Properties

Label 966.4.a.m.1.3
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 1.3
Root \(-11.8868\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.32009 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.32009 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -2.64018 q^{10} +64.4402 q^{11} -12.0000 q^{12} +49.6970 q^{13} +14.0000 q^{14} -3.96026 q^{15} +16.0000 q^{16} +4.18938 q^{17} -18.0000 q^{18} +98.3525 q^{19} +5.28035 q^{20} +21.0000 q^{21} -128.880 q^{22} -23.0000 q^{23} +24.0000 q^{24} -123.257 q^{25} -99.3940 q^{26} -27.0000 q^{27} -28.0000 q^{28} +4.52857 q^{29} +7.92053 q^{30} +215.412 q^{31} -32.0000 q^{32} -193.321 q^{33} -8.37875 q^{34} -9.24062 q^{35} +36.0000 q^{36} -181.747 q^{37} -196.705 q^{38} -149.091 q^{39} -10.5607 q^{40} +48.0909 q^{41} -42.0000 q^{42} +58.4393 q^{43} +257.761 q^{44} +11.8808 q^{45} +46.0000 q^{46} -178.330 q^{47} -48.0000 q^{48} +49.0000 q^{49} +246.515 q^{50} -12.5681 q^{51} +198.788 q^{52} -54.2750 q^{53} +54.0000 q^{54} +85.0667 q^{55} +56.0000 q^{56} -295.057 q^{57} -9.05713 q^{58} +278.903 q^{59} -15.8411 q^{60} +151.982 q^{61} -430.825 q^{62} -63.0000 q^{63} +64.0000 q^{64} +65.6044 q^{65} +386.641 q^{66} -786.112 q^{67} +16.7575 q^{68} +69.0000 q^{69} +18.4812 q^{70} +788.157 q^{71} -72.0000 q^{72} +244.133 q^{73} +363.494 q^{74} +369.772 q^{75} +393.410 q^{76} -451.081 q^{77} +298.182 q^{78} -271.610 q^{79} +21.1214 q^{80} +81.0000 q^{81} -96.1818 q^{82} -557.327 q^{83} +84.0000 q^{84} +5.53035 q^{85} -116.879 q^{86} -13.5857 q^{87} -515.521 q^{88} -98.1740 q^{89} -23.7616 q^{90} -347.879 q^{91} -92.0000 q^{92} -646.237 q^{93} +356.659 q^{94} +129.834 q^{95} +96.0000 q^{96} -471.995 q^{97} -98.0000 q^{98} +579.962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 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
\(5\) 1.32009 0.118072 0.0590361 0.998256i \(-0.481197\pi\)
0.0590361 + 0.998256i \(0.481197\pi\)
\(6\) 6.00000 0.408248
\(7\) −7.00000 −0.377964
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) −2.64018 −0.0834897
\(11\) 64.4402 1.76631 0.883157 0.469078i \(-0.155414\pi\)
0.883157 + 0.469078i \(0.155414\pi\)
\(12\) −12.0000 −0.288675
\(13\) 49.6970 1.06027 0.530133 0.847914i \(-0.322142\pi\)
0.530133 + 0.847914i \(0.322142\pi\)
\(14\) 14.0000 0.267261
\(15\) −3.96026 −0.0681691
\(16\) 16.0000 0.250000
\(17\) 4.18938 0.0597690 0.0298845 0.999553i \(-0.490486\pi\)
0.0298845 + 0.999553i \(0.490486\pi\)
\(18\) −18.0000 −0.235702
\(19\) 98.3525 1.18756 0.593779 0.804628i \(-0.297635\pi\)
0.593779 + 0.804628i \(0.297635\pi\)
\(20\) 5.28035 0.0590361
\(21\) 21.0000 0.218218
\(22\) −128.880 −1.24897
\(23\) −23.0000 −0.208514
\(24\) 24.0000 0.204124
\(25\) −123.257 −0.986059
\(26\) −99.3940 −0.749721
\(27\) −27.0000 −0.192450
\(28\) −28.0000 −0.188982
\(29\) 4.52857 0.0289977 0.0144989 0.999895i \(-0.495385\pi\)
0.0144989 + 0.999895i \(0.495385\pi\)
\(30\) 7.92053 0.0482028
\(31\) 215.412 1.24804 0.624020 0.781409i \(-0.285499\pi\)
0.624020 + 0.781409i \(0.285499\pi\)
\(32\) −32.0000 −0.176777
\(33\) −193.321 −1.01978
\(34\) −8.37875 −0.0422631
\(35\) −9.24062 −0.0446271
\(36\) 36.0000 0.166667
\(37\) −181.747 −0.807542 −0.403771 0.914860i \(-0.632301\pi\)
−0.403771 + 0.914860i \(0.632301\pi\)
\(38\) −196.705 −0.839730
\(39\) −149.091 −0.612145
\(40\) −10.5607 −0.0417449
\(41\) 48.0909 0.183184 0.0915919 0.995797i \(-0.470804\pi\)
0.0915919 + 0.995797i \(0.470804\pi\)
\(42\) −42.0000 −0.154303
\(43\) 58.4393 0.207254 0.103627 0.994616i \(-0.466955\pi\)
0.103627 + 0.994616i \(0.466955\pi\)
\(44\) 257.761 0.883157
\(45\) 11.8808 0.0393574
\(46\) 46.0000 0.147442
\(47\) −178.330 −0.553448 −0.276724 0.960949i \(-0.589249\pi\)
−0.276724 + 0.960949i \(0.589249\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) 246.515 0.697249
\(51\) −12.5681 −0.0345076
\(52\) 198.788 0.530133
\(53\) −54.2750 −0.140665 −0.0703325 0.997524i \(-0.522406\pi\)
−0.0703325 + 0.997524i \(0.522406\pi\)
\(54\) 54.0000 0.136083
\(55\) 85.0667 0.208553
\(56\) 56.0000 0.133631
\(57\) −295.057 −0.685637
\(58\) −9.05713 −0.0205045
\(59\) 278.903 0.615426 0.307713 0.951479i \(-0.400436\pi\)
0.307713 + 0.951479i \(0.400436\pi\)
\(60\) −15.8411 −0.0340845
\(61\) 151.982 0.319005 0.159503 0.987197i \(-0.449011\pi\)
0.159503 + 0.987197i \(0.449011\pi\)
\(62\) −430.825 −0.882497
\(63\) −63.0000 −0.125988
\(64\) 64.0000 0.125000
\(65\) 65.6044 0.125188
\(66\) 386.641 0.721094
\(67\) −786.112 −1.43342 −0.716708 0.697373i \(-0.754352\pi\)
−0.716708 + 0.697373i \(0.754352\pi\)
\(68\) 16.7575 0.0298845
\(69\) 69.0000 0.120386
\(70\) 18.4812 0.0315561
\(71\) 788.157 1.31742 0.658711 0.752396i \(-0.271102\pi\)
0.658711 + 0.752396i \(0.271102\pi\)
\(72\) −72.0000 −0.117851
\(73\) 244.133 0.391420 0.195710 0.980662i \(-0.437299\pi\)
0.195710 + 0.980662i \(0.437299\pi\)
\(74\) 363.494 0.571018
\(75\) 369.772 0.569301
\(76\) 393.410 0.593779
\(77\) −451.081 −0.667604
\(78\) 298.182 0.432852
\(79\) −271.610 −0.386817 −0.193408 0.981118i \(-0.561954\pi\)
−0.193408 + 0.981118i \(0.561954\pi\)
