Properties

Label 4006.2.a.i.1.17
Level $4006$
Weight $2$
Character 4006.1
Self dual yes
Analytic conductor $31.988$
Analytic rank $0$
Dimension $46$
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] = [4006,2,Mod(1,4006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4006, 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("4006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4006.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: \(31.9880710497\)
Analytic rank: \(0\)
Dimension: \(46\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 4006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.354737 q^{3} +1.00000 q^{4} +2.50160 q^{5} -0.354737 q^{6} +4.23908 q^{7} +1.00000 q^{8} -2.87416 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.354737 q^{3} +1.00000 q^{4} +2.50160 q^{5} -0.354737 q^{6} +4.23908 q^{7} +1.00000 q^{8} -2.87416 q^{9} +2.50160 q^{10} +5.05191 q^{11} -0.354737 q^{12} +1.44576 q^{13} +4.23908 q^{14} -0.887411 q^{15} +1.00000 q^{16} +2.70292 q^{17} -2.87416 q^{18} +0.309796 q^{19} +2.50160 q^{20} -1.50376 q^{21} +5.05191 q^{22} -6.04785 q^{23} -0.354737 q^{24} +1.25801 q^{25} +1.44576 q^{26} +2.08378 q^{27} +4.23908 q^{28} +7.09884 q^{29} -0.887411 q^{30} +7.08818 q^{31} +1.00000 q^{32} -1.79210 q^{33} +2.70292 q^{34} +10.6045 q^{35} -2.87416 q^{36} -10.0196 q^{37} +0.309796 q^{38} -0.512863 q^{39} +2.50160 q^{40} -3.19650 q^{41} -1.50376 q^{42} -6.59282 q^{43} +5.05191 q^{44} -7.19001 q^{45} -6.04785 q^{46} -6.47974 q^{47} -0.354737 q^{48} +10.9698 q^{49} +1.25801 q^{50} -0.958825 q^{51} +1.44576 q^{52} +7.51170 q^{53} +2.08378 q^{54} +12.6379 q^{55} +4.23908 q^{56} -0.109896 q^{57} +7.09884 q^{58} -9.36687 q^{59} -0.887411 q^{60} -6.79492 q^{61} +7.08818 q^{62} -12.1838 q^{63} +1.00000 q^{64} +3.61671 q^{65} -1.79210 q^{66} +3.57920 q^{67} +2.70292 q^{68} +2.14539 q^{69} +10.6045 q^{70} -10.2708 q^{71} -2.87416 q^{72} -11.4207 q^{73} -10.0196 q^{74} -0.446264 q^{75} +0.309796 q^{76} +21.4155 q^{77} -0.512863 q^{78} +15.8549 q^{79} +2.50160 q^{80} +7.88329 q^{81} -3.19650 q^{82} -11.9598 q^{83} -1.50376 q^{84} +6.76163 q^{85} -6.59282 q^{86} -2.51822 q^{87} +5.05191 q^{88} +8.41688 q^{89} -7.19001 q^{90} +6.12868 q^{91} -6.04785 q^{92} -2.51444 q^{93} -6.47974 q^{94} +0.774988 q^{95} -0.354737 q^{96} +13.0362 q^{97} +10.9698 q^{98} -14.5200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 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
\(3\) −0.354737 −0.204807 −0.102404 0.994743i \(-0.532653\pi\)
−0.102404 + 0.994743i \(0.532653\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.50160 1.11875 0.559375 0.828915i \(-0.311041\pi\)
0.559375 + 0.828915i \(0.311041\pi\)
\(6\) −0.354737 −0.144821
\(7\) 4.23908 1.60222 0.801110 0.598517i \(-0.204243\pi\)
0.801110 + 0.598517i \(0.204243\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.87416 −0.958054
\(10\) 2.50160 0.791076
\(11\) 5.05191 1.52321 0.761605 0.648042i \(-0.224412\pi\)
0.761605 + 0.648042i \(0.224412\pi\)
\(12\) −0.354737 −0.102404
\(13\) 1.44576 0.400981 0.200490 0.979696i \(-0.435746\pi\)
0.200490 + 0.979696i \(0.435746\pi\)
\(14\) 4.23908 1.13294
\(15\) −0.887411 −0.229128
\(16\) 1.00000 0.250000
\(17\) 2.70292 0.655554 0.327777 0.944755i \(-0.393700\pi\)
0.327777 + 0.944755i \(0.393700\pi\)
\(18\) −2.87416 −0.677446
\(19\) 0.309796 0.0710722 0.0355361 0.999368i \(-0.488686\pi\)
0.0355361 + 0.999368i \(0.488686\pi\)
\(20\) 2.50160 0.559375
\(21\) −1.50376 −0.328147
\(22\) 5.05191 1.07707
\(23\) −6.04785 −1.26106 −0.630532 0.776163i \(-0.717163\pi\)
−0.630532 + 0.776163i \(0.717163\pi\)
\(24\) −0.354737 −0.0724104
\(25\) 1.25801 0.251603
\(26\) 1.44576 0.283536
\(27\) 2.08378 0.401024
\(28\) 4.23908 0.801110
\(29\) 7.09884 1.31822 0.659110 0.752046i \(-0.270933\pi\)
0.659110 + 0.752046i \(0.270933\pi\)
\(30\) −0.887411 −0.162018
\(31\) 7.08818 1.27307 0.636537 0.771246i \(-0.280366\pi\)
0.636537 + 0.771246i \(0.280366\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.79210 −0.311965
\(34\) 2.70292 0.463547
\(35\) 10.6045 1.79249
\(36\) −2.87416 −0.479027
\(37\) −10.0196 −1.64721 −0.823605 0.567163i \(-0.808041\pi\)
−0.823605 + 0.567163i \(0.808041\pi\)
\(38\) 0.309796 0.0502556
\(39\) −0.512863 −0.0821239
\(40\) 2.50160 0.395538
\(41\) −3.19650 −0.499209 −0.249605 0.968348i \(-0.580301\pi\)
−0.249605 + 0.968348i \(0.580301\pi\)
\(42\) −1.50376 −0.232035
\(43\) −6.59282 −1.00540 −0.502698 0.864462i \(-0.667659\pi\)
−0.502698 + 0.864462i \(0.667659\pi\)
\(44\) 5.05191 0.761605
\(45\) −7.19001 −1.07182
\(46\) −6.04785 −0.891707
\(47\) −6.47974 −0.945167 −0.472583 0.881286i \(-0.656678\pi\)
−0.472583 + 0.881286i \(0.656678\pi\)
\(48\) −0.354737 −0.0512019
\(49\) 10.9698 1.56711
\(50\) 1.25801 0.177910
\(51\) −0.958825 −0.134262
\(52\) 1.44576 0.200490
\(53\) 7.51170 1.03181 0.515906 0.856645i \(-0.327455\pi\)
0.515906 + 0.856645i \(0.327455\pi\)
\(54\) 2.08378 0.283567
\(55\) 12.6379 1.70409
\(56\) 4.23908 0.566471
\(57\) −0.109896 −0.0145561
\(58\) 7.09884 0.932123
\(59\) −9.36687 −1.21946 −0.609731 0.792608i \(-0.708723\pi\)
−0.609731 + 0.792608i \(0.708723\pi\)
\(60\) −0.887411 −0.114564
