Properties

Label 9036.2.a.i.1.1
Level 9036
Weight 2
Character 9036.1
Self dual yes
Analytic conductor 72.153
Analytic rank 1
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 9036.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.1528232664\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1004)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.40474\)
Character \(\chi\) = 9036.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.59588 q^{5} +1.10443 q^{7} +O(q^{10})\) \(q-2.59588 q^{5} +1.10443 q^{7} +5.46000 q^{11} -2.10841 q^{13} +1.93466 q^{17} -4.08955 q^{19} +2.90552 q^{23} +1.73858 q^{25} -5.78201 q^{29} -1.15076 q^{31} -2.86696 q^{35} -1.95339 q^{37} -2.94481 q^{41} -6.50361 q^{43} +11.0399 q^{47} -5.78024 q^{49} -0.0920517 q^{53} -14.1735 q^{55} -1.65539 q^{59} +5.04551 q^{61} +5.47318 q^{65} +8.55699 q^{67} +7.42422 q^{71} -10.9708 q^{73} +6.03016 q^{77} -7.18613 q^{79} +6.37870 q^{83} -5.02213 q^{85} -13.8905 q^{89} -2.32859 q^{91} +10.6160 q^{95} -2.75331 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 2q^{5} - 6q^{7} + O(q^{10}) \) \( 7q + 2q^{5} - 6q^{7} + 5q^{11} - q^{13} + 8q^{17} - 15q^{19} + 5q^{23} - 9q^{25} - 21q^{31} + 7q^{35} - q^{37} + 10q^{41} - 23q^{43} + 10q^{47} - 13q^{49} + q^{53} - 23q^{55} + 4q^{59} + 3q^{61} - 4q^{65} - 28q^{67} + 18q^{71} - 7q^{73} - 6q^{77} - 30q^{79} - 13q^{83} + q^{85} - 18q^{91} - 2q^{97} + O(q^{100}) \)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −2.59588 −1.16091 −0.580456 0.814292i \(-0.697126\pi\)
−0.580456 + 0.814292i \(0.697126\pi\)
\(6\) 0 0
\(7\) 1.10443 0.417434 0.208717 0.977976i \(-0.433071\pi\)
0.208717 + 0.977976i \(0.433071\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.46000 1.64625 0.823125 0.567860i \(-0.192228\pi\)
0.823125 + 0.567860i \(0.192228\pi\)
\(12\) 0 0
\(13\) −2.10841 −0.584768 −0.292384 0.956301i \(-0.594449\pi\)
−0.292384 + 0.956301i \(0.594449\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.93466 0.469223 0.234612 0.972089i \(-0.424618\pi\)
0.234612 + 0.972089i \(0.424618\pi\)
\(18\) 0 0
\(19\) −4.08955 −0.938207 −0.469104 0.883143i \(-0.655423\pi\)
−0.469104 + 0.883143i \(0.655423\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.90552 0.605842 0.302921 0.953016i \(-0.402038\pi\)
0.302921 + 0.953016i \(0.402038\pi\)
\(24\) 0 0
\(25\) 1.73858 0.347717
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5.78201 −1.07369 −0.536846 0.843680i \(-0.680384\pi\)
−0.536846 + 0.843680i \(0.680384\pi\)
\(30\) 0 0
\(31\) −1.15076 −0.206682 −0.103341 0.994646i \(-0.532953\pi\)
−0.103341 + 0.994646i \(0.532953\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.86696 −0.484604
\(36\) 0 0
\(37\) −1.95339 −0.321136 −0.160568 0.987025i \(-0.551333\pi\)
−0.160568 + 0.987025i \(0.551333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.94481 −0.459902 −0.229951 0.973202i \(-0.573857\pi\)
−0.229951 + 0.973202i \(0.573857\pi\)
\(42\) 0 0
\(43\) −6.50361 −0.991792 −0.495896 0.868382i \(-0.665160\pi\)
−0.495896 + 0.868382i \(0.665160\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.0399 1.61033 0.805164 0.593052i \(-0.202077\pi\)
0.805164 + 0.593052i \(0.202077\pi\)
\(48\) 0 0
\(49\) −5.78024 −0.825749
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.0920517 −0.0126443 −0.00632214 0.999980i \(-0.502012\pi\)
−0.00632214 + 0.999980i \(0.502012\pi\)
\(54\) 0 0
\(55\) −14.1735 −1.91115
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.65539 −0.215513 −0.107757 0.994177i \(-0.534367\pi\)
−0.107757 + 0.994177i \(0.534367\pi\)
\(60\) 0 0
\(61\) 5.04551 0.646011 0.323006 0.946397i \(-0.395307\pi\)
0.323006 + 0.946397i \(0.395307\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.47318 0.678865
\(66\) 0 0
\(67\) 8.55699 1.04540 0.522701 0.852516i \(-0.324924\pi\)
0.522701 + 0.852516i \(0.324924\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.42422 0.881093 0.440546 0.897730i \(-0.354785\pi\)
0.440546 + 0.897730i \(0.354785\pi\)
\(72\) 0 0
