Properties

Label 3630.2.a.c.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

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +7.00000 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -7.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} +2.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -7.00000 q^{26} -1.00000 q^{27} -1.00000 q^{28} +9.00000 q^{29} -1.00000 q^{30} -1.00000 q^{32} -1.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -7.00000 q^{37} +7.00000 q^{38} -7.00000 q^{39} +1.00000 q^{40} +12.0000 q^{41} -1.00000 q^{42} -12.0000 q^{43} -1.00000 q^{45} -2.00000 q^{46} +2.00000 q^{47} -1.00000 q^{48} -6.00000 q^{49} -1.00000 q^{50} -1.00000 q^{51} +7.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} +1.00000 q^{56} +7.00000 q^{57} -9.00000 q^{58} -10.0000 q^{59} +1.00000 q^{60} +2.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} -7.00000 q^{65} -6.00000 q^{67} +1.00000 q^{68} -2.00000 q^{69} -1.00000 q^{70} +5.00000 q^{71} -1.00000 q^{72} -4.00000 q^{73} +7.00000 q^{74} -1.00000 q^{75} -7.00000 q^{76} +7.00000 q^{78} +14.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} -1.00000 q^{83} +1.00000 q^{84} -1.00000 q^{85} +12.0000 q^{86} -9.00000 q^{87} -8.00000 q^{89} +1.00000 q^{90} -7.00000 q^{91} +2.00000 q^{92} -2.00000 q^{94} +7.00000 q^{95} +1.00000 q^{96} +6.00000 q^{98} +O(q^{100})\)

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
\(13\) 7.00000 1.94145 0.970725 0.240192i \(-0.0772105\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 1.00000 0.267261
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) −1.00000 −0.235702
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) −7.00000 −1.37281
\(27\) −1.00000 −0.192450
\(28\) −1.00000 −0.188982
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) −1.00000 −0.182574
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) 1.00000 0.169031
\(36\) 1.00000 0.166667
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 7.00000 1.13555
\(39\) −7.00000 −1.12090
\(40\) 1.00000 0.158114
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) −1.00000 −0.154303
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) −2.00000 −0.294884
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.00000 −0.857143
\(50\) −1.00000 −0.141421
\(51\) −1.00000 −0.140028
\(52\) 7.00000 0.970725
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 7.00000 0.927173
\(58\) −9.00000 −1.18176
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 1.00000 0.129099
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) −7.00000 −0.868243
\(66\) 0 0
\(67\) −6.00000 −0.733017 −0.366508 0.930415i \(-0.619447\pi\)
−0.366508 + 0.930415i \(0.619447\pi\)
\(68\) 1.00000 0.121268
\(69\) −2.00000 −0.240772
\(70\) −1.00000 −0.119523
\(71\) 5.00000 0.593391 0.296695 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) −1.00000 −0.117851
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 7.00000 0.813733
\(75\) −1.00000 −0.115470
\(76\) −7.00000 −0.802955
\(77\) 0 0
\(78\) 7.00000 0.792594
\(79\) 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
\(82\) −12.0000 −1.32518
\(83\) −1.00000 −0.109764 −0.0548821 0.998493i \(-0.517478\pi\)
−0.0548821 + 0.998493i \(0.517478\pi\)
\(84\) 1.00000 0.109109
\(85\) −1.00000 −0.108465
\(86\) 12.0000 1.29399
\(87\) −9.00000 −0.964901
\(88\) 0 0
\(89\) −8.00000 −0.847998 −0.423999 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) 1.00000 0.105409
\(91\) −7.00000 −0.733799
\(92\) 2.00000 0.208514
\(93\) 0 0
\(94\) −2.00000 −0.206284
\(95\) 7.00000 0.718185
\(96\) 1.00000 0.102062
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 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 \(0.231839\pi\)
\(102\) 1.00000 0.0990148
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) −7.00000 −0.686406
\(105\) −1.00000 −0.0975900
\(106\) −6.00000 −0.582772
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 7.00000 0.664411
\(112\) −1.00000 −0.0944911
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −7.00000 −0.655610
\(115\) −2.00000 −0.186501
\(116\) 9.00000 0.835629
\(117\) 7.00000 0.647150
\(118\) 10.0000 0.920575
