Properties

Label 966.4.a.m.1.5
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.9958450655\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \( x^{5} - x^{4} - 351x^{3} - 663x^{2} + 18451x - 19243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.11377\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.6576 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.6576 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -43.3153 q^{10} -7.67965 q^{11} -12.0000 q^{12} +63.7565 q^{13} +14.0000 q^{14} -64.9729 q^{15} +16.0000 q^{16} +9.23862 q^{17} -18.0000 q^{18} -145.686 q^{19} +86.6306 q^{20} +21.0000 q^{21} +15.3593 q^{22} -23.0000 q^{23} +24.0000 q^{24} +344.054 q^{25} -127.513 q^{26} -27.0000 q^{27} -28.0000 q^{28} +223.788 q^{29} +129.946 q^{30} +165.935 q^{31} -32.0000 q^{32} +23.0389 q^{33} -18.4772 q^{34} -151.604 q^{35} +36.0000 q^{36} +292.555 q^{37} +291.371 q^{38} -191.269 q^{39} -173.261 q^{40} -335.500 q^{41} -42.0000 q^{42} +121.574 q^{43} -30.7186 q^{44} +194.919 q^{45} +46.0000 q^{46} +140.326 q^{47} -48.0000 q^{48} +49.0000 q^{49} -688.107 q^{50} -27.7159 q^{51} +255.026 q^{52} -91.7378 q^{53} +54.0000 q^{54} -166.323 q^{55} +56.0000 q^{56} +437.057 q^{57} -447.576 q^{58} +10.3736 q^{59} -259.892 q^{60} +10.9004 q^{61} -331.869 q^{62} -63.0000 q^{63} +64.0000 q^{64} +1380.81 q^{65} -46.0779 q^{66} -444.657 q^{67} +36.9545 q^{68} +69.0000 q^{69} +303.207 q^{70} -345.504 q^{71} -72.0000 q^{72} +283.982 q^{73} -585.110 q^{74} -1032.16 q^{75} -582.743 q^{76} +53.7575 q^{77} +382.539 q^{78} -308.066 q^{79} +346.522 q^{80} +81.0000 q^{81} +671.001 q^{82} -139.248 q^{83} +84.0000 q^{84} +200.087 q^{85} -243.148 q^{86} -671.364 q^{87} +61.4372 q^{88} +888.786 q^{89} -389.838 q^{90} -446.295 q^{91} -92.0000 q^{92} -497.804 q^{93} -280.651 q^{94} -3155.21 q^{95} +96.0000 q^{96} -778.098 q^{97} -98.0000 q^{98} -69.1168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 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
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) 21.6576 1.93712 0.968559 0.248783i \(-0.0800304\pi\)
0.968559 + 0.248783i \(0.0800304\pi\)
\(6\) 6.00000 0.408248
\(7\) −7.00000 −0.377964
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) −43.3153 −1.36975
\(11\) −7.67965 −0.210500 −0.105250 0.994446i \(-0.533564\pi\)
−0.105250 + 0.994446i \(0.533564\pi\)
\(12\) −12.0000 −0.288675
\(13\) 63.7565 1.36022 0.680110 0.733110i \(-0.261932\pi\)
0.680110 + 0.733110i \(0.261932\pi\)
\(14\) 14.0000 0.267261
\(15\) −64.9729 −1.11840
\(16\) 16.0000 0.250000
\(17\) 9.23862 0.131806 0.0659028 0.997826i \(-0.479007\pi\)
0.0659028 + 0.997826i \(0.479007\pi\)
\(18\) −18.0000 −0.235702
\(19\) −145.686 −1.75908 −0.879542 0.475821i \(-0.842151\pi\)
−0.879542 + 0.475821i \(0.842151\pi\)
\(20\) 86.6306 0.968559
\(21\) 21.0000 0.218218
\(22\) 15.3593 0.148846
\(23\) −23.0000 −0.208514
\(24\) 24.0000 0.204124
\(25\) 344.054 2.75243
\(26\) −127.513 −0.961821
\(27\) −27.0000 −0.192450
\(28\) −28.0000 −0.188982
\(29\) 223.788 1.43298 0.716489 0.697598i \(-0.245748\pi\)
0.716489 + 0.697598i \(0.245748\pi\)
\(30\) 129.946 0.790825
\(31\) 165.935 0.961378 0.480689 0.876891i \(-0.340387\pi\)
0.480689 + 0.876891i \(0.340387\pi\)
\(32\) −32.0000 −0.176777
\(33\) 23.0389 0.121532
\(34\) −18.4772 −0.0932006
\(35\) −151.604 −0.732162
\(36\) 36.0000 0.166667
\(37\) 292.555 1.29988 0.649942 0.759984i \(-0.274793\pi\)
0.649942 + 0.759984i \(0.274793\pi\)
\(38\) 291.371 1.24386
\(39\) −191.269 −0.785323
\(40\) −173.261 −0.684875
\(41\) −335.500 −1.27796 −0.638980 0.769223i \(-0.720643\pi\)
−0.638980 + 0.769223i \(0.720643\pi\)
\(42\) −42.0000 −0.154303
\(43\) 121.574 0.431159 0.215580 0.976486i \(-0.430836\pi\)
0.215580 + 0.976486i \(0.430836\pi\)
\(44\) −30.7186 −0.105250
\(45\) 194.919 0.645706
\(46\) 46.0000 0.147442
\(47\) 140.326 0.435502 0.217751 0.976004i \(-0.430128\pi\)
0.217751 + 0.976004i \(0.430128\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) −688.107 −1.94626
\(51\) −27.7159 −0.0760980
\(52\) 255.026 0.680110
\(53\) −91.7378 −0.237758 −0.118879 0.992909i \(-0.537930\pi\)
−0.118879 + 0.992909i \(0.537930\pi\)
\(54\) 54.0000 0.136083
\(55\) −166.323 −0.407764
\(56\) 56.0000 0.133631
\(57\) 437.057 1.01561
\(58\) −447.576 −1.01327
\(59\) 10.3736 0.0228902 0.0114451 0.999935i \(-0.496357\pi\)
0.0114451 + 0.999935i \(0.496357\pi\)
\(60\) −259.892 −0.559198
\(61\) 10.9004 0.0228795 0.0114398 0.999935i \(-0.496359\pi\)
0.0114398 + 0.999935i \(0.496359\pi\)
\(62\) −331.869 −0.679797
\(63\) −63.0000 −0.125988
\(64\) 64.0000 0.125000
\(65\) 1380.81 2.63491
\(66\) −46.0779 −0.0859363
\(67\) −444.657 −0.810799 −0.405399 0.914140i \(-0.632868\pi\)
−0.405399 + 0.914140i \(0.632868\pi\)
\(68\) 36.9545 0.0659028
\(69\) 69.0000 0.120386
\(70\) 303.207 0.517717
\(71\) −345.504 −0.577519 −0.288759 0.957402i \(-0.593243\pi\)
−0.288759 + 0.957402i \(0.593243\pi\)
\(72\) −72.0000 −0.117851
\(73\) 283.982 0.455309 0.227655 0.973742i \(-0.426894\pi\)
0.227655 + 0.973742i \(0.426894\pi\)
\(74\) −585.110 −0.919157
