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Properties

Label 3630.2.a.q.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 $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3630,2,Mod(1,3630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3630, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3630.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3630.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +5.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.00000 q^{29} -1.00000 q^{30} +10.0000 q^{31} +1.00000 q^{32} +5.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -7.00000 q^{37} -1.00000 q^{38} +1.00000 q^{39} +1.00000 q^{40} -2.00000 q^{41} -1.00000 q^{42} +6.00000 q^{43} +1.00000 q^{45} -6.00000 q^{47} -1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} -5.00000 q^{51} -1.00000 q^{52} +8.00000 q^{53} -1.00000 q^{54} +1.00000 q^{56} +1.00000 q^{57} +1.00000 q^{58} -4.00000 q^{59} -1.00000 q^{60} +4.00000 q^{61} +10.0000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} +14.0000 q^{67} +5.00000 q^{68} +1.00000 q^{70} -1.00000 q^{71} +1.00000 q^{72} +2.00000 q^{73} -7.00000 q^{74} -1.00000 q^{75} -1.00000 q^{76} +1.00000 q^{78} +6.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +17.0000 q^{83} -1.00000 q^{84} +5.00000 q^{85} +6.00000 q^{86} -1.00000 q^{87} +1.00000 q^{90} -1.00000 q^{91} -10.0000 q^{93} -6.00000 q^{94} -1.00000 q^{95} -1.00000 q^{96} -2.00000 q^{97} -6.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350 −0.138675 − 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.00000 −0.258199
\(16\) 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
\(19\) −1.00000 −0.229416 −0.114708 − 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) 1.00000 0.188982
\(29\) 1.00000 0.185695 0.0928477 − 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) −1.00000 −0.182574
\(31\) 10.0000 1.79605 0.898027 − 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 5.00000 0.857493
\(35\) 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 \(0.695152\pi\)
\(38\) −1.00000 −0.162221
\(39\) 1.00000 0.160128
\(40\) 1.00000 0.158114
\(41\) −2.00000 −0.312348 −0.156174 − 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) −1.00000 −0.154303
\(43\) 6.00000 0.914991 0.457496 − 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 − 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.00000 −0.857143
\(50\) 1.00000 0.141421
\(51\) −5.00000 −0.700140
\(52\) −1.00000 −0.138675
\(53\) 8.00000 1.09888 0.549442 − 0.835532i \(-0.314840\pi\)
0.549442 + 0.835532i \(0.314840\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 1.00000 0.132453
\(58\) 1.00000 0.131306
\(59\) −4.00000 −0.520756 −0.260378 − 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) −1.00000 −0.129099
\(61\) 4.00000 0.512148 0.256074 − 0.966657i \(-0.417571\pi\)
0.256074 + 0.966657i \(0.417571\pi\)
\(62\) 10.0000 1.27000
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 14.0000 1.71037 0.855186 − 0.518321i \(-0.173443\pi\)
0.855186 + 0.518321i \(0.173443\pi\)
\(68\) 5.00000 0.606339
\(69\) 0 0
\(70\) 1.00000 0.119523
\(71\) −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 \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −7.00000 −0.813733
\(75\) −1.00000 −0.115470
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 6.00000 0.675053 0.337526 − 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −2.00000 −0.220863
\(83\) 17.0000 1.86599 0.932996 − 0.359886i \(-0.117184\pi\)
0.932996 + 0.359886i \(0.117184\pi\)
\(84\) −1.00000 −0.109109
\(85\) 5.00000 0.542326
\(86\) 6.00000 0.646997
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 1.00000 0.105409
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −10.0000 −1.03695
\(94\) −6.00000 −0.618853
\(95\) −1.00000 −0.102598
\(96\) −1.00000 −0.102062
\(97\) −2.00000 −0.203069 −0.101535 − 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 3.00000 0.298511 0.149256 − 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) −5.00000 −0.495074
\(103\) −1.00000 −0.0985329 −0.0492665 − 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −1.00000 −0.0975900
\(106\) 8.00000 0.777029
\(107\) −8.00000 −0.773389 −0.386695 − 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −8.00000 −0.766261 −0.383131 − 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) 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 \(0.408930\pi\)
