Properties

Label 3630.2.a.u.1.1
Level $3630$
Weight $2$
Character 3630.1
Self dual yes
Analytic conductor $28.986$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3630.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.9856959337\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 3630.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +5.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +1.00000 q^{18} +5.00000 q^{19} -1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{24} +1.00000 q^{25} +5.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -3.00000 q^{29} -1.00000 q^{30} +2.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} +5.00000 q^{37} +5.00000 q^{38} +5.00000 q^{39} -1.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} +2.00000 q^{43} -1.00000 q^{45} -6.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} -3.00000 q^{51} +5.00000 q^{52} +1.00000 q^{54} -1.00000 q^{56} +5.00000 q^{57} -3.00000 q^{58} -1.00000 q^{60} +8.00000 q^{61} +2.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -5.00000 q^{65} +2.00000 q^{67} -3.00000 q^{68} +1.00000 q^{70} +9.00000 q^{71} +1.00000 q^{72} +14.0000 q^{73} +5.00000 q^{74} +1.00000 q^{75} +5.00000 q^{76} +5.00000 q^{78} +14.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -3.00000 q^{83} -1.00000 q^{84} +3.00000 q^{85} +2.00000 q^{86} -3.00000 q^{87} -12.0000 q^{89} -1.00000 q^{90} -5.00000 q^{91} +2.00000 q^{93} -6.00000 q^{94} -5.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} -6.00000 q^{98} +O(q^{100})\)

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
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −1.00000 −0.267261
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 1.00000 0.235702
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) −1.00000 −0.223607
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 5.00000 0.980581
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) −1.00000 −0.182574
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 1.00000 0.169031
\(36\) 1.00000 0.166667
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) 5.00000 0.811107
\(39\) 5.00000 0.800641
\(40\) −1.00000 −0.158114
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) −1.00000 −0.154303
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) 1.00000 0.141421
\(51\) −3.00000 −0.420084
\(52\) 5.00000 0.693375
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 5.00000 0.662266
\(58\) −3.00000 −0.393919
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −1.00000 −0.129099
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 2.00000 0.254000
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) −5.00000 −0.620174
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) 1.00000 0.119523
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) 1.00000 0.117851
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 5.00000 0.581238
\(75\) 1.00000 0.115470
\(76\) 5.00000 0.573539
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −3.00000 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) −1.00000 −0.109109
\(85\) 3.00000 0.325396
\(86\) 2.00000 0.215666
\(87\) −3.00000 −0.321634
\(88\) 0 0
\(89\) −12.0000 −1.27200 −0.635999 0.771690i \(-0.719412\pi\)
−0.635999 + 0.771690i \(0.719412\pi\)
\(90\) −1.00000 −0.105409
\(91\) −5.00000 −0.524142
\(92\) 0 0
\(93\) 2.00000 0.207390
\(94\) −6.00000 −0.618853
\(95\) −5.00000 −0.512989
\(96\) 1.00000 0.102062
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 15.0000 1.49256 0.746278 0.665635i \(-0.231839\pi\)
0.746278 + 0.665635i \(0.231839\pi\)
\(102\) −3.00000 −0.297044
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) 5.00000 0.490290
\(105\) 1.00000 0.0975900
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 1.00000 0.0962250
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) −1.00000 −0.0944911
