Properties

Label 7350.2.a.bt.1.1
Level 7350
Weight 2
Character 7350.1
Self dual yes
Analytic conductor 58.690
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7350.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.6900454856\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1050)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7350.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} +1.00000 q^{16} +5.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -2.00000 q^{22} -5.00000 q^{23} -1.00000 q^{24} +4.00000 q^{26} -1.00000 q^{27} -6.00000 q^{29} -11.0000 q^{31} +1.00000 q^{32} +2.00000 q^{33} +5.00000 q^{34} +1.00000 q^{36} -8.00000 q^{37} -4.00000 q^{38} -4.00000 q^{39} +5.00000 q^{41} -2.00000 q^{44} -5.00000 q^{46} +1.00000 q^{47} -1.00000 q^{48} -5.00000 q^{51} +4.00000 q^{52} -12.0000 q^{53} -1.00000 q^{54} +4.00000 q^{57} -6.00000 q^{58} -2.00000 q^{59} +10.0000 q^{61} -11.0000 q^{62} +1.00000 q^{64} +2.00000 q^{66} +5.00000 q^{68} +5.00000 q^{69} -1.00000 q^{71} +1.00000 q^{72} -2.00000 q^{73} -8.00000 q^{74} -4.00000 q^{76} -4.00000 q^{78} +9.00000 q^{79} +1.00000 q^{81} +5.00000 q^{82} -6.00000 q^{83} +6.00000 q^{87} -2.00000 q^{88} +11.0000 q^{89} -5.00000 q^{92} +11.0000 q^{93} +1.00000 q^{94} -1.00000 q^{96} +1.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) −1.00000 −0.288675
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.00000 1.21268 0.606339 0.795206i \(-0.292637\pi\)
0.606339 + 0.795206i \(0.292637\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) −5.00000 −1.04257 −0.521286 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) 4.00000 0.784465
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −11.0000 −1.97566 −0.987829 0.155543i \(-0.950287\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.00000 0.348155
\(34\) 5.00000 0.857493
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) −4.00000 −0.648886
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) −5.00000 −0.737210
\(47\) 1.00000 0.145865 0.0729325 0.997337i \(-0.476764\pi\)
0.0729325 + 0.997337i \(0.476764\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 0 0
\(51\) −5.00000 −0.700140
\(52\) 4.00000 0.554700
\(53\) −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
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) −6.00000 −0.787839
\(59\) −2.00000 −0.260378 −0.130189 0.991489i \(-0.541558\pi\)
−0.130189 + 0.991489i \(0.541558\pi\)
\(60\) 0 0
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) −11.0000 −1.39700
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 2.00000 0.246183
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 5.00000 0.606339
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) −1.00000 −0.118678 −0.0593391 0.998238i \(-0.518899\pi\)
−0.0593391 + 0.998238i \(0.518899\pi\)
\(72\) 1.00000 0.117851
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) 9.00000 1.01258 0.506290 0.862364i \(-0.331017\pi\)
0.506290 + 0.862364i \(0.331017\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 5.00000 0.552158
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 6.00000 0.643268
\(88\) −2.00000 −0.213201
\(89\) 11.0000 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.00000 −0.521286
\(93\) 11.0000 1.14065
\(94\) 1.00000 0.103142
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 1.00000 0.101535 0.0507673 0.998711i \(-0.483833\pi\)
0.0507673 + 0.998711i \(0.483833\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) −5.00000 −0.495074
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) −2.00000 −0.193347 −0.0966736 0.995316i \(-0.530820\pi\)
−0.0966736 + 0.995316i \(0.530820\pi\)
\(108\) −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
