↑

Properties

Label 4830.2.a.n.1.1
Level $4830$
Weight $2$
Character 4830.1
Self dual yes
Analytic conductor $38.568$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4830,2,Mod(1,4830)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4830, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4830.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4830.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: \(38.5677441763\)
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 \(\chi\) \(=\) 4830.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.00000 q^{11} +1.00000 q^{12} +6.00000 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} +1.00000 q^{20} -1.00000 q^{21} -4.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +6.00000 q^{29} -1.00000 q^{30} -1.00000 q^{32} +4.00000 q^{33} -2.00000 q^{34} -1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +6.00000 q^{39} -1.00000 q^{40} -6.00000 q^{41} +1.00000 q^{42} +12.0000 q^{43} +4.00000 q^{44} +1.00000 q^{45} -1.00000 q^{46} +8.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.00000 q^{51} +6.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} +4.00000 q^{55} +1.00000 q^{56} -6.00000 q^{58} +1.00000 q^{60} -2.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +6.00000 q^{65} -4.00000 q^{66} +4.00000 q^{67} +2.00000 q^{68} +1.00000 q^{69} +1.00000 q^{70} -12.0000 q^{71} -1.00000 q^{72} -14.0000 q^{73} +6.00000 q^{74} +1.00000 q^{75} -4.00000 q^{77} -6.00000 q^{78} -4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +4.00000 q^{83} -1.00000 q^{84} +2.00000 q^{85} -12.0000 q^{86} +6.00000 q^{87} -4.00000 q^{88} +10.0000 q^{89} -1.00000 q^{90} -6.00000 q^{91} +1.00000 q^{92} -8.00000 q^{94} -1.00000 q^{96} +14.0000 q^{97} -1.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

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
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 4.00000 1.20605 0.603023 − 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 1.00000 0.288675
\(13\) 6.00000 1.66410 0.832050 − 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 1.00000 0.267261
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 − 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.00000 −0.218218
\(22\) −4.00000 −0.852803
\(23\) 1.00000 0.208514
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) −6.00000 −1.17670
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) 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
\(33\) 4.00000 0.696311
\(34\) −2.00000 −0.342997
\(35\) −1.00000 −0.169031
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 6.00000 0.960769
\(40\) −1.00000 −0.158114
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 1.00000 0.154303
\(43\) 12.0000 1.82998 0.914991 − 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) 4.00000 0.603023
\(45\) 1.00000 0.149071
\(46\) −1.00000 −0.147442
\(47\) 8.00000 1.16692 0.583460 − 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) 2.00000 0.280056
\(52\) 6.00000 0.832050
\(53\) −10.0000 −1.37361 −0.686803 − 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) −1.00000 −0.136083
\(55\) 4.00000 0.539360
\(56\) 1.00000 0.133631
\(57\) 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
\(61\) −2.00000 −0.256074 −0.128037 − 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) −4.00000 −0.492366
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 2.00000 0.242536
\(69\) 1.00000 0.120386
\(70\) 1.00000 0.119523
\(71\) −12.0000 −1.42414 −0.712069 − 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) −1.00000 −0.117851
\(73\) −14.0000 −1.63858 −0.819288 − 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 6.00000 0.697486
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) −6.00000 −0.679366
\(79\) −4.00000 −0.450035 −0.225018 − 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) −1.00000 −0.109109
\(85\) 2.00000 0.216930
\(86\) −12.0000 −1.29399
\(87\) 6.00000 0.643268
\(88\) −4.00000 −0.426401
\(89\) 10.0000 1.06000 0.529999 − 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −1.00000 −0.105409
\(91\) −6.00000 −0.628971
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 14.0000 1.42148 0.710742 − 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −1.00000 −0.101015
\(99\) 4.00000 0.402015
\(100\) 1.00000 0.100000
