Properties

Label 8001.2.a.l.1.6
Level 8001
Weight 2
Character 8001.1
Self dual yes
Analytic conductor 63.888
Analytic rank 1
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.118870813.1
Defining polynomial: \(x^{7} - 9 x^{5} - 3 x^{4} + 20 x^{3} + 7 x^{2} - 13 x - 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2667)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.14753\) of defining polynomial
Character \(\chi\) \(=\) 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.15625 q^{2} +2.64943 q^{4} +0.239094 q^{5} +1.00000 q^{7} +1.40032 q^{8} +O(q^{10})\) \(q+2.15625 q^{2} +2.64943 q^{4} +0.239094 q^{5} +1.00000 q^{7} +1.40032 q^{8} +0.515547 q^{10} +3.99784 q^{11} -1.61682 q^{13} +2.15625 q^{14} -2.27940 q^{16} -4.61421 q^{17} -4.17289 q^{19} +0.633462 q^{20} +8.62035 q^{22} -5.22408 q^{23} -4.94283 q^{25} -3.48627 q^{26} +2.64943 q^{28} -9.10130 q^{29} -6.57815 q^{31} -7.71560 q^{32} -9.94939 q^{34} +0.239094 q^{35} -0.353708 q^{37} -8.99781 q^{38} +0.334809 q^{40} +7.72038 q^{41} -7.33166 q^{43} +10.5920 q^{44} -11.2644 q^{46} -3.52396 q^{47} +1.00000 q^{49} -10.6580 q^{50} -4.28365 q^{52} +0.655025 q^{53} +0.955860 q^{55} +1.40032 q^{56} -19.6247 q^{58} +11.8415 q^{59} -7.05891 q^{61} -14.1842 q^{62} -12.0780 q^{64} -0.386572 q^{65} -0.167504 q^{67} -12.2250 q^{68} +0.515547 q^{70} -6.98566 q^{71} -2.79662 q^{73} -0.762683 q^{74} -11.0558 q^{76} +3.99784 q^{77} +14.2526 q^{79} -0.544990 q^{80} +16.6471 q^{82} +6.75526 q^{83} -1.10323 q^{85} -15.8089 q^{86} +5.59827 q^{88} +11.9943 q^{89} -1.61682 q^{91} -13.8408 q^{92} -7.59856 q^{94} -0.997714 q^{95} -1.79091 q^{97} +2.15625 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 2q^{2} + 4q^{4} + 8q^{5} + 7q^{7} + 9q^{8} + O(q^{10}) \) \( 7q + 2q^{2} + 4q^{4} + 8q^{5} + 7q^{7} + 9q^{8} + 3q^{11} - 23q^{13} + 2q^{14} + 2q^{16} - 3q^{17} - 9q^{19} + 9q^{20} - 19q^{22} - 12q^{23} + 3q^{25} - 18q^{26} + 4q^{28} + 9q^{29} - 33q^{31} - 10q^{32} - 2q^{34} + 8q^{35} - 33q^{37} + 3q^{38} - 9q^{40} + 3q^{41} - 9q^{43} - 2q^{44} - 32q^{46} - 11q^{47} + 7q^{49} - 29q^{50} - 21q^{52} - q^{53} - 16q^{55} + 9q^{56} - 5q^{58} + 30q^{59} - 19q^{61} - 3q^{62} - 21q^{64} - 14q^{65} - 30q^{67} - 24q^{68} - 8q^{71} - 20q^{73} + 9q^{74} - 42q^{76} + 3q^{77} + 8q^{79} - 12q^{80} + 10q^{82} + 34q^{83} - 28q^{85} - 24q^{86} - q^{88} + 12q^{89} - 23q^{91} - 60q^{92} - 3q^{94} - 12q^{95} + 7q^{97} + 2q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.15625 1.52470 0.762350 0.647164i \(-0.224045\pi\)
0.762350 + 0.647164i \(0.224045\pi\)
\(3\) 0 0
\(4\) 2.64943 1.32471
\(5\) 0.239094 0.106926 0.0534631 0.998570i \(-0.482974\pi\)
0.0534631 + 0.998570i \(0.482974\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.40032 0.495090
\(9\) 0 0
\(10\) 0.515547 0.163030
\(11\) 3.99784 1.20539 0.602697 0.797970i \(-0.294093\pi\)
0.602697 + 0.797970i \(0.294093\pi\)
\(12\) 0 0
\(13\) −1.61682 −0.448425 −0.224213 0.974540i \(-0.571981\pi\)
−0.224213 + 0.974540i \(0.571981\pi\)
\(14\) 2.15625 0.576283
\(15\) 0 0
\(16\) −2.27940 −0.569849
\(17\) −4.61421 −1.11911 −0.559555 0.828793i \(-0.689028\pi\)
−0.559555 + 0.828793i \(0.689028\pi\)
\(18\) 0 0
\(19\) −4.17289 −0.957328 −0.478664 0.877998i \(-0.658879\pi\)
−0.478664 + 0.877998i \(0.658879\pi\)
\(20\) 0.633462 0.141646
\(21\) 0 0
\(22\) 8.62035 1.83786
\(23\) −5.22408 −1.08930 −0.544648 0.838665i \(-0.683337\pi\)
−0.544648 + 0.838665i \(0.683337\pi\)
\(24\) 0 0
\(25\) −4.94283 −0.988567
\(26\) −3.48627 −0.683714
\(27\) 0 0
\(28\) 2.64943 0.500694
\(29\) −9.10130 −1.69007 −0.845035 0.534712i \(-0.820420\pi\)
−0.845035 + 0.534712i \(0.820420\pi\)
\(30\) 0 0
\(31\) −6.57815 −1.18147 −0.590736 0.806865i \(-0.701162\pi\)
−0.590736 + 0.806865i \(0.701162\pi\)
\(32\) −7.71560 −1.36394
\(33\) 0 0
\(34\) −9.94939 −1.70631
\(35\) 0.239094 0.0404143
\(36\) 0 0
\(37\) −0.353708 −0.0581492 −0.0290746 0.999577i \(-0.509256\pi\)
−0.0290746 + 0.999577i \(0.509256\pi\)
\(38\) −8.99781 −1.45964
\(39\) 0 0
\(40\) 0.334809 0.0529380
\(41\) 7.72038 1.20572 0.602860 0.797847i \(-0.294028\pi\)
0.602860 + 0.797847i \(0.294028\pi\)
\(42\) 0 0
\(43\) −7.33166 −1.11807 −0.559034 0.829145i \(-0.688828\pi\)
−0.559034 + 0.829145i \(0.688828\pi\)
\(44\) 10.5920 1.59680
\(45\) 0 0
\(46\) −11.2644 −1.66085
\(47\) −3.52396 −0.514023 −0.257011 0.966408i \(-0.582738\pi\)
−0.257011 + 0.966408i \(0.582738\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −10.6580 −1.50727
\(51\) 0 0
\(52\) −4.28365 −0.594035
\(53\) 0.655025 0.0899745 0.0449873 0.998988i \(-0.485675\pi\)
