Properties

Label 9800.2.a.ce.1.3
Level $9800$
Weight $2$
Character 9800.1
Self dual yes
Analytic conductor $78.253$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(78.2533939809\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1944.1
Defining polynomial: \(x^{3} - 9 x - 6\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.28995\) of defining polynomial
Character \(\chi\) \(=\) 9800.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.28995 q^{3} +7.82374 q^{9} +O(q^{10})\) \(q+3.28995 q^{3} +7.82374 q^{9} +5.82374 q^{11} -2.75615 q^{13} -2.00000 q^{17} -0.756152 q^{19} +0.533794 q^{23} +15.8698 q^{27} -0.823739 q^{29} -2.57989 q^{31} +19.1598 q^{33} -4.75615 q^{37} -9.06759 q^{39} +6.06759 q^{41} -0.710055 q^{43} +12.8913 q^{47} -6.57989 q^{51} +8.40363 q^{53} -2.48770 q^{57} +8.00000 q^{59} +9.40363 q^{61} -11.8698 q^{67} +1.75615 q^{69} -3.51230 q^{73} -9.51230 q^{79} +28.7397 q^{81} +6.71005 q^{83} -2.71005 q^{87} +1.75615 q^{89} -8.48770 q^{93} +2.00000 q^{97} +45.5634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 9q^{9} + O(q^{10}) \) \( 3q + 9q^{9} + 3q^{11} - 3q^{13} - 6q^{17} + 3q^{19} - 3q^{23} + 18q^{27} + 12q^{29} + 12q^{31} + 18q^{33} - 9q^{37} - 18q^{39} + 9q^{41} - 12q^{43} + 15q^{47} - 9q^{53} - 18q^{57} + 24q^{59} - 6q^{61} - 6q^{67} - 18q^{79} + 27q^{81} + 30q^{83} - 18q^{87} - 36q^{93} + 6q^{97} + 63q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.28995 1.89945 0.949725 0.313084i \(-0.101362\pi\)
0.949725 + 0.313084i \(0.101362\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 7.82374 2.60791
\(10\) 0 0
\(11\) 5.82374 1.75592 0.877962 0.478731i \(-0.158903\pi\)
0.877962 + 0.478731i \(0.158903\pi\)
\(12\) 0 0
\(13\) −2.75615 −0.764419 −0.382209 0.924076i \(-0.624837\pi\)
−0.382209 + 0.924076i \(0.624837\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −0.756152 −0.173473 −0.0867365 0.996231i \(-0.527644\pi\)
−0.0867365 + 0.996231i \(0.527644\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.533794 0.111304 0.0556518 0.998450i \(-0.482276\pi\)
0.0556518 + 0.998450i \(0.482276\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 15.8698 3.05415
\(28\) 0 0
\(29\) −0.823739 −0.152964 −0.0764822 0.997071i \(-0.524369\pi\)
−0.0764822 + 0.997071i \(0.524369\pi\)
\(30\) 0 0
\(31\) −2.57989 −0.463362 −0.231681 0.972792i \(-0.574423\pi\)
−0.231681 + 0.972792i \(0.574423\pi\)
\(32\) 0 0
\(33\) 19.1598 3.33529
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.75615 −0.781906 −0.390953 0.920411i \(-0.627855\pi\)
−0.390953 + 0.920411i \(0.627855\pi\)
\(38\) 0 0
\(39\) −9.06759 −1.45198
\(40\) 0 0
\(41\) 6.06759 0.947598 0.473799 0.880633i \(-0.342882\pi\)
0.473799 + 0.880633i \(0.342882\pi\)
\(42\) 0 0
\(43\) −0.710055 −0.108282 −0.0541412 0.998533i \(-0.517242\pi\)
−0.0541412 + 0.998533i \(0.517242\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.8913 1.88039 0.940197 0.340632i \(-0.110641\pi\)
0.940197 + 0.340632i \(0.110641\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −6.57989 −0.921369
\(52\) 0 0
\(53\) 8.40363 1.15433 0.577164 0.816629i \(-0.304159\pi\)
0.577164 + 0.816629i \(0.304159\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.48770 −0.329504
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) 9.40363 1.20401 0.602006 0.798492i \(-0.294368\pi\)
0.602006 + 0.798492i \(0.294368\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −11.8698 −1.45013 −0.725066 0.688680i \(-0.758191\pi\)
−0.725066 + 0.688680i \(0.758191\pi\)
\(68\) 0 0
\(69\) 1.75615 0.211416
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −3.51230 −0.411084 −0.205542 0.978648i \(-0.565896\pi\)
−0.205542 + 0.978648i \(0.565896\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −9.51230 −1.07022 −0.535109 0.844783i \(-0.679729\pi\)
−0.535109 + 0.844783i \(0.679729\pi\)
\(80\) 0 0
\(81\) 28.7397 3.19330
\(82\) 0 0
\(83\) 6.71005 0.736524 0.368262 0.929722i \(-0.379953\pi\)