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 5.00000 0.468293
\(115\) 0 0
\(116\) −3.00000 −0.278543
\(117\) 5.00000 0.462250
\(118\) 0 0
\(119\) 3.00000 0.275010
\(120\) −1.00000 −0.0912871
\(121\) 0 0
\(122\) 8.00000 0.724286
\(123\) 6.00000 0.541002
\(124\) 2.00000 0.179605
\(125\) −1.00000 −0.0894427
\(126\) −1.00000 −0.0890871
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.00000 0.176090
\(130\) −5.00000 −0.438529
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) −5.00000 −0.433555
\(134\) 2.00000 0.172774
\(135\) −1.00000 −0.0860663
\(136\) −3.00000 −0.257248
\(137\) 15.0000 1.28154 0.640768 0.767734i \(-0.278616\pi\)
0.640768 + 0.767734i \(0.278616\pi\)
\(138\) 0 0
\(139\) 23.0000 1.95083 0.975417 0.220366i \(-0.0707252\pi\)
0.975417 + 0.220366i \(0.0707252\pi\)
\(140\) 1.00000 0.0845154
\(141\) −6.00000 −0.505291
\(142\) 9.00000 0.755263
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 3.00000 0.249136
\(146\) 14.0000 1.15865
\(147\) −6.00000 −0.494872
\(148\) 5.00000 0.410997
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 1.00000 0.0816497
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 5.00000 0.405554
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 5.00000 0.400320
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 14.0000 1.11378
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −3.00000 −0.232845
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 12.0000 0.923077
\(170\) 3.00000 0.230089
\(171\) 5.00000 0.382360
\(172\) 2.00000 0.152499
\(173\) 12.0000 0.912343 0.456172 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(174\) −3.00000 −0.227429
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) −12.0000 −0.899438
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −5.00000 −0.370625
\(183\) 8.00000 0.591377
\(184\) 0 0
\(185\) −5.00000 −0.367607
\(186\) 2.00000 0.146647
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) −1.00000 −0.0727393
\(190\) −5.00000 −0.362738
\(191\) −21.0000 −1.51951 −0.759753 0.650211i \(-0.774680\pi\)
−0.759753 + 0.650211i \(0.774680\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) −10.0000 −0.717958
\(195\) −5.00000 −0.358057
\(196\) −6.00000 −0.428571
\(197\) −24.0000 −1.70993 −0.854965 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 1.00000 0.0707107
\(201\) 2.00000 0.141069
\(202\) 15.0000 1.05540
\(203\) 3.00000 0.210559
\(204\) −3.00000 −0.210042
\(205\) −6.00000 −0.419058
\(206\) −1.00000 −0.0696733
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) 0 0
\(210\) 1.00000 0.0690066
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 0 0
\(213\) 9.00000 0.616670
\(214\) 0 0
\(215\) −2.00000 −0.136399
\(216\) 1.00000 0.0680414
\(217\) −2.00000 −0.135769
\(218\) −16.0000 −1.08366
\(219\) 14.0000 0.946032
\(220\) 0 0
\(221\) −15.0000 −1.00901
\(222\) 5.00000 0.335578
\(223\) 5.00000 0.334825 0.167412 0.985887i \(-0.446459\pi\)
0.167412 + 0.985887i \(0.446459\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.00000 0.0666667
\(226\) 18.0000 1.19734
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 5.00000 0.331133
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 −0.196960
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 5.00000 0.326860
\(235\) 6.00000 0.391397
\(236\) 0 0
\(237\) 14.0000 0.909398
\(238\) 3.00000 0.194461
\(239\) −21.0000 −1.35838 −0.679189 0.733964i \(-0.737668\pi\)
−0.679189 + 0.733964i \(0.737668\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −7.00000 −0.450910 −0.225455 0.974254i \(-0.572387\pi\)
−0.225455 + 0.974254i \(0.572387\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 8.00000 0.512148
\(245\) 6.00000 0.383326
\(246\) 6.00000 0.382546
\(247\) 25.0000 1.59071
\(248\) 2.00000 0.127000
\(249\) −3.00000 −0.190117
\(250\) −1.00000 −0.0632456
