Properties

Label 5610.2.a.c.1.1
Level $5610$
Weight $2$
Character 5610.1
Self dual yes
Analytic conductor $44.796$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.7960755339\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5610.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -6.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +8.00000 q^{19} -1.00000 q^{20} +1.00000 q^{22} -8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} -1.00000 q^{27} +6.00000 q^{29} -1.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} -8.00000 q^{38} +6.00000 q^{39} +1.00000 q^{40} +2.00000 q^{41} -4.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} +8.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -6.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} -8.00000 q^{57} -6.00000 q^{58} -4.00000 q^{59} +1.00000 q^{60} +14.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} -1.00000 q^{66} +4.00000 q^{67} -1.00000 q^{68} +8.00000 q^{69} +8.00000 q^{71} -1.00000 q^{72} +2.00000 q^{73} -10.0000 q^{74} -1.00000 q^{75} +8.00000 q^{76} -6.00000 q^{78} -16.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +4.00000 q^{83} +1.00000 q^{85} +4.00000 q^{86} -6.00000 q^{87} +1.00000 q^{88} -6.00000 q^{89} +1.00000 q^{90} -8.00000 q^{92} -4.00000 q^{93} -4.00000 q^{94} -8.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} +7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) −1.00000 −0.288675
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) 8.00000 1.83533 0.917663 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 6.00000 1.17670
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −1.00000 −0.182574
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) −8.00000 −1.29777
\(39\) 6.00000 0.960769
\(40\) 1.00000 0.158114
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −1.00000 −0.150756
\(45\) −1.00000 −0.149071
\(46\) 8.00000 1.17954
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) −1.00000 −0.144338
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) 1.00000 0.140028
\(52\) −6.00000 −0.832050
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 1.00000 0.136083
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) −8.00000 −1.05963
\(58\) −6.00000 −0.787839
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 1.00000 0.129099
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) −1.00000 −0.123091
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −1.00000 −0.121268
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −10.0000 −1.16248
\(75\) −1.00000 −0.115470
\(76\) 8.00000 0.917663
\(77\) 0 0
\(78\) −6.00000 −0.679366
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −2.00000 −0.220863
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 1.00000 0.108465
\(86\) 4.00000 0.431331
\(87\) −6.00000 −0.643268
\(88\) 1.00000 0.106600
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) −8.00000 −0.834058
\(93\) −4.00000 −0.414781
\(94\) −4.00000 −0.412568
\(95\) −8.00000 −0.820783
\(96\) 1.00000 0.102062
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 7.00000 0.707107
\(99\) −1.00000 −0.100504
\(100\) 1.00000 0.100000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −10.0000 −0.949158
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 8.00000 0.749269
\(115\) 8.00000 0.746004
\(116\) 6.00000 0.557086
\(117\) −6.00000 −0.554700
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) −14.0000 −1.26750
\(123\) −2.00000 −0.180334
\(124\) 4.00000 0.359211
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.00000 0.352180
\(130\) −6.00000 −0.526235
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 1.00000 0.0860663
\(136\) 1.00000 0.0857493
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) −8.00000 −0.681005
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) −8.00000 −0.671345
\(143\) 6.00000 0.501745
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) −2.00000 −0.165521
