Properties

Label 6026.2.a.g.1.17
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
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] = [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: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.44805 q^{3} +1.00000 q^{4} +3.26245 q^{5} +1.44805 q^{6} -3.72778 q^{7} +1.00000 q^{8} -0.903151 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.44805 q^{3} +1.00000 q^{4} +3.26245 q^{5} +1.44805 q^{6} -3.72778 q^{7} +1.00000 q^{8} -0.903151 q^{9} +3.26245 q^{10} -4.09702 q^{11} +1.44805 q^{12} -2.98138 q^{13} -3.72778 q^{14} +4.72419 q^{15} +1.00000 q^{16} -1.49368 q^{17} -0.903151 q^{18} -1.05316 q^{19} +3.26245 q^{20} -5.39802 q^{21} -4.09702 q^{22} -1.00000 q^{23} +1.44805 q^{24} +5.64360 q^{25} -2.98138 q^{26} -5.65196 q^{27} -3.72778 q^{28} -4.90034 q^{29} +4.72419 q^{30} +6.60489 q^{31} +1.00000 q^{32} -5.93269 q^{33} -1.49368 q^{34} -12.1617 q^{35} -0.903151 q^{36} -8.08086 q^{37} -1.05316 q^{38} -4.31719 q^{39} +3.26245 q^{40} +2.30886 q^{41} -5.39802 q^{42} -6.47442 q^{43} -4.09702 q^{44} -2.94649 q^{45} -1.00000 q^{46} -8.29223 q^{47} +1.44805 q^{48} +6.89637 q^{49} +5.64360 q^{50} -2.16293 q^{51} -2.98138 q^{52} +0.309487 q^{53} -5.65196 q^{54} -13.3663 q^{55} -3.72778 q^{56} -1.52503 q^{57} -4.90034 q^{58} +12.9613 q^{59} +4.72419 q^{60} -13.5111 q^{61} +6.60489 q^{62} +3.36675 q^{63} +1.00000 q^{64} -9.72662 q^{65} -5.93269 q^{66} +13.0224 q^{67} -1.49368 q^{68} -1.44805 q^{69} -12.1617 q^{70} +7.82972 q^{71} -0.903151 q^{72} +4.03401 q^{73} -8.08086 q^{74} +8.17221 q^{75} -1.05316 q^{76} +15.2728 q^{77} -4.31719 q^{78} -2.73118 q^{79} +3.26245 q^{80} -5.47486 q^{81} +2.30886 q^{82} -0.859840 q^{83} -5.39802 q^{84} -4.87307 q^{85} -6.47442 q^{86} -7.09594 q^{87} -4.09702 q^{88} +13.3306 q^{89} -2.94649 q^{90} +11.1139 q^{91} -1.00000 q^{92} +9.56421 q^{93} -8.29223 q^{94} -3.43588 q^{95} +1.44805 q^{96} +2.53866 q^{97} +6.89637 q^{98} +3.70023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 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
\(3\) 1.44805 0.836032 0.418016 0.908440i \(-0.362726\pi\)
0.418016 + 0.908440i \(0.362726\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.26245 1.45901 0.729507 0.683974i \(-0.239750\pi\)
0.729507 + 0.683974i \(0.239750\pi\)
\(6\) 1.44805 0.591164
\(7\) −3.72778 −1.40897 −0.704485 0.709719i \(-0.748822\pi\)
−0.704485 + 0.709719i \(0.748822\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.903151 −0.301050
\(10\) 3.26245 1.03168
\(11\) −4.09702 −1.23530 −0.617649 0.786454i \(-0.711915\pi\)
−0.617649 + 0.786454i \(0.711915\pi\)
\(12\) 1.44805 0.418016
\(13\) −2.98138 −0.826886 −0.413443 0.910530i \(-0.635674\pi\)
−0.413443 + 0.910530i \(0.635674\pi\)
\(14\) −3.72778 −0.996292
\(15\) 4.72419 1.21978
\(16\) 1.00000 0.250000
\(17\) −1.49368 −0.362272 −0.181136 0.983458i \(-0.557977\pi\)
−0.181136 + 0.983458i \(0.557977\pi\)
\(18\) −0.903151 −0.212875
\(19\) −1.05316 −0.241611 −0.120806 0.992676i \(-0.538548\pi\)
−0.120806 + 0.992676i \(0.538548\pi\)
\(20\) 3.26245 0.729507
\(21\) −5.39802 −1.17794
\(22\) −4.09702 −0.873488
\(23\) −1.00000 −0.208514
\(24\) 1.44805 0.295582
\(25\) 5.64360 1.12872
\(26\) −2.98138 −0.584697
\(27\) −5.65196 −1.08772
\(28\) −3.72778 −0.704485
\(29\) −4.90034 −0.909971 −0.454985 0.890499i \(-0.650356\pi\)
−0.454985 + 0.890499i \(0.650356\pi\)
\(30\) 4.72419 0.862516
\(31\) 6.60489 1.18627 0.593136 0.805102i \(-0.297889\pi\)
0.593136 + 0.805102i \(0.297889\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.93269 −1.03275
\(34\) −1.49368 −0.256165
\(35\) −12.1617 −2.05571
\(36\) −0.903151 −0.150525
\(37\) −8.08086 −1.32849 −0.664243 0.747517i \(-0.731246\pi\)
−0.664243 + 0.747517i \(0.731246\pi\)
\(38\) −1.05316 −0.170845
\(39\) −4.31719 −0.691304
\(40\) 3.26245 0.515839
\(41\) 2.30886 0.360583 0.180291 0.983613i \(-0.442296\pi\)
0.180291 + 0.983613i \(0.442296\pi\)
\(42\) −5.39802 −0.832932
\(43\) −6.47442 −0.987340 −0.493670 0.869649i \(-0.664345\pi\)
−0.493670 + 0.869649i \(0.664345\pi\)
\(44\) −4.09702 −0.617649
\(45\) −2.94649 −0.439236
\(46\) −1.00000 −0.147442
\(47\) −8.29223 −1.20955 −0.604773 0.796398i \(-0.706736\pi\)
−0.604773 + 0.796398i \(0.706736\pi\)
\(48\) 1.44805 0.209008
\(49\) 6.89637 0.985196
\(50\) 5.64360 0.798125
\(51\) −2.16293 −0.302871
\(52\) −2.98138 −0.413443
\(53\) 0.309487 0.0425113 0.0212557 0.999774i \(-0.493234\pi\)
0.0212557 + 0.999774i \(0.493234\pi\)
\(54\) −5.65196 −0.769134
\(55\) −13.3663 −1.80232
\(56\) −3.72778 −0.498146
\(57\) −1.52503 −0.201995
\(58\) −4.90034 −0.643446
\(59\) 12.9613 1.68742 0.843712 0.536796i \(-0.180366\pi\)
0.843712 + 0.536796i \(0.180366\pi\)
\(60\) 4.72419 0.609891
\(61\) −13.5111 −1.72991 −0.864957 0.501847i \(-0.832654\pi\)
−0.864957 + 0.501847i \(0.832654\pi\)
\(62\) 6.60489 0.838822
\(63\) 3.36675 0.424171
\(64\) 1.00000 0.125000
\(65\) −9.72662 −1.20644
\(66\) −5.93269 −0.730264
\(67\) 13.0224 1.59094 0.795471 0.605992i \(-0.207224\pi\)
0.795471 + 0.605992i \(0.207224\pi\)
\(68\) −1.49368 −0.181136
\(69\) −1.44805 −0.174325
