Properties

Label 6014.2.a.e.1.14
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, 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("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.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: \(48.0220317756\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.436625 q^{3} +1.00000 q^{4} -0.0518544 q^{5} +0.436625 q^{6} +0.167384 q^{7} +1.00000 q^{8} -2.80936 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.436625 q^{3} +1.00000 q^{4} -0.0518544 q^{5} +0.436625 q^{6} +0.167384 q^{7} +1.00000 q^{8} -2.80936 q^{9} -0.0518544 q^{10} +1.44287 q^{11} +0.436625 q^{12} +4.01294 q^{13} +0.167384 q^{14} -0.0226409 q^{15} +1.00000 q^{16} -2.41030 q^{17} -2.80936 q^{18} -2.67873 q^{19} -0.0518544 q^{20} +0.0730839 q^{21} +1.44287 q^{22} -6.72568 q^{23} +0.436625 q^{24} -4.99731 q^{25} +4.01294 q^{26} -2.53651 q^{27} +0.167384 q^{28} -8.89627 q^{29} -0.0226409 q^{30} +1.00000 q^{31} +1.00000 q^{32} +0.629995 q^{33} -2.41030 q^{34} -0.00867957 q^{35} -2.80936 q^{36} -7.01316 q^{37} -2.67873 q^{38} +1.75215 q^{39} -0.0518544 q^{40} -2.01690 q^{41} +0.0730839 q^{42} +2.30133 q^{43} +1.44287 q^{44} +0.145677 q^{45} -6.72568 q^{46} +2.67590 q^{47} +0.436625 q^{48} -6.97198 q^{49} -4.99731 q^{50} -1.05240 q^{51} +4.01294 q^{52} -7.23535 q^{53} -2.53651 q^{54} -0.0748193 q^{55} +0.167384 q^{56} -1.16960 q^{57} -8.89627 q^{58} +8.40917 q^{59} -0.0226409 q^{60} +2.45239 q^{61} +1.00000 q^{62} -0.470241 q^{63} +1.00000 q^{64} -0.208088 q^{65} +0.629995 q^{66} -12.3169 q^{67} -2.41030 q^{68} -2.93660 q^{69} -0.00867957 q^{70} -3.10491 q^{71} -2.80936 q^{72} +5.71496 q^{73} -7.01316 q^{74} -2.18195 q^{75} -2.67873 q^{76} +0.241513 q^{77} +1.75215 q^{78} +10.4456 q^{79} -0.0518544 q^{80} +7.32057 q^{81} -2.01690 q^{82} +8.37850 q^{83} +0.0730839 q^{84} +0.124985 q^{85} +2.30133 q^{86} -3.88434 q^{87} +1.44287 q^{88} +6.86237 q^{89} +0.145677 q^{90} +0.671700 q^{91} -6.72568 q^{92} +0.436625 q^{93} +2.67590 q^{94} +0.138904 q^{95} +0.436625 q^{96} -1.00000 q^{97} -6.97198 q^{98} -4.05355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 0.436625 0.252086 0.126043 0.992025i \(-0.459772\pi\)
0.126043 + 0.992025i \(0.459772\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.0518544 −0.0231900 −0.0115950 0.999933i \(-0.503691\pi\)
−0.0115950 + 0.999933i \(0.503691\pi\)
\(6\) 0.436625 0.178252
\(7\) 0.167384 0.0632651 0.0316325 0.999500i \(-0.489929\pi\)
0.0316325 + 0.999500i \(0.489929\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.80936 −0.936453
\(10\) −0.0518544 −0.0163978
\(11\) 1.44287 0.435043 0.217521 0.976056i \(-0.430203\pi\)
0.217521 + 0.976056i \(0.430203\pi\)
\(12\) 0.436625 0.126043
\(13\) 4.01294 1.11299 0.556495 0.830851i \(-0.312146\pi\)
0.556495 + 0.830851i \(0.312146\pi\)
\(14\) 0.167384 0.0447352
\(15\) −0.0226409 −0.00584586
\(16\) 1.00000 0.250000
\(17\) −2.41030 −0.584584 −0.292292 0.956329i \(-0.594418\pi\)
−0.292292 + 0.956329i \(0.594418\pi\)
\(18\) −2.80936 −0.662172
\(19\) −2.67873 −0.614543 −0.307271 0.951622i \(-0.599416\pi\)
−0.307271 + 0.951622i \(0.599416\pi\)
\(20\) −0.0518544 −0.0115950
\(21\) 0.0730839 0.0159482
\(22\) 1.44287 0.307622
\(23\) −6.72568 −1.40240 −0.701201 0.712964i \(-0.747352\pi\)
−0.701201 + 0.712964i \(0.747352\pi\)
\(24\) 0.436625 0.0891258
\(25\) −4.99731 −0.999462
\(26\) 4.01294 0.787002
\(27\) −2.53651 −0.488152
\(28\) 0.167384 0.0316325
\(29\) −8.89627 −1.65200 −0.825998 0.563673i \(-0.809388\pi\)
−0.825998 + 0.563673i \(0.809388\pi\)
\(30\) −0.0226409 −0.00413365
\(31\) 1.00000 0.179605
\(32\) 1.00000 0.176777
\(33\) 0.629995 0.109668
\(34\) −2.41030 −0.413363
\(35\) −0.00867957 −0.00146711
\(36\) −2.80936 −0.468226
\(37\) −7.01316 −1.15296 −0.576478 0.817113i \(-0.695573\pi\)
−0.576478 + 0.817113i \(0.695573\pi\)
\(38\) −2.67873 −0.434547
\(39\) 1.75215 0.280569
\(40\) −0.0518544 −0.00819889
\(41\) −2.01690 −0.314986 −0.157493 0.987520i \(-0.550341\pi\)
−0.157493 + 0.987520i \(0.550341\pi\)
\(42\) 0.0730839 0.0112771
\(43\) 2.30133 0.350949 0.175475 0.984484i \(-0.443854\pi\)
0.175475 + 0.984484i \(0.443854\pi\)
\(44\) 1.44287 0.217521
\(45\) 0.145677 0.0217163
\(46\) −6.72568 −0.991648
\(47\) 2.67590 0.390320 0.195160 0.980771i \(-0.437477\pi\)
0.195160 + 0.980771i \(0.437477\pi\)
\(48\) 0.436625 0.0630215
\(49\) −6.97198 −0.995998
\(50\) −4.99731 −0.706727
\(51\) −1.05240 −0.147365
\(52\) 4.01294 0.556495
\(53\) −7.23535 −0.993852 −0.496926 0.867793i \(-0.665538\pi\)
−0.496926 + 0.867793i \(0.665538\pi\)
\(54\) −2.53651 −0.345176
\(55\) −0.0748193 −0.0100886
\(56\) 0.167384 0.0223676
\(57\) −1.16960 −0.154917
\(58\) −8.89627 −1.16814
\(59\) 8.40917 1.09478 0.547390 0.836877i \(-0.315621\pi\)
0.547390 + 0.836877i \(0.315621\pi\)
\(60\) −0.0226409 −0.00292293
\(61\) 2.45239 0.313996 0.156998 0.987599i \(-0.449818\pi\)
0.156998 + 0.987599i \(0.449818\pi\)
\(62\) 1.00000 0.127000
\(63\) −0.470241 −0.0592447
\(64\) 1.00000 0.125000
\(65\) −0.208088 −0.0258102
\(66\) 0.629995 0.0775470
\(67\) −12.3169 −1.50475 −0.752374 0.658737i \(-0.771091\pi\)
−0.752374 + 0.658737i \(0.771091\pi\)
\(68\) −2.41030 −0.292292
\(69\) −2.93660 −0.353526
