Properties

Label 6018.2.a.x.1.2
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $10$
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] = [6018,2,Mod(1,6018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6018.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: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.78078\) of defining polynomial
Character \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.78078 q^{5} +1.00000 q^{6} +3.42043 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.78078 q^{5} +1.00000 q^{6} +3.42043 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.78078 q^{10} -6.40684 q^{11} -1.00000 q^{12} -1.09916 q^{13} -3.42043 q^{14} +2.78078 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +6.34964 q^{19} -2.78078 q^{20} -3.42043 q^{21} +6.40684 q^{22} -0.0945846 q^{23} +1.00000 q^{24} +2.73271 q^{25} +1.09916 q^{26} -1.00000 q^{27} +3.42043 q^{28} -3.02228 q^{29} -2.78078 q^{30} -2.51109 q^{31} -1.00000 q^{32} +6.40684 q^{33} -1.00000 q^{34} -9.51144 q^{35} +1.00000 q^{36} -4.03293 q^{37} -6.34964 q^{38} +1.09916 q^{39} +2.78078 q^{40} +3.94277 q^{41} +3.42043 q^{42} -4.15125 q^{43} -6.40684 q^{44} -2.78078 q^{45} +0.0945846 q^{46} +3.44949 q^{47} -1.00000 q^{48} +4.69932 q^{49} -2.73271 q^{50} -1.00000 q^{51} -1.09916 q^{52} +0.825282 q^{53} +1.00000 q^{54} +17.8160 q^{55} -3.42043 q^{56} -6.34964 q^{57} +3.02228 q^{58} -1.00000 q^{59} +2.78078 q^{60} -1.88013 q^{61} +2.51109 q^{62} +3.42043 q^{63} +1.00000 q^{64} +3.05651 q^{65} -6.40684 q^{66} -6.99934 q^{67} +1.00000 q^{68} +0.0945846 q^{69} +9.51144 q^{70} -8.64966 q^{71} -1.00000 q^{72} +6.87094 q^{73} +4.03293 q^{74} -2.73271 q^{75} +6.34964 q^{76} -21.9141 q^{77} -1.09916 q^{78} +6.85217 q^{79} -2.78078 q^{80} +1.00000 q^{81} -3.94277 q^{82} -0.152814 q^{83} -3.42043 q^{84} -2.78078 q^{85} +4.15125 q^{86} +3.02228 q^{87} +6.40684 q^{88} -9.59621 q^{89} +2.78078 q^{90} -3.75958 q^{91} -0.0945846 q^{92} +2.51109 q^{93} -3.44949 q^{94} -17.6569 q^{95} +1.00000 q^{96} +1.52877 q^{97} -4.69932 q^{98} -6.40684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −2.78078 −1.24360 −0.621800 0.783176i \(-0.713598\pi\)
−0.621800 + 0.783176i \(0.713598\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.42043 1.29280 0.646400 0.762999i \(-0.276274\pi\)
0.646400 + 0.762999i \(0.276274\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.78078 0.879358
\(11\) −6.40684 −1.93173 −0.965867 0.259038i \(-0.916595\pi\)
−0.965867 + 0.259038i \(0.916595\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.09916 −0.304851 −0.152425 0.988315i \(-0.548708\pi\)
−0.152425 + 0.988315i \(0.548708\pi\)
\(14\) −3.42043 −0.914147
\(15\) 2.78078 0.717993
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) 6.34964 1.45671 0.728354 0.685201i \(-0.240286\pi\)
0.728354 + 0.685201i \(0.240286\pi\)
\(20\) −2.78078 −0.621800
\(21\) −3.42043 −0.746398
\(22\) 6.40684 1.36594
\(23\) −0.0945846 −0.0197223 −0.00986113 0.999951i \(-0.503139\pi\)
−0.00986113 + 0.999951i \(0.503139\pi\)
\(24\) 1.00000 0.204124
\(25\) 2.73271 0.546543
\(26\) 1.09916 0.215562
\(27\) −1.00000 −0.192450
\(28\) 3.42043 0.646400
\(29\) −3.02228 −0.561223 −0.280612 0.959821i \(-0.590537\pi\)
−0.280612 + 0.959821i \(0.590537\pi\)
\(30\) −2.78078 −0.507698
\(31\) −2.51109 −0.451006 −0.225503 0.974243i \(-0.572402\pi\)
−0.225503 + 0.974243i \(0.572402\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.40684 1.11529
\(34\) −1.00000 −0.171499
\(35\) −9.51144 −1.60773
\(36\) 1.00000 0.166667
\(37\) −4.03293 −0.663010 −0.331505 0.943453i \(-0.607556\pi\)
−0.331505 + 0.943453i \(0.607556\pi\)
\(38\) −6.34964 −1.03005
\(39\) 1.09916 0.176006
\(40\) 2.78078 0.439679
\(41\) 3.94277 0.615757 0.307879 0.951426i \(-0.400381\pi\)
0.307879 + 0.951426i \(0.400381\pi\)
\(42\) 3.42043 0.527783
\(43\) −4.15125 −0.633060 −0.316530 0.948583i \(-0.602518\pi\)
−0.316530 + 0.948583i \(0.602518\pi\)
\(44\) −6.40684 −0.965867
\(45\) −2.78078 −0.414534
\(46\) 0.0945846 0.0139457
\(47\) 3.44949 0.503159 0.251580 0.967837i \(-0.419050\pi\)
0.251580 + 0.967837i \(0.419050\pi\)
\(48\) −1.00000 −0.144338
\(49\) 4.69932 0.671331
\(50\) −2.73271 −0.386464
\(51\) −1.00000 −0.140028
\(52\) −1.09916 −0.152425
\(53\) 0.825282 0.113361 0.0566806 0.998392i \(-0.481948\pi\)
0.0566806 + 0.998392i \(0.481948\pi\)
\(54\) 1.00000 0.136083
\(55\) 17.8160 2.40231
\(56\) −3.42043 −0.457074
\(57\) −6.34964 −0.841031
\(58\) 3.02228 0.396845
\(59\) −1.00000 −0.130189
\(60\) 2.78078 0.358997
\(61\) −1.88013 −0.240726 −0.120363 0.992730i \(-0.538406\pi\)
−0.120363 + 0.992730i \(0.538406\pi\)
\(62\) 2.51109 0.318909
\(63\) 3.42043 0.430933
\(64\) 1.00000 0.125000
\(65\) 3.05651 0.379113
\(66\) −6.40684 −0.788627
\(67\) −6.99934 −0.855106 −0.427553 0.903990i \(-0.640624\pi\)
−0.427553 + 0.903990i \(0.640624\pi\)
\(68\) 1.00000 0.121268
\(69\) 0.0945846 0.0113866
\(70\) 9.51144 1.13683
\(71\) −8.64966 −1.02653 −0.513263 0.858231i \(-0.671563\pi\)
−0.513263 + 0.858231i \(0.671563\pi\)
\(72\) −1.00000 −0.117851
\(73\) 6.87094 0.804183 0.402091 0.915600i \(-0.368283\pi\)
