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Properties

Label 366.2.a.c.1.1
Level $366$
Weight $2$
Character 366.1
Self dual yes
Analytic conductor $2.923$
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] = [366,2,Mod(1,366)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(366, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("366.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 366 = 2 \cdot 3 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 366.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: \(2.92252471398\)
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 \(\chi\) \(=\) 366.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +6.00000 q^{11} +1.00000 q^{12} +2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +3.00000 q^{17} -1.00000 q^{18} +1.00000 q^{20} -2.00000 q^{21} -6.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{27} -2.00000 q^{28} +6.00000 q^{29} -1.00000 q^{30} -1.00000 q^{32} +6.00000 q^{33} -3.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +3.00000 q^{37} -1.00000 q^{40} +12.0000 q^{41} +2.00000 q^{42} +1.00000 q^{43} +6.00000 q^{44} +1.00000 q^{45} +1.00000 q^{46} -12.0000 q^{47} +1.00000 q^{48} -3.00000 q^{49} +4.00000 q^{50} +3.00000 q^{51} -2.00000 q^{53} -1.00000 q^{54} +6.00000 q^{55} +2.00000 q^{56} -6.00000 q^{58} +1.00000 q^{60} -1.00000 q^{61} -2.00000 q^{63} +1.00000 q^{64} -6.00000 q^{66} +4.00000 q^{67} +3.00000 q^{68} -1.00000 q^{69} +2.00000 q^{70} -13.0000 q^{71} -1.00000 q^{72} -9.00000 q^{73} -3.00000 q^{74} -4.00000 q^{75} -12.0000 q^{77} -14.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} +3.00000 q^{83} -2.00000 q^{84} +3.00000 q^{85} -1.00000 q^{86} +6.00000 q^{87} -6.00000 q^{88} -9.00000 q^{89} -1.00000 q^{90} -1.00000 q^{92} +12.0000 q^{94} -1.00000 q^{96} -1.00000 q^{97} +3.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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 0.223607 − 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) −1.00000 −0.408248
\(7\) −2.00000 −0.755929 −0.377964 − 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 6.00000 1.80907 0.904534 − 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 2.00000 0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 − 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.00000 −0.436436
\(22\) −6.00000 −1.27920
\(23\) −1.00000 −0.208514 −0.104257 − 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −2.00000 −0.377964
\(29\) 6.00000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −1.00000 −0.182574
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.00000 1.04447
\(34\) −3.00000 −0.514496
\(35\) −2.00000 −0.338062
\(36\) 1.00000 0.166667
\(37\) 3.00000 0.493197 0.246598 − 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 12.0000 1.87409 0.937043 − 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 2.00000 0.308607
\(43\) 1.00000 0.152499 0.0762493 − 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 6.00000 0.904534
\(45\) 1.00000 0.149071
\(46\) 1.00000 0.147442
\(47\) −12.0000 −1.75038 −0.875190 − 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) 4.00000 0.565685
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 − 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) −1.00000 −0.136083
\(55\) 6.00000 0.809040
\(56\) 2.00000 0.267261
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 1.00000 0.129099
\(61\) −1.00000 −0.128037
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.00000 −0.738549
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 3.00000 0.363803
\(69\) −1.00000 −0.120386
\(70\) 2.00000 0.239046
\(71\) −13.0000 −1.54282 −0.771408 − 0.636341i \(-0.780447\pi\)
−0.771408 + 0.636341i \(0.780447\pi\)
\(72\) −1.00000 −0.117851
\(73\) −9.00000 −1.05337 −0.526685 − 0.850060i \(-0.676565\pi\)
−0.526685 + 0.850060i \(0.676565\pi\)
\(74\) −3.00000 −0.348743
\(75\) −4.00000 −0.461880
\(76\) 0 0
\(77\) −12.0000 −1.36753
\(78\) 0 0
\(79\) −14.0000 −1.57512 −0.787562 − 0.616236i \(-0.788657\pi\)
−0.787562 + 0.616236i \(0.788657\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −12.0000 −1.32518
\(83\) 3.00000 0.329293 0.164646 − 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) −2.00000 −0.218218
\(85\) 3.00000 0.325396
\(86\) −1.00000 −0.107833
\(87\) 6.00000 0.643268
\(88\) −6.00000 −0.639602
\(89\) −9.00000 −0.953998 −0.476999 − 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −1.00000 −0.104257
\(93\) 0 0
\(94\) 12.0000 1.23771