\(119\) −1.00000 −0.0916698
\(120\) −1.00000 −0.0912871
\(121\) 0 0
\(122\) −2.00000 −0.181071
\(123\) −12.0000 −1.08200
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 1.00000 0.0890871
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.0000 1.05654
\(130\) 7.00000 0.613941
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 7.00000 0.606977
\(134\) 6.00000 0.518321
\(135\) 1.00000 0.0860663
\(136\) −1.00000 −0.0857493
\(137\) −7.00000 −0.598050 −0.299025 0.954245i \(-0.596661\pi\)
−0.299025 + 0.954245i \(0.596661\pi\)
\(138\) 2.00000 0.170251
\(139\) 19.0000 1.61156 0.805779 0.592216i \(-0.201747\pi\)
0.805779 + 0.592216i \(0.201747\pi\)
\(140\) 1.00000 0.0845154
\(141\) −2.00000 −0.168430
\(142\) −5.00000 −0.419591
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −9.00000 −0.747409
\(146\) 4.00000 0.331042
\(147\) 6.00000 0.494872
\(148\) −7.00000 −0.575396
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 1.00000 0.0816497
\(151\) 6.00000 0.488273 0.244137 0.969741i \(-0.421495\pi\)
0.244137 + 0.969741i \(0.421495\pi\)
\(152\) 7.00000 0.567775
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) −7.00000 −0.560449
\(157\) −1.00000 −0.0798087 −0.0399043 0.999204i \(-0.512705\pi\)
−0.0399043 + 0.999204i \(0.512705\pi\)
\(158\) −14.0000 −1.11378
\(159\) −6.00000 −0.475831
\(160\) 1.00000 0.0790569
\(161\) −2.00000 −0.157622
\(162\) −1.00000 −0.0785674
\(163\) 10.0000 0.783260 0.391630 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) 12.0000 0.937043
\(165\) 0 0
\(166\) 1.00000 0.0776151
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 36.0000 2.76923
\(170\) 1.00000 0.0766965
\(171\) −7.00000 −0.535303
\(172\) −12.0000 −0.914991
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 9.00000 0.682288
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) 10.0000 0.751646
\(178\) 8.00000 0.599625
\(179\) −14.0000 −1.04641 −0.523205 0.852207i \(-0.675264\pi\)
−0.523205 + 0.852207i \(0.675264\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 7.00000 0.518875
\(183\) −2.00000 −0.147844
\(184\) −2.00000 −0.147442
\(185\) 7.00000 0.514650
\(186\) 0 0
\(187\) 0 0
\(188\) 2.00000 0.145865
\(189\) 1.00000 0.0727393
\(190\) −7.00000 −0.507833
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −20.0000 −1.43963 −0.719816 0.694165i \(-0.755774\pi\)
−0.719816 + 0.694165i \(0.755774\pi\)
\(194\) 0 0
\(195\) 7.00000 0.501280
\(196\) −6.00000 −0.428571
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 6.00000 0.423207
\(202\) −15.0000 −1.05540
\(203\) −9.00000 −0.631676
\(204\) −1.00000 −0.0700140
\(205\) −12.0000 −0.838116
\(206\) 7.00000 0.487713
\(207\) 2.00000 0.139010
\(208\) 7.00000 0.485363
\(209\) 0 0
\(210\) 1.00000 0.0690066
\(211\) 21.0000 1.44570 0.722850 0.691005i \(-0.242832\pi\)
0.722850 + 0.691005i \(0.242832\pi\)
\(212\) 6.00000 0.412082
\(213\) −5.00000 −0.342594
\(214\) 12.0000 0.820303
\(215\) 12.0000 0.818393
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −4.00000 −0.270914
\(219\) 4.00000 0.270295
\(220\) 0 0
\(221\) 7.00000 0.470871
\(222\) −7.00000 −0.469809
\(223\) 3.00000 0.200895 0.100447 0.994942i \(-0.467973\pi\)
0.100447 + 0.994942i \(0.467973\pi\)
\(224\) 1.00000 0.0668153
\(225\) 1.00000 0.0666667
\(226\) −6.00000 −0.399114
\(227\) 20.0000 1.32745 0.663723 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) 7.00000 0.463586
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 2.00000 0.131876
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) 22.0000 1.44127 0.720634 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) −7.00000 −0.457604
\(235\) −2.00000 −0.130466
\(236\) −10.0000 −0.650945
\(237\) −14.0000 −0.909398
\(238\) 1.00000 0.0648204
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 1.00000 0.0645497
\(241\) −21.0000 −1.35273 −0.676364 0.736567i \(-0.736446\pi\)
−0.676364 + 0.736567i \(0.736446\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 2.00000 0.128037
\(245\) 6.00000 0.383326
\(246\) 12.0000 0.765092
\(247\) −49.0000 −3.11780
\(248\) 0 0
\(249\) 1.00000 0.0633724
\(250\) 1.00000 0.0632456
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 0 0