\(61\) −6.79492 −0.870001 −0.435000 0.900430i \(-0.643252\pi\)
−0.435000 + 0.900430i \(0.643252\pi\)
\(62\) 7.08818 0.900200
\(63\) −12.1838 −1.53501
\(64\) 1.00000 0.125000
\(65\) 3.61671 0.448598
\(66\) −1.79210 −0.220592
\(67\) 3.57920 0.437268 0.218634 0.975807i \(-0.429840\pi\)
0.218634 + 0.975807i \(0.429840\pi\)
\(68\) 2.70292 0.327777
\(69\) 2.14539 0.258275
\(70\) 10.6045 1.26748
\(71\) −10.2708 −1.21891 −0.609457 0.792819i \(-0.708613\pi\)
−0.609457 + 0.792819i \(0.708613\pi\)
\(72\) −2.87416 −0.338723
\(73\) −11.4207 −1.33670 −0.668349 0.743848i \(-0.732999\pi\)
−0.668349 + 0.743848i \(0.732999\pi\)
\(74\) −10.0196 −1.16475
\(75\) −0.446264 −0.0515302
\(76\) 0.309796 0.0355361
\(77\) 21.4155 2.44052
\(78\) −0.512863 −0.0580704
\(79\) 15.8549 1.78382 0.891909 0.452215i \(-0.149366\pi\)
0.891909 + 0.452215i \(0.149366\pi\)
\(80\) 2.50160 0.279688
\(81\) 7.88329 0.875921
\(82\) −3.19650 −0.352994
\(83\) −11.9598 −1.31276 −0.656379 0.754431i \(-0.727913\pi\)
−0.656379 + 0.754431i \(0.727913\pi\)
\(84\) −1.50376 −0.164073
\(85\) 6.76163 0.733402
\(86\) −6.59282 −0.710922
\(87\) −2.51822 −0.269981
\(88\) 5.05191 0.538536
\(89\) 8.41688 0.892187 0.446094 0.894986i \(-0.352815\pi\)
0.446094 + 0.894986i \(0.352815\pi\)
\(90\) −7.19001 −0.757894
\(91\) 6.12868 0.642460
\(92\) −6.04785 −0.630532
\(93\) −2.51444 −0.260735
\(94\) −6.47974 −0.668334
\(95\) 0.774988 0.0795120
\(96\) −0.354737 −0.0362052
\(97\) 13.0362 1.32363 0.661814 0.749668i \(-0.269787\pi\)
0.661814 + 0.749668i \(0.269787\pi\)
\(98\) 10.9698 1.10812
\(99\) −14.5200 −1.45932
\(100\) 1.25801 0.125801
\(101\) 13.4570 1.33902 0.669509 0.742804i \(-0.266505\pi\)
0.669509 + 0.742804i \(0.266505\pi\)
\(102\) −0.958825 −0.0949379
\(103\) −19.4082 −1.91235 −0.956175 0.292795i \(-0.905415\pi\)
−0.956175 + 0.292795i \(0.905415\pi\)
\(104\) 1.44576 0.141768
\(105\) −3.76180 −0.367114
\(106\) 7.51170 0.729601
\(107\) −6.49107 −0.627516 −0.313758 0.949503i \(-0.601588\pi\)
−0.313758 + 0.949503i \(0.601588\pi\)
\(108\) 2.08378 0.200512
\(109\) 1.54816 0.148287 0.0741433 0.997248i \(-0.476378\pi\)
0.0741433 + 0.997248i \(0.476378\pi\)
\(110\) 12.6379 1.20497
\(111\) 3.55432 0.337361
\(112\) 4.23908 0.400555
\(113\) −16.0403 −1.50894 −0.754472 0.656332i \(-0.772107\pi\)
−0.754472 + 0.656332i \(0.772107\pi\)
\(114\) −0.109896 −0.0102927
\(115\) −15.1293 −1.41082
\(116\) 7.09884 0.659110
\(117\) −4.15534 −0.384161
\(118\) −9.36687 −0.862290
\(119\) 11.4579 1.05034
\(120\) −0.887411 −0.0810091
\(121\) 14.5218 1.32017
\(122\) −6.79492 −0.615184
\(123\) 1.13392 0.102242
\(124\) 7.08818 0.636537
\(125\) −9.36096 −0.837270
\(126\) −12.1838 −1.08542
\(127\) −15.5297 −1.37804 −0.689021 0.724741i \(-0.741959\pi\)
−0.689021 + 0.724741i \(0.741959\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.33872 0.205913
\(130\) 3.61671 0.317206
\(131\) 5.60410 0.489632 0.244816 0.969570i \(-0.421272\pi\)
0.244816 + 0.969570i \(0.421272\pi\)
\(132\) −1.79210 −0.155982
\(133\) 1.31325 0.113873
\(134\) 3.57920 0.309196
\(135\) 5.21279 0.448646
\(136\) 2.70292 0.231773
\(137\) −16.7378 −1.43000 −0.715001 0.699123i \(-0.753574\pi\)
−0.715001 + 0.699123i \(0.753574\pi\)
\(138\) 2.14539 0.182628
\(139\) 5.63400 0.477870 0.238935 0.971036i \(-0.423202\pi\)
0.238935 + 0.971036i \(0.423202\pi\)
\(140\) 10.6045 0.896243
\(141\) 2.29860 0.193577
\(142\) −10.2708 −0.861903
\(143\) 7.30384 0.610778
\(144\) −2.87416 −0.239513
\(145\) 17.7585 1.47476
\(146\) −11.4207 −0.945188
\(147\) −3.89139 −0.320956
\(148\) −10.0196 −0.823605
\(149\) −11.6511 −0.954494 −0.477247 0.878769i \(-0.658365\pi\)
−0.477247 + 0.878769i \(0.658365\pi\)
\(150\) −0.446264 −0.0364373
\(151\) −18.8620 −1.53497 −0.767485 0.641066i \(-0.778492\pi\)
−0.767485 + 0.641066i \(0.778492\pi\)
\(152\) 0.309796 0.0251278
\(153\) −7.76863 −0.628056
\(154\) 21.4155 1.72571
\(155\) 17.7318 1.42425
\(156\) −0.512863 −0.0410619
\(157\) 6.74126 0.538011 0.269006 0.963139i \(-0.413305\pi\)
0.269006 + 0.963139i \(0.413305\pi\)
\(158\) 15.8549 1.26135
\(159\) −2.66468 −0.211323
\(160\) 2.50160 0.197769
\(161\) −25.6373 −2.02050
\(162\) 7.88329 0.619370
\(163\) 16.2878 1.27576 0.637878 0.770137i \(-0.279812\pi\)
0.637878 + 0.770137i \(0.279812\pi\)
\(164\) −3.19650 −0.249605
\(165\) −4.48312 −0.349011
\(166\) −11.9598 −0.928260
\(167\) 12.3546 0.956025 0.478013 0.878353i \(-0.341357\pi\)
0.478013 + 0.878353i \(0.341357\pi\)
\(168\) −1.50376 −0.116017
\(169\) −10.9098 −0.839214
\(170\) 6.76163 0.518593
\(171\) −0.890405 −0.0680910
\(172\) −6.59282 −0.502698
\(173\) −5.34997 −0.406751 −0.203376 0.979101i \(-0.565191\pi\)
−0.203376 + 0.979101i \(0.565191\pi\)
\(174\) −2.51822 −0.190906
\(175\) 5.33282 0.403123
\(176\) 5.05191 0.380802
\(177\) 3.32277 0.249755
\(178\) 8.41688 0.630872
\(179\) 16.1423 1.20653 0.603265 0.797541i \(-0.293866\pi\)
0.603265 + 0.797541i \(0.293866\pi\)
\(180\) −7.19001 −0.535912
\(181\) −16.4804 −1.22498 −0.612490 0.790478i \(-0.709832\pi\)
−0.612490 + 0.790478i \(0.709832\pi\)
\(182\) 6.12868 0.454288
\(183\) 2.41041 0.178183
\(184\) −6.04785 −0.445853
\(185\) −25.0650 −1.84282
\(186\) −2.51444 −0.184368
