Properties

Label 966.4.a.m.1.2
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 1.2
Root \(5.91860\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.3402 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.3402 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +20.6804 q^{10} -0.432547 q^{11} -12.0000 q^{12} +58.4854 q^{13} +14.0000 q^{14} +31.0206 q^{15} +16.0000 q^{16} +119.180 q^{17} -18.0000 q^{18} -124.465 q^{19} -41.3608 q^{20} +21.0000 q^{21} +0.865093 q^{22} -23.0000 q^{23} +24.0000 q^{24} -18.0804 q^{25} -116.971 q^{26} -27.0000 q^{27} -28.0000 q^{28} -263.013 q^{29} -62.0412 q^{30} -298.993 q^{31} -32.0000 q^{32} +1.29764 q^{33} -238.361 q^{34} +72.3814 q^{35} +36.0000 q^{36} +258.142 q^{37} +248.930 q^{38} -175.456 q^{39} +82.7216 q^{40} +468.112 q^{41} -42.0000 q^{42} -495.967 q^{43} -1.73019 q^{44} -93.0618 q^{45} +46.0000 q^{46} -429.041 q^{47} -48.0000 q^{48} +49.0000 q^{49} +36.1607 q^{50} -357.541 q^{51} +233.941 q^{52} +606.504 q^{53} +54.0000 q^{54} +4.47262 q^{55} +56.0000 q^{56} +373.395 q^{57} +526.026 q^{58} +389.469 q^{59} +124.082 q^{60} -532.099 q^{61} +597.986 q^{62} -63.0000 q^{63} +64.0000 q^{64} -604.750 q^{65} -2.59528 q^{66} +322.037 q^{67} +476.721 q^{68} +69.0000 q^{69} -144.763 q^{70} -547.122 q^{71} -72.0000 q^{72} -568.864 q^{73} -516.284 q^{74} +54.2411 q^{75} -497.860 q^{76} +3.02783 q^{77} +350.912 q^{78} +439.699 q^{79} -165.443 q^{80} +81.0000 q^{81} -936.224 q^{82} +305.368 q^{83} +84.0000 q^{84} -1232.35 q^{85} +991.935 q^{86} +789.039 q^{87} +3.46037 q^{88} -263.162 q^{89} +186.124 q^{90} -409.397 q^{91} -92.0000 q^{92} +896.979 q^{93} +858.082 q^{94} +1286.99 q^{95} +96.0000 q^{96} -902.223 q^{97} -98.0000 q^{98} -3.89292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 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
\(5\) −10.3402 −0.924855 −0.462428 0.886657i \(-0.653021\pi\)
−0.462428 + 0.886657i \(0.653021\pi\)
\(6\) 6.00000 0.408248
\(7\) −7.00000 −0.377964
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) 20.6804 0.653971
\(11\) −0.432547 −0.0118562 −0.00592808 0.999982i \(-0.501887\pi\)
−0.00592808 + 0.999982i \(0.501887\pi\)
\(12\) −12.0000 −0.288675
\(13\) 58.4854 1.24776 0.623881 0.781519i \(-0.285555\pi\)
0.623881 + 0.781519i \(0.285555\pi\)
\(14\) 14.0000 0.267261
\(15\) 31.0206 0.533965
\(16\) 16.0000 0.250000
\(17\) 119.180 1.70032 0.850161 0.526523i \(-0.176505\pi\)
0.850161 + 0.526523i \(0.176505\pi\)
\(18\) −18.0000 −0.235702
\(19\) −124.465 −1.50285 −0.751427 0.659816i \(-0.770634\pi\)
−0.751427 + 0.659816i \(0.770634\pi\)
\(20\) −41.3608 −0.462428
\(21\) 21.0000 0.218218
\(22\) 0.865093 0.00838357
\(23\) −23.0000 −0.208514
\(24\) 24.0000 0.204124
\(25\) −18.0804 −0.144643
\(26\) −116.971 −0.882302
\(27\) −27.0000 −0.192450
\(28\) −28.0000 −0.188982
\(29\) −263.013 −1.68415 −0.842074 0.539363i \(-0.818665\pi\)
−0.842074 + 0.539363i \(0.818665\pi\)
\(30\) −62.0412 −0.377571
\(31\) −298.993 −1.73228 −0.866140 0.499801i \(-0.833407\pi\)
−0.866140 + 0.499801i \(0.833407\pi\)
\(32\) −32.0000 −0.176777
\(33\) 1.29764 0.00684515
\(34\) −238.361 −1.20231
\(35\) 72.3814 0.349562
\(36\) 36.0000 0.166667
\(37\) 258.142 1.14698 0.573490 0.819213i \(-0.305589\pi\)
0.573490 + 0.819213i \(0.305589\pi\)
\(38\) 248.930 1.06268
\(39\) −175.456 −0.720396
\(40\) 82.7216 0.326986
\(41\) 468.112 1.78309 0.891547 0.452929i \(-0.149621\pi\)
0.891547 + 0.452929i \(0.149621\pi\)
\(42\) −42.0000 −0.154303
\(43\) −495.967 −1.75894 −0.879469 0.475957i \(-0.842102\pi\)
−0.879469 + 0.475957i \(0.842102\pi\)
\(44\) −1.73019 −0.00592808
\(45\) −93.0618 −0.308285
\(46\) 46.0000 0.147442
\(47\) −429.041 −1.33153 −0.665767 0.746160i \(-0.731895\pi\)
−0.665767 + 0.746160i \(0.731895\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) 36.1607 0.102278
\(51\) −357.541 −0.981681
\(52\) 233.941 0.623881
\(53\) 606.504 1.57188 0.785941 0.618301i \(-0.212179\pi\)
0.785941 + 0.618301i \(0.212179\pi\)
\(54\) 54.0000 0.136083
\(55\) 4.47262 0.0109652
\(56\) 56.0000 0.133631
\(57\) 373.395 0.867674
\(58\) 526.026 1.19087
\(59\) 389.469 0.859399 0.429700 0.902972i \(-0.358619\pi\)
0.429700 + 0.902972i \(0.358619\pi\)
\(60\) 124.082 0.266983
\(61\) −532.099 −1.11686 −0.558429 0.829553i \(-0.688596\pi\)
−0.558429 + 0.829553i \(0.688596\pi\)
\(62\) 597.986 1.22491
\(63\) −63.0000 −0.125988
\(64\) 64.0000 0.125000
\(65\) −604.750 −1.15400
\(66\) −2.59528 −0.00484025
\(67\) 322.037 0.587210 0.293605 0.955927i \(-0.405145\pi\)
0.293605 + 0.955927i \(0.405145\pi\)
\(68\) 476.721 0.850161
\(69\) 69.0000 0.120386
\(70\) −144.763 −0.247178
\(71\) −547.122 −0.914527 −0.457264 0.889331i \(-0.651170\pi\)
−0.457264 + 0.889331i \(0.651170\pi\)
\(72\) −72.0000 −0.117851
\(73\) −568.864 −0.912061 −0.456030 0.889964i \(-0.650729\pi\)
−0.456030 + 0.889964i \(0.650729\pi\)
\(74\) −516.284 −0.811037
\(75\) 54.2411 0.0835096
\(76\) −497.860 −0.751427
\(77\) 3.02783 0.00448121
\(78\) 350.912 0.509397
\(79\) 439.699 0.626203 0.313101 0.949720i \(-0.398632\pi\)
