Properties

Label 8007.2.a.c.1.5
Level $8007$
Weight $2$
Character 8007.1
Self dual yes
Analytic conductor $63.936$
Analytic rank $1$
Dimension $39$
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] = [8007,2,Mod(1,8007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8007, 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("8007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8007.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: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(39\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 8007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.20952 q^{2} -1.00000 q^{3} +2.88199 q^{4} -2.30853 q^{5} +2.20952 q^{6} -2.22002 q^{7} -1.94877 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.20952 q^{2} -1.00000 q^{3} +2.88199 q^{4} -2.30853 q^{5} +2.20952 q^{6} -2.22002 q^{7} -1.94877 q^{8} +1.00000 q^{9} +5.10076 q^{10} -3.84505 q^{11} -2.88199 q^{12} -1.58168 q^{13} +4.90519 q^{14} +2.30853 q^{15} -1.45813 q^{16} +1.00000 q^{17} -2.20952 q^{18} -0.738095 q^{19} -6.65316 q^{20} +2.22002 q^{21} +8.49572 q^{22} -4.94002 q^{23} +1.94877 q^{24} +0.329329 q^{25} +3.49477 q^{26} -1.00000 q^{27} -6.39808 q^{28} +10.1642 q^{29} -5.10076 q^{30} -0.840905 q^{31} +7.11930 q^{32} +3.84505 q^{33} -2.20952 q^{34} +5.12500 q^{35} +2.88199 q^{36} -8.92908 q^{37} +1.63084 q^{38} +1.58168 q^{39} +4.49879 q^{40} +0.805630 q^{41} -4.90519 q^{42} -1.73261 q^{43} -11.0814 q^{44} -2.30853 q^{45} +10.9151 q^{46} -3.65706 q^{47} +1.45813 q^{48} -2.07149 q^{49} -0.727660 q^{50} -1.00000 q^{51} -4.55839 q^{52} +0.966170 q^{53} +2.20952 q^{54} +8.87642 q^{55} +4.32631 q^{56} +0.738095 q^{57} -22.4580 q^{58} +13.0182 q^{59} +6.65316 q^{60} +2.83262 q^{61} +1.85800 q^{62} -2.22002 q^{63} -12.8140 q^{64} +3.65137 q^{65} -8.49572 q^{66} -1.20484 q^{67} +2.88199 q^{68} +4.94002 q^{69} -11.3238 q^{70} +14.3800 q^{71} -1.94877 q^{72} -4.59489 q^{73} +19.7290 q^{74} -0.329329 q^{75} -2.12718 q^{76} +8.53610 q^{77} -3.49477 q^{78} +7.33466 q^{79} +3.36614 q^{80} +1.00000 q^{81} -1.78006 q^{82} -0.714138 q^{83} +6.39808 q^{84} -2.30853 q^{85} +3.82824 q^{86} -10.1642 q^{87} +7.49310 q^{88} -3.74781 q^{89} +5.10076 q^{90} +3.51138 q^{91} -14.2371 q^{92} +0.840905 q^{93} +8.08035 q^{94} +1.70392 q^{95} -7.11930 q^{96} +18.5380 q^{97} +4.57701 q^{98} -3.84505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20952 −1.56237 −0.781184 0.624301i \(-0.785384\pi\)
−0.781184 + 0.624301i \(0.785384\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.88199 1.44099
\(5\) −2.30853 −1.03241 −0.516204 0.856466i \(-0.672655\pi\)
−0.516204 + 0.856466i \(0.672655\pi\)
\(6\) 2.20952 0.902033
\(7\) −2.22002 −0.839090 −0.419545 0.907735i \(-0.637810\pi\)
−0.419545 + 0.907735i \(0.637810\pi\)
\(8\) −1.94877 −0.688993
\(9\) 1.00000 0.333333
\(10\) 5.10076 1.61300
\(11\) −3.84505 −1.15933 −0.579663 0.814856i \(-0.696816\pi\)
−0.579663 + 0.814856i \(0.696816\pi\)
\(12\) −2.88199 −0.831958
\(13\) −1.58168 −0.438680 −0.219340 0.975648i \(-0.570390\pi\)
−0.219340 + 0.975648i \(0.570390\pi\)
\(14\) 4.90519 1.31097
\(15\) 2.30853 0.596061
\(16\) −1.45813 −0.364533
\(17\) 1.00000 0.242536
\(18\) −2.20952 −0.520789
\(19\) −0.738095 −0.169331 −0.0846653 0.996409i \(-0.526982\pi\)
−0.0846653 + 0.996409i \(0.526982\pi\)
\(20\) −6.65316 −1.48769
\(21\) 2.22002 0.484449
\(22\) 8.49572 1.81129
\(23\) −4.94002 −1.03007 −0.515033 0.857171i \(-0.672220\pi\)
−0.515033 + 0.857171i \(0.672220\pi\)
\(24\) 1.94877 0.397790
\(25\) 0.329329 0.0658658
\(26\) 3.49477 0.685380
\(27\) −1.00000 −0.192450
\(28\) −6.39808 −1.20912
\(29\) 10.1642 1.88744 0.943720 0.330744i \(-0.107300\pi\)
0.943720 + 0.330744i \(0.107300\pi\)
\(30\) −5.10076 −0.931266
\(31\) −0.840905 −0.151031 −0.0755155 0.997145i \(-0.524060\pi\)
−0.0755155 + 0.997145i \(0.524060\pi\)
\(32\) 7.11930 1.25853
\(33\) 3.84505 0.669337
\(34\) −2.20952 −0.378930
\(35\) 5.12500 0.866283
\(36\) 2.88199 0.480331
\(37\) −8.92908 −1.46793 −0.733966 0.679186i \(-0.762333\pi\)
−0.733966 + 0.679186i \(0.762333\pi\)
\(38\) 1.63084 0.264557
\(39\) 1.58168 0.253272
\(40\) 4.49879 0.711322
\(41\) 0.805630 0.125818 0.0629091 0.998019i \(-0.479962\pi\)
0.0629091 + 0.998019i \(0.479962\pi\)
\(42\) −4.90519 −0.756887
\(43\) −1.73261 −0.264221 −0.132110 0.991235i \(-0.542175\pi\)
−0.132110 + 0.991235i \(0.542175\pi\)
\(44\) −11.0814 −1.67058
\(45\) −2.30853 −0.344136
\(46\) 10.9151 1.60934
\(47\) −3.65706 −0.533437 −0.266718 0.963774i \(-0.585939\pi\)
−0.266718 + 0.963774i \(0.585939\pi\)
\(48\) 1.45813 0.210463
\(49\) −2.07149 −0.295928
\(50\) −0.727660 −0.102907
\(51\) −1.00000 −0.140028
\(52\) −4.55839 −0.632135
\(53\) 0.966170 0.132714 0.0663568 0.997796i \(-0.478862\pi\)
0.0663568 + 0.997796i \(0.478862\pi\)
\(54\) 2.20952 0.300678
\(55\) 8.87642 1.19690
\(56\) 4.32631 0.578127
\(57\) 0.738095 0.0977631
\(58\) −22.4580 −2.94888
\(59\) 13.0182 1.69483 0.847415 0.530931i \(-0.178158\pi\)
0.847415 + 0.530931i \(0.178158\pi\)
\(60\) 6.65316 0.858919
\(61\) 2.83262 0.362679 0.181340 0.983421i \(-0.441957\pi\)
0.181340 + 0.983421i \(0.441957\pi\)