\(80\) 21.1214 0.0295181
\(81\) 81.0000 0.111111
\(82\) −96.1818 −0.129531
\(83\) −557.327 −0.737043 −0.368521 0.929619i \(-0.620136\pi\)
−0.368521 + 0.929619i \(0.620136\pi\)
\(84\) 84.0000 0.109109
\(85\) 5.53035 0.00705706
\(86\) −116.879 −0.146550
\(87\) −13.5857 −0.0167418
\(88\) −515.521 −0.624486
\(89\) −98.1740 −0.116926 −0.0584630 0.998290i \(-0.518620\pi\)
−0.0584630 + 0.998290i \(0.518620\pi\)
\(90\) −23.7616 −0.0278299
\(91\) −347.879 −0.400743
\(92\) −92.0000 −0.104257
\(93\) −646.237 −0.720556
\(94\) 356.659 0.391347
\(95\) 129.834 0.140218
\(96\) 96.0000 0.102062
\(97\) −471.995 −0.494060 −0.247030 0.969008i \(-0.579455\pi\)
−0.247030 + 0.969008i \(0.579455\pi\)
\(98\) −98.0000 −0.101015
\(99\) 579.962 0.588771
\(100\) −493.029 −0.493029
\(101\) 573.054 0.564564 0.282282 0.959331i \(-0.408909\pi\)
0.282282 + 0.959331i \(0.408909\pi\)
\(102\) 25.1363 0.0244006
\(103\) −1020.62 −0.976352 −0.488176 0.872745i \(-0.662338\pi\)
−0.488176 + 0.872745i \(0.662338\pi\)
\(104\) −397.576 −0.374861
\(105\) 27.7219 0.0257655
\(106\) 108.550 0.0994652
\(107\) 767.973 0.693857 0.346929 0.937891i \(-0.387225\pi\)
0.346929 + 0.937891i \(0.387225\pi\)
\(108\) −108.000 −0.0962250
\(109\) −391.544 −0.344065 −0.172033 0.985091i \(-0.555033\pi\)
−0.172033 + 0.985091i \(0.555033\pi\)
\(110\) −170.133 −0.147469
\(111\) 545.241 0.466234
\(112\) −112.000 −0.0944911
\(113\) 1626.94 1.35442 0.677211 0.735789i \(-0.263188\pi\)
0.677211 + 0.735789i \(0.263188\pi\)
\(114\) 590.115 0.484819
\(115\) −30.3620 −0.0246198
\(116\) 18.1143 0.0144989
\(117\) 447.273 0.353422
\(118\) −557.807 −0.435172
\(119\) −29.3256 −0.0225906
\(120\) 31.6821 0.0241014
\(121\) 2821.54 2.11986
\(122\) −303.964 −0.225571
\(123\) −144.273 −0.105761
\(124\) 861.650 0.624020
\(125\) −327.722 −0.234498
\(126\) 126.000 0.0890871
\(127\) −109.756 −0.0766870 −0.0383435 0.999265i \(-0.512208\pi\)
−0.0383435 + 0.999265i \(0.512208\pi\)
\(128\) −128.000 −0.0883883
\(129\) −175.318 −0.119658
\(130\) −131.209 −0.0885213
\(131\) −940.188 −0.627058 −0.313529 0.949579i \(-0.601511\pi\)
−0.313529 + 0.949579i \(0.601511\pi\)
\(132\) −773.282 −0.509891
\(133\) −688.467 −0.448855
\(134\) 1572.22 1.01358
\(135\) −35.6424 −0.0227230
\(136\) −33.5150 −0.0211315
\(137\) 3072.89 1.91631 0.958156 0.286246i \(-0.0924073\pi\)
0.958156 + 0.286246i \(0.0924073\pi\)
\(138\) −138.000 −0.0851257
\(139\) −2424.58 −1.47950 −0.739748 0.672885i \(-0.765055\pi\)
−0.739748 + 0.672885i \(0.765055\pi\)
\(140\) −36.9625 −0.0223136
\(141\) 534.989 0.319533
\(142\) −1576.31 −0.931559
\(143\) 3202.48 1.87276
\(144\) 144.000 0.0833333
\(145\) 5.97810 0.00342382
\(146\) −488.267 −0.276776
\(147\) −147.000 −0.0824786
\(148\) −726.989 −0.403771
\(149\) 1085.32 0.596733 0.298367 0.954451i \(-0.403558\pi\)
0.298367 + 0.954451i \(0.403558\pi\)
\(150\) −739.544 −0.402557
\(151\) −457.345 −0.246478 −0.123239 0.992377i \(-0.539328\pi\)
−0.123239 + 0.992377i \(0.539328\pi\)
\(152\) −786.820 −0.419865
\(153\) 37.7044 0.0199230
\(154\) 902.163 0.472067
\(155\) 284.363 0.147359
\(156\) −596.364 −0.306073
\(157\) 2146.20 1.09099 0.545495 0.838114i \(-0.316342\pi\)
0.545495 + 0.838114i \(0.316342\pi\)
\(158\) 543.220 0.273521
\(159\) 162.825 0.0812130
\(160\) −42.2428 −0.0208724
\(161\) 161.000 0.0788110
\(162\) −162.000 −0.0785674
\(163\) 2029.78 0.975368 0.487684 0.873020i \(-0.337842\pi\)
0.487684 + 0.873020i \(0.337842\pi\)
\(164\) 192.364 0.0915919
\(165\) −255.200 −0.120408
\(166\) 1114.65 0.521168
\(167\) 2279.37 1.05619 0.528093 0.849186i \(-0.322907\pi\)
0.528093 + 0.849186i \(0.322907\pi\)
\(168\) −168.000 −0.0771517
\(169\) 272.790 0.124165
\(170\) −11.0607 −0.00499010
\(171\) 885.172 0.395853
\(172\) 233.757 0.103627
\(173\) 1755.72 0.771589 0.385794 0.922585i \(-0.373927\pi\)
0.385794 + 0.922585i \(0.373927\pi\)
\(174\) 27.1714 0.0118383
\(175\) 862.802 0.372695
\(176\) 1031.04 0.441578
\(177\) −836.710 −0.355316
\(178\) 196.348 0.0826792
\(179\) 3606.36 1.50588 0.752939 0.658091i \(-0.228636\pi\)
0.752939 + 0.658091i \(0.228636\pi\)
\(180\) 47.5232 0.0196787
\(181\) −799.117 −0.328165 −0.164083 0.986447i \(-0.552466\pi\)
−0.164083 + 0.986447i \(0.552466\pi\)
\(182\) 695.758 0.283368
\(183\) −455.947 −0.184178
\(184\) 184.000 0.0737210
\(185\) −239.922 −0.0953483
\(186\) 1292.47 0.509510
\(187\) 269.964 0.105571
\(188\) −713.318 −0.276724
\(189\) 189.000 0.0727393
\(190\) −259.668 −0.0991489
\(191\) 3519.29 1.33323 0.666616 0.745402i \(-0.267742\pi\)
0.666616 + 0.745402i \(0.267742\pi\)
\(192\) −192.000 −0.0721688
\(193\) 3430.06 1.27928 0.639640 0.768675i \(-0.279083\pi\)
0.639640 + 0.768675i \(0.279083\pi\)
\(194\) 943.990 0.349353
\(195\) −196.813 −0.0722774
\(196\) 196.000 0.0714286
\(197\) 3300.61 1.19370 0.596850 0.802353i \(-0.296419\pi\)
0.596850 + 0.802353i \(0.296419\pi\)
\(198\) −1159.92 −0.416324
\(199\) 2302.94 0.820356 0.410178 0.912005i \(-0.365467\pi\)
0.410178 + 0.912005i \(0.365467\pi\)
\(200\) 986.059 0.348624
\(201\) 2358.34 0.827583
\(202\) −1146.11 −0.399207
\(203\) −31.7000 −0.0109601
