Properties

Label 4016.2.a.g.1.2
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 7
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: \(7\)
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 1.2
Root \(-0.844838\)
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.844838 q^{3} -2.47034 q^{5} +0.972158 q^{7} -2.28625 q^{9} +O(q^{10})\) \(q-0.844838 q^{3} -2.47034 q^{5} +0.972158 q^{7} -2.28625 q^{9} -3.50942 q^{11} +2.87894 q^{13} +2.08704 q^{15} -2.27070 q^{17} +6.78729 q^{19} -0.821315 q^{21} -3.58090 q^{23} +1.10259 q^{25} +4.46602 q^{27} -7.60769 q^{29} +0.279626 q^{31} +2.96489 q^{33} -2.40156 q^{35} -9.37051 q^{37} -2.43223 q^{39} -10.4728 q^{41} +5.70457 q^{43} +5.64782 q^{45} +8.12711 q^{47} -6.05491 q^{49} +1.91837 q^{51} +1.01555 q^{53} +8.66946 q^{55} -5.73416 q^{57} -12.3081 q^{59} +9.95423 q^{61} -2.22260 q^{63} -7.11196 q^{65} +4.50345 q^{67} +3.02528 q^{69} -9.82624 q^{71} +6.37302 q^{73} -0.931509 q^{75} -3.41171 q^{77} -1.13734 q^{79} +3.08569 q^{81} +1.53106 q^{83} +5.60940 q^{85} +6.42726 q^{87} +15.3254 q^{89} +2.79878 q^{91} -0.236239 q^{93} -16.7669 q^{95} -0.254712 q^{97} +8.02340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + O(q^{10}) \) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + 5q^{11} - q^{13} + 6q^{15} - 8q^{17} + 15q^{19} - 3q^{21} + 5q^{23} - 9q^{25} + 9q^{27} + 21q^{31} + 7q^{35} - q^{37} + 23q^{39} - 10q^{41} + 23q^{43} - 4q^{45} + 10q^{47} - 13q^{49} + 20q^{51} - q^{53} + 23q^{55} - 6q^{57} + 4q^{59} + 3q^{61} + 4q^{63} + 4q^{65} + 28q^{67} + 18q^{69} + 18q^{71} - 7q^{73} - 11q^{75} + 6q^{77} + 30q^{79} - 5q^{81} - 13q^{83} + q^{85} + 7q^{87} + 18q^{91} + 36q^{93} - 2q^{97} + 10q^{99} + O(q^{100}) \)

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
\(3\) −0.844838 −0.487767 −0.243884 0.969805i \(-0.578421\pi\)
−0.243884 + 0.969805i \(0.578421\pi\)
\(4\) 0 0
\(5\) −2.47034 −1.10477 −0.552385 0.833589i \(-0.686282\pi\)
−0.552385 + 0.833589i \(0.686282\pi\)
\(6\) 0 0
\(7\) 0.972158 0.367441 0.183721 0.982979i \(-0.441186\pi\)
0.183721 + 0.982979i \(0.441186\pi\)
\(8\) 0 0
\(9\) −2.28625 −0.762083
\(10\) 0 0
\(11\) −3.50942 −1.05813 −0.529064 0.848582i \(-0.677457\pi\)
−0.529064 + 0.848582i \(0.677457\pi\)
\(12\) 0 0
\(13\) 2.87894 0.798473 0.399237 0.916848i \(-0.369275\pi\)
0.399237 + 0.916848i \(0.369275\pi\)
\(14\) 0 0
\(15\) 2.08704 0.538871
\(16\) 0 0
\(17\) −2.27070 −0.550725 −0.275362 0.961340i \(-0.588798\pi\)
−0.275362 + 0.961340i \(0.588798\pi\)
\(18\) 0 0
\(19\) 6.78729 1.55711 0.778556 0.627576i \(-0.215953\pi\)
0.778556 + 0.627576i \(0.215953\pi\)
\(20\) 0 0
\(21\) −0.821315 −0.179226
\(22\) 0 0
\(23\) −3.58090 −0.746670 −0.373335 0.927697i \(-0.621786\pi\)
−0.373335 + 0.927697i \(0.621786\pi\)
\(24\) 0 0
\(25\) 1.10259 0.220518
\(26\) 0 0
\(27\) 4.46602 0.859486
\(28\) 0 0
\(29\) −7.60769 −1.41271 −0.706356 0.707857i \(-0.749662\pi\)
−0.706356 + 0.707857i \(0.749662\pi\)
\(30\) 0 0
\(31\) 0.279626 0.0502224 0.0251112 0.999685i \(-0.492006\pi\)
0.0251112 + 0.999685i \(0.492006\pi\)
\(32\) 0 0
\(33\) 2.96489 0.516121
\(34\) 0 0
\(35\) −2.40156 −0.405938
\(36\) 0 0
\(37\) −9.37051 −1.54050 −0.770251 0.637741i \(-0.779869\pi\)
−0.770251 + 0.637741i \(0.779869\pi\)
\(38\) 0 0
\(39\) −2.43223 −0.389469
\(40\) 0 0
\(41\) −10.4728 −1.63558 −0.817791 0.575516i \(-0.804801\pi\)
−0.817791 + 0.575516i \(0.804801\pi\)
\(42\) 0 0
\(43\) 5.70457 0.869939 0.434970 0.900445i \(-0.356759\pi\)
0.434970 + 0.900445i \(0.356759\pi\)
\(44\) 0 0
\(45\) 5.64782 0.841927
\(46\) 0 0
\(47\) 8.12711 1.18546 0.592730 0.805401i \(-0.298050\pi\)
0.592730 + 0.805401i \(0.298050\pi\)
\(48\) 0 0
\(49\) −6.05491 −0.864987
\(50\) 0 0
\(51\) 1.91837 0.268626
\(52\) 0 0
\(53\) 1.01555 0.139497 0.0697484 0.997565i \(-0.477780\pi\)
0.0697484 + 0.997565i \(0.477780\pi\)
\(54\) 0 0
\(55\) 8.66946 1.16899
\(56\) 0 0
\(57\) −5.73416 −0.759508
\(58\) 0 0
\(59\) −12.3081 −1.60238 −0.801188 0.598413i \(-0.795798\pi\)
−0.801188 + 0.598413i \(0.795798\pi\)
\(60\) 0 0
\(61\) 9.95423 1.27451 0.637255 0.770653i \(-0.280070\pi\)
0.637255 + 0.770653i \(0.280070\pi\)
\(62\) 0 0
\(63\) −2.22260 −0.280021
\(64\) 0 0
\(65\) −7.11196 −0.882130
