Properties

Label 4016.2.a.m.1.4
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 23
CM no
Inner twists 1

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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: \(23\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 2008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.67736 q^{3} +4.29688 q^{5} +4.01755 q^{7} +4.16827 q^{9} +O(q^{10})\) \(q-2.67736 q^{3} +4.29688 q^{5} +4.01755 q^{7} +4.16827 q^{9} -4.88107 q^{11} -3.92210 q^{13} -11.5043 q^{15} +0.345632 q^{17} -3.26874 q^{19} -10.7564 q^{21} -7.48325 q^{23} +13.4632 q^{25} -3.12789 q^{27} -10.5555 q^{29} +9.70877 q^{31} +13.0684 q^{33} +17.2630 q^{35} +4.92845 q^{37} +10.5009 q^{39} +7.39986 q^{41} +4.90581 q^{43} +17.9106 q^{45} -1.34062 q^{47} +9.14073 q^{49} -0.925381 q^{51} +1.36208 q^{53} -20.9734 q^{55} +8.75160 q^{57} +0.330955 q^{59} +9.87403 q^{61} +16.7463 q^{63} -16.8528 q^{65} +11.0820 q^{67} +20.0354 q^{69} +10.1094 q^{71} +13.6687 q^{73} -36.0459 q^{75} -19.6100 q^{77} +8.91873 q^{79} -4.13032 q^{81} -3.12340 q^{83} +1.48514 q^{85} +28.2609 q^{87} -7.28030 q^{89} -15.7573 q^{91} -25.9939 q^{93} -14.0454 q^{95} +2.84471 q^{97} -20.3456 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −2.67736 −1.54578 −0.772888 0.634542i \(-0.781189\pi\)
−0.772888 + 0.634542i \(0.781189\pi\)
\(4\) 0 0
\(5\) 4.29688 1.92162 0.960812 0.277200i \(-0.0894063\pi\)
0.960812 + 0.277200i \(0.0894063\pi\)
\(6\) 0 0
\(7\) 4.01755 1.51849 0.759246 0.650804i \(-0.225568\pi\)
0.759246 + 0.650804i \(0.225568\pi\)
\(8\) 0 0
\(9\) 4.16827 1.38942
\(10\) 0 0
\(11\) −4.88107 −1.47170 −0.735849 0.677146i \(-0.763217\pi\)
−0.735849 + 0.677146i \(0.763217\pi\)
\(12\) 0 0
\(13\) −3.92210 −1.08780 −0.543898 0.839151i \(-0.683052\pi\)
−0.543898 + 0.839151i \(0.683052\pi\)
\(14\) 0 0
\(15\) −11.5043 −2.97040
\(16\) 0 0
\(17\) 0.345632 0.0838280 0.0419140 0.999121i \(-0.486654\pi\)
0.0419140 + 0.999121i \(0.486654\pi\)
\(18\) 0 0
\(19\) −3.26874 −0.749900 −0.374950 0.927045i \(-0.622340\pi\)
−0.374950 + 0.927045i \(0.622340\pi\)
\(20\) 0 0
\(21\) −10.7564 −2.34725
\(22\) 0 0
\(23\) −7.48325 −1.56037 −0.780183 0.625551i \(-0.784874\pi\)
−0.780183 + 0.625551i \(0.784874\pi\)
\(24\) 0 0
\(25\) 13.4632 2.69264
\(26\) 0 0
\(27\) −3.12789 −0.601962
\(28\) 0 0
\(29\) −10.5555 −1.96011 −0.980053 0.198735i \(-0.936317\pi\)
−0.980053 + 0.198735i \(0.936317\pi\)
\(30\) 0 0
\(31\) 9.70877 1.74375 0.871873 0.489731i \(-0.162905\pi\)
0.871873 + 0.489731i \(0.162905\pi\)
\(32\) 0 0
\(33\) 13.0684 2.27492
\(34\) 0 0
\(35\) 17.2630 2.91797
\(36\) 0 0
\(37\) 4.92845 0.810232 0.405116 0.914265i \(-0.367231\pi\)
0.405116 + 0.914265i \(0.367231\pi\)
\(38\) 0 0
\(39\) 10.5009 1.68149
\(40\) 0 0
\(41\) 7.39986 1.15566 0.577832 0.816156i \(-0.303899\pi\)
0.577832 + 0.816156i \(0.303899\pi\)
\(42\) 0 0
\(43\) 4.90581 0.748129 0.374064 0.927403i \(-0.377964\pi\)
0.374064 + 0.927403i \(0.377964\pi\)
\(44\) 0 0
\(45\) 17.9106 2.66995
\(46\) 0 0
\(47\) −1.34062 −0.195550 −0.0977750 0.995209i \(-0.531173\pi\)
−0.0977750 + 0.995209i \(0.531173\pi\)
\(48\) 0 0
\(49\) 9.14073 1.30582
\(50\) 0 0
\(51\) −0.925381 −0.129579
\(52\) 0 0
\(53\) 1.36208 0.187096 0.0935479 0.995615i \(-0.470179\pi\)
0.0935479 + 0.995615i \(0.470179\pi\)
\(54\) 0 0
\(55\) −20.9734 −2.82805
\(56\) 0 0
\(57\) 8.75160 1.15918
\(58\) 0 0
\(59\) 0.330955 0.0430867 0.0215434 0.999768i \(-0.493142\pi\)
0.0215434 + 0.999768i \(0.493142\pi\)
\(60\) 0 0
\(61\) 9.87403 1.26424 0.632120 0.774871i \(-0.282185\pi\)
0.632120 + 0.774871i \(0.282185\pi\)
\(62\) 0 0
\(63\) 16.7463 2.10983
\(64\) 0 0
\(65\) −16.8528 −2.09034
\(66\) 0 0
\(67\) 11.0820 1.35389 0.676943 0.736035i \(-0.263304\pi\)
0.676943 + 0.736035i \(0.263304\pi\)
\(68\) 0 0
\(69\) 20.0354 2.41198
\(70\) 0 0
\(71\) 10.1094 1.19977 0.599884 0.800087i \(-0.295213\pi\)
0.599884 + 0.800087i \(0.295213\pi\)
\(72\) 0 0
\(73\) 13.6687 1.59980 0.799900 0.600133i \(-0.204886\pi\)
0.799900 + 0.600133i \(0.204886\pi\)
\(74\) 0 0
\(75\) −36.0459 −4.16222
\(76\) 0 0
\(77\) −19.6100 −2.23476
\(78\) 0 0
