Properties

Label 7098.2.a.q.1.1
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7098.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.6778153547\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{10} +3.00000 q^{11} -1.00000 q^{12} -1.00000 q^{14} +4.00000 q^{15} +1.00000 q^{16} -5.00000 q^{17} +1.00000 q^{18} -3.00000 q^{19} -4.00000 q^{20} +1.00000 q^{21} +3.00000 q^{22} +6.00000 q^{23} -1.00000 q^{24} +11.0000 q^{25} -1.00000 q^{27} -1.00000 q^{28} -9.00000 q^{29} +4.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} -3.00000 q^{33} -5.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} -4.00000 q^{37} -3.00000 q^{38} -4.00000 q^{40} -5.00000 q^{41} +1.00000 q^{42} +3.00000 q^{44} -4.00000 q^{45} +6.00000 q^{46} +3.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} +11.0000 q^{50} +5.00000 q^{51} -11.0000 q^{53} -1.00000 q^{54} -12.0000 q^{55} -1.00000 q^{56} +3.00000 q^{57} -9.00000 q^{58} -2.00000 q^{59} +4.00000 q^{60} -1.00000 q^{61} +4.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -3.00000 q^{66} -2.00000 q^{67} -5.00000 q^{68} -6.00000 q^{69} +4.00000 q^{70} -6.00000 q^{71} +1.00000 q^{72} -12.0000 q^{73} -4.00000 q^{74} -11.0000 q^{75} -3.00000 q^{76} -3.00000 q^{77} +11.0000 q^{79} -4.00000 q^{80} +1.00000 q^{81} -5.00000 q^{82} -6.00000 q^{83} +1.00000 q^{84} +20.0000 q^{85} +9.00000 q^{87} +3.00000 q^{88} -7.00000 q^{89} -4.00000 q^{90} +6.00000 q^{92} -4.00000 q^{93} +3.00000 q^{94} +12.0000 q^{95} -1.00000 q^{96} +12.0000 q^{97} +1.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)

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
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −4.00000 −1.26491
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) 4.00000 1.03280
\(16\) 1.00000 0.250000
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) −4.00000 −0.894427
\(21\) 1.00000 0.218218
\(22\) 3.00000 0.639602
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −1.00000 −0.204124
\(25\) 11.0000 2.20000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.00000 −0.188982
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 4.00000 0.730297
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.00000 −0.522233
\(34\) −5.00000 −0.857493
\(35\) 4.00000 0.676123
\(36\) 1.00000 0.166667
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) −3.00000 −0.486664
\(39\) 0 0
\(40\) −4.00000 −0.632456
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 1.00000 0.154303
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 3.00000 0.452267
\(45\) −4.00000 −0.596285
\(46\) 6.00000 0.884652
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) 11.0000 1.55563
\(51\) 5.00000 0.700140
\(52\) 0 0
\(53\) −11.0000 −1.51097 −0.755483 0.655168i \(-0.772598\pi\)
−0.755483 + 0.655168i \(0.772598\pi\)
\(54\) −1.00000 −0.136083
\(55\) −12.0000 −1.61808
\(56\) −1.00000 −0.133631
\(57\) 3.00000 0.397360
\(58\) −9.00000 −1.18176
\(59\) −2.00000 −0.260378 −0.130189 0.991489i \(-0.541558\pi\)
−0.130189 + 0.991489i \(0.541558\pi\)
\(60\) 4.00000 0.516398
\(61\) −1.00000 −0.128037 −0.0640184 0.997949i \(-0.520392\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 4.00000 0.508001
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 −0.369274
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) −5.00000 −0.606339
\(69\) −6.00000 −0.722315
\(70\) 4.00000 0.478091
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 1.00000 0.117851
\(73\) −12.0000 −1.40449 −0.702247 0.711934i \(-0.747820\pi\)
−0.702247 + 0.711934i \(0.747820\pi\)
\(74\) −4.00000 −0.464991
\(75\) −11.0000 −1.27017
\(76\) −3.00000 −0.344124
\(77\) −3.00000 −0.341882
\(78\) 0 0
\(79\) 11.0000 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) −4.00000 −0.447214
\(81\) 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 \(0.606810\pi\)
\(84\) 1.00000 0.109109
\(85\) 20.0000 2.16930
\(86\) 0 0
\(87\) 9.00000 0.964901
\(88\) 3.00000 0.319801
\(89\) −7.00000 −0.741999 −0.370999 0.928633i \(-0.620985\pi\)
−0.370999 + 0.928633i \(0.620985\pi\)
\(90\) −4.00000 −0.421637
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) −4.00000 −0.414781
\(94\) 3.00000 0.309426
\(95\) 12.0000 1.23117
\(96\) −1.00000 −0.102062
\(97\) 12.0000 1.21842 0.609208 0.793011i \(-0.291488\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(98\) 1.00000 0.101015