\(254\) −8.00000 −0.501965
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) −9.00000 −0.561405 −0.280702 0.959795i \(-0.590567\pi\)
−0.280702 + 0.959795i \(0.590567\pi\)
\(258\) −12.0000 −0.747087
\(259\) 7.00000 0.434959
\(260\) −7.00000 −0.434122
\(261\) 9.00000 0.557086
\(262\) −6.00000 −0.370681
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −7.00000 −0.429198
\(267\) 8.00000 0.489592
\(268\) −6.00000 −0.366508
\(269\) 21.0000 1.28039 0.640196 0.768211i \(-0.278853\pi\)
0.640196 + 0.768211i \(0.278853\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 1.00000 0.0606339
\(273\) 7.00000 0.423659
\(274\) 7.00000 0.422885
\(275\) 0 0
\(276\) −2.00000 −0.120386
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) −19.0000 −1.13954
\(279\) 0 0
\(280\) −1.00000 −0.0597614
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 2.00000 0.119098
\(283\) −24.0000 −1.42665 −0.713326 0.700832i \(-0.752812\pi\)
−0.713326 + 0.700832i \(0.752812\pi\)
\(284\) 5.00000 0.296695
\(285\) −7.00000 −0.414644
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) −1.00000 −0.0589256
\(289\) −16.0000 −0.941176
\(290\) 9.00000 0.528498
\(291\) 0 0
\(292\) −4.00000 −0.234082
\(293\) 28.0000 1.63578 0.817889 0.575376i \(-0.195144\pi\)
0.817889 + 0.575376i \(0.195144\pi\)
\(294\) −6.00000 −0.349927
\(295\) 10.0000 0.582223
\(296\) 7.00000 0.406867
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 14.0000 0.809641
\(300\) −1.00000 −0.0577350
\(301\) 12.0000 0.691669
\(302\) −6.00000 −0.345261
\(303\) −15.0000 −0.861727
\(304\) −7.00000 −0.401478
\(305\) −2.00000 −0.114520
\(306\) −1.00000 −0.0571662
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 7.00000 0.396297
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 1.00000 0.0564333
\(315\) 1.00000 0.0563436
\(316\) 14.0000 0.787562
\(317\) −10.0000 −0.561656 −0.280828 0.959758i \(-0.590609\pi\)
−0.280828 + 0.959758i \(0.590609\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 12.0000 0.669775
\(322\) 2.00000 0.111456
\(323\) −7.00000 −0.389490
\(324\) 1.00000 0.0555556
\(325\) 7.00000 0.388290
\(326\) −10.0000 −0.553849
\(327\) −4.00000 −0.221201
\(328\) −12.0000 −0.662589
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) 29.0000 1.59398 0.796992 0.603990i \(-0.206423\pi\)
0.796992 + 0.603990i \(0.206423\pi\)
\(332\) −1.00000 −0.0548821
\(333\) −7.00000 −0.383598
\(334\) −8.00000 −0.437741
\(335\) 6.00000 0.327815
\(336\) 1.00000 0.0545545
\(337\) −20.0000 −1.08947 −0.544735 0.838608i \(-0.683370\pi\)
−0.544735 + 0.838608i \(0.683370\pi\)
\(338\) −36.0000 −1.95814
\(339\) −6.00000 −0.325875
\(340\) −1.00000 −0.0542326
\(341\) 0 0
\(342\) 7.00000 0.378517
\(343\) 13.0000 0.701934
\(344\) 12.0000 0.646997
\(345\) 2.00000 0.107676
\(346\) −6.00000 −0.322562
\(347\) 17.0000 0.912608 0.456304 0.889824i \(-0.349173\pi\)
0.456304 + 0.889824i \(0.349173\pi\)
\(348\) −9.00000 −0.482451
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 1.00000 0.0534522
\(351\) −7.00000 −0.373632
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) −10.0000 −0.531494
\(355\) −5.00000 −0.265372
\(356\) −8.00000 −0.423999
\(357\) 1.00000 0.0529256
\(358\) 14.0000 0.739923
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) 1.00000 0.0527046
\(361\) 30.0000 1.57895
\(362\) −2.00000 −0.105118
\(363\) 0 0
\(364\) −7.00000 −0.366900
\(365\) 4.00000 0.209370
\(366\) 2.00000 0.104542
\(367\) 37.0000 1.93138 0.965692 0.259690i \(-0.0836203\pi\)
0.965692 + 0.259690i \(0.0836203\pi\)
\(368\) 2.00000 0.104257
\(369\) 12.0000 0.624695
\(370\) −7.00000 −0.363913
\(371\) −6.00000 −0.311504
\(372\) 0 0
\(373\) 33.0000 1.70868 0.854338 0.519718i \(-0.173963\pi\)
0.854338 + 0.519718i \(0.173963\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) −2.00000 −0.103142
\(377\) 63.0000 3.24467
\(378\) −1.00000 −0.0514344
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 7.00000 0.359092
\(381\) −8.00000 −0.409852
\(382\) −3.00000 −0.153493
\(383\) −34.0000 −1.73732 −0.868659 0.495410i \(-0.835018\pi\)
−0.868659 + 0.495410i \(0.835018\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 20.0000 1.01797