\(187\) 13.6549 0.998546
\(188\) −6.47974 −0.472583
\(189\) 8.83331 0.642529
\(190\) 0.774988 0.0562235
\(191\) 25.8262 1.86872 0.934358 0.356337i \(-0.115974\pi\)
0.934358 + 0.356337i \(0.115974\pi\)
\(192\) −0.354737 −0.0256009
\(193\) 24.2074 1.74249 0.871245 0.490849i \(-0.163313\pi\)
0.871245 + 0.490849i \(0.163313\pi\)
\(194\) 13.0362 0.935947
\(195\) −1.28298 −0.0918761
\(196\) 10.9698 0.783556
\(197\) −7.28644 −0.519137 −0.259569 0.965725i \(-0.583580\pi\)
−0.259569 + 0.965725i \(0.583580\pi\)
\(198\) −14.5200 −1.03189
\(199\) 7.55110 0.535283 0.267642 0.963519i \(-0.413756\pi\)
0.267642 + 0.963519i \(0.413756\pi\)
\(200\) 1.25801 0.0889551
\(201\) −1.26967 −0.0895558
\(202\) 13.4570 0.946829
\(203\) 30.0925 2.11208
\(204\) −0.958825 −0.0671312
\(205\) −7.99637 −0.558491
\(206\) −19.4082 −1.35224
\(207\) 17.3825 1.20817
\(208\) 1.44576 0.100245
\(209\) 1.56506 0.108258
\(210\) −3.76180 −0.259589
\(211\) 16.1594 1.11246 0.556230 0.831029i \(-0.312248\pi\)
0.556230 + 0.831029i \(0.312248\pi\)
\(212\) 7.51170 0.515906
\(213\) 3.64342 0.249643
\(214\) −6.49107 −0.443721
\(215\) −16.4926 −1.12479
\(216\) 2.08378 0.141783
\(217\) 30.0473 2.03975
\(218\) 1.54816 0.104854
\(219\) 4.05136 0.273766
\(220\) 12.6379 0.852046
\(221\) 3.90777 0.262865
\(222\) 3.55432 0.238550
\(223\) −17.6469 −1.18172 −0.590861 0.806774i \(-0.701212\pi\)
−0.590861 + 0.806774i \(0.701212\pi\)
\(224\) 4.23908 0.283235
\(225\) −3.61574 −0.241049
\(226\) −16.0403 −1.06698
\(227\) −1.29779 −0.0861371 −0.0430686 0.999072i \(-0.513713\pi\)
−0.0430686 + 0.999072i \(0.513713\pi\)
\(228\) −0.109896 −0.00727806
\(229\) 23.9469 1.58245 0.791227 0.611523i \(-0.209443\pi\)
0.791227 + 0.611523i \(0.209443\pi\)
\(230\) −15.1293 −0.997597
\(231\) −7.59685 −0.499836
\(232\) 7.09884 0.466061
\(233\) 7.87004 0.515584 0.257792 0.966200i \(-0.417005\pi\)
0.257792 + 0.966200i \(0.417005\pi\)
\(234\) −4.15534 −0.271643
\(235\) −16.2097 −1.05741
\(236\) −9.36687 −0.609731
\(237\) −5.62432 −0.365339
\(238\) 11.4579 0.742705
\(239\) 19.2985 1.24831 0.624157 0.781299i \(-0.285443\pi\)
0.624157 + 0.781299i \(0.285443\pi\)
\(240\) −0.887411 −0.0572821
\(241\) 6.99523 0.450602 0.225301 0.974289i \(-0.427663\pi\)
0.225301 + 0.974289i \(0.427663\pi\)
\(242\) 14.5218 0.933498
\(243\) −9.04784 −0.580419
\(244\) −6.79492 −0.435000
\(245\) 27.4420 1.75321
\(246\) 1.13392 0.0722958
\(247\) 0.447890 0.0284986
\(248\) 7.08818 0.450100
\(249\) 4.24258 0.268863
\(250\) −9.36096 −0.592039
\(251\) 15.3312 0.967696 0.483848 0.875152i \(-0.339239\pi\)
0.483848 + 0.875152i \(0.339239\pi\)
\(252\) −12.1838 −0.767507
\(253\) −30.5532 −1.92086
\(254\) −15.5297 −0.974423
\(255\) −2.39860 −0.150206
\(256\) 1.00000 0.0625000
\(257\) −24.6485 −1.53753 −0.768766 0.639530i \(-0.779129\pi\)
−0.768766 + 0.639530i \(0.779129\pi\)
\(258\) 2.33872 0.145602
\(259\) −42.4738 −2.63919
\(260\) 3.61671 0.224299
\(261\) −20.4032 −1.26293
\(262\) 5.60410 0.346222
\(263\) 10.2955 0.634848 0.317424 0.948284i \(-0.397182\pi\)
0.317424 + 0.948284i \(0.397182\pi\)
\(264\) −1.79210 −0.110296
\(265\) 18.7913 1.15434
\(266\) 1.31325 0.0805206
\(267\) −2.98578 −0.182727
\(268\) 3.57920 0.218634
\(269\) 14.6922 0.895801 0.447901 0.894083i \(-0.352172\pi\)
0.447901 + 0.894083i \(0.352172\pi\)
\(270\) 5.21279 0.317241
\(271\) −6.98204 −0.424129 −0.212064 0.977256i \(-0.568019\pi\)
−0.212064 + 0.977256i \(0.568019\pi\)
\(272\) 2.70292 0.163889
\(273\) −2.17407 −0.131581
\(274\) −16.7378 −1.01116
\(275\) 6.35538 0.383244
\(276\) 2.14539 0.129138
\(277\) 16.0138 0.962177 0.481089 0.876672i \(-0.340242\pi\)
0.481089 + 0.876672i \(0.340242\pi\)
\(278\) 5.63400 0.337905
\(279\) −20.3726 −1.21967
\(280\) 10.6045 0.633739
\(281\) 17.5241 1.04540 0.522700 0.852517i \(-0.324925\pi\)
0.522700 + 0.852517i \(0.324925\pi\)
\(282\) 2.29860 0.136880
\(283\) −6.47177 −0.384707 −0.192353 0.981326i \(-0.561612\pi\)
−0.192353 + 0.981326i \(0.561612\pi\)
\(284\) −10.2708 −0.609457
\(285\) −0.274917 −0.0162847
\(286\) 7.30384 0.431885
\(287\) −13.5502 −0.799843
\(288\) −2.87416 −0.169362
\(289\) −9.69422 −0.570248
\(290\) 17.7585 1.04281
\(291\) −4.62443 −0.271089
\(292\) −11.4207 −0.668349
\(293\) −15.8101 −0.923636 −0.461818 0.886975i \(-0.652803\pi\)
−0.461818 + 0.886975i \(0.652803\pi\)
\(294\) −3.89139 −0.226950
\(295\) −23.4322 −1.36427
\(296\) −10.0196 −0.582377
\(297\) 10.5271 0.610843
\(298\) −11.6511 −0.674929
\(299\) −8.74372 −0.505662
\(300\) −0.446264 −0.0257651
\(301\) −27.9475 −1.61087
\(302\) −18.8620 −1.08539
\(303\) −4.77368 −0.274241
\(304\) 0.309796 0.0177680
\(305\) −16.9982 −0.973314
\(306\) −7.76863 −0.444103
\(307\) −11.6136 −0.662825 −0.331412 0.943486i \(-0.607525\pi\)
−0.331412 + 0.943486i \(0.607525\pi\)
\(308\) 21.4155 1.22026
\(309\) 6.88482 0.391664
\(310\) 17.7318 1.00710
\(311\) −18.7925 −1.06562 −0.532812 0.846234i \(-0.678865\pi\)
−0.532812 + 0.846234i \(0.678865\pi\)
\(312\) −0.512863 −0.0290352
\(313\) −3.58821 −0.202818 −0.101409 0.994845i \(-0.532335\pi\)
−0.101409 + 0.994845i \(0.532335\pi\)
\(314\) 6.74126 0.380431
\(315\) −30.4790 −1.71730
\(316\) 15.8549 0.891909
