Properties

Label 966.4.a.f.1.2
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
Analytic rank $0$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.12197.1
Defining polynomial: \( x^{3} - x^{2} - 15x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.272991\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.81897 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.81897 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +9.63795 q^{10} +43.0349 q^{11} -12.0000 q^{12} +48.6845 q^{13} +14.0000 q^{14} -14.4569 q^{15} +16.0000 q^{16} -24.7735 q^{17} +18.0000 q^{18} +63.2479 q^{19} +19.2759 q^{20} -21.0000 q^{21} +86.0698 q^{22} -23.0000 q^{23} -24.0000 q^{24} -101.777 q^{25} +97.3689 q^{26} -27.0000 q^{27} +28.0000 q^{28} -4.70005 q^{29} -28.9138 q^{30} -88.4310 q^{31} +32.0000 q^{32} -129.105 q^{33} -49.5470 q^{34} +33.7328 q^{35} +36.0000 q^{36} -168.863 q^{37} +126.496 q^{38} -146.053 q^{39} +38.5518 q^{40} +465.750 q^{41} -42.0000 q^{42} +254.877 q^{43} +172.140 q^{44} +43.3708 q^{45} -46.0000 q^{46} -513.188 q^{47} -48.0000 q^{48} +49.0000 q^{49} -203.555 q^{50} +74.3206 q^{51} +194.738 q^{52} +428.489 q^{53} -54.0000 q^{54} +207.384 q^{55} +56.0000 q^{56} -189.744 q^{57} -9.40009 q^{58} +158.984 q^{59} -57.8277 q^{60} -28.2878 q^{61} -176.862 q^{62} +63.0000 q^{63} +64.0000 q^{64} +234.609 q^{65} -258.209 q^{66} +797.236 q^{67} -99.0941 q^{68} +69.0000 q^{69} +67.4656 q^{70} -778.422 q^{71} +72.0000 q^{72} +526.081 q^{73} -337.726 q^{74} +305.332 q^{75} +252.992 q^{76} +301.244 q^{77} -292.107 q^{78} -108.025 q^{79} +77.1036 q^{80} +81.0000 q^{81} +931.500 q^{82} +409.259 q^{83} -84.0000 q^{84} -119.383 q^{85} +509.754 q^{86} +14.1001 q^{87} +344.279 q^{88} +888.952 q^{89} +86.7415 q^{90} +340.791 q^{91} -92.0000 q^{92} +265.293 q^{93} -1026.38 q^{94} +304.790 q^{95} -96.0000 q^{96} -255.899 q^{97} +98.0000 q^{98} +387.314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9} + 18 q^{10} + 53 q^{11} - 36 q^{12} + 61 q^{13} + 42 q^{14} - 27 q^{15} + 48 q^{16} - 2 q^{17} + 54 q^{18} + 63 q^{19} + 36 q^{20} - 63 q^{21} + 106 q^{22} - 69 q^{23} - 72 q^{24} - 72 q^{25} + 122 q^{26} - 81 q^{27} + 84 q^{28} + 312 q^{29} - 54 q^{30} + 220 q^{31} + 96 q^{32} - 159 q^{33} - 4 q^{34} + 63 q^{35} + 108 q^{36} - 44 q^{37} + 126 q^{38} - 183 q^{39} + 72 q^{40} + 171 q^{41} - 126 q^{42} - 627 q^{43} + 212 q^{44} + 81 q^{45} - 138 q^{46} + 353 q^{47} - 144 q^{48} + 147 q^{49} - 144 q^{50} + 6 q^{51} + 244 q^{52} - 504 q^{53} - 162 q^{54} + 1181 q^{55} + 168 q^{56} - 189 q^{57} + 624 q^{58} + 538 q^{59} - 108 q^{60} + 256 q^{61} + 440 q^{62} + 189 q^{63} + 192 q^{64} + 244 q^{65} - 318 q^{66} + 1113 q^{67} - 8 q^{68} + 207 q^{69} + 126 q^{70} + 53 q^{71} + 216 q^{72} + 360 q^{73} - 88 q^{74} + 216 q^{75} + 252 q^{76} + 371 q^{77} - 366 q^{78} + 134 q^{79} + 144 q^{80} + 243 q^{81} + 342 q^{82} + 1506 q^{83} - 252 q^{84} + 577 q^{85} - 1254 q^{86} - 936 q^{87} + 424 q^{88} + 2381 q^{89} + 162 q^{90} + 427 q^{91} - 276 q^{92} - 660 q^{93} + 706 q^{94} + 945 q^{95} - 288 q^{96} - 88 q^{97} + 294 q^{98} + 477 q^{99}+O(q^{100}) \) 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
\(5\) 4.81897 0.431022 0.215511 0.976501i \(-0.430858\pi\)
0.215511 + 0.976501i \(0.430858\pi\)
\(6\) −6.00000 −0.408248
\(7\) 7.00000 0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 9.63795 0.304779
\(11\) 43.0349 1.17959 0.589796 0.807553i \(-0.299208\pi\)
0.589796 + 0.807553i \(0.299208\pi\)
\(12\) −12.0000 −0.288675
\(13\) 48.6845 1.03866 0.519332 0.854572i \(-0.326181\pi\)
0.519332 + 0.854572i \(0.326181\pi\)
\(14\) 14.0000 0.267261
\(15\) −14.4569 −0.248851
\(16\) 16.0000 0.250000
\(17\) −24.7735 −0.353439 −0.176719 0.984261i \(-0.556549\pi\)
−0.176719 + 0.984261i \(0.556549\pi\)
\(18\) 18.0000 0.235702
\(19\) 63.2479 0.763687 0.381844 0.924227i \(-0.375289\pi\)
0.381844 + 0.924227i \(0.375289\pi\)
\(20\) 19.2759 0.215511
\(21\) −21.0000 −0.218218
\(22\) 86.0698 0.834097
\(23\) −23.0000 −0.208514
\(24\) −24.0000 −0.204124
\(25\) −101.777 −0.814220
\(26\) 97.3689 0.734447
\(27\) −27.0000 −0.192450
\(28\) 28.0000 0.188982
\(29\) −4.70005 −0.0300957 −0.0150479 0.999887i \(-0.504790\pi\)
−0.0150479 + 0.999887i \(0.504790\pi\)
\(30\) −28.9138 −0.175964
\(31\) −88.4310 −0.512345 −0.256172 0.966631i \(-0.582461\pi\)
−0.256172 + 0.966631i \(0.582461\pi\)
\(32\) 32.0000 0.176777
\(33\) −129.105 −0.681037
\(34\) −49.5470 −0.249919
\(35\) 33.7328 0.162911
\(36\) 36.0000 0.166667
\(37\) −168.863 −0.750294 −0.375147 0.926965i \(-0.622408\pi\)
−0.375147 + 0.926965i \(0.622408\pi\)
\(38\) 126.496 0.540009
\(39\) −146.053 −0.599673
\(40\) 38.5518 0.152389
\(41\) 465.750 1.77410 0.887048 0.461677i \(-0.152752\pi\)
0.887048 + 0.461677i \(0.152752\pi\)
\(42\) −42.0000 −0.154303
\(43\) 254.877 0.903915 0.451958 0.892039i \(-0.350726\pi\)
0.451958 + 0.892039i \(0.350726\pi\)
\(44\) 172.140 0.589796
\(45\) 43.3708 0.143674
\(46\) −46.0000 −0.147442
\(47\) −513.188 −1.59268 −0.796342 0.604847i \(-0.793234\pi\)
−0.796342 + 0.604847i \(0.793234\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) −203.555 −0.575740
\(51\) 74.3206 0.204058
\(52\) 194.738 0.519332
\(53\) 428.489 1.11052 0.555259 0.831677i \(-0.312619\pi\)
