Properties

Label 4034.2.a.a.1.14
Level $4034$
Weight $2$
Character 4034.1
Self dual yes
Analytic conductor $32.212$
Analytic rank $1$
Dimension $33$
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] = [4034,2,Mod(1,4034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4034, 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("4034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4034.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: \(32.2116521754\)
Analytic rank: \(1\)
Dimension: \(33\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 4034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.945997 q^{3} +1.00000 q^{4} -2.44770 q^{5} -0.945997 q^{6} +2.03235 q^{7} +1.00000 q^{8} -2.10509 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.945997 q^{3} +1.00000 q^{4} -2.44770 q^{5} -0.945997 q^{6} +2.03235 q^{7} +1.00000 q^{8} -2.10509 q^{9} -2.44770 q^{10} -2.80078 q^{11} -0.945997 q^{12} -1.99090 q^{13} +2.03235 q^{14} +2.31551 q^{15} +1.00000 q^{16} +5.52248 q^{17} -2.10509 q^{18} +2.90068 q^{19} -2.44770 q^{20} -1.92260 q^{21} -2.80078 q^{22} +6.12514 q^{23} -0.945997 q^{24} +0.991226 q^{25} -1.99090 q^{26} +4.82940 q^{27} +2.03235 q^{28} -3.04955 q^{29} +2.31551 q^{30} -0.837606 q^{31} +1.00000 q^{32} +2.64953 q^{33} +5.52248 q^{34} -4.97458 q^{35} -2.10509 q^{36} +6.35990 q^{37} +2.90068 q^{38} +1.88339 q^{39} -2.44770 q^{40} +3.39380 q^{41} -1.92260 q^{42} -12.3524 q^{43} -2.80078 q^{44} +5.15262 q^{45} +6.12514 q^{46} -8.79264 q^{47} -0.945997 q^{48} -2.86955 q^{49} +0.991226 q^{50} -5.22425 q^{51} -1.99090 q^{52} -7.11992 q^{53} +4.82940 q^{54} +6.85545 q^{55} +2.03235 q^{56} -2.74404 q^{57} -3.04955 q^{58} +0.529488 q^{59} +2.31551 q^{60} -7.57201 q^{61} -0.837606 q^{62} -4.27828 q^{63} +1.00000 q^{64} +4.87312 q^{65} +2.64953 q^{66} -0.246931 q^{67} +5.52248 q^{68} -5.79436 q^{69} -4.97458 q^{70} -1.27323 q^{71} -2.10509 q^{72} -7.08356 q^{73} +6.35990 q^{74} -0.937697 q^{75} +2.90068 q^{76} -5.69216 q^{77} +1.88339 q^{78} -8.73964 q^{79} -2.44770 q^{80} +1.74667 q^{81} +3.39380 q^{82} -15.0794 q^{83} -1.92260 q^{84} -13.5174 q^{85} -12.3524 q^{86} +2.88487 q^{87} -2.80078 q^{88} +10.3602 q^{89} +5.15262 q^{90} -4.04621 q^{91} +6.12514 q^{92} +0.792373 q^{93} -8.79264 q^{94} -7.10000 q^{95} -0.945997 q^{96} +1.35477 q^{97} -2.86955 q^{98} +5.89589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 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
\(3\) −0.945997 −0.546172 −0.273086 0.961990i \(-0.588044\pi\)