\(317\) 19.8340 1.11399 0.556993 0.830517i \(-0.311955\pi\)
0.556993 + 0.830517i \(0.311955\pi\)
\(318\) −2.66468 −0.149428
\(319\) 35.8627 2.00793
\(320\) 2.50160 0.139844
\(321\) 2.30262 0.128520
\(322\) −25.6373 −1.42871
\(323\) 0.837355 0.0465917
\(324\) 7.88329 0.437961
\(325\) 1.81878 0.100888
\(326\) 16.2878 0.902096
\(327\) −0.549189 −0.0303702
\(328\) −3.19650 −0.176497
\(329\) −27.4681 −1.51437
\(330\) −4.48312 −0.246788
\(331\) 14.8735 0.817519 0.408760 0.912642i \(-0.365961\pi\)
0.408760 + 0.912642i \(0.365961\pi\)
\(332\) −11.9598 −0.656379
\(333\) 28.7979 1.57812
\(334\) 12.3546 0.676012
\(335\) 8.95373 0.489194
\(336\) −1.50376 −0.0820367
\(337\) −12.2061 −0.664908 −0.332454 0.943120i \(-0.607877\pi\)
−0.332454 + 0.943120i \(0.607877\pi\)
\(338\) −10.9098 −0.593414
\(339\) 5.69008 0.309043
\(340\) 6.76163 0.366701
\(341\) 35.8089 1.93916
\(342\) −0.890405 −0.0481476
\(343\) 16.8282 0.908637
\(344\) −6.59282 −0.355461
\(345\) 5.36692 0.288946
\(346\) −5.34997 −0.287616
\(347\) 25.9128 1.39107 0.695535 0.718492i \(-0.255167\pi\)
0.695535 + 0.718492i \(0.255167\pi\)
\(348\) −2.51822 −0.134991
\(349\) −1.96325 −0.105090 −0.0525452 0.998619i \(-0.516733\pi\)
−0.0525452 + 0.998619i \(0.516733\pi\)
\(350\) 5.33282 0.285051
\(351\) 3.01264 0.160803
\(352\) 5.05191 0.269268
\(353\) 7.06061 0.375798 0.187899 0.982188i \(-0.439832\pi\)
0.187899 + 0.982188i \(0.439832\pi\)
\(354\) 3.32277 0.176603
\(355\) −25.6934 −1.36366
\(356\) 8.41688 0.446094
\(357\) −4.06454 −0.215118
\(358\) 16.1423 0.853146
\(359\) 8.10653 0.427847 0.213923 0.976850i \(-0.431376\pi\)
0.213923 + 0.976850i \(0.431376\pi\)
\(360\) −7.19001 −0.378947
\(361\) −18.9040 −0.994949
\(362\) −16.4804 −0.866192
\(363\) −5.15143 −0.270380
\(364\) 6.12868 0.321230
\(365\) −28.5702 −1.49543
\(366\) 2.41041 0.125994
\(367\) 30.2287 1.57792 0.788962 0.614441i \(-0.210619\pi\)
0.788962 + 0.614441i \(0.210619\pi\)
\(368\) −6.04785 −0.315266
\(369\) 9.18725 0.478269
\(370\) −25.0650 −1.30307
\(371\) 31.8427 1.65319
\(372\) −2.51444 −0.130368
\(373\) −3.53242 −0.182902 −0.0914508 0.995810i \(-0.529150\pi\)
−0.0914508 + 0.995810i \(0.529150\pi\)
\(374\) 13.6549 0.706079
\(375\) 3.32068 0.171479
\(376\) −6.47974 −0.334167
\(377\) 10.2632 0.528581
\(378\) 8.83331 0.454337
\(379\) 37.2454 1.91317 0.956584 0.291456i \(-0.0941398\pi\)
0.956584 + 0.291456i \(0.0941398\pi\)
\(380\) 0.774988 0.0397560
\(381\) 5.50898 0.282233
\(382\) 25.8262 1.32138
\(383\) −36.2812 −1.85388 −0.926940 0.375209i \(-0.877571\pi\)
−0.926940 + 0.375209i \(0.877571\pi\)
\(384\) −0.354737 −0.0181026
\(385\) 53.5729 2.73033
\(386\) 24.2074 1.23213
\(387\) 18.9488 0.963224
\(388\) 13.0362 0.661814
\(389\) −25.5490 −1.29539 −0.647693 0.761901i \(-0.724266\pi\)
−0.647693 + 0.761901i \(0.724266\pi\)
\(390\) −1.28298 −0.0649662
\(391\) −16.3468 −0.826696
\(392\) 10.9698 0.554058
\(393\) −1.98798 −0.100280
\(394\) −7.28644 −0.367086
\(395\) 39.6627 1.99565
\(396\) −14.5200 −0.729658
\(397\) 17.4966 0.878127 0.439064 0.898456i \(-0.355310\pi\)
0.439064 + 0.898456i \(0.355310\pi\)
\(398\) 7.55110 0.378502
\(399\) −0.465859 −0.0233221
\(400\) 1.25801 0.0629007
\(401\) −30.2755 −1.51189 −0.755943 0.654638i \(-0.772821\pi\)
−0.755943 + 0.654638i \(0.772821\pi\)
\(402\) −1.26967 −0.0633255
\(403\) 10.2478 0.510479
\(404\) 13.4570 0.669509
\(405\) 19.7209 0.979937
\(406\) 30.0925 1.49347
\(407\) −50.6181 −2.50905
\(408\) −0.958825 −0.0474689
\(409\) 29.7996 1.47350 0.736749 0.676167i \(-0.236360\pi\)
0.736749 + 0.676167i \(0.236360\pi\)
\(410\) −7.99637 −0.394912
\(411\) 5.93750 0.292875
\(412\) −19.4082 −0.956175
\(413\) −39.7069 −1.95385
\(414\) 17.3825 0.854303
\(415\) −29.9187 −1.46865
\(416\) 1.44576 0.0708841
\(417\) −1.99859 −0.0978713
\(418\) 1.56506 0.0765498
\(419\) −8.07295 −0.394389 −0.197195 0.980364i \(-0.563183\pi\)
−0.197195 + 0.980364i \(0.563183\pi\)
\(420\) −3.76180 −0.183557
\(421\) −23.5149 −1.14605 −0.573023 0.819539i \(-0.694230\pi\)
−0.573023 + 0.819539i \(0.694230\pi\)
\(422\) 16.1594 0.786627
\(423\) 18.6238 0.905521
\(424\) 7.51170 0.364800
\(425\) 3.40031 0.164939
\(426\) 3.64342 0.176524
\(427\) −28.8042 −1.39393
\(428\) −6.49107 −0.313758
\(429\) −2.59094 −0.125092
\(430\) −16.4926 −0.795345
\(431\) −12.5117 −0.602667 −0.301334 0.953519i \(-0.597432\pi\)
−0.301334 + 0.953519i \(0.597432\pi\)
\(432\) 2.08378 0.100256
\(433\) −12.9160 −0.620705 −0.310353 0.950621i \(-0.600447\pi\)
−0.310353 + 0.950621i \(0.600447\pi\)
\(434\) 30.0473 1.44232
\(435\) −6.29958 −0.302042
\(436\) 1.54816 0.0741433
\(437\) −1.87360 −0.0896265
\(438\) 4.05136 0.193581
\(439\) −7.03100 −0.335571 −0.167786 0.985824i \(-0.553662\pi\)
−0.167786 + 0.985824i \(0.553662\pi\)
\(440\) 12.6379 0.602487
\(441\) −31.5289 −1.50138
\(442\) 3.90777 0.185873
\(443\) 33.5400 1.59353 0.796767 0.604287i \(-0.206542\pi\)
0.796767 + 0.604287i \(0.206542\pi\)
\(444\) 3.55432 0.168680
\(445\) 21.0557 0.998135
\(446\) −17.6469 −0.835603
\(447\) 4.13307 0.195488
\(448\) 4.23908 0.200278
\(449\) −22.6121 −1.06713 −0.533566 0.845759i \(-0.679148\pi\)
−0.533566 + 0.845759i \(0.679148\pi\)
\(450\) −3.61574 −0.170448
\(451\) −16.1484 −0.760400