\(147\) 7.00000 0.577350
\(148\) 10.0000 0.821995
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 1.00000 0.0816497
\(151\) −4.00000 −0.325515 −0.162758 0.986666i \(-0.552039\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) −8.00000 −0.648886
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 6.00000 0.480384
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 16.0000 1.27289
\(159\) 6.00000 0.475831
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 2.00000 0.156174
\(165\) −1.00000 −0.0778499
\(166\) −4.00000 −0.310460
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) −1.00000 −0.0766965
\(171\) 8.00000 0.611775
\(172\) −4.00000 −0.304997
\(173\) −22.0000 −1.67263 −0.836315 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 4.00000 0.300658
\(178\) 6.00000 0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −14.0000 −1.03491
\(184\) 8.00000 0.589768
\(185\) −10.0000 −0.735215
\(186\) 4.00000 0.293294
\(187\) 1.00000 0.0731272
\(188\) 4.00000 0.291730
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 10.0000 0.719816 0.359908 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) 10.0000 0.717958
\(195\) −6.00000 −0.429669
\(196\) −7.00000 −0.500000
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 1.00000 0.0710669
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −4.00000 −0.282138
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 1.00000 0.0700140
\(205\) −2.00000 −0.139686
\(206\) 8.00000 0.557386
\(207\) −8.00000 −0.556038
\(208\) −6.00000 −0.416025
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −6.00000 −0.412082
\(213\) −8.00000 −0.548151
\(214\) −8.00000 −0.546869
\(215\) 4.00000 0.272798
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −2.00000 −0.135147
\(220\) 1.00000 0.0674200
\(221\) 6.00000 0.403604
\(222\) 10.0000 0.671156
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 2.00000 0.133038
\(227\) −8.00000 −0.530979 −0.265489 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) −8.00000 −0.529813
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 6.00000 0.392232
\(235\) −4.00000 −0.260931
\(236\) −4.00000 −0.260378
\(237\) 16.0000 1.03931
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 1.00000 0.0645497
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 14.0000 0.896258
\(245\) 7.00000 0.447214
\(246\) 2.00000 0.127515
\(247\) −48.0000 −3.05417
\(248\) −4.00000 −0.254000
\(249\) −4.00000 −0.253490
\(250\) 1.00000 0.0632456
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −16.0000 −1.00393
\(255\) −1.00000 −0.0626224
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 6.00000 0.371391
\(262\) 4.00000 0.247121
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 4.00000 0.244339
\(269\) −30.0000 −1.82913 −0.914566 0.404436i \(-0.867468\pi\)
−0.914566 + 0.404436i \(0.867468\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) −1.00000 −0.0603023
\(276\) 8.00000 0.481543
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 12.0000 0.719712
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 4.00000 0.238197
\(283\) −28.0000 −1.66443 −0.832214 0.554455i \(-0.812927\pi\)
−0.832214 + 0.554455i \(0.812927\pi\)
\(284\) 8.00000 0.474713
\(285\) 8.00000 0.473879
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 6.00000 0.352332
\(291\) 10.0000 0.586210
\(292\) 2.00000 0.117041
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) −7.00000 −0.408248
\(295\) 4.00000 0.232889
\(296\) −10.0000 −0.581238
\(297\) 1.00000 0.0580259
\(298\) 6.00000 0.347571
\(299\) 48.0000 2.77591
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) 4.00000 0.230174
\(303\) 6.00000 0.344691
\(304\) 8.00000 0.458831
\(305\) −14.0000 −0.801638
\(306\) 1.00000 0.0571662
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 4.00000 0.227185
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −6.00000 −0.339683
\(313\) 30.0000 1.69570 0.847850 0.530236i \(-0.177897\pi\)