0.368262 + 0.929722i \(0.379953\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.71005 −0.290548
\(88\) 0 0
\(89\) 1.75615 0.186152 0.0930758 0.995659i \(-0.470330\pi\)
0.0930758 + 0.995659i \(0.470330\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −8.48770 −0.880133
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 45.5634 4.57929
\(100\) 0 0
\(101\) 2.33604 0.232445 0.116222 0.993223i \(-0.462921\pi\)
0.116222 + 0.993223i \(0.462921\pi\)
\(102\) 0 0
\(103\) 2.22236 0.218975 0.109488 0.993988i \(-0.465079\pi\)
0.109488 + 0.993988i \(0.465079\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.8698 −1.53419 −0.767097 0.641531i \(-0.778300\pi\)
−0.767097 + 0.641531i \(0.778300\pi\)
\(108\) 0 0
\(109\) −3.26845 −0.313061 −0.156531 0.987673i \(-0.550031\pi\)
−0.156531 + 0.987673i \(0.550031\pi\)
\(110\) 0 0
\(111\) −15.6475 −1.48519
\(112\) 0 0
\(113\) 13.1598 1.23797 0.618984 0.785404i \(-0.287545\pi\)
0.618984 + 0.785404i \(0.287545\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −21.5634 −1.99354
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 22.9159 2.08327
\(122\) 0 0
\(123\) 19.9620 1.79992
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.9159 −1.05737 −0.528684 0.848819i \(-0.677314\pi\)
−0.528684 + 0.848819i \(0.677314\pi\)
\(128\) 0 0
\(129\) −2.33604 −0.205677
\(130\) 0 0
\(131\) 21.5634 1.88400 0.942002 0.335608i \(-0.108942\pi\)
0.942002 + 0.335608i \(0.108942\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.00000 −0.341743 −0.170872 0.985293i \(-0.554658\pi\)
−0.170872 + 0.985293i \(0.554658\pi\)
\(138\) 0 0
\(139\) 6.57989 0.558099 0.279049 0.960277i \(-0.409981\pi\)
0.279049 + 0.960277i \(0.409981\pi\)
\(140\) 0 0
\(141\) 42.4118 3.57171
\(142\) 0 0
\(143\) −16.0511 −1.34226
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.108674 0.00890294 0.00445147 0.999990i \(-0.498583\pi\)
0.00445147 + 0.999990i \(0.498583\pi\)
\(150\) 0 0
\(151\) −13.0676 −1.06343 −0.531713 0.846925i \(-0.678451\pi\)
−0.531713 + 0.846925i \(0.678451\pi\)
\(152\) 0 0
\(153\) −15.6475 −1.26502
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.89133 −0.709605 −0.354803 0.934941i \(-0.615452\pi\)
−0.354803 + 0.934941i \(0.615452\pi\)
\(158\) 0 0
\(159\) 27.6475 2.19259
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 11.5123 0.901713 0.450857 0.892596i \(-0.351119\pi\)
0.450857 + 0.892596i \(0.351119\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.46621 −0.113458 −0.0567292 0.998390i \(-0.518067\pi\)
−0.0567292 + 0.998390i \(0.518067\pi\)
\(168\) 0 0
\(169\) −5.40363 −0.415664
\(170\) 0 0
\(171\) −5.91593 −0.452403
\(172\) 0 0
\(173\) 11.2438 0.854854 0.427427 0.904050i \(-0.359420\pi\)
0.427427 + 0.904050i \(0.359420\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 26.3196 1.97830
\(178\) 0 0
\(179\) 7.33604 0.548321 0.274161 0.961684i \(-0.411600\pi\)
0.274161 + 0.961684i \(0.411600\pi\)
\(180\) 0 0
\(181\) −18.4712 −1.37295 −0.686477 0.727151i \(-0.740844\pi\)
−0.686477 + 0.727151i \(0.740844\pi\)
\(182\) 0 0
\(183\) 30.9374 2.28696
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −11.6475 −0.851748
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 14.5799 1.05496 0.527482 0.849566i \(-0.323136\pi\)
0.527482 + 0.849566i \(0.323136\pi\)
\(192\) 0 0
\(193\) 18.8073 1.35378 0.676888 0.736086i \(-0.263328\pi\)
0.676888 + 0.736086i \(0.263328\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.75615 −0.196368 −0.0981838 0.995168i \(-0.531303\pi\)
−0.0981838 + 0.995168i \(0.531303\pi\)
\(198\) 0 0
\(199\) 15.0246 1.06507 0.532533 0.846409i \(-0.321240\pi\)
0.532533 + 0.846409i \(0.321240\pi\)
\(200\) 0 0
\(201\) −39.0511 −2.75445
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 4.17626 0.290270
\(208\) 0 0
\(209\) −4.40363 −0.304605
\(210\) 0 0
\(211\) −21.9159 −1.50875 −0.754377 0.656441i \(-0.772061\pi\)
−0.754377 + 0.656441i \(0.772061\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −11.5553 −0.780834
