Properties

Label 8006.2.a.b.1.19
Level $8006$
Weight $2$
Character 8006.1
Self dual yes
Analytic conductor $63.928$
Analytic rank $1$
Dimension $75$
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] = [8006,2,Mod(1,8006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8006, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8006 = 2 \cdot 4003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8006.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: \(63.9282318582\)
Analytic rank: \(1\)
Dimension: \(75\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 8006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.72100 q^{3} +1.00000 q^{4} +1.49175 q^{5} +1.72100 q^{6} -1.07018 q^{7} -1.00000 q^{8} -0.0381718 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.72100 q^{3} +1.00000 q^{4} +1.49175 q^{5} +1.72100 q^{6} -1.07018 q^{7} -1.00000 q^{8} -0.0381718 q^{9} -1.49175 q^{10} +1.68870 q^{11} -1.72100 q^{12} +3.00150 q^{13} +1.07018 q^{14} -2.56729 q^{15} +1.00000 q^{16} -0.629551 q^{17} +0.0381718 q^{18} -0.905993 q^{19} +1.49175 q^{20} +1.84178 q^{21} -1.68870 q^{22} -0.523921 q^{23} +1.72100 q^{24} -2.77469 q^{25} -3.00150 q^{26} +5.22868 q^{27} -1.07018 q^{28} +0.474981 q^{29} +2.56729 q^{30} -0.660364 q^{31} -1.00000 q^{32} -2.90625 q^{33} +0.629551 q^{34} -1.59644 q^{35} -0.0381718 q^{36} +1.31640 q^{37} +0.905993 q^{38} -5.16557 q^{39} -1.49175 q^{40} +1.65916 q^{41} -1.84178 q^{42} -3.20887 q^{43} +1.68870 q^{44} -0.0569426 q^{45} +0.523921 q^{46} +3.81130 q^{47} -1.72100 q^{48} -5.85471 q^{49} +2.77469 q^{50} +1.08346 q^{51} +3.00150 q^{52} -7.66072 q^{53} -5.22868 q^{54} +2.51911 q^{55} +1.07018 q^{56} +1.55921 q^{57} -0.474981 q^{58} -8.83103 q^{59} -2.56729 q^{60} +0.188979 q^{61} +0.660364 q^{62} +0.0408507 q^{63} +1.00000 q^{64} +4.47748 q^{65} +2.90625 q^{66} +12.0430 q^{67} -0.629551 q^{68} +0.901666 q^{69} +1.59644 q^{70} +2.26035 q^{71} +0.0381718 q^{72} -2.11853 q^{73} -1.31640 q^{74} +4.77524 q^{75} -0.905993 q^{76} -1.80722 q^{77} +5.16557 q^{78} +5.32571 q^{79} +1.49175 q^{80} -8.88403 q^{81} -1.65916 q^{82} -7.15493 q^{83} +1.84178 q^{84} -0.939131 q^{85} +3.20887 q^{86} -0.817440 q^{87} -1.68870 q^{88} -10.0856 q^{89} +0.0569426 q^{90} -3.21215 q^{91} -0.523921 q^{92} +1.13648 q^{93} -3.81130 q^{94} -1.35151 q^{95} +1.72100 q^{96} -8.68119 q^{97} +5.85471 q^{98} -0.0644607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 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
\(3\) −1.72100 −0.993618 −0.496809 0.867860i \(-0.665495\pi\)
−0.496809 + 0.867860i \(0.665495\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.49175 0.667129 0.333565 0.942727i \(-0.391748\pi\)
0.333565 + 0.942727i \(0.391748\pi\)
\(6\) 1.72100 0.702594
\(7\) −1.07018 −0.404490 −0.202245 0.979335i \(-0.564824\pi\)
−0.202245 + 0.979335i \(0.564824\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.0381718 −0.0127239
\(10\) −1.49175 −0.471732
\(11\) 1.68870 0.509162 0.254581 0.967051i \(-0.418062\pi\)
0.254581 + 0.967051i \(0.418062\pi\)
\(12\) −1.72100 −0.496809
\(13\) 3.00150 0.832467 0.416233 0.909258i \(-0.363350\pi\)
0.416233 + 0.909258i \(0.363350\pi\)
\(14\) 1.07018 0.286018
\(15\) −2.56729 −0.662871
\(16\) 1.00000 0.250000
\(17\) −0.629551 −0.152689 −0.0763443 0.997082i \(-0.524325\pi\)
−0.0763443 + 0.997082i \(0.524325\pi\)
\(18\) 0.0381718 0.00899718
\(19\) −0.905993 −0.207849 −0.103925 0.994585i \(-0.533140\pi\)
−0.103925 + 0.994585i \(0.533140\pi\)
\(20\) 1.49175 0.333565
\(21\) 1.84178 0.401909
\(22\) −1.68870 −0.360032
\(23\) −0.523921 −0.109245 −0.0546225 0.998507i \(-0.517396\pi\)
−0.0546225 + 0.998507i \(0.517396\pi\)
\(24\) 1.72100 0.351297
\(25\) −2.77469 −0.554939
\(26\) −3.00150 −0.588643
\(27\) 5.22868 1.00626
\(28\) −1.07018 −0.202245
\(29\) 0.474981 0.0882017 0.0441008 0.999027i \(-0.485958\pi\)
0.0441008 + 0.999027i \(0.485958\pi\)
\(30\) 2.56729 0.468721
\(31\) −0.660364 −0.118605 −0.0593025 0.998240i \(-0.518888\pi\)
−0.0593025 + 0.998240i \(0.518888\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.90625 −0.505913
\(34\) 0.629551 0.107967
\(35\) −1.59644 −0.269847
\(36\) −0.0381718 −0.00636196
\(37\) 1.31640 0.216415 0.108207 0.994128i \(-0.465489\pi\)
0.108207 + 0.994128i \(0.465489\pi\)
\(38\) 0.905993 0.146971
\(39\) −5.16557 −0.827154
\(40\) −1.49175 −0.235866
\(41\) 1.65916 0.259117 0.129558 0.991572i \(-0.458644\pi\)
0.129558 + 0.991572i \(0.458644\pi\)
\(42\) −1.84178 −0.284192
\(43\) −3.20887 −0.489348 −0.244674 0.969605i \(-0.578681\pi\)
−0.244674 + 0.969605i \(0.578681\pi\)
\(44\) 1.68870 0.254581
\(45\) −0.0569426 −0.00848850
\(46\) 0.523921 0.0772479
\(47\) 3.81130 0.555935 0.277967 0.960590i \(-0.410339\pi\)
0.277967 + 0.960590i \(0.410339\pi\)
\(48\) −1.72100 −0.248404
\(49\) −5.85471 −0.836388
\(50\) 2.77469 0.392401
\(51\) 1.08346 0.151714
\(52\) 3.00150 0.416233
\(53\) −7.66072 −1.05228 −0.526141 0.850398i \(-0.676361\pi\)
−0.526141 + 0.850398i \(0.676361\pi\)
\(54\) −5.22868 −0.711534
\(55\) 2.51911 0.339677
\(56\) 1.07018 0.143009
\(57\) 1.55921 0.206522
\(58\) −0.474981 −0.0623680
\(59\) −8.83103 −1.14970 −0.574851 0.818258i \(-0.694940\pi\)
−0.574851 + 0.818258i \(0.694940\pi\)
\(60\) −2.56729 −0.331436