\(204\) −50.2725 −0.0172538
\(205\) 63.4842 0.0216289
\(206\) 2041.23 0.690385
\(207\) −207.000 −0.0695048
\(208\) 795.152 0.265067
\(209\) 6337.85 2.09760
\(210\) −55.4437 −0.0182189
\(211\) −1154.09 −0.376544 −0.188272 0.982117i \(-0.560289\pi\)
−0.188272 + 0.982117i \(0.560289\pi\)
\(212\) −217.100 −0.0703325
\(213\) −2364.47 −0.760614
\(214\) −1535.95 −0.490631
\(215\) 77.1450 0.0244709
\(216\) 216.000 0.0680414
\(217\) −1507.89 −0.471714
\(218\) 783.088 0.243291
\(219\) −732.400 −0.225986
\(220\) 340.267 0.104276
\(221\) 208.199 0.0633711
\(222\) −1090.48 −0.329678
\(223\) −1900.87 −0.570815 −0.285407 0.958406i \(-0.592129\pi\)
−0.285407 + 0.958406i \(0.592129\pi\)
\(224\) 224.000 0.0668153
\(225\) −1109.32 −0.328686
\(226\) −3253.88 −0.957721
\(227\) −4795.12 −1.40204 −0.701020 0.713142i \(-0.747272\pi\)
−0.701020 + 0.713142i \(0.747272\pi\)
\(228\) −1180.23 −0.342818
\(229\) 758.647 0.218920 0.109460 0.993991i \(-0.465088\pi\)
0.109460 + 0.993991i \(0.465088\pi\)
\(230\) 60.7241 0.0174088
\(231\) 1353.24 0.385441
\(232\) −36.2285 −0.0102522
\(233\) −275.301 −0.0774058 −0.0387029 0.999251i \(-0.512323\pi\)
−0.0387029 + 0.999251i \(0.512323\pi\)
\(234\) −894.546 −0.249907
\(235\) −235.411 −0.0653468
\(236\) 1115.61 0.307713
\(237\) 814.830 0.223329
\(238\) 58.6513 0.0159739
\(239\) −4853.13 −1.31348 −0.656742 0.754115i \(-0.728066\pi\)
−0.656742 + 0.754115i \(0.728066\pi\)
\(240\) −63.3642 −0.0170423
\(241\) −236.715 −0.0632703 −0.0316352 0.999499i \(-0.510071\pi\)
−0.0316352 + 0.999499i \(0.510071\pi\)
\(242\) −5643.07 −1.49897
\(243\) −243.000 −0.0641500
\(244\) 607.929 0.159503
\(245\) 64.6843 0.0168675
\(246\) 288.545 0.0747845
\(247\) 4887.82 1.25913
\(248\) −1723.30 −0.441248
\(249\) 1671.98 0.425532
\(250\) 655.443 0.165815
\(251\) 363.718 0.0914649 0.0457324 0.998954i \(-0.485438\pi\)
0.0457324 + 0.998954i \(0.485438\pi\)
\(252\) −252.000 −0.0629941
\(253\) −1482.12 −0.368302
\(254\) 219.511 0.0542259
\(255\) −16.5910 −0.00407440
\(256\) 256.000 0.0625000
\(257\) −6206.34 −1.50638 −0.753192 0.657800i \(-0.771487\pi\)
−0.753192 + 0.657800i \(0.771487\pi\)
\(258\) 350.636 0.0846109
\(259\) 1272.23 0.305222
\(260\) 262.418 0.0625940
\(261\) 40.7571 0.00966590
\(262\) 1880.38 0.443397
\(263\) −470.117 −0.110223 −0.0551115 0.998480i \(-0.517551\pi\)
−0.0551115 + 0.998480i \(0.517551\pi\)
\(264\) 1546.56 0.360547
\(265\) −71.6478 −0.0166086
\(266\) 1376.93 0.317388
\(267\) 294.522 0.0675073
\(268\) −3144.45 −0.716708
\(269\) 539.902 0.122373 0.0611866 0.998126i \(-0.480512\pi\)
0.0611866 + 0.998126i \(0.480512\pi\)
\(270\) 71.2848 0.0160676
\(271\) 6303.85 1.41303 0.706516 0.707697i \(-0.250266\pi\)
0.706516 + 0.707697i \(0.250266\pi\)
\(272\) 67.0300 0.0149422
\(273\) 1043.64 0.231369
\(274\) −6145.78 −1.35504
\(275\) −7942.73 −1.74169
\(276\) 276.000 0.0601929
\(277\) −2631.75 −0.570854 −0.285427 0.958401i \(-0.592135\pi\)
−0.285427 + 0.958401i \(0.592135\pi\)
\(278\) 4849.15 1.04616
\(279\) 1938.71 0.416013
\(280\) 73.9249 0.0157781
\(281\) 7037.97 1.49413 0.747064 0.664752i \(-0.231463\pi\)
0.747064 + 0.664752i \(0.231463\pi\)
\(282\) −1069.98 −0.225944
\(283\) 845.902 0.177681 0.0888404 0.996046i \(-0.471684\pi\)
0.0888404 + 0.996046i \(0.471684\pi\)
\(284\) 3152.63 0.658711
\(285\) −389.502 −0.0809547
\(286\) −6404.96 −1.32424
\(287\) −336.636 −0.0692370
\(288\) −288.000 −0.0589256
\(289\) −4895.45 −0.996428
\(290\) −11.9562 −0.00242101
\(291\) 1415.98 0.285246
\(292\) 976.533 0.195710
\(293\) 4035.41 0.804612 0.402306 0.915505i \(-0.368209\pi\)
0.402306 + 0.915505i \(0.368209\pi\)
\(294\) 294.000 0.0583212
\(295\) 368.177 0.0726647
\(296\) 1453.98 0.285509
\(297\) −1739.88 −0.339927
\(298\) −2170.65 −0.421954
\(299\) −1143.03 −0.221081
\(300\) 1479.09 0.284651
\(301\) −409.075 −0.0783345
\(302\) 914.690 0.174286
\(303\) −1719.16 −0.325951
\(304\) 1573.64 0.296890
\(305\) 200.630 0.0376657
\(306\) −75.4088 −0.0140877
\(307\) −8115.36 −1.50869 −0.754345 0.656478i \(-0.772046\pi\)
−0.754345 + 0.656478i \(0.772046\pi\)
\(308\) −1804.33 −0.333802
\(309\) 3061.85 0.563697
\(310\) −568.727 −0.104198
\(311\) −3967.19 −0.723340 −0.361670 0.932306i \(-0.617793\pi\)
−0.361670 + 0.932306i \(0.617793\pi\)
\(312\) 1192.73 0.216426
\(313\) 3727.82 0.673192 0.336596 0.941649i \(-0.390724\pi\)
0.336596 + 0.941649i \(0.390724\pi\)
\(314\) −4292.40 −0.771446
\(315\) −83.1656 −0.0148757
\(316\) −1086.44 −0.193408
\(317\) 3634.46 0.643948 0.321974 0.946749i \(-0.395654\pi\)
0.321974 + 0.946749i \(0.395654\pi\)
\(318\) −325.650 −0.0574263
\(319\) 291.822 0.0512190
\(320\) 84.4856 0.0147590
\(321\) −2303.92 −0.400599
\(322\) −322.000 −0.0557278
\(323\) 412.035 0.0709792
\(324\) 324.000 0.0555556
\(325\) −6125.52 −1.04549
\(326\) −4059.57 −0.689689
\(327\) 1174.63 0.198646
\(328\) −384.727 −0.0647653
\(329\) 1248.31 0.209184
\(330\) 510.400 0.0851413
\(331\) 6897.03 1.14530 0.572651 0.819799i \(-0.305915\pi\)
0.572651 + 0.819799i \(0.305915\pi\)
\(332\) −2229.31 −0.368521
\(333\) −1635.72 −0.269181
\(334\) −4558.75 −0.746837
\(335\) −1037.74 −0.169247