\(114\) 1.00000 0.0936586
\(115\) 0 0
\(116\) 1.00000 0.0928477
\(117\) −1.00000 −0.0924500
\(118\) −4.00000 −0.368230
\(119\) 5.00000 0.458349
\(120\) −1.00000 −0.0912871
\(121\) 0 0
\(122\) 4.00000 0.362143
\(123\) 2.00000 0.180334
\(124\) 10.0000 0.898027
\(125\) 1.00000 0.0894427
\(126\) 1.00000 0.0890871
\(127\) −12.0000 −1.06483 −0.532414 − 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.00000 −0.528271
\(130\) −1.00000 −0.0877058
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 14.0000 1.20942
\(135\) −1.00000 −0.0860663
\(136\) 5.00000 0.428746
\(137\) −15.0000 −1.28154 −0.640768 − 0.767734i \(-0.721384\pi\)
−0.640768 + 0.767734i \(0.721384\pi\)
\(138\) 0 0
\(139\) −3.00000 −0.254457 −0.127228 − 0.991873i \(-0.540608\pi\)
−0.127228 + 0.991873i \(0.540608\pi\)
\(140\) 1.00000 0.0845154
\(141\) 6.00000 0.505291
\(142\) −1.00000 −0.0839181
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 1.00000 0.0830455
\(146\) 2.00000 0.165521
\(147\) 6.00000 0.494872
\(148\) −7.00000 −0.575396
\(149\) 10.0000 0.819232 0.409616 − 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 20.0000 1.62758 0.813788 − 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 5.00000 0.404226
\(154\) 0 0
\(155\) 10.0000 0.803219
\(156\) 1.00000 0.0800641
\(157\) −17.0000 −1.35675 −0.678374 − 0.734717i \(-0.737315\pi\)
−0.678374 + 0.734717i \(0.737315\pi\)
\(158\) 6.00000 0.477334
\(159\) −8.00000 −0.634441
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 12.0000 0.939913 0.469956 − 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) 17.0000 1.31946
\(167\) 12.0000 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.0000 −0.923077
\(170\) 5.00000 0.383482
\(171\) −1.00000 −0.0764719
\(172\) 6.00000 0.457496
\(173\) 16.0000 1.21646 0.608229 − 0.793762i \(-0.291880\pi\)
0.608229 + 0.793762i \(0.291880\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 4.00000 0.300658
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 1.00000 0.0745356
\(181\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) −1.00000 −0.0741249
\(183\) −4.00000 −0.295689
\(184\) 0 0
\(185\) −7.00000 −0.514650
\(186\) −10.0000 −0.733236
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) −1.00000 −0.0727393
\(190\) −1.00000 −0.0725476
\(191\) −19.0000 −1.37479 −0.687396 − 0.726283i \(-0.741246\pi\)
−0.687396 + 0.726283i \(0.741246\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −16.0000 −1.15171 −0.575853 − 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) −2.00000 −0.143592
\(195\) 1.00000 0.0716115
\(196\) −6.00000 −0.428571
\(197\) 28.0000 1.99492 0.997459 − 0.0712470i \(-0.0226979\pi\)
0.997459 + 0.0712470i \(0.0226979\pi\)
\(198\) 0 0
\(199\) 12.0000 0.850657 0.425329 − 0.905039i \(-0.360158\pi\)
0.425329 + 0.905039i \(0.360158\pi\)
\(200\) 1.00000 0.0707107
\(201\) −14.0000 −0.987484
\(202\) 3.00000 0.211079
\(203\) 1.00000 0.0701862
\(204\) −5.00000 −0.350070
\(205\) −2.00000 −0.139686
\(206\) −1.00000 −0.0696733
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) −1.00000 −0.0690066
\(211\) −9.00000 −0.619586 −0.309793 − 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) 8.00000 0.549442
\(213\) 1.00000 0.0685189
\(214\) −8.00000 −0.546869
\(215\) 6.00000 0.409197
\(216\) −1.00000 −0.0680414
\(217\) 10.0000 0.678844
\(218\) −8.00000 −0.541828
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) −5.00000 −0.336336
\(222\) 7.00000 0.469809
\(223\) 13.0000 0.870544 0.435272 − 0.900299i \(-0.356652\pi\)
0.435272 + 0.900299i \(0.356652\pi\)
\(224\) 1.00000 0.0668153
\(225\) 1.00000 0.0666667
\(226\) 6.00000 0.399114
\(227\) 8.00000 0.530979 0.265489 − 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 1.00000 0.0662266
\(229\) 8.00000 0.528655 0.264327 − 0.964433i \(-0.414850\pi\)
0.264327 + 0.964433i \(0.414850\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000 0.0656532
\(233\) 14.0000 0.917170 0.458585 − 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −6.00000 −0.391397
\(236\) −4.00000 −0.260378
\(237\) −6.00000 −0.389742
\(238\) 5.00000 0.324102
\(239\) 3.00000 0.194054 0.0970269 − 0.995282i \(-0.469067\pi\)
0.0970269 + 0.995282i \(0.469067\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −17.0000 −1.09507 −0.547533 − 0.836784i \(-0.684433\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 4.00000 0.256074
\(245\) −6.00000 −0.383326
\(246\) 2.00000 0.127515