−0.273086 + 0.961990i \(0.588044\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.44770 −1.09464 −0.547322 0.836922i \(-0.684353\pi\)
−0.547322 + 0.836922i \(0.684353\pi\)
\(6\) −0.945997 −0.386202
\(7\) 2.03235 0.768156 0.384078 0.923301i \(-0.374519\pi\)
0.384078 + 0.923301i \(0.374519\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.10509 −0.701697
\(10\) −2.44770 −0.774030
\(11\) −2.80078 −0.844466 −0.422233 0.906487i \(-0.638754\pi\)
−0.422233 + 0.906487i \(0.638754\pi\)
\(12\) −0.945997 −0.273086
\(13\) −1.99090 −0.552177 −0.276088 0.961132i \(-0.589038\pi\)
−0.276088 + 0.961132i \(0.589038\pi\)
\(14\) 2.03235 0.543169
\(15\) 2.31551 0.597863
\(16\) 1.00000 0.250000
\(17\) 5.52248 1.33940 0.669699 0.742632i \(-0.266423\pi\)
0.669699 + 0.742632i \(0.266423\pi\)
\(18\) −2.10509 −0.496174
\(19\) 2.90068 0.665463 0.332731 0.943022i \(-0.392030\pi\)
0.332731 + 0.943022i \(0.392030\pi\)
\(20\) −2.44770 −0.547322
\(21\) −1.92260 −0.419545
\(22\) −2.80078 −0.597128
\(23\) 6.12514 1.27718 0.638590 0.769547i \(-0.279518\pi\)
0.638590 + 0.769547i \(0.279518\pi\)
\(24\) −0.945997 −0.193101
\(25\) 0.991226 0.198245
\(26\) −1.99090 −0.390448
\(27\) 4.82940 0.929418
\(28\) 2.03235 0.384078
\(29\) −3.04955 −0.566287 −0.283144 0.959078i \(-0.591377\pi\)
−0.283144 + 0.959078i \(0.591377\pi\)
\(30\) 2.31551 0.422753
\(31\) −0.837606 −0.150439 −0.0752193 0.997167i \(-0.523966\pi\)
−0.0752193 + 0.997167i \(0.523966\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.64953 0.461223
\(34\) 5.52248 0.947098
\(35\) −4.97458 −0.840858
\(36\) −2.10509 −0.350848
\(37\) 6.35990 1.04556 0.522781 0.852467i \(-0.324895\pi\)
0.522781 + 0.852467i \(0.324895\pi\)
\(38\) 2.90068 0.470553
\(39\) 1.88339 0.301583
\(40\) −2.44770 −0.387015
\(41\) 3.39380 0.530023 0.265011 0.964245i \(-0.414624\pi\)
0.265011 + 0.964245i \(0.414624\pi\)
\(42\) −1.92260 −0.296663
\(43\) −12.3524 −1.88372 −0.941859 0.336009i \(-0.890923\pi\)
−0.941859 + 0.336009i \(0.890923\pi\)
\(44\) −2.80078 −0.422233
\(45\) 5.15262 0.768108
\(46\) 6.12514 0.903102
\(47\) −8.79264 −1.28254 −0.641269 0.767316i \(-0.721592\pi\)
−0.641269 + 0.767316i \(0.721592\pi\)
\(48\) −0.945997 −0.136543
\(49\) −2.86955 −0.409936
\(50\) 0.991226 0.140181
\(51\) −5.22425 −0.731541
\(52\) −1.99090 −0.276088
\(53\) −7.11992 −0.977996 −0.488998 0.872285i \(-0.662638\pi\)
−0.488998 + 0.872285i \(0.662638\pi\)
\(54\) 4.82940 0.657198
\(55\) 6.85545 0.924389
\(56\) 2.03235 0.271584
\(57\) −2.74404 −0.363457
\(58\) −3.04955 −0.400426
\(59\) 0.529488 0.0689335 0.0344667 0.999406i \(-0.489027\pi\)
0.0344667 + 0.999406i \(0.489027\pi\)