\(79\) 8.91873 1.00344 0.501718 0.865031i \(-0.332702\pi\)
0.501718 + 0.865031i \(0.332702\pi\)
\(80\) 0 0
\(81\) −4.13032 −0.458925
\(82\) 0 0
\(83\) −3.12340 −0.342838 −0.171419 0.985198i \(-0.554835\pi\)
−0.171419 + 0.985198i \(0.554835\pi\)
\(84\) 0 0
\(85\) 1.48514 0.161086
\(86\) 0 0
\(87\) 28.2609 3.02989
\(88\) 0 0
\(89\) −7.28030 −0.771710 −0.385855 0.922559i \(-0.626094\pi\)
−0.385855 + 0.922559i \(0.626094\pi\)
\(90\) 0 0
\(91\) −15.7573 −1.65181
\(92\) 0 0
\(93\) −25.9939 −2.69544
\(94\) 0 0
\(95\) −14.0454 −1.44103
\(96\) 0 0
\(97\) 2.84471 0.288837 0.144418 0.989517i \(-0.453869\pi\)
0.144418 + 0.989517i \(0.453869\pi\)
\(98\) 0 0
\(99\) −20.3456 −2.04481
\(100\) 0 0
\(101\) 2.85666 0.284248 0.142124 0.989849i \(-0.454607\pi\)
0.142124 + 0.989849i \(0.454607\pi\)
\(102\) 0 0
\(103\) 2.89586 0.285338 0.142669 0.989770i \(-0.454432\pi\)
0.142669 + 0.989770i \(0.454432\pi\)
\(104\) 0 0
\(105\) −46.2192 −4.51053
\(106\) 0 0
\(107\) 12.3609 1.19498 0.597488 0.801878i \(-0.296166\pi\)
0.597488 + 0.801878i \(0.296166\pi\)
\(108\) 0 0
\(109\) 2.64043 0.252908 0.126454 0.991973i \(-0.459640\pi\)
0.126454 + 0.991973i \(0.459640\pi\)
\(110\) 0 0
\(111\) −13.1953 −1.25244
\(112\) 0 0
\(113\) −2.02036 −0.190060 −0.0950299 0.995474i \(-0.530295\pi\)
−0.0950299 + 0.995474i \(0.530295\pi\)
\(114\) 0 0
\(115\) −32.1547 −2.99844
\(116\) 0 0
\(117\) −16.3484 −1.51141
\(118\) 0 0
\(119\) 1.38859 0.127292
\(120\) 0 0
\(121\) 12.8248 1.16589
\(122\) 0 0
\(123\) −19.8121 −1.78640
\(124\) 0 0
\(125\) 36.3654 3.25262
\(126\) 0 0
\(127\) 1.08326 0.0961240 0.0480620 0.998844i \(-0.484695\pi\)
0.0480620 + 0.998844i \(0.484695\pi\)
\(128\) 0 0
\(129\) −13.1346 −1.15644
\(130\) 0 0
\(131\) 10.8410 0.947181 0.473590 0.880745i \(-0.342958\pi\)
0.473590 + 0.880745i \(0.342958\pi\)
\(132\) 0 0
\(133\) −13.1323 −1.13872
\(134\) 0 0
\(135\) −13.4402 −1.15675
\(136\) 0 0
\(137\) −4.67905 −0.399758 −0.199879 0.979821i \(-0.564055\pi\)
−0.199879 + 0.979821i \(0.564055\pi\)
\(138\) 0 0
\(139\) 8.19070 0.694726 0.347363 0.937731i \(-0.387077\pi\)
0.347363 + 0.937731i \(0.387077\pi\)
\(140\) 0 0
\(141\) 3.58933 0.302276
\(142\) 0 0
\(143\) 19.1441 1.60091
\(144\) 0 0
\(145\) −45.3557 −3.76659
\(146\) 0 0
\(147\) −24.4730 −2.01850
\(148\) 0 0
\(149\) −11.2822 −0.924273 −0.462136 0.886809i \(-0.652917\pi\)
−0.462136 + 0.886809i \(0.652917\pi\)
\(150\) 0 0
\(151\) 2.55491 0.207916 0.103958 0.994582i \(-0.466849\pi\)
0.103958 + 0.994582i \(0.466849\pi\)
\(152\) 0 0
\(153\) 1.44069 0.116473
\(154\) 0 0
\(155\) 41.7175 3.35083
\(156\) 0 0
\(157\) 12.5622 1.00257 0.501286 0.865281i \(-0.332860\pi\)
0.501286 + 0.865281i \(0.332860\pi\)
\(158\) 0 0
\(159\) −3.64678 −0.289208
\(160\) 0 0
\(161\) −30.0644 −2.36940
\(162\) 0 0
\(163\) 6.55995 0.513815 0.256908 0.966436i \(-0.417296\pi\)
0.256908 + 0.966436i \(0.417296\pi\)
\(164\) 0 0
\(165\) 56.1534 4.37153
\(166\) 0 0
\(167\) 21.9818 1.70100 0.850502 0.525972i \(-0.176298\pi\)
0.850502 + 0.525972i \(0.176298\pi\)
\(168\) 0 0
\(169\) 2.38290 0.183300
\(170\) 0 0
\(171\) −13.6250 −1.04193
\(172\) 0 0
\(173\) 11.5338 0.876900 0.438450 0.898756i \(-0.355528\pi\)
0.438450 + 0.898756i \(0.355528\pi\)
\(174\) 0 0
\(175\) 54.0891 4.08875
\(176\) 0 0
\(177\) −0.886087 −0.0666024
\(178\) 0 0
\(179\) 12.1386 0.907278 0.453639 0.891185i \(-0.350126\pi\)
0.453639 + 0.891185i \(0.350126\pi\)
\(180\) 0 0
\(181\) 5.83347 0.433598 0.216799 0.976216i \(-0.430438\pi\)
0.216799 + 0.976216i \(0.430438\pi\)
\(182\) 0 0
\(183\) −26.4364 −1.95423
\(184\) 0 0
\(185\) 21.1770 1.55696
\(186\) 0 0
\(187\) −1.68705 −0.123369
\(188\) 0 0
\(189\) −12.5665 −0.914075
\(190\) 0 0
\(191\) −12.2293 −0.884879 −0.442440 0.896798i \(-0.645887\pi\)
−0.442440 + 0.896798i \(0.645887\pi\)
\(192\) 0 0
\(193\) −5.50148 −0.396005 −0.198003 0.980201i \(-0.563445\pi\)
−0.198003 + 0.980201i \(0.563445\pi\)
\(194\) 0 0
\(195\) 45.1211 3.23119
\(196\) 0 0
\(197\) −9.94394 −0.708477 −0.354238 0.935155i \(-0.615260\pi\)
−0.354238 + 0.935155i \(0.615260\pi\)
\(198\) 0 0
\(199\) −17.1814 −1.21796 −0.608979 0.793187i \(-0.708421\pi\)
