Properties

Label 6029.2.a.b.1.4
Level $6029$
Weight $2$
Character 6029.1
Self dual yes
Analytic conductor $48.142$
Analytic rank $0$
Dimension $268$
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] = [6029,2,Mod(1,6029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6029 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6029.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: \(48.1418073786\)
Analytic rank: \(0\)
Dimension: \(268\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 6029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.76187 q^{2} -2.45998 q^{3} +5.62792 q^{4} +2.94480 q^{5} +6.79415 q^{6} +1.83308 q^{7} -10.0198 q^{8} +3.05151 q^{9} +O(q^{10})\) \(q-2.76187 q^{2} -2.45998 q^{3} +5.62792 q^{4} +2.94480 q^{5} +6.79415 q^{6} +1.83308 q^{7} -10.0198 q^{8} +3.05151 q^{9} -8.13315 q^{10} -1.81301 q^{11} -13.8446 q^{12} +1.02382 q^{13} -5.06274 q^{14} -7.24415 q^{15} +16.4177 q^{16} +0.386297 q^{17} -8.42787 q^{18} +7.64280 q^{19} +16.5731 q^{20} -4.50936 q^{21} +5.00729 q^{22} -8.13701 q^{23} +24.6486 q^{24} +3.67184 q^{25} -2.82767 q^{26} -0.126714 q^{27} +10.3165 q^{28} -2.16417 q^{29} +20.0074 q^{30} +6.43282 q^{31} -25.3037 q^{32} +4.45996 q^{33} -1.06690 q^{34} +5.39807 q^{35} +17.1737 q^{36} -0.190632 q^{37} -21.1084 q^{38} -2.51859 q^{39} -29.5064 q^{40} -3.89847 q^{41} +12.4542 q^{42} -2.13094 q^{43} -10.2035 q^{44} +8.98608 q^{45} +22.4734 q^{46} -4.51809 q^{47} -40.3872 q^{48} -3.63980 q^{49} -10.1412 q^{50} -0.950283 q^{51} +5.76201 q^{52} -6.91539 q^{53} +0.349966 q^{54} -5.33894 q^{55} -18.3672 q^{56} -18.8011 q^{57} +5.97716 q^{58} +4.87745 q^{59} -40.7695 q^{60} +2.72175 q^{61} -17.7666 q^{62} +5.59368 q^{63} +37.0503 q^{64} +3.01496 q^{65} -12.3178 q^{66} +1.23528 q^{67} +2.17405 q^{68} +20.0169 q^{69} -14.9088 q^{70} +3.41889 q^{71} -30.5757 q^{72} -8.92070 q^{73} +0.526500 q^{74} -9.03267 q^{75} +43.0131 q^{76} -3.32339 q^{77} +6.95602 q^{78} +8.79434 q^{79} +48.3467 q^{80} -8.84282 q^{81} +10.7671 q^{82} +3.31980 q^{83} -25.3783 q^{84} +1.13757 q^{85} +5.88537 q^{86} +5.32382 q^{87} +18.1660 q^{88} +9.66287 q^{89} -24.8184 q^{90} +1.87676 q^{91} -45.7945 q^{92} -15.8246 q^{93} +12.4784 q^{94} +22.5065 q^{95} +62.2468 q^{96} +6.75489 q^{97} +10.0527 q^{98} -5.53241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76187 −1.95294 −0.976468 0.215661i \(-0.930809\pi\)
−0.976468 + 0.215661i \(0.930809\pi\)
\(3\) −2.45998 −1.42027 −0.710136 0.704065i \(-0.751366\pi\)
−0.710136 + 0.704065i \(0.751366\pi\)
\(4\) 5.62792 2.81396
\(5\) 2.94480 1.31695 0.658477 0.752601i \(-0.271201\pi\)
0.658477 + 0.752601i \(0.271201\pi\)
\(6\) 6.79415 2.77370
\(7\) 1.83308 0.692841 0.346420 0.938079i \(-0.387397\pi\)
0.346420 + 0.938079i \(0.387397\pi\)
\(8\) −10.0198 −3.54255
\(9\) 3.05151 1.01717
\(10\) −8.13315 −2.57193
\(11\) −1.81301 −0.546642 −0.273321 0.961923i \(-0.588122\pi\)
−0.273321 + 0.961923i \(0.588122\pi\)
\(12\) −13.8446 −3.99659
\(13\) 1.02382 0.283958 0.141979 0.989870i \(-0.454653\pi\)
0.141979 + 0.989870i \(0.454653\pi\)
\(14\) −5.06274 −1.35307
\(15\) −7.24415 −1.87043
\(16\) 16.4177 4.10442
\(17\) 0.386297 0.0936907 0.0468453 0.998902i \(-0.485083\pi\)
0.0468453 + 0.998902i \(0.485083\pi\)
\(18\) −8.42787 −1.98647
\(19\) 7.64280 1.75338 0.876689 0.481057i \(-0.159747\pi\)
0.876689 + 0.481057i \(0.159747\pi\)
\(20\) 16.5731 3.70586
\(21\) −4.50936 −0.984022
\(22\) 5.00729 1.06756
\(23\) −8.13701 −1.69668 −0.848342 0.529449i \(-0.822399\pi\)
−0.848342 + 0.529449i \(0.822399\pi\)
\(24\) 24.6486 5.03138
\(25\) 3.67184 0.734369
\(26\) −2.82767 −0.554552
\(27\) −0.126714 −0.0243860
\(28\) 10.3165 1.94963
\(29\) −2.16417 −0.401877 −0.200938 0.979604i \(-0.564399\pi\)
−0.200938 + 0.979604i \(0.564399\pi\)
\(30\) 20.0074 3.65284
\(31\) 6.43282 1.15537 0.577684 0.816260i \(-0.303957\pi\)
0.577684 + 0.816260i \(0.303957\pi\)
\(32\) −25.3037 −4.47311
\(33\) 4.45996 0.776380
\(34\) −1.06690 −0.182972
\(35\) 5.39807 0.912440
\(36\) 17.1737 2.86228
\(37\) −0.190632 −0.0313396 −0.0156698 0.999877i \(-0.504988\pi\)
−0.0156698 + 0.999877i \(0.504988\pi\)
\(38\) −21.1084 −3.42424
\(39\) −2.51859 −0.403297
\(40\) −29.5064 −4.66538
\(41\) −3.89847 −0.608839 −0.304419 0.952538i \(-0.598462\pi\)
−0.304419 + 0.952538i \(0.598462\pi\)
\(42\) 12.4542 1.92173
\(43\) −2.13094 −0.324965 −0.162483 0.986711i \(-0.551950\pi\)
−0.162483 + 0.986711i \(0.551950\pi\)
\(44\) −10.2035 −1.53823
\(45\) 8.98608 1.33957
\(46\) 22.4734 3.31352
\(47\) −4.51809 −0.659031 −0.329516 0.944150i \(-0.606885\pi\)
−0.329516 + 0.944150i \(0.606885\pi\)
\(48\) −40.3872 −5.82938
\(49\) −3.63980 −0.519971
\(50\) −10.1412 −1.43418
\(51\) −0.950283 −0.133066
\(52\) 5.76201 0.799047
\(53\) −6.91539 −0.949902 −0.474951 0.880012i \(-0.657534\pi\)
−0.474951 + 0.880012i \(0.657534\pi\)
\(54\) 0.349966 0.0476244
\(55\) −5.33894 −0.719903
\(56\) −18.3672 −2.45442
\(57\) −18.8011 −2.49027
\(58\) 5.97716 0.784839
\(59\) 4.87745 0.634990 0.317495 0.948260i \(-0.397158\pi\)
0.317495 + 0.948260i \(0.397158\pi\)
\(60\) −40.7695 −5.26332
\(61\) 2.72175 0.348484 0.174242 0.984703i \(-0.444252\pi\)