0.0449873 + 0.998988i \(0.485675\pi\)
\(54\) 0 0
\(55\) 0.955860 0.128888
\(56\) 1.40032 0.187126
\(57\) 0 0
\(58\) −19.6247 −2.57685
\(59\) 11.8415 1.54163 0.770814 0.637060i \(-0.219850\pi\)
0.770814 + 0.637060i \(0.219850\pi\)
\(60\) 0 0
\(61\) −7.05891 −0.903801 −0.451901 0.892068i \(-0.649254\pi\)
−0.451901 + 0.892068i \(0.649254\pi\)
\(62\) −14.1842 −1.80139
\(63\) 0 0
\(64\) −12.0780 −1.50975
\(65\) −0.386572 −0.0479484
\(66\) 0 0
\(67\) −0.167504 −0.0204638 −0.0102319 0.999948i \(-0.503257\pi\)
−0.0102319 + 0.999948i \(0.503257\pi\)
\(68\) −12.2250 −1.48250
\(69\) 0 0
\(70\) 0.515547 0.0616197
\(71\) −6.98566 −0.829045 −0.414523 0.910039i \(-0.636051\pi\)
−0.414523 + 0.910039i \(0.636051\pi\)
\(72\) 0 0
\(73\) −2.79662 −0.327320 −0.163660 0.986517i \(-0.552330\pi\)
−0.163660 + 0.986517i \(0.552330\pi\)
\(74\) −0.762683 −0.0886601
\(75\) 0 0
\(76\) −11.0558 −1.26818
\(77\) 3.99784 0.455596
\(78\) 0 0
\(79\) 14.2526 1.60354 0.801770 0.597633i \(-0.203892\pi\)
0.801770 + 0.597633i \(0.203892\pi\)
\(80\) −0.544990 −0.0609317
\(81\) 0 0
\(82\) 16.6471 1.83836
\(83\) 6.75526 0.741486 0.370743 0.928735i \(-0.379103\pi\)
0.370743 + 0.928735i \(0.379103\pi\)
\(84\) 0 0
\(85\) −1.10323 −0.119662
\(86\) −15.8089 −1.70472
\(87\) 0 0
\(88\) 5.59827 0.596778
\(89\) 11.9943 1.27140 0.635698 0.771938i \(-0.280712\pi\)
0.635698 + 0.771938i \(0.280712\pi\)
\(90\) 0 0
\(91\) −1.61682 −0.169489
\(92\) −13.8408 −1.44300
\(93\) 0 0
\(94\) −7.59856 −0.783731
\(95\) −0.997714 −0.102363
\(96\) 0 0
\(97\) −1.79091 −0.181840 −0.0909199 0.995858i \(-0.528981\pi\)
−0.0909199 + 0.995858i \(0.528981\pi\)
\(98\) 2.15625 0.217814
\(99\) 0 0
\(100\) −13.0957 −1.30957
\(101\) 11.0925 1.10375 0.551873 0.833928i \(-0.313913\pi\)
0.551873 + 0.833928i \(0.313913\pi\)
\(102\) 0 0
\(103\) 14.5981 1.43839 0.719197 0.694806i \(-0.244510\pi\)
0.719197 + 0.694806i \(0.244510\pi\)
\(104\) −2.26407 −0.222011
\(105\) 0 0
\(106\) 1.41240 0.137184
\(107\) −10.6926 −1.03369 −0.516845 0.856079i \(-0.672894\pi\)
−0.516845 + 0.856079i \(0.672894\pi\)
\(108\) 0 0
\(109\) −19.1750 −1.83664 −0.918318 0.395844i \(-0.870452\pi\)
−0.918318 + 0.395844i \(0.870452\pi\)
\(110\) 2.06107 0.196516
\(111\) 0 0
\(112\) −2.27940 −0.215383
\(113\) 13.9603 1.31327 0.656636 0.754208i \(-0.271979\pi\)
0.656636 + 0.754208i \(0.271979\pi\)
\(114\) 0 0
\(115\) −1.24905 −0.116474
\(116\) −24.1132 −2.23886
\(117\) 0 0
\(118\) 25.5332 2.35052
\(119\) −4.61421 −0.422984
\(120\) 0 0
\(121\) 4.98272 0.452974
\(122\) −15.2208 −1.37803
\(123\) 0 0
\(124\) −17.4283 −1.56511
\(125\) −2.37727 −0.212630
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −10.6120 −0.937978
\(129\) 0 0
\(130\) −0.833547 −0.0731069
\(131\) 1.23738 0.108111 0.0540553 0.998538i \(-0.482785\pi\)
0.0540553 + 0.998538i \(0.482785\pi\)
\(132\) 0 0
\(133\) −4.17289 −0.361836
\(134\) −0.361180 −0.0312012
\(135\) 0 0
\(136\) −6.46139 −0.554059
\(137\) 5.10054 0.435769 0.217884 0.975975i \(-0.430084\pi\)
0.217884 + 0.975975i \(0.430084\pi\)
\(138\) 0 0
\(139\) 12.5215 1.06206 0.531032 0.847352i \(-0.321805\pi\)
0.531032 + 0.847352i \(0.321805\pi\)
\(140\) 0.633462 0.0535373
\(141\) 0 0
\(142\) −15.0628 −1.26405
\(143\) −6.46379 −0.540529
\(144\) 0 0
\(145\) −2.17607 −0.180713
\(146\) −6.03022 −0.499065
\(147\) 0 0
\(148\) −0.937122 −0.0770310
\(149\) −9.58767 −0.785452 −0.392726 0.919655i \(-0.628468\pi\)
−0.392726 + 0.919655i \(0.628468\pi\)
\(150\) 0 0
\(151\) −17.1326 −1.39423 −0.697117 0.716957i \(-0.745534\pi\)
−0.697117 + 0.716957i \(0.745534\pi\)
\(152\) −5.84341 −0.473963
\(153\) 0 0
\(154\) 8.62035 0.694648
\(155\) −1.57280 −0.126330
\(156\) 0 0
\(157\) 7.98480 0.637257 0.318628 0.947880i \(-0.396778\pi\)
0.318628 + 0.947880i \(0.396778\pi\)
\(158\) 30.7322 2.44492
\(159\) 0 0
\(160\) −1.84476 −0.145841
\(161\) −5.22408 −0.411715
\(162\) 0 0
\(163\) 5.01915 0.393130 0.196565 0.980491i \(-0.437021\pi\)
0.196565 + 0.980491i \(0.437021\pi\)
\(164\) 20.4546 1.59723
\(165\) 0 0
\(166\) 14.5661 1.13055
\(167\) −7.58516 −0.586958 −0.293479 0.955966i \(-0.594813\pi\)
−0.293479 + 0.955966i \(0.594813\pi\)
\(168\) 0 0
\(169\) −10.3859 −0.798915
\(170\) −2.37884 −0.182449
\(171\) 0 0
\(172\) −19.4247 −1.48112
\(173\) 4.01343 0.305135 0.152568 0.988293i \(-0.451246\pi\)
0.152568 + 0.988293i \(0.451246\pi\)
\(174\) 0 0
\(175\) −4.94283 −0.373643
\(176\) −9.11266 −0.686893
\(177\) 0 0
\(178\) 25.8628 1.93850
\(179\) 24.8302 1.85590 0.927948 0.372711i \(-0.121572\pi\)
0.927948 + 0.372711i \(0.121572\pi\)
\(180\) 0 0
