Properties

Label 4017.2.a.g.1.20
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $0$
Dimension $24$
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] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, 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("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.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: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.86289 q^{2} -1.00000 q^{3} +1.47035 q^{4} +4.02931 q^{5} -1.86289 q^{6} +3.22519 q^{7} -0.986675 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.86289 q^{2} -1.00000 q^{3} +1.47035 q^{4} +4.02931 q^{5} -1.86289 q^{6} +3.22519 q^{7} -0.986675 q^{8} +1.00000 q^{9} +7.50616 q^{10} -3.00398 q^{11} -1.47035 q^{12} -1.00000 q^{13} +6.00816 q^{14} -4.02931 q^{15} -4.77877 q^{16} +4.28605 q^{17} +1.86289 q^{18} -6.27499 q^{19} +5.92451 q^{20} -3.22519 q^{21} -5.59607 q^{22} +7.70305 q^{23} +0.986675 q^{24} +11.2354 q^{25} -1.86289 q^{26} -1.00000 q^{27} +4.74216 q^{28} -5.15412 q^{29} -7.50616 q^{30} +6.62744 q^{31} -6.92896 q^{32} +3.00398 q^{33} +7.98443 q^{34} +12.9953 q^{35} +1.47035 q^{36} +7.68405 q^{37} -11.6896 q^{38} +1.00000 q^{39} -3.97562 q^{40} +1.36900 q^{41} -6.00816 q^{42} +10.8702 q^{43} -4.41690 q^{44} +4.02931 q^{45} +14.3499 q^{46} +5.13698 q^{47} +4.77877 q^{48} +3.40183 q^{49} +20.9302 q^{50} -4.28605 q^{51} -1.47035 q^{52} -0.715373 q^{53} -1.86289 q^{54} -12.1040 q^{55} -3.18221 q^{56} +6.27499 q^{57} -9.60154 q^{58} +4.67528 q^{59} -5.92451 q^{60} +1.19246 q^{61} +12.3462 q^{62} +3.22519 q^{63} -3.35034 q^{64} -4.02931 q^{65} +5.59607 q^{66} -1.94836 q^{67} +6.30200 q^{68} -7.70305 q^{69} +24.2088 q^{70} +8.42340 q^{71} -0.986675 q^{72} -12.1934 q^{73} +14.3145 q^{74} -11.2354 q^{75} -9.22644 q^{76} -9.68839 q^{77} +1.86289 q^{78} +4.74780 q^{79} -19.2552 q^{80} +1.00000 q^{81} +2.55030 q^{82} -10.7359 q^{83} -4.74216 q^{84} +17.2698 q^{85} +20.2499 q^{86} +5.15412 q^{87} +2.96395 q^{88} -3.76088 q^{89} +7.50616 q^{90} -3.22519 q^{91} +11.3262 q^{92} -6.62744 q^{93} +9.56962 q^{94} -25.2839 q^{95} +6.92896 q^{96} -8.35697 q^{97} +6.33724 q^{98} -3.00398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86289 1.31726 0.658630 0.752467i \(-0.271136\pi\)
0.658630 + 0.752467i \(0.271136\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.47035 0.735176
\(5\) 4.02931 1.80196 0.900982 0.433857i \(-0.142848\pi\)
0.900982 + 0.433857i \(0.142848\pi\)
\(6\) −1.86289 −0.760521
\(7\) 3.22519 1.21901 0.609503 0.792784i \(-0.291369\pi\)
0.609503 + 0.792784i \(0.291369\pi\)
\(8\) −0.986675 −0.348842
\(9\) 1.00000 0.333333
\(10\) 7.50616 2.37366
\(11\) −3.00398 −0.905733 −0.452867 0.891578i \(-0.649599\pi\)
−0.452867 + 0.891578i \(0.649599\pi\)
\(12\) −1.47035 −0.424454
\(13\) −1.00000 −0.277350
\(14\) 6.00816 1.60575
\(15\) −4.02931 −1.04036
\(16\) −4.77877 −1.19469
\(17\) 4.28605 1.03952 0.519760 0.854312i \(-0.326021\pi\)
0.519760 + 0.854312i \(0.326021\pi\)
\(18\) 1.86289 0.439087
\(19\) −6.27499 −1.43958 −0.719791 0.694191i \(-0.755762\pi\)
−0.719791 + 0.694191i \(0.755762\pi\)
\(20\) 5.92451 1.32476
\(21\) −3.22519 −0.703794
\(22\) −5.59607 −1.19309
\(23\) 7.70305 1.60620 0.803099 0.595846i \(-0.203183\pi\)
0.803099 + 0.595846i \(0.203183\pi\)
\(24\) 0.986675 0.201404
\(25\) 11.2354 2.24707
\(26\) −1.86289 −0.365342
\(27\) −1.00000 −0.192450
\(28\) 4.74216 0.896184
\(29\) −5.15412 −0.957095 −0.478548 0.878062i \(-0.658837\pi\)
−0.478548 + 0.878062i \(0.658837\pi\)
\(30\) −7.50616 −1.37043
\(31\) 6.62744 1.19032 0.595162 0.803606i \(-0.297088\pi\)
0.595162 + 0.803606i \(0.297088\pi\)
\(32\) −6.92896 −1.22488
\(33\) 3.00398 0.522925
\(34\) 7.98443 1.36932
\(35\) 12.9953 2.19660
\(36\) 1.47035 0.245059
\(37\) 7.68405 1.26325 0.631625 0.775274i \(-0.282388\pi\)
0.631625 + 0.775274i \(0.282388\pi\)
\(38\) −11.6896 −1.89630
\(39\) 1.00000 0.160128
\(40\) −3.97562 −0.628601
\(41\) 1.36900 0.213802 0.106901 0.994270i \(-0.465907\pi\)
0.106901 + 0.994270i \(0.465907\pi\)
\(42\) −6.00816 −0.927080
\(43\) 10.8702 1.65768 0.828841 0.559484i \(-0.189001\pi\)
0.828841 + 0.559484i \(0.189001\pi\)
\(44\) −4.41690 −0.665873
\(45\) 4.02931 0.600654
\(46\) 14.3499 2.11578
\(47\) 5.13698 0.749305 0.374653 0.927165i \(-0.377762\pi\)
0.374653 + 0.927165i \(0.377762\pi\)
\(48\) 4.77877 0.689756
\(49\) 3.40183 0.485976
\(50\) 20.9302 2.95998
\(51\) −4.28605 −0.600167
\(52\) −1.47035 −0.203901
\(53\) −0.715373 −0.0982640 −0.0491320 0.998792i \(-0.515645\pi\)
−0.0491320 + 0.998792i \(0.515645\pi\)
\(54\) −1.86289 −0.253507
\(55\) −12.1040 −1.63210
\(56\) −3.18221 −0.425241
\(57\) 6.27499 0.831143
\(58\) −9.60154 −1.26074
\(59\) 4.67528 0.608670 0.304335 0.952565i \(-0.401566\pi\)
0.304335 + 0.952565i \(0.401566\pi\)
\(60\) −5.92451 −0.764851
\(61\) 1.19246 0.152679 0.0763395 0.997082i \(-0.475677\pi\)
0.0763395 + 0.997082i \(0.475677\pi\)
\(62\) 12.3462 1.56797
\(63\) 3.22519 0.406335
\(64\) −3.35034 −0.418793
\(65\) −4.02931 −0.499775
\(66\) 5.59607 0.688829
\(67\) −1.94836 −0.238030 −0.119015 0.992892i \(-0.537974\pi\)