\(99\) 3.00000 0.301511
\(100\) 11.0000 1.10000
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 5.00000 0.495074
\(103\) 20.0000 1.97066 0.985329 0.170664i \(-0.0545913\pi\)
0.985329 + 0.170664i \(0.0545913\pi\)
\(104\) 0 0
\(105\) −4.00000 −0.390360
\(106\) −11.0000 −1.06841
\(107\) 17.0000 1.64345 0.821726 0.569883i \(-0.193011\pi\)
0.821726 + 0.569883i \(0.193011\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −12.0000 −1.14416
\(111\) 4.00000 0.379663
\(112\) −1.00000 −0.0944911
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 3.00000 0.280976
\(115\) −24.0000 −2.23801
\(116\) −9.00000 −0.835629
\(117\) 0 0
\(118\) −2.00000 −0.184115
\(119\) 5.00000 0.458349
\(120\) 4.00000 0.365148
\(121\) −2.00000 −0.181818
\(122\) −1.00000 −0.0905357
\(123\) 5.00000 0.450835
\(124\) 4.00000 0.359211
\(125\) −24.0000 −2.14663
\(126\) −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
\(129\) 0 0
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −3.00000 −0.261116
\(133\) 3.00000 0.260133
\(134\) −2.00000 −0.172774
\(135\) 4.00000 0.344265
\(136\) −5.00000 −0.428746
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) −6.00000 −0.510754
\(139\) 13.0000 1.10265 0.551323 0.834292i \(-0.314123\pi\)
0.551323 + 0.834292i \(0.314123\pi\)
\(140\) 4.00000 0.338062
\(141\) −3.00000 −0.252646
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 36.0000 2.98964
\(146\) −12.0000 −0.993127
\(147\) −1.00000 −0.0824786
\(148\) −4.00000 −0.328798
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) −11.0000 −0.898146
\(151\) 11.0000 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) −3.00000 −0.243332
\(153\) −5.00000 −0.404226
\(154\) −3.00000 −0.241747
\(155\) −16.0000 −1.28515
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 11.0000 0.875113
\(159\) 11.0000 0.872357
\(160\) −4.00000 −0.316228
\(161\) −6.00000 −0.472866
\(162\) 1.00000 0.0785674
\(163\) −20.0000 −1.56652 −0.783260 0.621694i \(-0.786445\pi\)
−0.783260 + 0.621694i \(0.786445\pi\)
\(164\) −5.00000 −0.390434
\(165\) 12.0000 0.934199
\(166\) −6.00000 −0.465690
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) 20.0000 1.53393
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 9.00000 0.682288
\(175\) −11.0000 −0.831522
\(176\) 3.00000 0.226134
\(177\) 2.00000 0.150329
\(178\) −7.00000 −0.524672
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) −4.00000 −0.298142
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 0 0
\(183\) 1.00000 0.0739221
\(184\) 6.00000 0.442326
\(185\) 16.0000 1.17634
\(186\) −4.00000 −0.293294
\(187\) −15.0000 −1.09691
\(188\) 3.00000 0.218797
\(189\) 1.00000 0.0727393
\(190\) 12.0000 0.870572
\(191\) −6.00000 −0.434145 −0.217072 0.976156i \(-0.569651\pi\)
−0.217072 + 0.976156i \(0.569651\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −13.0000 −0.935760 −0.467880 0.883792i \(-0.654982\pi\)
−0.467880 + 0.883792i \(0.654982\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 19.0000 1.35369 0.676847 0.736124i \(-0.263346\pi\)
0.676847 + 0.736124i \(0.263346\pi\)
\(198\) 3.00000 0.213201
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 11.0000 0.777817
\(201\) 2.00000 0.141069
\(202\) 10.0000 0.703598
\(203\) 9.00000 0.631676
\(204\) 5.00000 0.350070
\(205\) 20.0000 1.39686
\(206\) 20.0000 1.39347
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) −9.00000 −0.622543
\(210\) −4.00000 −0.276026
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −11.0000 −0.755483
\(213\) 6.00000 0.411113
\(214\) 17.0000 1.16210
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −4.00000 −0.271538
\(218\) 2.00000 0.135457
\(219\) 12.0000 0.810885
\(220\) −12.0000 −0.809040
\(221\) 0 0
\(222\) 4.00000 0.268462
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 11.0000 0.733333
\(226\) 12.0000 0.798228
\(227\) −14.0000 −0.929213 −0.464606 0.885517i \(-0.653804\pi\)
−0.464606 + 0.885517i \(0.653804\pi\)
\(228\) 3.00000 0.198680
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) −24.0000 −1.58251
\(231\) 3.00000 0.197386
\(232\) −9.00000 −0.590879
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) −2.00000 −0.130189
\(237\) −11.0000 −0.714527
\(238\) 5.00000 0.324102
\(239\) 26.0000 1.68180 0.840900 0.541190i \(-0.182026\pi\)