\(111\) 8.00000 0.759326
\(112\) 0 0
\(113\) −5.00000 −0.470360 −0.235180 0.971952i \(-0.575568\pi\)
−0.235180 + 0.971952i \(0.575568\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 4.00000 0.369800
\(118\) −2.00000 −0.184115
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 10.0000 0.905357
\(123\) −5.00000 −0.450835
\(124\) −11.0000 −0.987829
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 2.00000 0.174078
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 5.00000 0.428746
\(137\) −23.0000 −1.96502 −0.982511 0.186203i \(-0.940382\pi\)
−0.982511 + 0.186203i \(0.940382\pi\)
\(138\) 5.00000 0.425628
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 0 0
\(141\) −1.00000 −0.0842152
\(142\) −1.00000 −0.0839181
\(143\) −8.00000 −0.668994
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) −8.00000 −0.657596
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) −4.00000 −0.324443
\(153\) 5.00000 0.404226
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 9.00000 0.716002
\(159\) 12.0000 0.951662
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −24.0000 −1.87983 −0.939913 0.341415i \(-0.889094\pi\)
−0.939913 + 0.341415i \(0.889094\pi\)
\(164\) 5.00000 0.390434
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) −16.0000 −1.23812 −0.619059 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 0 0
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) 2.00000 0.150329
\(178\) 11.0000 0.824485
\(179\) 22.0000 1.64436 0.822179 0.569230i \(-0.192758\pi\)
0.822179 + 0.569230i \(0.192758\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) −10.0000 −0.739221
\(184\) −5.00000 −0.368605
\(185\) 0 0
\(186\) 11.0000 0.806559
\(187\) −10.0000 −0.731272
\(188\) 1.00000 0.0729325
\(189\) 0 0
\(190\) 0 0
\(191\) −25.0000 −1.80894 −0.904468 0.426541i \(-0.859732\pi\)
−0.904468 + 0.426541i \(0.859732\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −11.0000 −0.791797 −0.395899 0.918294i \(-0.629567\pi\)
−0.395899 + 0.918294i \(0.629567\pi\)
\(194\) 1.00000 0.0717958
\(195\) 0 0
\(196\) 0 0
\(197\) 24.0000 1.70993 0.854965 0.518686i \(-0.173579\pi\)
0.854965 + 0.518686i \(0.173579\pi\)
\(198\) −2.00000 −0.142134
\(199\) 5.00000 0.354441 0.177220 0.984171i \(-0.443289\pi\)
0.177220 + 0.984171i \(0.443289\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 12.0000 0.844317
\(203\) 0 0
\(204\) −5.00000 −0.350070
\(205\) 0 0
\(206\) −13.0000 −0.905753
\(207\) −5.00000 −0.347524
\(208\) 4.00000 0.277350
\(209\) 8.00000 0.553372
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −12.0000 −0.824163
\(213\) 1.00000 0.0685189
\(214\) −2.00000 −0.136717
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 4.00000 0.270914
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 20.0000 1.34535
\(222\) 8.00000 0.536925
\(223\) −21.0000 −1.40626 −0.703132 0.711059i \(-0.748216\pi\)
−0.703132 + 0.711059i \(0.748216\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −5.00000 −0.332595
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 4.00000 0.264906
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 4.00000 0.261488
\(235\) 0 0
\(236\) −2.00000 −0.130189
\(237\) −9.00000 −0.584613
\(238\) 0 0
\(239\) 11.0000 0.711531 0.355765 0.934575i \(-0.384220\pi\)
0.355765 + 0.934575i \(0.384220\pi\)
\(240\) 0 0
\(241\) −6.00000 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) −7.00000 −0.449977
\(243\) −1.00000 −0.0641500
\(244\) 10.0000 0.640184
\(245\) 0 0
\(246\) −5.00000 −0.318788
\(247\) −16.0000 −1.01806
\(248\) −11.0000 −0.698501
\(249\) 6.00000 0.380235
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) 10.0000 0.628695
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 6.00000 0.370681