\(101\) −2.00000 −0.199007 −0.0995037 − 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) −2.00000 −0.198030
\(103\) −16.0000 −1.57653 −0.788263 − 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) −6.00000 −0.588348
\(105\) −1.00000 −0.0975900
\(106\) 10.0000 0.971286
\(107\) −4.00000 −0.386695 −0.193347 − 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 1.00000 0.0962250
\(109\) −18.0000 −1.72409 −0.862044 − 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) −4.00000 −0.381385
\(111\) −6.00000 −0.569495
\(112\) −1.00000 −0.0944911
\(113\) 18.0000 1.69330 0.846649 − 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 6.00000 0.557086
\(117\) 6.00000 0.554700
\(118\) 0 0
\(119\) −2.00000 −0.183340
\(120\) −1.00000 −0.0912871
\(121\) 5.00000 0.454545
\(122\) 2.00000 0.181071
\(123\) −6.00000 −0.541002
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 1.00000 0.0890871
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.0000 1.05654
\(130\) −6.00000 −0.526235
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 1.00000 0.0860663
\(136\) −2.00000 −0.171499
\(137\) −6.00000 −0.512615 −0.256307 − 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −1.00000 −0.0851257
\(139\) −12.0000 −1.01783 −0.508913 − 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 8.00000 0.673722
\(142\) 12.0000 1.00702
\(143\) 24.0000 2.00698
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) 14.0000 1.15865
\(147\) 1.00000 0.0824786
\(148\) −6.00000 −0.493197
\(149\) 22.0000 1.80231 0.901155 − 0.433497i \(-0.142720\pi\)
0.901155 + 0.433497i \(0.142720\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 4.00000 0.322329
\(155\) 0 0
\(156\) 6.00000 0.480384
\(157\) 10.0000 0.798087 0.399043 − 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) 4.00000 0.318223
\(159\) −10.0000 −0.793052
\(160\) −1.00000 −0.0790569
\(161\) −1.00000 −0.0788110
\(162\) −1.00000 −0.0785674
\(163\) 4.00000 0.313304 0.156652 − 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −6.00000 −0.468521
\(165\) 4.00000 0.311400
\(166\) −4.00000 −0.310460
\(167\) −8.00000 −0.619059 −0.309529 − 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 1.00000 0.0771517
\(169\) 23.0000 1.76923
\(170\) −2.00000 −0.153393
\(171\) 0 0
\(172\) 12.0000 0.914991
\(173\) 18.0000 1.36851 0.684257 − 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) −6.00000 −0.454859
\(175\) −1.00000 −0.0755929
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) −10.0000 −0.749532
\(179\) 16.0000 1.19590 0.597948 − 0.801535i \(-0.295983\pi\)
0.597948 + 0.801535i \(0.295983\pi\)
\(180\) 1.00000 0.0745356
\(181\) −2.00000 −0.148659 −0.0743294 − 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 6.00000 0.444750
\(183\) −2.00000 −0.147844
\(184\) −1.00000 −0.0737210
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) 8.00000 0.585018
\(188\) 8.00000 0.583460
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) 10.0000 0.719816 0.359908 − 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) −14.0000 −1.00514
\(195\) 6.00000 0.429669
\(196\) 1.00000 0.0714286
\(197\) 10.0000 0.712470 0.356235 − 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) −4.00000 −0.284268
\(199\) −20.0000 −1.41776 −0.708881 − 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 4.00000 0.282138
\(202\) 2.00000 0.140720
\(203\) −6.00000 −0.421117
\(204\) 2.00000 0.140028
\(205\) −6.00000 −0.419058
\(206\) 16.0000 1.11477
\(207\) 1.00000 0.0695048
\(208\) 6.00000 0.416025
\(209\) 0 0
\(210\) 1.00000 0.0690066
\(211\) −12.0000 −0.826114 −0.413057 − 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −10.0000 −0.686803
\(213\) −12.0000 −0.822226
\(214\) 4.00000 0.273434
\(215\) 12.0000 0.818393
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 18.0000 1.21911
\(219\) −14.0000 −0.946032
\(220\) 4.00000 0.269680
\(221\) 12.0000 0.807207
\(222\) 6.00000 0.402694
\(223\) 16.0000 1.07144 0.535720 − 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 1.00000 0.0668153
\(225\) 1.00000 0.0666667
\(226\) −18.0000 −1.19734
\(227\) −4.00000 −0.265489 −0.132745 − 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) 6.00000 0.396491 0.198246 − 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) −1.00000 −0.0659380
\(231\) −4.00000 −0.263181
\(232\) −6.00000 −0.393919