\(75\) −1032.16 −1.58912
\(76\) −582.743 −0.879542
\(77\) 53.7575 0.0795616
\(78\) 382.539 0.555308
\(79\) −308.066 −0.438736 −0.219368 0.975642i \(-0.570400\pi\)
−0.219368 + 0.975642i \(0.570400\pi\)
\(80\) 346.522 0.484280
\(81\) 81.0000 0.111111
\(82\) 671.001 0.903654
\(83\) −139.248 −0.184150 −0.0920750 0.995752i \(-0.529350\pi\)
−0.0920750 + 0.995752i \(0.529350\pi\)
\(84\) 84.0000 0.109109
\(85\) 200.087 0.255323
\(86\) −243.148 −0.304876
\(87\) −671.364 −0.827331
\(88\) 61.4372 0.0744230
\(89\) 888.786 1.05855 0.529276 0.848450i \(-0.322464\pi\)
0.529276 + 0.848450i \(0.322464\pi\)
\(90\) −389.838 −0.456583
\(91\) −446.295 −0.514115
\(92\) −92.0000 −0.104257
\(93\) −497.804 −0.555052
\(94\) −280.651 −0.307947
\(95\) −3155.21 −3.40755
\(96\) 96.0000 0.102062
\(97\) −778.098 −0.814473 −0.407237 0.913323i \(-0.633508\pi\)
−0.407237 + 0.913323i \(0.633508\pi\)
\(98\) −98.0000 −0.101015
\(99\) −69.1168 −0.0701667
\(100\) 1376.21 1.37621
\(101\) 1405.96 1.38514 0.692568 0.721353i \(-0.256479\pi\)
0.692568 + 0.721353i \(0.256479\pi\)
\(102\) 55.4317 0.0538094
\(103\) 809.058 0.773969 0.386984 0.922086i \(-0.373517\pi\)
0.386984 + 0.922086i \(0.373517\pi\)
\(104\) −510.052 −0.480910
\(105\) 454.811 0.422714
\(106\) 183.476 0.168120
\(107\) 380.224 0.343529 0.171765 0.985138i \(-0.445053\pi\)
0.171765 + 0.985138i \(0.445053\pi\)
\(108\) −108.000 −0.0962250
\(109\) −1836.52 −1.61382 −0.806912 0.590671i \(-0.798863\pi\)
−0.806912 + 0.590671i \(0.798863\pi\)
\(110\) 332.646 0.288332
\(111\) −877.664 −0.750488
\(112\) −112.000 −0.0944911
\(113\) −1682.63 −1.40078 −0.700392 0.713759i \(-0.746991\pi\)
−0.700392 + 0.713759i \(0.746991\pi\)
\(114\) −874.114 −0.718143
\(115\) −498.126 −0.403917
\(116\) 895.152 0.716489
\(117\) 573.808 0.453407
\(118\) −20.7471 −0.0161858
\(119\) −64.6703 −0.0498178
\(120\) 519.784 0.395413
\(121\) −1272.02 −0.955690
\(122\) −21.8007 −0.0161783
\(123\) 1006.50 0.737831
\(124\) 663.738 0.480689
\(125\) 4744.19 3.39466
\(126\) 126.000 0.0890871
\(127\) 2608.82 1.82280 0.911400 0.411521i \(-0.135002\pi\)
0.911400 + 0.411521i \(0.135002\pi\)
\(128\) −128.000 −0.0883883
\(129\) −364.722 −0.248930
\(130\) −2761.63 −1.86316
\(131\) 2139.80 1.42714 0.713569 0.700585i \(-0.247077\pi\)
0.713569 + 0.700585i \(0.247077\pi\)
\(132\) 92.1558 0.0607661
\(133\) 1019.80 0.664871
\(134\) 889.314 0.573321
\(135\) −584.756 −0.372799
\(136\) −73.9090 −0.0466003
\(137\) −1087.17 −0.677983 −0.338991 0.940790i \(-0.610086\pi\)
−0.338991 + 0.940790i \(0.610086\pi\)
\(138\) −138.000 −0.0851257
\(139\) 1485.73 0.906603 0.453301 0.891357i \(-0.350246\pi\)
0.453301 + 0.891357i \(0.350246\pi\)
\(140\) −606.414 −0.366081
\(141\) −420.977 −0.251437
\(142\) 691.009 0.408367
\(143\) −489.627 −0.286326
\(144\) 144.000 0.0833333
\(145\) 4846.72 2.77585
\(146\) −567.964 −0.321952
\(147\) −147.000 −0.0824786
\(148\) 1170.22 0.649942
\(149\) 1551.38 0.852980 0.426490 0.904492i \(-0.359750\pi\)
0.426490 + 0.904492i \(0.359750\pi\)
\(150\) 2064.32 1.12367
\(151\) 2830.68 1.52555 0.762774 0.646665i \(-0.223837\pi\)
0.762774 + 0.646665i \(0.223837\pi\)
\(152\) 1165.49 0.621930
\(153\) 83.1476 0.0439352
\(154\) −107.515 −0.0562585
\(155\) 3593.75 1.86230
\(156\) −765.078 −0.392662
\(157\) −2463.32 −1.25219 −0.626096 0.779746i \(-0.715348\pi\)
−0.626096 + 0.779746i \(0.715348\pi\)
\(158\) 616.132 0.310233
\(159\) 275.213 0.137269
\(160\) −693.045 −0.342437
\(161\) 161.000 0.0788110
\(162\) −162.000 −0.0785674
\(163\) 1464.76 0.703858 0.351929 0.936027i \(-0.385526\pi\)
0.351929 + 0.936027i \(0.385526\pi\)
\(164\) −1342.00 −0.638980
\(165\) 498.969 0.235422
\(166\) 278.496 0.130214
\(167\) 2390.35 1.10761 0.553805 0.832646i \(-0.313175\pi\)
0.553805 + 0.832646i \(0.313175\pi\)
\(168\) −168.000 −0.0771517
\(169\) 1867.89 0.850199
\(170\) −400.173 −0.180541
\(171\) −1311.17 −0.586361
\(172\) 486.296 0.215580
\(173\) 2785.56 1.22418 0.612088 0.790790i \(-0.290330\pi\)
0.612088 + 0.790790i \(0.290330\pi\)
\(174\) 1342.73 0.585011
\(175\) −2408.38 −1.04032
\(176\) −122.874 −0.0526250
\(177\) −31.1207 −0.0132157
\(178\) −1777.57 −0.748509
\(179\) 2809.84 1.17328 0.586641 0.809847i \(-0.300450\pi\)
0.586641 + 0.809847i \(0.300450\pi\)
\(180\) 779.675 0.322853
\(181\) 125.390 0.0514925 0.0257463 0.999669i \(-0.491804\pi\)
0.0257463 + 0.999669i \(0.491804\pi\)
\(182\) 892.591 0.363534
\(183\) −32.7011 −0.0132095
\(184\) 184.000 0.0737210
\(185\) 6336.05 2.51803
\(186\) 995.607 0.392481
\(187\) −70.9493 −0.0277451
\(188\) 561.303 0.217751
\(189\) 189.000 0.0727393
\(190\) 6310.42 2.40950
\(191\) 2966.84 1.12394 0.561972 0.827157i \(-0.310043\pi\)
0.561972 + 0.827157i \(0.310043\pi\)
\(192\) −192.000 −0.0721688
\(193\) 2844.63 1.06094 0.530468 0.847705i \(-0.322016\pi\)
0.530468 + 0.847705i \(0.322016\pi\)
\(194\) 1556.20 0.575920
\(195\) −4142.44 −1.52126
\(196\) 196.000 0.0714286
\(197\) −2906.03 −1.05100 −0.525498 0.850795i \(-0.676121\pi\)
−0.525498 + 0.850795i \(0.676121\pi\)
\(198\) 138.234 0.0496153
\(199\) −3752.84 −1.33684 −0.668422 0.743783i \(-0.733030\pi\)