\(336\) 336.000 0.0545545
\(337\) 4212.94 0.680990 0.340495 0.940246i \(-0.389405\pi\)
0.340495 + 0.940246i \(0.389405\pi\)
\(338\) −545.579 −0.0877976
\(339\) −4880.82 −0.781976
\(340\) 22.1214 0.00352853
\(341\) 13881.2 2.20443
\(342\) −1770.34 −0.279910
\(343\) −343.000 −0.0539949
\(344\) −467.514 −0.0732752
\(345\) 91.0861 0.0142142
\(346\) −3511.44 −0.545595
\(347\) −7267.35 −1.12430 −0.562150 0.827035i \(-0.690026\pi\)
−0.562150 + 0.827035i \(0.690026\pi\)
\(348\) −54.3428 −0.00837092
\(349\) −10426.0 −1.59911 −0.799555 0.600592i \(-0.794932\pi\)
−0.799555 + 0.600592i \(0.794932\pi\)
\(350\) −1725.60 −0.263535
\(351\) −1341.82 −0.204048
\(352\) −2062.09 −0.312243
\(353\) 11400.4 1.71893 0.859465 0.511194i \(-0.170797\pi\)
0.859465 + 0.511194i \(0.170797\pi\)
\(354\) 1673.42 0.251246
\(355\) 1040.44 0.155551
\(356\) −392.696 −0.0584630
\(357\) 87.9769 0.0130427
\(358\) −7212.72 −1.06482
\(359\) 4721.56 0.694135 0.347067 0.937840i \(-0.387178\pi\)
0.347067 + 0.937840i \(0.387178\pi\)
\(360\) −95.0463 −0.0139150
\(361\) 2814.21 0.410294
\(362\) 1598.23 0.232048
\(363\) −8464.61 −1.22390
\(364\) −1391.52 −0.200371
\(365\) 322.277 0.0462158
\(366\) 911.893 0.130233
\(367\) −4227.00 −0.601220 −0.300610 0.953747i \(-0.597190\pi\)
−0.300610 + 0.953747i \(0.597190\pi\)
\(368\) −368.000 −0.0521286
\(369\) 432.818 0.0610613
\(370\) 479.844 0.0674214
\(371\) 379.925 0.0531664
\(372\) −2584.95 −0.360278
\(373\) −4755.63 −0.660154 −0.330077 0.943954i \(-0.607075\pi\)
−0.330077 + 0.943954i \(0.607075\pi\)
\(374\) −539.928 −0.0746498
\(375\) 983.165 0.135388
\(376\) 1426.64 0.195673
\(377\) 225.056 0.0307453
\(378\) −378.000 −0.0514344
\(379\) −4677.74 −0.633983 −0.316992 0.948428i \(-0.602673\pi\)
−0.316992 + 0.948428i \(0.602673\pi\)
\(380\) 519.336 0.0701088
\(381\) 329.267 0.0442752
\(382\) −7038.59 −0.942737
\(383\) 11024.4 1.47082 0.735408 0.677625i \(-0.236991\pi\)
0.735408 + 0.677625i \(0.236991\pi\)
\(384\) 384.000 0.0510310
\(385\) −595.467 −0.0788255
\(386\) −6860.12 −0.904588
\(387\) 525.953 0.0690845
\(388\) −1887.98 −0.247030
\(389\) 8450.89 1.10148 0.550742 0.834676i \(-0.314345\pi\)
0.550742 + 0.834676i \(0.314345\pi\)
\(390\) 393.626 0.0511078
\(391\) −96.3557 −0.0124627
\(392\) −392.000 −0.0505076
\(393\) 2820.56 0.362032
\(394\) −6601.22 −0.844073
\(395\) −358.549 −0.0456723
\(396\) 2319.85 0.294386
\(397\) −2871.53 −0.363017 −0.181509 0.983389i \(-0.558098\pi\)
−0.181509 + 0.983389i \(0.558098\pi\)
\(398\) −4605.87 −0.580079
\(399\) 2065.40 0.259146
\(400\) −1972.12 −0.246515
\(401\) −8506.36 −1.05932 −0.529660 0.848210i \(-0.677681\pi\)
−0.529660 + 0.848210i \(0.677681\pi\)
\(402\) −4716.67 −0.585190
\(403\) 10705.3 1.32325
\(404\) 2292.21 0.282282
\(405\) 106.927 0.0131191
\(406\) 63.3999 0.00774996
\(407\) −11711.8 −1.42637
\(408\) 100.545 0.0122003
\(409\) 10411.5 1.25872 0.629359 0.777115i \(-0.283318\pi\)
0.629359 + 0.777115i \(0.283318\pi\)
\(410\) −126.968 −0.0152940
\(411\) −9218.67 −1.10638
\(412\) −4082.46 −0.488176
\(413\) −1952.32 −0.232609
\(414\) 414.000 0.0491473
\(415\) −735.720 −0.0870243
\(416\) −1590.30 −0.187430
\(417\) 7273.73 0.854187
\(418\) −12675.7 −1.48323
\(419\) −7981.20 −0.930566 −0.465283 0.885162i \(-0.654047\pi\)
−0.465283 + 0.885162i \(0.654047\pi\)
\(420\) 110.887 0.0128827
\(421\) 9347.17 1.08207 0.541037 0.840999i \(-0.318032\pi\)
0.541037 + 0.840999i \(0.318032\pi\)
\(422\) 2308.18 0.266257
\(423\) −1604.97 −0.184483
\(424\) 434.200 0.0497326
\(425\) −516.371 −0.0589358
\(426\) 4728.94 0.537836
\(427\) −1063.88 −0.120573
\(428\) 3071.89 0.346929
\(429\) −9607.45 −1.08124
\(430\) −154.290 −0.0173035
\(431\) −58.4868 −0.00653645 −0.00326822 0.999995i \(-0.501040\pi\)
−0.00326822 + 0.999995i \(0.501040\pi\)
\(432\) −432.000 −0.0481125
\(433\) −10719.3 −1.18969 −0.594844 0.803841i \(-0.702786\pi\)
−0.594844 + 0.803841i \(0.702786\pi\)
\(434\) 3015.77 0.333552
\(435\) −17.9343 −0.00197675
\(436\) −1566.18 −0.172033
\(437\) −2262.11 −0.247623
\(438\) 1464.80 0.159796
\(439\) −6982.84 −0.759163 −0.379582 0.925158i \(-0.623932\pi\)
−0.379582 + 0.925158i \(0.623932\pi\)
\(440\) −680.534 −0.0737345
\(441\) 441.000 0.0476190
\(442\) −416.399 −0.0448101
\(443\) −1339.35 −0.143644 −0.0718222 0.997417i \(-0.522881\pi\)
−0.0718222 + 0.997417i \(0.522881\pi\)
\(444\) 2180.97 0.233117
\(445\) −129.598 −0.0138057
\(446\) 3801.74 0.403627
\(447\) −3255.97 −0.344524
\(448\) −448.000 −0.0472456
\(449\) 6645.51 0.698488 0.349244 0.937032i \(-0.386438\pi\)
0.349244 + 0.937032i \(0.386438\pi\)
\(450\) 2218.63 0.232416
\(451\) 3098.99 0.323560
\(452\) 6507.76 0.677211
\(453\) 1372.03 0.142304
\(454\) 9590.23 0.991392
\(455\) −459.231 −0.0473166
\(456\) 2360.46 0.242409
\(457\) −10413.9 −1.06596 −0.532979 0.846128i \(-0.678928\pi\)
−0.532979 + 0.846128i \(0.678928\pi\)
\(458\) −1517.29 −0.154800
\(459\) −113.113 −0.0115025
\(460\) −121.448 −0.0123099
\(461\) −11343.1 −1.14599 −0.572994 0.819560i \(-0.694218\pi\)
−0.572994 + 0.819560i \(0.694218\pi\)
\(462\) −2706.49 −0.272548
