Properties

Label 3630.2.a.l.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

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +5.00000 q^{13} -3.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +7.00000 q^{17} -1.00000 q^{18} +7.00000 q^{19} +1.00000 q^{20} +3.00000 q^{21} -1.00000 q^{24} +1.00000 q^{25} -5.00000 q^{26} +1.00000 q^{27} +3.00000 q^{28} -7.00000 q^{29} -1.00000 q^{30} +6.00000 q^{31} -1.00000 q^{32} -7.00000 q^{34} +3.00000 q^{35} +1.00000 q^{36} -5.00000 q^{37} -7.00000 q^{38} +5.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} -3.00000 q^{42} -6.00000 q^{43} +1.00000 q^{45} -10.0000 q^{47} +1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} +7.00000 q^{51} +5.00000 q^{52} -12.0000 q^{53} -1.00000 q^{54} -3.00000 q^{56} +7.00000 q^{57} +7.00000 q^{58} +1.00000 q^{60} -12.0000 q^{61} -6.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +5.00000 q^{65} -2.00000 q^{67} +7.00000 q^{68} -3.00000 q^{70} -9.00000 q^{71} -1.00000 q^{72} +6.00000 q^{73} +5.00000 q^{74} +1.00000 q^{75} +7.00000 q^{76} -5.00000 q^{78} +10.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} -13.0000 q^{83} +3.00000 q^{84} +7.00000 q^{85} +6.00000 q^{86} -7.00000 q^{87} +4.00000 q^{89} -1.00000 q^{90} +15.0000 q^{91} +6.00000 q^{93} +10.0000 q^{94} +7.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)

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
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) −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 \(0.256123\pi\)
\(14\) −3.00000 −0.801784
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) −1.00000 −0.235702
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 1.00000 0.223607
\(21\) 3.00000 0.654654
\(22\) 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
\(28\) 3.00000 0.566947
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) −1.00000 −0.182574
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −7.00000 −1.20049
\(35\) 3.00000 0.507093
\(36\) 1.00000 0.166667
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) −7.00000 −1.13555
\(39\) 5.00000 0.800641
\(40\) −1.00000 −0.158114
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) −3.00000 −0.462910
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −10.0000 −1.45865 −0.729325 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) 1.00000 0.144338
\(49\) 2.00000 0.285714
\(50\) −1.00000 −0.141421
\(51\) 7.00000 0.980196
\(52\) 5.00000 0.693375
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −3.00000 −0.400892
\(57\) 7.00000 0.927173
\(58\) 7.00000 0.919145
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 1.00000 0.129099
\(61\) −12.0000 −1.53644 −0.768221 0.640184i \(-0.778858\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) −6.00000 −0.762001
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) 5.00000 0.620174
\(66\) 0 0
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) 7.00000 0.848875
\(69\) 0 0
\(70\) −3.00000 −0.358569
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) −1.00000 −0.117851
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 5.00000 0.581238
\(75\) 1.00000 0.115470
\(76\) 7.00000 0.802955
\(77\) 0 0
\(78\) −5.00000 −0.566139
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −10.0000 −1.10432
\(83\) −13.0000 −1.42694 −0.713468 0.700688i \(-0.752876\pi\)
−0.713468 + 0.700688i \(0.752876\pi\)
\(84\) 3.00000 0.327327
\(85\) 7.00000 0.759257
\(86\) 6.00000 0.646997
\(87\) −7.00000 −0.750479
\(88\) 0 0
\(89\) 4.00000 0.423999 0.212000 0.977270i \(-0.432002\pi\)
0.212000 + 0.977270i \(0.432002\pi\)
\(90\) −1.00000 −0.105409
\(91\) 15.0000 1.57243
\(92\) 0 0
\(93\) 6.00000 0.622171
\(94\) 10.0000 1.03142
\(95\) 7.00000 0.718185
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 3.00000 0.298511 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) −7.00000 −0.693103
\(103\) −3.00000 −0.295599 −0.147799 0.989017i \(-0.547219\pi\)
−0.147799 + 0.989017i \(0.547219\pi\)
\(104\) −5.00000 −0.490290
\(105\) 3.00000 0.292770
\(106\) 12.0000 1.16554
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 1.00000 0.0962250