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 0 0
\(254\) −4.00000 −0.250982
\(255\) 3.00000 0.187867
\(256\) 1.00000 0.0625000
\(257\) −27.0000 −1.68421 −0.842107 0.539311i \(-0.818685\pi\)
−0.842107 + 0.539311i \(0.818685\pi\)
\(258\) 2.00000 0.124515
\(259\) −5.00000 −0.310685
\(260\) −5.00000 −0.310087
\(261\) −3.00000 −0.185695
\(262\) −12.0000 −0.741362
\(263\) 18.0000 1.10993 0.554964 0.831875i \(-0.312732\pi\)
0.554964 + 0.831875i \(0.312732\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −5.00000 −0.306570
\(267\) −12.0000 −0.734388
\(268\) 2.00000 0.122169
\(269\) 15.0000 0.914566 0.457283 0.889321i \(-0.348823\pi\)
0.457283 + 0.889321i \(0.348823\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) −3.00000 −0.181902
\(273\) −5.00000 −0.302614
\(274\) 15.0000 0.906183
\(275\) 0 0
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 23.0000 1.37945
\(279\) 2.00000 0.119737
\(280\) 1.00000 0.0597614
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) −6.00000 −0.357295
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) 9.00000 0.534052
\(285\) −5.00000 −0.296174
\(286\) 0 0
\(287\) −6.00000 −0.354169
\(288\) 1.00000 0.0589256
\(289\) −8.00000 −0.470588
\(290\) 3.00000 0.176166
\(291\) −10.0000 −0.586210
\(292\) 14.0000 0.819288
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) −6.00000 −0.349927
\(295\) 0 0
\(296\) 5.00000 0.290619
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) −2.00000 −0.115278
\(302\) 20.0000 1.15087
\(303\) 15.0000 0.861727
\(304\) 5.00000 0.286770
\(305\) −8.00000 −0.458079
\(306\) −3.00000 −0.171499
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) 0 0
\(309\) −1.00000 −0.0568880
\(310\) −2.00000 −0.113592
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 5.00000 0.283069
\(313\) −34.0000 −1.92179 −0.960897 0.276907i \(-0.910691\pi\)
−0.960897 + 0.276907i \(0.910691\pi\)
\(314\) −13.0000 −0.733632
\(315\) 1.00000 0.0563436
\(316\) 14.0000 0.787562
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 0 0
\(323\) −15.0000 −0.834622
\(324\) 1.00000 0.0555556
\(325\) 5.00000 0.277350
\(326\) −16.0000 −0.886158
\(327\) −16.0000 −0.884802
\(328\) 6.00000 0.331295
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) −13.0000 −0.714545 −0.357272 0.934000i \(-0.616293\pi\)
−0.357272 + 0.934000i \(0.616293\pi\)
\(332\) −3.00000 −0.164646
\(333\) 5.00000 0.273998
\(334\) 12.0000 0.656611
\(335\) −2.00000 −0.109272
\(336\) −1.00000 −0.0545545
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 12.0000 0.652714
\(339\) 18.0000 0.977626
\(340\) 3.00000 0.162698
\(341\) 0 0
\(342\) 5.00000 0.270369
\(343\) 13.0000 0.701934
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) 12.0000 0.645124
\(347\) −21.0000 −1.12734 −0.563670 0.826000i \(-0.690611\pi\)
−0.563670 + 0.826000i \(0.690611\pi\)
\(348\) −3.00000 −0.160817
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) −9.00000 −0.477670
\(356\) −12.0000 −0.635999
\(357\) 3.00000 0.158777
\(358\) 12.0000 0.634220
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 6.00000 0.315789
\(362\) −16.0000 −0.840941
\(363\) 0 0
\(364\) −5.00000 −0.262071
\(365\) −14.0000 −0.732793
\(366\) 8.00000 0.418167
\(367\) 23.0000 1.20059 0.600295 0.799779i \(-0.295050\pi\)
0.600295 + 0.799779i \(0.295050\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) −5.00000 −0.259938
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) −13.0000 −0.673114 −0.336557 0.941663i \(-0.609263\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) −6.00000 −0.309426
\(377\) −15.0000 −0.772539
\(378\) −1.00000 −0.0514344
\(379\) 5.00000 0.256833 0.128416 0.991720i \(-0.459011\pi\)
0.128416 + 0.991720i \(0.459011\pi\)
\(380\) −5.00000 −0.256495
\(381\) −4.00000 −0.204926
\(382\) −21.0000 −1.07445
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −4.00000 −0.203595