\(70\) −0.00867957 −0.00103741
\(71\) −3.10491 −0.368485 −0.184243 0.982881i \(-0.558983\pi\)
−0.184243 + 0.982881i \(0.558983\pi\)
\(72\) −2.80936 −0.331086
\(73\) 5.71496 0.668885 0.334443 0.942416i \(-0.391452\pi\)
0.334443 + 0.942416i \(0.391452\pi\)
\(74\) −7.01316 −0.815263
\(75\) −2.18195 −0.251950
\(76\) −2.67873 −0.307271
\(77\) 0.241513 0.0275230
\(78\) 1.75215 0.198392
\(79\) 10.4456 1.17523 0.587613 0.809142i \(-0.300068\pi\)
0.587613 + 0.809142i \(0.300068\pi\)
\(80\) −0.0518544 −0.00579749
\(81\) 7.32057 0.813396
\(82\) −2.01690 −0.222729
\(83\) 8.37850 0.919660 0.459830 0.888007i \(-0.347910\pi\)
0.459830 + 0.888007i \(0.347910\pi\)
\(84\) 0.0730839 0.00797411
\(85\) 0.124985 0.0135565
\(86\) 2.30133 0.248159
\(87\) −3.88434 −0.416445
\(88\) 1.44287 0.153811
\(89\) 6.86237 0.727409 0.363705 0.931514i \(-0.381512\pi\)
0.363705 + 0.931514i \(0.381512\pi\)
\(90\) 0.145677 0.0153558
\(91\) 0.671700 0.0704133
\(92\) −6.72568 −0.701201
\(93\) 0.436625 0.0452759
\(94\) 2.67590 0.275998
\(95\) 0.138904 0.0142512
\(96\) 0.436625 0.0445629
\(97\) −1.00000 −0.101535
\(98\) −6.97198 −0.704277
\(99\) −4.05355 −0.407397
\(100\) −4.99731 −0.499731
\(101\) −8.14646 −0.810603 −0.405302 0.914183i \(-0.632834\pi\)
−0.405302 + 0.914183i \(0.632834\pi\)
\(102\) −1.05240 −0.104203
\(103\) −1.69987 −0.167494 −0.0837468 0.996487i \(-0.526689\pi\)
−0.0837468 + 0.996487i \(0.526689\pi\)
\(104\) 4.01294 0.393501
\(105\) −0.00378972 −0.000369839 0
\(106\) −7.23535 −0.702759
\(107\) 8.05896 0.779089 0.389544 0.921008i \(-0.372632\pi\)
0.389544 + 0.921008i \(0.372632\pi\)
\(108\) −2.53651 −0.244076
\(109\) −8.16312 −0.781885 −0.390942 0.920415i \(-0.627851\pi\)
−0.390942 + 0.920415i \(0.627851\pi\)
\(110\) −0.0748193 −0.00713374
\(111\) −3.06212 −0.290644
\(112\) 0.167384 0.0158163
\(113\) 5.18278 0.487555 0.243777 0.969831i \(-0.421613\pi\)
0.243777 + 0.969831i \(0.421613\pi\)
\(114\) −1.16960 −0.109543
\(115\) 0.348756 0.0325217
\(116\) −8.89627 −0.825998
\(117\) −11.2738 −1.04226
\(118\) 8.40917 0.774127
\(119\) −0.403445 −0.0369837
\(120\) −0.0226409 −0.00206682
\(121\) −8.91812 −0.810738
\(122\) 2.45239 0.222029
\(123\) −0.880628 −0.0794036
\(124\) 1.00000 0.0898027
\(125\) 0.518404 0.0463675
\(126\) −0.470241 −0.0418924
\(127\) −5.95977 −0.528844 −0.264422 0.964407i \(-0.585181\pi\)
−0.264422 + 0.964407i \(0.585181\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.00482 0.0884694
\(130\) −0.208088 −0.0182506
\(131\) 8.22326 0.718470 0.359235 0.933247i \(-0.383038\pi\)
0.359235 + 0.933247i \(0.383038\pi\)
\(132\) 0.629995 0.0548340
\(133\) −0.448375 −0.0388791
\(134\) −12.3169 −1.06402
\(135\) 0.131529 0.0113202
\(136\) −2.41030 −0.206682
\(137\) 6.09300 0.520560 0.260280 0.965533i \(-0.416185\pi\)
0.260280 + 0.965533i \(0.416185\pi\)
\(138\) −2.93660 −0.249980
\(139\) 11.1137 0.942648 0.471324 0.881960i \(-0.343776\pi\)
0.471324 + 0.881960i \(0.343776\pi\)
\(140\) −0.00867957 −0.000733557 0
\(141\) 1.16837 0.0983942
\(142\) −3.10491 −0.260558
\(143\) 5.79016 0.484198
\(144\) −2.80936 −0.234113
\(145\) 0.461310 0.0383097
\(146\) 5.71496 0.472973
\(147\) −3.04414 −0.251077
\(148\) −7.01316 −0.576478
\(149\) 11.4942 0.941638 0.470819 0.882230i \(-0.343959\pi\)
0.470819 + 0.882230i \(0.343959\pi\)
\(150\) −2.18195 −0.178156
\(151\) −14.5521 −1.18423 −0.592116 0.805852i \(-0.701707\pi\)
−0.592116 + 0.805852i \(0.701707\pi\)
\(152\) −2.67873 −0.217274
\(153\) 6.77140 0.547435
\(154\) 0.241513 0.0194617
\(155\) −0.0518544 −0.00416504
\(156\) 1.75215 0.140284
\(157\) 17.1344 1.36748 0.683739 0.729727i \(-0.260353\pi\)
0.683739 + 0.729727i \(0.260353\pi\)
\(158\) 10.4456 0.831010
\(159\) −3.15914 −0.250536
\(160\) −0.0518544 −0.00409945
\(161\) −1.12577 −0.0887230
\(162\) 7.32057 0.575158
\(163\) −17.9962 −1.40957 −0.704787 0.709419i \(-0.748957\pi\)
−0.704787 + 0.709419i \(0.748957\pi\)
\(164\) −2.01690 −0.157493
\(165\) −0.0326680 −0.00254320
\(166\) 8.37850 0.650298
\(167\) −15.8941 −1.22993 −0.614963 0.788556i \(-0.710829\pi\)
−0.614963 + 0.788556i \(0.710829\pi\)
\(168\) 0.0730839 0.00563855
\(169\) 3.10369 0.238746
\(170\) 0.124985 0.00958588
\(171\) 7.52551 0.575490
\(172\) 2.30133 0.175475
\(173\) 11.2740 0.857150 0.428575 0.903506i \(-0.359016\pi\)
0.428575 + 0.903506i \(0.359016\pi\)
\(174\) −3.88434 −0.294471
\(175\) −0.836468 −0.0632310
\(176\) 1.44287 0.108761
\(177\) 3.67166 0.275979
\(178\) 6.86237 0.514356
\(179\) −14.9204 −1.11521 −0.557603 0.830108i \(-0.688279\pi\)
−0.557603 + 0.830108i \(0.688279\pi\)
\(180\) 0.145677 0.0108582
\(181\) −18.1697 −1.35054 −0.675272 0.737569i \(-0.735974\pi\)
−0.675272 + 0.737569i \(0.735974\pi\)
\(182\) 0.671700 0.0497898
\(183\) 1.07078 0.0791540
\(184\) −6.72568 −0.495824
\(185\) 0.363663 0.0267370
\(186\) 0.436625 0.0320149
\(187\) −3.47776 −0.254319
\(188\) 2.67590 0.195160
\(189\) −0.424571 −0.0308830
\(190\) 0.138904 0.0100771
\(191\) −15.2353 −1.10239 −0.551195 0.834376i \(-0.685828\pi\)
−0.551195 + 0.834376i \(0.685828\pi\)
\(192\) 0.436625 0.0315107
\(193\) −9.63153 −0.693293 −0.346646 0.937996i \(-0.612680\pi\)
−0.346646 + 0.937996i \(0.612680\pi\)
\(194\) −1.00000 −0.0717958
\(195\) −0.0908567 −0.00650638