\(60\) 2.31551 0.298932
\(61\) −7.57201 −0.969496 −0.484748 0.874654i \(-0.661089\pi\)
−0.484748 + 0.874654i \(0.661089\pi\)
\(62\) −0.837606 −0.106376
\(63\) −4.27828 −0.539013
\(64\) 1.00000 0.125000
\(65\) 4.87312 0.604437
\(66\) 2.64953 0.326134
\(67\) −0.246931 −0.0301674 −0.0150837 0.999886i \(-0.504801\pi\)
−0.0150837 + 0.999886i \(0.504801\pi\)
\(68\) 5.52248 0.669699
\(69\) −5.79436 −0.697559
\(70\) −4.97458 −0.594576
\(71\) −1.27323 −0.151105 −0.0755525 0.997142i \(-0.524072\pi\)
−0.0755525 + 0.997142i \(0.524072\pi\)
\(72\) −2.10509 −0.248087
\(73\) −7.08356 −0.829068 −0.414534 0.910034i \(-0.636055\pi\)
−0.414534 + 0.910034i \(0.636055\pi\)
\(74\) 6.35990 0.739324
\(75\) −0.937697 −0.108276
\(76\) 2.90068 0.332731
\(77\) −5.69216 −0.648682
\(78\) 1.88339 0.213252
\(79\) −8.73964 −0.983286 −0.491643 0.870797i \(-0.663603\pi\)
−0.491643 + 0.870797i \(0.663603\pi\)
\(80\) −2.44770 −0.273661
\(81\) 1.74667 0.194075
\(82\) 3.39380 0.374783
\(83\) −15.0794 −1.65518 −0.827588 0.561336i \(-0.810288\pi\)
−0.827588 + 0.561336i \(0.810288\pi\)
\(84\) −1.92260 −0.209773
\(85\) −13.5174 −1.46616
\(86\) −12.3524 −1.33199
\(87\) 2.88487 0.309290
\(88\) −2.80078 −0.298564
\(89\) 10.3602 1.09818 0.549089 0.835764i \(-0.314975\pi\)
0.549089 + 0.835764i \(0.314975\pi\)
\(90\) 5.15262 0.543134
\(91\) −4.04621 −0.424158
\(92\) 6.12514 0.638590
\(93\) 0.792373 0.0821653
\(94\) −8.79264 −0.906892
\(95\) −7.10000 −0.728445
\(96\) −0.945997 −0.0965504
\(97\) 1.35477 0.137556 0.0687778 0.997632i \(-0.478090\pi\)
0.0687778 + 0.997632i \(0.478090\pi\)
\(98\) −2.86955 −0.289868
\(99\) 5.89589 0.592559
\(100\) 0.991226 0.0991226
\(101\) −2.66728 −0.265404 −0.132702 0.991156i \(-0.542365\pi\)
−0.132702 + 0.991156i \(0.542365\pi\)
\(102\) −5.22425 −0.517278
\(103\) −15.3143 −1.50896 −0.754480 0.656323i \(-0.772111\pi\)
−0.754480 + 0.656323i \(0.772111\pi\)
\(104\) −1.99090 −0.195224
\(105\) 4.70594 0.459253
\(106\) −7.11992 −0.691548
\(107\) 14.4192 1.39396 0.696980 0.717090i \(-0.254526\pi\)
0.696980 + 0.717090i \(0.254526\pi\)
\(108\) 4.82940 0.464709
\(109\) −2.62093 −0.251039 −0.125520 0.992091i \(-0.540060\pi\)
−0.125520 + 0.992091i \(0.540060\pi\)
\(110\) 6.85545 0.653642
\(111\) −6.01645 −0.571056
\(112\) 2.03235 0.192039
\(113\) −11.3017 −1.06318 −0.531589 0.847003i \(-0.678405\pi\)
−0.531589 + 0.847003i \(0.678405\pi\)
\(114\) −2.74404 −0.257003
\(115\) −14.9925 −1.39806
\(116\) −3.04955 −0.283144
\(117\) 4.19103 0.387460
\(118\) 0.529488 0.0487433
\(119\) 11.2236 1.02887
\(120\) 2.31551 0.211377
\(121\) −3.15565 −0.286877