\(62\) 1.85800 0.235966
\(63\) −2.22002 −0.279697
\(64\) −12.8140 −1.60175
\(65\) 3.65137 0.452897
\(66\) −8.49572 −1.04575
\(67\) −1.20484 −0.147195 −0.0735974 0.997288i \(-0.523448\pi\)
−0.0735974 + 0.997288i \(0.523448\pi\)
\(68\) 2.88199 0.349492
\(69\) 4.94002 0.594708
\(70\) −11.3238 −1.35345
\(71\) 14.3800 1.70660 0.853298 0.521423i \(-0.174599\pi\)
0.853298 + 0.521423i \(0.174599\pi\)
\(72\) −1.94877 −0.229664
\(73\) −4.59489 −0.537791 −0.268895 0.963169i \(-0.586659\pi\)
−0.268895 + 0.963169i \(0.586659\pi\)
\(74\) 19.7290 2.29345
\(75\) −0.329329 −0.0380276
\(76\) −2.12718 −0.244004
\(77\) 8.53610 0.972779
\(78\) −3.49477 −0.395704
\(79\) 7.33466 0.825214 0.412607 0.910909i \(-0.364618\pi\)
0.412607 + 0.910909i \(0.364618\pi\)
\(80\) 3.36614 0.376346
\(81\) 1.00000 0.111111
\(82\) −1.78006 −0.196574
\(83\) −0.714138 −0.0783868 −0.0391934 0.999232i \(-0.512479\pi\)
−0.0391934 + 0.999232i \(0.512479\pi\)
\(84\) 6.39808 0.698087
\(85\) −2.30853 −0.250396
\(86\) 3.82824 0.412810
\(87\) −10.1642 −1.08971
\(88\) 7.49310 0.798767
\(89\) −3.74781 −0.397267 −0.198633 0.980074i \(-0.563650\pi\)
−0.198633 + 0.980074i \(0.563650\pi\)
\(90\) 5.10076 0.537667
\(91\) 3.51138 0.368092
\(92\) −14.2371 −1.48432
\(93\) 0.840905 0.0871978
\(94\) 8.08035 0.833425
\(95\) 1.70392 0.174818
\(96\) −7.11930 −0.726611
\(97\) 18.5380 1.88224 0.941122 0.338067i \(-0.109773\pi\)
0.941122 + 0.338067i \(0.109773\pi\)
\(98\) 4.57701 0.462348
\(99\) −3.84505 −0.386442
\(100\) 0.949122 0.0949122
\(101\) −13.8732 −1.38043 −0.690216 0.723604i \(-0.742484\pi\)
−0.690216 + 0.723604i \(0.742484\pi\)
\(102\) 2.20952 0.218775
\(103\) 2.31242 0.227849 0.113925 0.993489i \(-0.463658\pi\)
0.113925 + 0.993489i \(0.463658\pi\)
\(104\) 3.08233 0.302248
\(105\) −5.12500 −0.500149
\(106\) −2.13477 −0.207348
\(107\) −1.17716 −0.113800 −0.0569001 0.998380i \(-0.518122\pi\)
−0.0569001 + 0.998380i \(0.518122\pi\)
\(108\) −2.88199 −0.277319
\(109\) −19.9146 −1.90747 −0.953734 0.300650i \(-0.902796\pi\)
−0.953734 + 0.300650i \(0.902796\pi\)
\(110\) −19.6127 −1.86999
\(111\) 8.92908 0.847511
\(112\) 3.23708 0.305876
\(113\) 9.41079 0.885293 0.442646 0.896696i \(-0.354040\pi\)
0.442646 + 0.896696i \(0.354040\pi\)
\(114\) −1.63084 −0.152742
\(115\) 11.4042 1.06345
\(116\) 29.2930 2.71979
\(117\) −1.58168 −0.146227
\(118\) −28.7641 −2.64795
\(119\) −2.22002 −0.203509
\(120\) −4.49879 −0.410682
\(121\) 3.78439 0.344036
\(122\) −6.25873 −0.566639
\(123\) −0.805630 −0.0726412
\(124\) −2.42348 −0.217635
\(125\) 10.7824 0.964407
\(126\) 4.90519 0.436989
\(127\) −5.42283 −0.481199 −0.240599 0.970625i \(-0.577344\pi\)
−0.240599 + 0.970625i \(0.577344\pi\)
\(128\) 14.0742 1.24399
\(129\) 1.73261 0.152548
\(130\) −8.06779 −0.707592
\(131\) −5.15483 −0.450379 −0.225190 0.974315i \(-0.572300\pi\)
−0.225190 + 0.974315i \(0.572300\pi\)
\(132\) 11.0814 0.964510
\(133\) 1.63859 0.142084
\(134\) 2.66212 0.229973
\(135\) 2.30853 0.198687
\(136\) −1.94877 −0.167105
\(137\) 1.80324 0.154061 0.0770307 0.997029i \(-0.475456\pi\)
0.0770307 + 0.997029i \(0.475456\pi\)
\(138\) −10.9151 −0.929153
\(139\) 8.52112 0.722752 0.361376 0.932420i \(-0.382307\pi\)
0.361376 + 0.932420i \(0.382307\pi\)
\(140\) 14.7702 1.24831
\(141\) 3.65706 0.307980
\(142\) −31.7730 −2.66633
\(143\) 6.08165 0.508574
\(144\) −1.45813 −0.121511
\(145\) −23.4644 −1.94861
\(146\) 10.1525 0.840227
\(147\) 2.07149 0.170854
\(148\) −25.7335 −2.11528
\(149\) 21.9483 1.79808 0.899038 0.437870i \(-0.144267\pi\)
0.899038 + 0.437870i \(0.144267\pi\)
\(150\) 0.727660 0.0594132
\(151\) 6.83500 0.556224 0.278112 0.960549i \(-0.410291\pi\)
0.278112 + 0.960549i \(0.410291\pi\)
\(152\) 1.43837 0.116668
\(153\) 1.00000 0.0808452
\(154\) −18.8607 −1.51984
\(155\) 1.94126 0.155926
\(156\) 4.55839 0.364964
\(157\) 1.00000 0.0798087
\(158\) −16.2061 −1.28929
\(159\) −0.966170 −0.0766223
\(160\) −16.4352 −1.29931
\(161\) 10.9670 0.864317
\(162\) −2.20952 −0.173596
\(163\) 7.96902 0.624182 0.312091 0.950052i \(-0.398971\pi\)
0.312091 + 0.950052i \(0.398971\pi\)
\(164\) 2.32181 0.181303
\(165\) −8.87642 −0.691029
\(166\) 1.57790 0.122469
\(167\) 6.96414 0.538901 0.269450 0.963014i \(-0.413158\pi\)
0.269450 + 0.963014i \(0.413158\pi\)
\(168\) −4.32631 −0.333782
\(169\) −10.4983 −0.807559
\(170\) 5.10076 0.391210
\(171\) −0.738095 −0.0564435
\(172\) −4.99336 −0.380740
\(173\) −4.40945 −0.335244 −0.167622 0.985851i \(-0.553609\pi\)
−0.167622 + 0.985851i \(0.553609\pi\)
\(174\) 22.4580 1.70253
\(175\) −0.731118 −0.0552674
\(176\) 5.60658 0.422612
\(177\) −13.0182 −0.978510
\(178\) 8.28086 0.620677
\(179\) 7.09049 0.529968 0.264984 0.964253i \(-0.414633\pi\)
0.264984 + 0.964253i \(0.414633\pi\)
\(180\) −6.65316 −0.495897
\(181\) 3.58628 0.266566 0.133283 0.991078i \(-0.457448\pi\)
0.133283 + 0.991078i \(0.457448\pi\)
\(182\) −7.75847 −0.575096
\(183\) −2.83262 −0.209393
\(184\) 9.62694 0.709707
\(185\) 20.6131 1.51550
\(186\) −1.85800 −0.136235
\(187\) −3.84505 −0.281178
\(188\) −10.5396 −0.768679
\(189\) 2.22002 0.161483
\(190\) −3.76484 −0.273130
\(191\) −10.7272 −0.776194 −0.388097 0.921619i \(-0.626867\pi\)