\(196\) −6.97198 −0.497999
\(197\) −14.4162 −1.02711 −0.513557 0.858055i \(-0.671673\pi\)
−0.513557 + 0.858055i \(0.671673\pi\)
\(198\) −4.05355 −0.288073
\(199\) −13.4697 −0.954840 −0.477420 0.878675i \(-0.658428\pi\)
−0.477420 + 0.878675i \(0.658428\pi\)
\(200\) −4.99731 −0.353363
\(201\) −5.37787 −0.379325
\(202\) −8.14646 −0.573183
\(203\) −1.48909 −0.104514
\(204\) −1.05240 −0.0736827
\(205\) 0.104585 0.00730452
\(206\) −1.69987 −0.118436
\(207\) 18.8949 1.31328
\(208\) 4.01294 0.278247
\(209\) −3.86507 −0.267352
\(210\) −0.00378972 −0.000261516 0
\(211\) −10.0648 −0.692891 −0.346445 0.938070i \(-0.612611\pi\)
−0.346445 + 0.938070i \(0.612611\pi\)
\(212\) −7.23535 −0.496926
\(213\) −1.35568 −0.0928899
\(214\) 8.05896 0.550899
\(215\) −0.119334 −0.00813851
\(216\) −2.53651 −0.172588
\(217\) 0.167384 0.0113627
\(218\) −8.16312 −0.552876
\(219\) 2.49530 0.168616
\(220\) −0.0748193 −0.00504431
\(221\) −9.67240 −0.650636
\(222\) −3.06212 −0.205516
\(223\) 15.0134 1.00537 0.502685 0.864470i \(-0.332346\pi\)
0.502685 + 0.864470i \(0.332346\pi\)
\(224\) 0.167384 0.0111838
\(225\) 14.0392 0.935949
\(226\) 5.18278 0.344753
\(227\) −6.02369 −0.399807 −0.199903 0.979816i \(-0.564063\pi\)
−0.199903 + 0.979816i \(0.564063\pi\)
\(228\) −1.16960 −0.0774587
\(229\) −5.78767 −0.382460 −0.191230 0.981545i \(-0.561248\pi\)
−0.191230 + 0.981545i \(0.561248\pi\)
\(230\) 0.348756 0.0229963
\(231\) 0.105451 0.00693816
\(232\) −8.89627 −0.584069
\(233\) −9.17116 −0.600823 −0.300411 0.953810i \(-0.597124\pi\)
−0.300411 + 0.953810i \(0.597124\pi\)
\(234\) −11.2738 −0.736991
\(235\) −0.138757 −0.00905151
\(236\) 8.40917 0.547390
\(237\) 4.56083 0.296258
\(238\) −0.403445 −0.0261515
\(239\) 12.6834 0.820424 0.410212 0.911990i \(-0.365455\pi\)
0.410212 + 0.911990i \(0.365455\pi\)
\(240\) −0.0226409 −0.00146147
\(241\) −19.0267 −1.22562 −0.612810 0.790230i \(-0.709961\pi\)
−0.612810 + 0.790230i \(0.709961\pi\)
\(242\) −8.91812 −0.573278
\(243\) 10.8059 0.693198
\(244\) 2.45239 0.156998
\(245\) 0.361528 0.0230972
\(246\) −0.880628 −0.0561468
\(247\) −10.7496 −0.683979
\(248\) 1.00000 0.0635001
\(249\) 3.65827 0.231833
\(250\) 0.518404 0.0327868
\(251\) −30.2633 −1.91020 −0.955100 0.296284i \(-0.904252\pi\)
−0.955100 + 0.296284i \(0.904252\pi\)
\(252\) −0.470241 −0.0296224
\(253\) −9.70431 −0.610105
\(254\) −5.95977 −0.373950
\(255\) 0.0545715 0.00341740
\(256\) 1.00000 0.0625000
\(257\) −5.99771 −0.374127 −0.187063 0.982348i \(-0.559897\pi\)
−0.187063 + 0.982348i \(0.559897\pi\)
\(258\) 1.00482 0.0625573
\(259\) −1.17389 −0.0729418
\(260\) −0.208088 −0.0129051
\(261\) 24.9928 1.54702
\(262\) 8.22326 0.508035
\(263\) 2.57774 0.158950 0.0794752 0.996837i \(-0.474676\pi\)
0.0794752 + 0.996837i \(0.474676\pi\)
\(264\) 0.629995 0.0387735
\(265\) 0.375184 0.0230474
\(266\) −0.448375 −0.0274917
\(267\) 2.99628 0.183370
\(268\) −12.3169 −0.752374
\(269\) 29.2747 1.78491 0.892454 0.451138i \(-0.148982\pi\)
0.892454 + 0.451138i \(0.148982\pi\)
\(270\) 0.131529 0.00800462
\(271\) −3.85462 −0.234152 −0.117076 0.993123i \(-0.537352\pi\)
−0.117076 + 0.993123i \(0.537352\pi\)
\(272\) −2.41030 −0.146146
\(273\) 0.293282 0.0177502
\(274\) 6.09300 0.368091
\(275\) −7.21049 −0.434809
\(276\) −2.93660 −0.176763
\(277\) −17.9316 −1.07741 −0.538703 0.842496i \(-0.681086\pi\)
−0.538703 + 0.842496i \(0.681086\pi\)
\(278\) 11.1137 0.666553
\(279\) −2.80936 −0.168192
\(280\) −0.00867957 −0.000518703 0
\(281\) −1.64814 −0.0983200 −0.0491600 0.998791i \(-0.515654\pi\)
−0.0491600 + 0.998791i \(0.515654\pi\)
\(282\) 1.16837 0.0695752
\(283\) 14.2618 0.847773 0.423887 0.905715i \(-0.360665\pi\)
0.423887 + 0.905715i \(0.360665\pi\)
\(284\) −3.10491 −0.184243
\(285\) 0.0606489 0.00359253
\(286\) 5.79016 0.342380
\(287\) −0.337595 −0.0199276
\(288\) −2.80936 −0.165543
\(289\) −11.1904 −0.658262
\(290\) 0.461310 0.0270891
\(291\) −0.436625 −0.0255954
\(292\) 5.71496 0.334443
\(293\) 10.7623 0.628741 0.314371 0.949300i \(-0.398207\pi\)
0.314371 + 0.949300i \(0.398207\pi\)
\(294\) −3.04414 −0.177538
\(295\) −0.436052 −0.0253879
\(296\) −7.01316 −0.407632
\(297\) −3.65987 −0.212367
\(298\) 11.4942 0.665838
\(299\) −26.9898 −1.56086
\(300\) −2.18195 −0.125975
\(301\) 0.385205 0.0222028
\(302\) −14.5521 −0.837379
\(303\) −3.55695 −0.204342
\(304\) −2.67873 −0.153636
\(305\) −0.127167 −0.00728157
\(306\) 6.77140 0.387095
\(307\) −8.22255 −0.469286 −0.234643 0.972082i \(-0.575392\pi\)
−0.234643 + 0.972082i \(0.575392\pi\)
\(308\) 0.241513 0.0137615
\(309\) −0.742209 −0.0422228
\(310\) −0.0518544 −0.00294513
\(311\) 5.16135 0.292673 0.146337 0.989235i \(-0.453252\pi\)
0.146337 + 0.989235i \(0.453252\pi\)
\(312\) 1.75215 0.0991961
\(313\) 3.16198 0.178726 0.0893629 0.995999i \(-0.471517\pi\)
0.0893629 + 0.995999i \(0.471517\pi\)
\(314\) 17.1344 0.966953
\(315\) 0.0243840 0.00137388
\(316\) 10.4456 0.587613
\(317\) 19.3097 1.08454 0.542270 0.840204i \(-0.317565\pi\)
0.542270 + 0.840204i \(0.317565\pi\)
\(318\) −3.15914 −0.177156
\(319\) −12.8362 −0.718689
\(320\) −0.0518544 −0.00289875
\(321\) 3.51875 0.196397
\(322\) −1.12577 −0.0627367
\(323\) 6.45655 0.359252
\(324\) 7.32057 0.406698
\(325\) −20.0539 −1.11239
\(326\) −17.9962 −0.996719