0.555259 + 0.831677i \(0.312619\pi\)
\(54\) −54.0000 −0.136083
\(55\) 207.384 0.508430
\(56\) 56.0000 0.133631
\(57\) −189.744 −0.440915
\(58\) −9.40009 −0.0212809
\(59\) 158.984 0.350812 0.175406 0.984496i \(-0.443876\pi\)
0.175406 + 0.984496i \(0.443876\pi\)
\(60\) −57.8277 −0.124425
\(61\) −28.2878 −0.0593752 −0.0296876 0.999559i \(-0.509451\pi\)
−0.0296876 + 0.999559i \(0.509451\pi\)
\(62\) −176.862 −0.362282
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) 234.609 0.447687
\(66\) −258.209 −0.481566
\(67\) 797.236 1.45370 0.726850 0.686796i \(-0.240984\pi\)
0.726850 + 0.686796i \(0.240984\pi\)
\(68\) −99.0941 −0.176719
\(69\) 69.0000 0.120386
\(70\) 67.4656 0.115196
\(71\) −778.422 −1.30115 −0.650576 0.759442i \(-0.725472\pi\)
−0.650576 + 0.759442i \(0.725472\pi\)
\(72\) 72.0000 0.117851
\(73\) 526.081 0.843468 0.421734 0.906720i \(-0.361422\pi\)
0.421734 + 0.906720i \(0.361422\pi\)
\(74\) −337.726 −0.530538
\(75\) 305.332 0.470090
\(76\) 252.992 0.381844
\(77\) 301.244 0.445844
\(78\) −292.107 −0.424033
\(79\) −108.025 −0.153845 −0.0769223 0.997037i \(-0.524509\pi\)
−0.0769223 + 0.997037i \(0.524509\pi\)
\(80\) 77.1036 0.107756
\(81\) 81.0000 0.111111
\(82\) 931.500 1.25448
\(83\) 409.259 0.541229 0.270615 0.962688i \(-0.412773\pi\)
0.270615 + 0.962688i \(0.412773\pi\)
\(84\) −84.0000 −0.109109
\(85\) −119.383 −0.152340
\(86\) 509.754 0.639165
\(87\) 14.1001 0.0173758
\(88\) 344.279 0.417049
\(89\) 888.952 1.05875 0.529375 0.848388i \(-0.322427\pi\)
0.529375 + 0.848388i \(0.322427\pi\)
\(90\) 86.7415 0.101593
\(91\) 340.791 0.392578
\(92\) −92.0000 −0.104257
\(93\) 265.293 0.295802
\(94\) −1026.38 −1.12620
\(95\) 304.790 0.329166
\(96\) −96.0000 −0.102062
\(97\) −255.899 −0.267862 −0.133931 0.990991i \(-0.542760\pi\)
−0.133931 + 0.990991i \(0.542760\pi\)
\(98\) 98.0000 0.101015
\(99\) 387.314 0.393197
\(100\) −407.110 −0.407110
\(101\) 726.548 0.715784 0.357892 0.933763i \(-0.383496\pi\)
0.357892 + 0.933763i \(0.383496\pi\)
\(102\) 148.641 0.144291
\(103\) 623.121 0.596097 0.298048 0.954551i \(-0.403664\pi\)
0.298048 + 0.954551i \(0.403664\pi\)
\(104\) 389.476 0.367223
\(105\) −101.198 −0.0940567
\(106\) 856.978 0.785255
\(107\) −34.0096 −0.0307274 −0.0153637 0.999882i \(-0.504891\pi\)
−0.0153637 + 0.999882i \(0.504891\pi\)
\(108\) −108.000 −0.0962250
\(109\) −177.207 −0.155719 −0.0778596 0.996964i \(-0.524809\pi\)
−0.0778596 + 0.996964i \(0.524809\pi\)
\(110\) 414.768 0.359514
\(111\) 506.589 0.433183
\(112\) 112.000 0.0944911
\(113\) −1011.65 −0.842196 −0.421098 0.907015i \(-0.638355\pi\)
−0.421098 + 0.907015i \(0.638355\pi\)
\(114\) −379.487 −0.311774
\(115\) −110.836 −0.0898743
\(116\) −18.8002 −0.0150479
\(117\) 438.160 0.346222
\(118\) 317.967 0.248062
\(119\) −173.415 −0.133587
\(120\) −115.655 −0.0879820
\(121\) 521.001 0.391436
\(122\) −56.5757 −0.0419846
\(123\) −1397.25 −1.02427
\(124\) −353.724 −0.256172
\(125\) −1092.83 −0.781969
\(126\) 126.000 0.0890871
\(127\) −1522.05 −1.06346 −0.531731 0.846913i \(-0.678458\pi\)
−0.531731 + 0.846913i \(0.678458\pi\)
\(128\) 128.000 0.0883883
\(129\) −764.631 −0.521876
\(130\) 469.218 0.316563
\(131\) 2533.05 1.68941 0.844707 0.535228i \(-0.179774\pi\)
0.844707 + 0.535228i \(0.179774\pi\)
\(132\) −516.419 −0.340519
\(133\) 442.735 0.288647
\(134\) 1594.47 1.02792
\(135\) −130.112 −0.0829502
\(136\) −198.188 −0.124960
\(137\) 18.5942 0.0115957 0.00579783 0.999983i \(-0.498154\pi\)
0.00579783 + 0.999983i \(0.498154\pi\)
\(138\) 138.000 0.0851257
\(139\) 2684.26 1.63796 0.818979 0.573824i \(-0.194541\pi\)
0.818979 + 0.573824i \(0.194541\pi\)
\(140\) 134.931 0.0814555
\(141\) 1539.56 0.919537
\(142\) −1556.84 −0.920053
\(143\) 2095.13 1.22520
\(144\) 144.000 0.0833333
\(145\) −22.6494 −0.0129719
\(146\) 1052.16 0.596422
\(147\) −147.000 −0.0824786
\(148\) −675.452 −0.375147
\(149\) 71.6799 0.0394111 0.0197055 0.999806i \(-0.493727\pi\)
0.0197055 + 0.999806i \(0.493727\pi\)
\(150\) 610.665 0.332404
\(151\) −1287.00 −0.693604 −0.346802 0.937938i \(-0.612732\pi\)
−0.346802 + 0.937938i \(0.612732\pi\)
\(152\) 505.983 0.270004
\(153\) −222.962 −0.117813
\(154\) 602.488 0.315259
\(155\) −426.147 −0.220832
\(156\) −584.214 −0.299837
\(157\) −1520.90 −0.773128 −0.386564 0.922262i \(-0.626338\pi\)
−0.386564 + 0.922262i \(0.626338\pi\)
\(158\) −216.049 −0.108785
\(159\) −1285.47 −0.641158
\(160\) 154.207 0.0761947
\(161\) −161.000 −0.0788110
\(162\) 162.000 0.0785674
\(163\) 2629.34 1.26347 0.631736 0.775184i \(-0.282343\pi\)
0.631736 + 0.775184i \(0.282343\pi\)
\(164\) 1863.00 0.887048
\(165\) −622.152 −0.293542
\(166\) 818.518 0.382707
\(167\) 254.418 0.117889 0.0589445 0.998261i \(-0.481227\pi\)
0.0589445 + 0.998261i \(0.481227\pi\)
\(168\) −168.000 −0.0771517
\(169\) 173.177 0.0788242
\(170\) −238.766 −0.107721
\(171\) 569.231 0.254562
\(172\) 1019.51 0.451958
\(173\) −1451.24 −0.637780 −0.318890 0.947792i \(-0.603310\pi\)
−0.318890 + 0.947792i \(0.603310\pi\)
\(174\) 28.2003 0.0122865
\(175\) −712.442 −0.307746
\(176\) 688.558 0.294898
\(177\) −476.951 −0.202541
\(178\) 1777.90 0.748649
\(179\) 1382.02 0.577078 0.288539 0.957468i \(-0.406830\pi\)
0.288539 + 0.957468i \(0.406830\pi\)
\(180\) 173.483 0.0718370