\(70\) −12.1617 −1.45360
\(71\) 7.82972 0.929217 0.464609 0.885516i \(-0.346195\pi\)
0.464609 + 0.885516i \(0.346195\pi\)
\(72\) −0.903151 −0.106437
\(73\) 4.03401 0.472146 0.236073 0.971735i \(-0.424140\pi\)
0.236073 + 0.971735i \(0.424140\pi\)
\(74\) −8.08086 −0.939381
\(75\) 8.17221 0.943646
\(76\) −1.05316 −0.120806
\(77\) 15.2728 1.74050
\(78\) −4.31719 −0.488825
\(79\) −2.73118 −0.307282 −0.153641 0.988127i \(-0.549100\pi\)
−0.153641 + 0.988127i \(0.549100\pi\)
\(80\) 3.26245 0.364753
\(81\) −5.47486 −0.608318
\(82\) 2.30886 0.254970
\(83\) −0.859840 −0.0943797 −0.0471898 0.998886i \(-0.515027\pi\)
−0.0471898 + 0.998886i \(0.515027\pi\)
\(84\) −5.39802 −0.588972
\(85\) −4.87307 −0.528559
\(86\) −6.47442 −0.698155
\(87\) −7.09594 −0.760765
\(88\) −4.09702 −0.436744
\(89\) 13.3306 1.41304 0.706522 0.707691i \(-0.250263\pi\)
0.706522 + 0.707691i \(0.250263\pi\)
\(90\) −2.94649 −0.310587
\(91\) 11.1139 1.16506
\(92\) −1.00000 −0.104257
\(93\) 9.56421 0.991762
\(94\) −8.29223 −0.855278
\(95\) −3.43588 −0.352514
\(96\) 1.44805 0.147791
\(97\) 2.53866 0.257762 0.128881 0.991660i \(-0.458861\pi\)
0.128881 + 0.991660i \(0.458861\pi\)
\(98\) 6.89637 0.696639
\(99\) 3.70023 0.371887
\(100\) 5.64360 0.564360
\(101\) −17.8685 −1.77798 −0.888990 0.457928i \(-0.848592\pi\)
−0.888990 + 0.457928i \(0.848592\pi\)
\(102\) −2.16293 −0.214162
\(103\) 0.452882 0.0446238 0.0223119 0.999751i \(-0.492897\pi\)
0.0223119 + 0.999751i \(0.492897\pi\)
\(104\) −2.98138 −0.292348
\(105\) −17.6108 −1.71864
\(106\) 0.309487 0.0300600
\(107\) −9.35237 −0.904128 −0.452064 0.891986i \(-0.649312\pi\)
−0.452064 + 0.891986i \(0.649312\pi\)
\(108\) −5.65196 −0.543860
\(109\) −9.43508 −0.903716 −0.451858 0.892090i \(-0.649239\pi\)
−0.451858 + 0.892090i \(0.649239\pi\)
\(110\) −13.3663 −1.27443
\(111\) −11.7015 −1.11066
\(112\) −3.72778 −0.352242
\(113\) −13.2693 −1.24827 −0.624135 0.781316i \(-0.714549\pi\)
−0.624135 + 0.781316i \(0.714549\pi\)
\(114\) −1.52503 −0.142832
\(115\) −3.26245 −0.304225
\(116\) −4.90034 −0.454985
\(117\) 2.69264 0.248934
\(118\) 12.9613 1.19319
\(119\) 5.56813 0.510430
\(120\) 4.72419 0.431258
\(121\) 5.78558 0.525962
\(122\) −13.5111 −1.22323
\(123\) 3.34334 0.301459
\(124\) 6.60489 0.593136
\(125\) 2.09971 0.187804
\(126\) 3.36675 0.299934
\(127\) 2.35002 0.208531 0.104265 0.994550i \(-0.466751\pi\)
0.104265 + 0.994550i \(0.466751\pi\)
\(128\) 1.00000 0.0883883
\(129\) −9.37529 −0.825448
\(130\) −9.72662 −0.853081
\(131\) 1.00000 0.0873704
\(132\) −5.93269 −0.516374
\(133\) 3.92595 0.340423
\(134\) 13.0224 1.12497
\(135\) −18.4392 −1.58700
\(136\) −1.49368 −0.128082
\(137\) 4.91743 0.420125 0.210062 0.977688i \(-0.432633\pi\)
0.210062 + 0.977688i \(0.432633\pi\)
\(138\) −1.44805 −0.123266
\(139\) −15.7808 −1.33851 −0.669255 0.743032i \(-0.733387\pi\)
−0.669255 + 0.743032i \(0.733387\pi\)
\(140\) −12.1617 −1.02785
\(141\) −12.0076 −1.01122
\(142\) 7.82972 0.657056
\(143\) 12.2148 1.02145
\(144\) −0.903151 −0.0752626
\(145\) −15.9871 −1.32766
\(146\) 4.03401 0.333857
\(147\) 9.98629 0.823656
\(148\) −8.08086 −0.664243
\(149\) −18.4294 −1.50979 −0.754896 0.655845i \(-0.772313\pi\)
−0.754896 + 0.655845i \(0.772313\pi\)
\(150\) 8.17221 0.667258
\(151\) 1.03384 0.0841327 0.0420663 0.999115i \(-0.486606\pi\)
0.0420663 + 0.999115i \(0.486606\pi\)
\(152\) −1.05316 −0.0854224
\(153\) 1.34902 0.109062
\(154\) 15.2728 1.23072
\(155\) 21.5481 1.73079
\(156\) −4.31719 −0.345652
\(157\) 4.32678 0.345314 0.172657 0.984982i \(-0.444765\pi\)
0.172657 + 0.984982i \(0.444765\pi\)
\(158\) −2.73118 −0.217281
\(159\) 0.448153 0.0355408
\(160\) 3.26245 0.257920
\(161\) 3.72778 0.293791
\(162\) −5.47486 −0.430146
\(163\) −13.6321 −1.06775 −0.533876 0.845563i \(-0.679265\pi\)
−0.533876 + 0.845563i \(0.679265\pi\)
\(164\) 2.30886 0.180291
\(165\) −19.3551 −1.50679
\(166\) −0.859840 −0.0667365
\(167\) 1.13278 0.0876575 0.0438288 0.999039i \(-0.486044\pi\)
0.0438288 + 0.999039i \(0.486044\pi\)
\(168\) −5.39802 −0.416466
\(169\) −4.11137 −0.316259
\(170\) −4.87307 −0.373748
\(171\) 0.951161 0.0727371
\(172\) −6.47442 −0.493670
\(173\) −9.88200 −0.751314 −0.375657 0.926759i \(-0.622583\pi\)
−0.375657 + 0.926759i \(0.622583\pi\)
\(174\) −7.09594 −0.537942
\(175\) −21.0381 −1.59033
\(176\) −4.09702 −0.308825
\(177\) 18.7687 1.41074
\(178\) 13.3306 0.999173
\(179\) 21.2799 1.59054 0.795269 0.606257i \(-0.207330\pi\)
0.795269 + 0.606257i \(0.207330\pi\)
\(180\) −2.94649 −0.219618
\(181\) 22.6914 1.68664 0.843319 0.537413i \(-0.180598\pi\)
0.843319 + 0.537413i \(0.180598\pi\)
\(182\) 11.1139 0.823820
\(183\) −19.5647 −1.44626
\(184\) −1.00000 −0.0737210
\(185\) −26.3634 −1.93828
\(186\) 9.56421 0.701282
\(187\) 6.11965 0.447513
\(188\) −8.29223 −0.604773
\(189\) 21.0693 1.53256
\(190\) −3.43588 −0.249265
\(191\) 3.53360 0.255682 0.127841 0.991795i \(-0.459195\pi\)
0.127841 + 0.991795i \(0.459195\pi\)
\(192\) 1.44805 0.104504
\(193\) 11.5607 0.832157 0.416078 0.909329i \(-0.363404\pi\)
0.416078 + 0.909329i \(0.363404\pi\)
\(194\) 2.53866 0.182266
