Properties

Label 4016.2.a.g.1.5
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 7
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
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 1.5
Root \(1.40474\)
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.40474 q^{3} +2.59588 q^{5} -1.10443 q^{7} -1.02671 q^{9} +O(q^{10})\) \(q+1.40474 q^{3} +2.59588 q^{5} -1.10443 q^{7} -1.02671 q^{9} +5.46000 q^{11} -2.10841 q^{13} +3.64653 q^{15} -1.93466 q^{17} +4.08955 q^{19} -1.55143 q^{21} +2.90552 q^{23} +1.73858 q^{25} -5.65647 q^{27} +5.78201 q^{29} +1.15076 q^{31} +7.66987 q^{33} -2.86696 q^{35} -1.95339 q^{37} -2.96177 q^{39} +2.94481 q^{41} +6.50361 q^{43} -2.66521 q^{45} +11.0399 q^{47} -5.78024 q^{49} -2.71769 q^{51} +0.0920517 q^{53} +14.1735 q^{55} +5.74475 q^{57} -1.65539 q^{59} +5.04551 q^{61} +1.13392 q^{63} -5.47318 q^{65} -8.55699 q^{67} +4.08149 q^{69} +7.42422 q^{71} -10.9708 q^{73} +2.44226 q^{75} -6.03016 q^{77} +7.18613 q^{79} -4.86575 q^{81} +6.37870 q^{83} -5.02213 q^{85} +8.12221 q^{87} +13.8905 q^{89} +2.32859 q^{91} +1.61651 q^{93} +10.6160 q^{95} -2.75331 q^{97} -5.60582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + O(q^{10}) \) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + 5q^{11} - q^{13} + 6q^{15} - 8q^{17} + 15q^{19} - 3q^{21} + 5q^{23} - 9q^{25} + 9q^{27} + 21q^{31} + 7q^{35} - q^{37} + 23q^{39} - 10q^{41} + 23q^{43} - 4q^{45} + 10q^{47} - 13q^{49} + 20q^{51} - q^{53} + 23q^{55} - 6q^{57} + 4q^{59} + 3q^{61} + 4q^{63} + 4q^{65} + 28q^{67} + 18q^{69} + 18q^{71} - 7q^{73} - 11q^{75} + 6q^{77} + 30q^{79} - 5q^{81} - 13q^{83} + q^{85} + 7q^{87} + 18q^{91} + 36q^{93} - 2q^{97} + 10q^{99} + O(q^{100}) \)

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
\(3\) 1.40474 0.811027 0.405513 0.914089i \(-0.367093\pi\)
0.405513 + 0.914089i \(0.367093\pi\)
\(4\) 0 0
\(5\) 2.59588 1.16091 0.580456 0.814292i \(-0.302874\pi\)
0.580456 + 0.814292i \(0.302874\pi\)
\(6\) 0 0
\(7\) −1.10443 −0.417434 −0.208717 0.977976i \(-0.566929\pi\)
−0.208717 + 0.977976i \(0.566929\pi\)
\(8\) 0 0
\(9\) −1.02671 −0.342236
\(10\) 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
\(15\) 3.64653 0.941530
\(16\) 0 0
\(17\) −1.93466 −0.469223 −0.234612 0.972089i \(-0.575382\pi\)
−0.234612 + 0.972089i \(0.575382\pi\)
\(18\) 0 0
\(19\) 4.08955 0.938207 0.469104 0.883143i \(-0.344577\pi\)
0.469104 + 0.883143i \(0.344577\pi\)
\(20\) 0 0
\(21\) −1.55143 −0.338550
\(22\) 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
\(27\) −5.65647 −1.08859
\(28\) 0 0
\(29\) 5.78201 1.07369 0.536846 0.843680i \(-0.319616\pi\)
0.536846 + 0.843680i \(0.319616\pi\)
\(30\) 0 0
\(31\) 1.15076 0.206682 0.103341 0.994646i \(-0.467047\pi\)
0.103341 + 0.994646i \(0.467047\pi\)
\(32\) 0 0
\(33\) 7.66987 1.33515
\(34\) 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
\(39\) −2.96177 −0.474263
\(40\) 0 0
\(41\) 2.94481 0.459902 0.229951 0.973202i \(-0.426143\pi\)
0.229951 + 0.973202i \(0.426143\pi\)
\(42\) 0 0
\(43\) 6.50361 0.991792 0.495896 0.868382i \(-0.334840\pi\)
0.495896 + 0.868382i \(0.334840\pi\)
\(44\) 0 0
\(45\) −2.66521 −0.397306
\(46\) 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
\(51\) −2.71769 −0.380552
\(52\) 0 0
\(53\) 0.0920517 0.0126443 0.00632214 0.999980i \(-0.497988\pi\)