\(463\) −11385.2 −1.14280 −0.571399 0.820673i \(-0.693599\pi\)
−0.571399 + 0.820673i \(0.693599\pi\)
\(464\) 72.4570 0.00724943
\(465\) −853.090 −0.0850776
\(466\) 550.602 0.0547342
\(467\) 5768.99 0.571643 0.285821 0.958283i \(-0.407734\pi\)
0.285821 + 0.958283i \(0.407734\pi\)
\(468\) 1789.09 0.176711
\(469\) 5502.78 0.541780
\(470\) 470.822 0.0462072
\(471\) −6438.60 −0.629883
\(472\) −2231.23 −0.217586
\(473\) 3765.84 0.366075
\(474\) −1629.66 −0.157917
\(475\) −12122.7 −1.17100
\(476\) −117.303 −0.0112953
\(477\) −488.475 −0.0468884
\(478\) 9706.25 0.928773
\(479\) 7271.68 0.693636 0.346818 0.937932i \(-0.387262\pi\)
0.346818 + 0.937932i \(0.387262\pi\)
\(480\) 126.728 0.0120507
\(481\) −9032.28 −0.856209
\(482\) 473.430 0.0447389
\(483\) −483.000 −0.0455016
\(484\) 11286.1 1.05993
\(485\) −623.075 −0.0583348
\(486\) 486.000 0.0453609
\(487\) 19893.5 1.85105 0.925525 0.378686i \(-0.123624\pi\)
0.925525 + 0.378686i \(0.123624\pi\)
\(488\) −1215.86 −0.112785
\(489\) −6089.35 −0.563129
\(490\) −129.369 −0.0119271
\(491\) −16272.8 −1.49568 −0.747840 0.663879i \(-0.768909\pi\)
−0.747840 + 0.663879i \(0.768909\pi\)
\(492\) −577.091 −0.0528806
\(493\) 18.9719 0.00173316
\(494\) −9775.64 −0.890338
\(495\) 765.600 0.0695175
\(496\) 3446.60 0.312010
\(497\) −5517.10 −0.497939
\(498\) −3343.96 −0.300896
\(499\) 3349.75 0.300512 0.150256 0.988647i \(-0.451990\pi\)
0.150256 + 0.988647i \(0.451990\pi\)
\(500\) −1310.89 −0.117249
\(501\) −6838.12 −0.609790
\(502\) −727.436 −0.0646754
\(503\) −5070.47 −0.449466 −0.224733 0.974420i \(-0.572151\pi\)
−0.224733 + 0.974420i \(0.572151\pi\)
\(504\) 504.000 0.0445435
\(505\) 756.481 0.0666593
\(506\) 2964.25 0.260429
\(507\) −818.369 −0.0716864
\(508\) −439.023 −0.0383435
\(509\) 5396.50 0.469933 0.234966 0.972004i \(-0.424502\pi\)
0.234966 + 0.972004i \(0.424502\pi\)
\(510\) 33.1821 0.00288103
\(511\) −1708.93 −0.147943
\(512\) −512.000 −0.0441942
\(513\) −2655.52 −0.228546
\(514\) 12412.7 1.06517
\(515\) −1347.30 −0.115280
\(516\) −701.271 −0.0598290
\(517\) −11491.6 −0.977562
\(518\) −2544.46 −0.215825
\(519\) −5267.16 −0.445477
\(520\) −524.835 −0.0442607
\(521\) −1966.79 −0.165387 −0.0826937 0.996575i \(-0.526352\pi\)
−0.0826937 + 0.996575i \(0.526352\pi\)
\(522\) −81.5142 −0.00683482
\(523\) −10824.3 −0.904997 −0.452498 0.891765i \(-0.649467\pi\)
−0.452498 + 0.891765i \(0.649467\pi\)
\(524\) −3760.75 −0.313529
\(525\) −2588.40 −0.215176
\(526\) 940.234 0.0779394
\(527\) 902.444 0.0745940
\(528\) −3093.13 −0.254945
\(529\) 529.000 0.0434783
\(530\) 143.296 0.0117441
\(531\) 2510.13 0.205142
\(532\) −2753.87 −0.224427
\(533\) 2389.97 0.194224
\(534\) −589.044 −0.0477349
\(535\) 1013.79 0.0819253
\(536\) 6288.90 0.506789
\(537\) −10819.1 −0.869419
\(538\) −1079.80 −0.0865310
\(539\) 3157.57 0.252330
\(540\) −142.570 −0.0113615
\(541\) 20837.7 1.65598 0.827988 0.560746i \(-0.189485\pi\)
0.827988 + 0.560746i \(0.189485\pi\)
\(542\) −12607.7 −0.999164
\(543\) 2397.35 0.189466
\(544\) −134.060 −0.0105658
\(545\) −516.873 −0.0406246
\(546\) −2087.27 −0.163603
\(547\) −3961.09 −0.309623 −0.154812 0.987944i \(-0.549477\pi\)
−0.154812 + 0.987944i \(0.549477\pi\)
\(548\) 12291.6 0.958156
\(549\) 1367.84 0.106335
\(550\) 15885.5 1.23156
\(551\) 445.396 0.0344365
\(552\) −552.000 −0.0425628
\(553\) 1901.27 0.146203
\(554\) 5263.50 0.403654
\(555\) 719.767 0.0550494
\(556\) −9698.30 −0.739748
\(557\) 23969.4 1.82337 0.911684 0.410892i \(-0.134783\pi\)
0.911684 + 0.410892i \(0.134783\pi\)
\(558\) −3877.42 −0.294166
\(559\) 2904.25 0.219744
\(560\) −147.850 −0.0111568
\(561\) −809.893 −0.0609513
\(562\) −14075.9 −1.05651
\(563\) 18626.2 1.39432 0.697158 0.716917i \(-0.254447\pi\)
0.697158 + 0.716917i \(0.254447\pi\)
\(564\) 2139.96 0.159767
\(565\) 2147.71 0.159920
\(566\) −1691.80 −0.125639
\(567\) −567.000 −0.0419961
\(568\) −6305.26 −0.465779
\(569\) −12481.6 −0.919604 −0.459802 0.888022i \(-0.652080\pi\)
−0.459802 + 0.888022i \(0.652080\pi\)
\(570\) 779.004 0.0572436
\(571\) −1957.23 −0.143446 −0.0717229 0.997425i \(-0.522850\pi\)
−0.0717229 + 0.997425i \(0.522850\pi\)
\(572\) 12809.9 0.936381
\(573\) −10557.9 −0.769741
\(574\) 673.273 0.0489580
\(575\) 2834.92 0.205608
\(576\) 576.000 0.0416667
\(577\) 1351.24 0.0974916 0.0487458 0.998811i \(-0.484478\pi\)
0.0487458 + 0.998811i \(0.484478\pi\)
\(578\) 9790.90 0.704581
\(579\) −10290.2 −0.738593
\(580\) 23.9124 0.00171191
\(581\) 3901.29 0.278576
\(582\) −2831.97 −0.201699
\(583\) −3497.49 −0.248459
\(584\) −1953.07 −0.138388
\(585\) 590.440 0.0417293
\(586\) −8070.83 −0.568947
\(587\) −7715.19 −0.542487 −0.271244 0.962511i \(-0.587435\pi\)
−0.271244 + 0.962511i \(0.587435\pi\)
\(588\) −588.000 −0.0412393
\(589\) 21186.3 1.48212
\(590\) −736.354 −0.0513817
\(591\) −9901.83 −0.689183
\(592\) −2907.95 −0.201885
\(593\) −4037.63 −0.279605 −0.139802 0.990179i \(-0.544647\pi\)
−0.139802 + 0.990179i \(0.544647\pi\)
\(594\) 3479.77 0.240365
\(595\) −38.7124 −0.00266732
\(596\) 4341.30 0.298367
\(597\) −6908.81 −0.473633
\(598\) 2286.06 0.156328
\(599\) 9342.69 0.637282 0.318641 0.947875i \(-0.396774\pi\)