\(387\) 2.00000 0.101666
\(388\) −10.0000 −0.507673
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) −5.00000 −0.253185
\(391\) 0 0
\(392\) −6.00000 −0.303046
\(393\) −12.0000 −0.605320
\(394\) −24.0000 −1.20910
\(395\) −14.0000 −0.704416
\(396\) 0 0
\(397\) 29.0000 1.45547 0.727734 0.685859i \(-0.240573\pi\)
0.727734 + 0.685859i \(0.240573\pi\)
\(398\) −16.0000 −0.802008
\(399\) −5.00000 −0.250313
\(400\) 1.00000 0.0500000
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 2.00000 0.0997509
\(403\) 10.0000 0.498135
\(404\) 15.0000 0.746278
\(405\) −1.00000 −0.0496904
\(406\) 3.00000 0.148888
\(407\) 0 0
\(408\) −3.00000 −0.148522
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) −6.00000 −0.296319
\(411\) 15.0000 0.739895
\(412\) −1.00000 −0.0492665
\(413\) 0 0
\(414\) 0 0
\(415\) 3.00000 0.147264
\(416\) 5.00000 0.245145
\(417\) 23.0000 1.12631
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 1.00000 0.0487950
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 5.00000 0.243396
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) −3.00000 −0.145521
\(426\) 9.00000 0.436051
\(427\) −8.00000 −0.387147
\(428\) 0 0
\(429\) 0 0
\(430\) −2.00000 −0.0964486
\(431\) −15.0000 −0.722525 −0.361262 0.932464i \(-0.617654\pi\)
−0.361262 + 0.932464i \(0.617654\pi\)
\(432\) 1.00000 0.0481125
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −2.00000 −0.0960031
\(435\) 3.00000 0.143839
\(436\) −16.0000 −0.766261
\(437\) 0 0
\(438\) 14.0000 0.668946
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −15.0000 −0.713477
\(443\) −9.00000 −0.427603 −0.213801 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 5.00000 0.237289
\(445\) 12.0000 0.568855
\(446\) 5.00000 0.236757
\(447\) −6.00000 −0.283790
\(448\) −1.00000 −0.0472456
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) 20.0000 0.939682
\(454\) 0 0
\(455\) 5.00000 0.234404
\(456\) 5.00000 0.234146
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 20.0000 0.934539
\(459\) −3.00000 −0.140028
\(460\) 0 0
\(461\) −3.00000 −0.139724 −0.0698620 0.997557i \(-0.522256\pi\)
−0.0698620 + 0.997557i \(0.522256\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) −3.00000 −0.139272
\(465\) −2.00000 −0.0927478
\(466\) 6.00000 0.277945
\(467\) 33.0000 1.52706 0.763529 0.645774i \(-0.223465\pi\)
0.763529 + 0.645774i \(0.223465\pi\)
\(468\) 5.00000 0.231125
\(469\) −2.00000 −0.0923514
\(470\) 6.00000 0.276759
\(471\) −13.0000 −0.599008
\(472\) 0 0
\(473\) 0 0
\(474\) 14.0000 0.643041
\(475\) 5.00000 0.229416
\(476\) 3.00000 0.137505
\(477\) 0 0
\(478\) −21.0000 −0.960518
\(479\) −21.0000 −0.959514 −0.479757 0.877401i \(-0.659275\pi\)
−0.479757 + 0.877401i \(0.659275\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 25.0000 1.13990
\(482\) −7.00000 −0.318841
\(483\) 0 0
\(484\) 0 0
\(485\) 10.0000 0.454077
\(486\) 1.00000 0.0453609
\(487\) −25.0000 −1.13286 −0.566429 0.824110i \(-0.691675\pi\)
−0.566429 + 0.824110i \(0.691675\pi\)
\(488\) 8.00000 0.362143
\(489\) −16.0000 −0.723545
\(490\) 6.00000 0.271052
\(491\) 18.0000 0.812329 0.406164 0.913800i \(-0.366866\pi\)
0.406164 + 0.913800i \(0.366866\pi\)
\(492\) 6.00000 0.270501
\(493\) 9.00000 0.405340
\(494\) 25.0000 1.12480
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) −9.00000 −0.403705
\(498\) −3.00000 −0.134433
\(499\) 5.00000 0.223831 0.111915 0.993718i \(-0.464301\pi\)
0.111915 + 0.993718i \(0.464301\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 12.0000 0.536120
\(502\) −24.0000 −1.07117
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −4.00000 −0.177471
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 3.00000 0.132842
\(511\) −14.0000 −0.619324
\(512\) 1.00000 0.0441942
\(513\) 5.00000 0.220755
\(514\) −27.0000 −1.19092
\(515\) 1.00000 0.0440653
\(516\) 2.00000 0.0880451