\(263\) 21.0000 1.29492 0.647458 0.762101i \(-0.275832\pi\)
0.647458 + 0.762101i \(0.275832\pi\)
\(264\) 2.00000 0.123091
\(265\) 0 0
\(266\) 0 0
\(267\) −11.0000 −0.673189
\(268\) 0 0
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) −9.00000 −0.546711 −0.273356 0.961913i \(-0.588134\pi\)
−0.273356 + 0.961913i \(0.588134\pi\)
\(272\) 5.00000 0.303170
\(273\) 0 0
\(274\) −23.0000 −1.38948
\(275\) 0 0
\(276\) 5.00000 0.300965
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 2.00000 0.119952
\(279\) −11.0000 −0.658553
\(280\) 0 0
\(281\) −29.0000 −1.72999 −0.864997 0.501776i \(-0.832680\pi\)
−0.864997 + 0.501776i \(0.832680\pi\)
\(282\) −1.00000 −0.0595491
\(283\) 26.0000 1.54554 0.772770 0.634686i \(-0.218871\pi\)
0.772770 + 0.634686i \(0.218871\pi\)
\(284\) −1.00000 −0.0593391
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) −1.00000 −0.0586210
\(292\) −2.00000 −0.117041
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −8.00000 −0.464991
\(297\) 2.00000 0.116052
\(298\) 18.0000 1.04271
\(299\) −20.0000 −1.15663
\(300\) 0 0
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) −12.0000 −0.689382
\(304\) −4.00000 −0.229416
\(305\) 0 0
\(306\) 5.00000 0.285831
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 13.0000 0.739544
\(310\) 0 0
\(311\) 29.0000 1.64444 0.822220 0.569170i \(-0.192736\pi\)
0.822220 + 0.569170i \(0.192736\pi\)
\(312\) −4.00000 −0.226455
\(313\) 1.00000 0.0565233 0.0282617 0.999601i \(-0.491003\pi\)
0.0282617 + 0.999601i \(0.491003\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 9.00000 0.506290
\(317\) −4.00000 −0.224662 −0.112331 0.993671i \(-0.535832\pi\)
−0.112331 + 0.993671i \(0.535832\pi\)
\(318\) 12.0000 0.672927
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 2.00000 0.111629
\(322\) 0 0
\(323\) −20.0000 −1.11283
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −24.0000 −1.32924
\(327\) −4.00000 −0.221201
\(328\) 5.00000 0.276079
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) −6.00000 −0.329293
\(333\) −8.00000 −0.438397
\(334\) −16.0000 −0.875481
\(335\) 0 0
\(336\) 0 0
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) 3.00000 0.163178
\(339\) 5.00000 0.271563
\(340\) 0 0
\(341\) 22.0000 1.19137
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) 18.0000 0.966291 0.483145 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) 6.00000 0.321634
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) −2.00000 −0.106600
\(353\) −9.00000 −0.479022 −0.239511 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(354\) 2.00000 0.106299
\(355\) 0 0
\(356\) 11.0000 0.582999
\(357\) 0 0
\(358\) 22.0000 1.16274
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −22.0000 −1.15629
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 0 0
\(366\) −10.0000 −0.522708
\(367\) 4.00000 0.208798 0.104399 0.994535i \(-0.466708\pi\)
0.104399 + 0.994535i \(0.466708\pi\)
\(368\) −5.00000 −0.260643
\(369\) 5.00000 0.260290
\(370\) 0 0
\(371\) 0 0
\(372\) 11.0000 0.570323
\(373\) 32.0000 1.65690 0.828449 0.560065i \(-0.189224\pi\)
0.828449 + 0.560065i \(0.189224\pi\)
\(374\) −10.0000 −0.517088
\(375\) 0 0
\(376\) 1.00000 0.0515711
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) −2.00000 −0.102733 −0.0513665 0.998680i \(-0.516358\pi\)
−0.0513665 + 0.998680i \(0.516358\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −25.0000 −1.27911
\(383\) −3.00000 −0.153293 −0.0766464 0.997058i \(-0.524421\pi\)
−0.0766464 + 0.997058i \(0.524421\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −11.0000 −0.559885
\(387\) 0 0
\(388\) 1.00000 0.0507673
\(389\) 24.0000 1.21685 0.608424 0.793612i \(-0.291802\pi\)
0.608424 + 0.793612i \(0.291802\pi\)
\(390\) 0 0
\(391\) −25.0000 −1.26430