0.00632214 + 0.999980i \(0.497988\pi\)
\(54\) 0 0
\(55\) 14.1735 1.91115
\(56\) 0 0
\(57\) 5.74475 0.760911
\(58\) 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
\(63\) 1.13392 0.142861
\(64\) 0 0
\(65\) −5.47318 −0.678865
\(66\) 0 0
\(67\) −8.55699 −1.04540 −0.522701 0.852516i \(-0.675076\pi\)
−0.522701 + 0.852516i \(0.675076\pi\)
\(68\) 0 0
\(69\) 4.08149 0.491354
\(70\) 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
\(75\) 2.44226 0.282008
\(76\) 0 0
\(77\) −6.03016 −0.687201
\(78\) 0 0
\(79\) 7.18613 0.808503 0.404251 0.914648i \(-0.367532\pi\)
0.404251 + 0.914648i \(0.367532\pi\)
\(80\) 0 0
\(81\) −4.86575 −0.540639
\(82\) 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
\(87\) 8.12221 0.870793
\(88\) 0 0
\(89\) 13.8905 1.47239 0.736197 0.676768i \(-0.236620\pi\)
0.736197 + 0.676768i \(0.236620\pi\)
\(90\) 0 0
\(91\) 2.32859 0.244102
\(92\) 0 0
\(93\) 1.61651 0.167625
\(94\) 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
\(99\) −5.60582 −0.563406
\(100\) 0 0
\(101\) −3.06894 −0.305370 −0.152685 0.988275i \(-0.548792\pi\)
−0.152685 + 0.988275i \(0.548792\pi\)
\(102\) 0 0
\(103\) 2.79994 0.275886 0.137943 0.990440i \(-0.455951\pi\)
0.137943 + 0.990440i \(0.455951\pi\)
\(104\) 0 0
\(105\) −4.02733 −0.393027
\(106\) 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
\(111\) −2.74401 −0.260450
\(112\) 0 0
\(113\) 5.92000 0.556907 0.278453 0.960450i \(-0.410178\pi\)
0.278453 + 0.960450i \(0.410178\pi\)
\(114\) 0 0
\(115\) 7.54237 0.703329
\(116\) 0 0
\(117\) 2.16472 0.200129
\(118\) 0 0
\(119\) 2.13668 0.195870
\(120\) 0 0
\(121\) 18.8116 1.71014
\(122\) 0 0
\(123\) 4.13669 0.372993
\(124\) 0 0
\(125\) −8.46624 −0.757243
\(126\) 0 0
\(127\) −6.21223 −0.551246 −0.275623 0.961266i \(-0.588884\pi\)
−0.275623 + 0.961266i \(0.588884\pi\)
\(128\) 0 0
\(129\) 9.13588 0.804370
\(130\) 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
\(135\) −14.6835 −1.26376
\(136\) 0 0
\(137\) 13.1926 1.12712 0.563561 0.826074i \(-0.309431\pi\)
0.563561 + 0.826074i \(0.309431\pi\)
\(138\) 0 0
\(139\) −18.3023 −1.55238 −0.776189 0.630500i \(-0.782850\pi\)
−0.776189 + 0.630500i \(0.782850\pi\)
\(140\) 0 0
\(141\) 15.5081 1.30602
\(142\) 0 0
\(143\) −11.5119 −0.962675
\(144\) 0 0
\(145\) 15.0094 1.24646
\(146\) 0 0
\(147\) −8.11973 −0.669704
\(148\) 0 0
\(149\) −9.18031 −0.752080 −0.376040 0.926603i \(-0.622715\pi\)
−0.376040 + 0.926603i \(0.622715\pi\)
\(150\) 0 0
\(151\) 8.48773 0.690721 0.345361 0.938470i \(-0.387757\pi\)
0.345361 + 0.938470i \(0.387757\pi\)
\(152\) 0 0
\(153\) 1.98633 0.160585
\(154\) 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
\(159\) 0.129309 0.0102548
\(160\) 0 0
\(161\) −3.20893 −0.252899
\(162\) 0 0
\(163\) −9.22646 −0.722672 −0.361336 0.932436i \(-0.617679\pi\)
−0.361336 + 0.932436i \(0.617679\pi\)
\(164\) 0 0
\(165\) 19.9101 1.55000
\(166\) 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
\(171\) −4.19877 −0.321088
\(172\) 0 0
\(173\) 20.0022 1.52074 0.760370 0.649490i \(-0.225018\pi\)
0.760370 + 0.649490i \(0.225018\pi\)
\(174\) 0 0
\(175\) −1.92014 −0.145149
\(176\) 0 0
\(177\) −2.32539 −0.174787
\(178\) 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
\(183\) 7.08762 0.523932
\(184\) 0 0