\(66\) 0 0
\(67\) 4.50345 0.550184 0.275092 0.961418i \(-0.411292\pi\)
0.275092 + 0.961418i \(0.411292\pi\)
\(68\) 0 0
\(69\) 3.02528 0.364201
\(70\) 0 0
\(71\) −9.82624 −1.16616 −0.583080 0.812415i \(-0.698153\pi\)
−0.583080 + 0.812415i \(0.698153\pi\)
\(72\) 0 0
\(73\) 6.37302 0.745906 0.372953 0.927850i \(-0.378345\pi\)
0.372953 + 0.927850i \(0.378345\pi\)
\(74\) 0 0
\(75\) −0.931509 −0.107561
\(76\) 0 0
\(77\) −3.41171 −0.388800
\(78\) 0 0
\(79\) −1.13734 −0.127961 −0.0639806 0.997951i \(-0.520380\pi\)
−0.0639806 + 0.997951i \(0.520380\pi\)
\(80\) 0 0
\(81\) 3.08569 0.342854
\(82\) 0 0
\(83\) 1.53106 0.168055 0.0840277 0.996463i \(-0.473222\pi\)
0.0840277 + 0.996463i \(0.473222\pi\)
\(84\) 0 0
\(85\) 5.60940 0.608425
\(86\) 0 0
\(87\) 6.42726 0.689074
\(88\) 0 0
\(89\) 15.3254 1.62449 0.812243 0.583320i \(-0.198246\pi\)
0.812243 + 0.583320i \(0.198246\pi\)
\(90\) 0 0
\(91\) 2.79878 0.293392
\(92\) 0 0
\(93\) −0.236239 −0.0244968
\(94\) 0 0
\(95\) −16.7669 −1.72025
\(96\) 0 0
\(97\) −0.254712 −0.0258621 −0.0129310 0.999916i \(-0.504116\pi\)
−0.0129310 + 0.999916i \(0.504116\pi\)
\(98\) 0 0
\(99\) 8.02340 0.806382
\(100\) 0 0
\(101\) 10.7612 1.07078 0.535391 0.844604i \(-0.320164\pi\)
0.535391 + 0.844604i \(0.320164\pi\)
\(102\) 0 0
\(103\) 4.73867 0.466915 0.233458 0.972367i \(-0.424996\pi\)
0.233458 + 0.972367i \(0.424996\pi\)
\(104\) 0 0
\(105\) 2.02893 0.198003
\(106\) 0 0
\(107\) 5.02191 0.485486 0.242743 0.970091i \(-0.421953\pi\)
0.242743 + 0.970091i \(0.421953\pi\)
\(108\) 0 0
\(109\) 0.0232276 0.00222480 0.00111240 0.999999i \(-0.499646\pi\)
0.00111240 + 0.999999i \(0.499646\pi\)
\(110\) 0 0
\(111\) 7.91655 0.751406
\(112\) 0 0
\(113\) 9.83680 0.925369 0.462684 0.886523i \(-0.346886\pi\)
0.462684 + 0.886523i \(0.346886\pi\)
\(114\) 0 0
\(115\) 8.84605 0.824899
\(116\) 0 0
\(117\) −6.58197 −0.608503
\(118\) 0 0
\(119\) −2.20748 −0.202359
\(120\) 0 0
\(121\) 1.31600 0.119637
\(122\) 0 0
\(123\) 8.84784 0.797783
\(124\) 0 0
\(125\) 9.62794 0.861149
\(126\) 0 0
\(127\) 6.24438 0.554099 0.277049 0.960856i \(-0.410643\pi\)
0.277049 + 0.960856i \(0.410643\pi\)
\(128\) 0 0
\(129\) −4.81944 −0.424328
\(130\) 0 0
\(131\) 21.8403 1.90820 0.954100 0.299489i \(-0.0968161\pi\)
0.954100 + 0.299489i \(0.0968161\pi\)
\(132\) 0 0
\(133\) 6.59832 0.572147
\(134\) 0 0
\(135\) −11.0326 −0.949535
\(136\) 0 0
\(137\) −8.61906 −0.736376 −0.368188 0.929751i \(-0.620022\pi\)
−0.368188 + 0.929751i \(0.620022\pi\)
\(138\) 0 0
\(139\) 5.86187 0.497197 0.248599 0.968607i \(-0.420030\pi\)
0.248599 + 0.968607i \(0.420030\pi\)
\(140\) 0 0
\(141\) −6.86608 −0.578229
\(142\) 0 0
\(143\) −10.1034 −0.844888
\(144\) 0 0
\(145\) 18.7936 1.56072
\(146\) 0 0
\(147\) 5.11541 0.421912
\(148\) 0 0
\(149\) −4.20332 −0.344349 −0.172175 0.985066i \(-0.555079\pi\)
−0.172175 + 0.985066i \(0.555079\pi\)
\(150\) 0 0
\(151\) 11.9027 0.968631 0.484316 0.874893i \(-0.339069\pi\)
0.484316 + 0.874893i \(0.339069\pi\)
\(152\) 0 0
\(153\) 5.19138 0.419698
\(154\) 0 0
\(155\) −0.690773 −0.0554842
\(156\) 0 0
\(157\) 14.3438 1.14476 0.572378 0.819990i \(-0.306021\pi\)
0.572378 + 0.819990i \(0.306021\pi\)
\(158\) 0 0
\(159\) −0.857977 −0.0680420
\(160\) 0 0
\(161\) −3.48120 −0.274357
\(162\) 0 0
\(163\) −6.38647 −0.500227 −0.250114 0.968217i \(-0.580468\pi\)
−0.250114 + 0.968217i \(0.580468\pi\)
\(164\) 0 0
\(165\) −7.32428 −0.570195
\(166\) 0 0
\(167\) −20.7849 −1.60838 −0.804191 0.594371i \(-0.797401\pi\)
−0.804191 + 0.594371i \(0.797401\pi\)
\(168\) 0 0
\(169\) −4.71172 −0.362440
\(170\) 0 0
\(171\) −15.5174 −1.18665
\(172\) 0 0
\(173\) 22.3065 1.69593 0.847964 0.530054i \(-0.177828\pi\)
0.847964 + 0.530054i \(0.177828\pi\)
\(174\) 0 0
\(175\) 1.07189 0.0810274
\(176\) 0 0
\(177\) 10.3983 0.781586
\(178\) 0 0
\(179\) 4.57389 0.341869 0.170934 0.985282i \(-0.445321\pi\)
0.170934 + 0.985282i \(0.445321\pi\)
\(180\) 0 0
\(181\) −23.4328 −1.74175 −0.870874 0.491507i \(-0.836446\pi\)
−0.870874 + 0.491507i \(0.836446\pi\)
\(182\) 0 0
\(183\) −8.40971 −0.621664
\(184\) 0 0
\(185\) 23.1484 1.70190
\(186\) 0 0
\(187\) 7.96882 0.582738
\(188\) 0 0
\(189\) 4.34168 0.315811
\(190\) 0 0
\(191\) −9.68497 −0.700780 −0.350390 0.936604i \(-0.613951\pi\)