0.402091 + 0.915600i \(0.368283\pi\)
\(74\) 4.03293 0.468819
\(75\) −2.73271 −0.315547
\(76\) 6.34964 0.728354
\(77\) −21.9141 −2.49735
\(78\) −1.09916 −0.124455
\(79\) 6.85217 0.770930 0.385465 0.922723i \(-0.374041\pi\)
0.385465 + 0.922723i \(0.374041\pi\)
\(80\) −2.78078 −0.310900
\(81\) 1.00000 0.111111
\(82\) −3.94277 −0.435406
\(83\) −0.152814 −0.0167735 −0.00838677 0.999965i \(-0.502670\pi\)
−0.00838677 + 0.999965i \(0.502670\pi\)
\(84\) −3.42043 −0.373199
\(85\) −2.78078 −0.301617
\(86\) 4.15125 0.447641
\(87\) 3.02228 0.324022
\(88\) 6.40684 0.682971
\(89\) −9.59621 −1.01720 −0.508598 0.861004i \(-0.669836\pi\)
−0.508598 + 0.861004i \(0.669836\pi\)
\(90\) 2.78078 0.293119
\(91\) −3.75958 −0.394111
\(92\) −0.0945846 −0.00986113
\(93\) 2.51109 0.260388
\(94\) −3.44949 −0.355787
\(95\) −17.6569 −1.81156
\(96\) 1.00000 0.102062
\(97\) 1.52877 0.155223 0.0776114 0.996984i \(-0.475271\pi\)
0.0776114 + 0.996984i \(0.475271\pi\)
\(98\) −4.69932 −0.474703
\(99\) −6.40684 −0.643911
\(100\) 2.73271 0.273271
\(101\) 7.28219 0.724605 0.362302 0.932061i \(-0.381991\pi\)
0.362302 + 0.932061i \(0.381991\pi\)
\(102\) 1.00000 0.0990148
\(103\) −3.54082 −0.348887 −0.174444 0.984667i \(-0.555813\pi\)
−0.174444 + 0.984667i \(0.555813\pi\)
\(104\) 1.09916 0.107781
\(105\) 9.51144 0.928221
\(106\) −0.825282 −0.0801585
\(107\) 7.81413 0.755420 0.377710 0.925924i \(-0.376712\pi\)
0.377710 + 0.925924i \(0.376712\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −5.99899 −0.574599 −0.287300 0.957841i \(-0.592758\pi\)
−0.287300 + 0.957841i \(0.592758\pi\)
\(110\) −17.8160 −1.69869
\(111\) 4.03293 0.382789
\(112\) 3.42043 0.323200
\(113\) −5.66954 −0.533346 −0.266673 0.963787i \(-0.585924\pi\)
−0.266673 + 0.963787i \(0.585924\pi\)
\(114\) 6.34964 0.594698
\(115\) 0.263019 0.0245266
\(116\) −3.02228 −0.280612
\(117\) −1.09916 −0.101617
\(118\) 1.00000 0.0920575
\(119\) 3.42043 0.313550
\(120\) −2.78078 −0.253849
\(121\) 30.0476 2.73160
\(122\) 1.88013 0.170219
\(123\) −3.94277 −0.355508
\(124\) −2.51109 −0.225503
\(125\) 6.30482 0.563920
\(126\) −3.42043 −0.304716
\(127\) −8.88937 −0.788804 −0.394402 0.918938i \(-0.629048\pi\)
−0.394402 + 0.918938i \(0.629048\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.15125 0.365497
\(130\) −3.05651 −0.268073
\(131\) 3.04262 0.265835 0.132917 0.991127i \(-0.457566\pi\)
0.132917 + 0.991127i \(0.457566\pi\)
\(132\) 6.40684 0.557644
\(133\) 21.7185 1.88323
\(134\) 6.99934 0.604651
\(135\) 2.78078 0.239331
\(136\) −1.00000 −0.0857493
\(137\) 0.484042 0.0413545 0.0206772 0.999786i \(-0.493418\pi\)
0.0206772 + 0.999786i \(0.493418\pi\)
\(138\) −0.0945846 −0.00805158
\(139\) −0.179257 −0.0152044 −0.00760221 0.999971i \(-0.502420\pi\)
−0.00760221 + 0.999971i \(0.502420\pi\)
\(140\) −9.51144 −0.803863
\(141\) −3.44949 −0.290499
\(142\) 8.64966 0.725864
\(143\) 7.04211 0.588891
\(144\) 1.00000 0.0833333
\(145\) 8.40428 0.697938
\(146\) −6.87094 −0.568643
\(147\) −4.69932 −0.387593
\(148\) −4.03293 −0.331505
\(149\) −8.32811 −0.682265 −0.341133 0.940015i \(-0.610811\pi\)
−0.341133 + 0.940015i \(0.610811\pi\)
\(150\) 2.73271 0.223125
\(151\) 7.36479 0.599338 0.299669 0.954043i \(-0.403124\pi\)
0.299669 + 0.954043i \(0.403124\pi\)
\(152\) −6.34964 −0.515024
\(153\) 1.00000 0.0808452
\(154\) 21.9141 1.76589
\(155\) 6.98279 0.560871
\(156\) 1.09916 0.0880029
\(157\) 9.87753 0.788313 0.394156 0.919043i \(-0.371037\pi\)
0.394156 + 0.919043i \(0.371037\pi\)
\(158\) −6.85217 −0.545130
\(159\) −0.825282 −0.0654491
\(160\) 2.78078 0.219840
\(161\) −0.323520 −0.0254969
\(162\) −1.00000 −0.0785674
\(163\) −21.8700 −1.71299 −0.856494 0.516156i \(-0.827362\pi\)
−0.856494 + 0.516156i \(0.827362\pi\)
\(164\) 3.94277 0.307879
\(165\) −17.8160 −1.38697
\(166\) 0.152814 0.0118607
\(167\) 21.1311 1.63517 0.817587 0.575806i \(-0.195312\pi\)
0.817587 + 0.575806i \(0.195312\pi\)
\(168\) 3.42043 0.263892
\(169\) −11.7919 −0.907066
\(170\) 2.78078 0.213276
\(171\) 6.34964 0.485569
\(172\) −4.15125 −0.316530
\(173\) 11.2828 0.857813 0.428906 0.903349i \(-0.358899\pi\)
0.428906 + 0.903349i \(0.358899\pi\)
\(174\) −3.02228 −0.229118
\(175\) 9.34705 0.706570
\(176\) −6.40684 −0.482934
\(177\) 1.00000 0.0751646
\(178\) 9.59621 0.719266
\(179\) 2.55732 0.191143 0.0955716 0.995423i \(-0.469532\pi\)
0.0955716 + 0.995423i \(0.469532\pi\)
\(180\) −2.78078 −0.207267
\(181\) 2.69513 0.200327 0.100164 0.994971i \(-0.468063\pi\)
0.100164 + 0.994971i \(0.468063\pi\)
\(182\) 3.75958 0.278679
\(183\) 1.88013 0.138983
\(184\) 0.0945846 0.00697287
\(185\) 11.2147 0.824520
\(186\) −2.51109 −0.184122
\(187\) −6.40684 −0.468514
\(188\) 3.44949 0.251580
\(189\) −3.42043 −0.248799
\(190\) 17.6569 1.28097
\(191\) 10.1874 0.737131 0.368566 0.929602i \(-0.379849\pi\)
0.368566 + 0.929602i \(0.379849\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −18.6070 −1.33936 −0.669681 0.742649i \(-0.733569\pi\)
−0.669681 + 0.742649i \(0.733569\pi\)
\(194\) −1.52877 −0.109759
\(195\) −3.05651 −0.218881
\(196\) 4.69932 0.335666
\(197\) −24.3322 −1.73359 −0.866797 0.498661i \(-0.833825\pi\)