0.840900 + 0.541190i \(0.182026\pi\)
\(240\) 4.00000 0.258199
\(241\) −12.0000 −0.772988 −0.386494 0.922292i \(-0.626314\pi\)
−0.386494 + 0.922292i \(0.626314\pi\)
\(242\) −2.00000 −0.128565
\(243\) −1.00000 −0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −4.00000 −0.255551
\(246\) 5.00000 0.318788
\(247\) 0 0
\(248\) 4.00000 0.254000
\(249\) 6.00000 0.380235
\(250\) −24.0000 −1.51789
\(251\) 14.0000 0.883672 0.441836 0.897096i \(-0.354327\pi\)
0.441836 + 0.897096i \(0.354327\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 18.0000 1.13165
\(254\) 8.00000 0.501965
\(255\) −20.0000 −1.25245
\(256\) 1.00000 0.0625000
\(257\) 7.00000 0.436648 0.218324 0.975876i \(-0.429941\pi\)
0.218324 + 0.975876i \(0.429941\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) −9.00000 −0.557086
\(262\) 12.0000 0.741362
\(263\) −26.0000 −1.60323 −0.801614 0.597841i \(-0.796025\pi\)
−0.801614 + 0.597841i \(0.796025\pi\)
\(264\) −3.00000 −0.184637
\(265\) 44.0000 2.70290
\(266\) 3.00000 0.183942
\(267\) 7.00000 0.428393
\(268\) −2.00000 −0.122169
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 4.00000 0.243432
\(271\) 12.0000 0.728948 0.364474 0.931214i \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(272\) −5.00000 −0.303170
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 33.0000 1.98997
\(276\) −6.00000 −0.361158
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 13.0000 0.779688
\(279\) 4.00000 0.239474
\(280\) 4.00000 0.239046
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) −3.00000 −0.178647
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −6.00000 −0.356034
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 5.00000 0.295141
\(288\) 1.00000 0.0589256
\(289\) 8.00000 0.470588
\(290\) 36.0000 2.11399
\(291\) −12.0000 −0.703452
\(292\) −12.0000 −0.702247
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 8.00000 0.465778
\(296\) −4.00000 −0.232495
\(297\) −3.00000 −0.174078
\(298\) −18.0000 −1.04271
\(299\) 0 0
\(300\) −11.0000 −0.635085
\(301\) 0 0
\(302\) 11.0000 0.632979
\(303\) −10.0000 −0.574485
\(304\) −3.00000 −0.172062
\(305\) 4.00000 0.229039
\(306\) −5.00000 −0.285831
\(307\) −21.0000 −1.19853 −0.599267 0.800549i \(-0.704541\pi\)
−0.599267 + 0.800549i \(0.704541\pi\)
\(308\) −3.00000 −0.170941
\(309\) −20.0000 −1.13776
\(310\) −16.0000 −0.908739
\(311\) −19.0000 −1.07739 −0.538696 0.842500i \(-0.681083\pi\)
−0.538696 + 0.842500i \(0.681083\pi\)
\(312\) 0 0
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) −2.00000 −0.112867
\(315\) 4.00000 0.225374
\(316\) 11.0000 0.618798
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 11.0000 0.616849
\(319\) −27.0000 −1.51171
\(320\) −4.00000 −0.223607
\(321\) −17.0000 −0.948847
\(322\) −6.00000 −0.334367
\(323\) 15.0000 0.834622
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −20.0000 −1.10770
\(327\) −2.00000 −0.110600
\(328\) −5.00000 −0.276079
\(329\) −3.00000 −0.165395
\(330\) 12.0000 0.660578
\(331\) −2.00000 −0.109930 −0.0549650 0.998488i \(-0.517505\pi\)
−0.0549650 + 0.998488i \(0.517505\pi\)
\(332\) −6.00000 −0.329293
\(333\) −4.00000 −0.219199
\(334\) 16.0000 0.875481
\(335\) 8.00000 0.437087
\(336\) 1.00000 0.0545545
\(337\) 31.0000 1.68868 0.844339 0.535810i \(-0.179994\pi\)
0.844339 + 0.535810i \(0.179994\pi\)
\(338\) 0 0
\(339\) −12.0000 −0.651751
\(340\) 20.0000 1.08465
\(341\) 12.0000 0.649836
\(342\) −3.00000 −0.162221
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 24.0000 1.29212
\(346\) −2.00000 −0.107521
\(347\) 11.0000 0.590511 0.295255 0.955418i \(-0.404595\pi\)
0.295255 + 0.955418i \(0.404595\pi\)
\(348\) 9.00000 0.482451
\(349\) 34.0000 1.81998 0.909989 0.414632i \(-0.136090\pi\)
0.909989 + 0.414632i \(0.136090\pi\)
\(350\) −11.0000 −0.587975
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 2.00000 0.106299
\(355\) 24.0000 1.27379
\(356\) −7.00000 −0.370999
\(357\) −5.00000 −0.264628
\(358\) 24.0000 1.26844
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) −4.00000 −0.210819
\(361\) −10.0000 −0.526316
\(362\) −5.00000 −0.262794
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) 48.0000 2.51243
\(366\) 1.00000 0.0522708
\(367\) 18.0000 0.939592 0.469796 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) 6.00000 0.312772
\(369\) −5.00000 −0.260290