\(327\) −3.56422 −0.197102
\(328\) −2.01690 −0.111364
\(329\) 0.447902 0.0246936
\(330\) −0.0326680 −0.00179831
\(331\) 7.59645 0.417538 0.208769 0.977965i \(-0.433054\pi\)
0.208769 + 0.977965i \(0.433054\pi\)
\(332\) 8.37850 0.459830
\(333\) 19.7025 1.07969
\(334\) −15.8941 −0.869688
\(335\) 0.638684 0.0348950
\(336\) 0.0730839 0.00398706
\(337\) −30.6571 −1.67000 −0.834999 0.550251i \(-0.814532\pi\)
−0.834999 + 0.550251i \(0.814532\pi\)
\(338\) 3.10369 0.168819
\(339\) 2.26293 0.122906
\(340\) 0.124985 0.00677824
\(341\) 1.44287 0.0781360
\(342\) 7.52551 0.406933
\(343\) −2.33868 −0.126277
\(344\) 2.30133 0.124079
\(345\) 0.152276 0.00819825
\(346\) 11.2740 0.606096
\(347\) 9.15064 0.491232 0.245616 0.969367i \(-0.421010\pi\)
0.245616 + 0.969367i \(0.421010\pi\)
\(348\) −3.88434 −0.208222
\(349\) 19.1348 1.02426 0.512131 0.858908i \(-0.328856\pi\)
0.512131 + 0.858908i \(0.328856\pi\)
\(350\) −0.836468 −0.0447111
\(351\) −10.1789 −0.543308
\(352\) 1.44287 0.0769054
\(353\) 10.3641 0.551624 0.275812 0.961212i \(-0.411053\pi\)
0.275812 + 0.961212i \(0.411053\pi\)
\(354\) 3.67166 0.195146
\(355\) 0.161003 0.00854516
\(356\) 6.86237 0.363705
\(357\) −0.176154 −0.00932308
\(358\) −14.9204 −0.788569
\(359\) 23.2049 1.22471 0.612355 0.790583i \(-0.290222\pi\)
0.612355 + 0.790583i \(0.290222\pi\)
\(360\) 0.145677 0.00767788
\(361\) −11.8244 −0.622337
\(362\) −18.1697 −0.954978
\(363\) −3.89388 −0.204376
\(364\) 0.671700 0.0352067
\(365\) −0.296345 −0.0155114
\(366\) 1.07078 0.0559704
\(367\) 6.11685 0.319297 0.159648 0.987174i \(-0.448964\pi\)
0.159648 + 0.987174i \(0.448964\pi\)
\(368\) −6.72568 −0.350600
\(369\) 5.66618 0.294970
\(370\) 0.363663 0.0189059
\(371\) −1.21108 −0.0628761
\(372\) 0.436625 0.0226380
\(373\) −23.0809 −1.19509 −0.597543 0.801837i \(-0.703856\pi\)
−0.597543 + 0.801837i \(0.703856\pi\)
\(374\) −3.47776 −0.179831
\(375\) 0.226348 0.0116886
\(376\) 2.67590 0.137999
\(377\) −35.7002 −1.83865
\(378\) −0.424571 −0.0218376
\(379\) 25.9370 1.33229 0.666146 0.745821i \(-0.267943\pi\)
0.666146 + 0.745821i \(0.267943\pi\)
\(380\) 0.138904 0.00712561
\(381\) −2.60219 −0.133314
\(382\) −15.2353 −0.779508
\(383\) 7.28337 0.372163 0.186081 0.982534i \(-0.440421\pi\)
0.186081 + 0.982534i \(0.440421\pi\)
\(384\) 0.436625 0.0222814
\(385\) −0.0125235 −0.000638258 0
\(386\) −9.63153 −0.490232
\(387\) −6.46526 −0.328648
\(388\) −1.00000 −0.0507673
\(389\) 32.8781 1.66699 0.833494 0.552528i \(-0.186337\pi\)
0.833494 + 0.552528i \(0.186337\pi\)
\(390\) −0.0908567 −0.00460071
\(391\) 16.2109 0.819822
\(392\) −6.97198 −0.352138
\(393\) 3.59049 0.181116
\(394\) −14.4162 −0.726280
\(395\) −0.541652 −0.0272535
\(396\) −4.05355 −0.203698
\(397\) 33.2627 1.66940 0.834702 0.550701i \(-0.185640\pi\)
0.834702 + 0.550701i \(0.185640\pi\)
\(398\) −13.4697 −0.675174
\(399\) −0.195772 −0.00980086
\(400\) −4.99731 −0.249866
\(401\) 13.1492 0.656642 0.328321 0.944566i \(-0.393517\pi\)
0.328321 + 0.944566i \(0.393517\pi\)
\(402\) −5.37787 −0.268224
\(403\) 4.01294 0.199899
\(404\) −8.14646 −0.405302
\(405\) −0.379603 −0.0188626
\(406\) −1.48909 −0.0739023
\(407\) −10.1191 −0.501585
\(408\) −1.05240 −0.0521015
\(409\) 31.2293 1.54419 0.772095 0.635507i \(-0.219209\pi\)
0.772095 + 0.635507i \(0.219209\pi\)
\(410\) 0.104585 0.00516508
\(411\) 2.66036 0.131226
\(412\) −1.69987 −0.0837468
\(413\) 1.40756 0.0692614
\(414\) 18.8949 0.928631
\(415\) −0.434462 −0.0213269
\(416\) 4.01294 0.196751
\(417\) 4.85251 0.237628
\(418\) −3.86507 −0.189047
\(419\) 24.4159 1.19279 0.596397 0.802689i \(-0.296598\pi\)
0.596397 + 0.802689i \(0.296598\pi\)
\(420\) −0.00378972 −0.000184919 0
\(421\) −0.0560206 −0.00273028 −0.00136514 0.999999i \(-0.500435\pi\)
−0.00136514 + 0.999999i \(0.500435\pi\)
\(422\) −10.0648 −0.489948
\(423\) −7.51756 −0.365516
\(424\) −7.23535 −0.351380
\(425\) 12.0450 0.584270
\(426\) −1.35568 −0.0656831
\(427\) 0.410490 0.0198650
\(428\) 8.05896 0.389544
\(429\) 2.52813 0.122059
\(430\) −0.119334 −0.00575479
\(431\) 3.31504 0.159680 0.0798400 0.996808i \(-0.474559\pi\)
0.0798400 + 0.996808i \(0.474559\pi\)
\(432\) −2.53651 −0.122038
\(433\) 28.7140 1.37991 0.689953 0.723854i \(-0.257631\pi\)
0.689953 + 0.723854i \(0.257631\pi\)
\(434\) 0.167384 0.00803467
\(435\) 0.201420 0.00965734
\(436\) −8.16312 −0.390942
\(437\) 18.0163 0.861836
\(438\) 2.49530 0.119230
\(439\) 14.8315 0.707871 0.353936 0.935270i \(-0.384843\pi\)
0.353936 + 0.935270i \(0.384843\pi\)
\(440\) −0.0748193 −0.00356687
\(441\) 19.5868 0.932705
\(442\) −9.67240 −0.460069
\(443\) −1.91418 −0.0909452 −0.0454726 0.998966i \(-0.514479\pi\)
−0.0454726 + 0.998966i \(0.514479\pi\)
\(444\) −3.06212 −0.145322
\(445\) −0.355844 −0.0168686
\(446\) 15.0134 0.710904
\(447\) 5.01864 0.237374
\(448\) 0.167384 0.00790813
\(449\) 24.7797 1.16943 0.584713 0.811240i \(-0.301207\pi\)
0.584713 + 0.811240i \(0.301207\pi\)
\(450\) 14.0392 0.661816
\(451\) −2.91013 −0.137032
\(452\) 5.18278 0.243777
\(453\) −6.35382 −0.298528
\(454\) −6.02369 −0.282706
\(455\) −0.0348306 −0.00163288
\(456\) −1.16960 −0.0547716
\(457\) −37.9094 −1.77332 −0.886662 0.462417i \(-0.846982\pi\)
−0.886662 + 0.462417i \(0.846982\pi\)
