Properties

Label 6026.2.a.b.1.1
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $1$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, 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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} -2.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} -2.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -3.00000 q^{10} -1.00000 q^{11} +4.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} +3.00000 q^{18} -8.00000 q^{19} +3.00000 q^{20} +1.00000 q^{22} -1.00000 q^{23} +4.00000 q^{25} -4.00000 q^{26} -2.00000 q^{28} +6.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} -6.00000 q^{35} -3.00000 q^{36} +2.00000 q^{37} +8.00000 q^{38} -3.00000 q^{40} +3.00000 q^{41} +3.00000 q^{43} -1.00000 q^{44} -9.00000 q^{45} +1.00000 q^{46} -12.0000 q^{47} -3.00000 q^{49} -4.00000 q^{50} +4.00000 q^{52} -2.00000 q^{53} -3.00000 q^{55} +2.00000 q^{56} -6.00000 q^{58} -4.00000 q^{59} +13.0000 q^{61} +4.00000 q^{62} +6.00000 q^{63} +1.00000 q^{64} +12.0000 q^{65} +4.00000 q^{67} +3.00000 q^{68} +6.00000 q^{70} -4.00000 q^{71} +3.00000 q^{72} -6.00000 q^{73} -2.00000 q^{74} -8.00000 q^{76} +2.00000 q^{77} +8.00000 q^{79} +3.00000 q^{80} +9.00000 q^{81} -3.00000 q^{82} -14.0000 q^{83} +9.00000 q^{85} -3.00000 q^{86} +1.00000 q^{88} +4.00000 q^{89} +9.00000 q^{90} -8.00000 q^{91} -1.00000 q^{92} +12.0000 q^{94} -24.0000 q^{95} -2.00000 q^{97} +3.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) −3.00000 −0.948683
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 3.00000 0.707107
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) −2.00000 −0.377964
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) −6.00000 −1.01419
\(36\) −3.00000 −0.500000
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 8.00000 1.29777
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) 3.00000 0.457496 0.228748 0.973486i \(-0.426537\pi\)
0.228748 + 0.973486i \(0.426537\pi\)
\(44\) −1.00000 −0.150756
\(45\) −9.00000 −1.34164
\(46\) 1.00000 0.147442
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) 4.00000 0.554700
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 2.00000 0.267261
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) 13.0000 1.66448 0.832240 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 4.00000 0.508001
\(63\) 6.00000 0.755929
\(64\) 1.00000 0.125000
\(65\) 12.0000 1.48842
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 3.00000 0.363803
\(69\) 0 0
\(70\) 6.00000 0.717137
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 3.00000 0.353553
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) −8.00000 −0.917663
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 3.00000 0.335410
\(81\) 9.00000 1.00000
\(82\) −3.00000 −0.331295
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 9.00000 0.976187
\(86\) −3.00000 −0.323498
\(87\) 0 0
\(88\) 1.00000 0.106600
\(89\) 4.00000 0.423999 0.212000 0.977270i \(-0.432002\pi\)
0.212000 + 0.977270i \(0.432002\pi\)
\(90\) 9.00000 0.948683
\(91\) −8.00000 −0.838628
\(92\) −1.00000 −0.104257
\(93\) 0 0
\(94\) 12.0000 1.23771
\(95\) −24.0000 −2.46235
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 3.00000 0.303046
\(99\) 3.00000 0.301511
\(100\) 4.00000 0.400000
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 5.00000 0.483368 0.241684 0.970355i \(-0.422300\pi\)
0.241684 + 0.970355i \(0.422300\pi\)
\(108\) 0 0
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 3.00000 0.286039
\(111\) 0 0
\(112\) −2.00000 −0.188982
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) −3.00000 −0.279751
\(116\) 6.00000 0.557086
\(117\) −12.0000 −1.10940
\(118\) 4.00000 0.368230
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) −13.0000 −1.17696
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) −3.00000 −0.268328
\(126\) −6.00000 −0.534522