−0.350390 + 0.936604i \(0.613951\pi\)
\(192\) 0 0
\(193\) −21.2162 −1.52718 −0.763588 0.645703i \(-0.776564\pi\)
−0.763588 + 0.645703i \(0.776564\pi\)
\(194\) 0 0
\(195\) 6.00845 0.430274
\(196\) 0 0
\(197\) 10.2301 0.728866 0.364433 0.931230i \(-0.381263\pi\)
0.364433 + 0.931230i \(0.381263\pi\)
\(198\) 0 0
\(199\) 2.03987 0.144602 0.0723011 0.997383i \(-0.476966\pi\)
0.0723011 + 0.997383i \(0.476966\pi\)
\(200\) 0 0
\(201\) −3.80468 −0.268362
\(202\) 0 0
\(203\) −7.39587 −0.519088
\(204\) 0 0
\(205\) 25.8715 1.80694
\(206\) 0 0
\(207\) 8.18684 0.569024
\(208\) 0 0
\(209\) −23.8194 −1.64762
\(210\) 0 0
\(211\) 12.1422 0.835901 0.417951 0.908470i \(-0.362749\pi\)
0.417951 + 0.908470i \(0.362749\pi\)
\(212\) 0 0
\(213\) 8.30158 0.568815
\(214\) 0 0
\(215\) −14.0922 −0.961083
\(216\) 0 0
\(217\) 0.271841 0.0184538
\(218\) 0 0
\(219\) −5.38417 −0.363828
\(220\) 0 0
\(221\) −6.53719 −0.439739
\(222\) 0 0
\(223\) 28.5639 1.91278 0.956389 0.292096i \(-0.0943528\pi\)
0.956389 + 0.292096i \(0.0943528\pi\)
\(224\) 0 0
\(225\) −2.52080 −0.168053
\(226\) 0 0
\(227\) 28.4032 1.88519 0.942593 0.333944i \(-0.108380\pi\)
0.942593 + 0.333944i \(0.108380\pi\)
\(228\) 0 0
\(229\) 19.7016 1.30192 0.650958 0.759114i \(-0.274367\pi\)
0.650958 + 0.759114i \(0.274367\pi\)
\(230\) 0 0
\(231\) 2.88234 0.189644
\(232\) 0 0
\(233\) −24.3686 −1.59644 −0.798221 0.602365i \(-0.794225\pi\)
−0.798221 + 0.602365i \(0.794225\pi\)
\(234\) 0 0
\(235\) −20.0767 −1.30966
\(236\) 0 0
\(237\) 0.960871 0.0624153
\(238\) 0 0
\(239\) 9.67986 0.626138 0.313069 0.949730i \(-0.398643\pi\)
0.313069 + 0.949730i \(0.398643\pi\)
\(240\) 0 0
\(241\) 7.49541 0.482822 0.241411 0.970423i \(-0.422390\pi\)
0.241411 + 0.970423i \(0.422390\pi\)
\(242\) 0 0
\(243\) −16.0050 −1.02672
\(244\) 0 0
\(245\) 14.9577 0.955612
\(246\) 0 0
\(247\) 19.5402 1.24331
\(248\) 0 0
\(249\) −1.29349 −0.0819719
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) 12.5669 0.790073
\(254\) 0 0
\(255\) −4.73903 −0.296770
\(256\) 0 0
\(257\) 22.0330 1.37438 0.687189 0.726479i \(-0.258844\pi\)
0.687189 + 0.726479i \(0.258844\pi\)
\(258\) 0 0
\(259\) −9.10961 −0.566044
\(260\) 0 0
\(261\) 17.3931 1.07660
\(262\) 0 0
\(263\) 0.437637 0.0269858 0.0134929 0.999909i \(-0.495705\pi\)
0.0134929 + 0.999909i \(0.495705\pi\)
\(264\) 0 0
\(265\) −2.50876 −0.154112
\(266\) 0 0
\(267\) −12.9474 −0.792371
\(268\) 0 0
\(269\) 0.166462 0.0101494 0.00507468 0.999987i \(-0.498385\pi\)
0.00507468 + 0.999987i \(0.498385\pi\)
\(270\) 0 0
\(271\) −27.1750 −1.65076 −0.825382 0.564574i \(-0.809040\pi\)
−0.825382 + 0.564574i \(0.809040\pi\)
\(272\) 0 0
\(273\) −2.36452 −0.143107
\(274\) 0 0
\(275\) −3.86945 −0.233336
\(276\) 0 0
\(277\) 26.0074 1.56263 0.781315 0.624137i \(-0.214549\pi\)
0.781315 + 0.624137i \(0.214549\pi\)
\(278\) 0 0
\(279\) −0.639296 −0.0382736
\(280\) 0 0
\(281\) −14.1033 −0.841335 −0.420668 0.907215i \(-0.638204\pi\)
−0.420668 + 0.907215i \(0.638204\pi\)
\(282\) 0 0
\(283\) 14.4293 0.857734 0.428867 0.903368i \(-0.358913\pi\)
0.428867 + 0.903368i \(0.358913\pi\)
\(284\) 0 0
\(285\) 14.1653 0.839082
\(286\) 0 0
\(287\) −10.1812 −0.600980
\(288\) 0 0
\(289\) −11.8439 −0.696702
\(290\) 0 0
\(291\) 0.215190 0.0126147
\(292\) 0 0
\(293\) 28.0623 1.63942 0.819710 0.572779i \(-0.194135\pi\)
0.819710 + 0.572779i \(0.194135\pi\)
\(294\) 0 0
\(295\) 30.4052 1.77026
\(296\) 0 0
\(297\) −15.6731 −0.909447
\(298\) 0 0
\(299\) −10.3092 −0.596196
\(300\) 0 0
\(301\) 5.54574 0.319651
\(302\) 0 0
\(303\) −9.09149 −0.522292
\(304\) 0 0
\(305\) −24.5904 −1.40804
\(306\) 0 0
\(307\) −22.0019 −1.25571 −0.627857 0.778329i \(-0.716068\pi\)
−0.627857 + 0.778329i \(0.716068\pi\)
\(308\) 0 0
\(309\) −4.00341 −0.227746
\(310\) 0 0
\(311\) 6.83660 0.387668 0.193834 0.981034i \(-0.437908\pi\)
0.193834 + 0.981034i \(0.437908\pi\)
\(312\) 0 0
\(313\) −22.1934 −1.25445 −0.627223 0.778839i \(-0.715809\pi\)
−0.627223 + 0.778839i \(0.715809\pi\)
\(314\) 0 0
\(315\) 5.49057 0.309359
\(316\) 0 0
\(317\) 14.4529 0.811755 0.405878 0.913927i \(-0.366966\pi\)
0.405878 + 0.913927i \(0.366966\pi\)
\(318\) 0 0
\(319\) 26.6985 1.49483
\(320\) 0 0
\(321\) −4.24270 −0.236804