0.313101 + 0.949720i \(0.398632\pi\)
\(80\) −165.443 −0.231214
\(81\) 81.0000 0.111111
\(82\) −936.224 −1.26084
\(83\) 305.368 0.403837 0.201919 0.979402i \(-0.435282\pi\)
0.201919 + 0.979402i \(0.435282\pi\)
\(84\) 84.0000 0.109109
\(85\) −1232.35 −1.57255
\(86\) 991.935 1.24376
\(87\) 789.039 0.972343
\(88\) 3.46037 0.00419178
\(89\) −263.162 −0.313428 −0.156714 0.987644i \(-0.550090\pi\)
−0.156714 + 0.987644i \(0.550090\pi\)
\(90\) 186.124 0.217990
\(91\) −409.397 −0.471610
\(92\) −92.0000 −0.104257
\(93\) 896.979 1.00013
\(94\) 858.082 0.941537
\(95\) 1286.99 1.38992
\(96\) 96.0000 0.102062
\(97\) −902.223 −0.944401 −0.472200 0.881491i \(-0.656540\pi\)
−0.472200 + 0.881491i \(0.656540\pi\)
\(98\) −98.0000 −0.101015
\(99\) −3.89292 −0.00395205
\(100\) −72.3215 −0.0723215
\(101\) 1386.53 1.36599 0.682996 0.730422i \(-0.260677\pi\)
0.682996 + 0.730422i \(0.260677\pi\)
\(102\) 715.082 0.694154
\(103\) 1344.50 1.28619 0.643097 0.765785i \(-0.277649\pi\)
0.643097 + 0.765785i \(0.277649\pi\)
\(104\) −467.883 −0.441151
\(105\) −217.144 −0.201820
\(106\) −1213.01 −1.11149
\(107\) −437.931 −0.395667 −0.197834 0.980236i \(-0.563391\pi\)
−0.197834 + 0.980236i \(0.563391\pi\)
\(108\) −108.000 −0.0962250
\(109\) 1053.37 0.925638 0.462819 0.886453i \(-0.346838\pi\)
0.462819 + 0.886453i \(0.346838\pi\)
\(110\) −8.94523 −0.00775359
\(111\) −774.425 −0.662209
\(112\) −112.000 −0.0944911
\(113\) 1327.22 1.10491 0.552454 0.833543i \(-0.313692\pi\)
0.552454 + 0.833543i \(0.313692\pi\)
\(114\) −746.790 −0.613538
\(115\) 237.824 0.192846
\(116\) −1052.05 −0.842074
\(117\) 526.368 0.415921
\(118\) −778.938 −0.607687
\(119\) −834.262 −0.642661
\(120\) −248.165 −0.188785
\(121\) −1330.81 −0.999859
\(122\) 1064.20 0.789737
\(123\) −1404.34 −1.02947
\(124\) −1195.97 −0.866140
\(125\) 1479.48 1.05863
\(126\) 126.000 0.0890871
\(127\) 63.6591 0.0444790 0.0222395 0.999753i \(-0.492920\pi\)
0.0222395 + 0.999753i \(0.492920\pi\)
\(128\) −128.000 −0.0883883
\(129\) 1487.90 1.01552
\(130\) 1209.50 0.816001
\(131\) −1056.98 −0.704954 −0.352477 0.935820i \(-0.614661\pi\)
−0.352477 + 0.935820i \(0.614661\pi\)
\(132\) 5.19056 0.00342258
\(133\) 871.255 0.568026
\(134\) −644.074 −0.415220
\(135\) 279.185 0.177988
\(136\) −953.443 −0.601155
\(137\) −1093.78 −0.682101 −0.341050 0.940045i \(-0.610783\pi\)
−0.341050 + 0.940045i \(0.610783\pi\)
\(138\) −138.000 −0.0851257
\(139\) 962.261 0.587179 0.293589 0.955932i \(-0.405150\pi\)
0.293589 + 0.955932i \(0.405150\pi\)
\(140\) 289.525 0.174781
\(141\) 1287.12 0.768761
\(142\) 1094.24 0.646668
\(143\) −25.2976 −0.0147937
\(144\) 144.000 0.0833333
\(145\) 2719.60 1.55759
\(146\) 1137.73 0.644924
\(147\) −147.000 −0.0824786
\(148\) 1032.57 0.573490
\(149\) 2538.33 1.39562 0.697812 0.716281i \(-0.254157\pi\)
0.697812 + 0.716281i \(0.254157\pi\)
\(150\) −108.482 −0.0590502
\(151\) 1727.52 0.931016 0.465508 0.885044i \(-0.345872\pi\)
0.465508 + 0.885044i \(0.345872\pi\)
\(152\) 995.720 0.531339
\(153\) 1072.62 0.566774
\(154\) −6.05565 −0.00316869
\(155\) 3091.64 1.60211
\(156\) −701.824 −0.360198
\(157\) 39.6442 0.0201526 0.0100763 0.999949i \(-0.496793\pi\)
0.0100763 + 0.999949i \(0.496793\pi\)
\(158\) −879.398 −0.442792
\(159\) −1819.51 −0.907527
\(160\) 330.886 0.163493
\(161\) 161.000 0.0788110
\(162\) −162.000 −0.0785674
\(163\) 2499.83 1.20124 0.600618 0.799536i \(-0.294921\pi\)
0.600618 + 0.799536i \(0.294921\pi\)
\(164\) 1872.45 0.891547
\(165\) −13.4178 −0.00633078
\(166\) −610.736 −0.285556
\(167\) −939.805 −0.435475 −0.217737 0.976007i \(-0.569868\pi\)
−0.217737 + 0.976007i \(0.569868\pi\)
\(168\) −168.000 −0.0771517
\(169\) 1223.54 0.556912
\(170\) 2464.70 1.11196
\(171\) −1120.19 −0.500952
\(172\) −1983.87 −0.879469
\(173\) 1206.62 0.530277 0.265139 0.964210i \(-0.414582\pi\)
0.265139 + 0.964210i \(0.414582\pi\)
\(174\) −1578.08 −0.687550
\(175\) 126.563 0.0546699
\(176\) −6.92075 −0.00296404
\(177\) −1168.41 −0.496174
\(178\) 526.323 0.221627
\(179\) −2544.71 −1.06257 −0.531287 0.847192i \(-0.678291\pi\)
−0.531287 + 0.847192i \(0.678291\pi\)
\(180\) −372.247 −0.154143
\(181\) −2097.40 −0.861320 −0.430660 0.902514i \(-0.641719\pi\)
−0.430660 + 0.902514i \(0.641719\pi\)
\(182\) 818.795 0.333479
\(183\) 1596.30 0.644818
\(184\) 184.000 0.0737210
\(185\) −2669.24 −1.06079
\(186\) −1793.96 −0.707201
\(187\) −51.5510 −0.0201593
\(188\) −1716.16 −0.665767
\(189\) 189.000 0.0727393
\(190\) −2573.99 −0.982824
\(191\) 2140.41 0.810862 0.405431 0.914126i \(-0.367122\pi\)
0.405431 + 0.914126i \(0.367122\pi\)
\(192\) −192.000 −0.0721688
\(193\) −561.409 −0.209384 −0.104692 0.994505i \(-0.533386\pi\)
−0.104692 + 0.994505i \(0.533386\pi\)
\(194\) 1804.45 0.667792
\(195\) 1814.25 0.666262
\(196\) 196.000 0.0714286
\(197\) 3481.52 1.25913 0.629563 0.776949i \(-0.283234\pi\)
0.629563 + 0.776949i \(0.283234\pi\)
\(198\) 7.78584 0.00279452
\(199\) 3869.17 1.37828 0.689141 0.724628i \(-0.257988\pi\)
0.689141 + 0.724628i \(0.257988\pi\)
\(200\) 144.643 0.0511390
\(201\) −966.111 −0.339026
\(202\) −2773.07 −0.965902