\(109\) −20.0000 −1.91565 −0.957826 0.287348i \(-0.907226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) −5.00000 −0.474579
\(112\) 3.00000 0.283473
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) −7.00000 −0.655610
\(115\) 0 0
\(116\) −7.00000 −0.649934
\(117\) 5.00000 0.462250
\(118\) 0 0
\(119\) 21.0000 1.92507
\(120\) −1.00000 −0.0912871
\(121\) 0 0
\(122\) 12.0000 1.08643
\(123\) 10.0000 0.901670
\(124\) 6.00000 0.538816
\(125\) 1.00000 0.0894427
\(126\) −3.00000 −0.267261
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.00000 −0.528271
\(130\) −5.00000 −0.438529
\(131\) −16.0000 −1.39793 −0.698963 0.715158i \(-0.746355\pi\)
−0.698963 + 0.715158i \(0.746355\pi\)
\(132\) 0 0
\(133\) 21.0000 1.82093
\(134\) 2.00000 0.172774
\(135\) 1.00000 0.0860663
\(136\) −7.00000 −0.600245
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 3.00000 0.253546
\(141\) −10.0000 −0.842152
\(142\) 9.00000 0.755263
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −7.00000 −0.581318
\(146\) −6.00000 −0.496564
\(147\) 2.00000 0.164957
\(148\) −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 \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) −7.00000 −0.567775
\(153\) 7.00000 0.565916
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) 5.00000 0.400320
\(157\) −11.0000 −0.877896 −0.438948 0.898513i \(-0.644649\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) −10.0000 −0.795557
\(159\) −12.0000 −0.951662
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 10.0000 0.780869
\(165\) 0 0
\(166\) 13.0000 1.00900
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) −3.00000 −0.231455
\(169\) 12.0000 0.923077
\(170\) −7.00000 −0.536875
\(171\) 7.00000 0.535303
\(172\) −6.00000 −0.457496
\(173\) 4.00000 0.304114 0.152057 0.988372i \(-0.451410\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 7.00000 0.530669
\(175\) 3.00000 0.226779
\(176\) 0 0
\(177\) 0 0
\(178\) −4.00000 −0.299813
\(179\) −16.0000 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) 1.00000 0.0745356
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) −15.0000 −1.11187
\(183\) −12.0000 −0.887066
\(184\) 0 0
\(185\) −5.00000 −0.367607
\(186\) −6.00000 −0.439941
\(187\) 0 0
\(188\) −10.0000 −0.729325
\(189\) 3.00000 0.218218
\(190\) −7.00000 −0.507833
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 1.00000 0.0721688
\(193\) 24.0000 1.72756 0.863779 0.503871i \(-0.168091\pi\)
0.863779 + 0.503871i \(0.168091\pi\)
\(194\) −2.00000 −0.143592
\(195\) 5.00000 0.358057
\(196\) 2.00000 0.142857
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 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
\(202\) −3.00000 −0.211079
\(203\) −21.0000 −1.47391
\(204\) 7.00000 0.490098
\(205\) 10.0000 0.698430
\(206\) 3.00000 0.209020
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) 0 0
\(210\) −3.00000 −0.207020
\(211\) 7.00000 0.481900 0.240950 0.970538i \(-0.422541\pi\)
0.240950 + 0.970538i \(0.422541\pi\)
\(212\) −12.0000 −0.824163
\(213\) −9.00000 −0.616670
\(214\) 0 0
\(215\) −6.00000 −0.409197
\(216\) −1.00000 −0.0680414
\(217\) 18.0000 1.22192
\(218\) 20.0000 1.35457
\(219\) 6.00000 0.405442
\(220\) 0 0
\(221\) 35.0000 2.35435
\(222\) 5.00000 0.335578
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) −3.00000 −0.200446
\(225\) 1.00000 0.0666667
\(226\) −10.0000 −0.665190
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 7.00000 0.463586
\(229\) 16.0000 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 7.00000 0.459573
\(233\) 2.00000 0.131024 0.0655122 0.997852i \(-0.479132\pi\)
0.0655122 + 0.997852i \(0.479132\pi\)
\(234\) −5.00000 −0.326860
\(235\) −10.0000 −0.652328
\(236\) 0 0
\(237\) 10.0000 0.649570
\(238\) −21.0000 −1.36123
\(239\) 3.00000 0.194054 0.0970269 0.995282i \(-0.469067\pi\)
0.0970269 + 0.995282i \(0.469067\pi\)
\(240\) 1.00000 0.0645497
\(241\) −25.0000 −1.61039 −0.805196 0.593009i \(-0.797940\pi\)
−0.805196 + 0.593009i \(0.797940\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −12.0000 −0.768221
\(245\) 2.00000 0.127775
\(246\) −10.0000 −0.637577
\(247\) 35.0000 2.22700
\(248\) −6.00000 −0.381000