\(195\) −14.0846 −1.00862
\(196\) 6.89637 0.492598
\(197\) 6.21116 0.442527 0.221263 0.975214i \(-0.428982\pi\)
0.221263 + 0.975214i \(0.428982\pi\)
\(198\) 3.70023 0.262964
\(199\) 1.35355 0.0959504 0.0479752 0.998849i \(-0.484723\pi\)
0.0479752 + 0.998849i \(0.484723\pi\)
\(200\) 5.64360 0.399063
\(201\) 18.8571 1.33008
\(202\) −17.8685 −1.25722
\(203\) 18.2674 1.28212
\(204\) −2.16293 −0.151435
\(205\) 7.53253 0.526095
\(206\) 0.452882 0.0315538
\(207\) 0.903151 0.0627733
\(208\) −2.98138 −0.206722
\(209\) 4.31481 0.298462
\(210\) −17.6108 −1.21526
\(211\) 5.48824 0.377826 0.188913 0.981994i \(-0.439504\pi\)
0.188913 + 0.981994i \(0.439504\pi\)
\(212\) 0.309487 0.0212557
\(213\) 11.3378 0.776855
\(214\) −9.35237 −0.639315
\(215\) −21.1225 −1.44054
\(216\) −5.65196 −0.384567
\(217\) −24.6216 −1.67142
\(218\) −9.43508 −0.639024
\(219\) 5.84146 0.394729
\(220\) −13.3663 −0.901158
\(221\) 4.45324 0.299557
\(222\) −11.7015 −0.785353
\(223\) 10.7643 0.720832 0.360416 0.932792i \(-0.382635\pi\)
0.360416 + 0.932792i \(0.382635\pi\)
\(224\) −3.72778 −0.249073
\(225\) −5.09702 −0.339801
\(226\) −13.2693 −0.882660
\(227\) 3.87295 0.257056 0.128528 0.991706i \(-0.458975\pi\)
0.128528 + 0.991706i \(0.458975\pi\)
\(228\) −1.52503 −0.100997
\(229\) −4.62184 −0.305420 −0.152710 0.988271i \(-0.548800\pi\)
−0.152710 + 0.988271i \(0.548800\pi\)
\(230\) −3.26245 −0.215120
\(231\) 22.1158 1.45511
\(232\) −4.90034 −0.321723
\(233\) 11.5937 0.759527 0.379764 0.925084i \(-0.376005\pi\)
0.379764 + 0.925084i \(0.376005\pi\)
\(234\) 2.69264 0.176023
\(235\) −27.0530 −1.76474
\(236\) 12.9613 0.843712
\(237\) −3.95488 −0.256897
\(238\) 5.56813 0.360928
\(239\) 11.6851 0.755844 0.377922 0.925837i \(-0.376639\pi\)
0.377922 + 0.925837i \(0.376639\pi\)
\(240\) 4.72419 0.304945
\(241\) −25.4567 −1.63981 −0.819904 0.572501i \(-0.805973\pi\)
−0.819904 + 0.572501i \(0.805973\pi\)
\(242\) 5.78558 0.371911
\(243\) 9.02800 0.579146
\(244\) −13.5111 −0.864957
\(245\) 22.4991 1.43741
\(246\) 3.34334 0.213163
\(247\) 3.13987 0.199785
\(248\) 6.60489 0.419411
\(249\) −1.24509 −0.0789044
\(250\) 2.09971 0.132797
\(251\) 7.69696 0.485828 0.242914 0.970048i \(-0.421897\pi\)
0.242914 + 0.970048i \(0.421897\pi\)
\(252\) 3.36675 0.212085
\(253\) 4.09702 0.257577
\(254\) 2.35002 0.147453
\(255\) −7.05645 −0.441892
\(256\) 1.00000 0.0625000
\(257\) 11.6785 0.728483 0.364241 0.931305i \(-0.381328\pi\)
0.364241 + 0.931305i \(0.381328\pi\)
\(258\) −9.37529 −0.583680
\(259\) 30.1237 1.87180
\(260\) −9.72662 −0.603219
\(261\) 4.42575 0.273947
\(262\) 1.00000 0.0617802
\(263\) 6.70714 0.413580 0.206790 0.978385i \(-0.433698\pi\)
0.206790 + 0.978385i \(0.433698\pi\)
\(264\) −5.93269 −0.365132
\(265\) 1.00969 0.0620246
\(266\) 3.92595 0.240715
\(267\) 19.3034 1.18135
\(268\) 13.0224 0.795471
\(269\) −10.4258 −0.635674 −0.317837 0.948145i \(-0.602956\pi\)
−0.317837 + 0.948145i \(0.602956\pi\)
\(270\) −18.4392 −1.12218
\(271\) −6.60454 −0.401197 −0.200599 0.979674i \(-0.564289\pi\)
−0.200599 + 0.979674i \(0.564289\pi\)
\(272\) −1.49368 −0.0905679
\(273\) 16.0935 0.974026
\(274\) 4.91743 0.297073
\(275\) −23.1219 −1.39431
\(276\) −1.44805 −0.0871624
\(277\) 31.1450 1.87132 0.935662 0.352898i \(-0.114804\pi\)
0.935662 + 0.352898i \(0.114804\pi\)
\(278\) −15.7808 −0.946470
\(279\) −5.96521 −0.357128
\(280\) −12.1617 −0.726802
\(281\) −6.42679 −0.383390 −0.191695 0.981455i \(-0.561398\pi\)
−0.191695 + 0.981455i \(0.561398\pi\)
\(282\) −12.0076 −0.715040
\(283\) 24.5134 1.45717 0.728585 0.684955i \(-0.240178\pi\)
0.728585 + 0.684955i \(0.240178\pi\)
\(284\) 7.82972 0.464609
\(285\) −4.97532 −0.294713
\(286\) 12.2148 0.722275
\(287\) −8.60692 −0.508050
\(288\) −0.903151 −0.0532187
\(289\) −14.7689 −0.868759
\(290\) −15.9871 −0.938797
\(291\) 3.67611 0.215498
\(292\) 4.03401 0.236073
\(293\) 24.0566 1.40540 0.702701 0.711485i \(-0.251977\pi\)
0.702701 + 0.711485i \(0.251977\pi\)
\(294\) 9.98629 0.582413
\(295\) 42.2858 2.46197
\(296\) −8.08086 −0.469691
\(297\) 23.1562 1.34366
\(298\) −18.4294 −1.06758
\(299\) 2.98138 0.172418
\(300\) 8.17221 0.471823
\(301\) 24.1353 1.39113
\(302\) 1.03384 0.0594908
\(303\) −25.8744 −1.48645
\(304\) −1.05316 −0.0604028
\(305\) −44.0792 −2.52397
\(306\) 1.34902 0.0771185
\(307\) 14.4246 0.823255 0.411628 0.911352i \(-0.364960\pi\)
0.411628 + 0.911352i \(0.364960\pi\)
\(308\) 15.2728 0.870249
\(309\) 0.655796 0.0373069
\(310\) 21.5481 1.22385
\(311\) −29.8190 −1.69088 −0.845441 0.534069i \(-0.820662\pi\)
−0.845441 + 0.534069i \(0.820662\pi\)
\(312\) −4.31719 −0.244413
\(313\) −16.6481 −0.941006 −0.470503 0.882398i \(-0.655928\pi\)
−0.470503 + 0.882398i \(0.655928\pi\)
\(314\) 4.32678 0.244174
\(315\) 10.9839 0.618871
\(316\) −2.73118 −0.153641
\(317\) 28.1380 1.58039 0.790195 0.612856i \(-0.209979\pi\)
0.790195 + 0.612856i \(0.209979\pi\)
\(318\) 0.448153 0.0251312
\(319\) 20.0768 1.12409
\(320\) 3.26245 0.182377
\(321\) −13.5427 −0.755880
\(322\) 3.72778 0.207741
\(323\) 1.57309 0.0875288
\(324\) −5.47486 −0.304159
\(325\) −16.8257 −0.933323
\(326\) −13.6321 −0.755014