0.847850 + 0.530236i \(0.177897\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) −6.00000 −0.336463
\(319\) −6.00000 −0.335936
\(320\) −1.00000 −0.0559017
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) 1.00000 0.0555556
\(325\) −6.00000 −0.332820
\(326\) −12.0000 −0.664619
\(327\) 2.00000 0.110600
\(328\) −2.00000 −0.110432
\(329\) 0 0
\(330\) 1.00000 0.0550482
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 4.00000 0.219529
\(333\) 10.0000 0.547997
\(334\) −12.0000 −0.656611
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) −23.0000 −1.25104
\(339\) 2.00000 0.108625
\(340\) 1.00000 0.0542326
\(341\) −4.00000 −0.216612
\(342\) −8.00000 −0.432590
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) −8.00000 −0.430706
\(346\) 22.0000 1.18273
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) −6.00000 −0.321634
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 6.00000 0.320256
\(352\) 1.00000 0.0533002
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) −4.00000 −0.212598
\(355\) −8.00000 −0.424596
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 1.00000 0.0527046
\(361\) 45.0000 2.36842
\(362\) 2.00000 0.105118
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 14.0000 0.731792
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) −8.00000 −0.417029
\(369\) 2.00000 0.104116
\(370\) 10.0000 0.519875
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) −1.00000 −0.0517088
\(375\) 1.00000 0.0516398
\(376\) −4.00000 −0.206284
\(377\) −36.0000 −1.85409
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −8.00000 −0.410391
\(381\) −16.0000 −0.819705
\(382\) 8.00000 0.409316
\(383\) −4.00000 −0.204390 −0.102195 0.994764i \(-0.532587\pi\)
−0.102195 + 0.994764i \(0.532587\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) −4.00000 −0.203331
\(388\) −10.0000 −0.507673
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 6.00000 0.303822
\(391\) 8.00000 0.404577
\(392\) 7.00000 0.353553
\(393\) 4.00000 0.201773
\(394\) −2.00000 −0.100759
\(395\) 16.0000 0.805047
\(396\) −1.00000 −0.0502519
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) −20.0000 −1.00251
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −34.0000 −1.69788 −0.848939 0.528490i \(-0.822758\pi\)
−0.848939 + 0.528490i \(0.822758\pi\)
\(402\) 4.00000 0.199502
\(403\) −24.0000 −1.19553
\(404\) −6.00000 −0.298511
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −10.0000 −0.495682
\(408\) −1.00000 −0.0495074
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 2.00000 0.0987730
\(411\) 2.00000 0.0986527
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) −4.00000 −0.196352
\(416\) 6.00000 0.294174
\(417\) 12.0000 0.587643
\(418\) 8.00000 0.391293
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 20.0000 0.973585
\(423\) 4.00000 0.194487
\(424\) 6.00000 0.291386
\(425\) −1.00000 −0.0485071
\(426\) 8.00000 0.387601
\(427\) 0 0
\(428\) 8.00000 0.386695
\(429\) −6.00000 −0.289683
\(430\) −4.00000 −0.192897
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) −2.00000 −0.0957826
\(437\) −64.0000 −3.06154
\(438\) 2.00000 0.0955637
\(439\) −40.0000 −1.90910 −0.954548 0.298057i \(-0.903661\pi\)
−0.954548 + 0.298057i \(0.903661\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −7.00000 −0.333333
\(442\) −6.00000 −0.285391
\(443\) −40.0000 −1.90046 −0.950229 0.311553i \(-0.899151\pi\)
−0.950229 + 0.311553i \(0.899151\pi\)
\(444\) −10.0000 −0.474579
\(445\) 6.00000 0.284427
\(446\) −16.0000 −0.757622
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −2.00000 −0.0941763
\(452\) −2.00000 −0.0940721
\(453\) 4.00000 0.187936
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) 8.00000 0.374634
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) −6.00000 −0.280362
\(459\) 1.00000 0.0466760
\(460\) 8.00000 0.373002
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 6.00000 0.278543
\(465\) 4.00000 0.185496
\(466\) 26.0000 1.20443