0.174242 + 0.984703i \(0.444252\pi\)
\(62\) −17.7666 −2.25636
\(63\) 5.59368 0.704737
\(64\) 37.0503 4.63129
\(65\) 3.01496 0.373960
\(66\) −12.3178 −1.51622
\(67\) 1.23528 0.150914 0.0754569 0.997149i \(-0.475958\pi\)
0.0754569 + 0.997149i \(0.475958\pi\)
\(68\) 2.17405 0.263642
\(69\) 20.0169 2.40975
\(70\) −14.9088 −1.78194
\(71\) 3.41889 0.405748 0.202874 0.979205i \(-0.434972\pi\)
0.202874 + 0.979205i \(0.434972\pi\)
\(72\) −30.5757 −3.60338
\(73\) −8.92070 −1.04409 −0.522044 0.852918i \(-0.674830\pi\)
−0.522044 + 0.852918i \(0.674830\pi\)
\(74\) 0.526500 0.0612043
\(75\) −9.03267 −1.04300
\(76\) 43.0131 4.93394
\(77\) −3.32339 −0.378736
\(78\) 6.95602 0.787614
\(79\) 8.79434 0.989441 0.494720 0.869052i \(-0.335270\pi\)
0.494720 + 0.869052i \(0.335270\pi\)
\(80\) 48.3467 5.40533
\(81\) −8.84282 −0.982535
\(82\) 10.7671 1.18902
\(83\) 3.31980 0.364396 0.182198 0.983262i \(-0.441679\pi\)
0.182198 + 0.983262i \(0.441679\pi\)
\(84\) −25.3783 −2.76900
\(85\) 1.13757 0.123386
\(86\) 5.88537 0.634636
\(87\) 5.32382 0.570774
\(88\) 18.1660 1.93651
\(89\) 9.66287 1.02426 0.512131 0.858907i \(-0.328856\pi\)
0.512131 + 0.858907i \(0.328856\pi\)
\(90\) −24.8184 −2.61609
\(91\) 1.87676 0.196738
\(92\) −45.7945 −4.77440
\(93\) −15.8246 −1.64094
\(94\) 12.4784 1.28705
\(95\) 22.5065 2.30912
\(96\) 62.2468 6.35303
\(97\) 6.75489 0.685855 0.342927 0.939362i \(-0.388581\pi\)
0.342927 + 0.939362i \(0.388581\pi\)
\(98\) 10.0527 1.01547
\(99\) −5.53241 −0.556028
\(100\) 20.6649 2.06649
\(101\) 17.7832 1.76950 0.884749 0.466068i \(-0.154330\pi\)
0.884749 + 0.466068i \(0.154330\pi\)
\(102\) 2.62456 0.259870
\(103\) 13.4400 1.32429 0.662143 0.749377i \(-0.269647\pi\)
0.662143 + 0.749377i \(0.269647\pi\)
\(104\) −10.2586 −1.00594
\(105\) −13.2791 −1.29591
\(106\) 19.0994 1.85510
\(107\) 12.8963 1.24673 0.623366 0.781930i \(-0.285765\pi\)
0.623366 + 0.781930i \(0.285765\pi\)
\(108\) −0.713134 −0.0686213
\(109\) −18.6677 −1.78805 −0.894023 0.448022i \(-0.852129\pi\)
−0.894023 + 0.448022i \(0.852129\pi\)
\(110\) 14.7455 1.40592
\(111\) 0.468950 0.0445108
\(112\) 30.0950 2.84371
\(113\) 14.7744 1.38986 0.694930 0.719077i \(-0.255435\pi\)
0.694930 + 0.719077i \(0.255435\pi\)
\(114\) 51.9263 4.86335
\(115\) −23.9619 −2.23445
\(116\) −12.1798 −1.13086
\(117\) 3.12421 0.288833
\(118\) −13.4709 −1.24009
\(119\) 0.708114 0.0649127
\(120\) 72.5853 6.62610
\(121\) −7.71301 −0.701182
\(122\) −7.51711 −0.680567
\(123\) 9.59017 0.864716
\(124\) 36.2034 3.25116
\(125\) −3.91115 −0.349824
\(126\) −15.4490 −1.37631
\(127\) 11.5885 1.02831 0.514156 0.857697i \(-0.328105\pi\)
0.514156 + 0.857697i \(0.328105\pi\)
\(128\) −51.7206 −4.57150
\(129\) 5.24207 0.461538
\(130\) −8.32692 −0.730319
\(131\) −19.3883 −1.69396 −0.846981 0.531623i \(-0.821582\pi\)
−0.846981 + 0.531623i \(0.821582\pi\)
\(132\) 25.1003 2.18470
\(133\) 14.0099 1.21481
\(134\) −3.41169 −0.294725
\(135\) −0.373146 −0.0321153
\(136\) −3.87063 −0.331904
\(137\) 8.52540 0.728374 0.364187 0.931326i \(-0.381347\pi\)
0.364187 + 0.931326i \(0.381347\pi\)
\(138\) −55.2840 −4.70609
\(139\) −15.7870 −1.33903 −0.669517 0.742797i \(-0.733499\pi\)
−0.669517 + 0.742797i \(0.733499\pi\)
\(140\) 30.3799 2.56757
\(141\) 11.1144 0.936003
\(142\) −9.44253 −0.792399
\(143\) −1.85620 −0.155223
\(144\) 50.0987 4.17489
\(145\) −6.37305 −0.529253
\(146\) 24.6378 2.03904
\(147\) 8.95384 0.738500
\(148\) −1.07286 −0.0881885
\(149\) 13.6573 1.11885 0.559424 0.828882i \(-0.311022\pi\)
0.559424 + 0.828882i \(0.311022\pi\)
\(150\) 24.9470 2.03692
\(151\) 11.9194 0.969990 0.484995 0.874517i \(-0.338821\pi\)
0.484995 + 0.874517i \(0.338821\pi\)
\(152\) −76.5797 −6.21143
\(153\) 1.17879 0.0952994
\(154\) 9.17878 0.739647
\(155\) 18.9434 1.52157
\(156\) −14.1744 −1.13486
\(157\) 13.3557 1.06590 0.532952 0.846145i \(-0.321083\pi\)
0.532952 + 0.846145i \(0.321083\pi\)
\(158\) −24.2888 −1.93231
\(159\) 17.0117 1.34912
\(160\) −74.5145 −5.89089
\(161\) −14.9158 −1.17553
\(162\) 24.4227 1.91883
\(163\) −12.6872 −0.993735 −0.496867 0.867827i \(-0.665516\pi\)
−0.496867 + 0.867827i \(0.665516\pi\)
\(164\) −21.9403 −1.71325
\(165\) 13.1337 1.02246
\(166\) −9.16886 −0.711642
\(167\) −6.11737 −0.473376 −0.236688 0.971586i \(-0.576062\pi\)
−0.236688 + 0.971586i \(0.576062\pi\)
\(168\) 45.1830 3.48595
\(169\) −11.9518 −0.919368
\(170\) −3.14181 −0.240966
\(171\) 23.3221 1.78348
\(172\) −11.9928 −0.914439
\(173\) 13.3940 1.01833 0.509164 0.860670i \(-0.329955\pi\)
0.509164 + 0.860670i \(0.329955\pi\)
\(174\) −14.7037 −1.11468
\(175\) 6.73080 0.508801
\(176\) −29.7653 −2.24365
\(177\) −11.9984 −0.901858
\(178\) −26.6876 −2.00032
\(179\) −14.8146 −1.10730 −0.553648 0.832751i \(-0.686765\pi\)
−0.553648 + 0.832751i \(0.686765\pi\)
\(180\) 50.5730 3.76949
\(181\) 20.4160 1.51751 0.758754 0.651377i \(-0.225808\pi\)
0.758754 + 0.651377i \(0.225808\pi\)
\(182\) −5.18336 −0.384216
\(183\) −6.69545 −0.494942
\(184\) 81.5316 6.01059
\(185\) −0.561372 −0.0412729
\(186\) 43.7055 3.20464
\(187\) −0.700358 −0.0512153
\(188\) −25.4275 −1.85449
\(189\) −0.232277 −0.0168956
