q^{73} -651.686 q^{74} -140.117 q^{76} +2015.85 q^{77} +606.056 q^{78} -773.967 q^{79} -760.771 q^{81} +144.754 q^{82} +22.4688 q^{83} -726.239 q^{84} -118.815 q^{86} -910.578 q^{87} +471.962 q^{88} +1172.86 q^{89} +1948.70 q^{91} -92.0000 q^{92} +697.661 q^{93} -958.572 q^{94} -170.031 q^{96} +1318.71 q^{97} -1649.14 q^{98} -72.7424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} + 12 q^{3} + 20 q^{4} - 24 q^{6} - 24 q^{7} - 40 q^{8} + 11 q^{9} - 54 q^{11} + 48 q^{12} + 36 q^{13} + 48 q^{14} + 80 q^{16} + 132 q^{17} - 22 q^{18} - 50 q^{19} - 158 q^{21} + 108 q^{22}+ \cdots - 1740 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 5.31348 1.02258 0.511289 0.859409i \(-0.329168\pi\)
0.511289 + 0.859409i \(0.329168\pi\)
\(4\) 4.00000 0.500000
\(5\) 0 0
\(6\) −10.6270 −0.723072
\(7\) −34.1697 −1.84499 −0.922495 0.386009i \(-0.873853\pi\)
−0.922495 + 0.386009i \(0.873853\pi\)
\(8\) −8.00000 −0.353553
\(9\) 1.23302 0.0456674
\(10\) 0 0
\(11\) −58.9953 −1.61707 −0.808534 0.588449i \(-0.799739\pi\)
−0.808534 + 0.588449i \(0.799739\pi\)
\(12\) 21.2539 0.511289
\(13\) −57.0300 −1.21671 −0.608357 0.793663i \(-0.708171\pi\)
−0.608357 + 0.793663i \(0.708171\pi\)
\(14\) 68.3394 1.30460
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 116.881 1.66751 0.833757 0.552132i \(-0.186186\pi\)
0.833757 + 0.552132i \(0.186186\pi\)
\(18\) −2.46604 −0.0322917
\(19\) −35.0292 −0.422960 −0.211480 0.977382i \(-0.567828\pi\)
−0.211480 + 0.977382i \(0.567828\pi\)
\(20\) 0 0
\(21\) −181.560 −1.88665
\(22\) 117.991 1.14344
\(23\) −23.0000 −0.208514
\(24\) −42.5078 −0.361536
\(25\) 0 0
\(26\) 114.060 0.860347
\(27\) −136.912 −0.975880
\(28\) −136.679 −0.922495
\(29\) −171.371 −1.09734 −0.548670 0.836039i \(-0.684866\pi\)
−0.548670 + 0.836039i \(0.684866\pi\)
\(30\) 0 0
\(31\) 131.300 0.760717 0.380359 0.924839i \(-0.375801\pi\)
0.380359 + 0.924839i \(0.375801\pi\)
\(32\) −32.0000 −0.176777
\(33\) −313.470 −1.65358
\(34\) −233.761 −1.17911
\(35\) 0 0
\(36\) 4.93208 0.0228337
\(37\) 325.843 1.44779 0.723896 0.689910i \(-0.242350\pi\)
0.723896 + 0.689910i \(0.242350\pi\)
\(38\) 70.0584 0.299078
\(39\) −303.028 −1.24419
\(40\) 0 0
\(41\) −72.3772 −0.275693 −0.137847 0.990454i \(-0.544018\pi\)
−0.137847 + 0.990454i \(0.544018\pi\)
\(42\) 363.120 1.33406
\(43\) 59.4075 0.210688 0.105344 0.994436i \(-0.466406\pi\)
0.105344 + 0.994436i \(0.466406\pi\)
\(44\) −235.981 −0.808534
\(45\) 0 0
\(46\) 46.0000 0.147442
\(47\) 479.286 1.48747 0.743735 0.668475i \(-0.233053\pi\)
0.743735 + 0.668475i \(0.233053\pi\)
\(48\) 85.0156 0.255645
\(49\) 824.568 2.40399
\(50\) 0 0
\(51\) 621.043 1.70516
\(52\) −228.120 −0.608357
\(53\) −230.887 −0.598392 −0.299196 0.954192i \(-0.596718\pi\)
−0.299196 + 0.954192i \(0.596718\pi\)
\(54\) 273.824 0.690052
\(55\) 0 0
\(56\) 273.358 0.652302
\(57\) −186.127 −0.432510
\(58\) 342.743 0.775937
\(59\) 495.740 1.09390 0.546948 0.837166i \(-0.315789\pi\)
0.546948 + 0.837166i \(0.315789\pi\)
\(60\) 0 0
\(61\) 267.995 0.562512 0.281256 0.959633i \(-0.409249\pi\)
0.281256 + 0.959633i \(0.409249\pi\)
\(62\) −262.601 −0.537908
\(63\) −42.1319 −0.0842559
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) 626.940 1.16926
\(67\) 11.1110 0.0202601 0.0101301 0.999949i \(-0.496775\pi\)
0.0101301 + 0.999949i \(0.496775\pi\)
\(68\) 467.523 0.833757
\(69\) −122.210 −0.213222
\(70\) 0 0
\(71\) −353.044 −0.590121 −0.295060 0.955479i \(-0.595340\pi\)
−0.295060 + 0.955479i \(0.595340\pi\)
\(72\) −9.86416 −0.0161459
\(73\) 466.427 0.747824 0.373912 0.927464i \(-0.378016\pi\)
0.373912 + 0.927464i \(0.378016\pi\)
\(74\) −651.686 −1.02374
\(75\) 0 0
\(76\) −140.117 −0.211480
\(77\) 2015.85 2.98348
\(78\) 606.056 0.879773
\(79\) −773.967 −1.10225 −0.551127 0.834421i \(-0.685802\pi\)
−0.551127 + 0.834421i \(0.685802\pi\)
\(80\) 0 0
\(81\) −760.771 −1.04358
\(82\) 144.754 0.194945
\(83\) 22.4688 0.0297141 0.0148571 0.999890i \(-0.495271\pi\)
0.0148571 + 0.999890i \(0.495271\pi\)
\(84\) −726.239 −0.943324
\(85\) 0 0
\(86\) −118.815 −0.148979
\(87\) −910.578 −1.12212
\(88\) 471.962 0.571720
\(89\) 1172.86 1.39688 0.698441 0.715667i \(-0.253877\pi\)
0.698441 + 0.715667i \(0.253877\pi\)
\(90\) 0 0
\(91\) 1948.70 2.24483
\(92\) −92.0000 −0.104257
\(93\) 697.661 0.777893
\(94\) −958.572 −1.05180
\(95\) 0 0
\(96\) −170.031 −0.180768
\(97\) 1318.71 1.38035 0.690177 0.723641i \(-0.257533\pi\)
0.690177 + 0.723641i \(0.257533\pi\)
\(98\) −1649.14 −1.69988
\(99\) −72.7424 −0.0738473
\(100\) 0 0
\(101\) −1452.56 −1.43104 −0.715522 0.698590i \(-0.753811\pi\)
−0.715522 + 0.698590i \(0.753811\pi\)