\(322\) 0 0
\(323\) −15.4119 −0.857540
\(324\) 0 0
\(325\) 3.17429 0.176078
\(326\) 0 0
\(327\) −0.0196236 −0.00108518
\(328\) 0 0
\(329\) 7.90083 0.435587
\(330\) 0 0
\(331\) −8.27651 −0.454918 −0.227459 0.973788i \(-0.573042\pi\)
−0.227459 + 0.973788i \(0.573042\pi\)
\(332\) 0 0
\(333\) 21.4233 1.17399
\(334\) 0 0
\(335\) −11.1251 −0.607827
\(336\) 0 0
\(337\) 6.45813 0.351797 0.175898 0.984408i \(-0.443717\pi\)
0.175898 + 0.984408i \(0.443717\pi\)
\(338\) 0 0
\(339\) −8.31050 −0.451364
\(340\) 0 0
\(341\) −0.981326 −0.0531418
\(342\) 0 0
\(343\) −12.6914 −0.685273
\(344\) 0 0
\(345\) −7.47348 −0.402358
\(346\) 0 0
\(347\) −15.2559 −0.818979 −0.409490 0.912315i \(-0.634293\pi\)
−0.409490 + 0.912315i \(0.634293\pi\)
\(348\) 0 0
\(349\) 1.41721 0.0758616 0.0379308 0.999280i \(-0.487923\pi\)
0.0379308 + 0.999280i \(0.487923\pi\)
\(350\) 0 0
\(351\) 12.8574 0.686277
\(352\) 0 0
\(353\) 13.5027 0.718674 0.359337 0.933208i \(-0.383003\pi\)
0.359337 + 0.933208i \(0.383003\pi\)
\(354\) 0 0
\(355\) 24.2742 1.28834
\(356\) 0 0
\(357\) 1.86496 0.0987041
\(358\) 0 0
\(359\) 5.44741 0.287503 0.143752 0.989614i \(-0.454083\pi\)
0.143752 + 0.989614i \(0.454083\pi\)
\(360\) 0 0
\(361\) 27.0673 1.42460
\(362\) 0 0
\(363\) −1.11181 −0.0583549
\(364\) 0 0
\(365\) −15.7435 −0.824055
\(366\) 0 0
\(367\) −6.36536 −0.332269 −0.166135 0.986103i \(-0.553129\pi\)
−0.166135 + 0.986103i \(0.553129\pi\)
\(368\) 0 0
\(369\) 23.9435 1.24645
\(370\) 0 0
\(371\) 0.987277 0.0512569
\(372\) 0 0
\(373\) −10.0940 −0.522646 −0.261323 0.965251i \(-0.584159\pi\)
−0.261323 + 0.965251i \(0.584159\pi\)
\(374\) 0 0
\(375\) −8.13404 −0.420040
\(376\) 0 0
\(377\) −21.9020 −1.12801
\(378\) 0 0
\(379\) 23.6557 1.21511 0.607557 0.794276i \(-0.292150\pi\)
0.607557 + 0.794276i \(0.292150\pi\)
\(380\) 0 0
\(381\) −5.27548 −0.270271
\(382\) 0 0
\(383\) 29.3212 1.49825 0.749123 0.662431i \(-0.230475\pi\)
0.749123 + 0.662431i \(0.230475\pi\)
\(384\) 0 0
\(385\) 8.42808 0.429535
\(386\) 0 0
\(387\) −13.0421 −0.662966
\(388\) 0 0
\(389\) 24.2891 1.23151 0.615753 0.787940i \(-0.288852\pi\)
0.615753 + 0.787940i \(0.288852\pi\)
\(390\) 0 0
\(391\) 8.13114 0.411210
\(392\) 0 0
\(393\) −18.4515 −0.930757
\(394\) 0 0
\(395\) 2.80963 0.141368
\(396\) 0 0
\(397\) −10.4398 −0.523961 −0.261980 0.965073i \(-0.584376\pi\)
−0.261980 + 0.965073i \(0.584376\pi\)
\(398\) 0 0
\(399\) −5.57451 −0.279074
\(400\) 0 0
\(401\) 27.6476 1.38066 0.690328 0.723496i \(-0.257466\pi\)
0.690328 + 0.723496i \(0.257466\pi\)
\(402\) 0 0
\(403\) 0.805027 0.0401012
\(404\) 0 0
\(405\) −7.62270 −0.378775
\(406\) 0 0
\(407\) 32.8850 1.63005
\(408\) 0 0
\(409\) −20.0738 −0.992587 −0.496294 0.868155i \(-0.665306\pi\)
−0.496294 + 0.868155i \(0.665306\pi\)
\(410\) 0 0
\(411\) 7.28170 0.359180
\(412\) 0 0
\(413\) −11.9654 −0.588779
\(414\) 0 0
\(415\) −3.78224 −0.185663
\(416\) 0 0
\(417\) −4.95233 −0.242516
\(418\) 0 0
\(419\) −5.41538 −0.264558 −0.132279 0.991212i \(-0.542230\pi\)
−0.132279 + 0.991212i \(0.542230\pi\)
\(420\) 0 0
\(421\) −23.1966 −1.13053 −0.565266 0.824909i \(-0.691226\pi\)
−0.565266 + 0.824909i \(0.691226\pi\)
\(422\) 0 0
\(423\) −18.5806 −0.903419
\(424\) 0 0
\(425\) −2.50365 −0.121445
\(426\) 0 0
\(427\) 9.67709 0.468307
\(428\) 0 0
\(429\) 8.53572 0.412109
\(430\) 0 0
\(431\) 31.4498 1.51488 0.757441 0.652904i \(-0.226449\pi\)
0.757441 + 0.652904i \(0.226449\pi\)
\(432\) 0 0
\(433\) −9.30587 −0.447211 −0.223606 0.974680i \(-0.571783\pi\)
−0.223606 + 0.974680i \(0.571783\pi\)
\(434\) 0 0
\(435\) −15.8775 −0.761269
\(436\) 0 0
\(437\) −24.3046 −1.16265
\(438\) 0 0
\(439\) 31.9914 1.52687 0.763434 0.645886i \(-0.223512\pi\)
0.763434 + 0.645886i \(0.223512\pi\)
\(440\) 0 0
\(441\) 13.8430 0.659192
\(442\) 0 0
\(443\) 9.46628 0.449757 0.224878 0.974387i \(-0.427802\pi\)
0.224878 + 0.974387i \(0.427802\pi\)
\(444\) 0 0
\(445\) −37.8589 −1.79468
\(446\) 0 0
\(447\) 3.55112 0.167962
\(448\) 0 0
\(449\) −20.4021 −0.962835 −0.481418 0.876491i \(-0.659878\pi\)
−0.481418 + 0.876491i \(0.659878\pi\)
\(450\) 0 0
\(451\) 36.7535 1.73066
\(452\) 0 0
\(453\) −10.0559 −0.472467
\(454\) 0 0
\(455\) −6.91395 −0.324131
\(456\) 0 0
\(457\) 5.97184 0.279351 0.139675 0.990197i \(-0.455394\pi\)