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −1.00000 −0.101535 −0.0507673 − 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 3.00000 0.303046
\(99\) 6.00000 0.603023
\(100\) −4.00000 −0.400000
\(101\) 12.0000 1.19404 0.597022 − 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) −3.00000 −0.297044
\(103\) −5.00000 −0.492665 −0.246332 − 0.969185i \(-0.579225\pi\)
−0.246332 + 0.969185i \(0.579225\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 2.00000 0.194257
\(107\) −15.0000 −1.45010 −0.725052 − 0.688694i \(-0.758184\pi\)
−0.725052 + 0.688694i \(0.758184\pi\)
\(108\) 1.00000 0.0962250
\(109\) −8.00000 −0.766261 −0.383131 − 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) −6.00000 −0.572078
\(111\) 3.00000 0.284747
\(112\) −2.00000 −0.188982
\(113\) 4.00000 0.376288 0.188144 − 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) 0 0
\(119\) −6.00000 −0.550019
\(120\) −1.00000 −0.0912871
\(121\) 25.0000 2.27273
\(122\) 1.00000 0.0905357
\(123\) 12.0000 1.08200
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 2.00000 0.178174
\(127\) −15.0000 −1.33103 −0.665517 − 0.746382i \(-0.731789\pi\)
−0.665517 + 0.746382i \(0.731789\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.00000 0.0880451
\(130\) 0 0
\(131\) −7.00000 −0.611593 −0.305796 − 0.952097i \(-0.598923\pi\)
−0.305796 + 0.952097i \(0.598923\pi\)
\(132\) 6.00000 0.522233
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 1.00000 0.0860663
\(136\) −3.00000 −0.257248
\(137\) −4.00000 −0.341743 −0.170872 − 0.985293i \(-0.554658\pi\)
−0.170872 + 0.985293i \(0.554658\pi\)
\(138\) 1.00000 0.0851257
\(139\) 11.0000 0.933008 0.466504 − 0.884519i \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(140\) −2.00000 −0.169031
\(141\) −12.0000 −1.01058
\(142\) 13.0000 1.09094
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) 9.00000 0.744845
\(147\) −3.00000 −0.247436
\(148\) 3.00000 0.246598
\(149\) −6.00000 −0.491539 −0.245770 − 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 4.00000 0.326599
\(151\) 6.00000 0.488273 0.244137 − 0.969741i \(-0.421495\pi\)
0.244137 + 0.969741i \(0.421495\pi\)
\(152\) 0 0
\(153\) 3.00000 0.242536
\(154\) 12.0000 0.966988
\(155\) 0 0
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 − 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 14.0000 1.11378
\(159\) −2.00000 −0.158610
\(160\) −1.00000 −0.0790569
\(161\) 2.00000 0.157622
\(162\) −1.00000 −0.0785674
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 12.0000 0.937043
\(165\) 6.00000 0.467099
\(166\) −3.00000 −0.232845
\(167\) 14.0000 1.08335 0.541676 − 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 2.00000 0.154303
\(169\) −13.0000 −1.00000
\(170\) −3.00000 −0.230089
\(171\) 0 0
\(172\) 1.00000 0.0762493
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −6.00000 −0.454859
\(175\) 8.00000 0.604743
\(176\) 6.00000 0.452267
\(177\) 0 0
\(178\) 9.00000 0.674579
\(179\) −21.0000 −1.56961 −0.784807 − 0.619740i \(-0.787238\pi\)
−0.784807 + 0.619740i \(0.787238\pi\)
\(180\) 1.00000 0.0745356
\(181\) 21.0000 1.56092 0.780459 − 0.625207i \(-0.214986\pi\)
0.780459 + 0.625207i \(0.214986\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 1.00000 0.0737210
\(185\) 3.00000 0.220564
\(186\) 0 0
\(187\) 18.0000 1.31629
\(188\) −12.0000 −0.875190
\(189\) −2.00000 −0.145479
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 − 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 1.00000 0.0721688
\(193\) 12.0000 0.863779 0.431889 − 0.901927i \(-0.357847\pi\)
0.431889 + 0.901927i \(0.357847\pi\)
\(194\) 1.00000 0.0717958
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 26.0000 1.85242 0.926212 − 0.377004i \(-0.123046\pi\)
0.926212 + 0.377004i \(0.123046\pi\)
\(198\) −6.00000 −0.426401
\(199\) −7.00000 −0.496217 −0.248108 − 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) 4.00000 0.282843
\(201\) 4.00000 0.282138
\(202\) −12.0000 −0.844317
\(203\) −12.0000 −0.842235
\(204\) 3.00000 0.210042
\(205\) 12.0000 0.838116
\(206\) 5.00000 0.348367
\(207\) −1.00000 −0.0695048
\(208\) 0 0
\(209\) 0 0
\(210\) 2.00000 0.138013
\(211\) −12.0000 −0.826114 −0.413057 − 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −2.00000 −0.137361
\(213\) −13.0000 −0.890745
\(214\) 15.0000 1.02538
\(215\) 1.00000 0.0681994
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 8.00000 0.541828
\(219\) −9.00000 −0.608164
\(220\) 6.00000 0.404520
\(221\) 0 0
\(222\) −3.00000 −0.201347
\(223\) −2.00000 −0.133930 −0.0669650 − 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) 2.00000 0.133631