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 24.0000 1.20910
\(395\) 0 0
\(396\) −2.00000 −0.100504
\(397\) 34.0000 1.70641 0.853206 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) 5.00000 0.250627
\(399\) 0 0
\(400\) 0 0
\(401\) −6.00000 −0.299626 −0.149813 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 0 0
\(403\) −44.0000 −2.19180
\(404\) 12.0000 0.597022
\(405\) 0 0
\(406\) 0 0
\(407\) 16.0000 0.793091
\(408\) −5.00000 −0.247537
\(409\) −35.0000 −1.73064 −0.865319 0.501221i \(-0.832884\pi\)
−0.865319 + 0.501221i \(0.832884\pi\)
\(410\) 0 0
\(411\) 23.0000 1.13451
\(412\) −13.0000 −0.640464
\(413\) 0 0
\(414\) −5.00000 −0.245737
\(415\) 0 0
\(416\) 4.00000 0.196116
\(417\) −2.00000 −0.0979404
\(418\) 8.00000 0.391293
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) −16.0000 −0.778868
\(423\) 1.00000 0.0486217
\(424\) −12.0000 −0.582772
\(425\) 0 0
\(426\) 1.00000 0.0484502
\(427\) 0 0
\(428\) −2.00000 −0.0966736
\(429\) 8.00000 0.386244
\(430\) 0 0
\(431\) −3.00000 −0.144505 −0.0722525 0.997386i \(-0.523019\pi\)
−0.0722525 + 0.997386i \(0.523019\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 9.00000 0.432512 0.216256 0.976337i \(-0.430615\pi\)
0.216256 + 0.976337i \(0.430615\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4.00000 0.191565
\(437\) 20.0000 0.956730
\(438\) 2.00000 0.0955637
\(439\) 35.0000 1.67046 0.835229 0.549902i \(-0.185335\pi\)
0.835229 + 0.549902i \(0.185335\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 20.0000 0.951303
\(443\) 8.00000 0.380091 0.190046 0.981775i \(-0.439136\pi\)
0.190046 + 0.981775i \(0.439136\pi\)
\(444\) 8.00000 0.379663
\(445\) 0 0
\(446\) −21.0000 −0.994379
\(447\) −18.0000 −0.851371
\(448\) 0 0
\(449\) 37.0000 1.74614 0.873069 0.487597i \(-0.162126\pi\)
0.873069 + 0.487597i \(0.162126\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) −5.00000 −0.235180
\(453\) 16.0000 0.751746
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −14.0000 −0.654892 −0.327446 0.944870i \(-0.606188\pi\)
−0.327446 + 0.944870i \(0.606188\pi\)
\(458\) −14.0000 −0.654177
\(459\) −5.00000 −0.233380
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 0 0
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −26.0000 −1.20443
\(467\) 34.0000 1.57333 0.786666 0.617379i \(-0.211805\pi\)
0.786666 + 0.617379i \(0.211805\pi\)
\(468\) 4.00000 0.184900
\(469\) 0 0
\(470\) 0 0
\(471\) −14.0000 −0.645086
\(472\) −2.00000 −0.0920575
\(473\) 0 0
\(474\) −9.00000 −0.413384
\(475\) 0 0
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 11.0000 0.503128
\(479\) −3.00000 −0.137073 −0.0685367 0.997649i \(-0.521833\pi\)
−0.0685367 + 0.997649i \(0.521833\pi\)
\(480\) 0 0
\(481\) −32.0000 −1.45907
\(482\) −6.00000 −0.273293
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 39.0000 1.76726 0.883629 0.468187i \(-0.155093\pi\)
0.883629 + 0.468187i \(0.155093\pi\)
\(488\) 10.0000 0.452679
\(489\) 24.0000 1.08532
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −5.00000 −0.225417
\(493\) −30.0000 −1.35113
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) −11.0000 −0.493915
\(497\) 0 0
\(498\) 6.00000 0.268866
\(499\) 22.0000 0.984855 0.492428 0.870353i \(-0.336110\pi\)
0.492428 + 0.870353i \(0.336110\pi\)
\(500\) 0 0
\(501\) 16.0000 0.714827
\(502\) −8.00000 −0.357057
\(503\) −8.00000 −0.356702 −0.178351 0.983967i \(-0.557076\pi\)
−0.178351 + 0.983967i \(0.557076\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 10.0000 0.444554
\(507\) −3.00000 −0.133235
\(508\) 0 0
\(509\) 2.00000 0.0886484 0.0443242 0.999017i \(-0.485887\pi\)
0.0443242 + 0.999017i \(0.485887\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 4.00000 0.176604
\(514\) 14.0000 0.617514