\(73\) −10.9708 −1.28403 −0.642017 0.766690i \(-0.721902\pi\)
−0.642017 + 0.766690i \(0.721902\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.03016 0.687201
\(78\) 0 0
\(79\) −7.18613 −0.808503 −0.404251 0.914648i \(-0.632468\pi\)
−0.404251 + 0.914648i \(0.632468\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.37870 0.700153 0.350077 0.936721i \(-0.386156\pi\)
0.350077 + 0.936721i \(0.386156\pi\)
\(84\) 0 0
\(85\) −5.02213 −0.544727
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −13.8905 −1.47239 −0.736197 0.676768i \(-0.763380\pi\)
−0.736197 + 0.676768i \(0.763380\pi\)
\(90\) 0 0
\(91\) −2.32859 −0.244102
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.6160 1.08918
\(96\) 0 0
\(97\) −2.75331 −0.279557 −0.139778 0.990183i \(-0.544639\pi\)
−0.139778 + 0.990183i \(0.544639\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.06894 0.305370 0.152685 0.988275i \(-0.451208\pi\)
0.152685 + 0.988275i \(0.451208\pi\)
\(102\) 0 0
\(103\) −2.79994 −0.275886 −0.137943 0.990440i \(-0.544049\pi\)
−0.137943 + 0.990440i \(0.544049\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.66878 −0.451348 −0.225674 0.974203i \(-0.572458\pi\)
−0.225674 + 0.974203i \(0.572458\pi\)
\(108\) 0 0
\(109\) −3.48753 −0.334045 −0.167022 0.985953i \(-0.553415\pi\)
−0.167022 + 0.985953i \(0.553415\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.92000 −0.556907 −0.278453 0.960450i \(-0.589822\pi\)
−0.278453 + 0.960450i \(0.589822\pi\)
\(114\) 0 0
\(115\) −7.54237 −0.703329
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.13668 0.195870
\(120\) 0 0
\(121\) 18.8116 1.71014
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 8.46624 0.757243
\(126\) 0 0
\(127\) 6.21223 0.551246 0.275623 0.961266i \(-0.411116\pi\)
0.275623 + 0.961266i \(0.411116\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 21.0021 1.83497 0.917483 0.397775i \(-0.130218\pi\)
0.917483 + 0.397775i \(0.130218\pi\)
\(132\) 0 0
\(133\) −4.51661 −0.391639
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −13.1926 −1.12712 −0.563561 0.826074i \(-0.690569\pi\)
−0.563561 + 0.826074i \(0.690569\pi\)
\(138\) 0 0
\(139\) 18.3023 1.55238 0.776189 0.630500i \(-0.217150\pi\)
0.776189 + 0.630500i \(0.217150\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −11.5119 −0.962675
\(144\) 0 0
\(145\) 15.0094 1.24646
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.18031 0.752080 0.376040 0.926603i \(-0.377285\pi\)
0.376040 + 0.926603i \(0.377285\pi\)
\(150\) 0 0
\(151\) −8.48773 −0.690721 −0.345361 0.938470i \(-0.612243\pi\)
−0.345361 + 0.938470i \(0.612243\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.98723 0.239940
\(156\) 0 0
\(157\) −3.28279 −0.261995 −0.130997 0.991383i \(-0.541818\pi\)
−0.130997 + 0.991383i \(0.541818\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.20893 0.252899
\(162\) 0 0
\(163\) 9.22646 0.722672 0.361336 0.932436i \(-0.382321\pi\)
0.361336 + 0.932436i \(0.382321\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.73551 −0.366445 −0.183222 0.983071i \(-0.558653\pi\)
−0.183222 + 0.983071i \(0.558653\pi\)
\(168\) 0 0
\(169\) −8.55460 −0.658046
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −20.0022 −1.52074 −0.760370 0.649490i \(-0.774982\pi\)
−0.760370 + 0.649490i \(0.774982\pi\)
\(174\) 0 0
\(175\) 1.92014 0.145149
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −17.0679 −1.27571 −0.637857 0.770154i \(-0.720179\pi\)
−0.637857 + 0.770154i \(0.720179\pi\)
\(180\) 0 0
\(181\) −2.50078 −0.185881 −0.0929406 0.995672i \(-0.529627\pi\)
−0.0929406 + 0.995672i \(0.529627\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.07077 0.372810
\(186\) 0 0
\(187\) 10.5632 0.772459
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.68883 0.556344 0.278172 0.960531i \(-0.410272\pi\)
0.278172 + 0.960531i \(0.410272\pi\)
\(192\) 0 0
\(193\) −15.5929 −1.12240 −0.561200 0.827680i \(-0.689660\pi\)