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) 4.00000 0.184506
\(471\) 2.00000 0.0921551
\(472\) 4.00000 0.184115
\(473\) 4.00000 0.183920
\(474\) −16.0000 −0.734904
\(475\) 8.00000 0.367065
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 8.00000 0.365911
\(479\) −32.0000 −1.46212 −0.731059 0.682315i \(-0.760973\pi\)
−0.731059 + 0.682315i \(0.760973\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −60.0000 −2.73576
\(482\) 14.0000 0.637683
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 10.0000 0.454077
\(486\) 1.00000 0.0453609
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −14.0000 −0.633750
\(489\) −12.0000 −0.542659
\(490\) −7.00000 −0.316228
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −2.00000 −0.0901670
\(493\) −6.00000 −0.270226
\(494\) 48.0000 2.15962
\(495\) 1.00000 0.0449467
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) 8.00000 0.358129 0.179065 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −12.0000 −0.536120
\(502\) 20.0000 0.892644
\(503\) −4.00000 −0.178351 −0.0891756 0.996016i \(-0.528423\pi\)
−0.0891756 + 0.996016i \(0.528423\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) −8.00000 −0.355643
\(507\) −23.0000 −1.02147
\(508\) 16.0000 0.709885
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 1.00000 0.0442807
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −8.00000 −0.353209
\(514\) −6.00000 −0.264649
\(515\) 8.00000 0.352522
\(516\) 4.00000 0.176090
\(517\) −4.00000 −0.175920
\(518\) 0 0
\(519\) 22.0000 0.965693
\(520\) −6.00000 −0.263117
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) −6.00000 −0.262613
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) −4.00000 −0.174243
\(528\) 1.00000 0.0435194
\(529\) 41.0000 1.78261
\(530\) −6.00000 −0.260623
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) −6.00000 −0.259645
\(535\) −8.00000 −0.345870
\(536\) −4.00000 −0.172774
\(537\) −12.0000 −0.517838
\(538\) 30.0000 1.29339
\(539\) 7.00000 0.301511
\(540\) 1.00000 0.0430331
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) −20.0000 −0.859074
\(543\) 2.00000 0.0858282
\(544\) 1.00000 0.0428746
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −36.0000 −1.53925 −0.769624 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 14.0000 0.597505
\(550\) 1.00000 0.0426401
\(551\) 48.0000 2.04487
\(552\) −8.00000 −0.340503
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 10.0000 0.424476
\(556\) −12.0000 −0.508913
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) −4.00000 −0.169334
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) −1.00000 −0.0422200
\(562\) 18.0000 0.759284
\(563\) −36.0000 −1.51722 −0.758610 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) −4.00000 −0.168430
\(565\) 2.00000 0.0841406
\(566\) 28.0000 1.17693
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) 38.0000 1.59304 0.796521 0.604610i \(-0.206671\pi\)
0.796521 + 0.604610i \(0.206671\pi\)
\(570\) −8.00000 −0.335083
\(571\) −44.0000 −1.84134 −0.920671 0.390339i \(-0.872358\pi\)
−0.920671 + 0.390339i \(0.872358\pi\)
\(572\) 6.00000 0.250873
\(573\) 8.00000 0.334205
\(574\) 0 0
\(575\) −8.00000 −0.333623
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −10.0000 −0.415586
\(580\) −6.00000 −0.249136
\(581\) 0 0
\(582\) −10.0000 −0.414513
\(583\) 6.00000 0.248495
\(584\) −2.00000 −0.0827606
\(585\) 6.00000 0.248069
\(586\) −26.0000 −1.07405
\(587\) 8.00000 0.330195 0.165098 0.986277i \(-0.447206\pi\)
0.165098 + 0.986277i \(0.447206\pi\)
\(588\) 7.00000 0.288675
\(589\) 32.0000 1.31854
\(590\) −4.00000 −0.164677
\(591\) −2.00000 −0.0822690
\(592\) 10.0000 0.410997
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −20.0000 −0.818546
\(598\) −48.0000 −1.96287
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 1.00000 0.0408248
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) −4.00000 −0.162758
\(605\) −1.00000 −0.0406558
\(606\) −6.00000 −0.243733