\(190\) −62.1600 −4.50956
\(191\) 24.6524 1.78379 0.891894 0.452245i \(-0.149377\pi\)
0.891894 + 0.452245i \(0.149377\pi\)
\(192\) −91.1431 −6.57769
\(193\) −4.74669 −0.341674 −0.170837 0.985299i \(-0.554647\pi\)
−0.170837 + 0.985299i \(0.554647\pi\)
\(194\) −18.6561 −1.33943
\(195\) −7.41674 −0.531124
\(196\) −20.4845 −1.46318
\(197\) 11.1113 0.791650 0.395825 0.918326i \(-0.370459\pi\)
0.395825 + 0.918326i \(0.370459\pi\)
\(198\) 15.2798 1.08589
\(199\) 11.8476 0.839852 0.419926 0.907558i \(-0.362056\pi\)
0.419926 + 0.907558i \(0.362056\pi\)
\(200\) −36.7913 −2.60154
\(201\) −3.03877 −0.214338
\(202\) −49.1150 −3.45572
\(203\) −3.96711 −0.278437
\(204\) −5.34812 −0.374443
\(205\) −11.4802 −0.801813
\(206\) −37.1196 −2.58625
\(207\) −24.8302 −1.72582
\(208\) 16.8088 1.16548
\(209\) −13.8564 −0.958471
\(210\) 36.6753 2.53083
\(211\) 7.34636 0.505744 0.252872 0.967500i \(-0.418625\pi\)
0.252872 + 0.967500i \(0.418625\pi\)
\(212\) −38.9193 −2.67299
\(213\) −8.41041 −0.576272
\(214\) −35.6179 −2.43479
\(215\) −6.27519 −0.427964
\(216\) 1.26965 0.0863887
\(217\) 11.7919 0.800486
\(218\) 51.5579 3.49194
\(219\) 21.9448 1.48289
\(220\) −30.0471 −2.02578
\(221\) 0.395500 0.0266042
\(222\) −1.29518 −0.0869267
\(223\) −1.75697 −0.117656 −0.0588278 0.998268i \(-0.518736\pi\)
−0.0588278 + 0.998268i \(0.518736\pi\)
\(224\) −46.3839 −3.09916
\(225\) 11.2047 0.746978
\(226\) −40.8050 −2.71431
\(227\) −3.50337 −0.232527 −0.116263 0.993218i \(-0.537092\pi\)
−0.116263 + 0.993218i \(0.537092\pi\)
\(228\) −105.811 −7.00753
\(229\) −5.41895 −0.358095 −0.179047 0.983840i \(-0.557302\pi\)
−0.179047 + 0.983840i \(0.557302\pi\)
\(230\) 66.1795 4.36375
\(231\) 8.17549 0.537908
\(232\) 21.6847 1.42367
\(233\) −3.32322 −0.217711 −0.108856 0.994058i \(-0.534719\pi\)
−0.108856 + 0.994058i \(0.534719\pi\)
\(234\) −8.62866 −0.564073
\(235\) −13.3049 −0.867914
\(236\) 27.4499 1.78684
\(237\) −21.6339 −1.40527
\(238\) −1.95572 −0.126770
\(239\) 11.7022 0.756951 0.378476 0.925611i \(-0.376448\pi\)
0.378476 + 0.925611i \(0.376448\pi\)
\(240\) −118.932 −7.67703
\(241\) 20.8848 1.34531 0.672655 0.739956i \(-0.265154\pi\)
0.672655 + 0.739956i \(0.265154\pi\)
\(242\) 21.3023 1.36936
\(243\) 22.1333 1.41985
\(244\) 15.3178 0.980621
\(245\) −10.7185 −0.684779
\(246\) −26.4868 −1.68874
\(247\) 7.82489 0.497886
\(248\) −64.4558 −4.09295
\(249\) −8.16665 −0.517541
\(250\) 10.8021 0.683185
\(251\) 9.50454 0.599921 0.299961 0.953952i \(-0.403026\pi\)
0.299961 + 0.953952i \(0.403026\pi\)
\(252\) 31.4808 1.98310
\(253\) 14.7525 0.927479
\(254\) −32.0059 −2.00823
\(255\) −2.79839 −0.175242
\(256\) 68.7450 4.29656
\(257\) −7.58262 −0.472991 −0.236496 0.971633i \(-0.575999\pi\)
−0.236496 + 0.971633i \(0.575999\pi\)
\(258\) −14.4779 −0.901355
\(259\) −0.349444 −0.0217134
\(260\) 16.9680 1.05231
\(261\) −6.60399 −0.408777
\(262\) 53.5479 3.30820
\(263\) 19.0591 1.17523 0.587617 0.809139i \(-0.300066\pi\)
0.587617 + 0.809139i \(0.300066\pi\)
\(264\) −44.6881 −2.75037
\(265\) −20.3644 −1.25098
\(266\) −38.6935 −2.37245
\(267\) −23.7705 −1.45473
\(268\) 6.95207 0.424665
\(269\) −13.1532 −0.801965 −0.400983 0.916086i \(-0.631331\pi\)
−0.400983 + 0.916086i \(0.631331\pi\)
\(270\) 1.03058 0.0627191
\(271\) 8.42874 0.512009 0.256005 0.966676i \(-0.417594\pi\)
0.256005 + 0.966676i \(0.417594\pi\)
\(272\) 6.34209 0.384546
\(273\) −4.61679 −0.279421
\(274\) −23.5460 −1.42247
\(275\) −6.65708 −0.401437
\(276\) 112.654 6.78094
\(277\) −30.5960 −1.83834 −0.919169 0.393864i \(-0.871138\pi\)
−0.919169 + 0.393864i \(0.871138\pi\)
\(278\) 43.6015 2.61505
\(279\) 19.6298 1.17521
\(280\) −54.0878 −3.23236
\(281\) 0.107479 0.00641168 0.00320584 0.999995i \(-0.498980\pi\)
0.00320584 + 0.999995i \(0.498980\pi\)
\(282\) −30.6966 −1.82795
\(283\) −2.69680 −0.160308 −0.0801542 0.996782i \(-0.525541\pi\)
−0.0801542 + 0.996782i \(0.525541\pi\)
\(284\) 19.2412 1.14176
\(285\) −55.3656 −3.27958
\(286\) 5.12659 0.303141
\(287\) −7.14623 −0.421828
\(288\) −77.2146 −4.54992
\(289\) −16.8508 −0.991222
\(290\) 17.6015 1.03360
\(291\) −16.6169 −0.974100
\(292\) −50.2050 −2.93803
\(293\) −19.1515 −1.11884 −0.559421 0.828884i \(-0.688976\pi\)
−0.559421 + 0.828884i \(0.688976\pi\)
\(294\) −24.7293 −1.44224
\(295\) 14.3631 0.836253
\(296\) 1.91010 0.111022
\(297\) 0.229732 0.0133304
\(298\) −37.7196 −2.18504
\(299\) −8.33087 −0.481787
\(300\) −50.8352 −2.93497
\(301\) −3.90619 −0.225149
\(302\) −32.9199 −1.89433
\(303\) −43.7464 −2.51317
\(304\) 125.477 7.19659
\(305\) 8.01500 0.458938
\(306\) −3.25566 −0.186114
\(307\) −4.68317 −0.267283 −0.133641 0.991030i \(-0.542667\pi\)
−0.133641 + 0.991030i \(0.542667\pi\)
\(308\) −18.7038 −1.06575
\(309\) −33.0623 −1.88085
\(310\) −52.3191 −2.97152
\(311\) 17.4852 0.991496 0.495748 0.868466i \(-0.334894\pi\)
0.495748 + 0.868466i \(0.334894\pi\)
\(312\) 25.2359 1.42870
\(313\) −21.1255 −1.19409 −0.597043 0.802209i \(-0.703658\pi\)
−0.597043 + 0.802209i \(0.703658\pi\)
\(314\) −36.8868 −2.08164
\(315\) 16.4723 0.928106
\(316\) 49.4939 2.78425
\(317\) 13.5889 0.763228 0.381614 0.924322i \(-0.375368\pi\)