\(247\) 1.00000 0.0636285
\(248\) 10.0000 0.635001
\(249\) −17.0000 −1.07733
\(250\) 1.00000 0.0632456
\(251\) 24.0000 1.51487 0.757433 − 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) −12.0000 −0.752947
\(255\) −5.00000 −0.313112
\(256\) 1.00000 0.0625000
\(257\) −21.0000 −1.30994 −0.654972 − 0.755653i \(-0.727320\pi\)
−0.654972 + 0.755653i \(0.727320\pi\)
\(258\) −6.00000 −0.373544
\(259\) −7.00000 −0.434959
\(260\) −1.00000 −0.0620174
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) −2.00000 −0.123325 −0.0616626 − 0.998097i \(-0.519640\pi\)
−0.0616626 + 0.998097i \(0.519640\pi\)
\(264\) 0 0
\(265\) 8.00000 0.491436
\(266\) −1.00000 −0.0613139
\(267\) 0 0
\(268\) 14.0000 0.855186
\(269\) −19.0000 −1.15845 −0.579225 − 0.815168i \(-0.696645\pi\)
−0.579225 + 0.815168i \(0.696645\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −14.0000 −0.850439 −0.425220 − 0.905090i \(-0.639803\pi\)
−0.425220 + 0.905090i \(0.639803\pi\)
\(272\) 5.00000 0.303170
\(273\) 1.00000 0.0605228
\(274\) −15.0000 −0.906183
\(275\) 0 0
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −3.00000 −0.179928
\(279\) 10.0000 0.598684
\(280\) 1.00000 0.0597614
\(281\) 24.0000 1.43172 0.715860 − 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 6.00000 0.357295
\(283\) 28.0000 1.66443 0.832214 − 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) −1.00000 −0.0593391
\(285\) 1.00000 0.0592349
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) 1.00000 0.0589256
\(289\) 8.00000 0.470588
\(290\) 1.00000 0.0587220
\(291\) 2.00000 0.117242
\(292\) 2.00000 0.117041
\(293\) 12.0000 0.701047 0.350524 − 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 6.00000 0.349927
\(295\) −4.00000 −0.232889
\(296\) −7.00000 −0.406867
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 6.00000 0.345834
\(302\) 20.0000 1.15087
\(303\) −3.00000 −0.172345
\(304\) −1.00000 −0.0573539
\(305\) 4.00000 0.229039
\(306\) 5.00000 0.285831
\(307\) 18.0000 1.02731 0.513657 − 0.857996i \(-0.328290\pi\)
0.513657 + 0.857996i \(0.328290\pi\)
\(308\) 0 0
\(309\) 1.00000 0.0568880
\(310\) 10.0000 0.567962
\(311\) −16.0000 −0.907277 −0.453638 − 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 1.00000 0.0566139
\(313\) −22.0000 −1.24351 −0.621757 − 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) −17.0000 −0.959366
\(315\) 1.00000 0.0563436
\(316\) 6.00000 0.337526
\(317\) −12.0000 −0.673987 −0.336994 − 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) −8.00000 −0.448618
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 8.00000 0.446516
\(322\) 0 0
\(323\) −5.00000 −0.278207
\(324\) 1.00000 0.0555556
\(325\) −1.00000 −0.0554700
\(326\) 12.0000 0.664619
\(327\) 8.00000 0.442401
\(328\) −2.00000 −0.110432
\(329\) −6.00000 −0.330791
\(330\) 0 0
\(331\) −9.00000 −0.494685 −0.247342 − 0.968928i \(-0.579557\pi\)
−0.247342 + 0.968928i \(0.579557\pi\)
\(332\) 17.0000 0.932996
\(333\) −7.00000 −0.383598
\(334\) 12.0000 0.656611
\(335\) 14.0000 0.764902
\(336\) −1.00000 −0.0545545
\(337\) 34.0000 1.85210 0.926049 − 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) −12.0000 −0.652714
\(339\) −6.00000 −0.325875
\(340\) 5.00000 0.271163
\(341\) 0 0
\(342\) −1.00000 −0.0540738
\(343\) −13.0000 −0.701934
\(344\) 6.00000 0.323498
\(345\) 0 0
\(346\) 16.0000 0.860165
\(347\) 7.00000 0.375780 0.187890 − 0.982190i \(-0.439835\pi\)
0.187890 + 0.982190i \(0.439835\pi\)
\(348\) −1.00000 −0.0536056
\(349\) 2.00000 0.107058 0.0535288 − 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 1.00000 0.0534522
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −14.0000 −0.745145 −0.372572 − 0.928003i \(-0.621524\pi\)
−0.372572 + 0.928003i \(0.621524\pi\)
\(354\) 4.00000 0.212598
\(355\) −1.00000 −0.0530745
\(356\) 0 0
\(357\) −5.00000 −0.264628
\(358\) 12.0000 0.634220
\(359\) −24.0000 −1.26667 −0.633336 − 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 1.00000 0.0527046
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) −1.00000 −0.0524142
\(365\) 2.00000 0.104685
\(366\) −4.00000 −0.209083
\(367\) −9.00000 −0.469796 −0.234898 − 0.972020i \(-0.575476\pi\)
−0.234898 + 0.972020i \(0.575476\pi\)
\(368\) 0 0
\(369\) −2.00000 −0.104116
\(370\) −7.00000 −0.363913
\(371\) 8.00000 0.415339
\(372\) −10.0000 −0.518476
\(373\) 1.00000 0.0517780 0.0258890 − 0.999665i \(-0.491758\pi\)
0.0258890 + 0.999665i \(0.491758\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) −6.00000 −0.309426