−0.119015 + 0.992892i \(0.537974\pi\)
\(68\) 6.30200 0.764230
\(69\) −7.70305 −0.927338
\(70\) 24.2088 2.89350
\(71\) 8.42340 0.999674 0.499837 0.866120i \(-0.333393\pi\)
0.499837 + 0.866120i \(0.333393\pi\)
\(72\) −0.986675 −0.116281
\(73\) −12.1934 −1.42712 −0.713562 0.700592i \(-0.752919\pi\)
−0.713562 + 0.700592i \(0.752919\pi\)
\(74\) 14.3145 1.66403
\(75\) −11.2354 −1.29735
\(76\) −9.22644 −1.05835
\(77\) −9.68839 −1.10409
\(78\) 1.86289 0.210931
\(79\) 4.74780 0.534170 0.267085 0.963673i \(-0.413940\pi\)
0.267085 + 0.963673i \(0.413940\pi\)
\(80\) −19.2552 −2.15279
\(81\) 1.00000 0.111111
\(82\) 2.55030 0.281633
\(83\) −10.7359 −1.17842 −0.589209 0.807980i \(-0.700561\pi\)
−0.589209 + 0.807980i \(0.700561\pi\)
\(84\) −4.74216 −0.517412
\(85\) 17.2698 1.87318
\(86\) 20.2499 2.18360
\(87\) 5.15412 0.552579
\(88\) 2.96395 0.315958
\(89\) −3.76088 −0.398652 −0.199326 0.979933i \(-0.563875\pi\)
−0.199326 + 0.979933i \(0.563875\pi\)
\(90\) 7.50616 0.791218
\(91\) −3.22519 −0.338092
\(92\) 11.3262 1.18084
\(93\) −6.62744 −0.687234
\(94\) 9.56962 0.987031
\(95\) −25.2839 −2.59407
\(96\) 6.92896 0.707184
\(97\) −8.35697 −0.848521 −0.424261 0.905540i \(-0.639466\pi\)
−0.424261 + 0.905540i \(0.639466\pi\)
\(98\) 6.33724 0.640158
\(99\) −3.00398 −0.301911
\(100\) 16.5199 1.65199
\(101\) −8.27275 −0.823170 −0.411585 0.911371i \(-0.635025\pi\)
−0.411585 + 0.911371i \(0.635025\pi\)
\(102\) −7.98443 −0.790577
\(103\) 1.00000 0.0985329
\(104\) 0.986675 0.0967514
\(105\) −12.9953 −1.26821
\(106\) −1.33266 −0.129439
\(107\) 10.1157 0.977917 0.488959 0.872307i \(-0.337377\pi\)
0.488959 + 0.872307i \(0.337377\pi\)
\(108\) −1.47035 −0.141485
\(109\) −14.5820 −1.39670 −0.698351 0.715756i \(-0.746082\pi\)
−0.698351 + 0.715756i \(0.746082\pi\)
\(110\) −22.5483 −2.14990
\(111\) −7.68405 −0.729338
\(112\) −15.4124 −1.45634
\(113\) −7.92776 −0.745780 −0.372890 0.927875i \(-0.621633\pi\)
−0.372890 + 0.927875i \(0.621633\pi\)
\(114\) 11.6896 1.09483
\(115\) 31.0380 2.89431
\(116\) −7.57836 −0.703633
\(117\) −1.00000 −0.0924500
\(118\) 8.70953 0.801777
\(119\) 13.8233 1.26718
\(120\) 3.97562 0.362923
\(121\) −1.97612 −0.179647
\(122\) 2.22142 0.201118
\(123\) −1.36900 −0.123439
\(124\) 9.74467 0.875097
\(125\) 25.1242 2.24718
\(126\) 6.00816 0.535250
\(127\) 4.36807 0.387604 0.193802 0.981041i \(-0.437918\pi\)
0.193802 + 0.981041i \(0.437918\pi\)
\(128\) 7.61661 0.673220
\(129\) −10.8702 −0.957063
\(130\) −7.50616 −0.658334
\(131\) 12.5592 1.09730 0.548651 0.836052i \(-0.315142\pi\)
0.548651 + 0.836052i \(0.315142\pi\)
\(132\) 4.41690 0.384442
\(133\) −20.2380 −1.75486
\(134\) −3.62957 −0.313547
\(135\) −4.02931 −0.346788
\(136\) −4.22894 −0.362628
\(137\) −13.2503 −1.13205 −0.566024 0.824389i \(-0.691519\pi\)
−0.566024 + 0.824389i \(0.691519\pi\)
\(138\) −14.3499 −1.22155
\(139\) 12.9235 1.09616 0.548080 0.836426i \(-0.315359\pi\)
0.548080 + 0.836426i \(0.315359\pi\)
\(140\) 19.1076 1.61489
\(141\) −5.13698 −0.432612
\(142\) 15.6919 1.31683
\(143\) 3.00398 0.251205
\(144\) −4.77877 −0.398231
\(145\) −20.7675 −1.72465
\(146\) −22.7149 −1.87990
\(147\) −3.40183 −0.280579
\(148\) 11.2983 0.928711
\(149\) 1.14194 0.0935514 0.0467757 0.998905i \(-0.485105\pi\)
0.0467757 + 0.998905i \(0.485105\pi\)
\(150\) −20.9302 −1.70894
\(151\) −10.3512 −0.842366 −0.421183 0.906976i \(-0.638385\pi\)
−0.421183 + 0.906976i \(0.638385\pi\)
\(152\) 6.19137 0.502187
\(153\) 4.28605 0.346507
\(154\) −18.0484 −1.45438
\(155\) 26.7040 2.14492
\(156\) 1.47035 0.117722
\(157\) −11.7224 −0.935552 −0.467776 0.883847i \(-0.654945\pi\)
−0.467776 + 0.883847i \(0.654945\pi\)
\(158\) 8.84462 0.703641
\(159\) 0.715373 0.0567327
\(160\) −27.9189 −2.20719
\(161\) 24.8438 1.95796
\(162\) 1.86289 0.146362
\(163\) 13.6038 1.06553 0.532766 0.846262i \(-0.321152\pi\)
0.532766 + 0.846262i \(0.321152\pi\)
\(164\) 2.01292 0.157182
\(165\) 12.1040 0.942292
\(166\) −19.9998 −1.55229
\(167\) −7.81237 −0.604540 −0.302270 0.953222i \(-0.597744\pi\)
−0.302270 + 0.953222i \(0.597744\pi\)
\(168\) 3.18221 0.245513
\(169\) 1.00000 0.0769231
\(170\) 32.1718 2.46746
\(171\) −6.27499 −0.479860
\(172\) 15.9829 1.21869
\(173\) 11.6753 0.887653 0.443826 0.896113i \(-0.353621\pi\)
0.443826 + 0.896113i \(0.353621\pi\)
\(174\) 9.60154 0.727891
\(175\) 36.2361 2.73919
\(176\) 14.3553 1.08207
\(177\) −4.67528 −0.351416
\(178\) −7.00609 −0.525129
\(179\) −26.0265 −1.94531 −0.972654 0.232258i \(-0.925389\pi\)
−0.972654 + 0.232258i \(0.925389\pi\)
\(180\) 5.92451 0.441587
\(181\) −7.07137 −0.525611 −0.262805 0.964849i \(-0.584648\pi\)
−0.262805 + 0.964849i \(0.584648\pi\)
\(182\) −6.00816 −0.445355
\(183\) −1.19246 −0.0881492
\(184\) −7.60041 −0.560309
\(185\) 30.9614 2.27633
\(186\) −12.3462 −0.905266
\(187\) −12.8752 −0.941528
\(188\) 7.55317 0.550871
\(189\) −3.22519 −0.234598
\(190\) −47.1011 −3.41707
\(191\) 10.1201 0.732264 0.366132 0.930563i \(-0.380682\pi\)
0.366132 + 0.930563i \(0.380682\pi\)
\(192\) 3.35034 0.241790
\(193\) −17.7397 −1.27693 −0.638465 0.769651i \(-0.720430\pi\)
−0.638465 + 0.769651i \(0.720430\pi\)