−0.388097 + 0.921619i \(0.626867\pi\)
\(192\) 12.8140 0.924770
\(193\) −17.2369 −1.24074 −0.620370 0.784309i \(-0.713017\pi\)
−0.620370 + 0.784309i \(0.713017\pi\)
\(194\) −40.9600 −2.94076
\(195\) −3.65137 −0.261480
\(196\) −5.97002 −0.426430
\(197\) 23.5952 1.68109 0.840545 0.541741i \(-0.182235\pi\)
0.840545 + 0.541741i \(0.182235\pi\)
\(198\) 8.49572 0.603764
\(199\) 2.59595 0.184022 0.0920110 0.995758i \(-0.470671\pi\)
0.0920110 + 0.995758i \(0.470671\pi\)
\(200\) −0.641785 −0.0453811
\(201\) 1.20484 0.0849830
\(202\) 30.6531 2.15674
\(203\) −22.5647 −1.58373
\(204\) −2.88199 −0.201779
\(205\) −1.85982 −0.129896
\(206\) −5.10934 −0.355985
\(207\) −4.94002 −0.343355
\(208\) 2.30630 0.159913
\(209\) 2.83801 0.196309
\(210\) 11.3238 0.781416
\(211\) 26.1164 1.79793 0.898963 0.438025i \(-0.144322\pi\)
0.898963 + 0.438025i \(0.144322\pi\)
\(212\) 2.78449 0.191239
\(213\) −14.3800 −0.985304
\(214\) 2.60096 0.177798
\(215\) 3.99979 0.272783
\(216\) 1.94877 0.132597
\(217\) 1.86683 0.126729
\(218\) 44.0016 2.98017
\(219\) 4.59489 0.310494
\(220\) 25.5817 1.72472
\(221\) −1.58168 −0.106396
\(222\) −19.7290 −1.32412
\(223\) 11.2118 0.750798 0.375399 0.926863i \(-0.377506\pi\)
0.375399 + 0.926863i \(0.377506\pi\)
\(224\) −15.8050 −1.05602
\(225\) 0.329329 0.0219553
\(226\) −20.7933 −1.38315
\(227\) 16.0179 1.06314 0.531572 0.847013i \(-0.321602\pi\)
0.531572 + 0.847013i \(0.321602\pi\)
\(228\) 2.12718 0.140876
\(229\) −8.93746 −0.590604 −0.295302 0.955404i \(-0.595420\pi\)
−0.295302 + 0.955404i \(0.595420\pi\)
\(230\) −25.1978 −1.66150
\(231\) −8.53610 −0.561634
\(232\) −19.8076 −1.30043
\(233\) −1.19361 −0.0781958 −0.0390979 0.999235i \(-0.512448\pi\)
−0.0390979 + 0.999235i \(0.512448\pi\)
\(234\) 3.49477 0.228460
\(235\) 8.44245 0.550724
\(236\) 37.5184 2.44224
\(237\) −7.33466 −0.476438
\(238\) 4.90519 0.317956
\(239\) 26.4181 1.70885 0.854423 0.519578i \(-0.173911\pi\)
0.854423 + 0.519578i \(0.173911\pi\)
\(240\) −3.36614 −0.217284
\(241\) 8.65381 0.557441 0.278720 0.960372i \(-0.410090\pi\)
0.278720 + 0.960372i \(0.410090\pi\)
\(242\) −8.36170 −0.537510
\(243\) −1.00000 −0.0641500
\(244\) 8.16356 0.522618
\(245\) 4.78212 0.305518
\(246\) 1.78006 0.113492
\(247\) 1.16743 0.0742820
\(248\) 1.63873 0.104059
\(249\) 0.714138 0.0452566
\(250\) −23.8240 −1.50676
\(251\) −13.1035 −0.827083 −0.413541 0.910485i \(-0.635708\pi\)
−0.413541 + 0.910485i \(0.635708\pi\)
\(252\) −6.39808 −0.403041
\(253\) 18.9946 1.19418
\(254\) 11.9819 0.751809
\(255\) 2.30853 0.144566
\(256\) −5.46923 −0.341827
\(257\) −6.26798 −0.390986 −0.195493 0.980705i \(-0.562631\pi\)
−0.195493 + 0.980705i \(0.562631\pi\)
\(258\) −3.82824 −0.238336
\(259\) 19.8228 1.23173
\(260\) 10.5232 0.652621
\(261\) 10.1642 0.629147
\(262\) 11.3897 0.703658
\(263\) −25.6283 −1.58031 −0.790155 0.612907i \(-0.790000\pi\)
−0.790155 + 0.612907i \(0.790000\pi\)
\(264\) −7.49310 −0.461168
\(265\) −2.23044 −0.137015
\(266\) −3.62050 −0.221987
\(267\) 3.74781 0.229362
\(268\) −3.47234 −0.212107
\(269\) −27.5743 −1.68123 −0.840617 0.541631i \(-0.817807\pi\)
−0.840617 + 0.541631i \(0.817807\pi\)
\(270\) −5.10076 −0.310422
\(271\) 25.5444 1.55171 0.775857 0.630908i \(-0.217318\pi\)
0.775857 + 0.630908i \(0.217318\pi\)
\(272\) −1.45813 −0.0884122
\(273\) −3.51138 −0.212518
\(274\) −3.98430 −0.240701
\(275\) −1.26629 −0.0763599
\(276\) 14.2371 0.856970
\(277\) 4.16094 0.250006 0.125003 0.992156i \(-0.460106\pi\)
0.125003 + 0.992156i \(0.460106\pi\)
\(278\) −18.8276 −1.12920
\(279\) −0.840905 −0.0503437
\(280\) −9.98743 −0.596863
\(281\) −24.7320 −1.47539 −0.737693 0.675136i \(-0.764085\pi\)
−0.737693 + 0.675136i \(0.764085\pi\)
\(282\) −8.08035 −0.481178
\(283\) 26.0154 1.54645 0.773226 0.634130i \(-0.218642\pi\)
0.773226 + 0.634130i \(0.218642\pi\)
\(284\) 41.4431 2.45919
\(285\) −1.70392 −0.100931
\(286\) −13.4375 −0.794579
\(287\) −1.78852 −0.105573
\(288\) 7.11930 0.419509
\(289\) 1.00000 0.0588235
\(290\) 51.8450 3.04444
\(291\) −18.5380 −1.08671
\(292\) −13.2424 −0.774953
\(293\) −19.0533 −1.11310 −0.556552 0.830813i \(-0.687876\pi\)
−0.556552 + 0.830813i \(0.687876\pi\)
\(294\) −4.57701 −0.266937
\(295\) −30.0530 −1.74976
\(296\) 17.4007 1.01139
\(297\) 3.84505 0.223112
\(298\) −48.4953 −2.80926
\(299\) 7.81355 0.451869
\(300\) −0.949122 −0.0547976
\(301\) 3.84643 0.221705
\(302\) −15.1021 −0.869027
\(303\) 13.8732 0.796993
\(304\) 1.07624 0.0617265
\(305\) −6.53919 −0.374433
\(306\) −2.20952 −0.126310
\(307\) −24.7473 −1.41240 −0.706201 0.708012i \(-0.749592\pi\)
−0.706201 + 0.708012i \(0.749592\pi\)
\(308\) 24.6009 1.40177
\(309\) −2.31242 −0.131549
\(310\) −4.28925 −0.243613
\(311\) 19.3519 1.09735 0.548673 0.836037i \(-0.315133\pi\)
0.548673 + 0.836037i \(0.315133\pi\)
\(312\) −3.08233 −0.174503
\(313\) −22.0735 −1.24767 −0.623834 0.781557i \(-0.714426\pi\)
−0.623834 + 0.781557i \(0.714426\pi\)
\(314\) −2.20952 −0.124691
\(315\) 5.12500 0.288761
\(316\) 21.1384 1.18913
\(317\) 17.5284 0.984491 0.492246 0.870456i \(-0.336176\pi\)
0.492246 + 0.870456i \(0.336176\pi\)
\(318\) 2.13477 0.119712
\(319\) −39.0818 −2.18816
\(320\) 29.5815 1.65366