−0.608979 + 0.793187i \(0.708421\pi\)
\(200\) 0 0
\(201\) −29.6706 −2.09281
\(202\) 0 0
\(203\) −42.4073 −2.97641
\(204\) 0 0
\(205\) 31.7963 2.22075
\(206\) 0 0
\(207\) −31.1922 −2.16801
\(208\) 0 0
\(209\) 15.9549 1.10363
\(210\) 0 0
\(211\) 3.36612 0.231733 0.115867 0.993265i \(-0.463035\pi\)
0.115867 + 0.993265i \(0.463035\pi\)
\(212\) 0 0
\(213\) −27.0666 −1.85457
\(214\) 0 0
\(215\) 21.0797 1.43762
\(216\) 0 0
\(217\) 39.0055 2.64787
\(218\) 0 0
\(219\) −36.5961 −2.47293
\(220\) 0 0
\(221\) −1.35560 −0.0911877
\(222\) 0 0
\(223\) −6.42756 −0.430421 −0.215210 0.976568i \(-0.569044\pi\)
−0.215210 + 0.976568i \(0.569044\pi\)
\(224\) 0 0
\(225\) 56.1183 3.74122
\(226\) 0 0
\(227\) −6.11613 −0.405942 −0.202971 0.979185i \(-0.565060\pi\)
−0.202971 + 0.979185i \(0.565060\pi\)
\(228\) 0 0
\(229\) −18.0264 −1.19122 −0.595608 0.803275i \(-0.703089\pi\)
−0.595608 + 0.803275i \(0.703089\pi\)
\(230\) 0 0
\(231\) 52.5030 3.45444
\(232\) 0 0
\(233\) −13.2752 −0.869689 −0.434845 0.900506i \(-0.643197\pi\)
−0.434845 + 0.900506i \(0.643197\pi\)
\(234\) 0 0
\(235\) −5.76050 −0.375774
\(236\) 0 0
\(237\) −23.8787 −1.55109
\(238\) 0 0
\(239\) 4.87379 0.315259 0.157630 0.987498i \(-0.449615\pi\)
0.157630 + 0.987498i \(0.449615\pi\)
\(240\) 0 0
\(241\) 14.7989 0.953280 0.476640 0.879099i \(-0.341854\pi\)
0.476640 + 0.879099i \(0.341854\pi\)
\(242\) 0 0
\(243\) 20.4420 1.31136
\(244\) 0 0
\(245\) 39.2766 2.50929
\(246\) 0 0
\(247\) 12.8203 0.815739
\(248\) 0 0
\(249\) 8.36248 0.529950
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 36.5263 2.29639
\(254\) 0 0
\(255\) −3.97626 −0.249003
\(256\) 0 0
\(257\) −0.551631 −0.0344098 −0.0172049 0.999852i \(-0.505477\pi\)
−0.0172049 + 0.999852i \(0.505477\pi\)
\(258\) 0 0
\(259\) 19.8003 1.23033
\(260\) 0 0
\(261\) −43.9982 −2.72342
\(262\) 0 0
\(263\) −25.8398 −1.59335 −0.796676 0.604407i \(-0.793410\pi\)
−0.796676 + 0.604407i \(0.793410\pi\)
\(264\) 0 0
\(265\) 5.85269 0.359528
\(266\) 0 0
\(267\) 19.4920 1.19289
\(268\) 0 0
\(269\) 17.6689 1.07729 0.538647 0.842532i \(-0.318936\pi\)
0.538647 + 0.842532i \(0.318936\pi\)
\(270\) 0 0
\(271\) 7.60636 0.462053 0.231027 0.972947i \(-0.425792\pi\)
0.231027 + 0.972947i \(0.425792\pi\)
\(272\) 0 0
\(273\) 42.1879 2.55333
\(274\) 0 0
\(275\) −65.7148 −3.96275
\(276\) 0 0
\(277\) −21.6033 −1.29802 −0.649009 0.760781i \(-0.724816\pi\)
−0.649009 + 0.760781i \(0.724816\pi\)
\(278\) 0 0
\(279\) 40.4688 2.42280
\(280\) 0 0
\(281\) −22.6953 −1.35389 −0.676943 0.736035i \(-0.736696\pi\)
−0.676943 + 0.736035i \(0.736696\pi\)
\(282\) 0 0
\(283\) −23.1542 −1.37638 −0.688188 0.725533i \(-0.741593\pi\)
−0.688188 + 0.725533i \(0.741593\pi\)
\(284\) 0 0
\(285\) 37.6046 2.22751
\(286\) 0 0
\(287\) 29.7293 1.75487
\(288\) 0 0
\(289\) −16.8805 −0.992973
\(290\) 0 0
\(291\) −7.61633 −0.446477
\(292\) 0 0
\(293\) 19.7530 1.15398 0.576991 0.816751i \(-0.304227\pi\)
0.576991 + 0.816751i \(0.304227\pi\)
\(294\) 0 0
\(295\) 1.42208 0.0827965
\(296\) 0 0
\(297\) 15.2674 0.885907
\(298\) 0 0
\(299\) 29.3501 1.69736
\(300\) 0 0
\(301\) 19.7093 1.13603
\(302\) 0 0
\(303\) −7.64831 −0.439384
\(304\) 0 0
\(305\) 42.4275 2.42939
\(306\) 0 0
\(307\) 4.29451 0.245101 0.122550 0.992462i \(-0.460893\pi\)
0.122550 + 0.992462i \(0.460893\pi\)
\(308\) 0 0
\(309\) −7.75327 −0.441068
\(310\) 0 0
\(311\) 15.9165 0.902540 0.451270 0.892387i \(-0.350971\pi\)
0.451270 + 0.892387i \(0.350971\pi\)
\(312\) 0 0
\(313\) 21.1655 1.19635 0.598173 0.801367i \(-0.295893\pi\)
0.598173 + 0.801367i \(0.295893\pi\)
\(314\) 0 0
\(315\) 71.9567 4.05430
\(316\) 0 0
\(317\) 14.6269 0.821530 0.410765 0.911741i \(-0.365262\pi\)
0.410765 + 0.911741i \(0.365262\pi\)
\(318\) 0 0
\(319\) 51.5221 2.88468
\(320\) 0 0
\(321\) −33.0947 −1.84716
\(322\) 0 0
\(323\) −1.12978 −0.0628626
\(324\) 0 0
\(325\) −52.8041 −2.92904
\(326\) 0 0
\(327\) −7.06939 −0.390938
\(328\) 0 0
\(329\) −5.38602 −0.296941
\(330\) 0 0
\(331\) −10.2268 −0.562114 −0.281057 0.959691i \(-0.590685\pi\)
−0.281057 + 0.959691i \(0.590685\pi\)
\(332\) 0 0
\(333\) 20.5431 1.12576