\(515\) 0 0
\(516\) 0 0
\(517\) −2.00000 −0.0879599
\(518\) 0 0
\(519\) −2.00000 −0.0877903
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) −6.00000 −0.262613
\(523\) 14.0000 0.612177 0.306089 0.952003i \(-0.400980\pi\)
0.306089 + 0.952003i \(0.400980\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 21.0000 0.915644
\(527\) −55.0000 −2.39584
\(528\) 2.00000 0.0870388
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) −2.00000 −0.0867926
\(532\) 0 0
\(533\) 20.0000 0.866296
\(534\) −11.0000 −0.476017
\(535\) 0 0
\(536\) 0 0
\(537\) −22.0000 −0.949370
\(538\) −24.0000 −1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) −9.00000 −0.386583
\(543\) 22.0000 0.944110
\(544\) 5.00000 0.214373
\(545\) 0 0
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) −23.0000 −0.982511
\(549\) 10.0000 0.426790
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) 5.00000 0.212814
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 2.00000 0.0848189
\(557\) −38.0000 −1.61011 −0.805056 0.593199i \(-0.797865\pi\)
−0.805056 + 0.593199i \(0.797865\pi\)
\(558\) −11.0000 −0.465667
\(559\) 0 0
\(560\) 0 0
\(561\) 10.0000 0.422200
\(562\) −29.0000 −1.22329
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) −1.00000 −0.0421076
\(565\) 0 0
\(566\) 26.0000 1.09286
\(567\) 0 0
\(568\) −1.00000 −0.0419591
\(569\) 9.00000 0.377300 0.188650 0.982044i \(-0.439589\pi\)
0.188650 + 0.982044i \(0.439589\pi\)
\(570\) 0 0
\(571\) −44.0000 −1.84134 −0.920671 0.390339i \(-0.872358\pi\)
−0.920671 + 0.390339i \(0.872358\pi\)
\(572\) −8.00000 −0.334497
\(573\) 25.0000 1.04439
\(574\) 0 0
\(575\) 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
\(579\) 11.0000 0.457144
\(580\) 0 0
\(581\) 0 0
\(582\) −1.00000 −0.0414513
\(583\) 24.0000 0.993978
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) −6.00000 −0.247647 −0.123823 0.992304i \(-0.539516\pi\)
−0.123823 + 0.992304i \(0.539516\pi\)
\(588\) 0 0
\(589\) 44.0000 1.81299
\(590\) 0 0
\(591\) −24.0000 −0.987228
\(592\) −8.00000 −0.328798
\(593\) −9.00000 −0.369586 −0.184793 0.982777i \(-0.559161\pi\)
−0.184793 + 0.982777i \(0.559161\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) −5.00000 −0.204636
\(598\) −20.0000 −0.817861
\(599\) 17.0000 0.694601 0.347301 0.937754i \(-0.387098\pi\)
0.347301 + 0.937754i \(0.387098\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −16.0000 −0.651031
\(605\) 0 0
\(606\) −12.0000 −0.487467
\(607\) 27.0000 1.09590 0.547948 0.836512i \(-0.315409\pi\)
0.547948 + 0.836512i \(0.315409\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) 0 0
\(611\) 4.00000 0.161823
\(612\) 5.00000 0.202113
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) 0 0
\(617\) −29.0000 −1.16750 −0.583748 0.811935i \(-0.698414\pi\)
−0.583748 + 0.811935i \(0.698414\pi\)
\(618\) 13.0000 0.522937
\(619\) −14.0000 −0.562708 −0.281354 0.959604i \(-0.590783\pi\)
−0.281354 + 0.959604i \(0.590783\pi\)
\(620\) 0 0
\(621\) 5.00000 0.200643
\(622\) 29.0000 1.16279
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 0 0
\(626\) 1.00000 0.0399680
\(627\) −8.00000 −0.319489
\(628\) 14.0000 0.558661
\(629\) −40.0000 −1.59490
\(630\) 0 0
\(631\) 33.0000 1.31371 0.656855 0.754017i \(-0.271887\pi\)
0.656855 + 0.754017i \(0.271887\pi\)
\(632\) 9.00000 0.358001
\(633\) 16.0000 0.635943
\(634\) −4.00000 −0.158860
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) 0 0
\(638\) 12.0000 0.475085
\(639\) −1.00000 −0.0395594
\(640\) 0 0
\(641\) −15.0000 −0.592464 −0.296232 0.955116i \(-0.595730\pi\)
−0.296232 + 0.955116i \(0.595730\pi\)
\(642\) 2.00000 0.0789337
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −20.0000 −0.786889
\(647\) 28.0000 1.10079 0.550397 0.834903i \(-0.314476\pi\)