\(225\) −4.00000 −0.266667
\(226\) −4.00000 −0.266076
\(227\) 14.0000 0.929213 0.464606 − 0.885517i \(-0.346196\pi\)
0.464606 + 0.885517i \(0.346196\pi\)
\(228\) 0 0
\(229\) 18.0000 1.18947 0.594737 − 0.803921i \(-0.297256\pi\)
0.594737 + 0.803921i \(0.297256\pi\)
\(230\) 1.00000 0.0659380
\(231\) −12.0000 −0.789542
\(232\) −6.00000 −0.393919
\(233\) 26.0000 1.70332 0.851658 − 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) 0 0
\(237\) −14.0000 −0.909398
\(238\) 6.00000 0.388922
\(239\) 6.00000 0.388108 0.194054 − 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 1.00000 0.0645497
\(241\) 25.0000 1.61039 0.805196 − 0.593009i \(-0.202060\pi\)
0.805196 + 0.593009i \(0.202060\pi\)
\(242\) −25.0000 −1.60706
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −3.00000 −0.191663
\(246\) −12.0000 −0.765092
\(247\) 0 0
\(248\) 0 0
\(249\) 3.00000 0.190117
\(250\) 9.00000 0.569210
\(251\) −10.0000 −0.631194 −0.315597 − 0.948893i \(-0.602205\pi\)
−0.315597 + 0.948893i \(0.602205\pi\)
\(252\) −2.00000 −0.125988
\(253\) −6.00000 −0.377217
\(254\) 15.0000 0.941184
\(255\) 3.00000 0.187867
\(256\) 1.00000 0.0625000
\(257\) −28.0000 −1.74659 −0.873296 − 0.487190i \(-0.838022\pi\)
−0.873296 + 0.487190i \(0.838022\pi\)
\(258\) −1.00000 −0.0622573
\(259\) −6.00000 −0.372822
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 7.00000 0.432461
\(263\) −12.0000 −0.739952 −0.369976 − 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) −6.00000 −0.369274
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) −9.00000 −0.550791
\(268\) 4.00000 0.244339
\(269\) 2.00000 0.121942 0.0609711 − 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −17.0000 −1.03268 −0.516338 − 0.856385i \(-0.672705\pi\)
−0.516338 + 0.856385i \(0.672705\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) 4.00000 0.241649
\(275\) −24.0000 −1.44725
\(276\) −1.00000 −0.0601929
\(277\) −18.0000 −1.08152 −0.540758 − 0.841178i \(-0.681862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) −11.0000 −0.659736
\(279\) 0 0
\(280\) 2.00000 0.119523
\(281\) 26.0000 1.55103 0.775515 − 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 12.0000 0.714590
\(283\) 24.0000 1.42665 0.713326 − 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) −13.0000 −0.771408
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) −1.00000 −0.0589256
\(289\) −8.00000 −0.470588
\(290\) −6.00000 −0.352332
\(291\) −1.00000 −0.0586210
\(292\) −9.00000 −0.526685
\(293\) −31.0000 −1.81104 −0.905520 − 0.424304i \(-0.860519\pi\)
−0.905520 + 0.424304i \(0.860519\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) −3.00000 −0.174371
\(297\) 6.00000 0.348155
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) −4.00000 −0.230940
\(301\) −2.00000 −0.115278
\(302\) −6.00000 −0.345261
\(303\) 12.0000 0.689382
\(304\) 0 0
\(305\) −1.00000 −0.0572598
\(306\) −3.00000 −0.171499
\(307\) −29.0000 −1.65512 −0.827559 − 0.561379i \(-0.810271\pi\)
−0.827559 + 0.561379i \(0.810271\pi\)
\(308\) −12.0000 −0.683763
\(309\) −5.00000 −0.284440
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −2.00000 −0.113047 −0.0565233 − 0.998401i \(-0.518002\pi\)
−0.0565233 + 0.998401i \(0.518002\pi\)
\(314\) 2.00000 0.112867
\(315\) −2.00000 −0.112687
\(316\) −14.0000 −0.787562
\(317\) 21.0000 1.17948 0.589739 − 0.807594i \(-0.299231\pi\)
0.589739 + 0.807594i \(0.299231\pi\)
\(318\) 2.00000 0.112154
\(319\) 36.0000 2.01561
\(320\) 1.00000 0.0559017
\(321\) −15.0000 −0.837218
\(322\) −2.00000 −0.111456
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) −8.00000 −0.442401
\(328\) −12.0000 −0.662589
\(329\) 24.0000 1.32316
\(330\) −6.00000 −0.330289
\(331\) 17.0000 0.934405 0.467202 − 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 3.00000 0.164646
\(333\) 3.00000 0.164399
\(334\) −14.0000 −0.766046
\(335\) 4.00000 0.218543
\(336\) −2.00000 −0.109109
\(337\) −6.00000 −0.326841 −0.163420 − 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 13.0000 0.707107
\(339\) 4.00000 0.217250
\(340\) 3.00000 0.162698
\(341\) 0 0
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) −1.00000 −0.0539164
\(345\) −1.00000 −0.0538382
\(346\) −6.00000 −0.322562
\(347\) −7.00000 −0.375780 −0.187890 − 0.982190i \(-0.560165\pi\)
−0.187890 + 0.982190i \(0.560165\pi\)
\(348\) 6.00000 0.321634
\(349\) −11.0000 −0.588817 −0.294408 − 0.955680i \(-0.595123\pi\)
−0.294408 + 0.955680i \(0.595123\pi\)
\(350\) −8.00000 −0.427618
\(351\) 0 0
\(352\) −6.00000 −0.319801