\(61\) 0.188979 0.0241963 0.0120981 0.999927i \(-0.496149\pi\)
0.0120981 + 0.999927i \(0.496149\pi\)
\(62\) 0.660364 0.0838663
\(63\) 0.0408507 0.00514671
\(64\) 1.00000 0.125000
\(65\) 4.47748 0.555363
\(66\) 2.90625 0.357734
\(67\) 12.0430 1.47128 0.735642 0.677370i \(-0.236880\pi\)
0.735642 + 0.677370i \(0.236880\pi\)
\(68\) −0.629551 −0.0763443
\(69\) 0.901666 0.108548
\(70\) 1.59644 0.190811
\(71\) 2.26035 0.268254 0.134127 0.990964i \(-0.457177\pi\)
0.134127 + 0.990964i \(0.457177\pi\)
\(72\) 0.0381718 0.00449859
\(73\) −2.11853 −0.247955 −0.123978 0.992285i \(-0.539565\pi\)
−0.123978 + 0.992285i \(0.539565\pi\)
\(74\) −1.31640 −0.153028
\(75\) 4.77524 0.551397
\(76\) −0.905993 −0.103925
\(77\) −1.80722 −0.205951
\(78\) 5.16557 0.584886
\(79\) 5.32571 0.599189 0.299594 0.954067i \(-0.403149\pi\)
0.299594 + 0.954067i \(0.403149\pi\)
\(80\) 1.49175 0.166782
\(81\) −8.88403 −0.987114
\(82\) −1.65916 −0.183223
\(83\) −7.15493 −0.785355 −0.392678 0.919676i \(-0.628451\pi\)
−0.392678 + 0.919676i \(0.628451\pi\)
\(84\) 1.84178 0.200954
\(85\) −0.939131 −0.101863
\(86\) 3.20887 0.346021
\(87\) −0.817440 −0.0876387
\(88\) −1.68870 −0.180016
\(89\) −10.0856 −1.06907 −0.534534 0.845147i \(-0.679513\pi\)
−0.534534 + 0.845147i \(0.679513\pi\)
\(90\) 0.0569426 0.00600228
\(91\) −3.21215 −0.336725
\(92\) −0.523921 −0.0546225
\(93\) 1.13648 0.117848
\(94\) −3.81130 −0.393105
\(95\) −1.35151 −0.138662
\(96\) 1.72100 0.175648
\(97\) −8.68119 −0.881442 −0.440721 0.897644i \(-0.645277\pi\)
−0.440721 + 0.897644i \(0.645277\pi\)
\(98\) 5.85471 0.591415
\(99\) −0.0644607 −0.00647855
\(100\) −2.77469 −0.277469
\(101\) 19.4422 1.93458 0.967288 0.253682i \(-0.0816416\pi\)
0.967288 + 0.253682i \(0.0816416\pi\)
\(102\) −1.08346 −0.107278
\(103\) −4.58818 −0.452086 −0.226043 0.974117i \(-0.572579\pi\)
−0.226043 + 0.974117i \(0.572579\pi\)
\(104\) −3.00150 −0.294321
\(105\) 2.74746 0.268125
\(106\) 7.66072 0.744075
\(107\) 8.88578 0.859020 0.429510 0.903062i \(-0.358686\pi\)
0.429510 + 0.903062i \(0.358686\pi\)
\(108\) 5.22868 0.503130
\(109\) 12.5508 1.20215 0.601073 0.799194i \(-0.294740\pi\)
0.601073 + 0.799194i \(0.294740\pi\)
\(110\) −2.51911 −0.240188
\(111\) −2.26552 −0.215034
\(112\) −1.07018 −0.101123
\(113\) 6.53956 0.615190 0.307595 0.951517i \(-0.400476\pi\)
0.307595 + 0.951517i \(0.400476\pi\)
\(114\) −1.55921 −0.146033
\(115\) −0.781557 −0.0728806
\(116\) 0.474981 0.0441008
\(117\) −0.114573 −0.0105922
\(118\) 8.83103 0.812962
\(119\) 0.673734 0.0617611
\(120\) 2.56729 0.234360
\(121\) −8.14829 −0.740754
\(122\) −0.188979 −0.0171093
\(123\) −2.85540 −0.257463
\(124\) −0.660364 −0.0593025
\(125\) −11.5979 −1.03734
\(126\) −0.0408507 −0.00363927
\(127\) 5.39811 0.479005 0.239502 0.970896i \(-0.423016\pi\)
0.239502 + 0.970896i \(0.423016\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.52245 0.486224
\(130\) −4.47748 −0.392701
\(131\) 2.39765 0.209484 0.104742 0.994499i \(-0.466598\pi\)
0.104742 + 0.994499i \(0.466598\pi\)
\(132\) −2.90625 −0.252956
\(133\) 0.969576 0.0840729
\(134\) −12.0430 −1.04036
\(135\) 7.79987 0.671306
\(136\) 0.629551 0.0539836
\(137\) −21.9377 −1.87426 −0.937131 0.348977i \(-0.886529\pi\)
−0.937131 + 0.348977i \(0.886529\pi\)
\(138\) −0.901666 −0.0767549
\(139\) −8.36040 −0.709119 −0.354560 0.935033i \(-0.615369\pi\)
−0.354560 + 0.935033i \(0.615369\pi\)
\(140\) −1.59644 −0.134924
\(141\) −6.55923 −0.552387
\(142\) −2.26035 −0.189684
\(143\) 5.06864 0.423861
\(144\) −0.0381718 −0.00318098
\(145\) 0.708550 0.0588419
\(146\) 2.11853 0.175331
\(147\) 10.0759 0.831049
\(148\) 1.31640 0.108207
\(149\) −22.2698 −1.82441 −0.912206 0.409731i \(-0.865622\pi\)
−0.912206 + 0.409731i \(0.865622\pi\)
\(150\) −4.77524 −0.389896
\(151\) 4.25695 0.346426 0.173213 0.984884i \(-0.444585\pi\)
0.173213 + 0.984884i \(0.444585\pi\)
\(152\) 0.905993 0.0734857
\(153\) 0.0240311 0.00194280
\(154\) 1.80722 0.145630
\(155\) −0.985096 −0.0791248
\(156\) −5.16557 −0.413577
\(157\) 4.51315 0.360189 0.180094 0.983649i \(-0.442360\pi\)
0.180094 + 0.983649i \(0.442360\pi\)
\(158\) −5.32571 −0.423691
\(159\) 13.1841 1.04557
\(160\) −1.49175 −0.117933
\(161\) 0.560690 0.0441886
\(162\) 8.88403 0.697995
\(163\) −10.2065 −0.799432 −0.399716 0.916639i \(-0.630891\pi\)
−0.399716 + 0.916639i \(0.630891\pi\)
\(164\) 1.65916 0.129558
\(165\) −4.33538 −0.337509
\(166\) 7.15493 0.555330
\(167\) 6.46771 0.500486 0.250243 0.968183i \(-0.419489\pi\)
0.250243 + 0.968183i \(0.419489\pi\)
\(168\) −1.84178 −0.142096
\(169\) −3.99099 −0.306999
\(170\) 0.939131 0.0720281
\(171\) 0.0345834 0.00264466
\(172\) −3.20887 −0.244674
\(173\) 10.4767 0.796530 0.398265 0.917270i \(-0.369612\pi\)
0.398265 + 0.917270i \(0.369612\pi\)
\(174\) 0.817440 0.0619699
\(175\) 2.96942 0.224467
\(176\) 1.68870 0.127291
\(177\) 15.1982 1.14236
\(178\) 10.0856 0.755945
\(179\) 6.70309 0.501012 0.250506 0.968115i \(-0.419403\pi\)
0.250506 + 0.968115i \(0.419403\pi\)
\(180\) −0.0569426 −0.00424425
\(181\) 3.66864 0.272688 0.136344 0.990662i \(-0.456465\pi\)
0.136344 + 0.990662i \(0.456465\pi\)
\(182\) 3.21215 0.238100
\(183\) −0.325232 −0.0240418
\(184\) 0.523921 0.0386240
\(185\) 1.96373 0.144377
\(186\) −1.13648 −0.0833311
\(187\) −1.06312 −0.0777433