\(220\) 0 0
\(221\) 5.51230 0.370798
\(222\) 0 0
\(223\) −18.8073 −1.25943 −0.629714 0.776827i \(-0.716828\pi\)
−0.629714 + 0.776827i \(0.716828\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.6721 −1.10657 −0.553283 0.832994i \(-0.686625\pi\)
−0.553283 + 0.832994i \(0.686625\pi\)
\(228\) 0 0
\(229\) 19.5123 1.28941 0.644705 0.764432i \(-0.276980\pi\)
0.644705 + 0.764432i \(0.276980\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −31.2950 −2.03283
\(238\) 0 0
\(239\) −16.0922 −1.04092 −0.520459 0.853887i \(-0.674239\pi\)
−0.520459 + 0.853887i \(0.674239\pi\)
\(240\) 0 0
\(241\) 0.891326 0.0574153 0.0287077 0.999588i \(-0.490861\pi\)
0.0287077 + 0.999588i \(0.490861\pi\)
\(242\) 0 0
\(243\) 46.9424 3.01136
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.08407 0.132606
\(248\) 0 0
\(249\) 22.0757 1.39899
\(250\) 0 0
\(251\) 17.4712 1.10277 0.551387 0.834250i \(-0.314099\pi\)
0.551387 + 0.834250i \(0.314099\pi\)
\(252\) 0 0
\(253\) 3.10867 0.195441
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.02461 0.438183 0.219091 0.975704i \(-0.429691\pi\)
0.219091 + 0.975704i \(0.429691\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −6.44472 −0.398918
\(262\) 0 0
\(263\) −17.7776 −1.09622 −0.548108 0.836407i \(-0.684652\pi\)
−0.548108 + 0.836407i \(0.684652\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 5.77764 0.353586
\(268\) 0 0
\(269\) −9.40363 −0.573349 −0.286675 0.958028i \(-0.592550\pi\)
−0.286675 + 0.958028i \(0.592550\pi\)
\(270\) 0 0
\(271\) 7.02461 0.426714 0.213357 0.976974i \(-0.431560\pi\)
0.213357 + 0.976974i \(0.431560\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −27.1598 −1.63187 −0.815937 0.578141i \(-0.803778\pi\)
−0.815937 + 0.578141i \(0.803778\pi\)
\(278\) 0 0
\(279\) −20.1844 −1.20841
\(280\) 0 0
\(281\) −0.620977 −0.0370444 −0.0185222 0.999828i \(-0.505896\pi\)
−0.0185222 + 0.999828i \(0.505896\pi\)
\(282\) 0 0
\(283\) −3.15978 −0.187829 −0.0939147 0.995580i \(-0.529938\pi\)
−0.0939147 + 0.995580i \(0.529938\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 6.57989 0.385720
\(292\) 0 0
\(293\) −11.2438 −0.656873 −0.328436 0.944526i \(-0.606522\pi\)
−0.328436 + 0.944526i \(0.606522\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 92.4218 5.36286
\(298\) 0 0
\(299\) −1.47122 −0.0850826
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 7.68545 0.441518
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −23.5173 −1.34220 −0.671102 0.741365i \(-0.734179\pi\)
−0.671102 + 0.741365i \(0.734179\pi\)
\(308\) 0 0
\(309\) 7.31144 0.415933
\(310\) 0 0
\(311\) −29.1598 −1.65350 −0.826750 0.562570i \(-0.809813\pi\)
−0.826750 + 0.562570i \(0.809813\pi\)
\(312\) 0 0
\(313\) 24.1844 1.36698 0.683491 0.729959i \(-0.260461\pi\)
0.683491 + 0.729959i \(0.260461\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.1352 −0.681579 −0.340790 0.940140i \(-0.610694\pi\)
−0.340790 + 0.940140i \(0.610694\pi\)
\(318\) 0 0
\(319\) −4.79724 −0.268594
\(320\) 0 0
\(321\) −52.2109 −2.91413
\(322\) 0 0
\(323\) 1.51230 0.0841468
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −10.7530 −0.594644
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.82374 −0.100242 −0.0501209 0.998743i \(-0.515961\pi\)
−0.0501209 + 0.998743i \(0.515961\pi\)
\(332\) 0 0
\(333\) −37.2109 −2.03914
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 17.7827 0.968683 0.484341 0.874879i \(-0.339059\pi\)
0.484341 + 0.874879i \(0.339059\pi\)
\(338\) 0 0
\(339\) 43.2950 2.35146
\(340\) 0 0
\(341\) −15.0246 −0.813628
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.28995 0.0692479 0.0346239 0.999400i \(-0.488977\pi\)
0.0346239 + 0.999400i \(0.488977\pi\)
\(348\) 0 0
\(349\) 1.31144 0.0701995 0.0350998 0.999384i \(-0.488825\pi\)
0.0350998 + 0.999384i \(0.488825\pi\)
\(350\) 0 0
\(351\) −43.7397 −2.33465
\(352\) 0 0
\(353\) 11.0246 0.586781 0.293390 0.955993i \(-0.405216\pi\)