0.381614 + 0.924322i \(0.375368\pi\)
\(318\) −46.9842 −2.63474
\(319\) 3.92366 0.219683
\(320\) 109.106 6.09920
\(321\) −31.7246 −1.77070
\(322\) 41.1956 2.29574
\(323\) 2.95239 0.164275
\(324\) −49.7667 −2.76482
\(325\) 3.75932 0.208530
\(326\) 35.0403 1.94070
\(327\) 45.9223 2.53951
\(328\) 39.0621 2.15684
\(329\) −8.28204 −0.456604
\(330\) −36.2736 −1.99679
\(331\) 8.58074 0.471640 0.235820 0.971797i \(-0.424222\pi\)
0.235820 + 0.971797i \(0.424222\pi\)
\(332\) 18.6836 1.02540
\(333\) −0.581714 −0.0318777
\(334\) 16.8954 0.924474
\(335\) 3.63766 0.198747
\(336\) −74.0331 −4.03884
\(337\) −0.139185 −0.00758190 −0.00379095 0.999993i \(-0.501207\pi\)
−0.00379095 + 0.999993i \(0.501207\pi\)
\(338\) 33.0093 1.79547
\(339\) −36.3448 −1.97398
\(340\) 6.40213 0.347204
\(341\) −11.6627 −0.631573
\(342\) −64.4125 −3.48303
\(343\) −19.5037 −1.05310
\(344\) 21.3517 1.15121
\(345\) 58.9457 3.17353
\(346\) −36.9925 −1.98873
\(347\) 16.4244 0.881710 0.440855 0.897578i \(-0.354675\pi\)
0.440855 + 0.897578i \(0.354675\pi\)
\(348\) 29.9621 1.60613
\(349\) −12.2741 −0.657015 −0.328507 0.944501i \(-0.606546\pi\)
−0.328507 + 0.944501i \(0.606546\pi\)
\(350\) −18.5896 −0.993655
\(351\) −0.129732 −0.00692461
\(352\) 45.8759 2.44519
\(353\) −25.6029 −1.36270 −0.681352 0.731956i \(-0.738608\pi\)
−0.681352 + 0.731956i \(0.738608\pi\)
\(354\) 33.1381 1.76127
\(355\) 10.0679 0.534351
\(356\) 54.3819 2.88223
\(357\) −1.74195 −0.0921937
\(358\) 40.9160 2.16248
\(359\) 23.4877 1.23963 0.619816 0.784747i \(-0.287207\pi\)
0.619816 + 0.784747i \(0.287207\pi\)
\(360\) −90.0392 −4.74548
\(361\) 39.4124 2.07434
\(362\) −56.3863 −2.96360
\(363\) 18.9739 0.995869
\(364\) 10.5622 0.553612
\(365\) −26.2697 −1.37502
\(366\) 18.4920 0.966590
\(367\) −4.70148 −0.245415 −0.122708 0.992443i \(-0.539158\pi\)
−0.122708 + 0.992443i \(0.539158\pi\)
\(368\) −133.591 −6.96389
\(369\) −11.8962 −0.619293
\(370\) 1.55044 0.0806033
\(371\) −12.6765 −0.658131
\(372\) −89.0597 −4.61753
\(373\) −4.91089 −0.254276 −0.127138 0.991885i \(-0.540579\pi\)
−0.127138 + 0.991885i \(0.540579\pi\)
\(374\) 1.93430 0.100020
\(375\) 9.62137 0.496845
\(376\) 45.2706 2.33465
\(377\) −2.21573 −0.114116
\(378\) 0.641518 0.0329961
\(379\) 13.4160 0.689133 0.344566 0.938762i \(-0.388026\pi\)
0.344566 + 0.938762i \(0.388026\pi\)
\(380\) 126.665 6.49777
\(381\) −28.5075 −1.46048
\(382\) −68.0868 −3.48362
\(383\) −7.51654 −0.384077 −0.192039 0.981387i \(-0.561510\pi\)
−0.192039 + 0.981387i \(0.561510\pi\)
\(384\) 127.232 6.49277
\(385\) −9.78673 −0.498778
\(386\) 13.1097 0.667268
\(387\) −6.50258 −0.330545
\(388\) 38.0160 1.92997
\(389\) −23.5109 −1.19205 −0.596025 0.802966i \(-0.703254\pi\)
−0.596025 + 0.802966i \(0.703254\pi\)
\(390\) 20.4841 1.03725
\(391\) −3.14330 −0.158963
\(392\) 36.4702 1.84203
\(393\) 47.6948 2.40589
\(394\) −30.6881 −1.54604
\(395\) 25.8976 1.30305
\(396\) −31.1360 −1.56464
\(397\) 22.6065 1.13459 0.567295 0.823515i \(-0.307990\pi\)
0.567295 + 0.823515i \(0.307990\pi\)
\(398\) −32.7215 −1.64018
\(399\) −34.4641 −1.72536
\(400\) 60.2831 3.01415
\(401\) 3.13021 0.156315 0.0781575 0.996941i \(-0.475096\pi\)
0.0781575 + 0.996941i \(0.475096\pi\)
\(402\) 8.39269 0.418589
\(403\) 6.58608 0.328076
\(404\) 100.083 4.97930
\(405\) −26.0403 −1.29395
\(406\) 10.9566 0.543769
\(407\) 0.345616 0.0171316
\(408\) 9.52169 0.471394
\(409\) −9.96785 −0.492878 −0.246439 0.969158i \(-0.579261\pi\)
−0.246439 + 0.969158i \(0.579261\pi\)
\(410\) 31.7068 1.56589
\(411\) −20.9723 −1.03449
\(412\) 75.6395 3.72649
\(413\) 8.94078 0.439947
\(414\) 68.5777 3.37041
\(415\) 9.77615 0.479892
\(416\) −25.9066 −1.27018
\(417\) 38.8357 1.90179
\(418\) 38.2697 1.87183
\(419\) −34.0577 −1.66383 −0.831913 0.554906i \(-0.812754\pi\)
−0.831913 + 0.554906i \(0.812754\pi\)
\(420\) −74.7340 −3.64665
\(421\) 26.5540 1.29416 0.647082 0.762421i \(-0.275989\pi\)
0.647082 + 0.762421i \(0.275989\pi\)
\(422\) −20.2897 −0.987687
\(423\) −13.7870 −0.670347
\(424\) 69.2912 3.36508
\(425\) 1.41842 0.0688035
\(426\) 23.2284 1.12542
\(427\) 4.98919 0.241444
\(428\) 72.5793 3.50825
\(429\) 4.56622 0.220459
\(430\) 17.3312 0.835787
\(431\) 40.6580 1.95843 0.979214 0.202829i \(-0.0650135\pi\)
0.979214 + 0.202829i \(0.0650135\pi\)
\(432\) −2.08034 −0.100090
\(433\) −34.8815 −1.67630 −0.838149 0.545441i \(-0.816362\pi\)
−0.838149 + 0.545441i \(0.816362\pi\)
\(434\) −32.5677 −1.56330
\(435\) 15.6776 0.751683
\(436\) −105.061 −5.03149
\(437\) −62.1895 −2.97493
\(438\) −60.6085 −2.89599
\(439\) 17.2156 0.821654 0.410827 0.911713i \(-0.365240\pi\)
0.410827 + 0.911713i \(0.365240\pi\)
\(440\) 53.4954 2.55029
\(441\) −11.1069 −0.528899
\(442\) −1.09232 −0.0519563
\(443\) 3.24573 0.154209 0.0771046 0.997023i \(-0.475432\pi\)
0.0771046 + 0.997023i \(0.475432\pi\)
\(444\) 2.63922 0.125252
\(445\) 28.4552 1.34891
\(446\) 4.85253 0.229774
\(447\) −33.5967 −1.58907
\(448\) 67.9164 3.20875
\(449\) 16.8128 0.793447 0.396724 0.917938i \(-0.370147\pi\)
0.396724 + 0.917938i \(0.370147\pi\)
\(450\) −30.9458 −1.45880
\(451\) 7.06795 0.332817
\(452\) 83.1493 3.91101