\(377\) −1.00000 −0.0515026
\(378\) −1.00000 −0.0514344
\(379\) −23.0000 −1.18143 −0.590715 − 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) −1.00000 −0.0512989
\(381\) 12.0000 0.614779
\(382\) −19.0000 −0.972125
\(383\) 6.00000 0.306586 0.153293 − 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −16.0000 −0.814379
\(387\) 6.00000 0.304997
\(388\) −2.00000 −0.101535
\(389\) −38.0000 −1.92668 −0.963338 − 0.268290i \(-0.913542\pi\)
−0.963338 + 0.268290i \(0.913542\pi\)
\(390\) 1.00000 0.0506370
\(391\) 0 0
\(392\) −6.00000 −0.303046
\(393\) 0 0
\(394\) 28.0000 1.41062
\(395\) 6.00000 0.301893
\(396\) 0 0
\(397\) −15.0000 −0.752828 −0.376414 − 0.926451i \(-0.622843\pi\)
−0.376414 + 0.926451i \(0.622843\pi\)
\(398\) 12.0000 0.601506
\(399\) 1.00000 0.0500626
\(400\) 1.00000 0.0500000
\(401\) 22.0000 1.09863 0.549314 − 0.835616i \(-0.314889\pi\)
0.549314 + 0.835616i \(0.314889\pi\)
\(402\) −14.0000 −0.698257
\(403\) −10.0000 −0.498135
\(404\) 3.00000 0.149256
\(405\) 1.00000 0.0496904
\(406\) 1.00000 0.0496292
\(407\) 0 0
\(408\) −5.00000 −0.247537
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) −2.00000 −0.0987730
\(411\) 15.0000 0.739895
\(412\) −1.00000 −0.0492665
\(413\) −4.00000 −0.196827
\(414\) 0 0
\(415\) 17.0000 0.834497
\(416\) −1.00000 −0.0490290
\(417\) 3.00000 0.146911
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 − 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) −1.00000 −0.0487950
\(421\) 10.0000 0.487370 0.243685 − 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −9.00000 −0.438113
\(423\) −6.00000 −0.291730
\(424\) 8.00000 0.388514
\(425\) 5.00000 0.242536
\(426\) 1.00000 0.0484502
\(427\) 4.00000 0.193574
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) 9.00000 0.433515 0.216757 − 0.976226i \(-0.430452\pi\)
0.216757 + 0.976226i \(0.430452\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 4.00000 0.192228 0.0961139 − 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 10.0000 0.480015
\(435\) −1.00000 −0.0479463
\(436\) −8.00000 −0.383131
\(437\) 0 0
\(438\) −2.00000 −0.0955637
\(439\) −38.0000 −1.81364 −0.906821 − 0.421517i \(-0.861498\pi\)
−0.906821 + 0.421517i \(0.861498\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −5.00000 −0.237826
\(443\) 29.0000 1.37783 0.688916 − 0.724841i \(-0.258087\pi\)
0.688916 + 0.724841i \(0.258087\pi\)
\(444\) 7.00000 0.332205
\(445\) 0 0
\(446\) 13.0000 0.615568
\(447\) −10.0000 −0.472984
\(448\) 1.00000 0.0472456
\(449\) −38.0000 −1.79333 −0.896665 − 0.442709i \(-0.854018\pi\)
−0.896665 + 0.442709i \(0.854018\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −20.0000 −0.939682
\(454\) 8.00000 0.375459
\(455\) −1.00000 −0.0468807
\(456\) 1.00000 0.0468293
\(457\) −40.0000 −1.87112 −0.935561 − 0.353166i \(-0.885105\pi\)
−0.935561 + 0.353166i \(0.885105\pi\)
\(458\) 8.00000 0.373815
\(459\) −5.00000 −0.233380
\(460\) 0 0
\(461\) 25.0000 1.16437 0.582183 − 0.813058i \(-0.302199\pi\)
0.582183 + 0.813058i \(0.302199\pi\)
\(462\) 0 0
\(463\) −40.0000 −1.85896 −0.929479 − 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 1.00000 0.0464238
\(465\) −10.0000 −0.463739
\(466\) 14.0000 0.648537
\(467\) 11.0000 0.509019 0.254510 − 0.967070i \(-0.418086\pi\)
0.254510 + 0.967070i \(0.418086\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 14.0000 0.646460
\(470\) −6.00000 −0.276759
\(471\) 17.0000 0.783319
\(472\) −4.00000 −0.184115
\(473\) 0 0
\(474\) −6.00000 −0.275589
\(475\) −1.00000 −0.0458831
\(476\) 5.00000 0.229175
\(477\) 8.00000 0.366295
\(478\) 3.00000 0.137217
\(479\) 35.0000 1.59919 0.799595 − 0.600539i \(-0.205047\pi\)
0.799595 + 0.600539i \(0.205047\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 7.00000 0.319173
\(482\) −17.0000 −0.774329
\(483\) 0 0
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) −1.00000 −0.0453609
\(487\) −41.0000 −1.85789 −0.928944 − 0.370221i \(-0.879282\pi\)
−0.928944 + 0.370221i \(0.879282\pi\)
\(488\) 4.00000 0.181071
\(489\) −12.0000 −0.542659
\(490\) −6.00000 −0.271052
\(491\) −38.0000 −1.71492 −0.857458 − 0.514554i \(-0.827958\pi\)
−0.857458 + 0.514554i \(0.827958\pi\)
\(492\) 2.00000 0.0901670
\(493\) 5.00000 0.225189
\(494\) 1.00000 0.0449921
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) −1.00000 −0.0448561
\(498\) −17.0000 −0.761788
\(499\) −31.0000 −1.38775 −0.693875 − 0.720095i \(-0.744098\pi\)