\(233\) −10.0000 −0.655122 −0.327561 − 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) −6.00000 −0.392232
\(235\) 8.00000 0.521862
\(236\) 0 0
\(237\) −4.00000 −0.259828
\(238\) 2.00000 0.129641
\(239\) 12.0000 0.776215 0.388108 − 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 1.00000 0.0645497
\(241\) −14.0000 −0.901819 −0.450910 − 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) −5.00000 −0.321412
\(243\) 1.00000 0.0641500
\(244\) −2.00000 −0.128037
\(245\) 1.00000 0.0638877
\(246\) 6.00000 0.382546
\(247\) 0 0
\(248\) 0 0
\(249\) 4.00000 0.253490
\(250\) −1.00000 −0.0632456
\(251\) −20.0000 −1.26239 −0.631194 − 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 4.00000 0.251478
\(254\) 8.00000 0.501965
\(255\) 2.00000 0.125245
\(256\) 1.00000 0.0625000
\(257\) 22.0000 1.37232 0.686161 − 0.727450i \(-0.259294\pi\)
0.686161 + 0.727450i \(0.259294\pi\)
\(258\) −12.0000 −0.747087
\(259\) 6.00000 0.372822
\(260\) 6.00000 0.372104
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 − 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) −4.00000 −0.246183
\(265\) −10.0000 −0.614295
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 4.00000 0.244339
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 8.00000 0.485965 0.242983 − 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 2.00000 0.121268
\(273\) −6.00000 −0.363137
\(274\) 6.00000 0.362473
\(275\) 4.00000 0.241209
\(276\) 1.00000 0.0601929
\(277\) 14.0000 0.841178 0.420589 − 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 12.0000 0.719712
\(279\) 0 0
\(280\) 1.00000 0.0597614
\(281\) −22.0000 −1.31241 −0.656205 − 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) −8.00000 −0.476393
\(283\) −12.0000 −0.713326 −0.356663 − 0.934233i \(-0.616086\pi\)
−0.356663 + 0.934233i \(0.616086\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) −24.0000 −1.41915
\(287\) 6.00000 0.354169
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) −6.00000 −0.352332
\(291\) 14.0000 0.820695
\(292\) −14.0000 −0.819288
\(293\) 30.0000 1.75262 0.876309 − 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 0 0
\(296\) 6.00000 0.348743
\(297\) 4.00000 0.232104
\(298\) −22.0000 −1.27443
\(299\) 6.00000 0.346989
\(300\) 1.00000 0.0577350
\(301\) −12.0000 −0.691669
\(302\) 0 0
\(303\) −2.00000 −0.114897
\(304\) 0 0
\(305\) −2.00000 −0.114520
\(306\) −2.00000 −0.114332
\(307\) 12.0000 0.684876 0.342438 − 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) −4.00000 −0.227921
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) −28.0000 −1.58773 −0.793867 − 0.608091i \(-0.791935\pi\)
−0.793867 + 0.608091i \(0.791935\pi\)
\(312\) −6.00000 −0.339683
\(313\) −2.00000 −0.113047 −0.0565233 − 0.998401i \(-0.518002\pi\)
−0.0565233 + 0.998401i \(0.518002\pi\)
\(314\) −10.0000 −0.564333
\(315\) −1.00000 −0.0563436
\(316\) −4.00000 −0.225018
\(317\) 26.0000 1.46031 0.730153 − 0.683284i \(-0.239449\pi\)
0.730153 + 0.683284i \(0.239449\pi\)
\(318\) 10.0000 0.560772
\(319\) 24.0000 1.34374
\(320\) 1.00000 0.0559017
\(321\) −4.00000 −0.223258
\(322\) 1.00000 0.0557278
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 6.00000 0.332820
\(326\) −4.00000 −0.221540
\(327\) −18.0000 −0.995402
\(328\) 6.00000 0.331295
\(329\) −8.00000 −0.441054
\(330\) −4.00000 −0.220193
\(331\) 20.0000 1.09930 0.549650 − 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 4.00000 0.219529
\(333\) −6.00000 −0.328798
\(334\) 8.00000 0.437741
\(335\) 4.00000 0.218543
\(336\) −1.00000 −0.0545545
\(337\) −18.0000 −0.980522 −0.490261 − 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) −23.0000 −1.25104
\(339\) 18.0000 0.977626
\(340\) 2.00000 0.108465
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −12.0000 −0.646997
\(345\) 1.00000 0.0538382
\(346\) −18.0000 −0.967686
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 6.00000 0.321634
\(349\) −2.00000 −0.107058 −0.0535288 − 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 1.00000 0.0534522
\(351\) 6.00000 0.320256
\(352\) −4.00000 −0.213201
\(353\) −26.0000 −1.38384 −0.691920 − 0.721974i \(-0.743235\pi\)
−0.691920 + 0.721974i \(0.743235\pi\)
\(354\) 0 0
\(355\) −12.0000 −0.636894
\(356\) 10.0000 0.529999
\(357\) −2.00000 −0.105851
\(358\) −16.0000 −0.845626
\(359\) 32.0000 1.68890 0.844448 − 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −19.0000 −1.00000