\(321\) 1.17716 0.0657026
\(322\) −24.2317 −1.35038
\(323\) −0.738095 −0.0410687
\(324\) 2.88199 0.160110
\(325\) −0.520895 −0.0288940
\(326\) −17.6077 −0.975202
\(327\) 19.9146 1.10128
\(328\) −1.56998 −0.0866879
\(329\) 8.11876 0.447602
\(330\) 19.6127 1.07964
\(331\) 6.98992 0.384201 0.192100 0.981375i \(-0.438470\pi\)
0.192100 + 0.981375i \(0.438470\pi\)
\(332\) −2.05813 −0.112955
\(333\) −8.92908 −0.489311
\(334\) −15.3874 −0.841961
\(335\) 2.78142 0.151965
\(336\) −3.23708 −0.176597
\(337\) −6.01148 −0.327466 −0.163733 0.986505i \(-0.552354\pi\)
−0.163733 + 0.986505i \(0.552354\pi\)
\(338\) 23.1962 1.26170
\(339\) −9.41079 −0.511124
\(340\) −6.65316 −0.360818
\(341\) 3.23332 0.175094
\(342\) 1.63084 0.0881855
\(343\) 20.1389 1.08740
\(344\) 3.37645 0.182046
\(345\) −11.4042 −0.613981
\(346\) 9.74277 0.523775
\(347\) 5.53277 0.297014 0.148507 0.988911i \(-0.452553\pi\)
0.148507 + 0.988911i \(0.452553\pi\)
\(348\) −29.2930 −1.57027
\(349\) 10.0050 0.535557 0.267779 0.963480i \(-0.413710\pi\)
0.267779 + 0.963480i \(0.413710\pi\)
\(350\) 1.61542 0.0863479
\(351\) 1.58168 0.0844241
\(352\) −27.3741 −1.45904
\(353\) −2.60373 −0.138582 −0.0692912 0.997596i \(-0.522074\pi\)
−0.0692912 + 0.997596i \(0.522074\pi\)
\(354\) 28.7641 1.52879
\(355\) −33.1968 −1.76190
\(356\) −10.8011 −0.572459
\(357\) 2.22002 0.117496
\(358\) −15.6666 −0.828005
\(359\) −9.61828 −0.507633 −0.253817 0.967252i \(-0.581686\pi\)
−0.253817 + 0.967252i \(0.581686\pi\)
\(360\) 4.49879 0.237107
\(361\) −18.4552 −0.971327
\(362\) −7.92396 −0.416474
\(363\) −3.78439 −0.198629
\(364\) 10.1197 0.530419
\(365\) 10.6075 0.555220
\(366\) 6.25873 0.327149
\(367\) −10.0218 −0.523136 −0.261568 0.965185i \(-0.584240\pi\)
−0.261568 + 0.965185i \(0.584240\pi\)
\(368\) 7.20319 0.375492
\(369\) 0.805630 0.0419394
\(370\) −45.5451 −2.36778
\(371\) −2.14492 −0.111359
\(372\) 2.42348 0.125651
\(373\) −5.66337 −0.293238 −0.146619 0.989193i \(-0.546839\pi\)
−0.146619 + 0.989193i \(0.546839\pi\)
\(374\) 8.49572 0.439303
\(375\) −10.7824 −0.556801
\(376\) 7.12675 0.367534
\(377\) −16.0765 −0.827983
\(378\) −4.90519 −0.252296
\(379\) 10.8505 0.557352 0.278676 0.960385i \(-0.410104\pi\)
0.278676 + 0.960385i \(0.410104\pi\)
\(380\) 4.91066 0.251912
\(381\) 5.42283 0.277820
\(382\) 23.7020 1.21270
\(383\) 34.6746 1.77179 0.885895 0.463885i \(-0.153545\pi\)
0.885895 + 0.463885i \(0.153545\pi\)
\(384\) −14.0742 −0.718220
\(385\) −19.7059 −1.00430
\(386\) 38.0853 1.93849
\(387\) −1.73261 −0.0880735
\(388\) 53.4261 2.71230
\(389\) 2.83589 0.143785 0.0718927 0.997412i \(-0.477096\pi\)
0.0718927 + 0.997412i \(0.477096\pi\)
\(390\) 8.06779 0.408528
\(391\) −4.94002 −0.249827
\(392\) 4.03686 0.203892
\(393\) 5.15483 0.260027
\(394\) −52.1342 −2.62648
\(395\) −16.9323 −0.851957
\(396\) −11.0814 −0.556860
\(397\) 25.4417 1.27688 0.638440 0.769672i \(-0.279580\pi\)
0.638440 + 0.769672i \(0.279580\pi\)
\(398\) −5.73580 −0.287510
\(399\) −1.63859 −0.0820320
\(400\) −0.480205 −0.0240102
\(401\) 22.7176 1.13446 0.567232 0.823558i \(-0.308014\pi\)
0.567232 + 0.823558i \(0.308014\pi\)
\(402\) −2.66212 −0.132775
\(403\) 1.33005 0.0662544
\(404\) −39.9823 −1.98919
\(405\) −2.30853 −0.114712
\(406\) 49.8572 2.47437
\(407\) 34.3328 1.70181
\(408\) 1.94877 0.0964783
\(409\) −14.6619 −0.724983 −0.362491 0.931987i \(-0.618074\pi\)
−0.362491 + 0.931987i \(0.618074\pi\)
\(410\) 4.10932 0.202945
\(411\) −1.80324 −0.0889474
\(412\) 6.66436 0.328329
\(413\) −28.9008 −1.42212
\(414\) 10.9151 0.536447
\(415\) 1.64861 0.0809271
\(416\) −11.2605 −0.552091
\(417\) −8.52112 −0.417281
\(418\) −6.27065 −0.306707
\(419\) 29.9080 1.46110 0.730550 0.682859i \(-0.239264\pi\)
0.730550 + 0.682859i \(0.239264\pi\)
\(420\) −14.7702 −0.720711
\(421\) −0.799668 −0.0389734 −0.0194867 0.999810i \(-0.506203\pi\)
−0.0194867 + 0.999810i \(0.506203\pi\)
\(422\) −57.7047 −2.80902
\(423\) −3.65706 −0.177812
\(424\) −1.88284 −0.0914388
\(425\) 0.329329 0.0159748
\(426\) 31.7730 1.53941
\(427\) −6.28848 −0.304321
\(428\) −3.39255 −0.163985
\(429\) −6.08165 −0.293625
\(430\) −8.83762 −0.426188
\(431\) 17.5388 0.844812 0.422406 0.906407i \(-0.361186\pi\)
0.422406 + 0.906407i \(0.361186\pi\)
\(432\) 1.45813 0.0701543
\(433\) −15.2755 −0.734096 −0.367048 0.930202i \(-0.619632\pi\)
−0.367048 + 0.930202i \(0.619632\pi\)
\(434\) −4.12480 −0.197997
\(435\) 23.4644 1.12503
\(436\) −57.3935 −2.74865
\(437\) 3.64620 0.174422
\(438\) −10.1525 −0.485105
\(439\) −17.6320 −0.841529 −0.420764 0.907170i \(-0.638238\pi\)
−0.420764 + 0.907170i \(0.638238\pi\)
\(440\) −17.2981 −0.824653
\(441\) −2.07149 −0.0986426
\(442\) 3.49477 0.166229
\(443\) 2.01022 0.0955083 0.0477542 0.998859i \(-0.484794\pi\)
0.0477542 + 0.998859i \(0.484794\pi\)
\(444\) 25.7335 1.22126
\(445\) 8.65194 0.410141
\(446\) −24.7727 −1.17302
\(447\) −21.9483 −1.03812
\(448\) 28.4474 1.34401
\(449\) 7.55031 0.356321 0.178161 0.984001i \(-0.442985\pi\)
0.178161 + 0.984001i \(0.442985\pi\)
\(450\) −0.727660 −0.0343022
\(451\) −3.09769 −0.145864
\(452\) 27.1218 1.27570
\(453\) −6.83500 −0.321136
\(454\) −35.3918 −1.66102
\(455\) −8.10614 −0.380022