\(458\) −5.78767 −0.270440
\(459\) 6.11376 0.285366
\(460\) 0.348756 0.0162608
\(461\) 11.7897 0.549100 0.274550 0.961573i \(-0.411471\pi\)
0.274550 + 0.961573i \(0.411471\pi\)
\(462\) 0.105451 0.00490602
\(463\) 2.21085 0.102747 0.0513735 0.998680i \(-0.483640\pi\)
0.0513735 + 0.998680i \(0.483640\pi\)
\(464\) −8.89627 −0.412999
\(465\) −0.0226409 −0.00104995
\(466\) −9.17116 −0.424846
\(467\) 2.05186 0.0949489 0.0474745 0.998872i \(-0.484883\pi\)
0.0474745 + 0.998872i \(0.484883\pi\)
\(468\) −11.2738 −0.521131
\(469\) −2.06164 −0.0951979
\(470\) −0.138757 −0.00640039
\(471\) 7.48134 0.344722
\(472\) 8.40917 0.387063
\(473\) 3.32053 0.152678
\(474\) 4.56083 0.209486
\(475\) 13.3864 0.614212
\(476\) −0.403445 −0.0184919
\(477\) 20.3267 0.930695
\(478\) 12.6834 0.580127
\(479\) −30.3350 −1.38604 −0.693021 0.720917i \(-0.743721\pi\)
−0.693021 + 0.720917i \(0.743721\pi\)
\(480\) −0.0226409 −0.00103341
\(481\) −28.1434 −1.28323
\(482\) −19.0267 −0.866644
\(483\) −0.491539 −0.0223658
\(484\) −8.91812 −0.405369
\(485\) 0.0518544 0.00235459
\(486\) 10.8059 0.490165
\(487\) 29.1251 1.31979 0.659893 0.751360i \(-0.270602\pi\)
0.659893 + 0.751360i \(0.270602\pi\)
\(488\) 2.45239 0.111014
\(489\) −7.85761 −0.355334
\(490\) 0.361528 0.0163322
\(491\) −39.9149 −1.80134 −0.900668 0.434508i \(-0.856922\pi\)
−0.900668 + 0.434508i \(0.856922\pi\)
\(492\) −0.880628 −0.0397018
\(493\) 21.4427 0.965731
\(494\) −10.7496 −0.483647
\(495\) 0.210194 0.00944752
\(496\) 1.00000 0.0449013
\(497\) −0.519711 −0.0233122
\(498\) 3.65827 0.163931
\(499\) 24.9423 1.11657 0.558284 0.829650i \(-0.311460\pi\)
0.558284 + 0.829650i \(0.311460\pi\)
\(500\) 0.518404 0.0231837
\(501\) −6.93978 −0.310047
\(502\) −30.2633 −1.35072
\(503\) −2.92782 −0.130545 −0.0652725 0.997867i \(-0.520792\pi\)
−0.0652725 + 0.997867i \(0.520792\pi\)
\(504\) −0.470241 −0.0209462
\(505\) 0.422430 0.0187979
\(506\) −9.70431 −0.431409
\(507\) 1.35515 0.0601844
\(508\) −5.95977 −0.264422
\(509\) −32.7470 −1.45149 −0.725743 0.687966i \(-0.758504\pi\)
−0.725743 + 0.687966i \(0.758504\pi\)
\(510\) 0.0545715 0.00241647
\(511\) 0.956590 0.0423171
\(512\) 1.00000 0.0441942
\(513\) 6.79463 0.299990
\(514\) −5.99771 −0.264547
\(515\) 0.0881459 0.00388417
\(516\) 1.00482 0.0442347
\(517\) 3.86098 0.169806
\(518\) −1.17389 −0.0515777
\(519\) 4.92254 0.216075
\(520\) −0.208088 −0.00912528
\(521\) −22.6993 −0.994472 −0.497236 0.867615i \(-0.665652\pi\)
−0.497236 + 0.867615i \(0.665652\pi\)
\(522\) 24.9928 1.09391
\(523\) 8.33624 0.364518 0.182259 0.983251i \(-0.441659\pi\)
0.182259 + 0.983251i \(0.441659\pi\)
\(524\) 8.22326 0.359235
\(525\) −0.365223 −0.0159396
\(526\) 2.57774 0.112395
\(527\) −2.41030 −0.104994
\(528\) 0.629995 0.0274170
\(529\) 22.2348 0.966731
\(530\) 0.375184 0.0162970
\(531\) −23.6244 −1.02521
\(532\) −0.448375 −0.0194395
\(533\) −8.09368 −0.350576
\(534\) 2.99628 0.129662
\(535\) −0.417892 −0.0180670
\(536\) −12.3169 −0.532008
\(537\) −6.51464 −0.281127
\(538\) 29.2747 1.26212
\(539\) −10.0597 −0.433301
\(540\) 0.131529 0.00566012
\(541\) 44.4243 1.90995 0.954975 0.296687i \(-0.0958818\pi\)
0.954975 + 0.296687i \(0.0958818\pi\)
\(542\) −3.85462 −0.165570
\(543\) −7.93335 −0.340453
\(544\) −2.41030 −0.103341
\(545\) 0.423293 0.0181319
\(546\) 0.293282 0.0125513
\(547\) −19.7025 −0.842416 −0.421208 0.906964i \(-0.638394\pi\)
−0.421208 + 0.906964i \(0.638394\pi\)
\(548\) 6.09300 0.260280
\(549\) −6.88964 −0.294043
\(550\) −7.21049 −0.307456
\(551\) 23.8307 1.01522
\(552\) −2.93660 −0.124990
\(553\) 1.74843 0.0743507
\(554\) −17.9316 −0.761841
\(555\) 0.158784 0.00674002
\(556\) 11.1137 0.471324
\(557\) 18.9453 0.802740 0.401370 0.915916i \(-0.368534\pi\)
0.401370 + 0.915916i \(0.368534\pi\)
\(558\) −2.80936 −0.118930
\(559\) 9.23510 0.390603
\(560\) −0.00867957 −0.000366779 0
\(561\) −1.51848 −0.0641102
\(562\) −1.64814 −0.0695228
\(563\) 39.0032 1.64379 0.821895 0.569639i \(-0.192917\pi\)
0.821895 + 0.569639i \(0.192917\pi\)
\(564\) 1.16837 0.0491971
\(565\) −0.268750 −0.0113064
\(566\) 14.2618 0.599466
\(567\) 1.22534 0.0514596
\(568\) −3.10491 −0.130279
\(569\) −37.2867 −1.56314 −0.781569 0.623818i \(-0.785580\pi\)
−0.781569 + 0.623818i \(0.785580\pi\)
\(570\) 0.0606489 0.00254030
\(571\) −17.3027 −0.724096 −0.362048 0.932159i \(-0.617922\pi\)
−0.362048 + 0.932159i \(0.617922\pi\)
\(572\) 5.79016 0.242099
\(573\) −6.65214 −0.277897
\(574\) −0.337595 −0.0140910
\(575\) 33.6103 1.40165
\(576\) −2.80936 −0.117057
\(577\) −34.6438 −1.44224 −0.721120 0.692810i \(-0.756373\pi\)
−0.721120 + 0.692810i \(0.756373\pi\)
\(578\) −11.1904 −0.465461
\(579\) −4.20537 −0.174769
\(580\) 0.461310 0.0191549
\(581\) 1.40242 0.0581824
\(582\) −0.436625 −0.0180987
\(583\) −10.4397 −0.432368
\(584\) 5.71496 0.236487
\(585\) 0.584595 0.0241700
\(586\) 10.7623 0.444587
\(587\) 16.2036 0.668795 0.334397 0.942432i \(-0.391467\pi\)
0.334397 + 0.942432i \(0.391467\pi\)
\(588\) −3.04414 −0.125538
\(589\) −2.67873 −0.110375
\(590\) −0.436052 −0.0179520
\(591\) −6.29450 −0.258921
\(592\) −7.01316 −0.288239
\(593\) −28.7224 −1.17949 −0.589743 0.807591i \(-0.700771\pi\)
−0.589743 + 0.807591i \(0.700771\pi\)
\(594\) −3.65987 −0.150166