\(387\) −12.0000 −0.609994
\(388\) 0 0
\(389\) −22.0000 −1.11544 −0.557722 0.830028i \(-0.688325\pi\)
−0.557722 + 0.830028i \(0.688325\pi\)
\(390\) −7.00000 −0.354459
\(391\) 2.00000 0.101144
\(392\) 6.00000 0.303046
\(393\) −6.00000 −0.302660
\(394\) 12.0000 0.604551
\(395\) −14.0000 −0.704416
\(396\) 0 0
\(397\) 1.00000 0.0501886 0.0250943 0.999685i \(-0.492011\pi\)
0.0250943 + 0.999685i \(0.492011\pi\)
\(398\) −24.0000 −1.20301
\(399\) −7.00000 −0.350438
\(400\) 1.00000 0.0500000
\(401\) 32.0000 1.59800 0.799002 0.601329i \(-0.205362\pi\)
0.799002 + 0.601329i \(0.205362\pi\)
\(402\) −6.00000 −0.299253
\(403\) 0 0
\(404\) 15.0000 0.746278
\(405\) −1.00000 −0.0496904
\(406\) 9.00000 0.446663
\(407\) 0 0
\(408\) 1.00000 0.0495074
\(409\) −26.0000 −1.28562 −0.642809 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 12.0000 0.592638
\(411\) 7.00000 0.345285
\(412\) −7.00000 −0.344865
\(413\) 10.0000 0.492068
\(414\) −2.00000 −0.0982946
\(415\) 1.00000 0.0490881
\(416\) −7.00000 −0.343203
\(417\) −19.0000 −0.930434
\(418\) 0 0
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −32.0000 −1.55958 −0.779792 0.626038i \(-0.784675\pi\)
−0.779792 + 0.626038i \(0.784675\pi\)
\(422\) −21.0000 −1.02226
\(423\) 2.00000 0.0972433
\(424\) −6.00000 −0.291386
\(425\) 1.00000 0.0485071
\(426\) 5.00000 0.242251
\(427\) −2.00000 −0.0967868
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) −12.0000 −0.578691
\(431\) −33.0000 −1.58955 −0.794777 0.606902i \(-0.792412\pi\)
−0.794777 + 0.606902i \(0.792412\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 28.0000 1.34559 0.672797 0.739827i \(-0.265093\pi\)
0.672797 + 0.739827i \(0.265093\pi\)
\(434\) 0 0
\(435\) 9.00000 0.431517
\(436\) 4.00000 0.191565
\(437\) −14.0000 −0.669711
\(438\) −4.00000 −0.191127
\(439\) 18.0000 0.859093 0.429547 0.903045i \(-0.358673\pi\)
0.429547 + 0.903045i \(0.358673\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −7.00000 −0.332956
\(443\) 39.0000 1.85295 0.926473 0.376361i \(-0.122825\pi\)
0.926473 + 0.376361i \(0.122825\pi\)
\(444\) 7.00000 0.332205
\(445\) 8.00000 0.379236
\(446\) −3.00000 −0.142054
\(447\) −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
\(452\) 6.00000 0.282216
\(453\) −6.00000 −0.281905
\(454\) −20.0000 −0.938647
\(455\) 7.00000 0.328165
\(456\) −7.00000 −0.327805
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) 8.00000 0.373815
\(459\) −1.00000 −0.0466760
\(460\) −2.00000 −0.0932505
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) 0 0
\(463\) 36.0000 1.67306 0.836531 0.547920i \(-0.184580\pi\)
0.836531 + 0.547920i \(0.184580\pi\)
\(464\) 9.00000 0.417815
\(465\) 0 0
\(466\) −22.0000 −1.01913
\(467\) −11.0000 −0.509019 −0.254510 0.967070i \(-0.581914\pi\)
−0.254510 + 0.967070i \(0.581914\pi\)
\(468\) 7.00000 0.323575
\(469\) 6.00000 0.277054
\(470\) 2.00000 0.0922531
\(471\) 1.00000 0.0460776
\(472\) 10.0000 0.460287
\(473\) 0 0
\(474\) 14.0000 0.643041
\(475\) −7.00000 −0.321182
\(476\) −1.00000 −0.0458349
\(477\) 6.00000 0.274721
\(478\) −9.00000 −0.411650
\(479\) −3.00000 −0.137073 −0.0685367 0.997649i \(-0.521833\pi\)
−0.0685367 + 0.997649i \(0.521833\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −49.0000 −2.23421
\(482\) 21.0000 0.956524
\(483\) 2.00000 0.0910032
\(484\) 0 0
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 25.0000 1.13286 0.566429 0.824110i \(-0.308325\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) −2.00000 −0.0905357
\(489\) −10.0000 −0.452216
\(490\) −6.00000 −0.271052
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) −12.0000 −0.541002
\(493\) 9.00000 0.405340
\(494\) 49.0000 2.20461
\(495\) 0 0
\(496\) 0 0
\(497\) −5.00000 −0.224281
\(498\) −1.00000 −0.0448111
\(499\) 3.00000 0.134298 0.0671492 0.997743i \(-0.478610\pi\)
0.0671492 + 0.997743i \(0.478610\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −8.00000 −0.357414
\(502\) 12.0000 0.535586
\(503\) 2.00000 0.0891756 0.0445878 0.999005i \(-0.485803\pi\)
0.0445878 + 0.999005i \(0.485803\pi\)
\(504\) 1.00000 0.0445435
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) −36.0000 −1.59882
\(508\) 8.00000 0.354943