−0.668422 + 0.743783i \(0.733030\pi\)
\(200\) −2752.43 −0.973131
\(201\) 1333.97 0.468115
\(202\) −2811.93 −0.979439
\(203\) −1566.52 −0.541615
\(204\) −110.863 −0.0380490
\(205\) −7266.15 −2.47556
\(206\) −1618.12 −0.547279
\(207\) −207.000 −0.0695048
\(208\) 1020.10 0.340055
\(209\) 1118.81 0.370287
\(210\) −909.621 −0.298904
\(211\) −2467.89 −0.805195 −0.402598 0.915377i \(-0.631893\pi\)
−0.402598 + 0.915377i \(0.631893\pi\)
\(212\) −366.951 −0.118879
\(213\) 1036.51 0.333431
\(214\) −760.447 −0.242912
\(215\) 2633.00 0.835207
\(216\) 216.000 0.0680414
\(217\) −1161.54 −0.363367
\(218\) 3673.04 1.14115
\(219\) −851.946 −0.262873
\(220\) −665.292 −0.203882
\(221\) 589.022 0.179285
\(222\) 1755.33 0.530675
\(223\) −5855.47 −1.75835 −0.879173 0.476504i \(-0.841904\pi\)
−0.879173 + 0.476504i \(0.841904\pi\)
\(224\) 224.000 0.0668153
\(225\) 3096.48 0.917476
\(226\) 3365.26 0.990503
\(227\) 3318.38 0.970258 0.485129 0.874443i \(-0.338773\pi\)
0.485129 + 0.874443i \(0.338773\pi\)
\(228\) 1748.23 0.507804
\(229\) −4276.81 −1.23415 −0.617073 0.786906i \(-0.711682\pi\)
−0.617073 + 0.786906i \(0.711682\pi\)
\(230\) 996.252 0.285613
\(231\) −161.273 −0.0459349
\(232\) −1790.30 −0.506635
\(233\) 4982.08 1.40080 0.700401 0.713750i \(-0.253005\pi\)
0.700401 + 0.713750i \(0.253005\pi\)
\(234\) −1147.62 −0.320607
\(235\) 3039.13 0.843620
\(236\) 41.4943 0.0114451
\(237\) 924.198 0.253304
\(238\) 129.341 0.0352265
\(239\) 5664.37 1.53305 0.766523 0.642217i \(-0.221985\pi\)
0.766523 + 0.642217i \(0.221985\pi\)
\(240\) −1039.57 −0.279599
\(241\) 3584.05 0.957962 0.478981 0.877825i \(-0.341006\pi\)
0.478981 + 0.877825i \(0.341006\pi\)
\(242\) 2544.05 0.675775
\(243\) −243.000 −0.0641500
\(244\) 43.6015 0.0114398
\(245\) 1061.22 0.276731
\(246\) −2013.00 −0.521725
\(247\) −9288.41 −2.39274
\(248\) −1327.48 −0.339899
\(249\) 417.744 0.106319
\(250\) −9488.37 −2.40039
\(251\) −4147.76 −1.04305 −0.521523 0.853237i \(-0.674636\pi\)
−0.521523 + 0.853237i \(0.674636\pi\)
\(252\) −252.000 −0.0629941
\(253\) 176.632 0.0438923
\(254\) −5217.65 −1.28891
\(255\) −600.260 −0.147411
\(256\) 256.000 0.0625000
\(257\) 5416.54 1.31469 0.657343 0.753591i \(-0.271680\pi\)
0.657343 + 0.753591i \(0.271680\pi\)
\(258\) 729.443 0.176020
\(259\) −2047.88 −0.491310
\(260\) 5523.26 1.31745
\(261\) 2014.09 0.477660
\(262\) −4279.60 −1.00914
\(263\) −5233.81 −1.22711 −0.613556 0.789651i \(-0.710261\pi\)
−0.613556 + 0.789651i \(0.710261\pi\)
\(264\) −184.312 −0.0429681
\(265\) −1986.82 −0.460565
\(266\) −2039.60 −0.470135
\(267\) −2666.36 −0.611155
\(268\) −1778.63 −0.405399
\(269\) 2204.45 0.499656 0.249828 0.968290i \(-0.419626\pi\)
0.249828 + 0.968290i \(0.419626\pi\)
\(270\) 1169.51 0.263608
\(271\) 8283.32 1.85674 0.928369 0.371659i \(-0.121211\pi\)
0.928369 + 0.371659i \(0.121211\pi\)
\(272\) 147.818 0.0329514
\(273\) 1338.89 0.296824
\(274\) 2174.35 0.479406
\(275\) −2642.21 −0.579387
\(276\) 276.000 0.0601929
\(277\) 340.659 0.0738925 0.0369463 0.999317i \(-0.488237\pi\)
0.0369463 + 0.999317i \(0.488237\pi\)
\(278\) −2971.46 −0.641065
\(279\) 1493.41 0.320459
\(280\) 1212.83 0.258858
\(281\) 1603.50 0.340415 0.170207 0.985408i \(-0.445556\pi\)
0.170207 + 0.985408i \(0.445556\pi\)
\(282\) 841.954 0.177793
\(283\) 7515.82 1.57869 0.789345 0.613950i \(-0.210421\pi\)
0.789345 + 0.613950i \(0.210421\pi\)
\(284\) −1382.02 −0.288759
\(285\) 9465.63 1.96735
\(286\) 979.254 0.202463
\(287\) 2348.50 0.483023
\(288\) −288.000 −0.0589256
\(289\) −4827.65 −0.982627
\(290\) −9693.44 −1.96282
\(291\) 2334.29 0.470236
\(292\) 1135.93 0.227655
\(293\) −1807.73 −0.360439 −0.180220 0.983626i \(-0.557681\pi\)
−0.180220 + 0.983626i \(0.557681\pi\)
\(294\) 294.000 0.0583212
\(295\) 224.667 0.0443411
\(296\) −2340.44 −0.459578
\(297\) 207.350 0.0405108
\(298\) −3102.76 −0.603148
\(299\) −1466.40 −0.283626
\(300\) −4128.64 −0.794558
\(301\) −851.017 −0.162963
\(302\) −5661.37 −1.07873
\(303\) −4217.89 −0.799709
\(304\) −2330.97 −0.439771
\(305\) 236.076 0.0443203
\(306\) −166.295 −0.0310669
\(307\) −9486.62 −1.76362 −0.881808 0.471609i \(-0.843674\pi\)
−0.881808 + 0.471609i \(0.843674\pi\)
\(308\) 215.030 0.0397808
\(309\) −2427.17 −0.446851
\(310\) −7187.50 −1.31685
\(311\) 2011.36 0.366732 0.183366 0.983045i \(-0.441301\pi\)
0.183366 + 0.983045i \(0.441301\pi\)
\(312\) 1530.16 0.277654
\(313\) −8481.05 −1.53156 −0.765778 0.643105i \(-0.777646\pi\)
−0.765778 + 0.643105i \(0.777646\pi\)
\(314\) 4926.63 0.885433
\(315\) −1364.43 −0.244054
\(316\) −1232.26 −0.219368
\(317\) −1379.68 −0.244450 −0.122225 0.992502i \(-0.539003\pi\)
−0.122225 + 0.992502i \(0.539003\pi\)
\(318\) −550.427 −0.0970642
\(319\) −1718.61 −0.301642
\(320\) 1386.09 0.242140
\(321\) −1140.67 −0.198337
\(322\) −322.000 −0.0557278
\(323\) −1345.93 −0.231857
\(324\) 324.000 0.0555556
\(325\) 21935.6 3.74391
\(326\) −2929.52 −0.497703
\(327\) 5509.56 0.931742
\(328\) 2684.00 0.451827
\(329\) −982.280 −0.164604
\(330\) −997.939 −0.166469
\(331\) −447.040 −0.0742343 −0.0371171 0.999311i \(-0.511817\pi\)