\(203\) 1841.09 0.636548
\(204\) −1430.16 −0.490841
\(205\) −4840.37 −1.64910
\(206\) −2689.01 −0.909476
\(207\) −207.000 −0.0695048
\(208\) 935.766 0.311941
\(209\) 53.8369 0.0178181
\(210\) 434.288 0.142708
\(211\) 3412.74 1.11347 0.556737 0.830689i \(-0.312053\pi\)
0.556737 + 0.830689i \(0.312053\pi\)
\(212\) 2426.02 0.785941
\(213\) 1641.37 0.528003
\(214\) 875.862 0.279779
\(215\) 5128.40 1.62676
\(216\) 216.000 0.0680414
\(217\) 2092.95 0.654741
\(218\) −2106.74 −0.654525
\(219\) 1706.59 0.526579
\(220\) 17.8905 0.00548261
\(221\) 6970.30 2.12160
\(222\) 1548.85 0.468253
\(223\) −3712.10 −1.11471 −0.557356 0.830274i \(-0.688184\pi\)
−0.557356 + 0.830274i \(0.688184\pi\)
\(224\) 224.000 0.0668153
\(225\) −162.723 −0.0482143
\(226\) −2654.44 −0.781288
\(227\) 1753.63 0.512741 0.256371 0.966579i \(-0.417473\pi\)
0.256371 + 0.966579i \(0.417473\pi\)
\(228\) 1493.58 0.433837
\(229\) −1415.43 −0.408446 −0.204223 0.978924i \(-0.565467\pi\)
−0.204223 + 0.978924i \(0.565467\pi\)
\(230\) −475.649 −0.136362
\(231\) −9.08348 −0.00258722
\(232\) 2104.10 0.595436
\(233\) 3163.07 0.889354 0.444677 0.895691i \(-0.353318\pi\)
0.444677 + 0.895691i \(0.353318\pi\)
\(234\) −1052.74 −0.294101
\(235\) 4436.37 1.23148
\(236\) 1557.88 0.429700
\(237\) −1319.10 −0.361538
\(238\) 1668.52 0.454430
\(239\) 4143.03 1.12130 0.560649 0.828053i \(-0.310552\pi\)
0.560649 + 0.828053i \(0.310552\pi\)
\(240\) 496.329 0.133491
\(241\) −2878.68 −0.769427 −0.384714 0.923036i \(-0.625700\pi\)
−0.384714 + 0.923036i \(0.625700\pi\)
\(242\) 2661.63 0.707007
\(243\) −243.000 −0.0641500
\(244\) −2128.40 −0.558429
\(245\) −506.670 −0.132122
\(246\) 2808.67 0.727945
\(247\) −7279.38 −1.87521
\(248\) 2391.94 0.612454
\(249\) −916.104 −0.233156
\(250\) −2958.96 −0.748564
\(251\) 5977.97 1.50329 0.751645 0.659568i \(-0.229261\pi\)
0.751645 + 0.659568i \(0.229261\pi\)
\(252\) −252.000 −0.0629941
\(253\) 9.94857 0.00247218
\(254\) −127.318 −0.0314514
\(255\) 3697.04 0.907913
\(256\) 256.000 0.0625000
\(257\) −3868.37 −0.938920 −0.469460 0.882954i \(-0.655551\pi\)
−0.469460 + 0.882954i \(0.655551\pi\)
\(258\) −2975.80 −0.718083
\(259\) −1806.99 −0.433518
\(260\) −2419.00 −0.577000
\(261\) −2367.12 −0.561382
\(262\) 2113.97 0.498478
\(263\) 3073.54 0.720618 0.360309 0.932833i \(-0.382671\pi\)
0.360309 + 0.932833i \(0.382671\pi\)
\(264\) −10.3811 −0.00242013
\(265\) −6271.37 −1.45376
\(266\) −1742.51 −0.401655
\(267\) 789.485 0.180958
\(268\) 1288.15 0.293605
\(269\) −2508.94 −0.568672 −0.284336 0.958725i \(-0.591773\pi\)
−0.284336 + 0.958725i \(0.591773\pi\)
\(270\) −558.371 −0.125857
\(271\) −1653.33 −0.370601 −0.185300 0.982682i \(-0.559326\pi\)
−0.185300 + 0.982682i \(0.559326\pi\)
\(272\) 1906.89 0.425080
\(273\) 1228.19 0.272284
\(274\) 2187.56 0.482318
\(275\) 7.82060 0.00171491
\(276\) 276.000 0.0601929
\(277\) 6688.13 1.45073 0.725363 0.688367i \(-0.241672\pi\)
0.725363 + 0.688367i \(0.241672\pi\)
\(278\) −1924.52 −0.415198
\(279\) −2690.94 −0.577427
\(280\) −579.051 −0.123589
\(281\) 2244.31 0.476457 0.238228 0.971209i \(-0.423433\pi\)
0.238228 + 0.971209i \(0.423433\pi\)
\(282\) −2574.25 −0.543596
\(283\) 3553.67 0.746444 0.373222 0.927742i \(-0.378253\pi\)
0.373222 + 0.927742i \(0.378253\pi\)
\(284\) −2188.49 −0.457264
\(285\) −3860.98 −0.802472
\(286\) 50.5953 0.0104607
\(287\) −3276.78 −0.673946
\(288\) −288.000 −0.0589256
\(289\) 9290.95 1.89109
\(290\) −5439.21 −1.10138
\(291\) 2706.67 0.545250
\(292\) −2275.45 −0.456030
\(293\) −8467.65 −1.68835 −0.844173 0.536070i \(-0.819908\pi\)
−0.844173 + 0.536070i \(0.819908\pi\)
\(294\) 294.000 0.0583212
\(295\) −4027.19 −0.794820
\(296\) −2065.13 −0.405519
\(297\) 11.6788 0.00228172
\(298\) −5076.66 −0.986856
\(299\) −1345.16 −0.260177
\(300\) 216.964 0.0417548
\(301\) 3471.77 0.664816
\(302\) −3455.03 −0.658328
\(303\) −4159.60 −0.788656
\(304\) −1991.44 −0.375714
\(305\) 5502.01 1.03293
\(306\) −2145.25 −0.400770
\(307\) 5968.27 1.10954 0.554768 0.832005i \(-0.312807\pi\)
0.554768 + 0.832005i \(0.312807\pi\)
\(308\) 12.1113 0.00224060
\(309\) −4033.51 −0.742584
\(310\) −6183.29 −1.13286
\(311\) 4875.47 0.888947 0.444473 0.895792i \(-0.353391\pi\)
0.444473 + 0.895792i \(0.353391\pi\)
\(312\) 1403.65 0.254699
\(313\) 1656.71 0.299177 0.149589 0.988748i \(-0.452205\pi\)
0.149589 + 0.988748i \(0.452205\pi\)
\(314\) −79.2885 −0.0142500
\(315\) 651.432 0.116521
\(316\) 1758.80 0.313101
\(317\) 6464.34 1.14534 0.572671 0.819785i \(-0.305907\pi\)
0.572671 + 0.819785i \(0.305907\pi\)
\(318\) 3639.03 0.641718
\(319\) 113.765 0.0199675
\(320\) −661.772 −0.115607
\(321\) 1313.79 0.228439
\(322\) −322.000 −0.0557278
\(323\) −14833.8 −2.55534
\(324\) 324.000 0.0555556
\(325\) −1057.44 −0.180480
\(326\) −4999.65 −0.849402
\(327\) −3160.11 −0.534418
\(328\) −3744.90 −0.630419
\(329\) 3003.29 0.503272
\(330\) 26.8357 0.00447653
\(331\) 4283.23 0.711262 0.355631 0.934627i \(-0.384266\pi\)
0.355631 + 0.934627i \(0.384266\pi\)
\(332\) 1221.47 0.201919
\(333\) 2323.28 0.382327
\(334\) 1879.61 0.307927