−0.693875 + 0.720095i \(0.744098\pi\)
\(500\) 1.00000 0.0447214
\(501\) −12.0000 −0.536120
\(502\) 24.0000 1.07117
\(503\) −36.0000 −1.60516 −0.802580 − 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 1.00000 0.0445435
\(505\) 3.00000 0.133498
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −12.0000 −0.532414
\(509\) 30.0000 1.32973 0.664863 − 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −5.00000 −0.221404
\(511\) 2.00000 0.0884748
\(512\) 1.00000 0.0441942
\(513\) 1.00000 0.0441511
\(514\) −21.0000 −0.926270
\(515\) −1.00000 −0.0440653
\(516\) −6.00000 −0.264135
\(517\) 0 0
\(518\) −7.00000 −0.307562
\(519\) −16.0000 −0.702322
\(520\) −1.00000 −0.0438529
\(521\) −28.0000 −1.22670 −0.613351 − 0.789810i \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) 1.00000 0.0437688
\(523\) −16.0000 −0.699631 −0.349816 − 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 0 0
\(525\) −1.00000 −0.0436436
\(526\) −2.00000 −0.0872041
\(527\) 50.0000 2.17803
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 8.00000 0.347498
\(531\) −4.00000 −0.173585
\(532\) −1.00000 −0.0433555
\(533\) 2.00000 0.0866296
\(534\) 0 0
\(535\) −8.00000 −0.345870
\(536\) 14.0000 0.604708
\(537\) −12.0000 −0.517838
\(538\) −19.0000 −0.819148
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 22.0000 0.945854 0.472927 − 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) −14.0000 −0.601351
\(543\) 0 0
\(544\) 5.00000 0.214373
\(545\) −8.00000 −0.342682
\(546\) 1.00000 0.0427960
\(547\) −2.00000 −0.0855138 −0.0427569 − 0.999086i \(-0.513614\pi\)
−0.0427569 + 0.999086i \(0.513614\pi\)
\(548\) −15.0000 −0.640768
\(549\) 4.00000 0.170716
\(550\) 0 0
\(551\) −1.00000 −0.0426014
\(552\) 0 0
\(553\) 6.00000 0.255146
\(554\) −2.00000 −0.0849719
\(555\) 7.00000 0.297133
\(556\) −3.00000 −0.127228
\(557\) 38.0000 1.61011 0.805056 − 0.593199i \(-0.202135\pi\)
0.805056 + 0.593199i \(0.202135\pi\)
\(558\) 10.0000 0.423334
\(559\) −6.00000 −0.253773
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) 24.0000 1.01238
\(563\) 3.00000 0.126435 0.0632175 − 0.998000i \(-0.479864\pi\)
0.0632175 + 0.998000i \(0.479864\pi\)
\(564\) 6.00000 0.252646
\(565\) 6.00000 0.252422
\(566\) 28.0000 1.17693
\(567\) 1.00000 0.0419961
\(568\) −1.00000 −0.0419591
\(569\) −30.0000 −1.25767 −0.628833 − 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 1.00000 0.0418854
\(571\) −8.00000 −0.334790 −0.167395 − 0.985890i \(-0.553535\pi\)
−0.167395 + 0.985890i \(0.553535\pi\)
\(572\) 0 0
\(573\) 19.0000 0.793736
\(574\) −2.00000 −0.0834784
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 34.0000 1.41544 0.707719 − 0.706494i \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) 8.00000 0.332756
\(579\) 16.0000 0.664937
\(580\) 1.00000 0.0415227
\(581\) 17.0000 0.705279
\(582\) 2.00000 0.0829027
\(583\) 0 0
\(584\) 2.00000 0.0827606
\(585\) −1.00000 −0.0413449
\(586\) 12.0000 0.495715
\(587\) 5.00000 0.206372 0.103186 − 0.994662i \(-0.467096\pi\)
0.103186 + 0.994662i \(0.467096\pi\)
\(588\) 6.00000 0.247436
\(589\) −10.0000 −0.412043
\(590\) −4.00000 −0.164677
\(591\) −28.0000 −1.15177
\(592\) −7.00000 −0.287698
\(593\) −18.0000 −0.739171 −0.369586 − 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) 5.00000 0.204980
\(596\) 10.0000 0.409616
\(597\) −12.0000 −0.491127
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 − 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −22.0000 −0.897399 −0.448699 − 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 6.00000 0.244542
\(603\) 14.0000 0.570124
\(604\) 20.0000 0.813788
\(605\) 0 0
\(606\) −3.00000 −0.121867
\(607\) 3.00000 0.121766 0.0608831 − 0.998145i \(-0.480608\pi\)
0.0608831 + 0.998145i \(0.480608\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −1.00000 −0.0405220
\(610\) 4.00000 0.161955
\(611\) 6.00000 0.242734
\(612\) 5.00000 0.202113
\(613\) −25.0000 −1.00974 −0.504870 − 0.863195i \(-0.668460\pi\)
−0.504870 + 0.863195i \(0.668460\pi\)
\(614\) 18.0000 0.726421
\(615\) 2.00000 0.0806478
\(616\) 0 0
\(617\) 9.00000 0.362326 0.181163 − 0.983453i \(-0.442014\pi\)
0.181163 + 0.983453i \(0.442014\pi\)
\(618\) 1.00000 0.0402259
\(619\) −7.00000 −0.281354 −0.140677 − 0.990056i \(-0.544928\pi\)
−0.140677 + 0.990056i \(0.544928\pi\)
\(620\) 10.0000 0.401610
\(621\) 0 0
\(622\) −16.0000 −0.641542
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 1.00000 0.0400000