−0.0371171 + 0.999311i \(0.511817\pi\)
\(332\) −556.992 −0.0920750
\(333\) 2632.99 0.433295
\(334\) −4780.70 −0.783199
\(335\) −9630.23 −1.57061
\(336\) 336.000 0.0545545
\(337\) −7611.82 −1.23039 −0.615196 0.788374i \(-0.710923\pi\)
−0.615196 + 0.788374i \(0.710923\pi\)
\(338\) −3735.77 −0.601181
\(339\) 5047.89 0.808743
\(340\) 800.347 0.127661
\(341\) −1274.32 −0.202370
\(342\) 2622.34 0.414620
\(343\) −343.000 −0.0539949
\(344\) −972.591 −0.152438
\(345\) 1494.38 0.233202
\(346\) −5571.13 −0.865623
\(347\) −1936.99 −0.299663 −0.149832 0.988712i \(-0.547873\pi\)
−0.149832 + 0.988712i \(0.547873\pi\)
\(348\) −2685.46 −0.413665
\(349\) −4777.25 −0.732724 −0.366362 0.930472i \(-0.619397\pi\)
−0.366362 + 0.930472i \(0.619397\pi\)
\(350\) 4816.75 0.735618
\(351\) −1721.42 −0.261774
\(352\) 245.749 0.0372115
\(353\) −9788.48 −1.47589 −0.737943 0.674863i \(-0.764203\pi\)
−0.737943 + 0.674863i \(0.764203\pi\)
\(354\) 62.2414 0.00934490
\(355\) −7482.81 −1.11872
\(356\) 3555.14 0.529276
\(357\) 194.011 0.0287623
\(358\) −5619.68 −0.829635
\(359\) 7786.60 1.14474 0.572369 0.819996i \(-0.306024\pi\)
0.572369 + 0.819996i \(0.306024\pi\)
\(360\) −1559.35 −0.228292
\(361\) 14365.3 2.09438
\(362\) −250.779 −0.0364107
\(363\) 3816.07 0.551768
\(364\) −1785.18 −0.257057
\(365\) 6150.38 0.881988
\(366\) 65.4022 0.00934052
\(367\) 1369.04 0.194723 0.0973614 0.995249i \(-0.468960\pi\)
0.0973614 + 0.995249i \(0.468960\pi\)
\(368\) −368.000 −0.0521286
\(369\) −3019.50 −0.425987
\(370\) −12672.1 −1.78052
\(371\) 642.165 0.0898640
\(372\) −1991.21 −0.277526
\(373\) 11348.7 1.57537 0.787687 0.616076i \(-0.211278\pi\)
0.787687 + 0.616076i \(0.211278\pi\)
\(374\) 141.899 0.0196187
\(375\) −14232.6 −1.95991
\(376\) −1122.61 −0.153973
\(377\) 14267.9 1.94917
\(378\) −378.000 −0.0514344
\(379\) 1931.79 0.261819 0.130910 0.991394i \(-0.458210\pi\)
0.130910 + 0.991394i \(0.458210\pi\)
\(380\) −12620.8 −1.70378
\(381\) −7826.47 −1.05239
\(382\) −5933.68 −0.794748
\(383\) 2075.41 0.276890 0.138445 0.990370i \(-0.455790\pi\)
0.138445 + 0.990370i \(0.455790\pi\)
\(384\) 384.000 0.0510310
\(385\) 1164.26 0.154120
\(386\) −5689.25 −0.750195
\(387\) 1094.17 0.143720
\(388\) −3112.39 −0.407237
\(389\) −7434.25 −0.968975 −0.484488 0.874798i \(-0.660994\pi\)
−0.484488 + 0.874798i \(0.660994\pi\)
\(390\) 8284.89 1.07570
\(391\) −212.488 −0.0274834
\(392\) −392.000 −0.0505076
\(393\) −6419.40 −0.823959
\(394\) 5812.06 0.743166
\(395\) −6671.99 −0.849884
\(396\) −276.467 −0.0350833
\(397\) −2829.73 −0.357733 −0.178866 0.983873i \(-0.557243\pi\)
−0.178866 + 0.983873i \(0.557243\pi\)
\(398\) 7505.68 0.945291
\(399\) −3059.40 −0.383864
\(400\) 5504.86 0.688107
\(401\) 5719.37 0.712248 0.356124 0.934439i \(-0.384098\pi\)
0.356124 + 0.934439i \(0.384098\pi\)
\(402\) −2667.94 −0.331007
\(403\) 10579.4 1.30769
\(404\) 5623.86 0.692568
\(405\) 1754.27 0.215235
\(406\) 3133.03 0.382980
\(407\) −2246.72 −0.273626
\(408\) 221.727 0.0269047
\(409\) −2913.31 −0.352209 −0.176105 0.984371i \(-0.556350\pi\)
−0.176105 + 0.984371i \(0.556350\pi\)
\(410\) 14532.3 1.75049
\(411\) 3261.52 0.391433
\(412\) 3236.23 0.386984
\(413\) −72.6150 −0.00865169
\(414\) 414.000 0.0491473
\(415\) −3015.78 −0.356720
\(416\) −2040.21 −0.240455
\(417\) −4457.18 −0.523427
\(418\) −2237.63 −0.261833
\(419\) 11518.7 1.34301 0.671507 0.740998i \(-0.265647\pi\)
0.671507 + 0.740998i \(0.265647\pi\)
\(420\) 1819.24 0.211357
\(421\) −10074.9 −1.16632 −0.583162 0.812356i \(-0.698185\pi\)
−0.583162 + 0.812356i \(0.698185\pi\)
\(422\) 4935.77 0.569359
\(423\) 1262.93 0.145167
\(424\) 733.902 0.0840600
\(425\) 3178.58 0.362785
\(426\) −2073.03 −0.235771
\(427\) −76.3026 −0.00864764
\(428\) 1520.89 0.171765
\(429\) 1468.88 0.165311
\(430\) −5266.01 −0.590580
\(431\) −4889.20 −0.546414 −0.273207 0.961955i \(-0.588084\pi\)
−0.273207 + 0.961955i \(0.588084\pi\)
\(432\) −432.000 −0.0481125
\(433\) −12480.8 −1.38520 −0.692600 0.721322i \(-0.743535\pi\)
−0.692600 + 0.721322i \(0.743535\pi\)
\(434\) 2323.08 0.256939
\(435\) −14540.2 −1.60264
\(436\) −7346.09 −0.806912
\(437\) 3350.77 0.366794
\(438\) 1703.89 0.185879
\(439\) 10614.2 1.15396 0.576978 0.816759i \(-0.304232\pi\)
0.576978 + 0.816759i \(0.304232\pi\)
\(440\) 1330.58 0.144166
\(441\) 441.000 0.0476190
\(442\) −1178.04 −0.126773
\(443\) 8956.50 0.960578 0.480289 0.877110i \(-0.340532\pi\)
0.480289 + 0.877110i \(0.340532\pi\)
\(444\) −3510.66 −0.375244
\(445\) 19249.0 2.05054
\(446\) 11710.9 1.24334
\(447\) −4654.14 −0.492468
\(448\) −448.000 −0.0472456
\(449\) 1848.59 0.194300 0.0971498 0.995270i \(-0.469027\pi\)
0.0971498 + 0.995270i \(0.469027\pi\)
\(450\) −6192.97 −0.648754
\(451\) 2576.52 0.269011
\(452\) −6730.52 −0.700392
\(453\) −8492.05 −0.880775
\(454\) −6636.76 −0.686076
\(455\) −9665.70 −0.995902
\(456\) −3496.46 −0.359071
\(457\) 13880.5 1.42079 0.710395 0.703803i \(-0.248516\pi\)
0.710395 + 0.703803i \(0.248516\pi\)
\(458\) 8553.62 0.872673
\(459\) −249.443 −0.0253660
\(460\) −1992.50 −0.201959
\(461\) 6171.03 0.623457 0.311729 0.950171i \(-0.399092\pi\)