0.550397 + 0.834903i \(0.314476\pi\)
\(648\) 1.00000 0.0392837
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) −24.0000 −0.939913
\(653\) −28.0000 −1.09572 −0.547862 0.836569i \(-0.684558\pi\)
−0.547862 + 0.836569i \(0.684558\pi\)
\(654\) −4.00000 −0.156412
\(655\) 0 0
\(656\) 5.00000 0.195217
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) −14.0000 −0.545363 −0.272681 0.962104i \(-0.587910\pi\)
−0.272681 + 0.962104i \(0.587910\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 10.0000 0.388661
\(663\) −20.0000 −0.776736
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) 30.0000 1.16160
\(668\) −16.0000 −0.619059
\(669\) 21.0000 0.811907
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) −13.0000 −0.500741
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 5.00000 0.192024
\(679\) 0 0
\(680\) 0 0
\(681\) 18.0000 0.689761
\(682\) 22.0000 0.842424
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) −4.00000 −0.152944
\(685\) 0 0
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) 0 0
\(689\) −48.0000 −1.82865
\(690\) 0 0
\(691\) −2.00000 −0.0760836 −0.0380418 0.999276i \(-0.512112\pi\)
−0.0380418 + 0.999276i \(0.512112\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) 18.0000 0.683271
\(695\) 0 0
\(696\) 6.00000 0.227429
\(697\) 25.0000 0.946943
\(698\) −4.00000 −0.151402
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −4.00000 −0.150970
\(703\) 32.0000 1.20690
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) −9.00000 −0.338719
\(707\) 0 0
\(708\) 2.00000 0.0751646
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 9.00000 0.337526
\(712\) 11.0000 0.412242
\(713\) 55.0000 2.05977
\(714\) 0 0
\(715\) 0 0
\(716\) 22.0000 0.822179
\(717\) −11.0000 −0.410803
\(718\) −20.0000 −0.746393
\(719\) −3.00000 −0.111881 −0.0559406 0.998434i \(-0.517816\pi\)
−0.0559406 + 0.998434i \(0.517816\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) 6.00000 0.223142
\(724\) −22.0000 −0.817624
\(725\) 0 0
\(726\) 7.00000 0.259794
\(727\) 33.0000 1.22390 0.611951 0.790896i \(-0.290385\pi\)
0.611951 + 0.790896i \(0.290385\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) −10.0000 −0.369611
\(733\) −30.0000 −1.10808 −0.554038 0.832492i \(-0.686914\pi\)
−0.554038 + 0.832492i \(0.686914\pi\)
\(734\) 4.00000 0.147643
\(735\) 0 0
\(736\) −5.00000 −0.184302
\(737\) 0 0
\(738\) 5.00000 0.184053
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) 33.0000 1.21065 0.605326 0.795977i \(-0.293043\pi\)
0.605326 + 0.795977i \(0.293043\pi\)
\(744\) 11.0000 0.403280
\(745\) 0 0
\(746\) 32.0000 1.17160
\(747\) −6.00000 −0.219529
\(748\) −10.0000 −0.365636
\(749\) 0 0
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 1.00000 0.0364662
\(753\) 8.00000 0.291536
\(754\) −24.0000 −0.874028
\(755\) 0 0
\(756\) 0 0
\(757\) −28.0000 −1.01768 −0.508839 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) −2.00000 −0.0726433
\(759\) −10.0000 −0.362977
\(760\) 0 0
\(761\) 17.0000 0.616250 0.308125 0.951346i \(-0.400299\pi\)
0.308125 + 0.951346i \(0.400299\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −25.0000 −0.904468
\(765\) 0 0
\(766\) −3.00000 −0.108394
\(767\) −8.00000 −0.288863
\(768\) −1.00000 −0.0360844
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −14.0000 −0.504198
\(772\) −11.0000 −0.395899
\(773\) 4.00000 0.143870 0.0719350 0.997409i \(-0.477083\pi\)
0.0719350 + 0.997409i \(0.477083\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.00000 0.0358979
\(777\) 0 0
\(778\) 24.0000 0.860442
\(779\) −20.0000 −0.716574
\(780\) 0 0
\(781\) 2.00000 0.0715656
\(782\) −25.0000 −0.893998
\(783\) 6.00000 0.214423
\(784\) 0 0
\(785\) 0 0
\(786\) −6.00000 −0.214013