\(181\) 7.31346 0.543606 0.271803 0.962353i \(-0.412380\pi\)
0.271803 + 0.962353i \(0.412380\pi\)
\(182\) −3.48627 −0.258420
\(183\) 0 0
\(184\) −7.31540 −0.539299
\(185\) −0.0845694 −0.00621767
\(186\) 0 0
\(187\) −18.4469 −1.34897
\(188\) −9.33648 −0.680933
\(189\) 0 0
\(190\) −2.15132 −0.156073
\(191\) 12.4008 0.897293 0.448646 0.893709i \(-0.351906\pi\)
0.448646 + 0.893709i \(0.351906\pi\)
\(192\) 0 0
\(193\) 16.0448 1.15493 0.577465 0.816415i \(-0.304042\pi\)
0.577465 + 0.816415i \(0.304042\pi\)
\(194\) −3.86166 −0.277251
\(195\) 0 0
\(196\) 2.64943 0.189245
\(197\) −12.1872 −0.868304 −0.434152 0.900840i \(-0.642952\pi\)
−0.434152 + 0.900840i \(0.642952\pi\)
\(198\) 0 0
\(199\) 13.7816 0.976950 0.488475 0.872578i \(-0.337553\pi\)
0.488475 + 0.872578i \(0.337553\pi\)
\(200\) −6.92157 −0.489429
\(201\) 0 0
\(202\) 23.9183 1.68288
\(203\) −9.10130 −0.638786
\(204\) 0 0
\(205\) 1.84590 0.128923
\(206\) 31.4772 2.19312
\(207\) 0 0
\(208\) 3.68537 0.255535
\(209\) −16.6826 −1.15396
\(210\) 0 0
\(211\) −12.3776 −0.852111 −0.426056 0.904697i \(-0.640097\pi\)
−0.426056 + 0.904697i \(0.640097\pi\)
\(212\) 1.73544 0.119190
\(213\) 0 0
\(214\) −23.0559 −1.57607
\(215\) −1.75296 −0.119551
\(216\) 0 0
\(217\) −6.57815 −0.446554
\(218\) −41.3462 −2.80032
\(219\) 0 0
\(220\) 2.53248 0.170740
\(221\) 7.46034 0.501837
\(222\) 0 0
\(223\) −16.9298 −1.13370 −0.566852 0.823819i \(-0.691839\pi\)
−0.566852 + 0.823819i \(0.691839\pi\)
\(224\) −7.71560 −0.515520
\(225\) 0 0
\(226\) 30.1019 2.00235
\(227\) 14.4225 0.957256 0.478628 0.878018i \(-0.341134\pi\)
0.478628 + 0.878018i \(0.341134\pi\)
\(228\) 0 0
\(229\) −16.4164 −1.08483 −0.542414 0.840111i \(-0.682490\pi\)
−0.542414 + 0.840111i \(0.682490\pi\)
\(230\) −2.69326 −0.177588
\(231\) 0 0
\(232\) −12.7448 −0.836736
\(233\) 7.64997 0.501167 0.250583 0.968095i \(-0.419378\pi\)
0.250583 + 0.968095i \(0.419378\pi\)
\(234\) 0 0
\(235\) −0.842559 −0.0549625
\(236\) 31.3731 2.04221
\(237\) 0 0
\(238\) −9.94939 −0.644923
\(239\) −8.03695 −0.519867 −0.259933 0.965627i \(-0.583701\pi\)
−0.259933 + 0.965627i \(0.583701\pi\)
\(240\) 0 0
\(241\) −22.8036 −1.46891 −0.734456 0.678657i \(-0.762562\pi\)
−0.734456 + 0.678657i \(0.762562\pi\)
\(242\) 10.7440 0.690650
\(243\) 0 0
\(244\) −18.7021 −1.19728
\(245\) 0.239094 0.0152752
\(246\) 0 0
\(247\) 6.74682 0.429290
\(248\) −9.21155 −0.584934
\(249\) 0 0
\(250\) −5.12600 −0.324197
\(251\) 2.22670 0.140548 0.0702739 0.997528i \(-0.477613\pi\)
0.0702739 + 0.997528i \(0.477613\pi\)
\(252\) 0 0
\(253\) −20.8850 −1.31303
\(254\) −2.15625 −0.135295
\(255\) 0 0
\(256\) 1.27383 0.0796142
\(257\) −12.7786 −0.797110 −0.398555 0.917144i \(-0.630488\pi\)
−0.398555 + 0.917144i \(0.630488\pi\)
\(258\) 0 0
\(259\) −0.353708 −0.0219783
\(260\) −1.02419 −0.0635178
\(261\) 0 0
\(262\) 2.66811 0.164836
\(263\) −1.91222 −0.117912 −0.0589562 0.998261i \(-0.518777\pi\)
−0.0589562 + 0.998261i \(0.518777\pi\)
\(264\) 0 0
\(265\) 0.156612 0.00962063
\(266\) −8.99781 −0.551691
\(267\) 0 0
\(268\) −0.443788 −0.0271087
\(269\) −7.78586 −0.474712 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(270\) 0 0
\(271\) −10.3228 −0.627064 −0.313532 0.949578i \(-0.601512\pi\)
−0.313532 + 0.949578i \(0.601512\pi\)
\(272\) 10.5176 0.637723
\(273\) 0 0
\(274\) 10.9981 0.664417
\(275\) −19.7607 −1.19161
\(276\) 0 0
\(277\) −13.1278 −0.788776 −0.394388 0.918944i \(-0.629043\pi\)
−0.394388 + 0.918944i \(0.629043\pi\)
\(278\) 26.9996 1.61933
\(279\) 0 0
\(280\) 0.334809 0.0200087
\(281\) −18.1404 −1.08216 −0.541081 0.840970i \(-0.681985\pi\)
−0.541081 + 0.840970i \(0.681985\pi\)
\(282\) 0 0
\(283\) −19.1287 −1.13708 −0.568542 0.822655i \(-0.692492\pi\)
−0.568542 + 0.822655i \(0.692492\pi\)
\(284\) −18.5080 −1.09825
\(285\) 0 0
\(286\) −13.9376 −0.824145
\(287\) 7.72038 0.455720
\(288\) 0 0
\(289\) 4.29089 0.252406
\(290\) −4.69215 −0.275533
\(291\) 0 0
\(292\) −7.40944 −0.433604
\(293\) 26.6893 1.55921 0.779603 0.626274i \(-0.215421\pi\)
0.779603 + 0.626274i \(0.215421\pi\)
\(294\) 0 0
\(295\) 2.83122 0.164840
\(296\) −0.495306 −0.0287891
\(297\) 0 0
\(298\) −20.6734 −1.19758
\(299\) 8.44639 0.488468
\(300\) 0 0
\(301\) −7.33166 −0.422590
\(302\) −36.9423 −2.12579
\(303\) 0 0
\(304\) 9.51168 0.545532
\(305\) −1.68774 −0.0966400
\(306\) 0 0
\(307\) 9.45867 0.539835 0.269917 0.962883i \(-0.413004\pi\)
0.269917 + 0.962883i \(0.413004\pi\)
\(308\) 10.5920 0.603534
\(309\) 0 0
\(310\) −3.39135 −0.192616
\(311\) −1.98631 −0.112633 −0.0563167 0.998413i \(-0.517936\pi\)
−0.0563167 + 0.998413i \(0.517936\pi\)
\(312\) 0 0