\(509\) −14.0000 −0.620539 −0.310270 0.950649i \(-0.600419\pi\)
−0.310270 + 0.950649i \(0.600419\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 4.00000 0.176950
\(512\) −1.00000 −0.0441942
\(513\) 7.00000 0.309058
\(514\) 9.00000 0.396973
\(515\) 7.00000 0.308457
\(516\) 12.0000 0.528271
\(517\) 0 0
\(518\) −7.00000 −0.307562
\(519\) −6.00000 −0.263371
\(520\) 7.00000 0.306970
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −9.00000 −0.393919
\(523\) −14.0000 −0.612177 −0.306089 0.952003i \(-0.599020\pi\)
−0.306089 + 0.952003i \(0.599020\pi\)
\(524\) 6.00000 0.262111
\(525\) 1.00000 0.0436436
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 6.00000 0.260623
\(531\) −10.0000 −0.433963
\(532\) 7.00000 0.303488
\(533\) 84.0000 3.63844
\(534\) −8.00000 −0.346194
\(535\) 12.0000 0.518805
\(536\) 6.00000 0.259161
\(537\) 14.0000 0.604145
\(538\) −21.0000 −0.905374
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) −2.00000 −0.0859074
\(543\) −2.00000 −0.0858282
\(544\) −1.00000 −0.0428746
\(545\) −4.00000 −0.171341
\(546\) −7.00000 −0.299572
\(547\) −10.0000 −0.427569 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(548\) −7.00000 −0.299025
\(549\) 2.00000 0.0853579
\(550\) 0 0
\(551\) −63.0000 −2.68389
\(552\) 2.00000 0.0851257
\(553\) −14.0000 −0.595341
\(554\) −6.00000 −0.254916
\(555\) −7.00000 −0.297133
\(556\) 19.0000 0.805779
\(557\) −42.0000 −1.77960 −0.889799 0.456354i \(-0.849155\pi\)
−0.889799 + 0.456354i \(0.849155\pi\)
\(558\) 0 0
\(559\) −84.0000 −3.55282
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) −22.0000 −0.928014
\(563\) 37.0000 1.55936 0.779682 0.626176i \(-0.215381\pi\)
0.779682 + 0.626176i \(0.215381\pi\)
\(564\) −2.00000 −0.0842152
\(565\) −6.00000 −0.252422
\(566\) 24.0000 1.00880
\(567\) −1.00000 −0.0419961
\(568\) −5.00000 −0.209795
\(569\) −32.0000 −1.34151 −0.670755 0.741679i \(-0.734030\pi\)
−0.670755 + 0.741679i \(0.734030\pi\)
\(570\) 7.00000 0.293198
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) 12.0000 0.500870
\(575\) 2.00000 0.0834058
\(576\) 1.00000 0.0416667
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 16.0000 0.665512
\(579\) 20.0000 0.831172
\(580\) −9.00000 −0.373705
\(581\) 1.00000 0.0414870
\(582\) 0 0
\(583\) 0 0
\(584\) 4.00000 0.165521
\(585\) −7.00000 −0.289414
\(586\) −28.0000 −1.15667
\(587\) −21.0000 −0.866763 −0.433381 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) 6.00000 0.247436
\(589\) 0 0
\(590\) −10.0000 −0.411693
\(591\) 12.0000 0.493614
\(592\) −7.00000 −0.287698
\(593\) −14.0000 −0.574911 −0.287456 0.957794i \(-0.592809\pi\)
−0.287456 + 0.957794i \(0.592809\pi\)
\(594\) 0 0
\(595\) 1.00000 0.0409960
\(596\) 6.00000 0.245770
\(597\) −24.0000 −0.982255
\(598\) −14.0000 −0.572503
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 1.00000 0.0408248
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) −12.0000 −0.489083
\(603\) −6.00000 −0.244339
\(604\) 6.00000 0.244137
\(605\) 0 0
\(606\) 15.0000 0.609333
\(607\) −23.0000 −0.933541 −0.466771 0.884378i \(-0.654583\pi\)
−0.466771 + 0.884378i \(0.654583\pi\)
\(608\) 7.00000 0.283887
\(609\) 9.00000 0.364698
\(610\) 2.00000 0.0809776
\(611\) 14.0000 0.566379
\(612\) 1.00000 0.0404226
\(613\) 23.0000 0.928961 0.464481 0.885583i \(-0.346241\pi\)
0.464481 + 0.885583i \(0.346241\pi\)
\(614\) −4.00000 −0.161427
\(615\) 12.0000 0.483887
\(616\) 0 0
\(617\) −39.0000 −1.57008 −0.785040 0.619445i \(-0.787358\pi\)
−0.785040 + 0.619445i \(0.787358\pi\)
\(618\) −7.00000 −0.281581
\(619\) −9.00000 −0.361741 −0.180870 0.983507i \(-0.557891\pi\)
−0.180870 + 0.983507i \(0.557891\pi\)
\(620\) 0 0
\(621\) −2.00000 −0.0802572
\(622\) −24.0000 −0.962312
\(623\) 8.00000 0.320513
\(624\) −7.00000 −0.280224
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) −1.00000 −0.0399043
\(629\) −7.00000 −0.279108
\(630\) −1.00000 −0.0398410
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) −14.0000 −0.556890
\(633\) −21.0000 −0.834675
\(634\) 10.0000 0.397151
\(635\) −8.00000 −0.317470
\(636\) −6.00000 −0.237915
\(637\) −42.0000 −1.66410
\(638\) 0 0
\(639\) 5.00000 0.197797
\(640\) 1.00000 0.0395285