\(787\) −40.0000 −1.42585 −0.712923 0.701242i \(-0.752629\pi\)
−0.712923 + 0.701242i \(0.752629\pi\)
\(788\) 24.0000 0.854965
\(789\) −21.0000 −0.747620
\(790\) 0 0
\(791\) 0 0
\(792\) −2.00000 −0.0710669
\(793\) 40.0000 1.42044
\(794\) 34.0000 1.20661
\(795\) 0 0
\(796\) 5.00000 0.177220
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) 5.00000 0.176887
\(800\) 0 0
\(801\) 11.0000 0.388666
\(802\) −6.00000 −0.211867
\(803\) 4.00000 0.141157
\(804\) 0 0
\(805\) 0 0
\(806\) −44.0000 −1.54983
\(807\) 24.0000 0.844840
\(808\) 12.0000 0.422159
\(809\) 10.0000 0.351581 0.175791 0.984428i \(-0.443752\pi\)
0.175791 + 0.984428i \(0.443752\pi\)
\(810\) 0 0
\(811\) −48.0000 −1.68551 −0.842754 0.538299i \(-0.819067\pi\)
−0.842754 + 0.538299i \(0.819067\pi\)
\(812\) 0 0
\(813\) 9.00000 0.315644
\(814\) 16.0000 0.560800
\(815\) 0 0
\(816\) −5.00000 −0.175035
\(817\) 0 0
\(818\) −35.0000 −1.22375
\(819\) 0 0
\(820\) 0 0
\(821\) 52.0000 1.81481 0.907406 0.420255i \(-0.138059\pi\)
0.907406 + 0.420255i \(0.138059\pi\)
\(822\) 23.0000 0.802217
\(823\) −20.0000 −0.697156 −0.348578 0.937280i \(-0.613335\pi\)
−0.348578 + 0.937280i \(0.613335\pi\)
\(824\) −13.0000 −0.452876
\(825\) 0 0
\(826\) 0 0
\(827\) 30.0000 1.04320 0.521601 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) −5.00000 −0.173762
\(829\) 26.0000 0.903017 0.451509 0.892267i \(-0.350886\pi\)
0.451509 + 0.892267i \(0.350886\pi\)
\(830\) 0 0
\(831\) −2.00000 −0.0693792
\(832\) 4.00000 0.138675
\(833\) 0 0
\(834\) −2.00000 −0.0692543
\(835\) 0 0
\(836\) 8.00000 0.276686
\(837\) 11.0000 0.380216
\(838\) 0 0
\(839\) −9.00000 −0.310715 −0.155357 0.987858i \(-0.549653\pi\)
−0.155357 + 0.987858i \(0.549653\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 28.0000 0.964944
\(843\) 29.0000 0.998813
\(844\) −16.0000 −0.550743
\(845\) 0 0
\(846\) 1.00000 0.0343807
\(847\) 0 0
\(848\) −12.0000 −0.412082
\(849\) −26.0000 −0.892318
\(850\) 0 0
\(851\) 40.0000 1.37118
\(852\) 1.00000 0.0342594
\(853\) −20.0000 −0.684787 −0.342393 0.939557i \(-0.611238\pi\)
−0.342393 + 0.939557i \(0.611238\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −2.00000 −0.0683586
\(857\) −58.0000 −1.98124 −0.990621 0.136637i \(-0.956370\pi\)
−0.990621 + 0.136637i \(0.956370\pi\)
\(858\) 8.00000 0.273115
\(859\) −10.0000 −0.341196 −0.170598 0.985341i \(-0.554570\pi\)
−0.170598 + 0.985341i \(0.554570\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −3.00000 −0.102180
\(863\) −51.0000 −1.73606 −0.868030 0.496512i \(-0.834614\pi\)
−0.868030 + 0.496512i \(0.834614\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) 9.00000 0.305832
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) −18.0000 −0.610608
\(870\) 0 0
\(871\) 0 0
\(872\) 4.00000 0.135457
\(873\) 1.00000 0.0338449
\(874\) 20.0000 0.676510
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −22.0000 −0.742887 −0.371444 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 35.0000 1.18119
\(879\) 18.0000 0.607125
\(880\) 0 0
\(881\) 39.0000 1.31394 0.656972 0.753915i \(-0.271837\pi\)
0.656972 + 0.753915i \(0.271837\pi\)
\(882\) 0 0
\(883\) −2.00000 −0.0673054 −0.0336527 0.999434i \(-0.510714\pi\)
−0.0336527 + 0.999434i \(0.510714\pi\)
\(884\) 20.0000 0.672673
\(885\) 0 0
\(886\) 8.00000 0.268765
\(887\) −56.0000 −1.88030 −0.940148 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) 8.00000 0.268462
\(889\) 0 0
\(890\) 0 0
\(891\) −2.00000 −0.0670025
\(892\) −21.0000 −0.703132
\(893\) −4.00000 −0.133855
\(894\) −18.0000 −0.602010
\(895\) 0 0
\(896\) 0 0
\(897\) 20.0000 0.667781
\(898\) 37.0000 1.23471
\(899\) 66.0000 2.20122
\(900\) 0 0
\(901\) −60.0000 −1.99889
\(902\) −10.0000 −0.332964
\(903\) 0 0
\(904\) −5.00000 −0.166298
\(905\) 0 0
\(906\) 16.0000 0.531564