\(127\) −18.0000 −1.59724 −0.798621 0.601834i \(-0.794437\pi\)
−0.798621 + 0.601834i \(0.794437\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −12.0000 −1.05247
\(131\) −1.00000 −0.0873704
\(132\) 0 0
\(133\) 16.0000 1.38738
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) 1.00000 0.0848189 0.0424094 0.999100i \(-0.486497\pi\)
0.0424094 + 0.999100i \(0.486497\pi\)
\(140\) −6.00000 −0.507093
\(141\) 0 0
\(142\) 4.00000 0.335673
\(143\) −4.00000 −0.334497
\(144\) −3.00000 −0.250000
\(145\) 18.0000 1.49482
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) −7.00000 −0.569652 −0.284826 0.958579i \(-0.591936\pi\)
−0.284826 + 0.958579i \(0.591936\pi\)
\(152\) 8.00000 0.648886
\(153\) −9.00000 −0.727607
\(154\) −2.00000 −0.161165
\(155\) −12.0000 −0.963863
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −8.00000 −0.636446
\(159\) 0 0
\(160\) −3.00000 −0.237171
\(161\) 2.00000 0.157622
\(162\) −9.00000 −0.707107
\(163\) −9.00000 −0.704934 −0.352467 0.935824i \(-0.614657\pi\)
−0.352467 + 0.935824i \(0.614657\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) 14.0000 1.08661
\(167\) 1.00000 0.0773823 0.0386912 0.999251i \(-0.487681\pi\)
0.0386912 + 0.999251i \(0.487681\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) −9.00000 −0.690268
\(171\) 24.0000 1.83533
\(172\) 3.00000 0.228748
\(173\) −13.0000 −0.988372 −0.494186 0.869356i \(-0.664534\pi\)
−0.494186 + 0.869356i \(0.664534\pi\)
\(174\) 0 0
\(175\) −8.00000 −0.604743
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) −4.00000 −0.299813
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) −9.00000 −0.670820
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 8.00000 0.592999
\(183\) 0 0
\(184\) 1.00000 0.0737210
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −3.00000 −0.219382
\(188\) −12.0000 −0.875190
\(189\) 0 0
\(190\) 24.0000 1.74114
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) −21.0000 −1.51161 −0.755807 0.654795i \(-0.772755\pi\)
−0.755807 + 0.654795i \(0.772755\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 7.00000 0.498729 0.249365 0.968410i \(-0.419778\pi\)
0.249365 + 0.968410i \(0.419778\pi\)
\(198\) −3.00000 −0.213201
\(199\) 3.00000 0.212664 0.106332 0.994331i \(-0.466089\pi\)
0.106332 + 0.994331i \(0.466089\pi\)
\(200\) −4.00000 −0.282843
\(201\) 0 0
\(202\) 12.0000 0.844317
\(203\) −12.0000 −0.842235
\(204\) 0 0
\(205\) 9.00000 0.628587
\(206\) 1.00000 0.0696733
\(207\) 3.00000 0.208514
\(208\) 4.00000 0.277350
\(209\) 8.00000 0.553372
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −2.00000 −0.137361
\(213\) 0 0
\(214\) −5.00000 −0.341793
\(215\) 9.00000 0.613795
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) −5.00000 −0.338643
\(219\) 0 0
\(220\) −3.00000 −0.202260
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 10.0000 0.669650 0.334825 0.942280i \(-0.391323\pi\)
0.334825 + 0.942280i \(0.391323\pi\)
\(224\) 2.00000 0.133631
\(225\) −12.0000 −0.800000
\(226\) 18.0000 1.19734
\(227\) −2.00000 −0.132745 −0.0663723 0.997795i \(-0.521143\pi\)
−0.0663723 + 0.997795i \(0.521143\pi\)
\(228\) 0 0
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 3.00000 0.197814
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −1.00000 −0.0655122 −0.0327561 0.999463i \(-0.510428\pi\)
−0.0327561 + 0.999463i \(0.510428\pi\)
\(234\) 12.0000 0.784465
\(235\) −36.0000 −2.34838
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) 6.00000 0.388922
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −3.00000 −0.193247 −0.0966235 0.995321i \(-0.530804\pi\)
−0.0966235 + 0.995321i \(0.530804\pi\)
\(242\) 10.0000 0.642824
\(243\) 0 0
\(244\) 13.0000 0.832240
\(245\) −9.00000 −0.574989
\(246\) 0 0
\(247\) −32.0000 −2.03611
\(248\) 4.00000 0.254000
\(249\) 0 0
\(250\) 3.00000 0.189737
\(251\) 26.0000 1.64111 0.820553 0.571571i \(-0.193666\pi\)
0.820553 + 0.571571i \(0.193666\pi\)
\(252\) 6.00000 0.377964