\(353\) 6.00000 0.319348 0.159674 − 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) −13.0000 −0.689968
\(356\) −9.00000 −0.476999
\(357\) −6.00000 −0.317554
\(358\) 21.0000 1.10988
\(359\) 25.0000 1.31945 0.659725 − 0.751507i \(-0.270673\pi\)
0.659725 + 0.751507i \(0.270673\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −19.0000 −1.00000
\(362\) −21.0000 −1.10374
\(363\) 25.0000 1.31216
\(364\) 0 0
\(365\) −9.00000 −0.471082
\(366\) 1.00000 0.0522708
\(367\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 12.0000 0.624695
\(370\) −3.00000 −0.155963
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) −13.0000 −0.673114 −0.336557 − 0.941663i \(-0.609263\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) −18.0000 −0.930758
\(375\) −9.00000 −0.464758
\(376\) 12.0000 0.618853
\(377\) 0 0
\(378\) 2.00000 0.102869
\(379\) 32.0000 1.64373 0.821865 − 0.569683i \(-0.192934\pi\)
0.821865 + 0.569683i \(0.192934\pi\)
\(380\) 0 0
\(381\) −15.0000 −0.768473
\(382\) −4.00000 −0.204658
\(383\) 24.0000 1.22634 0.613171 − 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −12.0000 −0.611577
\(386\) −12.0000 −0.610784
\(387\) 1.00000 0.0508329
\(388\) −1.00000 −0.0507673
\(389\) 2.00000 0.101404 0.0507020 − 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) 0 0
\(391\) −3.00000 −0.151717
\(392\) 3.00000 0.151523
\(393\) −7.00000 −0.353103
\(394\) −26.0000 −1.30986
\(395\) −14.0000 −0.704416
\(396\) 6.00000 0.301511
\(397\) −35.0000 −1.75660 −0.878300 − 0.478110i \(-0.841322\pi\)
−0.878300 + 0.478110i \(0.841322\pi\)
\(398\) 7.00000 0.350878
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 27.0000 1.34832 0.674158 − 0.738587i \(-0.264507\pi\)
0.674158 + 0.738587i \(0.264507\pi\)
\(402\) −4.00000 −0.199502
\(403\) 0 0
\(404\) 12.0000 0.597022
\(405\) 1.00000 0.0496904
\(406\) 12.0000 0.595550
\(407\) 18.0000 0.892227
\(408\) −3.00000 −0.148522
\(409\) 20.0000 0.988936 0.494468 − 0.869196i \(-0.335363\pi\)
0.494468 + 0.869196i \(0.335363\pi\)
\(410\) −12.0000 −0.592638
\(411\) −4.00000 −0.197305
\(412\) −5.00000 −0.246332
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) 3.00000 0.147264
\(416\) 0 0
\(417\) 11.0000 0.538672
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 − 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) −2.00000 −0.0975900
\(421\) −37.0000 −1.80327 −0.901635 − 0.432498i \(-0.857632\pi\)
−0.901635 + 0.432498i \(0.857632\pi\)
\(422\) 12.0000 0.584151
\(423\) −12.0000 −0.583460
\(424\) 2.00000 0.0971286
\(425\) −12.0000 −0.582086
\(426\) 13.0000 0.629852
\(427\) 2.00000 0.0967868
\(428\) −15.0000 −0.725052
\(429\) 0 0
\(430\) −1.00000 −0.0482243
\(431\) 2.00000 0.0963366 0.0481683 − 0.998839i \(-0.484662\pi\)
0.0481683 + 0.998839i \(0.484662\pi\)
\(432\) 1.00000 0.0481125
\(433\) 16.0000 0.768911 0.384455 − 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) −8.00000 −0.383131
\(437\) 0 0
\(438\) 9.00000 0.430037
\(439\) 3.00000 0.143182 0.0715911 − 0.997434i \(-0.477192\pi\)
0.0715911 + 0.997434i \(0.477192\pi\)
\(440\) −6.00000 −0.286039
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) 15.0000 0.712672 0.356336 − 0.934358i \(-0.384026\pi\)
0.356336 + 0.934358i \(0.384026\pi\)
\(444\) 3.00000 0.142374
\(445\) −9.00000 −0.426641
\(446\) 2.00000 0.0947027
\(447\) −6.00000 −0.283790
\(448\) −2.00000 −0.0944911
\(449\) 18.0000 0.849473 0.424736 − 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 4.00000 0.188562
\(451\) 72.0000 3.39035
\(452\) 4.00000 0.188144
\(453\) 6.00000 0.281905
\(454\) −14.0000 −0.657053
\(455\) 0 0
\(456\) 0 0
\(457\) 2.00000 0.0935561 0.0467780 − 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) −18.0000 −0.841085
\(459\) 3.00000 0.140028
\(460\) −1.00000 −0.0466252
\(461\) −13.0000 −0.605470 −0.302735 − 0.953075i \(-0.597900\pi\)
−0.302735 + 0.953075i \(0.597900\pi\)
\(462\) 12.0000 0.558291
\(463\) −29.0000 −1.34774 −0.673872 − 0.738848i \(-0.735370\pi\)
−0.673872 + 0.738848i \(0.735370\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −26.0000 −1.20443
\(467\) −20.0000 −0.925490 −0.462745 − 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) 12.0000 0.553519
\(471\) −2.00000 −0.0921551
\(472\) 0 0
\(473\) 6.00000 0.275880
\(474\) 14.0000 0.643041
\(475\) 0 0
\(476\) −6.00000 −0.275010
\(477\) −2.00000 −0.0915737
\(478\) −6.00000 −0.274434
\(479\) 22.0000 1.00521 0.502603 − 0.864517i \(-0.332376\pi\)
0.502603 + 0.864517i \(0.332376\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 0 0
\(482\) −25.0000 −1.13872
\(483\) 2.00000 0.0910032
\(484\) 25.0000 1.13636