\(907\) −18.0000 −0.597680 −0.298840 0.954303i \(-0.596600\pi\)
−0.298840 + 0.954303i \(0.596600\pi\)
\(908\) −18.0000 −0.597351
\(909\) 12.0000 0.398015
\(910\) 0 0
\(911\) 51.0000 1.68971 0.844853 0.534999i \(-0.179688\pi\)
0.844853 + 0.534999i \(0.179688\pi\)
\(912\) 4.00000 0.132453
\(913\) 12.0000 0.397142
\(914\) −14.0000 −0.463079
\(915\) 0 0
\(916\) −14.0000 −0.462573
\(917\) 0 0
\(918\) −5.00000 −0.165025
\(919\) 43.0000 1.41844 0.709220 0.704988i \(-0.249047\pi\)
0.709220 + 0.704988i \(0.249047\pi\)
\(920\) 0 0
\(921\) 28.0000 0.922631
\(922\) 20.0000 0.658665
\(923\) −4.00000 −0.131662
\(924\) 0 0
\(925\) 0 0
\(926\) −13.0000 −0.427207
\(927\) −13.0000 −0.426976
\(928\) −6.00000 −0.196960
\(929\) 34.0000 1.11550 0.557752 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −26.0000 −0.851658
\(933\) −29.0000 −0.949417
\(934\) 34.0000 1.11251
\(935\) 0 0
\(936\) 4.00000 0.130744
\(937\) 30.0000 0.980057 0.490029 0.871706i \(-0.336986\pi\)
0.490029 + 0.871706i \(0.336986\pi\)
\(938\) 0 0
\(939\) −1.00000 −0.0326338
\(940\) 0 0
\(941\) 36.0000 1.17357 0.586783 0.809744i \(-0.300394\pi\)
0.586783 + 0.809744i \(0.300394\pi\)
\(942\) −14.0000 −0.456145
\(943\) −25.0000 −0.814112
\(944\) −2.00000 −0.0650945
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) −9.00000 −0.292306
\(949\) −8.00000 −0.259691
\(950\) 0 0
\(951\) 4.00000 0.129709
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) −12.0000 −0.388514
\(955\) 0 0
\(956\) 11.0000 0.355765
\(957\) −12.0000 −0.387905
\(958\) −3.00000 −0.0969256
\(959\) 0 0
\(960\) 0 0
\(961\) 90.0000 2.90323
\(962\) −32.0000 −1.03172
\(963\) −2.00000 −0.0644491
\(964\) −6.00000 −0.193247
\(965\) 0 0
\(966\) 0 0
\(967\) 1.00000 0.0321578 0.0160789 0.999871i \(-0.494882\pi\)
0.0160789 + 0.999871i \(0.494882\pi\)
\(968\) −7.00000 −0.224989
\(969\) 20.0000 0.642493
\(970\) 0 0
\(971\) 6.00000 0.192549 0.0962746 0.995355i \(-0.469307\pi\)
0.0962746 + 0.995355i \(0.469307\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 39.0000 1.24964
\(975\) 0 0
\(976\) 10.0000 0.320092
\(977\) 33.0000 1.05576 0.527882 0.849318i \(-0.322986\pi\)
0.527882 + 0.849318i \(0.322986\pi\)
\(978\) 24.0000 0.767435
\(979\) −22.0000 −0.703123
\(980\) 0 0
\(981\) 4.00000 0.127710
\(982\) 12.0000 0.382935
\(983\) −16.0000 −0.510321 −0.255160 0.966899i \(-0.582128\pi\)
−0.255160 + 0.966899i \(0.582128\pi\)
\(984\) −5.00000 −0.159394
\(985\) 0 0
\(986\) −30.0000 −0.955395
\(987\) 0 0
\(988\) −16.0000 −0.509028
\(989\) 0 0
\(990\) 0 0
\(991\) 37.0000 1.17534 0.587672 0.809099i \(-0.300045\pi\)
0.587672 + 0.809099i \(0.300045\pi\)
\(992\) −11.0000 −0.349250
\(993\) −10.0000 −0.317340
\(994\) 0 0
\(995\) 0 0
\(996\) 6.00000 0.190117
\(997\) −4.00000 −0.126681 −0.0633406 0.997992i \(-0.520175\pi\)
−0.0633406 + 0.997992i \(0.520175\pi\)
\(998\) 22.0000 0.696398
\(999\) 8.00000 0.253109
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 7350.2.a.bt.1.1 1
5.4 even 2 7350.2.a.z.1.1 1
7.2 even 3 1050.2.i.j.151.1 2
7.4 even 3 1050.2.i.j.751.1 yes 2
7.6 odd 2 7350.2.a.cn.1.1 1
35.2 odd 12 1050.2.o.f.949.2 4
35.4 even 6 1050.2.i.k.751.1 yes 2
35.9 even 6 1050.2.i.k.151.1 yes 2
35.18 odd 12 1050.2.o.f.499.2 4
35.23 odd 12 1050.2.o.f.949.1 4
35.32 odd 12 1050.2.o.f.499.1 4
35.34 odd 2 7350.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.j.151.1 2 7.2 even 3
1050.2.i.j.751.1 yes 2 7.4 even 3
1050.2.i.k.151.1 yes 2 35.9 even 6
1050.2.i.k.751.1 yes 2 35.4 even 6
1050.2.o.f.499.1 4 35.32 odd 12
1050.2.o.f.499.2 4 35.18 odd 12
1050.2.o.f.949.1 4 35.23 odd 12
1050.2.o.f.949.2 4 35.2 odd 12
7350.2.a.h.1.1 1 35.34 odd 2
7350.2.a.z.1.1 1 5.4 even 2
7350.2.a.bt.1.1 1 1.1 even 1 trivial
7350.2.a.cn.1.1 1 7.6 odd 2