\(452\) −16.0403 −0.754472
\(453\) 6.69106 0.314373
\(454\) −1.29779 −0.0609081
\(455\) 15.3315 0.718752
\(456\) −0.109896 −0.00514636
\(457\) −13.0858 −0.612126 −0.306063 0.952011i \(-0.599012\pi\)
−0.306063 + 0.952011i \(0.599012\pi\)
\(458\) 23.9469 1.11896
\(459\) 5.63230 0.262893
\(460\) −15.1293 −0.705408
\(461\) −17.0440 −0.793817 −0.396909 0.917858i \(-0.629917\pi\)
−0.396909 + 0.917858i \(0.629917\pi\)
\(462\) −7.59685 −0.353437
\(463\) −16.6959 −0.775925 −0.387962 0.921675i \(-0.626821\pi\)
−0.387962 + 0.921675i \(0.626821\pi\)
\(464\) 7.09884 0.329555
\(465\) −6.29013 −0.291698
\(466\) 7.87004 0.364573
\(467\) −32.5843 −1.50782 −0.753912 0.656976i \(-0.771835\pi\)
−0.753912 + 0.656976i \(0.771835\pi\)
\(468\) −4.15534 −0.192081
\(469\) 15.1725 0.700601
\(470\) −16.2097 −0.747699
\(471\) −2.39137 −0.110189
\(472\) −9.36687 −0.431145
\(473\) −33.3064 −1.53143
\(474\) −5.62432 −0.258334
\(475\) 0.389729 0.0178820
\(476\) 11.4579 0.525171
\(477\) −21.5898 −0.988531
\(478\) 19.2985 0.882691
\(479\) 38.3198 1.75088 0.875439 0.483329i \(-0.160572\pi\)
0.875439 + 0.483329i \(0.160572\pi\)
\(480\) −0.887411 −0.0405046
\(481\) −14.4859 −0.660500
\(482\) 6.99523 0.318624
\(483\) 9.09450 0.413814
\(484\) 14.5218 0.660083
\(485\) 32.6115 1.48081
\(486\) −9.04784 −0.410418
\(487\) −14.7907 −0.670233 −0.335116 0.942177i \(-0.608776\pi\)
−0.335116 + 0.942177i \(0.608776\pi\)
\(488\) −6.79492 −0.307592
\(489\) −5.77787 −0.261284
\(490\) 27.4420 1.23970
\(491\) 16.2154 0.731793 0.365896 0.930656i \(-0.380762\pi\)
0.365896 + 0.930656i \(0.380762\pi\)
\(492\) 1.13392 0.0511209
\(493\) 19.1876 0.864165
\(494\) 0.447890 0.0201515
\(495\) −36.3233 −1.63261
\(496\) 7.08818 0.318269
\(497\) −43.5385 −1.95297
\(498\) 4.24258 0.190115
\(499\) −20.0826 −0.899022 −0.449511 0.893275i \(-0.648402\pi\)
−0.449511 + 0.893275i \(0.648402\pi\)
\(500\) −9.36096 −0.418635
\(501\) −4.38262 −0.195801
\(502\) 15.3312 0.684264
\(503\) 27.8342 1.24107 0.620533 0.784180i \(-0.286916\pi\)
0.620533 + 0.784180i \(0.286916\pi\)
\(504\) −12.1838 −0.542709
\(505\) 33.6640 1.49803
\(506\) −30.5532 −1.35826
\(507\) 3.87010 0.171877
\(508\) −15.5297 −0.689021
\(509\) 13.3063 0.589793 0.294897 0.955529i \(-0.404715\pi\)
0.294897 + 0.955529i \(0.404715\pi\)
\(510\) −2.39860 −0.106212
\(511\) −48.4134 −2.14168
\(512\) 1.00000 0.0441942
\(513\) 0.645548 0.0285017
\(514\) −24.6485 −1.08720
\(515\) −48.5517 −2.13944
\(516\) 2.33872 0.102956
\(517\) −32.7351 −1.43969
\(518\) −42.4738 −1.86619
\(519\) 1.89783 0.0833056
\(520\) 3.61671 0.158603
\(521\) −4.20936 −0.184416 −0.0922078 0.995740i \(-0.529392\pi\)
−0.0922078 + 0.995740i \(0.529392\pi\)
\(522\) −20.4032 −0.893024
\(523\) 19.9416 0.871987 0.435993 0.899950i \(-0.356397\pi\)
0.435993 + 0.899950i \(0.356397\pi\)
\(524\) 5.60410 0.244816
\(525\) −1.89175 −0.0825627
\(526\) 10.2955 0.448906
\(527\) 19.1588 0.834570
\(528\) −1.79210 −0.0779911
\(529\) 13.5765 0.590281
\(530\) 18.7913 0.816241
\(531\) 26.9219 1.16831
\(532\) 1.31325 0.0569367
\(533\) −4.62136 −0.200173
\(534\) −2.98578 −0.129207
\(535\) −16.2381 −0.702034
\(536\) 3.57920 0.154598
\(537\) −5.72626 −0.247106
\(538\) 14.6922 0.633427
\(539\) 55.4184 2.38704
\(540\) 5.21279 0.224323
\(541\) 16.8684 0.725228 0.362614 0.931939i \(-0.381884\pi\)
0.362614 + 0.931939i \(0.381884\pi\)
\(542\) −6.98204 −0.299904
\(543\) 5.84621 0.250885
\(544\) 2.70292 0.115887
\(545\) 3.87288 0.165896
\(546\) −2.17407 −0.0930415
\(547\) −31.6926 −1.35508 −0.677538 0.735488i \(-0.736953\pi\)
−0.677538 + 0.735488i \(0.736953\pi\)
\(548\) −16.7378 −0.715001
\(549\) 19.5297 0.833508
\(550\) 6.35538 0.270994
\(551\) 2.19919 0.0936888
\(552\) 2.14539 0.0913141
\(553\) 67.2102 2.85807
\(554\) 16.0138 0.680362
\(555\) 8.89149 0.377423
\(556\) 5.63400 0.238935
\(557\) 47.1291 1.99693 0.998463 0.0554225i \(-0.0176506\pi\)
0.998463 + 0.0554225i \(0.0176506\pi\)
\(558\) −20.3726 −0.862440
\(559\) −9.53162 −0.403145
\(560\) 10.6045 0.448121
\(561\) −4.84390 −0.204510
\(562\) 17.5241 0.739209
\(563\) 35.3170 1.48843 0.744216 0.667939i \(-0.232823\pi\)
0.744216 + 0.667939i \(0.232823\pi\)
\(564\) 2.29860 0.0967886
\(565\) −40.1264 −1.68813
\(566\) −6.47177 −0.272029
\(567\) 33.4179 1.40342
\(568\) −10.2708 −0.430952
\(569\) 3.88606 0.162912 0.0814560 0.996677i \(-0.474043\pi\)
0.0814560 + 0.996677i \(0.474043\pi\)
\(570\) −0.274917 −0.0115150
\(571\) −38.2602 −1.60114 −0.800569 0.599241i \(-0.795469\pi\)
−0.800569 + 0.599241i \(0.795469\pi\)
\(572\) 7.30384 0.305389
\(573\) −9.16149 −0.382727
\(574\) −13.5502 −0.565575
\(575\) −7.60828 −0.317287
\(576\) −2.87416 −0.119757
\(577\) −40.4946 −1.68581 −0.842907 0.538060i \(-0.819157\pi\)
−0.842907 + 0.538060i \(0.819157\pi\)
\(578\) −9.69422 −0.403227
\(579\) −8.58727 −0.356875
\(580\) 17.7585 0.737380
\(581\) −50.6985 −2.10333
\(582\) −4.62443 −0.191689
\(583\) 37.9485 1.57166
\(584\) −11.4207 −0.472594
\(585\) −10.3950 −0.429781
\(586\) −15.8101 −0.653109
\(587\) −30.8235 −1.27222 −0.636110 0.771598i \(-0.719458\pi\)
−0.636110 + 0.771598i \(0.719458\pi\)
\(588\) −3.89139 −0.160478
\(589\) 2.19589 0.0904802
\(590\) −23.4322 −0.964688