0.139675 + 0.990197i \(0.455394\pi\)
\(458\) 0 0
\(459\) −10.1410 −0.473341
\(460\) 0 0
\(461\) 6.01449 0.280123 0.140061 0.990143i \(-0.455270\pi\)
0.140061 + 0.990143i \(0.455270\pi\)
\(462\) 0 0
\(463\) −11.4730 −0.533197 −0.266598 0.963808i \(-0.585900\pi\)
−0.266598 + 0.963808i \(0.585900\pi\)
\(464\) 0 0
\(465\) 0.583591 0.0270634
\(466\) 0 0
\(467\) 26.1886 1.21187 0.605933 0.795516i \(-0.292800\pi\)
0.605933 + 0.795516i \(0.292800\pi\)
\(468\) 0 0
\(469\) 4.37806 0.202160
\(470\) 0 0
\(471\) −12.1181 −0.558374
\(472\) 0 0
\(473\) −20.0197 −0.920508
\(474\) 0 0
\(475\) 7.48360 0.343371
\(476\) 0 0
\(477\) −2.32181 −0.106308
\(478\) 0 0
\(479\) 5.68587 0.259794 0.129897 0.991527i \(-0.458535\pi\)
0.129897 + 0.991527i \(0.458535\pi\)
\(480\) 0 0
\(481\) −26.9771 −1.23005
\(482\) 0 0
\(483\) 2.94105 0.133822
\(484\) 0 0
\(485\) 0.629226 0.0285717
\(486\) 0 0
\(487\) −16.9258 −0.766983 −0.383491 0.923544i \(-0.625278\pi\)
−0.383491 + 0.923544i \(0.625278\pi\)
\(488\) 0 0
\(489\) 5.39553 0.243994
\(490\) 0 0
\(491\) −0.457098 −0.0206285 −0.0103143 0.999947i \(-0.503283\pi\)
−0.0103143 + 0.999947i \(0.503283\pi\)
\(492\) 0 0
\(493\) 17.2748 0.778016
\(494\) 0 0
\(495\) −19.8205 −0.890867
\(496\) 0 0
\(497\) −9.55266 −0.428495
\(498\) 0 0
\(499\) −20.9818 −0.939274 −0.469637 0.882860i \(-0.655615\pi\)
−0.469637 + 0.882860i \(0.655615\pi\)
\(500\) 0 0
\(501\) 17.5598 0.784516
\(502\) 0 0
\(503\) −7.22680 −0.322227 −0.161113 0.986936i \(-0.551509\pi\)
−0.161113 + 0.986936i \(0.551509\pi\)
\(504\) 0 0
\(505\) −26.5839 −1.18297
\(506\) 0 0
\(507\) 3.98064 0.176786
\(508\) 0 0
\(509\) −27.1215 −1.20214 −0.601069 0.799197i \(-0.705258\pi\)
−0.601069 + 0.799197i \(0.705258\pi\)
\(510\) 0 0
\(511\) 6.19558 0.274077
\(512\) 0 0
\(513\) 30.3122 1.33832
\(514\) 0 0
\(515\) −11.7061 −0.515834
\(516\) 0 0
\(517\) −28.5214 −1.25437
\(518\) 0 0
\(519\) −18.8453 −0.827218
\(520\) 0 0
\(521\) 8.03645 0.352083 0.176042 0.984383i \(-0.443671\pi\)
0.176042 + 0.984383i \(0.443671\pi\)
\(522\) 0 0
\(523\) −35.6907 −1.56064 −0.780322 0.625378i \(-0.784945\pi\)
−0.780322 + 0.625378i \(0.784945\pi\)
\(524\) 0 0
\(525\) −0.905574 −0.0395225
\(526\) 0 0
\(527\) −0.634947 −0.0276587
\(528\) 0 0
\(529\) −10.1771 −0.442484
\(530\) 0 0
\(531\) 28.1393 1.22114
\(532\) 0 0
\(533\) −30.1506 −1.30597
\(534\) 0 0
\(535\) −12.4058 −0.536351
\(536\) 0 0
\(537\) −3.86420 −0.166752
\(538\) 0 0
\(539\) 21.2492 0.915268
\(540\) 0 0
\(541\) −23.7224 −1.01991 −0.509953 0.860202i \(-0.670337\pi\)
−0.509953 + 0.860202i \(0.670337\pi\)
\(542\) 0 0
\(543\) 19.7969 0.849567
\(544\) 0 0
\(545\) −0.0573801 −0.00245789
\(546\) 0 0
\(547\) −0.652965 −0.0279188 −0.0139594 0.999903i \(-0.504444\pi\)
−0.0139594 + 0.999903i \(0.504444\pi\)
\(548\) 0 0
\(549\) −22.7579 −0.971282
\(550\) 0 0
\(551\) −51.6356 −2.19975
\(552\) 0 0
\(553\) −1.10568 −0.0470182
\(554\) 0 0
\(555\) −19.5566 −0.830131
\(556\) 0 0
\(557\) 10.7803 0.456776 0.228388 0.973570i \(-0.426655\pi\)
0.228388 + 0.973570i \(0.426655\pi\)
\(558\) 0 0
\(559\) 16.4231 0.694623
\(560\) 0 0
\(561\) −6.73236 −0.284240
\(562\) 0 0
\(563\) 17.4873 0.737000 0.368500 0.929628i \(-0.379871\pi\)
0.368500 + 0.929628i \(0.379871\pi\)
\(564\) 0 0
\(565\) −24.3003 −1.02232
\(566\) 0 0
\(567\) 2.99977 0.125979
\(568\) 0 0
\(569\) 3.99957 0.167671 0.0838353 0.996480i \(-0.473283\pi\)
0.0838353 + 0.996480i \(0.473283\pi\)
\(570\) 0 0
\(571\) −39.9033 −1.66990 −0.834950 0.550325i \(-0.814504\pi\)
−0.834950 + 0.550325i \(0.814504\pi\)
\(572\) 0 0
\(573\) 8.18223 0.341817
\(574\) 0 0
\(575\) −3.94827 −0.164654
\(576\) 0 0
\(577\) −8.27664 −0.344561 −0.172280 0.985048i \(-0.555114\pi\)
−0.172280 + 0.985048i \(0.555114\pi\)
\(578\) 0 0
\(579\) 17.9243 0.744907
\(580\) 0 0
\(581\) 1.48843 0.0617505
\(582\) 0 0
\(583\) −3.56400 −0.147606
\(584\) 0 0
\(585\) 16.2597 0.672256
\(586\) 0 0
\(587\) −39.2614 −1.62049 −0.810246 0.586090i \(-0.800667\pi\)
−0.810246 + 0.586090i \(0.800667\pi\)
\(588\) 0 0
\(589\) 1.89791 0.0782018
\(590\) 0 0
\(591\) −8.64280 −0.355517
\(592\) 0 0
\(593\) 24.9457 1.02440 0.512198 0.858868i \(-0.328831\pi\)
0.512198 + 0.858868i \(0.328831\pi\)