\(188\) 3.81130 0.277967
\(189\) −5.59564 −0.407023
\(190\) 1.35151 0.0980489
\(191\) 3.49506 0.252894 0.126447 0.991973i \(-0.459643\pi\)
0.126447 + 0.991973i \(0.459643\pi\)
\(192\) −1.72100 −0.124202
\(193\) −25.3685 −1.82607 −0.913034 0.407885i \(-0.866267\pi\)
−0.913034 + 0.407885i \(0.866267\pi\)
\(194\) 8.68119 0.623273
\(195\) −7.70573 −0.551818
\(196\) −5.85471 −0.418194
\(197\) 24.2370 1.72681 0.863406 0.504509i \(-0.168327\pi\)
0.863406 + 0.504509i \(0.168327\pi\)
\(198\) 0.0644607 0.00458102
\(199\) −8.57145 −0.607614 −0.303807 0.952734i \(-0.598258\pi\)
−0.303807 + 0.952734i \(0.598258\pi\)
\(200\) 2.77469 0.196200
\(201\) −20.7259 −1.46189
\(202\) −19.4422 −1.36795
\(203\) −0.508315 −0.0356767
\(204\) 1.08346 0.0758571
\(205\) 2.47504 0.172864
\(206\) 4.58818 0.319673
\(207\) 0.0199990 0.00139003
\(208\) 3.00150 0.208117
\(209\) −1.52995 −0.105829
\(210\) −2.74746 −0.189593
\(211\) 5.44236 0.374667 0.187334 0.982296i \(-0.440015\pi\)
0.187334 + 0.982296i \(0.440015\pi\)
\(212\) −7.66072 −0.526141
\(213\) −3.89005 −0.266542
\(214\) −8.88578 −0.607419
\(215\) −4.78682 −0.326458
\(216\) −5.22868 −0.355767
\(217\) 0.706709 0.0479745
\(218\) −12.5508 −0.850046
\(219\) 3.64598 0.246373
\(220\) 2.51911 0.169839
\(221\) −1.88960 −0.127108
\(222\) 2.26552 0.152052
\(223\) 7.72095 0.517033 0.258517 0.966007i \(-0.416766\pi\)
0.258517 + 0.966007i \(0.416766\pi\)
\(224\) 1.07018 0.0715045
\(225\) 0.105915 0.00706100
\(226\) −6.53956 −0.435005
\(227\) −22.1025 −1.46699 −0.733497 0.679692i \(-0.762113\pi\)
−0.733497 + 0.679692i \(0.762113\pi\)
\(228\) 1.55921 0.103261
\(229\) 2.43523 0.160924 0.0804622 0.996758i \(-0.474360\pi\)
0.0804622 + 0.996758i \(0.474360\pi\)
\(230\) 0.781557 0.0515343
\(231\) 3.11021 0.204637
\(232\) −0.474981 −0.0311840
\(233\) −28.6314 −1.87571 −0.937853 0.347033i \(-0.887189\pi\)
−0.937853 + 0.347033i \(0.887189\pi\)
\(234\) 0.114573 0.00748985
\(235\) 5.68549 0.370880
\(236\) −8.83103 −0.574851
\(237\) −9.16552 −0.595365
\(238\) −0.673734 −0.0436717
\(239\) −3.85355 −0.249265 −0.124633 0.992203i \(-0.539775\pi\)
−0.124633 + 0.992203i \(0.539775\pi\)
\(240\) −2.56729 −0.165718
\(241\) 22.0678 1.42151 0.710756 0.703438i \(-0.248353\pi\)
0.710756 + 0.703438i \(0.248353\pi\)
\(242\) 8.14829 0.523792
\(243\) −0.396669 −0.0254463
\(244\) 0.188979 0.0120981
\(245\) −8.73375 −0.557979
\(246\) 2.85540 0.182054
\(247\) −2.71934 −0.173027
\(248\) 0.660364 0.0419332
\(249\) 12.3136 0.780343
\(250\) 11.5979 0.733514
\(251\) 10.4314 0.658423 0.329211 0.944256i \(-0.393217\pi\)
0.329211 + 0.944256i \(0.393217\pi\)
\(252\) 0.0408507 0.00257335
\(253\) −0.884746 −0.0556235
\(254\) −5.39811 −0.338707
\(255\) 1.61624 0.101213
\(256\) 1.00000 0.0625000
\(257\) 15.8546 0.988986 0.494493 0.869182i \(-0.335354\pi\)
0.494493 + 0.869182i \(0.335354\pi\)
\(258\) −5.52245 −0.343813
\(259\) −1.40879 −0.0875377
\(260\) 4.47748 0.277681
\(261\) −0.0181309 −0.00112227
\(262\) −2.39765 −0.148127
\(263\) 28.5821 1.76245 0.881224 0.472700i \(-0.156720\pi\)
0.881224 + 0.472700i \(0.156720\pi\)
\(264\) 2.90625 0.178867
\(265\) −11.4279 −0.702008
\(266\) −0.969576 −0.0594485
\(267\) 17.3572 1.06224
\(268\) 12.0430 0.735642
\(269\) 0.791621 0.0482660 0.0241330 0.999709i \(-0.492317\pi\)
0.0241330 + 0.999709i \(0.492317\pi\)
\(270\) −7.79987 −0.474685
\(271\) 6.60941 0.401493 0.200747 0.979643i \(-0.435663\pi\)
0.200747 + 0.979643i \(0.435663\pi\)
\(272\) −0.629551 −0.0381722
\(273\) 5.52810 0.334576
\(274\) 21.9377 1.32530
\(275\) −4.68563 −0.282554
\(276\) 0.901666 0.0542739
\(277\) 7.34257 0.441172 0.220586 0.975367i \(-0.429203\pi\)
0.220586 + 0.975367i \(0.429203\pi\)
\(278\) 8.36040 0.501423
\(279\) 0.0252073 0.00150912
\(280\) 1.59644 0.0954054
\(281\) 5.23271 0.312157 0.156079 0.987745i \(-0.450115\pi\)
0.156079 + 0.987745i \(0.450115\pi\)
\(282\) 6.55923 0.390596
\(283\) 22.4417 1.33402 0.667010 0.745048i \(-0.267574\pi\)
0.667010 + 0.745048i \(0.267574\pi\)
\(284\) 2.26035 0.134127
\(285\) 2.32595 0.137777
\(286\) −5.06864 −0.299715
\(287\) −1.77560 −0.104810
\(288\) 0.0381718 0.00224929
\(289\) −16.6037 −0.976686
\(290\) −0.708550 −0.0416075
\(291\) 14.9403 0.875816
\(292\) −2.11853 −0.123978
\(293\) −18.2607 −1.06680 −0.533399 0.845864i \(-0.679086\pi\)
−0.533399 + 0.845864i \(0.679086\pi\)
\(294\) −10.0759 −0.587641
\(295\) −13.1736 −0.767000
\(296\) −1.31640 −0.0765142
\(297\) 8.82968 0.512350
\(298\) 22.2698 1.29005
\(299\) −1.57255 −0.0909429
\(300\) 4.77524 0.275698
\(301\) 3.43407 0.197936
\(302\) −4.25695 −0.244960
\(303\) −33.4600 −1.92223
\(304\) −0.905993 −0.0519623
\(305\) 0.281909 0.0161420
\(306\) −0.0240311 −0.00137377
\(307\) 19.9080 1.13621 0.568104 0.822957i \(-0.307677\pi\)
0.568104 + 0.822957i \(0.307677\pi\)
\(308\) −1.80722 −0.102976
\(309\) 7.89623 0.449201
\(310\) 0.985096 0.0559497
\(311\) −32.6917 −1.85377 −0.926887 0.375341i \(-0.877526\pi\)
−0.926887 + 0.375341i \(0.877526\pi\)
\(312\) 5.16557 0.292443
\(313\) 5.08826 0.287605 0.143803 0.989606i \(-0.454067\pi\)
0.143803 + 0.989606i \(0.454067\pi\)
\(314\) −4.51315 −0.254692
\(315\) 0.0609389 0.00343352
\(316\) 5.32571 0.299594
\(317\) 0.0528738 0.00296969 0.00148484 0.999999i \(-0.499527\pi\)