\(253\) 1.00000 0.0628695
\(254\) 18.0000 1.12942
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −8.00000 −0.499026 −0.249513 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) 12.0000 0.744208
\(261\) −18.0000 −1.11417
\(262\) 1.00000 0.0617802
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −16.0000 −0.981023
\(267\) 0 0
\(268\) 4.00000 0.244339
\(269\) 20.0000 1.21942 0.609711 0.792624i \(-0.291286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) 0 0
\(271\) 3.00000 0.182237 0.0911185 0.995840i \(-0.470956\pi\)
0.0911185 + 0.995840i \(0.470956\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) −4.00000 −0.241209
\(276\) 0 0
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) −1.00000 −0.0599760
\(279\) 12.0000 0.718421
\(280\) 6.00000 0.358569
\(281\) −13.0000 −0.775515 −0.387757 0.921761i \(-0.626750\pi\)
−0.387757 + 0.921761i \(0.626750\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) −4.00000 −0.237356
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) −6.00000 −0.354169
\(288\) 3.00000 0.176777
\(289\) −8.00000 −0.470588
\(290\) −18.0000 −1.05700
\(291\) 0 0
\(292\) −6.00000 −0.351123
\(293\) −8.00000 −0.467365 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(294\) 0 0
\(295\) −12.0000 −0.698667
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 0 0
\(299\) −4.00000 −0.231326
\(300\) 0 0
\(301\) −6.00000 −0.345834
\(302\) 7.00000 0.402805
\(303\) 0 0
\(304\) −8.00000 −0.458831
\(305\) 39.0000 2.23313
\(306\) 9.00000 0.514496
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 2.00000 0.113961
\(309\) 0 0
\(310\) 12.0000 0.681554
\(311\) −13.0000 −0.737162 −0.368581 0.929596i \(-0.620156\pi\)
−0.368581 + 0.929596i \(0.620156\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −2.00000 −0.112867
\(315\) 18.0000 1.01419
\(316\) 8.00000 0.450035
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) 0 0
\(319\) −6.00000 −0.335936
\(320\) 3.00000 0.167705
\(321\) 0 0
\(322\) −2.00000 −0.111456
\(323\) −24.0000 −1.33540
\(324\) 9.00000 0.500000
\(325\) 16.0000 0.887520
\(326\) 9.00000 0.498464
\(327\) 0 0
\(328\) −3.00000 −0.165647
\(329\) 24.0000 1.32316
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −14.0000 −0.768350
\(333\) −6.00000 −0.328798
\(334\) −1.00000 −0.0547176
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) −3.00000 −0.163178
\(339\) 0 0
\(340\) 9.00000 0.488094
\(341\) 4.00000 0.216612
\(342\) −24.0000 −1.29777
\(343\) 20.0000 1.07990
\(344\) −3.00000 −0.161749
\(345\) 0 0
\(346\) 13.0000 0.698884
\(347\) 25.0000 1.34207 0.671035 0.741426i \(-0.265850\pi\)
0.671035 + 0.741426i \(0.265850\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 8.00000 0.427618
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) 5.00000 0.266123 0.133062 0.991108i \(-0.457519\pi\)
0.133062 + 0.991108i \(0.457519\pi\)
\(354\) 0 0
\(355\) −12.0000 −0.636894
\(356\) 4.00000 0.212000
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) 3.00000 0.158334 0.0791670 0.996861i \(-0.474774\pi\)
0.0791670 + 0.996861i \(0.474774\pi\)
\(360\) 9.00000 0.474342
\(361\) 45.0000 2.36842
\(362\) 8.00000 0.420471
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) −18.0000 −0.942163
\(366\) 0 0
\(367\) 36.0000 1.87918 0.939592 0.342296i \(-0.111204\pi\)
0.939592 + 0.342296i \(0.111204\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −9.00000 −0.468521
\(370\) −6.00000 −0.311925
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) 6.00000 0.310668 0.155334 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 3.00000 0.155126
\(375\) 0 0
\(376\) 12.0000 0.618853
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) −24.0000 −1.23117
\(381\) 0 0
\(382\) 12.0000 0.613973
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) 6.00000 0.305788
\(386\) 21.0000 1.06887
\(387\) −9.00000 −0.457496
\(388\) −2.00000 −0.101535