\(185\) −5.07077 −0.372810
\(186\) 0 0
\(187\) −10.5632 −0.772459
\(188\) 0 0
\(189\) 6.24716 0.454414
\(190\) 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
\(195\) −7.68839 −0.550577
\(196\) 0 0
\(197\) 11.8677 0.845540 0.422770 0.906237i \(-0.361058\pi\)
0.422770 + 0.906237i \(0.361058\pi\)
\(198\) 0 0
\(199\) 17.6493 1.25113 0.625564 0.780173i \(-0.284869\pi\)
0.625564 + 0.780173i \(0.284869\pi\)
\(200\) 0 0
\(201\) −12.0203 −0.847849
\(202\) 0 0
\(203\) −6.38580 −0.448195
\(204\) 0 0
\(205\) 7.64437 0.533906
\(206\) 0 0
\(207\) −2.98312 −0.207341
\(208\) 0 0
\(209\) 22.3289 1.54452
\(210\) 0 0
\(211\) −9.98934 −0.687695 −0.343847 0.939026i \(-0.611730\pi\)
−0.343847 + 0.939026i \(0.611730\pi\)
\(212\) 0 0
\(213\) 10.4291 0.714590
\(214\) 0 0
\(215\) 16.8826 1.15138
\(216\) 0 0
\(217\) −1.27093 −0.0862761
\(218\) 0 0
\(219\) −15.4111 −1.04139
\(220\) 0 0
\(221\) 4.07905 0.274387
\(222\) 0 0
\(223\) −8.67597 −0.580986 −0.290493 0.956877i \(-0.593819\pi\)
−0.290493 + 0.956877i \(0.593819\pi\)
\(224\) 0 0
\(225\) −1.78502 −0.119001
\(226\) 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
\(231\) −8.47081 −0.557338
\(232\) 0 0
\(233\) 13.2713 0.869434 0.434717 0.900567i \(-0.356848\pi\)
0.434717 + 0.900567i \(0.356848\pi\)
\(234\) 0 0
\(235\) 28.6581 1.86945
\(236\) 0 0
\(237\) 10.0946 0.655717
\(238\) 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
\(243\) 10.1343 0.650117
\(244\) 0 0
\(245\) −15.0048 −0.958622
\(246\) 0 0
\(247\) −8.62246 −0.548634
\(248\) 0 0
\(249\) 8.96041 0.567843
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) 15.8641 0.997368
\(254\) 0 0
\(255\) −7.05478 −0.441788
\(256\) 0 0
\(257\) 1.65887 0.103478 0.0517388 0.998661i \(-0.483524\pi\)
0.0517388 + 0.998661i \(0.483524\pi\)
\(258\) 0 0
\(259\) 2.15738 0.134053
\(260\) 0 0
\(261\) −5.93643 −0.367456
\(262\) 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
\(267\) 19.5126 1.19415
\(268\) 0 0
\(269\) −31.3225 −1.90977 −0.954883 0.296981i \(-0.904020\pi\)
−0.954883 + 0.296981i \(0.904020\pi\)
\(270\) 0 0
\(271\) −3.81449 −0.231714 −0.115857 0.993266i \(-0.536961\pi\)
−0.115857 + 0.993266i \(0.536961\pi\)
\(272\) 0 0
\(273\) 3.27106 0.197973
\(274\) 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
\(279\) −1.18149 −0.0707341
\(280\) 0 0
\(281\) 1.78573 0.106528 0.0532638 0.998580i \(-0.483038\pi\)
0.0532638 + 0.998580i \(0.483038\pi\)
\(282\) 0 0
\(283\) −24.2483 −1.44141 −0.720707 0.693240i \(-0.756183\pi\)
−0.720707 + 0.693240i \(0.756183\pi\)
\(284\) 0 0
\(285\) 14.9127 0.883351
\(286\) 0 0
\(287\) −3.25233 −0.191979
\(288\) 0 0
\(289\) −13.2571 −0.779830
\(290\) 0 0
\(291\) −3.86769 −0.226728
\(292\) 0 0
\(293\) 7.10405 0.415023 0.207511 0.978233i \(-0.433464\pi\)
0.207511 + 0.978233i \(0.433464\pi\)
\(294\) 0 0
\(295\) −4.29719 −0.250192
\(296\) 0 0
\(297\) −30.8843 −1.79209
\(298\) 0 0
\(299\) −6.12603 −0.354277
\(300\) 0 0
\(301\) −7.18276 −0.414008
\(302\) 0 0
\(303\) −4.31105 −0.247664
\(304\) 0 0
\(305\) 13.0975 0.749962
\(306\) 0 0
\(307\) −22.0293 −1.25728 −0.628638 0.777698i \(-0.716387\pi\)
−0.628638 + 0.777698i \(0.716387\pi\)
\(308\) 0 0
\(309\) 3.93319 0.223751
\(310\) 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
\(315\) 2.94353 0.165849