\(249\) −13.0000 −0.823842
\(250\) −1.00000 −0.0632456
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 3.00000 0.188982
\(253\) 0 0
\(254\) −4.00000 −0.250982
\(255\) 7.00000 0.438357
\(256\) 1.00000 0.0625000
\(257\) 17.0000 1.06043 0.530215 0.847863i \(-0.322111\pi\)
0.530215 + 0.847863i \(0.322111\pi\)
\(258\) 6.00000 0.373544
\(259\) −15.0000 −0.932055
\(260\) 5.00000 0.310087
\(261\) −7.00000 −0.433289
\(262\) 16.0000 0.988483
\(263\) −22.0000 −1.35658 −0.678289 0.734795i \(-0.737278\pi\)
−0.678289 + 0.734795i \(0.737278\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) −21.0000 −1.28759
\(267\) 4.00000 0.244796
\(268\) −2.00000 −0.122169
\(269\) −19.0000 −1.15845 −0.579225 0.815168i \(-0.696645\pi\)
−0.579225 + 0.815168i \(0.696645\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 7.00000 0.424437
\(273\) 15.0000 0.907841
\(274\) −3.00000 −0.181237
\(275\) 0 0
\(276\) 0 0
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) −5.00000 −0.299880
\(279\) 6.00000 0.359211
\(280\) −3.00000 −0.179284
\(281\) 4.00000 0.238620 0.119310 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 10.0000 0.595491
\(283\) 24.0000 1.42665 0.713326 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) −9.00000 −0.534052
\(285\) 7.00000 0.414644
\(286\) 0 0
\(287\) 30.0000 1.77084
\(288\) −1.00000 −0.0589256
\(289\) 32.0000 1.88235
\(290\) 7.00000 0.411054
\(291\) 2.00000 0.117242
\(292\) 6.00000 0.351123
\(293\) −16.0000 −0.934730 −0.467365 0.884064i \(-0.654797\pi\)
−0.467365 + 0.884064i \(0.654797\pi\)
\(294\) −2.00000 −0.116642
\(295\) 0 0
\(296\) 5.00000 0.290619
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) −18.0000 −1.03750
\(302\) 20.0000 1.15087
\(303\) 3.00000 0.172345
\(304\) 7.00000 0.401478
\(305\) −12.0000 −0.687118
\(306\) −7.00000 −0.400163
\(307\) 34.0000 1.94048 0.970241 0.242140i \(-0.0778494\pi\)
0.970241 + 0.242140i \(0.0778494\pi\)
\(308\) 0 0
\(309\) −3.00000 −0.170664
\(310\) −6.00000 −0.340777
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −5.00000 −0.283069
\(313\) −2.00000 −0.113047 −0.0565233 0.998401i \(-0.518002\pi\)
−0.0565233 + 0.998401i \(0.518002\pi\)
\(314\) 11.0000 0.620766
\(315\) 3.00000 0.169031
\(316\) 10.0000 0.562544
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 12.0000 0.672927
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 0 0
\(323\) 49.0000 2.72643
\(324\) 1.00000 0.0555556
\(325\) 5.00000 0.277350
\(326\) −4.00000 −0.221540
\(327\) −20.0000 −1.10600
\(328\) −10.0000 −0.552158
\(329\) −30.0000 −1.65395
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) −13.0000 −0.713468
\(333\) −5.00000 −0.273998
\(334\) −16.0000 −0.875481
\(335\) −2.00000 −0.109272
\(336\) 3.00000 0.163663
\(337\) −6.00000 −0.326841 −0.163420 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) −12.0000 −0.652714
\(339\) 10.0000 0.543125
\(340\) 7.00000 0.379628
\(341\) 0 0
\(342\) −7.00000 −0.378517
\(343\) −15.0000 −0.809924
\(344\) 6.00000 0.323498
\(345\) 0 0
\(346\) −4.00000 −0.215041
\(347\) −3.00000 −0.161048 −0.0805242 0.996753i \(-0.525659\pi\)
−0.0805242 + 0.996753i \(0.525659\pi\)
\(348\) −7.00000 −0.375239
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) −3.00000 −0.160357
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) −9.00000 −0.477670
\(356\) 4.00000 0.212000
\(357\) 21.0000 1.11144
\(358\) 16.0000 0.845626
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 30.0000 1.57895
\(362\) 8.00000 0.420471
\(363\) 0 0
\(364\) 15.0000 0.786214
\(365\) 6.00000 0.314054
\(366\) 12.0000 0.627250
\(367\) −27.0000 −1.40939 −0.704694 0.709511i \(-0.748916\pi\)
−0.704694 + 0.709511i \(0.748916\pi\)
\(368\) 0 0
\(369\) 10.0000 0.520579
\(370\) 5.00000 0.259938
\(371\) −36.0000 −1.86903
\(372\) 6.00000 0.311086
\(373\) −29.0000 −1.50156 −0.750782 0.660551i \(-0.770323\pi\)
−0.750782 + 0.660551i \(0.770323\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 10.0000 0.515711
\(377\) −35.0000 −1.80259
\(378\) −3.00000 −0.154303
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 7.00000 0.359092
\(381\) 4.00000 0.204926
\(382\) 3.00000 0.153493