\(517\) 0 0
\(518\) −5.00000 −0.219687
\(519\) 12.0000 0.526742
\(520\) −5.00000 −0.219265
\(521\) −36.0000 −1.57719 −0.788594 0.614914i \(-0.789191\pi\)
−0.788594 + 0.614914i \(0.789191\pi\)
\(522\) −3.00000 −0.131306
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −12.0000 −0.524222
\(525\) −1.00000 −0.0436436
\(526\) 18.0000 0.784837
\(527\) −6.00000 −0.261364
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) −5.00000 −0.216777
\(533\) 30.0000 1.29944
\(534\) −12.0000 −0.519291
\(535\) 0 0
\(536\) 2.00000 0.0863868
\(537\) 12.0000 0.517838
\(538\) 15.0000 0.646696
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 2.00000 0.0859074
\(543\) −16.0000 −0.686626
\(544\) −3.00000 −0.128624
\(545\) 16.0000 0.685365
\(546\) −5.00000 −0.213980
\(547\) −46.0000 −1.96682 −0.983409 0.181402i \(-0.941936\pi\)
−0.983409 + 0.181402i \(0.941936\pi\)
\(548\) 15.0000 0.640768
\(549\) 8.00000 0.341432
\(550\) 0 0
\(551\) −15.0000 −0.639021
\(552\) 0 0
\(553\) −14.0000 −0.595341
\(554\) −22.0000 −0.934690
\(555\) −5.00000 −0.212238
\(556\) 23.0000 0.975417
\(557\) −6.00000 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) 2.00000 0.0846668
\(559\) 10.0000 0.422955
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) 0 0
\(563\) −9.00000 −0.379305 −0.189652 0.981851i \(-0.560736\pi\)
−0.189652 + 0.981851i \(0.560736\pi\)
\(564\) −6.00000 −0.252646
\(565\) −18.0000 −0.757266
\(566\) −16.0000 −0.672530
\(567\) −1.00000 −0.0419961
\(568\) 9.00000 0.377632
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) −5.00000 −0.209427
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) −21.0000 −0.877288
\(574\) −6.00000 −0.250435
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −8.00000 −0.332756
\(579\) −4.00000 −0.166234
\(580\) 3.00000 0.124568
\(581\) 3.00000 0.124461
\(582\) −10.0000 −0.414513
\(583\) 0 0
\(584\) 14.0000 0.579324
\(585\) −5.00000 −0.206725
\(586\) −12.0000 −0.495715
\(587\) −33.0000 −1.36206 −0.681028 0.732257i \(-0.738467\pi\)
−0.681028 + 0.732257i \(0.738467\pi\)
\(588\) −6.00000 −0.247436
\(589\) 10.0000 0.412043
\(590\) 0 0
\(591\) −24.0000 −0.987228
\(592\) 5.00000 0.205499
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) −3.00000 −0.122988
\(596\) −6.00000 −0.245770
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 1.00000 0.0408248
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −2.00000 −0.0815139
\(603\) 2.00000 0.0814463
\(604\) 20.0000 0.813788
\(605\) 0 0
\(606\) 15.0000 0.609333
\(607\) 5.00000 0.202944 0.101472 0.994838i \(-0.467645\pi\)
0.101472 + 0.994838i \(0.467645\pi\)
\(608\) 5.00000 0.202777
\(609\) 3.00000 0.121566
\(610\) −8.00000 −0.323911
\(611\) −30.0000 −1.21367
\(612\) −3.00000 −0.121268
\(613\) 5.00000 0.201948 0.100974 0.994889i \(-0.467804\pi\)
0.100974 + 0.994889i \(0.467804\pi\)
\(614\) −22.0000 −0.887848
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) 15.0000 0.603877 0.301939 0.953327i \(-0.402366\pi\)
0.301939 + 0.953327i \(0.402366\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 29.0000 1.16561 0.582804 0.812613i \(-0.301955\pi\)
0.582804 + 0.812613i \(0.301955\pi\)
\(620\) −2.00000 −0.0803219
\(621\) 0 0
\(622\) 0 0
\(623\) 12.0000 0.480770
\(624\) 5.00000 0.200160
\(625\) 1.00000 0.0400000
\(626\) −34.0000 −1.35891
\(627\) 0 0
\(628\) −13.0000 −0.518756
\(629\) −15.0000 −0.598089
\(630\) 1.00000 0.0398410
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) 14.0000 0.556890
\(633\) 5.00000 0.198732
\(634\) −12.0000 −0.476581
\(635\) 4.00000 0.158735
\(636\) 0 0
\(637\) −30.0000 −1.18864
\(638\) 0 0
\(639\) 9.00000 0.356034
\(640\) −1.00000 −0.0395285
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 0 0
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) 0 0
\(645\) −2.00000 −0.0787499
\(646\) −15.0000 −0.590167