\(194\) −15.5681 −1.11772
\(195\) 4.02931 0.288545
\(196\) 5.00189 0.357278
\(197\) −13.0312 −0.928434 −0.464217 0.885721i \(-0.653664\pi\)
−0.464217 + 0.885721i \(0.653664\pi\)
\(198\) −5.59607 −0.397696
\(199\) 20.8216 1.47600 0.738002 0.674798i \(-0.235769\pi\)
0.738002 + 0.674798i \(0.235769\pi\)
\(200\) −11.0856 −0.783873
\(201\) 1.94836 0.137426
\(202\) −15.4112 −1.08433
\(203\) −16.6230 −1.16671
\(204\) −6.30200 −0.441228
\(205\) 5.51614 0.385264
\(206\) 1.86289 0.129794
\(207\) 7.70305 0.535399
\(208\) 4.77877 0.331348
\(209\) 18.8499 1.30388
\(210\) −24.2088 −1.67056
\(211\) −5.21341 −0.358906 −0.179453 0.983767i \(-0.557433\pi\)
−0.179453 + 0.983767i \(0.557433\pi\)
\(212\) −1.05185 −0.0722413
\(213\) −8.42340 −0.577162
\(214\) 18.8443 1.28817
\(215\) 43.7992 2.98708
\(216\) 0.986675 0.0671347
\(217\) 21.3747 1.45101
\(218\) −27.1646 −1.83982
\(219\) 12.1934 0.823951
\(220\) −17.7971 −1.19988
\(221\) −4.28605 −0.288311
\(222\) −14.3145 −0.960728
\(223\) 0.912908 0.0611329 0.0305664 0.999533i \(-0.490269\pi\)
0.0305664 + 0.999533i \(0.490269\pi\)
\(224\) −22.3472 −1.49314
\(225\) 11.2354 0.749024
\(226\) −14.7685 −0.982387
\(227\) −16.4016 −1.08861 −0.544305 0.838887i \(-0.683207\pi\)
−0.544305 + 0.838887i \(0.683207\pi\)
\(228\) 9.22644 0.611036
\(229\) 25.9445 1.71446 0.857231 0.514932i \(-0.172183\pi\)
0.857231 + 0.514932i \(0.172183\pi\)
\(230\) 57.8203 3.81256
\(231\) 9.68839 0.637449
\(232\) 5.08544 0.333875
\(233\) −10.7098 −0.701622 −0.350811 0.936446i \(-0.614094\pi\)
−0.350811 + 0.936446i \(0.614094\pi\)
\(234\) −1.86289 −0.121781
\(235\) 20.6985 1.35022
\(236\) 6.87431 0.447480
\(237\) −4.74780 −0.308403
\(238\) 25.7513 1.66921
\(239\) −3.15424 −0.204031 −0.102015 0.994783i \(-0.532529\pi\)
−0.102015 + 0.994783i \(0.532529\pi\)
\(240\) 19.2552 1.24291
\(241\) −0.587519 −0.0378454 −0.0189227 0.999821i \(-0.506024\pi\)
−0.0189227 + 0.999821i \(0.506024\pi\)
\(242\) −3.68129 −0.236642
\(243\) −1.00000 −0.0641500
\(244\) 1.75334 0.112246
\(245\) 13.7071 0.875712
\(246\) −2.55030 −0.162601
\(247\) 6.27499 0.399268
\(248\) −6.53913 −0.415235
\(249\) 10.7359 0.680360
\(250\) 46.8036 2.96012
\(251\) −18.6666 −1.17822 −0.589112 0.808051i \(-0.700522\pi\)
−0.589112 + 0.808051i \(0.700522\pi\)
\(252\) 4.74216 0.298728
\(253\) −23.1398 −1.45479
\(254\) 8.13723 0.510575
\(255\) −17.2698 −1.08148
\(256\) 20.8896 1.30560
\(257\) 25.3211 1.57948 0.789742 0.613439i \(-0.210214\pi\)
0.789742 + 0.613439i \(0.210214\pi\)
\(258\) −20.2499 −1.26070
\(259\) 24.7825 1.53991
\(260\) −5.92451 −0.367422
\(261\) −5.15412 −0.319032
\(262\) 23.3964 1.44543
\(263\) −9.86212 −0.608124 −0.304062 0.952652i \(-0.598343\pi\)
−0.304062 + 0.952652i \(0.598343\pi\)
\(264\) −2.96395 −0.182418
\(265\) −2.88246 −0.177068
\(266\) −37.7012 −2.31161
\(267\) 3.76088 0.230162
\(268\) −2.86477 −0.174994
\(269\) 23.6713 1.44326 0.721631 0.692278i \(-0.243393\pi\)
0.721631 + 0.692278i \(0.243393\pi\)
\(270\) −7.50616 −0.456810
\(271\) −9.87442 −0.599828 −0.299914 0.953966i \(-0.596958\pi\)
−0.299914 + 0.953966i \(0.596958\pi\)
\(272\) −20.4820 −1.24191
\(273\) 3.22519 0.195197
\(274\) −24.6838 −1.49120
\(275\) −33.7508 −2.03525
\(276\) −11.3262 −0.681757
\(277\) 16.4259 0.986934 0.493467 0.869764i \(-0.335729\pi\)
0.493467 + 0.869764i \(0.335729\pi\)
\(278\) 24.0751 1.44393
\(279\) 6.62744 0.396775
\(280\) −12.8221 −0.766269
\(281\) −22.0337 −1.31442 −0.657211 0.753706i \(-0.728264\pi\)
−0.657211 + 0.753706i \(0.728264\pi\)
\(282\) −9.56962 −0.569862
\(283\) 5.97027 0.354896 0.177448 0.984130i \(-0.443216\pi\)
0.177448 + 0.984130i \(0.443216\pi\)
\(284\) 12.3854 0.734936
\(285\) 25.2839 1.49769
\(286\) 5.59607 0.330903
\(287\) 4.41529 0.260626
\(288\) −6.92896 −0.408293
\(289\) 1.37022 0.0806014
\(290\) −38.6876 −2.27181
\(291\) 8.35697 0.489894
\(292\) −17.9285 −1.04919
\(293\) −14.3699 −0.839500 −0.419750 0.907640i \(-0.637882\pi\)
−0.419750 + 0.907640i \(0.637882\pi\)
\(294\) −6.33724 −0.369595
\(295\) 18.8382 1.09680
\(296\) −7.58166 −0.440675
\(297\) 3.00398 0.174308
\(298\) 2.12731 0.123232
\(299\) −7.70305 −0.445479
\(300\) −16.5199 −0.953778
\(301\) 35.0583 2.02073
\(302\) −19.2831 −1.10962
\(303\) 8.27275 0.475257
\(304\) 29.9867 1.71986
\(305\) 4.80480 0.275122
\(306\) 7.98443 0.456440
\(307\) −13.9995 −0.798994 −0.399497 0.916734i \(-0.630815\pi\)
−0.399497 + 0.916734i \(0.630815\pi\)
\(308\) −14.2453 −0.811704
\(309\) −1.00000 −0.0568880
\(310\) 49.7466 2.82542
\(311\) 11.4607 0.649879 0.324939 0.945735i \(-0.394656\pi\)
0.324939 + 0.945735i \(0.394656\pi\)
\(312\) −0.986675 −0.0558595
\(313\) −23.7411 −1.34193 −0.670964 0.741490i \(-0.734119\pi\)
−0.670964 + 0.741490i \(0.734119\pi\)
\(314\) −21.8376 −1.23237
\(315\) 12.9953 0.732201
\(316\) 6.98094 0.392709
\(317\) −23.4510 −1.31714 −0.658571 0.752519i \(-0.728839\pi\)
−0.658571 + 0.752519i \(0.728839\pi\)
\(318\) 1.33266 0.0747318
\(319\) 15.4828 0.866873
\(320\) −13.4996 −0.754649
\(321\) −10.1157 −0.564601
\(322\) 46.2812 2.57915
\(323\) −26.8949 −1.49647
\(324\) 1.47035 0.0816862