\(102\) −1242.09 −1.20573
\(103\) −481.080 −0.460216 −0.230108 0.973165i \(-0.573908\pi\)
−0.230108 + 0.973165i \(0.573908\pi\)
\(104\) 456.240 0.430174
\(105\) 0 0
\(106\) 461.774 0.423127
\(107\) 176.518 0.159483 0.0797415 0.996816i \(-0.474591\pi\)
0.0797415 + 0.996816i \(0.474591\pi\)
\(108\) −547.649 −0.487940
\(109\) −336.029 −0.295282 −0.147641 0.989041i \(-0.547168\pi\)
−0.147641 + 0.989041i \(0.547168\pi\)
\(110\) 0 0
\(111\) 1731.36 1.48048
\(112\) −546.715 −0.461247
\(113\) 1140.89 0.949790 0.474895 0.880043i \(-0.342486\pi\)
0.474895 + 0.880043i \(0.342486\pi\)
\(114\) 372.253 0.305831
\(115\) 0 0
\(116\) −685.486 −0.548670
\(117\) −70.3192 −0.0555642
\(118\) −991.481 −0.773502
\(119\) −3993.78 −3.07654
\(120\) 0 0
\(121\) 2149.45 1.61491
\(122\) −535.990 −0.397756
\(123\) −384.575 −0.281918
\(124\) 525.201 0.380359
\(125\) 0 0
\(126\) 84.2638 0.0595779
\(127\) 1919.42 1.34111 0.670556 0.741859i \(-0.266056\pi\)
0.670556 + 0.741859i \(0.266056\pi\)
\(128\) −128.000 −0.0883883
\(129\) 315.660 0.215445
\(130\) 0 0
\(131\) −2728.18 −1.81956 −0.909778 0.415094i \(-0.863749\pi\)
−0.909778 + 0.415094i \(0.863749\pi\)
\(132\) −1253.88 −0.826790
\(133\) 1196.94 0.780358
\(134\) −22.2221 −0.0143261
\(135\) 0 0
\(136\) −935.045 −0.589555
\(137\) −1498.15 −0.934271 −0.467136 0.884186i \(-0.654714\pi\)
−0.467136 + 0.884186i \(0.654714\pi\)
\(138\) 244.420 0.150771
\(139\) −3070.10 −1.87340 −0.936700 0.350132i \(-0.886137\pi\)
−0.936700 + 0.350132i \(0.886137\pi\)
\(140\) 0 0
\(141\) 2546.68 1.52105
\(142\) 706.087 0.417278
\(143\) 3364.51 1.96751
\(144\) 19.7283 0.0114169
\(145\) 0 0
\(146\) −932.854 −0.528791
\(147\) 4381.32 2.45827
\(148\) 1303.37 0.723896
\(149\) −2446.56 −1.34517 −0.672585 0.740020i \(-0.734816\pi\)
−0.672585 + 0.740020i \(0.734816\pi\)
\(150\) 0 0
\(151\) 1398.67 0.753789 0.376895 0.926256i \(-0.376992\pi\)
0.376895 + 0.926256i \(0.376992\pi\)
\(152\) 280.234 0.149539
\(153\) 144.116 0.0761510
\(154\) −4031.70 −2.10964
\(155\) 0 0
\(156\) −1212.11 −0.622093
\(157\) −1629.82 −0.828495 −0.414248 0.910164i \(-0.635955\pi\)
−0.414248 + 0.910164i \(0.635955\pi\)
\(158\) 1547.93 0.779412
\(159\) −1226.81 −0.611903
\(160\) 0 0
\(161\) 785.903 0.384707
\(162\) 1521.54 0.737924
\(163\) −209.019 −0.100439 −0.0502197 0.998738i \(-0.515992\pi\)
−0.0502197 + 0.998738i \(0.515992\pi\)
\(164\) −289.509 −0.137847
\(165\) 0 0
\(166\) −44.9376 −0.0210111
\(167\) 891.381 0.413037 0.206518 0.978443i \(-0.433787\pi\)
0.206518 + 0.978443i \(0.433787\pi\)
\(168\) 1452.48 0.667031
\(169\) 1055.43 0.480394
\(170\) 0 0
\(171\) −43.1917 −0.0193155
\(172\) 237.630 0.105344
\(173\) 1198.99 0.526922 0.263461 0.964670i \(-0.415136\pi\)
0.263461 + 0.964670i \(0.415136\pi\)
\(174\) 1821.16 0.793457
\(175\) 0 0
\(176\) −943.925 −0.404267
\(177\) 2634.10 1.11860
\(178\) −2345.71 −0.987745
\(179\) −1993.46 −0.832392 −0.416196 0.909275i \(-0.636637\pi\)
−0.416196 + 0.909275i \(0.636637\pi\)
\(180\) 0 0
\(181\) −1964.42 −0.806707 −0.403354 0.915044i \(-0.632156\pi\)
−0.403354 + 0.915044i \(0.632156\pi\)
\(182\) −3897.40 −1.58733
\(183\) 1423.98 0.575213
\(184\) 184.000 0.0737210
\(185\) 0 0
\(186\) −1395.32 −0.550054
\(187\) −6895.41 −2.69648
\(188\) 1917.14 0.743735
\(189\) 4678.25 1.80049
\(190\) 0 0
\(191\) −1282.64 −0.485910 −0.242955 0.970038i \(-0.578117\pi\)
−0.242955 + 0.970038i \(0.578117\pi\)
\(192\) 340.062 0.127822
\(193\) 561.448 0.209399 0.104699 0.994504i \(-0.466612\pi\)
0.104699 + 0.994504i \(0.466612\pi\)
\(194\) −2637.41 −0.976058
\(195\) 0 0
\(196\) 3298.27 1.20199
\(197\) 4599.35 1.66340 0.831701 0.555224i \(-0.187367\pi\)
0.831701 + 0.555224i \(0.187367\pi\)
\(198\) 145.485 0.0522180
\(199\) 331.109 0.117948 0.0589740 0.998260i \(-0.481217\pi\)
0.0589740 + 0.998260i \(0.481217\pi\)
\(200\) 0 0
\(201\) 59.0382 0.0207176
\(202\) 2905.13 1.01190
\(203\) 5855.71 2.02458
\(204\) 2484.17 0.852582
\(205\) 0 0
\(206\) 962.160 0.325422
\(207\) −28.3595 −0.00952231
\(208\) −912.481 −0.304179
\(209\) 2066.56 0.683956
\(210\) 0 0
\(211\) −3949.25 −1.28852 −0.644260 0.764807i \(-0.722834\pi\)
−0.644260 + 0.764807i \(0.722834\pi\)
\(212\) −923.549 −0.299196
\(213\) −1875.89 −0.603445
\(214\) −353.037 −0.112772
\(215\) 0 0
\(216\) 1095.30 0.345026
\(217\) −4486.49 −1.40352
\(218\) 672.059 0.208796
\(219\) 2478.35 0.764709
\(220\) 0 0
\(221\) −6665.71 −2.02889
\(222\) −3462.72 −1.04686
\(223\) −3592.14 −1.07869 −0.539344 0.842085i \(-0.681328\pi\)
−0.539344 + 0.842085i \(0.681328\pi\)
\(224\) 1093.43 0.326151
\(225\) 0 0
\(226\) −2281.79 −0.671603