\(362\) 2.00000 0.105118
\(363\) 5.00000 0.262432
\(364\) −6.00000 −0.314485
\(365\) −14.0000 −0.732793
\(366\) 2.00000 0.104542
\(367\) −8.00000 −0.417597 −0.208798 − 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 1.00000 0.0521286
\(369\) −6.00000 −0.312348
\(370\) 6.00000 0.311925
\(371\) 10.0000 0.519174
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 − 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) −8.00000 −0.413670
\(375\) 1.00000 0.0516398
\(376\) −8.00000 −0.412568
\(377\) 36.0000 1.85409
\(378\) 1.00000 0.0514344
\(379\) −16.0000 −0.821865 −0.410932 − 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) −8.00000 −0.409852
\(382\) 0 0
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −4.00000 −0.203859
\(386\) −10.0000 −0.508987
\(387\) 12.0000 0.609994
\(388\) 14.0000 0.710742
\(389\) 6.00000 0.304212 0.152106 − 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) −6.00000 −0.303822
\(391\) 2.00000 0.101144
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) −10.0000 −0.503793
\(395\) −4.00000 −0.201262
\(396\) 4.00000 0.201008
\(397\) −2.00000 −0.100377 −0.0501886 − 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 2.00000 0.0998752 0.0499376 − 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −4.00000 −0.199502
\(403\) 0 0
\(404\) −2.00000 −0.0995037
\(405\) 1.00000 0.0496904
\(406\) 6.00000 0.297775
\(407\) −24.0000 −1.18964
\(408\) −2.00000 −0.0990148
\(409\) 10.0000 0.494468 0.247234 − 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 6.00000 0.296319
\(411\) −6.00000 −0.295958
\(412\) −16.0000 −0.788263
\(413\) 0 0
\(414\) −1.00000 −0.0491473
\(415\) 4.00000 0.196352
\(416\) −6.00000 −0.294174
\(417\) −12.0000 −0.587643
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 − 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −18.0000 −0.877266 −0.438633 − 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) 12.0000 0.584151
\(423\) 8.00000 0.388973
\(424\) 10.0000 0.485643
\(425\) 2.00000 0.0970143
\(426\) 12.0000 0.581402
\(427\) 2.00000 0.0967868
\(428\) −4.00000 −0.193347
\(429\) 24.0000 1.15873
\(430\) −12.0000 −0.578691
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 1.00000 0.0481125
\(433\) 14.0000 0.672797 0.336399 − 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) −18.0000 −0.862044
\(437\) 0 0
\(438\) 14.0000 0.668946
\(439\) −16.0000 −0.763638 −0.381819 − 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) −4.00000 −0.190693
\(441\) 1.00000 0.0476190
\(442\) −12.0000 −0.570782
\(443\) 4.00000 0.190046 0.0950229 − 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) −6.00000 −0.284747
\(445\) 10.0000 0.474045
\(446\) −16.0000 −0.757622
\(447\) 22.0000 1.04056
\(448\) −1.00000 −0.0472456
\(449\) 18.0000 0.849473 0.424736 − 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −24.0000 −1.13012
\(452\) 18.0000 0.846649
\(453\) 0 0
\(454\) 4.00000 0.187729
\(455\) −6.00000 −0.281284
\(456\) 0 0
\(457\) −42.0000 −1.96468 −0.982339 − 0.187112i \(-0.940087\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) −6.00000 −0.280362
\(459\) 2.00000 0.0933520
\(460\) 1.00000 0.0466252
\(461\) 38.0000 1.76984 0.884918 − 0.465746i \(-0.154214\pi\)
0.884918 + 0.465746i \(0.154214\pi\)
\(462\) 4.00000 0.186097
\(463\) 16.0000 0.743583 0.371792 − 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 10.0000 0.463241
\(467\) −20.0000 −0.925490 −0.462745 − 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 6.00000 0.277350
\(469\) −4.00000 −0.184703
\(470\) −8.00000 −0.369012
\(471\) 10.0000 0.460776
\(472\) 0 0
\(473\) 48.0000 2.20704
\(474\) 4.00000 0.183726
\(475\) 0 0
\(476\) −2.00000 −0.0916698
\(477\) −10.0000 −0.457869
\(478\) −12.0000 −0.548867
\(479\) −24.0000 −1.09659 −0.548294 − 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −36.0000 −1.64146
\(482\) 14.0000 0.637683
\(483\) −1.00000 −0.0455016
\(484\) 5.00000 0.227273
\(485\) 14.0000 0.635707
\(486\) −1.00000 −0.0453609
\(487\) 40.0000 1.81257 0.906287 − 0.422664i \(-0.138905\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(488\) 2.00000 0.0905357
\(489\) 4.00000 0.180886
\(490\) −1.00000 −0.0451754
\(491\) 24.0000 1.08310 0.541552 − 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) −6.00000 −0.270501