\(370\) 16.0000 0.831800
\(371\) 11.0000 0.571092
\(372\) −4.00000 −0.207390
\(373\) 34.0000 1.76045 0.880227 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(374\) −15.0000 −0.775632
\(375\) 24.0000 1.23935
\(376\) 3.00000 0.154713
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 18.0000 0.924598 0.462299 0.886724i \(-0.347025\pi\)
0.462299 + 0.886724i \(0.347025\pi\)
\(380\) 12.0000 0.615587
\(381\) −8.00000 −0.409852
\(382\) −6.00000 −0.306987
\(383\) 11.0000 0.562074 0.281037 0.959697i \(-0.409322\pi\)
0.281037 + 0.959697i \(0.409322\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 12.0000 0.611577
\(386\) −13.0000 −0.661683
\(387\) 0 0
\(388\) 12.0000 0.609208
\(389\) −26.0000 −1.31825 −0.659126 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 0 0
\(391\) −30.0000 −1.51717
\(392\) 1.00000 0.0505076
\(393\) −12.0000 −0.605320
\(394\) 19.0000 0.957206
\(395\) −44.0000 −2.21388
\(396\) 3.00000 0.150756
\(397\) 23.0000 1.15434 0.577168 0.816625i \(-0.304158\pi\)
0.577168 + 0.816625i \(0.304158\pi\)
\(398\) 0 0
\(399\) −3.00000 −0.150188
\(400\) 11.0000 0.550000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 2.00000 0.0997509
\(403\) 0 0
\(404\) 10.0000 0.497519
\(405\) −4.00000 −0.198762
\(406\) 9.00000 0.446663
\(407\) −12.0000 −0.594818
\(408\) 5.00000 0.247537
\(409\) 2.00000 0.0988936 0.0494468 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) 20.0000 0.987730
\(411\) −18.0000 −0.887875
\(412\) 20.0000 0.985329
\(413\) 2.00000 0.0984136
\(414\) 6.00000 0.294884
\(415\) 24.0000 1.17811
\(416\) 0 0
\(417\) −13.0000 −0.636613
\(418\) −9.00000 −0.440204
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) −4.00000 −0.195180
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) 14.0000 0.681509
\(423\) 3.00000 0.145865
\(424\) −11.0000 −0.534207
\(425\) −55.0000 −2.66789
\(426\) 6.00000 0.290701
\(427\) 1.00000 0.0483934
\(428\) 17.0000 0.821726
\(429\) 0 0
\(430\) 0 0
\(431\) −38.0000 −1.83040 −0.915198 0.403005i \(-0.867966\pi\)
−0.915198 + 0.403005i \(0.867966\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) −4.00000 −0.192006
\(435\) −36.0000 −1.72607
\(436\) 2.00000 0.0957826
\(437\) −18.0000 −0.861057
\(438\) 12.0000 0.573382
\(439\) 40.0000 1.90910 0.954548 0.298057i \(-0.0963387\pi\)
0.954548 + 0.298057i \(0.0963387\pi\)
\(440\) −12.0000 −0.572078
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −15.0000 −0.712672 −0.356336 0.934358i \(-0.615974\pi\)
−0.356336 + 0.934358i \(0.615974\pi\)
\(444\) 4.00000 0.189832
\(445\) 28.0000 1.32733
\(446\) 16.0000 0.757622
\(447\) 18.0000 0.851371
\(448\) −1.00000 −0.0472456
\(449\) −20.0000 −0.943858 −0.471929 0.881636i \(-0.656442\pi\)
−0.471929 + 0.881636i \(0.656442\pi\)
\(450\) 11.0000 0.518545
\(451\) −15.0000 −0.706322
\(452\) 12.0000 0.564433
\(453\) −11.0000 −0.516825
\(454\) −14.0000 −0.657053
\(455\) 0 0
\(456\) 3.00000 0.140488
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) 5.00000 0.233635
\(459\) 5.00000 0.233380
\(460\) −24.0000 −1.11901
\(461\) 32.0000 1.49039 0.745194 0.666847i \(-0.232357\pi\)
0.745194 + 0.666847i \(0.232357\pi\)
\(462\) 3.00000 0.139573
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) −9.00000 −0.417815
\(465\) 16.0000 0.741982
\(466\) 4.00000 0.185296
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 2.00000 0.0923514
\(470\) −12.0000 −0.553519
\(471\) 2.00000 0.0921551
\(472\) −2.00000 −0.0920575
\(473\) 0 0
\(474\) −11.0000 −0.505247
\(475\) −33.0000 −1.51414
\(476\) 5.00000 0.229175
\(477\) −11.0000 −0.503655
\(478\) 26.0000 1.18921
\(479\) 33.0000 1.50781 0.753904 0.656984i \(-0.228168\pi\)
0.753904 + 0.656984i \(0.228168\pi\)
\(480\) 4.00000 0.182574
\(481\) 0 0
\(482\) −12.0000 −0.546585
\(483\) 6.00000 0.273009
\(484\) −2.00000 −0.0909091
\(485\) −48.0000 −2.17957
\(486\) −1.00000 −0.0453609
\(487\) 21.0000 0.951601 0.475800 0.879553i \(-0.342158\pi\)
0.475800 + 0.879553i \(0.342158\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 20.0000 0.904431
\(490\) −4.00000 −0.180702
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 5.00000 0.225417
\(493\) 45.0000 2.02670
\(494\) 0 0
\(495\) −12.0000 −0.539360
\(496\) 4.00000 0.179605
\(497\) 6.00000 0.269137
\(498\) 6.00000 0.268866