\(227\) −3349.51 −0.979359 −0.489680 0.871902i \(-0.662886\pi\)
−0.489680 + 0.871902i \(0.662886\pi\)
\(228\) −744.507 −0.216255
\(229\) 2763.74 0.797525 0.398763 0.917054i \(-0.369440\pi\)
0.398763 + 0.917054i \(0.369440\pi\)
\(230\) 0 0
\(231\) 10711.2 3.05084
\(232\) 1370.97 0.387968
\(233\) 2085.17 0.586285 0.293142 0.956069i \(-0.405299\pi\)
0.293142 + 0.956069i \(0.405299\pi\)
\(234\) 140.638 0.0392898
\(235\) 0 0
\(236\) 1982.96 0.546948
\(237\) −4112.45 −1.12714
\(238\) 7987.55 2.17545
\(239\) 4763.85 1.28932 0.644660 0.764469i \(-0.276999\pi\)
0.644660 + 0.764469i \(0.276999\pi\)
\(240\) 0 0
\(241\) 6928.92 1.85200 0.925998 0.377528i \(-0.123226\pi\)
0.925998 + 0.377528i \(0.123226\pi\)
\(242\) −4298.89 −1.14191
\(243\) −345.709 −0.0912645
\(244\) 1071.98 0.281256
\(245\) 0 0
\(246\) 769.149 0.199346
\(247\) 1997.72 0.514622
\(248\) −1050.40 −0.268954
\(249\) 119.387 0.0303850
\(250\) 0 0
\(251\) 4718.91 1.18667 0.593336 0.804955i \(-0.297810\pi\)
0.593336 + 0.804955i \(0.297810\pi\)
\(252\) −168.528 −0.0421280
\(253\) 1356.89 0.337182
\(254\) −3838.84 −0.948309
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 7890.24 1.91510 0.957548 0.288275i \(-0.0930817\pi\)
0.957548 + 0.288275i \(0.0930817\pi\)
\(258\) −631.321 −0.152342
\(259\) −11134.0 −2.67116
\(260\) 0 0
\(261\) −211.304 −0.0501127
\(262\) 5456.35 1.28662
\(263\) 129.509 0.0303645 0.0151822 0.999885i \(-0.495167\pi\)
0.0151822 + 0.999885i \(0.495167\pi\)
\(264\) 2507.76 0.584629
\(265\) 0 0
\(266\) −2393.87 −0.551796
\(267\) 6231.95 1.42842
\(268\) 44.4441 0.0101301
\(269\) 5625.75 1.27512 0.637561 0.770400i \(-0.279943\pi\)
0.637561 + 0.770400i \(0.279943\pi\)
\(270\) 0 0
\(271\) 5008.19 1.12260 0.561302 0.827611i \(-0.310301\pi\)
0.561302 + 0.827611i \(0.310301\pi\)
\(272\) 1870.09 0.416878
\(273\) 10354.4 2.29551
\(274\) 2996.29 0.660630
\(275\) 0 0
\(276\) −488.840 −0.106611
\(277\) −6191.44 −1.34299 −0.671494 0.741010i \(-0.734347\pi\)
−0.671494 + 0.741010i \(0.734347\pi\)
\(278\) 6140.21 1.32469
\(279\) 161.896 0.0347400
\(280\) 0 0
\(281\) 7739.13 1.64298 0.821491 0.570221i \(-0.193142\pi\)
0.821491 + 0.570221i \(0.193142\pi\)
\(282\) −5093.35 −1.07555
\(283\) 4201.98 0.882621 0.441310 0.897354i \(-0.354514\pi\)
0.441310 + 0.897354i \(0.354514\pi\)
\(284\) −1412.17 −0.295060
\(285\) 0 0
\(286\) −6729.01 −1.39124
\(287\) 2473.11 0.508651
\(288\) −39.4566 −0.00807293
\(289\) 8748.09 1.78060
\(290\) 0 0
\(291\) 7006.91 1.41152
\(292\) 1865.71 0.373912
\(293\) −3293.70 −0.656724 −0.328362 0.944552i \(-0.606497\pi\)
−0.328362 + 0.944552i \(0.606497\pi\)
\(294\) −8762.64 −1.73826
\(295\) 0 0
\(296\) −2606.74 −0.511871
\(297\) 8077.18 1.57807
\(298\) 4893.12 0.951178
\(299\) 1311.69 0.253703
\(300\) 0 0
\(301\) −2029.94 −0.388716
\(302\) −2797.34 −0.533009
\(303\) −7718.16 −1.46336
\(304\) −560.467 −0.105740
\(305\) 0 0
\(306\) −288.232 −0.0538469
\(307\) 1088.67 0.202390 0.101195 0.994867i \(-0.467733\pi\)
0.101195 + 0.994867i \(0.467733\pi\)
\(308\) 8063.41 1.49174
\(309\) −2556.21 −0.470607
\(310\) 0 0
\(311\) 3853.58 0.702625 0.351313 0.936258i \(-0.385735\pi\)
0.351313 + 0.936258i \(0.385735\pi\)
\(312\) 2424.22 0.439886
\(313\) −8534.78 −1.54126 −0.770630 0.637282i \(-0.780058\pi\)
−0.770630 + 0.637282i \(0.780058\pi\)
\(314\) 3259.64 0.585835
\(315\) 0 0
\(316\) −3095.87 −0.551127
\(317\) 4063.86 0.720029 0.360015 0.932947i \(-0.382772\pi\)
0.360015 + 0.932947i \(0.382772\pi\)
\(318\) 2453.63 0.432681
\(319\) 10110.1 1.77447
\(320\) 0 0
\(321\) 937.926 0.163084
\(322\) −1571.81 −0.272029
\(323\) −4094.23 −0.705292
\(324\) −3043.08 −0.521791
\(325\) 0 0
\(326\) 418.038 0.0710214
\(327\) −1785.48 −0.301949
\(328\) 579.018 0.0974723
\(329\) −16377.1 −2.74437
\(330\) 0 0
\(331\) −7528.47 −1.25016 −0.625079 0.780562i \(-0.714933\pi\)
−0.625079 + 0.780562i \(0.714933\pi\)
\(332\) 89.8753 0.0148571
\(333\) 401.771 0.0661169
\(334\) −1782.76 −0.292061
\(335\) 0 0
\(336\) −2904.96 −0.471662
\(337\) 5076.22 0.820533 0.410266 0.911966i \(-0.365436\pi\)
0.410266 + 0.911966i \(0.365436\pi\)
\(338\) −2110.85 −0.339690
\(339\) 6062.11 0.971235
\(340\) 0 0
\(341\) −7746.10 −1.23013
\(342\) 86.3834 0.0136581
\(343\) −16455.0 −2.59034
\(344\) −475.260 −0.0744893
\(345\) 0 0
\(346\) −2397.98 −0.372590
\(347\) 1637.97 0.253404 0.126702 0.991941i \(-0.459561\pi\)
0.126702 + 0.991941i \(0.459561\pi\)
\(348\) −3642.31 −0.561059
\(349\) −9786.85 −1.50108 −0.750542 0.660823i \(-0.770208\pi\)
−0.750542 + 0.660823i \(0.770208\pi\)
\(350\) 0 0
\(351\) 7808.11 1.18737