\(325\) −11.2354 −0.623225
\(326\) 25.3424 1.40358
\(327\) 14.5820 0.806386
\(328\) −1.35076 −0.0745833
\(329\) 16.5677 0.913408
\(330\) 22.5483 1.24124
\(331\) −21.6288 −1.18883 −0.594413 0.804160i \(-0.702616\pi\)
−0.594413 + 0.804160i \(0.702616\pi\)
\(332\) −15.7856 −0.866345
\(333\) 7.68405 0.421083
\(334\) −14.5536 −0.796336
\(335\) −7.85054 −0.428921
\(336\) 15.4124 0.840817
\(337\) 15.6903 0.854704 0.427352 0.904085i \(-0.359446\pi\)
0.427352 + 0.904085i \(0.359446\pi\)
\(338\) 1.86289 0.101328
\(339\) 7.92776 0.430577
\(340\) 25.3927 1.37711
\(341\) −19.9087 −1.07812
\(342\) −11.6896 −0.632101
\(343\) −11.6048 −0.626598
\(344\) −10.7253 −0.578270
\(345\) −31.0380 −1.67103
\(346\) 21.7497 1.16927
\(347\) 4.44235 0.238478 0.119239 0.992866i \(-0.461955\pi\)
0.119239 + 0.992866i \(0.461955\pi\)
\(348\) 7.57836 0.406243
\(349\) −33.5600 −1.79642 −0.898212 0.439563i \(-0.855133\pi\)
−0.898212 + 0.439563i \(0.855133\pi\)
\(350\) 67.5039 3.60823
\(351\) 1.00000 0.0533761
\(352\) 20.8144 1.10941
\(353\) −26.8168 −1.42731 −0.713657 0.700496i \(-0.752962\pi\)
−0.713657 + 0.700496i \(0.752962\pi\)
\(354\) −8.70953 −0.462906
\(355\) 33.9405 1.80138
\(356\) −5.52981 −0.293079
\(357\) −13.8233 −0.731607
\(358\) −48.4844 −2.56248
\(359\) 10.5956 0.559215 0.279608 0.960114i \(-0.409796\pi\)
0.279608 + 0.960114i \(0.409796\pi\)
\(360\) −3.97562 −0.209534
\(361\) 20.3755 1.07239
\(362\) −13.1732 −0.692367
\(363\) 1.97612 0.103719
\(364\) −4.74216 −0.248557
\(365\) −49.1309 −2.57163
\(366\) −2.22142 −0.116116
\(367\) −23.0186 −1.20156 −0.600781 0.799413i \(-0.705144\pi\)
−0.600781 + 0.799413i \(0.705144\pi\)
\(368\) −36.8111 −1.91891
\(369\) 1.36900 0.0712674
\(370\) 57.6777 2.99852
\(371\) −2.30721 −0.119784
\(372\) −9.74467 −0.505238
\(373\) −16.6741 −0.863352 −0.431676 0.902029i \(-0.642078\pi\)
−0.431676 + 0.902029i \(0.642078\pi\)
\(374\) −23.9851 −1.24024
\(375\) −25.1242 −1.29741
\(376\) −5.06853 −0.261389
\(377\) 5.15412 0.265450
\(378\) −6.00816 −0.309027
\(379\) 16.4198 0.843427 0.421713 0.906729i \(-0.361429\pi\)
0.421713 + 0.906729i \(0.361429\pi\)
\(380\) −37.1762 −1.90710
\(381\) −4.36807 −0.223783
\(382\) 18.8526 0.964582
\(383\) 12.9842 0.663464 0.331732 0.943374i \(-0.392367\pi\)
0.331732 + 0.943374i \(0.392367\pi\)
\(384\) −7.61661 −0.388684
\(385\) −39.0375 −1.98954
\(386\) −33.0470 −1.68205
\(387\) 10.8702 0.552561
\(388\) −12.2877 −0.623812
\(389\) 29.9070 1.51634 0.758172 0.652054i \(-0.226093\pi\)
0.758172 + 0.652054i \(0.226093\pi\)
\(390\) 7.50616 0.380089
\(391\) 33.0157 1.66967
\(392\) −3.35651 −0.169529
\(393\) −12.5592 −0.633527
\(394\) −24.2757 −1.22299
\(395\) 19.1304 0.962554
\(396\) −4.41690 −0.221958
\(397\) 3.42665 0.171979 0.0859894 0.996296i \(-0.472595\pi\)
0.0859894 + 0.996296i \(0.472595\pi\)
\(398\) 38.7883 1.94428
\(399\) 20.2380 1.01317
\(400\) −53.6912 −2.68456
\(401\) −31.5411 −1.57509 −0.787543 0.616260i \(-0.788647\pi\)
−0.787543 + 0.616260i \(0.788647\pi\)
\(402\) 3.62957 0.181026
\(403\) −6.62744 −0.330136
\(404\) −12.1639 −0.605175
\(405\) 4.02931 0.200218
\(406\) −30.9668 −1.53685
\(407\) −23.0827 −1.14417
\(408\) 4.22894 0.209364
\(409\) 31.5101 1.55808 0.779038 0.626977i \(-0.215708\pi\)
0.779038 + 0.626977i \(0.215708\pi\)
\(410\) 10.2759 0.507493
\(411\) 13.2503 0.653588
\(412\) 1.47035 0.0724390
\(413\) 15.0787 0.741973
\(414\) 14.3499 0.705260
\(415\) −43.2583 −2.12347
\(416\) 6.92896 0.339720
\(417\) −12.9235 −0.632868
\(418\) 35.1153 1.71755
\(419\) 20.3897 0.996104 0.498052 0.867147i \(-0.334049\pi\)
0.498052 + 0.867147i \(0.334049\pi\)
\(420\) −19.1076 −0.932358
\(421\) −21.3544 −1.04075 −0.520376 0.853937i \(-0.674208\pi\)
−0.520376 + 0.853937i \(0.674208\pi\)
\(422\) −9.71199 −0.472772
\(423\) 5.13698 0.249768
\(424\) 0.705840 0.0342786
\(425\) 48.1553 2.33588
\(426\) −15.6919 −0.760273
\(427\) 3.84591 0.186117
\(428\) 14.8736 0.718941
\(429\) −3.00398 −0.145033
\(430\) 81.5931 3.93477
\(431\) 3.08838 0.148762 0.0743810 0.997230i \(-0.476302\pi\)
0.0743810 + 0.997230i \(0.476302\pi\)
\(432\) 4.77877 0.229919
\(433\) −19.0477 −0.915375 −0.457688 0.889113i \(-0.651322\pi\)
−0.457688 + 0.889113i \(0.651322\pi\)
\(434\) 39.8188 1.91136
\(435\) 20.7675 0.995727
\(436\) −21.4407 −1.02682
\(437\) −48.3366 −2.31225
\(438\) 22.7149 1.08536
\(439\) 32.9555 1.57288 0.786441 0.617665i \(-0.211921\pi\)
0.786441 + 0.617665i \(0.211921\pi\)
\(440\) 11.9427 0.569345
\(441\) 3.40183 0.161992
\(442\) −7.98443 −0.379781
\(443\) 17.7006 0.840980 0.420490 0.907297i \(-0.361858\pi\)
0.420490 + 0.907297i \(0.361858\pi\)
\(444\) −11.2983 −0.536192
\(445\) −15.1537 −0.718356
\(446\) 1.70065 0.0805279
\(447\) −1.14194 −0.0540119
\(448\) −10.8055 −0.510511
\(449\) 10.8535 0.512210 0.256105 0.966649i \(-0.417561\pi\)
0.256105 + 0.966649i \(0.417561\pi\)
\(450\) 20.9302 0.986660
\(451\) −4.11245 −0.193648
\(452\) −11.6566 −0.548280
\(453\) 10.3512 0.486340
\(454\) −30.5543 −1.43398
\(455\) −12.9953 −0.609228
\(456\) −6.19137 −0.289938
\(457\) 10.0687 0.470994 0.235497 0.971875i \(-0.424328\pi\)