\(327\) −13.6625 −0.755536
\(328\) 2.30886 0.127485
\(329\) 30.9116 1.70421
\(330\) −19.3551 −1.06546
\(331\) −30.9825 −1.70295 −0.851477 0.524392i \(-0.824293\pi\)
−0.851477 + 0.524392i \(0.824293\pi\)
\(332\) −0.859840 −0.0471898
\(333\) 7.29824 0.399941
\(334\) 1.13278 0.0619832
\(335\) 42.4850 2.32121
\(336\) −5.39802 −0.294486
\(337\) −20.9581 −1.14166 −0.570830 0.821068i \(-0.693379\pi\)
−0.570830 + 0.821068i \(0.693379\pi\)
\(338\) −4.11137 −0.223629
\(339\) −19.2146 −1.04359
\(340\) −4.87307 −0.264279
\(341\) −27.0604 −1.46540
\(342\) 0.951161 0.0514329
\(343\) 0.386296 0.0208580
\(344\) −6.47442 −0.349078
\(345\) −4.72419 −0.254342
\(346\) −9.88200 −0.531260
\(347\) 10.7389 0.576493 0.288246 0.957556i \(-0.406928\pi\)
0.288246 + 0.957556i \(0.406928\pi\)
\(348\) −7.09594 −0.380382
\(349\) −24.0172 −1.28561 −0.642805 0.766030i \(-0.722230\pi\)
−0.642805 + 0.766030i \(0.722230\pi\)
\(350\) −21.0381 −1.12453
\(351\) 16.8506 0.899421
\(352\) −4.09702 −0.218372
\(353\) −24.8423 −1.32222 −0.661112 0.750287i \(-0.729915\pi\)
−0.661112 + 0.750287i \(0.729915\pi\)
\(354\) 18.7687 0.997544
\(355\) 25.5441 1.35574
\(356\) 13.3306 0.706522
\(357\) 8.06293 0.426736
\(358\) 21.2799 1.12468
\(359\) −32.2827 −1.70382 −0.851908 0.523692i \(-0.824554\pi\)
−0.851908 + 0.523692i \(0.824554\pi\)
\(360\) −2.94649 −0.155294
\(361\) −17.8909 −0.941624
\(362\) 22.6914 1.19263
\(363\) 8.37781 0.439721
\(364\) 11.1139 0.582529
\(365\) 13.1608 0.688867
\(366\) −19.5647 −1.02266
\(367\) 24.4870 1.27821 0.639106 0.769119i \(-0.279305\pi\)
0.639106 + 0.769119i \(0.279305\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −2.08525 −0.108554
\(370\) −26.3634 −1.37057
\(371\) −1.15370 −0.0598972
\(372\) 9.56421 0.495881
\(373\) 12.3106 0.637417 0.318709 0.947853i \(-0.396751\pi\)
0.318709 + 0.947853i \(0.396751\pi\)
\(374\) 6.11965 0.316440
\(375\) 3.04048 0.157010
\(376\) −8.29223 −0.427639
\(377\) 14.6098 0.752442
\(378\) 21.0693 1.08369
\(379\) 19.3124 0.992012 0.496006 0.868319i \(-0.334799\pi\)
0.496006 + 0.868319i \(0.334799\pi\)
\(380\) −3.43588 −0.176257
\(381\) 3.40295 0.174338
\(382\) 3.53360 0.180795
\(383\) −26.5607 −1.35719 −0.678594 0.734514i \(-0.737410\pi\)
−0.678594 + 0.734514i \(0.737410\pi\)
\(384\) 1.44805 0.0738955
\(385\) 49.8268 2.53941
\(386\) 11.5607 0.588424
\(387\) 5.84738 0.297239
\(388\) 2.53866 0.128881
\(389\) −9.58462 −0.485960 −0.242980 0.970031i \(-0.578125\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(390\) −14.0846 −0.713203
\(391\) 1.49368 0.0755388
\(392\) 6.89637 0.348319
\(393\) 1.44805 0.0730445
\(394\) 6.21116 0.312914
\(395\) −8.91034 −0.448328
\(396\) 3.70023 0.185943
\(397\) 5.00689 0.251289 0.125644 0.992075i \(-0.459900\pi\)
0.125644 + 0.992075i \(0.459900\pi\)
\(398\) 1.35355 0.0678472
\(399\) 5.68497 0.284604
\(400\) 5.64360 0.282180
\(401\) −14.9221 −0.745175 −0.372587 0.927997i \(-0.621529\pi\)
−0.372587 + 0.927997i \(0.621529\pi\)
\(402\) 18.8571 0.940507
\(403\) −19.6917 −0.980913
\(404\) −17.8685 −0.888990
\(405\) −17.8615 −0.887544
\(406\) 18.2674 0.906597
\(407\) 33.1075 1.64108
\(408\) −2.16293 −0.107081
\(409\) 30.3856 1.50247 0.751235 0.660034i \(-0.229458\pi\)
0.751235 + 0.660034i \(0.229458\pi\)
\(410\) 7.53253 0.372005
\(411\) 7.12069 0.351238
\(412\) 0.452882 0.0223119
\(413\) −48.3171 −2.37753
\(414\) 0.903151 0.0443875
\(415\) −2.80519 −0.137701
\(416\) −2.98138 −0.146174
\(417\) −22.8514 −1.11904
\(418\) 4.31481 0.211044
\(419\) −5.78674 −0.282701 −0.141350 0.989960i \(-0.545144\pi\)
−0.141350 + 0.989960i \(0.545144\pi\)
\(420\) −17.6108 −0.859318
\(421\) −9.77900 −0.476599 −0.238300 0.971192i \(-0.576590\pi\)
−0.238300 + 0.971192i \(0.576590\pi\)
\(422\) 5.48824 0.267164
\(423\) 7.48914 0.364134
\(424\) 0.309487 0.0150300
\(425\) −8.42975 −0.408903
\(426\) 11.3378 0.549320
\(427\) 50.3663 2.43740
\(428\) −9.35237 −0.452064
\(429\) 17.6876 0.853966
\(430\) −21.1225 −1.01862
\(431\) 16.1958 0.780125 0.390063 0.920788i \(-0.372453\pi\)
0.390063 + 0.920788i \(0.372453\pi\)
\(432\) −5.65196 −0.271930
\(433\) 28.6150 1.37515 0.687575 0.726113i \(-0.258675\pi\)
0.687575 + 0.726113i \(0.258675\pi\)
\(434\) −24.6216 −1.18187
\(435\) −23.1502 −1.10997
\(436\) −9.43508 −0.451858
\(437\) 1.05316 0.0503794
\(438\) 5.84146 0.279116
\(439\) 7.14980 0.341241 0.170621 0.985337i \(-0.445423\pi\)
0.170621 + 0.985337i \(0.445423\pi\)
\(440\) −13.3663 −0.637215
\(441\) −6.22847 −0.296594
\(442\) 4.45324 0.211819
\(443\) −41.1251 −1.95391 −0.976956 0.213440i \(-0.931533\pi\)
−0.976956 + 0.213440i \(0.931533\pi\)
\(444\) −11.7015 −0.555328
\(445\) 43.4906 2.06165
\(446\) 10.7643 0.509705
\(447\) −26.6866 −1.26223
\(448\) −3.72778 −0.176121
\(449\) −10.1368 −0.478385 −0.239192 0.970972i \(-0.576883\pi\)
−0.239192 + 0.970972i \(0.576883\pi\)
\(450\) −5.09702 −0.240276
\(451\) −9.45943 −0.445427
\(452\) −13.2693 −0.624135
\(453\) 1.49705 0.0703376
\(454\) 3.87295 0.181766
\(455\) 36.2587 1.69984
\(456\) −1.52503 −0.0714159
\(457\) −27.1345 −1.26930 −0.634650 0.772800i \(-0.718856\pi\)
−0.634650 + 0.772800i \(0.718856\pi\)