\(181\) 825.918 0.339171 0.169586 0.985515i \(-0.445757\pi\)
0.169586 + 0.985515i \(0.445757\pi\)
\(182\) 681.582 0.277595
\(183\) 84.8635 0.0342803
\(184\) −184.000 −0.0737210
\(185\) −813.746 −0.323393
\(186\) 530.586 0.209164
\(187\) −1066.13 −0.416914
\(188\) −2052.75 −0.796342
\(189\) −189.000 −0.0727393
\(190\) 609.580 0.232756
\(191\) 1746.50 0.661636 0.330818 0.943695i \(-0.392675\pi\)
0.330818 + 0.943695i \(0.392675\pi\)
\(192\) −192.000 −0.0721688
\(193\) 2592.01 0.966720 0.483360 0.875422i \(-0.339416\pi\)
0.483360 + 0.875422i \(0.339416\pi\)
\(194\) −511.798 −0.189407
\(195\) −703.827 −0.258472
\(196\) 196.000 0.0714286
\(197\) −2101.75 −0.760120 −0.380060 0.924962i \(-0.624097\pi\)
−0.380060 + 0.924962i \(0.624097\pi\)
\(198\) 774.628 0.278032
\(199\) 3228.44 1.15004 0.575020 0.818139i \(-0.304994\pi\)
0.575020 + 0.818139i \(0.304994\pi\)
\(200\) −814.220 −0.287870
\(201\) −2391.71 −0.839294
\(202\) 1453.10 0.506136
\(203\) −32.9003 −0.0113751
\(204\) 297.282 0.102029
\(205\) 2244.44 0.764675
\(206\) 1246.24 0.421504
\(207\) −207.000 −0.0695048
\(208\) 778.951 0.259666
\(209\) 2721.87 0.900839
\(210\) −202.397 −0.0665082
\(211\) −2689.98 −0.877658 −0.438829 0.898570i \(-0.644607\pi\)
−0.438829 + 0.898570i \(0.644607\pi\)
\(212\) 1713.96 0.555259
\(213\) 2335.27 0.751220
\(214\) −68.0193 −0.0217276
\(215\) 1228.24 0.389607
\(216\) −216.000 −0.0680414
\(217\) −619.017 −0.193648
\(218\) −354.415 −0.110110
\(219\) −1578.24 −0.486976
\(220\) 829.536 0.254215
\(221\) −1206.09 −0.367105
\(222\) 1013.18 0.306306
\(223\) −2592.25 −0.778429 −0.389214 0.921147i \(-0.627253\pi\)
−0.389214 + 0.921147i \(0.627253\pi\)
\(224\) 224.000 0.0668153
\(225\) −915.997 −0.271407
\(226\) −2023.30 −0.595522
\(227\) 5463.45 1.59745 0.798726 0.601695i \(-0.205508\pi\)
0.798726 + 0.601695i \(0.205508\pi\)
\(228\) −758.975 −0.220458
\(229\) 663.825 0.191558 0.0957790 0.995403i \(-0.469466\pi\)
0.0957790 + 0.995403i \(0.469466\pi\)
\(230\) −221.673 −0.0635507
\(231\) −903.733 −0.257408
\(232\) −37.6004 −0.0106405
\(233\) −3961.76 −1.11392 −0.556961 0.830539i \(-0.688033\pi\)
−0.556961 + 0.830539i \(0.688033\pi\)
\(234\) 876.320 0.244816
\(235\) −2473.04 −0.686482
\(236\) 635.935 0.175406
\(237\) 324.074 0.0888222
\(238\) −346.829 −0.0944605
\(239\) −2991.95 −0.809763 −0.404881 0.914369i \(-0.632687\pi\)
−0.404881 + 0.914369i \(0.632687\pi\)
\(240\) −231.311 −0.0622127
\(241\) −5740.49 −1.53435 −0.767173 0.641441i \(-0.778337\pi\)
−0.767173 + 0.641441i \(0.778337\pi\)
\(242\) 1042.00 0.276787
\(243\) −243.000 −0.0641500
\(244\) −113.151 −0.0296876
\(245\) 236.130 0.0615746
\(246\) −2794.50 −0.724272
\(247\) 3079.19 0.793215
\(248\) −707.448 −0.181141
\(249\) −1227.78 −0.312479
\(250\) −2185.67 −0.552936
\(251\) 1505.93 0.378698 0.189349 0.981910i \(-0.439362\pi\)
0.189349 + 0.981910i \(0.439362\pi\)
\(252\) 252.000 0.0629941
\(253\) −989.802 −0.245962
\(254\) −3044.09 −0.751982
\(255\) 358.149 0.0879535
\(256\) 256.000 0.0625000
\(257\) −5987.31 −1.45322 −0.726611 0.687050i \(-0.758906\pi\)
−0.726611 + 0.687050i \(0.758906\pi\)
\(258\) −1529.26 −0.369022
\(259\) −1182.04 −0.283585
\(260\) 938.437 0.223844
\(261\) −42.3004 −0.0100319
\(262\) 5066.09 1.19460
\(263\) −1898.18 −0.445046 −0.222523 0.974927i \(-0.571429\pi\)
−0.222523 + 0.974927i \(0.571429\pi\)
\(264\) −1032.84 −0.240783
\(265\) 2064.88 0.478658
\(266\) 885.470 0.204104
\(267\) −2666.86 −0.611269
\(268\) 3188.94 0.726850
\(269\) 4317.05 0.978496 0.489248 0.872145i \(-0.337271\pi\)
0.489248 + 0.872145i \(0.337271\pi\)
\(270\) −260.225 −0.0586547
\(271\) −5978.25 −1.34005 −0.670024 0.742340i \(-0.733716\pi\)
−0.670024 + 0.742340i \(0.733716\pi\)
\(272\) −396.376 −0.0883597
\(273\) −1022.37 −0.226655
\(274\) 37.1883 0.00819938
\(275\) −4379.98 −0.960447
\(276\) 276.000 0.0601929
\(277\) 4212.43 0.913719 0.456859 0.889539i \(-0.348974\pi\)
0.456859 + 0.889539i \(0.348974\pi\)
\(278\) 5368.52 1.15821
\(279\) −795.879 −0.170782
\(280\) 269.863 0.0575978
\(281\) 4850.74 1.02979 0.514895 0.857253i \(-0.327831\pi\)
0.514895 + 0.857253i \(0.327831\pi\)
\(282\) 3079.13 0.650211
\(283\) 689.593 0.144848 0.0724241 0.997374i \(-0.476926\pi\)
0.0724241 + 0.997374i \(0.476926\pi\)
\(284\) −3113.69 −0.650576
\(285\) −914.370 −0.190044
\(286\) 4190.26 0.866347
\(287\) 3260.25 0.670545
\(288\) 288.000 0.0589256
\(289\) −4299.27 −0.875081
\(290\) −45.2988 −0.00917254
\(291\) 767.696 0.154650
\(292\) 2104.32 0.421734
\(293\) −1099.32 −0.219191 −0.109596 0.993976i \(-0.534956\pi\)
−0.109596 + 0.993976i \(0.534956\pi\)
\(294\) −294.000 −0.0583212
\(295\) 766.138 0.151208
\(296\) −1350.90 −0.265269
\(297\) −1161.94 −0.227012
\(298\) 143.360 0.0278678
\(299\) −1119.74 −0.216577
\(300\) 1221.33 0.235045
\(301\) 1784.14 0.341648
\(302\) −2573.99 −0.490452
\(303\) −2179.64 −0.413258
\(304\) 1011.97 0.190922
\(305\) −136.318 −0.0255920
\(306\) −445.923 −0.0833064
\(307\) −3586.44 −0.666739 −0.333369 0.942796i \(-0.608186\pi\)
−0.333369 + 0.942796i \(0.608186\pi\)
\(308\) 1204.98 0.222922
\(309\) −1869.36 −0.344157
\(310\) −852.294 −0.156152
\(311\) 1271.25 0.231787 0.115894 0.993262i \(-0.463027\pi\)
0.115894 + 0.993262i \(0.463027\pi\)
\(312\) −1168.43 −0.212017