\(334\) 0 0
\(335\) 47.6182 2.60166
\(336\) 0 0
\(337\) 19.9429 1.08636 0.543181 0.839616i \(-0.317220\pi\)
0.543181 + 0.839616i \(0.317220\pi\)
\(338\) 0 0
\(339\) 5.40925 0.293790
\(340\) 0 0
\(341\) −47.3892 −2.56627
\(342\) 0 0
\(343\) 8.60049 0.464383
\(344\) 0 0
\(345\) 86.0897 4.63491
\(346\) 0 0
\(347\) −36.2758 −1.94739 −0.973693 0.227864i \(-0.926826\pi\)
−0.973693 + 0.227864i \(0.926826\pi\)
\(348\) 0 0
\(349\) −32.9190 −1.76211 −0.881056 0.473011i \(-0.843167\pi\)
−0.881056 + 0.473011i \(0.843167\pi\)
\(350\) 0 0
\(351\) 12.2679 0.654812
\(352\) 0 0
\(353\) −8.34949 −0.444398 −0.222199 0.975001i \(-0.571324\pi\)
−0.222199 + 0.975001i \(0.571324\pi\)
\(354\) 0 0
\(355\) 43.4390 2.30550
\(356\) 0 0
\(357\) −3.71777 −0.196765
\(358\) 0 0
\(359\) −23.3855 −1.23424 −0.617119 0.786870i \(-0.711700\pi\)
−0.617119 + 0.786870i \(0.711700\pi\)
\(360\) 0 0
\(361\) −8.31534 −0.437649
\(362\) 0 0
\(363\) −34.3367 −1.80221
\(364\) 0 0
\(365\) 58.7328 3.07422
\(366\) 0 0
\(367\) −9.95074 −0.519424 −0.259712 0.965686i \(-0.583628\pi\)
−0.259712 + 0.965686i \(0.583628\pi\)
\(368\) 0 0
\(369\) 30.8446 1.60571
\(370\) 0 0
\(371\) 5.47222 0.284103
\(372\) 0 0
\(373\) −16.1591 −0.836688 −0.418344 0.908289i \(-0.637389\pi\)
−0.418344 + 0.908289i \(0.637389\pi\)
\(374\) 0 0
\(375\) −97.3634 −5.02782
\(376\) 0 0
\(377\) 41.3997 2.13220
\(378\) 0 0
\(379\) −15.0285 −0.771962 −0.385981 0.922507i \(-0.626137\pi\)
−0.385981 + 0.922507i \(0.626137\pi\)
\(380\) 0 0
\(381\) −2.90029 −0.148586
\(382\) 0 0
\(383\) −15.6944 −0.801944 −0.400972 0.916090i \(-0.631328\pi\)
−0.400972 + 0.916090i \(0.631328\pi\)
\(384\) 0 0
\(385\) −84.2617 −4.29437
\(386\) 0 0
\(387\) 20.4487 1.03947
\(388\) 0 0
\(389\) 3.70628 0.187916 0.0939580 0.995576i \(-0.470048\pi\)
0.0939580 + 0.995576i \(0.470048\pi\)
\(390\) 0 0
\(391\) −2.58645 −0.130802
\(392\) 0 0
\(393\) −29.0252 −1.46413
\(394\) 0 0
\(395\) 38.3227 1.92823
\(396\) 0 0
\(397\) 0.520696 0.0261330 0.0130665 0.999915i \(-0.495841\pi\)
0.0130665 + 0.999915i \(0.495841\pi\)
\(398\) 0 0
\(399\) 35.1600 1.76020
\(400\) 0 0
\(401\) −1.47427 −0.0736217 −0.0368109 0.999322i \(-0.511720\pi\)
−0.0368109 + 0.999322i \(0.511720\pi\)
\(402\) 0 0
\(403\) −38.0788 −1.89684
\(404\) 0 0
\(405\) −17.7475 −0.881882
\(406\) 0 0
\(407\) −24.0561 −1.19242
\(408\) 0 0
\(409\) 23.3081 1.15251 0.576256 0.817269i \(-0.304513\pi\)
0.576256 + 0.817269i \(0.304513\pi\)
\(410\) 0 0
\(411\) 12.5275 0.617937
\(412\) 0 0
\(413\) 1.32963 0.0654268
\(414\) 0 0
\(415\) −13.4209 −0.658806
\(416\) 0 0
\(417\) −21.9295 −1.07389
\(418\) 0 0
\(419\) 16.5740 0.809691 0.404846 0.914385i \(-0.367325\pi\)
0.404846 + 0.914385i \(0.367325\pi\)
\(420\) 0 0
\(421\) −15.7926 −0.769686 −0.384843 0.922982i \(-0.625744\pi\)
−0.384843 + 0.922982i \(0.625744\pi\)
\(422\) 0 0
\(423\) −5.58808 −0.271702
\(424\) 0 0
\(425\) 4.65331 0.225719
\(426\) 0 0
\(427\) 39.6694 1.91974
\(428\) 0 0
\(429\) −51.2556 −2.47464
\(430\) 0 0
\(431\) 9.47799 0.456539 0.228269 0.973598i \(-0.426693\pi\)
0.228269 + 0.973598i \(0.426693\pi\)
\(432\) 0 0
\(433\) −31.5164 −1.51458 −0.757291 0.653078i \(-0.773477\pi\)
−0.757291 + 0.653078i \(0.773477\pi\)
\(434\) 0 0
\(435\) 121.434 5.82230
\(436\) 0 0
\(437\) 24.4608 1.17012
\(438\) 0 0
\(439\) 31.6164 1.50897 0.754485 0.656318i \(-0.227887\pi\)
0.754485 + 0.656318i \(0.227887\pi\)
\(440\) 0 0
\(441\) 38.1010 1.81434
\(442\) 0 0
\(443\) −6.80425 −0.323279 −0.161640 0.986850i \(-0.551678\pi\)
−0.161640 + 0.986850i \(0.551678\pi\)
\(444\) 0 0
\(445\) −31.2826 −1.48294
\(446\) 0 0
\(447\) 30.2065 1.42872
\(448\) 0 0
\(449\) 32.7833 1.54714 0.773571 0.633710i \(-0.218469\pi\)
0.773571 + 0.633710i \(0.218469\pi\)
\(450\) 0 0
\(451\) −36.1192 −1.70079
\(452\) 0 0
\(453\) −6.84043 −0.321391
\(454\) 0 0
\(455\) −67.7071 −3.17416
\(456\) 0 0
\(457\) −16.4517 −0.769578 −0.384789 0.923004i \(-0.625726\pi\)
−0.384789 + 0.923004i \(0.625726\pi\)
\(458\) 0 0
\(459\) −1.08110 −0.0504613
\(460\) 0 0
\(461\) 16.4167 0.764602 0.382301 0.924038i \(-0.375132\pi\)
0.382301 + 0.924038i \(0.375132\pi\)