0.235497 + 0.971875i \(0.424328\pi\)
\(458\) 48.3317 2.25839
\(459\) −4.28605 −0.200056
\(460\) 45.6368 2.12783
\(461\) −12.4728 −0.580916 −0.290458 0.956888i \(-0.593808\pi\)
−0.290458 + 0.956888i \(0.593808\pi\)
\(462\) 18.0484 0.839687
\(463\) 41.9870 1.95130 0.975650 0.219335i \(-0.0703887\pi\)
0.975650 + 0.219335i \(0.0703887\pi\)
\(464\) 24.6303 1.14343
\(465\) −26.7040 −1.23837
\(466\) −19.9512 −0.924220
\(467\) −18.8748 −0.873421 −0.436711 0.899602i \(-0.643857\pi\)
−0.436711 + 0.899602i \(0.643857\pi\)
\(468\) −1.47035 −0.0679670
\(469\) −6.28381 −0.290160
\(470\) 38.5590 1.77859
\(471\) 11.7224 0.540141
\(472\) −4.61298 −0.212330
\(473\) −32.6537 −1.50142
\(474\) −8.84462 −0.406247
\(475\) −70.5017 −3.23484
\(476\) 20.3251 0.931601
\(477\) −0.715373 −0.0327547
\(478\) −5.87599 −0.268762
\(479\) −11.5599 −0.528187 −0.264094 0.964497i \(-0.585073\pi\)
−0.264094 + 0.964497i \(0.585073\pi\)
\(480\) 27.9189 1.27432
\(481\) −7.68405 −0.350363
\(482\) −1.09448 −0.0498523
\(483\) −24.8438 −1.13043
\(484\) −2.90559 −0.132072
\(485\) −33.6728 −1.52900
\(486\) −1.86289 −0.0845023
\(487\) 6.09228 0.276068 0.138034 0.990428i \(-0.455922\pi\)
0.138034 + 0.990428i \(0.455922\pi\)
\(488\) −1.17657 −0.0532609
\(489\) −13.6038 −0.615185
\(490\) 25.5347 1.15354
\(491\) 12.5778 0.567627 0.283813 0.958880i \(-0.408400\pi\)
0.283813 + 0.958880i \(0.408400\pi\)
\(492\) −2.01292 −0.0907492
\(493\) −22.0908 −0.994919
\(494\) 11.6896 0.525940
\(495\) −12.1040 −0.544033
\(496\) −31.6710 −1.42207
\(497\) 27.1670 1.21861
\(498\) 19.9998 0.896212
\(499\) −31.4576 −1.40823 −0.704117 0.710084i \(-0.748657\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(500\) 36.9414 1.65207
\(501\) 7.81237 0.349031
\(502\) −34.7737 −1.55203
\(503\) −35.1741 −1.56833 −0.784167 0.620549i \(-0.786910\pi\)
−0.784167 + 0.620549i \(0.786910\pi\)
\(504\) −3.18221 −0.141747
\(505\) −33.3335 −1.48332
\(506\) −43.1068 −1.91633
\(507\) −1.00000 −0.0444116
\(508\) 6.42260 0.284957
\(509\) 18.2079 0.807052 0.403526 0.914968i \(-0.367785\pi\)
0.403526 + 0.914968i \(0.367785\pi\)
\(510\) −32.1718 −1.42459
\(511\) −39.3259 −1.73967
\(512\) 23.6817 1.04659
\(513\) 6.27499 0.277048
\(514\) 47.1703 2.08059
\(515\) 4.02931 0.177553
\(516\) −15.9829 −0.703610
\(517\) −15.4314 −0.678671
\(518\) 46.1670 2.02846
\(519\) −11.6753 −0.512487
\(520\) 3.97562 0.174343
\(521\) −19.3930 −0.849622 −0.424811 0.905282i \(-0.639659\pi\)
−0.424811 + 0.905282i \(0.639659\pi\)
\(522\) −9.60154 −0.420248
\(523\) −31.5819 −1.38098 −0.690490 0.723342i \(-0.742605\pi\)
−0.690490 + 0.723342i \(0.742605\pi\)
\(524\) 18.4664 0.806709
\(525\) −36.2361 −1.58147
\(526\) −18.3720 −0.801058
\(527\) 28.4055 1.23737
\(528\) −14.3553 −0.624735
\(529\) 36.3370 1.57987
\(530\) −5.36970 −0.233245
\(531\) 4.67528 0.202890
\(532\) −29.7570 −1.29013
\(533\) −1.36900 −0.0592981
\(534\) 7.00609 0.303183
\(535\) 40.7591 1.76217
\(536\) 1.92239 0.0830348
\(537\) 26.0265 1.12312
\(538\) 44.0969 1.90115
\(539\) −10.2190 −0.440165
\(540\) −5.92451 −0.254950
\(541\) 33.8590 1.45571 0.727855 0.685731i \(-0.240517\pi\)
0.727855 + 0.685731i \(0.240517\pi\)
\(542\) −18.3949 −0.790130
\(543\) 7.07137 0.303462
\(544\) −29.6979 −1.27329
\(545\) −58.7554 −2.51680
\(546\) 6.00816 0.257126
\(547\) −45.2902 −1.93647 −0.968234 0.250047i \(-0.919554\pi\)
−0.968234 + 0.250047i \(0.919554\pi\)
\(548\) −19.4826 −0.832254
\(549\) 1.19246 0.0508930
\(550\) −62.8739 −2.68095
\(551\) 32.3420 1.37782
\(552\) 7.60041 0.323495
\(553\) 15.3126 0.651156
\(554\) 30.5995 1.30005
\(555\) −30.9614 −1.31424
\(556\) 19.0021 0.805870
\(557\) −17.7246 −0.751017 −0.375509 0.926819i \(-0.622532\pi\)
−0.375509 + 0.926819i \(0.622532\pi\)
\(558\) 12.3462 0.522656
\(559\) −10.8702 −0.459758
\(560\) −62.1015 −2.62427
\(561\) 12.8752 0.543591
\(562\) −41.0464 −1.73144
\(563\) 40.3638 1.70113 0.850566 0.525869i \(-0.176260\pi\)
0.850566 + 0.525869i \(0.176260\pi\)
\(564\) −7.55317 −0.318046
\(565\) −31.9434 −1.34387
\(566\) 11.1219 0.467490
\(567\) 3.22519 0.135445
\(568\) −8.31116 −0.348728
\(569\) 30.9042 1.29557 0.647785 0.761823i \(-0.275695\pi\)
0.647785 + 0.761823i \(0.275695\pi\)
\(570\) 47.1011 1.97285
\(571\) −36.1512 −1.51288 −0.756441 0.654062i \(-0.773064\pi\)
−0.756441 + 0.654062i \(0.773064\pi\)
\(572\) 4.41690 0.184680
\(573\) −10.1201 −0.422773
\(574\) 8.22519 0.343313
\(575\) 86.5465 3.60924
\(576\) −3.35034 −0.139598
\(577\) 36.4780 1.51860 0.759299 0.650741i \(-0.225542\pi\)
0.759299 + 0.650741i \(0.225542\pi\)
\(578\) 2.55258 0.106173
\(579\) 17.7397 0.737235
\(580\) −30.5356 −1.26792
\(581\) −34.6253 −1.43650
\(582\) 15.5681 0.645318
\(583\) 2.14896 0.0890009
\(584\) 12.0309 0.497842
\(585\) −4.02931 −0.166592
\(586\) −26.7696 −1.10584
\(587\) −19.8035 −0.817378 −0.408689 0.912674i \(-0.634014\pi\)
−0.408689 + 0.912674i \(0.634014\pi\)
\(588\) −5.00189 −0.206275
\(589\) −41.5871 −1.71357
\(590\) 35.0934 1.44477
\(591\) 13.0312 0.536032
\(592\) −36.7203 −1.50919
\(593\) 12.4830 0.512616 0.256308 0.966595i \(-0.417494\pi\)
0.256308 + 0.966595i \(0.417494\pi\)