0.293390 + 0.955993i \(0.405216\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.2274 0.539780 0.269890 0.962891i \(-0.413013\pi\)
0.269890 + 0.962891i \(0.413013\pi\)
\(360\) 0 0
\(361\) −18.4282 −0.969907
\(362\) 0 0
\(363\) 75.3922 3.95706
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −17.3411 −0.905196 −0.452598 0.891715i \(-0.649503\pi\)
−0.452598 + 0.891715i \(0.649503\pi\)
\(368\) 0 0
\(369\) 47.4712 2.47125
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 17.7827 0.920751 0.460375 0.887724i \(-0.347715\pi\)
0.460375 + 0.887724i \(0.347715\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.27035 0.116929
\(378\) 0 0
\(379\) −33.2109 −1.70593 −0.852964 0.521969i \(-0.825198\pi\)
−0.852964 + 0.521969i \(0.825198\pi\)
\(380\) 0 0
\(381\) −39.2028 −2.00842
\(382\) 0 0
\(383\) −14.7612 −0.754260 −0.377130 0.926160i \(-0.623089\pi\)
−0.377130 + 0.926160i \(0.623089\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.55528 −0.282391
\(388\) 0 0
\(389\) −22.8073 −1.15637 −0.578187 0.815904i \(-0.696240\pi\)
−0.578187 + 0.815904i \(0.696240\pi\)
\(390\) 0 0
\(391\) −1.06759 −0.0539902
\(392\) 0 0
\(393\) 70.9424 3.57857
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 14.2703 0.716208 0.358104 0.933682i \(-0.383423\pi\)
0.358104 + 0.933682i \(0.383423\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.4877 −0.573668 −0.286834 0.957980i \(-0.592603\pi\)
−0.286834 + 0.957980i \(0.592603\pi\)
\(402\) 0 0
\(403\) 7.11057 0.354203
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −27.6986 −1.37297
\(408\) 0 0
\(409\) 1.79913 0.0889614 0.0444807 0.999010i \(-0.485837\pi\)
0.0444807 + 0.999010i \(0.485837\pi\)
\(410\) 0 0
\(411\) −13.1598 −0.649124
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 21.6475 1.06008
\(418\) 0 0
\(419\) 27.4282 1.33996 0.669978 0.742381i \(-0.266303\pi\)
0.669978 + 0.742381i \(0.266303\pi\)
\(420\) 0 0
\(421\) 2.91593 0.142114 0.0710569 0.997472i \(-0.477363\pi\)
0.0710569 + 0.997472i \(0.477363\pi\)
\(422\) 0 0
\(423\) 100.858 4.90390
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −52.8073 −2.54956
\(430\) 0 0
\(431\) 14.5799 0.702289 0.351144 0.936321i \(-0.385793\pi\)
0.351144 + 0.936321i \(0.385793\pi\)
\(432\) 0 0
\(433\) −21.1598 −1.01687 −0.508437 0.861099i \(-0.669777\pi\)
−0.508437 + 0.861099i \(0.669777\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.403629 −0.0193082
\(438\) 0 0
\(439\) −30.9424 −1.47680 −0.738401 0.674362i \(-0.764419\pi\)
−0.738401 + 0.674362i \(0.764419\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −37.5173 −1.78250 −0.891251 0.453511i \(-0.850171\pi\)
−0.891251 + 0.453511i \(0.850171\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.357532 0.0169107
\(448\) 0 0
\(449\) 31.0922 1.46733 0.733666 0.679511i \(-0.237808\pi\)
0.733666 + 0.679511i \(0.237808\pi\)
\(450\) 0 0
\(451\) 35.3360 1.66391
\(452\) 0 0
\(453\) −42.9916 −2.01992
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4.35252 0.203602 0.101801 0.994805i \(-0.467539\pi\)
0.101801 + 0.994805i \(0.467539\pi\)
\(458\) 0 0
\(459\) −31.7397 −1.48148
\(460\) 0 0
\(461\) 37.2950 1.73700 0.868500 0.495690i \(-0.165085\pi\)
0.868500 + 0.495690i \(0.165085\pi\)
\(462\) 0 0
\(463\) 9.81873 0.456315 0.228158 0.973624i \(-0.426730\pi\)
0.228158 + 0.973624i \(0.426730\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 22.8022 1.05516 0.527581 0.849505i \(-0.323099\pi\)
0.527581 + 0.849505i \(0.323099\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −29.2520 −1.34786
\(472\) 0 0
\(473\) −4.13517 −0.190136
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 65.7478 3.01038
\(478\) 0 0
\(479\) −20.4447 −0.934143 −0.467071 0.884220i \(-0.654691\pi\)
−0.467071 + 0.884220i \(0.654691\pi\)
\(480\) 0 0
\(481\) 13.1087 0.597704
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 42.8073 1.93978 0.969891 0.243539i \(-0.0783085\pi\)