\(499\) −40.0000 −1.79065 −0.895323 0.445418i \(-0.853055\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) −24.0000 −1.07331
\(501\) −16.0000 −0.714827
\(502\) 14.0000 0.624851
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −40.0000 −1.77998
\(506\) 18.0000 0.800198
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −20.0000 −0.885615
\(511\) 12.0000 0.530849
\(512\) 1.00000 0.0441942
\(513\) 3.00000 0.132453
\(514\) 7.00000 0.308757
\(515\) −80.0000 −3.52522
\(516\) 0 0
\(517\) 9.00000 0.395820
\(518\) 4.00000 0.175750
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) −5.00000 −0.219054 −0.109527 0.993984i \(-0.534934\pi\)
−0.109527 + 0.993984i \(0.534934\pi\)
\(522\) −9.00000 −0.393919
\(523\) 27.0000 1.18063 0.590314 0.807174i \(-0.299004\pi\)
0.590314 + 0.807174i \(0.299004\pi\)
\(524\) 12.0000 0.524222
\(525\) 11.0000 0.480079
\(526\) −26.0000 −1.13365
\(527\) −20.0000 −0.871214
\(528\) −3.00000 −0.130558
\(529\) 13.0000 0.565217
\(530\) 44.0000 1.91124
\(531\) −2.00000 −0.0867926
\(532\) 3.00000 0.130066
\(533\) 0 0
\(534\) 7.00000 0.302920
\(535\) −68.0000 −2.93990
\(536\) −2.00000 −0.0863868
\(537\) −24.0000 −1.03568
\(538\) −24.0000 −1.03471
\(539\) 3.00000 0.129219
\(540\) 4.00000 0.172133
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 12.0000 0.515444
\(543\) 5.00000 0.214571
\(544\) −5.00000 −0.214373
\(545\) −8.00000 −0.342682
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 18.0000 0.768922
\(549\) −1.00000 −0.0426790
\(550\) 33.0000 1.40712
\(551\) 27.0000 1.15024
\(552\) −6.00000 −0.255377
\(553\) −11.0000 −0.467768
\(554\) 14.0000 0.594803
\(555\) −16.0000 −0.679162
\(556\) 13.0000 0.551323
\(557\) −11.0000 −0.466085 −0.233042 0.972467i \(-0.574868\pi\)
−0.233042 + 0.972467i \(0.574868\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) 4.00000 0.169031
\(561\) 15.0000 0.633300
\(562\) −30.0000 −1.26547
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) −3.00000 −0.126323
\(565\) −48.0000 −2.01938
\(566\) −4.00000 −0.168133
\(567\) −1.00000 −0.0419961
\(568\) −6.00000 −0.251754
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) −12.0000 −0.502625
\(571\) 38.0000 1.59025 0.795125 0.606445i \(-0.207405\pi\)
0.795125 + 0.606445i \(0.207405\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 5.00000 0.208696
\(575\) 66.0000 2.75239
\(576\) 1.00000 0.0416667
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 8.00000 0.332756
\(579\) 13.0000 0.540262
\(580\) 36.0000 1.49482
\(581\) 6.00000 0.248922
\(582\) −12.0000 −0.497416
\(583\) −33.0000 −1.36672
\(584\) −12.0000 −0.496564
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −12.0000 −0.494451
\(590\) 8.00000 0.329355
\(591\) −19.0000 −0.781556
\(592\) −4.00000 −0.164399
\(593\) −41.0000 −1.68367 −0.841834 0.539736i \(-0.818524\pi\)
−0.841834 + 0.539736i \(0.818524\pi\)
\(594\) −3.00000 −0.123091
\(595\) −20.0000 −0.819920
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) 0 0
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) −11.0000 −0.449073
\(601\) −44.0000 −1.79480 −0.897399 0.441221i \(-0.854546\pi\)
−0.897399 + 0.441221i \(0.854546\pi\)
\(602\) 0 0
\(603\) −2.00000 −0.0814463
\(604\) 11.0000 0.447584
\(605\) 8.00000 0.325246
\(606\) −10.0000 −0.406222
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −3.00000 −0.121666
\(609\) −9.00000 −0.364698
\(610\) 4.00000 0.161955
\(611\) 0 0
\(612\) −5.00000 −0.202113
\(613\) −8.00000 −0.323117 −0.161558 0.986863i \(-0.551652\pi\)
−0.161558 + 0.986863i \(0.551652\pi\)
\(614\) −21.0000 −0.847491
\(615\) −20.0000 −0.806478
\(616\) −3.00000 −0.120873
\(617\) −10.0000 −0.402585 −0.201292 0.979531i \(-0.564514\pi\)
−0.201292 + 0.979531i \(0.564514\pi\)
\(618\) −20.0000 −0.804518
\(619\) −17.0000 −0.683288 −0.341644 0.939829i \(-0.610984\pi\)
−0.341644 + 0.939829i \(0.610984\pi\)
\(620\) −16.0000 −0.642575
\(621\) −6.00000 −0.240772
\(622\) −19.0000 −0.761831
\(623\) 7.00000 0.280449
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) −14.0000 −0.559553
\(627\) 9.00000 0.359425
\(628\) −2.00000 −0.0798087
\(629\) 20.0000 0.797452
\(630\) 4.00000 0.159364
\(631\) 13.0000 0.517522 0.258761 0.965941i \(-0.416686\pi\)
0.258761 + 0.965941i \(0.416686\pi\)
\(632\) 11.0000 0.437557
\(633\) −14.0000 −0.556450
\(634\) 18.0000 0.714871
\(635\) −32.0000 −1.26988
\(636\) 11.0000 0.436178