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) −8.00000 −0.324443
\(609\) 0 0
\(610\) 14.0000 0.566843
\(611\) −24.0000 −0.970936
\(612\) −1.00000 −0.0404226
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) −28.0000 −1.12999
\(615\) 2.00000 0.0806478
\(616\) 0 0
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) −8.00000 −0.321807
\(619\) −40.0000 −1.60774 −0.803868 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(620\) −4.00000 −0.160644
\(621\) 8.00000 0.321029
\(622\) 8.00000 0.320771
\(623\) 0 0
\(624\) 6.00000 0.240192
\(625\) 1.00000 0.0400000
\(626\) −30.0000 −1.19904
\(627\) 8.00000 0.319489
\(628\) −2.00000 −0.0798087
\(629\) −10.0000 −0.398726
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 16.0000 0.636446
\(633\) 20.0000 0.794929
\(634\) −2.00000 −0.0794301
\(635\) −16.0000 −0.634941
\(636\) 6.00000 0.237915
\(637\) 42.0000 1.66410
\(638\) 6.00000 0.237542
\(639\) 8.00000 0.316475
\(640\) 1.00000 0.0395285
\(641\) −2.00000 −0.0789953 −0.0394976 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 8.00000 0.315735
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 8.00000 0.314756
\(647\) −28.0000 −1.10079 −0.550397 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 4.00000 0.157014
\(650\) 6.00000 0.235339
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 4.00000 0.156293
\(656\) 2.00000 0.0780869
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 4.00000 0.155818 0.0779089 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) −1.00000 −0.0389249
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 20.0000 0.777322
\(663\) −6.00000 −0.233021
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) −48.0000 −1.85857
\(668\) 12.0000 0.464294
\(669\) −16.0000 −0.618596
\(670\) 4.00000 0.154533
\(671\) −14.0000 −0.540464
\(672\) 0 0
\(673\) −38.0000 −1.46479 −0.732396 0.680879i \(-0.761598\pi\)
−0.732396 + 0.680879i \(0.761598\pi\)
\(674\) −26.0000 −1.00148
\(675\) −1.00000 −0.0384900
\(676\) 23.0000 0.884615
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 0 0
\(680\) −1.00000 −0.0383482
\(681\) 8.00000 0.306561
\(682\) 4.00000 0.153168
\(683\) −44.0000 −1.68361 −0.841807 0.539779i \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) 8.00000 0.305888
\(685\) 2.00000 0.0764161
\(686\) 0 0
\(687\) −6.00000 −0.228914
\(688\) −4.00000 −0.152499
\(689\) 36.0000 1.37149
\(690\) 8.00000 0.304555
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) −22.0000 −0.836315
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 12.0000 0.455186
\(696\) 6.00000 0.227429
\(697\) −2.00000 −0.0757554
\(698\) 10.0000 0.378506
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) −6.00000 −0.226455
\(703\) 80.0000 3.01726
\(704\) −1.00000 −0.0376889
\(705\) 4.00000 0.150649
\(706\) 18.0000 0.677439
\(707\) 0 0
\(708\) 4.00000 0.150329
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 8.00000 0.300235
\(711\) −16.0000 −0.600047
\(712\) 6.00000 0.224860
\(713\) −32.0000 −1.19841
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) 12.0000 0.448461
\(717\) 8.00000 0.298765
\(718\) 16.0000 0.597115
\(719\) 40.0000 1.49175 0.745874 0.666087i \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) −45.0000 −1.67473
\(723\) 14.0000 0.520666
\(724\) −2.00000 −0.0743294
\(725\) 6.00000 0.222834
\(726\) 1.00000 0.0371135
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 2.00000 0.0740233
\(731\) 4.00000 0.147945
\(732\) −14.0000 −0.517455
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 16.0000 0.590571
\(735\) −7.00000 −0.258199
\(736\) 8.00000 0.294884
\(737\) −4.00000 −0.147342
\(738\) −2.00000 −0.0736210
\(739\) −48.0000 −1.76571 −0.882854 0.469647i \(-0.844381\pi\)
−0.882854 + 0.469647i \(0.844381\pi\)
\(740\) −10.0000 −0.367607
\(741\) 48.0000 1.76332
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 4.00000 0.146647
\(745\) 6.00000 0.219823
\(746\) 6.00000 0.219676
\(747\) 4.00000 0.146352
\(748\) 1.00000 0.0365636