\(458\) −4.62184 −0.215965
\(459\) 8.44224 0.394050
\(460\) −3.26245 −0.152113
\(461\) 23.7116 1.10436 0.552180 0.833725i \(-0.313796\pi\)
0.552180 + 0.833725i \(0.313796\pi\)
\(462\) 22.1158 1.02892
\(463\) 9.48950 0.441015 0.220507 0.975385i \(-0.429229\pi\)
0.220507 + 0.975385i \(0.429229\pi\)
\(464\) −4.90034 −0.227493
\(465\) 31.2028 1.44699
\(466\) 11.5937 0.537067
\(467\) −4.43197 −0.205087 −0.102544 0.994729i \(-0.532698\pi\)
−0.102544 + 0.994729i \(0.532698\pi\)
\(468\) 2.69264 0.124467
\(469\) −48.5448 −2.24159
\(470\) −27.0530 −1.24786
\(471\) 6.26539 0.288694
\(472\) 12.9613 0.596594
\(473\) 26.5259 1.21966
\(474\) −3.95488 −0.181654
\(475\) −5.94360 −0.272711
\(476\) 5.56813 0.255215
\(477\) −0.279514 −0.0127980
\(478\) 11.6851 0.534462
\(479\) 11.3773 0.519844 0.259922 0.965630i \(-0.416303\pi\)
0.259922 + 0.965630i \(0.416303\pi\)
\(480\) 4.72419 0.215629
\(481\) 24.0921 1.09851
\(482\) −25.4567 −1.15952
\(483\) 5.39802 0.245618
\(484\) 5.78558 0.262981
\(485\) 8.28227 0.376079
\(486\) 9.02800 0.409518
\(487\) 29.6295 1.34264 0.671320 0.741168i \(-0.265728\pi\)
0.671320 + 0.741168i \(0.265728\pi\)
\(488\) −13.5111 −0.611617
\(489\) −19.7400 −0.892675
\(490\) 22.4991 1.01641
\(491\) 24.8058 1.11947 0.559735 0.828671i \(-0.310903\pi\)
0.559735 + 0.828671i \(0.310903\pi\)
\(492\) 3.34334 0.150729
\(493\) 7.31956 0.329656
\(494\) 3.13987 0.141269
\(495\) 12.0718 0.542588
\(496\) 6.60489 0.296568
\(497\) −29.1875 −1.30924
\(498\) −1.24509 −0.0557939
\(499\) 9.82637 0.439889 0.219944 0.975512i \(-0.429412\pi\)
0.219944 + 0.975512i \(0.429412\pi\)
\(500\) 2.09971 0.0939019
\(501\) 1.64033 0.0732845
\(502\) 7.69696 0.343532
\(503\) −28.3634 −1.26466 −0.632330 0.774699i \(-0.717901\pi\)
−0.632330 + 0.774699i \(0.717901\pi\)
\(504\) 3.36675 0.149967
\(505\) −58.2950 −2.59410
\(506\) 4.09702 0.182135
\(507\) −5.95346 −0.264403
\(508\) 2.35002 0.104265
\(509\) −16.1797 −0.717154 −0.358577 0.933500i \(-0.616738\pi\)
−0.358577 + 0.933500i \(0.616738\pi\)
\(510\) −7.05645 −0.312465
\(511\) −15.0379 −0.665239
\(512\) 1.00000 0.0441942
\(513\) 5.95241 0.262805
\(514\) 11.6785 0.515115
\(515\) 1.47751 0.0651067
\(516\) −9.37529 −0.412724
\(517\) 33.9734 1.49415
\(518\) 30.1237 1.32356
\(519\) −14.3096 −0.628123
\(520\) −9.72662 −0.426540
\(521\) −38.6356 −1.69265 −0.846327 0.532663i \(-0.821191\pi\)
−0.846327 + 0.532663i \(0.821191\pi\)
\(522\) 4.42575 0.193710
\(523\) 3.34181 0.146127 0.0730636 0.997327i \(-0.476722\pi\)
0.0730636 + 0.997327i \(0.476722\pi\)
\(524\) 1.00000 0.0436852
\(525\) −30.4642 −1.32957
\(526\) 6.70714 0.292445
\(527\) −9.86561 −0.429753
\(528\) −5.93269 −0.258187
\(529\) 1.00000 0.0434783
\(530\) 1.00969 0.0438580
\(531\) −11.7061 −0.507999
\(532\) 3.92595 0.170211
\(533\) −6.88358 −0.298161
\(534\) 19.3034 0.835341
\(535\) −30.5117 −1.31913
\(536\) 13.0224 0.562483
\(537\) 30.8144 1.32974
\(538\) −10.4258 −0.449489
\(539\) −28.2546 −1.21701
\(540\) −18.4392 −0.793499
\(541\) −8.49344 −0.365162 −0.182581 0.983191i \(-0.558445\pi\)
−0.182581 + 0.983191i \(0.558445\pi\)
\(542\) −6.60454 −0.283689
\(543\) 32.8583 1.41008
\(544\) −1.49368 −0.0640412
\(545\) −30.7815 −1.31853
\(546\) 16.0935 0.688740
\(547\) 16.8274 0.719489 0.359745 0.933051i \(-0.382864\pi\)
0.359745 + 0.933051i \(0.382864\pi\)
\(548\) 4.91743 0.210062
\(549\) 12.2025 0.520791
\(550\) −23.1219 −0.985923
\(551\) 5.16084 0.219859
\(552\) −1.44805 −0.0616331
\(553\) 10.1812 0.432951
\(554\) 31.1450 1.32323
\(555\) −38.1756 −1.62046
\(556\) −15.7808 −0.669255
\(557\) −6.60948 −0.280053 −0.140026 0.990148i \(-0.544719\pi\)
−0.140026 + 0.990148i \(0.544719\pi\)
\(558\) −5.96521 −0.252528
\(559\) 19.3027 0.816418
\(560\) −12.1617 −0.513926
\(561\) 8.86156 0.374135
\(562\) −6.42679 −0.271098
\(563\) 3.80207 0.160238 0.0801191 0.996785i \(-0.474470\pi\)
0.0801191 + 0.996785i \(0.474470\pi\)
\(564\) −12.0076 −0.505610
\(565\) −43.2904 −1.82124
\(566\) 24.5134 1.03038
\(567\) 20.4091 0.857102
\(568\) 7.82972 0.328528
\(569\) 1.92744 0.0808026 0.0404013 0.999184i \(-0.487136\pi\)
0.0404013 + 0.999184i \(0.487136\pi\)
\(570\) −4.97532 −0.208393
\(571\) 4.28832 0.179461 0.0897303 0.995966i \(-0.471399\pi\)
0.0897303 + 0.995966i \(0.471399\pi\)
\(572\) 12.2148 0.510726
\(573\) 5.11682 0.213758
\(574\) −8.60692 −0.359246
\(575\) −5.64360 −0.235354
\(576\) −0.903151 −0.0376313
\(577\) −30.6857 −1.27746 −0.638732 0.769429i \(-0.720541\pi\)
−0.638732 + 0.769429i \(0.720541\pi\)
\(578\) −14.7689 −0.614306
\(579\) 16.7405 0.695710
\(580\) −15.9871 −0.663830
\(581\) 3.20530 0.132978
\(582\) 3.67611 0.152380
\(583\) −1.26797 −0.0525141
\(584\) 4.03401 0.166929
\(585\) 8.78460 0.363199
\(586\) 24.0566 0.993769
\(587\) 40.7625 1.68245 0.841224 0.540687i \(-0.181835\pi\)
0.841224 + 0.540687i \(0.181835\pi\)
\(588\) 9.98629 0.411828
\(589\) −6.95599 −0.286617
\(590\) 42.2858 1.74088
\(591\) 8.99407 0.369966
\(592\) −8.08086 −0.332121
\(593\) −34.7883 −1.42858 −0.714291 0.699848i \(-0.753251\pi\)
−0.714291 + 0.699848i \(0.753251\pi\)
\(594\) 23.1562 0.950110