\(352\) 1887.85 0.285860
\(353\) −11697.5 −1.76372 −0.881860 0.471512i \(-0.843708\pi\)
−0.881860 + 0.471512i \(0.843708\pi\)
\(354\) −5268.21 −0.790967
\(355\) 0 0
\(356\) 4691.43 0.698441
\(357\) −21220.8 −3.14601
\(358\) 3986.92 0.588590
\(359\) 1498.68 0.220327 0.110164 0.993913i \(-0.464863\pi\)
0.110164 + 0.993913i \(0.464863\pi\)
\(360\) 0 0
\(361\) −5631.96 −0.821105
\(362\) 3928.84 0.570428
\(363\) 11421.0 1.65137
\(364\) 7794.80 1.12241
\(365\) 0 0
\(366\) −2847.97 −0.406737
\(367\) 750.417 0.106734 0.0533671 0.998575i \(-0.483005\pi\)
0.0533671 + 0.998575i \(0.483005\pi\)
\(368\) −368.000 −0.0521286
\(369\) −89.2426 −0.0125902
\(370\) 0 0
\(371\) 7889.34 1.10403
\(372\) 2790.64 0.388947
\(373\) −12191.6 −1.69238 −0.846190 0.532882i \(-0.821109\pi\)
−0.846190 + 0.532882i \(0.821109\pi\)
\(374\) 13790.8 1.90670
\(375\) 0 0
\(376\) −3834.29 −0.525900
\(377\) 9773.32 1.33515
\(378\) −9356.50 −1.27314
\(379\) 2267.64 0.307337 0.153668 0.988122i \(-0.450891\pi\)
0.153668 + 0.988122i \(0.450891\pi\)
\(380\) 0 0
\(381\) 10198.8 1.37139
\(382\) 2565.29 0.343590
\(383\) 7320.76 0.976693 0.488346 0.872650i \(-0.337600\pi\)
0.488346 + 0.872650i \(0.337600\pi\)
\(384\) −680.125 −0.0903841
\(385\) 0 0
\(386\) −1122.90 −0.148067
\(387\) 73.2507 0.00962155
\(388\) 5274.82 0.690177
\(389\) −3099.78 −0.404024 −0.202012 0.979383i \(-0.564748\pi\)
−0.202012 + 0.979383i \(0.564748\pi\)
\(390\) 0 0
\(391\) −2688.26 −0.347701
\(392\) −6596.54 −0.849938
\(393\) −14496.1 −1.86064
\(394\) −9198.70 −1.17620
\(395\) 0 0
\(396\) −290.970 −0.0369237
\(397\) 6476.52 0.818759 0.409380 0.912364i \(-0.365745\pi\)
0.409380 + 0.912364i \(0.365745\pi\)
\(398\) −662.217 −0.0834019
\(399\) 6359.89 0.797977
\(400\) 0 0
\(401\) 9038.72 1.12562 0.562808 0.826588i \(-0.309721\pi\)
0.562808 + 0.826588i \(0.309721\pi\)
\(402\) −118.076 −0.0146495
\(403\) −7488.06 −0.925576
\(404\) −5810.25 −0.715522
\(405\) 0 0
\(406\) −11711.4 −1.43160
\(407\) −19223.2 −2.34118
\(408\) −4968.34 −0.602866
\(409\) 1463.62 0.176948 0.0884738 0.996079i \(-0.471801\pi\)
0.0884738 + 0.996079i \(0.471801\pi\)
\(410\) 0 0
\(411\) −7960.36 −0.955366
\(412\) −1924.32 −0.230108
\(413\) −16939.3 −2.01823
\(414\) 56.7189 0.00673329
\(415\) 0 0
\(416\) 1824.96 0.215087
\(417\) −16312.9 −1.91570
\(418\) −4133.12 −0.483630
\(419\) −3240.74 −0.377853 −0.188926 0.981991i \(-0.560501\pi\)
−0.188926 + 0.981991i \(0.560501\pi\)
\(420\) 0 0
\(421\) 11983.1 1.38722 0.693608 0.720352i \(-0.256020\pi\)
0.693608 + 0.720352i \(0.256020\pi\)
\(422\) 7898.50 0.911121
\(423\) 590.969 0.0679289
\(424\) 1847.10 0.211564
\(425\) 0 0
\(426\) 3751.78 0.426700
\(427\) −9157.30 −1.03783
\(428\) 706.074 0.0797415
\(429\) 17877.2 2.01194
\(430\) 0 0
\(431\) −7554.30 −0.844265 −0.422132 0.906534i \(-0.638718\pi\)
−0.422132 + 0.906534i \(0.638718\pi\)
\(432\) −2190.60 −0.243970
\(433\) 13051.5 1.44854 0.724268 0.689519i \(-0.242178\pi\)
0.724268 + 0.689519i \(0.242178\pi\)
\(434\) 8972.98 0.992435
\(435\) 0 0
\(436\) −1344.12 −0.147641
\(437\) 805.671 0.0881933
\(438\) −4956.70 −0.540731
\(439\) −6821.34 −0.741606 −0.370803 0.928712i \(-0.620917\pi\)
−0.370803 + 0.928712i \(0.620917\pi\)
\(440\) 0 0
\(441\) 1016.71 0.109784
\(442\) 13331.4 1.43464
\(443\) 10760.1 1.15402 0.577008 0.816739i \(-0.304220\pi\)
0.577008 + 0.816739i \(0.304220\pi\)
\(444\) 6925.44 0.740240
\(445\) 0 0
\(446\) 7184.28 0.762748
\(447\) −12999.7 −1.37554
\(448\) −2186.86 −0.230624
\(449\) 7503.52 0.788671 0.394335 0.918967i \(-0.370975\pi\)
0.394335 + 0.918967i \(0.370975\pi\)
\(450\) 0 0
\(451\) 4269.92 0.445815
\(452\) 4563.57 0.474895
\(453\) 7431.80 0.770809
\(454\) 6699.01 0.692512
\(455\) 0 0
\(456\) 1489.01 0.152915
\(457\) 18746.2 1.91884 0.959421 0.281977i \(-0.0909903\pi\)
0.959421 + 0.281977i \(0.0909903\pi\)
\(458\) −5527.48 −0.563935
\(459\) −16002.4 −1.62729
\(460\) 0 0
\(461\) −3461.92 −0.349756 −0.174878 0.984590i \(-0.555953\pi\)
−0.174878 + 0.984590i \(0.555953\pi\)
\(462\) −21422.4 −2.15727
\(463\) −12567.6 −1.26148 −0.630741 0.775993i \(-0.717249\pi\)
−0.630741 + 0.775993i \(0.717249\pi\)
\(464\) −2741.94 −0.274335
\(465\) 0 0
\(466\) −4170.35 −0.414566
\(467\) 15137.8 1.49999 0.749995 0.661443i \(-0.230056\pi\)
0.749995 + 0.661443i \(0.230056\pi\)
\(468\) −281.277 −0.0277821
\(469\) −379.661 −0.0373797
\(470\) 0 0
\(471\) −8660.01 −0.847202
\(472\) −3965.92 −0.386751
\(473\) −3504.77 −0.340696
\(474\) 8224.91 0.797010
\(475\) 0 0
\(476\) −15975.1 −1.53827
\(477\) −284.689 −0.0273270
\(478\) −9527.69 −0.911687
\(479\) 10179.6 0.971021 0.485511 0.874231i \(-0.338634\pi\)