−0.561200 + 0.827680i \(0.689660\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.8677 −0.845540 −0.422770 0.906237i \(-0.638942\pi\)
−0.422770 + 0.906237i \(0.638942\pi\)
\(198\) 0 0
\(199\) −17.6493 −1.25113 −0.625564 0.780173i \(-0.715131\pi\)
−0.625564 + 0.780173i \(0.715131\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.38580 −0.448195
\(204\) 0 0
\(205\) 7.64437 0.533906
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −22.3289 −1.54452
\(210\) 0 0
\(211\) 9.98934 0.687695 0.343847 0.939026i \(-0.388270\pi\)
0.343847 + 0.939026i \(0.388270\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 16.8826 1.15138
\(216\) 0 0
\(217\) −1.27093 −0.0862761
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.07905 −0.274387
\(222\) 0 0
\(223\) 8.67597 0.580986 0.290493 0.956877i \(-0.406181\pi\)
0.290493 + 0.956877i \(0.406181\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.23123 0.479954 0.239977 0.970779i \(-0.422860\pi\)
0.239977 + 0.970779i \(0.422860\pi\)
\(228\) 0 0
\(229\) 1.43014 0.0945064 0.0472532 0.998883i \(-0.484953\pi\)
0.0472532 + 0.998883i \(0.484953\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.2713 −0.869434 −0.434717 0.900567i \(-0.643152\pi\)
−0.434717 + 0.900567i \(0.643152\pi\)
\(234\) 0 0
\(235\) −28.6581 −1.86945
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −24.5612 −1.58873 −0.794367 0.607438i \(-0.792197\pi\)
−0.794367 + 0.607438i \(0.792197\pi\)
\(240\) 0 0
\(241\) −14.2498 −0.917909 −0.458954 0.888460i \(-0.651776\pi\)
−0.458954 + 0.888460i \(0.651776\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 15.0048 0.958622
\(246\) 0 0
\(247\) 8.62246 0.548634
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) 15.8641 0.997368
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.65887 −0.103478 −0.0517388 0.998661i \(-0.516476\pi\)
−0.0517388 + 0.998661i \(0.516476\pi\)
\(258\) 0 0
\(259\) −2.15738 −0.134053
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −11.5458 −0.711947 −0.355973 0.934496i \(-0.615851\pi\)
−0.355973 + 0.934496i \(0.615851\pi\)
\(264\) 0 0
\(265\) 0.238955 0.0146789
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 31.3225 1.90977 0.954883 0.296981i \(-0.0959799\pi\)
0.954883 + 0.296981i \(0.0959799\pi\)
\(270\) 0 0
\(271\) 3.81449 0.231714 0.115857 0.993266i \(-0.463039\pi\)
0.115857 + 0.993266i \(0.463039\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9.49266 0.572429
\(276\) 0 0
\(277\) −23.9064 −1.43640 −0.718198 0.695839i \(-0.755033\pi\)
−0.718198 + 0.695839i \(0.755033\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.78573 −0.106528 −0.0532638 0.998580i \(-0.516962\pi\)
−0.0532638 + 0.998580i \(0.516962\pi\)
\(282\) 0 0
\(283\) 24.2483 1.44141 0.720707 0.693240i \(-0.243817\pi\)
0.720707 + 0.693240i \(0.243817\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.25233 −0.191979
\(288\) 0 0
\(289\) −13.2571 −0.779830
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.10405 −0.415023 −0.207511 0.978233i \(-0.566536\pi\)
−0.207511 + 0.978233i \(0.566536\pi\)
\(294\) 0 0
\(295\) 4.29719 0.250192
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.12603 −0.354277
\(300\) 0 0
\(301\) −7.18276 −0.414008
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −13.0975 −0.749962
\(306\) 0 0
\(307\) 22.0293 1.25728 0.628638 0.777698i \(-0.283613\pi\)
0.628638 + 0.777698i \(0.283613\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 28.7818 1.63207 0.816033 0.578005i \(-0.196168\pi\)
0.816033 + 0.578005i \(0.196168\pi\)
\(312\) 0 0
\(313\) −6.68002 −0.377577 −0.188788 0.982018i \(-0.560456\pi\)
−0.188788 + 0.982018i \(0.560456\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −21.9722 −1.23408 −0.617042 0.786930i \(-0.711669\pi\)
−0.617042 + 0.786930i \(0.711669\pi\)
\(318\) 0 0
\(319\) −31.5697 −1.76757
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7.91187 −0.440228
\(324\) 0 0
\(325\) −3.66565 −0.203334
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 12.1927 0.672205
\(330\) 0 0