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) 4.00000 0.179787
\(496\) 0 0
\(497\) 12.0000 0.538274
\(498\) −4.00000 −0.179244
\(499\) −20.0000 −0.895323 −0.447661 − 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.00000 −0.357414
\(502\) 20.0000 0.892644
\(503\) 24.0000 1.07011 0.535054 − 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 1.00000 0.0445435
\(505\) −2.00000 −0.0889988
\(506\) −4.00000 −0.177822
\(507\) 23.0000 1.02147
\(508\) −8.00000 −0.354943
\(509\) 14.0000 0.620539 0.310270 − 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 14.0000 0.619324
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −22.0000 −0.970378
\(515\) −16.0000 −0.705044
\(516\) 12.0000 0.528271
\(517\) 32.0000 1.40736
\(518\) −6.00000 −0.263625
\(519\) 18.0000 0.790112
\(520\) −6.00000 −0.263117
\(521\) −6.00000 −0.262865 −0.131432 − 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −6.00000 −0.262613
\(523\) 36.0000 1.57417 0.787085 − 0.616844i \(-0.211589\pi\)
0.787085 + 0.616844i \(0.211589\pi\)
\(524\) 0 0
\(525\) −1.00000 −0.0436436
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 4.00000 0.174078
\(529\) 1.00000 0.0434783
\(530\) 10.0000 0.434372
\(531\) 0 0
\(532\) 0 0
\(533\) −36.0000 −1.55933
\(534\) −10.0000 −0.432742
\(535\) −4.00000 −0.172935
\(536\) −4.00000 −0.172774
\(537\) 16.0000 0.690451
\(538\) −6.00000 −0.258678
\(539\) 4.00000 0.172292
\(540\) 1.00000 0.0430331
\(541\) −34.0000 −1.46177 −0.730887 − 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) −8.00000 −0.343629
\(543\) −2.00000 −0.0858282
\(544\) −2.00000 −0.0857493
\(545\) −18.0000 −0.771035
\(546\) 6.00000 0.256776
\(547\) 4.00000 0.171028 0.0855138 − 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −6.00000 −0.256307
\(549\) −2.00000 −0.0853579
\(550\) −4.00000 −0.170561
\(551\) 0 0
\(552\) −1.00000 −0.0425628
\(553\) 4.00000 0.170097
\(554\) −14.0000 −0.594803
\(555\) −6.00000 −0.254686
\(556\) −12.0000 −0.508913
\(557\) 30.0000 1.27114 0.635570 − 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) 72.0000 3.04528
\(560\) −1.00000 −0.0422577
\(561\) 8.00000 0.337760
\(562\) 22.0000 0.928014
\(563\) 36.0000 1.51722 0.758610 − 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 8.00000 0.336861
\(565\) 18.0000 0.757266
\(566\) 12.0000 0.504398
\(567\) −1.00000 −0.0419961
\(568\) 12.0000 0.503509
\(569\) 26.0000 1.08998 0.544988 − 0.838444i \(-0.316534\pi\)
0.544988 + 0.838444i \(0.316534\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 − 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 24.0000 1.00349
\(573\) 0 0
\(574\) −6.00000 −0.250435
\(575\) 1.00000 0.0417029
\(576\) 1.00000 0.0416667
\(577\) 18.0000 0.749350 0.374675 − 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 13.0000 0.540729
\(579\) 10.0000 0.415586
\(580\) 6.00000 0.249136
\(581\) −4.00000 −0.165948
\(582\) −14.0000 −0.580319
\(583\) −40.0000 −1.65663
\(584\) 14.0000 0.579324
\(585\) 6.00000 0.248069
\(586\) −30.0000 −1.23929
\(587\) 12.0000 0.495293 0.247647 − 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 1.00000 0.0412393
\(589\) 0 0
\(590\) 0 0
\(591\) 10.0000 0.411345
\(592\) −6.00000 −0.246598
\(593\) −10.0000 −0.410651 −0.205325 − 0.978694i \(-0.565825\pi\)
−0.205325 + 0.978694i \(0.565825\pi\)
\(594\) −4.00000 −0.164122
\(595\) −2.00000 −0.0819920
\(596\) 22.0000 0.901155
\(597\) −20.0000 −0.818546
\(598\) −6.00000 −0.245358
\(599\) −28.0000 −1.14405 −0.572024 − 0.820237i \(-0.693842\pi\)
−0.572024 + 0.820237i \(0.693842\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 26.0000 1.06056 0.530281 − 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 12.0000 0.489083
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) 5.00000 0.203279
\(606\) 2.00000 0.0812444
\(607\) −24.0000 −0.974130 −0.487065 − 0.873366i \(-0.661933\pi\)
−0.487065 + 0.873366i \(0.661933\pi\)
\(608\) 0 0
\(609\) −6.00000 −0.243132
\(610\) 2.00000 0.0809776
\(611\) 48.0000 1.94187
\(612\) 2.00000 0.0808452
\(613\) −14.0000 −0.565455 −0.282727 − 0.959200i \(-0.591239\pi\)
−0.282727 + 0.959200i \(0.591239\pi\)
\(614\) −12.0000 −0.484281
\(615\) −6.00000 −0.241943
\(616\) 4.00000 0.161165
\(617\) 42.0000 1.69086 0.845428 − 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 16.0000 0.643614