−0.866797 + 0.498661i \(0.833825\pi\)
\(198\) 6.40684 0.455314
\(199\) −3.70805 −0.262857 −0.131428 0.991326i \(-0.541956\pi\)
−0.131428 + 0.991326i \(0.541956\pi\)
\(200\) −2.73271 −0.193232
\(201\) 6.99934 0.493695
\(202\) −7.28219 −0.512373
\(203\) −10.3375 −0.725549
\(204\) −1.00000 −0.0700140
\(205\) −10.9640 −0.765756
\(206\) 3.54082 0.246700
\(207\) −0.0945846 −0.00657409
\(208\) −1.09916 −0.0762127
\(209\) −40.6811 −2.81397
\(210\) −9.51144 −0.656352
\(211\) −5.01235 −0.345064 −0.172532 0.985004i \(-0.555195\pi\)
−0.172532 + 0.985004i \(0.555195\pi\)
\(212\) 0.825282 0.0566806
\(213\) 8.64966 0.592665
\(214\) −7.81413 −0.534163
\(215\) 11.5437 0.787273
\(216\) 1.00000 0.0680414
\(217\) −8.58901 −0.583060
\(218\) 5.99899 0.406303
\(219\) −6.87094 −0.464295
\(220\) 17.8160 1.20115
\(221\) −1.09916 −0.0739372
\(222\) −4.03293 −0.270673
\(223\) 1.38896 0.0930118 0.0465059 0.998918i \(-0.485191\pi\)
0.0465059 + 0.998918i \(0.485191\pi\)
\(224\) −3.42043 −0.228537
\(225\) 2.73271 0.182181
\(226\) 5.66954 0.377132
\(227\) −8.74677 −0.580544 −0.290272 0.956944i \(-0.593746\pi\)
−0.290272 + 0.956944i \(0.593746\pi\)
\(228\) −6.34964 −0.420515
\(229\) 13.4870 0.891244 0.445622 0.895221i \(-0.352982\pi\)
0.445622 + 0.895221i \(0.352982\pi\)
\(230\) −0.263019 −0.0173429
\(231\) 21.9141 1.44184
\(232\) 3.02228 0.198422
\(233\) −6.74729 −0.442030 −0.221015 0.975270i \(-0.570937\pi\)
−0.221015 + 0.975270i \(0.570937\pi\)
\(234\) 1.09916 0.0718541
\(235\) −9.59225 −0.625730
\(236\) −1.00000 −0.0650945
\(237\) −6.85217 −0.445096
\(238\) −3.42043 −0.221713
\(239\) −3.39472 −0.219586 −0.109793 0.993954i \(-0.535019\pi\)
−0.109793 + 0.993954i \(0.535019\pi\)
\(240\) 2.78078 0.179498
\(241\) 13.6691 0.880507 0.440254 0.897874i \(-0.354889\pi\)
0.440254 + 0.897874i \(0.354889\pi\)
\(242\) −30.0476 −1.93153
\(243\) −1.00000 −0.0641500
\(244\) −1.88013 −0.120363
\(245\) −13.0678 −0.834868
\(246\) 3.94277 0.251382
\(247\) −6.97925 −0.444079
\(248\) 2.51109 0.159455
\(249\) 0.152814 0.00968421
\(250\) −6.30482 −0.398752
\(251\) 17.2811 1.09077 0.545385 0.838185i \(-0.316383\pi\)
0.545385 + 0.838185i \(0.316383\pi\)
\(252\) 3.42043 0.215467
\(253\) 0.605988 0.0380982
\(254\) 8.88937 0.557768
\(255\) 2.78078 0.174139
\(256\) 1.00000 0.0625000
\(257\) 29.6761 1.85115 0.925573 0.378570i \(-0.123584\pi\)
0.925573 + 0.378570i \(0.123584\pi\)
\(258\) −4.15125 −0.258446
\(259\) −13.7944 −0.857139
\(260\) 3.05651 0.189556
\(261\) −3.02228 −0.187074
\(262\) −3.04262 −0.187973
\(263\) 21.9414 1.35297 0.676484 0.736458i \(-0.263503\pi\)
0.676484 + 0.736458i \(0.263503\pi\)
\(264\) −6.40684 −0.394314
\(265\) −2.29492 −0.140976
\(266\) −21.7185 −1.33165
\(267\) 9.59621 0.587279
\(268\) −6.99934 −0.427553
\(269\) −1.06146 −0.0647184 −0.0323592 0.999476i \(-0.510302\pi\)
−0.0323592 + 0.999476i \(0.510302\pi\)
\(270\) −2.78078 −0.169233
\(271\) −4.15826 −0.252597 −0.126298 0.991992i \(-0.540310\pi\)
−0.126298 + 0.991992i \(0.540310\pi\)
\(272\) 1.00000 0.0606339
\(273\) 3.75958 0.227540
\(274\) −0.484042 −0.0292420
\(275\) −17.5081 −1.05578
\(276\) 0.0945846 0.00569332
\(277\) −0.918785 −0.0552045 −0.0276022 0.999619i \(-0.508787\pi\)
−0.0276022 + 0.999619i \(0.508787\pi\)
\(278\) 0.179257 0.0107511
\(279\) −2.51109 −0.150335
\(280\) 9.51144 0.568417
\(281\) 20.3440 1.21362 0.606811 0.794846i \(-0.292448\pi\)
0.606811 + 0.794846i \(0.292448\pi\)
\(282\) 3.44949 0.205414
\(283\) −28.9503 −1.72092 −0.860459 0.509519i \(-0.829823\pi\)
−0.860459 + 0.509519i \(0.829823\pi\)
\(284\) −8.64966 −0.513263
\(285\) 17.6569 1.04591
\(286\) −7.04211 −0.416409
\(287\) 13.4860 0.796051
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −8.40428 −0.493516
\(291\) −1.52877 −0.0896180
\(292\) 6.87094 0.402091
\(293\) −21.5847 −1.26099 −0.630497 0.776192i \(-0.717149\pi\)
−0.630497 + 0.776192i \(0.717149\pi\)
\(294\) 4.69932 0.274070
\(295\) 2.78078 0.161903
\(296\) 4.03293 0.234410
\(297\) 6.40684 0.371762
\(298\) 8.32811 0.482435
\(299\) 0.103963 0.00601235
\(300\) −2.73271 −0.157773
\(301\) −14.1990 −0.818419
\(302\) −7.36479 −0.423796
\(303\) −7.28219 −0.418351
\(304\) 6.34964 0.364177
\(305\) 5.22821 0.299367
\(306\) −1.00000 −0.0571662
\(307\) 13.7268 0.783429 0.391714 0.920087i \(-0.371882\pi\)
0.391714 + 0.920087i \(0.371882\pi\)
\(308\) −21.9141 −1.24867
\(309\) 3.54082 0.201430
\(310\) −6.98279 −0.396596
\(311\) −13.7718 −0.780926 −0.390463 0.920619i \(-0.627685\pi\)
−0.390463 + 0.920619i \(0.627685\pi\)
\(312\) −1.09916 −0.0622274
\(313\) 19.3987 1.09648 0.548239 0.836321i \(-0.315298\pi\)
0.548239 + 0.836321i \(0.315298\pi\)
\(314\) −9.87753 −0.557421
\(315\) −9.51144 −0.535909
\(316\) 6.85217 0.385465
\(317\) 21.2894 1.19573 0.597866 0.801596i \(-0.296016\pi\)
0.597866 + 0.801596i \(0.296016\pi\)
\(318\) 0.825282 0.0462795
\(319\) 19.3633 1.08413
\(320\) −2.78078 −0.155450
\(321\) −7.81413 −0.436142
\(322\) 0.323520 0.0180291
\(323\) 6.34964 0.353304
\(324\) 1.00000 0.0555556
\(325\) −3.00368 −0.166614
\(326\) 21.8700 1.21127
\(327\) 5.99899 0.331745
\(328\) −3.94277 −0.217703
\(329\) 11.7987 0.650484