\(485\) −1.00000 −0.0454077
\(486\) −1.00000 −0.0453609
\(487\) 16.0000 0.725029 0.362515 − 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 1.00000 0.0452679
\(489\) −4.00000 −0.180886
\(490\) 3.00000 0.135526
\(491\) −32.0000 −1.44414 −0.722070 − 0.691820i \(-0.756809\pi\)
−0.722070 + 0.691820i \(0.756809\pi\)
\(492\) 12.0000 0.541002
\(493\) 18.0000 0.810679
\(494\) 0 0
\(495\) 6.00000 0.269680
\(496\) 0 0
\(497\) 26.0000 1.16626
\(498\) −3.00000 −0.134433
\(499\) 5.00000 0.223831 0.111915 − 0.993718i \(-0.464301\pi\)
0.111915 + 0.993718i \(0.464301\pi\)
\(500\) −9.00000 −0.402492
\(501\) 14.0000 0.625474
\(502\) 10.0000 0.446322
\(503\) −32.0000 −1.42681 −0.713405 − 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 2.00000 0.0890871
\(505\) 12.0000 0.533993
\(506\) 6.00000 0.266733
\(507\) −13.0000 −0.577350
\(508\) −15.0000 −0.665517
\(509\) −4.00000 −0.177297 −0.0886484 − 0.996063i \(-0.528255\pi\)
−0.0886484 + 0.996063i \(0.528255\pi\)
\(510\) −3.00000 −0.132842
\(511\) 18.0000 0.796273
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 28.0000 1.23503
\(515\) −5.00000 −0.220326
\(516\) 1.00000 0.0440225
\(517\) −72.0000 −3.16656
\(518\) 6.00000 0.263625
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 − 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) −6.00000 −0.262613
\(523\) 1.00000 0.0437269 0.0218635 − 0.999761i \(-0.493040\pi\)
0.0218635 + 0.999761i \(0.493040\pi\)
\(524\) −7.00000 −0.305796
\(525\) 8.00000 0.349149
\(526\) 12.0000 0.523225
\(527\) 0 0
\(528\) 6.00000 0.261116
\(529\) −22.0000 −0.956522
\(530\) 2.00000 0.0868744
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 9.00000 0.389468
\(535\) −15.0000 −0.648507
\(536\) −4.00000 −0.172774
\(537\) −21.0000 −0.906217
\(538\) −2.00000 −0.0862261
\(539\) −18.0000 −0.775315
\(540\) 1.00000 0.0430331
\(541\) −21.0000 −0.902861 −0.451430 − 0.892306i \(-0.649086\pi\)
−0.451430 + 0.892306i \(0.649086\pi\)
\(542\) 17.0000 0.730213
\(543\) 21.0000 0.901196
\(544\) −3.00000 −0.128624
\(545\) −8.00000 −0.342682
\(546\) 0 0
\(547\) −44.0000 −1.88130 −0.940652 − 0.339372i \(-0.889785\pi\)
−0.940652 + 0.339372i \(0.889785\pi\)
\(548\) −4.00000 −0.170872
\(549\) −1.00000 −0.0426790
\(550\) 24.0000 1.02336
\(551\) 0 0
\(552\) 1.00000 0.0425628
\(553\) 28.0000 1.19068
\(554\) 18.0000 0.764747
\(555\) 3.00000 0.127343
\(556\) 11.0000 0.466504
\(557\) 26.0000 1.10166 0.550828 − 0.834619i \(-0.314312\pi\)
0.550828 + 0.834619i \(0.314312\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −2.00000 −0.0845154
\(561\) 18.0000 0.759961
\(562\) −26.0000 −1.09674
\(563\) 40.0000 1.68580 0.842900 − 0.538071i \(-0.180847\pi\)
0.842900 + 0.538071i \(0.180847\pi\)
\(564\) −12.0000 −0.505291
\(565\) 4.00000 0.168281
\(566\) −24.0000 −1.00880
\(567\) −2.00000 −0.0839921
\(568\) 13.0000 0.545468
\(569\) −24.0000 −1.00613 −0.503066 − 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 36.0000 1.50655 0.753277 − 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) 0 0
\(573\) 4.00000 0.167102
\(574\) 24.0000 1.00174
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) −28.0000 −1.16566 −0.582828 − 0.812596i \(-0.698054\pi\)
−0.582828 + 0.812596i \(0.698054\pi\)
\(578\) 8.00000 0.332756
\(579\) 12.0000 0.498703
\(580\) 6.00000 0.249136
\(581\) −6.00000 −0.248922
\(582\) 1.00000 0.0414513
\(583\) −12.0000 −0.496989
\(584\) 9.00000 0.372423
\(585\) 0 0
\(586\) 31.0000 1.28060
\(587\) 18.0000 0.742940 0.371470 − 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) −3.00000 −0.123718
\(589\) 0 0
\(590\) 0 0
\(591\) 26.0000 1.06950
\(592\) 3.00000 0.123299
\(593\) −15.0000 −0.615976 −0.307988 − 0.951390i \(-0.599656\pi\)
−0.307988 + 0.951390i \(0.599656\pi\)
\(594\) −6.00000 −0.246183
\(595\) −6.00000 −0.245976
\(596\) −6.00000 −0.245770
\(597\) −7.00000 −0.286491
\(598\) 0 0
\(599\) 33.0000 1.34834 0.674172 − 0.738575i \(-0.264501\pi\)
0.674172 + 0.738575i \(0.264501\pi\)
\(600\) 4.00000 0.163299
\(601\) 13.0000 0.530281 0.265141 − 0.964210i \(-0.414582\pi\)
0.265141 + 0.964210i \(0.414582\pi\)
\(602\) 2.00000 0.0815139
\(603\) 4.00000 0.162893
\(604\) 6.00000 0.244137
\(605\) 25.0000 1.01639
\(606\) −12.0000 −0.487467
\(607\) −21.0000 −0.852364 −0.426182 − 0.904638i \(-0.640142\pi\)
−0.426182 + 0.904638i \(0.640142\pi\)
\(608\) 0 0
\(609\) −12.0000 −0.486265
\(610\) 1.00000 0.0404888
\(611\) 0 0
\(612\) 3.00000 0.121268
\(613\) −16.0000 −0.646234 −0.323117 − 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 29.0000 1.17034
\(615\) 12.0000 0.483887