\(619\) −40.0000 −1.60774 −0.803868 − 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 28.0000 1.12270
\(623\) −10.0000 −0.400642
\(624\) 6.00000 0.240192
\(625\) 1.00000 0.0400000
\(626\) 2.00000 0.0799361
\(627\) 0 0
\(628\) 10.0000 0.399043
\(629\) −12.0000 −0.478471
\(630\) 1.00000 0.0398410
\(631\) −44.0000 −1.75161 −0.875806 − 0.482663i \(-0.839670\pi\)
−0.875806 + 0.482663i \(0.839670\pi\)
\(632\) 4.00000 0.159111
\(633\) −12.0000 −0.476957
\(634\) −26.0000 −1.03259
\(635\) −8.00000 −0.317470
\(636\) −10.0000 −0.396526
\(637\) 6.00000 0.237729
\(638\) −24.0000 −0.950169
\(639\) −12.0000 −0.474713
\(640\) −1.00000 −0.0395285
\(641\) 18.0000 0.710957 0.355479 − 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 4.00000 0.157867
\(643\) −44.0000 −1.73519 −0.867595 − 0.497271i \(-0.834335\pi\)
−0.867595 + 0.497271i \(0.834335\pi\)
\(644\) −1.00000 −0.0394055
\(645\) 12.0000 0.472500
\(646\) 0 0
\(647\) −48.0000 −1.88707 −0.943537 − 0.331266i \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) −6.00000 −0.235339
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −14.0000 −0.547862 −0.273931 − 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) 18.0000 0.703856
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) −14.0000 −0.546192
\(658\) 8.00000 0.311872
\(659\) −36.0000 −1.40236 −0.701180 − 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 4.00000 0.155700
\(661\) 22.0000 0.855701 0.427850 − 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) −20.0000 −0.777322
\(663\) 12.0000 0.466041
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 6.00000 0.232321
\(668\) −8.00000 −0.309529
\(669\) 16.0000 0.618596
\(670\) −4.00000 −0.154533
\(671\) −8.00000 −0.308837
\(672\) 1.00000 0.0385758
\(673\) −14.0000 −0.539660 −0.269830 − 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) 18.0000 0.693334
\(675\) 1.00000 0.0384900
\(676\) 23.0000 0.884615
\(677\) 22.0000 0.845529 0.422764 − 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) −18.0000 −0.691286
\(679\) −14.0000 −0.537271
\(680\) −2.00000 −0.0766965
\(681\) −4.00000 −0.153280
\(682\) 0 0
\(683\) −4.00000 −0.153056 −0.0765279 − 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 1.00000 0.0381802
\(687\) 6.00000 0.228914
\(688\) 12.0000 0.457496
\(689\) −60.0000 −2.28582
\(690\) −1.00000 −0.0380693
\(691\) 4.00000 0.152167 0.0760836 − 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) 18.0000 0.684257
\(693\) −4.00000 −0.151947
\(694\) 4.00000 0.151838
\(695\) −12.0000 −0.455186
\(696\) −6.00000 −0.227429
\(697\) −12.0000 −0.454532
\(698\) 2.00000 0.0757011
\(699\) −10.0000 −0.378235
\(700\) −1.00000 −0.0377964
\(701\) −18.0000 −0.679851 −0.339925 − 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) −6.00000 −0.226455
\(703\) 0 0
\(704\) 4.00000 0.150756
\(705\) 8.00000 0.301297
\(706\) 26.0000 0.978523
\(707\) 2.00000 0.0752177
\(708\) 0 0
\(709\) 14.0000 0.525781 0.262891 − 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 12.0000 0.450352
\(711\) −4.00000 −0.150012
\(712\) −10.0000 −0.374766
\(713\) 0 0
\(714\) 2.00000 0.0748481
\(715\) 24.0000 0.897549
\(716\) 16.0000 0.597948
\(717\) 12.0000 0.448148
\(718\) −32.0000 −1.19423
\(719\) −4.00000 −0.149175 −0.0745874 − 0.997214i \(-0.523764\pi\)
−0.0745874 + 0.997214i \(0.523764\pi\)
\(720\) 1.00000 0.0372678
\(721\) 16.0000 0.595871
\(722\) 19.0000 0.707107
\(723\) −14.0000 −0.520666
\(724\) −2.00000 −0.0743294
\(725\) 6.00000 0.222834
\(726\) −5.00000 −0.185567
\(727\) −8.00000 −0.296704 −0.148352 − 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 6.00000 0.222375
\(729\) 1.00000 0.0370370
\(730\) 14.0000 0.518163
\(731\) 24.0000 0.887672
\(732\) −2.00000 −0.0739221
\(733\) 26.0000 0.960332 0.480166 − 0.877178i \(-0.340576\pi\)
0.480166 + 0.877178i \(0.340576\pi\)
\(734\) 8.00000 0.295285
\(735\) 1.00000 0.0368856
\(736\) −1.00000 −0.0368605
\(737\) 16.0000 0.589368
\(738\) 6.00000 0.220863
\(739\) 44.0000 1.61857 0.809283 − 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) −6.00000 −0.220564
\(741\) 0 0
\(742\) −10.0000 −0.367112
\(743\) 16.0000 0.586983 0.293492 − 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 0 0
\(745\) 22.0000 0.806018
\(746\) 14.0000 0.512576
\(747\) 4.00000 0.146352
\(748\) 8.00000 0.292509
\(749\) 4.00000 0.146157
\(750\) −1.00000 −0.0365148