\(335\) −3329.93 −0.543085
\(336\) 336.000 0.0545545
\(337\) −11333.3 −1.83194 −0.915969 0.401249i \(-0.868576\pi\)
−0.915969 + 0.401249i \(0.868576\pi\)
\(338\) −2447.07 −0.393796
\(339\) −3981.67 −0.637919
\(340\) −4929.39 −0.786276
\(341\) 129.328 0.0205382
\(342\) 2240.37 0.354226
\(343\) −343.000 −0.0539949
\(344\) 3967.74 0.621878
\(345\) −713.473 −0.111339
\(346\) −2413.25 −0.374963
\(347\) 3090.87 0.478175 0.239087 0.970998i \(-0.423152\pi\)
0.239087 + 0.970998i \(0.423152\pi\)
\(348\) 3156.16 0.486171
\(349\) −7158.14 −1.09790 −0.548949 0.835856i \(-0.684972\pi\)
−0.548949 + 0.835856i \(0.684972\pi\)
\(350\) −253.125 −0.0386574
\(351\) −1579.10 −0.240132
\(352\) 13.8415 0.00209589
\(353\) −1301.42 −0.196225 −0.0981126 0.995175i \(-0.531281\pi\)
−0.0981126 + 0.995175i \(0.531281\pi\)
\(354\) 2336.81 0.350848
\(355\) 5657.35 0.845805
\(356\) −1052.65 −0.156714
\(357\) 2502.79 0.371041
\(358\) 5089.42 0.751353
\(359\) −5035.04 −0.740221 −0.370111 0.928988i \(-0.620680\pi\)
−0.370111 + 0.928988i \(0.620680\pi\)
\(360\) 744.494 0.108995
\(361\) 8632.55 1.25857
\(362\) 4194.81 0.609045
\(363\) 3992.44 0.577269
\(364\) −1637.59 −0.235805
\(365\) 5882.16 0.843524
\(366\) −3192.59 −0.455955
\(367\) −7217.30 −1.02654 −0.513269 0.858228i \(-0.671566\pi\)
−0.513269 + 0.858228i \(0.671566\pi\)
\(368\) −368.000 −0.0521286
\(369\) 4213.01 0.594364
\(370\) 5338.47 0.750092
\(371\) −4245.53 −0.594116
\(372\) 3587.91 0.500066
\(373\) 870.591 0.120851 0.0604256 0.998173i \(-0.480754\pi\)
0.0604256 + 0.998173i \(0.480754\pi\)
\(374\) 103.102 0.0142548
\(375\) −4438.44 −0.611200
\(376\) 3432.33 0.470768
\(377\) −15382.4 −2.10142
\(378\) −378.000 −0.0514344
\(379\) −12466.8 −1.68965 −0.844823 0.535045i \(-0.820295\pi\)
−0.844823 + 0.535045i \(0.820295\pi\)
\(380\) 5147.97 0.694962
\(381\) −190.977 −0.0256799
\(382\) −4280.82 −0.573366
\(383\) −3629.39 −0.484212 −0.242106 0.970250i \(-0.577838\pi\)
−0.242106 + 0.970250i \(0.577838\pi\)
\(384\) 384.000 0.0510310
\(385\) −31.3083 −0.00414447
\(386\) 1122.82 0.148057
\(387\) −4463.71 −0.586312
\(388\) −3608.89 −0.472200
\(389\) 11031.1 1.43779 0.718896 0.695118i \(-0.244648\pi\)
0.718896 + 0.695118i \(0.244648\pi\)
\(390\) −3628.50 −0.471119
\(391\) −2741.15 −0.354542
\(392\) −392.000 −0.0505076
\(393\) 3170.95 0.407006
\(394\) −6963.04 −0.890337
\(395\) −4546.57 −0.579147
\(396\) −15.5717 −0.00197603
\(397\) 12002.9 1.51740 0.758698 0.651442i \(-0.225836\pi\)
0.758698 + 0.651442i \(0.225836\pi\)
\(398\) −7738.33 −0.974592
\(399\) −2613.77 −0.327950
\(400\) −289.286 −0.0361607
\(401\) −3705.09 −0.461404 −0.230702 0.973024i \(-0.574102\pi\)
−0.230702 + 0.973024i \(0.574102\pi\)
\(402\) 1932.22 0.239728
\(403\) −17486.7 −2.16148
\(404\) 5546.13 0.682996
\(405\) −837.556 −0.102762
\(406\) −3682.18 −0.450107
\(407\) −111.658 −0.0135988
\(408\) 2860.33 0.347077
\(409\) 8490.89 1.02652 0.513261 0.858233i \(-0.328437\pi\)
0.513261 + 0.858233i \(0.328437\pi\)
\(410\) 9680.74 1.16609
\(411\) 3281.34 0.393811
\(412\) 5378.02 0.643097
\(413\) −2726.28 −0.324822
\(414\) 414.000 0.0491473
\(415\) −3157.57 −0.373491
\(416\) −1871.53 −0.220575
\(417\) −2886.78 −0.339008
\(418\) −107.674 −0.0125993
\(419\) 1659.99 0.193546 0.0967730 0.995306i \(-0.469148\pi\)
0.0967730 + 0.995306i \(0.469148\pi\)
\(420\) −868.576 −0.100910
\(421\) 2439.98 0.282464 0.141232 0.989977i \(-0.454894\pi\)
0.141232 + 0.989977i \(0.454894\pi\)
\(422\) −6825.48 −0.787345
\(423\) −3861.37 −0.443845
\(424\) −4852.04 −0.555745
\(425\) −2154.82 −0.245940
\(426\) −3282.73 −0.373354
\(427\) 3724.69 0.422132
\(428\) −1751.72 −0.197834
\(429\) 75.8929 0.00854113
\(430\) −10256.8 −1.15029
\(431\) 8536.40 0.954023 0.477012 0.878897i \(-0.341720\pi\)
0.477012 + 0.878897i \(0.341720\pi\)
\(432\) −432.000 −0.0481125
\(433\) −6078.77 −0.674658 −0.337329 0.941387i \(-0.609523\pi\)
−0.337329 + 0.941387i \(0.609523\pi\)
\(434\) −4185.90 −0.462971
\(435\) −8158.81 −0.899276
\(436\) 4213.48 0.462819
\(437\) 2862.70 0.313367
\(438\) −3413.18 −0.372347
\(439\) −8767.75 −0.953216 −0.476608 0.879116i \(-0.658134\pi\)
−0.476608 + 0.879116i \(0.658134\pi\)
\(440\) −35.7809 −0.00387679
\(441\) 441.000 0.0476190
\(442\) −13940.6 −1.50020
\(443\) 2691.45 0.288656 0.144328 0.989530i \(-0.453898\pi\)
0.144328 + 0.989530i \(0.453898\pi\)
\(444\) −3097.70 −0.331105
\(445\) 2721.14 0.289875
\(446\) 7424.20 0.788220
\(447\) −7614.99 −0.805764
\(448\) −448.000 −0.0472456
\(449\) 11532.1 1.21210 0.606050 0.795427i \(-0.292753\pi\)
0.606050 + 0.795427i \(0.292753\pi\)
\(450\) 325.447 0.0340927
\(451\) −202.480 −0.0211406
\(452\) 5308.89 0.552454
\(453\) −5182.55 −0.537522
\(454\) −3507.25 −0.362563
\(455\) 4233.25 0.436171
\(456\) −2987.16 −0.306769
\(457\) −2710.86 −0.277480 −0.138740 0.990329i \(-0.544305\pi\)
−0.138740 + 0.990329i \(0.544305\pi\)
\(458\) 2830.85 0.288815
\(459\) −3217.87 −0.327227
\(460\) 951.298 0.0964228
\(461\) −17646.7 −1.78284 −0.891418 0.453182i \(-0.850289\pi\)
−0.891418 + 0.453182i \(0.850289\pi\)
\(462\) 18.1670 0.00182944