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 4.00000 0.145865
\(753\) 20.0000 0.728841
\(754\) 36.0000 1.31104
\(755\) 4.00000 0.145575
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 0 0
\(759\) −8.00000 −0.290382
\(760\) 8.00000 0.290191
\(761\) 54.0000 1.95750 0.978749 0.205061i \(-0.0657392\pi\)
0.978749 + 0.205061i \(0.0657392\pi\)
\(762\) 16.0000 0.579619
\(763\) 0 0
\(764\) −8.00000 −0.289430
\(765\) 1.00000 0.0361551
\(766\) 4.00000 0.144526
\(767\) 24.0000 0.866590
\(768\) −1.00000 −0.0360844
\(769\) 10.0000 0.360609 0.180305 0.983611i \(-0.442292\pi\)
0.180305 + 0.983611i \(0.442292\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 10.0000 0.359908
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 4.00000 0.143777
\(775\) 4.00000 0.143684
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) −30.0000 −1.07555
\(779\) 16.0000 0.573259
\(780\) −6.00000 −0.214834
\(781\) −8.00000 −0.286263
\(782\) −8.00000 −0.286079
\(783\) −6.00000 −0.214423
\(784\) −7.00000 −0.250000
\(785\) 2.00000 0.0713831
\(786\) −4.00000 −0.142675
\(787\) 4.00000 0.142585 0.0712923 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) 2.00000 0.0712470
\(789\) 24.0000 0.854423
\(790\) −16.0000 −0.569254
\(791\) 0 0
\(792\) 1.00000 0.0355335
\(793\) −84.0000 −2.98293
\(794\) 22.0000 0.780751
\(795\) −6.00000 −0.212798
\(796\) 20.0000 0.708881
\(797\) −22.0000 −0.779280 −0.389640 0.920967i \(-0.627401\pi\)
−0.389640 + 0.920967i \(0.627401\pi\)
\(798\) 0 0
\(799\) −4.00000 −0.141510
\(800\) −1.00000 −0.0353553
\(801\) −6.00000 −0.212000
\(802\) 34.0000 1.20058
\(803\) −2.00000 −0.0705785
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) 24.0000 0.845364
\(807\) 30.0000 1.05605
\(808\) 6.00000 0.211079
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 1.00000 0.0351364
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) −20.0000 −0.701431
\(814\) 10.0000 0.350500
\(815\) −12.0000 −0.420342
\(816\) 1.00000 0.0350070
\(817\) −32.0000 −1.11954
\(818\) 14.0000 0.489499
\(819\) 0 0
\(820\) −2.00000 −0.0698430
\(821\) −10.0000 −0.349002 −0.174501 0.984657i \(-0.555831\pi\)
−0.174501 + 0.984657i \(0.555831\pi\)
\(822\) −2.00000 −0.0697580
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 8.00000 0.278693
\(825\) 1.00000 0.0348155
\(826\) 0 0
\(827\) −32.0000 −1.11275 −0.556375 0.830932i \(-0.687808\pi\)
−0.556375 + 0.830932i \(0.687808\pi\)
\(828\) −8.00000 −0.278019
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) 4.00000 0.138842
\(831\) 10.0000 0.346896
\(832\) −6.00000 −0.208013
\(833\) 7.00000 0.242536
\(834\) −12.0000 −0.415526
\(835\) −12.0000 −0.415277
\(836\) −8.00000 −0.276686
\(837\) −4.00000 −0.138260
\(838\) 20.0000 0.690889
\(839\) 16.0000 0.552381 0.276191 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 26.0000 0.896019
\(843\) 18.0000 0.619953
\(844\) −20.0000 −0.688428
\(845\) −23.0000 −0.791224
\(846\) −4.00000 −0.137523
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) 28.0000 0.960958
\(850\) 1.00000 0.0342997
\(851\) −80.0000 −2.74236
\(852\) −8.00000 −0.274075
\(853\) 6.00000 0.205436 0.102718 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) 0 0
\(855\) −8.00000 −0.273594
\(856\) −8.00000 −0.273434
\(857\) 38.0000 1.29806 0.649028 0.760765i \(-0.275176\pi\)
0.649028 + 0.760765i \(0.275176\pi\)
\(858\) 6.00000 0.204837
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 4.00000 0.136399
\(861\) 0 0
\(862\) −24.0000 −0.817443
\(863\) 4.00000 0.136162 0.0680808 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) 1.00000 0.0340207
\(865\) 22.0000 0.748022
\(866\) −26.0000 −0.883516
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 16.0000 0.542763
\(870\) −6.00000 −0.203419
\(871\) −24.0000 −0.813209
\(872\) 2.00000 0.0677285
\(873\) −10.0000 −0.338449
\(874\) 64.0000 2.16483
\(875\) 0 0
\(876\) −2.00000 −0.0675737
\(877\) 22.0000 0.742887 0.371444 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(878\) 40.0000 1.34993