\(751\) −52.0000 −1.89751 −0.948753 − 0.316017i \(-0.897654\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) 8.00000 0.291730
\(753\) −20.0000 −0.728841
\(754\) −36.0000 −1.31104
\(755\) 0 0
\(756\) −1.00000 −0.0363696
\(757\) 26.0000 0.944986 0.472493 − 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 16.0000 0.581146
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) −30.0000 −1.08750 −0.543750 − 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) 8.00000 0.289809
\(763\) 18.0000 0.651644
\(764\) 0 0
\(765\) 2.00000 0.0723102
\(766\) 0 0
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 2.00000 0.0721218 0.0360609 − 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 4.00000 0.144150
\(771\) 22.0000 0.792311
\(772\) 10.0000 0.359908
\(773\) 22.0000 0.791285 0.395643 − 0.918405i \(-0.370522\pi\)
0.395643 + 0.918405i \(0.370522\pi\)
\(774\) −12.0000 −0.431331
\(775\) 0 0
\(776\) −14.0000 −0.502571
\(777\) 6.00000 0.215249
\(778\) −6.00000 −0.215110
\(779\) 0 0
\(780\) 6.00000 0.214834
\(781\) −48.0000 −1.71758
\(782\) −2.00000 −0.0715199
\(783\) 6.00000 0.214423
\(784\) 1.00000 0.0357143
\(785\) 10.0000 0.356915
\(786\) 0 0
\(787\) −28.0000 −0.998092 −0.499046 − 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) 10.0000 0.356235
\(789\) −24.0000 −0.854423
\(790\) 4.00000 0.142314
\(791\) −18.0000 −0.640006
\(792\) −4.00000 −0.142134
\(793\) −12.0000 −0.426132
\(794\) 2.00000 0.0709773
\(795\) −10.0000 −0.354663
\(796\) −20.0000 −0.708881
\(797\) −10.0000 −0.354218 −0.177109 − 0.984191i \(-0.556675\pi\)
−0.177109 + 0.984191i \(0.556675\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) −1.00000 −0.0353553
\(801\) 10.0000 0.353333
\(802\) −2.00000 −0.0706225
\(803\) −56.0000 −1.97620
\(804\) 4.00000 0.141069
\(805\) −1.00000 −0.0352454
\(806\) 0 0
\(807\) 6.00000 0.211210
\(808\) 2.00000 0.0703598
\(809\) 50.0000 1.75791 0.878953 − 0.476908i \(-0.158243\pi\)
0.878953 + 0.476908i \(0.158243\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 36.0000 1.26413 0.632065 − 0.774915i \(-0.282207\pi\)
0.632065 + 0.774915i \(0.282207\pi\)
\(812\) −6.00000 −0.210559
\(813\) 8.00000 0.280572
\(814\) 24.0000 0.841200
\(815\) 4.00000 0.140114
\(816\) 2.00000 0.0700140
\(817\) 0 0
\(818\) −10.0000 −0.349642
\(819\) −6.00000 −0.209657
\(820\) −6.00000 −0.209529
\(821\) −18.0000 −0.628204 −0.314102 − 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 6.00000 0.209274
\(823\) −56.0000 −1.95204 −0.976019 − 0.217687i \(-0.930149\pi\)
−0.976019 + 0.217687i \(0.930149\pi\)
\(824\) 16.0000 0.557386
\(825\) 4.00000 0.139262
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 − 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 1.00000 0.0347524
\(829\) −34.0000 −1.18087 −0.590434 − 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) −4.00000 −0.138842
\(831\) 14.0000 0.485655
\(832\) 6.00000 0.208013
\(833\) 2.00000 0.0692959
\(834\) 12.0000 0.415526
\(835\) −8.00000 −0.276851
\(836\) 0 0
\(837\) 0 0
\(838\) −20.0000 −0.690889
\(839\) −24.0000 −0.828572 −0.414286 − 0.910147i \(-0.635969\pi\)
−0.414286 + 0.910147i \(0.635969\pi\)
\(840\) 1.00000 0.0345033
\(841\) 7.00000 0.241379
\(842\) 18.0000 0.620321
\(843\) −22.0000 −0.757720
\(844\) −12.0000 −0.413057
\(845\) 23.0000 0.791224
\(846\) −8.00000 −0.275046
\(847\) −5.00000 −0.171802
\(848\) −10.0000 −0.343401
\(849\) −12.0000 −0.411839
\(850\) −2.00000 −0.0685994
\(851\) −6.00000 −0.205677
\(852\) −12.0000 −0.411113
\(853\) −26.0000 −0.890223 −0.445112 − 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) −2.00000 −0.0684386
\(855\) 0 0
\(856\) 4.00000 0.136717
\(857\) −42.0000 −1.43469 −0.717346 − 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) −24.0000 −0.819346
\(859\) −20.0000 −0.682391 −0.341196 − 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 12.0000 0.409197
\(861\) 6.00000 0.204479
\(862\) 0 0
\(863\) −32.0000 −1.08929 −0.544646 − 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 18.0000 0.612018
\(866\) −14.0000 −0.475739
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) −16.0000 −0.542763
\(870\) −6.00000 −0.203419
\(871\) 24.0000 0.813209
\(872\) 18.0000 0.609557
\(873\) 14.0000 0.473828
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) −14.0000 −0.473016
\(877\) 30.0000 1.01303 0.506514 − 0.862232i \(-0.330934\pi\)