\(637\) 0 0
\(638\) −27.0000 −1.06894
\(639\) −6.00000 −0.237356
\(640\) −4.00000 −0.158114
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −17.0000 −0.670936
\(643\) 17.0000 0.670415 0.335207 0.942144i \(-0.391194\pi\)
0.335207 + 0.942144i \(0.391194\pi\)
\(644\) −6.00000 −0.236433
\(645\) 0 0
\(646\) 15.0000 0.590167
\(647\) 15.0000 0.589711 0.294855 0.955542i \(-0.404729\pi\)
0.294855 + 0.955542i \(0.404729\pi\)
\(648\) 1.00000 0.0392837
\(649\) −6.00000 −0.235521
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) −20.0000 −0.783260
\(653\) −27.0000 −1.05659 −0.528296 0.849060i \(-0.677169\pi\)
−0.528296 + 0.849060i \(0.677169\pi\)
\(654\) −2.00000 −0.0782062
\(655\) −48.0000 −1.87552
\(656\) −5.00000 −0.195217
\(657\) −12.0000 −0.468165
\(658\) −3.00000 −0.116952
\(659\) 39.0000 1.51922 0.759612 0.650376i \(-0.225389\pi\)
0.759612 + 0.650376i \(0.225389\pi\)
\(660\) 12.0000 0.467099
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) −2.00000 −0.0777322
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) −12.0000 −0.465340
\(666\) −4.00000 −0.154997
\(667\) −54.0000 −2.09089
\(668\) 16.0000 0.619059
\(669\) −16.0000 −0.618596
\(670\) 8.00000 0.309067
\(671\) −3.00000 −0.115814
\(672\) 1.00000 0.0385758
\(673\) 23.0000 0.886585 0.443292 0.896377i \(-0.353810\pi\)
0.443292 + 0.896377i \(0.353810\pi\)
\(674\) 31.0000 1.19408
\(675\) −11.0000 −0.423390
\(676\) 0 0
\(677\) −26.0000 −0.999261 −0.499631 0.866239i \(-0.666531\pi\)
−0.499631 + 0.866239i \(0.666531\pi\)
\(678\) −12.0000 −0.460857
\(679\) −12.0000 −0.460518
\(680\) 20.0000 0.766965
\(681\) 14.0000 0.536481
\(682\) 12.0000 0.459504
\(683\) 20.0000 0.765279 0.382639 0.923898i \(-0.375015\pi\)
0.382639 + 0.923898i \(0.375015\pi\)
\(684\) −3.00000 −0.114708
\(685\) −72.0000 −2.75098
\(686\) −1.00000 −0.0381802
\(687\) −5.00000 −0.190762
\(688\) 0 0
\(689\) 0 0
\(690\) 24.0000 0.913664
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) −2.00000 −0.0760286
\(693\) −3.00000 −0.113961
\(694\) 11.0000 0.417554
\(695\) −52.0000 −1.97247
\(696\) 9.00000 0.341144
\(697\) 25.0000 0.946943
\(698\) 34.0000 1.28692
\(699\) −4.00000 −0.151294
\(700\) −11.0000 −0.415761
\(701\) −21.0000 −0.793159 −0.396580 0.918000i \(-0.629803\pi\)
−0.396580 + 0.918000i \(0.629803\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) 3.00000 0.113067
\(705\) 12.0000 0.451946
\(706\) 18.0000 0.677439
\(707\) −10.0000 −0.376089
\(708\) 2.00000 0.0751646
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 24.0000 0.900704
\(711\) 11.0000 0.412532
\(712\) −7.00000 −0.262336
\(713\) 24.0000 0.898807
\(714\) −5.00000 −0.187120
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) −26.0000 −0.970988
\(718\) 20.0000 0.746393
\(719\) −1.00000 −0.0372937 −0.0186469 0.999826i \(-0.505936\pi\)
−0.0186469 + 0.999826i \(0.505936\pi\)
\(720\) −4.00000 −0.149071
\(721\) −20.0000 −0.744839
\(722\) −10.0000 −0.372161
\(723\) 12.0000 0.446285
\(724\) −5.00000 −0.185824
\(725\) −99.0000 −3.67677
\(726\) 2.00000 0.0742270
\(727\) 12.0000 0.445055 0.222528 0.974926i \(-0.428569\pi\)
0.222528 + 0.974926i \(0.428569\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 48.0000 1.77656
\(731\) 0 0
\(732\) 1.00000 0.0369611
\(733\) −13.0000 −0.480166 −0.240083 0.970752i \(-0.577175\pi\)
−0.240083 + 0.970752i \(0.577175\pi\)
\(734\) 18.0000 0.664392
\(735\) 4.00000 0.147542
\(736\) 6.00000 0.221163
\(737\) −6.00000 −0.221013
\(738\) −5.00000 −0.184053
\(739\) 54.0000 1.98642 0.993211 0.116326i \(-0.0371118\pi\)
0.993211 + 0.116326i \(0.0371118\pi\)
\(740\) 16.0000 0.588172
\(741\) 0 0
\(742\) 11.0000 0.403823
\(743\) −28.0000 −1.02722 −0.513610 0.858024i \(-0.671692\pi\)
−0.513610 + 0.858024i \(0.671692\pi\)
\(744\) −4.00000 −0.146647
\(745\) 72.0000 2.63788
\(746\) 34.0000 1.24483
\(747\) −6.00000 −0.219529
\(748\) −15.0000 −0.548454
\(749\) −17.0000 −0.621166
\(750\) 24.0000 0.876356
\(751\) 31.0000 1.13121 0.565603 0.824678i \(-0.308643\pi\)
0.565603 + 0.824678i \(0.308643\pi\)
\(752\) 3.00000 0.109399
\(753\) −14.0000 −0.510188
\(754\) 0 0
\(755\) −44.0000 −1.60132
\(756\) 1.00000 0.0363696
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 18.0000 0.653789
\(759\) −18.0000 −0.653359
\(760\) 12.0000 0.435286
\(761\) 26.0000 0.942499 0.471250 0.882000i \(-0.343803\pi\)