\(389\) −34.0000 −1.72387 −0.861934 0.507020i \(-0.830747\pi\)
−0.861934 + 0.507020i \(0.830747\pi\)
\(390\) 0 0
\(391\) −3.00000 −0.151717
\(392\) 3.00000 0.151523
\(393\) 0 0
\(394\) −7.00000 −0.352655
\(395\) 24.0000 1.20757
\(396\) 3.00000 0.150756
\(397\) −26.0000 −1.30490 −0.652451 0.757831i \(-0.726259\pi\)
−0.652451 + 0.757831i \(0.726259\pi\)
\(398\) −3.00000 −0.150376
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −26.0000 −1.29838 −0.649189 0.760627i \(-0.724892\pi\)
−0.649189 + 0.760627i \(0.724892\pi\)
\(402\) 0 0
\(403\) −16.0000 −0.797017
\(404\) −12.0000 −0.597022
\(405\) 27.0000 1.34164
\(406\) 12.0000 0.595550
\(407\) −2.00000 −0.0991363
\(408\) 0 0
\(409\) 5.00000 0.247234 0.123617 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) −9.00000 −0.444478
\(411\) 0 0
\(412\) −1.00000 −0.0492665
\(413\) 8.00000 0.393654
\(414\) −3.00000 −0.147442
\(415\) −42.0000 −2.06170
\(416\) −4.00000 −0.196116
\(417\) 0 0
\(418\) −8.00000 −0.391293
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 0 0
\(421\) −26.0000 −1.26716 −0.633581 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) 20.0000 0.973585
\(423\) 36.0000 1.75038
\(424\) 2.00000 0.0971286
\(425\) 12.0000 0.582086
\(426\) 0 0
\(427\) −26.0000 −1.25823
\(428\) 5.00000 0.241684
\(429\) 0 0
\(430\) −9.00000 −0.434019
\(431\) −34.0000 −1.63772 −0.818861 0.573992i \(-0.805394\pi\)
−0.818861 + 0.573992i \(0.805394\pi\)
\(432\) 0 0
\(433\) −15.0000 −0.720854 −0.360427 0.932787i \(-0.617369\pi\)
−0.360427 + 0.932787i \(0.617369\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) 5.00000 0.239457
\(437\) 8.00000 0.382692
\(438\) 0 0
\(439\) −11.0000 −0.525001 −0.262501 0.964932i \(-0.584547\pi\)
−0.262501 + 0.964932i \(0.584547\pi\)
\(440\) 3.00000 0.143019
\(441\) 9.00000 0.428571
\(442\) −12.0000 −0.570782
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 12.0000 0.568855
\(446\) −10.0000 −0.473514
\(447\) 0 0
\(448\) −2.00000 −0.0944911
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 12.0000 0.565685
\(451\) −3.00000 −0.141264
\(452\) −18.0000 −0.846649
\(453\) 0 0
\(454\) 2.00000 0.0938647
\(455\) −24.0000 −1.12514
\(456\) 0 0
\(457\) −32.0000 −1.49690 −0.748448 0.663193i \(-0.769201\pi\)
−0.748448 + 0.663193i \(0.769201\pi\)
\(458\) 8.00000 0.373815
\(459\) 0 0
\(460\) −3.00000 −0.139876
\(461\) −27.0000 −1.25752 −0.628758 0.777601i \(-0.716436\pi\)
−0.628758 + 0.777601i \(0.716436\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 1.00000 0.0463241
\(467\) 9.00000 0.416470 0.208235 0.978079i \(-0.433228\pi\)
0.208235 + 0.978079i \(0.433228\pi\)
\(468\) −12.0000 −0.554700
\(469\) −8.00000 −0.369406
\(470\) 36.0000 1.66056
\(471\) 0 0
\(472\) 4.00000 0.184115
\(473\) −3.00000 −0.137940
\(474\) 0 0
\(475\) −32.0000 −1.46826
\(476\) −6.00000 −0.275010
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −9.00000 −0.411220 −0.205610 0.978634i \(-0.565918\pi\)
−0.205610 + 0.978634i \(0.565918\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 3.00000 0.136646
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) −6.00000 −0.272446
\(486\) 0 0
\(487\) −31.0000 −1.40474 −0.702372 0.711810i \(-0.747876\pi\)
−0.702372 + 0.711810i \(0.747876\pi\)
\(488\) −13.0000 −0.588482
\(489\) 0 0
\(490\) 9.00000 0.406579
\(491\) 35.0000 1.57953 0.789764 0.613411i \(-0.210203\pi\)
0.789764 + 0.613411i \(0.210203\pi\)
\(492\) 0 0
\(493\) 18.0000 0.810679
\(494\) 32.0000 1.43975
\(495\) 9.00000 0.404520
\(496\) −4.00000 −0.179605
\(497\) 8.00000 0.358849
\(498\) 0 0
\(499\) 11.0000 0.492428 0.246214 0.969216i \(-0.420813\pi\)
0.246214 + 0.969216i \(0.420813\pi\)
\(500\) −3.00000 −0.134164
\(501\) 0 0
\(502\) −26.0000 −1.16044
\(503\) −33.0000 −1.47140 −0.735699 0.677309i \(-0.763146\pi\)
−0.735699 + 0.677309i \(0.763146\pi\)
\(504\) −6.00000 −0.267261
\(505\) −36.0000 −1.60198
\(506\) −1.00000 −0.0444554
\(507\) 0 0