0.311729 + 0.950171i \(0.399092\pi\)
\(462\) 322.545 0.0324809
\(463\) 11742.8 1.17869 0.589346 0.807880i \(-0.299385\pi\)
0.589346 + 0.807880i \(0.299385\pi\)
\(464\) 3580.61 0.358245
\(465\) −10781.3 −1.07520
\(466\) −9964.15 −0.990516
\(467\) −2037.06 −0.201850 −0.100925 0.994894i \(-0.532180\pi\)
−0.100925 + 0.994894i \(0.532180\pi\)
\(468\) 2295.23 0.226703
\(469\) 3112.60 0.306453
\(470\) −6078.25 −0.596529
\(471\) 7389.95 0.722953
\(472\) −82.9885 −0.00809292
\(473\) −933.645 −0.0907591
\(474\) −1848.40 −0.179113
\(475\) −50123.7 −4.84175
\(476\) −258.681 −0.0249089
\(477\) −825.640 −0.0792526
\(478\) −11328.7 −1.08403
\(479\) 18344.6 1.74986 0.874931 0.484247i \(-0.160907\pi\)
0.874931 + 0.484247i \(0.160907\pi\)
\(480\) 2079.13 0.197706
\(481\) 18652.3 1.76813
\(482\) −7168.10 −0.677382
\(483\) −483.000 −0.0455016
\(484\) −5088.09 −0.477845
\(485\) −16851.8 −1.57773
\(486\) 486.000 0.0453609
\(487\) −5695.34 −0.529940 −0.264970 0.964257i \(-0.585362\pi\)
−0.264970 + 0.964257i \(0.585362\pi\)
\(488\) −87.2030 −0.00808913
\(489\) −4394.28 −0.406373
\(490\) −2122.45 −0.195679
\(491\) 4.86414 0.000447078 0 0.000223539 1.00000i \(-0.499929\pi\)
0.000223539 1.00000i \(0.499929\pi\)
\(492\) 4026.00 0.368915
\(493\) 2067.49 0.188875
\(494\) 18576.8 1.69192
\(495\) −1496.91 −0.135921
\(496\) 2654.95 0.240345
\(497\) 2418.53 0.218282
\(498\) −835.488 −0.0751789
\(499\) −20659.3 −1.85338 −0.926689 0.375830i \(-0.877358\pi\)
−0.926689 + 0.375830i \(0.877358\pi\)
\(500\) 18976.7 1.69733
\(501\) −7171.05 −0.639479
\(502\) 8295.53 0.737545
\(503\) −17141.4 −1.51948 −0.759741 0.650226i \(-0.774674\pi\)
−0.759741 + 0.650226i \(0.774674\pi\)
\(504\) 504.000 0.0445435
\(505\) 30449.9 2.68317
\(506\) −353.264 −0.0310365
\(507\) −5603.66 −0.490863
\(508\) 10435.3 0.911400
\(509\) −11323.8 −0.986084 −0.493042 0.870005i \(-0.664115\pi\)
−0.493042 + 0.870005i \(0.664115\pi\)
\(510\) 1200.52 0.104235
\(511\) −1987.87 −0.172091
\(512\) −512.000 −0.0441942
\(513\) 3933.51 0.338536
\(514\) −10833.1 −0.929624
\(515\) 17522.3 1.49927
\(516\) −1458.89 −0.124465
\(517\) −1077.65 −0.0916733
\(518\) 4095.77 0.347409
\(519\) −8356.69 −0.706779
\(520\) −11046.5 −0.931581
\(521\) 9820.14 0.825774 0.412887 0.910782i \(-0.364520\pi\)
0.412887 + 0.910782i \(0.364520\pi\)
\(522\) −4028.18 −0.337756
\(523\) 3490.61 0.291842 0.145921 0.989296i \(-0.453385\pi\)
0.145921 + 0.989296i \(0.453385\pi\)
\(524\) 8559.20 0.713569
\(525\) 7225.13 0.600629
\(526\) 10467.6 0.867699
\(527\) 1533.01 0.126715
\(528\) 368.623 0.0303831
\(529\) 529.000 0.0434783
\(530\) 3973.65 0.325669
\(531\) 93.3621 0.00763008
\(532\) 4079.20 0.332436
\(533\) −21390.3 −1.73831
\(534\) 5332.71 0.432152
\(535\) 8234.75 0.665457
\(536\) 3557.26 0.286661
\(537\) −8429.52 −0.677394
\(538\) −4408.89 −0.353310
\(539\) −376.303 −0.0300714
\(540\) −2339.03 −0.186399
\(541\) 2812.06 0.223475 0.111737 0.993738i \(-0.464358\pi\)
0.111737 + 0.993738i \(0.464358\pi\)
\(542\) −16566.6 −1.31291
\(543\) −376.169 −0.0297292
\(544\) −295.636 −0.0233001
\(545\) −39774.7 −3.12617
\(546\) −2677.77 −0.209887
\(547\) 21225.6 1.65912 0.829560 0.558417i \(-0.188591\pi\)
0.829560 + 0.558417i \(0.188591\pi\)
\(548\) −4348.70 −0.338991
\(549\) 98.1034 0.00762650
\(550\) 5284.42 0.409688
\(551\) −32602.7 −2.52073
\(552\) −552.000 −0.0425628
\(553\) 2156.46 0.165827
\(554\) −681.318 −0.0522499
\(555\) −19008.1 −1.45379
\(556\) 5942.91 0.453301
\(557\) −9319.31 −0.708926 −0.354463 0.935070i \(-0.615336\pi\)
−0.354463 + 0.935070i \(0.615336\pi\)
\(558\) −2986.82 −0.226599
\(559\) 7751.12 0.586471
\(560\) −2425.66 −0.183041
\(561\) 212.848 0.0160186
\(562\) −3206.99 −0.240709
\(563\) −11813.9 −0.884362 −0.442181 0.896926i \(-0.645795\pi\)
−0.442181 + 0.896926i \(0.645795\pi\)
\(564\) −1683.91 −0.125719
\(565\) −36441.8 −2.71348
\(566\) −15031.6 −1.11630
\(567\) −567.000 −0.0419961
\(568\) 2764.04 0.204184
\(569\) 331.923 0.0244551 0.0122275 0.999925i \(-0.496108\pi\)
0.0122275 + 0.999925i \(0.496108\pi\)
\(570\) −18931.3 −1.39113
\(571\) 9252.25 0.678099 0.339050 0.940768i \(-0.389895\pi\)
0.339050 + 0.940768i \(0.389895\pi\)
\(572\) −1958.51 −0.143163
\(573\) −8900.52 −0.648909
\(574\) −4697.01 −0.341549
\(575\) −7913.23 −0.573921
\(576\) 576.000 0.0416667
\(577\) −4323.91 −0.311970 −0.155985 0.987759i \(-0.549855\pi\)
−0.155985 + 0.987759i \(0.549855\pi\)
\(578\) 9655.30 0.694822
\(579\) −8533.88 −0.612532
\(580\) 19386.9 1.38793
\(581\) 974.735 0.0696021
\(582\) −4668.59 −0.332507
\(583\) 704.514 0.0500480
\(584\) −2271.86 −0.160976
\(585\) 12427.3 0.878303
\(586\) 3615.46 0.254869
\(587\) −18758.3 −1.31898 −0.659489 0.751714i \(-0.729227\pi\)
−0.659489 + 0.751714i \(0.729227\pi\)
\(588\) −588.000 −0.0412393
\(589\) −24174.3 −1.69114
\(590\) −449.334 −0.0313539
\(591\) 8718.10 0.606793
\(592\) 4680.88 0.324971
\(593\) −13282.8 −0.919832 −0.459916 0.887962i \(-0.652121\pi\)
−0.459916 + 0.887962i \(0.652121\pi\)
\(594\) −414.701 −0.0286454
\(595\) −1400.61 −0.0965030
\(596\) 6205.52 0.426490
\(597\) 11258.5 0.771827