\(591\) 2.58477 0.106323
\(592\) −10.0196 −0.411803
\(593\) −31.2460 −1.28312 −0.641560 0.767073i \(-0.721713\pi\)
−0.641560 + 0.767073i \(0.721713\pi\)
\(594\) 10.5271 0.431932
\(595\) 28.6631 1.17507
\(596\) −11.6511 −0.477247
\(597\) −2.67865 −0.109630
\(598\) −8.74372 −0.357557
\(599\) 18.7749 0.767122 0.383561 0.923516i \(-0.374698\pi\)
0.383561 + 0.923516i \(0.374698\pi\)
\(600\) −0.446264 −0.0182187
\(601\) −19.8542 −0.809871 −0.404935 0.914345i \(-0.632706\pi\)
−0.404935 + 0.914345i \(0.632706\pi\)
\(602\) −27.9475 −1.13905
\(603\) −10.2872 −0.418927
\(604\) −18.8620 −0.767485
\(605\) 36.3278 1.47694
\(606\) −4.77368 −0.193918
\(607\) 28.0675 1.13923 0.569613 0.821913i \(-0.307093\pi\)
0.569613 + 0.821913i \(0.307093\pi\)
\(608\) 0.309796 0.0125639
\(609\) −10.6749 −0.432570
\(610\) −16.9982 −0.688237
\(611\) −9.36813 −0.378994
\(612\) −7.76863 −0.314028
\(613\) 8.57039 0.346155 0.173077 0.984908i \(-0.444629\pi\)
0.173077 + 0.984908i \(0.444629\pi\)
\(614\) −11.6136 −0.468688
\(615\) 2.83661 0.114383
\(616\) 21.4155 0.862853
\(617\) 11.8838 0.478423 0.239211 0.970968i \(-0.423111\pi\)
0.239211 + 0.970968i \(0.423111\pi\)
\(618\) 6.88482 0.276948
\(619\) −2.01662 −0.0810547 −0.0405274 0.999178i \(-0.512904\pi\)
−0.0405274 + 0.999178i \(0.512904\pi\)
\(620\) 17.7318 0.712127
\(621\) −12.6024 −0.505717
\(622\) −18.7925 −0.753509
\(623\) 35.6798 1.42948
\(624\) −0.512863 −0.0205310
\(625\) −29.7075 −1.18830
\(626\) −3.58821 −0.143414
\(627\) −0.555186 −0.0221720
\(628\) 6.74126 0.269006
\(629\) −27.0822 −1.07984
\(630\) −30.4790 −1.21431
\(631\) −6.64381 −0.264486 −0.132243 0.991217i \(-0.542218\pi\)
−0.132243 + 0.991217i \(0.542218\pi\)
\(632\) 15.8549 0.630675
\(633\) −5.73234 −0.227840
\(634\) 19.8340 0.787707
\(635\) −38.8493 −1.54169
\(636\) −2.66468 −0.105661
\(637\) 15.8596 0.628382
\(638\) 35.8627 1.41982
\(639\) 29.5198 1.16779
\(640\) 2.50160 0.0988845
\(641\) −24.0254 −0.948946 −0.474473 0.880270i \(-0.657361\pi\)
−0.474473 + 0.880270i \(0.657361\pi\)
\(642\) 2.30262 0.0908773
\(643\) −13.2150 −0.521148 −0.260574 0.965454i \(-0.583912\pi\)
−0.260574 + 0.965454i \(0.583912\pi\)
\(644\) −25.6373 −1.01025
\(645\) 5.85054 0.230365
\(646\) 0.837355 0.0329453
\(647\) 1.28356 0.0504619 0.0252309 0.999682i \(-0.491968\pi\)
0.0252309 + 0.999682i \(0.491968\pi\)
\(648\) 7.88329 0.309685
\(649\) −47.3206 −1.85750
\(650\) 1.81878 0.0713386
\(651\) −10.6589 −0.417755
\(652\) 16.2878 0.637878
\(653\) 14.8806 0.582324 0.291162 0.956674i \(-0.405958\pi\)
0.291162 + 0.956674i \(0.405958\pi\)
\(654\) −0.549189 −0.0214750
\(655\) 14.0192 0.547776
\(656\) −3.19650 −0.124802
\(657\) 32.8251 1.28063
\(658\) −27.4681 −1.07082
\(659\) −25.0699 −0.976583 −0.488291 0.872681i \(-0.662380\pi\)
−0.488291 + 0.872681i \(0.662380\pi\)
\(660\) −4.48312 −0.174505
\(661\) −9.12341 −0.354859 −0.177430 0.984133i \(-0.556778\pi\)
−0.177430 + 0.984133i \(0.556778\pi\)
\(662\) 14.8735 0.578073
\(663\) −1.38623 −0.0538367
\(664\) −11.9598 −0.464130
\(665\) 3.28523 0.127396
\(666\) 28.7979 1.11590
\(667\) −42.9327 −1.66236
\(668\) 12.3546 0.478013
\(669\) 6.25999 0.242025
\(670\) 8.95373 0.345913
\(671\) −34.3274 −1.32519
\(672\) −1.50376 −0.0580087
\(673\) −42.0482 −1.62084 −0.810419 0.585850i \(-0.800761\pi\)
−0.810419 + 0.585850i \(0.800761\pi\)
\(674\) −12.2061 −0.470161
\(675\) 2.62143 0.100899
\(676\) −10.9098 −0.419607
\(677\) −6.22762 −0.239347 −0.119673 0.992813i \(-0.538185\pi\)
−0.119673 + 0.992813i \(0.538185\pi\)
\(678\) 5.69008 0.218526
\(679\) 55.2616 2.12075
\(680\) 6.76163 0.259297
\(681\) 0.460373 0.0176415
\(682\) 35.8089 1.37119
\(683\) −28.8127 −1.10249 −0.551244 0.834344i \(-0.685847\pi\)
−0.551244 + 0.834344i \(0.685847\pi\)
\(684\) −0.890405 −0.0340455
\(685\) −41.8712 −1.59982
\(686\) 16.8282 0.642504
\(687\) −8.49483 −0.324098
\(688\) −6.59282 −0.251349
\(689\) 10.8601 0.413737
\(690\) 5.36692 0.204315
\(691\) 8.66669 0.329697 0.164848 0.986319i \(-0.447287\pi\)
0.164848 + 0.986319i \(0.447287\pi\)
\(692\) −5.34997 −0.203376
\(693\) −61.5515 −2.33815
\(694\) 25.9128 0.983636
\(695\) 14.0940 0.534617
\(696\) −2.51822 −0.0954529
\(697\) −8.63988 −0.327259
\(698\) −1.96325 −0.0743101
\(699\) −2.79180 −0.105595
\(700\) 5.33282 0.201562
\(701\) 9.38131 0.354327 0.177164 0.984181i \(-0.443308\pi\)
0.177164 + 0.984181i \(0.443308\pi\)
\(702\) 3.01264 0.113705
\(703\) −3.10403 −0.117071
\(704\) 5.05191 0.190401
\(705\) 5.75019 0.216565
\(706\) 7.06061 0.265730
\(707\) 57.0451 2.14540
\(708\) 3.32277 0.124877
\(709\) 17.7703 0.667379 0.333690 0.942683i \(-0.391706\pi\)
0.333690 + 0.942683i \(0.391706\pi\)
\(710\) −25.6934 −0.964255
\(711\) −45.5696 −1.70899
\(712\) 8.41688 0.315436
\(713\) −42.8682 −1.60543
\(714\) −4.06454 −0.152111
\(715\) 18.2713 0.683308
\(716\) 16.1423 0.603265
\(717\) −6.84588 −0.255664
\(718\) 8.10653 0.302533
\(719\) 28.9435 1.07941 0.539704 0.841855i \(-0.318536\pi\)
0.539704 + 0.841855i \(0.318536\pi\)
\(720\) −7.19001 −0.267956
\(721\) −82.2730 −3.06401
\(722\) −18.9040 −0.703535
\(723\) −2.48146 −0.0922867
\(724\) −16.4804 −0.612490
\(725\) 8.93044 0.331668
\(726\) −5.15143 −0.191187