\(313\) −7502.44 −1.35483 −0.677417 0.735599i \(-0.736901\pi\)
−0.677417 + 0.735599i \(0.736901\pi\)
\(314\) −3041.80 −0.546684
\(315\) 303.595 0.0543037
\(316\) −432.099 −0.0769223
\(317\) −7578.44 −1.34274 −0.671369 0.741123i \(-0.734293\pi\)
−0.671369 + 0.741123i \(0.734293\pi\)
\(318\) −2570.93 −0.453367
\(319\) −202.266 −0.0355007
\(320\) 308.414 0.0538778
\(321\) 102.029 0.0177405
\(322\) −322.000 −0.0557278
\(323\) −1566.87 −0.269917
\(324\) 324.000 0.0555556
\(325\) −4954.98 −0.845701
\(326\) 5258.68 0.893410
\(327\) 531.622 0.0899045
\(328\) 3726.00 0.627238
\(329\) −3592.32 −0.601978
\(330\) −1244.30 −0.207566
\(331\) −5168.33 −0.858240 −0.429120 0.903248i \(-0.641176\pi\)
−0.429120 + 0.903248i \(0.641176\pi\)
\(332\) 1637.04 0.270615
\(333\) −1519.77 −0.250098
\(334\) 508.836 0.0833601
\(335\) 3841.86 0.626577
\(336\) −336.000 −0.0545545
\(337\) −3372.75 −0.545180 −0.272590 0.962130i \(-0.587880\pi\)
−0.272590 + 0.962130i \(0.587880\pi\)
\(338\) 346.354 0.0557372
\(339\) 3034.95 0.486242
\(340\) −477.532 −0.0761700
\(341\) −3805.62 −0.604357
\(342\) 1138.46 0.180003
\(343\) 343.000 0.0539949
\(344\) 2039.01 0.319582
\(345\) 332.509 0.0518890
\(346\) −2902.48 −0.450978
\(347\) 4931.32 0.762903 0.381451 0.924389i \(-0.375424\pi\)
0.381451 + 0.924389i \(0.375424\pi\)
\(348\) 56.4005 0.00868789
\(349\) −8112.70 −1.24431 −0.622153 0.782895i \(-0.713742\pi\)
−0.622153 + 0.782895i \(0.713742\pi\)
\(350\) −1424.88 −0.217609
\(351\) −1314.48 −0.199891
\(352\) 1377.12 0.208524
\(353\) 1934.09 0.291618 0.145809 0.989313i \(-0.453421\pi\)
0.145809 + 0.989313i \(0.453421\pi\)
\(354\) −953.902 −0.143218
\(355\) −3751.20 −0.560825
\(356\) 3555.81 0.529375
\(357\) 520.244 0.0771267
\(358\) 2764.04 0.408056
\(359\) −308.167 −0.0453049 −0.0226524 0.999743i \(-0.507211\pi\)
−0.0226524 + 0.999743i \(0.507211\pi\)
\(360\) 346.966 0.0507964
\(361\) −2858.70 −0.416782
\(362\) 1651.84 0.239830
\(363\) −1563.00 −0.225996
\(364\) 1363.16 0.196289
\(365\) 2535.17 0.363553
\(366\) 169.727 0.0242398
\(367\) −6831.82 −0.971711 −0.485856 0.874039i \(-0.661492\pi\)
−0.485856 + 0.874039i \(0.661492\pi\)
\(368\) −368.000 −0.0521286
\(369\) 4191.75 0.591365
\(370\) −1627.49 −0.228674
\(371\) 2999.42 0.419737
\(372\) 1061.17 0.147901
\(373\) −10390.3 −1.44232 −0.721162 0.692766i \(-0.756392\pi\)
−0.721162 + 0.692766i \(0.756392\pi\)
\(374\) −2132.25 −0.294802
\(375\) 3278.50 0.451470
\(376\) −4105.50 −0.563099
\(377\) −228.819 −0.0312594
\(378\) −378.000 −0.0514344
\(379\) 4526.85 0.613532 0.306766 0.951785i \(-0.400753\pi\)
0.306766 + 0.951785i \(0.400753\pi\)
\(380\) 1219.16 0.164583
\(381\) 4566.14 0.613990
\(382\) 3493.00 0.467847
\(383\) −1271.78 −0.169674 −0.0848369 0.996395i \(-0.527037\pi\)
−0.0848369 + 0.996395i \(0.527037\pi\)
\(384\) −384.000 −0.0510310
\(385\) 1451.69 0.192168
\(386\) 5184.02 0.683575
\(387\) 2293.89 0.301305
\(388\) −1023.60 −0.133931
\(389\) −9955.76 −1.29763 −0.648813 0.760948i \(-0.724734\pi\)
−0.648813 + 0.760948i \(0.724734\pi\)
\(390\) −1407.65 −0.182768
\(391\) 569.791 0.0736971
\(392\) 392.000 0.0505076
\(393\) −7599.14 −0.975384
\(394\) −4203.51 −0.537486
\(395\) −520.568 −0.0663104
\(396\) 1549.26 0.196599
\(397\) 6168.22 0.779784 0.389892 0.920861i \(-0.372512\pi\)
0.389892 + 0.920861i \(0.372512\pi\)
\(398\) 6456.88 0.813201
\(399\) −1328.21 −0.166650
\(400\) −1628.44 −0.203555
\(401\) −5134.86 −0.639458 −0.319729 0.947509i \(-0.603592\pi\)
−0.319729 + 0.947509i \(0.603592\pi\)
\(402\) −4783.42 −0.593470
\(403\) −4305.22 −0.532154
\(404\) 2906.19 0.357892
\(405\) 390.337 0.0478913
\(406\) −65.8006 −0.00804343
\(407\) −7266.99 −0.885041
\(408\) 594.565 0.0721454
\(409\) −6805.93 −0.822816 −0.411408 0.911451i \(-0.634963\pi\)
−0.411408 + 0.911451i \(0.634963\pi\)
\(410\) 4488.87 0.540707
\(411\) −55.7825 −0.00669476
\(412\) 2492.49 0.298048
\(413\) 1112.89 0.132594
\(414\) −414.000 −0.0491473
\(415\) 1972.21 0.233282
\(416\) 1557.90 0.183612
\(417\) −8052.79 −0.945675
\(418\) 5443.73 0.636989
\(419\) 9403.51 1.09640 0.548200 0.836347i \(-0.315313\pi\)
0.548200 + 0.836347i \(0.315313\pi\)
\(420\) −404.794 −0.0470284
\(421\) 2153.32 0.249279 0.124639 0.992202i \(-0.460223\pi\)
0.124639 + 0.992202i \(0.460223\pi\)
\(422\) −5379.96 −0.620598
\(423\) −4618.69 −0.530895
\(424\) 3427.91 0.392628
\(425\) 2521.39 0.287777
\(426\) 4670.53 0.531193
\(427\) −198.015 −0.0224417
\(428\) −136.039 −0.0153637
\(429\) −6285.39 −0.707369
\(430\) 2456.49 0.275494
\(431\) 6346.56 0.709287 0.354644 0.935002i \(-0.384602\pi\)
0.354644 + 0.935002i \(0.384602\pi\)
\(432\) −432.000 −0.0481125
\(433\) −718.947 −0.0797931 −0.0398965 0.999204i \(-0.512703\pi\)
−0.0398965 + 0.999204i \(0.512703\pi\)
\(434\) −1238.03 −0.136930
\(435\) 67.9482 0.00748935
\(436\) −708.830 −0.0778596
\(437\) −1454.70 −0.159240
\(438\) −3156.49 −0.344344
\(439\) 7477.10 0.812898 0.406449 0.913673i \(-0.366767\pi\)
0.406449 + 0.913673i \(0.366767\pi\)
\(440\) 1659.07 0.179757
\(441\) 441.000 0.0476190
\(442\) −2412.17 −0.259582
\(443\) 12703.0 1.36239 0.681196 0.732101i \(-0.261460\pi\)
0.681196 + 0.732101i \(0.261460\pi\)
\(444\) 2026.35 0.216591
\(445\) 4283.84 0.456345
\(446\) −5184.49 −0.550432