0.506514 + 0.862232i \(0.330934\pi\)
\(878\) 16.0000 0.539974
\(879\) 30.0000 1.01187
\(880\) 4.00000 0.134840
\(881\) 18.0000 0.606435 0.303218 − 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) −1.00000 −0.0336718
\(883\) −12.0000 −0.403832 −0.201916 − 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) −4.00000 −0.134383
\(887\) −24.0000 −0.805841 −0.402921 − 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) 6.00000 0.201347
\(889\) 8.00000 0.268311
\(890\) −10.0000 −0.335201
\(891\) 4.00000 0.134005
\(892\) 16.0000 0.535720
\(893\) 0 0
\(894\) −22.0000 −0.735790
\(895\) 16.0000 0.534821
\(896\) 1.00000 0.0334077
\(897\) 6.00000 0.200334
\(898\) −18.0000 −0.600668
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) −20.0000 −0.666297
\(902\) 24.0000 0.799113
\(903\) −12.0000 −0.399335
\(904\) −18.0000 −0.598671
\(905\) −2.00000 −0.0664822
\(906\) 0 0
\(907\) 52.0000 1.72663 0.863316 − 0.504664i \(-0.168384\pi\)
0.863316 + 0.504664i \(0.168384\pi\)
\(908\) −4.00000 −0.132745
\(909\) −2.00000 −0.0663358
\(910\) 6.00000 0.198898
\(911\) −40.0000 −1.32526 −0.662630 − 0.748947i \(-0.730560\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(912\) 0 0
\(913\) 16.0000 0.529523
\(914\) 42.0000 1.38924
\(915\) −2.00000 −0.0661180
\(916\) 6.00000 0.198246
\(917\) 0 0
\(918\) −2.00000 −0.0660098
\(919\) −36.0000 −1.18753 −0.593765 − 0.804638i \(-0.702359\pi\)
−0.593765 + 0.804638i \(0.702359\pi\)
\(920\) −1.00000 −0.0329690
\(921\) 12.0000 0.395413
\(922\) −38.0000 −1.25146
\(923\) −72.0000 −2.36991
\(924\) −4.00000 −0.131590
\(925\) −6.00000 −0.197279
\(926\) −16.0000 −0.525793
\(927\) −16.0000 −0.525509
\(928\) −6.00000 −0.196960
\(929\) −54.0000 −1.77168 −0.885841 − 0.463988i \(-0.846418\pi\)
−0.885841 + 0.463988i \(0.846418\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −10.0000 −0.327561
\(933\) −28.0000 −0.916679
\(934\) 20.0000 0.654420
\(935\) 8.00000 0.261628
\(936\) −6.00000 −0.196116
\(937\) −2.00000 −0.0653372 −0.0326686 − 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 4.00000 0.130605
\(939\) −2.00000 −0.0652675
\(940\) 8.00000 0.260931
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) −10.0000 −0.325818
\(943\) −6.00000 −0.195387
\(944\) 0 0
\(945\) −1.00000 −0.0325300
\(946\) −48.0000 −1.56061
\(947\) −4.00000 −0.129983 −0.0649913 − 0.997886i \(-0.520702\pi\)
−0.0649913 + 0.997886i \(0.520702\pi\)
\(948\) −4.00000 −0.129914
\(949\) −84.0000 −2.72676
\(950\) 0 0
\(951\) 26.0000 0.843108
\(952\) 2.00000 0.0648204
\(953\) 34.0000 1.10137 0.550684 − 0.834714i \(-0.314367\pi\)
0.550684 + 0.834714i \(0.314367\pi\)
\(954\) 10.0000 0.323762
\(955\) 0 0
\(956\) 12.0000 0.388108
\(957\) 24.0000 0.775810
\(958\) 24.0000 0.775405
\(959\) 6.00000 0.193750
\(960\) 1.00000 0.0322749
\(961\) −31.0000 −1.00000
\(962\) 36.0000 1.16069
\(963\) −4.00000 −0.128898
\(964\) −14.0000 −0.450910
\(965\) 10.0000 0.321911
\(966\) 1.00000 0.0321745
\(967\) −8.00000 −0.257263 −0.128631 − 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) −5.00000 −0.160706
\(969\) 0 0
\(970\) −14.0000 −0.449513
\(971\) −36.0000 −1.15529 −0.577647 − 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 1.00000 0.0320750
\(973\) 12.0000 0.384702
\(974\) −40.0000 −1.28168
\(975\) 6.00000 0.192154
\(976\) −2.00000 −0.0640184
\(977\) −14.0000 −0.447900 −0.223950 − 0.974601i \(-0.571895\pi\)
−0.223950 + 0.974601i \(0.571895\pi\)
\(978\) −4.00000 −0.127906
\(979\) 40.0000 1.27841
\(980\) 1.00000 0.0319438
\(981\) −18.0000 −0.574696
\(982\) −24.0000 −0.765871
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 6.00000 0.191273
\(985\) 10.0000 0.318626
\(986\) −12.0000 −0.382158
\(987\) −8.00000 −0.254643
\(988\) 0 0
\(989\) 12.0000 0.381578
\(990\) −4.00000 −0.127128
\(991\) −48.0000 −1.52477 −0.762385 − 0.647124i \(-0.775972\pi\)
−0.762385 + 0.647124i \(0.775972\pi\)
\(992\) 0 0
\(993\) 20.0000 0.634681
\(994\) −12.0000 −0.380617
\(995\) −20.0000 −0.634043
\(996\) 4.00000 0.126745
\(997\) 14.0000 0.443384 0.221692 − 0.975117i \(-0.428842\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(998\) 20.0000 0.633089
\(999\) −6.00000 −0.189832
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 4830.2.a.n.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4830.2.a.n.1.1 ✓ 1 1.1 even 1 trivial