\(594\) 0 0
\(595\) 5.45322 0.223560
\(596\) 0 0
\(597\) −1.72335 −0.0705322
\(598\) 0 0
\(599\) 12.0175 0.491020 0.245510 0.969394i \(-0.421045\pi\)
0.245510 + 0.969394i \(0.421045\pi\)
\(600\) 0 0
\(601\) −11.9326 −0.486742 −0.243371 0.969933i \(-0.578253\pi\)
−0.243371 + 0.969933i \(0.578253\pi\)
\(602\) 0 0
\(603\) −10.2960 −0.419286
\(604\) 0 0
\(605\) −3.25098 −0.132171
\(606\) 0 0
\(607\) 38.2623 1.55302 0.776509 0.630106i \(-0.216989\pi\)
0.776509 + 0.630106i \(0.216989\pi\)
\(608\) 0 0
\(609\) 6.24831 0.253194
\(610\) 0 0
\(611\) 23.3974 0.946558
\(612\) 0 0
\(613\) 32.5152 1.31328 0.656639 0.754205i \(-0.271977\pi\)
0.656639 + 0.754205i \(0.271977\pi\)
\(614\) 0 0
\(615\) −21.8572 −0.881367
\(616\) 0 0
\(617\) −16.0903 −0.647770 −0.323885 0.946096i \(-0.604989\pi\)
−0.323885 + 0.946096i \(0.604989\pi\)
\(618\) 0 0
\(619\) −44.4841 −1.78797 −0.893984 0.448099i \(-0.852101\pi\)
−0.893984 + 0.448099i \(0.852101\pi\)
\(620\) 0 0
\(621\) −15.9924 −0.641752
\(622\) 0 0
\(623\) 14.8987 0.596903
\(624\) 0 0
\(625\) −29.2972 −1.17189
\(626\) 0 0
\(627\) 20.1235 0.803657
\(628\) 0 0
\(629\) 21.2776 0.848393
\(630\) 0 0
\(631\) 42.6044 1.69606 0.848028 0.529952i \(-0.177790\pi\)
0.848028 + 0.529952i \(0.177790\pi\)
\(632\) 0 0
\(633\) −10.2582 −0.407725
\(634\) 0 0
\(635\) −15.4257 −0.612152
\(636\) 0 0
\(637\) −17.4317 −0.690669
\(638\) 0 0
\(639\) 22.4652 0.888711
\(640\) 0 0
\(641\) −26.8680 −1.06122 −0.530612 0.847615i \(-0.678038\pi\)
−0.530612 + 0.847615i \(0.678038\pi\)
\(642\) 0 0
\(643\) −4.23302 −0.166934 −0.0834670 0.996511i \(-0.526599\pi\)
−0.0834670 + 0.996511i \(0.526599\pi\)
\(644\) 0 0
\(645\) 11.9057 0.468785
\(646\) 0 0
\(647\) 6.04546 0.237672 0.118836 0.992914i \(-0.462084\pi\)
0.118836 + 0.992914i \(0.462084\pi\)
\(648\) 0 0
\(649\) 43.1942 1.69552
\(650\) 0 0
\(651\) −0.229662 −0.00900114
\(652\) 0 0
\(653\) −1.66383 −0.0651106 −0.0325553 0.999470i \(-0.510365\pi\)
−0.0325553 + 0.999470i \(0.510365\pi\)
\(654\) 0 0
\(655\) −53.9531 −2.10812
\(656\) 0 0
\(657\) −14.5703 −0.568442
\(658\) 0 0
\(659\) 7.82120 0.304671 0.152335 0.988329i \(-0.451321\pi\)
0.152335 + 0.988329i \(0.451321\pi\)
\(660\) 0 0
\(661\) 22.4534 0.873336 0.436668 0.899623i \(-0.356159\pi\)
0.436668 + 0.899623i \(0.356159\pi\)
\(662\) 0 0
\(663\) 5.52287 0.214490
\(664\) 0 0
\(665\) −16.3001 −0.632091
\(666\) 0 0
\(667\) 27.2424 1.05483
\(668\) 0 0
\(669\) −24.1318 −0.932990
\(670\) 0 0
\(671\) −34.9336 −1.34859
\(672\) 0 0
\(673\) −24.6777 −0.951256 −0.475628 0.879647i \(-0.657779\pi\)
−0.475628 + 0.879647i \(0.657779\pi\)
\(674\) 0 0
\(675\) 4.92419 0.189532
\(676\) 0 0
\(677\) 38.6413 1.48510 0.742552 0.669788i \(-0.233615\pi\)
0.742552 + 0.669788i \(0.233615\pi\)
\(678\) 0 0
\(679\) −0.247620 −0.00950279
\(680\) 0 0
\(681\) −23.9961 −0.919532
\(682\) 0 0
\(683\) −13.3316 −0.510120 −0.255060 0.966925i \(-0.582095\pi\)
−0.255060 + 0.966925i \(0.582095\pi\)
\(684\) 0 0
\(685\) 21.2920 0.813526
\(686\) 0 0
\(687\) −16.6446 −0.635032
\(688\) 0 0
\(689\) 2.92371 0.111385
\(690\) 0 0
\(691\) 21.1199 0.803439 0.401720 0.915763i \(-0.368413\pi\)
0.401720 + 0.915763i \(0.368413\pi\)
\(692\) 0 0
\(693\) 7.80001 0.296298
\(694\) 0 0
\(695\) −14.4808 −0.549289
\(696\) 0 0
\(697\) 23.7806 0.900755
\(698\) 0 0
\(699\) 20.5875 0.778692
\(700\) 0 0
\(701\) −20.8009 −0.785638 −0.392819 0.919616i \(-0.628500\pi\)
−0.392819 + 0.919616i \(0.628500\pi\)
\(702\) 0 0
\(703\) −63.6003 −2.39873
\(704\) 0 0
\(705\) 16.9616 0.638810
\(706\) 0 0
\(707\) 10.4616 0.393449
\(708\) 0 0
\(709\) 28.0183 1.05225 0.526125 0.850407i \(-0.323645\pi\)
0.526125 + 0.850407i \(0.323645\pi\)
\(710\) 0 0
\(711\) 2.60025 0.0975171
\(712\) 0 0
\(713\) −1.00131 −0.0374995
\(714\) 0 0
\(715\) 24.9588 0.933407
\(716\) 0 0
\(717\) −8.17791 −0.305410
\(718\) 0 0
\(719\) 23.5265 0.877391 0.438695 0.898636i \(-0.355441\pi\)
0.438695 + 0.898636i \(0.355441\pi\)
\(720\) 0 0
\(721\) 4.60674 0.171564
\(722\) 0 0
\(723\) −6.33240 −0.235505
\(724\) 0 0
\(725\) −8.38816 −0.311528
\(726\) 0 0
\(727\) −13.6375 −0.505786 −0.252893 0.967494i \(-0.581382\pi\)
−0.252893 + 0.967494i \(0.581382\pi\)
\(728\) 0 0
\(729\) 4.26454 0.157946