\(330\) 17.8160 0.980737
\(331\) 10.7517 0.590964 0.295482 0.955348i \(-0.404520\pi\)
0.295482 + 0.955348i \(0.404520\pi\)
\(332\) −0.152814 −0.00838677
\(333\) −4.03293 −0.221003
\(334\) −21.1311 −1.15624
\(335\) 19.4636 1.06341
\(336\) −3.42043 −0.186600
\(337\) 27.6531 1.50636 0.753181 0.657813i \(-0.228518\pi\)
0.753181 + 0.657813i \(0.228518\pi\)
\(338\) 11.7919 0.641392
\(339\) 5.66954 0.307927
\(340\) −2.78078 −0.150809
\(341\) 16.0882 0.871223
\(342\) −6.34964 −0.343349
\(343\) −7.86931 −0.424903
\(344\) 4.15125 0.223820
\(345\) −0.263019 −0.0141604
\(346\) −11.2828 −0.606565
\(347\) 17.0845 0.917147 0.458573 0.888657i \(-0.348361\pi\)
0.458573 + 0.888657i \(0.348361\pi\)
\(348\) 3.02228 0.162011
\(349\) 12.8542 0.688072 0.344036 0.938957i \(-0.388206\pi\)
0.344036 + 0.938957i \(0.388206\pi\)
\(350\) −9.34705 −0.499621
\(351\) 1.09916 0.0586686
\(352\) 6.40684 0.341486
\(353\) 24.7686 1.31830 0.659149 0.752012i \(-0.270916\pi\)
0.659149 + 0.752012i \(0.270916\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 24.0528 1.27659
\(356\) −9.59621 −0.508598
\(357\) −3.42043 −0.181028
\(358\) −2.55732 −0.135159
\(359\) 6.82217 0.360061 0.180030 0.983661i \(-0.442380\pi\)
0.180030 + 0.983661i \(0.442380\pi\)
\(360\) 2.78078 0.146560
\(361\) 21.3179 1.12200
\(362\) −2.69513 −0.141653
\(363\) −30.0476 −1.57709
\(364\) −3.75958 −0.197056
\(365\) −19.1065 −1.00008
\(366\) −1.88013 −0.0982759
\(367\) 32.6009 1.70175 0.850877 0.525365i \(-0.176071\pi\)
0.850877 + 0.525365i \(0.176071\pi\)
\(368\) −0.0945846 −0.00493056
\(369\) 3.94277 0.205252
\(370\) −11.2147 −0.583024
\(371\) 2.82282 0.146553
\(372\) 2.51109 0.130194
\(373\) 12.2917 0.636438 0.318219 0.948017i \(-0.396915\pi\)
0.318219 + 0.948017i \(0.396915\pi\)
\(374\) 6.40684 0.331290
\(375\) −6.30482 −0.325579
\(376\) −3.44949 −0.177894
\(377\) 3.32196 0.171089
\(378\) 3.42043 0.175928
\(379\) 6.21412 0.319198 0.159599 0.987182i \(-0.448980\pi\)
0.159599 + 0.987182i \(0.448980\pi\)
\(380\) −17.6569 −0.905781
\(381\) 8.88937 0.455416
\(382\) −10.1874 −0.521231
\(383\) −24.5786 −1.25591 −0.627953 0.778251i \(-0.716107\pi\)
−0.627953 + 0.778251i \(0.716107\pi\)
\(384\) 1.00000 0.0510310
\(385\) 60.9383 3.10570
\(386\) 18.6070 0.947071
\(387\) −4.15125 −0.211020
\(388\) 1.52877 0.0776114
\(389\) 19.3063 0.978869 0.489434 0.872040i \(-0.337203\pi\)
0.489434 + 0.872040i \(0.337203\pi\)
\(390\) 3.05651 0.154772
\(391\) −0.0945846 −0.00478335
\(392\) −4.69932 −0.237351
\(393\) −3.04262 −0.153480
\(394\) 24.3322 1.22584
\(395\) −19.0544 −0.958729
\(396\) −6.40684 −0.321956
\(397\) −23.0737 −1.15803 −0.579017 0.815316i \(-0.696563\pi\)
−0.579017 + 0.815316i \(0.696563\pi\)
\(398\) 3.70805 0.185868
\(399\) −21.7185 −1.08728
\(400\) 2.73271 0.136636
\(401\) 6.62545 0.330859 0.165429 0.986222i \(-0.447099\pi\)
0.165429 + 0.986222i \(0.447099\pi\)
\(402\) −6.99934 −0.349095
\(403\) 2.76008 0.137490
\(404\) 7.28219 0.362302
\(405\) −2.78078 −0.138178
\(406\) 10.3375 0.513041
\(407\) 25.8384 1.28076
\(408\) 1.00000 0.0495074
\(409\) 4.87099 0.240855 0.120427 0.992722i \(-0.461573\pi\)
0.120427 + 0.992722i \(0.461573\pi\)
\(410\) 10.9640 0.541471
\(411\) −0.484042 −0.0238760
\(412\) −3.54082 −0.174444
\(413\) −3.42043 −0.168308
\(414\) 0.0945846 0.00464858
\(415\) 0.424942 0.0208596
\(416\) 1.09916 0.0538906
\(417\) 0.179257 0.00877827
\(418\) 40.6811 1.98978
\(419\) −13.5440 −0.661669 −0.330834 0.943689i \(-0.607330\pi\)
−0.330834 + 0.943689i \(0.607330\pi\)
\(420\) 9.51144 0.464111
\(421\) 16.4086 0.799709 0.399854 0.916579i \(-0.369061\pi\)
0.399854 + 0.916579i \(0.369061\pi\)
\(422\) 5.01235 0.243997
\(423\) 3.44949 0.167720
\(424\) −0.825282 −0.0400792
\(425\) 2.73271 0.132556
\(426\) −8.64966 −0.419078
\(427\) −6.43084 −0.311210
\(428\) 7.81413 0.377710
\(429\) −7.04211 −0.339996
\(430\) −11.5437 −0.556686
\(431\) 5.11972 0.246608 0.123304 0.992369i \(-0.460651\pi\)
0.123304 + 0.992369i \(0.460651\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −26.7697 −1.28647 −0.643234 0.765670i \(-0.722408\pi\)
−0.643234 + 0.765670i \(0.722408\pi\)
\(434\) 8.58901 0.412286
\(435\) −8.40428 −0.402954
\(436\) −5.99899 −0.287300
\(437\) −0.600578 −0.0287296
\(438\) 6.87094 0.328306
\(439\) 25.7731 1.23008 0.615042 0.788495i \(-0.289139\pi\)
0.615042 + 0.788495i \(0.289139\pi\)
\(440\) −17.8160 −0.849343
\(441\) 4.69932 0.223777
\(442\) 1.09916 0.0522815
\(443\) 6.33359 0.300918 0.150459 0.988616i \(-0.451925\pi\)
0.150459 + 0.988616i \(0.451925\pi\)
\(444\) 4.03293 0.191395
\(445\) 26.6849 1.26499
\(446\) −1.38896 −0.0657693
\(447\) 8.32811 0.393906
\(448\) 3.42043 0.161600
\(449\) −6.05616 −0.285808 −0.142904 0.989737i \(-0.545644\pi\)
−0.142904 + 0.989737i \(0.545644\pi\)
\(450\) −2.73271 −0.128821
\(451\) −25.2607 −1.18948
\(452\) −5.66954 −0.266673
\(453\) −7.36479 −0.346028
\(454\) 8.74677 0.410506
\(455\) 10.4546 0.490117
\(456\) 6.34964 0.297349
\(457\) 24.5777 1.14970 0.574849 0.818259i \(-0.305061\pi\)
0.574849 + 0.818259i \(0.305061\pi\)
\(458\) −13.4870 −0.630205
\(459\) −1.00000 −0.0466760
\(460\) 0.263019 0.0122633