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −24.0000 −1.22157
\(387\) −6.00000 −0.304997
\(388\) 2.00000 0.101535
\(389\) 34.0000 1.72387 0.861934 0.507020i \(-0.169253\pi\)
0.861934 + 0.507020i \(0.169253\pi\)
\(390\) −5.00000 −0.253185
\(391\) 0 0
\(392\) −2.00000 −0.101015
\(393\) −16.0000 −0.807093
\(394\) 12.0000 0.604551
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) 35.0000 1.75660 0.878300 0.478110i \(-0.158678\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) 16.0000 0.802008
\(399\) 21.0000 1.05131
\(400\) 1.00000 0.0500000
\(401\) −34.0000 −1.69788 −0.848939 0.528490i \(-0.822758\pi\)
−0.848939 + 0.528490i \(0.822758\pi\)
\(402\) 2.00000 0.0997509
\(403\) 30.0000 1.49441
\(404\) 3.00000 0.149256
\(405\) 1.00000 0.0496904
\(406\) 21.0000 1.04221
\(407\) 0 0
\(408\) −7.00000 −0.346552
\(409\) −6.00000 −0.296681 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) −10.0000 −0.493865
\(411\) 3.00000 0.147979
\(412\) −3.00000 −0.147799
\(413\) 0 0
\(414\) 0 0
\(415\) −13.0000 −0.638145
\(416\) −5.00000 −0.245145
\(417\) 5.00000 0.244851
\(418\) 0 0
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) 3.00000 0.146385
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) −7.00000 −0.340755
\(423\) −10.0000 −0.486217
\(424\) 12.0000 0.582772
\(425\) 7.00000 0.339550
\(426\) 9.00000 0.436051
\(427\) −36.0000 −1.74216
\(428\) 0 0
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) 1.00000 0.0481683 0.0240842 0.999710i \(-0.492333\pi\)
0.0240842 + 0.999710i \(0.492333\pi\)
\(432\) 1.00000 0.0481125
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) −18.0000 −0.864028
\(435\) −7.00000 −0.335624
\(436\) −20.0000 −0.957826
\(437\) 0 0
\(438\) −6.00000 −0.286691
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) −35.0000 −1.66478
\(443\) 15.0000 0.712672 0.356336 0.934358i \(-0.384026\pi\)
0.356336 + 0.934358i \(0.384026\pi\)
\(444\) −5.00000 −0.237289
\(445\) 4.00000 0.189618
\(446\) 1.00000 0.0473514
\(447\) −6.00000 −0.283790
\(448\) 3.00000 0.141737
\(449\) 22.0000 1.03824 0.519122 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) 10.0000 0.470360
\(453\) −20.0000 −0.939682
\(454\) 0 0
\(455\) 15.0000 0.703211
\(456\) −7.00000 −0.327805
\(457\) −4.00000 −0.187112 −0.0935561 0.995614i \(-0.529823\pi\)
−0.0935561 + 0.995614i \(0.529823\pi\)
\(458\) −16.0000 −0.747631
\(459\) 7.00000 0.326732
\(460\) 0 0
\(461\) 33.0000 1.53696 0.768482 0.639872i \(-0.221013\pi\)
0.768482 + 0.639872i \(0.221013\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) −7.00000 −0.324967
\(465\) 6.00000 0.278243
\(466\) −2.00000 −0.0926482
\(467\) −7.00000 −0.323921 −0.161961 0.986797i \(-0.551782\pi\)
−0.161961 + 0.986797i \(0.551782\pi\)
\(468\) 5.00000 0.231125
\(469\) −6.00000 −0.277054
\(470\) 10.0000 0.461266
\(471\) −11.0000 −0.506853
\(472\) 0 0
\(473\) 0 0
\(474\) −10.0000 −0.459315
\(475\) 7.00000 0.321182
\(476\) 21.0000 0.962533
\(477\) −12.0000 −0.549442
\(478\) −3.00000 −0.137217
\(479\) 3.00000 0.137073 0.0685367 0.997649i \(-0.478167\pi\)
0.0685367 + 0.997649i \(0.478167\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −25.0000 −1.13990
\(482\) 25.0000 1.13872
\(483\) 0 0
\(484\) 0 0
\(485\) 2.00000 0.0908153
\(486\) −1.00000 −0.0453609
\(487\) 29.0000 1.31412 0.657058 0.753840i \(-0.271801\pi\)
0.657058 + 0.753840i \(0.271801\pi\)
\(488\) 12.0000 0.543214
\(489\) 4.00000 0.180886
\(490\) −2.00000 −0.0903508
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 10.0000 0.450835
\(493\) −49.0000 −2.20685
\(494\) −35.0000 −1.57472
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) −27.0000 −1.21112
\(498\) 13.0000 0.582544
\(499\) 33.0000 1.47728 0.738641 0.674099i \(-0.235468\pi\)
0.738641 + 0.674099i \(0.235468\pi\)
\(500\) 1.00000 0.0447214
\(501\) 16.0000 0.714827
\(502\) 12.0000 0.535586
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) −3.00000 −0.133631
\(505\) 3.00000 0.133498
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) 4.00000 0.177471
\(509\) −2.00000 −0.0886484 −0.0443242 0.999017i \(-0.514113\pi\)
−0.0443242 + 0.999017i \(0.514113\pi\)
\(510\) −7.00000 −0.309965
\(511\) 18.0000 0.796273