\(463\) 9616.38 0.965251 0.482625 0.875827i \(-0.339683\pi\)
0.482625 + 0.875827i \(0.339683\pi\)
\(464\) −4208.21 −0.421037
\(465\) −9274.93 −0.924978
\(466\) −6326.14 −0.628869
\(467\) −18488.3 −1.83198 −0.915992 0.401197i \(-0.868594\pi\)
−0.915992 + 0.401197i \(0.868594\pi\)
\(468\) 2105.47 0.207960
\(469\) −2254.26 −0.221945
\(470\) −8872.74 −0.870785
\(471\) −118.933 −0.0116351
\(472\) −3115.75 −0.303844
\(473\) 214.529 0.0208542
\(474\) 2638.19 0.255646
\(475\) 2250.37 0.217377
\(476\) −3337.05 −0.321331
\(477\) 5458.54 0.523961
\(478\) −8286.06 −0.792878
\(479\) 15943.0 1.52078 0.760388 0.649469i \(-0.225009\pi\)
0.760388 + 0.649469i \(0.225009\pi\)
\(480\) −992.659 −0.0943926
\(481\) 15097.5 1.43116
\(482\) 5757.35 0.544067
\(483\) −483.000 −0.0455016
\(484\) −5323.25 −0.499930
\(485\) 9329.16 0.873434
\(486\) 486.000 0.0453609
\(487\) 5277.63 0.491072 0.245536 0.969387i \(-0.421036\pi\)
0.245536 + 0.969387i \(0.421036\pi\)
\(488\) 4256.79 0.394869
\(489\) −7499.48 −0.693534
\(490\) 1013.34 0.0934245
\(491\) 13895.3 1.27716 0.638579 0.769556i \(-0.279522\pi\)
0.638579 + 0.769556i \(0.279522\pi\)
\(492\) −5617.35 −0.514735
\(493\) −31346.0 −2.86359
\(494\) 14558.8 1.32597
\(495\) 40.2535 0.00365508
\(496\) −4783.89 −0.433070
\(497\) 3829.85 0.345659
\(498\) 1832.21 0.164866
\(499\) 12826.2 1.15066 0.575329 0.817922i \(-0.304874\pi\)
0.575329 + 0.817922i \(0.304874\pi\)
\(500\) 5917.92 0.529314
\(501\) 2819.41 0.251421
\(502\) −11955.9 −1.06299
\(503\) −509.018 −0.0451213 −0.0225606 0.999745i \(-0.507182\pi\)
−0.0225606 + 0.999745i \(0.507182\pi\)
\(504\) 504.000 0.0445435
\(505\) −14337.0 −1.26334
\(506\) −19.8971 −0.00174809
\(507\) −3670.61 −0.321533
\(508\) 254.636 0.0222395
\(509\) 10162.0 0.884919 0.442460 0.896788i \(-0.354106\pi\)
0.442460 + 0.896788i \(0.354106\pi\)
\(510\) −7394.09 −0.641991
\(511\) 3982.04 0.344727
\(512\) −512.000 −0.0441942
\(513\) 3360.56 0.289225
\(514\) 7736.74 0.663917
\(515\) −13902.4 −1.18954
\(516\) 5951.61 0.507761
\(517\) 185.580 0.0157869
\(518\) 3613.99 0.306543
\(519\) −3619.87 −0.306156
\(520\) 4838.00 0.408001
\(521\) 17924.5 1.50727 0.753635 0.657293i \(-0.228299\pi\)
0.753635 + 0.657293i \(0.228299\pi\)
\(522\) 4734.23 0.396957
\(523\) 1260.42 0.105381 0.0526905 0.998611i \(-0.483220\pi\)
0.0526905 + 0.998611i \(0.483220\pi\)
\(524\) −4227.93 −0.352477
\(525\) −379.688 −0.0315637
\(526\) −6147.08 −0.509554
\(527\) −35634.1 −2.94543
\(528\) 20.7622 0.00171129
\(529\) 529.000 0.0434783
\(530\) 12542.7 1.02797
\(531\) 3505.22 0.286466
\(532\) 3485.02 0.284013
\(533\) 27377.7 2.22488
\(534\) −1578.97 −0.127956
\(535\) 4528.29 0.365935
\(536\) −2576.30 −0.207610
\(537\) 7634.13 0.613477
\(538\) 5017.88 0.402112
\(539\) −21.1948 −0.00169374
\(540\) 1116.74 0.0889942
\(541\) −1465.06 −0.116429 −0.0582143 0.998304i \(-0.518541\pi\)
−0.0582143 + 0.998304i \(0.518541\pi\)
\(542\) 3306.66 0.262054
\(543\) 6292.21 0.497283
\(544\) −3813.77 −0.300577
\(545\) −10892.1 −0.856081
\(546\) −2456.38 −0.192534
\(547\) 120.094 0.00938732 0.00469366 0.999989i \(-0.498506\pi\)
0.00469366 + 0.999989i \(0.498506\pi\)
\(548\) −4375.11 −0.341050
\(549\) −4788.89 −0.372286
\(550\) −15.6412 −0.00121262
\(551\) 32735.9 2.53103
\(552\) −552.000 −0.0425628
\(553\) −3077.89 −0.236682
\(554\) −13376.3 −1.02582
\(555\) 8007.71 0.612447
\(556\) 3849.04 0.293589
\(557\) −16526.2 −1.25716 −0.628581 0.777744i \(-0.716364\pi\)
−0.628581 + 0.777744i \(0.716364\pi\)
\(558\) 5381.87 0.408302
\(559\) −29006.8 −2.19474
\(560\) 1158.10 0.0873906
\(561\) 154.653 0.0116390
\(562\) −4488.62 −0.336906
\(563\) −15277.5 −1.14364 −0.571820 0.820379i \(-0.693762\pi\)
−0.571820 + 0.820379i \(0.693762\pi\)
\(564\) 5148.49 0.384381
\(565\) −13723.7 −1.02188
\(566\) −7107.34 −0.527816
\(567\) −567.000 −0.0419961
\(568\) 4376.98 0.323334
\(569\) 3979.82 0.293221 0.146611 0.989194i \(-0.453164\pi\)
0.146611 + 0.989194i \(0.453164\pi\)
\(570\) 7721.96 0.567434
\(571\) 10846.2 0.794919 0.397459 0.917620i \(-0.369892\pi\)
0.397459 + 0.917620i \(0.369892\pi\)
\(572\) −101.191 −0.00739683
\(573\) −6421.23 −0.468151
\(574\) 6553.57 0.476552
\(575\) 415.848 0.0301601
\(576\) 576.000 0.0416667
\(577\) −14286.1 −1.03074 −0.515372 0.856967i \(-0.672346\pi\)
−0.515372 + 0.856967i \(0.672346\pi\)
\(578\) −18581.9 −1.33721
\(579\) 1684.23 0.120888
\(580\) 10878.4 0.778796
\(581\) −2137.58 −0.152636
\(582\) −5413.34 −0.385550
\(583\) −262.341 −0.0186365
\(584\) 4550.91 0.322462
\(585\) −5442.75 −0.384667
\(586\) 16935.3 1.19384
\(587\) 3676.60 0.258517 0.129259 0.991611i \(-0.458740\pi\)
0.129259 + 0.991611i \(0.458740\pi\)
\(588\) −588.000 −0.0412393
\(589\) 37214.2 2.60337
\(590\) 8054.37 0.562023
\(591\) −10444.6 −0.726957
\(592\) 4130.27 0.286745
\(593\) 25212.1 1.74593 0.872965 0.487783i \(-0.162194\pi\)
0.872965 + 0.487783i \(0.162194\pi\)
\(594\) −23.3575 −0.00161342
\(595\) 8626.43 0.594369
\(596\) 10153.3 0.697812
\(597\) −11607.5 −0.795751
\(598\) 2690.33 0.183973
\(599\) −7943.80 −0.541862 −0.270931 0.962599i \(-0.587331\pi\)