\(122\) −7.57201 −0.685537
\(123\) −3.21053 −0.289483
\(124\) −0.837606 −0.0752193
\(125\) 9.81227 0.877636
\(126\) −4.27828 −0.381140
\(127\) −1.86707 −0.165676 −0.0828380 0.996563i \(-0.526398\pi\)
−0.0828380 + 0.996563i \(0.526398\pi\)
\(128\) 1.00000 0.0883883
\(129\) 11.6853 1.02883
\(130\) 4.87312 0.427401
\(131\) −4.97772 −0.434905 −0.217453 0.976071i \(-0.569775\pi\)
−0.217453 + 0.976071i \(0.569775\pi\)
\(132\) 2.64953 0.230612
\(133\) 5.89521 0.511179
\(134\) −0.246931 −0.0213315
\(135\) −11.8209 −1.01738
\(136\) 5.52248 0.473549
\(137\) −16.0530 −1.37150 −0.685751 0.727836i \(-0.740526\pi\)
−0.685751 + 0.727836i \(0.740526\pi\)
\(138\) −5.79436 −0.493249
\(139\) −16.7441 −1.42022 −0.710110 0.704091i \(-0.751355\pi\)
−0.710110 + 0.704091i \(0.751355\pi\)
\(140\) −4.97458 −0.420429
\(141\) 8.31781 0.700486
\(142\) −1.27323 −0.106847
\(143\) 5.57607 0.466294
\(144\) −2.10509 −0.175424
\(145\) 7.46438 0.619883
\(146\) −7.08356 −0.586240
\(147\) 2.71459 0.223895
\(148\) 6.35990 0.522781
\(149\) −9.63045 −0.788957 −0.394479 0.918905i \(-0.629075\pi\)
−0.394479 + 0.918905i \(0.629075\pi\)
\(150\) −0.937697 −0.0765626
\(151\) 11.0569 0.899798 0.449899 0.893080i \(-0.351460\pi\)
0.449899 + 0.893080i \(0.351460\pi\)
\(152\) 2.90068 0.235277
\(153\) −11.6253 −0.939851
\(154\) −5.69216 −0.458687
\(155\) 2.05021 0.164677
\(156\) 1.88339 0.150792
\(157\) 23.6561 1.88796 0.943982 0.329997i \(-0.107048\pi\)
0.943982 + 0.329997i \(0.107048\pi\)
\(158\) −8.73964 −0.695288
\(159\) 6.73542 0.534154
\(160\) −2.44770 −0.193508
\(161\) 12.4484 0.981073
\(162\) 1.74667 0.137231
\(163\) 1.48955 0.116671 0.0583354 0.998297i \(-0.481421\pi\)
0.0583354 + 0.998297i \(0.481421\pi\)
\(164\) 3.39380 0.265011
\(165\) −6.48524 −0.504875
\(166\) −15.0794 −1.17039
\(167\) 10.1098 0.782321 0.391160 0.920323i \(-0.372074\pi\)
0.391160 + 0.920323i \(0.372074\pi\)
\(168\) −1.92260 −0.148332
\(169\) −9.03631 −0.695101
\(170\) −13.5174 −1.03673
\(171\) −6.10620 −0.466953
\(172\) −12.3524 −0.941859
\(173\) −7.11640 −0.541050 −0.270525 0.962713i \(-0.587197\pi\)
−0.270525 + 0.962713i \(0.587197\pi\)
\(174\) 2.88487 0.218701
\(175\) 2.01452 0.152283
\(176\) −2.80078 −0.211116
\(177\) −0.500894 −0.0376495
\(178\) 10.3602 0.776530
\(179\) −24.0359 −1.79653 −0.898263 0.439458i \(-0.855170\pi\)
−0.898263 + 0.439458i \(0.855170\pi\)
\(180\) 5.15262 0.384054
\(181\) −10.7648 −0.800145 −0.400072 0.916484i \(-0.631015\pi\)
−0.400072 + 0.916484i \(0.631015\pi\)
\(182\) −4.04621 −0.299925
\(183\) 7.16310 0.529511
\(184\) 6.12514 0.451551
\(185\) −15.5671 −1.14452