\(316\) 0 0
\(317\) 21.9722 1.23408 0.617042 0.786930i \(-0.288331\pi\)
0.617042 + 0.786930i \(0.288331\pi\)
\(318\) 0 0
\(319\) 31.5697 1.76757
\(320\) 0 0
\(321\) −6.55842 −0.366055
\(322\) 0 0
\(323\) −7.91187 −0.440228
\(324\) 0 0
\(325\) −3.66565 −0.203334
\(326\) 0 0
\(327\) −4.89907 −0.270919
\(328\) 0 0
\(329\) −12.1927 −0.672205
\(330\) 0 0
\(331\) 28.3052 1.55580 0.777898 0.628391i \(-0.216286\pi\)
0.777898 + 0.628391i \(0.216286\pi\)
\(332\) 0 0
\(333\) 2.00556 0.109904
\(334\) 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
\(339\) 8.31606 0.451666
\(340\) 0 0
\(341\) 6.28313 0.340251
\(342\) 0 0
\(343\) 14.1148 0.762129
\(344\) 0 0
\(345\) 10.5951 0.570419
\(346\) 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
\(351\) 11.9262 0.636572
\(352\) 0 0
\(353\) 17.2047 0.915712 0.457856 0.889026i \(-0.348618\pi\)
0.457856 + 0.889026i \(0.348618\pi\)
\(354\) 0 0
\(355\) 19.2724 1.02287
\(356\) 0 0
\(357\) 3.00148 0.158855
\(358\) 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
\(363\) 26.4253 1.38697
\(364\) 0 0
\(365\) −28.4788 −1.49065
\(366\) 0 0
\(367\) −8.66133 −0.452118 −0.226059 0.974114i \(-0.572584\pi\)
−0.226059 + 0.974114i \(0.572584\pi\)
\(368\) 0 0
\(369\) −3.02346 −0.157395
\(370\) 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
\(375\) −11.8929 −0.614145
\(376\) 0 0
\(377\) −12.1909 −0.627861
\(378\) 0 0
\(379\) 4.78961 0.246026 0.123013 0.992405i \(-0.460744\pi\)
0.123013 + 0.992405i \(0.460744\pi\)
\(380\) 0 0
\(381\) −8.72657 −0.447075
\(382\) 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
\(387\) −6.67731 −0.339427
\(388\) 0 0
\(389\) 19.9287 1.01043 0.505214 0.862994i \(-0.331414\pi\)
0.505214 + 0.862994i \(0.331414\pi\)
\(390\) 0 0
\(391\) −5.62117 −0.284275
\(392\) 0 0
\(393\) 29.5025 1.48821
\(394\) 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
\(399\) −6.34465 −0.317630
\(400\) 0 0
\(401\) 7.41181 0.370128 0.185064 0.982726i \(-0.440751\pi\)
0.185064 + 0.982726i \(0.440751\pi\)
\(402\) 0 0
\(403\) −2.42627 −0.120861
\(404\) 0 0
\(405\) −12.6309 −0.627634
\(406\) 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
\(411\) 18.5322 0.914126
\(412\) 0 0
\(413\) 1.82826 0.0899626
\(414\) 0 0
\(415\) 16.5583 0.812816
\(416\) 0 0
\(417\) −25.7099 −1.25902
\(418\) 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
\(423\) −11.3347 −0.551112
\(424\) 0 0
\(425\) −3.36356 −0.163157
\(426\) 0 0
\(427\) −5.57239 −0.269667
\(428\) 0 0
\(429\) −16.1712 −0.780755
\(430\) 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
\(435\) 21.0843 1.01091
\(436\) 0 0
\(437\) 11.8823 0.568405
\(438\) 0 0
\(439\) 24.6780 1.17782 0.588908 0.808200i \(-0.299558\pi\)
0.588908 + 0.808200i \(0.299558\pi\)
\(440\) 0 0
\(441\) 5.93462 0.282601
\(442\) 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
\(447\) −12.8959 −0.609957
\(448\) 0 0
\(449\) 23.1886 1.09434 0.547169 0.837022i \(-0.315705\pi\)
0.547169 + 0.837022i \(0.315705\pi\)
\(450\) 0 0
\(451\) 16.0787 0.757114
\(452\) 0 0
\(453\) 11.9230 0.560193
\(454\) 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
\(459\) 10.9433 0.510791
\(460\) 0 0
\(461\) −8.18616 −0.381267 −0.190634 0.981661i \(-0.561054\pi\)
−0.190634 + 0.981661i \(0.561054\pi\)
\(462\) 0 0