\(313\) −20.0441 −1.13296 −0.566480 0.824075i \(-0.691695\pi\)
−0.566480 + 0.824075i \(0.691695\pi\)
\(314\) 17.2173 0.971626
\(315\) 0 0
\(316\) 37.7611 2.12423
\(317\) 27.2490 1.53046 0.765228 0.643760i \(-0.222626\pi\)
0.765228 + 0.643760i \(0.222626\pi\)
\(318\) 0 0
\(319\) −36.3855 −2.03720
\(320\) −2.88778 −0.161432
\(321\) 0 0
\(322\) −11.2644 −0.627742
\(323\) 19.2546 1.07135
\(324\) 0 0
\(325\) 7.99168 0.443298
\(326\) 10.8226 0.599406
\(327\) 0 0
\(328\) 10.8110 0.596940
\(329\) −3.52396 −0.194282
\(330\) 0 0
\(331\) 34.0423 1.87113 0.935567 0.353150i \(-0.114889\pi\)
0.935567 + 0.353150i \(0.114889\pi\)
\(332\) 17.8976 0.982256
\(333\) 0 0
\(334\) −16.3555 −0.894935
\(335\) −0.0400491 −0.00218812
\(336\) 0 0
\(337\) −13.1131 −0.714318 −0.357159 0.934044i \(-0.616255\pi\)
−0.357159 + 0.934044i \(0.616255\pi\)
\(338\) −22.3946 −1.21811
\(339\) 0 0
\(340\) −2.92292 −0.158518
\(341\) −26.2984 −1.42414
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −10.2667 −0.553543
\(345\) 0 0
\(346\) 8.65396 0.465240
\(347\) 8.22380 0.441477 0.220738 0.975333i \(-0.429153\pi\)
0.220738 + 0.975333i \(0.429153\pi\)
\(348\) 0 0
\(349\) −22.6433 −1.21207 −0.606035 0.795438i \(-0.707241\pi\)
−0.606035 + 0.795438i \(0.707241\pi\)
\(350\) −10.6580 −0.569694
\(351\) 0 0
\(352\) −30.8457 −1.64408
\(353\) 22.9217 1.22000 0.610000 0.792401i \(-0.291169\pi\)
0.610000 + 0.792401i \(0.291169\pi\)
\(354\) 0 0
\(355\) −1.67023 −0.0886466
\(356\) 31.7781 1.68423
\(357\) 0 0
\(358\) 53.5402 2.82969
\(359\) −22.9728 −1.21246 −0.606230 0.795289i \(-0.707319\pi\)
−0.606230 + 0.795289i \(0.707319\pi\)
\(360\) 0 0
\(361\) −1.58696 −0.0835240
\(362\) 15.7697 0.828836
\(363\) 0 0
\(364\) −4.28365 −0.224524
\(365\) −0.668655 −0.0349990
\(366\) 0 0
\(367\) −2.80411 −0.146373 −0.0731866 0.997318i \(-0.523317\pi\)
−0.0731866 + 0.997318i \(0.523317\pi\)
\(368\) 11.9077 0.620734
\(369\) 0 0
\(370\) −0.182353 −0.00948008
\(371\) 0.655025 0.0340072
\(372\) 0 0
\(373\) −35.2417 −1.82475 −0.912374 0.409358i \(-0.865753\pi\)
−0.912374 + 0.409358i \(0.865753\pi\)
\(374\) −39.7761 −2.05677
\(375\) 0 0
\(376\) −4.93469 −0.254487
\(377\) 14.7152 0.757870
\(378\) 0 0
\(379\) −8.26039 −0.424308 −0.212154 0.977236i \(-0.568048\pi\)
−0.212154 + 0.977236i \(0.568048\pi\)
\(380\) −2.64337 −0.135602
\(381\) 0 0
\(382\) 26.7393 1.36810
\(383\) 6.69505 0.342101 0.171050 0.985262i \(-0.445284\pi\)
0.171050 + 0.985262i \(0.445284\pi\)
\(384\) 0 0
\(385\) 0.955860 0.0487151
\(386\) 34.5966 1.76092
\(387\) 0 0
\(388\) −4.74489 −0.240885
\(389\) 13.4050 0.679658 0.339829 0.940487i \(-0.389631\pi\)
0.339829 + 0.940487i \(0.389631\pi\)
\(390\) 0 0
\(391\) 24.1050 1.21904
\(392\) 1.40032 0.0707271
\(393\) 0 0
\(394\) −26.2787 −1.32390
\(395\) 3.40771 0.171460
\(396\) 0 0
\(397\) 1.27937 0.0642097 0.0321048 0.999485i \(-0.489779\pi\)
0.0321048 + 0.999485i \(0.489779\pi\)
\(398\) 29.7165 1.48956
\(399\) 0 0
\(400\) 11.2667 0.563334
\(401\) 25.8637 1.29157 0.645785 0.763519i \(-0.276530\pi\)
0.645785 + 0.763519i \(0.276530\pi\)
\(402\) 0 0
\(403\) 10.6357 0.529802
\(404\) 29.3888 1.46215
\(405\) 0 0
\(406\) −19.6247 −0.973958
\(407\) −1.41407 −0.0700927
\(408\) 0 0
\(409\) −8.40634 −0.415667 −0.207833 0.978164i \(-0.566641\pi\)
−0.207833 + 0.978164i \(0.566641\pi\)
\(410\) 3.98022 0.196569
\(411\) 0 0
\(412\) 38.6766 1.90546
\(413\) 11.8415 0.582681
\(414\) 0 0
\(415\) 1.61514 0.0792843
\(416\) 12.4747 0.611625
\(417\) 0 0
\(418\) −35.9718 −1.75944
\(419\) −12.0193 −0.587183 −0.293592 0.955931i \(-0.594851\pi\)
−0.293592 + 0.955931i \(0.594851\pi\)
\(420\) 0 0
\(421\) 27.5197 1.34123 0.670614 0.741807i \(-0.266031\pi\)
0.670614 + 0.741807i \(0.266031\pi\)
\(422\) −26.6893 −1.29922
\(423\) 0 0
\(424\) 0.917247 0.0445455
\(425\) 22.8073 1.10631
\(426\) 0 0
\(427\) −7.05891 −0.341605
\(428\) −28.3292 −1.36934
\(429\) 0 0
\(430\) −3.77981 −0.182279
\(431\) −35.4733 −1.70869 −0.854345 0.519707i \(-0.826041\pi\)
−0.854345 + 0.519707i \(0.826041\pi\)
\(432\) 0 0
\(433\) 26.5237 1.27465 0.637323 0.770597i \(-0.280042\pi\)
0.637323 + 0.770597i \(0.280042\pi\)
\(434\) −14.1842 −0.680862
\(435\) 0 0
\(436\) −50.8028 −2.43301
\(437\) 21.7995 1.04281
\(438\) 0 0
\(439\) −32.6301 −1.55735 −0.778674 0.627428i \(-0.784108\pi\)
−0.778674 + 0.627428i \(0.784108\pi\)
\(440\) 1.33851 0.0638111
\(441\) 0 0
\(442\) 16.0864 0.765151
\(443\) −16.0947 −0.764681 −0.382340 0.924022i \(-0.624882\pi\)
−0.382340 + 0.924022i \(0.624882\pi\)
\(444\) 0 0
\(445\) 2.86777 0.135945
\(446\) −36.5050 −1.72856
\(447\) 0 0
\(448\) −12.0780 −0.570632