\(186\) 0.792373 0.0580996
\(187\) −15.4672 −1.13108
\(188\) −8.79264 −0.641269
\(189\) 9.81503 0.713939
\(190\) −7.10000 −0.515088
\(191\) 21.1184 1.52807 0.764037 0.645173i \(-0.223215\pi\)
0.764037 + 0.645173i \(0.223215\pi\)
\(192\) −0.945997 −0.0682715
\(193\) 16.5811 1.19354 0.596768 0.802414i \(-0.296451\pi\)
0.596768 + 0.802414i \(0.296451\pi\)
\(194\) 1.35477 0.0972665
\(195\) −4.60996 −0.330126
\(196\) −2.86955 −0.204968
\(197\) 17.8425 1.27122 0.635612 0.772008i \(-0.280748\pi\)
0.635612 + 0.772008i \(0.280748\pi\)
\(198\) 5.89589 0.419002
\(199\) −2.34031 −0.165901 −0.0829503 0.996554i \(-0.526434\pi\)
−0.0829503 + 0.996554i \(0.526434\pi\)
\(200\) 0.991226 0.0700903
\(201\) 0.233596 0.0164766
\(202\) −2.66728 −0.187669
\(203\) −6.19775 −0.434997
\(204\) −5.22425 −0.365771
\(205\) −8.30700 −0.580186
\(206\) −15.3143 −1.06700
\(207\) −12.8940 −0.896192
\(208\) −1.99090 −0.138044
\(209\) −8.12417 −0.561960
\(210\) 4.70594 0.324741
\(211\) 17.8337 1.22772 0.613861 0.789414i \(-0.289615\pi\)
0.613861 + 0.789414i \(0.289615\pi\)
\(212\) −7.11992 −0.488998
\(213\) 1.20448 0.0825293
\(214\) 14.4192 0.985679
\(215\) 30.2349 2.06200
\(216\) 4.82940 0.328599
\(217\) −1.70231 −0.115560
\(218\) −2.62093 −0.177512
\(219\) 6.70103 0.452813
\(220\) 6.85545 0.462195
\(221\) −10.9947 −0.739585
\(222\) −6.01645 −0.403798
\(223\) −3.72901 −0.249713 −0.124856 0.992175i \(-0.539847\pi\)
−0.124856 + 0.992175i \(0.539847\pi\)
\(224\) 2.03235 0.135792
\(225\) −2.08662 −0.139108
\(226\) −11.3017 −0.751780
\(227\) −27.0598 −1.79602 −0.898010 0.439975i \(-0.854987\pi\)
−0.898010 + 0.439975i \(0.854987\pi\)
\(228\) −2.74404 −0.181728
\(229\) −13.4293 −0.887430 −0.443715 0.896168i \(-0.646340\pi\)
−0.443715 + 0.896168i \(0.646340\pi\)
\(230\) −14.9925 −0.988575
\(231\) 5.38477 0.354292
\(232\) −3.04955 −0.200213
\(233\) 25.4347 1.66629 0.833143 0.553058i \(-0.186539\pi\)
0.833143 + 0.553058i \(0.186539\pi\)
\(234\) 4.19103 0.273976
\(235\) 21.5217 1.40392
\(236\) 0.529488 0.0344667
\(237\) 8.26767 0.537043
\(238\) 11.2236 0.727519
\(239\) −15.9974 −1.03478 −0.517391 0.855749i \(-0.673097\pi\)
−0.517391 + 0.855749i \(0.673097\pi\)
\(240\) 2.31551 0.149466
\(241\) 29.8860 1.92512 0.962562 0.271061i \(-0.0873745\pi\)
0.962562 + 0.271061i \(0.0873745\pi\)
\(242\) −3.15565 −0.202853
\(243\) −16.1405 −1.03542
\(244\) −7.57201 −0.484748
\(245\) 7.02379 0.448734
\(246\) −3.21053 −0.204696
\(247\) −5.77498 −0.367453
\(248\) −0.837606 −0.0531881
\(249\) 14.2650 0.904010
\(250\) 9.81227 0.620582
\(251\) 22.8719 1.44366 0.721831 0.692070i \(-0.243301\pi\)