\(512\) −1.00000 −0.0441942
\(513\) 7.00000 0.309058
\(514\) −17.0000 −0.749838
\(515\) −3.00000 −0.132196
\(516\) −6.00000 −0.264135
\(517\) 0 0
\(518\) 15.0000 0.659062
\(519\) 4.00000 0.175581
\(520\) −5.00000 −0.219265
\(521\) 8.00000 0.350486 0.175243 0.984525i \(-0.443929\pi\)
0.175243 + 0.984525i \(0.443929\pi\)
\(522\) 7.00000 0.306382
\(523\) −12.0000 −0.524723 −0.262362 0.964970i \(-0.584501\pi\)
−0.262362 + 0.964970i \(0.584501\pi\)
\(524\) −16.0000 −0.698963
\(525\) 3.00000 0.130931
\(526\) 22.0000 0.959246
\(527\) 42.0000 1.82955
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 12.0000 0.521247
\(531\) 0 0
\(532\) 21.0000 0.910465
\(533\) 50.0000 2.16574
\(534\) −4.00000 −0.173097
\(535\) 0 0
\(536\) 2.00000 0.0863868
\(537\) −16.0000 −0.690451
\(538\) 19.0000 0.819148
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 26.0000 1.11783 0.558914 0.829226i \(-0.311218\pi\)
0.558914 + 0.829226i \(0.311218\pi\)
\(542\) −22.0000 −0.944981
\(543\) −8.00000 −0.343313
\(544\) −7.00000 −0.300123
\(545\) −20.0000 −0.856706
\(546\) −15.0000 −0.641941
\(547\) 38.0000 1.62476 0.812381 0.583127i \(-0.198171\pi\)
0.812381 + 0.583127i \(0.198171\pi\)
\(548\) 3.00000 0.128154
\(549\) −12.0000 −0.512148
\(550\) 0 0
\(551\) −49.0000 −2.08747
\(552\) 0 0
\(553\) 30.0000 1.27573
\(554\) −26.0000 −1.10463
\(555\) −5.00000 −0.212238
\(556\) 5.00000 0.212047
\(557\) 42.0000 1.77960 0.889799 0.456354i \(-0.150845\pi\)
0.889799 + 0.456354i \(0.150845\pi\)
\(558\) −6.00000 −0.254000
\(559\) −30.0000 −1.26886
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) −4.00000 −0.168730
\(563\) −15.0000 −0.632175 −0.316087 0.948730i \(-0.602369\pi\)
−0.316087 + 0.948730i \(0.602369\pi\)
\(564\) −10.0000 −0.421076
\(565\) 10.0000 0.420703
\(566\) −24.0000 −1.00880
\(567\) 3.00000 0.125988
\(568\) 9.00000 0.377632
\(569\) 2.00000 0.0838444 0.0419222 0.999121i \(-0.486652\pi\)
0.0419222 + 0.999121i \(0.486652\pi\)
\(570\) −7.00000 −0.293198
\(571\) 24.0000 1.00437 0.502184 0.864761i \(-0.332530\pi\)
0.502184 + 0.864761i \(0.332530\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) −30.0000 −1.25218
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 42.0000 1.74848 0.874241 0.485491i \(-0.161359\pi\)
0.874241 + 0.485491i \(0.161359\pi\)
\(578\) −32.0000 −1.33102
\(579\) 24.0000 0.997406
\(580\) −7.00000 −0.290659
\(581\) −39.0000 −1.61799
\(582\) −2.00000 −0.0829027
\(583\) 0 0
\(584\) −6.00000 −0.248282
\(585\) 5.00000 0.206725
\(586\) 16.0000 0.660954
\(587\) 7.00000 0.288921 0.144460 0.989511i \(-0.453855\pi\)
0.144460 + 0.989511i \(0.453855\pi\)
\(588\) 2.00000 0.0824786
\(589\) 42.0000 1.73058
\(590\) 0 0
\(591\) −12.0000 −0.493614
\(592\) −5.00000 −0.205499
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 0 0
\(595\) 21.0000 0.860916
\(596\) −6.00000 −0.245770
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) 8.00000 0.326871 0.163436 0.986554i \(-0.447742\pi\)
0.163436 + 0.986554i \(0.447742\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 18.0000 0.733625
\(603\) −2.00000 −0.0814463
\(604\) −20.0000 −0.813788
\(605\) 0 0
\(606\) −3.00000 −0.121867
\(607\) 33.0000 1.33943 0.669714 0.742619i \(-0.266417\pi\)
0.669714 + 0.742619i \(0.266417\pi\)
\(608\) −7.00000 −0.283887
\(609\) −21.0000 −0.850963
\(610\) 12.0000 0.485866
\(611\) −50.0000 −2.02278
\(612\) 7.00000 0.282958
\(613\) −3.00000 −0.121169 −0.0605844 0.998163i \(-0.519296\pi\)
−0.0605844 + 0.998163i \(0.519296\pi\)
\(614\) −34.0000 −1.37213
\(615\) 10.0000 0.403239
\(616\) 0 0
\(617\) 3.00000 0.120775 0.0603877 0.998175i \(-0.480766\pi\)
0.0603877 + 0.998175i \(0.480766\pi\)
\(618\) 3.00000 0.120678
\(619\) 25.0000 1.00483 0.502417 0.864625i \(-0.332444\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(620\) 6.00000 0.240966
\(621\) 0 0
\(622\) 8.00000 0.320771
\(623\) 12.0000 0.480770
\(624\) 5.00000 0.200160
\(625\) 1.00000 0.0400000
\(626\) 2.00000 0.0799361
\(627\) 0 0
\(628\) −11.0000 −0.438948
\(629\) −35.0000 −1.39554
\(630\) −3.00000 −0.119523
\(631\) 4.00000 0.159237 0.0796187 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) −10.0000 −0.397779