\(453\) −29.3216 −1.37765
\(454\) 9.67585 0.454110
\(455\) 5.52668 0.259095
\(456\) 188.385 8.82192
\(457\) 12.6947 0.593834 0.296917 0.954903i \(-0.404042\pi\)
0.296917 + 0.954903i \(0.404042\pi\)
\(458\) 14.9664 0.699336
\(459\) −0.0489490 −0.00228474
\(460\) −134.855 −6.28767
\(461\) −22.0799 −1.02836 −0.514181 0.857682i \(-0.671904\pi\)
−0.514181 + 0.857682i \(0.671904\pi\)
\(462\) −22.5796 −1.05050
\(463\) −20.5139 −0.953363 −0.476681 0.879076i \(-0.658160\pi\)
−0.476681 + 0.879076i \(0.658160\pi\)
\(464\) −35.5306 −1.64947
\(465\) −46.6003 −2.16104
\(466\) 9.17830 0.425177
\(467\) 22.6108 1.04631 0.523153 0.852239i \(-0.324756\pi\)
0.523153 + 0.852239i \(0.324756\pi\)
\(468\) 17.5828 0.812766
\(469\) 2.26438 0.104559
\(470\) 36.7463 1.69498
\(471\) −32.8549 −1.51387
\(472\) −48.8713 −2.24948
\(473\) 3.86340 0.177640
\(474\) 59.7501 2.74441
\(475\) 28.0632 1.28763
\(476\) 3.98521 0.182662
\(477\) −21.1024 −0.966212
\(478\) −32.3199 −1.47828
\(479\) 26.3057 1.20194 0.600969 0.799272i \(-0.294781\pi\)
0.600969 + 0.799272i \(0.294781\pi\)
\(480\) 183.304 8.36665
\(481\) −0.195173 −0.00889914
\(482\) −57.6811 −2.62730
\(483\) 36.6927 1.66957
\(484\) −43.4082 −1.97310
\(485\) 19.8918 0.903240
\(486\) −61.1293 −2.77288
\(487\) 23.1266 1.04797 0.523983 0.851729i \(-0.324446\pi\)
0.523983 + 0.851729i \(0.324446\pi\)
\(488\) −27.2715 −1.23452
\(489\) 31.2102 1.41137
\(490\) 29.6030 1.33733
\(491\) −21.3535 −0.963672 −0.481836 0.876262i \(-0.660030\pi\)
−0.481836 + 0.876262i \(0.660030\pi\)
\(492\) 53.9727 2.43328
\(493\) −0.836012 −0.0376521
\(494\) −21.6113 −0.972339
\(495\) −16.2918 −0.732263
\(496\) 105.612 4.74211
\(497\) 6.26712 0.281119
\(498\) 22.5552 1.01072
\(499\) 20.0004 0.895342 0.447671 0.894198i \(-0.352254\pi\)
0.447671 + 0.894198i \(0.352254\pi\)
\(500\) −22.0117 −0.984392
\(501\) 15.0486 0.672322
\(502\) −26.2503 −1.17161
\(503\) −13.2405 −0.590365 −0.295182 0.955441i \(-0.595380\pi\)
−0.295182 + 0.955441i \(0.595380\pi\)
\(504\) −56.0478 −2.49657
\(505\) 52.3681 2.33035
\(506\) −40.7443 −1.81131
\(507\) 29.4012 1.30575
\(508\) 65.2191 2.89363
\(509\) 0.401532 0.0177976 0.00889881 0.999960i \(-0.497167\pi\)
0.00889881 + 0.999960i \(0.497167\pi\)
\(510\) 7.72879 0.342237
\(511\) −16.3524 −0.723387
\(512\) −86.4235 −3.81941
\(513\) −0.968446 −0.0427579
\(514\) 20.9422 0.923722
\(515\) 39.5782 1.74402
\(516\) 29.5020 1.29875
\(517\) 8.19133 0.360254
\(518\) 0.965118 0.0424049
\(519\) −32.9490 −1.44630
\(520\) −30.2094 −1.32477
\(521\) 11.4530 0.501767 0.250884 0.968017i \(-0.419279\pi\)
0.250884 + 0.968017i \(0.419279\pi\)
\(522\) 18.2394 0.798315
\(523\) 1.66959 0.0730060 0.0365030 0.999334i \(-0.488378\pi\)
0.0365030 + 0.999334i \(0.488378\pi\)
\(524\) −109.116 −4.76674
\(525\) −16.5576 −0.722635
\(526\) −52.6387 −2.29516
\(527\) 2.48498 0.108247
\(528\) 73.2222 3.18659
\(529\) 43.2109 1.87874
\(530\) 56.2439 2.44308
\(531\) 14.8836 0.645893
\(532\) 78.8466 3.41843
\(533\) −3.99135 −0.172885
\(534\) 65.6509 2.84099
\(535\) 37.9770 1.64189
\(536\) −12.3773 −0.534620
\(537\) 36.4437 1.57266
\(538\) 36.3275 1.56619
\(539\) 6.59898 0.284238
\(540\) −2.10004 −0.0903712
\(541\) 10.1682 0.437166 0.218583 0.975818i \(-0.429857\pi\)
0.218583 + 0.975818i \(0.429857\pi\)
\(542\) −23.2791 −0.999921
\(543\) −50.2230 −2.15527
\(544\) −9.77475 −0.419089
\(545\) −54.9727 −2.35477
\(546\) 12.7510 0.545691
\(547\) −21.0758 −0.901136 −0.450568 0.892742i \(-0.648778\pi\)
−0.450568 + 0.892742i \(0.648778\pi\)
\(548\) 47.9803 2.04962
\(549\) 8.30544 0.354468
\(550\) 18.3860 0.783981
\(551\) −16.5403 −0.704642
\(552\) −200.566 −8.53666
\(553\) 16.1208 0.685525
\(554\) 84.5023 3.59016
\(555\) 1.38096 0.0586187
\(556\) −88.8478 −3.76799
\(557\) −10.5110 −0.445365 −0.222682 0.974891i \(-0.571481\pi\)
−0.222682 + 0.974891i \(0.571481\pi\)
\(558\) −54.2150 −2.29510
\(559\) −2.18171 −0.0922764
\(560\) 88.6236 3.74503
\(561\) 1.72287 0.0727396
\(562\) −0.296844 −0.0125216
\(563\) 31.6828 1.33527 0.667636 0.744488i \(-0.267306\pi\)
0.667636 + 0.744488i \(0.267306\pi\)
\(564\) 62.5511 2.63388
\(565\) 43.5077 1.83038
\(566\) 7.44822 0.313072
\(567\) −16.2096 −0.680741
\(568\) −34.2568 −1.43738
\(569\) −42.4671 −1.78032 −0.890158 0.455653i \(-0.849406\pi\)
−0.890158 + 0.455653i \(0.849406\pi\)
\(570\) 152.913 6.40480
\(571\) −10.2811 −0.430253 −0.215126 0.976586i \(-0.569016\pi\)
−0.215126 + 0.976586i \(0.569016\pi\)
\(572\) −10.4466 −0.436792
\(573\) −60.6445 −2.53346
\(574\) 19.7369 0.823804
\(575\) −29.8778 −1.24599
\(576\) 113.059 4.71081
\(577\) −19.6631 −0.818585 −0.409293 0.912403i \(-0.634224\pi\)
−0.409293 + 0.912403i \(0.634224\pi\)
\(578\) 46.5396 1.93579
\(579\) 11.6768 0.485270
\(580\) −35.8670 −1.48930
\(581\) 6.08548 0.252468
\(582\) 45.8937 1.90236
\(583\) 12.5376 0.519256
\(584\) 89.3840 3.69874
\(585\) 9.20018 0.380381
\(586\) 52.8939 2.18503
\(587\) −8.83037 −0.364468 −0.182234 0.983255i \(-0.558333\pi\)
−0.182234 + 0.983255i \(0.558333\pi\)
\(588\) 50.3915 2.07811
\(589\) 49.1647 2.02580
\(590\) −39.6690 −1.63315
\(591\) −27.3337 −1.12436
\(592\) −3.12973 −0.128631