\(647\) 36.0000 1.41531 0.707653 0.706560i \(-0.249754\pi\)
0.707653 + 0.706560i \(0.249754\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 5.00000 0.196116
\(651\) −2.00000 −0.0783862
\(652\) −16.0000 −0.626608
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) −16.0000 −0.625650
\(655\) 12.0000 0.468879
\(656\) 6.00000 0.234261
\(657\) 14.0000 0.546192
\(658\) 6.00000 0.233904
\(659\) 18.0000 0.701180 0.350590 0.936529i \(-0.385981\pi\)
0.350590 + 0.936529i \(0.385981\pi\)
\(660\) 0 0
\(661\) 26.0000 1.01128 0.505641 0.862744i \(-0.331256\pi\)
0.505641 + 0.862744i \(0.331256\pi\)
\(662\) −13.0000 −0.505259
\(663\) −15.0000 −0.582552
\(664\) −3.00000 −0.116423
\(665\) 5.00000 0.193892
\(666\) 5.00000 0.193746
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) 5.00000 0.193311
\(670\) −2.00000 −0.0772667
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) 32.0000 1.23351 0.616755 0.787155i \(-0.288447\pi\)
0.616755 + 0.787155i \(0.288447\pi\)
\(674\) 14.0000 0.539260
\(675\) 1.00000 0.0384900
\(676\) 12.0000 0.461538
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 18.0000 0.691286
\(679\) 10.0000 0.383765
\(680\) 3.00000 0.115045
\(681\) 0 0
\(682\) 0 0
\(683\) 33.0000 1.26271 0.631355 0.775494i \(-0.282499\pi\)
0.631355 + 0.775494i \(0.282499\pi\)
\(684\) 5.00000 0.191180
\(685\) −15.0000 −0.573121
\(686\) 13.0000 0.496342
\(687\) 20.0000 0.763048
\(688\) 2.00000 0.0762493
\(689\) 0 0
\(690\) 0 0
\(691\) 29.0000 1.10321 0.551606 0.834105i \(-0.314015\pi\)
0.551606 + 0.834105i \(0.314015\pi\)
\(692\) 12.0000 0.456172
\(693\) 0 0
\(694\) −21.0000 −0.797149
\(695\) −23.0000 −0.872440
\(696\) −3.00000 −0.113715
\(697\) −18.0000 −0.681799
\(698\) 2.00000 0.0757011
\(699\) 6.00000 0.226941
\(700\) −1.00000 −0.0377964
\(701\) −3.00000 −0.113308 −0.0566542 0.998394i \(-0.518043\pi\)
−0.0566542 + 0.998394i \(0.518043\pi\)
\(702\) 5.00000 0.188713
\(703\) 25.0000 0.942893
\(704\) 0 0
\(705\) 6.00000 0.225973
\(706\) −18.0000 −0.677439
\(707\) −15.0000 −0.564133
\(708\) 0 0
\(709\) −46.0000 −1.72757 −0.863783 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) −9.00000 −0.337764
\(711\) 14.0000 0.525041
\(712\) −12.0000 −0.449719
\(713\) 0 0
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −21.0000 −0.784259
\(718\) 24.0000 0.895672
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 1.00000 0.0372419
\(722\) 6.00000 0.223297
\(723\) −7.00000 −0.260333
\(724\) −16.0000 −0.594635
\(725\) −3.00000 −0.111417
\(726\) 0 0
\(727\) 53.0000 1.96566 0.982831 0.184510i \(-0.0590699\pi\)
0.982831 + 0.184510i \(0.0590699\pi\)
\(728\) −5.00000 −0.185312
\(729\) 1.00000 0.0370370
\(730\) −14.0000 −0.518163
\(731\) −6.00000 −0.221918
\(732\) 8.00000 0.295689
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 23.0000 0.848945
\(735\) 6.00000 0.221313
\(736\) 0 0
\(737\) 0 0
\(738\) 6.00000 0.220863
\(739\) −25.0000 −0.919640 −0.459820 0.888012i \(-0.652086\pi\)
−0.459820 + 0.888012i \(0.652086\pi\)
\(740\) −5.00000 −0.183804
\(741\) 25.0000 0.918398
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 2.00000 0.0733236
\(745\) 6.00000 0.219823
\(746\) −13.0000 −0.475964
\(747\) −3.00000 −0.109764
\(748\) 0 0
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) −22.0000 −0.802791 −0.401396 0.915905i \(-0.631475\pi\)
−0.401396 + 0.915905i \(0.631475\pi\)
\(752\) −6.00000 −0.218797
\(753\) −24.0000 −0.874609
\(754\) −15.0000 −0.546268
\(755\) −20.0000 −0.727875
\(756\) −1.00000 −0.0363696
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 5.00000 0.181608
\(759\) 0 0
\(760\) −5.00000 −0.181369
\(761\) −12.0000 −0.435000 −0.217500 0.976060i \(-0.569790\pi\)
−0.217500 + 0.976060i \(0.569790\pi\)
\(762\) −4.00000 −0.144905
\(763\) 16.0000 0.579239
\(764\) −21.0000 −0.759753
\(765\) 3.00000 0.108465
\(766\) −6.00000 −0.216789