0.00148484 + 0.999999i \(0.499527\pi\)
\(318\) −13.1841 −0.739326
\(319\) 0.802100 0.0449090
\(320\) 1.49175 0.0833911
\(321\) −15.2924 −0.853538
\(322\) −0.560690 −0.0312460
\(323\) 0.570369 0.0317362
\(324\) −8.88403 −0.493557
\(325\) −8.32825 −0.461968
\(326\) 10.2065 0.565284
\(327\) −21.5998 −1.19447
\(328\) −1.65916 −0.0916116
\(329\) −4.07878 −0.224870
\(330\) 4.33538 0.238655
\(331\) −12.8595 −0.706821 −0.353410 0.935468i \(-0.614978\pi\)
−0.353410 + 0.935468i \(0.614978\pi\)
\(332\) −7.15493 −0.392678
\(333\) −0.0502493 −0.00275365
\(334\) −6.46771 −0.353897
\(335\) 17.9651 0.981537
\(336\) 1.84178 0.100477
\(337\) −17.2499 −0.939662 −0.469831 0.882756i \(-0.655685\pi\)
−0.469831 + 0.882756i \(0.655685\pi\)
\(338\) 3.99099 0.217081
\(339\) −11.2546 −0.611264
\(340\) −0.939131 −0.0509315
\(341\) −1.11516 −0.0603892
\(342\) −0.0345834 −0.00187005
\(343\) 13.7569 0.742801
\(344\) 3.20887 0.173011
\(345\) 1.34506 0.0724154
\(346\) −10.4767 −0.563232
\(347\) 27.2330 1.46194 0.730971 0.682409i \(-0.239068\pi\)
0.730971 + 0.682409i \(0.239068\pi\)
\(348\) −0.817440 −0.0438194
\(349\) −22.2712 −1.19215 −0.596074 0.802929i \(-0.703274\pi\)
−0.596074 + 0.802929i \(0.703274\pi\)
\(350\) −2.96942 −0.158722
\(351\) 15.6939 0.837678
\(352\) −1.68870 −0.0900081
\(353\) −7.04399 −0.374914 −0.187457 0.982273i \(-0.560025\pi\)
−0.187457 + 0.982273i \(0.560025\pi\)
\(354\) −15.1982 −0.807773
\(355\) 3.37187 0.178960
\(356\) −10.0856 −0.534534
\(357\) −1.15949 −0.0613669
\(358\) −6.70309 −0.354269
\(359\) −19.4730 −1.02775 −0.513874 0.857866i \(-0.671790\pi\)
−0.513874 + 0.857866i \(0.671790\pi\)
\(360\) 0.0569426 0.00300114
\(361\) −18.1792 −0.956799
\(362\) −3.66864 −0.192820
\(363\) 14.0232 0.736026
\(364\) −3.21215 −0.168362
\(365\) −3.16031 −0.165418
\(366\) 0.325232 0.0170001
\(367\) −24.0895 −1.25746 −0.628730 0.777624i \(-0.716425\pi\)
−0.628730 + 0.777624i \(0.716425\pi\)
\(368\) −0.523921 −0.0273113
\(369\) −0.0633330 −0.00329698
\(370\) −1.96373 −0.102090
\(371\) 8.19836 0.425638
\(372\) 1.13648 0.0589240
\(373\) −7.50688 −0.388691 −0.194346 0.980933i \(-0.562258\pi\)
−0.194346 + 0.980933i \(0.562258\pi\)
\(374\) 1.06312 0.0549728
\(375\) 19.9599 1.03072
\(376\) −3.81130 −0.196553
\(377\) 1.42566 0.0734250
\(378\) 5.59564 0.287808
\(379\) 4.26329 0.218990 0.109495 0.993987i \(-0.465077\pi\)
0.109495 + 0.993987i \(0.465077\pi\)
\(380\) −1.35151 −0.0693311
\(381\) −9.29012 −0.475947
\(382\) −3.49506 −0.178823
\(383\) 2.04896 0.104697 0.0523484 0.998629i \(-0.483329\pi\)
0.0523484 + 0.998629i \(0.483329\pi\)
\(384\) 1.72100 0.0878242
\(385\) −2.69591 −0.137396
\(386\) 25.3685 1.29122
\(387\) 0.122488 0.00622642
\(388\) −8.68119 −0.440721
\(389\) 21.7457 1.10255 0.551276 0.834323i \(-0.314141\pi\)
0.551276 + 0.834323i \(0.314141\pi\)
\(390\) 7.70573 0.390195
\(391\) 0.329835 0.0166805
\(392\) 5.85471 0.295708
\(393\) −4.12635 −0.208147
\(394\) −24.2370 −1.22104
\(395\) 7.94460 0.399736
\(396\) −0.0644607 −0.00323927
\(397\) −19.7781 −0.992635 −0.496318 0.868141i \(-0.665315\pi\)
−0.496318 + 0.868141i \(0.665315\pi\)
\(398\) 8.57145 0.429648
\(399\) −1.66864 −0.0835363
\(400\) −2.77469 −0.138735
\(401\) −30.2560 −1.51091 −0.755456 0.655200i \(-0.772584\pi\)
−0.755456 + 0.655200i \(0.772584\pi\)
\(402\) 20.7259 1.03372
\(403\) −1.98208 −0.0987347
\(404\) 19.4422 0.967288
\(405\) −13.2527 −0.658533
\(406\) 0.508315 0.0252273
\(407\) 2.22301 0.110190
\(408\) −1.08346 −0.0536390
\(409\) −3.90825 −0.193251 −0.0966253 0.995321i \(-0.530805\pi\)
−0.0966253 + 0.995321i \(0.530805\pi\)
\(410\) −2.47504 −0.122234
\(411\) 37.7547 1.86230
\(412\) −4.58818 −0.226043
\(413\) 9.45079 0.465043
\(414\) −0.0199990 −0.000982897 0
\(415\) −10.6733 −0.523934
\(416\) −3.00150 −0.147161
\(417\) 14.3882 0.704594
\(418\) 1.52995 0.0748324
\(419\) 3.60625 0.176177 0.0880885 0.996113i \(-0.471924\pi\)
0.0880885 + 0.996113i \(0.471924\pi\)
\(420\) 2.74746 0.134063
\(421\) −11.7802 −0.574134 −0.287067 0.957911i \(-0.592680\pi\)
−0.287067 + 0.957911i \(0.592680\pi\)
\(422\) −5.44236 −0.264930
\(423\) −0.145484 −0.00707368
\(424\) 7.66072 0.372038
\(425\) 1.74681 0.0847328
\(426\) 3.89005 0.188474
\(427\) −0.202242 −0.00978716
\(428\) 8.88578 0.429510
\(429\) −8.72311 −0.421156
\(430\) 4.78682 0.230841
\(431\) −12.9393 −0.623262 −0.311631 0.950203i \(-0.600875\pi\)
−0.311631 + 0.950203i \(0.600875\pi\)
\(432\) 5.22868 0.251565
\(433\) 1.56045 0.0749906 0.0374953 0.999297i \(-0.488062\pi\)
0.0374953 + 0.999297i \(0.488062\pi\)
\(434\) −0.706709 −0.0339231
\(435\) −1.21941 −0.0584664
\(436\) 12.5508 0.601073
\(437\) 0.474669 0.0227065
\(438\) −3.64598 −0.174212
\(439\) −29.9307 −1.42852 −0.714258 0.699883i \(-0.753236\pi\)
−0.714258 + 0.699883i \(0.753236\pi\)
\(440\) −2.51911 −0.120094
\(441\) 0.223485 0.0106421
\(442\) 1.88960 0.0898791
\(443\) 29.5035 1.40175 0.700877 0.713282i \(-0.252792\pi\)
0.700877 + 0.713282i \(0.252792\pi\)
\(444\) −2.26552 −0.107517
\(445\) −15.0451 −0.713206
\(446\) −7.72095 −0.365598
\(447\) 38.3262 1.81277
\(448\) −1.07018 −0.0505613
\(449\) 16.6803 0.787190 0.393595 0.919284i \(-0.371231\pi\)
0.393595 + 0.919284i \(0.371231\pi\)
\(450\) −0.105915 −0.00499288
\(451\) 2.80182 0.131933
\(452\) 6.53956 0.307595