\(730\) 0 0
\(731\) −12.9534 −0.479097
\(732\) 0 0
\(733\) −45.2947 −1.67300 −0.836498 0.547970i \(-0.815401\pi\)
−0.836498 + 0.547970i \(0.815401\pi\)
\(734\) 0 0
\(735\) −12.6368 −0.466116
\(736\) 0 0
\(737\) −15.8045 −0.582165
\(738\) 0 0
\(739\) 38.2582 1.40735 0.703676 0.710521i \(-0.251541\pi\)
0.703676 + 0.710521i \(0.251541\pi\)
\(740\) 0 0
\(741\) −16.5083 −0.606447
\(742\) 0 0
\(743\) 21.5410 0.790264 0.395132 0.918624i \(-0.370699\pi\)
0.395132 + 0.918624i \(0.370699\pi\)
\(744\) 0 0
\(745\) 10.3836 0.380427
\(746\) 0 0
\(747\) −3.50038 −0.128072
\(748\) 0 0
\(749\) 4.88209 0.178388
\(750\) 0 0
\(751\) 2.05259 0.0748999 0.0374500 0.999299i \(-0.488077\pi\)
0.0374500 + 0.999299i \(0.488077\pi\)
\(752\) 0 0
\(753\) 0.844838 0.0307876
\(754\) 0 0
\(755\) −29.4038 −1.07012
\(756\) 0 0
\(757\) −24.1139 −0.876434 −0.438217 0.898869i \(-0.644390\pi\)
−0.438217 + 0.898869i \(0.644390\pi\)
\(758\) 0 0
\(759\) −10.6170 −0.385372
\(760\) 0 0
\(761\) −23.7308 −0.860239 −0.430120 0.902772i \(-0.641529\pi\)
−0.430120 + 0.902772i \(0.641529\pi\)
\(762\) 0 0
\(763\) 0.0225809 0.000817483 0
\(764\) 0 0
\(765\) −12.8245 −0.463670
\(766\) 0 0
\(767\) −35.4342 −1.27945
\(768\) 0 0
\(769\) 37.2832 1.34447 0.672233 0.740340i \(-0.265335\pi\)
0.672233 + 0.740340i \(0.265335\pi\)
\(770\) 0 0
\(771\) −18.6143 −0.670376
\(772\) 0 0
\(773\) 0.720896 0.0259288 0.0129644 0.999916i \(-0.495873\pi\)
0.0129644 + 0.999916i \(0.495873\pi\)
\(774\) 0 0
\(775\) 0.308313 0.0110749
\(776\) 0 0
\(777\) 7.69614 0.276097
\(778\) 0 0
\(779\) −71.0821 −2.54678
\(780\) 0 0
\(781\) 34.4844 1.23395
\(782\) 0 0
\(783\) −33.9761 −1.21421
\(784\) 0 0
\(785\) −35.4340 −1.26469
\(786\) 0 0
\(787\) 50.8920 1.81410 0.907051 0.421020i \(-0.138328\pi\)
0.907051 + 0.421020i \(0.138328\pi\)
\(788\) 0 0
\(789\) −0.369732 −0.0131628
\(790\) 0 0
\(791\) 9.56293 0.340018
\(792\) 0 0
\(793\) 28.6576 1.01766
\(794\) 0 0
\(795\) 2.11950 0.0751708
\(796\) 0 0
\(797\) −14.0627 −0.498126 −0.249063 0.968487i \(-0.580123\pi\)
−0.249063 + 0.968487i \(0.580123\pi\)
\(798\) 0 0
\(799\) −18.4542 −0.652863
\(800\) 0 0
\(801\) −35.0376 −1.23799
\(802\) 0 0
\(803\) −22.3656 −0.789265
\(804\) 0 0
\(805\) 8.59976 0.303102
\(806\) 0 0
\(807\) −0.140633 −0.00495053
\(808\) 0 0
\(809\) −44.6840 −1.57100 −0.785502 0.618859i \(-0.787595\pi\)
−0.785502 + 0.618859i \(0.787595\pi\)
\(810\) 0 0
\(811\) −9.73808 −0.341950 −0.170975 0.985275i \(-0.554692\pi\)
−0.170975 + 0.985275i \(0.554692\pi\)
\(812\) 0 0
\(813\) 22.9585 0.805189
\(814\) 0 0
\(815\) 15.7768 0.552636
\(816\) 0 0
\(817\) 38.7186 1.35459
\(818\) 0 0
\(819\) −6.39871 −0.223589
\(820\) 0 0
\(821\) 37.0650 1.29358 0.646788 0.762670i \(-0.276112\pi\)
0.646788 + 0.762670i \(0.276112\pi\)
\(822\) 0 0
\(823\) 53.7145 1.87237 0.936185 0.351508i \(-0.114331\pi\)
0.936185 + 0.351508i \(0.114331\pi\)
\(824\) 0 0
\(825\) 3.26905 0.113814
\(826\) 0 0
\(827\) −33.6240 −1.16922 −0.584611 0.811314i \(-0.698753\pi\)
−0.584611 + 0.811314i \(0.698753\pi\)
\(828\) 0 0
\(829\) −4.34280 −0.150832 −0.0754159 0.997152i \(-0.524028\pi\)
−0.0754159 + 0.997152i \(0.524028\pi\)
\(830\) 0 0
\(831\) −21.9720 −0.762200
\(832\) 0 0
\(833\) 13.7489 0.476370
\(834\) 0 0
\(835\) 51.3458 1.77689
\(836\) 0 0
\(837\) 1.24882 0.0431655
\(838\) 0 0
\(839\) −20.3087 −0.701135 −0.350567 0.936538i \(-0.614011\pi\)
−0.350567 + 0.936538i \(0.614011\pi\)
\(840\) 0 0
\(841\) 28.8769 0.995755
\(842\) 0 0
\(843\) 11.9150 0.410376
\(844\) 0 0
\(845\) 11.6396 0.400413
\(846\) 0 0
\(847\) 1.27936 0.0439595
\(848\) 0 0
\(849\) −12.1904 −0.418375
\(850\) 0 0
\(851\) 33.5549 1.15025
\(852\) 0 0
\(853\) 4.46704 0.152948 0.0764742 0.997072i \(-0.475634\pi\)
0.0764742 + 0.997072i \(0.475634\pi\)
\(854\) 0 0
\(855\) 38.3334 1.31097
\(856\) 0 0
\(857\) 28.2401 0.964664 0.482332 0.875989i \(-0.339790\pi\)
0.482332 + 0.875989i \(0.339790\pi\)
\(858\) 0 0
\(859\) 44.2974 1.51141 0.755703 0.654914i \(-0.227295\pi\)
0.755703 + 0.654914i \(0.227295\pi\)
\(860\) 0 0
\(861\) 8.60150 0.293138
\(862\) 0 0
\(863\) 8.12320 0.276517 0.138259 0.990396i \(-0.455850\pi\)
0.138259 + 0.990396i \(0.455850\pi\)
\(864\) 0 0
\(865\) −55.1046 −1.87361
\(866\) 0 0