\(331\) −28.3052 −1.55580 −0.777898 0.628391i \(-0.783714\pi\)
−0.777898 + 0.628391i \(0.783714\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −22.2129 −1.21362
\(336\) 0 0
\(337\) −17.4431 −0.950188 −0.475094 0.879935i \(-0.657586\pi\)
−0.475094 + 0.879935i \(0.657586\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.28313 −0.340251
\(342\) 0 0
\(343\) −14.1148 −0.762129
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −20.2757 −1.08846 −0.544228 0.838938i \(-0.683177\pi\)
−0.544228 + 0.838938i \(0.683177\pi\)
\(348\) 0 0
\(349\) 27.1505 1.45333 0.726667 0.686989i \(-0.241068\pi\)
0.726667 + 0.686989i \(0.241068\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −17.2047 −0.915712 −0.457856 0.889026i \(-0.651382\pi\)
−0.457856 + 0.889026i \(0.651382\pi\)
\(354\) 0 0
\(355\) −19.2724 −1.02287
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 23.5600 1.24345 0.621725 0.783235i \(-0.286432\pi\)
0.621725 + 0.783235i \(0.286432\pi\)
\(360\) 0 0
\(361\) −2.27558 −0.119767
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 28.4788 1.49065
\(366\) 0 0
\(367\) 8.66133 0.452118 0.226059 0.974114i \(-0.427416\pi\)
0.226059 + 0.974114i \(0.427416\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.101664 −0.00527815
\(372\) 0 0
\(373\) −17.6387 −0.913297 −0.456649 0.889647i \(-0.650950\pi\)
−0.456649 + 0.889647i \(0.650950\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.1909 0.627861
\(378\) 0 0
\(379\) −4.78961 −0.246026 −0.123013 0.992405i \(-0.539256\pi\)
−0.123013 + 0.992405i \(0.539256\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −30.4931 −1.55813 −0.779063 0.626946i \(-0.784305\pi\)
−0.779063 + 0.626946i \(0.784305\pi\)
\(384\) 0 0
\(385\) −15.6536 −0.797780
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −19.9287 −1.01043 −0.505214 0.862994i \(-0.668586\pi\)
−0.505214 + 0.862994i \(0.668586\pi\)
\(390\) 0 0
\(391\) 5.62117 0.284275
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 18.6543 0.938601
\(396\) 0 0
\(397\) −4.65870 −0.233814 −0.116907 0.993143i \(-0.537298\pi\)
−0.116907 + 0.993143i \(0.537298\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.41181 −0.370128 −0.185064 0.982726i \(-0.559249\pi\)
−0.185064 + 0.982726i \(0.559249\pi\)
\(402\) 0 0
\(403\) 2.42627 0.120861
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.6655 −0.528670
\(408\) 0 0
\(409\) −5.64037 −0.278899 −0.139449 0.990229i \(-0.544533\pi\)
−0.139449 + 0.990229i \(0.544533\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.82826 −0.0899626
\(414\) 0 0
\(415\) −16.5583 −0.812816
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13.5560 −0.662255 −0.331128 0.943586i \(-0.607429\pi\)
−0.331128 + 0.943586i \(0.607429\pi\)
\(420\) 0 0
\(421\) 27.7306 1.35151 0.675753 0.737129i \(-0.263819\pi\)
0.675753 + 0.737129i \(0.263819\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.36356 0.163157
\(426\) 0 0
\(427\) 5.57239 0.269667
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.2175 −0.588496 −0.294248 0.955729i \(-0.595069\pi\)
−0.294248 + 0.955729i \(0.595069\pi\)
\(432\) 0 0
\(433\) −15.3759 −0.738920 −0.369460 0.929247i \(-0.620457\pi\)
−0.369460 + 0.929247i \(0.620457\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −11.8823 −0.568405
\(438\) 0 0
\(439\) −24.6780 −1.17782 −0.588908 0.808200i \(-0.700442\pi\)
−0.588908 + 0.808200i \(0.700442\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.76904 −0.274095 −0.137048 0.990564i \(-0.543761\pi\)
−0.137048 + 0.990564i \(0.543761\pi\)
\(444\) 0 0
\(445\) 36.0581 1.70932
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −23.1886 −1.09434 −0.547169 0.837022i \(-0.684295\pi\)
−0.547169 + 0.837022i \(0.684295\pi\)
\(450\) 0 0
\(451\) −16.0787 −0.757114
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.04472 0.283381
\(456\) 0 0
\(457\) −26.5427 −1.24162 −0.620808 0.783963i \(-0.713195\pi\)
−0.620808 + 0.783963i \(0.713195\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8.18616 0.381267 0.190634 0.981661i \(-0.438946\pi\)