\(463\) −9.28673 −0.431591 −0.215796 0.976439i \(-0.569234\pi\)
−0.215796 + 0.976439i \(0.569234\pi\)
\(464\) 0 0
\(465\) 4.19627 0.194598
\(466\) 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
\(471\) −4.61146 −0.212485
\(472\) 0 0
\(473\) 35.5097 1.63274
\(474\) 0 0
\(475\) 7.11003 0.326230
\(476\) 0 0
\(477\) −0.0945102 −0.00432733
\(478\) 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
\(483\) −4.50771 −0.205108
\(484\) 0 0
\(485\) −7.14727 −0.324541
\(486\) 0 0
\(487\) 19.8582 0.899860 0.449930 0.893064i \(-0.351449\pi\)
0.449930 + 0.893064i \(0.351449\pi\)
\(488\) 0 0
\(489\) −12.9608 −0.586106
\(490\) 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
\(495\) −14.5520 −0.654065
\(496\) 0 0
\(497\) −8.19950 −0.367798
\(498\) 0 0
\(499\) −17.1660 −0.768455 −0.384228 0.923238i \(-0.625532\pi\)
−0.384228 + 0.923238i \(0.625532\pi\)
\(500\) 0 0
\(501\) −6.65216 −0.297196
\(502\) 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
\(507\) −12.0170 −0.533693
\(508\) 0 0
\(509\) 27.6050 1.22357 0.611785 0.791024i \(-0.290452\pi\)
0.611785 + 0.791024i \(0.290452\pi\)
\(510\) 0 0
\(511\) 12.1164 0.535999
\(512\) 0 0
\(513\) −23.1324 −1.02132
\(514\) 0 0
\(515\) 7.26831 0.320280
\(516\) 0 0
\(517\) 60.2775 2.65100
\(518\) 0 0
\(519\) 28.0979 1.23336
\(520\) 0 0
\(521\) −9.19886 −0.403009 −0.201505 0.979488i \(-0.564583\pi\)
−0.201505 + 0.979488i \(0.564583\pi\)
\(522\) 0 0
\(523\) 31.1408 1.36169 0.680847 0.732426i \(-0.261612\pi\)
0.680847 + 0.732426i \(0.261612\pi\)
\(524\) 0 0
\(525\) −2.69729 −0.117719
\(526\) 0 0
\(527\) −2.22632 −0.0969800
\(528\) 0 0
\(529\) −14.5580 −0.632955
\(530\) 0 0
\(531\) 1.69960 0.0737564
\(532\) 0 0
\(533\) −6.20887 −0.268936
\(534\) 0 0
\(535\) −12.1196 −0.523976
\(536\) 0 0
\(537\) −23.9760 −1.03464
\(538\) 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
\(543\) −3.51294 −0.150755
\(544\) 0 0
\(545\) −9.05321 −0.387797
\(546\) 0 0
\(547\) 36.6986 1.56912 0.784560 0.620053i \(-0.212889\pi\)
0.784560 + 0.620053i \(0.212889\pi\)
\(548\) 0 0
\(549\) −5.18026 −0.221088
\(550\) 0 0
\(551\) 23.6458 1.00735
\(552\) 0 0
\(553\) −7.93655 −0.337496
\(554\) 0 0
\(555\) −7.12310 −0.302359
\(556\) 0 0
\(557\) −2.25209 −0.0954243 −0.0477121 0.998861i \(-0.515193\pi\)
−0.0477121 + 0.998861i \(0.515193\pi\)
\(558\) 0 0
\(559\) −13.7123 −0.579969
\(560\) 0 0
\(561\) −14.8386 −0.626485
\(562\) 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
\(567\) 5.37386 0.225681
\(568\) 0 0
\(569\) 17.7973 0.746102 0.373051 0.927811i \(-0.378312\pi\)
0.373051 + 0.927811i \(0.378312\pi\)
\(570\) 0 0
\(571\) 20.8568 0.872828 0.436414 0.899746i \(-0.356248\pi\)
0.436414 + 0.899746i \(0.356248\pi\)
\(572\) 0 0
\(573\) 10.8008 0.451210
\(574\) 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
\(579\) −21.9039 −0.910297
\(580\) 0 0
\(581\) −7.04480 −0.292268
\(582\) 0 0
\(583\) 0.502602 0.0208157
\(584\) 0 0
\(585\) 5.61936 0.232332
\(586\) 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
\(591\) 16.6711 0.685756
\(592\) 0 0
\(593\) 9.51454 0.390715 0.195358 0.980732i \(-0.437413\pi\)
0.195358 + 0.980732i \(0.437413\pi\)
\(594\) 0 0
\(595\) 5.54657 0.227387
\(596\) 0 0
\(597\) 24.7927 1.01470
\(598\) 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