\(867\) 10.0062 0.339828
\(868\) 0 0
\(869\) 3.99142 0.135399
\(870\) 0 0
\(871\) 12.9651 0.439307
\(872\) 0 0
\(873\) 0.582335 0.0197091
\(874\) 0 0
\(875\) 9.35987 0.316421
\(876\) 0 0
\(877\) 9.21603 0.311203 0.155602 0.987820i \(-0.450268\pi\)
0.155602 + 0.987820i \(0.450268\pi\)
\(878\) 0 0
\(879\) −23.7081 −0.799655
\(880\) 0 0
\(881\) −27.3672 −0.922025 −0.461013 0.887394i \(-0.652514\pi\)
−0.461013 + 0.887394i \(0.652514\pi\)
\(882\) 0 0
\(883\) −28.6386 −0.963765 −0.481883 0.876236i \(-0.660047\pi\)
−0.481883 + 0.876236i \(0.660047\pi\)
\(884\) 0 0
\(885\) −25.6874 −0.863474
\(886\) 0 0
\(887\) −31.8728 −1.07018 −0.535092 0.844794i \(-0.679723\pi\)
−0.535092 + 0.844794i \(0.679723\pi\)
\(888\) 0 0
\(889\) 6.07052 0.203599
\(890\) 0 0
\(891\) −10.8290 −0.362784
\(892\) 0 0
\(893\) 55.1610 1.84589
\(894\) 0 0
\(895\) −11.2991 −0.377687
\(896\) 0 0
\(897\) 8.70959 0.290805
\(898\) 0 0
\(899\) −2.12731 −0.0709498
\(900\) 0 0
\(901\) −2.30601 −0.0768244
\(902\) 0 0
\(903\) −4.68525 −0.155915
\(904\) 0 0
\(905\) 57.8871 1.92423
\(906\) 0 0
\(907\) −50.8857 −1.68963 −0.844816 0.535057i \(-0.820290\pi\)
−0.844816 + 0.535057i \(0.820290\pi\)
\(908\) 0 0
\(909\) −24.6028 −0.816025
\(910\) 0 0
\(911\) −18.1844 −0.602477 −0.301239 0.953549i \(-0.597400\pi\)
−0.301239 + 0.953549i \(0.597400\pi\)
\(912\) 0 0
\(913\) −5.37312 −0.177824
\(914\) 0 0
\(915\) 20.7749 0.686796
\(916\) 0 0
\(917\) 21.2323 0.701151
\(918\) 0 0
\(919\) −2.57600 −0.0849745 −0.0424872 0.999097i \(-0.513528\pi\)
−0.0424872 + 0.999097i \(0.513528\pi\)
\(920\) 0 0
\(921\) 18.5880 0.612496
\(922\) 0 0
\(923\) −28.2891 −0.931148
\(924\) 0 0
\(925\) −10.3318 −0.339708
\(926\) 0 0
\(927\) −10.8338 −0.355828
\(928\) 0 0
\(929\) 23.1992 0.761142 0.380571 0.924752i \(-0.375727\pi\)
0.380571 + 0.924752i \(0.375727\pi\)
\(930\) 0 0
\(931\) −41.0964 −1.34688
\(932\) 0 0
\(933\) −5.77582 −0.189092
\(934\) 0 0
\(935\) −19.6857 −0.643792
\(936\) 0 0
\(937\) −15.9033 −0.519539 −0.259769 0.965671i \(-0.583647\pi\)
−0.259769 + 0.965671i \(0.583647\pi\)
\(938\) 0 0
\(939\) 18.7498 0.611878
\(940\) 0 0
\(941\) −4.26329 −0.138979 −0.0694896 0.997583i \(-0.522137\pi\)
−0.0694896 + 0.997583i \(0.522137\pi\)
\(942\) 0 0
\(943\) 37.5022 1.22124
\(944\) 0 0
\(945\) −10.7254 −0.348898
\(946\) 0 0
\(947\) 7.78149 0.252864 0.126432 0.991975i \(-0.459647\pi\)
0.126432 + 0.991975i \(0.459647\pi\)
\(948\) 0 0
\(949\) 18.3475 0.595586
\(950\) 0 0
\(951\) −12.2103 −0.395947
\(952\) 0 0
\(953\) 18.4808 0.598650 0.299325 0.954151i \(-0.403238\pi\)
0.299325 + 0.954151i \(0.403238\pi\)
\(954\) 0 0
\(955\) 23.9252 0.774201
\(956\) 0 0
\(957\) −22.5559 −0.729130
\(958\) 0 0
\(959\) −8.37908 −0.270575
\(960\) 0 0
\(961\) −30.9218 −0.997478
\(962\) 0 0
\(963\) −11.4813 −0.369981
\(964\) 0 0
\(965\) 52.4113 1.68718
\(966\) 0 0
\(967\) 8.95512 0.287977 0.143989 0.989579i \(-0.454007\pi\)
0.143989 + 0.989579i \(0.454007\pi\)
\(968\) 0 0
\(969\) 13.0205 0.418280
\(970\) 0 0
\(971\) 2.19052 0.0702972 0.0351486 0.999382i \(-0.488810\pi\)
0.0351486 + 0.999382i \(0.488810\pi\)
\(972\) 0 0
\(973\) 5.69866 0.182691
\(974\) 0 0
\(975\) −2.68176 −0.0858850
\(976\) 0 0
\(977\) −25.8102 −0.825741 −0.412871 0.910790i \(-0.635474\pi\)
−0.412871 + 0.910790i \(0.635474\pi\)
\(978\) 0 0
\(979\) −53.7831 −1.71891
\(980\) 0 0
\(981\) −0.0531041 −0.00169548
\(982\) 0 0
\(983\) −21.6394 −0.690188 −0.345094 0.938568i \(-0.612153\pi\)
−0.345094 + 0.938568i \(0.612153\pi\)
\(984\) 0 0
\(985\) −25.2719 −0.805230
\(986\) 0 0
\(987\) −6.67492 −0.212465
\(988\) 0 0
\(989\) −20.4275 −0.649557
\(990\) 0 0
\(991\) 46.4242 1.47471 0.737357 0.675503i \(-0.236073\pi\)
0.737357 + 0.675503i \(0.236073\pi\)
\(992\) 0 0
\(993\) 6.99231 0.221894
\(994\) 0 0
\(995\) −5.03916 −0.159752
\(996\) 0 0
\(997\) 7.29268 0.230961 0.115481 0.993310i \(-0.463159\pi\)
0.115481 + 0.993310i \(0.463159\pi\)
\(998\) 0 0
\(999\) −41.8489 −1.32404
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.1.2 7
4.3 odd 2 1004.2.a.a.1.6 7
12.11 even 2 9036.2.a.i.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1004.2.a.a.1.6 7 4.3 odd 2
4016.2.a.g.1.2 7 1.1 even 1 trivial
9036.2.a.i.1.7 7 12.11 even 2