\(727\) −8.66942 −0.321531 −0.160766 0.986993i \(-0.551396\pi\)
−0.160766 + 0.986993i \(0.551396\pi\)
\(728\) 6.12868 0.227144
\(729\) −20.4403 −0.757047
\(730\) −28.5702 −1.05743
\(731\) −17.8199 −0.659092
\(732\) 2.41041 0.0890913
\(733\) −12.5526 −0.463641 −0.231820 0.972759i \(-0.574468\pi\)
−0.231820 + 0.972759i \(0.574468\pi\)
\(734\) 30.2287 1.11576
\(735\) −9.73470 −0.359070
\(736\) −6.04785 −0.222927
\(737\) 18.0818 0.666051
\(738\) 9.18725 0.338187
\(739\) −25.8355 −0.950373 −0.475186 0.879885i \(-0.657619\pi\)
−0.475186 + 0.879885i \(0.657619\pi\)
\(740\) −25.0650 −0.921409
\(741\) −0.158883 −0.00583672
\(742\) 31.8427 1.16898
\(743\) 20.2761 0.743857 0.371928 0.928261i \(-0.378697\pi\)
0.371928 + 0.928261i \(0.378697\pi\)
\(744\) −2.51444 −0.0921838
\(745\) −29.1464 −1.06784
\(746\) −3.53242 −0.129331
\(747\) 34.3744 1.25769
\(748\) 13.6549 0.499273
\(749\) −27.5162 −1.00542
\(750\) 3.32068 0.121254
\(751\) 21.7713 0.794446 0.397223 0.917722i \(-0.369974\pi\)
0.397223 + 0.917722i \(0.369974\pi\)
\(752\) −6.47974 −0.236292
\(753\) −5.43854 −0.198191
\(754\) 10.2632 0.373764
\(755\) −47.1853 −1.71725
\(756\) 8.83331 0.321264
\(757\) −12.1926 −0.443147 −0.221574 0.975144i \(-0.571119\pi\)
−0.221574 + 0.975144i \(0.571119\pi\)
\(758\) 37.2454 1.35281
\(759\) 10.8383 0.393407
\(760\) 0.774988 0.0281118
\(761\) −29.6438 −1.07459 −0.537294 0.843395i \(-0.680553\pi\)
−0.537294 + 0.843395i \(0.680553\pi\)
\(762\) 5.50898 0.199569
\(763\) 6.56276 0.237588
\(764\) 25.8262 0.934358
\(765\) −19.4340 −0.702639
\(766\) −36.2812 −1.31089
\(767\) −13.5422 −0.488981
\(768\) −0.354737 −0.0128005
\(769\) 10.7597 0.388005 0.194002 0.981001i \(-0.437853\pi\)
0.194002 + 0.981001i \(0.437853\pi\)
\(770\) 53.5729 1.93063
\(771\) 8.74374 0.314898
\(772\) 24.2074 0.871245
\(773\) 43.5593 1.56672 0.783360 0.621569i \(-0.213504\pi\)
0.783360 + 0.621569i \(0.213504\pi\)
\(774\) 18.9488 0.681102
\(775\) 8.91704 0.320309
\(776\) 13.0362 0.467973
\(777\) 15.0670 0.540527
\(778\) −25.5490 −0.915976
\(779\) −0.990264 −0.0354799
\(780\) −1.28298 −0.0459381
\(781\) −51.8870 −1.85666
\(782\) −16.3468 −0.584562
\(783\) 14.7924 0.528638
\(784\) 10.9698 0.391778
\(785\) 16.8640 0.601900
\(786\) −1.98798 −0.0709089
\(787\) 29.0027 1.03384 0.516918 0.856035i \(-0.327079\pi\)
0.516918 + 0.856035i \(0.327079\pi\)
\(788\) −7.28644 −0.259569
\(789\) −3.65220 −0.130022
\(790\) 39.6627 1.41114
\(791\) −67.9960 −2.41766
\(792\) −14.5200 −0.515946
\(793\) −9.82381 −0.348854
\(794\) 17.4966 0.620930
\(795\) −6.66596 −0.236417
\(796\) 7.55110 0.267642
\(797\) 43.8518 1.55331 0.776655 0.629926i \(-0.216915\pi\)
0.776655 + 0.629926i \(0.216915\pi\)
\(798\) −0.465859 −0.0164912
\(799\) −17.5142 −0.619608
\(800\) 1.25801 0.0444775
\(801\) −24.1915 −0.854763
\(802\) −30.2755 −1.06906
\(803\) −57.6966 −2.03607
\(804\) −1.26967 −0.0447779
\(805\) −64.1343 −2.26044
\(806\) 10.2478 0.360963
\(807\) −5.21188 −0.183467
\(808\) 13.4570 0.473414
\(809\) −47.9146 −1.68459 −0.842294 0.539018i \(-0.818795\pi\)
−0.842294 + 0.539018i \(0.818795\pi\)
\(810\) 19.7209 0.692920
\(811\) 22.3056 0.783255 0.391628 0.920124i \(-0.371912\pi\)
0.391628 + 0.920124i \(0.371912\pi\)
\(812\) 30.0925 1.05604
\(813\) 2.47679 0.0868648
\(814\) −50.6181 −1.77416
\(815\) 40.7455 1.42725
\(816\) −0.958825 −0.0335656
\(817\) −2.04243 −0.0714557
\(818\) 29.7996 1.04192
\(819\) −17.6148 −0.615511
\(820\) −7.99637 −0.279245
\(821\) −19.2376 −0.671397 −0.335699 0.941969i \(-0.608972\pi\)
−0.335699 + 0.941969i \(0.608972\pi\)
\(822\) 5.93750 0.207094
\(823\) 0.114474 0.00399032 0.00199516 0.999998i \(-0.499365\pi\)
0.00199516 + 0.999998i \(0.499365\pi\)
\(824\) −19.4082 −0.676118
\(825\) −2.25449 −0.0784912
\(826\) −39.7069 −1.38158
\(827\) 27.2801 0.948622 0.474311 0.880357i \(-0.342697\pi\)
0.474311 + 0.880357i \(0.342697\pi\)
\(828\) 17.3825 0.604083
\(829\) −52.3424 −1.81793 −0.908964 0.416876i \(-0.863125\pi\)
−0.908964 + 0.416876i \(0.863125\pi\)
\(830\) −29.9187 −1.03849
\(831\) −5.68069 −0.197061
\(832\) 1.44576 0.0501226
\(833\) 29.6504 1.02733
\(834\) −1.99859 −0.0692054
\(835\) 30.9062 1.06955
\(836\) 1.56506 0.0541289
\(837\) 14.7702 0.510534
\(838\) −8.07295 −0.278875
\(839\) −18.9473 −0.654132 −0.327066 0.945001i \(-0.606060\pi\)
−0.327066 + 0.945001i \(0.606060\pi\)
\(840\) −3.76180 −0.129795
\(841\) 21.3935 0.737706
\(842\) −23.5149 −0.810377
\(843\) −6.21644 −0.214106
\(844\) 16.1594 0.556230
\(845\) −27.2919 −0.938872
\(846\) 18.6238 0.640300
\(847\) 61.5591 2.11520
\(848\) 7.51170 0.257953
\(849\) 2.29578 0.0787908
\(850\) 3.40031 0.116630
\(851\) 60.5970 2.07724
\(852\) 3.64342 0.124821
\(853\) 10.8118 0.370190 0.185095 0.982721i \(-0.440741\pi\)
0.185095 + 0.982721i \(0.440741\pi\)
\(854\) −28.8042 −0.985660
\(855\) −2.22744 −0.0761768
\(856\) −6.49107 −0.221860
\(857\) 3.33892 0.114055 0.0570277 0.998373i \(-0.481838\pi\)
0.0570277 + 0.998373i \(0.481838\pi\)
\(858\) −2.59094 −0.0884533
\(859\) −27.3932 −0.934643 −0.467321 0.884087i \(-0.654781\pi\)
−0.467321 + 0.884087i \(0.654781\pi\)
\(860\) −16.4926 −0.562394
\(861\) 4.80676 0.163814
\(862\) −12.5117 −0.426150