0.969891 + 0.243539i \(0.0783085\pi\)
\(488\) 0 0
\(489\) 37.8748 1.71276
\(490\) 0 0
\(491\) −18.8502 −0.850699 −0.425350 0.905029i \(-0.639849\pi\)
−0.425350 + 0.905029i \(0.639849\pi\)
\(492\) 0 0
\(493\) 1.64748 0.0741986
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 27.7397 1.24180 0.620899 0.783890i \(-0.286768\pi\)
0.620899 + 0.783890i \(0.286768\pi\)
\(500\) 0 0
\(501\) −4.82374 −0.215509
\(502\) 0 0
\(503\) −14.7101 −0.655889 −0.327944 0.944697i \(-0.606356\pi\)
−0.327944 + 0.944697i \(0.606356\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −17.7776 −0.789533
\(508\) 0 0
\(509\) −13.9835 −0.619809 −0.309904 0.950768i \(-0.600297\pi\)
−0.309904 + 0.950768i \(0.600297\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −12.0000 −0.529813
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 75.0757 3.30183
\(518\) 0 0
\(519\) 36.9916 1.62375
\(520\) 0 0
\(521\) 20.7232 0.907899 0.453950 0.891027i \(-0.350015\pi\)
0.453950 + 0.891027i \(0.350015\pi\)
\(522\) 0 0
\(523\) 22.3525 0.977408 0.488704 0.872450i \(-0.337470\pi\)
0.488704 + 0.872450i \(0.337470\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.15978 0.224764
\(528\) 0 0
\(529\) −22.7151 −0.987611
\(530\) 0 0
\(531\) 62.5899 2.71617
\(532\) 0 0
\(533\) −16.7232 −0.724362
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 24.1352 1.04151
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 32.6556 1.40397 0.701987 0.712190i \(-0.252296\pi\)
0.701987 + 0.712190i \(0.252296\pi\)
\(542\) 0 0
\(543\) −60.7693 −2.60786
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −31.1648 −1.33251 −0.666255 0.745724i \(-0.732104\pi\)
−0.666255 + 0.745724i \(0.732104\pi\)
\(548\) 0 0
\(549\) 73.5715 3.13996
\(550\) 0 0
\(551\) 0.622871 0.0265352
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 44.7232 1.89498 0.947491 0.319782i \(-0.103610\pi\)
0.947491 + 0.319782i \(0.103610\pi\)
\(558\) 0 0
\(559\) 1.95702 0.0827731
\(560\) 0 0
\(561\) −38.3196 −1.61785
\(562\) 0 0
\(563\) 32.4927 1.36940 0.684702 0.728823i \(-0.259932\pi\)
0.684702 + 0.728823i \(0.259932\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 34.6740 1.45361 0.726804 0.686845i \(-0.241005\pi\)
0.726804 + 0.686845i \(0.241005\pi\)
\(570\) 0 0
\(571\) 3.11057 0.130173 0.0650866 0.997880i \(-0.479268\pi\)
0.0650866 + 0.997880i \(0.479268\pi\)
\(572\) 0 0
\(573\) 47.9670 2.00385
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −0.672083 −0.0279792 −0.0139896 0.999902i \(-0.504453\pi\)
−0.0139896 + 0.999902i \(0.504453\pi\)
\(578\) 0 0
\(579\) 61.8748 2.57143
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 48.9405 2.02691
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.67208 0.192838 0.0964188 0.995341i \(-0.469261\pi\)
0.0964188 + 0.995341i \(0.469261\pi\)
\(588\) 0 0
\(589\) 1.95079 0.0803808
\(590\) 0 0
\(591\) −9.06759 −0.372991
\(592\) 0 0
\(593\) −20.1844 −0.828873 −0.414437 0.910078i \(-0.636021\pi\)
−0.414437 + 0.910078i \(0.636021\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 49.4301 2.02304
\(598\) 0 0
\(599\) 21.5123 0.878969 0.439484 0.898250i \(-0.355161\pi\)
0.439484 + 0.898250i \(0.355161\pi\)
\(600\) 0 0
\(601\) 5.29495 0.215986 0.107993 0.994152i \(-0.465558\pi\)
0.107993 + 0.994152i \(0.465558\pi\)
\(602\) 0 0
\(603\) −92.8665 −3.78182
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −36.7182 −1.49034 −0.745172 0.666872i \(-0.767633\pi\)
−0.745172 + 0.666872i \(0.767633\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −35.5304 −1.43741
\(612\) 0 0
\(613\) −40.7232 −1.64479 −0.822397 0.568914i \(-0.807364\pi\)
−0.822397 + 0.568914i \(0.807364\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −16.8073 −0.676635 −0.338317 0.941032i \(-0.609858\pi\)
−0.338317 + 0.941032i \(0.609858\pi\)
\(618\) 0 0
\(619\) −35.7908 −1.43855 −0.719276 0.694724i \(-0.755526\pi\)
−0.719276 + 0.694724i \(0.755526\pi\)
\(620\) 0 0
\(621\) 8.47122 0.339938