\(456\) −1.43837 −0.0673580
\(457\) −2.56504 −0.119988 −0.0599938 0.998199i \(-0.519108\pi\)
−0.0599938 + 0.998199i \(0.519108\pi\)
\(458\) 19.7475 0.922741
\(459\) −1.00000 −0.0466760
\(460\) 32.8667 1.53242
\(461\) −19.3695 −0.902127 −0.451064 0.892492i \(-0.648955\pi\)
−0.451064 + 0.892492i \(0.648955\pi\)
\(462\) 18.8607 0.877479
\(463\) 12.2330 0.568515 0.284257 0.958748i \(-0.408253\pi\)
0.284257 + 0.958748i \(0.408253\pi\)
\(464\) −14.8207 −0.688034
\(465\) −1.94126 −0.0900237
\(466\) 2.63730 0.122171
\(467\) 10.2642 0.474972 0.237486 0.971391i \(-0.423677\pi\)
0.237486 + 0.971391i \(0.423677\pi\)
\(468\) −4.55839 −0.210712
\(469\) 2.67478 0.123510
\(470\) −18.6538 −0.860434
\(471\) −1.00000 −0.0460776
\(472\) −25.3695 −1.16773
\(473\) 6.66197 0.306318
\(474\) 16.2061 0.744371
\(475\) −0.243076 −0.0111531
\(476\) −6.39808 −0.293255
\(477\) 0.966170 0.0442379
\(478\) −58.3714 −2.66985
\(479\) 10.5901 0.483874 0.241937 0.970292i \(-0.422217\pi\)
0.241937 + 0.970292i \(0.422217\pi\)
\(480\) 16.4352 0.750159
\(481\) 14.1230 0.643953
\(482\) −19.1208 −0.870928
\(483\) −10.9670 −0.499014
\(484\) 10.9066 0.495753
\(485\) −42.7955 −1.94324
\(486\) 2.20952 0.100226
\(487\) 6.55707 0.297129 0.148565 0.988903i \(-0.452535\pi\)
0.148565 + 0.988903i \(0.452535\pi\)
\(488\) −5.52011 −0.249883
\(489\) −7.96902 −0.360372
\(490\) −10.5662 −0.477332
\(491\) 22.9432 1.03541 0.517705 0.855559i \(-0.326786\pi\)
0.517705 + 0.855559i \(0.326786\pi\)
\(492\) −2.32181 −0.104675
\(493\) 10.1642 0.457772
\(494\) −2.57947 −0.116056
\(495\) 8.87642 0.398966
\(496\) 1.22615 0.0550557
\(497\) −31.9240 −1.43199
\(498\) −1.57790 −0.0707075
\(499\) 11.6637 0.522137 0.261069 0.965320i \(-0.415925\pi\)
0.261069 + 0.965320i \(0.415925\pi\)
\(500\) 31.0747 1.38970
\(501\) −6.96414 −0.311135
\(502\) 28.9524 1.29221
\(503\) −5.18372 −0.231130 −0.115565 0.993300i \(-0.536868\pi\)
−0.115565 + 0.993300i \(0.536868\pi\)
\(504\) 4.32631 0.192709
\(505\) 32.0267 1.42517
\(506\) −41.9690 −1.86575
\(507\) 10.4983 0.466245
\(508\) −15.6285 −0.693404
\(509\) 2.41208 0.106914 0.0534568 0.998570i \(-0.482976\pi\)
0.0534568 + 0.998570i \(0.482976\pi\)
\(510\) −5.10076 −0.225865
\(511\) 10.2008 0.451255
\(512\) −16.0640 −0.709934
\(513\) 0.738095 0.0325877
\(514\) 13.8492 0.610863
\(515\) −5.33830 −0.235233
\(516\) 4.99336 0.219820
\(517\) 14.0616 0.618427
\(518\) −43.7989 −1.92441
\(519\) 4.40945 0.193553
\(520\) −7.11567 −0.312043
\(521\) 18.1932 0.797058 0.398529 0.917156i \(-0.369521\pi\)
0.398529 + 0.917156i \(0.369521\pi\)
\(522\) −22.4580 −0.982959
\(523\) −20.7596 −0.907755 −0.453878 0.891064i \(-0.649960\pi\)
−0.453878 + 0.891064i \(0.649960\pi\)
\(524\) −14.8561 −0.648993
\(525\) 0.731118 0.0319086
\(526\) 56.6263 2.46903
\(527\) −0.840905 −0.0366304
\(528\) −5.60658 −0.243995
\(529\) 1.40378 0.0610340
\(530\) 4.92820 0.214067
\(531\) 13.0182 0.564943
\(532\) 4.72239 0.204741
\(533\) −1.27425 −0.0551940
\(534\) −8.28086 −0.358348
\(535\) 2.71751 0.117488
\(536\) 2.34796 0.101416
\(537\) −7.09049 −0.305977
\(538\) 60.9260 2.62670
\(539\) 7.96500 0.343077
\(540\) 6.65316 0.286306
\(541\) −9.05763 −0.389418 −0.194709 0.980861i \(-0.562376\pi\)
−0.194709 + 0.980861i \(0.562376\pi\)
\(542\) −56.4410 −2.42435
\(543\) −3.58628 −0.153902
\(544\) 7.11930 0.305238
\(545\) 45.9734 1.96929
\(546\) 7.75847 0.332032
\(547\) −18.4935 −0.790727 −0.395364 0.918525i \(-0.629381\pi\)
−0.395364 + 0.918525i \(0.629381\pi\)
\(548\) 5.19692 0.222001
\(549\) 2.83262 0.120893
\(550\) 2.79789 0.119302
\(551\) −7.50213 −0.319601
\(552\) −9.62694 −0.409750
\(553\) −16.2831 −0.692429
\(554\) −9.19368 −0.390602
\(555\) −20.6131 −0.874977
\(556\) 24.5577 1.04148
\(557\) 12.9092 0.546981 0.273491 0.961875i \(-0.411822\pi\)
0.273491 + 0.961875i \(0.411822\pi\)
\(558\) 1.85800 0.0786553
\(559\) 2.74044 0.115908
\(560\) −7.47292 −0.315788
\(561\) 3.84505 0.162338
\(562\) 54.6458 2.30510
\(563\) −16.5522 −0.697593 −0.348796 0.937199i \(-0.613410\pi\)
−0.348796 + 0.937199i \(0.613410\pi\)
\(564\) 10.5396 0.443797
\(565\) −21.7251 −0.913983
\(566\) −57.4815 −2.41613
\(567\) −2.22002 −0.0932322
\(568\) −28.0233 −1.17583
\(569\) −28.5553 −1.19710 −0.598550 0.801086i \(-0.704256\pi\)
−0.598550 + 0.801086i \(0.704256\pi\)
\(570\) 3.76484 0.157692
\(571\) 27.1517 1.13626 0.568132 0.822937i \(-0.307666\pi\)
0.568132 + 0.822937i \(0.307666\pi\)
\(572\) 17.5272 0.732851
\(573\) 10.7272 0.448136
\(574\) 3.95177 0.164944
\(575\) −1.62689 −0.0678461
\(576\) −12.8140 −0.533916
\(577\) −9.37529 −0.390298 −0.195149 0.980774i \(-0.562519\pi\)
−0.195149 + 0.980774i \(0.562519\pi\)
\(578\) −2.20952 −0.0919040
\(579\) 17.2369 0.716341
\(580\) −67.6239 −2.80793
\(581\) 1.58540 0.0657736
\(582\) 40.9600 1.69785
\(583\) −3.71497 −0.153858
\(584\) 8.95436 0.370534
\(585\) 3.65137 0.150966
\(586\) 42.0986 1.73908
\(587\) 43.4149 1.79192 0.895962 0.444131i \(-0.146487\pi\)
0.895962 + 0.444131i \(0.146487\pi\)
\(588\) 5.97002 0.246199
\(589\) 0.620668 0.0255742
\(590\) 66.4028 2.73376
\(591\) −23.5952 −0.970578
\(592\) 13.0198 0.535109
\(593\) −35.4407 −1.45538 −0.727688 0.685908i \(-0.759405\pi\)