0.471250 + 0.882000i \(0.343803\pi\)
\(762\) −8.00000 −0.289809
\(763\) −2.00000 −0.0724049
\(764\) −6.00000 −0.217072
\(765\) 20.0000 0.723102
\(766\) 11.0000 0.397446
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 4.00000 0.144244 0.0721218 0.997396i \(-0.477023\pi\)
0.0721218 + 0.997396i \(0.477023\pi\)
\(770\) 12.0000 0.432450
\(771\) −7.00000 −0.252099
\(772\) −13.0000 −0.467880
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) 44.0000 1.58053
\(776\) 12.0000 0.430775
\(777\) −4.00000 −0.143499
\(778\) −26.0000 −0.932145
\(779\) 15.0000 0.537431
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) −30.0000 −1.07280
\(783\) 9.00000 0.321634
\(784\) 1.00000 0.0357143
\(785\) 8.00000 0.285532
\(786\) −12.0000 −0.428026
\(787\) 11.0000 0.392108 0.196054 0.980593i \(-0.437187\pi\)
0.196054 + 0.980593i \(0.437187\pi\)
\(788\) 19.0000 0.676847
\(789\) 26.0000 0.925625
\(790\) −44.0000 −1.56545
\(791\) −12.0000 −0.426671
\(792\) 3.00000 0.106600
\(793\) 0 0
\(794\) 23.0000 0.816239
\(795\) −44.0000 −1.56052
\(796\) 0 0
\(797\) −2.00000 −0.0708436 −0.0354218 0.999372i \(-0.511277\pi\)
−0.0354218 + 0.999372i \(0.511277\pi\)
\(798\) −3.00000 −0.106199
\(799\) −15.0000 −0.530662
\(800\) 11.0000 0.388909
\(801\) −7.00000 −0.247333
\(802\) −18.0000 −0.635602
\(803\) −36.0000 −1.27041
\(804\) 2.00000 0.0705346
\(805\) 24.0000 0.845889
\(806\) 0 0
\(807\) 24.0000 0.844840
\(808\) 10.0000 0.351799
\(809\) −50.0000 −1.75791 −0.878953 0.476908i \(-0.841757\pi\)
−0.878953 + 0.476908i \(0.841757\pi\)
\(810\) −4.00000 −0.140546
\(811\) −24.0000 −0.842754 −0.421377 0.906886i \(-0.638453\pi\)
−0.421377 + 0.906886i \(0.638453\pi\)
\(812\) 9.00000 0.315838
\(813\) −12.0000 −0.420858
\(814\) −12.0000 −0.420600
\(815\) 80.0000 2.80228
\(816\) 5.00000 0.175035
\(817\) 0 0
\(818\) 2.00000 0.0699284
\(819\) 0 0
\(820\) 20.0000 0.698430
\(821\) 15.0000 0.523504 0.261752 0.965135i \(-0.415700\pi\)
0.261752 + 0.965135i \(0.415700\pi\)
\(822\) −18.0000 −0.627822
\(823\) −16.0000 −0.557725 −0.278862 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) 20.0000 0.696733
\(825\) −33.0000 −1.14891
\(826\) 2.00000 0.0695889
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 6.00000 0.208514
\(829\) 5.00000 0.173657 0.0868286 0.996223i \(-0.472327\pi\)
0.0868286 + 0.996223i \(0.472327\pi\)
\(830\) 24.0000 0.833052
\(831\) −14.0000 −0.485655
\(832\) 0 0
\(833\) −5.00000 −0.173240
\(834\) −13.0000 −0.450153
\(835\) −64.0000 −2.21481
\(836\) −9.00000 −0.311272
\(837\) −4.00000 −0.138260
\(838\) 18.0000 0.621800
\(839\) −44.0000 −1.51905 −0.759524 0.650479i \(-0.774568\pi\)
−0.759524 + 0.650479i \(0.774568\pi\)
\(840\) −4.00000 −0.138013
\(841\) 52.0000 1.79310
\(842\) 18.0000 0.620321
\(843\) 30.0000 1.03325
\(844\) 14.0000 0.481900
\(845\) 0 0
\(846\) 3.00000 0.103142
\(847\) 2.00000 0.0687208
\(848\) −11.0000 −0.377742
\(849\) 4.00000 0.137280
\(850\) −55.0000 −1.88648
\(851\) −24.0000 −0.822709
\(852\) 6.00000 0.205557
\(853\) −49.0000 −1.67773 −0.838864 0.544341i \(-0.816780\pi\)
−0.838864 + 0.544341i \(0.816780\pi\)
\(854\) 1.00000 0.0342193
\(855\) 12.0000 0.410391
\(856\) 17.0000 0.581048
\(857\) 10.0000 0.341593 0.170797 0.985306i \(-0.445366\pi\)
0.170797 + 0.985306i \(0.445366\pi\)
\(858\) 0 0
\(859\) −5.00000 −0.170598 −0.0852989 0.996355i \(-0.527185\pi\)
−0.0852989 + 0.996355i \(0.527185\pi\)
\(860\) 0 0
\(861\) −5.00000 −0.170400
\(862\) −38.0000 −1.29429
\(863\) 14.0000 0.476566 0.238283 0.971196i \(-0.423415\pi\)
0.238283 + 0.971196i \(0.423415\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 8.00000 0.272008
\(866\) 34.0000 1.15537
\(867\) −8.00000 −0.271694
\(868\) −4.00000 −0.135769
\(869\) 33.0000 1.11945
\(870\) −36.0000 −1.22051
\(871\) 0 0
\(872\) 2.00000 0.0677285
\(873\) 12.0000 0.406138
\(874\) −18.0000 −0.608859
\(875\) 24.0000 0.811348
\(876\) 12.0000 0.405442
\(877\) −42.0000 −1.41824 −0.709120 0.705088i \(-0.750907\pi\)
−0.709120 + 0.705088i \(0.750907\pi\)
\(878\) 40.0000 1.34993
\(879\) 24.0000 0.809500
\(880\) −12.0000 −0.404520
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) 1.00000 0.0336718
\(883\) −8.00000 −0.269221 −0.134611 0.990899i \(-0.542978\pi\)
−0.134611 + 0.990899i \(0.542978\pi\)
\(884\) 0 0
\(885\) −8.00000 −0.268917
\(886\) −15.0000 −0.503935