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −14.4877 −0.578583
\(628\) 0 0
\(629\) 9.51230 0.379280
\(630\) 0 0
\(631\) −32.4447 −1.29160 −0.645802 0.763505i \(-0.723477\pi\)
−0.645802 + 0.763505i \(0.723477\pi\)
\(632\) 0 0
\(633\) −72.1022 −2.86581
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16.9078 0.667818 0.333909 0.942605i \(-0.391632\pi\)
0.333909 + 0.942605i \(0.391632\pi\)
\(642\) 0 0
\(643\) −0.135174 −0.00533075 −0.00266538 0.999996i \(-0.500848\pi\)
−0.00266538 + 0.999996i \(0.500848\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.08908 0.160758 0.0803791 0.996764i \(-0.474387\pi\)
0.0803791 + 0.996764i \(0.474387\pi\)
\(648\) 0 0
\(649\) 46.5899 1.82881
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −31.9159 −1.24897 −0.624483 0.781038i \(-0.714690\pi\)
−0.624483 + 0.781038i \(0.714690\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −27.4793 −1.07207
\(658\) 0 0
\(659\) 4.70505 0.183283 0.0916413 0.995792i \(-0.470789\pi\)
0.0916413 + 0.995792i \(0.470789\pi\)
\(660\) 0 0
\(661\) 4.51420 0.175582 0.0877910 0.996139i \(-0.472019\pi\)
0.0877910 + 0.996139i \(0.472019\pi\)
\(662\) 0 0
\(663\) 18.1352 0.704312
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.439706 −0.0170255
\(668\) 0 0
\(669\) −61.8748 −2.39222
\(670\) 0 0
\(671\) 54.7643 2.11415
\(672\) 0 0
\(673\) −46.9424 −1.80950 −0.904749 0.425945i \(-0.859942\pi\)
−0.904749 + 0.425945i \(0.859942\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.4036 0.399844 0.199922 0.979812i \(-0.435931\pi\)
0.199922 + 0.979812i \(0.435931\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −54.8502 −2.10187
\(682\) 0 0
\(683\) −5.06258 −0.193714 −0.0968571 0.995298i \(-0.530879\pi\)
−0.0968571 + 0.995298i \(0.530879\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 64.1944 2.44917
\(688\) 0 0
\(689\) −23.1617 −0.882390
\(690\) 0 0
\(691\) −4.44472 −0.169085 −0.0845425 0.996420i \(-0.526943\pi\)
−0.0845425 + 0.996420i \(0.526943\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −12.1352 −0.459653
\(698\) 0 0
\(699\) −59.2190 −2.23987
\(700\) 0 0
\(701\) 21.7562 0.821719 0.410859 0.911699i \(-0.365229\pi\)
0.410859 + 0.911699i \(0.365229\pi\)
\(702\) 0 0
\(703\) 3.59637 0.135640
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −41.0081 −1.54009 −0.770046 0.637988i \(-0.779767\pi\)
−0.770046 + 0.637988i \(0.779767\pi\)
\(710\) 0 0
\(711\) −74.4218 −2.79103
\(712\) 0 0
\(713\) −1.37713 −0.0515739
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −52.9424 −1.97717
\(718\) 0 0
\(719\) 23.7397 0.885340 0.442670 0.896685i \(-0.354031\pi\)
0.442670 + 0.896685i \(0.354031\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 2.93241 0.109058
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 28.8534 1.07011 0.535056 0.844817i \(-0.320291\pi\)
0.535056 + 0.844817i \(0.320291\pi\)
\(728\) 0 0
\(729\) 68.2190 2.52663
\(730\) 0 0
\(731\) 1.42011 0.0525247
\(732\) 0 0
\(733\) −46.8584 −1.73075 −0.865377 0.501122i \(-0.832921\pi\)
−0.865377 + 0.501122i \(0.832921\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −69.1268 −2.54632
\(738\) 0 0
\(739\) 16.1433 0.593841 0.296920 0.954902i \(-0.404040\pi\)
0.296920 + 0.954902i \(0.404040\pi\)
\(740\) 0 0
\(741\) 6.85647 0.251879
\(742\) 0 0
\(743\) 16.2243 0.595210 0.297605 0.954689i \(-0.403812\pi\)
0.297605 + 0.954689i \(0.403812\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 52.4977 1.92079
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 21.5123 0.784995 0.392498 0.919753i \(-0.371611\pi\)
0.392498 + 0.919753i \(0.371611\pi\)
\(752\) 0 0
\(753\) 57.4793 2.09466
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.840220 −0.0305383 −0.0152692 0.999883i \(-0.504861\pi\)
−0.0152692 + 0.999883i \(0.504861\pi\)
\(758\) 0 0
\(759\) 10.2274 0.371230
\(760\) 0 0
\(761\) −28.8913 −1.04731 −0.523655 0.851930i \(-0.675432\pi\)