\(462\) 0 0
\(463\) 4.17134 0.193859 0.0969293 0.995291i \(-0.469098\pi\)
0.0969293 + 0.995291i \(0.469098\pi\)
\(464\) 0 0
\(465\) −111.693 −5.17963
\(466\) 0 0
\(467\) 13.6901 0.633501 0.316751 0.948509i \(-0.397408\pi\)
0.316751 + 0.948509i \(0.397408\pi\)
\(468\) 0 0
\(469\) 44.5227 2.05587
\(470\) 0 0
\(471\) −33.6336 −1.54975
\(472\) 0 0
\(473\) −23.9456 −1.10102
\(474\) 0 0
\(475\) −44.0077 −2.01921
\(476\) 0 0
\(477\) 5.67751 0.259955
\(478\) 0 0
\(479\) 15.4423 0.705578 0.352789 0.935703i \(-0.385233\pi\)
0.352789 + 0.935703i \(0.385233\pi\)
\(480\) 0 0
\(481\) −19.3299 −0.881367
\(482\) 0 0
\(483\) 80.4932 3.66257
\(484\) 0 0
\(485\) 12.2234 0.555036
\(486\) 0 0
\(487\) 27.7327 1.25669 0.628343 0.777936i \(-0.283733\pi\)
0.628343 + 0.777936i \(0.283733\pi\)
\(488\) 0 0
\(489\) −17.5634 −0.794243
\(490\) 0 0
\(491\) 34.8181 1.57132 0.785660 0.618658i \(-0.212323\pi\)
0.785660 + 0.618658i \(0.212323\pi\)
\(492\) 0 0
\(493\) −3.64831 −0.164312
\(494\) 0 0
\(495\) −87.4228 −3.92936
\(496\) 0 0
\(497\) 40.6152 1.82184
\(498\) 0 0
\(499\) −7.95889 −0.356289 −0.178144 0.984004i \(-0.557009\pi\)
−0.178144 + 0.984004i \(0.557009\pi\)
\(500\) 0 0
\(501\) −58.8533 −2.62937
\(502\) 0 0
\(503\) 3.50633 0.156339 0.0781697 0.996940i \(-0.475092\pi\)
0.0781697 + 0.996940i \(0.475092\pi\)
\(504\) 0 0
\(505\) 12.2747 0.546218
\(506\) 0 0
\(507\) −6.37988 −0.283340
\(508\) 0 0
\(509\) −26.4551 −1.17260 −0.586300 0.810094i \(-0.699416\pi\)
−0.586300 + 0.810094i \(0.699416\pi\)
\(510\) 0 0
\(511\) 54.9147 2.42928
\(512\) 0 0
\(513\) 10.2243 0.451412
\(514\) 0 0
\(515\) 12.4432 0.548312
\(516\) 0 0
\(517\) 6.54367 0.287790
\(518\) 0 0
\(519\) −30.8802 −1.35549
\(520\) 0 0
\(521\) −32.3080 −1.41544 −0.707720 0.706493i \(-0.750276\pi\)
−0.707720 + 0.706493i \(0.750276\pi\)
\(522\) 0 0
\(523\) 1.08738 0.0475479 0.0237739 0.999717i \(-0.492432\pi\)
0.0237739 + 0.999717i \(0.492432\pi\)
\(524\) 0 0
\(525\) −144.816 −6.32030
\(526\) 0 0
\(527\) 3.35566 0.146175
\(528\) 0 0
\(529\) 32.9991 1.43474
\(530\) 0 0
\(531\) 1.37951 0.0598657
\(532\) 0 0
\(533\) −29.0230 −1.25713
\(534\) 0 0
\(535\) 53.1134 2.29629
\(536\) 0 0
\(537\) −32.4993 −1.40245
\(538\) 0 0
\(539\) −44.6165 −1.92177
\(540\) 0 0
\(541\) −14.5224 −0.624369 −0.312184 0.950022i \(-0.601061\pi\)
−0.312184 + 0.950022i \(0.601061\pi\)
\(542\) 0 0
\(543\) −15.6183 −0.670246
\(544\) 0 0
\(545\) 11.3456 0.485993
\(546\) 0 0
\(547\) 26.7522 1.14384 0.571920 0.820309i \(-0.306199\pi\)
0.571920 + 0.820309i \(0.306199\pi\)
\(548\) 0 0
\(549\) 41.1576 1.75657
\(550\) 0 0
\(551\) 34.5032 1.46988
\(552\) 0 0
\(553\) 35.8315 1.52371
\(554\) 0 0
\(555\) −56.6985 −2.40672
\(556\) 0 0
\(557\) 17.5837 0.745047 0.372523 0.928023i \(-0.378493\pi\)
0.372523 + 0.928023i \(0.378493\pi\)
\(558\) 0 0
\(559\) −19.2411 −0.813811
\(560\) 0 0
\(561\) 4.51685 0.190702
\(562\) 0 0
\(563\) −33.8164 −1.42519 −0.712595 0.701575i \(-0.752480\pi\)
−0.712595 + 0.701575i \(0.752480\pi\)
\(564\) 0 0
\(565\) −8.68127 −0.365224
\(566\) 0 0
\(567\) −16.5938 −0.696874
\(568\) 0 0
\(569\) 16.5754 0.694877 0.347439 0.937703i \(-0.387051\pi\)
0.347439 + 0.937703i \(0.387051\pi\)
\(570\) 0 0
\(571\) −19.8103 −0.829034 −0.414517 0.910041i \(-0.636050\pi\)
−0.414517 + 0.910041i \(0.636050\pi\)
\(572\) 0 0
\(573\) 32.7422 1.36783
\(574\) 0 0
\(575\) −100.749 −4.20151
\(576\) 0 0
\(577\) −4.26144 −0.177406 −0.0887031 0.996058i \(-0.528272\pi\)
−0.0887031 + 0.996058i \(0.528272\pi\)
\(578\) 0 0
\(579\) 14.7295 0.612135
\(580\) 0 0
\(581\) −12.5484 −0.520596
\(582\) 0 0
\(583\) −6.64840 −0.275348
\(584\) 0 0
\(585\) −70.2471 −2.90436
\(586\) 0 0
\(587\) −20.7936 −0.858244 −0.429122 0.903247i \(-0.641177\pi\)
−0.429122 + 0.903247i \(0.641177\pi\)
\(588\) 0 0
\(589\) −31.7355 −1.30764
\(590\) 0 0
\(591\) 26.6235 1.09515
\(592\) 0 0
\(593\) −34.8668 −1.43181 −0.715904 0.698199i \(-0.753985\pi\)
−0.715904 + 0.698199i \(0.753985\pi\)
\(594\) 0 0
\(595\) 5.96662 0.244608
\(596\) 0 0
\(597\) 46.0009 1.88269
\(598\) 0 0
\(599\) −14.5394 −0.594064 −0.297032 0.954868i \(-0.595997\pi\)