\(593\) 29.6565 1.21784 0.608922 0.793230i \(-0.291602\pi\)
0.608922 + 0.793230i \(0.291602\pi\)
\(594\) −0.634491 −0.0260335
\(595\) 2.08526 0.0854871
\(596\) 76.8621 3.14840
\(597\) −29.1448 −1.19282
\(598\) 23.0088 0.940899
\(599\) −38.4774 −1.57214 −0.786071 0.618136i \(-0.787888\pi\)
−0.786071 + 0.618136i \(0.787888\pi\)
\(600\) 90.5060 3.69489
\(601\) −9.23740 −0.376801 −0.188401 0.982092i \(-0.560330\pi\)
−0.188401 + 0.982092i \(0.560330\pi\)
\(602\) 10.7884 0.439702
\(603\) 3.76948 0.153505
\(604\) 67.0816 2.72951
\(605\) −22.7133 −0.923425
\(606\) 120.822 4.90806
\(607\) 23.9098 0.970469 0.485234 0.874384i \(-0.338734\pi\)
0.485234 + 0.874384i \(0.338734\pi\)
\(608\) −193.391 −7.84306
\(609\) 9.75902 0.395455
\(610\) −22.1364 −0.896276
\(611\) −4.62573 −0.187137
\(612\) 6.63413 0.268169
\(613\) 3.55509 0.143589 0.0717944 0.997419i \(-0.477127\pi\)
0.0717944 + 0.997419i \(0.477127\pi\)
\(614\) 12.9343 0.521986
\(615\) 28.2411 1.13879
\(616\) 33.2999 1.34169
\(617\) 16.5606 0.666705 0.333352 0.942802i \(-0.391820\pi\)
0.333352 + 0.942802i \(0.391820\pi\)
\(618\) 91.3136 3.67317
\(619\) −9.77712 −0.392976 −0.196488 0.980506i \(-0.562954\pi\)
−0.196488 + 0.980506i \(0.562954\pi\)
\(620\) 106.612 4.28163
\(621\) 1.03107 0.0413754
\(622\) −48.2919 −1.93633
\(623\) 17.7129 0.709650
\(624\) −41.3494 −1.65530
\(625\) −29.8768 −1.19507
\(626\) 58.3460 2.33198
\(627\) 34.0866 1.36129
\(628\) 75.1651 2.99941
\(629\) −0.0736403 −0.00293623
\(630\) −45.4942 −1.81253
\(631\) 36.1880 1.44062 0.720310 0.693652i \(-0.243999\pi\)
0.720310 + 0.693652i \(0.243999\pi\)
\(632\) −88.1180 −3.50514
\(633\) −18.0719 −0.718294
\(634\) −37.5307 −1.49054
\(635\) 34.1258 1.35424
\(636\) 95.7407 3.79637
\(637\) −3.72652 −0.147650
\(638\) −10.8366 −0.429026
\(639\) 10.4328 0.412714
\(640\) −152.307 −6.02046
\(641\) −3.00417 −0.118658 −0.0593288 0.998238i \(-0.518896\pi\)
−0.0593288 + 0.998238i \(0.518896\pi\)
\(642\) 87.6193 3.45806
\(643\) 42.9281 1.69292 0.846459 0.532453i \(-0.178730\pi\)
0.846459 + 0.532453i \(0.178730\pi\)
\(644\) −83.9451 −3.30790
\(645\) 15.4368 0.607825
\(646\) −8.15411 −0.320819
\(647\) −27.3258 −1.07429 −0.537144 0.843491i \(-0.680497\pi\)
−0.537144 + 0.843491i \(0.680497\pi\)
\(648\) 88.6037 3.48068
\(649\) −8.84285 −0.347112
\(650\) −10.3828 −0.407246
\(651\) −29.0079 −1.13691
\(652\) −71.4023 −2.79633
\(653\) 2.76399 0.108163 0.0540817 0.998537i \(-0.482777\pi\)
0.0540817 + 0.998537i \(0.482777\pi\)
\(654\) −126.831 −4.95950
\(655\) −57.0946 −2.23087
\(656\) −64.0038 −2.49893
\(657\) −27.2216 −1.06202
\(658\) 22.8739 0.891718
\(659\) 18.7322 0.729705 0.364852 0.931065i \(-0.381119\pi\)
0.364852 + 0.931065i \(0.381119\pi\)
\(660\) 73.9154 2.87715
\(661\) −17.7576 −0.690689 −0.345344 0.938476i \(-0.612238\pi\)
−0.345344 + 0.938476i \(0.612238\pi\)
\(662\) −23.6989 −0.921083
\(663\) −0.972923 −0.0377852
\(664\) −33.2639 −1.29089
\(665\) 41.2563 1.59985
\(666\) 1.60662 0.0622552
\(667\) 17.6099 0.681857
\(668\) −34.4281 −1.33206
\(669\) 4.32212 0.167103
\(670\) −10.0467 −0.388139
\(671\) −4.93455 −0.190496
\(672\) 114.104 4.40164
\(673\) −51.7364 −1.99429 −0.997145 0.0755122i \(-0.975941\pi\)
−0.997145 + 0.0755122i \(0.975941\pi\)
\(674\) 0.384411 0.0148070
\(675\) −0.465272 −0.0179083
\(676\) −67.2637 −2.58707
\(677\) 4.51667 0.173590 0.0867949 0.996226i \(-0.472338\pi\)
0.0867949 + 0.996226i \(0.472338\pi\)
\(678\) 100.380 3.85505
\(679\) 12.3823 0.475188
\(680\) −11.3982 −0.437102
\(681\) 8.61822 0.330251
\(682\) 32.2110 1.23342
\(683\) −26.7038 −1.02179 −0.510896 0.859642i \(-0.670686\pi\)
−0.510896 + 0.859642i \(0.670686\pi\)
\(684\) 131.255 5.01865
\(685\) 25.1056 0.959236
\(686\) 53.8665 2.05663
\(687\) 13.3305 0.508591
\(688\) −34.9850 −1.33379
\(689\) −7.08015 −0.269732
\(690\) −162.800 −6.19771
\(691\) 31.3020 1.19078 0.595392 0.803435i \(-0.296997\pi\)
0.595392 + 0.803435i \(0.296997\pi\)
\(692\) 75.3804 2.86553
\(693\) −10.1414 −0.385239
\(694\) −45.3621 −1.72192
\(695\) −46.4895 −1.76345
\(696\) −53.3439 −2.02199
\(697\) −1.50597 −0.0570425
\(698\) 33.8993 1.28311
\(699\) 8.17506 0.309209
\(700\) 37.8804 1.43175
\(701\) 3.47270 0.131162 0.0655811 0.997847i \(-0.479110\pi\)
0.0655811 + 0.997847i \(0.479110\pi\)
\(702\) 0.358304 0.0135233
\(703\) −1.45696 −0.0549503
\(704\) −67.1725 −2.53166
\(705\) 32.7297 1.23267
\(706\) 70.7118 2.66127
\(707\) 32.5982 1.22598
\(708\) −67.5263 −2.53779
\(709\) 43.1219 1.61948 0.809739 0.586790i \(-0.199609\pi\)
0.809739 + 0.586790i \(0.199609\pi\)
\(710\) −27.8064 −1.04355
\(711\) 26.8360 1.00643
\(712\) −96.8204 −3.62850
\(713\) −52.3439 −1.96029
\(714\) 4.81103 0.180048
\(715\) −5.46614 −0.204422
\(716\) −83.3755 −3.11589
\(717\) −28.7872 −1.07508
\(718\) −64.8699 −2.42092
\(719\) −44.7395 −1.66850 −0.834251 0.551386i \(-0.814099\pi\)
−0.834251 + 0.551386i \(0.814099\pi\)
\(720\) 147.531 5.49814
\(721\) 24.6367 0.917520
\(722\) −108.852 −4.05105
\(723\) −51.3763 −1.91070
\(724\) 114.900 4.27021
\(725\) −7.94650 −0.295126
\(726\) −52.4033 −1.94487
\(727\) 37.4335 1.38833 0.694167 0.719814i \(-0.255773\pi\)