\(447\) −215.040 −0.0227540
\(448\) 448.000 0.0472456
\(449\) 634.326 0.0666719 0.0333359 0.999444i \(-0.489387\pi\)
0.0333359 + 0.999444i \(0.489387\pi\)
\(450\) −1831.99 −0.191913
\(451\) 20043.5 2.09271
\(452\) −4046.60 −0.421098
\(453\) 3860.99 0.400453
\(454\) 10926.9 1.12957
\(455\) 1642.26 0.169210
\(456\) −1517.95 −0.155887
\(457\) 1586.41 0.162384 0.0811918 0.996698i \(-0.474127\pi\)
0.0811918 + 0.996698i \(0.474127\pi\)
\(458\) 1327.65 0.135452
\(459\) 668.885 0.0680194
\(460\) −443.346 −0.0449372
\(461\) 12274.6 1.24010 0.620051 0.784562i \(-0.287112\pi\)
0.620051 + 0.784562i \(0.287112\pi\)
\(462\) −1807.47 −0.182015
\(463\) −11981.2 −1.20262 −0.601312 0.799014i \(-0.705355\pi\)
−0.601312 + 0.799014i \(0.705355\pi\)
\(464\) −75.2007 −0.00752394
\(465\) 1278.44 0.127497
\(466\) −7923.52 −0.787661
\(467\) 4935.51 0.489054 0.244527 0.969643i \(-0.421367\pi\)
0.244527 + 0.969643i \(0.421367\pi\)
\(468\) 1752.64 0.173111
\(469\) 5580.65 0.549447
\(470\) −4946.08 −0.485416
\(471\) 4562.71 0.446366
\(472\) 1271.87 0.124031
\(473\) 10968.6 1.06625
\(474\) 648.148 0.0628068
\(475\) −6437.21 −0.621809
\(476\) −693.659 −0.0667937
\(477\) 3856.40 0.370173
\(478\) −5983.91 −0.572589
\(479\) −7814.60 −0.745424 −0.372712 0.927947i \(-0.621572\pi\)
−0.372712 + 0.927947i \(0.621572\pi\)
\(480\) −462.621 −0.0439910
\(481\) −8221.00 −0.779304
\(482\) −11481.0 −1.08495
\(483\) 483.000 0.0455016
\(484\) 2084.00 0.195718
\(485\) −1233.17 −0.115454
\(486\) −486.000 −0.0453609
\(487\) −1993.13 −0.185457 −0.0927284 0.995691i \(-0.529559\pi\)
−0.0927284 + 0.995691i \(0.529559\pi\)
\(488\) −226.303 −0.0209923
\(489\) −7888.02 −0.729466
\(490\) 472.259 0.0435398
\(491\) −2069.52 −0.190216 −0.0951081 0.995467i \(-0.530320\pi\)
−0.0951081 + 0.995467i \(0.530320\pi\)
\(492\) −5589.00 −0.512137
\(493\) 116.437 0.0106370
\(494\) 6158.38 0.560888
\(495\) 1866.46 0.169477
\(496\) −1414.90 −0.128086
\(497\) −5448.96 −0.491789
\(498\) −2455.56 −0.220956
\(499\) −16681.6 −1.49654 −0.748268 0.663397i \(-0.769114\pi\)
−0.748268 + 0.663397i \(0.769114\pi\)
\(500\) −4371.34 −0.390984
\(501\) −763.254 −0.0680632
\(502\) 3011.85 0.267780
\(503\) 547.940 0.0485714 0.0242857 0.999705i \(-0.492269\pi\)
0.0242857 + 0.999705i \(0.492269\pi\)
\(504\) 504.000 0.0445435
\(505\) 3501.21 0.308519
\(506\) −1979.60 −0.173921
\(507\) −519.531 −0.0455092
\(508\) −6088.18 −0.531731
\(509\) 12549.1 1.09279 0.546395 0.837528i \(-0.316000\pi\)
0.546395 + 0.837528i \(0.316000\pi\)
\(510\) 716.298 0.0621925
\(511\) 3682.57 0.318801
\(512\) 512.000 0.0441942
\(513\) −1707.69 −0.146972
\(514\) −11974.6 −1.02758
\(515\) 3002.81 0.256931
\(516\) −3058.52 −0.260938
\(517\) −22085.0 −1.87872
\(518\) −2364.08 −0.200525
\(519\) 4353.73 0.368222
\(520\) 1876.87 0.158281
\(521\) 15526.1 1.30559 0.652794 0.757536i \(-0.273597\pi\)
0.652794 + 0.757536i \(0.273597\pi\)
\(522\) −84.6008 −0.00709363
\(523\) 15227.7 1.27316 0.636579 0.771212i \(-0.280349\pi\)
0.636579 + 0.771212i \(0.280349\pi\)
\(524\) 10132.2 0.844707
\(525\) 2137.33 0.177677
\(526\) −3796.37 −0.314695
\(527\) 2190.75 0.181083
\(528\) −2065.67 −0.170259
\(529\) 529.000 0.0434783
\(530\) 4129.75 0.338462
\(531\) 1430.85 0.116937
\(532\) 1770.94 0.144323
\(533\) 22674.8 1.84269
\(534\) −5333.71 −0.432233
\(535\) −163.892 −0.0132442
\(536\) 6377.89 0.513960
\(537\) −4146.06 −0.333176
\(538\) 8634.11 0.691901
\(539\) 2108.71 0.168513
\(540\) −520.449 −0.0414751
\(541\) −18557.1 −1.47473 −0.737367 0.675493i \(-0.763931\pi\)
−0.737367 + 0.675493i \(0.763931\pi\)
\(542\) −11956.5 −0.947557
\(543\) −2477.75 −0.195821
\(544\) −792.753 −0.0624798
\(545\) −853.958 −0.0671184
\(546\) −2044.75 −0.160269
\(547\) −2032.79 −0.158895 −0.0794476 0.996839i \(-0.525316\pi\)
−0.0794476 + 0.996839i \(0.525316\pi\)
\(548\) 74.3766 0.00579783
\(549\) −254.591 −0.0197917
\(550\) −8759.96 −0.679138
\(551\) −297.268 −0.0229837
\(552\) 552.000 0.0425628
\(553\) −756.172 −0.0581478
\(554\) 8424.85 0.646097
\(555\) 2441.24 0.186711
\(556\) 10737.0 0.818979
\(557\) −11605.7 −0.882855 −0.441428 0.897297i \(-0.645528\pi\)
−0.441428 + 0.897297i \(0.645528\pi\)
\(558\) −1591.76 −0.120761
\(559\) 12408.5 0.938865
\(560\) 539.725 0.0407278
\(561\) 3198.38 0.240705
\(562\) 9701.48 0.728171
\(563\) 154.171 0.0115409 0.00577047 0.999983i \(-0.498163\pi\)
0.00577047 + 0.999983i \(0.498163\pi\)
\(564\) 6158.26 0.459768
\(565\) −4875.12 −0.363005
\(566\) 1379.19 0.102423
\(567\) 567.000 0.0419961
\(568\) −6227.38 −0.460026
\(569\) −20639.0 −1.52062 −0.760309 0.649562i \(-0.774952\pi\)
−0.760309 + 0.649562i \(0.774952\pi\)
\(570\) −1828.74 −0.134382
\(571\) −22691.0 −1.66303 −0.831515 0.555502i \(-0.812526\pi\)
−0.831515 + 0.555502i \(0.812526\pi\)
\(572\) 8380.52 0.612600
\(573\) −5239.51 −0.381996
\(574\) 6520.50 0.474147
\(575\) 2340.88 0.169777
\(576\) 576.000 0.0416667
\(577\) −53.9391 −0.00389171 −0.00194585 0.999998i \(-0.500619\pi\)
−0.00194585 + 0.999998i \(0.500619\pi\)
\(578\) −8598.55 −0.618776
\(579\) −7776.03 −0.558136
\(580\) −90.5976 −0.00648597
\(581\) 2864.81 0.204565
\(582\) 1535.39 0.109354
\(583\) 18440.0 1.30996
\(584\) 4208.65 0.298211
\(585\) 2111.48 0.149229
\(586\) −2198.64 −0.154991