\(594\) 5.59607 0.229610
\(595\) 55.6985 2.28341
\(596\) 1.67905 0.0687767
\(597\) −20.8216 −0.852172
\(598\) −14.3499 −0.586812
\(599\) −27.9247 −1.14097 −0.570487 0.821307i \(-0.693245\pi\)
−0.570487 + 0.821307i \(0.693245\pi\)
\(600\) 11.0856 0.452570
\(601\) 30.9818 1.26378 0.631888 0.775060i \(-0.282280\pi\)
0.631888 + 0.775060i \(0.282280\pi\)
\(602\) 65.3096 2.66182
\(603\) −1.94836 −0.0793432
\(604\) −15.2198 −0.619287
\(605\) −7.96241 −0.323718
\(606\) 15.4112 0.626038
\(607\) 19.9205 0.808550 0.404275 0.914638i \(-0.367524\pi\)
0.404275 + 0.914638i \(0.367524\pi\)
\(608\) 43.4792 1.76331
\(609\) 16.6230 0.673598
\(610\) 8.95080 0.362407
\(611\) −5.13698 −0.207820
\(612\) 6.30200 0.254743
\(613\) −4.77158 −0.192722 −0.0963611 0.995346i \(-0.530720\pi\)
−0.0963611 + 0.995346i \(0.530720\pi\)
\(614\) −26.0795 −1.05248
\(615\) −5.51614 −0.222432
\(616\) 9.55929 0.385155
\(617\) 11.7537 0.473185 0.236593 0.971609i \(-0.423969\pi\)
0.236593 + 0.971609i \(0.423969\pi\)
\(618\) −1.86289 −0.0749363
\(619\) 18.8643 0.758221 0.379110 0.925351i \(-0.376230\pi\)
0.379110 + 0.925351i \(0.376230\pi\)
\(620\) 39.2643 1.57689
\(621\) −7.70305 −0.309113
\(622\) 21.3501 0.856060
\(623\) −12.1295 −0.485959
\(624\) −4.77877 −0.191304
\(625\) 45.0564 1.80226
\(626\) −44.2271 −1.76767
\(627\) −18.8499 −0.752793
\(628\) −17.2361 −0.687796
\(629\) 32.9342 1.31317
\(630\) 24.2088 0.964500
\(631\) −44.0957 −1.75542 −0.877712 0.479188i \(-0.840931\pi\)
−0.877712 + 0.479188i \(0.840931\pi\)
\(632\) −4.68454 −0.186341
\(633\) 5.21341 0.207214
\(634\) −43.6867 −1.73502
\(635\) 17.6003 0.698448
\(636\) 1.05185 0.0417085
\(637\) −3.40183 −0.134786
\(638\) 28.8428 1.14190
\(639\) 8.42340 0.333225
\(640\) 30.6897 1.21312
\(641\) 35.5445 1.40392 0.701962 0.712214i \(-0.252307\pi\)
0.701962 + 0.712214i \(0.252307\pi\)
\(642\) −18.8443 −0.743726
\(643\) −3.11861 −0.122986 −0.0614931 0.998108i \(-0.519586\pi\)
−0.0614931 + 0.998108i \(0.519586\pi\)
\(644\) 36.5291 1.43945
\(645\) −43.7992 −1.72459
\(646\) −50.1022 −1.97125
\(647\) 30.4158 1.19577 0.597884 0.801583i \(-0.296008\pi\)
0.597884 + 0.801583i \(0.296008\pi\)
\(648\) −0.986675 −0.0387603
\(649\) −14.0444 −0.551293
\(650\) −20.9302 −0.820950
\(651\) −21.3747 −0.837742
\(652\) 20.0024 0.783354
\(653\) 12.5016 0.489225 0.244613 0.969621i \(-0.421339\pi\)
0.244613 + 0.969621i \(0.421339\pi\)
\(654\) 27.1646 1.06222
\(655\) 50.6049 1.97730
\(656\) −6.54215 −0.255428
\(657\) −12.1934 −0.475708
\(658\) 30.8638 1.20320
\(659\) 4.29862 0.167451 0.0837253 0.996489i \(-0.473318\pi\)
0.0837253 + 0.996489i \(0.473318\pi\)
\(660\) 17.7971 0.692751
\(661\) −46.2020 −1.79705 −0.898525 0.438923i \(-0.855360\pi\)
−0.898525 + 0.438923i \(0.855360\pi\)
\(662\) −40.2920 −1.56599
\(663\) 4.28605 0.166456
\(664\) 10.5929 0.411082
\(665\) −81.5453 −3.16219
\(666\) 14.3145 0.554677
\(667\) −39.7024 −1.53728
\(668\) −11.4869 −0.444443
\(669\) −0.912908 −0.0352951
\(670\) −14.6247 −0.565000
\(671\) −3.58213 −0.138286
\(672\) 22.3472 0.862062
\(673\) −17.5086 −0.674906 −0.337453 0.941342i \(-0.609565\pi\)
−0.337453 + 0.941342i \(0.609565\pi\)
\(674\) 29.2292 1.12587
\(675\) −11.2354 −0.432449
\(676\) 1.47035 0.0565520
\(677\) −29.3931 −1.12967 −0.564835 0.825204i \(-0.691060\pi\)
−0.564835 + 0.825204i \(0.691060\pi\)
\(678\) 14.7685 0.567182
\(679\) −26.9528 −1.03435
\(680\) −17.0397 −0.653443
\(681\) 16.4016 0.628510
\(682\) −37.0877 −1.42016
\(683\) 9.36032 0.358163 0.179081 0.983834i \(-0.442687\pi\)
0.179081 + 0.983834i \(0.442687\pi\)
\(684\) −9.22644 −0.352782
\(685\) −53.3895 −2.03991
\(686\) −21.6184 −0.825393
\(687\) −25.9445 −0.989845
\(688\) −51.9459 −1.98042
\(689\) 0.715373 0.0272535
\(690\) −57.8203 −2.20118
\(691\) −41.4899 −1.57835 −0.789176 0.614167i \(-0.789492\pi\)
−0.789176 + 0.614167i \(0.789492\pi\)
\(692\) 17.1667 0.652581
\(693\) −9.68839 −0.368032
\(694\) 8.27561 0.314138
\(695\) 52.0729 1.97524
\(696\) −5.08544 −0.192763
\(697\) 5.86761 0.222252
\(698\) −62.5185 −2.36636
\(699\) 10.7098 0.405082
\(700\) 53.2799 2.01379
\(701\) 12.3887 0.467914 0.233957 0.972247i \(-0.424833\pi\)
0.233957 + 0.972247i \(0.424833\pi\)
\(702\) 1.86289 0.0703102
\(703\) −48.2173 −1.81855
\(704\) 10.0644 0.379315
\(705\) −20.6985 −0.779550
\(706\) −49.9567 −1.88014
\(707\) −26.6812 −1.00345
\(708\) −6.87431 −0.258352
\(709\) 10.5147 0.394886 0.197443 0.980314i \(-0.436736\pi\)
0.197443 + 0.980314i \(0.436736\pi\)
\(710\) 63.2274 2.37288
\(711\) 4.74780 0.178057
\(712\) 3.71076 0.139067
\(713\) 51.0515 1.91189
\(714\) −25.7513 −0.963718
\(715\) 12.1040 0.452663
\(716\) −38.2680 −1.43014
\(717\) 3.15424 0.117797
\(718\) 19.7385 0.736632
\(719\) −8.30235 −0.309626 −0.154813 0.987944i \(-0.549477\pi\)
−0.154813 + 0.987944i \(0.549477\pi\)
\(720\) −19.2552 −0.717597
\(721\) 3.22519 0.120112
\(722\) 37.9572 1.41262
\(723\) 0.587519 0.0218501
\(724\) −10.3974 −0.386417
\(725\) −57.9083 −2.15066
\(726\) 3.68129 0.136626
\(727\) −22.7577 −0.844038 −0.422019 0.906587i \(-0.638678\pi\)
−0.422019 + 0.906587i \(0.638678\pi\)
\(728\) 3.18221 0.117941