\(461\) 23.1601 1.07867 0.539336 0.842090i \(-0.318675\pi\)
0.539336 + 0.842090i \(0.318675\pi\)
\(462\) −21.9141 −1.01954
\(463\) −6.15000 −0.285815 −0.142907 0.989736i \(-0.545645\pi\)
−0.142907 + 0.989736i \(0.545645\pi\)
\(464\) −3.02228 −0.140306
\(465\) −6.98279 −0.323819
\(466\) 6.74729 0.312562
\(467\) 38.5003 1.78158 0.890791 0.454413i \(-0.150151\pi\)
0.890791 + 0.454413i \(0.150151\pi\)
\(468\) −1.09916 −0.0508085
\(469\) −23.9407 −1.10548
\(470\) 9.59225 0.442458
\(471\) −9.87753 −0.455132
\(472\) 1.00000 0.0460287
\(473\) 26.5964 1.22290
\(474\) 6.85217 0.314731
\(475\) 17.3518 0.796153
\(476\) 3.42043 0.156775
\(477\) 0.825282 0.0377871
\(478\) 3.39472 0.155271
\(479\) 3.10423 0.141836 0.0709180 0.997482i \(-0.477407\pi\)
0.0709180 + 0.997482i \(0.477407\pi\)
\(480\) −2.78078 −0.126924
\(481\) 4.43282 0.202119
\(482\) −13.6691 −0.622612
\(483\) 0.323520 0.0147207
\(484\) 30.0476 1.36580
\(485\) −4.25116 −0.193035
\(486\) 1.00000 0.0453609
\(487\) 28.9801 1.31321 0.656606 0.754234i \(-0.271991\pi\)
0.656606 + 0.754234i \(0.271991\pi\)
\(488\) 1.88013 0.0851094
\(489\) 21.8700 0.988994
\(490\) 13.0678 0.590341
\(491\) 41.1935 1.85904 0.929519 0.368775i \(-0.120223\pi\)
0.929519 + 0.368775i \(0.120223\pi\)
\(492\) −3.94277 −0.177754
\(493\) −3.02228 −0.136117
\(494\) 6.97925 0.314011
\(495\) 17.8160 0.800769
\(496\) −2.51109 −0.112751
\(497\) −29.5855 −1.32709
\(498\) −0.152814 −0.00684777
\(499\) −16.5558 −0.741141 −0.370570 0.928804i \(-0.620838\pi\)
−0.370570 + 0.928804i \(0.620838\pi\)
\(500\) 6.30482 0.281960
\(501\) −21.1311 −0.944068
\(502\) −17.2811 −0.771291
\(503\) 8.40763 0.374878 0.187439 0.982276i \(-0.439981\pi\)
0.187439 + 0.982276i \(0.439981\pi\)
\(504\) −3.42043 −0.152358
\(505\) −20.2501 −0.901119
\(506\) −0.605988 −0.0269395
\(507\) 11.7919 0.523695
\(508\) −8.88937 −0.394402
\(509\) 14.7215 0.652517 0.326258 0.945281i \(-0.394212\pi\)
0.326258 + 0.945281i \(0.394212\pi\)
\(510\) −2.78078 −0.123135
\(511\) 23.5015 1.03965
\(512\) −1.00000 −0.0441942
\(513\) −6.34964 −0.280344
\(514\) −29.6761 −1.30896
\(515\) 9.84622 0.433876
\(516\) 4.15125 0.182749
\(517\) −22.1003 −0.971970
\(518\) 13.7944 0.606089
\(519\) −11.2828 −0.495258
\(520\) −3.05651 −0.134037
\(521\) 4.13825 0.181300 0.0906500 0.995883i \(-0.471106\pi\)
0.0906500 + 0.995883i \(0.471106\pi\)
\(522\) 3.02228 0.132282
\(523\) 20.0157 0.875227 0.437614 0.899163i \(-0.355824\pi\)
0.437614 + 0.899163i \(0.355824\pi\)
\(524\) 3.04262 0.132917
\(525\) −9.34705 −0.407939
\(526\) −21.9414 −0.956693
\(527\) −2.51109 −0.109385
\(528\) 6.40684 0.278822
\(529\) −22.9911 −0.999611
\(530\) 2.29492 0.0996852
\(531\) −1.00000 −0.0433963
\(532\) 21.7185 0.941616
\(533\) −4.33372 −0.187714
\(534\) −9.59621 −0.415269
\(535\) −21.7293 −0.939441
\(536\) 6.99934 0.302325
\(537\) −2.55732 −0.110357
\(538\) 1.06146 0.0457628
\(539\) −30.1078 −1.29683
\(540\) 2.78078 0.119666
\(541\) 6.61115 0.284236 0.142118 0.989850i \(-0.454609\pi\)
0.142118 + 0.989850i \(0.454609\pi\)
\(542\) 4.15826 0.178613
\(543\) −2.69513 −0.115659
\(544\) −1.00000 −0.0428746
\(545\) 16.6819 0.714572
\(546\) −3.75958 −0.160895
\(547\) 4.21646 0.180283 0.0901414 0.995929i \(-0.471268\pi\)
0.0901414 + 0.995929i \(0.471268\pi\)
\(548\) 0.484042 0.0206772
\(549\) −1.88013 −0.0802419
\(550\) 17.5081 0.746546
\(551\) −19.1904 −0.817538
\(552\) −0.0945846 −0.00402579
\(553\) 23.4374 0.996658
\(554\) 0.918785 0.0390355
\(555\) −11.2147 −0.476037
\(556\) −0.179257 −0.00760221
\(557\) 39.5624 1.67631 0.838155 0.545432i \(-0.183634\pi\)
0.838155 + 0.545432i \(0.183634\pi\)
\(558\) 2.51109 0.106303
\(559\) 4.56287 0.192989
\(560\) −9.51144 −0.401932
\(561\) 6.40684 0.270497
\(562\) −20.3440 −0.858160
\(563\) −25.9702 −1.09452 −0.547258 0.836964i \(-0.684328\pi\)
−0.547258 + 0.836964i \(0.684328\pi\)
\(564\) −3.44949 −0.145250
\(565\) 15.7657 0.663269
\(566\) 28.9503 1.21687
\(567\) 3.42043 0.143644
\(568\) 8.64966 0.362932
\(569\) −26.7710 −1.12230 −0.561149 0.827715i \(-0.689640\pi\)
−0.561149 + 0.827715i \(0.689640\pi\)
\(570\) −17.6569 −0.739567
\(571\) 17.2078 0.720124 0.360062 0.932928i \(-0.382756\pi\)
0.360062 + 0.932928i \(0.382756\pi\)
\(572\) 7.04211 0.294446
\(573\) −10.1874 −0.425583
\(574\) −13.4860 −0.562893
\(575\) −0.258473 −0.0107791
\(576\) 1.00000 0.0416667
\(577\) 24.0676 1.00195 0.500973 0.865463i \(-0.332976\pi\)
0.500973 + 0.865463i \(0.332976\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 18.6070 0.773280
\(580\) 8.40428 0.348969
\(581\) −0.522690 −0.0216848
\(582\) 1.52877 0.0633695
\(583\) −5.28745 −0.218984
\(584\) −6.87094 −0.284321
\(585\) 3.05651 0.126371
\(586\) 21.5847 0.891657
\(587\) 25.2960 1.04408 0.522039 0.852922i \(-0.325172\pi\)
0.522039 + 0.852922i \(0.325172\pi\)
\(588\) −4.69932 −0.193797
\(589\) −15.9445 −0.656983
\(590\) −2.78078 −0.114483
\(591\) 24.3322 1.00089
\(592\) −4.03293 −0.165753
\(593\) 16.3906 0.673082 0.336541 0.941669i \(-0.390743\pi\)
0.336541 + 0.941669i \(0.390743\pi\)
\(594\) −6.40684 −0.262876
\(595\) −9.51144 −0.389931
\(596\) −8.32811 −0.341133
\(597\) 3.70805 0.151760