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −1.00000 −0.0360609 −0.0180305 0.999837i \(-0.505740\pi\)
−0.0180305 + 0.999837i \(0.505740\pi\)
\(770\) 0 0
\(771\) −27.0000 −0.972381
\(772\) −4.00000 −0.143963
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 2.00000 0.0718885
\(775\) 2.00000 0.0718421
\(776\) −10.0000 −0.358979
\(777\) −5.00000 −0.179374
\(778\) 6.00000 0.215110
\(779\) 30.0000 1.07486
\(780\) −5.00000 −0.179029
\(781\) 0 0
\(782\) 0 0
\(783\) −3.00000 −0.107211
\(784\) −6.00000 −0.214286
\(785\) 13.0000 0.463990
\(786\) −12.0000 −0.428026
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) −24.0000 −0.854965
\(789\) 18.0000 0.640817
\(790\) −14.0000 −0.498098
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 40.0000 1.42044
\(794\) 29.0000 1.02917
\(795\) 0 0
\(796\) −16.0000 −0.567105
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) −5.00000 −0.176998
\(799\) 18.0000 0.636794
\(800\) 1.00000 0.0353553
\(801\) −12.0000 −0.423999
\(802\) −30.0000 −1.05934
\(803\) 0 0
\(804\) 2.00000 0.0705346
\(805\) 0 0
\(806\) 10.0000 0.352235
\(807\) 15.0000 0.528025
\(808\) 15.0000 0.527698
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 29.0000 1.01833 0.509164 0.860670i \(-0.329955\pi\)
0.509164 + 0.860670i \(0.329955\pi\)
\(812\) 3.00000 0.105279
\(813\) 2.00000 0.0701431
\(814\) 0 0
\(815\) 16.0000 0.560456
\(816\) −3.00000 −0.105021
\(817\) 10.0000 0.349856
\(818\) 14.0000 0.489499
\(819\) −5.00000 −0.174714
\(820\) −6.00000 −0.209529
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 15.0000 0.523185
\(823\) 41.0000 1.42917 0.714585 0.699549i \(-0.246616\pi\)
0.714585 + 0.699549i \(0.246616\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 0 0
\(826\) 0 0
\(827\) −33.0000 −1.14752 −0.573761 0.819023i \(-0.694516\pi\)
−0.573761 + 0.819023i \(0.694516\pi\)
\(828\) 0 0
\(829\) 44.0000 1.52818 0.764092 0.645108i \(-0.223188\pi\)
0.764092 + 0.645108i \(0.223188\pi\)
\(830\) 3.00000 0.104132
\(831\) −22.0000 −0.763172
\(832\) 5.00000 0.173344
\(833\) 18.0000 0.623663
\(834\) 23.0000 0.796425
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) 2.00000 0.0691301
\(838\) −30.0000 −1.03633
\(839\) 45.0000 1.55357 0.776786 0.629764i \(-0.216849\pi\)
0.776786 + 0.629764i \(0.216849\pi\)
\(840\) 1.00000 0.0345033
\(841\) −20.0000 −0.689655
\(842\) −10.0000 −0.344623
\(843\) 0 0
\(844\) 5.00000 0.172107
\(845\) −12.0000 −0.412813
\(846\) −6.00000 −0.206284
\(847\) 0 0
\(848\) 0 0
\(849\) −16.0000 −0.549119
\(850\) −3.00000 −0.102899
\(851\) 0 0
\(852\) 9.00000 0.308335
\(853\) −31.0000 −1.06142 −0.530710 0.847554i \(-0.678075\pi\)
−0.530710 + 0.847554i \(0.678075\pi\)
\(854\) −8.00000 −0.273754
\(855\) −5.00000 −0.170996
\(856\) 0 0
\(857\) −39.0000 −1.33221 −0.666107 0.745856i \(-0.732041\pi\)
−0.666107 + 0.745856i \(0.732041\pi\)
\(858\) 0 0
\(859\) 44.0000 1.50126 0.750630 0.660722i \(-0.229750\pi\)
0.750630 + 0.660722i \(0.229750\pi\)
\(860\) −2.00000 −0.0681994
\(861\) −6.00000 −0.204479
\(862\) −15.0000 −0.510902
\(863\) 42.0000 1.42970 0.714848 0.699280i \(-0.246496\pi\)
0.714848 + 0.699280i \(0.246496\pi\)
\(864\) 1.00000 0.0340207
\(865\) −12.0000 −0.408012
\(866\) −16.0000 −0.543702
\(867\) −8.00000 −0.271694
\(868\) −2.00000 −0.0678844
\(869\) 0 0
\(870\) 3.00000 0.101710
\(871\) 10.0000 0.338837
\(872\) −16.0000 −0.541828
\(873\) −10.0000 −0.338449
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 14.0000 0.473016
\(877\) −25.0000 −0.844190 −0.422095 0.906552i \(-0.638705\pi\)
−0.422095 + 0.906552i \(0.638705\pi\)
\(878\) 26.0000 0.877457
\(879\) −12.0000 −0.404750
\(880\) 0 0
\(881\) −6.00000 −0.202145 −0.101073 0.994879i \(-0.532227\pi\)
−0.101073 + 0.994879i \(0.532227\pi\)
\(882\) −6.00000 −0.202031
\(883\) 2.00000 0.0673054 0.0336527 0.999434i \(-0.489286\pi\)
0.0336527 + 0.999434i \(0.489286\pi\)