−0.297032 + 0.954868i \(0.595997\pi\)
\(600\) 0 0
\(601\) 22.9360 0.935579 0.467790 0.883840i \(-0.345051\pi\)
0.467790 + 0.883840i \(0.345051\pi\)
\(602\) 0 0
\(603\) 46.1929 1.88112
\(604\) 0 0
\(605\) 55.1068 2.24041
\(606\) 0 0
\(607\) −38.8454 −1.57669 −0.788343 0.615235i \(-0.789061\pi\)
−0.788343 + 0.615235i \(0.789061\pi\)
\(608\) 0 0
\(609\) 113.540 4.60086
\(610\) 0 0
\(611\) 5.25806 0.212718
\(612\) 0 0
\(613\) −3.80742 −0.153780 −0.0768901 0.997040i \(-0.524499\pi\)
−0.0768901 + 0.997040i \(0.524499\pi\)
\(614\) 0 0
\(615\) −85.1303 −3.43279
\(616\) 0 0
\(617\) 4.05826 0.163380 0.0816898 0.996658i \(-0.473968\pi\)
0.0816898 + 0.996658i \(0.473968\pi\)
\(618\) 0 0
\(619\) −18.6601 −0.750014 −0.375007 0.927022i \(-0.622360\pi\)
−0.375007 + 0.927022i \(0.622360\pi\)
\(620\) 0 0
\(621\) 23.4068 0.939282
\(622\) 0 0
\(623\) −29.2490 −1.17184
\(624\) 0 0
\(625\) 88.9419 3.55768
\(626\) 0 0
\(627\) −42.7172 −1.70596
\(628\) 0 0
\(629\) 1.70343 0.0679202
\(630\) 0 0
\(631\) 1.64043 0.0653045 0.0326523 0.999467i \(-0.489605\pi\)
0.0326523 + 0.999467i \(0.489605\pi\)
\(632\) 0 0
\(633\) −9.01233 −0.358208
\(634\) 0 0
\(635\) 4.65465 0.184714
\(636\) 0 0
\(637\) −35.8509 −1.42046
\(638\) 0 0
\(639\) 42.1388 1.66699
\(640\) 0 0
\(641\) −15.0740 −0.595386 −0.297693 0.954662i \(-0.596217\pi\)
−0.297693 + 0.954662i \(0.596217\pi\)
\(642\) 0 0
\(643\) −34.7735 −1.37133 −0.685666 0.727916i \(-0.740489\pi\)
−0.685666 + 0.727916i \(0.740489\pi\)
\(644\) 0 0
\(645\) −56.4380 −2.22224
\(646\) 0 0
\(647\) 30.2866 1.19069 0.595344 0.803471i \(-0.297016\pi\)
0.595344 + 0.803471i \(0.297016\pi\)
\(648\) 0 0
\(649\) −1.61542 −0.0634106
\(650\) 0 0
\(651\) −104.432 −4.09301
\(652\) 0 0
\(653\) 15.7825 0.617618 0.308809 0.951124i \(-0.400070\pi\)
0.308809 + 0.951124i \(0.400070\pi\)
\(654\) 0 0
\(655\) 46.5824 1.82013
\(656\) 0 0
\(657\) 56.9749 2.22280
\(658\) 0 0
\(659\) 5.44667 0.212172 0.106086 0.994357i \(-0.466168\pi\)
0.106086 + 0.994357i \(0.466168\pi\)
\(660\) 0 0
\(661\) 12.6197 0.490851 0.245425 0.969416i \(-0.421072\pi\)
0.245425 + 0.969416i \(0.421072\pi\)
\(662\) 0 0
\(663\) 3.62944 0.140956
\(664\) 0 0
\(665\) −56.4281 −2.18819
\(666\) 0 0
\(667\) 78.9894 3.05848
\(668\) 0 0
\(669\) 17.2089 0.665334
\(670\) 0 0
\(671\) −48.1958 −1.86058
\(672\) 0 0
\(673\) −2.25268 −0.0868345 −0.0434172 0.999057i \(-0.513824\pi\)
−0.0434172 + 0.999057i \(0.513824\pi\)
\(674\) 0 0
\(675\) −42.1114 −1.62087
\(676\) 0 0
\(677\) −3.09785 −0.119060 −0.0595299 0.998227i \(-0.518960\pi\)
−0.0595299 + 0.998227i \(0.518960\pi\)
\(678\) 0 0
\(679\) 11.4288 0.438596
\(680\) 0 0
\(681\) 16.3751 0.627495
\(682\) 0 0
\(683\) −12.1587 −0.465239 −0.232620 0.972568i \(-0.574730\pi\)
−0.232620 + 0.972568i \(0.574730\pi\)
\(684\) 0 0
\(685\) −20.1053 −0.768185
\(686\) 0 0
\(687\) 48.2632 1.84135
\(688\) 0 0
\(689\) −5.34221 −0.203522
\(690\) 0 0
\(691\) −6.64379 −0.252742 −0.126371 0.991983i \(-0.540333\pi\)
−0.126371 + 0.991983i \(0.540333\pi\)
\(692\) 0 0
\(693\) −81.7396 −3.10503
\(694\) 0 0
\(695\) 35.1945 1.33500
\(696\) 0 0
\(697\) 2.55763 0.0968770
\(698\) 0 0
\(699\) 35.5426 1.34434
\(700\) 0 0
\(701\) −11.3048 −0.426976 −0.213488 0.976946i \(-0.568482\pi\)
−0.213488 + 0.976946i \(0.568482\pi\)
\(702\) 0 0
\(703\) −16.1098 −0.607594
\(704\) 0 0
\(705\) 15.4229 0.580862
\(706\) 0 0
\(707\) 11.4768 0.431629
\(708\) 0 0
\(709\) 26.9207 1.01103 0.505514 0.862818i \(-0.331303\pi\)
0.505514 + 0.862818i \(0.331303\pi\)
\(710\) 0 0
\(711\) 37.1757 1.39420
\(712\) 0 0
\(713\) −72.6532 −2.72088
\(714\) 0 0
\(715\) 82.2598 3.07634
\(716\) 0 0
\(717\) −13.0489 −0.487320
\(718\) 0 0
\(719\) 28.7292 1.07142 0.535709 0.844403i \(-0.320045\pi\)
0.535709 + 0.844403i \(0.320045\pi\)
\(720\) 0 0
\(721\) 11.6343 0.433283
\(722\) 0 0
\(723\) −39.6220 −1.47356
\(724\) 0 0
\(725\) −142.111 −5.27786
\(726\) 0 0
\(727\) −33.9674 −1.25978 −0.629891 0.776684i \(-0.716900\pi\)
−0.629891 + 0.776684i \(0.716900\pi\)
\(728\) 0 0
\(729\) −42.3398 −1.56814
\(730\) 0 0
\(731\) 1.69560 0.0627141
\(732\) 0 0