0.190634 + 0.981661i \(0.438946\pi\)
\(462\) 0 0
\(463\) 9.28673 0.431591 0.215796 0.976439i \(-0.430766\pi\)
0.215796 + 0.976439i \(0.430766\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −30.6019 −1.41609 −0.708043 0.706170i \(-0.750422\pi\)
−0.708043 + 0.706170i \(0.750422\pi\)
\(468\) 0 0
\(469\) 9.45056 0.436386
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −35.5097 −1.63274
\(474\) 0 0
\(475\) −7.11003 −0.326230
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 14.7624 0.674509 0.337255 0.941413i \(-0.390502\pi\)
0.337255 + 0.941413i \(0.390502\pi\)
\(480\) 0 0
\(481\) 4.11855 0.187790
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.14727 0.324541
\(486\) 0 0
\(487\) −19.8582 −0.899860 −0.449930 0.893064i \(-0.648551\pi\)
−0.449930 + 0.893064i \(0.648551\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 13.3227 0.601246 0.300623 0.953743i \(-0.402805\pi\)
0.300623 + 0.953743i \(0.402805\pi\)
\(492\) 0 0
\(493\) −11.1862 −0.503801
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.19950 0.367798
\(498\) 0 0
\(499\) 17.1660 0.768455 0.384228 0.923238i \(-0.374468\pi\)
0.384228 + 0.923238i \(0.374468\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.93373 −0.130809 −0.0654043 0.997859i \(-0.520834\pi\)
−0.0654043 + 0.997859i \(0.520834\pi\)
\(504\) 0 0
\(505\) −7.96658 −0.354508
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −27.6050 −1.22357 −0.611785 0.791024i \(-0.709548\pi\)
−0.611785 + 0.791024i \(0.709548\pi\)
\(510\) 0 0
\(511\) −12.1164 −0.535999
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.26831 0.320280
\(516\) 0 0
\(517\) 60.2775 2.65100
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.19886 0.403009 0.201505 0.979488i \(-0.435417\pi\)
0.201505 + 0.979488i \(0.435417\pi\)
\(522\) 0 0
\(523\) −31.1408 −1.36169 −0.680847 0.732426i \(-0.738388\pi\)
−0.680847 + 0.732426i \(0.738388\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.22632 −0.0969800
\(528\) 0 0
\(529\) −14.5580 −0.632955
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.20887 0.268936
\(534\) 0 0
\(535\) 12.1196 0.523976
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −31.5601 −1.35939
\(540\) 0 0
\(541\) −35.1556 −1.51146 −0.755728 0.654885i \(-0.772717\pi\)
−0.755728 + 0.654885i \(0.772717\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.05321 0.387797
\(546\) 0 0
\(547\) −36.6986 −1.56912 −0.784560 0.620053i \(-0.787111\pi\)
−0.784560 + 0.620053i \(0.787111\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 23.6458 1.00735
\(552\) 0 0
\(553\) −7.93655 −0.337496
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.25209 0.0954243 0.0477121 0.998861i \(-0.484807\pi\)
0.0477121 + 0.998861i \(0.484807\pi\)
\(558\) 0 0
\(559\) 13.7123 0.579969
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.40947 0.185837 0.0929184 0.995674i \(-0.470380\pi\)
0.0929184 + 0.995674i \(0.470380\pi\)
\(564\) 0 0
\(565\) 15.3676 0.646520
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.7973 −0.746102 −0.373051 0.927811i \(-0.621688\pi\)
−0.373051 + 0.927811i \(0.621688\pi\)
\(570\) 0 0
\(571\) −20.8568 −0.872828 −0.436414 0.899746i \(-0.643752\pi\)
−0.436414 + 0.899746i \(0.643752\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.05148 0.210661
\(576\) 0 0
\(577\) −36.6443 −1.52552 −0.762761 0.646680i \(-0.776157\pi\)
−0.762761 + 0.646680i \(0.776157\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.04480 0.292268
\(582\) 0 0
\(583\) −0.502602 −0.0208157
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.48348 −0.143779 −0.0718893 0.997413i \(-0.522903\pi\)
−0.0718893 + 0.997413i \(0.522903\pi\)
\(588\) 0 0
\(589\) 4.70608 0.193911
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9.51454 −0.390715 −0.195358 0.980732i \(-0.562587\pi\)
−0.195358 + 0.980732i \(0.562587\pi\)
\(594\) 0 0
\(595\) −5.54657 −0.227387
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 43.5907 1.78107 0.890534 0.454917i \(-0.150331\pi\)