\(641\) −34.0000 −1.34292 −0.671460 0.741041i \(-0.734332\pi\)
−0.671460 + 0.741041i \(0.734332\pi\)
\(642\) −12.0000 −0.473602
\(643\) 8.00000 0.315489 0.157745 0.987480i \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(644\) −2.00000 −0.0788110
\(645\) −12.0000 −0.472500
\(646\) 7.00000 0.275411
\(647\) 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
\(650\) −7.00000 −0.274563
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) 20.0000 0.782660 0.391330 0.920250i \(-0.372015\pi\)
0.391330 + 0.920250i \(0.372015\pi\)
\(654\) 4.00000 0.156412
\(655\) −6.00000 −0.234439
\(656\) 12.0000 0.468521
\(657\) −4.00000 −0.156055
\(658\) 2.00000 0.0779681
\(659\) 14.0000 0.545363 0.272681 0.962104i \(-0.412090\pi\)
0.272681 + 0.962104i \(0.412090\pi\)
\(660\) 0 0
\(661\) 20.0000 0.777910 0.388955 0.921257i \(-0.372836\pi\)
0.388955 + 0.921257i \(0.372836\pi\)
\(662\) −29.0000 −1.12712
\(663\) −7.00000 −0.271857
\(664\) 1.00000 0.0388075
\(665\) −7.00000 −0.271448
\(666\) 7.00000 0.271244
\(667\) 18.0000 0.696963
\(668\) 8.00000 0.309529
\(669\) −3.00000 −0.115987
\(670\) −6.00000 −0.231800
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) −32.0000 −1.23351 −0.616755 0.787155i \(-0.711553\pi\)
−0.616755 + 0.787155i \(0.711553\pi\)
\(674\) 20.0000 0.770371
\(675\) −1.00000 −0.0384900
\(676\) 36.0000 1.38462
\(677\) −12.0000 −0.461197 −0.230599 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 6.00000 0.230429
\(679\) 0 0
\(680\) 1.00000 0.0383482
\(681\) −20.0000 −0.766402
\(682\) 0 0
\(683\) −19.0000 −0.727015 −0.363507 0.931591i \(-0.618421\pi\)
−0.363507 + 0.931591i \(0.618421\pi\)
\(684\) −7.00000 −0.267652
\(685\) 7.00000 0.267456
\(686\) −13.0000 −0.496342
\(687\) 8.00000 0.305219
\(688\) −12.0000 −0.457496
\(689\) 42.0000 1.60007
\(690\) −2.00000 −0.0761387
\(691\) 11.0000 0.418460 0.209230 0.977866i \(-0.432904\pi\)
0.209230 + 0.977866i \(0.432904\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −17.0000 −0.645311
\(695\) −19.0000 −0.720711
\(696\) 9.00000 0.341144
\(697\) 12.0000 0.454532
\(698\) −10.0000 −0.378506
\(699\) −22.0000 −0.832116
\(700\) −1.00000 −0.0377964
\(701\) 45.0000 1.69963 0.849813 0.527084i \(-0.176715\pi\)
0.849813 + 0.527084i \(0.176715\pi\)
\(702\) 7.00000 0.264198
\(703\) 49.0000 1.84807
\(704\) 0 0
\(705\) 2.00000 0.0753244
\(706\) −18.0000 −0.677439
\(707\) −15.0000 −0.564133
\(708\) 10.0000 0.375823
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) 5.00000 0.187647
\(711\) 14.0000 0.525041
\(712\) 8.00000 0.299813
\(713\) 0 0
\(714\) −1.00000 −0.0374241
\(715\) 0 0
\(716\) −14.0000 −0.523205
\(717\) −9.00000 −0.336111
\(718\) −16.0000 −0.597115
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 7.00000 0.260694
\(722\) −30.0000 −1.11648
\(723\) 21.0000 0.780998
\(724\) 2.00000 0.0743294
\(725\) 9.00000 0.334252
\(726\) 0 0
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) 7.00000 0.259437
\(729\) 1.00000 0.0370370
\(730\) −4.00000 −0.148047
\(731\) −12.0000 −0.443836
\(732\) −2.00000 −0.0739221
\(733\) −10.0000 −0.369358 −0.184679 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) −37.0000 −1.36569
\(735\) −6.00000 −0.221313
\(736\) −2.00000 −0.0737210
\(737\) 0 0
\(738\) −12.0000 −0.441726
\(739\) −21.0000 −0.772497 −0.386249 0.922395i \(-0.626229\pi\)
−0.386249 + 0.922395i \(0.626229\pi\)
\(740\) 7.00000 0.257325
\(741\) 49.0000 1.80006
\(742\) 6.00000 0.220267
\(743\) −10.0000 −0.366864 −0.183432 0.983032i \(-0.558721\pi\)
−0.183432 + 0.983032i \(0.558721\pi\)
\(744\) 0 0
\(745\) −6.00000 −0.219823
\(746\) −33.0000 −1.20822
\(747\) −1.00000 −0.0365881
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) −1.00000 −0.0365148
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 2.00000 0.0729325
\(753\) 12.0000 0.437304
\(754\) −63.0000 −2.29432
\(755\) −6.00000 −0.218362
\(756\) 1.00000 0.0363696
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) −11.0000 −0.399538
\(759\) 0 0
\(760\) −7.00000 −0.253917
\(761\) 44.0000 1.59500 0.797499 0.603320i \(-0.206156\pi\)
0.797499 + 0.603320i \(0.206156\pi\)
\(762\) 8.00000 0.289809
\(763\) −4.00000 −0.144810
\(764\) 3.00000 0.108536