\(633\) 7.00000 0.278225
\(634\) −12.0000 −0.476581
\(635\) 4.00000 0.158735
\(636\) −12.0000 −0.475831
\(637\) 10.0000 0.396214
\(638\) 0 0
\(639\) −9.00000 −0.356034
\(640\) −1.00000 −0.0395285
\(641\) −26.0000 −1.02694 −0.513469 0.858108i \(-0.671640\pi\)
−0.513469 + 0.858108i \(0.671640\pi\)
\(642\) 0 0
\(643\) −44.0000 −1.73519 −0.867595 0.497271i \(-0.834335\pi\)
−0.867595 + 0.497271i \(0.834335\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) −49.0000 −1.92788
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) −5.00000 −0.196116
\(651\) 18.0000 0.705476
\(652\) 4.00000 0.156652
\(653\) 30.0000 1.17399 0.586995 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 20.0000 0.782062
\(655\) −16.0000 −0.625172
\(656\) 10.0000 0.390434
\(657\) 6.00000 0.234082
\(658\) 30.0000 1.16952
\(659\) −42.0000 −1.63609 −0.818044 0.575156i \(-0.804941\pi\)
−0.818044 + 0.575156i \(0.804941\pi\)
\(660\) 0 0
\(661\) −30.0000 −1.16686 −0.583432 0.812162i \(-0.698291\pi\)
−0.583432 + 0.812162i \(0.698291\pi\)
\(662\) 17.0000 0.660724
\(663\) 35.0000 1.35929
\(664\) 13.0000 0.504498
\(665\) 21.0000 0.814345
\(666\) 5.00000 0.193746
\(667\) 0 0
\(668\) 16.0000 0.619059
\(669\) −1.00000 −0.0386622
\(670\) 2.00000 0.0772667
\(671\) 0 0
\(672\) −3.00000 −0.115728
\(673\) −16.0000 −0.616755 −0.308377 0.951264i \(-0.599786\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(674\) 6.00000 0.231111
\(675\) 1.00000 0.0384900
\(676\) 12.0000 0.461538
\(677\) −10.0000 −0.384331 −0.192166 0.981363i \(-0.561551\pi\)
−0.192166 + 0.981363i \(0.561551\pi\)
\(678\) −10.0000 −0.384048
\(679\) 6.00000 0.230259
\(680\) −7.00000 −0.268438
\(681\) 0 0
\(682\) 0 0
\(683\) 25.0000 0.956598 0.478299 0.878197i \(-0.341253\pi\)
0.478299 + 0.878197i \(0.341253\pi\)
\(684\) 7.00000 0.267652
\(685\) 3.00000 0.114624
\(686\) 15.0000 0.572703
\(687\) 16.0000 0.610438
\(688\) −6.00000 −0.228748
\(689\) −60.0000 −2.28582
\(690\) 0 0
\(691\) −31.0000 −1.17930 −0.589648 0.807661i \(-0.700733\pi\)
−0.589648 + 0.807661i \(0.700733\pi\)
\(692\) 4.00000 0.152057
\(693\) 0 0
\(694\) 3.00000 0.113878
\(695\) 5.00000 0.189661
\(696\) 7.00000 0.265334
\(697\) 70.0000 2.65144
\(698\) 14.0000 0.529908
\(699\) 2.00000 0.0756469
\(700\) 3.00000 0.113389
\(701\) 33.0000 1.24639 0.623196 0.782065i \(-0.285834\pi\)
0.623196 + 0.782065i \(0.285834\pi\)
\(702\) −5.00000 −0.188713
\(703\) −35.0000 −1.32005
\(704\) 0 0
\(705\) −10.0000 −0.376622
\(706\) −6.00000 −0.225813
\(707\) 9.00000 0.338480
\(708\) 0 0
\(709\) 30.0000 1.12667 0.563337 0.826227i \(-0.309517\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(710\) 9.00000 0.337764
\(711\) 10.0000 0.375029
\(712\) −4.00000 −0.149906
\(713\) 0 0
\(714\) −21.0000 −0.785905
\(715\) 0 0
\(716\) −16.0000 −0.597948
\(717\) 3.00000 0.112037
\(718\) −24.0000 −0.895672
\(719\) 4.00000 0.149175 0.0745874 0.997214i \(-0.476236\pi\)
0.0745874 + 0.997214i \(0.476236\pi\)
\(720\) 1.00000 0.0372678
\(721\) −9.00000 −0.335178
\(722\) −30.0000 −1.11648
\(723\) −25.0000 −0.929760
\(724\) −8.00000 −0.297318
\(725\) −7.00000 −0.259973
\(726\) 0 0
\(727\) 7.00000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(728\) −15.0000 −0.555937
\(729\) 1.00000 0.0370370
\(730\) −6.00000 −0.222070
\(731\) −42.0000 −1.55343
\(732\) −12.0000 −0.443533
\(733\) −46.0000 −1.69905 −0.849524 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) 27.0000 0.996588
\(735\) 2.00000 0.0737711
\(736\) 0 0
\(737\) 0 0
\(738\) −10.0000 −0.368105
\(739\) −27.0000 −0.993211 −0.496606 0.867976i \(-0.665420\pi\)
−0.496606 + 0.867976i \(0.665420\pi\)
\(740\) −5.00000 −0.183804
\(741\) 35.0000 1.28576
\(742\) 36.0000 1.32160
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) −6.00000 −0.219971
\(745\) −6.00000 −0.219823
\(746\) 29.0000 1.06177
\(747\) −13.0000 −0.475645
\(748\) 0 0
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) −46.0000 −1.67856 −0.839282 0.543696i \(-0.817024\pi\)
−0.839282 + 0.543696i \(0.817024\pi\)
\(752\) −10.0000 −0.364662
\(753\) −12.0000 −0.437304
\(754\) 35.0000 1.27462
\(755\) −20.0000 −0.727875
\(756\) 3.00000 0.109109