−0.727688 + 0.685908i \(0.759405\pi\)
\(594\) −8.49572 −0.348583
\(595\) 5.12500 0.210105
\(596\) 63.2547 2.59102
\(597\) −2.59595 −0.106245
\(598\) −17.2642 −0.705986
\(599\) −40.3090 −1.64698 −0.823490 0.567330i \(-0.807976\pi\)
−0.823490 + 0.567330i \(0.807976\pi\)
\(600\) 0.641785 0.0262008
\(601\) 9.33407 0.380745 0.190372 0.981712i \(-0.439030\pi\)
0.190372 + 0.981712i \(0.439030\pi\)
\(602\) −8.49878 −0.346384
\(603\) −1.20484 −0.0490650
\(604\) 19.6984 0.801515
\(605\) −8.73640 −0.355185
\(606\) −30.6531 −1.24520
\(607\) −23.1494 −0.939605 −0.469802 0.882772i \(-0.655675\pi\)
−0.469802 + 0.882772i \(0.655675\pi\)
\(608\) −5.25472 −0.213107
\(609\) 22.5647 0.914369
\(610\) 14.4485 0.585002
\(611\) 5.78432 0.234008
\(612\) 2.88199 0.116497
\(613\) −25.7877 −1.04155 −0.520777 0.853693i \(-0.674358\pi\)
−0.520777 + 0.853693i \(0.674358\pi\)
\(614\) 54.6796 2.20669
\(615\) 1.85982 0.0749954
\(616\) −16.6349 −0.670238
\(617\) 5.01790 0.202013 0.101007 0.994886i \(-0.467794\pi\)
0.101007 + 0.994886i \(0.467794\pi\)
\(618\) 5.10934 0.205528
\(619\) −24.1372 −0.970156 −0.485078 0.874471i \(-0.661209\pi\)
−0.485078 + 0.874471i \(0.661209\pi\)
\(620\) 5.59468 0.224688
\(621\) 4.94002 0.198236
\(622\) −42.7584 −1.71446
\(623\) 8.32022 0.333343
\(624\) −2.30630 −0.0923260
\(625\) −26.5382 −1.06153
\(626\) 48.7718 1.94932
\(627\) −2.83801 −0.113339
\(628\) 2.88199 0.115004
\(629\) −8.92908 −0.356026
\(630\) −11.3238 −0.451151
\(631\) 36.2545 1.44327 0.721635 0.692274i \(-0.243391\pi\)
0.721635 + 0.692274i \(0.243391\pi\)
\(632\) −14.2935 −0.568567
\(633\) −26.1164 −1.03803
\(634\) −38.7293 −1.53814
\(635\) 12.5188 0.496793
\(636\) −2.78449 −0.110412
\(637\) 3.27645 0.129818
\(638\) 86.3520 3.41871
\(639\) 14.3800 0.568866
\(640\) −32.4907 −1.28431
\(641\) −22.4900 −0.888303 −0.444151 0.895952i \(-0.646495\pi\)
−0.444151 + 0.895952i \(0.646495\pi\)
\(642\) −2.60096 −0.102652
\(643\) −31.6183 −1.24690 −0.623452 0.781862i \(-0.714270\pi\)
−0.623452 + 0.781862i \(0.714270\pi\)
\(644\) 31.6066 1.24548
\(645\) −3.99979 −0.157492
\(646\) 1.63084 0.0641644
\(647\) −32.6741 −1.28455 −0.642275 0.766474i \(-0.722009\pi\)
−0.642275 + 0.766474i \(0.722009\pi\)
\(648\) −1.94877 −0.0765548
\(649\) −50.0557 −1.96486
\(650\) 1.15093 0.0451431
\(651\) −1.86683 −0.0731668
\(652\) 22.9666 0.899442
\(653\) −1.21932 −0.0477157 −0.0238579 0.999715i \(-0.507595\pi\)
−0.0238579 + 0.999715i \(0.507595\pi\)
\(654\) −44.0016 −1.72060
\(655\) 11.9001 0.464975
\(656\) −1.17471 −0.0458649
\(657\) −4.59489 −0.179264
\(658\) −17.9386 −0.699318
\(659\) 22.5867 0.879854 0.439927 0.898033i \(-0.355004\pi\)
0.439927 + 0.898033i \(0.355004\pi\)
\(660\) −25.5817 −0.995767
\(661\) 21.1970 0.824466 0.412233 0.911078i \(-0.364749\pi\)
0.412233 + 0.911078i \(0.364749\pi\)
\(662\) −15.4444 −0.600263
\(663\) 1.58168 0.0614276
\(664\) 1.39169 0.0540079
\(665\) −3.78274 −0.146688
\(666\) 19.7290 0.764483
\(667\) −50.2112 −1.94419
\(668\) 20.0705 0.776552
\(669\) −11.2118 −0.433473
\(670\) −6.14560 −0.237425
\(671\) −10.8915 −0.420463
\(672\) 15.8050 0.609692
\(673\) −41.1885 −1.58770 −0.793851 0.608113i \(-0.791927\pi\)
−0.793851 + 0.608113i \(0.791927\pi\)
\(674\) 13.2825 0.511622
\(675\) −0.329329 −0.0126759
\(676\) −30.2559 −1.16369
\(677\) 22.6867 0.871920 0.435960 0.899966i \(-0.356409\pi\)
0.435960 + 0.899966i \(0.356409\pi\)
\(678\) 20.7933 0.798564
\(679\) −41.1547 −1.57937
\(680\) 4.49879 0.172521
\(681\) −16.0179 −0.613806
\(682\) −7.14409 −0.273561
\(683\) −21.3664 −0.817562 −0.408781 0.912632i \(-0.634046\pi\)
−0.408781 + 0.912632i \(0.634046\pi\)
\(684\) −2.12718 −0.0813347
\(685\) −4.16285 −0.159054
\(686\) −44.4974 −1.69892
\(687\) 8.93746 0.340985
\(688\) 2.52637 0.0963170
\(689\) −1.52818 −0.0582189
\(690\) 25.1978 0.959265
\(691\) −50.4409 −1.91886 −0.959432 0.281940i \(-0.909022\pi\)
−0.959432 + 0.281940i \(0.909022\pi\)
\(692\) −12.7080 −0.483085
\(693\) 8.53610 0.324260
\(694\) −12.2248 −0.464046
\(695\) −19.6713 −0.746174
\(696\) 19.8076 0.750805
\(697\) 0.805630 0.0305154
\(698\) −22.1063 −0.836738
\(699\) 1.19361 0.0451463
\(700\) −2.10707 −0.0796399
\(701\) −19.9321 −0.752824 −0.376412 0.926452i \(-0.622842\pi\)
−0.376412 + 0.926452i \(0.622842\pi\)
\(702\) −3.49477 −0.131901
\(703\) 6.59051 0.248566
\(704\) 49.2704 1.85695
\(705\) −8.44245 −0.317961
\(706\) 5.75299 0.216517
\(707\) 30.7988 1.15831
\(708\) −37.5184 −1.41003
\(709\) 2.87595 0.108009 0.0540044 0.998541i \(-0.482802\pi\)
0.0540044 + 0.998541i \(0.482802\pi\)
\(710\) 73.3491 2.75274
\(711\) 7.33466 0.275071
\(712\) 7.30360 0.273714
\(713\) 4.15409 0.155572
\(714\) −4.90519 −0.183572
\(715\) −14.0397 −0.525055
\(716\) 20.4347 0.763680
\(717\) −26.4181 −0.986603
\(718\) 21.2518 0.793110
\(719\) −33.1529 −1.23640 −0.618198 0.786022i \(-0.712137\pi\)
−0.618198 + 0.786022i \(0.712137\pi\)
\(720\) 3.36614 0.125449
\(721\) −5.13362 −0.191186
\(722\) 40.7772 1.51757
\(723\) −8.65381 −0.321839
\(724\) 10.3356 0.384120
\(725\) 3.34736 0.124318
\(726\) 8.36170 0.310332
\(727\) 0.721276 0.0267507 0.0133753 0.999911i \(-0.495742\pi\)