\(765\) −1.00000 −0.0361551
\(766\) 34.0000 1.22847
\(767\) −70.0000 −2.52755
\(768\) −1.00000 −0.0360844
\(769\) 49.0000 1.76699 0.883493 0.468445i \(-0.155186\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 0 0
\(771\) 9.00000 0.324127
\(772\) −20.0000 −0.719816
\(773\) −14.0000 −0.503545 −0.251773 0.967786i \(-0.581013\pi\)
−0.251773 + 0.967786i \(0.581013\pi\)
\(774\) 12.0000 0.431331
\(775\) 0 0
\(776\) 0 0
\(777\) −7.00000 −0.251124
\(778\) 22.0000 0.788738
\(779\) −84.0000 −3.00961
\(780\) 7.00000 0.250640
\(781\) 0 0
\(782\) −2.00000 −0.0715199
\(783\) −9.00000 −0.321634
\(784\) −6.00000 −0.214286
\(785\) 1.00000 0.0356915
\(786\) 6.00000 0.214013
\(787\) 6.00000 0.213877 0.106938 0.994266i \(-0.465895\pi\)
0.106938 + 0.994266i \(0.465895\pi\)
\(788\) −12.0000 −0.427482
\(789\) 0 0
\(790\) 14.0000 0.498098
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) 14.0000 0.497155
\(794\) −1.00000 −0.0354887
\(795\) 6.00000 0.212798
\(796\) 24.0000 0.850657
\(797\) −30.0000 −1.06265 −0.531327 0.847167i \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) 7.00000 0.247797
\(799\) 2.00000 0.0707549
\(800\) −1.00000 −0.0353553
\(801\) −8.00000 −0.282666
\(802\) −32.0000 −1.12996
\(803\) 0 0
\(804\) 6.00000 0.211604
\(805\) 2.00000 0.0704907
\(806\) 0 0
\(807\) −21.0000 −0.739235
\(808\) −15.0000 −0.527698
\(809\) 28.0000 0.984428 0.492214 0.870474i \(-0.336188\pi\)
0.492214 + 0.870474i \(0.336188\pi\)
\(810\) 1.00000 0.0351364
\(811\) −43.0000 −1.50993 −0.754967 0.655763i \(-0.772347\pi\)
−0.754967 + 0.655763i \(0.772347\pi\)
\(812\) −9.00000 −0.315838
\(813\) −2.00000 −0.0701431
\(814\) 0 0
\(815\) −10.0000 −0.350285
\(816\) −1.00000 −0.0350070
\(817\) 84.0000 2.93879
\(818\) 26.0000 0.909069
\(819\) −7.00000 −0.244600
\(820\) −12.0000 −0.419058
\(821\) −22.0000 −0.767805 −0.383903 0.923374i \(-0.625420\pi\)
−0.383903 + 0.923374i \(0.625420\pi\)
\(822\) −7.00000 −0.244153
\(823\) 23.0000 0.801730 0.400865 0.916137i \(-0.368710\pi\)
0.400865 + 0.916137i \(0.368710\pi\)
\(824\) 7.00000 0.243857
\(825\) 0 0
\(826\) −10.0000 −0.347945
\(827\) −15.0000 −0.521601 −0.260801 0.965393i \(-0.583986\pi\)
−0.260801 + 0.965393i \(0.583986\pi\)
\(828\) 2.00000 0.0695048
\(829\) −26.0000 −0.903017 −0.451509 0.892267i \(-0.649114\pi\)
−0.451509 + 0.892267i \(0.649114\pi\)
\(830\) −1.00000 −0.0347105
\(831\) −6.00000 −0.208138
\(832\) 7.00000 0.242681
\(833\) −6.00000 −0.207888
\(834\) 19.0000 0.657916
\(835\) −8.00000 −0.276851
\(836\) 0 0
\(837\) 0 0
\(838\) −26.0000 −0.898155
\(839\) −39.0000 −1.34643 −0.673215 0.739447i \(-0.735087\pi\)
−0.673215 + 0.739447i \(0.735087\pi\)
\(840\) 1.00000 0.0345033
\(841\) 52.0000 1.79310
\(842\) 32.0000 1.10279
\(843\) −22.0000 −0.757720
\(844\) 21.0000 0.722850
\(845\) −36.0000 −1.23844
\(846\) −2.00000 −0.0687614
\(847\) 0 0
\(848\) 6.00000 0.206041
\(849\) 24.0000 0.823678
\(850\) −1.00000 −0.0342997
\(851\) −14.0000 −0.479914
\(852\) −5.00000 −0.171297
\(853\) 39.0000 1.33533 0.667667 0.744460i \(-0.267293\pi\)
0.667667 + 0.744460i \(0.267293\pi\)
\(854\) 2.00000 0.0684386
\(855\) 7.00000 0.239395
\(856\) 12.0000 0.410152
\(857\) −31.0000 −1.05894 −0.529470 0.848329i \(-0.677609\pi\)
−0.529470 + 0.848329i \(0.677609\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 12.0000 0.409197
\(861\) 12.0000 0.408959
\(862\) 33.0000 1.12398
\(863\) 30.0000 1.02121 0.510606 0.859815i \(-0.329421\pi\)
0.510606 + 0.859815i \(0.329421\pi\)
\(864\) 1.00000 0.0340207
\(865\) −6.00000 −0.204006
\(866\) −28.0000 −0.951479
\(867\) 16.0000 0.543388
\(868\) 0 0
\(869\) 0 0
\(870\) −9.00000 −0.305129
\(871\) −42.0000 −1.42312
\(872\) −4.00000 −0.135457
\(873\) 0 0
\(874\) 14.0000 0.473557
\(875\) 1.00000 0.0338062
\(876\) 4.00000 0.135147
\(877\) 5.00000 0.168838 0.0844190 0.996430i \(-0.473097\pi\)
0.0844190 + 0.996430i \(0.473097\pi\)
\(878\) −18.0000 −0.607471
\(879\) −28.0000 −0.944417
\(880\) 0 0
\(881\) 12.0000 0.404290 0.202145 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) 6.00000 0.202031
\(883\) −16.0000 −0.538443 −0.269221 0.963078i \(-0.586766\pi\)
−0.269221 + 0.963078i \(0.586766\pi\)