0.485511 + 0.874231i \(0.338634\pi\)
\(480\) 0 0
\(481\) −18582.8 −1.76155
\(482\) −13857.8 −1.30956
\(483\) 4175.88 0.393393
\(484\) 8597.79 0.807456
\(485\) 0 0
\(486\) 691.419 0.0645337
\(487\) 10705.5 0.996123 0.498061 0.867142i \(-0.334045\pi\)
0.498061 + 0.867142i \(0.334045\pi\)
\(488\) −2143.96 −0.198878
\(489\) −1110.62 −0.102707
\(490\) 0 0
\(491\) 1389.39 0.127704 0.0638518 0.997959i \(-0.479661\pi\)
0.0638518 + 0.997959i \(0.479661\pi\)
\(492\) −1538.30 −0.140959
\(493\) −20030.0 −1.82983
\(494\) −3995.43 −0.363893
\(495\) 0 0
\(496\) 2100.80 0.190179
\(497\) 12063.4 1.08877
\(498\) −238.775 −0.0214855
\(499\) 6024.03 0.540426 0.270213 0.962801i \(-0.412906\pi\)
0.270213 + 0.962801i \(0.412906\pi\)
\(500\) 0 0
\(501\) 4736.33 0.422363
\(502\) −9437.82 −0.839104
\(503\) 897.694 0.0795749 0.0397875 0.999208i \(-0.487332\pi\)
0.0397875 + 0.999208i \(0.487332\pi\)
\(504\) 337.055 0.0297890
\(505\) 0 0
\(506\) −2713.78 −0.238424
\(507\) 5607.98 0.491241
\(508\) 7677.69 0.670556
\(509\) −2501.06 −0.217795 −0.108897 0.994053i \(-0.534732\pi\)
−0.108897 + 0.994053i \(0.534732\pi\)
\(510\) 0 0
\(511\) −15937.7 −1.37973
\(512\) −512.000 −0.0441942
\(513\) 4795.92 0.412759
\(514\) −15780.5 −1.35418
\(515\) 0 0
\(516\) 1262.64 0.107722
\(517\) −28275.6 −2.40534
\(518\) 22267.9 1.88880
\(519\) 6370.80 0.538819
\(520\) 0 0
\(521\) −2231.18 −0.187619 −0.0938097 0.995590i \(-0.529905\pi\)
−0.0938097 + 0.995590i \(0.529905\pi\)
\(522\) 422.609 0.0354350
\(523\) 19156.5 1.60163 0.800816 0.598910i \(-0.204399\pi\)
0.800816 + 0.598910i \(0.204399\pi\)
\(524\) −10912.7 −0.909778
\(525\) 0 0
\(526\) −259.018 −0.0214709
\(527\) 15346.5 1.26851
\(528\) −5015.52 −0.413395
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) 611.258 0.0499554
\(532\) 4787.75 0.390179
\(533\) 4127.68 0.335440
\(534\) −12463.9 −1.01005
\(535\) 0 0
\(536\) −88.8883 −0.00716304
\(537\) −10592.2 −0.851187
\(538\) −11251.5 −0.901648
\(539\) −48645.6 −3.88741
\(540\) 0 0
\(541\) −3507.07 −0.278708 −0.139354 0.990243i \(-0.544503\pi\)
−0.139354 + 0.990243i \(0.544503\pi\)
\(542\) −10016.4 −0.793801
\(543\) −10437.9 −0.824922
\(544\) −3740.18 −0.294777
\(545\) 0 0
\(546\) −20708.7 −1.62317
\(547\) 18849.4 1.47339 0.736694 0.676227i \(-0.236386\pi\)
0.736694 + 0.676227i \(0.236386\pi\)
\(548\) −5992.58 −0.467136
\(549\) 330.443 0.0256885
\(550\) 0 0
\(551\) 6003.00 0.464132
\(552\) 977.679 0.0753855
\(553\) 26446.2 2.03365
\(554\) 12382.9 0.949635
\(555\) 0 0
\(556\) −12280.4 −0.936700
\(557\) 532.356 0.0404966 0.0202483 0.999795i \(-0.493554\pi\)
0.0202483 + 0.999795i \(0.493554\pi\)
\(558\) −323.792 −0.0245649
\(559\) −3388.01 −0.256347
\(560\) 0 0
\(561\) −36638.6 −2.75737
\(562\) −15478.3 −1.16176
\(563\) 820.550 0.0614246 0.0307123 0.999528i \(-0.490222\pi\)
0.0307123 + 0.999528i \(0.490222\pi\)
\(564\) 10186.7 0.760527
\(565\) 0 0
\(566\) −8403.96 −0.624107
\(567\) 25995.3 1.92540
\(568\) 2824.35 0.208639
\(569\) 24200.5 1.78302 0.891508 0.453006i \(-0.149648\pi\)
0.891508 + 0.453006i \(0.149648\pi\)
\(570\) 0 0
\(571\) 18192.0 1.33329 0.666646 0.745374i \(-0.267729\pi\)
0.666646 + 0.745374i \(0.267729\pi\)
\(572\) 13458.0 0.983756
\(573\) −6815.29 −0.496881
\(574\) −4946.21 −0.359671
\(575\) 0 0
\(576\) 78.9133 0.00570843
\(577\) −21178.1 −1.52800 −0.763998 0.645218i \(-0.776766\pi\)
−0.763998 + 0.645218i \(0.776766\pi\)
\(578\) −17496.2 −1.25907
\(579\) 2983.24 0.214127
\(580\) 0 0
\(581\) −767.752 −0.0548223
\(582\) −14013.8 −0.998096
\(583\) 13621.3 0.967641
\(584\) −3731.42 −0.264396
\(585\) 0 0
\(586\) 6587.40 0.464374
\(587\) −10093.9 −0.709745 −0.354873 0.934915i \(-0.615476\pi\)
−0.354873 + 0.934915i \(0.615476\pi\)
\(588\) 17525.3 1.22913
\(589\) −4599.34 −0.321753
\(590\) 0 0
\(591\) 24438.5 1.70096
\(592\) 5213.49 0.361948
\(593\) −14438.3 −0.999851 −0.499926 0.866068i \(-0.666639\pi\)
−0.499926 + 0.866068i \(0.666639\pi\)
\(594\) −16154.4 −1.11586
\(595\) 0 0
\(596\) −9786.25 −0.672585
\(597\) 1759.34 0.120611
\(598\) −2623.38 −0.179395
\(599\) 3466.27 0.236440 0.118220 0.992987i \(-0.462281\pi\)
0.118220 + 0.992987i \(0.462281\pi\)
\(600\) 0 0
\(601\) 12108.7 0.821839 0.410919 0.911672i \(-0.365208\pi\)
0.410919 + 0.911672i \(0.365208\pi\)
\(602\) 4059.87 0.274864
\(603\) 13.7001 0.000925228 0
\(604\) 5594.68 0.376895
\(605\) 0 0
\(606\) 15436.3 1.03475
\(607\) −5997.00 −0.401006 −0.200503 0.979693i \(-0.564258\pi\)
−0.200503 + 0.979693i \(0.564258\pi\)
\(608\) 1120.93 0.0747695
\(609\) 31114.2 2.07029
\(610\) 0 0
\(611\) −27333.7 −1.80983