\(595\) 0.0209204 0.000857652 0
\(596\) 11.4942 0.470819
\(597\) −5.88120 −0.240702
\(598\) −26.9898 −1.10369
\(599\) 29.1516 1.19110 0.595551 0.803318i \(-0.296934\pi\)
0.595551 + 0.803318i \(0.296934\pi\)
\(600\) −2.18195 −0.0890779
\(601\) 18.9082 0.771280 0.385640 0.922649i \(-0.373981\pi\)
0.385640 + 0.922649i \(0.373981\pi\)
\(602\) 0.385205 0.0156998
\(603\) 34.6025 1.40912
\(604\) −14.5521 −0.592116
\(605\) 0.462443 0.0188010
\(606\) −3.55695 −0.144491
\(607\) 2.47095 0.100293 0.0501463 0.998742i \(-0.484031\pi\)
0.0501463 + 0.998742i \(0.484031\pi\)
\(608\) −2.67873 −0.108637
\(609\) −0.650175 −0.0263464
\(610\) −0.127167 −0.00514885
\(611\) 10.7382 0.434422
\(612\) 6.77140 0.273718
\(613\) −33.5553 −1.35529 −0.677643 0.735391i \(-0.736998\pi\)
−0.677643 + 0.735391i \(0.736998\pi\)
\(614\) −8.22255 −0.331835
\(615\) 0.0456644 0.00184137
\(616\) 0.241513 0.00973085
\(617\) −18.1789 −0.731855 −0.365927 0.930643i \(-0.619248\pi\)
−0.365927 + 0.930643i \(0.619248\pi\)
\(618\) −0.742209 −0.0298560
\(619\) −7.06561 −0.283991 −0.141995 0.989867i \(-0.545352\pi\)
−0.141995 + 0.989867i \(0.545352\pi\)
\(620\) −0.0518544 −0.00208252
\(621\) 17.0598 0.684586
\(622\) 5.16135 0.206951
\(623\) 1.14865 0.0460196
\(624\) 1.75215 0.0701422
\(625\) 24.9597 0.998387
\(626\) 3.16198 0.126378
\(627\) −1.68759 −0.0673957
\(628\) 17.1344 0.683739
\(629\) 16.9038 0.674000
\(630\) 0.0243840 0.000971483 0
\(631\) −35.1955 −1.40111 −0.700556 0.713598i \(-0.747065\pi\)
−0.700556 + 0.713598i \(0.747065\pi\)
\(632\) 10.4456 0.415505
\(633\) −4.39456 −0.174668
\(634\) 19.3097 0.766886
\(635\) 0.309040 0.0122639
\(636\) −3.15914 −0.125268
\(637\) −27.9782 −1.10853
\(638\) −12.8362 −0.508190
\(639\) 8.72281 0.345069
\(640\) −0.0518544 −0.00204972
\(641\) 1.00332 0.0396287 0.0198144 0.999804i \(-0.493692\pi\)
0.0198144 + 0.999804i \(0.493692\pi\)
\(642\) 3.51875 0.138874
\(643\) 23.0459 0.908840 0.454420 0.890788i \(-0.349847\pi\)
0.454420 + 0.890788i \(0.349847\pi\)
\(644\) −1.12577 −0.0443615
\(645\) −0.0521042 −0.00205160
\(646\) 6.45655 0.254029
\(647\) 13.5997 0.534660 0.267330 0.963605i \(-0.413859\pi\)
0.267330 + 0.963605i \(0.413859\pi\)
\(648\) 7.32057 0.287579
\(649\) 12.1334 0.476276
\(650\) −20.0539 −0.786579
\(651\) 0.0730839 0.00286439
\(652\) −17.9962 −0.704787
\(653\) −36.2061 −1.41686 −0.708428 0.705784i \(-0.750595\pi\)
−0.708428 + 0.705784i \(0.750595\pi\)
\(654\) −3.56422 −0.139372
\(655\) −0.426412 −0.0166613
\(656\) −2.01690 −0.0787466
\(657\) −16.0554 −0.626379
\(658\) 0.447902 0.0174610
\(659\) 1.77337 0.0690807 0.0345404 0.999403i \(-0.489003\pi\)
0.0345404 + 0.999403i \(0.489003\pi\)
\(660\) −0.0326680 −0.00127160
\(661\) −10.7087 −0.416520 −0.208260 0.978074i \(-0.566780\pi\)
−0.208260 + 0.978074i \(0.566780\pi\)
\(662\) 7.59645 0.295244
\(663\) −4.22321 −0.164016
\(664\) 8.37850 0.325149
\(665\) 0.0232502 0.000901605 0
\(666\) 19.7025 0.763455
\(667\) 59.8335 2.31676
\(668\) −15.8941 −0.614963
\(669\) 6.55522 0.253439
\(670\) 0.638684 0.0246745
\(671\) 3.53849 0.136602
\(672\) 0.0730839 0.00281927
\(673\) 0.333170 0.0128428 0.00642138 0.999979i \(-0.497956\pi\)
0.00642138 + 0.999979i \(0.497956\pi\)
\(674\) −30.6571 −1.18087
\(675\) 12.6757 0.487890
\(676\) 3.10369 0.119373
\(677\) −27.9940 −1.07590 −0.537948 0.842978i \(-0.680800\pi\)
−0.537948 + 0.842978i \(0.680800\pi\)
\(678\) 2.26293 0.0869074
\(679\) −0.167384 −0.00642359
\(680\) 0.124985 0.00479294
\(681\) −2.63010 −0.100786
\(682\) 1.44287 0.0552505
\(683\) −4.98843 −0.190877 −0.0954385 0.995435i \(-0.530425\pi\)
−0.0954385 + 0.995435i \(0.530425\pi\)
\(684\) 7.52551 0.287745
\(685\) −0.315948 −0.0120718
\(686\) −2.33868 −0.0892912
\(687\) −2.52704 −0.0964127
\(688\) 2.30133 0.0877374
\(689\) −29.0350 −1.10615
\(690\) 0.152276 0.00579704
\(691\) 17.4931 0.665470 0.332735 0.943020i \(-0.392029\pi\)
0.332735 + 0.943020i \(0.392029\pi\)
\(692\) 11.2740 0.428575
\(693\) −0.678497 −0.0257740
\(694\) 9.15064 0.347354
\(695\) −0.576292 −0.0218600
\(696\) −3.88434 −0.147235
\(697\) 4.86133 0.184136
\(698\) 19.1348 0.724262
\(699\) −4.00436 −0.151459
\(700\) −0.836468 −0.0316155
\(701\) −7.33980 −0.277220 −0.138610 0.990347i \(-0.544264\pi\)
−0.138610 + 0.990347i \(0.544264\pi\)
\(702\) −10.1789 −0.384177
\(703\) 18.7864 0.708541
\(704\) 1.44287 0.0543803
\(705\) −0.0605849 −0.00228176
\(706\) 10.3641 0.390057
\(707\) −1.36358 −0.0512829
\(708\) 3.67166 0.137989
\(709\) −8.51845 −0.319917 −0.159959 0.987124i \(-0.551136\pi\)
−0.159959 + 0.987124i \(0.551136\pi\)
\(710\) 0.161003 0.00604234
\(711\) −29.3455 −1.10054
\(712\) 6.86237 0.257178
\(713\) −6.72568 −0.251879
\(714\) −0.176154 −0.00659241
\(715\) −0.300245 −0.0112285
\(716\) −14.9204 −0.557603
\(717\) 5.53791 0.206817
\(718\) 23.2049 0.866001
\(719\) −34.7296 −1.29519 −0.647597 0.761983i \(-0.724226\pi\)
−0.647597 + 0.761983i \(0.724226\pi\)
\(720\) 0.145677 0.00542908
\(721\) −0.284531 −0.0105965
\(722\) −11.8244 −0.440059
\(723\) −8.30756 −0.308961
\(724\) −18.1697 −0.675272
\(725\) 44.4574 1.65111
\(726\) −3.89388 −0.144515
\(727\) −31.8181 −1.18007 −0.590035 0.807378i \(-0.700886\pi\)
−0.590035 + 0.807378i \(0.700886\pi\)
\(728\) 0.671700 0.0248949