\(449\) −33.1478 −1.56434 −0.782171 0.623064i \(-0.785888\pi\)
−0.782171 + 0.623064i \(0.785888\pi\)
\(450\) 0 0
\(451\) 30.8648 1.45337
\(452\) 36.9867 1.73971
\(453\) 0 0
\(454\) 31.0986 1.45953
\(455\) −0.386572 −0.0181228
\(456\) 0 0
\(457\) −20.7795 −0.972026 −0.486013 0.873952i \(-0.661549\pi\)
−0.486013 + 0.873952i \(0.661549\pi\)
\(458\) −35.3980 −1.65404
\(459\) 0 0
\(460\) −3.30925 −0.154295
\(461\) −26.0027 −1.21106 −0.605532 0.795821i \(-0.707040\pi\)
−0.605532 + 0.795821i \(0.707040\pi\)
\(462\) 0 0
\(463\) 1.40695 0.0653867 0.0326934 0.999465i \(-0.489592\pi\)
0.0326934 + 0.999465i \(0.489592\pi\)
\(464\) 20.7455 0.963084
\(465\) 0 0
\(466\) 16.4953 0.764129
\(467\) 4.52880 0.209568 0.104784 0.994495i \(-0.466585\pi\)
0.104784 + 0.994495i \(0.466585\pi\)
\(468\) 0 0
\(469\) −0.167504 −0.00773460
\(470\) −1.81677 −0.0838013
\(471\) 0 0
\(472\) 16.5819 0.763244
\(473\) −29.3108 −1.34771
\(474\) 0 0
\(475\) 20.6259 0.946382
\(476\) −12.2250 −0.560332
\(477\) 0 0
\(478\) −17.3297 −0.792641
\(479\) −1.74794 −0.0798653 −0.0399327 0.999202i \(-0.512714\pi\)
−0.0399327 + 0.999202i \(0.512714\pi\)
\(480\) 0 0
\(481\) 0.571882 0.0260756
\(482\) −49.1704 −2.23965
\(483\) 0 0
\(484\) 13.2013 0.600061
\(485\) −0.428197 −0.0194434
\(486\) 0 0
\(487\) −25.2382 −1.14365 −0.571827 0.820375i \(-0.693765\pi\)
−0.571827 + 0.820375i \(0.693765\pi\)
\(488\) −9.88477 −0.447463
\(489\) 0 0
\(490\) 0.515547 0.0232900
\(491\) 27.1705 1.22619 0.613093 0.790010i \(-0.289925\pi\)
0.613093 + 0.790010i \(0.289925\pi\)
\(492\) 0 0
\(493\) 41.9953 1.89137
\(494\) 14.5478 0.654539
\(495\) 0 0
\(496\) 14.9942 0.673260
\(497\) −6.98566 −0.313350
\(498\) 0 0
\(499\) −18.9409 −0.847909 −0.423955 0.905683i \(-0.639358\pi\)
−0.423955 + 0.905683i \(0.639358\pi\)
\(500\) −6.29841 −0.281673
\(501\) 0 0
\(502\) 4.80132 0.214293
\(503\) 2.52810 0.112722 0.0563611 0.998410i \(-0.482050\pi\)
0.0563611 + 0.998410i \(0.482050\pi\)
\(504\) 0 0
\(505\) 2.65216 0.118019
\(506\) −45.0334 −2.00198
\(507\) 0 0
\(508\) −2.64943 −0.117549
\(509\) −34.9093 −1.54733 −0.773663 0.633598i \(-0.781578\pi\)
−0.773663 + 0.633598i \(0.781578\pi\)
\(510\) 0 0
\(511\) −2.79662 −0.123715
\(512\) 23.9707 1.05937
\(513\) 0 0
\(514\) −27.5540 −1.21535
\(515\) 3.49032 0.153802
\(516\) 0 0
\(517\) −14.0882 −0.619600
\(518\) −0.762683 −0.0335104
\(519\) 0 0
\(520\) −0.541327 −0.0237387
\(521\) −8.56576 −0.375273 −0.187636 0.982239i \(-0.560083\pi\)
−0.187636 + 0.982239i \(0.560083\pi\)
\(522\) 0 0
\(523\) 2.00260 0.0875675 0.0437838 0.999041i \(-0.486059\pi\)
0.0437838 + 0.999041i \(0.486059\pi\)
\(524\) 3.27835 0.143215
\(525\) 0 0
\(526\) −4.12322 −0.179781
\(527\) 30.3530 1.32220
\(528\) 0 0
\(529\) 4.29098 0.186564
\(530\) 0.337696 0.0146686
\(531\) 0 0
\(532\) −11.0558 −0.479328
\(533\) −12.4825 −0.540676
\(534\) 0 0
\(535\) −2.55653 −0.110528
\(536\) −0.234559 −0.0101314
\(537\) 0 0
\(538\) −16.7883 −0.723794
\(539\) 3.99784 0.172199
\(540\) 0 0
\(541\) −14.8542 −0.638632 −0.319316 0.947648i \(-0.603453\pi\)
−0.319316 + 0.947648i \(0.603453\pi\)
\(542\) −22.2585 −0.956085
\(543\) 0 0
\(544\) 35.6014 1.52640
\(545\) −4.58464 −0.196384
\(546\) 0 0
\(547\) 9.86356 0.421735 0.210868 0.977515i \(-0.432371\pi\)
0.210868 + 0.977515i \(0.432371\pi\)
\(548\) 13.5135 0.577268
\(549\) 0 0
\(550\) −42.6090 −1.81685
\(551\) 37.9788 1.61795
\(552\) 0 0
\(553\) 14.2526 0.606081
\(554\) −28.3069 −1.20265
\(555\) 0 0
\(556\) 33.1749 1.40693
\(557\) 1.50087 0.0635939 0.0317970 0.999494i \(-0.489877\pi\)
0.0317970 + 0.999494i \(0.489877\pi\)
\(558\) 0 0
\(559\) 11.8540 0.501370
\(560\) −0.544990 −0.0230300
\(561\) 0 0
\(562\) −39.1152 −1.64997
\(563\) −40.5430 −1.70868 −0.854341 0.519713i \(-0.826039\pi\)
−0.854341 + 0.519713i \(0.826039\pi\)
\(564\) 0 0
\(565\) 3.33782 0.140423
\(566\) −41.2463 −1.73371
\(567\) 0 0
\(568\) −9.78219 −0.410452
\(569\) −3.51593 −0.147396 −0.0736978 0.997281i \(-0.523480\pi\)
−0.0736978 + 0.997281i \(0.523480\pi\)
\(570\) 0 0
\(571\) −39.7252 −1.66245 −0.831224 0.555937i \(-0.812359\pi\)
−0.831224 + 0.555937i \(0.812359\pi\)
\(572\) −17.1253 −0.716046
\(573\) 0 0
\(574\) 16.6471 0.694836
\(575\) 25.8217 1.07684
\(576\) 0 0
\(577\) 34.1969 1.42364 0.711818 0.702364i \(-0.247872\pi\)
0.711818 + 0.702364i \(0.247872\pi\)
\(578\) 9.25225 0.384843
\(579\) 0 0
\(580\) −5.76533 −0.239392
\(581\) 6.75526 0.280256
\(582\) 0 0
\(583\) 2.61868 0.108455
\(584\) −3.91618 −0.162053
\(585\) 0 0
\(586\) 57.5489 2.37732
\(587\) 14.5520 0.600625 0.300313 0.953841i \(-0.402909\pi\)