\(598\) −0.103963 −0.00425137
\(599\) 27.7346 1.13321 0.566603 0.823991i \(-0.308257\pi\)
0.566603 + 0.823991i \(0.308257\pi\)
\(600\) 2.73271 0.111563
\(601\) −27.9576 −1.14042 −0.570208 0.821501i \(-0.693137\pi\)
−0.570208 + 0.821501i \(0.693137\pi\)
\(602\) 14.1990 0.578710
\(603\) −6.99934 −0.285035
\(604\) 7.36479 0.299669
\(605\) −83.5556 −3.39702
\(606\) 7.28219 0.295819
\(607\) −6.68756 −0.271440 −0.135720 0.990747i \(-0.543335\pi\)
−0.135720 + 0.990747i \(0.543335\pi\)
\(608\) −6.34964 −0.257512
\(609\) 10.3375 0.418896
\(610\) −5.22821 −0.211684
\(611\) −3.79152 −0.153389
\(612\) 1.00000 0.0404226
\(613\) −13.7819 −0.556644 −0.278322 0.960488i \(-0.589778\pi\)
−0.278322 + 0.960488i \(0.589778\pi\)
\(614\) −13.7268 −0.553968
\(615\) 10.9640 0.442109
\(616\) 21.9141 0.882945
\(617\) −19.6056 −0.789290 −0.394645 0.918834i \(-0.629132\pi\)
−0.394645 + 0.918834i \(0.629132\pi\)
\(618\) −3.54082 −0.142433
\(619\) 32.6087 1.31065 0.655327 0.755345i \(-0.272531\pi\)
0.655327 + 0.755345i \(0.272531\pi\)
\(620\) 6.98279 0.280436
\(621\) 0.0945846 0.00379555
\(622\) 13.7718 0.552198
\(623\) −32.8231 −1.31503
\(624\) 1.09916 0.0440015
\(625\) −31.1958 −1.24783
\(626\) −19.3987 −0.775328
\(627\) 40.6811 1.62465
\(628\) 9.87753 0.394156
\(629\) −4.03293 −0.160804
\(630\) 9.51144 0.378945
\(631\) 14.7811 0.588427 0.294213 0.955740i \(-0.404942\pi\)
0.294213 + 0.955740i \(0.404942\pi\)
\(632\) −6.85217 −0.272565
\(633\) 5.01235 0.199223
\(634\) −21.2894 −0.845510
\(635\) 24.7193 0.980957
\(636\) −0.825282 −0.0327246
\(637\) −5.16528 −0.204656
\(638\) −19.3633 −0.766599
\(639\) −8.64966 −0.342175
\(640\) 2.78078 0.109920
\(641\) −7.44836 −0.294192 −0.147096 0.989122i \(-0.546993\pi\)
−0.147096 + 0.989122i \(0.546993\pi\)
\(642\) 7.81413 0.308399
\(643\) 34.2894 1.35224 0.676121 0.736791i \(-0.263660\pi\)
0.676121 + 0.736791i \(0.263660\pi\)
\(644\) −0.323520 −0.0127485
\(645\) −11.5437 −0.454533
\(646\) −6.34964 −0.249823
\(647\) 17.0872 0.671767 0.335884 0.941904i \(-0.390965\pi\)
0.335884 + 0.941904i \(0.390965\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 6.40684 0.251490
\(650\) 3.00368 0.117814
\(651\) 8.58901 0.336630
\(652\) −21.8700 −0.856494
\(653\) −25.2629 −0.988615 −0.494307 0.869287i \(-0.664578\pi\)
−0.494307 + 0.869287i \(0.664578\pi\)
\(654\) −5.99899 −0.234579
\(655\) −8.46083 −0.330592
\(656\) 3.94277 0.153939
\(657\) 6.87094 0.268061
\(658\) −11.7987 −0.459962
\(659\) −35.6885 −1.39023 −0.695113 0.718900i \(-0.744646\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(660\) −17.8160 −0.693486
\(661\) −17.9778 −0.699257 −0.349628 0.936889i \(-0.613692\pi\)
−0.349628 + 0.936889i \(0.613692\pi\)
\(662\) −10.7517 −0.417875
\(663\) 1.09916 0.0426877
\(664\) 0.152814 0.00593034
\(665\) −60.3942 −2.34199
\(666\) 4.03293 0.156273
\(667\) 0.285861 0.0110686
\(668\) 21.1311 0.817587
\(669\) −1.38896 −0.0537004
\(670\) −19.4636 −0.751944
\(671\) 12.0457 0.465018
\(672\) 3.42043 0.131946
\(673\) 35.5902 1.37190 0.685950 0.727649i \(-0.259387\pi\)
0.685950 + 0.727649i \(0.259387\pi\)
\(674\) −27.6531 −1.06516
\(675\) −2.73271 −0.105182
\(676\) −11.7919 −0.453533
\(677\) 44.9411 1.72723 0.863614 0.504153i \(-0.168195\pi\)
0.863614 + 0.504153i \(0.168195\pi\)
\(678\) −5.66954 −0.217737
\(679\) 5.22904 0.200672
\(680\) 2.78078 0.106638
\(681\) 8.74677 0.335177
\(682\) −16.0882 −0.616048
\(683\) −27.0493 −1.03501 −0.517507 0.855679i \(-0.673140\pi\)
−0.517507 + 0.855679i \(0.673140\pi\)
\(684\) 6.34964 0.242785
\(685\) −1.34601 −0.0514285
\(686\) 7.86931 0.300452
\(687\) −13.4870 −0.514560
\(688\) −4.15125 −0.158265
\(689\) −0.907114 −0.0345583
\(690\) 0.263019 0.0100129
\(691\) 27.0426 1.02875 0.514374 0.857566i \(-0.328024\pi\)
0.514374 + 0.857566i \(0.328024\pi\)
\(692\) 11.2828 0.428906
\(693\) −21.9141 −0.832449
\(694\) −17.0845 −0.648521
\(695\) 0.498475 0.0189082
\(696\) −3.02228 −0.114559
\(697\) 3.94277 0.149343
\(698\) −12.8542 −0.486540
\(699\) 6.74729 0.255206
\(700\) 9.34705 0.353285
\(701\) 33.6517 1.27101 0.635504 0.772098i \(-0.280793\pi\)
0.635504 + 0.772098i \(0.280793\pi\)
\(702\) −1.09916 −0.0414850
\(703\) −25.6077 −0.965812
\(704\) −6.40684 −0.241467
\(705\) 9.59225 0.361265
\(706\) −24.7686 −0.932178
\(707\) 24.9082 0.936769
\(708\) 1.00000 0.0375823
\(709\) −20.0642 −0.753526 −0.376763 0.926310i \(-0.622963\pi\)
−0.376763 + 0.926310i \(0.622963\pi\)
\(710\) −24.0528 −0.902684
\(711\) 6.85217 0.256977
\(712\) 9.59621 0.359633
\(713\) 0.237511 0.00889485
\(714\) 3.42043 0.128006
\(715\) −19.5825 −0.732345
\(716\) 2.55732 0.0955716
\(717\) 3.39472 0.126778
\(718\) −6.82217 −0.254601
\(719\) 21.6002 0.805550 0.402775 0.915299i \(-0.368046\pi\)
0.402775 + 0.915299i \(0.368046\pi\)
\(720\) −2.78078 −0.103633
\(721\) −12.1111 −0.451041
\(722\) −21.3179 −0.793372
\(723\) −13.6691 −0.508361
\(724\) 2.69513 0.100164
\(725\) −8.25902 −0.306732
\(726\) 30.0476 1.11517
\(727\) −14.9641 −0.554988 −0.277494 0.960727i \(-0.589504\pi\)
−0.277494 + 0.960727i \(0.589504\pi\)
\(728\) 3.75958 0.139339
\(729\) 1.00000 0.0370370
\(730\) 19.1065 0.707165