\(603\) 8.78553 0.357774
\(604\) 0 0
\(605\) 48.8325 1.98532
\(606\) 0 0
\(607\) −19.3315 −0.784641 −0.392320 0.919829i \(-0.628328\pi\)
−0.392320 + 0.919829i \(0.628328\pi\)
\(608\) 0 0
\(609\) −8.97039 −0.363498
\(610\) 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
\(615\) 10.7383 0.433012
\(616\) 0 0
\(617\) −29.4697 −1.18641 −0.593203 0.805053i \(-0.702137\pi\)
−0.593203 + 0.805053i \(0.702137\pi\)
\(618\) 0 0
\(619\) −17.3548 −0.697547 −0.348773 0.937207i \(-0.613402\pi\)
−0.348773 + 0.937207i \(0.613402\pi\)
\(620\) 0 0
\(621\) −16.4350 −0.659513
\(622\) 0 0
\(623\) −15.3411 −0.614627
\(624\) 0 0
\(625\) −30.6702 −1.22681
\(626\) 0 0
\(627\) 31.3663 1.25265
\(628\) 0 0
\(629\) 3.77914 0.150684
\(630\) 0 0
\(631\) 17.7649 0.707211 0.353605 0.935395i \(-0.384956\pi\)
0.353605 + 0.935395i \(0.384956\pi\)
\(632\) 0 0
\(633\) −14.0324 −0.557739
\(634\) 0 0
\(635\) −16.1262 −0.639949
\(636\) 0 0
\(637\) 12.1871 0.482872
\(638\) 0 0
\(639\) −7.62250 −0.301542
\(640\) 0 0
\(641\) −19.1757 −0.757395 −0.378698 0.925520i \(-0.623628\pi\)
−0.378698 + 0.925520i \(0.623628\pi\)
\(642\) 0 0
\(643\) −35.7582 −1.41016 −0.705082 0.709126i \(-0.749090\pi\)
−0.705082 + 0.709126i \(0.749090\pi\)
\(644\) 0 0
\(645\) 23.7156 0.933802
\(646\) 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
\(651\) −1.78532 −0.0699722
\(652\) 0 0
\(653\) −11.8660 −0.464351 −0.232176 0.972674i \(-0.574584\pi\)
−0.232176 + 0.972674i \(0.574584\pi\)
\(654\) 0 0
\(655\) 54.5190 2.13023
\(656\) 0 0
\(657\) 11.2638 0.439443
\(658\) 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
\(663\) 5.73000 0.222535
\(664\) 0 0
\(665\) −11.7246 −0.454659
\(666\) 0 0
\(667\) 16.7997 0.650488
\(668\) 0 0
\(669\) −12.1875 −0.471195
\(670\) 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
\(675\) −9.83425 −0.378521
\(676\) 0 0
\(677\) −44.1231 −1.69579 −0.847895 0.530165i \(-0.822130\pi\)
−0.847895 + 0.530165i \(0.822130\pi\)
\(678\) 0 0
\(679\) 3.04083 0.116696
\(680\) 0 0
\(681\) 10.1580 0.389255
\(682\) 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
\(687\) 2.00898 0.0766472
\(688\) 0 0
\(689\) −0.194083 −0.00739397
\(690\) 0 0
\(691\) −2.94258 −0.111941 −0.0559705 0.998432i \(-0.517825\pi\)
−0.0559705 + 0.998432i \(0.517825\pi\)
\(692\) 0 0
\(693\) 6.19121 0.235185
\(694\) 0 0
\(695\) −47.5105 −1.80217
\(696\) 0 0
\(697\) −5.69719 −0.215797
\(698\) 0 0
\(699\) 18.6428 0.705134
\(700\) 0 0
\(701\) −16.1032 −0.608209 −0.304104 0.952639i \(-0.598357\pi\)
−0.304104 + 0.952639i \(0.598357\pi\)
\(702\) 0 0
\(703\) −7.98849 −0.301292
\(704\) 0 0
\(705\) 40.2572 1.51617
\(706\) 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
\(711\) −7.37806 −0.276699
\(712\) 0 0
\(713\) 3.34354 0.125217
\(714\) 0 0
\(715\) −29.8835 −1.11758
\(716\) 0 0
\(717\) −34.5021 −1.28851
\(718\) 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
\(723\) −20.0172 −0.744449
\(724\) 0 0
\(725\) 10.0525 0.373341
\(726\) 0 0
\(727\) −8.63762 −0.320352 −0.160176 0.987088i \(-0.551206\pi\)
−0.160176 + 0.987088i \(0.551206\pi\)
\(728\) 0 0
\(729\) 28.8333 1.06790
\(730\) 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
\(735\) −21.0778 −0.777468
\(736\) 0 0
\(737\) −46.7211 −1.72099
\(738\) 0 0
\(739\) 13.6956 0.503803 0.251901 0.967753i \(-0.418944\pi\)