0.300313 + 0.953841i \(0.402909\pi\)
\(588\) 0 0
\(589\) 27.4499 1.13105
\(590\) 6.10483 0.251332
\(591\) 0 0
\(592\) 0.806240 0.0331363
\(593\) 22.6700 0.930947 0.465473 0.885062i \(-0.345884\pi\)
0.465473 + 0.885062i \(0.345884\pi\)
\(594\) 0 0
\(595\) −1.10323 −0.0452280
\(596\) −25.4018 −1.04050
\(597\) 0 0
\(598\) 18.2126 0.744767
\(599\) −19.5665 −0.799466 −0.399733 0.916632i \(-0.630897\pi\)
−0.399733 + 0.916632i \(0.630897\pi\)
\(600\) 0 0
\(601\) 7.31719 0.298475 0.149237 0.988801i \(-0.452318\pi\)
0.149237 + 0.988801i \(0.452318\pi\)
\(602\) −15.8089 −0.644323
\(603\) 0 0
\(604\) −45.3917 −1.84696
\(605\) 1.19134 0.0484348
\(606\) 0 0
\(607\) 25.1482 1.02074 0.510368 0.859956i \(-0.329509\pi\)
0.510368 + 0.859956i \(0.329509\pi\)
\(608\) 32.1964 1.30574
\(609\) 0 0
\(610\) −3.63920 −0.147347
\(611\) 5.69762 0.230501
\(612\) 0 0
\(613\) 40.8861 1.65137 0.825686 0.564129i \(-0.190788\pi\)
0.825686 + 0.564129i \(0.190788\pi\)
\(614\) 20.3953 0.823087
\(615\) 0 0
\(616\) 5.59827 0.225561
\(617\) −23.3040 −0.938185 −0.469092 0.883149i \(-0.655419\pi\)
−0.469092 + 0.883149i \(0.655419\pi\)
\(618\) 0 0
\(619\) 36.2218 1.45588 0.727939 0.685642i \(-0.240478\pi\)
0.727939 + 0.685642i \(0.240478\pi\)
\(620\) −4.16701 −0.167351
\(621\) 0 0
\(622\) −4.28299 −0.171732
\(623\) 11.9943 0.480543
\(624\) 0 0
\(625\) 24.1458 0.965831
\(626\) −43.2202 −1.72743
\(627\) 0 0
\(628\) 21.1551 0.844182
\(629\) 1.63208 0.0650753
\(630\) 0 0
\(631\) 44.1474 1.75748 0.878741 0.477299i \(-0.158384\pi\)
0.878741 + 0.477299i \(0.158384\pi\)
\(632\) 19.9582 0.793896
\(633\) 0 0
\(634\) 58.7557 2.33349
\(635\) −0.239094 −0.00948816
\(636\) 0 0
\(637\) −1.61682 −0.0640608
\(638\) −78.4564 −3.10612
\(639\) 0 0
\(640\) −2.53727 −0.100294
\(641\) −20.5976 −0.813557 −0.406779 0.913527i \(-0.633348\pi\)
−0.406779 + 0.913527i \(0.633348\pi\)
\(642\) 0 0
\(643\) −3.13591 −0.123668 −0.0618342 0.998086i \(-0.519695\pi\)
−0.0618342 + 0.998086i \(0.519695\pi\)
\(644\) −13.8408 −0.545404
\(645\) 0 0
\(646\) 41.5178 1.63349
\(647\) −6.98764 −0.274712 −0.137356 0.990522i \(-0.543861\pi\)
−0.137356 + 0.990522i \(0.543861\pi\)
\(648\) 0 0
\(649\) 47.3403 1.85827
\(650\) 17.2321 0.675897
\(651\) 0 0
\(652\) 13.2979 0.520784
\(653\) −18.7511 −0.733786 −0.366893 0.930263i \(-0.619578\pi\)
−0.366893 + 0.930263i \(0.619578\pi\)
\(654\) 0 0
\(655\) 0.295851 0.0115598
\(656\) −17.5978 −0.687079
\(657\) 0 0
\(658\) −7.59856 −0.296223
\(659\) −28.0273 −1.09179 −0.545895 0.837854i \(-0.683810\pi\)
−0.545895 + 0.837854i \(0.683810\pi\)
\(660\) 0 0
\(661\) −46.8900 −1.82381 −0.911905 0.410401i \(-0.865389\pi\)
−0.911905 + 0.410401i \(0.865389\pi\)
\(662\) 73.4038 2.85292
\(663\) 0 0
\(664\) 9.45956 0.367102
\(665\) −0.997714 −0.0386897
\(666\) 0 0
\(667\) 47.5459 1.84098
\(668\) −20.0963 −0.777550
\(669\) 0 0
\(670\) −0.0863560 −0.00333622
\(671\) −28.2204 −1.08944
\(672\) 0 0
\(673\) 30.2264 1.16514 0.582571 0.812780i \(-0.302047\pi\)
0.582571 + 0.812780i \(0.302047\pi\)
\(674\) −28.2752 −1.08912
\(675\) 0 0
\(676\) −27.5166 −1.05833
\(677\) 4.66520 0.179298 0.0896491 0.995973i \(-0.471425\pi\)
0.0896491 + 0.995973i \(0.471425\pi\)
\(678\) 0 0
\(679\) −1.79091 −0.0687290
\(680\) −1.54488 −0.0592434
\(681\) 0 0
\(682\) −56.7060 −2.17138
\(683\) 34.8003 1.33160 0.665798 0.746132i \(-0.268091\pi\)
0.665798 + 0.746132i \(0.268091\pi\)
\(684\) 0 0
\(685\) 1.21951 0.0465951
\(686\) 2.15625 0.0823261
\(687\) 0 0
\(688\) 16.7118 0.637130
\(689\) −1.05906 −0.0403469
\(690\) 0 0
\(691\) 36.6726 1.39509 0.697546 0.716540i \(-0.254275\pi\)
0.697546 + 0.716540i \(0.254275\pi\)
\(692\) 10.6333 0.404216
\(693\) 0 0
\(694\) 17.7326 0.673120
\(695\) 2.99383 0.113562
\(696\) 0 0
\(697\) −35.6234 −1.34933
\(698\) −48.8247 −1.84804
\(699\) 0 0
\(700\) −13.0957 −0.494970
\(701\) 11.0457 0.417192 0.208596 0.978002i \(-0.433111\pi\)
0.208596 + 0.978002i \(0.433111\pi\)
\(702\) 0 0
\(703\) 1.47598 0.0556678
\(704\) −48.2859 −1.81984
\(705\) 0 0
\(706\) 49.4250 1.86014
\(707\) 11.0925 0.417177
\(708\) 0 0
\(709\) −7.73369 −0.290445 −0.145222 0.989399i \(-0.546390\pi\)
−0.145222 + 0.989399i \(0.546390\pi\)
\(710\) −3.60144 −0.135160
\(711\) 0 0
\(712\) 16.7960 0.629455
\(713\) 34.3648 1.28697
\(714\) 0 0
\(715\) −1.54545 −0.0577967
\(716\) 65.7857 2.45853
\(717\) 0 0
\(718\) −49.5353 −1.84864
\(719\) 50.9775 1.90114 0.950571 0.310509i \(-0.100499\pi\)
0.950571 + 0.310509i \(0.100499\pi\)
\(720\) 0 0
\(721\) 14.5981 0.543662
\(722\) −3.42188 −0.127349
\(723\) 0 0
\(724\) 19.3765 0.720121
\(725\) 44.9862 1.67075