\(587\) 17794.4 1.25120 0.625600 0.780144i \(-0.284854\pi\)
0.625600 + 0.780144i \(0.284854\pi\)
\(588\) −588.000 −0.0412393
\(589\) −5593.08 −0.391271
\(590\) 1532.28 0.106920
\(591\) 6305.26 0.438856
\(592\) −2701.81 −0.187574
\(593\) −27738.6 −1.92089 −0.960444 0.278474i \(-0.910171\pi\)
−0.960444 + 0.278474i \(0.910171\pi\)
\(594\) −2323.88 −0.160522
\(595\) −835.681 −0.0575791
\(596\) 286.720 0.0197055
\(597\) −9685.32 −0.663976
\(598\) −2239.49 −0.153143
\(599\) 2927.43 0.199686 0.0998428 0.995003i \(-0.468166\pi\)
0.0998428 + 0.995003i \(0.468166\pi\)
\(600\) 2442.66 0.166202
\(601\) −9902.60 −0.672106 −0.336053 0.941843i \(-0.609092\pi\)
−0.336053 + 0.941843i \(0.609092\pi\)
\(602\) 3568.28 0.241582
\(603\) 7175.12 0.484567
\(604\) −5147.98 −0.346802
\(605\) 2510.69 0.168717
\(606\) −4359.29 −0.292218
\(607\) 4754.02 0.317891 0.158946 0.987287i \(-0.449191\pi\)
0.158946 + 0.987287i \(0.449191\pi\)
\(608\) 2023.93 0.135002
\(609\) 98.7010 0.00656743
\(610\) −272.637 −0.0180963
\(611\) −24984.3 −1.65426
\(612\) −891.847 −0.0589065
\(613\) −24542.3 −1.61706 −0.808529 0.588457i \(-0.799736\pi\)
−0.808529 + 0.588457i \(0.799736\pi\)
\(614\) −7172.88 −0.471456
\(615\) −6733.31 −0.441485
\(616\) 2409.95 0.157630
\(617\) 24061.2 1.56996 0.784981 0.619520i \(-0.212673\pi\)
0.784981 + 0.619520i \(0.212673\pi\)
\(618\) −3738.73 −0.243355
\(619\) 668.751 0.0434239 0.0217119 0.999764i \(-0.493088\pi\)
0.0217119 + 0.999764i \(0.493088\pi\)
\(620\) −1704.59 −0.110416
\(621\) 621.000 0.0401286
\(622\) 2542.49 0.163898
\(623\) 6222.66 0.400170
\(624\) −2336.85 −0.149918
\(625\) 7455.84 0.477174
\(626\) −15004.9 −0.958013
\(627\) −8165.60 −0.520100
\(628\) −6083.61 −0.386564
\(629\) 4183.33 0.265183
\(630\) 607.191 0.0383985
\(631\) −22237.5 −1.40295 −0.701476 0.712693i \(-0.747475\pi\)
−0.701476 + 0.712693i \(0.747475\pi\)
\(632\) −864.197 −0.0543923
\(633\) 8069.94 0.506716
\(634\) −15156.9 −0.949459
\(635\) −7334.70 −0.458376
\(636\) −5141.87 −0.320579
\(637\) 2385.54 0.148381
\(638\) −404.532 −0.0251028
\(639\) −7005.80 −0.433717
\(640\) 616.829 0.0380973
\(641\) −6268.56 −0.386261 −0.193131 0.981173i \(-0.561864\pi\)
−0.193131 + 0.981173i \(0.561864\pi\)
\(642\) 204.058 0.0125444
\(643\) −3657.99 −0.224350 −0.112175 0.993688i \(-0.535782\pi\)
−0.112175 + 0.993688i \(0.535782\pi\)
\(644\) −644.000 −0.0394055
\(645\) −3684.73 −0.224940
\(646\) −3133.75 −0.190860
\(647\) 29876.0 1.81537 0.907687 0.419647i \(-0.137846\pi\)
0.907687 + 0.419647i \(0.137846\pi\)
\(648\) 648.000 0.0392837
\(649\) 6841.84 0.413815
\(650\) −9909.96 −0.598001
\(651\) 1857.05 0.111803
\(652\) 10517.4 0.631736
\(653\) −15406.4 −0.923274 −0.461637 0.887069i \(-0.652738\pi\)
−0.461637 + 0.887069i \(0.652738\pi\)
\(654\) 1063.24 0.0635721
\(655\) 12206.7 0.728175
\(656\) 7452.00 0.443524
\(657\) 4734.73 0.281156
\(658\) −7184.63 −0.425663
\(659\) 11969.6 0.707543 0.353772 0.935332i \(-0.384899\pi\)
0.353772 + 0.935332i \(0.384899\pi\)
\(660\) −2488.61 −0.146771
\(661\) 19192.9 1.12938 0.564688 0.825304i \(-0.308996\pi\)
0.564688 + 0.825304i \(0.308996\pi\)
\(662\) −10336.7 −0.606867
\(663\) 3618.26 0.211948
\(664\) 3274.07 0.191353
\(665\) 2133.53 0.124413
\(666\) −3039.53 −0.176846
\(667\) 108.101 0.00627540
\(668\) 1017.67 0.0589445
\(669\) 7776.74 0.449426
\(670\) 7683.72 0.443057
\(671\) −1217.36 −0.0700385
\(672\) −672.000 −0.0385758
\(673\) −17503.4 −1.00253 −0.501267 0.865293i \(-0.667133\pi\)
−0.501267 + 0.865293i \(0.667133\pi\)
\(674\) −6745.51 −0.385500
\(675\) 2747.99 0.156697
\(676\) 692.708 0.0394121
\(677\) −27542.0 −1.56355 −0.781776 0.623560i \(-0.785686\pi\)
−0.781776 + 0.623560i \(0.785686\pi\)
\(678\) 6069.91 0.343825
\(679\) −1791.29 −0.101242
\(680\) −955.064 −0.0538603
\(681\) −16390.3 −0.922290
\(682\) −7611.24 −0.427345
\(683\) 4505.08 0.252389 0.126195 0.992005i \(-0.459724\pi\)
0.126195 + 0.992005i \(0.459724\pi\)
\(684\) 2276.92 0.127281
\(685\) 89.6048 0.00499799
\(686\) 686.000 0.0381802
\(687\) −1991.47 −0.110596
\(688\) 4078.03 0.225979
\(689\) 20860.8 1.15346
\(690\) 665.018 0.0366910
\(691\) −19738.4 −1.08666 −0.543332 0.839518i \(-0.682838\pi\)
−0.543332 + 0.839518i \(0.682838\pi\)
\(692\) −5804.97 −0.318890
\(693\) 2711.20 0.148615
\(694\) 9862.65 0.539454
\(695\) 12935.4 0.705996
\(696\) 112.801 0.00614327
\(697\) −11538.3 −0.627035
\(698\) −16225.4 −0.879858
\(699\) 11885.3 0.643123
\(700\) −2849.77 −0.153873
\(701\) 16160.7 0.870727 0.435364 0.900255i \(-0.356620\pi\)
0.435364 + 0.900255i \(0.356620\pi\)
\(702\) −2628.96 −0.141344
\(703\) −10680.2 −0.572990
\(704\) 2754.23 0.147449
\(705\) 7419.12 0.396341
\(706\) 3868.18 0.206205
\(707\) 5085.83 0.270541
\(708\) −1907.80 −0.101271
\(709\) −19644.9 −1.04059 −0.520295 0.853987i \(-0.674178\pi\)
−0.520295 + 0.853987i \(0.674178\pi\)
\(710\) −7502.39 −0.396563
\(711\) −972.222 −0.0512815
\(712\) 7111.62 0.374325
\(713\) 2033.91 0.106831
\(714\) 1040.49 0.0545368
\(715\) 10096.4 0.528088
\(716\) 5528.08 0.288539
\(717\) 8975.86 0.467517
\(718\) −616.334 −0.0320354
\(719\) 8964.56 0.464982 0.232491 0.972599i \(-0.425312\pi\)
0.232491 + 0.972599i \(0.425312\pi\)
\(720\) 693.932 0.0359185
\(721\) 4361.85 0.225303
\(722\) −5717.41 −0.294709