0.0133753 + 0.999911i \(0.495742\pi\)
\(728\) −6.84285 −0.253613
\(729\) 1.00000 0.0370370
\(730\) −23.4374 −0.867457
\(731\) −1.73261 −0.0640829
\(732\) −8.16356 −0.301734
\(733\) 8.87008 0.327624 0.163812 0.986492i \(-0.447621\pi\)
0.163812 + 0.986492i \(0.447621\pi\)
\(734\) 22.1435 0.817330
\(735\) −4.78212 −0.176391
\(736\) −35.1695 −1.29636
\(737\) 4.63268 0.170647
\(738\) −1.78006 −0.0655248
\(739\) −27.6014 −1.01533 −0.507667 0.861554i \(-0.669492\pi\)
−0.507667 + 0.861554i \(0.669492\pi\)
\(740\) 59.4066 2.18383
\(741\) −1.16743 −0.0428867
\(742\) 4.73925 0.173983
\(743\) −33.0066 −1.21089 −0.605447 0.795885i \(-0.707006\pi\)
−0.605447 + 0.795885i \(0.707006\pi\)
\(744\) −1.63873 −0.0600787
\(745\) −50.6684 −1.85635
\(746\) 12.5133 0.458146
\(747\) −0.714138 −0.0261289
\(748\) −11.0814 −0.405175
\(749\) 2.61332 0.0954887
\(750\) 23.8240 0.869928
\(751\) 44.7830 1.63416 0.817078 0.576528i \(-0.195593\pi\)
0.817078 + 0.576528i \(0.195593\pi\)
\(752\) 5.33247 0.194455
\(753\) 13.1035 0.477516
\(754\) 35.5214 1.29361
\(755\) −15.7788 −0.574250
\(756\) 6.39808 0.232696
\(757\) −7.22520 −0.262604 −0.131302 0.991342i \(-0.541916\pi\)
−0.131302 + 0.991342i \(0.541916\pi\)
\(758\) −23.9744 −0.870789
\(759\) −18.9946 −0.689461
\(760\) −3.32054 −0.120448
\(761\) 8.01954 0.290708 0.145354 0.989380i \(-0.453568\pi\)
0.145354 + 0.989380i \(0.453568\pi\)
\(762\) −11.9819 −0.434057
\(763\) 44.2108 1.60054
\(764\) −30.9157 −1.11849
\(765\) −2.30853 −0.0834652
\(766\) −76.6143 −2.76819
\(767\) −20.5907 −0.743489
\(768\) 5.46923 0.197354
\(769\) 46.9365 1.69257 0.846287 0.532726i \(-0.178833\pi\)
0.846287 + 0.532726i \(0.178833\pi\)
\(770\) 43.5405 1.56909
\(771\) 6.26798 0.225736
\(772\) −49.6765 −1.78790
\(773\) 8.07146 0.290310 0.145155 0.989409i \(-0.453632\pi\)
0.145155 + 0.989409i \(0.453632\pi\)
\(774\) 3.82824 0.137603
\(775\) −0.276935 −0.00994778
\(776\) −36.1261 −1.29685
\(777\) −19.8228 −0.711138
\(778\) −6.26596 −0.224646
\(779\) −0.594632 −0.0213049
\(780\) −10.5232 −0.376791
\(781\) −55.2920 −1.97850
\(782\) 10.9151 0.390322
\(783\) −10.1642 −0.363238
\(784\) 3.02051 0.107875
\(785\) −2.30853 −0.0823951
\(786\) −11.3897 −0.406257
\(787\) 11.5758 0.412632 0.206316 0.978485i \(-0.433853\pi\)
0.206316 + 0.978485i \(0.433853\pi\)
\(788\) 68.0011 2.42244
\(789\) 25.6283 0.912392
\(790\) 37.4123 1.33107
\(791\) −20.8922 −0.742841
\(792\) 7.49310 0.266256
\(793\) −4.48031 −0.159100
\(794\) −56.2139 −1.99496
\(795\) 2.23044 0.0791054
\(796\) 7.48149 0.265174
\(797\) −31.6105 −1.11970 −0.559851 0.828594i \(-0.689141\pi\)
−0.559851 + 0.828594i \(0.689141\pi\)
\(798\) 3.62050 0.128164
\(799\) −3.65706 −0.129377
\(800\) 2.34459 0.0828939
\(801\) −3.74781 −0.132422
\(802\) −50.1950 −1.77245
\(803\) 17.6676 0.623475
\(804\) 3.47234 0.122460
\(805\) −25.3176 −0.892328
\(806\) −2.93877 −0.103514
\(807\) 27.5743 0.970661
\(808\) 27.0356 0.951108
\(809\) 18.2386 0.641237 0.320618 0.947208i \(-0.396109\pi\)
0.320618 + 0.947208i \(0.396109\pi\)
\(810\) 5.10076 0.179222
\(811\) −56.8141 −1.99501 −0.997507 0.0705716i \(-0.977518\pi\)
−0.997507 + 0.0705716i \(0.977518\pi\)
\(812\) −65.0312 −2.28215
\(813\) −25.5444 −0.895883
\(814\) −75.8590 −2.65886
\(815\) −18.3968 −0.644410
\(816\) 1.45813 0.0510448
\(817\) 1.27883 0.0447406
\(818\) 32.3957 1.13269
\(819\) 3.51138 0.122697
\(820\) −5.35999 −0.187179
\(821\) −9.61418 −0.335537 −0.167769 0.985826i \(-0.553656\pi\)
−0.167769 + 0.985826i \(0.553656\pi\)
\(822\) 3.98430 0.138969
\(823\) −18.9976 −0.662215 −0.331107 0.943593i \(-0.607422\pi\)
−0.331107 + 0.943593i \(0.607422\pi\)
\(824\) −4.50636 −0.156987
\(825\) 1.26629 0.0440864
\(826\) 63.8569 2.22187
\(827\) −46.1651 −1.60532 −0.802659 0.596438i \(-0.796582\pi\)
−0.802659 + 0.596438i \(0.796582\pi\)
\(828\) −14.2371 −0.494772
\(829\) −46.1714 −1.60360 −0.801800 0.597592i \(-0.796124\pi\)
−0.801800 + 0.597592i \(0.796124\pi\)
\(830\) −3.64264 −0.126438
\(831\) −4.16094 −0.144341
\(832\) 20.2677 0.702656
\(833\) −2.07149 −0.0717730
\(834\) 18.8276 0.651946
\(835\) −16.0769 −0.556366
\(836\) 8.17911 0.282880
\(837\) 0.840905 0.0290659
\(838\) −66.0823 −2.28277
\(839\) 17.6093 0.607941 0.303971 0.952681i \(-0.401688\pi\)
0.303971 + 0.952681i \(0.401688\pi\)
\(840\) 9.98743 0.344599
\(841\) 74.3106 2.56243
\(842\) 1.76688 0.0608908
\(843\) 24.7320 0.851814
\(844\) 75.2670 2.59080
\(845\) 24.2356 0.833731
\(846\) 8.08035 0.277808
\(847\) −8.40145 −0.288677
\(848\) −1.40880 −0.0483785
\(849\) −26.0154 −0.892845
\(850\) −0.727660 −0.0249585
\(851\) 44.1098 1.51207
\(852\) −41.4431 −1.41982
\(853\) −16.2066 −0.554904 −0.277452 0.960740i \(-0.589490\pi\)
−0.277452 + 0.960740i \(0.589490\pi\)
\(854\) 13.8945 0.475461
\(855\) 1.70392 0.0582727
\(856\) 2.29401 0.0784075
\(857\) −34.2031 −1.16836 −0.584178 0.811626i \(-0.698583\pi\)
−0.584178 + 0.811626i \(0.698583\pi\)
\(858\) 13.4375 0.458750
\(859\) 22.7029 0.774613 0.387306 0.921951i \(-0.373406\pi\)
0.387306 + 0.921951i \(0.373406\pi\)
\(860\) 11.5273 0.393079
\(861\) 1.78852 0.0609525
\(862\) −38.7523 −1.31991
\(863\) −21.9545 −0.747340 −0.373670 0.927562i \(-0.621901\pi\)