\(626\) −22.0000 −0.879297
\(627\) 0 0
\(628\) −17.0000 −0.678374
\(629\) −35.0000 −1.39554
\(630\) 1.00000 0.0398410
\(631\) 40.0000 1.59237 0.796187 − 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 6.00000 0.238667
\(633\) 9.00000 0.357718
\(634\) −12.0000 −0.476581
\(635\) −12.0000 −0.476205
\(636\) −8.00000 −0.317221
\(637\) 6.00000 0.237729
\(638\) 0 0
\(639\) −1.00000 −0.0395594
\(640\) 1.00000 0.0395285
\(641\) −2.00000 −0.0789953 −0.0394976 − 0.999220i \(-0.512576\pi\)
−0.0394976 + 0.999220i \(0.512576\pi\)
\(642\) 8.00000 0.315735
\(643\) 40.0000 1.57745 0.788723 − 0.614749i \(-0.210743\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) −5.00000 −0.196722
\(647\) −20.0000 −0.786281 −0.393141 − 0.919478i \(-0.628611\pi\)
−0.393141 + 0.919478i \(0.628611\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −1.00000 −0.0392232
\(651\) −10.0000 −0.391931
\(652\) 12.0000 0.469956
\(653\) 10.0000 0.391330 0.195665 − 0.980671i \(-0.437313\pi\)
0.195665 + 0.980671i \(0.437313\pi\)
\(654\) 8.00000 0.312825
\(655\) 0 0
\(656\) −2.00000 −0.0780869
\(657\) 2.00000 0.0780274
\(658\) −6.00000 −0.233904
\(659\) −30.0000 −1.16863 −0.584317 − 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) −34.0000 −1.32245 −0.661223 − 0.750189i \(-0.729962\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(662\) −9.00000 −0.349795
\(663\) 5.00000 0.194184
\(664\) 17.0000 0.659728
\(665\) −1.00000 −0.0387783
\(666\) −7.00000 −0.271244
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) −13.0000 −0.502609
\(670\) 14.0000 0.540867
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) −28.0000 −1.07932 −0.539660 − 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 34.0000 1.30963
\(675\) −1.00000 −0.0384900
\(676\) −12.0000 −0.461538
\(677\) −14.0000 −0.538064 −0.269032 − 0.963131i \(-0.586704\pi\)
−0.269032 + 0.963131i \(0.586704\pi\)
\(678\) −6.00000 −0.230429
\(679\) −2.00000 −0.0767530
\(680\) 5.00000 0.191741
\(681\) −8.00000 −0.306561
\(682\) 0 0
\(683\) 3.00000 0.114792 0.0573959 − 0.998351i \(-0.481720\pi\)
0.0573959 + 0.998351i \(0.481720\pi\)
\(684\) −1.00000 −0.0382360
\(685\) −15.0000 −0.573121
\(686\) −13.0000 −0.496342
\(687\) −8.00000 −0.305219
\(688\) 6.00000 0.228748
\(689\) −8.00000 −0.304776
\(690\) 0 0
\(691\) −15.0000 −0.570627 −0.285313 − 0.958434i \(-0.592098\pi\)
−0.285313 + 0.958434i \(0.592098\pi\)
\(692\) 16.0000 0.608229
\(693\) 0 0
\(694\) 7.00000 0.265716
\(695\) −3.00000 −0.113796
\(696\) −1.00000 −0.0379049
\(697\) −10.0000 −0.378777
\(698\) 2.00000 0.0757011
\(699\) −14.0000 −0.529529
\(700\) 1.00000 0.0377964
\(701\) −39.0000 −1.47301 −0.736505 − 0.676432i \(-0.763525\pi\)
−0.736505 + 0.676432i \(0.763525\pi\)
\(702\) 1.00000 0.0377426
\(703\) 7.00000 0.264010
\(704\) 0 0
\(705\) 6.00000 0.225973
\(706\) −14.0000 −0.526897
\(707\) 3.00000 0.112827
\(708\) 4.00000 0.150329
\(709\) −46.0000 −1.72757 −0.863783 − 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) −1.00000 −0.0375293
\(711\) 6.00000 0.225018
\(712\) 0 0
\(713\) 0 0
\(714\) −5.00000 −0.187120
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −3.00000 −0.112037
\(718\) −24.0000 −0.895672
\(719\) 20.0000 0.745874 0.372937 − 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 1.00000 0.0372678
\(721\) −1.00000 −0.0372419
\(722\) −18.0000 −0.669891
\(723\) 17.0000 0.632237
\(724\) 0 0
\(725\) 1.00000 0.0371391
\(726\) 0 0
\(727\) 13.0000 0.482143 0.241072 − 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) −1.00000 −0.0370625
\(729\) 1.00000 0.0370370
\(730\) 2.00000 0.0740233
\(731\) 30.0000 1.10959
\(732\) −4.00000 −0.147844
\(733\) −26.0000 −0.960332 −0.480166 − 0.877178i \(-0.659424\pi\)
−0.480166 + 0.877178i \(0.659424\pi\)
\(734\) −9.00000 −0.332196
\(735\) 6.00000 0.221313
\(736\) 0 0
\(737\) 0 0
\(738\) −2.00000 −0.0736210
\(739\) −19.0000 −0.698926 −0.349463 − 0.936950i \(-0.613636\pi\)
−0.349463 + 0.936950i \(0.613636\pi\)
\(740\) −7.00000 −0.257325
\(741\) −1.00000 −0.0367359
\(742\) 8.00000 0.293689
\(743\) −4.00000 −0.146746 −0.0733729 − 0.997305i \(-0.523376\pi\)
−0.0733729 + 0.997305i \(0.523376\pi\)
\(744\) −10.0000 −0.366618
\(745\) 10.0000 0.366372
\(746\) 1.00000 0.0366126
\(747\) 17.0000 0.621997
\(748\) 0 0
\(749\) −8.00000 −0.292314
\(750\) −1.00000 −0.0365148
\(751\) 2.00000 0.0729810 0.0364905 − 0.999334i \(-0.488382\pi\)
0.0364905 + 0.999334i \(0.488382\pi\)