\(453\) −7.32620 −0.344215
\(454\) 22.1025 1.03732
\(455\) −4.79171 −0.224639
\(456\) −1.55921 −0.0730167
\(457\) 12.9587 0.606185 0.303092 0.952961i \(-0.401981\pi\)
0.303092 + 0.952961i \(0.401981\pi\)
\(458\) −2.43523 −0.113791
\(459\) −3.29172 −0.153645
\(460\) −0.781557 −0.0364403
\(461\) −3.45467 −0.160900 −0.0804500 0.996759i \(-0.525636\pi\)
−0.0804500 + 0.996759i \(0.525636\pi\)
\(462\) −3.11021 −0.144700
\(463\) 7.47857 0.347559 0.173779 0.984785i \(-0.444402\pi\)
0.173779 + 0.984785i \(0.444402\pi\)
\(464\) 0.474981 0.0220504
\(465\) 1.69535 0.0786198
\(466\) 28.6314 1.32632
\(467\) −27.1896 −1.25818 −0.629091 0.777331i \(-0.716573\pi\)
−0.629091 + 0.777331i \(0.716573\pi\)
\(468\) −0.114573 −0.00529612
\(469\) −12.8882 −0.595120
\(470\) −5.68549 −0.262252
\(471\) −7.76712 −0.357890
\(472\) 8.83103 0.406481
\(473\) −5.41882 −0.249157
\(474\) 9.16552 0.420986
\(475\) 2.51385 0.115343
\(476\) 0.673734 0.0308805
\(477\) 0.292424 0.0133892
\(478\) 3.85355 0.176257
\(479\) −11.4309 −0.522291 −0.261145 0.965299i \(-0.584100\pi\)
−0.261145 + 0.965299i \(0.584100\pi\)
\(480\) 2.56729 0.117180
\(481\) 3.95118 0.180158
\(482\) −22.0678 −1.00516
\(483\) −0.964946 −0.0439065
\(484\) −8.14829 −0.370377
\(485\) −12.9501 −0.588035
\(486\) 0.396669 0.0179933
\(487\) −3.06882 −0.139062 −0.0695309 0.997580i \(-0.522150\pi\)
−0.0695309 + 0.997580i \(0.522150\pi\)
\(488\) −0.188979 −0.00855467
\(489\) 17.5653 0.794330
\(490\) 8.73375 0.394550
\(491\) −27.2157 −1.22823 −0.614113 0.789218i \(-0.710486\pi\)
−0.614113 + 0.789218i \(0.710486\pi\)
\(492\) −2.85540 −0.128732
\(493\) −0.299025 −0.0134674
\(494\) 2.71934 0.122349
\(495\) −0.0961591 −0.00432203
\(496\) −0.660364 −0.0296512
\(497\) −2.41898 −0.108506
\(498\) −12.3136 −0.551786
\(499\) 2.40788 0.107792 0.0538959 0.998547i \(-0.482836\pi\)
0.0538959 + 0.998547i \(0.482836\pi\)
\(500\) −11.5979 −0.518672
\(501\) −11.1309 −0.497292
\(502\) −10.4314 −0.465575
\(503\) 17.8861 0.797501 0.398751 0.917059i \(-0.369444\pi\)
0.398751 + 0.917059i \(0.369444\pi\)
\(504\) −0.0408507 −0.00181964
\(505\) 29.0029 1.29061
\(506\) 0.884746 0.0393317
\(507\) 6.86847 0.305039
\(508\) 5.39811 0.239502
\(509\) 29.7716 1.31960 0.659802 0.751439i \(-0.270640\pi\)
0.659802 + 0.751439i \(0.270640\pi\)
\(510\) −1.61624 −0.0715683
\(511\) 2.26721 0.100295
\(512\) −1.00000 −0.0441942
\(513\) −4.73715 −0.209150
\(514\) −15.8546 −0.699319
\(515\) −6.84439 −0.301600
\(516\) 5.52245 0.243112
\(517\) 6.43614 0.283061
\(518\) 1.40879 0.0618985
\(519\) −18.0304 −0.791446
\(520\) −4.47748 −0.196350
\(521\) −35.4047 −1.55111 −0.775554 0.631282i \(-0.782529\pi\)
−0.775554 + 0.631282i \(0.782529\pi\)
\(522\) 0.0181309 0.000793566 0
\(523\) −26.0379 −1.13856 −0.569280 0.822144i \(-0.692778\pi\)
−0.569280 + 0.822144i \(0.692778\pi\)
\(524\) 2.39765 0.104742
\(525\) −5.11037 −0.223035
\(526\) −28.5821 −1.24624
\(527\) 0.415733 0.0181096
\(528\) −2.90625 −0.126478
\(529\) −22.7255 −0.988066
\(530\) 11.4279 0.496394
\(531\) 0.337096 0.0146287
\(532\) 0.969576 0.0420365
\(533\) 4.97996 0.215706
\(534\) −17.3572 −0.751121
\(535\) 13.2553 0.573078
\(536\) −12.0430 −0.520178
\(537\) −11.5360 −0.497815
\(538\) −0.791621 −0.0341292
\(539\) −9.88686 −0.425857
\(540\) 7.79987 0.335653
\(541\) 11.8680 0.510243 0.255122 0.966909i \(-0.417884\pi\)
0.255122 + 0.966909i \(0.417884\pi\)
\(542\) −6.60941 −0.283899
\(543\) −6.31372 −0.270948
\(544\) 0.629551 0.0269918
\(545\) 18.7226 0.801987
\(546\) −5.52810 −0.236581
\(547\) −16.1838 −0.691971 −0.345986 0.938240i \(-0.612455\pi\)
−0.345986 + 0.938240i \(0.612455\pi\)
\(548\) −21.9377 −0.937131
\(549\) −0.00721366 −0.000307872 0
\(550\) 4.68563 0.199796
\(551\) −0.430329 −0.0183326
\(552\) −0.901666 −0.0383775
\(553\) −5.69947 −0.242366
\(554\) −7.34257 −0.311956
\(555\) −3.37958 −0.143455
\(556\) −8.36040 −0.354560
\(557\) −8.64260 −0.366199 −0.183099 0.983094i \(-0.558613\pi\)
−0.183099 + 0.983094i \(0.558613\pi\)
\(558\) −0.0252073 −0.00106711
\(559\) −9.63142 −0.407366
\(560\) −1.59644 −0.0674618
\(561\) 1.82963 0.0772471
\(562\) −5.23271 −0.220728
\(563\) 42.2887 1.78226 0.891128 0.453751i \(-0.149915\pi\)
0.891128 + 0.453751i \(0.149915\pi\)
\(564\) −6.55923 −0.276193
\(565\) 9.75536 0.410411
\(566\) −22.4417 −0.943295
\(567\) 9.50752 0.399278
\(568\) −2.26035 −0.0948422
\(569\) −22.5679 −0.946094 −0.473047 0.881037i \(-0.656846\pi\)
−0.473047 + 0.881037i \(0.656846\pi\)
\(570\) −2.32595 −0.0974232
\(571\) −37.8283 −1.58307 −0.791534 0.611126i \(-0.790717\pi\)
−0.791534 + 0.611126i \(0.790717\pi\)
\(572\) 5.06864 0.211930
\(573\) −6.01499 −0.251280
\(574\) 1.77560 0.0741120
\(575\) 1.45372 0.0606243
\(576\) −0.0381718 −0.00159049
\(577\) 3.15010 0.131140 0.0655701 0.997848i \(-0.479113\pi\)
0.0655701 + 0.997848i \(0.479113\pi\)
\(578\) 16.6037 0.690621
\(579\) 43.6592 1.81441
\(580\) 0.708550 0.0294210
\(581\) 7.65707 0.317669
\(582\) −14.9403 −0.619295
\(583\) −12.9367 −0.535782
\(584\) 2.11853 0.0876654
\(585\) −0.170913 −0.00706640
\(586\) 18.2607 0.754341
\(587\) −8.57414 −0.353893 −0.176946 0.984221i \(-0.556622\pi\)
−0.176946 + 0.984221i \(0.556622\pi\)
\(588\) 10.0759 0.415525
\(589\) 0.598285 0.0246519
\(590\) 13.1736 0.542351