\(733\) 9.35368 0.345486 0.172743 0.984967i \(-0.444737\pi\)
0.172743 + 0.984967i \(0.444737\pi\)
\(734\) 0 0
\(735\) −105.158 −3.87880
\(736\) 0 0
\(737\) −54.0922 −1.99251
\(738\) 0 0
\(739\) 3.87995 0.142726 0.0713632 0.997450i \(-0.477265\pi\)
0.0713632 + 0.997450i \(0.477265\pi\)
\(740\) 0 0
\(741\) −34.3247 −1.26095
\(742\) 0 0
\(743\) 1.00715 0.0369487 0.0184744 0.999829i \(-0.494119\pi\)
0.0184744 + 0.999829i \(0.494119\pi\)
\(744\) 0 0
\(745\) −48.4782 −1.77611
\(746\) 0 0
\(747\) −13.0192 −0.476347
\(748\) 0 0
\(749\) 49.6607 1.81456
\(750\) 0 0
\(751\) 7.10756 0.259359 0.129679 0.991556i \(-0.458605\pi\)
0.129679 + 0.991556i \(0.458605\pi\)
\(752\) 0 0
\(753\) −2.67736 −0.0975685
\(754\) 0 0
\(755\) 10.9782 0.399536
\(756\) 0 0
\(757\) −9.48536 −0.344751 −0.172376 0.985031i \(-0.555144\pi\)
−0.172376 + 0.985031i \(0.555144\pi\)
\(758\) 0 0
\(759\) −97.7941 −3.54970
\(760\) 0 0
\(761\) −13.9039 −0.504017 −0.252008 0.967725i \(-0.581091\pi\)
−0.252008 + 0.967725i \(0.581091\pi\)
\(762\) 0 0
\(763\) 10.6081 0.384038
\(764\) 0 0
\(765\) 6.19046 0.223817
\(766\) 0 0
\(767\) −1.29804 −0.0468695
\(768\) 0 0
\(769\) 39.6544 1.42997 0.714987 0.699138i \(-0.246433\pi\)
0.714987 + 0.699138i \(0.246433\pi\)
\(770\) 0 0
\(771\) 1.47692 0.0531898
\(772\) 0 0
\(773\) 42.2169 1.51844 0.759218 0.650836i \(-0.225582\pi\)
0.759218 + 0.650836i \(0.225582\pi\)
\(774\) 0 0
\(775\) 130.711 4.69529
\(776\) 0 0
\(777\) −53.0126 −1.90182
\(778\) 0 0
\(779\) −24.1882 −0.866633
\(780\) 0 0
\(781\) −49.3448 −1.76570
\(782\) 0 0
\(783\) 33.0164 1.17991
\(784\) 0 0
\(785\) 53.9783 1.92657
\(786\) 0 0
\(787\) −24.7090 −0.880782 −0.440391 0.897806i \(-0.645160\pi\)
−0.440391 + 0.897806i \(0.645160\pi\)
\(788\) 0 0
\(789\) 69.1826 2.46296
\(790\) 0 0
\(791\) −8.11692 −0.288604
\(792\) 0 0
\(793\) −38.7270 −1.37523
\(794\) 0 0
\(795\) −15.6698 −0.555750
\(796\) 0 0
\(797\) 13.7654 0.487595 0.243798 0.969826i \(-0.421607\pi\)
0.243798 + 0.969826i \(0.421607\pi\)
\(798\) 0 0
\(799\) −0.463362 −0.0163926
\(800\) 0 0
\(801\) −30.3463 −1.07223
\(802\) 0 0
\(803\) −66.7179 −2.35442
\(804\) 0 0
\(805\) −129.183 −4.55310
\(806\) 0 0
\(807\) −47.3061 −1.66526
\(808\) 0 0
\(809\) 22.0960 0.776854 0.388427 0.921479i \(-0.373019\pi\)
0.388427 + 0.921479i \(0.373019\pi\)
\(810\) 0 0
\(811\) 14.1728 0.497676 0.248838 0.968545i \(-0.419951\pi\)
0.248838 + 0.968545i \(0.419951\pi\)
\(812\) 0 0
\(813\) −20.3650 −0.714231
\(814\) 0 0
\(815\) 28.1874 0.987360
\(816\) 0 0
\(817\) −16.0358 −0.561022
\(818\) 0 0
\(819\) −65.6805 −2.29506
\(820\) 0 0
\(821\) 31.8108 1.11020 0.555102 0.831782i \(-0.312679\pi\)
0.555102 + 0.831782i \(0.312679\pi\)
\(822\) 0 0
\(823\) −45.4343 −1.58374 −0.791870 0.610690i \(-0.790892\pi\)
−0.791870 + 0.610690i \(0.790892\pi\)
\(824\) 0 0
\(825\) 175.942 6.12553
\(826\) 0 0
\(827\) 33.6944 1.17167 0.585835 0.810430i \(-0.300767\pi\)
0.585835 + 0.810430i \(0.300767\pi\)
\(828\) 0 0
\(829\) −30.1188 −1.04607 −0.523035 0.852311i \(-0.675200\pi\)
−0.523035 + 0.852311i \(0.675200\pi\)
\(830\) 0 0
\(831\) 57.8399 2.00644
\(832\) 0 0
\(833\) 3.15932 0.109464
\(834\) 0 0
\(835\) 94.4533 3.26869
\(836\) 0 0
\(837\) −30.3680 −1.04967
\(838\) 0 0
\(839\) −30.3559 −1.04800 −0.524001 0.851718i \(-0.675561\pi\)
−0.524001 + 0.851718i \(0.675561\pi\)
\(840\) 0 0
\(841\) 82.4185 2.84202
\(842\) 0 0
\(843\) 60.7635 2.09281
\(844\) 0 0
\(845\) 10.2390 0.352233
\(846\) 0 0
\(847\) 51.5245 1.77040
\(848\) 0 0
\(849\) 61.9922 2.12757
\(850\) 0 0
\(851\) −36.8809 −1.26426
\(852\) 0 0
\(853\) −26.6812 −0.913546 −0.456773 0.889583i \(-0.650995\pi\)
−0.456773 + 0.889583i \(0.650995\pi\)
\(854\) 0 0
\(855\) −58.5450 −2.00220
\(856\) 0 0
\(857\) 23.6142 0.806646 0.403323 0.915058i \(-0.367855\pi\)
0.403323 + 0.915058i \(0.367855\pi\)
\(858\) 0 0
\(859\) 29.0244 0.990301 0.495151 0.868807i \(-0.335113\pi\)
0.495151 + 0.868807i \(0.335113\pi\)
\(860\) 0 0
\(861\) −79.5962 −2.71263
\(862\) 0 0
\(863\) −48.4293 −1.64855 −0.824275 0.566189i \(-0.808417\pi\)
−0.824275 + 0.566189i \(0.808417\pi\)
\(864\) 0 0
\(865\) 49.5595 1.68507
\(866\) 0 0