−0.373670 + 0.927562i \(0.621901\pi\)
\(864\) −7.11930 −0.242204
\(865\) 10.1794 0.346109
\(866\) 33.7517 1.14693
\(867\) −1.00000 −0.0339618
\(868\) 5.38018 0.182615
\(869\) −28.2021 −0.956692
\(870\) −51.8450 −1.75771
\(871\) 1.90568 0.0645715
\(872\) 38.8088 1.31423
\(873\) 18.5380 0.627415
\(874\) −8.05636 −0.272511
\(875\) −23.9372 −0.809225
\(876\) 13.2424 0.447419
\(877\) 18.2044 0.614719 0.307360 0.951593i \(-0.400555\pi\)
0.307360 + 0.951593i \(0.400555\pi\)
\(878\) 38.9583 1.31478
\(879\) 19.0533 0.642651
\(880\) −12.9430 −0.436308
\(881\) −17.1771 −0.578711 −0.289356 0.957222i \(-0.593441\pi\)
−0.289356 + 0.957222i \(0.593441\pi\)
\(882\) 4.57701 0.154116
\(883\) −49.8843 −1.67874 −0.839370 0.543561i \(-0.817076\pi\)
−0.839370 + 0.543561i \(0.817076\pi\)
\(884\) −4.55839 −0.153315
\(885\) 30.0530 1.01022
\(886\) −4.44162 −0.149219
\(887\) −26.7693 −0.898825 −0.449413 0.893324i \(-0.648367\pi\)
−0.449413 + 0.893324i \(0.648367\pi\)
\(888\) −17.4007 −0.583929
\(889\) 12.0388 0.403769
\(890\) −19.1167 −0.640792
\(891\) −3.84505 −0.128814
\(892\) 32.3123 1.08189
\(893\) 2.69926 0.0903272
\(894\) 48.4953 1.62193
\(895\) −16.3686 −0.547143
\(896\) −31.2450 −1.04382
\(897\) −7.81355 −0.260887
\(898\) −16.6826 −0.556705
\(899\) −8.54711 −0.285062
\(900\) 0.949122 0.0316374
\(901\) 0.966170 0.0321878
\(902\) 6.84441 0.227894
\(903\) −3.84643 −0.128001
\(904\) −18.3394 −0.609960
\(905\) −8.27905 −0.275205
\(906\) 15.1021 0.501733
\(907\) −23.7621 −0.789007 −0.394503 0.918894i \(-0.629083\pi\)
−0.394503 + 0.918894i \(0.629083\pi\)
\(908\) 46.1633 1.53198
\(909\) −13.8732 −0.460144
\(910\) 17.9107 0.593733
\(911\) −8.54566 −0.283130 −0.141565 0.989929i \(-0.545213\pi\)
−0.141565 + 0.989929i \(0.545213\pi\)
\(912\) −1.07624 −0.0356378
\(913\) 2.74589 0.0908758
\(914\) 5.66752 0.187465
\(915\) 6.53919 0.216179
\(916\) −25.7576 −0.851056
\(917\) 11.4438 0.377909
\(918\) 2.20952 0.0729251
\(919\) −16.1680 −0.533334 −0.266667 0.963789i \(-0.585922\pi\)
−0.266667 + 0.963789i \(0.585922\pi\)
\(920\) −22.2241 −0.732707
\(921\) 24.7473 0.815450
\(922\) 42.7973 1.40945
\(923\) −22.7447 −0.748651
\(924\) −24.6009 −0.809311
\(925\) −2.94061 −0.0966866
\(926\) −27.0290 −0.888229
\(927\) 2.31242 0.0759498
\(928\) 72.3619 2.37539
\(929\) −36.0783 −1.18369 −0.591845 0.806052i \(-0.701600\pi\)
−0.591845 + 0.806052i \(0.701600\pi\)
\(930\) 4.28925 0.140650
\(931\) 1.52896 0.0501096
\(932\) −3.43996 −0.112680
\(933\) −19.3519 −0.633553
\(934\) −22.6790 −0.742080
\(935\) 8.87642 0.290290
\(936\) 3.08233 0.100749
\(937\) 20.1577 0.658524 0.329262 0.944239i \(-0.393200\pi\)
0.329262 + 0.944239i \(0.393200\pi\)
\(938\) −5.90998 −0.192968
\(939\) 22.0735 0.720341
\(940\) 24.3310 0.793590
\(941\) 19.2928 0.628926 0.314463 0.949270i \(-0.398176\pi\)
0.314463 + 0.949270i \(0.398176\pi\)
\(942\) 2.20952 0.0719901
\(943\) −3.97983 −0.129601
\(944\) −18.9823 −0.617821
\(945\) −5.12500 −0.166716
\(946\) −14.7198 −0.478581
\(947\) 10.3285 0.335631 0.167816 0.985818i \(-0.446329\pi\)
0.167816 + 0.985818i \(0.446329\pi\)
\(948\) −21.1384 −0.686543
\(949\) 7.26766 0.235918
\(950\) 0.537082 0.0174252
\(951\) −17.5284 −0.568396
\(952\) 4.32631 0.140216
\(953\) −14.1433 −0.458148 −0.229074 0.973409i \(-0.573570\pi\)
−0.229074 + 0.973409i \(0.573570\pi\)
\(954\) −2.13477 −0.0691158
\(955\) 24.7641 0.801349
\(956\) 76.1366 2.46243
\(957\) 39.0818 1.26333
\(958\) −23.3991 −0.755989
\(959\) −4.00324 −0.129271
\(960\) −29.5815 −0.954740
\(961\) −30.2929 −0.977190
\(962\) −31.2051 −1.00609
\(963\) −1.17716 −0.0379334
\(964\) 24.9402 0.803268
\(965\) 39.7920 1.28095
\(966\) 24.2317 0.779643
\(967\) −33.2309 −1.06863 −0.534317 0.845284i \(-0.679431\pi\)
−0.534317 + 0.845284i \(0.679431\pi\)
\(968\) −7.37490 −0.237038
\(969\) 0.738095 0.0237110
\(970\) 94.5576 3.03606
\(971\) 13.7675 0.441821 0.220910 0.975294i \(-0.429097\pi\)
0.220910 + 0.975294i \(0.429097\pi\)
\(972\) −2.88199 −0.0924397
\(973\) −18.9171 −0.606454
\(974\) −14.4880 −0.464225
\(975\) 0.520895 0.0166820
\(976\) −4.13032 −0.132208
\(977\) 16.4974 0.527800 0.263900 0.964550i \(-0.414991\pi\)
0.263900 + 0.964550i \(0.414991\pi\)
\(978\) 17.6077 0.563033
\(979\) 14.4105 0.460562
\(980\) 13.7820 0.440249
\(981\) −19.9146 −0.635823
\(982\) −50.6934 −1.61769
\(983\) −26.9699 −0.860205 −0.430102 0.902780i \(-0.641523\pi\)
−0.430102 + 0.902780i \(0.641523\pi\)
\(984\) 1.56998 0.0500493
\(985\) −54.4704 −1.73557
\(986\) −22.4580 −0.715208
\(987\) −8.11876 −0.258423
\(988\) 3.36453 0.107040
\(989\) 8.55912 0.272164
\(990\) −19.6127 −0.623331
\(991\) 45.0013 1.42951 0.714756 0.699373i \(-0.246538\pi\)
0.714756 + 0.699373i \(0.246538\pi\)
\(992\) −5.98666 −0.190077
\(993\) −6.98992 −0.221818
\(994\) 70.5368 2.23729
\(995\) −5.99284 −0.189986
\(996\) 2.05813 0.0652145
\(997\) −37.7485 −1.19551 −0.597754 0.801679i \(-0.703940\pi\)
−0.597754 + 0.801679i \(0.703940\pi\)
\(998\) −25.7711 −0.815770
\(999\) 8.92908 0.282504
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 8007.2.a.c.1.5 39
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.c.1.5 39 1.1 even 1 trivial