\(595\) 18.1658 0.744724
\(596\) −18.4294 −0.754896
\(597\) 1.96000 0.0802176
\(598\) 2.98138 0.121918
\(599\) −37.6513 −1.53839 −0.769195 0.639014i \(-0.779342\pi\)
−0.769195 + 0.639014i \(0.779342\pi\)
\(600\) 8.17221 0.333629
\(601\) −42.4996 −1.73360 −0.866798 0.498660i \(-0.833826\pi\)
−0.866798 + 0.498660i \(0.833826\pi\)
\(602\) 24.1353 0.983680
\(603\) −11.7612 −0.478954
\(604\) 1.03384 0.0420663
\(605\) 18.8752 0.767385
\(606\) −25.8744 −1.05108
\(607\) −7.17688 −0.291301 −0.145650 0.989336i \(-0.546527\pi\)
−0.145650 + 0.989336i \(0.546527\pi\)
\(608\) −1.05316 −0.0427112
\(609\) 26.4521 1.07189
\(610\) −44.0792 −1.78471
\(611\) 24.7223 1.00016
\(612\) 1.34902 0.0545310
\(613\) 40.2014 1.62372 0.811860 0.583852i \(-0.198455\pi\)
0.811860 + 0.583852i \(0.198455\pi\)
\(614\) 14.4246 0.582129
\(615\) 10.9075 0.439832
\(616\) 15.2728 0.615359
\(617\) 12.0681 0.485843 0.242922 0.970046i \(-0.421894\pi\)
0.242922 + 0.970046i \(0.421894\pi\)
\(618\) 0.655796 0.0263800
\(619\) 44.9348 1.80608 0.903041 0.429554i \(-0.141329\pi\)
0.903041 + 0.429554i \(0.141329\pi\)
\(620\) 21.5481 0.865394
\(621\) 5.65196 0.226805
\(622\) −29.8190 −1.19563
\(623\) −49.6937 −1.99094
\(624\) −4.31719 −0.172826
\(625\) −21.3678 −0.854712
\(626\) −16.6481 −0.665392
\(627\) 6.24806 0.249524
\(628\) 4.32678 0.172657
\(629\) 12.0703 0.481273
\(630\) 10.9839 0.437608
\(631\) 10.8493 0.431904 0.215952 0.976404i \(-0.430715\pi\)
0.215952 + 0.976404i \(0.430715\pi\)
\(632\) −2.73118 −0.108640
\(633\) 7.94725 0.315875
\(634\) 28.1380 1.11750
\(635\) 7.66684 0.304249
\(636\) 0.448153 0.0177704
\(637\) −20.5607 −0.814645
\(638\) 20.0768 0.794848
\(639\) −7.07142 −0.279741
\(640\) 3.26245 0.128960
\(641\) −34.3263 −1.35581 −0.677903 0.735151i \(-0.737111\pi\)
−0.677903 + 0.735151i \(0.737111\pi\)
\(642\) −13.5427 −0.534488
\(643\) −0.468965 −0.0184942 −0.00924710 0.999957i \(-0.502943\pi\)
−0.00924710 + 0.999957i \(0.502943\pi\)
\(644\) 3.72778 0.146895
\(645\) −30.5864 −1.20434
\(646\) 1.57309 0.0618922
\(647\) −49.1637 −1.93283 −0.966413 0.256995i \(-0.917267\pi\)
−0.966413 + 0.256995i \(0.917267\pi\)
\(648\) −5.47486 −0.215073
\(649\) −53.1029 −2.08447
\(650\) −16.8257 −0.659959
\(651\) −35.6533 −1.39736
\(652\) −13.6321 −0.533876
\(653\) 15.8344 0.619647 0.309823 0.950794i \(-0.399730\pi\)
0.309823 + 0.950794i \(0.399730\pi\)
\(654\) −13.6625 −0.534245
\(655\) 3.26245 0.127475
\(656\) 2.30886 0.0901457
\(657\) −3.64332 −0.142140
\(658\) 30.9116 1.20506
\(659\) −46.1821 −1.79900 −0.899499 0.436922i \(-0.856069\pi\)
−0.899499 + 0.436922i \(0.856069\pi\)
\(660\) −19.3551 −0.753397
\(661\) −10.7136 −0.416712 −0.208356 0.978053i \(-0.566811\pi\)
−0.208356 + 0.978053i \(0.566811\pi\)
\(662\) −30.9825 −1.20417
\(663\) 6.44852 0.250440
\(664\) −0.859840 −0.0333683
\(665\) 12.8082 0.496681
\(666\) 7.29824 0.282801
\(667\) 4.90034 0.189742
\(668\) 1.13278 0.0438288
\(669\) 15.5873 0.602638
\(670\) 42.4850 1.64134
\(671\) 55.3551 2.13696
\(672\) −5.39802 −0.208233
\(673\) −31.5207 −1.21503 −0.607517 0.794306i \(-0.707834\pi\)
−0.607517 + 0.794306i \(0.707834\pi\)
\(674\) −20.9581 −0.807276
\(675\) −31.8974 −1.22773
\(676\) −4.11137 −0.158129
\(677\) −22.0298 −0.846672 −0.423336 0.905973i \(-0.639141\pi\)
−0.423336 + 0.905973i \(0.639141\pi\)
\(678\) −19.2146 −0.737932
\(679\) −9.46359 −0.363179
\(680\) −4.87307 −0.186874
\(681\) 5.60822 0.214907
\(682\) −27.0604 −1.03619
\(683\) 19.4924 0.745855 0.372927 0.927861i \(-0.378354\pi\)
0.372927 + 0.927861i \(0.378354\pi\)
\(684\) 0.951161 0.0363685
\(685\) 16.0429 0.612967
\(686\) 0.386296 0.0147489
\(687\) −6.69266 −0.255341
\(688\) −6.47442 −0.246835
\(689\) −0.922699 −0.0351520
\(690\) −4.72419 −0.179847
\(691\) 27.8578 1.05976 0.529880 0.848073i \(-0.322237\pi\)
0.529880 + 0.848073i \(0.322237\pi\)
\(692\) −9.88200 −0.375657
\(693\) −13.7937 −0.523978
\(694\) 10.7389 0.407642
\(695\) −51.4842 −1.95291
\(696\) −7.09594 −0.268971
\(697\) −3.44870 −0.130629
\(698\) −24.0172 −0.909064
\(699\) 16.7882 0.634989
\(700\) −21.0381 −0.795166
\(701\) −0.0618821 −0.00233726 −0.00116863 0.999999i \(-0.500372\pi\)
−0.00116863 + 0.999999i \(0.500372\pi\)
\(702\) 16.8506 0.635986
\(703\) 8.51043 0.320977
\(704\) −4.09702 −0.154412
\(705\) −39.1741 −1.47538
\(706\) −24.8423 −0.934953
\(707\) 66.6098 2.50512
\(708\) 18.7687 0.705370
\(709\) 10.5171 0.394977 0.197488 0.980305i \(-0.436722\pi\)
0.197488 + 0.980305i \(0.436722\pi\)
\(710\) 25.5441 0.958653
\(711\) 2.46667 0.0925073
\(712\) 13.3306 0.499587
\(713\) −6.60489 −0.247355
\(714\) 8.06293 0.301748
\(715\) 39.8501 1.49031
\(716\) 21.2799 0.795269
\(717\) 16.9206 0.631910
\(718\) −32.2827 −1.20478
\(719\) 23.5496 0.878252 0.439126 0.898425i \(-0.355288\pi\)
0.439126 + 0.898425i \(0.355288\pi\)
\(720\) −2.94649 −0.109809
\(721\) −1.68825 −0.0628736
\(722\) −17.8909 −0.665829
\(723\) −36.8625 −1.37093
\(724\) 22.6914 0.843319
\(725\) −27.6556 −1.02710
\(726\) 8.37781 0.310930
\(727\) −27.8291 −1.03213 −0.516063 0.856551i \(-0.672603\pi\)
−0.516063 + 0.856551i \(0.672603\pi\)