\(723\) 17221.5 0.885855
\(724\) 3303.67 0.169586
\(725\) 478.359 0.0245046
\(726\) −3126.01 −0.159803
\(727\) −10420.1 −0.531581 −0.265791 0.964031i \(-0.585633\pi\)
−0.265791 + 0.964031i \(0.585633\pi\)
\(728\) 2726.33 0.138797
\(729\) 729.000 0.0370370
\(730\) 5070.34 0.257071
\(731\) −6314.20 −0.319479
\(732\) 339.454 0.0171401
\(733\) −30932.4 −1.55868 −0.779341 0.626600i \(-0.784446\pi\)
−0.779341 + 0.626600i \(0.784446\pi\)
\(734\) −13663.6 −0.687103
\(735\) −708.389 −0.0355501
\(736\) −736.000 −0.0368605
\(737\) 34309.0 1.71477
\(738\) 8383.50 0.418158
\(739\) −35846.9 −1.78437 −0.892185 0.451671i \(-0.850828\pi\)
−0.892185 + 0.451671i \(0.850828\pi\)
\(740\) −3254.98 −0.161697
\(741\) −9237.57 −0.457963
\(742\) 5998.85 0.296799
\(743\) −8603.86 −0.424825 −0.212412 0.977180i \(-0.568132\pi\)
−0.212412 + 0.977180i \(0.568132\pi\)
\(744\) 2122.34 0.104582
\(745\) 345.424 0.0169870
\(746\) −20780.5 −1.01988
\(747\) 3683.33 0.180410
\(748\) −4264.50 −0.208457
\(749\) −238.067 −0.0116139
\(750\) 6557.01 0.319237
\(751\) −16424.7 −0.798065 −0.399033 0.916937i \(-0.630654\pi\)
−0.399033 + 0.916937i \(0.630654\pi\)
\(752\) −8211.01 −0.398171
\(753\) −4517.78 −0.218641
\(754\) −457.638 −0.0221037
\(755\) −6202.00 −0.298959
\(756\) −756.000 −0.0363696
\(757\) 29277.3 1.40568 0.702842 0.711346i \(-0.251914\pi\)
0.702842 + 0.711346i \(0.251914\pi\)
\(758\) 9053.70 0.433833
\(759\) 2969.41 0.142006
\(760\) 2438.32 0.116378
\(761\) −4987.56 −0.237580 −0.118790 0.992919i \(-0.537902\pi\)
−0.118790 + 0.992919i \(0.537902\pi\)
\(762\) 9132.28 0.434157
\(763\) −1240.45 −0.0588563
\(764\) 6986.01 0.330818
\(765\) −1074.45 −0.0507800
\(766\) −2543.56 −0.119977
\(767\) 7740.03 0.364376
\(768\) −768.000 −0.0360844
\(769\) 23529.1 1.10336 0.551679 0.834057i \(-0.313987\pi\)
0.551679 + 0.834057i \(0.313987\pi\)
\(770\) 2903.38 0.135884
\(771\) 17961.9 0.839018
\(772\) 10368.0 0.483360
\(773\) 13327.5 0.620125 0.310063 0.950716i \(-0.399650\pi\)
0.310063 + 0.950716i \(0.399650\pi\)
\(774\) 4587.78 0.213055
\(775\) 9000.29 0.417161
\(776\) −2047.19 −0.0947034
\(777\) 3546.12 0.163728
\(778\) −19911.5 −0.917561
\(779\) 29457.7 1.35485
\(780\) −2815.31 −0.129236
\(781\) −33499.3 −1.53483
\(782\) 1139.58 0.0521117
\(783\) 126.901 0.00579193
\(784\) 784.000 0.0357143
\(785\) −7329.19 −0.333235
\(786\) −15198.3 −0.689701
\(787\) 13967.1 0.632624 0.316312 0.948655i \(-0.397555\pi\)
0.316312 + 0.948655i \(0.397555\pi\)
\(788\) −8407.01 −0.380060
\(789\) 5694.55 0.256947
\(790\) −1041.14 −0.0468885
\(791\) −7081.56 −0.318320
\(792\) 3098.51 0.139016
\(793\) −1377.18 −0.0616709
\(794\) 12336.4 0.551391
\(795\) −6194.63 −0.276353
\(796\) 12913.8 0.575020
\(797\) 24891.3 1.10627 0.553133 0.833093i \(-0.313432\pi\)
0.553133 + 0.833093i \(0.313432\pi\)
\(798\) −2656.41 −0.117840
\(799\) 12713.5 0.562917
\(800\) −3256.88 −0.143935
\(801\) 8000.57 0.352917
\(802\) −10269.7 −0.452165
\(803\) 22639.8 0.994947
\(804\) −9566.83 −0.419647
\(805\) −775.855 −0.0339693
\(806\) −8610.43 −0.376290
\(807\) −12951.2 −0.564935
\(808\) 5812.38 0.253068
\(809\) 44812.2 1.94748 0.973742 0.227656i \(-0.0731061\pi\)
0.973742 + 0.227656i \(0.0731061\pi\)
\(810\) 780.674 0.0338643
\(811\) −11709.4 −0.506994 −0.253497 0.967336i \(-0.581581\pi\)
−0.253497 + 0.967336i \(0.581581\pi\)
\(812\) −131.601 −0.00568756
\(813\) 17934.8 0.773677
\(814\) −14534.0 −0.625818
\(815\) 12670.7 0.544584
\(816\) 1189.13 0.0510145
\(817\) 16120.4 0.690309
\(818\) −13611.9 −0.581819
\(819\) 3067.12 0.130859
\(820\) 8977.75 0.382337
\(821\) 8677.96 0.368895 0.184448 0.982842i \(-0.440950\pi\)
0.184448 + 0.982842i \(0.440950\pi\)
\(822\) −111.565 −0.00473391
\(823\) 22764.2 0.964169 0.482084 0.876125i \(-0.339880\pi\)
0.482084 + 0.876125i \(0.339880\pi\)
\(824\) 4984.97 0.210752
\(825\) 13139.9 0.554514
\(826\) 2225.77 0.0937585
\(827\) −2370.25 −0.0996634 −0.0498317 0.998758i \(-0.515868\pi\)
−0.0498317 + 0.998758i \(0.515868\pi\)
\(828\) −828.000 −0.0347524
\(829\) 32978.6 1.38166 0.690830 0.723017i \(-0.257245\pi\)
0.690830 + 0.723017i \(0.257245\pi\)
\(830\) 3944.42 0.164955
\(831\) −12637.3 −0.527536
\(832\) 3115.81 0.129833
\(833\) −1213.90 −0.0504913
\(834\) −16105.6 −0.668693
\(835\) 1226.03 0.0508127
\(836\) 10887.5 0.450420
\(837\) 2387.64 0.0986008
\(838\) 18807.0 0.775272
\(839\) 21927.5 0.902289 0.451145 0.892451i \(-0.351016\pi\)
0.451145 + 0.892451i \(0.351016\pi\)
\(840\) −809.588 −0.0332541
\(841\) −24366.9 −0.999094
\(842\) 4306.64 0.176267
\(843\) −14552.2 −0.594549
\(844\) −10759.9 −0.438829
\(845\) 834.535 0.0339750
\(846\) −9237.38 −0.375399
\(847\) 3647.01 0.147949
\(848\) 6855.82 0.277630
\(849\) −2068.78 −0.0836282
\(850\) 5042.77 0.203489
\(851\) 3883.85 0.156447
\(852\) 9341.07 0.375610
\(853\) −21082.6 −0.846253 −0.423126 0.906071i \(-0.639067\pi\)
−0.423126 + 0.906071i \(0.639067\pi\)
\(854\) −396.030 −0.0158687
\(855\) 2743.11 0.109722
\(856\) −272.077 −0.0108638
\(857\) 34147.1 1.36108 0.680538 0.732713i \(-0.261746\pi\)
0.680538 + 0.732713i \(0.261746\pi\)
\(858\) −12570.8 −0.500186
\(859\) 15856.5 0.629822 0.314911 0.949121i \(-0.398025\pi\)
0.314911 + 0.949121i \(0.398025\pi\)
\(860\) 4912.98 0.194804