\(729\) −17.2436 −0.638651
\(730\) −0.296345 −0.0109682
\(731\) −5.54690 −0.205159
\(732\) 1.07078 0.0395770
\(733\) −18.4345 −0.680892 −0.340446 0.940264i \(-0.610578\pi\)
−0.340446 + 0.940264i \(0.610578\pi\)
\(734\) 6.11685 0.225777
\(735\) 0.157852 0.00582247
\(736\) −6.72568 −0.247912
\(737\) −17.7717 −0.654629
\(738\) 5.66618 0.208575
\(739\) 38.8606 1.42951 0.714756 0.699374i \(-0.246538\pi\)
0.714756 + 0.699374i \(0.246538\pi\)
\(740\) 0.363663 0.0133685
\(741\) −4.69354 −0.172422
\(742\) −1.21108 −0.0444601
\(743\) −22.4650 −0.824163 −0.412081 0.911147i \(-0.635198\pi\)
−0.412081 + 0.911147i \(0.635198\pi\)
\(744\) 0.436625 0.0160075
\(745\) −0.596022 −0.0218366
\(746\) −23.0809 −0.845054
\(747\) −23.5382 −0.861218
\(748\) −3.47776 −0.127159
\(749\) 1.34894 0.0492891
\(750\) 0.226348 0.00826508
\(751\) −50.4571 −1.84120 −0.920602 0.390502i \(-0.872302\pi\)
−0.920602 + 0.390502i \(0.872302\pi\)
\(752\) 2.67590 0.0975800
\(753\) −13.2137 −0.481534
\(754\) −35.7002 −1.30012
\(755\) 0.754590 0.0274623
\(756\) −0.424571 −0.0154415
\(757\) −4.61135 −0.167602 −0.0838012 0.996482i \(-0.526706\pi\)
−0.0838012 + 0.996482i \(0.526706\pi\)
\(758\) 25.9370 0.942073
\(759\) −4.23715 −0.153799
\(760\) 0.138904 0.00503857
\(761\) 19.5038 0.707013 0.353506 0.935432i \(-0.384989\pi\)
0.353506 + 0.935432i \(0.384989\pi\)
\(762\) −2.60219 −0.0942674
\(763\) −1.36637 −0.0494660
\(764\) −15.2353 −0.551195
\(765\) −0.351127 −0.0126950
\(766\) 7.28337 0.263159
\(767\) 33.7455 1.21848
\(768\) 0.436625 0.0157554
\(769\) −6.95524 −0.250812 −0.125406 0.992105i \(-0.540023\pi\)
−0.125406 + 0.992105i \(0.540023\pi\)
\(770\) −0.0125235 −0.000451316 0
\(771\) −2.61875 −0.0943120
\(772\) −9.63153 −0.346646
\(773\) 45.3298 1.63040 0.815199 0.579180i \(-0.196627\pi\)
0.815199 + 0.579180i \(0.196627\pi\)
\(774\) −6.46526 −0.232389
\(775\) −4.99731 −0.179509
\(776\) −1.00000 −0.0358979
\(777\) −0.512549 −0.0183876
\(778\) 32.8781 1.17874
\(779\) 5.40272 0.193572
\(780\) −0.0908567 −0.00325319
\(781\) −4.47999 −0.160307
\(782\) 16.2109 0.579701
\(783\) 22.5655 0.806426
\(784\) −6.97198 −0.248999
\(785\) −0.888496 −0.0317118
\(786\) 3.59049 0.128068
\(787\) −42.8113 −1.52606 −0.763030 0.646364i \(-0.776289\pi\)
−0.763030 + 0.646364i \(0.776289\pi\)
\(788\) −14.4162 −0.513557
\(789\) 1.12551 0.0400691
\(790\) −0.541652 −0.0192711
\(791\) 0.867512 0.0308452
\(792\) −4.05355 −0.144037
\(793\) 9.84130 0.349475
\(794\) 33.2627 1.18045
\(795\) 0.163815 0.00580992
\(796\) −13.4697 −0.477420
\(797\) −19.8725 −0.703921 −0.351960 0.936015i \(-0.614485\pi\)
−0.351960 + 0.936015i \(0.614485\pi\)
\(798\) −0.195772 −0.00693026
\(799\) −6.44973 −0.228175
\(800\) −4.99731 −0.176682
\(801\) −19.2788 −0.681185
\(802\) 13.1492 0.464316
\(803\) 8.24596 0.290994
\(804\) −5.37787 −0.189663
\(805\) 0.0583760 0.00205748
\(806\) 4.01294 0.141350
\(807\) 12.7821 0.449950
\(808\) −8.14646 −0.286592
\(809\) 51.7677 1.82006 0.910028 0.414546i \(-0.136060\pi\)
0.910028 + 0.414546i \(0.136060\pi\)
\(810\) −0.379603 −0.0133379
\(811\) 5.52449 0.193991 0.0969956 0.995285i \(-0.469077\pi\)
0.0969956 + 0.995285i \(0.469077\pi\)
\(812\) −1.48909 −0.0522568
\(813\) −1.68303 −0.0590263
\(814\) −10.1191 −0.354674
\(815\) 0.933183 0.0326880
\(816\) −1.05240 −0.0368413
\(817\) −6.16464 −0.215673
\(818\) 31.2293 1.09191
\(819\) −1.88705 −0.0659388
\(820\) 0.104585 0.00365226
\(821\) 49.7788 1.73729 0.868646 0.495433i \(-0.164990\pi\)
0.868646 + 0.495433i \(0.164990\pi\)
\(822\) 2.66036 0.0927906
\(823\) −22.4384 −0.782154 −0.391077 0.920358i \(-0.627897\pi\)
−0.391077 + 0.920358i \(0.627897\pi\)
\(824\) −1.69987 −0.0592179
\(825\) −3.14828 −0.109609
\(826\) 1.40756 0.0489752
\(827\) −32.2015 −1.11976 −0.559878 0.828575i \(-0.689152\pi\)
−0.559878 + 0.828575i \(0.689152\pi\)
\(828\) 18.8949 0.656641
\(829\) −10.9423 −0.380042 −0.190021 0.981780i \(-0.560856\pi\)
−0.190021 + 0.981780i \(0.560856\pi\)
\(830\) −0.434462 −0.0150804
\(831\) −7.82940 −0.271599
\(832\) 4.01294 0.139124
\(833\) 16.8046 0.582244
\(834\) 4.85251 0.168029
\(835\) 0.824180 0.0285219
\(836\) −3.86507 −0.133676
\(837\) −2.53651 −0.0876747
\(838\) 24.4159 0.843433
\(839\) −9.76043 −0.336967 −0.168484 0.985704i \(-0.553887\pi\)
−0.168484 + 0.985704i \(0.553887\pi\)
\(840\) −0.00378972 −0.000130758 0
\(841\) 50.1436 1.72909
\(842\) −0.0560206 −0.00193060
\(843\) −0.719622 −0.0247851
\(844\) −10.0648 −0.346445
\(845\) −0.160940 −0.00553650
\(846\) −7.51756 −0.258459
\(847\) −1.49275 −0.0512914
\(848\) −7.23535 −0.248463
\(849\) 6.22704 0.213712
\(850\) 12.0450 0.413141
\(851\) 47.1683 1.61691
\(852\) −1.35568 −0.0464449
\(853\) 17.0302 0.583104 0.291552 0.956555i \(-0.405828\pi\)
0.291552 + 0.956555i \(0.405828\pi\)
\(854\) 0.410490 0.0140467
\(855\) −0.390230 −0.0133456
\(856\) 8.05896 0.275449
\(857\) 27.0825 0.925119 0.462560 0.886588i \(-0.346931\pi\)
0.462560 + 0.886588i \(0.346931\pi\)
\(858\) 2.52813 0.0863090
\(859\) 40.8937 1.39528 0.697638 0.716450i \(-0.254234\pi\)
0.697638 + 0.716450i \(0.254234\pi\)
\(860\) −0.119334 −0.00406925
\(861\) −0.147403 −0.00502347
\(862\) 3.31504 0.112911
\(863\) −28.5694 −0.972512 −0.486256 0.873816i \(-0.661638\pi\)