−0.270931 + 0.962599i \(0.587331\pi\)
\(600\) −433.929 −0.0295251
\(601\) 15178.4 1.03018 0.515090 0.857136i \(-0.327758\pi\)
0.515090 + 0.857136i \(0.327758\pi\)
\(602\) −6943.54 −0.470096
\(603\) 2898.33 0.195737
\(604\) 6910.07 0.465508
\(605\) 13760.9 0.924725
\(606\) 8319.20 0.557664
\(607\) −10292.6 −0.688243 −0.344121 0.938925i \(-0.611823\pi\)
−0.344121 + 0.938925i \(0.611823\pi\)
\(608\) 3982.88 0.265670
\(609\) −5523.27 −0.367511
\(610\) −11004.0 −0.730393
\(611\) −25092.6 −1.66144
\(612\) 4290.49 0.283387
\(613\) −7009.66 −0.461855 −0.230928 0.972971i \(-0.574176\pi\)
−0.230928 + 0.972971i \(0.574176\pi\)
\(614\) −11936.5 −0.784560
\(615\) 14521.1 0.952110
\(616\) −24.2226 −0.00158435
\(617\) −19338.4 −1.26181 −0.630903 0.775861i \(-0.717316\pi\)
−0.630903 + 0.775861i \(0.717316\pi\)
\(618\) 8067.03 0.525086
\(619\) 15759.9 1.02334 0.511668 0.859183i \(-0.329028\pi\)
0.511668 + 0.859183i \(0.329028\pi\)
\(620\) 12366.6 0.801054
\(621\) 621.000 0.0401286
\(622\) −9750.94 −0.628580
\(623\) 1842.13 0.118465
\(624\) −2807.30 −0.180099
\(625\) −13038.1 −0.834435
\(626\) −3313.41 −0.211550
\(627\) −161.511 −0.0102873
\(628\) 158.577 0.0100763
\(629\) 30765.4 1.95023
\(630\) −1302.86 −0.0823926
\(631\) −25011.3 −1.57795 −0.788974 0.614427i \(-0.789387\pi\)
−0.788974 + 0.614427i \(0.789387\pi\)
\(632\) −3517.59 −0.221396
\(633\) −10238.2 −0.642864
\(634\) −12928.7 −0.809879
\(635\) −658.247 −0.0411366
\(636\) −7278.05 −0.453763
\(637\) 2865.78 0.178252
\(638\) −227.531 −0.0141192
\(639\) −4924.10 −0.304842
\(640\) 1323.54 0.0817464
\(641\) 28607.7 1.76277 0.881385 0.472398i \(-0.156612\pi\)
0.881385 + 0.472398i \(0.156612\pi\)
\(642\) −2627.59 −0.161530
\(643\) 15357.1 0.941873 0.470936 0.882167i \(-0.343916\pi\)
0.470936 + 0.882167i \(0.343916\pi\)
\(644\) 644.000 0.0394055
\(645\) −15385.2 −0.939212
\(646\) 29667.6 1.80690
\(647\) 12909.6 0.784435 0.392218 0.919872i \(-0.371708\pi\)
0.392218 + 0.919872i \(0.371708\pi\)
\(648\) −648.000 −0.0392837
\(649\) −168.464 −0.0101892
\(650\) 2114.87 0.127619
\(651\) −6278.85 −0.378015
\(652\) 9999.30 0.600618
\(653\) −3348.78 −0.200686 −0.100343 0.994953i \(-0.531994\pi\)
−0.100343 + 0.994953i \(0.531994\pi\)
\(654\) 6320.22 0.377890
\(655\) 10929.4 0.651981
\(656\) 7489.79 0.445773
\(657\) −5119.77 −0.304020
\(658\) −6006.58 −0.355867
\(659\) −17045.6 −1.00759 −0.503795 0.863823i \(-0.668063\pi\)
−0.503795 + 0.863823i \(0.668063\pi\)
\(660\) −53.6714 −0.00316539
\(661\) −10026.5 −0.589993 −0.294997 0.955498i \(-0.595318\pi\)
−0.294997 + 0.955498i \(0.595318\pi\)
\(662\) −8566.46 −0.502938
\(663\) −20910.9 −1.22491
\(664\) −2442.94 −0.142778
\(665\) −9008.95 −0.525342
\(666\) −4646.55 −0.270346
\(667\) 6049.30 0.351169
\(668\) −3759.22 −0.217737
\(669\) 11136.3 0.643579
\(670\) 6659.85 0.384019
\(671\) 230.158 0.0132416
\(672\) −672.000 −0.0385758
\(673\) −14133.9 −0.809539 −0.404770 0.914419i \(-0.632648\pi\)
−0.404770 + 0.914419i \(0.632648\pi\)
\(674\) 22666.6 1.29538
\(675\) 488.170 0.0278365
\(676\) 4894.15 0.278456
\(677\) 18169.1 1.03145 0.515726 0.856753i \(-0.327522\pi\)
0.515726 + 0.856753i \(0.327522\pi\)
\(678\) 7963.33 0.451077
\(679\) 6315.56 0.356950
\(680\) 9858.78 0.555981
\(681\) −5260.88 −0.296031
\(682\) −258.657 −0.0145227
\(683\) 3878.44 0.217283 0.108642 0.994081i \(-0.465350\pi\)
0.108642 + 0.994081i \(0.465350\pi\)
\(684\) −4480.74 −0.250476
\(685\) 11309.9 0.630844
\(686\) 686.000 0.0381802
\(687\) 4246.28 0.235816
\(688\) −7935.48 −0.439734
\(689\) 35471.6 1.96134
\(690\) 1426.95 0.0787289
\(691\) 21964.7 1.20923 0.604614 0.796518i \(-0.293327\pi\)
0.604614 + 0.796518i \(0.293327\pi\)
\(692\) 4826.50 0.265139
\(693\) 27.2504 0.00149374
\(694\) −6181.74 −0.338121
\(695\) −9949.96 −0.543056
\(696\) −6312.31 −0.343775
\(697\) 55789.8 3.03183
\(698\) 14316.3 0.776332
\(699\) −9489.21 −0.513469
\(700\) 506.250 0.0273349
\(701\) −12937.2 −0.697049 −0.348524 0.937300i \(-0.613317\pi\)
−0.348524 + 0.937300i \(0.613317\pi\)
\(702\) 3158.21 0.169799
\(703\) −32129.6 −1.72374
\(704\) −27.6830 −0.00148202
\(705\) −13309.1 −0.710993
\(706\) 2602.84 0.138752
\(707\) −9705.73 −0.516296
\(708\) −4673.63 −0.248087
\(709\) 25846.6 1.36910 0.684550 0.728966i \(-0.259999\pi\)
0.684550 + 0.728966i \(0.259999\pi\)
\(710\) −11314.7 −0.598075
\(711\) 3957.29 0.208734
\(712\) 2105.29 0.110813
\(713\) 6876.84 0.361205
\(714\) −5005.57 −0.262365
\(715\) 261.583 0.0136820
\(716\) −10178.8 −0.531287
\(717\) −12429.1 −0.647382
\(718\) 10070.1 0.523415
\(719\) 22479.5 1.16599 0.582993 0.812477i \(-0.301881\pi\)
0.582993 + 0.812477i \(0.301881\pi\)
\(720\) −1488.99 −0.0770713
\(721\) −9411.53 −0.486136
\(722\) −17265.1 −0.889945
\(723\) 8636.03 0.444229
\(724\) −8389.62 −0.430660
\(725\) 4755.37 0.243600
\(726\) −7984.88 −0.408191
\(727\) −18571.9 −0.947445 −0.473723 0.880674i \(-0.657090\pi\)
−0.473723 + 0.880674i \(0.657090\pi\)
\(728\) 3275.18 0.166739
\(729\) 729.000 0.0370370
\(730\) −11764.3 −0.596462
\(731\) −59109.5 −2.99076
\(732\) 6385.19 0.322409