\(752\) −6.00000 −0.218797
\(753\) −24.0000 −0.874609
\(754\) −1.00000 −0.0364179
\(755\) 20.0000 0.727875
\(756\) −1.00000 −0.0363696
\(757\) −30.0000 −1.09037 −0.545184 − 0.838316i \(-0.683540\pi\)
−0.545184 + 0.838316i \(0.683540\pi\)
\(758\) −23.0000 −0.835398
\(759\) 0 0
\(760\) −1.00000 −0.0362738
\(761\) −36.0000 −1.30500 −0.652499 − 0.757789i \(-0.726280\pi\)
−0.652499 + 0.757789i \(0.726280\pi\)
\(762\) 12.0000 0.434714
\(763\) −8.00000 −0.289619
\(764\) −19.0000 −0.687396
\(765\) 5.00000 0.180775
\(766\) 6.00000 0.216789
\(767\) 4.00000 0.144432
\(768\) −1.00000 −0.0360844
\(769\) −31.0000 −1.11789 −0.558944 − 0.829205i \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) 0 0
\(771\) 21.0000 0.756297
\(772\) −16.0000 −0.575853
\(773\) 32.0000 1.15096 0.575480 − 0.817816i \(-0.304815\pi\)
0.575480 + 0.817816i \(0.304815\pi\)
\(774\) 6.00000 0.215666
\(775\) 10.0000 0.359211
\(776\) −2.00000 −0.0717958
\(777\) 7.00000 0.251124
\(778\) −38.0000 −1.36237
\(779\) 2.00000 0.0716574
\(780\) 1.00000 0.0358057
\(781\) 0 0
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) −6.00000 −0.214286
\(785\) −17.0000 −0.606756
\(786\) 0 0
\(787\) −8.00000 −0.285169 −0.142585 − 0.989783i \(-0.545541\pi\)
−0.142585 + 0.989783i \(0.545541\pi\)
\(788\) 28.0000 0.997459
\(789\) 2.00000 0.0712019
\(790\) 6.00000 0.213470
\(791\) 6.00000 0.213335
\(792\) 0 0
\(793\) −4.00000 −0.142044
\(794\) −15.0000 −0.532330
\(795\) −8.00000 −0.283731
\(796\) 12.0000 0.425329
\(797\) 32.0000 1.13350 0.566749 − 0.823890i \(-0.308201\pi\)
0.566749 + 0.823890i \(0.308201\pi\)
\(798\) 1.00000 0.0353996
\(799\) −30.0000 −1.06132
\(800\) 1.00000 0.0353553
\(801\) 0 0
\(802\) 22.0000 0.776847
\(803\) 0 0
\(804\) −14.0000 −0.493742
\(805\) 0 0
\(806\) −10.0000 −0.352235
\(807\) 19.0000 0.668832
\(808\) 3.00000 0.105540
\(809\) 18.0000 0.632846 0.316423 − 0.948618i \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) 1.00000 0.0351364
\(811\) 39.0000 1.36948 0.684738 − 0.728790i \(-0.259917\pi\)
0.684738 + 0.728790i \(0.259917\pi\)
\(812\) 1.00000 0.0350931
\(813\) 14.0000 0.491001
\(814\) 0 0
\(815\) 12.0000 0.420342
\(816\) −5.00000 −0.175035
\(817\) −6.00000 −0.209913
\(818\) −22.0000 −0.769212
\(819\) −1.00000 −0.0349428
\(820\) −2.00000 −0.0698430
\(821\) −50.0000 −1.74501 −0.872506 − 0.488603i \(-0.837507\pi\)
−0.872506 + 0.488603i \(0.837507\pi\)
\(822\) 15.0000 0.523185
\(823\) 33.0000 1.15031 0.575154 − 0.818045i \(-0.304942\pi\)
0.575154 + 0.818045i \(0.304942\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 0 0
\(826\) −4.00000 −0.139178
\(827\) 3.00000 0.104320 0.0521601 − 0.998639i \(-0.483389\pi\)
0.0521601 + 0.998639i \(0.483389\pi\)
\(828\) 0 0
\(829\) 16.0000 0.555703 0.277851 − 0.960624i \(-0.410378\pi\)
0.277851 + 0.960624i \(0.410378\pi\)
\(830\) 17.0000 0.590079
\(831\) 2.00000 0.0693792
\(832\) −1.00000 −0.0346688
\(833\) −30.0000 −1.03944
\(834\) 3.00000 0.103882
\(835\) 12.0000 0.415277
\(836\) 0 0
\(837\) −10.0000 −0.345651
\(838\) −30.0000 −1.03633
\(839\) −13.0000 −0.448810 −0.224405 − 0.974496i \(-0.572044\pi\)
−0.224405 + 0.974496i \(0.572044\pi\)
\(840\) −1.00000 −0.0345033
\(841\) −28.0000 −0.965517
\(842\) 10.0000 0.344623
\(843\) −24.0000 −0.826604
\(844\) −9.00000 −0.309793
\(845\) −12.0000 −0.412813
\(846\) −6.00000 −0.206284
\(847\) 0 0
\(848\) 8.00000 0.274721
\(849\) −28.0000 −0.960958
\(850\) 5.00000 0.171499
\(851\) 0 0
\(852\) 1.00000 0.0342594
\(853\) −29.0000 −0.992941 −0.496471 − 0.868054i \(-0.665371\pi\)
−0.496471 + 0.868054i \(0.665371\pi\)
\(854\) 4.00000 0.136877
\(855\) −1.00000 −0.0341993
\(856\) −8.00000 −0.273434
\(857\) 57.0000 1.94708 0.973541 − 0.228510i \(-0.0733855\pi\)
0.973541 + 0.228510i \(0.0733855\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 − 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 6.00000 0.204598
\(861\) 2.00000 0.0681598
\(862\) 9.00000 0.306541
\(863\) 18.0000 0.612727 0.306364 − 0.951915i \(-0.400888\pi\)
0.306364 + 0.951915i \(0.400888\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 16.0000 0.544016
\(866\) 4.00000 0.135926
\(867\) −8.00000 −0.271694
\(868\) 10.0000 0.339422
\(869\) 0 0
\(870\) −1.00000 −0.0339032
\(871\) −14.0000 −0.474372
\(872\) −8.00000 −0.270914
\(873\) −2.00000 −0.0676897
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) −2.00000 −0.0675737
\(877\) −51.0000 −1.72215 −0.861074 − 0.508480i \(-0.830208\pi\)