\(867\) 45.1953 1.53491
\(868\) 0 0
\(869\) −43.5329 −1.47675
\(870\) 0 0
\(871\) −43.4649 −1.47275
\(872\) 0 0
\(873\) 11.8575 0.401317
\(874\) 0 0
\(875\) 146.100 4.93908
\(876\) 0 0
\(877\) −34.3861 −1.16114 −0.580569 0.814211i \(-0.697170\pi\)
−0.580569 + 0.814211i \(0.697170\pi\)
\(878\) 0 0
\(879\) −52.8859 −1.78380
\(880\) 0 0
\(881\) −56.7982 −1.91358 −0.956790 0.290780i \(-0.906085\pi\)
−0.956790 + 0.290780i \(0.906085\pi\)
\(882\) 0 0
\(883\) 1.65446 0.0556770 0.0278385 0.999612i \(-0.491138\pi\)
0.0278385 + 0.999612i \(0.491138\pi\)
\(884\) 0 0
\(885\) −3.80741 −0.127985
\(886\) 0 0
\(887\) 43.2107 1.45087 0.725436 0.688289i \(-0.241638\pi\)
0.725436 + 0.688289i \(0.241638\pi\)
\(888\) 0 0
\(889\) 4.35207 0.145964
\(890\) 0 0
\(891\) 20.1604 0.675399
\(892\) 0 0
\(893\) 4.38215 0.146643
\(894\) 0 0
\(895\) 52.1580 1.74345
\(896\) 0 0
\(897\) −78.5809 −2.62374
\(898\) 0 0
\(899\) −102.481 −3.41793
\(900\) 0 0
\(901\) 0.470777 0.0156839
\(902\) 0 0
\(903\) −52.7691 −1.75604
\(904\) 0 0
\(905\) 25.0657 0.833213
\(906\) 0 0
\(907\) −45.0162 −1.49474 −0.747369 0.664409i \(-0.768683\pi\)
−0.747369 + 0.664409i \(0.768683\pi\)
\(908\) 0 0
\(909\) 11.9073 0.394941
\(910\) 0 0
\(911\) 17.9780 0.595638 0.297819 0.954622i \(-0.403741\pi\)
0.297819 + 0.954622i \(0.403741\pi\)
\(912\) 0 0
\(913\) 15.2455 0.504554
\(914\) 0 0
\(915\) −113.594 −3.75530
\(916\) 0 0
\(917\) 43.5542 1.43829
\(918\) 0 0
\(919\) −3.36987 −0.111162 −0.0555809 0.998454i \(-0.517701\pi\)
−0.0555809 + 0.998454i \(0.517701\pi\)
\(920\) 0 0
\(921\) −11.4980 −0.378871
\(922\) 0 0
\(923\) −39.6502 −1.30510
\(924\) 0 0
\(925\) 66.3528 2.18167
\(926\) 0 0
\(927\) 12.0707 0.396455
\(928\) 0 0
\(929\) 42.8213 1.40492 0.702460 0.711723i \(-0.252085\pi\)
0.702460 + 0.711723i \(0.252085\pi\)
\(930\) 0 0
\(931\) −29.8787 −0.979234
\(932\) 0 0
\(933\) −42.6142 −1.39513
\(934\) 0 0
\(935\) −7.24907 −0.237070
\(936\) 0 0
\(937\) −6.08754 −0.198871 −0.0994356 0.995044i \(-0.531704\pi\)
−0.0994356 + 0.995044i \(0.531704\pi\)
\(938\) 0 0
\(939\) −56.6678 −1.84928
\(940\) 0 0
\(941\) 49.2223 1.60460 0.802300 0.596921i \(-0.203609\pi\)
0.802300 + 0.596921i \(0.203609\pi\)
\(942\) 0 0
\(943\) −55.3750 −1.80326
\(944\) 0 0
\(945\) −53.9966 −1.75651
\(946\) 0 0
\(947\) −1.53886 −0.0500062 −0.0250031 0.999687i \(-0.507960\pi\)
−0.0250031 + 0.999687i \(0.507960\pi\)
\(948\) 0 0
\(949\) −53.6100 −1.74026
\(950\) 0 0
\(951\) −39.1616 −1.26990
\(952\) 0 0
\(953\) 36.0563 1.16798 0.583989 0.811761i \(-0.301491\pi\)
0.583989 + 0.811761i \(0.301491\pi\)
\(954\) 0 0
\(955\) −52.5478 −1.70041
\(956\) 0 0
\(957\) −137.943 −4.45908
\(958\) 0 0
\(959\) −18.7983 −0.607030
\(960\) 0 0
\(961\) 63.2603 2.04065
\(962\) 0 0
\(963\) 51.5237 1.66033
\(964\) 0 0
\(965\) −23.6392 −0.760973
\(966\) 0 0
\(967\) 32.9184 1.05858 0.529292 0.848440i \(-0.322458\pi\)
0.529292 + 0.848440i \(0.322458\pi\)
\(968\) 0 0
\(969\) 3.02483 0.0971716
\(970\) 0 0
\(971\) −30.3151 −0.972858 −0.486429 0.873720i \(-0.661701\pi\)
−0.486429 + 0.873720i \(0.661701\pi\)
\(972\) 0 0
\(973\) 32.9066 1.05494
\(974\) 0 0
\(975\) 141.376 4.52765
\(976\) 0 0
\(977\) −40.0269 −1.28057 −0.640287 0.768136i \(-0.721185\pi\)
−0.640287 + 0.768136i \(0.721185\pi\)
\(978\) 0 0
\(979\) 35.5356 1.13572
\(980\) 0 0
\(981\) 11.0060 0.351396
\(982\) 0 0
\(983\) −5.34084 −0.170346 −0.0851732 0.996366i \(-0.527144\pi\)
−0.0851732 + 0.996366i \(0.527144\pi\)
\(984\) 0 0
\(985\) −42.7280 −1.36143
\(986\) 0 0
\(987\) 14.4203 0.459004
\(988\) 0 0
\(989\) −36.7114 −1.16735
\(990\) 0 0
\(991\) 32.3871 1.02881 0.514405 0.857547i \(-0.328013\pi\)
0.514405 + 0.857547i \(0.328013\pi\)
\(992\) 0 0
\(993\) 27.3808 0.868902
\(994\) 0 0
\(995\) −73.8265 −2.34046
\(996\) 0 0
\(997\) 26.0628 0.825416 0.412708 0.910863i \(-0.364583\pi\)
0.412708 + 0.910863i \(0.364583\pi\)
\(998\) 0 0
\(999\) −15.4156 −0.487729
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.m.1.4 23
4.3 odd 2 2008.2.a.d.1.20 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.20 23 4.3 odd 2
4016.2.a.m.1.4 23 1.1 even 1 trivial