\(733\) −31782.6 −1.60153 −0.800763 0.598981i \(-0.795572\pi\)
−0.800763 + 0.598981i \(0.795572\pi\)
\(734\) 14434.6 0.725873
\(735\) 1520.01 0.0762808
\(736\) 736.000 0.0368605
\(737\) −139.296 −0.00696206
\(738\) −8426.02 −0.420279
\(739\) −11096.6 −0.552363 −0.276181 0.961106i \(-0.589069\pi\)
−0.276181 + 0.961106i \(0.589069\pi\)
\(740\) −10676.9 −0.530395
\(741\) 21838.1 1.08265
\(742\) 8491.06 0.420103
\(743\) 27453.5 1.35555 0.677774 0.735271i \(-0.262945\pi\)
0.677774 + 0.735271i \(0.262945\pi\)
\(744\) −7175.83 −0.353600
\(745\) −26246.8 −1.29075
\(746\) −1741.18 −0.0854546
\(747\) 2748.31 0.134612
\(748\) −206.204 −0.0100796
\(749\) 3065.52 0.149548
\(750\) 8876.87 0.432183
\(751\) 10079.9 0.489775 0.244888 0.969551i \(-0.421249\pi\)
0.244888 + 0.969551i \(0.421249\pi\)
\(752\) −6864.66 −0.332883
\(753\) −17933.9 −0.867925
\(754\) 30764.8 1.48593
\(755\) −17862.9 −0.861055
\(756\) 756.000 0.0363696
\(757\) 30494.3 1.46411 0.732057 0.681244i \(-0.238561\pi\)
0.732057 + 0.681244i \(0.238561\pi\)
\(758\) 24933.6 1.19476
\(759\) −29.8457 −0.00142731
\(760\) −10295.9 −0.491412
\(761\) −19866.0 −0.946310 −0.473155 0.880979i \(-0.656885\pi\)
−0.473155 + 0.880979i \(0.656885\pi\)
\(762\) 381.954 0.0181585
\(763\) −7373.59 −0.349858
\(764\) 8561.64 0.405431
\(765\) −11091.1 −0.524184
\(766\) 7258.79 0.342390
\(767\) 22778.2 1.07233
\(768\) −768.000 −0.0360844
\(769\) −29343.9 −1.37603 −0.688016 0.725696i \(-0.741518\pi\)
−0.688016 + 0.725696i \(0.741518\pi\)
\(770\) 62.6166 0.00293058
\(771\) 11605.1 0.542086
\(772\) −2245.64 −0.104692
\(773\) −13207.1 −0.614523 −0.307261 0.951625i \(-0.599413\pi\)
−0.307261 + 0.951625i \(0.599413\pi\)
\(774\) 8927.41 0.414585
\(775\) 5405.90 0.250562
\(776\) 7217.78 0.333896
\(777\) 5420.98 0.250291
\(778\) −22062.3 −1.01667
\(779\) −58263.6 −2.67973
\(780\) 7257.00 0.333131
\(781\) 236.656 0.0108428
\(782\) 5482.29 0.250699
\(783\) 7101.35 0.324114
\(784\) 784.000 0.0357143
\(785\) −409.929 −0.0186382
\(786\) −6341.90 −0.287796
\(787\) 21714.2 0.983518 0.491759 0.870731i \(-0.336354\pi\)
0.491759 + 0.870731i \(0.336354\pi\)
\(788\) 13926.1 0.629563
\(789\) −9220.62 −0.416049
\(790\) 9093.15 0.409519
\(791\) −9290.56 −0.417616
\(792\) 31.1434 0.00139726
\(793\) −31120.0 −1.39357
\(794\) −24005.7 −1.07296
\(795\) 18814.1 0.839331
\(796\) 15476.7 0.689141
\(797\) 8315.34 0.369567 0.184783 0.982779i \(-0.440842\pi\)
0.184783 + 0.982779i \(0.440842\pi\)
\(798\) 5227.53 0.231896
\(799\) −51133.3 −2.26404
\(800\) 578.572 0.0255695
\(801\) −2368.46 −0.104476
\(802\) 7410.17 0.326262
\(803\) 246.060 0.0108135
\(804\) −3864.45 −0.169513
\(805\) −1664.77 −0.0728888
\(806\) 34973.4 1.52839
\(807\) 7526.82 0.328323
\(808\) −11092.3 −0.482951
\(809\) 9669.91 0.420242 0.210121 0.977675i \(-0.432614\pi\)
0.210121 + 0.977675i \(0.432614\pi\)
\(810\) 1675.11 0.0726635
\(811\) −9543.33 −0.413208 −0.206604 0.978425i \(-0.566241\pi\)
−0.206604 + 0.978425i \(0.566241\pi\)
\(812\) 7364.36 0.318274
\(813\) 4960.00 0.213966
\(814\) 223.317 0.00961578
\(815\) −25848.7 −1.11097
\(816\) −5720.66 −0.245420
\(817\) 61730.6 2.64343
\(818\) −16981.8 −0.725860
\(819\) −3684.58 −0.157203
\(820\) −19361.5 −0.824552
\(821\) 1330.39 0.0565543 0.0282772 0.999600i \(-0.490998\pi\)
0.0282772 + 0.999600i \(0.490998\pi\)
\(822\) −6562.67 −0.278467
\(823\) 28171.2 1.19318 0.596589 0.802547i \(-0.296522\pi\)
0.596589 + 0.802547i \(0.296522\pi\)
\(824\) −10756.0 −0.454738
\(825\) −23.4618 −0.000990103 0
\(826\) 5452.57 0.229684
\(827\) −26955.6 −1.13342 −0.566709 0.823918i \(-0.691784\pi\)
−0.566709 + 0.823918i \(0.691784\pi\)
\(828\) −828.000 −0.0347524
\(829\) 42904.8 1.79752 0.898762 0.438437i \(-0.144468\pi\)
0.898762 + 0.438437i \(0.144468\pi\)
\(830\) 6315.13 0.264098
\(831\) −20064.4 −0.837577
\(832\) 3743.06 0.155970
\(833\) 5839.84 0.242903
\(834\) 5773.56 0.239715
\(835\) 9717.76 0.402751
\(836\) 215.348 0.00890904
\(837\) 8072.81 0.333378
\(838\) −3319.98 −0.136858
\(839\) −20517.2 −0.844257 −0.422128 0.906536i \(-0.638717\pi\)
−0.422128 + 0.906536i \(0.638717\pi\)
\(840\) 1737.15 0.0713541
\(841\) 44786.8 1.83635
\(842\) −4879.96 −0.199732
\(843\) −6732.93 −0.275082
\(844\) 13651.0 0.556737
\(845\) −12651.6 −0.515063
\(846\) 7722.74 0.313846
\(847\) 9315.69 0.377911
\(848\) 9704.07 0.392971
\(849\) −10661.0 −0.430960
\(850\) 4309.65 0.173906
\(851\) −5937.26 −0.239162
\(852\) 6565.46 0.264001
\(853\) 40699.4 1.63367 0.816836 0.576870i \(-0.195726\pi\)
0.816836 + 0.576870i \(0.195726\pi\)
\(854\) −7449.39 −0.298493
\(855\) 11582.9 0.463308
\(856\) 3503.45 0.139890
\(857\) 4553.33 0.181492 0.0907461 0.995874i \(-0.471075\pi\)
0.0907461 + 0.995874i \(0.471075\pi\)
\(858\) −151.786 −0.00603949
\(859\) −33835.4 −1.34394 −0.671972 0.740576i \(-0.734553\pi\)
−0.671972 + 0.740576i \(0.734553\pi\)
\(860\) 20513.6 0.813381
\(861\) 9830.35 0.389103
\(862\) −17072.8 −0.674596
\(863\) 23062.8 0.909696 0.454848 0.890569i \(-0.349694\pi\)
0.454848 + 0.890569i \(0.349694\pi\)
\(864\) 864.000 0.0340207