\(598\) 2932.80 0.200554
\(599\) −13385.4 −0.913044 −0.456522 0.889712i \(-0.650905\pi\)
−0.456522 + 0.889712i \(0.650905\pi\)
\(600\) 8257.29 0.561837
\(601\) 4439.00 0.301282 0.150641 0.988589i \(-0.451866\pi\)
0.150641 + 0.988589i \(0.451866\pi\)
\(602\) 1702.03 0.115232
\(603\) −4001.92 −0.270266
\(604\) 11322.7 0.762774
\(605\) −27549.0 −1.85128
\(606\) 8435.79 0.565479
\(607\) 4029.43 0.269439 0.134720 0.990884i \(-0.456987\pi\)
0.134720 + 0.990884i \(0.456987\pi\)
\(608\) 4661.94 0.310965
\(609\) 4699.55 0.312702
\(610\) −472.153 −0.0313392
\(611\) 8946.67 0.592379
\(612\) 332.590 0.0219676
\(613\) −13906.1 −0.916253 −0.458127 0.888887i \(-0.651479\pi\)
−0.458127 + 0.888887i \(0.651479\pi\)
\(614\) 18973.2 1.24706
\(615\) 21798.4 1.42927
\(616\) −430.060 −0.0281293
\(617\) −4546.72 −0.296668 −0.148334 0.988937i \(-0.547391\pi\)
−0.148334 + 0.988937i \(0.547391\pi\)
\(618\) 4854.35 0.315972
\(619\) −5364.47 −0.348330 −0.174165 0.984717i \(-0.555723\pi\)
−0.174165 + 0.984717i \(0.555723\pi\)
\(620\) 14375.0 0.931152
\(621\) 621.000 0.0401286
\(622\) −4022.72 −0.259319
\(623\) −6221.50 −0.400095
\(624\) −3060.31 −0.196331
\(625\) 59741.2 3.82344
\(626\) 16962.1 1.08297
\(627\) −3356.44 −0.213785
\(628\) −9853.26 −0.626096
\(629\) 2702.80 0.171332
\(630\) 2728.86 0.172572
\(631\) −16148.1 −1.01877 −0.509386 0.860538i \(-0.670127\pi\)
−0.509386 + 0.860538i \(0.670127\pi\)
\(632\) 2464.53 0.155117
\(633\) 7403.66 0.464880
\(634\) 2759.36 0.172852
\(635\) 56501.0 3.53098
\(636\) 1100.85 0.0686347
\(637\) 3124.07 0.194317
\(638\) 3437.23 0.213293
\(639\) −3109.54 −0.192506
\(640\) −2772.18 −0.171219
\(641\) 14977.6 0.922902 0.461451 0.887166i \(-0.347329\pi\)
0.461451 + 0.887166i \(0.347329\pi\)
\(642\) 2281.34 0.140245
\(643\) −20284.5 −1.24408 −0.622038 0.782987i \(-0.713695\pi\)
−0.622038 + 0.782987i \(0.713695\pi\)
\(644\) 644.000 0.0394055
\(645\) −7899.01 −0.482207
\(646\) 2691.87 0.163948
\(647\) 9511.42 0.577948 0.288974 0.957337i \(-0.406686\pi\)
0.288974 + 0.957337i \(0.406686\pi\)
\(648\) −648.000 −0.0392837
\(649\) −79.6653 −0.00481840
\(650\) −43871.3 −2.64734
\(651\) 3484.63 0.209790
\(652\) 5859.04 0.351929
\(653\) −19219.0 −1.15176 −0.575878 0.817535i \(-0.695340\pi\)
−0.575878 + 0.817535i \(0.695340\pi\)
\(654\) −11019.1 −0.658841
\(655\) 46343.0 2.76454
\(656\) −5368.01 −0.319490
\(657\) 2555.84 0.151770
\(658\) 1964.56 0.116393
\(659\) −4176.90 −0.246902 −0.123451 0.992351i \(-0.539396\pi\)
−0.123451 + 0.992351i \(0.539396\pi\)
\(660\) 1995.88 0.117711
\(661\) 22086.9 1.29967 0.649833 0.760077i \(-0.274839\pi\)
0.649833 + 0.760077i \(0.274839\pi\)
\(662\) 894.080 0.0524916
\(663\) −1767.07 −0.103510
\(664\) 1113.98 0.0651068
\(665\) 22086.5 1.28793
\(666\) −5265.99 −0.306386
\(667\) −5147.12 −0.298797
\(668\) 9561.41 0.553805
\(669\) 17566.4 1.01518
\(670\) 19260.5 1.11059
\(671\) −83.7110 −0.00481614
\(672\) −672.000 −0.0385758
\(673\) 23118.0 1.32412 0.662059 0.749451i \(-0.269683\pi\)
0.662059 + 0.749451i \(0.269683\pi\)
\(674\) 15223.6 0.870018
\(675\) −9289.45 −0.529705
\(676\) 7471.55 0.425099
\(677\) −9447.78 −0.536348 −0.268174 0.963370i \(-0.586420\pi\)
−0.268174 + 0.963370i \(0.586420\pi\)
\(678\) −10095.8 −0.571867
\(679\) 5446.69 0.307842
\(680\) −1600.69 −0.0902703
\(681\) −9955.13 −0.560179
\(682\) 2548.64 0.143097
\(683\) 14305.1 0.801420 0.400710 0.916205i \(-0.368763\pi\)
0.400710 + 0.916205i \(0.368763\pi\)
\(684\) −5244.69 −0.293181
\(685\) −23545.6 −1.31333
\(686\) 686.000 0.0381802
\(687\) 12830.4 0.712535
\(688\) 1945.18 0.107790
\(689\) −5848.88 −0.323403
\(690\) −2988.76 −0.164898
\(691\) −17572.7 −0.967433 −0.483717 0.875225i \(-0.660713\pi\)
−0.483717 + 0.875225i \(0.660713\pi\)
\(692\) 11142.3 0.612088
\(693\) 483.818 0.0265205
\(694\) 3873.98 0.211894
\(695\) 32177.4 1.75620
\(696\) 5370.91 0.292506
\(697\) −3099.56 −0.168442
\(698\) 9554.51 0.518114
\(699\) −14946.2 −0.808753
\(700\) −9633.50 −0.520160
\(701\) 9881.83 0.532427 0.266214 0.963914i \(-0.414227\pi\)
0.266214 + 0.963914i \(0.414227\pi\)
\(702\) 3442.85 0.185103
\(703\) −42621.0 −2.28660
\(704\) −491.497 −0.0263125
\(705\) −9117.38 −0.487064
\(706\) 19577.0 1.04361
\(707\) −9841.75 −0.523532
\(708\) −124.483 −0.00660784
\(709\) −16184.5 −0.857293 −0.428646 0.903472i \(-0.641009\pi\)
−0.428646 + 0.903472i \(0.641009\pi\)
\(710\) 14965.6 0.791056
\(711\) −2772.59 −0.146245
\(712\) −7110.29 −0.374255
\(713\) −3816.49 −0.200461
\(714\) −388.022 −0.0203380
\(715\) −10604.2 −0.554648
\(716\) 11239.4 0.586641
\(717\) −16993.1 −0.885104
\(718\) −15573.2 −0.809452
\(719\) 25430.9 1.31907 0.659536 0.751673i \(-0.270753\pi\)
0.659536 + 0.751673i \(0.270753\pi\)
\(720\) 3118.70 0.161427
\(721\) −5663.40 −0.292533
\(722\) −28730.6 −1.48095
\(723\) −10752.1 −0.553080
\(724\) 501.559 0.0257463
\(725\) 76995.1 3.94417
\(726\) −7632.14 −0.390159
\(727\) 7539.07 0.384606 0.192303 0.981336i \(-0.438404\pi\)
0.192303 + 0.981336i \(0.438404\pi\)
\(728\) 3570.36 0.181767
\(729\) 729.000 0.0370370
\(730\) −12300.8 −0.623660