0.721831 + 0.692070i \(0.243301\pi\)
\(252\) −4.27828 −0.269506
\(253\) −17.1551 −1.07853
\(254\) −1.86707 −0.117151
\(255\) 12.7874 0.800777
\(256\) 1.00000 0.0625000
\(257\) 21.6713 1.35182 0.675909 0.736985i \(-0.263751\pi\)
0.675909 + 0.736985i \(0.263751\pi\)
\(258\) 11.6853 0.727495
\(259\) 12.9256 0.803155
\(260\) 4.87312 0.302218
\(261\) 6.41958 0.397362
\(262\) −4.97772 −0.307524
\(263\) −1.96752 −0.121323 −0.0606613 0.998158i \(-0.519321\pi\)
−0.0606613 + 0.998158i \(0.519321\pi\)
\(264\) 2.64953 0.163067
\(265\) 17.4274 1.07056
\(266\) 5.89521 0.361458
\(267\) −9.80071 −0.599794
\(268\) −0.246931 −0.0150837
\(269\) −7.94985 −0.484711 −0.242355 0.970188i \(-0.577920\pi\)
−0.242355 + 0.970188i \(0.577920\pi\)
\(270\) −11.8209 −0.719398
\(271\) −23.2965 −1.41516 −0.707582 0.706631i \(-0.750214\pi\)
−0.707582 + 0.706631i \(0.750214\pi\)
\(272\) 5.52248 0.334850
\(273\) 3.82770 0.231663
\(274\) −16.0530 −0.969799
\(275\) −2.77620 −0.167411
\(276\) −5.79436 −0.348780
\(277\) −27.0992 −1.62823 −0.814116 0.580702i \(-0.802778\pi\)
−0.814116 + 0.580702i \(0.802778\pi\)
\(278\) −16.7441 −1.00425
\(279\) 1.76324 0.105562
\(280\) −4.97458 −0.297288
\(281\) −10.1699 −0.606687 −0.303343 0.952881i \(-0.598103\pi\)
−0.303343 + 0.952881i \(0.598103\pi\)
\(282\) 8.31781 0.495319
\(283\) −19.4096 −1.15378 −0.576890 0.816822i \(-0.695734\pi\)
−0.576890 + 0.816822i \(0.695734\pi\)
\(284\) −1.27323 −0.0755525
\(285\) 6.71658 0.397856
\(286\) 5.57607 0.329720
\(287\) 6.89739 0.407140
\(288\) −2.10509 −0.124044
\(289\) 13.4978 0.793989
\(290\) 7.46438 0.438323
\(291\) −1.28160 −0.0751290
\(292\) −7.08356 −0.414534
\(293\) −4.93456 −0.288280 −0.144140 0.989557i \(-0.546042\pi\)
−0.144140 + 0.989557i \(0.546042\pi\)
\(294\) 2.71459 0.158318
\(295\) −1.29603 −0.0754576
\(296\) 6.35990 0.369662
\(297\) −13.5261 −0.784862
\(298\) −9.63045 −0.557877
\(299\) −12.1945 −0.705229
\(300\) −0.937697 −0.0541379
\(301\) −25.1043 −1.44699
\(302\) 11.0569 0.636253
\(303\) 2.52324 0.144956
\(304\) 2.90068 0.166366
\(305\) 18.5340 1.06125
\(306\) −11.6253 −0.664575
\(307\) −15.2499 −0.870360 −0.435180 0.900343i \(-0.643315\pi\)
−0.435180 + 0.900343i \(0.643315\pi\)
\(308\) −5.69216 −0.324341
\(309\) 14.4873 0.824152
\(310\) 2.05021 0.116444
\(311\) 21.6782 1.22926 0.614630 0.788815i \(-0.289305\pi\)
0.614630 + 0.788815i \(0.289305\pi\)
\(312\) 1.88339 0.106626
\(313\) −15.4715 −0.874499 −0.437249 0.899340i \(-0.644047\pi\)
−0.437249 + 0.899340i \(0.644047\pi\)
\(314\) 23.6561 1.33499
\(315\) 10.4719 0.590027