\(612\) 576.465 0.0380755
\(613\) −7989.11 −0.526390 −0.263195 0.964743i \(-0.584776\pi\)
−0.263195 + 0.964743i \(0.584776\pi\)
\(614\) −2177.34 −0.143111
\(615\) 0 0
\(616\) −16126.8 −1.05482
\(617\) −53.6752 −0.00350224 −0.00175112 0.999998i \(-0.500557\pi\)
−0.00175112 + 0.999998i \(0.500557\pi\)
\(618\) 5112.41 0.332769
\(619\) −40.1805 −0.00260903 −0.00130452 0.999999i \(-0.500415\pi\)
−0.00130452 + 0.999999i \(0.500415\pi\)
\(620\) 0 0
\(621\) 3148.98 0.203485
\(622\) −7707.16 −0.496831
\(623\) −40076.2 −2.57723
\(624\) −4848.44 −0.311047
\(625\) 0 0
\(626\) 17069.6 1.08984
\(627\) 10980.6 0.699399
\(628\) −6519.28 −0.414248
\(629\) 38084.8 2.41421
\(630\) 0 0
\(631\) −9418.81 −0.594227 −0.297113 0.954842i \(-0.596024\pi\)
−0.297113 + 0.954842i \(0.596024\pi\)
\(632\) 6191.74 0.389706
\(633\) −20984.2 −1.31761
\(634\) −8127.73 −0.509138
\(635\) 0 0
\(636\) −4907.25 −0.305952
\(637\) −47025.1 −2.92497
\(638\) −20220.2 −1.25474
\(639\) −435.310 −0.0269493
\(640\) 0 0
\(641\) 991.573 0.0610995 0.0305497 0.999533i \(-0.490274\pi\)
0.0305497 + 0.999533i \(0.490274\pi\)
\(642\) −1875.85 −0.115318
\(643\) 23370.9 1.43337 0.716687 0.697395i \(-0.245657\pi\)
0.716687 + 0.697395i \(0.245657\pi\)
\(644\) 3143.61 0.192353
\(645\) 0 0
\(646\) 8188.47 0.498717
\(647\) 17039.2 1.03536 0.517682 0.855573i \(-0.326795\pi\)
0.517682 + 0.855573i \(0.326795\pi\)
\(648\) 6086.17 0.368962
\(649\) −29246.4 −1.76891
\(650\) 0 0
\(651\) −23838.9 −1.43520
\(652\) −836.075 −0.0502197
\(653\) −31674.7 −1.89820 −0.949102 0.314968i \(-0.898006\pi\)
−0.949102 + 0.314968i \(0.898006\pi\)
\(654\) 3570.97 0.213510
\(655\) 0 0
\(656\) −1158.04 −0.0689233
\(657\) 575.114 0.0341512
\(658\) 32754.1 1.94056
\(659\) 25107.8 1.48416 0.742080 0.670311i \(-0.233839\pi\)
0.742080 + 0.670311i \(0.233839\pi\)
\(660\) 0 0
\(661\) −21628.9 −1.27272 −0.636358 0.771394i \(-0.719560\pi\)
−0.636358 + 0.771394i \(0.719560\pi\)
\(662\) 15056.9 0.883995
\(663\) −35418.1 −2.07470
\(664\) −179.751 −0.0105055
\(665\) 0 0
\(666\) −803.542 −0.0467517
\(667\) 3941.54 0.228811
\(668\) 3565.52 0.206518
\(669\) −19086.8 −1.10304
\(670\) 0 0
\(671\) −15810.4 −0.909621
\(672\) 5809.91 0.333515
\(673\) −21063.2 −1.20643 −0.603214 0.797579i \(-0.706114\pi\)
−0.603214 + 0.797579i \(0.706114\pi\)
\(674\) −10152.4 −0.580204
\(675\) 0 0
\(676\) 4221.71 0.240197
\(677\) −1518.27 −0.0861921 −0.0430960 0.999071i \(-0.513722\pi\)
−0.0430960 + 0.999071i \(0.513722\pi\)
\(678\) −12124.2 −0.686767
\(679\) −45059.8 −2.54674
\(680\) 0 0
\(681\) −17797.5 −1.00147
\(682\) 15492.2 0.869834
\(683\) −27013.3 −1.51337 −0.756687 0.653777i \(-0.773183\pi\)
−0.756687 + 0.653777i \(0.773183\pi\)
\(684\) −172.767 −0.00965775
\(685\) 0 0
\(686\) 32910.0 1.83165
\(687\) 14685.1 0.815532
\(688\) 950.521 0.0526719
\(689\) 13167.5 0.728073
\(690\) 0 0
\(691\) −29988.3 −1.65095 −0.825477 0.564435i \(-0.809094\pi\)
−0.825477 + 0.564435i \(0.809094\pi\)
\(692\) 4795.96 0.263461
\(693\) 2485.59 0.136248
\(694\) −3275.95 −0.179183
\(695\) 0 0
\(696\) 7284.62 0.396728
\(697\) −8459.50 −0.459722
\(698\) 19573.7 1.06143
\(699\) 11079.5 0.599522
\(700\) 0 0
\(701\) 7127.00 0.383999 0.191999 0.981395i \(-0.438503\pi\)
0.191999 + 0.981395i \(0.438503\pi\)
\(702\) −15616.2 −0.839596
\(703\) −11414.0 −0.612358
\(704\) −3775.70 −0.202134
\(705\) 0 0
\(706\) 23394.9 1.24714
\(707\) 49633.6 2.64026
\(708\) 10536.4 0.559298
\(709\) 19983.2 1.05851 0.529257 0.848462i \(-0.322471\pi\)
0.529257 + 0.848462i \(0.322471\pi\)
\(710\) 0 0
\(711\) −954.317 −0.0503371
\(712\) −9382.85 −0.493873
\(713\) −3019.91 −0.158620
\(714\) 42441.7 2.22456
\(715\) 0 0
\(716\) −7973.84 −0.416196
\(717\) 25312.6 1.31843
\(718\) −2997.36 −0.155795
\(719\) −10043.0 −0.520921 −0.260460 0.965485i \(-0.583874\pi\)
−0.260460 + 0.965485i \(0.583874\pi\)
\(720\) 0 0
\(721\) 16438.4 0.849093
\(722\) 11263.9 0.580609
\(723\) 36816.7 1.89381
\(724\) −7857.67 −0.403354
\(725\) 0 0
\(726\) −22842.1 −1.16770
\(727\) 6665.79 0.340056 0.170028 0.985439i \(-0.445614\pi\)
0.170028 + 0.985439i \(0.445614\pi\)
\(728\) −15589.6 −0.793666
\(729\) 18703.9 0.950257
\(730\) 0 0
\(731\) 6943.59 0.351324
\(732\) 5695.94 0.287606
\(733\) 18197.2 0.916955 0.458477 0.888706i \(-0.348395\pi\)
0.458477 + 0.888706i \(0.348395\pi\)
\(734\) −1500.83 −0.0754725
\(735\) 0 0
\(736\) 736.000 0.0368605
\(737\) −655.499 −0.0327620
\(738\) 178.485 0.00890261
\(739\) −1847.66 −0.0919722 −0.0459861 0.998942i \(-0.514643\pi\)
−0.0459861 + 0.998942i \(0.514643\pi\)
\(740\) 0 0
\(741\) 10614.8 0.526242
\(742\) −15778.7 −0.780665