\(731\) 1123.18 0.0568292
\(732\) −130.804 −0.00660474
\(733\) −24919.5 −1.25569 −0.627847 0.778337i \(-0.716064\pi\)
−0.627847 + 0.778337i \(0.716064\pi\)
\(734\) −2738.08 −0.137690
\(735\) −3183.67 −0.159771
\(736\) 736.000 0.0368605
\(737\) 3414.81 0.170673
\(738\) 6039.01 0.301218
\(739\) 2288.29 0.113905 0.0569527 0.998377i \(-0.481862\pi\)
0.0569527 + 0.998377i \(0.481862\pi\)
\(740\) 25344.2 1.25901
\(741\) 27865.2 1.38145
\(742\) −1284.33 −0.0635434
\(743\) −28920.9 −1.42800 −0.714002 0.700144i \(-0.753119\pi\)
−0.714002 + 0.700144i \(0.753119\pi\)
\(744\) 3982.43 0.196240
\(745\) 33599.2 1.65232
\(746\) −22697.4 −1.11396
\(747\) −1253.23 −0.0613833
\(748\) −283.797 −0.0138725
\(749\) −2661.57 −0.129842
\(750\) 28465.1 1.38587
\(751\) −23510.9 −1.14238 −0.571188 0.820819i \(-0.693517\pi\)
−0.571188 + 0.820819i \(0.693517\pi\)
\(752\) 2245.21 0.108876
\(753\) 12443.3 0.602203
\(754\) −28535.9 −1.37827
\(755\) 61305.9 2.95517
\(756\) 756.000 0.0363696
\(757\) −15189.4 −0.729284 −0.364642 0.931148i \(-0.618809\pi\)
−0.364642 + 0.931148i \(0.618809\pi\)
\(758\) −3863.58 −0.185134
\(759\) −529.896 −0.0253412
\(760\) 25241.7 1.20475
\(761\) 15513.6 0.738984 0.369492 0.929234i \(-0.379532\pi\)
0.369492 + 0.929234i \(0.379532\pi\)
\(762\) 15652.9 0.744155
\(763\) 12855.7 0.609968
\(764\) 11867.4 0.561972
\(765\) 1800.78 0.0851077
\(766\) −4150.83 −0.195791
\(767\) 661.382 0.0311358
\(768\) −768.000 −0.0360844
\(769\) 3335.24 0.156400 0.0782002 0.996938i \(-0.475083\pi\)
0.0782002 + 0.996938i \(0.475083\pi\)
\(770\) −2328.52 −0.108979
\(771\) −16249.6 −0.759035
\(772\) 11378.5 0.530468
\(773\) 15879.9 0.738887 0.369444 0.929253i \(-0.379548\pi\)
0.369444 + 0.929253i \(0.379548\pi\)
\(774\) −2188.33 −0.101625
\(775\) 57090.4 2.64613
\(776\) 6224.79 0.287960
\(777\) 6143.65 0.283658
\(778\) 14868.5 0.685169
\(779\) 48877.6 2.24804
\(780\) −16569.8 −0.760632
\(781\) 2653.35 0.121568
\(782\) 424.976 0.0194337
\(783\) −6042.28 −0.275777
\(784\) 784.000 0.0357143
\(785\) −53349.6 −2.42564
\(786\) 12838.8 0.582627
\(787\) −31903.3 −1.44502 −0.722509 0.691362i \(-0.757011\pi\)
−0.722509 + 0.691362i \(0.757011\pi\)
\(788\) −11624.1 −0.525498
\(789\) 15701.4 0.708473
\(790\) 13344.0 0.600959
\(791\) 11778.4 0.529446
\(792\) 552.935 0.0248077
\(793\) 694.969 0.0311212
\(794\) 5659.45 0.252955
\(795\) 5960.47 0.265907
\(796\) −15011.4 −0.668422
\(797\) −42935.1 −1.90821 −0.954103 0.299479i \(-0.903187\pi\)
−0.954103 + 0.299479i \(0.903187\pi\)
\(798\) 6118.80 0.271433
\(799\) 1296.42 0.0574016
\(800\) −11009.7 −0.486565
\(801\) 7999.07 0.352851
\(802\) −11438.7 −0.503636
\(803\) −2180.88 −0.0958427
\(804\) 5335.89 0.234057
\(805\) 3486.88 0.152666
\(806\) −21158.8 −0.924674
\(807\) −6613.34 −0.288476
\(808\) −11247.7 −0.489719
\(809\) 21015.4 0.913301 0.456650 0.889646i \(-0.349049\pi\)
0.456650 + 0.889646i \(0.349049\pi\)
\(810\) −3508.54 −0.152194
\(811\) −5737.75 −0.248434 −0.124217 0.992255i \(-0.539642\pi\)
−0.124217 + 0.992255i \(0.539642\pi\)
\(812\) −6266.06 −0.270808
\(813\) −24850.0 −1.07199
\(814\) 4493.44 0.193483
\(815\) 31723.3 1.36346
\(816\) −443.454 −0.0190245
\(817\) −17711.6 −0.758445
\(818\) 5826.61 0.249050
\(819\) −4016.66 −0.171372
\(820\) −29064.6 −1.23778
\(821\) −46055.2 −1.95778 −0.978891 0.204384i \(-0.934481\pi\)
−0.978891 + 0.204384i \(0.934481\pi\)
\(822\) −6523.05 −0.276785
\(823\) −39701.6 −1.68154 −0.840771 0.541391i \(-0.817898\pi\)
−0.840771 + 0.541391i \(0.817898\pi\)
\(824\) −6472.46 −0.273639
\(825\) 7926.63 0.334509
\(826\) 145.230 0.00611767
\(827\) −20446.2 −0.859714 −0.429857 0.902897i \(-0.641436\pi\)
−0.429857 + 0.902897i \(0.641436\pi\)
\(828\) −828.000 −0.0347524
\(829\) 18481.2 0.774282 0.387141 0.922020i \(-0.373463\pi\)
0.387141 + 0.922020i \(0.373463\pi\)
\(830\) 6031.56 0.252239
\(831\) −1021.98 −0.0426619
\(832\) 4080.41 0.170028
\(833\) 452.692 0.0188294
\(834\) 8914.37 0.370119
\(835\) 51769.4 2.14557
\(836\) 4475.26 0.185144
\(837\) −4480.23 −0.185017
\(838\) −23037.3 −0.949654
\(839\) 8223.46 0.338385 0.169193 0.985583i \(-0.445884\pi\)
0.169193 + 0.985583i \(0.445884\pi\)
\(840\) −3638.48 −0.149452
\(841\) 25692.1 1.05343
\(842\) 20149.9 0.824716
\(843\) −4810.49 −0.196538
\(844\) −9871.54 −0.402598
\(845\) 40454.0 1.64694
\(846\) −2525.86 −0.102649
\(847\) 8904.16 0.361217
\(848\) −1467.80 −0.0594394
\(849\) −22547.5 −0.911457
\(850\) −6357.16 −0.256528
\(851\) −6728.76 −0.271045
\(852\) 4146.05 0.166715
\(853\) −14330.6 −0.575231 −0.287615 0.957746i \(-0.592862\pi\)
−0.287615 + 0.957746i \(0.592862\pi\)
\(854\) 152.605 0.00611480
\(855\) −28396.9 −1.13585
\(856\) −3041.79 −0.121456
\(857\) −10483.2 −0.417853 −0.208927 0.977931i \(-0.566997\pi\)
−0.208927 + 0.977931i \(0.566997\pi\)
\(858\) −2937.76 −0.116892
\(859\) 6682.74 0.265439 0.132720 0.991154i \(-0.457629\pi\)
0.132720 + 0.991154i \(0.457629\pi\)
\(860\) 10532.0 0.417603
\(861\) −7045.51 −0.278874
\(862\) 9778.40 0.386373
\(863\) −8687.33 −0.342665 −0.171333 0.985213i \(-0.554807\pi\)
−0.171333 + 0.985213i \(0.554807\pi\)