−0.861074 + 0.508480i \(0.830208\pi\)
\(878\) −38.0000 −1.28244
\(879\) −12.0000 −0.404750
\(880\) 0 0
\(881\) −6.00000 −0.202145 −0.101073 − 0.994879i \(-0.532227\pi\)
−0.101073 + 0.994879i \(0.532227\pi\)
\(882\) −6.00000 −0.202031
\(883\) −22.0000 −0.740359 −0.370179 − 0.928960i \(-0.620704\pi\)
−0.370179 + 0.928960i \(0.620704\pi\)
\(884\) −5.00000 −0.168168
\(885\) 4.00000 0.134459
\(886\) 29.0000 0.974274
\(887\) −24.0000 −0.805841 −0.402921 − 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) 7.00000 0.234905
\(889\) −12.0000 −0.402467
\(890\) 0 0
\(891\) 0 0
\(892\) 13.0000 0.435272
\(893\) 6.00000 0.200782
\(894\) −10.0000 −0.334450
\(895\) 12.0000 0.401116
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −38.0000 −1.26808
\(899\) 10.0000 0.333519
\(900\) 1.00000 0.0333333
\(901\) 40.0000 1.33259
\(902\) 0 0
\(903\) −6.00000 −0.199667
\(904\) 6.00000 0.199557
\(905\) 0 0
\(906\) −20.0000 −0.664455
\(907\) 34.0000 1.12895 0.564476 − 0.825450i \(-0.309078\pi\)
0.564476 + 0.825450i \(0.309078\pi\)
\(908\) 8.00000 0.265489
\(909\) 3.00000 0.0995037
\(910\) −1.00000 −0.0331497
\(911\) −1.00000 −0.0331315 −0.0165657 − 0.999863i \(-0.505273\pi\)
−0.0165657 + 0.999863i \(0.505273\pi\)
\(912\) 1.00000 0.0331133
\(913\) 0 0
\(914\) −40.0000 −1.32308
\(915\) −4.00000 −0.132236
\(916\) 8.00000 0.264327
\(917\) 0 0
\(918\) −5.00000 −0.165025
\(919\) 20.0000 0.659739 0.329870 − 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 0 0
\(921\) −18.0000 −0.593120
\(922\) 25.0000 0.823331
\(923\) 1.00000 0.0329154
\(924\) 0 0
\(925\) −7.00000 −0.230159
\(926\) −40.0000 −1.31448
\(927\) −1.00000 −0.0328443
\(928\) 1.00000 0.0328266
\(929\) −24.0000 −0.787414 −0.393707 − 0.919236i \(-0.628808\pi\)
−0.393707 + 0.919236i \(0.628808\pi\)
\(930\) −10.0000 −0.327913
\(931\) 6.00000 0.196642
\(932\) 14.0000 0.458585
\(933\) 16.0000 0.523816
\(934\) 11.0000 0.359931
\(935\) 0 0
\(936\) −1.00000 −0.0326860
\(937\) 38.0000 1.24141 0.620703 − 0.784046i \(-0.286847\pi\)
0.620703 + 0.784046i \(0.286847\pi\)
\(938\) 14.0000 0.457116
\(939\) 22.0000 0.717943
\(940\) −6.00000 −0.195698
\(941\) 9.00000 0.293392 0.146696 − 0.989182i \(-0.453136\pi\)
0.146696 + 0.989182i \(0.453136\pi\)
\(942\) 17.0000 0.553890
\(943\) 0 0
\(944\) −4.00000 −0.130189
\(945\) −1.00000 −0.0325300
\(946\) 0 0
\(947\) 9.00000 0.292461 0.146230 − 0.989251i \(-0.453286\pi\)
0.146230 + 0.989251i \(0.453286\pi\)
\(948\) −6.00000 −0.194871
\(949\) −2.00000 −0.0649227
\(950\) −1.00000 −0.0324443
\(951\) 12.0000 0.389127
\(952\) 5.00000 0.162051
\(953\) 30.0000 0.971795 0.485898 − 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) 8.00000 0.259010
\(955\) −19.0000 −0.614826
\(956\) 3.00000 0.0970269
\(957\) 0 0
\(958\) 35.0000 1.13080
\(959\) −15.0000 −0.484375
\(960\) −1.00000 −0.0322749
\(961\) 69.0000 2.22581
\(962\) 7.00000 0.225689
\(963\) −8.00000 −0.257796
\(964\) −17.0000 −0.547533
\(965\) −16.0000 −0.515058
\(966\) 0 0
\(967\) 24.0000 0.771788 0.385894 − 0.922543i \(-0.373893\pi\)
0.385894 + 0.922543i \(0.373893\pi\)
\(968\) 0 0
\(969\) 5.00000 0.160623
\(970\) −2.00000 −0.0642161
\(971\) 24.0000 0.770197 0.385098 − 0.922876i \(-0.374168\pi\)
0.385098 + 0.922876i \(0.374168\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −3.00000 −0.0961756
\(974\) −41.0000 −1.31372
\(975\) 1.00000 0.0320256
\(976\) 4.00000 0.128037
\(977\) −18.0000 −0.575871 −0.287936 − 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) −12.0000 −0.383718
\(979\) 0 0
\(980\) −6.00000 −0.191663
\(981\) −8.00000 −0.255420
\(982\) −38.0000 −1.21263
\(983\) 46.0000 1.46717 0.733586 − 0.679597i \(-0.237845\pi\)
0.733586 + 0.679597i \(0.237845\pi\)
\(984\) 2.00000 0.0637577
\(985\) 28.0000 0.892154
\(986\) 5.00000 0.159232
\(987\) 6.00000 0.190982
\(988\) 1.00000 0.0318142
\(989\) 0 0
\(990\) 0 0
\(991\) 10.0000 0.317660 0.158830 − 0.987306i \(-0.449228\pi\)
0.158830 + 0.987306i \(0.449228\pi\)
\(992\) 10.0000 0.317500
\(993\) 9.00000 0.285606
\(994\) −1.00000 −0.0317181
\(995\) 12.0000 0.380426
\(996\) −17.0000 −0.538666
\(997\) −11.0000 −0.348373 −0.174187 − 0.984713i \(-0.555730\pi\)
−0.174187 + 0.984713i \(0.555730\pi\)
\(998\) −31.0000 −0.981288
\(999\) 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.q.1.1 yes 1
11.10 odd 2 3630.2.a.e.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3630.2.a.e.1.1 ✓ 1 11.10 odd 2
3630.2.a.q.1.1 yes 1 1.1 even 1 trivial