\(743\) 25291.0 1.24877 0.624385 0.781117i \(-0.285350\pi\)
0.624385 + 0.781117i \(0.285350\pi\)
\(744\) −5581.29 −0.275027
\(745\) 0 0
\(746\) 24383.2 1.19669
\(747\) 27.7045 0.00135697
\(748\) −27581.6 −1.34824
\(749\) −6031.58 −0.294245
\(750\) 0 0
\(751\) 15059.5 0.731731 0.365865 0.930668i \(-0.380773\pi\)
0.365865 + 0.930668i \(0.380773\pi\)
\(752\) 7668.58 0.371867
\(753\) 25073.8 1.21347
\(754\) −19546.6 −0.944094
\(755\) 0 0
\(756\) 18713.0 0.900245
\(757\) −23808.2 −1.14310 −0.571548 0.820569i \(-0.693657\pi\)
−0.571548 + 0.820569i \(0.693657\pi\)
\(758\) −4535.27 −0.217320
\(759\) 7209.81 0.344795
\(760\) 0 0
\(761\) 15673.8 0.746614 0.373307 0.927708i \(-0.378224\pi\)
0.373307 + 0.927708i \(0.378224\pi\)
\(762\) −20397.6 −0.969721
\(763\) 11482.0 0.544793
\(764\) −5130.57 −0.242955
\(765\) 0 0
\(766\) −14641.5 −0.690626
\(767\) −28272.1 −1.33096
\(768\) 1360.25 0.0639112
\(769\) 24213.5 1.13545 0.567724 0.823219i \(-0.307824\pi\)
0.567724 + 0.823219i \(0.307824\pi\)
\(770\) 0 0
\(771\) 41924.6 1.95834
\(772\) 2245.79 0.104699
\(773\) 34754.7 1.61713 0.808563 0.588410i \(-0.200246\pi\)
0.808563 + 0.588410i \(0.200246\pi\)
\(774\) −146.501 −0.00680347
\(775\) 0 0
\(776\) −10549.6 −0.488029
\(777\) −59160.0 −2.73147
\(778\) 6199.56 0.285688
\(779\) 2535.32 0.116607
\(780\) 0 0
\(781\) 20827.9 0.954266
\(782\) 5376.51 0.245861
\(783\) 23462.8 1.07087
\(784\) 13193.1 0.600997
\(785\) 0 0
\(786\) 28992.2 1.31567
\(787\) −7625.98 −0.345409 −0.172704 0.984974i \(-0.555251\pi\)
−0.172704 + 0.984974i \(0.555251\pi\)
\(788\) 18397.4 0.831701
\(789\) 688.142 0.0310501
\(790\) 0 0
\(791\) −38984.0 −1.75235
\(792\) 581.939 0.0261090
\(793\) −15283.8 −0.684417
\(794\) −12953.0 −0.578950
\(795\) 0 0
\(796\) 1324.43 0.0589740
\(797\) 1536.17 0.0682733 0.0341367 0.999417i \(-0.489132\pi\)
0.0341367 + 0.999417i \(0.489132\pi\)
\(798\) −12719.8 −0.564255
\(799\) 56019.3 2.48038
\(800\) 0 0
\(801\) 1446.16 0.0637920
\(802\) −18077.4 −0.795931
\(803\) −27517.0 −1.20928
\(804\) 236.153 0.0103588
\(805\) 0 0
\(806\) 14976.1 0.654481
\(807\) 29892.3 1.30391
\(808\) 11620.5 0.505950
\(809\) −2722.59 −0.118320 −0.0591601 0.998249i \(-0.518842\pi\)
−0.0591601 + 0.998249i \(0.518842\pi\)
\(810\) 0 0
\(811\) 828.222 0.0358604 0.0179302 0.999839i \(-0.494292\pi\)
0.0179302 + 0.999839i \(0.494292\pi\)
\(812\) 23422.8 1.01229
\(813\) 26610.9 1.14795
\(814\) 38446.4 1.65546
\(815\) 0 0
\(816\) 9936.68 0.426291
\(817\) −2081.00 −0.0891125
\(818\) −2927.25 −0.125121
\(819\) 2402.79 0.102515
\(820\) 0 0
\(821\) 32894.5 1.39832 0.699162 0.714963i \(-0.253556\pi\)
0.699162 + 0.714963i \(0.253556\pi\)
\(822\) 15920.7 0.675546
\(823\) −18307.6 −0.775412 −0.387706 0.921783i \(-0.626733\pi\)
−0.387706 + 0.921783i \(0.626733\pi\)
\(824\) 3848.64 0.162711
\(825\) 0 0
\(826\) 33878.6 1.42710
\(827\) −5237.10 −0.220208 −0.110104 0.993920i \(-0.535118\pi\)
−0.110104 + 0.993920i \(0.535118\pi\)
\(828\) −113.438 −0.00476116
\(829\) −2235.56 −0.0936601 −0.0468300 0.998903i \(-0.514912\pi\)
−0.0468300 + 0.998903i \(0.514912\pi\)
\(830\) 0 0
\(831\) −32898.1 −1.37331
\(832\) −3649.92 −0.152089
\(833\) 96376.0 4.00868
\(834\) 32625.8 1.35460
\(835\) 0 0
\(836\) 8266.23 0.341978
\(837\) −17976.6 −0.742369
\(838\) 6481.47 0.267182
\(839\) −23031.3 −0.947711 −0.473856 0.880603i \(-0.657138\pi\)
−0.473856 + 0.880603i \(0.657138\pi\)
\(840\) 0 0
\(841\) 4979.16 0.204156
\(842\) −23966.1 −0.980910
\(843\) 41121.7 1.68008
\(844\) −15797.0 −0.644260
\(845\) 0 0
\(846\) −1181.94 −0.0480330
\(847\) −73445.9 −2.97949
\(848\) −3694.19 −0.149598
\(849\) 22327.1 0.902550
\(850\) 0 0
\(851\) −7494.39 −0.301885
\(852\) −7503.55 −0.301722
\(853\) −4326.89 −0.173681 −0.0868405 0.996222i \(-0.527677\pi\)
−0.0868405 + 0.996222i \(0.527677\pi\)
\(854\) 18314.6 0.733856
\(855\) 0 0
\(856\) −1412.15 −0.0563858
\(857\) −20912.6 −0.833562 −0.416781 0.909007i \(-0.636842\pi\)
−0.416781 + 0.909007i \(0.636842\pi\)
\(858\) −35754.4 −1.42265
\(859\) −18002.3 −0.715054 −0.357527 0.933903i \(-0.616380\pi\)
−0.357527 + 0.933903i \(0.616380\pi\)
\(860\) 0 0
\(861\) 13140.8 0.520136
\(862\) 15108.6 0.596985
\(863\) −37389.4 −1.47480 −0.737399 0.675457i \(-0.763946\pi\)
−0.737399 + 0.675457i \(0.763946\pi\)
\(864\) 4381.19 0.172513
\(865\) 0 0
\(866\) −26103.0 −1.02427
\(867\) 46482.8 1.82080
\(868\) −17946.0 −0.701758
\(869\) 45660.4 1.78242
\(870\) 0 0
\(871\) −633.663 −0.0246508
\(872\) 2688.23 0.104398
\(873\) 1625.99 0.0630372
\(874\) −1611.34 −0.0623621
\(875\) 0 0
\(876\) 9913.39 0.382355