\(508\) −18.0000 −0.798621
\(509\) −13.0000 −0.576215 −0.288107 0.957598i \(-0.593026\pi\)
−0.288107 + 0.957598i \(0.593026\pi\)
\(510\) 0 0
\(511\) 12.0000 0.530849
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 8.00000 0.352865
\(515\) −3.00000 −0.132196
\(516\) 0 0
\(517\) 12.0000 0.527759
\(518\) 4.00000 0.175750
\(519\) 0 0
\(520\) −12.0000 −0.526235
\(521\) −35.0000 −1.53338 −0.766689 0.642019i \(-0.778097\pi\)
−0.766689 + 0.642019i \(0.778097\pi\)
\(522\) 18.0000 0.787839
\(523\) −8.00000 −0.349816 −0.174908 0.984585i \(-0.555963\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0 0
\(526\) 0 0
\(527\) −12.0000 −0.522728
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 6.00000 0.260623
\(531\) 12.0000 0.520756
\(532\) 16.0000 0.693688
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 15.0000 0.648507
\(536\) −4.00000 −0.172774
\(537\) 0 0
\(538\) −20.0000 −0.862261
\(539\) 3.00000 0.129219
\(540\) 0 0
\(541\) 5.00000 0.214967 0.107483 0.994207i \(-0.465721\pi\)
0.107483 + 0.994207i \(0.465721\pi\)
\(542\) −3.00000 −0.128861
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) 15.0000 0.642529
\(546\) 0 0
\(547\) 1.00000 0.0427569 0.0213785 0.999771i \(-0.493195\pi\)
0.0213785 + 0.999771i \(0.493195\pi\)
\(548\) 3.00000 0.128154
\(549\) −39.0000 −1.66448
\(550\) 4.00000 0.170561
\(551\) −48.0000 −2.04487
\(552\) 0 0
\(553\) −16.0000 −0.680389
\(554\) −6.00000 −0.254916
\(555\) 0 0
\(556\) 1.00000 0.0424094
\(557\) 9.00000 0.381342 0.190671 0.981654i \(-0.438934\pi\)
0.190671 + 0.981654i \(0.438934\pi\)
\(558\) −12.0000 −0.508001
\(559\) 12.0000 0.507546
\(560\) −6.00000 −0.253546
\(561\) 0 0
\(562\) 13.0000 0.548372
\(563\) 32.0000 1.34864 0.674320 0.738440i \(-0.264437\pi\)
0.674320 + 0.738440i \(0.264437\pi\)
\(564\) 0 0
\(565\) −54.0000 −2.27180
\(566\) 0 0
\(567\) −18.0000 −0.755929
\(568\) 4.00000 0.167836
\(569\) −36.0000 −1.50920 −0.754599 0.656186i \(-0.772169\pi\)
−0.754599 + 0.656186i \(0.772169\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) −4.00000 −0.167248
\(573\) 0 0
\(574\) 6.00000 0.250435
\(575\) −4.00000 −0.166812
\(576\) −3.00000 −0.125000
\(577\) 39.0000 1.62359 0.811796 0.583942i \(-0.198490\pi\)
0.811796 + 0.583942i \(0.198490\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) 18.0000 0.747409
\(581\) 28.0000 1.16164
\(582\) 0 0
\(583\) 2.00000 0.0828315
\(584\) 6.00000 0.248282
\(585\) −36.0000 −1.48842
\(586\) 8.00000 0.330477
\(587\) 14.0000 0.577842 0.288921 0.957353i \(-0.406704\pi\)
0.288921 + 0.957353i \(0.406704\pi\)
\(588\) 0 0
\(589\) 32.0000 1.31854
\(590\) 12.0000 0.494032
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) −18.0000 −0.737928
\(596\) 0 0
\(597\) 0 0
\(598\) 4.00000 0.163572
\(599\) −15.0000 −0.612883 −0.306442 0.951889i \(-0.599138\pi\)
−0.306442 + 0.951889i \(0.599138\pi\)
\(600\) 0 0
\(601\) 7.00000 0.285536 0.142768 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) 6.00000 0.244542
\(603\) −12.0000 −0.488678
\(604\) −7.00000 −0.284826
\(605\) −30.0000 −1.21967
\(606\) 0 0
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) 8.00000 0.324443
\(609\) 0 0
\(610\) −39.0000 −1.57906
\(611\) −48.0000 −1.94187
\(612\) −9.00000 −0.363803
\(613\) −19.0000 −0.767403 −0.383701 0.923457i \(-0.625351\pi\)
−0.383701 + 0.923457i \(0.625351\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) −2.00000 −0.0805823
\(617\) −13.0000 −0.523360 −0.261680 0.965155i \(-0.584277\pi\)
−0.261680 + 0.965155i \(0.584277\pi\)
\(618\) 0 0
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) −12.0000 −0.481932
\(621\) 0 0
\(622\) 13.0000 0.521253
\(623\) −8.00000 −0.320513
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) 6.00000 0.239236
\(630\) −18.0000 −0.717137
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) −8.00000 −0.318223
\(633\) 0 0
\(634\) 2.00000 0.0794301
\(635\) −54.0000 −2.14292
\(636\) 0 0