\(864\) 864.000 0.0340207
\(865\) 60328.8 2.37137
\(866\) 24961.7 0.979484
\(867\) 14482.9 0.567320
\(868\) −4646.17 −0.181683
\(869\) 2365.84 0.0923540
\(870\) 29080.3 1.13324
\(871\) −28349.8 −1.10287
\(872\) 14692.2 0.570573
\(873\) −7002.88 −0.271491
\(874\) −6701.54 −0.259363
\(875\) −33209.3 −1.28306
\(876\) −3407.78 −0.131436
\(877\) −18871.9 −0.726635 −0.363317 0.931665i \(-0.618356\pi\)
−0.363317 + 0.931665i \(0.618356\pi\)
\(878\) −21228.4 −0.815971
\(879\) 5423.19 0.208100
\(880\) −2661.17 −0.101941
\(881\) 21401.1 0.818411 0.409206 0.912442i \(-0.365806\pi\)
0.409206 + 0.912442i \(0.365806\pi\)
\(882\) −882.000 −0.0336718
\(883\) 7080.34 0.269844 0.134922 0.990856i \(-0.456922\pi\)
0.134922 + 0.990856i \(0.456922\pi\)
\(884\) 2356.09 0.0896423
\(885\) −674.001 −0.0256003
\(886\) −17913.0 −0.679231
\(887\) −32048.7 −1.21318 −0.606590 0.795015i \(-0.707463\pi\)
−0.606590 + 0.795015i \(0.707463\pi\)
\(888\) 7021.31 0.265338
\(889\) −18261.8 −0.688954
\(890\) −38498.0 −1.44995
\(891\) −622.051 −0.0233889
\(892\) −23421.9 −0.879173
\(893\) −20443.5 −0.766085
\(894\) 9308.28 0.348228
\(895\) 60854.5 2.27278
\(896\) 896.000 0.0334077
\(897\) 4399.20 0.163751
\(898\) −3697.19 −0.137391
\(899\) 37134.2 1.37763
\(900\) 12385.9 0.458738
\(901\) −847.531 −0.0313378
\(902\) −5153.05 −0.190219
\(903\) 2553.05 0.0940867
\(904\) 13461.0 0.495252
\(905\) 2715.65 0.0997471
\(906\) 16984.1 0.622802
\(907\) 49551.0 1.81402 0.907009 0.421111i \(-0.138360\pi\)
0.907009 + 0.421111i \(0.138360\pi\)
\(908\) 13273.5 0.485129
\(909\) 12653.7 0.461712
\(910\) 19331.4 0.704209
\(911\) 9888.98 0.359645 0.179822 0.983699i \(-0.442448\pi\)
0.179822 + 0.983699i \(0.442448\pi\)
\(912\) 6992.91 0.253902
\(913\) 1069.38 0.0387636
\(914\) −27760.9 −1.00465
\(915\) −708.229 −0.0255883
\(916\) −17107.2 −0.617073
\(917\) −14978.6 −0.539408
\(918\) 498.885 0.0179365
\(919\) 4847.06 0.173982 0.0869912 0.996209i \(-0.472275\pi\)
0.0869912 + 0.996209i \(0.472275\pi\)
\(920\) 3985.01 0.142806
\(921\) 28459.9 1.01822
\(922\) −12342.1 −0.440851
\(923\) −22028.1 −0.785553
\(924\) −645.090 −0.0229674
\(925\) 100655. 3.57784
\(926\) −23485.6 −0.833462
\(927\) 7281.52 0.257990
\(928\) −7161.22 −0.253317
\(929\) −6673.96 −0.235700 −0.117850 0.993031i \(-0.537600\pi\)
−0.117850 + 0.993031i \(0.537600\pi\)
\(930\) 21562.5 0.760282
\(931\) −7138.60 −0.251298
\(932\) 19928.3 0.700401
\(933\) −6034.08 −0.211733
\(934\) 4074.12 0.142729
\(935\) −1536.60 −0.0537455
\(936\) −4590.47 −0.160303
\(937\) −44446.7 −1.54964 −0.774819 0.632183i \(-0.782159\pi\)
−0.774819 + 0.632183i \(0.782159\pi\)
\(938\) −6225.20 −0.216695
\(939\) 25443.1 0.884245
\(940\) 12156.5 0.421810
\(941\) −39330.0 −1.36251 −0.681254 0.732047i \(-0.738565\pi\)
−0.681254 + 0.732047i \(0.738565\pi\)
\(942\) −14779.9 −0.511205
\(943\) 7716.51 0.266473
\(944\) 165.977 0.00572256
\(945\) 4093.30 0.140905
\(946\) 1867.29 0.0641763
\(947\) −5808.03 −0.199299 −0.0996493 0.995023i \(-0.531772\pi\)
−0.0996493 + 0.995023i \(0.531772\pi\)
\(948\) 3696.79 0.126652
\(949\) 18105.7 0.619321
\(950\) 100247. 3.42364
\(951\) 4139.04 0.141133
\(952\) 517.363 0.0176133
\(953\) 39453.8 1.34106 0.670532 0.741880i \(-0.266066\pi\)
0.670532 + 0.741880i \(0.266066\pi\)
\(954\) 1651.28 0.0560400
\(955\) 64254.8 2.17721
\(956\) 22657.5 0.766523
\(957\) 5155.84 0.174153
\(958\) −36689.1 −1.23734
\(959\) 7610.22 0.256253
\(960\) −4158.27 −0.139800
\(961\) −2256.73 −0.0757520
\(962\) −37304.5 −1.25026
\(963\) 3422.01 0.114510
\(964\) 14336.2 0.478981
\(965\) 61607.9 2.05516
\(966\) 966.000 0.0321745
\(967\) −16211.7 −0.539123 −0.269562 0.962983i \(-0.586879\pi\)
−0.269562 + 0.962983i \(0.586879\pi\)
\(968\) 10176.2 0.337887
\(969\) 4037.80 0.133863
\(970\) 33703.6 1.11562
\(971\) 40259.6 1.33058 0.665289 0.746586i \(-0.268308\pi\)
0.665289 + 0.746586i \(0.268308\pi\)
\(972\) −972.000 −0.0320750
\(973\) −10400.1 −0.342664
\(974\) 11390.7 0.374724
\(975\) −65806.9 −2.16155
\(976\) 174.406 0.00571988
\(977\) −28422.5 −0.930723 −0.465361 0.885121i \(-0.654076\pi\)
−0.465361 + 0.885121i \(0.654076\pi\)
\(978\) 8788.56 0.287349
\(979\) −6825.56 −0.222825
\(980\) 4244.90 0.138366
\(981\) −16528.7 −0.537941
\(982\) −9.72827 −0.000316132 0
\(983\) −16412.9 −0.532543 −0.266271 0.963898i \(-0.585792\pi\)
−0.266271 + 0.963898i \(0.585792\pi\)
\(984\) −8052.01 −0.260862
\(985\) −62937.8 −2.03590
\(986\) −4134.98 −0.133554
\(987\) 2946.84 0.0950344
\(988\) −37153.6 −1.19637
\(989\) −2796.20 −0.0899029
\(990\) 2993.82 0.0961108
\(991\) −34696.2 −1.11217 −0.556085 0.831126i \(-0.687697\pi\)
−0.556085 + 0.831126i \(0.687697\pi\)
\(992\) −5309.91 −0.169949
\(993\) 1341.12 0.0428592
\(994\) −4837.06 −0.154348
\(995\) −81277.7 −2.58962
\(996\) 1670.98 0.0531595
\(997\) 9210.31 0.292571 0.146286 0.989242i \(-0.453268\pi\)
0.146286 + 0.989242i \(0.453268\pi\)
\(998\) 41318.5 1.31054
\(999\) −7898.98 −0.250163
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 966.4.a.m.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.m.1.5 5 1.1 even 1 trivial