\(884\) 7.00000 0.235435
\(885\) −10.0000 −0.336146
\(886\) −39.0000 −1.31023
\(887\) 12.0000 0.402921 0.201460 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) −7.00000 −0.234905
\(889\) −8.00000 −0.268311
\(890\) −8.00000 −0.268161
\(891\) 0 0
\(892\) 3.00000 0.100447
\(893\) −14.0000 −0.468492
\(894\) 6.00000 0.200670
\(895\) 14.0000 0.467968
\(896\) 1.00000 0.0334077
\(897\) −14.0000 −0.467446
\(898\) −30.0000 −1.00111
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 6.00000 0.199889
\(902\) 0 0
\(903\) −12.0000 −0.399335
\(904\) −6.00000 −0.199557
\(905\) −2.00000 −0.0664822
\(906\) 6.00000 0.199337
\(907\) −22.0000 −0.730498 −0.365249 0.930910i \(-0.619016\pi\)
−0.365249 + 0.930910i \(0.619016\pi\)
\(908\) 20.0000 0.663723
\(909\) 15.0000 0.497519
\(910\) −7.00000 −0.232048
\(911\) 21.0000 0.695761 0.347881 0.937539i \(-0.386901\pi\)
0.347881 + 0.937539i \(0.386901\pi\)
\(912\) 7.00000 0.231793
\(913\) 0 0
\(914\) −2.00000 −0.0661541
\(915\) 2.00000 0.0661180
\(916\) −8.00000 −0.264327
\(917\) −6.00000 −0.198137
\(918\) 1.00000 0.0330049
\(919\) −30.0000 −0.989609 −0.494804 0.869004i \(-0.664760\pi\)
−0.494804 + 0.869004i \(0.664760\pi\)
\(920\) 2.00000 0.0659380
\(921\) −4.00000 −0.131804
\(922\) −21.0000 −0.691598
\(923\) 35.0000 1.15204
\(924\) 0 0
\(925\) −7.00000 −0.230159
\(926\) −36.0000 −1.18303
\(927\) −7.00000 −0.229910
\(928\) −9.00000 −0.295439
\(929\) 42.0000 1.37798 0.688988 0.724773i \(-0.258055\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(930\) 0 0
\(931\) 42.0000 1.37649
\(932\) 22.0000 0.720634
\(933\) −24.0000 −0.785725
\(934\) 11.0000 0.359931
\(935\) 0 0
\(936\) −7.00000 −0.228802
\(937\) 22.0000 0.718709 0.359354 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) −6.00000 −0.195907
\(939\) 0 0
\(940\) −2.00000 −0.0652328
\(941\) −7.00000 −0.228193 −0.114097 0.993470i \(-0.536397\pi\)
−0.114097 + 0.993470i \(0.536397\pi\)
\(942\) −1.00000 −0.0325818
\(943\) 24.0000 0.781548
\(944\) −10.0000 −0.325472
\(945\) −1.00000 −0.0325300
\(946\) 0 0
\(947\) −61.0000 −1.98223 −0.991117 0.132994i \(-0.957541\pi\)
−0.991117 + 0.132994i \(0.957541\pi\)
\(948\) −14.0000 −0.454699
\(949\) −28.0000 −0.908918
\(950\) 7.00000 0.227110
\(951\) 10.0000 0.324272
\(952\) 1.00000 0.0324102
\(953\) −54.0000 −1.74923 −0.874616 0.484817i \(-0.838886\pi\)
−0.874616 + 0.484817i \(0.838886\pi\)
\(954\) −6.00000 −0.194257
\(955\) −3.00000 −0.0970777
\(956\) 9.00000 0.291081
\(957\) 0 0
\(958\) 3.00000 0.0969256
\(959\) 7.00000 0.226042
\(960\) 1.00000 0.0322749
\(961\) −31.0000 −1.00000
\(962\) 49.0000 1.57982
\(963\) −12.0000 −0.386695
\(964\) −21.0000 −0.676364
\(965\) 20.0000 0.643823
\(966\) −2.00000 −0.0643489
\(967\) −48.0000 −1.54358 −0.771788 0.635880i \(-0.780637\pi\)
−0.771788 + 0.635880i \(0.780637\pi\)
\(968\) 0 0
\(969\) 7.00000 0.224872
\(970\) 0 0
\(971\) 32.0000 1.02693 0.513464 0.858111i \(-0.328362\pi\)
0.513464 + 0.858111i \(0.328362\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −19.0000 −0.609112
\(974\) −25.0000 −0.801052
\(975\) −7.00000 −0.224179
\(976\) 2.00000 0.0640184
\(977\) −2.00000 −0.0639857 −0.0319928 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) 10.0000 0.319765
\(979\) 0 0
\(980\) 6.00000 0.191663
\(981\) 4.00000 0.127710
\(982\) 36.0000 1.14881
\(983\) 16.0000 0.510321 0.255160 0.966899i \(-0.417872\pi\)
0.255160 + 0.966899i \(0.417872\pi\)
\(984\) 12.0000 0.382546
\(985\) 12.0000 0.382352
\(986\) −9.00000 −0.286618
\(987\) 2.00000 0.0636607
\(988\) −49.0000 −1.55890
\(989\) −24.0000 −0.763156
\(990\) 0 0
\(991\) −6.00000 −0.190596 −0.0952981 0.995449i \(-0.530380\pi\)
−0.0952981 + 0.995449i \(0.530380\pi\)
\(992\) 0 0
\(993\) −29.0000 −0.920287
\(994\) 5.00000 0.158590
\(995\) −24.0000 −0.760851
\(996\) 1.00000 0.0316862
\(997\) −31.0000 −0.981780 −0.490890 0.871222i \(-0.663328\pi\)
−0.490890 + 0.871222i \(0.663328\pi\)
\(998\) −3.00000 −0.0949633
\(999\) 7.00000 0.221470
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.c.1.1 1
11.10 odd 2 3630.2.a.o.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.c.1.1 1 1.1 even 1 trivial
3630.2.a.o.1.1 yes 1 11.10 odd 2