\(637\) −12.0000 −0.475457
\(638\) 6.00000 0.237542
\(639\) 12.0000 0.474713
\(640\) −3.00000 −0.118585
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) −24.0000 −0.946468 −0.473234 0.880937i \(-0.656913\pi\)
−0.473234 + 0.880937i \(0.656913\pi\)
\(644\) 2.00000 0.0788110
\(645\) 0 0
\(646\) 24.0000 0.944267
\(647\) 35.0000 1.37599 0.687996 0.725714i \(-0.258491\pi\)
0.687996 + 0.725714i \(0.258491\pi\)
\(648\) −9.00000 −0.353553
\(649\) 4.00000 0.157014
\(650\) −16.0000 −0.627572
\(651\) 0 0
\(652\) −9.00000 −0.352467
\(653\) 36.0000 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(654\) 0 0
\(655\) −3.00000 −0.117220
\(656\) 3.00000 0.117130
\(657\) 18.0000 0.702247
\(658\) −24.0000 −0.935617
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 0 0
\(661\) −42.0000 −1.63361 −0.816805 0.576913i \(-0.804257\pi\)
−0.816805 + 0.576913i \(0.804257\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) 14.0000 0.543305
\(665\) 48.0000 1.86136
\(666\) 6.00000 0.232495
\(667\) −6.00000 −0.232321
\(668\) 1.00000 0.0386912
\(669\) 0 0
\(670\) −12.0000 −0.463600
\(671\) −13.0000 −0.501859
\(672\) 0 0
\(673\) −32.0000 −1.23351 −0.616755 0.787155i \(-0.711553\pi\)
−0.616755 + 0.787155i \(0.711553\pi\)
\(674\) −22.0000 −0.847408
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −28.0000 −1.07613 −0.538064 0.842904i \(-0.680844\pi\)
−0.538064 + 0.842904i \(0.680844\pi\)
\(678\) 0 0
\(679\) 4.00000 0.153506
\(680\) −9.00000 −0.345134
\(681\) 0 0
\(682\) −4.00000 −0.153168
\(683\) 32.0000 1.22445 0.612223 0.790685i \(-0.290275\pi\)
0.612223 + 0.790685i \(0.290275\pi\)
\(684\) 24.0000 0.917663
\(685\) 9.00000 0.343872
\(686\) −20.0000 −0.763604
\(687\) 0 0
\(688\) 3.00000 0.114374
\(689\) −8.00000 −0.304776
\(690\) 0 0
\(691\) −16.0000 −0.608669 −0.304334 0.952565i \(-0.598434\pi\)
−0.304334 + 0.952565i \(0.598434\pi\)
\(692\) −13.0000 −0.494186
\(693\) −6.00000 −0.227921
\(694\) −25.0000 −0.948987
\(695\) 3.00000 0.113796
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) −2.00000 −0.0757011
\(699\) 0 0
\(700\) −8.00000 −0.302372
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) −16.0000 −0.603451
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) −5.00000 −0.188177
\(707\) 24.0000 0.902613
\(708\) 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
\(711\) −24.0000 −0.900070
\(712\) −4.00000 −0.149906
\(713\) 4.00000 0.149801
\(714\) 0 0
\(715\) −12.0000 −0.448775
\(716\) 4.00000 0.149487
\(717\) 0 0
\(718\) −3.00000 −0.111959
\(719\) −7.00000 −0.261056 −0.130528 0.991445i \(-0.541667\pi\)
−0.130528 + 0.991445i \(0.541667\pi\)
\(720\) −9.00000 −0.335410
\(721\) 2.00000 0.0744839
\(722\) −45.0000 −1.67473
\(723\) 0 0
\(724\) −8.00000 −0.297318
\(725\) 24.0000 0.891338
\(726\) 0 0
\(727\) −53.0000 −1.96566 −0.982831 0.184510i \(-0.940930\pi\)
−0.982831 + 0.184510i \(0.940930\pi\)
\(728\) 8.00000 0.296500
\(729\) −27.0000 −1.00000
\(730\) 18.0000 0.666210
\(731\) 9.00000 0.332877
\(732\) 0 0
\(733\) −40.0000 −1.47743 −0.738717 0.674016i \(-0.764568\pi\)
−0.738717 + 0.674016i \(0.764568\pi\)
\(734\) −36.0000 −1.32878
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −4.00000 −0.147342
\(738\) 9.00000 0.331295
\(739\) 16.0000 0.588570 0.294285 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(740\) 6.00000 0.220564
\(741\) 0 0
\(742\) −4.00000 −0.146845
\(743\) −19.0000 −0.697042 −0.348521 0.937301i \(-0.613316\pi\)
−0.348521 + 0.937301i \(0.613316\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −6.00000 −0.219676
\(747\) 42.0000 1.53670
\(748\) −3.00000 −0.109691
\(749\) −10.0000 −0.365392
\(750\) 0 0
\(751\) −23.0000 −0.839282 −0.419641 0.907690i \(-0.637844\pi\)
−0.419641 + 0.907690i \(0.637844\pi\)
\(752\) −12.0000 −0.437595
\(753\) 0 0
\(754\) −24.0000 −0.874028
\(755\) −21.0000 −0.764268
\(756\) 0 0
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) −29.0000 −1.05333