−0.486256 + 0.873816i \(0.661638\pi\)
\(864\) −2.53651 −0.0862939
\(865\) −0.584608 −0.0198773
\(866\) 28.7140 0.975741
\(867\) −4.88603 −0.165938
\(868\) 0.167384 0.00568137
\(869\) 15.0717 0.511273
\(870\) 0.201420 0.00682877
\(871\) −49.4269 −1.67477
\(872\) −8.16312 −0.276438
\(873\) 2.80936 0.0950824
\(874\) 18.0163 0.609410
\(875\) 0.0867724 0.00293344
\(876\) 2.49530 0.0843082
\(877\) 45.0926 1.52267 0.761335 0.648358i \(-0.224544\pi\)
0.761335 + 0.648358i \(0.224544\pi\)
\(878\) 14.8315 0.500541
\(879\) 4.69910 0.158497
\(880\) −0.0748193 −0.00252216
\(881\) 17.3979 0.586150 0.293075 0.956089i \(-0.405321\pi\)
0.293075 + 0.956089i \(0.405321\pi\)
\(882\) 19.5868 0.659522
\(883\) −57.7910 −1.94482 −0.972411 0.233273i \(-0.925057\pi\)
−0.972411 + 0.233273i \(0.925057\pi\)
\(884\) −9.67240 −0.325318
\(885\) −0.190391 −0.00639994
\(886\) −1.91418 −0.0643080
\(887\) −44.1040 −1.48087 −0.740435 0.672128i \(-0.765380\pi\)
−0.740435 + 0.672128i \(0.765380\pi\)
\(888\) −3.06212 −0.102758
\(889\) −0.997569 −0.0334574
\(890\) −0.355844 −0.0119279
\(891\) 10.5627 0.353862
\(892\) 15.0134 0.502685
\(893\) −7.16801 −0.239868
\(894\) 5.01864 0.167848
\(895\) 0.773689 0.0258616
\(896\) 0.167384 0.00559189
\(897\) −11.7844 −0.393470
\(898\) 24.7797 0.826909
\(899\) −8.89627 −0.296707
\(900\) 14.0392 0.467975
\(901\) 17.4394 0.580990
\(902\) −2.91013 −0.0968966
\(903\) 0.168190 0.00559702
\(904\) 5.18278 0.172377
\(905\) 0.942178 0.0313191
\(906\) −6.35382 −0.211091
\(907\) 45.2316 1.50189 0.750946 0.660364i \(-0.229598\pi\)
0.750946 + 0.660364i \(0.229598\pi\)
\(908\) −6.02369 −0.199903
\(909\) 22.8863 0.759092
\(910\) −0.0348306 −0.00115462
\(911\) 38.1427 1.26372 0.631862 0.775081i \(-0.282291\pi\)
0.631862 + 0.775081i \(0.282291\pi\)
\(912\) −1.16960 −0.0387294
\(913\) 12.0891 0.400091
\(914\) −37.9094 −1.25393
\(915\) −0.0555244 −0.00183558
\(916\) −5.78767 −0.191230
\(917\) 1.37644 0.0454540
\(918\) 6.11376 0.201784
\(919\) −57.3558 −1.89199 −0.945997 0.324175i \(-0.894913\pi\)
−0.945997 + 0.324175i \(0.894913\pi\)
\(920\) 0.348756 0.0114981
\(921\) −3.59017 −0.118300
\(922\) 11.7897 0.388272
\(923\) −12.4598 −0.410120
\(924\) 0.105451 0.00346908
\(925\) 35.0469 1.15234
\(926\) 2.21085 0.0726532
\(927\) 4.77556 0.156850
\(928\) −8.89627 −0.292034
\(929\) −32.0799 −1.05251 −0.526253 0.850328i \(-0.676403\pi\)
−0.526253 + 0.850328i \(0.676403\pi\)
\(930\) −0.0226409 −0.000742425 0
\(931\) 18.6761 0.612083
\(932\) −9.17116 −0.300411
\(933\) 2.25358 0.0737788
\(934\) 2.05186 0.0671390
\(935\) 0.180337 0.00589765
\(936\) −11.2738 −0.368495
\(937\) 41.7762 1.36477 0.682385 0.730993i \(-0.260943\pi\)
0.682385 + 0.730993i \(0.260943\pi\)
\(938\) −2.06164 −0.0673151
\(939\) 1.38060 0.0450543
\(940\) −0.138757 −0.00452576
\(941\) 54.8678 1.78864 0.894320 0.447428i \(-0.147660\pi\)
0.894320 + 0.447428i \(0.147660\pi\)
\(942\) 7.48134 0.243755
\(943\) 13.5650 0.441737
\(944\) 8.40917 0.273695
\(945\) 0.0220158 0.000716175 0
\(946\) 3.32053 0.107960
\(947\) 11.9073 0.386935 0.193468 0.981107i \(-0.438027\pi\)
0.193468 + 0.981107i \(0.438027\pi\)
\(948\) 4.56083 0.148129
\(949\) 22.9338 0.744462
\(950\) 13.3864 0.434314
\(951\) 8.43111 0.273397
\(952\) −0.403445 −0.0130757
\(953\) −22.7050 −0.735485 −0.367743 0.929928i \(-0.619869\pi\)
−0.367743 + 0.929928i \(0.619869\pi\)
\(954\) 20.3267 0.658101
\(955\) 0.790019 0.0255644
\(956\) 12.6834 0.410212
\(957\) −5.60461 −0.181171
\(958\) −30.3350 −0.980080
\(959\) 1.01987 0.0329332
\(960\) −0.0226409 −0.000730733 0
\(961\) 1.00000 0.0322581
\(962\) −28.1434 −0.907379
\(963\) −22.6405 −0.729580
\(964\) −19.0267 −0.612810
\(965\) 0.499437 0.0160774
\(966\) −0.491539 −0.0158150
\(967\) −23.2766 −0.748526 −0.374263 0.927323i \(-0.622104\pi\)
−0.374263 + 0.927323i \(0.622104\pi\)
\(968\) −8.91812 −0.286639
\(969\) 2.81909 0.0905623
\(970\) 0.0518544 0.00166494
\(971\) −51.7940 −1.66215 −0.831075 0.556160i \(-0.812274\pi\)
−0.831075 + 0.556160i \(0.812274\pi\)
\(972\) 10.8059 0.346599
\(973\) 1.86024 0.0596367
\(974\) 29.1251 0.933229
\(975\) −8.75605 −0.280418
\(976\) 2.45239 0.0784991
\(977\) 19.5000 0.623860 0.311930 0.950105i \(-0.399025\pi\)
0.311930 + 0.950105i \(0.399025\pi\)
\(978\) −7.85761 −0.251259
\(979\) 9.90152 0.316454
\(980\) 0.361528 0.0115486
\(981\) 22.9331 0.732198
\(982\) −39.9149 −1.27374
\(983\) 19.4762 0.621195 0.310598 0.950542i \(-0.399471\pi\)
0.310598 + 0.950542i \(0.399471\pi\)
\(984\) −0.880628 −0.0280734
\(985\) 0.747545 0.0238188
\(986\) 21.4427 0.682875
\(987\) 0.195565 0.00622491
\(988\) −10.7496 −0.341990
\(989\) −15.4780 −0.492172
\(990\) 0.210194 0.00668041
\(991\) 54.2510 1.72334 0.861671 0.507468i \(-0.169418\pi\)
0.861671 + 0.507468i \(0.169418\pi\)
\(992\) 1.00000 0.0317500
\(993\) 3.31680 0.105256
\(994\) −0.519711 −0.0164842
\(995\) 0.698462 0.0221427
\(996\) 3.65827 0.115917
\(997\) −31.1603 −0.986857 −0.493428 0.869786i \(-0.664256\pi\)
−0.493428 + 0.869786i \(0.664256\pi\)
\(998\) 24.9423 0.789533
\(999\) 17.7890 0.562818
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 6014.2.a.e.1.14 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.e.1.14 21 1.1 even 1 trivial