\(731\) −4.15125 −0.153540
\(732\) 1.88013 0.0694915
\(733\) −13.9674 −0.515898 −0.257949 0.966158i \(-0.583047\pi\)
−0.257949 + 0.966158i \(0.583047\pi\)
\(734\) −32.6009 −1.20332
\(735\) 13.0678 0.482011
\(736\) 0.0945846 0.00348644
\(737\) 44.8436 1.65184
\(738\) −3.94277 −0.145135
\(739\) −7.23539 −0.266158 −0.133079 0.991105i \(-0.542486\pi\)
−0.133079 + 0.991105i \(0.542486\pi\)
\(740\) 11.2147 0.412260
\(741\) 6.97925 0.256389
\(742\) −2.82282 −0.103629
\(743\) 41.5093 1.52283 0.761414 0.648265i \(-0.224505\pi\)
0.761414 + 0.648265i \(0.224505\pi\)
\(744\) −2.51109 −0.0920612
\(745\) 23.1586 0.848466
\(746\) −12.2917 −0.450030
\(747\) −0.152814 −0.00559118
\(748\) −6.40684 −0.234257
\(749\) 26.7276 0.976607
\(750\) 6.30482 0.230219
\(751\) −17.8437 −0.651125 −0.325562 0.945521i \(-0.605554\pi\)
−0.325562 + 0.945521i \(0.605554\pi\)
\(752\) 3.44949 0.125790
\(753\) −17.2811 −0.629757
\(754\) −3.32196 −0.120979
\(755\) −20.4798 −0.745337
\(756\) −3.42043 −0.124400
\(757\) −13.5549 −0.492662 −0.246331 0.969186i \(-0.579225\pi\)
−0.246331 + 0.969186i \(0.579225\pi\)
\(758\) −6.21412 −0.225707
\(759\) −0.605988 −0.0219960
\(760\) 17.6569 0.640484
\(761\) 5.51582 0.199948 0.0999742 0.994990i \(-0.468124\pi\)
0.0999742 + 0.994990i \(0.468124\pi\)
\(762\) −8.88937 −0.322028
\(763\) −20.5191 −0.742842
\(764\) 10.1874 0.368566
\(765\) −2.78078 −0.100539
\(766\) 24.5786 0.888060
\(767\) 1.09916 0.0396882
\(768\) −1.00000 −0.0360844
\(769\) −26.9607 −0.972229 −0.486115 0.873895i \(-0.661586\pi\)
−0.486115 + 0.873895i \(0.661586\pi\)
\(770\) −60.9383 −2.19606
\(771\) −29.6761 −1.06876
\(772\) −18.6070 −0.669681
\(773\) 19.2940 0.693957 0.346979 0.937873i \(-0.387208\pi\)
0.346979 + 0.937873i \(0.387208\pi\)
\(774\) 4.15125 0.149214
\(775\) −6.86210 −0.246494
\(776\) −1.52877 −0.0548796
\(777\) 13.7944 0.494870
\(778\) −19.3063 −0.692165
\(779\) 25.0352 0.896978
\(780\) −3.05651 −0.109440
\(781\) 55.4170 1.98298
\(782\) 0.0945846 0.00338234
\(783\) 3.02228 0.108007
\(784\) 4.69932 0.167833
\(785\) −27.4672 −0.980346
\(786\) 3.04262 0.108527
\(787\) −41.7477 −1.48814 −0.744072 0.668099i \(-0.767108\pi\)
−0.744072 + 0.668099i \(0.767108\pi\)
\(788\) −24.3322 −0.866797
\(789\) −21.9414 −0.781136
\(790\) 19.0544 0.677924
\(791\) −19.3923 −0.689509
\(792\) 6.40684 0.227657
\(793\) 2.06655 0.0733855
\(794\) 23.0737 0.818853
\(795\) 2.29492 0.0813926
\(796\) −3.70805 −0.131428
\(797\) −36.1574 −1.28076 −0.640381 0.768058i \(-0.721223\pi\)
−0.640381 + 0.768058i \(0.721223\pi\)
\(798\) 21.7185 0.768826
\(799\) 3.44949 0.122034
\(800\) −2.73271 −0.0966160
\(801\) −9.59621 −0.339065
\(802\) −6.62545 −0.233953
\(803\) −44.0210 −1.55347
\(804\) 6.99934 0.246848
\(805\) 0.899636 0.0317080
\(806\) −2.76008 −0.0972198
\(807\) 1.06146 0.0373652
\(808\) −7.28219 −0.256186
\(809\) 14.9124 0.524292 0.262146 0.965028i \(-0.415570\pi\)
0.262146 + 0.965028i \(0.415570\pi\)
\(810\) 2.78078 0.0977065
\(811\) 21.2737 0.747021 0.373510 0.927626i \(-0.378154\pi\)
0.373510 + 0.927626i \(0.378154\pi\)
\(812\) −10.3375 −0.362775
\(813\) 4.15826 0.145837
\(814\) −25.8384 −0.905634
\(815\) 60.8155 2.13027
\(816\) −1.00000 −0.0350070
\(817\) −26.3589 −0.922183
\(818\) −4.87099 −0.170310
\(819\) −3.75958 −0.131370
\(820\) −10.9640 −0.382878
\(821\) −42.2690 −1.47520 −0.737598 0.675240i \(-0.764040\pi\)
−0.737598 + 0.675240i \(0.764040\pi\)
\(822\) 0.484042 0.0168829
\(823\) −4.16450 −0.145166 −0.0725828 0.997362i \(-0.523124\pi\)
−0.0725828 + 0.997362i \(0.523124\pi\)
\(824\) 3.54082 0.123350
\(825\) 17.5081 0.609552
\(826\) 3.42043 0.119012
\(827\) 6.91461 0.240445 0.120222 0.992747i \(-0.461639\pi\)
0.120222 + 0.992747i \(0.461639\pi\)
\(828\) −0.0945846 −0.00328704
\(829\) 25.1055 0.871949 0.435974 0.899959i \(-0.356404\pi\)
0.435974 + 0.899959i \(0.356404\pi\)
\(830\) −0.424942 −0.0147500
\(831\) 0.918785 0.0318723
\(832\) −1.09916 −0.0381064
\(833\) 4.69932 0.162822
\(834\) −0.179257 −0.00620717
\(835\) −58.7608 −2.03350
\(836\) −40.6811 −1.40699
\(837\) 2.51109 0.0867961
\(838\) 13.5440 0.467871
\(839\) −18.4359 −0.636478 −0.318239 0.948010i \(-0.603092\pi\)
−0.318239 + 0.948010i \(0.603092\pi\)
\(840\) −9.51144 −0.328176
\(841\) −19.8658 −0.685028
\(842\) −16.4086 −0.565479
\(843\) −20.3440 −0.700685
\(844\) −5.01235 −0.172532
\(845\) 32.7905 1.12803
\(846\) −3.44949 −0.118596
\(847\) 102.776 3.53141
\(848\) 0.825282 0.0283403
\(849\) 28.9503 0.993573
\(850\) −2.73271 −0.0937313
\(851\) 0.381453 0.0130761
\(852\) 8.64966 0.296333
\(853\) 28.3342 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(854\) 6.43084 0.220059
\(855\) −17.6569 −0.603854
\(856\) −7.81413 −0.267081
\(857\) −54.2781 −1.85411 −0.927053 0.374931i \(-0.877666\pi\)
−0.927053 + 0.374931i \(0.877666\pi\)
\(858\) 7.04211 0.240414
\(859\) −20.7844 −0.709154 −0.354577 0.935027i \(-0.615375\pi\)
−0.354577 + 0.935027i \(0.615375\pi\)
\(860\) 11.5437 0.393637
\(861\) −13.4860 −0.459600
\(862\) −5.11972 −0.174378
\(863\) 16.8653 0.574102 0.287051 0.957915i \(-0.407325\pi\)
0.287051 + 0.957915i \(0.407325\pi\)
\(864\) 1.00000 0.0340207