\(759\) 0 0
\(760\) 24.0000 0.870572
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) −10.0000 −0.362024
\(764\) −12.0000 −0.434145
\(765\) −27.0000 −0.976187
\(766\) −18.0000 −0.650366
\(767\) −16.0000 −0.577727
\(768\) 0 0
\(769\) 4.00000 0.144244 0.0721218 0.997396i \(-0.477023\pi\)
0.0721218 + 0.997396i \(0.477023\pi\)
\(770\) −6.00000 −0.216225
\(771\) 0 0
\(772\) −21.0000 −0.755807
\(773\) 22.0000 0.791285 0.395643 0.918405i \(-0.370522\pi\)
0.395643 + 0.918405i \(0.370522\pi\)
\(774\) 9.00000 0.323498
\(775\) −16.0000 −0.574737
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 34.0000 1.21896
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 3.00000 0.107280
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) 6.00000 0.214149
\(786\) 0 0
\(787\) −45.0000 −1.60408 −0.802038 0.597272i \(-0.796251\pi\)
−0.802038 + 0.597272i \(0.796251\pi\)
\(788\) 7.00000 0.249365
\(789\) 0 0
\(790\) −24.0000 −0.853882
\(791\) 36.0000 1.28001
\(792\) −3.00000 −0.106600
\(793\) 52.0000 1.84657
\(794\) 26.0000 0.922705
\(795\) 0 0
\(796\) 3.00000 0.106332
\(797\) 27.0000 0.956389 0.478195 0.878254i \(-0.341291\pi\)
0.478195 + 0.878254i \(0.341291\pi\)
\(798\) 0 0
\(799\) −36.0000 −1.27359
\(800\) −4.00000 −0.141421
\(801\) −12.0000 −0.423999
\(802\) 26.0000 0.918092
\(803\) 6.00000 0.211735
\(804\) 0 0
\(805\) 6.00000 0.211472
\(806\) 16.0000 0.563576
\(807\) 0 0
\(808\) 12.0000 0.422159
\(809\) 38.0000 1.33601 0.668004 0.744157i \(-0.267149\pi\)
0.668004 + 0.744157i \(0.267149\pi\)
\(810\) −27.0000 −0.948683
\(811\) −30.0000 −1.05344 −0.526721 0.850038i \(-0.676579\pi\)
−0.526721 + 0.850038i \(0.676579\pi\)
\(812\) −12.0000 −0.421117
\(813\) 0 0
\(814\) 2.00000 0.0701000
\(815\) −27.0000 −0.945769
\(816\) 0 0
\(817\) −24.0000 −0.839654
\(818\) −5.00000 −0.174821
\(819\) 24.0000 0.838628
\(820\) 9.00000 0.314294
\(821\) 48.0000 1.67521 0.837606 0.546275i \(-0.183955\pi\)
0.837606 + 0.546275i \(0.183955\pi\)
\(822\) 0 0
\(823\) 30.0000 1.04573 0.522867 0.852414i \(-0.324862\pi\)
0.522867 + 0.852414i \(0.324862\pi\)
\(824\) 1.00000 0.0348367
\(825\) 0 0
\(826\) −8.00000 −0.278356
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 3.00000 0.104257
\(829\) 40.0000 1.38926 0.694629 0.719368i \(-0.255569\pi\)
0.694629 + 0.719368i \(0.255569\pi\)
\(830\) 42.0000 1.45784
\(831\) 0 0
\(832\) 4.00000 0.138675
\(833\) −9.00000 −0.311832
\(834\) 0 0
\(835\) 3.00000 0.103819
\(836\) 8.00000 0.276686
\(837\) 0 0
\(838\) −30.0000 −1.03633
\(839\) 30.0000 1.03572 0.517858 0.855467i \(-0.326730\pi\)
0.517858 + 0.855467i \(0.326730\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 26.0000 0.896019
\(843\) 0 0
\(844\) −20.0000 −0.688428
\(845\) 9.00000 0.309609
\(846\) −36.0000 −1.23771
\(847\) 20.0000 0.687208
\(848\) −2.00000 −0.0686803
\(849\) 0 0
\(850\) −12.0000 −0.411597
\(851\) −2.00000 −0.0685591
\(852\) 0 0
\(853\) 38.0000 1.30110 0.650548 0.759465i \(-0.274539\pi\)
0.650548 + 0.759465i \(0.274539\pi\)
\(854\) 26.0000 0.889702
\(855\) 72.0000 2.46235
\(856\) −5.00000 −0.170896
\(857\) 48.0000 1.63965 0.819824 0.572615i \(-0.194071\pi\)
0.819824 + 0.572615i \(0.194071\pi\)
\(858\) 0 0
\(859\) −16.0000 −0.545913 −0.272956 0.962026i \(-0.588002\pi\)
−0.272956 + 0.962026i \(0.588002\pi\)
\(860\) 9.00000 0.306897
\(861\) 0 0
\(862\) 34.0000 1.15804
\(863\) −8.00000 −0.272323 −0.136162 0.990687i \(-0.543477\pi\)
−0.136162 + 0.990687i \(0.543477\pi\)
\(864\) 0 0
\(865\) −39.0000 −1.32604
\(866\) 15.0000 0.509721
\(867\) 0 0
\(868\) 8.00000 0.271538
\(869\) −8.00000 −0.271381
\(870\) 0 0
\(871\) 16.0000 0.542139
\(872\) −5.00000 −0.169321
\(873\) 6.00000 0.203069
\(874\) −8.00000 −0.270604
\(875\) 6.00000 0.202837
\(876\) 0 0
\(877\) 4.00000 0.135070 0.0675352 0.997717i \(-0.478487\pi\)
0.0675352 + 0.997717i \(0.478487\pi\)
\(878\) 11.0000 0.371232
\(879\) 0 0
\(880\) −3.00000 −0.101130