\(726\) 0 0
\(727\) −6.89848 −0.255850 −0.127925 0.991784i \(-0.540832\pi\)
−0.127925 + 0.991784i \(0.540832\pi\)
\(728\) −2.26407 −0.0839122
\(729\) 0 0
\(730\) −1.44179 −0.0533630
\(731\) 33.8298 1.25124
\(732\) 0 0
\(733\) 6.77021 0.250063 0.125032 0.992153i \(-0.460097\pi\)
0.125032 + 0.992153i \(0.460097\pi\)
\(734\) −6.04636 −0.223175
\(735\) 0 0
\(736\) 40.3069 1.48573
\(737\) −0.669652 −0.0246670
\(738\) 0 0
\(739\) 10.2163 0.375814 0.187907 0.982187i \(-0.439830\pi\)
0.187907 + 0.982187i \(0.439830\pi\)
\(740\) −0.224060 −0.00823662
\(741\) 0 0
\(742\) 1.41240 0.0518508
\(743\) −3.12087 −0.114493 −0.0572467 0.998360i \(-0.518232\pi\)
−0.0572467 + 0.998360i \(0.518232\pi\)
\(744\) 0 0
\(745\) −2.29235 −0.0839854
\(746\) −75.9901 −2.78219
\(747\) 0 0
\(748\) −48.8736 −1.78699
\(749\) −10.6926 −0.390698
\(750\) 0 0
\(751\) 17.9651 0.655557 0.327778 0.944755i \(-0.393700\pi\)
0.327778 + 0.944755i \(0.393700\pi\)
\(752\) 8.03251 0.292916
\(753\) 0 0
\(754\) 31.7296 1.15552
\(755\) −4.09631 −0.149080
\(756\) 0 0
\(757\) −41.8801 −1.52216 −0.761080 0.648658i \(-0.775330\pi\)
−0.761080 + 0.648658i \(0.775330\pi\)
\(758\) −17.8115 −0.646942
\(759\) 0 0
\(760\) −1.39712 −0.0506790
\(761\) −47.4903 −1.72152 −0.860761 0.509010i \(-0.830012\pi\)
−0.860761 + 0.509010i \(0.830012\pi\)
\(762\) 0 0
\(763\) −19.1750 −0.694183
\(764\) 32.8551 1.18866
\(765\) 0 0
\(766\) 14.4362 0.521602
\(767\) −19.1455 −0.691305
\(768\) 0 0
\(769\) 44.5562 1.60674 0.803369 0.595481i \(-0.203039\pi\)
0.803369 + 0.595481i \(0.203039\pi\)
\(770\) 2.06107 0.0742760
\(771\) 0 0
\(772\) 42.5095 1.52995
\(773\) −28.7248 −1.03316 −0.516580 0.856239i \(-0.672795\pi\)
−0.516580 + 0.856239i \(0.672795\pi\)
\(774\) 0 0
\(775\) 32.5147 1.16796
\(776\) −2.50786 −0.0900270
\(777\) 0 0
\(778\) 28.9045 1.03628
\(779\) −32.2163 −1.15427
\(780\) 0 0
\(781\) −27.9275 −0.999326
\(782\) 51.9764 1.85867
\(783\) 0 0
\(784\) −2.27940 −0.0814070
\(785\) 1.90912 0.0681394
\(786\) 0 0
\(787\) −6.88490 −0.245420 −0.122710 0.992443i \(-0.539159\pi\)
−0.122710 + 0.992443i \(0.539159\pi\)
\(788\) −32.2891 −1.15025
\(789\) 0 0
\(790\) 7.34788 0.261426
\(791\) 13.9603 0.496370
\(792\) 0 0
\(793\) 11.4130 0.405287
\(794\) 2.75864 0.0979006
\(795\) 0 0
\(796\) 36.5132 1.29418
\(797\) −19.8500 −0.703123 −0.351562 0.936165i \(-0.614349\pi\)
−0.351562 + 0.936165i \(0.614349\pi\)
\(798\) 0 0
\(799\) 16.2603 0.575248
\(800\) 38.1370 1.34834
\(801\) 0 0
\(802\) 55.7686 1.96926
\(803\) −11.1804 −0.394549
\(804\) 0 0
\(805\) −1.24905 −0.0440231
\(806\) 22.9332 0.807789
\(807\) 0 0
\(808\) 15.5331 0.546454
\(809\) 18.8305 0.662046 0.331023 0.943623i \(-0.392606\pi\)
0.331023 + 0.943623i \(0.392606\pi\)
\(810\) 0 0
\(811\) −47.7100 −1.67533 −0.837663 0.546188i \(-0.816078\pi\)
−0.837663 + 0.546188i \(0.816078\pi\)
\(812\) −24.1132 −0.846208
\(813\) 0 0
\(814\) −3.04908 −0.106870
\(815\) 1.20005 0.0420359
\(816\) 0 0
\(817\) 30.5942 1.07036
\(818\) −18.1262 −0.633768
\(819\) 0 0
\(820\) 4.89057 0.170786
\(821\) −25.1137 −0.876475 −0.438238 0.898859i \(-0.644397\pi\)
−0.438238 + 0.898859i \(0.644397\pi\)
\(822\) 0 0
\(823\) 43.0088 1.49919 0.749597 0.661895i \(-0.230247\pi\)
0.749597 + 0.661895i \(0.230247\pi\)
\(824\) 20.4421 0.712134
\(825\) 0 0
\(826\) 25.5332 0.888413
\(827\) −13.8440 −0.481403 −0.240701 0.970599i \(-0.577377\pi\)
−0.240701 + 0.970599i \(0.577377\pi\)
\(828\) 0 0
\(829\) 12.5853 0.437105 0.218553 0.975825i \(-0.429867\pi\)
0.218553 + 0.975825i \(0.429867\pi\)
\(830\) 3.48266 0.120885
\(831\) 0 0
\(832\) 19.5280 0.677010
\(833\) −4.61421 −0.159873
\(834\) 0 0
\(835\) −1.81357 −0.0627611
\(836\) −44.1992 −1.52866
\(837\) 0 0
\(838\) −25.9167 −0.895279
\(839\) 4.46813 0.154257 0.0771284 0.997021i \(-0.475425\pi\)
0.0771284 + 0.997021i \(0.475425\pi\)
\(840\) 0 0
\(841\) 53.8337 1.85633
\(842\) 59.3394 2.04497
\(843\) 0 0
\(844\) −32.7936 −1.12880
\(845\) −2.48320 −0.0854248
\(846\) 0 0
\(847\) 4.98272 0.171208
\(848\) −1.49306 −0.0512719
\(849\) 0 0
\(850\) 49.1782 1.68680
\(851\) 1.84780 0.0633416
\(852\) 0 0
\(853\) −20.9580 −0.717589 −0.358795 0.933416i \(-0.616812\pi\)
−0.358795 + 0.933416i \(0.616812\pi\)
\(854\) −15.2208 −0.520845
\(855\) 0 0
\(856\) −14.9731 −0.511769
\(857\) 3.36198 0.114843 0.0574216 0.998350i \(-0.481712\pi\)
0.0574216 + 0.998350i \(0.481712\pi\)
\(858\) 0 0
\(859\) 31.0025 1.05779 0.528895 0.848687i \(-0.322607\pi\)
0.528895 + 0.848687i \(0.322607\pi\)
\(860\) −4.64432 −0.158370
\(861\) 0 0
\(862\) −76.4894 −2.60524
\(863\) −8.87723 −0.302185 −0.151092 0.988520i \(-0.548279\pi\)