\(591\) −41.7117 −1.71579
\(592\) 1.31640 0.0541037
\(593\) −37.8596 −1.55471 −0.777354 0.629063i \(-0.783439\pi\)
−0.777354 + 0.629063i \(0.783439\pi\)
\(594\) −8.82968 −0.362286
\(595\) 1.00504 0.0412026
\(596\) −22.2698 −0.912206
\(597\) 14.7514 0.603736
\(598\) 1.57255 0.0643063
\(599\) 14.6887 0.600166 0.300083 0.953913i \(-0.402986\pi\)
0.300083 + 0.953913i \(0.402986\pi\)
\(600\) −4.77524 −0.194948
\(601\) −6.03798 −0.246294 −0.123147 0.992388i \(-0.539299\pi\)
−0.123147 + 0.992388i \(0.539299\pi\)
\(602\) −3.43407 −0.139962
\(603\) −0.459702 −0.0187205
\(604\) 4.25695 0.173213
\(605\) −12.1552 −0.494178
\(606\) 33.4600 1.35922
\(607\) 35.8038 1.45323 0.726616 0.687044i \(-0.241092\pi\)
0.726616 + 0.687044i \(0.241092\pi\)
\(608\) 0.905993 0.0367429
\(609\) 0.874808 0.0354490
\(610\) −0.281909 −0.0114141
\(611\) 11.4396 0.462797
\(612\) 0.0240311 0.000971400 0
\(613\) 7.44892 0.300859 0.150429 0.988621i \(-0.451934\pi\)
0.150429 + 0.988621i \(0.451934\pi\)
\(614\) −19.9080 −0.803420
\(615\) −4.25954 −0.171761
\(616\) 1.80722 0.0728148
\(617\) −30.1387 −1.21334 −0.606670 0.794954i \(-0.707495\pi\)
−0.606670 + 0.794954i \(0.707495\pi\)
\(618\) −7.89623 −0.317633
\(619\) −44.4650 −1.78720 −0.893599 0.448866i \(-0.851828\pi\)
−0.893599 + 0.448866i \(0.851828\pi\)
\(620\) −0.985096 −0.0395624
\(621\) −2.73942 −0.109929
\(622\) 32.6917 1.31082
\(623\) 10.7934 0.432428
\(624\) −5.16557 −0.206788
\(625\) −3.42761 −0.137104
\(626\) −5.08826 −0.203368
\(627\) 2.63304 0.105153
\(628\) 4.51315 0.180094
\(629\) −0.828741 −0.0330441
\(630\) −0.0609389 −0.00242786
\(631\) −3.42615 −0.136393 −0.0681964 0.997672i \(-0.521724\pi\)
−0.0681964 + 0.997672i \(0.521724\pi\)
\(632\) −5.32571 −0.211845
\(633\) −9.36627 −0.372276
\(634\) −0.0528738 −0.00209988
\(635\) 8.05261 0.319558
\(636\) 13.1841 0.522783
\(637\) −17.5729 −0.696265
\(638\) −0.802100 −0.0317554
\(639\) −0.0862816 −0.00341325
\(640\) −1.49175 −0.0589664
\(641\) −48.4663 −1.91430 −0.957152 0.289585i \(-0.906483\pi\)
−0.957152 + 0.289585i \(0.906483\pi\)
\(642\) 15.2924 0.603542
\(643\) 19.4529 0.767149 0.383575 0.923510i \(-0.374693\pi\)
0.383575 + 0.923510i \(0.374693\pi\)
\(644\) 0.560690 0.0220943
\(645\) 8.23809 0.324375
\(646\) −0.570369 −0.0224409
\(647\) −9.69744 −0.381246 −0.190623 0.981663i \(-0.561051\pi\)
−0.190623 + 0.981663i \(0.561051\pi\)
\(648\) 8.88403 0.348998
\(649\) −14.9130 −0.585385
\(650\) 8.32825 0.326661
\(651\) −1.21624 −0.0476683
\(652\) −10.2065 −0.399716
\(653\) 46.3487 1.81377 0.906883 0.421384i \(-0.138455\pi\)
0.906883 + 0.421384i \(0.138455\pi\)
\(654\) 21.5998 0.844621
\(655\) 3.57669 0.139753
\(656\) 1.65916 0.0647792
\(657\) 0.0808681 0.00315496
\(658\) 4.07878 0.159007
\(659\) 14.3452 0.558811 0.279405 0.960173i \(-0.409863\pi\)
0.279405 + 0.960173i \(0.409863\pi\)
\(660\) −4.33538 −0.168755
\(661\) −32.0420 −1.24629 −0.623146 0.782106i \(-0.714146\pi\)
−0.623146 + 0.782106i \(0.714146\pi\)
\(662\) 12.8595 0.499798
\(663\) 3.25199 0.126297
\(664\) 7.15493 0.277665
\(665\) 1.44636 0.0560875
\(666\) 0.0502493 0.00194712
\(667\) −0.248852 −0.00963560
\(668\) 6.46771 0.250243
\(669\) −13.2877 −0.513733
\(670\) −17.9651 −0.694051
\(671\) 0.319129 0.0123198
\(672\) −1.84178 −0.0710481
\(673\) −25.3822 −0.978411 −0.489206 0.872169i \(-0.662713\pi\)
−0.489206 + 0.872169i \(0.662713\pi\)
\(674\) 17.2499 0.664442
\(675\) −14.5080 −0.558413
\(676\) −3.99099 −0.153499
\(677\) 2.61878 0.100648 0.0503240 0.998733i \(-0.483975\pi\)
0.0503240 + 0.998733i \(0.483975\pi\)
\(678\) 11.2546 0.432229
\(679\) 9.29045 0.356535
\(680\) 0.939131 0.0360140
\(681\) 38.0383 1.45763
\(682\) 1.11516 0.0427016
\(683\) −19.3856 −0.741770 −0.370885 0.928679i \(-0.620946\pi\)
−0.370885 + 0.928679i \(0.620946\pi\)
\(684\) 0.0345834 0.00132233
\(685\) −32.7255 −1.25038
\(686\) −13.7569 −0.525240
\(687\) −4.19102 −0.159897
\(688\) −3.20887 −0.122337
\(689\) −22.9937 −0.875989
\(690\) −1.34506 −0.0512054
\(691\) −33.2680 −1.26558 −0.632788 0.774325i \(-0.718089\pi\)
−0.632788 + 0.774325i \(0.718089\pi\)
\(692\) 10.4767 0.398265
\(693\) 0.0689846 0.00262051
\(694\) −27.2330 −1.03375
\(695\) −12.4716 −0.473074
\(696\) 0.817440 0.0309850
\(697\) −1.04452 −0.0395642
\(698\) 22.2712 0.842976
\(699\) 49.2746 1.86373
\(700\) 2.96942 0.112234
\(701\) 19.8226 0.748689 0.374345 0.927290i \(-0.377868\pi\)
0.374345 + 0.927290i \(0.377868\pi\)
\(702\) −15.6939 −0.592328
\(703\) −1.19265 −0.0449816
\(704\) 1.68870 0.0636453
\(705\) −9.78471 −0.368513
\(706\) 7.04399 0.265104
\(707\) −20.8067 −0.782517
\(708\) 15.1982 0.571182
\(709\) −16.1748 −0.607456 −0.303728 0.952759i \(-0.598231\pi\)
−0.303728 + 0.952759i \(0.598231\pi\)
\(710\) −3.37187 −0.126544
\(711\) −0.203292 −0.00762404
\(712\) 10.0856 0.377973
\(713\) 0.345979 0.0129570
\(714\) 1.15949 0.0433930
\(715\) 7.56112 0.282770
\(716\) 6.70309 0.250506
\(717\) 6.63194 0.247674
\(718\) 19.4730 0.726728
\(719\) 3.02187 0.112697 0.0563484 0.998411i \(-0.482054\pi\)
0.0563484 + 0.998411i \(0.482054\pi\)
\(720\) −0.0569426 −0.00212213
\(721\) 4.91018 0.182865
\(722\) 18.1792 0.676559
\(723\) −37.9786 −1.41244
\(724\) 3.66864 0.136344
\(725\) −1.31793 −0.0489465
\(726\) −14.0232 −0.520449