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) −1.00000 −0.0363216
\(759\) 0 0
\(760\) −7.00000 −0.253917
\(761\) −36.0000 −1.30500 −0.652499 0.757789i \(-0.726280\pi\)
−0.652499 + 0.757789i \(0.726280\pi\)
\(762\) −4.00000 −0.144905
\(763\) −60.0000 −2.17215
\(764\) −3.00000 −0.108536
\(765\) 7.00000 0.253086
\(766\) −6.00000 −0.216789
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 9.00000 0.324548 0.162274 0.986746i \(-0.448117\pi\)
0.162274 + 0.986746i \(0.448117\pi\)
\(770\) 0 0
\(771\) 17.0000 0.612240
\(772\) 24.0000 0.863779
\(773\) −12.0000 −0.431610 −0.215805 0.976436i \(-0.569238\pi\)
−0.215805 + 0.976436i \(0.569238\pi\)
\(774\) 6.00000 0.215666
\(775\) 6.00000 0.215526
\(776\) −2.00000 −0.0717958
\(777\) −15.0000 −0.538122
\(778\) −34.0000 −1.21896
\(779\) 70.0000 2.50801
\(780\) 5.00000 0.179029
\(781\) 0 0
\(782\) 0 0
\(783\) −7.00000 −0.250160
\(784\) 2.00000 0.0714286
\(785\) −11.0000 −0.392607
\(786\) 16.0000 0.570701
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) −12.0000 −0.427482
\(789\) −22.0000 −0.783221
\(790\) −10.0000 −0.355784
\(791\) 30.0000 1.06668
\(792\) 0 0
\(793\) −60.0000 −2.13066
\(794\) −35.0000 −1.24210
\(795\) −12.0000 −0.425596
\(796\) −16.0000 −0.567105
\(797\) 40.0000 1.41687 0.708436 0.705775i \(-0.249401\pi\)
0.708436 + 0.705775i \(0.249401\pi\)
\(798\) −21.0000 −0.743392
\(799\) −70.0000 −2.47642
\(800\) −1.00000 −0.0353553
\(801\) 4.00000 0.141333
\(802\) 34.0000 1.20058
\(803\) 0 0
\(804\) −2.00000 −0.0705346
\(805\) 0 0
\(806\) −30.0000 −1.05670
\(807\) −19.0000 −0.668832
\(808\) −3.00000 −0.105540
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −17.0000 −0.596951 −0.298475 0.954417i \(-0.596478\pi\)
−0.298475 + 0.954417i \(0.596478\pi\)
\(812\) −21.0000 −0.736956
\(813\) 22.0000 0.771574
\(814\) 0 0
\(815\) 4.00000 0.140114
\(816\) 7.00000 0.245049
\(817\) −42.0000 −1.46939
\(818\) 6.00000 0.209785
\(819\) 15.0000 0.524142
\(820\) 10.0000 0.349215
\(821\) 6.00000 0.209401 0.104701 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) −3.00000 −0.104637
\(823\) 11.0000 0.383436 0.191718 0.981450i \(-0.438594\pi\)
0.191718 + 0.981450i \(0.438594\pi\)
\(824\) 3.00000 0.104510
\(825\) 0 0
\(826\) 0 0
\(827\) −47.0000 −1.63435 −0.817175 0.576390i \(-0.804461\pi\)
−0.817175 + 0.576390i \(0.804461\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 13.0000 0.451237
\(831\) 26.0000 0.901930
\(832\) 5.00000 0.173344
\(833\) 14.0000 0.485071
\(834\) −5.00000 −0.173136
\(835\) 16.0000 0.553703
\(836\) 0 0
\(837\) 6.00000 0.207390
\(838\) 14.0000 0.483622
\(839\) 35.0000 1.20833 0.604167 0.796858i \(-0.293506\pi\)
0.604167 + 0.796858i \(0.293506\pi\)
\(840\) −3.00000 −0.103510
\(841\) 20.0000 0.689655
\(842\) 6.00000 0.206774
\(843\) 4.00000 0.137767
\(844\) 7.00000 0.240950
\(845\) 12.0000 0.412813
\(846\) 10.0000 0.343807
\(847\) 0 0
\(848\) −12.0000 −0.412082
\(849\) 24.0000 0.823678
\(850\) −7.00000 −0.240098
\(851\) 0 0
\(852\) −9.00000 −0.308335
\(853\) −7.00000 −0.239675 −0.119838 0.992793i \(-0.538237\pi\)
−0.119838 + 0.992793i \(0.538237\pi\)
\(854\) 36.0000 1.23189
\(855\) 7.00000 0.239395
\(856\) 0 0
\(857\) 51.0000 1.74213 0.871063 0.491171i \(-0.163431\pi\)
0.871063 + 0.491171i \(0.163431\pi\)
\(858\) 0 0
\(859\) −28.0000 −0.955348 −0.477674 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) −6.00000 −0.204598
\(861\) 30.0000 1.02240
\(862\) −1.00000 −0.0340601
\(863\) −30.0000 −1.02121 −0.510606 0.859815i \(-0.670579\pi\)
−0.510606 + 0.859815i \(0.670579\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 4.00000 0.136004
\(866\) 28.0000 0.951479
\(867\) 32.0000 1.08678
\(868\) 18.0000 0.610960
\(869\) 0 0
\(870\) 7.00000 0.237322
\(871\) −10.0000 −0.338837
\(872\) 20.0000 0.677285
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) 3.00000 0.101419
\(876\) 6.00000 0.202721
\(877\) 47.0000 1.58708 0.793539 0.608520i \(-0.208236\pi\)
0.793539 + 0.608520i \(0.208236\pi\)
\(878\) −26.0000 −0.877457
\(879\) −16.0000 −0.539667
\(880\) 0 0
\(881\) 26.0000 0.875962 0.437981 0.898984i \(-0.355694\pi\)
0.437981 + 0.898984i \(0.355694\pi\)