\(879\) −26.0000 −0.876958
\(880\) 1.00000 0.0337100
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 7.00000 0.235702
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) 6.00000 0.201802
\(885\) −4.00000 −0.134459
\(886\) 40.0000 1.34383
\(887\) −36.0000 −1.20876 −0.604381 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) 10.0000 0.335578
\(889\) 0 0
\(890\) −6.00000 −0.201120
\(891\) −1.00000 −0.0335013
\(892\) 16.0000 0.535720
\(893\) 32.0000 1.07084
\(894\) −6.00000 −0.200670
\(895\) −12.0000 −0.401116
\(896\) 0 0
\(897\) −48.0000 −1.60267
\(898\) −6.00000 −0.200223
\(899\) 24.0000 0.800445
\(900\) 1.00000 0.0333333
\(901\) 6.00000 0.199889
\(902\) 2.00000 0.0665927
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) 2.00000 0.0664822
\(906\) −4.00000 −0.132891
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) −8.00000 −0.265489
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) 24.0000 0.795155 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) −8.00000 −0.264906
\(913\) −4.00000 −0.132381
\(914\) −22.0000 −0.727695
\(915\) 14.0000 0.462826
\(916\) 6.00000 0.198246
\(917\) 0 0
\(918\) −1.00000 −0.0330049
\(919\) −60.0000 −1.97922 −0.989609 0.143787i \(-0.954072\pi\)
−0.989609 + 0.143787i \(0.954072\pi\)
\(920\) −8.00000 −0.263752
\(921\) −28.0000 −0.922631
\(922\) 6.00000 0.197599
\(923\) −48.0000 −1.57994
\(924\) 0 0
\(925\) 10.0000 0.328798
\(926\) −16.0000 −0.525793
\(927\) −8.00000 −0.262754
\(928\) −6.00000 −0.196960
\(929\) −10.0000 −0.328089 −0.164045 0.986453i \(-0.552454\pi\)
−0.164045 + 0.986453i \(0.552454\pi\)
\(930\) −4.00000 −0.131165
\(931\) −56.0000 −1.83533
\(932\) −26.0000 −0.851658
\(933\) 8.00000 0.261908
\(934\) 8.00000 0.261768
\(935\) −1.00000 −0.0327035
\(936\) 6.00000 0.196116
\(937\) −34.0000 −1.11073 −0.555366 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) 0 0
\(939\) −30.0000 −0.979013
\(940\) −4.00000 −0.130466
\(941\) 14.0000 0.456387 0.228193 0.973616i \(-0.426718\pi\)
0.228193 + 0.973616i \(0.426718\pi\)
\(942\) −2.00000 −0.0651635
\(943\) −16.0000 −0.521032
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) −4.00000 −0.130051
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 16.0000 0.519656
\(949\) −12.0000 −0.389536
\(950\) −8.00000 −0.259554
\(951\) −2.00000 −0.0648544
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 6.00000 0.194257
\(955\) 8.00000 0.258874
\(956\) −8.00000 −0.258738
\(957\) 6.00000 0.193952
\(958\) 32.0000 1.03387
\(959\) 0 0
\(960\) 1.00000 0.0322749
\(961\) −15.0000 −0.483871
\(962\) 60.0000 1.93448
\(963\) 8.00000 0.257796
\(964\) −14.0000 −0.450910
\(965\) −10.0000 −0.321911
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 8.00000 0.256997
\(970\) −10.0000 −0.321081
\(971\) −36.0000 −1.15529 −0.577647 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 16.0000 0.512673
\(975\) 6.00000 0.192154
\(976\) 14.0000 0.448129
\(977\) −2.00000 −0.0639857 −0.0319928 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) 12.0000 0.383718
\(979\) 6.00000 0.191761
\(980\) 7.00000 0.223607
\(981\) −2.00000 −0.0638551
\(982\) 12.0000 0.382935
\(983\) 8.00000 0.255160 0.127580 0.991828i \(-0.459279\pi\)
0.127580 + 0.991828i \(0.459279\pi\)
\(984\) 2.00000 0.0637577
\(985\) −2.00000 −0.0637253
\(986\) 6.00000 0.191079
\(987\) 0 0
\(988\) −48.0000 −1.52708
\(989\) 32.0000 1.01754
\(990\) −1.00000 −0.0317821
\(991\) −20.0000 −0.635321 −0.317660 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) −4.00000 −0.127000
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) −20.0000 −0.634043
\(996\) −4.00000 −0.126745
\(997\) 54.0000 1.71020 0.855099 0.518465i \(-0.173497\pi\)
0.855099 + 0.518465i \(0.173497\pi\)
\(998\) −8.00000 −0.253236
\(999\) −10.0000 −0.316386
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 5610.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.c.1.1 1 1.1 even 1 trivial