\(863\) 41.7515 1.42124 0.710619 0.703577i \(-0.248415\pi\)
0.710619 + 0.703577i \(0.248415\pi\)
\(864\) 2.08378 0.0708917
\(865\) −13.3835 −0.455053
\(866\) −12.9160 −0.438905
\(867\) 3.43890 0.116791
\(868\) 30.0473 1.01987
\(869\) 80.0977 2.71713
\(870\) −6.29958 −0.213576
\(871\) 5.17465 0.175336
\(872\) 1.54816 0.0524272
\(873\) −37.4682 −1.26811
\(874\) −1.87360 −0.0633755
\(875\) −39.6818 −1.34149
\(876\) 4.05136 0.136883
\(877\) −33.2160 −1.12162 −0.560812 0.827943i \(-0.689511\pi\)
−0.560812 + 0.827943i \(0.689511\pi\)
\(878\) −7.03100 −0.237285
\(879\) 5.60843 0.189168
\(880\) 12.6379 0.426023
\(881\) −6.70460 −0.225884 −0.112942 0.993602i \(-0.536027\pi\)
−0.112942 + 0.993602i \(0.536027\pi\)
\(882\) −31.5289 −1.06163
\(883\) −25.6609 −0.863559 −0.431780 0.901979i \(-0.642114\pi\)
−0.431780 + 0.901979i \(0.642114\pi\)
\(884\) 3.90777 0.131432
\(885\) 8.31226 0.279414
\(886\) 33.5400 1.12680
\(887\) −33.6357 −1.12938 −0.564689 0.825304i \(-0.691004\pi\)
−0.564689 + 0.825304i \(0.691004\pi\)
\(888\) 3.55432 0.119275
\(889\) −65.8318 −2.20793
\(890\) 21.0557 0.705788
\(891\) 39.8257 1.33421
\(892\) −17.6469 −0.590861
\(893\) −2.00740 −0.0671751
\(894\) 4.13307 0.138231
\(895\) 40.3816 1.34981
\(896\) 4.23908 0.141618
\(897\) 3.10172 0.103563
\(898\) −22.6121 −0.754576
\(899\) 50.3178 1.67819
\(900\) −3.61574 −0.120525
\(901\) 20.3035 0.676409
\(902\) −16.1484 −0.537684
\(903\) 9.91400 0.329917
\(904\) −16.0403 −0.533492
\(905\) −41.2275 −1.37045
\(906\) 6.69106 0.222296
\(907\) −36.4738 −1.21109 −0.605546 0.795810i \(-0.707045\pi\)
−0.605546 + 0.795810i \(0.707045\pi\)
\(908\) −1.29779 −0.0430686
\(909\) −38.6775 −1.28285
\(910\) 15.3315 0.508235
\(911\) −1.97399 −0.0654013 −0.0327006 0.999465i \(-0.510411\pi\)
−0.0327006 + 0.999465i \(0.510411\pi\)
\(912\) −0.109896 −0.00363903
\(913\) −60.4199 −1.99961
\(914\) −13.0858 −0.432838
\(915\) 6.02989 0.199342
\(916\) 23.9469 0.791227
\(917\) 23.7562 0.784499
\(918\) 5.63230 0.185893
\(919\) −28.9746 −0.955783 −0.477891 0.878419i \(-0.658599\pi\)
−0.477891 + 0.878419i \(0.658599\pi\)
\(920\) −15.1293 −0.498799
\(921\) 4.11978 0.135751
\(922\) −17.0440 −0.561314
\(923\) −14.8490 −0.488762
\(924\) −7.59685 −0.249918
\(925\) −12.6048 −0.414443
\(926\) −16.6959 −0.548662
\(927\) 55.7824 1.83214
\(928\) 7.09884 0.233031
\(929\) 45.3451 1.48772 0.743862 0.668334i \(-0.232992\pi\)
0.743862 + 0.668334i \(0.232992\pi\)
\(930\) −6.29013 −0.206261
\(931\) 3.39840 0.111378
\(932\) 7.87004 0.257792
\(933\) 6.66638 0.218248
\(934\) −32.5843 −1.06619
\(935\) 34.1592 1.11712
\(936\) −4.15534 −0.135822
\(937\) 36.7042 1.19907 0.599537 0.800347i \(-0.295352\pi\)
0.599537 + 0.800347i \(0.295352\pi\)
\(938\) 15.1725 0.495399
\(939\) 1.27287 0.0415386
\(940\) −16.2097 −0.528703
\(941\) −50.6447 −1.65097 −0.825484 0.564425i \(-0.809098\pi\)
−0.825484 + 0.564425i \(0.809098\pi\)
\(942\) −2.39137 −0.0779152
\(943\) 19.3319 0.629535
\(944\) −9.36687 −0.304866
\(945\) 22.0974 0.718830
\(946\) −33.3064 −1.08288
\(947\) −47.2660 −1.53594 −0.767969 0.640487i \(-0.778732\pi\)
−0.767969 + 0.640487i \(0.778732\pi\)
\(948\) −5.62432 −0.182670
\(949\) −16.5116 −0.535990
\(950\) 0.389729 0.0126445
\(951\) −7.03584 −0.228153
\(952\) 11.4579 0.371352
\(953\) 32.6629 1.05806 0.529028 0.848604i \(-0.322557\pi\)
0.529028 + 0.848604i \(0.322557\pi\)
\(954\) −21.5898 −0.698997
\(955\) 64.6068 2.09063
\(956\) 19.2985 0.624157
\(957\) −12.7218 −0.411238
\(958\) 38.3198 1.23806
\(959\) −70.9526 −2.29118
\(960\) −0.887411 −0.0286411
\(961\) 19.2423 0.620719
\(962\) −14.4859 −0.467044
\(963\) 18.6564 0.601194
\(964\) 6.99523 0.225301
\(965\) 60.5574 1.94941
\(966\) 9.09450 0.292611
\(967\) 31.4235 1.01051 0.505256 0.862969i \(-0.331398\pi\)
0.505256 + 0.862969i \(0.331398\pi\)
\(968\) 14.5218 0.466749
\(969\) −0.297041 −0.00954232
\(970\) 32.6115 1.04709
\(971\) −13.6162 −0.436966 −0.218483 0.975841i \(-0.570111\pi\)
−0.218483 + 0.975841i \(0.570111\pi\)
\(972\) −9.04784 −0.290210
\(973\) 23.8830 0.765653
\(974\) −14.7907 −0.473926
\(975\) −0.645190 −0.0206626
\(976\) −6.79492 −0.217500
\(977\) 23.1193 0.739651 0.369825 0.929101i \(-0.379417\pi\)
0.369825 + 0.929101i \(0.379417\pi\)
\(978\) −5.77787 −0.184756
\(979\) 42.5213 1.35899
\(980\) 27.4420 0.876603
\(981\) −4.44966 −0.142067
\(982\) 16.2154 0.517456
\(983\) −39.2107 −1.25063 −0.625314 0.780373i \(-0.715029\pi\)
−0.625314 + 0.780373i \(0.715029\pi\)
\(984\) 1.13392 0.0361479
\(985\) −18.2278 −0.580785
\(986\) 19.1876 0.611057
\(987\) 9.74395 0.310153
\(988\) 0.447890 0.0142493
\(989\) 39.8724 1.26787
\(990\) −36.3233 −1.15443
\(991\) 26.0106 0.826253 0.413127 0.910674i \(-0.364437\pi\)
0.413127 + 0.910674i \(0.364437\pi\)
\(992\) 7.08818 0.225050
\(993\) −5.27616 −0.167434
\(994\) −43.5385 −1.38096
\(995\) 18.8898 0.598848
\(996\) 4.24258 0.134431
\(997\) −10.5925 −0.335467 −0.167733 0.985832i \(-0.553645\pi\)
−0.167733 + 0.985832i \(0.553645\pi\)
\(998\) −20.0826 −0.635705
\(999\) −20.8786 −0.660571
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 4006.2.a.i.1.17 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.i.1.17 46 1.1 even 1 trivial