−0.523655 + 0.851930i \(0.675432\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −22.0492 −0.796151
\(768\) 0 0
\(769\) −27.3790 −0.987313 −0.493656 0.869657i \(-0.664340\pi\)
−0.493656 + 0.869657i \(0.664340\pi\)
\(770\) 0 0
\(771\) 23.1106 0.832307
\(772\) 0 0
\(773\) 38.2355 1.37524 0.687618 0.726073i \(-0.258657\pi\)
0.687618 + 0.726073i \(0.258657\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.58802 −0.164383
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −13.0726 −0.467176
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −7.33293 −0.261391 −0.130695 0.991423i \(-0.541721\pi\)
−0.130695 + 0.991423i \(0.541721\pi\)
\(788\) 0 0
\(789\) −58.4875 −2.08221
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −25.9178 −0.920369
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14.4877 −0.513181 −0.256590 0.966520i \(-0.582599\pi\)
−0.256590 + 0.966520i \(0.582599\pi\)
\(798\) 0 0
\(799\) −25.7827 −0.912125
\(800\) 0 0
\(801\) 13.7397 0.485467
\(802\) 0 0
\(803\) −20.4547 −0.721832
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −30.9374 −1.08905
\(808\) 0 0
\(809\) −11.3525 −0.399133 −0.199567 0.979884i \(-0.563953\pi\)
−0.199567 + 0.979884i \(0.563953\pi\)
\(810\) 0 0
\(811\) −28.7662 −1.01012 −0.505058 0.863085i \(-0.668529\pi\)
−0.505058 + 0.863085i \(0.668529\pi\)
\(812\) 0 0
\(813\) 23.1106 0.810523
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0.536909 0.0187841
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −16.0492 −0.560121 −0.280061 0.959982i \(-0.590355\pi\)
−0.280061 + 0.959982i \(0.590355\pi\)
\(822\) 0 0
\(823\) −14.0050 −0.488184 −0.244092 0.969752i \(-0.578490\pi\)
−0.244092 + 0.969752i \(0.578490\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −15.2899 −0.531683 −0.265842 0.964017i \(-0.585650\pi\)
−0.265842 + 0.964017i \(0.585650\pi\)
\(828\) 0 0
\(829\) −21.2950 −0.739604 −0.369802 0.929111i \(-0.620575\pi\)
−0.369802 + 0.929111i \(0.620575\pi\)
\(830\) 0 0
\(831\) −89.3542 −3.09966
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −40.9424 −1.41518
\(838\) 0 0
\(839\) 42.2274 1.45785 0.728925 0.684593i \(-0.240020\pi\)
0.728925 + 0.684593i \(0.240020\pi\)
\(840\) 0 0
\(841\) −28.3215 −0.976602
\(842\) 0 0
\(843\) −2.04298 −0.0703640
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −10.3955 −0.356773
\(850\) 0 0
\(851\) −2.53880 −0.0870290
\(852\) 0 0
\(853\) 13.2931 0.455146 0.227573 0.973761i \(-0.426921\pi\)
0.227573 + 0.973761i \(0.426921\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −38.4547 −1.31359 −0.656794 0.754070i \(-0.728088\pi\)
−0.656794 + 0.754070i \(0.728088\pi\)
\(858\) 0 0
\(859\) 8.00000 0.272956 0.136478 0.990643i \(-0.456422\pi\)
0.136478 + 0.990643i \(0.456422\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 47.0807 1.60265 0.801323 0.598232i \(-0.204130\pi\)
0.801323 + 0.598232i \(0.204130\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −42.7693 −1.45252
\(868\) 0 0
\(869\) −55.3972 −1.87922
\(870\) 0 0
\(871\) 32.7151 1.10851
\(872\) 0 0
\(873\) 15.6475 0.529587
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 4.57177 0.154378 0.0771888 0.997016i \(-0.475406\pi\)
0.0771888 + 0.997016i \(0.475406\pi\)
\(878\) 0 0
\(879\) −36.9916 −1.24770
\(880\) 0 0
\(881\) −14.2849 −0.481272 −0.240636 0.970615i \(-0.577356\pi\)
−0.240636 + 0.970615i \(0.577356\pi\)
\(882\) 0 0
\(883\) 15.9670 0.537334 0.268667 0.963233i \(-0.413417\pi\)
0.268667 + 0.963233i \(0.413417\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 7.16479 0.240570 0.120285 0.992739i \(-0.461619\pi\)
0.120285 + 0.992739i \(0.461619\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 167.372 5.60718
\(892\) 0 0
\(893\) −9.74780 −0.326198
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −4.84022 −0.161610
\(898\) 0 0
\(899\) 2.12516 0.0708779
\(900\) 0 0
\(901\) −16.8073 −0.559931
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −8.26534 −0.274446 −0.137223 0.990540i \(-0.543818\pi\)