0.318641 + 0.947875i \(0.396774\pi\)
\(600\) −2958.18 −0.201278
\(601\) −16985.7 −1.15284 −0.576422 0.817152i \(-0.695552\pi\)
−0.576422 + 0.817152i \(0.695552\pi\)
\(602\) 818.150 0.0553909
\(603\) −7075.01 −0.477805
\(604\) −1829.38 −0.123239
\(605\) 3724.68 0.250297
\(606\) 3438.32 0.230482
\(607\) 25384.2 1.69739 0.848693 0.528885i \(-0.177390\pi\)
0.848693 + 0.528885i \(0.177390\pi\)
\(608\) −3147.28 −0.209933
\(609\) 95.0999 0.00632782
\(610\) −401.260 −0.0266337
\(611\) −8862.44 −0.586802
\(612\) 150.818 0.00996150
\(613\) −2266.44 −0.149332 −0.0746661 0.997209i \(-0.523789\pi\)
−0.0746661 + 0.997209i \(0.523789\pi\)
\(614\) 16230.7 1.06681
\(615\) −190.453 −0.0124875
\(616\) 3608.65 0.236034
\(617\) −1099.45 −0.0717378 −0.0358689 0.999357i \(-0.511420\pi\)
−0.0358689 + 0.999357i \(0.511420\pi\)
\(618\) −6123.70 −0.398594
\(619\) −2805.62 −0.182177 −0.0910883 0.995843i \(-0.529035\pi\)
−0.0910883 + 0.995843i \(0.529035\pi\)
\(620\) 1137.45 0.0736794
\(621\) 621.000 0.0401286
\(622\) 7934.38 0.511478
\(623\) 687.218 0.0441939
\(624\) −2385.45 −0.153036
\(625\) 14974.5 0.958371
\(626\) −7455.64 −0.476018
\(627\) −19013.6 −1.21105
\(628\) 8584.80 0.545495
\(629\) −761.407 −0.0482660
\(630\) 166.331 0.0105187
\(631\) 185.699 0.0117156 0.00585780 0.999983i \(-0.498135\pi\)
0.00585780 + 0.999983i \(0.498135\pi\)
\(632\) 2172.88 0.136760
\(633\) 3462.27 0.217398
\(634\) −7268.92 −0.455340
\(635\) −144.887 −0.00905461
\(636\) 651.300 0.0406065
\(637\) 2435.15 0.151467
\(638\) −583.643 −0.0362173
\(639\) 7093.41 0.439141
\(640\) −168.971 −0.0104362
\(641\) 16123.9 0.993532 0.496766 0.867885i \(-0.334521\pi\)
0.496766 + 0.867885i \(0.334521\pi\)
\(642\) 4607.84 0.283266
\(643\) −1837.05 −0.112669 −0.0563345 0.998412i \(-0.517941\pi\)
−0.0563345 + 0.998412i \(0.517941\pi\)
\(644\) 644.000 0.0394055
\(645\) −231.435 −0.0141283
\(646\) −824.071 −0.0501898
\(647\) 3630.22 0.220585 0.110293 0.993899i \(-0.464821\pi\)
0.110293 + 0.993899i \(0.464821\pi\)
\(648\) −648.000 −0.0392837
\(649\) 17972.6 1.08703
\(650\) 12251.0 0.739270
\(651\) 4523.66 0.272344
\(652\) 8119.14 0.487684
\(653\) 4925.91 0.295200 0.147600 0.989047i \(-0.452845\pi\)
0.147600 + 0.989047i \(0.452845\pi\)
\(654\) −2349.26 −0.140464
\(655\) −1241.13 −0.0740382
\(656\) 769.455 0.0457960
\(657\) 2197.20 0.130473
\(658\) −2496.61 −0.147915
\(659\) −13887.7 −0.820924 −0.410462 0.911878i \(-0.634633\pi\)
−0.410462 + 0.911878i \(0.634633\pi\)
\(660\) −1020.80 −0.0602040
\(661\) −8936.52 −0.525855 −0.262928 0.964816i \(-0.584688\pi\)
−0.262928 + 0.964816i \(0.584688\pi\)
\(662\) −13794.1 −0.809851
\(663\) −624.598 −0.0365873
\(664\) 4458.61 0.260584
\(665\) −908.837 −0.0529973
\(666\) 3271.45 0.190339
\(667\) −104.157 −0.00604644
\(668\) 9117.49 0.528093
\(669\) 5702.61 0.329560
\(670\) 2075.47 0.119675
\(671\) 9793.76 0.563463
\(672\) −672.000 −0.0385758
\(673\) −3717.03 −0.212899 −0.106449 0.994318i \(-0.533948\pi\)
−0.106449 + 0.994318i \(0.533948\pi\)
\(674\) −8425.88 −0.481532
\(675\) 3327.95 0.189767
\(676\) 1091.16 0.0620823
\(677\) −22961.7 −1.30353 −0.651764 0.758422i \(-0.725971\pi\)
−0.651764 + 0.758422i \(0.725971\pi\)
\(678\) 9761.65 0.552941
\(679\) 3303.96 0.186737
\(680\) −44.2428 −0.00249505
\(681\) 14385.3 0.809468
\(682\) −27762.4 −1.55877
\(683\) −15542.6 −0.870748 −0.435374 0.900250i \(-0.643384\pi\)
−0.435374 + 0.900250i \(0.643384\pi\)
\(684\) 3540.69 0.197926
\(685\) 4056.49 0.226263
\(686\) 686.000 0.0381802
\(687\) −2275.94 −0.126394
\(688\) 935.028 0.0518134
\(689\) −2697.30 −0.149142
\(690\) −182.172 −0.0100510
\(691\) 2140.29 0.117830 0.0589151 0.998263i \(-0.481236\pi\)
0.0589151 + 0.998263i \(0.481236\pi\)
\(692\) 7022.87 0.385794
\(693\) −4059.73 −0.222535
\(694\) 14534.7 0.795000
\(695\) −3200.65 −0.174687
\(696\) 108.686 0.00591913
\(697\) 201.471 0.0109487
\(698\) 20852.0 1.13074
\(699\) 825.902 0.0446903
\(700\) 3451.21 0.186348
\(701\) 10755.5 0.579502 0.289751 0.957102i \(-0.406427\pi\)
0.289751 + 0.957102i \(0.406427\pi\)
\(702\) 2683.64 0.144284
\(703\) −17875.3 −0.959003
\(704\) 4124.17 0.220789
\(705\) 706.232 0.0377280
\(706\) −22800.8 −1.21547
\(707\) −4011.37 −0.213385
\(708\) −3346.84 −0.177658
\(709\) −27548.4 −1.45924 −0.729622 0.683851i \(-0.760304\pi\)
−0.729622 + 0.683851i \(0.760304\pi\)
\(710\) −2080.87 −0.109991
\(711\) −2444.49 −0.128939
\(712\) 785.392 0.0413396
\(713\) −4954.49 −0.260234
\(714\) −175.954 −0.00922256
\(715\) 4227.56 0.221121
\(716\) 14425.4 0.752939
\(717\) 14559.4 0.758340
\(718\) −9443.12 −0.490827
\(719\) 884.291 0.0458672 0.0229336 0.999737i \(-0.492699\pi\)
0.0229336 + 0.999737i \(0.492699\pi\)
\(720\) 190.093 0.00983936
\(721\) 7144.31 0.369027
\(722\) −5628.42 −0.290122
\(723\) 710.145 0.0365291
\(724\) −3196.47 −0.164083
\(725\) −558.179 −0.0285934
\(726\) 16929.2 0.865430
\(727\) −4136.68 −0.211033 −0.105516 0.994418i \(-0.533650\pi\)
−0.105516 + 0.994418i \(0.533650\pi\)
\(728\) 2783.03 0.141684
\(729\) 729.000 0.0370370
\(730\) −644.555 −0.0326795
\(731\) 244.824 0.0123873