\(616\) 12.0000 0.483494
\(617\) 7.00000 0.281809 0.140905 − 0.990023i \(-0.454999\pi\)
0.140905 + 0.990023i \(0.454999\pi\)
\(618\) 5.00000 0.201129
\(619\) −10.0000 −0.401934 −0.200967 − 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 0 0
\(621\) −1.00000 −0.0401286
\(622\) 0 0
\(623\) 18.0000 0.721155
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 2.00000 0.0799361
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) 9.00000 0.358854
\(630\) 2.00000 0.0796819
\(631\) −38.0000 −1.51276 −0.756378 − 0.654135i \(-0.773033\pi\)
−0.756378 + 0.654135i \(0.773033\pi\)
\(632\) 14.0000 0.556890
\(633\) −12.0000 −0.476957
\(634\) −21.0000 −0.834017
\(635\) −15.0000 −0.595257
\(636\) −2.00000 −0.0793052
\(637\) 0 0
\(638\) −36.0000 −1.42525
\(639\) −13.0000 −0.514272
\(640\) −1.00000 −0.0395285
\(641\) −15.0000 −0.592464 −0.296232 − 0.955116i \(-0.595730\pi\)
−0.296232 + 0.955116i \(0.595730\pi\)
\(642\) 15.0000 0.592003
\(643\) −11.0000 −0.433798 −0.216899 − 0.976194i \(-0.569594\pi\)
−0.216899 + 0.976194i \(0.569594\pi\)
\(644\) 2.00000 0.0788110
\(645\) 1.00000 0.0393750
\(646\) 0 0
\(647\) −3.00000 −0.117942 −0.0589711 − 0.998260i \(-0.518782\pi\)
−0.0589711 + 0.998260i \(0.518782\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −4.00000 −0.156532 −0.0782660 − 0.996933i \(-0.524938\pi\)
−0.0782660 + 0.996933i \(0.524938\pi\)
\(654\) 8.00000 0.312825
\(655\) −7.00000 −0.273513
\(656\) 12.0000 0.468521
\(657\) −9.00000 −0.351123
\(658\) −24.0000 −0.935617
\(659\) −13.0000 −0.506408 −0.253204 − 0.967413i \(-0.581484\pi\)
−0.253204 + 0.967413i \(0.581484\pi\)
\(660\) 6.00000 0.233550
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −17.0000 −0.660724
\(663\) 0 0
\(664\) −3.00000 −0.116423
\(665\) 0 0
\(666\) −3.00000 −0.116248
\(667\) −6.00000 −0.232321
\(668\) 14.0000 0.541676
\(669\) −2.00000 −0.0773245
\(670\) −4.00000 −0.154533
\(671\) −6.00000 −0.231627
\(672\) 2.00000 0.0771517
\(673\) −30.0000 −1.15642 −0.578208 − 0.815890i \(-0.696248\pi\)
−0.578208 + 0.815890i \(0.696248\pi\)
\(674\) 6.00000 0.231111
\(675\) −4.00000 −0.153960
\(676\) −13.0000 −0.500000
\(677\) 24.0000 0.922395 0.461197 − 0.887298i \(-0.347420\pi\)
0.461197 + 0.887298i \(0.347420\pi\)
\(678\) −4.00000 −0.153619
\(679\) 2.00000 0.0767530
\(680\) −3.00000 −0.115045
\(681\) 14.0000 0.536481
\(682\) 0 0
\(683\) 41.0000 1.56882 0.784411 − 0.620242i \(-0.212966\pi\)
0.784411 + 0.620242i \(0.212966\pi\)
\(684\) 0 0
\(685\) −4.00000 −0.152832
\(686\) −20.0000 −0.763604
\(687\) 18.0000 0.686743
\(688\) 1.00000 0.0381246
\(689\) 0 0
\(690\) 1.00000 0.0380693
\(691\) 46.0000 1.74992 0.874961 − 0.484193i \(-0.160887\pi\)
0.874961 + 0.484193i \(0.160887\pi\)
\(692\) 6.00000 0.228086
\(693\) −12.0000 −0.455842
\(694\) 7.00000 0.265716
\(695\) 11.0000 0.417254
\(696\) −6.00000 −0.227429
\(697\) 36.0000 1.36360
\(698\) 11.0000 0.416356
\(699\) 26.0000 0.983410
\(700\) 8.00000 0.302372
\(701\) −42.0000 −1.58632 −0.793159 − 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 6.00000 0.226134
\(705\) −12.0000 −0.451946
\(706\) −6.00000 −0.225813
\(707\) −24.0000 −0.902613
\(708\) 0 0
\(709\) −31.0000 −1.16423 −0.582115 − 0.813107i \(-0.697775\pi\)
−0.582115 + 0.813107i \(0.697775\pi\)
\(710\) 13.0000 0.487881
\(711\) −14.0000 −0.525041
\(712\) 9.00000 0.337289
\(713\) 0 0
\(714\) 6.00000 0.224544
\(715\) 0 0
\(716\) −21.0000 −0.784807
\(717\) 6.00000 0.224074
\(718\) −25.0000 −0.932992
\(719\) −48.0000 −1.79010 −0.895049 − 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 1.00000 0.0372678
\(721\) 10.0000 0.372419
\(722\) 19.0000 0.707107
\(723\) 25.0000 0.929760
\(724\) 21.0000 0.780459
\(725\) −24.0000 −0.891338
\(726\) −25.0000 −0.927837
\(727\) 32.0000 1.18681 0.593407 − 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 9.00000 0.333105
\(731\) 3.00000 0.110959
\(732\) −1.00000 −0.0369611
\(733\) 22.0000 0.812589 0.406294 − 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 0 0
\(735\) −3.00000 −0.110657
\(736\) 1.00000 0.0368605
\(737\) 24.0000 0.884051
\(738\) −12.0000 −0.441726
\(739\) −3.00000 −0.110357 −0.0551784 − 0.998477i \(-0.517573\pi\)
−0.0551784 + 0.998477i \(0.517573\pi\)
\(740\) 3.00000 0.110282
\(741\) 0 0
\(742\) −4.00000 −0.146845
\(743\) 1.00000 0.0366864 0.0183432 − 0.999832i \(-0.494161\pi\)
0.0183432 + 0.999832i \(0.494161\pi\)
\(744\) 0 0
\(745\) −6.00000 −0.219823
\(746\) 13.0000 0.475964
\(747\) 3.00000 0.109764
\(748\) 18.0000 0.658145
\(749\) 30.0000 1.09618
\(750\) 9.00000 0.328634