−0.151092 + 0.988520i \(0.548279\pi\)
\(864\) 0 0
\(865\) 0.959586 0.0326269
\(866\) 57.1917 1.94345
\(867\) 0 0
\(868\) −17.4283 −0.591556
\(869\) 56.9795 1.93290
\(870\) 0 0
\(871\) 0.270823 0.00917650
\(872\) −26.8513 −0.909299
\(873\) 0 0
\(874\) 47.0053 1.58998
\(875\) −2.37727 −0.0803665
\(876\) 0 0
\(877\) −19.3103 −0.652061 −0.326030 0.945359i \(-0.605711\pi\)
−0.326030 + 0.945359i \(0.605711\pi\)
\(878\) −70.3587 −2.37449
\(879\) 0 0
\(880\) −2.17878 −0.0734468
\(881\) −3.30078 −0.111206 −0.0556030 0.998453i \(-0.517708\pi\)
−0.0556030 + 0.998453i \(0.517708\pi\)
\(882\) 0 0
\(883\) 51.9315 1.74764 0.873818 0.486253i \(-0.161637\pi\)
0.873818 + 0.486253i \(0.161637\pi\)
\(884\) 19.7656 0.664790
\(885\) 0 0
\(886\) −34.7042 −1.16591
\(887\) −9.29948 −0.312246 −0.156123 0.987738i \(-0.549900\pi\)
−0.156123 + 0.987738i \(0.549900\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 6.18364 0.207276
\(891\) 0 0
\(892\) −44.8543 −1.50183
\(893\) 14.7051 0.492088
\(894\) 0 0
\(895\) 5.93675 0.198444
\(896\) −10.6120 −0.354522
\(897\) 0 0
\(898\) −71.4750 −2.38515
\(899\) 59.8698 1.99677
\(900\) 0 0
\(901\) −3.02242 −0.100691
\(902\) 66.5524 2.21595
\(903\) 0 0
\(904\) 19.5489 0.650187
\(905\) 1.74861 0.0581256
\(906\) 0 0
\(907\) −31.2600 −1.03797 −0.518985 0.854783i \(-0.673690\pi\)
−0.518985 + 0.854783i \(0.673690\pi\)
\(908\) 38.2114 1.26809
\(909\) 0 0
\(910\) −0.833547 −0.0276318
\(911\) 30.7338 1.01826 0.509128 0.860691i \(-0.329968\pi\)
0.509128 + 0.860691i \(0.329968\pi\)
\(912\) 0 0
\(913\) 27.0065 0.893783
\(914\) −44.8059 −1.48205
\(915\) 0 0
\(916\) −43.4941 −1.43709
\(917\) 1.23738 0.0408619
\(918\) 0 0
\(919\) 7.17530 0.236691 0.118346 0.992972i \(-0.462241\pi\)
0.118346 + 0.992972i \(0.462241\pi\)
\(920\) −1.74907 −0.0576651
\(921\) 0 0
\(922\) −56.0683 −1.84651
\(923\) 11.2946 0.371765
\(924\) 0 0
\(925\) 1.74832 0.0574844
\(926\) 3.03375 0.0996952
\(927\) 0 0
\(928\) 70.2220 2.30515
\(929\) −23.3488 −0.766051 −0.383025 0.923738i \(-0.625118\pi\)
−0.383025 + 0.923738i \(0.625118\pi\)
\(930\) 0 0
\(931\) −4.17289 −0.136761
\(932\) 20.2680 0.663902
\(933\) 0 0
\(934\) 9.76524 0.319529
\(935\) −4.41053 −0.144240
\(936\) 0 0
\(937\) −54.8510 −1.79191 −0.895953 0.444150i \(-0.853506\pi\)
−0.895953 + 0.444150i \(0.853506\pi\)
\(938\) −0.361180 −0.0117929
\(939\) 0 0
\(940\) −2.23230 −0.0728095
\(941\) 2.79391 0.0910788 0.0455394 0.998963i \(-0.485499\pi\)
0.0455394 + 0.998963i \(0.485499\pi\)
\(942\) 0 0
\(943\) −40.3319 −1.31339
\(944\) −26.9914 −0.878495
\(945\) 0 0
\(946\) −63.2014 −2.05486
\(947\) −6.53039 −0.212209 −0.106105 0.994355i \(-0.533838\pi\)
−0.106105 + 0.994355i \(0.533838\pi\)
\(948\) 0 0
\(949\) 4.52163 0.146778
\(950\) 44.4747 1.44295
\(951\) 0 0
\(952\) −6.46139 −0.209415
\(953\) −19.4446 −0.629873 −0.314937 0.949113i \(-0.601983\pi\)
−0.314937 + 0.949113i \(0.601983\pi\)
\(954\) 0 0
\(955\) 2.96497 0.0959440
\(956\) −21.2933 −0.688674
\(957\) 0 0
\(958\) −3.76899 −0.121771
\(959\) 5.10054 0.164705
\(960\) 0 0
\(961\) 12.2721 0.395874
\(962\) 1.23312 0.0397574
\(963\) 0 0
\(964\) −60.4165 −1.94589
\(965\) 3.83622 0.123492
\(966\) 0 0
\(967\) −4.67554 −0.150355 −0.0751777 0.997170i \(-0.523952\pi\)
−0.0751777 + 0.997170i \(0.523952\pi\)
\(968\) 6.97742 0.224263
\(969\) 0 0
\(970\) −0.923301 −0.0296454
\(971\) −4.75185 −0.152494 −0.0762470 0.997089i \(-0.524294\pi\)
−0.0762470 + 0.997089i \(0.524294\pi\)
\(972\) 0 0
\(973\) 12.5215 0.401422
\(974\) −54.4200 −1.74373
\(975\) 0 0
\(976\) 16.0901 0.515030
\(977\) 37.3562 1.19513 0.597565 0.801821i \(-0.296135\pi\)
0.597565 + 0.801821i \(0.296135\pi\)
\(978\) 0 0
\(979\) 47.9514 1.53253
\(980\) 0.633462 0.0202352
\(981\) 0 0
\(982\) 58.5864 1.86957
\(983\) −45.4192 −1.44865 −0.724324 0.689459i \(-0.757848\pi\)
−0.724324 + 0.689459i \(0.757848\pi\)
\(984\) 0 0
\(985\) −2.91389 −0.0928444
\(986\) 90.5524 2.88378
\(987\) 0 0
\(988\) 17.8752 0.568686
\(989\) 38.3011 1.21791
\(990\) 0 0
\(991\) −8.11368 −0.257739 −0.128870 0.991662i \(-0.541135\pi\)
−0.128870 + 0.991662i \(0.541135\pi\)
\(992\) 50.7544 1.61145
\(993\) 0 0
\(994\) −15.0628 −0.477764
\(995\) 3.29509 0.104461
\(996\) 0 0
\(997\) −33.0431 −1.04648 −0.523242 0.852184i \(-0.675278\pi\)
−0.523242 + 0.852184i \(0.675278\pi\)
\(998\) −40.8413 −1.29281
\(999\) 0 0
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 8001.2.a.l.1.6 7
3.2 odd 2 2667.2.a.j.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2667.2.a.j.1.2 7 3.2 odd 2
8001.2.a.l.1.6 7 1.1 even 1 trivial