\(732\) −1823.79 −0.0920889
\(733\) 18081.7 0.911137 0.455568 0.890201i \(-0.349436\pi\)
0.455568 + 0.890201i \(0.349436\pi\)
\(734\) 8454.01 0.425127
\(735\) −194.053 −0.00973844
\(736\) 736.000 0.0368605
\(737\) −50657.2 −2.53186
\(738\) −865.636 −0.0431769
\(739\) 21757.2 1.08302 0.541509 0.840695i \(-0.317853\pi\)
0.541509 + 0.840695i \(0.317853\pi\)
\(740\) −959.689 −0.0476741
\(741\) −14663.5 −0.726958
\(742\) −759.850 −0.0375943
\(743\) −29549.5 −1.45904 −0.729520 0.683959i \(-0.760257\pi\)
−0.729520 + 0.683959i \(0.760257\pi\)
\(744\) 5169.90 0.254755
\(745\) 1432.72 0.0704577
\(746\) 9511.26 0.466799
\(747\) −5015.94 −0.245681
\(748\) 1079.86 0.0527854
\(749\) −5375.81 −0.262253
\(750\) −1966.33 −0.0957336
\(751\) −12046.1 −0.585309 −0.292655 0.956218i \(-0.594539\pi\)
−0.292655 + 0.956218i \(0.594539\pi\)
\(752\) −2853.27 −0.138362
\(753\) −1091.15 −0.0528073
\(754\) −450.112 −0.0217402
\(755\) −603.736 −0.0291022
\(756\) 756.000 0.0363696
\(757\) 10608.7 0.509352 0.254676 0.967026i \(-0.418031\pi\)
0.254676 + 0.967026i \(0.418031\pi\)
\(758\) 9355.49 0.448294
\(759\) 4446.37 0.212639
\(760\) −1038.67 −0.0495744
\(761\) 36246.3 1.72658 0.863290 0.504708i \(-0.168400\pi\)
0.863290 + 0.504708i \(0.168400\pi\)
\(762\) −658.534 −0.0313073
\(763\) 2740.81 0.130044
\(764\) 14077.2 0.666616
\(765\) 49.7731 0.00235235
\(766\) −22048.9 −1.04002
\(767\) 13860.6 0.652515
\(768\) −768.000 −0.0360844
\(769\) 11694.1 0.548373 0.274187 0.961676i \(-0.411591\pi\)
0.274187 + 0.961676i \(0.411591\pi\)
\(770\) 1190.93 0.0557380
\(771\) 18619.0 0.869712
\(772\) 13720.2 0.639640
\(773\) 23735.6 1.10441 0.552206 0.833708i \(-0.313786\pi\)
0.552206 + 0.833708i \(0.313786\pi\)
\(774\) −1051.91 −0.0488501
\(775\) −26551.2 −1.23064
\(776\) 3775.96 0.174677
\(777\) −3816.69 −0.176220
\(778\) −16901.8 −0.778867
\(779\) 4729.86 0.217542
\(780\) −787.253 −0.0361387
\(781\) 50789.0 2.32698
\(782\) 192.711 0.00881246
\(783\) −122.271 −0.00558061
\(784\) 784.000 0.0357143
\(785\) 2833.17 0.128816
\(786\) −5641.13 −0.255995
\(787\) 15529.4 0.703385 0.351693 0.936116i \(-0.385606\pi\)
0.351693 + 0.936116i \(0.385606\pi\)
\(788\) 13202.4 0.596850
\(789\) 1410.35 0.0636373
\(790\) 717.098 0.0322952
\(791\) −11388.6 −0.511924
\(792\) −4639.69 −0.208162
\(793\) 7553.06 0.338231
\(794\) 5743.06 0.256692
\(795\) 214.943 0.00958901
\(796\) 9211.75 0.410178
\(797\) −1741.11 −0.0773816 −0.0386908 0.999251i \(-0.512319\pi\)
−0.0386908 + 0.999251i \(0.512319\pi\)
\(798\) −4130.80 −0.183244
\(799\) −747.090 −0.0330790
\(800\) 3944.24 0.174312
\(801\) −883.566 −0.0389754
\(802\) 17012.7 0.749052
\(803\) 15732.0 0.691370
\(804\) 9433.34 0.413792
\(805\) 212.534 0.00930540
\(806\) −21410.7 −0.935682
\(807\) −1619.71 −0.0706522
\(808\) −4584.43 −0.199604
\(809\) 21360.3 0.928292 0.464146 0.885759i \(-0.346361\pi\)
0.464146 + 0.885759i \(0.346361\pi\)
\(810\) −213.854 −0.00927663
\(811\) 15318.2 0.663249 0.331624 0.943411i \(-0.392403\pi\)
0.331624 + 0.943411i \(0.392403\pi\)
\(812\) −126.800 −0.00548005
\(813\) −18911.6 −0.815814
\(814\) 23423.6 1.00860
\(815\) 2679.49 0.115164
\(816\) −201.090 −0.00862691
\(817\) 5747.65 0.246126
\(818\) −20823.0 −0.890048
\(819\) −3130.91 −0.133581
\(820\) 253.937 0.0108145
\(821\) 8133.72 0.345760 0.172880 0.984943i \(-0.444693\pi\)
0.172880 + 0.984943i \(0.444693\pi\)
\(822\) 18437.3 0.782331
\(823\) 6099.29 0.258333 0.129166 0.991623i \(-0.458770\pi\)
0.129166 + 0.991623i \(0.458770\pi\)
\(824\) 8164.93 0.345193
\(825\) 23828.2 1.00556
\(826\) 3904.65 0.164479
\(827\) 3831.74 0.161116 0.0805579 0.996750i \(-0.474330\pi\)
0.0805579 + 0.996750i \(0.474330\pi\)
\(828\) −828.000 −0.0347524
\(829\) −32721.0 −1.37087 −0.685434 0.728135i \(-0.740387\pi\)
−0.685434 + 0.728135i \(0.740387\pi\)
\(830\) 1471.44 0.0615355
\(831\) 7895.25 0.329582
\(832\) 3180.61 0.132533
\(833\) 205.279 0.00853843
\(834\) −14547.5 −0.604001
\(835\) 3008.97 0.124706
\(836\) 25351.4 1.04880
\(837\) −5816.14 −0.240185
\(838\) 15962.4 0.658010
\(839\) 16329.1 0.671923 0.335962 0.941876i \(-0.390939\pi\)
0.335962 + 0.941876i \(0.390939\pi\)
\(840\) −221.775 −0.00910947
\(841\) −24368.5 −0.999159
\(842\) −18694.3 −0.765142
\(843\) −21113.9 −0.862635
\(844\) −4616.36 −0.188272
\(845\) 360.106 0.0146604
\(846\) 3209.93 0.130449
\(847\) −19750.8 −0.801233
\(848\) −868.400 −0.0351663
\(849\) −2537.71 −0.102584
\(850\) 1032.74 0.0416739
\(851\) 4180.18 0.168384
\(852\) −9457.88 −0.380307
\(853\) 2202.40 0.0884041 0.0442020 0.999023i \(-0.485925\pi\)
0.0442020 + 0.999023i \(0.485925\pi\)
\(854\) 2127.75 0.0852578
\(855\) 1168.51 0.0467392
\(856\) −6143.78 −0.245316
\(857\) −37826.0 −1.50771 −0.753857 0.657038i \(-0.771809\pi\)
−0.753857 + 0.657038i \(0.771809\pi\)
\(858\) 19214.9 0.764552
\(859\) 37600.5 1.49350 0.746748 0.665108i \(-0.231614\pi\)
0.746748 + 0.665108i \(0.231614\pi\)
\(860\) 308.580 0.0122355
\(861\) 1009.91 0.0399740
\(862\) 116.974 0.00462197
\(863\) 24679.4 0.973460 0.486730 0.873552i \(-0.338190\pi\)
0.486730 + 0.873552i \(0.338190\pi\)