0.890534 + 0.454917i \(0.150331\pi\)
\(600\) 0 0
\(601\) −19.6914 −0.803227 −0.401613 0.915809i \(-0.631550\pi\)
−0.401613 + 0.915809i \(0.631550\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −48.8325 −1.98532
\(606\) 0 0
\(607\) 19.3315 0.784641 0.392320 0.919829i \(-0.371672\pi\)
0.392320 + 0.919829i \(0.371672\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −23.2766 −0.941669
\(612\) 0 0
\(613\) 12.0543 0.486868 0.243434 0.969917i \(-0.421726\pi\)
0.243434 + 0.969917i \(0.421726\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 29.4697 1.18641 0.593203 0.805053i \(-0.297863\pi\)
0.593203 + 0.805053i \(0.297863\pi\)
\(618\) 0 0
\(619\) 17.3548 0.697547 0.348773 0.937207i \(-0.386598\pi\)
0.348773 + 0.937207i \(0.386598\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −15.3411 −0.614627
\(624\) 0 0
\(625\) −30.6702 −1.22681
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3.77914 −0.150684
\(630\) 0 0
\(631\) −17.7649 −0.707211 −0.353605 0.935395i \(-0.615044\pi\)
−0.353605 + 0.935395i \(0.615044\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −16.1262 −0.639949
\(636\) 0 0
\(637\) 12.1871 0.482872
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 19.1757 0.757395 0.378698 0.925520i \(-0.376372\pi\)
0.378698 + 0.925520i \(0.376372\pi\)
\(642\) 0 0
\(643\) 35.7582 1.41016 0.705082 0.709126i \(-0.250910\pi\)
0.705082 + 0.709126i \(0.250910\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.09564 0.357587 0.178793 0.983887i \(-0.442781\pi\)
0.178793 + 0.983887i \(0.442781\pi\)
\(648\) 0 0
\(649\) −9.03842 −0.354789
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11.8660 0.464351 0.232176 0.972674i \(-0.425416\pi\)
0.232176 + 0.972674i \(0.425416\pi\)
\(654\) 0 0
\(655\) −54.5190 −2.13023
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 16.8059 0.654666 0.327333 0.944909i \(-0.393850\pi\)
0.327333 + 0.944909i \(0.393850\pi\)
\(660\) 0 0
\(661\) −33.0205 −1.28435 −0.642175 0.766558i \(-0.721968\pi\)
−0.642175 + 0.766558i \(0.721968\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 11.7246 0.454659
\(666\) 0 0
\(667\) −16.7997 −0.650488
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 27.5485 1.06350
\(672\) 0 0
\(673\) 5.47289 0.210965 0.105482 0.994421i \(-0.466361\pi\)
0.105482 + 0.994421i \(0.466361\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 44.1231 1.69579 0.847895 0.530165i \(-0.177870\pi\)
0.847895 + 0.530165i \(0.177870\pi\)
\(678\) 0 0
\(679\) −3.04083 −0.116696
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −43.5772 −1.66744 −0.833718 0.552190i \(-0.813792\pi\)
−0.833718 + 0.552190i \(0.813792\pi\)
\(684\) 0 0
\(685\) 34.2464 1.30849
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.194083 0.00739397
\(690\) 0 0
\(691\) 2.94258 0.111941 0.0559705 0.998432i \(-0.482175\pi\)
0.0559705 + 0.998432i \(0.482175\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −47.5105 −1.80217
\(696\) 0 0
\(697\) −5.69719 −0.215797
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 16.1032 0.608209 0.304104 0.952639i \(-0.401643\pi\)
0.304104 + 0.952639i \(0.401643\pi\)
\(702\) 0 0
\(703\) 7.98849 0.301292
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.38941 0.127472
\(708\) 0 0
\(709\) −29.5366 −1.10927 −0.554635 0.832094i \(-0.687142\pi\)
−0.554635 + 0.832094i \(0.687142\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.34354 −0.125217
\(714\) 0 0
\(715\) 29.8835 1.11758
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −50.1400 −1.86990 −0.934952 0.354773i \(-0.884558\pi\)
−0.934952 + 0.354773i \(0.884558\pi\)
\(720\) 0 0
\(721\) −3.09233 −0.115164
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −10.0525 −0.373341
\(726\) 0 0
\(727\) 8.63762 0.320352 0.160176 0.987088i \(-0.448794\pi\)
0.160176 + 0.987088i \(0.448794\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12.5823 −0.465372
\(732\) 0 0
\(733\) 51.9558 1.91903 0.959515 0.281656i \(-0.0908838\pi\)