\(881\) −46.0000 −1.54978 −0.774890 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) −9.00000 −0.303046
\(883\) 47.0000 1.58168 0.790838 0.612026i \(-0.209645\pi\)
0.790838 + 0.612026i \(0.209645\pi\)
\(884\) 12.0000 0.403604
\(885\) 0 0
\(886\) 0 0
\(887\) −29.0000 −0.973725 −0.486862 0.873479i \(-0.661859\pi\)
−0.486862 + 0.873479i \(0.661859\pi\)
\(888\) 0 0
\(889\) 36.0000 1.20740
\(890\) −12.0000 −0.402241
\(891\) −9.00000 −0.301511
\(892\) 10.0000 0.334825
\(893\) 96.0000 3.21252
\(894\) 0 0
\(895\) 12.0000 0.401116
\(896\) 2.00000 0.0668153
\(897\) 0 0
\(898\) −6.00000 −0.200223
\(899\) −24.0000 −0.800445
\(900\) −12.0000 −0.400000
\(901\) −6.00000 −0.199889
\(902\) 3.00000 0.0998891
\(903\) 0 0
\(904\) 18.0000 0.598671
\(905\) −24.0000 −0.797787
\(906\) 0 0
\(907\) 23.0000 0.763702 0.381851 0.924224i \(-0.375287\pi\)
0.381851 + 0.924224i \(0.375287\pi\)
\(908\) −2.00000 −0.0663723
\(909\) 36.0000 1.19404
\(910\) 24.0000 0.795592
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) 14.0000 0.463332
\(914\) 32.0000 1.05847
\(915\) 0 0
\(916\) −8.00000 −0.264327
\(917\) 2.00000 0.0660458
\(918\) 0 0
\(919\) 25.0000 0.824674 0.412337 0.911031i \(-0.364713\pi\)
0.412337 + 0.911031i \(0.364713\pi\)
\(920\) 3.00000 0.0989071
\(921\) 0 0
\(922\) 27.0000 0.889198
\(923\) −16.0000 −0.526646
\(924\) 0 0
\(925\) 8.00000 0.263038
\(926\) 24.0000 0.788689
\(927\) 3.00000 0.0985329
\(928\) −6.00000 −0.196960
\(929\) 1.00000 0.0328089 0.0164045 0.999865i \(-0.494778\pi\)
0.0164045 + 0.999865i \(0.494778\pi\)
\(930\) 0 0
\(931\) 24.0000 0.786568
\(932\) −1.00000 −0.0327561
\(933\) 0 0
\(934\) −9.00000 −0.294489
\(935\) −9.00000 −0.294331
\(936\) 12.0000 0.392232
\(937\) 46.0000 1.50275 0.751377 0.659873i \(-0.229390\pi\)
0.751377 + 0.659873i \(0.229390\pi\)
\(938\) 8.00000 0.261209
\(939\) 0 0
\(940\) −36.0000 −1.17419
\(941\) −32.0000 −1.04317 −0.521585 0.853199i \(-0.674659\pi\)
−0.521585 + 0.853199i \(0.674659\pi\)
\(942\) 0 0
\(943\) −3.00000 −0.0976934
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) 3.00000 0.0975384
\(947\) −44.0000 −1.42981 −0.714904 0.699223i \(-0.753530\pi\)
−0.714904 + 0.699223i \(0.753530\pi\)
\(948\) 0 0
\(949\) −24.0000 −0.779073
\(950\) 32.0000 1.03822
\(951\) 0 0
\(952\) 6.00000 0.194461
\(953\) 12.0000 0.388718 0.194359 0.980930i \(-0.437737\pi\)
0.194359 + 0.980930i \(0.437737\pi\)
\(954\) −6.00000 −0.194257
\(955\) −36.0000 −1.16493
\(956\) 0 0
\(957\) 0 0
\(958\) 9.00000 0.290777
\(959\) −6.00000 −0.193750
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −8.00000 −0.257930
\(963\) −15.0000 −0.483368
\(964\) −3.00000 −0.0966235
\(965\) −63.0000 −2.02804
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) 10.0000 0.321412
\(969\) 0 0
\(970\) 6.00000 0.192648
\(971\) 48.0000 1.54039 0.770197 0.637806i \(-0.220158\pi\)
0.770197 + 0.637806i \(0.220158\pi\)
\(972\) 0 0
\(973\) −2.00000 −0.0641171
\(974\) 31.0000 0.993304
\(975\) 0 0
\(976\) 13.0000 0.416120
\(977\) 56.0000 1.79160 0.895799 0.444459i \(-0.146604\pi\)
0.895799 + 0.444459i \(0.146604\pi\)
\(978\) 0 0
\(979\) −4.00000 −0.127841
\(980\) −9.00000 −0.287494
\(981\) −15.0000 −0.478913
\(982\) −35.0000 −1.11689
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 0 0
\(985\) 21.0000 0.669116
\(986\) −18.0000 −0.573237
\(987\) 0 0
\(988\) −32.0000 −1.01806
\(989\) −3.00000 −0.0953945
\(990\) −9.00000 −0.286039
\(991\) −52.0000 −1.65183 −0.825917 0.563791i \(-0.809342\pi\)
−0.825917 + 0.563791i \(0.809342\pi\)
\(992\) 4.00000 0.127000
\(993\) 0 0
\(994\) −8.00000 −0.253745
\(995\) 9.00000 0.285319
\(996\) 0 0
\(997\) −4.00000 −0.126681 −0.0633406 0.997992i \(-0.520175\pi\)
−0.0633406 + 0.997992i \(0.520175\pi\)
\(998\) −11.0000 −0.348199
\(999\) 0 0
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 6026.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.b.1.1 1 1.1 even 1 trivial