\(864\) 864.000 0.0340207
\(865\) 2317.70 0.0911032
\(866\) 21438.5 0.841237
\(867\) 14686.3 0.575288
\(868\) −6031.55 −0.235857
\(869\) −17502.6 −0.683239
\(870\) 35.8686 0.00139777
\(871\) −39067.4 −1.51980
\(872\) 3132.35 0.121645
\(873\) −4247.95 −0.164687
\(874\) 4524.21 0.175096
\(875\) 2294.05 0.0886321
\(876\) −2929.60 −0.112993
\(877\) 47933.0 1.84559 0.922796 0.385290i \(-0.125899\pi\)
0.922796 + 0.385290i \(0.125899\pi\)
\(878\) 13965.7 0.536809
\(879\) −12106.2 −0.464543
\(880\) 1361.07 0.0521382
\(881\) −16010.3 −0.612259 −0.306130 0.951990i \(-0.599034\pi\)
−0.306130 + 0.951990i \(0.599034\pi\)
\(882\) −882.000 −0.0336718
\(883\) −24000.6 −0.914705 −0.457353 0.889285i \(-0.651202\pi\)
−0.457353 + 0.889285i \(0.651202\pi\)
\(884\) 832.797 0.0316855
\(885\) −1104.53 −0.0419530
\(886\) 2678.70 0.101572
\(887\) −32307.0 −1.22296 −0.611479 0.791261i \(-0.709425\pi\)
−0.611479 + 0.791261i \(0.709425\pi\)
\(888\) −4361.93 −0.164839
\(889\) 768.290 0.0289850
\(890\) 259.197 0.00976212
\(891\) 5219.65 0.196257
\(892\) −7603.48 −0.285407
\(893\) −17539.2 −0.657251
\(894\) 6511.95 0.243615
\(895\) 4760.71 0.177802
\(896\) 896.000 0.0334077
\(897\) 3429.09 0.127641
\(898\) −13291.0 −0.493905
\(899\) 975.509 0.0361903
\(900\) −4437.27 −0.164343
\(901\) −227.379 −0.00840741
\(902\) −6197.97 −0.228792
\(903\) 1227.22 0.0452264
\(904\) −13015.5 −0.478861
\(905\) −1054.90 −0.0387472
\(906\) −2744.07 −0.100624
\(907\) 41072.9 1.50364 0.751821 0.659367i \(-0.229176\pi\)
0.751821 + 0.659367i \(0.229176\pi\)
\(908\) −19180.5 −0.701020
\(909\) 5157.48 0.188188
\(910\) 918.461 0.0334579
\(911\) −15590.1 −0.566984 −0.283492 0.958975i \(-0.591493\pi\)
−0.283492 + 0.958975i \(0.591493\pi\)
\(912\) −4720.92 −0.171409
\(913\) −35914.2 −1.30185
\(914\) 20827.8 0.753746
\(915\) −601.890 −0.0217463
\(916\) 3034.59 0.109460
\(917\) 6581.32 0.237006
\(918\) 226.226 0.00813353
\(919\) −10020.8 −0.359689 −0.179845 0.983695i \(-0.557560\pi\)
−0.179845 + 0.983695i \(0.557560\pi\)
\(920\) 242.896 0.00870440
\(921\) 24346.1 0.871043
\(922\) 22686.2 0.810335
\(923\) 39169.0 1.39682
\(924\) 5412.98 0.192721
\(925\) 22401.7 0.796284
\(926\) 22770.4 0.808080
\(927\) −9185.55 −0.325451
\(928\) −144.914 −0.00512612
\(929\) −20010.9 −0.706712 −0.353356 0.935489i \(-0.614960\pi\)
−0.353356 + 0.935489i \(0.614960\pi\)
\(930\) 1706.18 0.0601590
\(931\) 4819.27 0.169651
\(932\) −1101.20 −0.0387029
\(933\) 11901.6 0.417620
\(934\) −11538.0 −0.404213
\(935\) 356.377 0.0124650
\(936\) −3578.18 −0.124954
\(937\) 26554.5 0.925826 0.462913 0.886404i \(-0.346804\pi\)
0.462913 + 0.886404i \(0.346804\pi\)
\(938\) −11005.6 −0.383097
\(939\) −11183.5 −0.388667
\(940\) −941.643 −0.0326734
\(941\) 42238.9 1.46328 0.731641 0.681691i \(-0.238755\pi\)
0.731641 + 0.681691i \(0.238755\pi\)
\(942\) 12877.2 0.445395
\(943\) −1106.09 −0.0381965
\(944\) 4462.45 0.153856
\(945\) 249.497 0.00858849
\(946\) −7531.67 −0.258854
\(947\) 24891.7 0.854141 0.427071 0.904218i \(-0.359546\pi\)
0.427071 + 0.904218i \(0.359546\pi\)
\(948\) 3259.32 0.111664
\(949\) 12132.7 0.415009
\(950\) 24245.3 0.828024
\(951\) −10903.4 −0.371784
\(952\) 234.605 0.00798697
\(953\) −25956.5 −0.882280 −0.441140 0.897438i \(-0.645426\pi\)
−0.441140 + 0.897438i \(0.645426\pi\)
\(954\) 976.951 0.0331551
\(955\) 4645.78 0.157418
\(956\) −19412.5 −0.656742
\(957\) −875.465 −0.0295713
\(958\) −14543.4 −0.490475
\(959\) −21510.2 −0.724298
\(960\) −253.457 −0.00852113
\(961\) 16611.5 0.557602
\(962\) 18064.6 0.605431
\(963\) 6911.76 0.231286
\(964\) −946.860 −0.0316352
\(965\) 4527.98 0.151047
\(966\) 966.000 0.0321745
\(967\) −3892.91 −0.129460 −0.0647298 0.997903i \(-0.520619\pi\)
−0.0647298 + 0.997903i \(0.520619\pi\)
\(968\) −22572.3 −0.749485
\(969\) −1236.11 −0.0409798
\(970\) 1246.15 0.0412489
\(971\) 54465.6 1.80009 0.900044 0.435800i \(-0.143534\pi\)
0.900044 + 0.435800i \(0.143534\pi\)
\(972\) −972.000 −0.0320750
\(973\) 16972.0 0.559197
\(974\) −39787.0 −1.30889
\(975\) 18376.6 0.603611
\(976\) 2431.72 0.0797513
\(977\) 41365.1 1.35454 0.677270 0.735735i \(-0.263163\pi\)
0.677270 + 0.735735i \(0.263163\pi\)
\(978\) 12178.7 0.398192
\(979\) −6326.35 −0.206528
\(980\) 258.737 0.00843373
\(981\) −3523.90 −0.114688
\(982\) 32545.5 1.05761
\(983\) −39193.0 −1.27168 −0.635840 0.771821i \(-0.719346\pi\)
−0.635840 + 0.771821i \(0.719346\pi\)
\(984\) 1154.18 0.0373923
\(985\) 4357.10 0.140943
\(986\) −37.9437 −0.00122553
\(987\) −3744.92 −0.120772
\(988\) 19551.3 0.629564
\(989\) −1344.10 −0.0432154
\(990\) −1531.20 −0.0491563
\(991\) −22273.1 −0.713955 −0.356977 0.934113i \(-0.616193\pi\)
−0.356977 + 0.934113i \(0.616193\pi\)
\(992\) −6893.20 −0.220624
\(993\) −20691.1 −0.661241
\(994\) 11034.2 0.352096
\(995\) 3040.08 0.0968613
\(996\) 6687.92 0.212766
\(997\) 52161.1 1.65693 0.828465 0.560041i \(-0.189215\pi\)
0.828465 + 0.560041i \(0.189215\pi\)
\(998\) −6699.49 −0.212494
\(999\) 4907.17 0.155411
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.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.m.1.3 5 1.1 even 1 trivial