\(728\) 11.1139 0.411910
\(729\) 29.4976 1.09250
\(730\) 13.1608 0.487102
\(731\) 9.67074 0.357685
\(732\) −19.5647 −0.723131
\(733\) −24.0836 −0.889549 −0.444774 0.895643i \(-0.646716\pi\)
−0.444774 + 0.895643i \(0.646716\pi\)
\(734\) 24.4870 0.903832
\(735\) 32.5798 1.20172
\(736\) −1.00000 −0.0368605
\(737\) −53.3531 −1.96529
\(738\) −2.08525 −0.0767590
\(739\) 1.37489 0.0505762 0.0252881 0.999680i \(-0.491950\pi\)
0.0252881 + 0.999680i \(0.491950\pi\)
\(740\) −26.3634 −0.969139
\(741\) 4.54668 0.167027
\(742\) −1.15370 −0.0423537
\(743\) 12.7805 0.468870 0.234435 0.972132i \(-0.424676\pi\)
0.234435 + 0.972132i \(0.424676\pi\)
\(744\) 9.56421 0.350641
\(745\) −60.1249 −2.20281
\(746\) 12.3106 0.450722
\(747\) 0.776565 0.0284130
\(748\) 6.11965 0.223757
\(749\) 34.8636 1.27389
\(750\) 3.04048 0.111023
\(751\) 21.2704 0.776168 0.388084 0.921624i \(-0.373137\pi\)
0.388084 + 0.921624i \(0.373137\pi\)
\(752\) −8.29223 −0.302387
\(753\) 11.1456 0.406168
\(754\) 14.6098 0.532057
\(755\) 3.37285 0.122751
\(756\) 21.0693 0.766282
\(757\) 50.6899 1.84236 0.921178 0.389141i \(-0.127228\pi\)
0.921178 + 0.389141i \(0.127228\pi\)
\(758\) 19.3124 0.701459
\(759\) 5.93269 0.215343
\(760\) −3.43588 −0.124632
\(761\) 23.0128 0.834214 0.417107 0.908857i \(-0.363044\pi\)
0.417107 + 0.908857i \(0.363044\pi\)
\(762\) 3.40295 0.123276
\(763\) 35.1719 1.27331
\(764\) 3.53360 0.127841
\(765\) 4.40112 0.159123
\(766\) −26.5607 −0.959677
\(767\) −38.6427 −1.39531
\(768\) 1.44805 0.0522520
\(769\) 19.8921 0.717327 0.358663 0.933467i \(-0.383233\pi\)
0.358663 + 0.933467i \(0.383233\pi\)
\(770\) 49.8268 1.79563
\(771\) 16.9110 0.609035
\(772\) 11.5607 0.416078
\(773\) −28.2713 −1.01685 −0.508423 0.861107i \(-0.669771\pi\)
−0.508423 + 0.861107i \(0.669771\pi\)
\(774\) 5.84738 0.210180
\(775\) 37.2753 1.33897
\(776\) 2.53866 0.0911328
\(777\) 43.6206 1.56488
\(778\) −9.58462 −0.343625
\(779\) −2.43159 −0.0871208
\(780\) −14.0846 −0.504311
\(781\) −32.0785 −1.14786
\(782\) 1.49368 0.0534140
\(783\) 27.6965 0.989793
\(784\) 6.89637 0.246299
\(785\) 14.1159 0.503818
\(786\) 1.44805 0.0516502
\(787\) −36.8594 −1.31389 −0.656947 0.753937i \(-0.728153\pi\)
−0.656947 + 0.753937i \(0.728153\pi\)
\(788\) 6.21116 0.221263
\(789\) 9.71227 0.345766
\(790\) −8.91034 −0.317016
\(791\) 49.4651 1.75878
\(792\) 3.70023 0.131482
\(793\) 40.2816 1.43044
\(794\) 5.00689 0.177688
\(795\) 1.46208 0.0518545
\(796\) 1.35355 0.0479752
\(797\) 2.54217 0.0900483 0.0450242 0.998986i \(-0.485664\pi\)
0.0450242 + 0.998986i \(0.485664\pi\)
\(798\) 5.68497 0.201246
\(799\) 12.3860 0.438184
\(800\) 5.64360 0.199531
\(801\) −12.0396 −0.425398
\(802\) −14.9221 −0.526918
\(803\) −16.5274 −0.583241
\(804\) 18.8571 0.665039
\(805\) 12.1617 0.428644
\(806\) −19.6917 −0.693610
\(807\) −15.0971 −0.531443
\(808\) −17.8685 −0.628611
\(809\) 29.3048 1.03030 0.515151 0.857099i \(-0.327736\pi\)
0.515151 + 0.857099i \(0.327736\pi\)
\(810\) −17.8615 −0.627589
\(811\) 40.2923 1.41485 0.707427 0.706786i \(-0.249856\pi\)
0.707427 + 0.706786i \(0.249856\pi\)
\(812\) 18.2674 0.641061
\(813\) −9.56370 −0.335414
\(814\) 33.1075 1.16042
\(815\) −44.4742 −1.55786
\(816\) −2.16293 −0.0757176
\(817\) 6.81859 0.238552
\(818\) 30.3856 1.06241
\(819\) −10.0376 −0.350741
\(820\) 7.53253 0.263047
\(821\) 2.95497 0.103129 0.0515646 0.998670i \(-0.483579\pi\)
0.0515646 + 0.998670i \(0.483579\pi\)
\(822\) 7.12069 0.248363
\(823\) 24.2496 0.845288 0.422644 0.906296i \(-0.361102\pi\)
0.422644 + 0.906296i \(0.361102\pi\)
\(824\) 0.452882 0.0157769
\(825\) −33.4817 −1.16568
\(826\) −48.3171 −1.68117
\(827\) 7.73882 0.269105 0.134553 0.990906i \(-0.457040\pi\)
0.134553 + 0.990906i \(0.457040\pi\)
\(828\) 0.903151 0.0313867
\(829\) −38.8842 −1.35050 −0.675252 0.737587i \(-0.735965\pi\)
−0.675252 + 0.737587i \(0.735965\pi\)
\(830\) −2.80519 −0.0973694
\(831\) 45.0996 1.56449
\(832\) −2.98138 −0.103361
\(833\) −10.3010 −0.356909
\(834\) −22.8514 −0.791279
\(835\) 3.69566 0.127893
\(836\) 4.31481 0.149231
\(837\) −37.3305 −1.29033
\(838\) −5.78674 −0.199900
\(839\) −18.4640 −0.637447 −0.318723 0.947848i \(-0.603254\pi\)
−0.318723 + 0.947848i \(0.603254\pi\)
\(840\) −17.6108 −0.607630
\(841\) −4.98664 −0.171953
\(842\) −9.77900 −0.337007
\(843\) −9.30632 −0.320527
\(844\) 5.48824 0.188913
\(845\) −13.4131 −0.461426
\(846\) 7.48914 0.257482
\(847\) −21.5674 −0.741064
\(848\) 0.309487 0.0106278
\(849\) 35.4966 1.21824
\(850\) −8.42975 −0.289138
\(851\) 8.08086 0.277008
\(852\) 11.3378 0.388428
\(853\) −46.8286 −1.60338 −0.801690 0.597740i \(-0.796066\pi\)
−0.801690 + 0.597740i \(0.796066\pi\)
\(854\) 50.3663 1.72350
\(855\) 3.10312 0.106124
\(856\) −9.35237 −0.319657
\(857\) 9.28335 0.317113 0.158557 0.987350i \(-0.449316\pi\)
0.158557 + 0.987350i \(0.449316\pi\)
\(858\) 17.6876 0.603845
\(859\) −16.0116 −0.546310 −0.273155 0.961970i \(-0.588067\pi\)
−0.273155 + 0.961970i \(0.588067\pi\)
\(860\) −21.1225 −0.720271
\(861\) −12.4632 −0.424746
\(862\) 16.1958 0.551632
\(863\) −29.3940 −1.00058 −0.500291 0.865857i \(-0.666774\pi\)