\(727\) 27.4998 1.01991 0.509956 0.860201i \(-0.329662\pi\)
0.509956 + 0.860201i \(0.329662\pi\)
\(728\) 3.21215 0.119050
\(729\) 27.3347 1.01240
\(730\) 3.16031 0.116968
\(731\) 2.02015 0.0747178
\(732\) −0.325232 −0.0120209
\(733\) −49.2084 −1.81755 −0.908776 0.417284i \(-0.862982\pi\)
−0.908776 + 0.417284i \(0.862982\pi\)
\(734\) 24.0895 0.889158
\(735\) 15.0307 0.554417
\(736\) 0.523921 0.0193120
\(737\) 20.3370 0.749123
\(738\) 0.0633330 0.00233132
\(739\) −7.21843 −0.265534 −0.132767 0.991147i \(-0.542386\pi\)
−0.132767 + 0.991147i \(0.542386\pi\)
\(740\) 1.96373 0.0721883
\(741\) 4.67997 0.171923
\(742\) −8.19836 −0.300971
\(743\) −32.8917 −1.20668 −0.603340 0.797484i \(-0.706164\pi\)
−0.603340 + 0.797484i \(0.706164\pi\)
\(744\) −1.13648 −0.0416655
\(745\) −33.2209 −1.21712
\(746\) 7.50688 0.274846
\(747\) 0.273116 0.00999281
\(748\) −1.06312 −0.0388717
\(749\) −9.50939 −0.347465
\(750\) −19.9599 −0.728832
\(751\) −47.9278 −1.74891 −0.874455 0.485106i \(-0.838781\pi\)
−0.874455 + 0.485106i \(0.838781\pi\)
\(752\) 3.81130 0.138984
\(753\) −17.9524 −0.654221
\(754\) −1.42566 −0.0519193
\(755\) 6.35029 0.231111
\(756\) −5.59564 −0.203511
\(757\) 41.9225 1.52370 0.761850 0.647753i \(-0.224291\pi\)
0.761850 + 0.647753i \(0.224291\pi\)
\(758\) −4.26329 −0.154850
\(759\) 1.52264 0.0552685
\(760\) 1.35151 0.0490245
\(761\) 16.0830 0.583009 0.291505 0.956569i \(-0.405844\pi\)
0.291505 + 0.956569i \(0.405844\pi\)
\(762\) 9.29012 0.336546
\(763\) −13.4316 −0.486257
\(764\) 3.49506 0.126447
\(765\) 0.0358483 0.00129610
\(766\) −2.04896 −0.0740318
\(767\) −26.5063 −0.957089
\(768\) −1.72100 −0.0621011
\(769\) −23.8882 −0.861429 −0.430715 0.902488i \(-0.641738\pi\)
−0.430715 + 0.902488i \(0.641738\pi\)
\(770\) 2.69591 0.0971537
\(771\) −27.2858 −0.982674
\(772\) −25.3685 −0.913034
\(773\) −15.1586 −0.545217 −0.272608 0.962125i \(-0.587886\pi\)
−0.272608 + 0.962125i \(0.587886\pi\)
\(774\) −0.122488 −0.00440275
\(775\) 1.83231 0.0658184
\(776\) 8.68119 0.311637
\(777\) 2.42451 0.0869790
\(778\) −21.7457 −0.779622
\(779\) −1.50318 −0.0538572
\(780\) −7.70573 −0.275909
\(781\) 3.81705 0.136585
\(782\) −0.329835 −0.0117949
\(783\) 2.48352 0.0887539
\(784\) −5.85471 −0.209097
\(785\) 6.73248 0.240292
\(786\) 4.12635 0.147182
\(787\) −22.6897 −0.808802 −0.404401 0.914582i \(-0.632520\pi\)
−0.404401 + 0.914582i \(0.632520\pi\)
\(788\) 24.2370 0.863406
\(789\) −49.1897 −1.75120
\(790\) −7.94460 −0.282656
\(791\) −6.99851 −0.248838
\(792\) 0.0644607 0.00229051
\(793\) 0.567221 0.0201426
\(794\) 19.7781 0.701899
\(795\) 19.6673 0.697527
\(796\) −8.57145 −0.303807
\(797\) 17.3969 0.616230 0.308115 0.951349i \(-0.400302\pi\)
0.308115 + 0.951349i \(0.400302\pi\)
\(798\) 1.66864 0.0590691
\(799\) −2.39941 −0.0848850
\(800\) 2.77469 0.0981002
\(801\) 0.384984 0.0136027
\(802\) 30.2560 1.06838
\(803\) −3.57756 −0.126249
\(804\) −20.7259 −0.730947
\(805\) 0.836407 0.0294795
\(806\) 1.98208 0.0698159
\(807\) −1.36238 −0.0479580
\(808\) −19.4422 −0.683976
\(809\) 9.85310 0.346416 0.173208 0.984885i \(-0.444587\pi\)
0.173208 + 0.984885i \(0.444587\pi\)
\(810\) 13.2527 0.465653
\(811\) −40.5571 −1.42415 −0.712077 0.702101i \(-0.752245\pi\)
−0.712077 + 0.702101i \(0.752245\pi\)
\(812\) −0.508315 −0.0178384
\(813\) −11.3748 −0.398931
\(814\) −2.22301 −0.0779163
\(815\) −15.2255 −0.533324
\(816\) 1.08346 0.0379285
\(817\) 2.90721 0.101710
\(818\) 3.90825 0.136649
\(819\) 0.122614 0.00428446
\(820\) 2.47504 0.0864322
\(821\) −27.5773 −0.962453 −0.481226 0.876596i \(-0.659809\pi\)
−0.481226 + 0.876596i \(0.659809\pi\)
\(822\) −37.7547 −1.31685
\(823\) −17.5605 −0.612122 −0.306061 0.952012i \(-0.599011\pi\)
−0.306061 + 0.952012i \(0.599011\pi\)
\(824\) 4.58818 0.159837
\(825\) 8.06395 0.280751
\(826\) −9.45079 −0.328835
\(827\) −14.2749 −0.496388 −0.248194 0.968710i \(-0.579837\pi\)
−0.248194 + 0.968710i \(0.579837\pi\)
\(828\) 0.0199990 0.000695013 0
\(829\) −43.2830 −1.50328 −0.751640 0.659573i \(-0.770737\pi\)
−0.751640 + 0.659573i \(0.770737\pi\)
\(830\) 10.6733 0.370477
\(831\) −12.6365 −0.438357
\(832\) 3.00150 0.104058
\(833\) 3.68584 0.127707
\(834\) −14.3882 −0.498223
\(835\) 9.64818 0.333889
\(836\) −1.52995 −0.0529145
\(837\) −3.45283 −0.119347
\(838\) −3.60625 −0.124576
\(839\) 30.2971 1.04597 0.522986 0.852342i \(-0.324818\pi\)
0.522986 + 0.852342i \(0.324818\pi\)
\(840\) −2.74746 −0.0947965
\(841\) −28.7744 −0.992220
\(842\) 11.7802 0.405974
\(843\) −9.00547 −0.310165
\(844\) 5.44236 0.187334
\(845\) −5.95354 −0.204808
\(846\) 0.145484 0.00500184
\(847\) 8.72014 0.299628
\(848\) −7.66072 −0.263070
\(849\) −38.6221 −1.32551
\(850\) −1.74681 −0.0599152
\(851\) −0.689689 −0.0236422
\(852\) −3.89005 −0.133271
\(853\) −40.2436 −1.37792 −0.688958 0.724802i \(-0.741931\pi\)
−0.688958 + 0.724802i \(0.741931\pi\)
\(854\) 0.202242 0.00692057
\(855\) 0.0515896 0.00176433
\(856\) −8.88578 −0.303710
\(857\) −33.2032 −1.13420 −0.567099 0.823650i \(-0.691934\pi\)
−0.567099 + 0.823650i \(0.691934\pi\)
\(858\) 8.72311 0.297802
\(859\) −10.7462 −0.366654 −0.183327 0.983052i \(-0.558687\pi\)
−0.183327 + 0.983052i \(0.558687\pi\)
\(860\) −4.78682 −0.163229
\(861\) 3.05580 0.104141
\(862\) 12.9393 0.440713