\(861\) −9780.75 −0.387139
\(862\) 12693.1 0.501542
\(863\) −34127.0 −1.34611 −0.673057 0.739590i \(-0.735019\pi\)
−0.673057 + 0.739590i \(0.735019\pi\)
\(864\) −864.000 −0.0340207
\(865\) −6993.50 −0.274897
\(866\) −1437.89 −0.0564222
\(867\) 12897.8 0.505228
\(868\) −2476.07 −0.0968240
\(869\) −4648.83 −0.181474
\(870\) 135.896 0.00529577
\(871\) 38813.0 1.50991
\(872\) −1417.66 −0.0550551
\(873\) −2303.09 −0.0892872
\(874\) −2909.40 −0.112600
\(875\) −7649.84 −0.295556
\(876\) −6312.97 −0.243488
\(877\) 22085.6 0.850373 0.425187 0.905106i \(-0.360208\pi\)
0.425187 + 0.905106i \(0.360208\pi\)
\(878\) 14954.2 0.574806
\(879\) 3297.96 0.126550
\(880\) 3318.14 0.127107
\(881\) 17543.1 0.670876 0.335438 0.942062i \(-0.391116\pi\)
0.335438 + 0.942062i \(0.391116\pi\)
\(882\) 882.000 0.0336718
\(883\) 2720.55 0.103685 0.0518424 0.998655i \(-0.483491\pi\)
0.0518424 + 0.998655i \(0.483491\pi\)
\(884\) −4824.34 −0.183552
\(885\) −2298.41 −0.0872998
\(886\) 25406.1 0.963356
\(887\) −9800.00 −0.370972 −0.185486 0.982647i \(-0.559386\pi\)
−0.185486 + 0.982647i \(0.559386\pi\)
\(888\) 4052.71 0.153153
\(889\) −10654.3 −0.401951
\(890\) 8567.67 0.322684
\(891\) 3485.83 0.131066
\(892\) −10369.0 −0.389214
\(893\) −32458.1 −1.21631
\(894\) −430.080 −0.0160895
\(895\) 6659.92 0.248733
\(896\) 896.000 0.0334077
\(897\) 3359.23 0.125041
\(898\) 1268.65 0.0471441
\(899\) 415.630 0.0154194
\(900\) −3663.99 −0.135703
\(901\) −10615.2 −0.392500
\(902\) 40087.0 1.47977
\(903\) −5352.41 −0.197250
\(904\) −8093.21 −0.297761
\(905\) 3980.08 0.146190
\(906\) 7721.97 0.283163
\(907\) −22361.9 −0.818650 −0.409325 0.912389i \(-0.634236\pi\)
−0.409325 + 0.912389i \(0.634236\pi\)
\(908\) 21853.8 0.798726
\(909\) 6538.93 0.238595
\(910\) 3284.53 0.119649
\(911\) 20460.4 0.744109 0.372055 0.928211i \(-0.378653\pi\)
0.372055 + 0.928211i \(0.378653\pi\)
\(912\) −3035.90 −0.110229
\(913\) 17612.4 0.638429
\(914\) 3172.83 0.114823
\(915\) 408.955 0.0147756
\(916\) 2655.30 0.0957790
\(917\) 17731.3 0.638539
\(918\) 1337.77 0.0480969
\(919\) 24141.2 0.866534 0.433267 0.901266i \(-0.357361\pi\)
0.433267 + 0.901266i \(0.357361\pi\)
\(920\) −886.691 −0.0317754
\(921\) 10759.3 0.384942
\(922\) 24549.3 0.876884
\(923\) −37897.1 −1.35146
\(924\) −3614.93 −0.128704
\(925\) 17186.4 0.610905
\(926\) −23962.5 −0.850384
\(927\) 5608.09 0.198699
\(928\) −150.401 −0.00532023
\(929\) −27309.5 −0.964475 −0.482237 0.876041i \(-0.660176\pi\)
−0.482237 + 0.876041i \(0.660176\pi\)
\(930\) 2556.88 0.0901542
\(931\) 3099.15 0.109098
\(932\) −15847.0 −0.556961
\(933\) −3813.74 −0.133822
\(934\) 9871.02 0.345813
\(935\) −5137.63 −0.179699
\(936\) 3505.28 0.122408
\(937\) −47133.7 −1.64332 −0.821659 0.569979i \(-0.806951\pi\)
−0.821659 + 0.569979i \(0.806951\pi\)
\(938\) 11161.3 0.388518
\(939\) 22507.3 0.782214
\(940\) −9892.16 −0.343241
\(941\) −20018.7 −0.693508 −0.346754 0.937956i \(-0.612716\pi\)
−0.346754 + 0.937956i \(0.612716\pi\)
\(942\) 9125.41 0.315628
\(943\) −10712.3 −0.369925
\(944\) 2543.74 0.0877030
\(945\) −910.786 −0.0313522
\(946\) 21937.2 0.753953
\(947\) −5601.37 −0.192207 −0.0961035 0.995371i \(-0.530638\pi\)
−0.0961035 + 0.995371i \(0.530638\pi\)
\(948\) 1296.30 0.0444111
\(949\) 25612.0 0.876080
\(950\) −12874.4 −0.439686
\(951\) 22735.3 0.775230
\(952\) −1387.32 −0.0472303
\(953\) 23276.4 0.791182 0.395591 0.918427i \(-0.370540\pi\)
0.395591 + 0.918427i \(0.370540\pi\)
\(954\) 7712.80 0.261752
\(955\) 8416.35 0.285180
\(956\) −11967.8 −0.404881
\(957\) 606.798 0.0204963
\(958\) −15629.2 −0.527094
\(959\) 130.159 0.00438275
\(960\) −925.243 −0.0311063
\(961\) −21971.0 −0.737503
\(962\) −16442.0 −0.551051
\(963\) −306.087 −0.0102425
\(964\) −22961.9 −0.767173
\(965\) 12490.8 0.416678
\(966\) 966.000 0.0321745
\(967\) 43459.8 1.44527 0.722634 0.691231i \(-0.242931\pi\)
0.722634 + 0.691231i \(0.242931\pi\)
\(968\) 4168.01 0.138393
\(969\) 4700.62 0.155837
\(970\) −2466.34 −0.0816385
\(971\) −53549.4 −1.76981 −0.884904 0.465774i \(-0.845776\pi\)
−0.884904 + 0.465774i \(0.845776\pi\)
\(972\) −972.000 −0.0320750
\(973\) 18789.8 0.619090
\(974\) −3986.27 −0.131138
\(975\) 14864.9 0.488266
\(976\) −452.605 −0.0148438
\(977\) 30132.4 0.986717 0.493358 0.869826i \(-0.335769\pi\)
0.493358 + 0.869826i \(0.335769\pi\)
\(978\) −15776.0 −0.515810
\(979\) 38255.9 1.24889
\(980\) 944.519 0.0307873
\(981\) −1594.87 −0.0519064
\(982\) −4139.04 −0.134503
\(983\) 10266.6 0.333117 0.166558 0.986032i \(-0.446735\pi\)
0.166558 + 0.986032i \(0.446735\pi\)
\(984\) −11178.0 −0.362136
\(985\) −10128.3 −0.327629
\(986\) 232.873 0.00752150
\(987\) 10776.9 0.347552
\(988\) 12316.8 0.396608
\(989\) −5862.17 −0.188479
\(990\) 3732.91 0.119838
\(991\) −8356.87 −0.267876 −0.133938 0.990990i \(-0.542762\pi\)
−0.133938 + 0.990990i \(0.542762\pi\)
\(992\) −2829.79 −0.0905706
\(993\) 15505.0 0.495505
\(994\) −10897.9 −0.347747
\(995\) 15557.8 0.495693
\(996\) −4911.11 −0.156239
\(997\) −25381.3 −0.806254 −0.403127 0.915144i \(-0.632077\pi\)
−0.403127 + 0.915144i \(0.632077\pi\)
\(998\) −33363.2 −1.05821
\(999\) 4559.30 0.144394
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.f.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.f.1.2 3 1.1 even 1 trivial