\(729\) 1.00000 0.0370370
\(730\) −91.5253 −3.38750
\(731\) 46.5900 1.72319
\(732\) −1.75334 −0.0648052
\(733\) 1.45793 0.0538500 0.0269250 0.999637i \(-0.491428\pi\)
0.0269250 + 0.999637i \(0.491428\pi\)
\(734\) −42.8811 −1.58277
\(735\) −13.7071 −0.505592
\(736\) −53.3741 −1.96740
\(737\) 5.85282 0.215591
\(738\) 2.55030 0.0938778
\(739\) 4.24653 0.156211 0.0781055 0.996945i \(-0.475113\pi\)
0.0781055 + 0.996945i \(0.475113\pi\)
\(740\) 45.5242 1.67350
\(741\) −6.27499 −0.230517
\(742\) −4.29807 −0.157787
\(743\) 10.3154 0.378436 0.189218 0.981935i \(-0.439405\pi\)
0.189218 + 0.981935i \(0.439405\pi\)
\(744\) 6.53913 0.239736
\(745\) 4.60123 0.168576
\(746\) −31.0620 −1.13726
\(747\) −10.7359 −0.392806
\(748\) −18.9311 −0.692189
\(749\) 32.6249 1.19209
\(750\) −46.8036 −1.70902
\(751\) −21.3927 −0.780629 −0.390315 0.920681i \(-0.627634\pi\)
−0.390315 + 0.920681i \(0.627634\pi\)
\(752\) −24.5484 −0.895189
\(753\) 18.6666 0.680248
\(754\) 9.60154 0.349667
\(755\) −41.7081 −1.51791
\(756\) −4.74216 −0.172471
\(757\) 49.9373 1.81500 0.907502 0.420049i \(-0.137987\pi\)
0.907502 + 0.420049i \(0.137987\pi\)
\(758\) 30.5882 1.11101
\(759\) 23.1398 0.839921
\(760\) 24.9470 0.904922
\(761\) 47.7800 1.73202 0.866011 0.500024i \(-0.166676\pi\)
0.866011 + 0.500024i \(0.166676\pi\)
\(762\) −8.13723 −0.294781
\(763\) −47.0296 −1.70259
\(764\) 14.8801 0.538343
\(765\) 17.2698 0.624392
\(766\) 24.1882 0.873955
\(767\) −4.67528 −0.168815
\(768\) −20.8896 −0.753788
\(769\) 12.1833 0.439342 0.219671 0.975574i \(-0.429502\pi\)
0.219671 + 0.975574i \(0.429502\pi\)
\(770\) −72.7226 −2.62074
\(771\) −25.3211 −0.911915
\(772\) −26.0836 −0.938768
\(773\) 25.6557 0.922770 0.461385 0.887200i \(-0.347353\pi\)
0.461385 + 0.887200i \(0.347353\pi\)
\(774\) 20.2499 0.727867
\(775\) 74.4617 2.67474
\(776\) 8.24561 0.296000
\(777\) −24.7825 −0.889067
\(778\) 55.7134 1.99742
\(779\) −8.59047 −0.307786
\(780\) 5.92451 0.212131
\(781\) −25.3037 −0.905438
\(782\) 61.5045 2.19940
\(783\) 5.15412 0.184193
\(784\) −16.2566 −0.580592
\(785\) −47.2334 −1.68583
\(786\) −23.3964 −0.834520
\(787\) −46.9197 −1.67251 −0.836253 0.548344i \(-0.815259\pi\)
−0.836253 + 0.548344i \(0.815259\pi\)
\(788\) −19.1604 −0.682563
\(789\) 9.86212 0.351101
\(790\) 35.6378 1.26793
\(791\) −25.5685 −0.909111
\(792\) 2.96395 0.105319
\(793\) −1.19246 −0.0423455
\(794\) 6.38347 0.226541
\(795\) 2.88246 0.102230
\(796\) 30.6151 1.08512
\(797\) 10.5564 0.373927 0.186963 0.982367i \(-0.440135\pi\)
0.186963 + 0.982367i \(0.440135\pi\)
\(798\) 37.7012 1.33461
\(799\) 22.0173 0.778918
\(800\) −77.8494 −2.75239
\(801\) −3.76088 −0.132884
\(802\) −58.7575 −2.07480
\(803\) 36.6286 1.29259
\(804\) 2.86477 0.101033
\(805\) 100.103 3.52818
\(806\) −12.3462 −0.434876
\(807\) −23.6713 −0.833268
\(808\) 8.16252 0.287156
\(809\) −3.61205 −0.126993 −0.0634964 0.997982i \(-0.520225\pi\)
−0.0634964 + 0.997982i \(0.520225\pi\)
\(810\) 7.50616 0.263739
\(811\) −20.6541 −0.725264 −0.362632 0.931932i \(-0.618122\pi\)
−0.362632 + 0.931932i \(0.618122\pi\)
\(812\) −24.4416 −0.857734
\(813\) 9.87442 0.346311
\(814\) −43.0005 −1.50717
\(815\) 54.8140 1.92005
\(816\) 20.4820 0.717015
\(817\) −68.2101 −2.38637
\(818\) 58.6998 2.05239
\(819\) −3.22519 −0.112697
\(820\) 8.11066 0.283237
\(821\) 20.3161 0.709036 0.354518 0.935049i \(-0.384645\pi\)
0.354518 + 0.935049i \(0.384645\pi\)
\(822\) 24.6838 0.860945
\(823\) −11.3908 −0.397057 −0.198529 0.980095i \(-0.563616\pi\)
−0.198529 + 0.980095i \(0.563616\pi\)
\(824\) −0.986675 −0.0343725
\(825\) 33.7508 1.17505
\(826\) 28.0899 0.977371
\(827\) −1.33613 −0.0464616 −0.0232308 0.999730i \(-0.507395\pi\)
−0.0232308 + 0.999730i \(0.507395\pi\)
\(828\) 11.3262 0.393612
\(829\) −34.1245 −1.18519 −0.592596 0.805500i \(-0.701897\pi\)
−0.592596 + 0.805500i \(0.701897\pi\)
\(830\) −80.5854 −2.79716
\(831\) −16.4259 −0.569807
\(832\) 3.35034 0.116152
\(833\) 14.5804 0.505182
\(834\) −24.0751 −0.833652
\(835\) −31.4785 −1.08936
\(836\) 27.7160 0.958579
\(837\) −6.62744 −0.229078
\(838\) 37.9838 1.31213
\(839\) −40.3995 −1.39474 −0.697372 0.716709i \(-0.745648\pi\)
−0.697372 + 0.716709i \(0.745648\pi\)
\(840\) 12.8221 0.442405
\(841\) −2.43509 −0.0839687
\(842\) −39.7809 −1.37094
\(843\) 22.0337 0.758882
\(844\) −7.66554 −0.263859
\(845\) 4.02931 0.138613
\(846\) 9.56962 0.329010
\(847\) −6.37336 −0.218991
\(848\) 3.41860 0.117395
\(849\) −5.97027 −0.204899
\(850\) 89.7079 3.07696
\(851\) 59.1906 2.02903
\(852\) −12.3854 −0.424316
\(853\) −34.2554 −1.17288 −0.586441 0.809992i \(-0.699471\pi\)
−0.586441 + 0.809992i \(0.699471\pi\)
\(854\) 7.16450 0.245164
\(855\) −25.2839 −0.864691
\(856\) −9.98086 −0.341139
\(857\) −24.1172 −0.823830 −0.411915 0.911222i \(-0.635140\pi\)
−0.411915 + 0.911222i \(0.635140\pi\)
\(858\) −5.59607 −0.191047
\(859\) −15.4801 −0.528174 −0.264087 0.964499i \(-0.585071\pi\)
−0.264087 + 0.964499i \(0.585071\pi\)
\(860\) 64.4003 2.19603
\(861\) −4.41529 −0.150473
\(862\) 5.75330 0.195958
\(863\) 12.6939 0.432105 0.216053 0.976382i \(-0.430682\pi\)
0.216053 + 0.976382i \(0.430682\pi\)