\(751\) −11.0000 −0.401396 −0.200698 − 0.979653i \(-0.564321\pi\)
−0.200698 + 0.979653i \(0.564321\pi\)
\(752\) −12.0000 −0.437595
\(753\) −10.0000 −0.364420
\(754\) 0 0
\(755\) 6.00000 0.218362
\(756\) −2.00000 −0.0727393
\(757\) −22.0000 −0.799604 −0.399802 − 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −32.0000 −1.16229
\(759\) −6.00000 −0.217786
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 − 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) 15.0000 0.543393
\(763\) 16.0000 0.579239
\(764\) 4.00000 0.144715
\(765\) 3.00000 0.108465
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −24.0000 −0.865462 −0.432731 − 0.901523i \(-0.642450\pi\)
−0.432731 + 0.901523i \(0.642450\pi\)
\(770\) 12.0000 0.432450
\(771\) −28.0000 −1.00840
\(772\) 12.0000 0.431889
\(773\) −39.0000 −1.40273 −0.701366 − 0.712801i \(-0.747426\pi\)
−0.701366 + 0.712801i \(0.747426\pi\)
\(774\) −1.00000 −0.0359443
\(775\) 0 0
\(776\) 1.00000 0.0358979
\(777\) −6.00000 −0.215249
\(778\) −2.00000 −0.0717035
\(779\) 0 0
\(780\) 0 0
\(781\) −78.0000 −2.79106
\(782\) 3.00000 0.107280
\(783\) 6.00000 0.214423
\(784\) −3.00000 −0.107143
\(785\) −2.00000 −0.0713831
\(786\) 7.00000 0.249682
\(787\) −20.0000 −0.712923 −0.356462 − 0.934310i \(-0.616017\pi\)
−0.356462 + 0.934310i \(0.616017\pi\)
\(788\) 26.0000 0.926212
\(789\) −12.0000 −0.427211
\(790\) 14.0000 0.498098
\(791\) −8.00000 −0.284447
\(792\) −6.00000 −0.213201
\(793\) 0 0
\(794\) 35.0000 1.24210
\(795\) −2.00000 −0.0709327
\(796\) −7.00000 −0.248108
\(797\) 6.00000 0.212531 0.106265 − 0.994338i \(-0.466111\pi\)
0.106265 + 0.994338i \(0.466111\pi\)
\(798\) 0 0
\(799\) −36.0000 −1.27359
\(800\) 4.00000 0.141421
\(801\) −9.00000 −0.317999
\(802\) −27.0000 −0.953403
\(803\) −54.0000 −1.90562
\(804\) 4.00000 0.141069
\(805\) 2.00000 0.0704907
\(806\) 0 0
\(807\) 2.00000 0.0704033
\(808\) −12.0000 −0.422159
\(809\) −46.0000 −1.61727 −0.808637 − 0.588308i \(-0.799794\pi\)
−0.808637 + 0.588308i \(0.799794\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 17.0000 0.596951 0.298475 − 0.954417i \(-0.403522\pi\)
0.298475 + 0.954417i \(0.403522\pi\)
\(812\) −12.0000 −0.421117
\(813\) −17.0000 −0.596216
\(814\) −18.0000 −0.630900
\(815\) −4.00000 −0.140114
\(816\) 3.00000 0.105021
\(817\) 0 0
\(818\) −20.0000 −0.699284
\(819\) 0 0
\(820\) 12.0000 0.419058
\(821\) −2.00000 −0.0698005 −0.0349002 − 0.999391i \(-0.511111\pi\)
−0.0349002 + 0.999391i \(0.511111\pi\)
\(822\) 4.00000 0.139516
\(823\) 46.0000 1.60346 0.801730 − 0.597687i \(-0.203913\pi\)
0.801730 + 0.597687i \(0.203913\pi\)
\(824\) 5.00000 0.174183
\(825\) −24.0000 −0.835573
\(826\) 0 0
\(827\) −17.0000 −0.591148 −0.295574 − 0.955320i \(-0.595511\pi\)
−0.295574 + 0.955320i \(0.595511\pi\)
\(828\) −1.00000 −0.0347524
\(829\) 38.0000 1.31979 0.659897 − 0.751356i \(-0.270600\pi\)
0.659897 + 0.751356i \(0.270600\pi\)
\(830\) −3.00000 −0.104132
\(831\) −18.0000 −0.624413
\(832\) 0 0
\(833\) −9.00000 −0.311832
\(834\) −11.0000 −0.380899
\(835\) 14.0000 0.484490
\(836\) 0 0
\(837\) 0 0
\(838\) −24.0000 −0.829066
\(839\) 24.0000 0.828572 0.414286 − 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 2.00000 0.0690066
\(841\) 7.00000 0.241379
\(842\) 37.0000 1.27510
\(843\) 26.0000 0.895488
\(844\) −12.0000 −0.413057
\(845\) −13.0000 −0.447214
\(846\) 12.0000 0.412568
\(847\) −50.0000 −1.71802
\(848\) −2.00000 −0.0686803
\(849\) 24.0000 0.823678
\(850\) 12.0000 0.411597
\(851\) −3.00000 −0.102839
\(852\) −13.0000 −0.445373
\(853\) 42.0000 1.43805 0.719026 − 0.694983i \(-0.244588\pi\)
0.719026 + 0.694983i \(0.244588\pi\)
\(854\) −2.00000 −0.0684386
\(855\) 0 0
\(856\) 15.0000 0.512689
\(857\) 46.0000 1.57133 0.785665 − 0.618652i \(-0.212321\pi\)
0.785665 + 0.618652i \(0.212321\pi\)
\(858\) 0 0
\(859\) −28.0000 −0.955348 −0.477674 − 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) 1.00000 0.0340997
\(861\) −24.0000 −0.817918
\(862\) −2.00000 −0.0681203
\(863\) 28.0000 0.953131 0.476566 − 0.879139i \(-0.341881\pi\)
0.476566 + 0.879139i \(0.341881\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 6.00000 0.204006
\(866\) −16.0000 −0.543702
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) −84.0000 −2.84950
\(870\) −6.00000 −0.203419
\(871\) 0 0
\(872\) 8.00000 0.270914
\(873\) −1.00000 −0.0338449
\(874\) 0 0
\(875\) 18.0000 0.608511
\(876\) −9.00000 −0.304082
\(877\) −1.00000 −0.0337676 −0.0168838 − 0.999857i \(-0.505375\pi\)
−0.0168838 + 0.999857i \(0.505375\pi\)
\(878\) −3.00000 −0.101245
\(879\) −31.0000 −1.04560