0.959515 + 0.281656i \(0.0908838\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 46.7211 1.72099
\(738\) 0 0
\(739\) −13.6956 −0.503803 −0.251901 0.967753i \(-0.581056\pi\)
−0.251901 + 0.967753i \(0.581056\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5.06676 0.185882 0.0929408 0.995672i \(-0.470373\pi\)
0.0929408 + 0.995672i \(0.470373\pi\)
\(744\) 0 0
\(745\) −23.8310 −0.873099
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.15633 −0.188408
\(750\) 0 0
\(751\) 5.63750 0.205715 0.102858 0.994696i \(-0.467201\pi\)
0.102858 + 0.994696i \(0.467201\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 22.0331 0.801867
\(756\) 0 0
\(757\) 50.6494 1.84088 0.920442 0.390880i \(-0.127829\pi\)
0.920442 + 0.390880i \(0.127829\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 26.9970 0.978640 0.489320 0.872104i \(-0.337245\pi\)
0.489320 + 0.872104i \(0.337245\pi\)
\(762\) 0 0
\(763\) −3.85172 −0.139442
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.49025 0.126025
\(768\) 0 0
\(769\) −24.1399 −0.870509 −0.435254 0.900308i \(-0.643342\pi\)
−0.435254 + 0.900308i \(0.643342\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 37.2454 1.33963 0.669813 0.742530i \(-0.266374\pi\)
0.669813 + 0.742530i \(0.266374\pi\)
\(774\) 0 0
\(775\) −2.00069 −0.0718668
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.0429 0.431483
\(780\) 0 0
\(781\) 40.5362 1.45050
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8.52171 0.304153
\(786\) 0 0
\(787\) −20.6348 −0.735550 −0.367775 0.929915i \(-0.619880\pi\)
−0.367775 + 0.929915i \(0.619880\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.53820 −0.232472
\(792\) 0 0
\(793\) −10.6380 −0.377767
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.94230 0.139644 0.0698218 0.997559i \(-0.477757\pi\)
0.0698218 + 0.997559i \(0.477757\pi\)
\(798\) 0 0
\(799\) 21.3583 0.755603
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −59.9005 −2.11384
\(804\) 0 0
\(805\) −8.32999 −0.293593
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 41.2905 1.45170 0.725849 0.687854i \(-0.241447\pi\)
0.725849 + 0.687854i \(0.241447\pi\)
\(810\) 0 0
\(811\) −9.94964 −0.349379 −0.174690 0.984624i \(-0.555892\pi\)
−0.174690 + 0.984624i \(0.555892\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −23.9508 −0.838958
\(816\) 0 0
\(817\) 26.5969 0.930506
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 4.35629 0.152036 0.0760178 0.997106i \(-0.475779\pi\)
0.0760178 + 0.997106i \(0.475779\pi\)
\(822\) 0 0
\(823\) 46.7715 1.63035 0.815175 0.579214i \(-0.196641\pi\)
0.815175 + 0.579214i \(0.196641\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 30.6169 1.06465 0.532327 0.846539i \(-0.321318\pi\)
0.532327 + 0.846539i \(0.321318\pi\)
\(828\) 0 0
\(829\) −19.8309 −0.688756 −0.344378 0.938831i \(-0.611910\pi\)
−0.344378 + 0.938831i \(0.611910\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −11.1828 −0.387460
\(834\) 0 0
\(835\) 12.2928 0.425410
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 11.4176 0.394180 0.197090 0.980385i \(-0.436851\pi\)
0.197090 + 0.980385i \(0.436851\pi\)
\(840\) 0 0
\(841\) 4.43163 0.152815
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 22.2067 0.763934
\(846\) 0 0
\(847\) 20.7760 0.713871
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −5.67561 −0.194557
\(852\) 0 0
\(853\) 24.4581 0.837428 0.418714 0.908118i \(-0.362481\pi\)
0.418714 + 0.908118i \(0.362481\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 56.4437 1.92808 0.964041 0.265754i \(-0.0856209\pi\)
0.964041 + 0.265754i \(0.0856209\pi\)
\(858\) 0 0
\(859\) 29.2843 0.999167 0.499583 0.866266i \(-0.333486\pi\)
0.499583 + 0.866266i \(0.333486\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 56.3958 1.91973 0.959867 0.280454i \(-0.0904850\pi\)
0.959867 + 0.280454i \(0.0904850\pi\)
\(864\) 0 0
\(865\) 51.9233 1.76544
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −39.2362 −1.33100