\(877\) −3952.88 −0.152200 −0.0760999 0.997100i \(-0.524247\pi\)
−0.0760999 + 0.997100i \(0.524247\pi\)
\(878\) 13642.7 0.524395
\(879\) −17501.0 −0.671552
\(880\) 0 0
\(881\) 51900.7 1.98477 0.992383 0.123188i \(-0.0393119\pi\)
0.992383 + 0.123188i \(0.0393119\pi\)
\(882\) −2033.42 −0.0776289
\(883\) 8033.47 0.306170 0.153085 0.988213i \(-0.451079\pi\)
0.153085 + 0.988213i \(0.451079\pi\)
\(884\) −26662.8 −1.01444
\(885\) 0 0
\(886\) −21520.2 −0.816012
\(887\) 16089.7 0.609062 0.304531 0.952502i \(-0.401500\pi\)
0.304531 + 0.952502i \(0.401500\pi\)
\(888\) −13850.9 −0.523429
\(889\) −65586.0 −2.47434
\(890\) 0 0
\(891\) 44881.9 1.68754
\(892\) −14368.6 −0.539344
\(893\) −16789.0 −0.629141
\(894\) 25999.5 0.972655
\(895\) 0 0
\(896\) 4373.72 0.163076
\(897\) 6969.64 0.259431
\(898\) −15007.0 −0.557675
\(899\) −22501.1 −0.834766
\(900\) 0 0
\(901\) −26986.2 −0.997827
\(902\) −8539.83 −0.315239
\(903\) −10786.0 −0.397493
\(904\) −9127.15 −0.335801
\(905\) 0 0
\(906\) −14863.6 −0.545044
\(907\) 10734.2 0.392969 0.196485 0.980507i \(-0.437047\pi\)
0.196485 + 0.980507i \(0.437047\pi\)
\(908\) −13398.0 −0.489680
\(909\) −1791.04 −0.0653521
\(910\) 0 0
\(911\) 7368.29 0.267972 0.133986 0.990983i \(-0.457222\pi\)
0.133986 + 0.990983i \(0.457222\pi\)
\(912\) −2978.03 −0.108128
\(913\) −1325.55 −0.0480498
\(914\) −37492.4 −1.35683
\(915\) 0 0
\(916\) 11055.0 0.398763
\(917\) 93221.0 3.35706
\(918\) 32004.8 1.15067
\(919\) −12106.3 −0.434549 −0.217275 0.976111i \(-0.569717\pi\)
−0.217275 + 0.976111i \(0.569717\pi\)
\(920\) 0 0
\(921\) 5784.62 0.206960
\(922\) 6923.83 0.247315
\(923\) 20134.1 0.718008
\(924\) 42844.7 1.52542
\(925\) 0 0
\(926\) 25135.2 0.892003
\(927\) −593.181 −0.0210169
\(928\) 5483.89 0.193984
\(929\) 14622.7 0.516421 0.258210 0.966089i \(-0.416867\pi\)
0.258210 + 0.966089i \(0.416867\pi\)
\(930\) 0 0
\(931\) −28883.9 −1.01679
\(932\) 8340.70 0.293142
\(933\) 20475.9 0.718490
\(934\) −30275.7 −1.06065
\(935\) 0 0
\(936\) 562.554 0.0196449
\(937\) −54950.3 −1.91585 −0.957924 0.287023i \(-0.907334\pi\)
−0.957924 + 0.287023i \(0.907334\pi\)
\(938\) 759.321 0.0264315
\(939\) −45349.4 −1.57606
\(940\) 0 0
\(941\) 36477.3 1.26368 0.631841 0.775098i \(-0.282299\pi\)
0.631841 + 0.775098i \(0.282299\pi\)
\(942\) 17320.0 0.599062
\(943\) 1664.68 0.0574860
\(944\) 7931.85 0.273474
\(945\) 0 0
\(946\) 7009.53 0.240909
\(947\) 20311.8 0.696985 0.348492 0.937312i \(-0.386694\pi\)
0.348492 + 0.937312i \(0.386694\pi\)
\(948\) −16449.8 −0.563571
\(949\) −26600.4 −0.909888
\(950\) 0 0
\(951\) 21593.2 0.736287
\(952\) 31950.2 1.08772
\(953\) −4320.54 −0.146858 −0.0734292 0.997300i \(-0.523394\pi\)
−0.0734292 + 0.997300i \(0.523394\pi\)
\(954\) 569.377 0.0193231
\(955\) 0 0
\(956\) 19055.4 0.644660
\(957\) 53719.8 1.81454
\(958\) −20359.3 −0.686616
\(959\) 51191.2 1.72372
\(960\) 0 0
\(961\) −12551.2 −0.421310
\(962\) 37165.7 1.24560
\(963\) 217.651 0.00728318
\(964\) 27715.7 0.925998
\(965\) 0 0
\(966\) −8351.75 −0.278171
\(967\) −19455.1 −0.646986 −0.323493 0.946231i \(-0.604857\pi\)
−0.323493 + 0.946231i \(0.604857\pi\)
\(968\) −17195.6 −0.570957
\(969\) −21754.6 −0.721217
\(970\) 0 0
\(971\) −19512.5 −0.644888 −0.322444 0.946588i \(-0.604504\pi\)
−0.322444 + 0.946588i \(0.604504\pi\)
\(972\) −1382.84 −0.0456322
\(973\) 104904. 3.45641
\(974\) −21411.0 −0.704365
\(975\) 0 0
\(976\) 4287.92 0.140628
\(977\) 23683.1 0.775526 0.387763 0.921759i \(-0.373248\pi\)
0.387763 + 0.921759i \(0.373248\pi\)
\(978\) 2221.23 0.0726249
\(979\) −69193.1 −2.25886
\(980\) 0 0
\(981\) −414.331 −0.0134848
\(982\) −2778.79 −0.0903001
\(983\) −19378.5 −0.628767 −0.314384 0.949296i \(-0.601798\pi\)
−0.314384 + 0.949296i \(0.601798\pi\)
\(984\) 3076.60 0.0996731
\(985\) 0 0
\(986\) 40060.0 1.29388
\(987\) −87019.1 −2.80633
\(988\) 7990.87 0.257311
\(989\) −1366.37 −0.0439314
\(990\) 0 0
\(991\) 2734.03 0.0876380 0.0438190 0.999039i \(-0.486048\pi\)
0.0438190 + 0.999039i \(0.486048\pi\)
\(992\) −4201.61 −0.134477
\(993\) −40002.3 −1.27838
\(994\) −24126.8 −0.769874
\(995\) 0 0
\(996\) 477.550 0.0151925
\(997\) 35626.3 1.13169 0.565846 0.824511i \(-0.308550\pi\)
0.565846 + 0.824511i \(0.308550\pi\)
\(998\) −12048.1 −0.382139
\(999\) −44611.9 −1.41287
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 1150.4.a.s.1.4 5
5.2 odd 4 1150.4.b.p.599.2 10
5.3 odd 4 1150.4.b.p.599.9 10
5.4 even 2 1150.4.a.t.1.2 yes 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1150.4.a.s.1.4 5 1.1 even 1 trivial
1150.4.a.t.1.2 yes 5 5.4 even 2
1150.4.b.p.599.2 10 5.2 odd 4
1150.4.b.p.599.9 10 5.3 odd 4