0.694167 + 0.719814i \(0.255773\pi\)
\(728\) −18.8048 −0.696953
\(729\) −27.9191 −1.03404
\(730\) 72.5534 2.68532
\(731\) −0.823174 −0.0304462
\(732\) −37.6815 −1.39275
\(733\) 15.3900 0.568443 0.284221 0.958759i \(-0.408265\pi\)
0.284221 + 0.958759i \(0.408265\pi\)
\(734\) 12.9849 0.479280
\(735\) 26.3673 0.972571
\(736\) 205.897 7.58946
\(737\) −2.23958 −0.0824958
\(738\) 32.8558 1.20944
\(739\) 5.01382 0.184437 0.0922183 0.995739i \(-0.470604\pi\)
0.0922183 + 0.995739i \(0.470604\pi\)
\(740\) −3.15936 −0.116140
\(741\) −19.2491 −0.707133
\(742\) 35.0108 1.28529
\(743\) 45.9362 1.68524 0.842618 0.538512i \(-0.181013\pi\)
0.842618 + 0.538512i \(0.181013\pi\)
\(744\) 158.560 5.81310
\(745\) 40.2180 1.47347
\(746\) 13.5632 0.496586
\(747\) 10.1304 0.370652
\(748\) −3.94156 −0.144118
\(749\) 23.6400 0.863787
\(750\) −26.5730 −0.970307
\(751\) 1.73530 0.0633219 0.0316610 0.999499i \(-0.489920\pi\)
0.0316610 + 0.999499i \(0.489920\pi\)
\(752\) −74.1765 −2.70494
\(753\) −23.3810 −0.852051
\(754\) 6.11956 0.222861
\(755\) 35.1003 1.27743
\(756\) −1.30723 −0.0475437
\(757\) 12.8895 0.468477 0.234238 0.972179i \(-0.424740\pi\)
0.234238 + 0.972179i \(0.424740\pi\)
\(758\) −37.0532 −1.34583
\(759\) −36.2908 −1.31727
\(760\) −225.512 −8.18017
\(761\) 20.2540 0.734209 0.367104 0.930180i \(-0.380349\pi\)
0.367104 + 0.930180i \(0.380349\pi\)
\(762\) 78.7339 2.85223
\(763\) −34.2195 −1.23883
\(764\) 138.742 5.01951
\(765\) 3.47129 0.125505
\(766\) 20.7597 0.750078
\(767\) 4.99365 0.180310
\(768\) −169.111 −6.10228
\(769\) −6.01347 −0.216851 −0.108426 0.994105i \(-0.534581\pi\)
−0.108426 + 0.994105i \(0.534581\pi\)
\(770\) 27.0297 0.974082
\(771\) 18.6531 0.671776
\(772\) −26.7140 −0.961458
\(773\) 19.5548 0.703337 0.351668 0.936125i \(-0.385615\pi\)
0.351668 + 0.936125i \(0.385615\pi\)
\(774\) 17.9593 0.645533
\(775\) 23.6203 0.848466
\(776\) −67.6829 −2.42968
\(777\) 0.859626 0.0308389
\(778\) 64.9341 2.32800
\(779\) −29.7952 −1.06752
\(780\) −41.7409 −1.49456
\(781\) −6.19847 −0.221799
\(782\) 8.68138 0.310446
\(783\) 0.274230 0.00980017
\(784\) −59.7570 −2.13418
\(785\) 39.3300 1.40375
\(786\) −131.727 −4.69854
\(787\) 54.7724 1.95243 0.976213 0.216814i \(-0.0695664\pi\)
0.976213 + 0.216814i \(0.0695664\pi\)
\(788\) 62.5337 2.22767
\(789\) −46.8850 −1.66915
\(790\) −71.5257 −2.54477
\(791\) 27.0828 0.962952
\(792\) 55.4339 1.96976
\(793\) 2.78659 0.0989548
\(794\) −62.4363 −2.21578
\(795\) 50.0961 1.77673
\(796\) 66.6772 2.36331
\(797\) −5.68298 −0.201302 −0.100651 0.994922i \(-0.532092\pi\)
−0.100651 + 0.994922i \(0.532092\pi\)
\(798\) 95.1853 3.36952
\(799\) −1.74532 −0.0617451
\(800\) −92.9114 −3.28491
\(801\) 29.4863 1.04185
\(802\) −8.64522 −0.305273
\(803\) 16.1733 0.570743
\(804\) −17.1020 −0.603140
\(805\) −43.9241 −1.54812
\(806\) −18.1899 −0.640712
\(807\) 32.3567 1.13901
\(808\) −178.185 −6.26854
\(809\) −44.0649 −1.54924 −0.774620 0.632427i \(-0.782059\pi\)
−0.774620 + 0.632427i \(0.782059\pi\)
\(810\) 71.9200 2.52701
\(811\) −48.6506 −1.70835 −0.854176 0.519984i \(-0.825938\pi\)
−0.854176 + 0.519984i \(0.825938\pi\)
\(812\) −22.3266 −0.783510
\(813\) −20.7345 −0.727192
\(814\) −0.954547 −0.0334569
\(815\) −37.3611 −1.30870
\(816\) −15.6014 −0.546159
\(817\) −16.2863 −0.569787
\(818\) 27.5299 0.962560
\(819\) 5.72695 0.200116
\(820\) −64.6097 −2.25627
\(821\) 33.1946 1.15850 0.579250 0.815150i \(-0.303345\pi\)
0.579250 + 0.815150i \(0.303345\pi\)
\(822\) 57.9228 2.02029
\(823\) 36.3943 1.26863 0.634313 0.773077i \(-0.281283\pi\)
0.634313 + 0.773077i \(0.281283\pi\)
\(824\) −134.667 −4.69135
\(825\) 16.3763 0.570149
\(826\) −24.6933 −0.859189
\(827\) 49.2420 1.71231 0.856156 0.516717i \(-0.172846\pi\)
0.856156 + 0.516717i \(0.172846\pi\)
\(828\) −139.742 −4.85638
\(829\) −31.6484 −1.09919 −0.549597 0.835430i \(-0.685219\pi\)
−0.549597 + 0.835430i \(0.685219\pi\)
\(830\) −27.0005 −0.937200
\(831\) 75.2657 2.61094
\(832\) 37.9330 1.31509
\(833\) −1.40604 −0.0487165
\(834\) −107.259 −3.71408
\(835\) −18.0144 −0.623415
\(836\) −77.9830 −2.69710
\(837\) −0.815125 −0.0281748
\(838\) 94.0628 3.24935
\(839\) −38.1706 −1.31780 −0.658898 0.752232i \(-0.728977\pi\)
−0.658898 + 0.752232i \(0.728977\pi\)
\(840\) 133.055 4.59083
\(841\) −24.3164 −0.838495
\(842\) −73.3387 −2.52742
\(843\) −0.264397 −0.00910633
\(844\) 41.3448 1.42315
\(845\) −35.1956 −1.21077
\(846\) 38.0779 1.30914
\(847\) −14.1386 −0.485808
\(848\) −113.535 −3.89879
\(849\) 6.63409 0.227681
\(850\) −3.91749 −0.134369
\(851\) 1.55117 0.0531735
\(852\) −47.3331 −1.62161
\(853\) 3.86153 0.132216 0.0661081 0.997812i \(-0.478942\pi\)
0.0661081 + 0.997812i \(0.478942\pi\)
\(854\) −13.7795 −0.471525
\(855\) 68.6789 2.34877
\(856\) −129.219 −4.41661
\(857\) −0.0133006 −0.000454339 0 −0.000227170 1.00000i \(-0.500072\pi\)
−0.000227170 1.00000i \(0.500072\pi\)
\(858\) −12.6113 −0.430543
\(859\) −4.54946 −0.155226 −0.0776128 0.996984i \(-0.524730\pi\)
−0.0776128 + 0.996984i \(0.524730\pi\)
\(860\) −35.3163 −1.20427
\(861\) 17.5796 0.599111
\(862\) −112.292 −3.82469
\(863\) −10.9433 −0.372515 −0.186257 0.982501i \(-0.559636\pi\)