\(316\) −8.73964 −0.491643
\(317\) −1.67493 −0.0940733 −0.0470367 0.998893i \(-0.514978\pi\)
−0.0470367 + 0.998893i \(0.514978\pi\)
\(318\) 6.73542 0.377704
\(319\) 8.54111 0.478210
\(320\) −2.44770 −0.136830
\(321\) −13.6406 −0.761342
\(322\) 12.4484 0.693724
\(323\) 16.0190 0.891320
\(324\) 1.74667 0.0970373
\(325\) −1.97343 −0.109466
\(326\) 1.48955 0.0824987
\(327\) 2.47939 0.137111
\(328\) 3.39380 0.187391
\(329\) −17.8697 −0.985190
\(330\) −6.48524 −0.357001
\(331\) 15.1393 0.832131 0.416066 0.909335i \(-0.363409\pi\)
0.416066 + 0.909335i \(0.363409\pi\)
\(332\) −15.0794 −0.827588
\(333\) −13.3882 −0.733667
\(334\) 10.1098 0.553184
\(335\) 0.604411 0.0330225
\(336\) −1.92260 −0.104886
\(337\) −14.3131 −0.779687 −0.389843 0.920881i \(-0.627471\pi\)
−0.389843 + 0.920881i \(0.627471\pi\)
\(338\) −9.03631 −0.491511
\(339\) 10.6914 0.580677
\(340\) −13.5174 −0.733082
\(341\) 2.34595 0.127040
\(342\) −6.10620 −0.330186
\(343\) −20.0584 −1.08305
\(344\) −12.3524 −0.665995
\(345\) 14.1828 0.763579
\(346\) −7.11640 −0.382580
\(347\) −29.7433 −1.59670 −0.798351 0.602192i \(-0.794294\pi\)
−0.798351 + 0.602192i \(0.794294\pi\)
\(348\) 2.88487 0.154645
\(349\) −18.8272 −1.00780 −0.503898 0.863763i \(-0.668101\pi\)
−0.503898 + 0.863763i \(0.668101\pi\)
\(350\) 2.01452 0.107681
\(351\) −9.61486 −0.513203
\(352\) −2.80078 −0.149282
\(353\) −14.7578 −0.785477 −0.392738 0.919650i \(-0.628472\pi\)
−0.392738 + 0.919650i \(0.628472\pi\)
\(354\) −0.500894 −0.0266222
\(355\) 3.11649 0.165406
\(356\) 10.3602 0.549089
\(357\) −10.6175 −0.561938
\(358\) −24.0359 −1.27034
\(359\) 22.4878 1.18686 0.593431 0.804885i \(-0.297773\pi\)
0.593431 + 0.804885i \(0.297773\pi\)
\(360\) 5.15262 0.271567
\(361\) −10.5860 −0.557160
\(362\) −10.7648 −0.565788
\(363\) 2.98524 0.156684
\(364\) −4.04621 −0.212079
\(365\) 17.3384 0.907534
\(366\) 7.16310 0.374421
\(367\) 37.2009 1.94187 0.970936 0.239341i \(-0.0769314\pi\)
0.970936 + 0.239341i \(0.0769314\pi\)
\(368\) 6.12514 0.319295
\(369\) −7.14426 −0.371915
\(370\) −15.5671 −0.809296
\(371\) −14.4702 −0.751254
\(372\) 0.792373 0.0410826
\(373\) −23.6565 −1.22489 −0.612444 0.790514i \(-0.709813\pi\)
−0.612444 + 0.790514i \(0.709813\pi\)
\(374\) −15.4672 −0.799792
\(375\) −9.28238 −0.479340
\(376\) −8.79264 −0.453446
\(377\) 6.07135 0.312691
\(378\) 9.81503 0.504831
\(379\) 11.7923 0.605732 0.302866 0.953033i \(-0.402057\pi\)
0.302866 + 0.953033i \(0.402057\pi\)
\(380\) −7.10000 −0.364222
\(381\) 1.76625 0.0904875
\(382\) 21.1184 1.08051
\(383\) −36.7542 −1.87805 −0.939025 0.343848i \(-0.888269\pi\)