0.251901 + 0.967753i \(0.418944\pi\)
\(740\) 0 0
\(741\) −12.1123 −0.444957
\(742\) 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
\(747\) −6.54906 −0.239618
\(748\) 0 0
\(749\) 5.15633 0.188408
\(750\) 0 0
\(751\) −5.63750 −0.205715 −0.102858 0.994696i \(-0.532799\pi\)
−0.102858 + 0.994696i \(0.532799\pi\)
\(752\) 0 0
\(753\) −1.40474 −0.0511915
\(754\) 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
\(759\) 22.2849 0.808892
\(760\) 0 0
\(761\) −26.9970 −0.978640 −0.489320 0.872104i \(-0.662755\pi\)
−0.489320 + 0.872104i \(0.662755\pi\)
\(762\) 0 0
\(763\) 3.85172 0.139442
\(764\) 0 0
\(765\) 5.15626 0.186425
\(766\) 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
\(771\) 2.33028 0.0839230
\(772\) 0 0
\(773\) −37.2454 −1.33963 −0.669813 0.742530i \(-0.733626\pi\)
−0.669813 + 0.742530i \(0.733626\pi\)
\(774\) 0 0
\(775\) 2.00069 0.0718668
\(776\) 0 0
\(777\) 3.03055 0.108720
\(778\) 0 0
\(779\) 12.0429 0.431483
\(780\) 0 0
\(781\) 40.5362 1.45050
\(782\) 0 0
\(783\) −32.7058 −1.16881
\(784\) 0 0
\(785\) −8.52171 −0.304153
\(786\) 0 0
\(787\) 20.6348 0.735550 0.367775 0.929915i \(-0.380120\pi\)
0.367775 + 0.929915i \(0.380120\pi\)
\(788\) 0 0
\(789\) −16.2189 −0.577408
\(790\) 0 0
\(791\) −6.53820 −0.232472
\(792\) 0 0
\(793\) −10.6380 −0.377767
\(794\) 0 0
\(795\) 0.335670 0.0119050
\(796\) 0 0
\(797\) −3.94230 −0.139644 −0.0698218 0.997559i \(-0.522243\pi\)
−0.0698218 + 0.997559i \(0.522243\pi\)
\(798\) 0 0
\(799\) −21.3583 −0.755603
\(800\) 0 0
\(801\) −14.2615 −0.503906
\(802\) 0 0
\(803\) −59.9005 −2.11384
\(804\) 0 0
\(805\) −8.32999 −0.293593
\(806\) 0 0
\(807\) −43.9999 −1.54887
\(808\) 0 0
\(809\) −41.2905 −1.45170 −0.725849 0.687854i \(-0.758553\pi\)
−0.725849 + 0.687854i \(0.758553\pi\)
\(810\) 0 0
\(811\) 9.94964 0.349379 0.174690 0.984624i \(-0.444108\pi\)
0.174690 + 0.984624i \(0.444108\pi\)
\(812\) 0 0
\(813\) −5.35837 −0.187926
\(814\) 0 0
\(815\) −23.9508 −0.838958
\(816\) 0 0
\(817\) 26.5969 0.930506
\(818\) 0 0
\(819\) −2.39078 −0.0835405
\(820\) 0 0
\(821\) −4.35629 −0.152036 −0.0760178 0.997106i \(-0.524221\pi\)
−0.0760178 + 0.997106i \(0.524221\pi\)
\(822\) 0 0
\(823\) −46.7715 −1.63035 −0.815175 0.579214i \(-0.803359\pi\)
−0.815175 + 0.579214i \(0.803359\pi\)
\(824\) 0 0
\(825\) 13.3347 0.464255
\(826\) 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
\(831\) −33.5822 −1.16495
\(832\) 0 0
\(833\) 11.1828 0.387460
\(834\) 0 0
\(835\) −12.2928 −0.425410
\(836\) 0 0
\(837\) −6.50923 −0.224992
\(838\) 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
\(843\) 2.50848 0.0863968
\(844\) 0 0
\(845\) −22.2067 −0.763934
\(846\) 0 0
\(847\) −20.7760 −0.713871
\(848\) 0 0
\(849\) −34.0626 −1.16903
\(850\) 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
\(855\) −10.8995 −0.372755
\(856\) 0 0
\(857\) −56.4437 −1.92808 −0.964041 0.265754i \(-0.914379\pi\)
−0.964041 + 0.265754i \(0.914379\pi\)
\(858\) 0 0
\(859\) −29.2843 −0.999167 −0.499583 0.866266i \(-0.666514\pi\)
−0.499583 + 0.866266i \(0.666514\pi\)
\(860\) 0 0
\(861\) −4.56867 −0.155700
\(862\) 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
\(867\) −18.6228 −0.632463
\(868\) 0 0
\(869\) 39.2362 1.33100
\(870\) 0 0
\(871\) 18.0417 0.611318