\(865\) −12476.7 −0.490430
\(866\) 12157.5 0.477055
\(867\) −27872.8 −1.09182
\(868\) 8371.80 0.327370
\(869\) −190.190 −0.00742435
\(870\) 16317.6 0.635884
\(871\) 18834.5 0.732699
\(872\) −8426.96 −0.327263
\(873\) −8120.01 −0.314800
\(874\) −5725.39 −0.221584
\(875\) −10356.4 −0.400124
\(876\) 6826.36 0.263289
\(877\) 455.054 0.0175212 0.00876060 0.999962i \(-0.497211\pi\)
0.00876060 + 0.999962i \(0.497211\pi\)
\(878\) 17535.5 0.674025
\(879\) 25403.0 0.974767
\(880\) 71.5619 0.00274131
\(881\) −11371.1 −0.434849 −0.217425 0.976077i \(-0.569766\pi\)
−0.217425 + 0.976077i \(0.569766\pi\)
\(882\) −882.000 −0.0336718
\(883\) 32228.8 1.22830 0.614149 0.789190i \(-0.289500\pi\)
0.614149 + 0.789190i \(0.289500\pi\)
\(884\) 27881.2 1.06080
\(885\) 12081.6 0.458889
\(886\) −5382.90 −0.204111
\(887\) 29855.0 1.13014 0.565069 0.825044i \(-0.308850\pi\)
0.565069 + 0.825044i \(0.308850\pi\)
\(888\) 6195.40 0.234126
\(889\) −445.613 −0.0168115
\(890\) −5442.29 −0.204973
\(891\) −35.0363 −0.00131735
\(892\) −14848.4 −0.557356
\(893\) 53400.6 2.00110
\(894\) 15230.0 0.569761
\(895\) 26312.8 0.982726
\(896\) 896.000 0.0334077
\(897\) 4035.49 0.150213
\(898\) −23064.2 −0.857084
\(899\) 78639.0 2.91742
\(900\) −650.893 −0.0241072
\(901\) 72283.4 2.67271
\(902\) 404.961 0.0149487
\(903\) −10415.3 −0.383832
\(904\) −10617.8 −0.390644
\(905\) 21687.6 0.796596
\(906\) 10365.1 0.380086
\(907\) −16902.8 −0.618795 −0.309397 0.950933i \(-0.600127\pi\)
−0.309397 + 0.950933i \(0.600127\pi\)
\(908\) 7014.51 0.256371
\(909\) 12478.8 0.455331
\(910\) −8466.50 −0.308419
\(911\) −43667.1 −1.58810 −0.794048 0.607855i \(-0.792030\pi\)
−0.794048 + 0.607855i \(0.792030\pi\)
\(912\) 5974.32 0.216918
\(913\) −132.086 −0.00478796
\(914\) 5421.71 0.196208
\(915\) −16506.0 −0.596363
\(916\) −5661.71 −0.204223
\(917\) 7398.88 0.266448
\(918\) 6435.74 0.231385
\(919\) 29867.2 1.07207 0.536033 0.844197i \(-0.319922\pi\)
0.536033 + 0.844197i \(0.319922\pi\)
\(920\) −1902.60 −0.0681812
\(921\) −17904.8 −0.640591
\(922\) 35293.3 1.26066
\(923\) −31998.6 −1.14111
\(924\) −36.3339 −0.00129361
\(925\) −4667.30 −0.165903
\(926\) −19232.8 −0.682535
\(927\) 12100.5 0.428731
\(928\) 8416.41 0.297718
\(929\) 15720.8 0.555201 0.277600 0.960697i \(-0.410461\pi\)
0.277600 + 0.960697i \(0.410461\pi\)
\(930\) 18549.9 0.654058
\(931\) −6098.79 −0.214694
\(932\) 12652.3 0.444677
\(933\) −14626.4 −0.513234
\(934\) 36976.6 1.29541
\(935\) 533.048 0.0186444
\(936\) −4210.95 −0.147050
\(937\) 19570.3 0.682321 0.341160 0.940005i \(-0.389180\pi\)
0.341160 + 0.940005i \(0.389180\pi\)
\(938\) 4508.52 0.156939
\(939\) −4970.12 −0.172730
\(940\) 17745.5 0.615738
\(941\) 4350.58 0.150717 0.0753586 0.997157i \(-0.475990\pi\)
0.0753586 + 0.997157i \(0.475990\pi\)
\(942\) 237.865 0.00822725
\(943\) −10766.6 −0.371801
\(944\) 6231.51 0.214850
\(945\) −1954.30 −0.0672733
\(946\) −429.058 −0.0147462
\(947\) 9017.19 0.309419 0.154709 0.987960i \(-0.450556\pi\)
0.154709 + 0.987960i \(0.450556\pi\)
\(948\) −5276.39 −0.180769
\(949\) −33270.2 −1.13804
\(950\) −4500.75 −0.153709
\(951\) −19393.0 −0.661264
\(952\) 6674.10 0.227215
\(953\) −49070.5 −1.66794 −0.833971 0.551808i \(-0.813938\pi\)
−0.833971 + 0.551808i \(0.813938\pi\)
\(954\) −10917.1 −0.370496
\(955\) −22132.3 −0.749930
\(956\) 16572.1 0.560649
\(957\) −341.296 −0.0115282
\(958\) −31885.9 −1.07535
\(959\) 7656.45 0.257810
\(960\) 1985.32 0.0667457
\(961\) 59605.7 2.00080
\(962\) −30195.0 −1.01198
\(963\) −3941.38 −0.131889
\(964\) −11514.7 −0.384714
\(965\) 5805.08 0.193650
\(966\) 966.000 0.0321745
\(967\) 8814.46 0.293127 0.146563 0.989201i \(-0.453179\pi\)
0.146563 + 0.989201i \(0.453179\pi\)
\(968\) 10646.5 0.353504
\(969\) 44501.4 1.47532
\(970\) −18658.3 −0.617611
\(971\) −12757.8 −0.421644 −0.210822 0.977524i \(-0.567614\pi\)
−0.210822 + 0.977524i \(0.567614\pi\)
\(972\) −972.000 −0.0320750
\(973\) −6735.82 −0.221933
\(974\) −10555.3 −0.347241
\(975\) 3172.31 0.104200
\(976\) −8513.58 −0.279214
\(977\) −34111.6 −1.11702 −0.558509 0.829498i \(-0.688627\pi\)
−0.558509 + 0.829498i \(0.688627\pi\)
\(978\) 14999.0 0.490403
\(979\) 113.830 0.00371605
\(980\) −2026.68 −0.0660611
\(981\) 9480.33 0.308546
\(982\) −27790.6 −0.903088
\(983\) 5868.96 0.190428 0.0952139 0.995457i \(-0.469646\pi\)
0.0952139 + 0.995457i \(0.469646\pi\)
\(984\) 11234.7 0.363972
\(985\) −35999.6 −1.16451
\(986\) 62691.9 2.02487
\(987\) −9009.87 −0.290565
\(988\) −29117.5 −0.937603
\(989\) 11407.2 0.366764
\(990\) −80.5071 −0.00258453
\(991\) 50157.4 1.60777 0.803886 0.594784i \(-0.202762\pi\)
0.803886 + 0.594784i \(0.202762\pi\)
\(992\) 9567.77 0.306227
\(993\) −12849.7 −0.410647
\(994\) −7659.71 −0.244418
\(995\) −40007.9 −1.27471
\(996\) −3664.42 −0.116578
\(997\) −22486.2 −0.714289 −0.357145 0.934049i \(-0.616250\pi\)
−0.357145 + 0.934049i \(0.616250\pi\)
\(998\) −25652.3 −0.813638
\(999\) −6969.83 −0.220736
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.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.m.1.2 5 1.1 even 1 trivial