\(887\) 39.0000 1.30949 0.654746 0.755849i \(-0.272776\pi\)
0.654746 + 0.755849i \(0.272776\pi\)
\(888\) 4.00000 0.134231
\(889\) −8.00000 −0.268311
\(890\) 28.0000 0.938562
\(891\) 3.00000 0.100504
\(892\) 16.0000 0.535720
\(893\) −9.00000 −0.301174
\(894\) 18.0000 0.602010
\(895\) −96.0000 −3.20893
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −20.0000 −0.667409
\(899\) −36.0000 −1.20067
\(900\) 11.0000 0.366667
\(901\) 55.0000 1.83232
\(902\) −15.0000 −0.499445
\(903\) 0 0
\(904\) 12.0000 0.399114
\(905\) 20.0000 0.664822
\(906\) −11.0000 −0.365451
\(907\) −14.0000 −0.464862 −0.232431 0.972613i \(-0.574668\pi\)
−0.232431 + 0.972613i \(0.574668\pi\)
\(908\) −14.0000 −0.464606
\(909\) 10.0000 0.331679
\(910\) 0 0
\(911\) −2.00000 −0.0662630 −0.0331315 0.999451i \(-0.510548\pi\)
−0.0331315 + 0.999451i \(0.510548\pi\)
\(912\) 3.00000 0.0993399
\(913\) −18.0000 −0.595713
\(914\) 2.00000 0.0661541
\(915\) −4.00000 −0.132236
\(916\) 5.00000 0.165205
\(917\) −12.0000 −0.396275
\(918\) 5.00000 0.165025
\(919\) −11.0000 −0.362857 −0.181428 0.983404i \(-0.558072\pi\)
−0.181428 + 0.983404i \(0.558072\pi\)
\(920\) −24.0000 −0.791257
\(921\) 21.0000 0.691974
\(922\) 32.0000 1.05386
\(923\) 0 0
\(924\) 3.00000 0.0986928
\(925\) −44.0000 −1.44671
\(926\) −1.00000 −0.0328620
\(927\) 20.0000 0.656886
\(928\) −9.00000 −0.295439
\(929\) 23.0000 0.754606 0.377303 0.926090i \(-0.376852\pi\)
0.377303 + 0.926090i \(0.376852\pi\)
\(930\) 16.0000 0.524661
\(931\) −3.00000 −0.0983210
\(932\) 4.00000 0.131024
\(933\) 19.0000 0.622032
\(934\) −12.0000 −0.392652
\(935\) 60.0000 1.96221
\(936\) 0 0
\(937\) 44.0000 1.43742 0.718709 0.695311i \(-0.244734\pi\)
0.718709 + 0.695311i \(0.244734\pi\)
\(938\) 2.00000 0.0653023
\(939\) 14.0000 0.456873
\(940\) −12.0000 −0.391397
\(941\) −48.0000 −1.56476 −0.782378 0.622804i \(-0.785993\pi\)
−0.782378 + 0.622804i \(0.785993\pi\)
\(942\) 2.00000 0.0651635
\(943\) −30.0000 −0.976934
\(944\) −2.00000 −0.0650945
\(945\) −4.00000 −0.130120
\(946\) 0 0
\(947\) −3.00000 −0.0974869 −0.0487435 0.998811i \(-0.515522\pi\)
−0.0487435 + 0.998811i \(0.515522\pi\)
\(948\) −11.0000 −0.357263
\(949\) 0 0
\(950\) −33.0000 −1.07066
\(951\) −18.0000 −0.583690
\(952\) 5.00000 0.162051
\(953\) 24.0000 0.777436 0.388718 0.921357i \(-0.372918\pi\)
0.388718 + 0.921357i \(0.372918\pi\)
\(954\) −11.0000 −0.356138
\(955\) 24.0000 0.776622
\(956\) 26.0000 0.840900
\(957\) 27.0000 0.872786
\(958\) 33.0000 1.06618
\(959\) −18.0000 −0.581250
\(960\) 4.00000 0.129099
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 17.0000 0.547817
\(964\) −12.0000 −0.386494
\(965\) 52.0000 1.67394
\(966\) 6.00000 0.193047
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) −2.00000 −0.0642824
\(969\) −15.0000 −0.481869
\(970\) −48.0000 −1.54119
\(971\) −50.0000 −1.60458 −0.802288 0.596937i \(-0.796384\pi\)
−0.802288 + 0.596937i \(0.796384\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −13.0000 −0.416761
\(974\) 21.0000 0.672883
\(975\) 0 0
\(976\) −1.00000 −0.0320092
\(977\) 4.00000 0.127971 0.0639857 0.997951i \(-0.479619\pi\)
0.0639857 + 0.997951i \(0.479619\pi\)
\(978\) 20.0000 0.639529
\(979\) −21.0000 −0.671163
\(980\) −4.00000 −0.127775
\(981\) 2.00000 0.0638551
\(982\) −20.0000 −0.638226
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 5.00000 0.159394
\(985\) −76.0000 −2.42156
\(986\) 45.0000 1.43309
\(987\) 3.00000 0.0954911
\(988\) 0 0
\(989\) 0 0
\(990\) −12.0000 −0.381385
\(991\) 33.0000 1.04828 0.524140 0.851632i \(-0.324387\pi\)
0.524140 + 0.851632i \(0.324387\pi\)
\(992\) 4.00000 0.127000
\(993\) 2.00000 0.0634681
\(994\) 6.00000 0.190308
\(995\) 0 0
\(996\) 6.00000 0.190117
\(997\) −13.0000 −0.411714 −0.205857 0.978582i \(-0.565998\pi\)
−0.205857 + 0.978582i \(0.565998\pi\)
\(998\) −40.0000 −1.26618
\(999\) 4.00000 0.126554
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 7098.2.a.q.1.1 1
13.4 even 6 546.2.l.h.211.1 2
13.10 even 6 546.2.l.h.295.1 yes 2
13.12 even 2 7098.2.a.g.1.1 1
39.17 odd 6 1638.2.r.a.757.1 2
39.23 odd 6 1638.2.r.a.1387.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.l.h.211.1 2 13.4 even 6
546.2.l.h.295.1 yes 2 13.10 even 6
1638.2.r.a.757.1 2 39.17 odd 6
1638.2.r.a.1387.1 2 39.23 odd 6
7098.2.a.g.1.1 1 13.12 even 2
7098.2.a.q.1.1 1 1.1 even 1 trivial