\(870\) 0 0
\(871\) −18.0417 −0.611318
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 9.35034 0.316099
\(876\) 0 0
\(877\) 2.55796 0.0863762 0.0431881 0.999067i \(-0.486249\pi\)
0.0431881 + 0.999067i \(0.486249\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 27.7786 0.935883 0.467942 0.883759i \(-0.344996\pi\)
0.467942 + 0.883759i \(0.344996\pi\)
\(882\) 0 0
\(883\) −13.4792 −0.453611 −0.226805 0.973940i \(-0.572828\pi\)
−0.226805 + 0.973940i \(0.572828\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −55.1525 −1.85184 −0.925920 0.377720i \(-0.876708\pi\)
−0.925920 + 0.377720i \(0.876708\pi\)
\(888\) 0 0
\(889\) 6.86095 0.230109
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −45.1480 −1.51082
\(894\) 0 0
\(895\) 44.3062 1.48099
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 6.65369 0.221913
\(900\) 0 0
\(901\) −0.178088 −0.00593299
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6.49171 0.215792
\(906\) 0 0
\(907\) 33.7611 1.12102 0.560509 0.828148i \(-0.310605\pi\)
0.560509 + 0.828148i \(0.310605\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −24.5552 −0.813549 −0.406775 0.913528i \(-0.633347\pi\)
−0.406775 + 0.913528i \(0.633347\pi\)
\(912\) 0 0
\(913\) 34.8277 1.15263
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 23.1953 0.765977
\(918\) 0 0
\(919\) −47.9060 −1.58027 −0.790136 0.612932i \(-0.789990\pi\)
−0.790136 + 0.612932i \(0.789990\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −15.6533 −0.515235
\(924\) 0 0
\(925\) −3.39613 −0.111664
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −23.8411 −0.782203 −0.391101 0.920348i \(-0.627906\pi\)
−0.391101 + 0.920348i \(0.627906\pi\)
\(930\) 0 0
\(931\) 23.6386 0.774724
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −27.4208 −0.896757
\(936\) 0 0
\(937\) 28.2056 0.921436 0.460718 0.887546i \(-0.347592\pi\)
0.460718 + 0.887546i \(0.347592\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −52.0125 −1.69556 −0.847780 0.530348i \(-0.822061\pi\)
−0.847780 + 0.530348i \(0.822061\pi\)
\(942\) 0 0
\(943\) −8.55619 −0.278628
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −13.7512 −0.446854 −0.223427 0.974721i \(-0.571724\pi\)
−0.223427 + 0.974721i \(0.571724\pi\)
\(948\) 0 0
\(949\) 23.1310 0.750862
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.03493 0.0335247 0.0167623 0.999860i \(-0.494664\pi\)
0.0167623 + 0.999860i \(0.494664\pi\)
\(954\) 0 0
\(955\) −19.9593 −0.645866
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −14.5703 −0.470499
\(960\) 0 0
\(961\) −29.6758 −0.957282
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 40.4772 1.30301
\(966\) 0 0
\(967\) −21.8068 −0.701259 −0.350630 0.936514i \(-0.614032\pi\)
−0.350630 + 0.936514i \(0.614032\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −46.6620 −1.49745 −0.748727 0.662878i \(-0.769335\pi\)
−0.748727 + 0.662878i \(0.769335\pi\)
\(972\) 0 0
\(973\) 20.2135 0.648015
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 6.84332 0.218937 0.109469 0.993990i \(-0.465085\pi\)
0.109469 + 0.993990i \(0.465085\pi\)
\(978\) 0 0
\(979\) −75.8422 −2.42393
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 25.4251 0.810934 0.405467 0.914110i \(-0.367109\pi\)
0.405467 + 0.914110i \(0.367109\pi\)
\(984\) 0 0
\(985\) 30.8072 0.981598
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −18.8964 −0.600869
\(990\) 0 0
\(991\) 0.474448 0.0150713 0.00753567 0.999972i \(-0.497601\pi\)
0.00753567 + 0.999972i \(0.497601\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 45.8155 1.45245
\(996\) 0 0
\(997\) −32.9430 −1.04331 −0.521657 0.853155i \(-0.674686\pi\)
−0.521657 + 0.853155i \(0.674686\pi\)
\(998\) 0 0
\(999\) 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 9036.2.a.i.1.1 7
3.2 odd 2 1004.2.a.a.1.3 7
12.11 even 2 4016.2.a.g.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1004.2.a.a.1.3 7 3.2 odd 2
4016.2.a.g.1.5 7 12.11 even 2
9036.2.a.i.1.1 7 1.1 even 1 trivial