\(884\) −15.0000 −0.504505
\(885\) 0 0
\(886\) −9.00000 −0.302361
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 5.00000 0.167789
\(889\) 4.00000 0.134156
\(890\) 12.0000 0.402241
\(891\) 0 0
\(892\) 5.00000 0.167412
\(893\) −30.0000 −1.00391
\(894\) −6.00000 −0.200670
\(895\) −12.0000 −0.401116
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 30.0000 1.00111
\(899\) −6.00000 −0.200111
\(900\) 1.00000 0.0333333
\(901\) 0 0
\(902\) 0 0
\(903\) −2.00000 −0.0665558
\(904\) 18.0000 0.598671
\(905\) 16.0000 0.531858
\(906\) 20.0000 0.664455
\(907\) −22.0000 −0.730498 −0.365249 0.930910i \(-0.619016\pi\)
−0.365249 + 0.930910i \(0.619016\pi\)
\(908\) 0 0
\(909\) 15.0000 0.497519
\(910\) 5.00000 0.165748
\(911\) −15.0000 −0.496972 −0.248486 0.968635i \(-0.579933\pi\)
−0.248486 + 0.968635i \(0.579933\pi\)
\(912\) 5.00000 0.165567
\(913\) 0 0
\(914\) 8.00000 0.264616
\(915\) −8.00000 −0.264472
\(916\) 20.0000 0.660819
\(917\) 12.0000 0.396275
\(918\) −3.00000 −0.0990148
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 0 0
\(921\) −22.0000 −0.724925
\(922\) −3.00000 −0.0987997
\(923\) 45.0000 1.48119
\(924\) 0 0
\(925\) 5.00000 0.164399
\(926\) 32.0000 1.05159
\(927\) −1.00000 −0.0328443
\(928\) −3.00000 −0.0984798
\(929\) −24.0000 −0.787414 −0.393707 0.919236i \(-0.628808\pi\)
−0.393707 + 0.919236i \(0.628808\pi\)
\(930\) −2.00000 −0.0655826
\(931\) −30.0000 −0.983210
\(932\) 6.00000 0.196537
\(933\) 0 0
\(934\) 33.0000 1.07979
\(935\) 0 0
\(936\) 5.00000 0.163430
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) −2.00000 −0.0653023
\(939\) −34.0000 −1.10955
\(940\) 6.00000 0.195698
\(941\) −3.00000 −0.0977972 −0.0488986 0.998804i \(-0.515571\pi\)
−0.0488986 + 0.998804i \(0.515571\pi\)
\(942\) −13.0000 −0.423563
\(943\) 0 0
\(944\) 0 0
\(945\) 1.00000 0.0325300
\(946\) 0 0
\(947\) 27.0000 0.877382 0.438691 0.898638i \(-0.355442\pi\)
0.438691 + 0.898638i \(0.355442\pi\)
\(948\) 14.0000 0.454699
\(949\) 70.0000 2.27230
\(950\) 5.00000 0.162221
\(951\) −12.0000 −0.389127
\(952\) 3.00000 0.0972306
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 0 0
\(955\) 21.0000 0.679544
\(956\) −21.0000 −0.679189
\(957\) 0 0
\(958\) −21.0000 −0.678479
\(959\) −15.0000 −0.484375
\(960\) −1.00000 −0.0322749
\(961\) −27.0000 −0.870968
\(962\) 25.0000 0.806032
\(963\) 0 0
\(964\) −7.00000 −0.225455
\(965\) 4.00000 0.128765
\(966\) 0 0
\(967\) −40.0000 −1.28631 −0.643157 0.765735i \(-0.722376\pi\)
−0.643157 + 0.765735i \(0.722376\pi\)
\(968\) 0 0
\(969\) −15.0000 −0.481869
\(970\) 10.0000 0.321081
\(971\) −60.0000 −1.92549 −0.962746 0.270408i \(-0.912841\pi\)
−0.962746 + 0.270408i \(0.912841\pi\)
\(972\) 1.00000 0.0320750
\(973\) −23.0000 −0.737346
\(974\) −25.0000 −0.801052
\(975\) 5.00000 0.160128
\(976\) 8.00000 0.256074
\(977\) −54.0000 −1.72761 −0.863807 0.503824i \(-0.831926\pi\)
−0.863807 + 0.503824i \(0.831926\pi\)
\(978\) −16.0000 −0.511624
\(979\) 0 0
\(980\) 6.00000 0.191663
\(981\) −16.0000 −0.510841
\(982\) 18.0000 0.574403
\(983\) 42.0000 1.33959 0.669796 0.742545i \(-0.266382\pi\)
0.669796 + 0.742545i \(0.266382\pi\)
\(984\) 6.00000 0.191273
\(985\) 24.0000 0.764704
\(986\) 9.00000 0.286618
\(987\) 6.00000 0.190982
\(988\) 25.0000 0.795356
\(989\) 0 0
\(990\) 0 0
\(991\) 50.0000 1.58830 0.794151 0.607720i \(-0.207916\pi\)
0.794151 + 0.607720i \(0.207916\pi\)
\(992\) 2.00000 0.0635001
\(993\) −13.0000 −0.412543
\(994\) −9.00000 −0.285463
\(995\) 16.0000 0.507234
\(996\) −3.00000 −0.0950586
\(997\) 23.0000 0.728417 0.364209 0.931317i \(-0.381339\pi\)
0.364209 + 0.931317i \(0.381339\pi\)
\(998\) 5.00000 0.158272
\(999\) 5.00000 0.158193
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 3630.2.a.u.1.1 yes 1
11.10 odd 2 3630.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.h.1.1 1 11.10 odd 2
3630.2.a.u.1.1 yes 1 1.1 even 1 trivial