\(865\) −31.3748 −1.06678
\(866\) 26.7697 0.909670
\(867\) −1.00000 −0.0339618
\(868\) −8.58901 −0.291530
\(869\) −43.9008 −1.48923
\(870\) 8.40428 0.284932
\(871\) 7.69337 0.260680
\(872\) 5.99899 0.203152
\(873\) 1.52877 0.0517410
\(874\) 0.600578 0.0203149
\(875\) 21.5652 0.729035
\(876\) −6.87094 −0.232148
\(877\) −7.45399 −0.251704 −0.125852 0.992049i \(-0.540166\pi\)
−0.125852 + 0.992049i \(0.540166\pi\)
\(878\) −25.7731 −0.869800
\(879\) 21.5847 0.728035
\(880\) 17.8160 0.600577
\(881\) −14.9966 −0.505247 −0.252623 0.967565i \(-0.581293\pi\)
−0.252623 + 0.967565i \(0.581293\pi\)
\(882\) −4.69932 −0.158234
\(883\) 45.1455 1.51927 0.759634 0.650351i \(-0.225378\pi\)
0.759634 + 0.650351i \(0.225378\pi\)
\(884\) −1.09916 −0.0369686
\(885\) −2.78078 −0.0934748
\(886\) −6.33359 −0.212781
\(887\) −19.1800 −0.644001 −0.322001 0.946739i \(-0.604355\pi\)
−0.322001 + 0.946739i \(0.604355\pi\)
\(888\) −4.03293 −0.135336
\(889\) −30.4054 −1.01977
\(890\) −26.6849 −0.894480
\(891\) −6.40684 −0.214637
\(892\) 1.38896 0.0465059
\(893\) 21.9030 0.732956
\(894\) −8.32811 −0.278534
\(895\) −7.11134 −0.237706
\(896\) −3.42043 −0.114268
\(897\) −0.103963 −0.00347123
\(898\) 6.05616 0.202097
\(899\) 7.58923 0.253115
\(900\) 2.73271 0.0910905
\(901\) 0.825282 0.0274941
\(902\) 25.2607 0.841089
\(903\) 14.1990 0.472515
\(904\) 5.66954 0.188566
\(905\) −7.49455 −0.249127
\(906\) 7.36479 0.244679
\(907\) 48.8641 1.62250 0.811252 0.584697i \(-0.198786\pi\)
0.811252 + 0.584697i \(0.198786\pi\)
\(908\) −8.74677 −0.290272
\(909\) 7.28219 0.241535
\(910\) −10.4546 −0.346565
\(911\) −52.1806 −1.72882 −0.864410 0.502788i \(-0.832308\pi\)
−0.864410 + 0.502788i \(0.832308\pi\)
\(912\) −6.34964 −0.210258
\(913\) 0.979056 0.0324020
\(914\) −24.5777 −0.812959
\(915\) −5.22821 −0.172839
\(916\) 13.4870 0.445622
\(917\) 10.4070 0.343671
\(918\) 1.00000 0.0330049
\(919\) 27.8217 0.917752 0.458876 0.888500i \(-0.348252\pi\)
0.458876 + 0.888500i \(0.348252\pi\)
\(920\) −0.263019 −0.00867147
\(921\) −13.7268 −0.452313
\(922\) −23.1601 −0.762737
\(923\) 9.50733 0.312938
\(924\) 21.9141 0.720922
\(925\) −11.0209 −0.362363
\(926\) 6.15000 0.202102
\(927\) −3.54082 −0.116296
\(928\) 3.02228 0.0992112
\(929\) −5.64580 −0.185233 −0.0926164 0.995702i \(-0.529523\pi\)
−0.0926164 + 0.995702i \(0.529523\pi\)
\(930\) 6.98279 0.228975
\(931\) 29.8390 0.977933
\(932\) −6.74729 −0.221015
\(933\) 13.7718 0.450868
\(934\) −38.5003 −1.25977
\(935\) 17.8160 0.582645
\(936\) 1.09916 0.0359270
\(937\) −41.9119 −1.36920 −0.684601 0.728918i \(-0.740024\pi\)
−0.684601 + 0.728918i \(0.740024\pi\)
\(938\) 23.9407 0.781693
\(939\) −19.3987 −0.633052
\(940\) −9.59225 −0.312865
\(941\) −5.59293 −0.182324 −0.0911621 0.995836i \(-0.529058\pi\)
−0.0911621 + 0.995836i \(0.529058\pi\)
\(942\) 9.87753 0.321827
\(943\) −0.372925 −0.0121441
\(944\) −1.00000 −0.0325472
\(945\) 9.51144 0.309407
\(946\) −26.5964 −0.864723
\(947\) 36.5743 1.18851 0.594253 0.804278i \(-0.297448\pi\)
0.594253 + 0.804278i \(0.297448\pi\)
\(948\) −6.85217 −0.222548
\(949\) −7.55223 −0.245156
\(950\) −17.3518 −0.562965
\(951\) −21.2894 −0.690356
\(952\) −3.42043 −0.110857
\(953\) 26.3468 0.853457 0.426728 0.904380i \(-0.359666\pi\)
0.426728 + 0.904380i \(0.359666\pi\)
\(954\) −0.825282 −0.0267195
\(955\) −28.3288 −0.916697
\(956\) −3.39472 −0.109793
\(957\) −19.3633 −0.625925
\(958\) −3.10423 −0.100293
\(959\) 1.65563 0.0534631
\(960\) 2.78078 0.0897492
\(961\) −24.6944 −0.796594
\(962\) −4.43282 −0.142920
\(963\) 7.81413 0.251807
\(964\) 13.6691 0.440254
\(965\) 51.7419 1.66563
\(966\) −0.323520 −0.0104091
\(967\) −26.9030 −0.865141 −0.432570 0.901600i \(-0.642393\pi\)
−0.432570 + 0.901600i \(0.642393\pi\)
\(968\) −30.0476 −0.965765
\(969\) −6.34964 −0.203980
\(970\) 4.25116 0.136497
\(971\) −36.5952 −1.17440 −0.587199 0.809443i \(-0.699769\pi\)
−0.587199 + 0.809443i \(0.699769\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −0.613137 −0.0196563
\(974\) −28.9801 −0.928581
\(975\) 3.00368 0.0961947
\(976\) −1.88013 −0.0601814
\(977\) 13.5085 0.432176 0.216088 0.976374i \(-0.430670\pi\)
0.216088 + 0.976374i \(0.430670\pi\)
\(978\) −21.8700 −0.699325
\(979\) 61.4814 1.96495
\(980\) −13.0678 −0.417434
\(981\) −5.99899 −0.191533
\(982\) −41.1935 −1.31454
\(983\) 25.3590 0.808827 0.404413 0.914576i \(-0.367476\pi\)
0.404413 + 0.914576i \(0.367476\pi\)
\(984\) 3.94277 0.125691
\(985\) 67.6623 2.15590
\(986\) 3.02228 0.0962490
\(987\) −11.7987 −0.375557
\(988\) −6.97925 −0.222039
\(989\) 0.392644 0.0124854
\(990\) −17.8160 −0.566229
\(991\) −38.2337 −1.21453 −0.607267 0.794498i \(-0.707734\pi\)
−0.607267 + 0.794498i \(0.707734\pi\)
\(992\) 2.51109 0.0797273
\(993\) −10.7517 −0.341193
\(994\) 29.5855 0.938396
\(995\) 10.3113 0.326889
\(996\) 0.152814 0.00484210
\(997\) −10.8817 −0.344628 −0.172314 0.985042i \(-0.555124\pi\)
−0.172314 + 0.985042i \(0.555124\pi\)
\(998\) 16.5558 0.524066
\(999\) 4.03293 0.127596
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 6018.2.a.x.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.x.1.2 10 1.1 even 1 trivial