\(872\) 0 0
\(873\) 2.82685 0.0956743
\(874\) 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
\(879\) 9.97933 0.336594
\(880\) 0 0
\(881\) −27.7786 −0.935883 −0.467942 0.883759i \(-0.655004\pi\)
−0.467942 + 0.883759i \(0.655004\pi\)
\(882\) 0 0
\(883\) 13.4792 0.453611 0.226805 0.973940i \(-0.427172\pi\)
0.226805 + 0.973940i \(0.427172\pi\)
\(884\) 0 0
\(885\) −6.03643 −0.202912
\(886\) 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
\(891\) −26.5670 −0.890027
\(892\) 0 0
\(893\) 45.1480 1.51082
\(894\) 0 0
\(895\) −44.3062 −1.48099
\(896\) 0 0
\(897\) −8.60547 −0.287328
\(898\) 0 0
\(899\) 6.65369 0.221913
\(900\) 0 0
\(901\) −0.178088 −0.00593299
\(902\) 0 0
\(903\) −10.0899 −0.335771
\(904\) 0 0
\(905\) −6.49171 −0.215792
\(906\) 0 0
\(907\) −33.7611 −1.12102 −0.560509 0.828148i \(-0.689395\pi\)
−0.560509 + 0.828148i \(0.689395\pi\)
\(908\) 0 0
\(909\) 3.15090 0.104509
\(910\) 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
\(915\) 18.3986 0.608239
\(916\) 0 0
\(917\) −23.1953 −0.765977
\(918\) 0 0
\(919\) 47.9060 1.58027 0.790136 0.612932i \(-0.210010\pi\)
0.790136 + 0.612932i \(0.210010\pi\)
\(920\) 0 0
\(921\) −30.9454 −1.01968
\(922\) 0 0
\(923\) −15.6533 −0.515235
\(924\) 0 0
\(925\) −3.39613 −0.111664
\(926\) 0 0
\(927\) −2.87472 −0.0944182
\(928\) 0 0
\(929\) 23.8411 0.782203 0.391101 0.920348i \(-0.372094\pi\)
0.391101 + 0.920348i \(0.372094\pi\)
\(930\) 0 0
\(931\) −23.6386 −0.774724
\(932\) 0 0
\(933\) 40.4309 1.32365
\(934\) 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
\(939\) −9.38368 −0.306225
\(940\) 0 0
\(941\) 52.0125 1.69556 0.847780 0.530348i \(-0.177939\pi\)
0.847780 + 0.530348i \(0.177939\pi\)
\(942\) 0 0
\(943\) 8.55619 0.278628
\(944\) 0 0
\(945\) 16.2169 0.527535
\(946\) 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
\(951\) 30.8653 1.00087
\(952\) 0 0
\(953\) −1.03493 −0.0335247 −0.0167623 0.999860i \(-0.505336\pi\)
−0.0167623 + 0.999860i \(0.505336\pi\)
\(954\) 0 0
\(955\) 19.9593 0.645866
\(956\) 0 0
\(957\) 44.3473 1.43354
\(958\) 0 0
\(959\) −14.5703 −0.470499
\(960\) 0 0
\(961\) −29.6758 −0.957282
\(962\) 0 0
\(963\) 4.79348 0.154468
\(964\) 0 0
\(965\) −40.4772 −1.30301
\(966\) 0 0
\(967\) 21.8068 0.701259 0.350630 0.936514i \(-0.385968\pi\)
0.350630 + 0.936514i \(0.385968\pi\)
\(968\) 0 0
\(969\) −11.1141 −0.357037
\(970\) 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
\(975\) −5.14928 −0.164909
\(976\) 0 0
\(977\) −6.84332 −0.218937 −0.109469 0.993990i \(-0.534915\pi\)
−0.109469 + 0.993990i \(0.534915\pi\)
\(978\) 0 0
\(979\) 75.8422 2.42393
\(980\) 0 0
\(981\) 3.58068 0.114322
\(982\) 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
\(987\) −17.1276 −0.545176
\(988\) 0 0
\(989\) 18.8964 0.600869
\(990\) 0 0
\(991\) −0.474448 −0.0150713 −0.00753567 0.999972i \(-0.502399\pi\)
−0.00753567 + 0.999972i \(0.502399\pi\)
\(992\) 0 0
\(993\) 39.7615 1.26179
\(994\) 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
\(999\) 11.0493 0.349585
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 4016.2.a.g.1.5 7
4.3 odd 2 1004.2.a.a.1.3 7
12.11 even 2 9036.2.a.i.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1004.2.a.a.1.3 7 4.3 odd 2
4016.2.a.g.1.5 7 1.1 even 1 trivial
9036.2.a.i.1.1 7 12.11 even 2