\(863\) −9.17913 −0.312461 −0.156231 0.987721i \(-0.549934\pi\)
−0.156231 + 0.987721i \(0.549934\pi\)
\(864\) −5.22868 −0.177883
\(865\) 15.6286 0.531388
\(866\) −1.56045 −0.0530263
\(867\) 28.5748 0.970453
\(868\) 0.706709 0.0239873
\(869\) 8.99353 0.305085
\(870\) 1.21941 0.0413420
\(871\) 36.1470 1.22480
\(872\) −12.5508 −0.425023
\(873\) 0.331377 0.0112154
\(874\) −0.474669 −0.0160559
\(875\) 12.4118 0.419596
\(876\) 3.64598 0.123186
\(877\) −22.2087 −0.749936 −0.374968 0.927038i \(-0.622346\pi\)
−0.374968 + 0.927038i \(0.622346\pi\)
\(878\) 29.9307 1.01011
\(879\) 31.4265 1.05999
\(880\) 2.51911 0.0849193
\(881\) −19.7013 −0.663755 −0.331877 0.943322i \(-0.607682\pi\)
−0.331877 + 0.943322i \(0.607682\pi\)
\(882\) −0.223485 −0.00752513
\(883\) 33.5175 1.12795 0.563977 0.825791i \(-0.309271\pi\)
0.563977 + 0.825791i \(0.309271\pi\)
\(884\) −1.88960 −0.0635541
\(885\) 22.6718 0.762104
\(886\) −29.5035 −0.991190
\(887\) 51.1726 1.71821 0.859103 0.511803i \(-0.171022\pi\)
0.859103 + 0.511803i \(0.171022\pi\)
\(888\) 2.26552 0.0760258
\(889\) −5.77695 −0.193753
\(890\) 15.0451 0.504313
\(891\) −15.0025 −0.502602
\(892\) 7.72095 0.258517
\(893\) −3.45301 −0.115551
\(894\) −38.3262 −1.28182
\(895\) 9.99930 0.334240
\(896\) 1.07018 0.0357522
\(897\) 2.70635 0.0903625
\(898\) −16.6803 −0.556628
\(899\) −0.313660 −0.0104612
\(900\) 0.105915 0.00353050
\(901\) 4.82282 0.160671
\(902\) −2.80182 −0.0932904
\(903\) −5.91002 −0.196673
\(904\) −6.53956 −0.217502
\(905\) 5.47268 0.181918
\(906\) 7.32620 0.243397
\(907\) 17.6063 0.584606 0.292303 0.956326i \(-0.405578\pi\)
0.292303 + 0.956326i \(0.405578\pi\)
\(908\) −22.1025 −0.733497
\(909\) −0.742145 −0.0246154
\(910\) 4.79171 0.158844
\(911\) −26.5176 −0.878566 −0.439283 0.898349i \(-0.644767\pi\)
−0.439283 + 0.898349i \(0.644767\pi\)
\(912\) 1.55921 0.0516306
\(913\) −12.0825 −0.399874
\(914\) −12.9587 −0.428637
\(915\) −0.485164 −0.0160390
\(916\) 2.43523 0.0804622
\(917\) −2.56592 −0.0847342
\(918\) 3.29172 0.108643
\(919\) 46.5952 1.53704 0.768518 0.639829i \(-0.220995\pi\)
0.768518 + 0.639829i \(0.220995\pi\)
\(920\) 0.781557 0.0257672
\(921\) −34.2615 −1.12896
\(922\) 3.45467 0.113773
\(923\) 6.78444 0.223313
\(924\) 3.11021 0.102318
\(925\) −3.65261 −0.120097
\(926\) −7.47857 −0.245761
\(927\) 0.175139 0.00575232
\(928\) −0.474981 −0.0155920
\(929\) −36.1551 −1.18621 −0.593105 0.805125i \(-0.702098\pi\)
−0.593105 + 0.805125i \(0.702098\pi\)
\(930\) −1.69535 −0.0555926
\(931\) 5.30433 0.173842
\(932\) −28.6314 −0.937853
\(933\) 56.2622 1.84194
\(934\) 27.1896 0.889670
\(935\) −1.58591 −0.0518648
\(936\) 0.114573 0.00374493
\(937\) −26.6691 −0.871241 −0.435620 0.900131i \(-0.643471\pi\)
−0.435620 + 0.900131i \(0.643471\pi\)
\(938\) 12.8882 0.420814
\(939\) −8.75687 −0.285770
\(940\) 5.68549 0.185440
\(941\) −25.1301 −0.819217 −0.409608 0.912261i \(-0.634335\pi\)
−0.409608 + 0.912261i \(0.634335\pi\)
\(942\) 7.76712 0.253066
\(943\) −0.869267 −0.0283072
\(944\) −8.83103 −0.287425
\(945\) −8.34727 −0.271537
\(946\) 5.41882 0.176181
\(947\) −36.6343 −1.19046 −0.595228 0.803557i \(-0.702938\pi\)
−0.595228 + 0.803557i \(0.702938\pi\)
\(948\) −9.16552 −0.297682
\(949\) −6.35877 −0.206415
\(950\) −2.51385 −0.0815601
\(951\) −0.0909955 −0.00295073
\(952\) −0.673734 −0.0218358
\(953\) −0.651456 −0.0211027 −0.0105514 0.999944i \(-0.503359\pi\)
−0.0105514 + 0.999944i \(0.503359\pi\)
\(954\) −0.292424 −0.00946756
\(955\) 5.21375 0.168713
\(956\) −3.85355 −0.124633
\(957\) −1.38041 −0.0446224
\(958\) 11.4309 0.369315
\(959\) 23.4773 0.758121
\(960\) −2.56729 −0.0828589
\(961\) −30.5639 −0.985933
\(962\) −3.95118 −0.127391
\(963\) −0.339186 −0.0109301
\(964\) 22.0678 0.710756
\(965\) −37.8434 −1.21822
\(966\) 0.964946 0.0310466
\(967\) −1.48564 −0.0477751 −0.0238875 0.999715i \(-0.507604\pi\)
−0.0238875 + 0.999715i \(0.507604\pi\)
\(968\) 8.14829 0.261896
\(969\) −0.981603 −0.0315336
\(970\) 12.9501 0.415804
\(971\) −10.2557 −0.329121 −0.164561 0.986367i \(-0.552621\pi\)
−0.164561 + 0.986367i \(0.552621\pi\)
\(972\) −0.396669 −0.0127232
\(973\) 8.94713 0.286832
\(974\) 3.06882 0.0983315
\(975\) 14.3329 0.459020
\(976\) 0.188979 0.00604907
\(977\) 43.6001 1.39489 0.697446 0.716637i \(-0.254320\pi\)
0.697446 + 0.716637i \(0.254320\pi\)
\(978\) −17.5653 −0.561676
\(979\) −17.0315 −0.544329
\(980\) −8.73375 −0.278989
\(981\) −0.479086 −0.0152960
\(982\) 27.2157 0.868487
\(983\) −16.7535 −0.534354 −0.267177 0.963648i \(-0.586091\pi\)
−0.267177 + 0.963648i \(0.586091\pi\)
\(984\) 2.85540 0.0910269
\(985\) 36.1554 1.15201
\(986\) 0.299025 0.00952289
\(987\) 7.01956 0.223435
\(988\) −2.71934 −0.0865137
\(989\) 1.68119 0.0534588
\(990\) 0.0961591 0.00305614
\(991\) 3.97479 0.126263 0.0631317 0.998005i \(-0.479891\pi\)
0.0631317 + 0.998005i \(0.479891\pi\)
\(992\) 0.660364 0.0209666
\(993\) 22.1311 0.702309
\(994\) 2.41898 0.0767255
\(995\) −12.7864 −0.405357
\(996\) 12.3136 0.390172
\(997\) 10.9747 0.347571 0.173785 0.984784i \(-0.444400\pi\)
0.173785 + 0.984784i \(0.444400\pi\)
\(998\) −2.40788 −0.0762203
\(999\) 6.88304 0.217770
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 8006.2.a.b.1.19 75
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8006.2.a.b.1.19 75 1.1 even 1 trivial