−0.500291 + 0.865857i \(0.666774\pi\)
\(864\) −5.65196 −0.192284
\(865\) −32.2396 −1.09618
\(866\) 28.6150 0.972378
\(867\) −21.3861 −0.726311
\(868\) −24.6216 −0.835711
\(869\) 11.1897 0.379584
\(870\) −23.1502 −0.784864
\(871\) −38.8248 −1.31553
\(872\) −9.43508 −0.319512
\(873\) −2.29280 −0.0775995
\(874\) 1.05316 0.0356236
\(875\) −7.82726 −0.264610
\(876\) 5.84146 0.197364
\(877\) −43.1526 −1.45716 −0.728579 0.684962i \(-0.759819\pi\)
−0.728579 + 0.684962i \(0.759819\pi\)
\(878\) 7.14980 0.241294
\(879\) 34.8352 1.17496
\(880\) −13.3663 −0.450579
\(881\) −23.2901 −0.784662 −0.392331 0.919824i \(-0.628331\pi\)
−0.392331 + 0.919824i \(0.628331\pi\)
\(882\) −6.22847 −0.209723
\(883\) −41.1780 −1.38575 −0.692875 0.721058i \(-0.743656\pi\)
−0.692875 + 0.721058i \(0.743656\pi\)
\(884\) 4.45324 0.149779
\(885\) 61.2319 2.05829
\(886\) −41.1251 −1.38162
\(887\) 1.71701 0.0576514 0.0288257 0.999584i \(-0.490823\pi\)
0.0288257 + 0.999584i \(0.490823\pi\)
\(888\) −11.7015 −0.392676
\(889\) −8.76037 −0.293814
\(890\) 43.4906 1.45781
\(891\) 22.4306 0.751455
\(892\) 10.7643 0.360416
\(893\) 8.73303 0.292240
\(894\) −26.6866 −0.892534
\(895\) 69.4248 2.32062
\(896\) −3.72778 −0.124537
\(897\) 4.31719 0.144147
\(898\) −10.1368 −0.338269
\(899\) −32.3662 −1.07947
\(900\) −5.09702 −0.169901
\(901\) −0.462276 −0.0154006
\(902\) −9.45943 −0.314965
\(903\) 34.9491 1.16303
\(904\) −13.2693 −0.441330
\(905\) 74.0296 2.46083
\(906\) 1.49705 0.0497362
\(907\) −45.4391 −1.50878 −0.754390 0.656426i \(-0.772067\pi\)
−0.754390 + 0.656426i \(0.772067\pi\)
\(908\) 3.87295 0.128528
\(909\) 16.1379 0.535261
\(910\) 36.2587 1.20196
\(911\) −10.0124 −0.331725 −0.165862 0.986149i \(-0.553041\pi\)
−0.165862 + 0.986149i \(0.553041\pi\)
\(912\) −1.52503 −0.0504986
\(913\) 3.52278 0.116587
\(914\) −27.1345 −0.897531
\(915\) −63.8289 −2.11012
\(916\) −4.62184 −0.152710
\(917\) −3.72778 −0.123102
\(918\) 8.44224 0.278635
\(919\) −41.9809 −1.38482 −0.692412 0.721503i \(-0.743452\pi\)
−0.692412 + 0.721503i \(0.743452\pi\)
\(920\) −3.26245 −0.107560
\(921\) 20.8875 0.688268
\(922\) 23.7116 0.780901
\(923\) −23.3434 −0.768357
\(924\) 22.1158 0.727556
\(925\) −45.6051 −1.49949
\(926\) 9.48950 0.311844
\(927\) −0.409021 −0.0134340
\(928\) −4.90034 −0.160862
\(929\) 28.0164 0.919188 0.459594 0.888129i \(-0.347995\pi\)
0.459594 + 0.888129i \(0.347995\pi\)
\(930\) 31.2028 1.02318
\(931\) −7.26297 −0.238034
\(932\) 11.5937 0.379764
\(933\) −43.1794 −1.41363
\(934\) −4.43197 −0.145019
\(935\) 19.9651 0.652928
\(936\) 2.69264 0.0880116
\(937\) 13.1822 0.430643 0.215321 0.976543i \(-0.430920\pi\)
0.215321 + 0.976543i \(0.430920\pi\)
\(938\) −48.5448 −1.58504
\(939\) −24.1073 −0.786711
\(940\) −27.0530 −0.882372
\(941\) −48.6416 −1.58567 −0.792835 0.609436i \(-0.791396\pi\)
−0.792835 + 0.609436i \(0.791396\pi\)
\(942\) 6.26539 0.204137
\(943\) −2.30886 −0.0751867
\(944\) 12.9613 0.421856
\(945\) 68.7375 2.23603
\(946\) 26.5259 0.862430
\(947\) 26.8422 0.872254 0.436127 0.899885i \(-0.356350\pi\)
0.436127 + 0.899885i \(0.356350\pi\)
\(948\) −3.95488 −0.128449
\(949\) −12.0269 −0.390411
\(950\) −5.94360 −0.192836
\(951\) 40.7453 1.32126
\(952\) 5.56813 0.180464
\(953\) −48.1239 −1.55889 −0.779443 0.626473i \(-0.784498\pi\)
−0.779443 + 0.626473i \(0.784498\pi\)
\(954\) −0.279514 −0.00904958
\(955\) 11.5282 0.373044
\(956\) 11.6851 0.377922
\(957\) 29.0722 0.939771
\(958\) 11.3773 0.367585
\(959\) −18.3311 −0.591943
\(960\) 4.72419 0.152473
\(961\) 12.6245 0.407243
\(962\) 24.0921 0.776762
\(963\) 8.44660 0.272188
\(964\) −25.4567 −0.819904
\(965\) 37.7162 1.21413
\(966\) 5.39802 0.173678
\(967\) 33.4321 1.07510 0.537552 0.843231i \(-0.319349\pi\)
0.537552 + 0.843231i \(0.319349\pi\)
\(968\) 5.78558 0.185956
\(969\) 2.27791 0.0731769
\(970\) 8.28227 0.265928
\(971\) −51.5788 −1.65524 −0.827622 0.561286i \(-0.810307\pi\)
−0.827622 + 0.561286i \(0.810307\pi\)
\(972\) 9.02800 0.289573
\(973\) 58.8275 1.88592
\(974\) 29.6295 0.949389
\(975\) −24.3645 −0.780288
\(976\) −13.5111 −0.432478
\(977\) 33.1159 1.05947 0.529735 0.848163i \(-0.322291\pi\)
0.529735 + 0.848163i \(0.322291\pi\)
\(978\) −19.7400 −0.631216
\(979\) −54.6159 −1.74553
\(980\) 22.4991 0.718707
\(981\) 8.52130 0.272064
\(982\) 24.8058 0.791585
\(983\) −35.9782 −1.14753 −0.573763 0.819022i \(-0.694517\pi\)
−0.573763 + 0.819022i \(0.694517\pi\)
\(984\) 3.34334 0.106582
\(985\) 20.2636 0.645652
\(986\) 7.31956 0.233102
\(987\) 44.7616 1.42478
\(988\) 3.13987 0.0998924
\(989\) 6.47442 0.205875
\(990\) 12.0718 0.383668
\(991\) −12.6716 −0.402526 −0.201263 0.979537i \(-0.564505\pi\)
−0.201263 + 0.979537i \(0.564505\pi\)
\(992\) 6.60489 0.209705
\(993\) −44.8643 −1.42372
\(994\) −29.1875 −0.925772
\(995\) 4.41588 0.139993
\(996\) −1.24509 −0.0394522
\(997\) 24.3353 0.770706 0.385353 0.922769i \(-0.374080\pi\)
0.385353 + 0.922769i \(0.374080\pi\)
\(998\) 9.82637 0.311048
\(999\) 45.6727 1.44502
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.g.1.17 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.g.1.17 21 1.1 even 1 trivial