−0.137223 + 0.990540i \(0.543818\pi\)
\(908\) 0 0
\(909\) 18.2766 0.606196
\(910\) 0 0
\(911\) 26.2274 0.868951 0.434476 0.900684i \(-0.356934\pi\)
0.434476 + 0.900684i \(0.356934\pi\)
\(912\) 0 0
\(913\) 39.0776 1.29328
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −18.7580 −0.618771 −0.309385 0.950937i \(-0.600123\pi\)
−0.309385 + 0.950937i \(0.600123\pi\)
\(920\) 0 0
\(921\) −77.3707 −2.54945
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 17.3871 0.571069
\(928\) 0 0
\(929\) −12.9078 −0.423491 −0.211746 0.977325i \(-0.567915\pi\)
−0.211746 + 0.977325i \(0.567915\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −95.9341 −3.14074
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.78265 −0.0582367 −0.0291183 0.999576i \(-0.509270\pi\)
−0.0291183 + 0.999576i \(0.509270\pi\)
\(938\) 0 0
\(939\) 79.5653 2.59652
\(940\) 0 0
\(941\) −45.1268 −1.47109 −0.735546 0.677475i \(-0.763074\pi\)
−0.735546 + 0.677475i \(0.763074\pi\)
\(942\) 0 0
\(943\) 3.23884 0.105471
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −22.0872 −0.717737 −0.358869 0.933388i \(-0.616837\pi\)
−0.358869 + 0.933388i \(0.616837\pi\)
\(948\) 0 0
\(949\) 9.68044 0.314240
\(950\) 0 0
\(951\) −39.9241 −1.29463
\(952\) 0 0
\(953\) 45.3442 1.46884 0.734421 0.678694i \(-0.237454\pi\)
0.734421 + 0.678694i \(0.237454\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −15.7827 −0.510181
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −24.3442 −0.785296
\(962\) 0 0
\(963\) −124.161 −4.00105
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 17.0296 0.547636 0.273818 0.961782i \(-0.411713\pi\)
0.273818 + 0.961782i \(0.411713\pi\)
\(968\) 0 0
\(969\) 4.97539 0.159833
\(970\) 0 0
\(971\) −29.2109 −0.937422 −0.468711 0.883352i \(-0.655281\pi\)
−0.468711 + 0.883352i \(0.655281\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −0.840220 −0.0268810 −0.0134405 0.999910i \(-0.504278\pi\)
−0.0134405 + 0.999910i \(0.504278\pi\)
\(978\) 0 0
\(979\) 10.2274 0.326868
\(980\) 0 0
\(981\) −25.5715 −0.816436
\(982\) 0 0
\(983\) −8.31645 −0.265253 −0.132627 0.991166i \(-0.542341\pi\)
−0.132627 + 0.991166i \(0.542341\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.379023 −0.0120522
\(990\) 0 0
\(991\) −20.2603 −0.643591 −0.321795 0.946809i \(-0.604286\pi\)
−0.321795 + 0.946809i \(0.604286\pi\)
\(992\) 0 0
\(993\) −6.00000 −0.190404
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 53.0776 1.68098 0.840492 0.541823i \(-0.182266\pi\)
0.840492 + 0.541823i \(0.182266\pi\)
\(998\) 0 0
\(999\) −75.4793 −2.38806
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 9800.2.a.ce.1.3 3
5.4 even 2 1960.2.a.w.1.1 3
7.2 even 3 1400.2.q.j.1201.1 6
7.4 even 3 1400.2.q.j.401.1 6
7.6 odd 2 9800.2.a.cf.1.1 3
20.19 odd 2 3920.2.a.cc.1.3 3
35.2 odd 12 1400.2.bh.i.249.6 12
35.4 even 6 280.2.q.e.121.3 yes 6
35.9 even 6 280.2.q.e.81.3 6
35.18 odd 12 1400.2.bh.i.849.6 12
35.19 odd 6 1960.2.q.w.361.1 6
35.23 odd 12 1400.2.bh.i.249.1 12
35.24 odd 6 1960.2.q.w.961.1 6
35.32 odd 12 1400.2.bh.i.849.1 12
35.34 odd 2 1960.2.a.v.1.3 3
105.44 odd 6 2520.2.bi.q.361.3 6
105.74 odd 6 2520.2.bi.q.1801.3 6
140.39 odd 6 560.2.q.l.401.1 6
140.79 odd 6 560.2.q.l.81.1 6
140.139 even 2 3920.2.a.cb.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.q.e.81.3 6 35.9 even 6
280.2.q.e.121.3 yes 6 35.4 even 6
560.2.q.l.81.1 6 140.79 odd 6
560.2.q.l.401.1 6 140.39 odd 6
1400.2.q.j.401.1 6 7.4 even 3
1400.2.q.j.1201.1 6 7.2 even 3
1400.2.bh.i.249.1 12 35.23 odd 12
1400.2.bh.i.249.6 12 35.2 odd 12
1400.2.bh.i.849.1 12 35.32 odd 12
1400.2.bh.i.849.6 12 35.18 odd 12
1960.2.a.v.1.3 3 35.34 odd 2
1960.2.a.w.1.1 3 5.4 even 2
1960.2.q.w.361.1 6 35.19 odd 6
1960.2.q.w.961.1 6 35.24 odd 6
2520.2.bi.q.361.3 6 105.44 odd 6
2520.2.bi.q.1801.3 6 105.74 odd 6
3920.2.a.cb.1.1 3 140.139 even 2
3920.2.a.cc.1.3 3 20.19 odd 2
9800.2.a.ce.1.3 3 1.1 even 1 trivial
9800.2.a.cf.1.1 3 7.6 odd 2