−0.186257 + 0.982501i \(0.559636\pi\)
\(864\) 3.20633 0.109081
\(865\) 39.4427 1.34109
\(866\) 96.3381 3.27370
\(867\) 41.4526 1.40780
\(868\) 66.3639 2.25254
\(869\) −15.9442 −0.540870
\(870\) −43.2995 −1.46799
\(871\) 1.26471 0.0428532
\(872\) 187.048 6.33424
\(873\) 20.6126 0.697631
\(874\) 171.759 5.80985
\(875\) −7.16948 −0.242373
\(876\) 123.503 4.17279
\(877\) 9.41049 0.317770 0.158885 0.987297i \(-0.449210\pi\)
0.158885 + 0.987297i \(0.449210\pi\)
\(878\) −47.5471 −1.60464
\(879\) 47.1123 1.58906
\(880\) −87.6529 −2.95478
\(881\) 7.89653 0.266041 0.133020 0.991113i \(-0.457532\pi\)
0.133020 + 0.991113i \(0.457532\pi\)
\(882\) 30.6758 1.03291
\(883\) −49.4232 −1.66322 −0.831611 0.555359i \(-0.812581\pi\)
−0.831611 + 0.555359i \(0.812581\pi\)
\(884\) 2.22584 0.0748632
\(885\) −35.3330 −1.18771
\(886\) −8.96428 −0.301161
\(887\) 19.4916 0.654464 0.327232 0.944944i \(-0.393884\pi\)
0.327232 + 0.944944i \(0.393884\pi\)
\(888\) −4.69881 −0.157682
\(889\) 21.2427 0.712457
\(890\) −78.5895 −2.63433
\(891\) 16.0321 0.537095
\(892\) −9.88810 −0.331078
\(893\) −34.5309 −1.15553
\(894\) 92.7896 3.10335
\(895\) −43.6261 −1.45826
\(896\) −94.8083 −3.16732
\(897\) 20.4938 0.684268
\(898\) −46.4349 −1.54955
\(899\) −13.9217 −0.464315
\(900\) 63.0590 2.10197
\(901\) −2.67139 −0.0889970
\(902\) −19.5208 −0.649970
\(903\) 9.60916 0.319773
\(904\) −148.037 −4.92365
\(905\) 60.1210 1.99849
\(906\) 80.9824 2.69046
\(907\) −23.5915 −0.783343 −0.391672 0.920105i \(-0.628103\pi\)
−0.391672 + 0.920105i \(0.628103\pi\)
\(908\) −19.7167 −0.654321
\(909\) 54.2657 1.79988
\(910\) −15.2640 −0.505995
\(911\) 31.6918 1.04999 0.524997 0.851104i \(-0.324066\pi\)
0.524997 + 0.851104i \(0.324066\pi\)
\(912\) −308.671 −10.2211
\(913\) −6.01882 −0.199194
\(914\) −35.0611 −1.15972
\(915\) −19.7168 −0.651816
\(916\) −30.4974 −1.00766
\(917\) −35.5404 −1.17365
\(918\) 0.135191 0.00446196
\(919\) 1.57127 0.0518316 0.0259158 0.999664i \(-0.491750\pi\)
0.0259158 + 0.999664i \(0.491750\pi\)
\(920\) 240.094 7.91567
\(921\) 11.5205 0.379614
\(922\) 60.9817 2.00832
\(923\) 3.50035 0.115215
\(924\) 46.0110 1.51365
\(925\) −0.699969 −0.0230149
\(926\) 56.6568 1.86186
\(927\) 41.0124 1.34702
\(928\) 54.7616 1.79764
\(929\) −0.256912 −0.00842900 −0.00421450 0.999991i \(-0.501342\pi\)
−0.00421450 + 0.999991i \(0.501342\pi\)
\(930\) 128.704 4.22037
\(931\) −27.8183 −0.911707
\(932\) −18.7028 −0.612631
\(933\) −43.0133 −1.40819
\(934\) −62.4482 −2.04337
\(935\) −2.06241 −0.0674482
\(936\) −31.3041 −1.02321
\(937\) 38.3170 1.25176 0.625881 0.779919i \(-0.284740\pi\)
0.625881 + 0.779919i \(0.284740\pi\)
\(938\) −6.25391 −0.204198
\(939\) 51.9685 1.69593
\(940\) −74.8788 −2.44228
\(941\) 41.8092 1.36294 0.681471 0.731845i \(-0.261340\pi\)
0.681471 + 0.731845i \(0.261340\pi\)
\(942\) 90.7409 2.95650
\(943\) 31.7219 1.03301
\(944\) 80.0763 2.60626
\(945\) −0.684008 −0.0222508
\(946\) −10.6702 −0.346919
\(947\) −30.1945 −0.981191 −0.490595 0.871388i \(-0.663221\pi\)
−0.490595 + 0.871388i \(0.663221\pi\)
\(948\) −121.754 −3.95439
\(949\) −9.13323 −0.296477
\(950\) −77.5068 −2.51465
\(951\) −33.4284 −1.08399
\(952\) −7.09520 −0.229957
\(953\) −0.688318 −0.0222968 −0.0111484 0.999938i \(-0.503549\pi\)
−0.0111484 + 0.999938i \(0.503549\pi\)
\(954\) 58.2820 1.88695
\(955\) 72.5965 2.34917
\(956\) 65.8590 2.13003
\(957\) −9.65212 −0.312009
\(958\) −72.6529 −2.34731
\(959\) 15.6278 0.504648
\(960\) −268.398 −8.66251
\(961\) 10.3811 0.334876
\(962\) 0.539043 0.0173795
\(963\) 39.3532 1.26814
\(964\) 117.538 3.78565
\(965\) −13.9781 −0.449969
\(966\) −101.340 −3.26057
\(967\) −36.3829 −1.17000 −0.584998 0.811035i \(-0.698905\pi\)
−0.584998 + 0.811035i \(0.698905\pi\)
\(968\) 77.2831 2.48397
\(969\) −7.26282 −0.233315
\(970\) −54.9385 −1.76397
\(971\) −19.8341 −0.636506 −0.318253 0.948006i \(-0.603096\pi\)
−0.318253 + 0.948006i \(0.603096\pi\)
\(972\) 124.565 3.99541
\(973\) −28.9389 −0.927737
\(974\) −63.8726 −2.04661
\(975\) −9.24787 −0.296169
\(976\) 44.6847 1.43032
\(977\) 25.0471 0.801329 0.400665 0.916225i \(-0.368779\pi\)
0.400665 + 0.916225i \(0.368779\pi\)
\(978\) −86.1984 −2.75632
\(979\) −17.5188 −0.559904
\(980\) −60.3228 −1.92694
\(981\) −56.9648 −1.81875
\(982\) 58.9757 1.88199
\(983\) 7.17206 0.228753 0.114377 0.993437i \(-0.463513\pi\)
0.114377 + 0.993437i \(0.463513\pi\)
\(984\) −96.0920 −3.06330
\(985\) 32.7207 1.04257
\(986\) 2.30896 0.0735321
\(987\) 20.3737 0.648501
\(988\) 44.0379 1.40103
\(989\) 17.3395 0.551363
\(990\) 44.9959 1.43006
\(991\) 14.5637 0.462630 0.231315 0.972879i \(-0.425697\pi\)
0.231315 + 0.972879i \(0.425697\pi\)
\(992\) −162.774 −5.16809
\(993\) −21.1085 −0.669857
\(994\) −17.3090 −0.549007
\(995\) 34.8887 1.10605
\(996\) −45.9613 −1.45634
\(997\) 6.17579 0.195589 0.0977946 0.995207i \(-0.468821\pi\)
0.0977946 + 0.995207i \(0.468821\pi\)
\(998\) −55.2386 −1.74855
\(999\) 0.0241556 0.000764249 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 6029.2.a.b.1.4 268
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6029.2.a.b.1.4 268 1.1 even 1 trivial