\(864\) 6.92896 0.235728
\(865\) 47.0432 1.59952
\(866\) −35.4838 −1.20579
\(867\) −1.37022 −0.0465353
\(868\) 31.4284 1.06675
\(869\) −14.2623 −0.483815
\(870\) 38.6876 1.31163
\(871\) 1.94836 0.0660175
\(872\) 14.3877 0.487228
\(873\) −8.35697 −0.282840
\(874\) −90.0456 −3.04584
\(875\) 81.0302 2.73932
\(876\) 17.9285 0.605749
\(877\) 14.1833 0.478936 0.239468 0.970904i \(-0.423027\pi\)
0.239468 + 0.970904i \(0.423027\pi\)
\(878\) 61.3925 2.07190
\(879\) 14.3699 0.484686
\(880\) 57.8420 1.94985
\(881\) 17.5865 0.592503 0.296251 0.955110i \(-0.404263\pi\)
0.296251 + 0.955110i \(0.404263\pi\)
\(882\) 6.33724 0.213386
\(883\) −12.3300 −0.414939 −0.207470 0.978241i \(-0.566523\pi\)
−0.207470 + 0.978241i \(0.566523\pi\)
\(884\) −6.30200 −0.211959
\(885\) −18.8382 −0.633238
\(886\) 32.9742 1.10779
\(887\) 47.5421 1.59631 0.798154 0.602454i \(-0.205810\pi\)
0.798154 + 0.602454i \(0.205810\pi\)
\(888\) 7.58166 0.254424
\(889\) 14.0879 0.472491
\(890\) −28.2297 −0.946262
\(891\) −3.00398 −0.100637
\(892\) 1.34230 0.0449434
\(893\) −32.2345 −1.07869
\(894\) −2.12731 −0.0711478
\(895\) −104.869 −3.50537
\(896\) 24.5650 0.820659
\(897\) 7.70305 0.257197
\(898\) 20.2189 0.674715
\(899\) −34.1586 −1.13925
\(900\) 16.5199 0.550664
\(901\) −3.06612 −0.102147
\(902\) −7.66104 −0.255085
\(903\) −35.0583 −1.16667
\(904\) 7.82212 0.260160
\(905\) −28.4928 −0.947132
\(906\) 19.2831 0.640637
\(907\) −35.1217 −1.16620 −0.583098 0.812402i \(-0.698160\pi\)
−0.583098 + 0.812402i \(0.698160\pi\)
\(908\) −24.1161 −0.800320
\(909\) −8.27275 −0.274390
\(910\) −24.2088 −0.802513
\(911\) 18.7016 0.619611 0.309806 0.950800i \(-0.399736\pi\)
0.309806 + 0.950800i \(0.399736\pi\)
\(912\) −29.9867 −0.992960
\(913\) 32.2504 1.06733
\(914\) 18.7569 0.620422
\(915\) −4.80480 −0.158842
\(916\) 38.1476 1.26043
\(917\) 40.5057 1.33762
\(918\) −7.98443 −0.263526
\(919\) −2.01636 −0.0665136 −0.0332568 0.999447i \(-0.510588\pi\)
−0.0332568 + 0.999447i \(0.510588\pi\)
\(920\) −30.6244 −1.00966
\(921\) 13.9995 0.461300
\(922\) −23.2354 −0.765218
\(923\) −8.42340 −0.277260
\(924\) 14.2453 0.468637
\(925\) 86.3330 2.83861
\(926\) 78.2170 2.57037
\(927\) 1.00000 0.0328443
\(928\) 35.7127 1.17233
\(929\) −33.0752 −1.08516 −0.542580 0.840004i \(-0.682553\pi\)
−0.542580 + 0.840004i \(0.682553\pi\)
\(930\) −49.7466 −1.63126
\(931\) −21.3465 −0.699602
\(932\) −15.7472 −0.515816
\(933\) −11.4607 −0.375208
\(934\) −35.1616 −1.15052
\(935\) −51.8782 −1.69660
\(936\) 0.986675 0.0322505
\(937\) −18.5285 −0.605301 −0.302651 0.953102i \(-0.597872\pi\)
−0.302651 + 0.953102i \(0.597872\pi\)
\(938\) −11.7060 −0.382216
\(939\) 23.7411 0.774762
\(940\) 30.4341 0.992650
\(941\) −56.5431 −1.84325 −0.921627 0.388077i \(-0.873139\pi\)
−0.921627 + 0.388077i \(0.873139\pi\)
\(942\) 21.8376 0.711507
\(943\) 10.5455 0.343409
\(944\) −22.3421 −0.727173
\(945\) −12.9953 −0.422737
\(946\) −60.8302 −1.97776
\(947\) −34.6953 −1.12744 −0.563722 0.825964i \(-0.690631\pi\)
−0.563722 + 0.825964i \(0.690631\pi\)
\(948\) −6.98094 −0.226730
\(949\) 12.1934 0.395813
\(950\) −131.337 −4.26113
\(951\) 23.4510 0.760452
\(952\) −13.6391 −0.442046
\(953\) −16.7212 −0.541653 −0.270826 0.962628i \(-0.587297\pi\)
−0.270826 + 0.962628i \(0.587297\pi\)
\(954\) −1.33266 −0.0431464
\(955\) 40.7770 1.31951
\(956\) −4.63784 −0.149998
\(957\) −15.4828 −0.500489
\(958\) −21.5349 −0.695761
\(959\) −42.7346 −1.37997
\(960\) 13.4996 0.435697
\(961\) 12.9230 0.416871
\(962\) −14.3145 −0.461519
\(963\) 10.1157 0.325972
\(964\) −0.863859 −0.0278230
\(965\) −71.4787 −2.30098
\(966\) −46.2812 −1.48907
\(967\) 50.9499 1.63844 0.819220 0.573480i \(-0.194407\pi\)
0.819220 + 0.573480i \(0.194407\pi\)
\(968\) 1.94979 0.0626686
\(969\) 26.8949 0.863989
\(970\) −62.7287 −2.01410
\(971\) 5.49879 0.176465 0.0882323 0.996100i \(-0.471878\pi\)
0.0882323 + 0.996100i \(0.471878\pi\)
\(972\) −1.47035 −0.0471616
\(973\) 41.6808 1.33623
\(974\) 11.3492 0.363653
\(975\) 11.2354 0.359819
\(976\) −5.69849 −0.182404
\(977\) −38.9037 −1.24464 −0.622320 0.782763i \(-0.713810\pi\)
−0.622320 + 0.782763i \(0.713810\pi\)
\(978\) −25.3424 −0.810360
\(979\) 11.2976 0.361072
\(980\) 20.1542 0.643802
\(981\) −14.5820 −0.465567
\(982\) 23.4310 0.747712
\(983\) −9.84743 −0.314084 −0.157042 0.987592i \(-0.550196\pi\)
−0.157042 + 0.987592i \(0.550196\pi\)
\(984\) 1.35076 0.0430607
\(985\) −52.5068 −1.67300
\(986\) −41.1527 −1.31057
\(987\) −16.5677 −0.527356
\(988\) 9.22644 0.293532
\(989\) 83.7333 2.66256
\(990\) −22.5483 −0.716633
\(991\) −5.08594 −0.161560 −0.0807801 0.996732i \(-0.525741\pi\)
−0.0807801 + 0.996732i \(0.525741\pi\)
\(992\) −45.9213 −1.45800
\(993\) 21.6288 0.686369
\(994\) 50.6092 1.60523
\(995\) 83.8968 2.65971
\(996\) 15.7856 0.500185
\(997\) −31.2027 −0.988199 −0.494099 0.869405i \(-0.664502\pi\)
−0.494099 + 0.869405i \(0.664502\pi\)
\(998\) −58.6020 −1.85501
\(999\) −7.68405 −0.243113
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 4017.2.a.g.1.20 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.g.1.20 24 1.1 even 1 trivial