\(880\) 6.00000 0.202260
\(881\) −34.0000 −1.14549 −0.572745 − 0.819734i \(-0.694121\pi\)
−0.572745 + 0.819734i \(0.694121\pi\)
\(882\) 3.00000 0.101015
\(883\) −41.0000 −1.37976 −0.689880 − 0.723924i \(-0.742337\pi\)
−0.689880 + 0.723924i \(0.742337\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −15.0000 −0.503935
\(887\) 29.0000 0.973725 0.486862 − 0.873479i \(-0.338141\pi\)
0.486862 + 0.873479i \(0.338141\pi\)
\(888\) −3.00000 −0.100673
\(889\) 30.0000 1.00617
\(890\) 9.00000 0.301681
\(891\) 6.00000 0.201008
\(892\) −2.00000 −0.0669650
\(893\) 0 0
\(894\) 6.00000 0.200670
\(895\) −21.0000 −0.701953
\(896\) 2.00000 0.0668153
\(897\) 0 0
\(898\) −18.0000 −0.600668
\(899\) 0 0
\(900\) −4.00000 −0.133333
\(901\) −6.00000 −0.199889
\(902\) −72.0000 −2.39734
\(903\) −2.00000 −0.0665558
\(904\) −4.00000 −0.133038
\(905\) 21.0000 0.698064
\(906\) −6.00000 −0.199337
\(907\) 23.0000 0.763702 0.381851 − 0.924224i \(-0.375287\pi\)
0.381851 + 0.924224i \(0.375287\pi\)
\(908\) 14.0000 0.464606
\(909\) 12.0000 0.398015
\(910\) 0 0
\(911\) 40.0000 1.32526 0.662630 − 0.748947i \(-0.269440\pi\)
0.662630 + 0.748947i \(0.269440\pi\)
\(912\) 0 0
\(913\) 18.0000 0.595713
\(914\) −2.00000 −0.0661541
\(915\) −1.00000 −0.0330590
\(916\) 18.0000 0.594737
\(917\) 14.0000 0.462321
\(918\) −3.00000 −0.0990148
\(919\) 17.0000 0.560778 0.280389 − 0.959886i \(-0.409536\pi\)
0.280389 + 0.959886i \(0.409536\pi\)
\(920\) 1.00000 0.0329690
\(921\) −29.0000 −0.955582
\(922\) 13.0000 0.428132
\(923\) 0 0
\(924\) −12.0000 −0.394771
\(925\) −12.0000 −0.394558
\(926\) 29.0000 0.952999
\(927\) −5.00000 −0.164222
\(928\) −6.00000 −0.196960
\(929\) 28.0000 0.918650 0.459325 − 0.888268i \(-0.348091\pi\)
0.459325 + 0.888268i \(0.348091\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 26.0000 0.851658
\(933\) 0 0
\(934\) 20.0000 0.654420
\(935\) 18.0000 0.588663
\(936\) 0 0
\(937\) 47.0000 1.53542 0.767712 − 0.640796i \(-0.221395\pi\)
0.767712 + 0.640796i \(0.221395\pi\)
\(938\) 8.00000 0.261209
\(939\) −2.00000 −0.0652675
\(940\) −12.0000 −0.391397
\(941\) 44.0000 1.43436 0.717180 − 0.696888i \(-0.245433\pi\)
0.717180 + 0.696888i \(0.245433\pi\)
\(942\) 2.00000 0.0651635
\(943\) −12.0000 −0.390774
\(944\) 0 0
\(945\) −2.00000 −0.0650600
\(946\) −6.00000 −0.195077
\(947\) −32.0000 −1.03986 −0.519930 − 0.854209i \(-0.674042\pi\)
−0.519930 + 0.854209i \(0.674042\pi\)
\(948\) −14.0000 −0.454699
\(949\) 0 0
\(950\) 0 0
\(951\) 21.0000 0.680972
\(952\) 6.00000 0.194461
\(953\) −17.0000 −0.550684 −0.275342 − 0.961346i \(-0.588791\pi\)
−0.275342 + 0.961346i \(0.588791\pi\)
\(954\) 2.00000 0.0647524
\(955\) 4.00000 0.129437
\(956\) 6.00000 0.194054
\(957\) 36.0000 1.16371
\(958\) −22.0000 −0.710788
\(959\) 8.00000 0.258333
\(960\) 1.00000 0.0322749
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) −15.0000 −0.483368
\(964\) 25.0000 0.805196
\(965\) 12.0000 0.386294
\(966\) −2.00000 −0.0643489
\(967\) 33.0000 1.06121 0.530604 − 0.847620i \(-0.321965\pi\)
0.530604 + 0.847620i \(0.321965\pi\)
\(968\) −25.0000 −0.803530
\(969\) 0 0
\(970\) 1.00000 0.0321081
\(971\) −19.0000 −0.609739 −0.304870 − 0.952394i \(-0.598613\pi\)
−0.304870 + 0.952394i \(0.598613\pi\)
\(972\) 1.00000 0.0320750
\(973\) −22.0000 −0.705288
\(974\) −16.0000 −0.512673
\(975\) 0 0
\(976\) −1.00000 −0.0320092
\(977\) 24.0000 0.767828 0.383914 − 0.923369i \(-0.374576\pi\)
0.383914 + 0.923369i \(0.374576\pi\)
\(978\) 4.00000 0.127906
\(979\) −54.0000 −1.72585
\(980\) −3.00000 −0.0958315
\(981\) −8.00000 −0.255420
\(982\) 32.0000 1.02116
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) −12.0000 −0.382546
\(985\) 26.0000 0.828429
\(986\) −18.0000 −0.573237
\(987\) 24.0000 0.763928
\(988\) 0 0
\(989\) −1.00000 −0.0317982
\(990\) −6.00000 −0.190693
\(991\) −4.00000 −0.127064 −0.0635321 − 0.997980i \(-0.520237\pi\)
−0.0635321 + 0.997980i \(0.520237\pi\)
\(992\) 0 0
\(993\) 17.0000 0.539479
\(994\) −26.0000 −0.824670
\(995\) −7.00000 −0.221915
\(996\) 3.00000 0.0950586
\(997\) 23.0000 0.728417 0.364209 − 0.931317i \(-0.381339\pi\)
0.364209 + 0.931317i \(0.381339\pi\)
\(998\) −5.00000 −0.158272
\(999\) 3.00000 0.0949158
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 366.2.a.c.1.1 ✓ 1
3.2 odd 2 1098.2.a.i.1.1 1
4.3 odd 2 2928.2.a.e.1.1 1
5.4 even 2 9150.2.a.v.1.1 1
12.11 even 2 8784.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
366.2.a.c.1.1 ✓ 1 1.1 even 1 trivial
1098.2.a.i.1.1 1 3.2 odd 2
2928.2.a.e.1.1 1 4.3 odd 2
8784.2.a.h.1.1 1 12.11 even 2
9150.2.a.v.1.1 1 5.4 even 2