\(882\) −2.00000 −0.0673435
\(883\) −14.0000 −0.471138 −0.235569 0.971858i \(-0.575695\pi\)
−0.235569 + 0.971858i \(0.575695\pi\)
\(884\) 35.0000 1.17718
\(885\) 0 0
\(886\) −15.0000 −0.503935
\(887\) 16.0000 0.537227 0.268614 0.963248i \(-0.413434\pi\)
0.268614 + 0.963248i \(0.413434\pi\)
\(888\) 5.00000 0.167789
\(889\) 12.0000 0.402467
\(890\) −4.00000 −0.134080
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) −70.0000 −2.34246
\(894\) 6.00000 0.200670
\(895\) −16.0000 −0.534821
\(896\) −3.00000 −0.100223
\(897\) 0 0
\(898\) −22.0000 −0.734150
\(899\) −42.0000 −1.40078
\(900\) 1.00000 0.0333333
\(901\) −84.0000 −2.79845
\(902\) 0 0
\(903\) −18.0000 −0.599002
\(904\) −10.0000 −0.332595
\(905\) −8.00000 −0.265929
\(906\) 20.0000 0.664455
\(907\) 6.00000 0.199227 0.0996134 0.995026i \(-0.468239\pi\)
0.0996134 + 0.995026i \(0.468239\pi\)
\(908\) 0 0
\(909\) 3.00000 0.0995037
\(910\) −15.0000 −0.497245
\(911\) −57.0000 −1.88849 −0.944247 0.329238i \(-0.893208\pi\)
−0.944247 + 0.329238i \(0.893208\pi\)
\(912\) 7.00000 0.231793
\(913\) 0 0
\(914\) 4.00000 0.132308
\(915\) −12.0000 −0.396708
\(916\) 16.0000 0.528655
\(917\) −48.0000 −1.58510
\(918\) −7.00000 −0.231034
\(919\) −48.0000 −1.58337 −0.791687 0.610927i \(-0.790797\pi\)
−0.791687 + 0.610927i \(0.790797\pi\)
\(920\) 0 0
\(921\) 34.0000 1.12034
\(922\) −33.0000 −1.08680
\(923\) −45.0000 −1.48119
\(924\) 0 0
\(925\) −5.00000 −0.164399
\(926\) 8.00000 0.262896
\(927\) −3.00000 −0.0985329
\(928\) 7.00000 0.229786
\(929\) −16.0000 −0.524943 −0.262471 0.964940i \(-0.584538\pi\)
−0.262471 + 0.964940i \(0.584538\pi\)
\(930\) −6.00000 −0.196748
\(931\) 14.0000 0.458831
\(932\) 2.00000 0.0655122
\(933\) −8.00000 −0.261908
\(934\) 7.00000 0.229047
\(935\) 0 0
\(936\) −5.00000 −0.163430
\(937\) 18.0000 0.588034 0.294017 0.955800i \(-0.405008\pi\)
0.294017 + 0.955800i \(0.405008\pi\)
\(938\) 6.00000 0.195907
\(939\) −2.00000 −0.0652675
\(940\) −10.0000 −0.326164
\(941\) 33.0000 1.07577 0.537885 0.843018i \(-0.319224\pi\)
0.537885 + 0.843018i \(0.319224\pi\)
\(942\) 11.0000 0.358399
\(943\) 0 0
\(944\) 0 0
\(945\) 3.00000 0.0975900
\(946\) 0 0
\(947\) 3.00000 0.0974869 0.0487435 0.998811i \(-0.484478\pi\)
0.0487435 + 0.998811i \(0.484478\pi\)
\(948\) 10.0000 0.324785
\(949\) 30.0000 0.973841
\(950\) −7.00000 −0.227110
\(951\) 12.0000 0.389127
\(952\) −21.0000 −0.680614
\(953\) 18.0000 0.583077 0.291539 0.956559i \(-0.405833\pi\)
0.291539 + 0.956559i \(0.405833\pi\)
\(954\) 12.0000 0.388514
\(955\) −3.00000 −0.0970777
\(956\) 3.00000 0.0970269
\(957\) 0 0
\(958\) −3.00000 −0.0969256
\(959\) 9.00000 0.290625
\(960\) 1.00000 0.0322749
\(961\) 5.00000 0.161290
\(962\) 25.0000 0.806032
\(963\) 0 0
\(964\) −25.0000 −0.805196
\(965\) 24.0000 0.772587
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) 0 0
\(969\) 49.0000 1.57411
\(970\) −2.00000 −0.0642161
\(971\) 48.0000 1.54039 0.770197 0.637806i \(-0.220158\pi\)
0.770197 + 0.637806i \(0.220158\pi\)
\(972\) 1.00000 0.0320750
\(973\) 15.0000 0.480878
\(974\) −29.0000 −0.929220
\(975\) 5.00000 0.160128
\(976\) −12.0000 −0.384111
\(977\) 42.0000 1.34370 0.671850 0.740688i \(-0.265500\pi\)
0.671850 + 0.740688i \(0.265500\pi\)
\(978\) −4.00000 −0.127906
\(979\) 0 0
\(980\) 2.00000 0.0638877
\(981\) −20.0000 −0.638551
\(982\) 30.0000 0.957338
\(983\) −14.0000 −0.446531 −0.223265 0.974758i \(-0.571672\pi\)
−0.223265 + 0.974758i \(0.571672\pi\)
\(984\) −10.0000 −0.318788
\(985\) −12.0000 −0.382352
\(986\) 49.0000 1.56048
\(987\) −30.0000 −0.954911
\(988\) 35.0000 1.11350
\(989\) 0 0
\(990\) 0 0
\(991\) −34.0000 −1.08005 −0.540023 0.841650i \(-0.681584\pi\)
−0.540023 + 0.841650i \(0.681584\pi\)
\(992\) −6.00000 −0.190500
\(993\) −17.0000 −0.539479
\(994\) 27.0000 0.856388
\(995\) −16.0000 −0.507234
\(996\) −13.0000 −0.411921
\(997\) 23.0000 0.728417 0.364209 0.931317i \(-0.381339\pi\)
0.364209 + 0.931317i \(0.381339\pi\)
\(998\) −33.0000 −1.04460
\(999\) −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.l.1.1 1
11.10 odd 2 3630.2.a.y.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.l.1.1 1 1.1 even 1 trivial
3630.2.a.y.1.1 yes 1 11.10 odd 2