−0.939025 + 0.343848i \(0.888269\pi\)
\(384\) −0.945997 −0.0482752
\(385\) 13.9327 0.710075
\(386\) 16.5811 0.843958
\(387\) 26.0028 1.32180
\(388\) 1.35477 0.0687778
\(389\) 28.9807 1.46938 0.734690 0.678403i \(-0.237328\pi\)
0.734690 + 0.678403i \(0.237328\pi\)
\(390\) −4.60996 −0.233434
\(391\) 33.8260 1.71065
\(392\) −2.86955 −0.144934
\(393\) 4.70891 0.237533
\(394\) 17.8425 0.898891
\(395\) 21.3920 1.07635
\(396\) 5.89589 0.296279
\(397\) −34.8860 −1.75088 −0.875439 0.483329i \(-0.839428\pi\)
−0.875439 + 0.483329i \(0.839428\pi\)
\(398\) −2.34031 −0.117309
\(399\) −5.57685 −0.279192
\(400\) 0.991226 0.0495613
\(401\) 0.263485 0.0131578 0.00657891 0.999978i \(-0.497906\pi\)
0.00657891 + 0.999978i \(0.497906\pi\)
\(402\) 0.233596 0.0116507
\(403\) 1.66759 0.0830686
\(404\) −2.66728 −0.132702
\(405\) −4.27533 −0.212443
\(406\) −6.19775 −0.307589
\(407\) −17.8127 −0.882941
\(408\) −5.22425 −0.258639
\(409\) −6.03471 −0.298397 −0.149199 0.988807i \(-0.547669\pi\)
−0.149199 + 0.988807i \(0.547669\pi\)
\(410\) −8.30700 −0.410254
\(411\) 15.1861 0.749076
\(412\) −15.3143 −0.754480
\(413\) 1.07611 0.0529517
\(414\) −12.8940 −0.633704
\(415\) 36.9097 1.81183
\(416\) −1.99090 −0.0976120
\(417\) 15.8399 0.775683
\(418\) −8.12417 −0.397366
\(419\) 17.2897 0.844658 0.422329 0.906443i \(-0.361213\pi\)
0.422329 + 0.906443i \(0.361213\pi\)
\(420\) 4.70594 0.229626
\(421\) −21.0468 −1.02576 −0.512879 0.858461i \(-0.671421\pi\)
−0.512879 + 0.858461i \(0.671421\pi\)
\(422\) 17.8337 0.868131
\(423\) 18.5093 0.899953
\(424\) −7.11992 −0.345774
\(425\) 5.47403 0.265529
\(426\) 1.20448 0.0583570
\(427\) −15.3890 −0.744725
\(428\) 14.4192 0.696980
\(429\) −5.27494 −0.254677
\(430\) 30.2349 1.45805
\(431\) −37.9200 −1.82654 −0.913272 0.407350i \(-0.866453\pi\)
−0.913272 + 0.407350i \(0.866453\pi\)
\(432\) 4.82940 0.232355
\(433\) −31.0593 −1.49262 −0.746308 0.665601i \(-0.768175\pi\)
−0.746308 + 0.665601i \(0.768175\pi\)
\(434\) −1.70231 −0.0817135
\(435\) −7.06128 −0.338562
\(436\) −2.62093 −0.125520
\(437\) 17.7671 0.849915
\(438\) 6.70103 0.320187
\(439\) 14.5169 0.692854 0.346427 0.938077i \(-0.387395\pi\)
0.346427 + 0.938077i \(0.387395\pi\)
\(440\) 6.85545 0.326821
\(441\) 6.04066 0.287651
\(442\) −10.9947 −0.522965
\(443\) 2.05491 0.0976315 0.0488157 0.998808i \(-0.484455\pi\)
0.0488157 + 0.998808i \(0.484455\pi\)
\(444\) −6.01645 −0.285528
\(445\) −25.3586 −1.20211
\(446\) −3.72901 −0.176574
\(447\) 9.11038 0.430906
\(448\) 2.03235 0.0960195
\(449\) 14.0686 0.663937 0.331969 0.943290i \(-0.392287\pi\)
0.331969 + 0.943290i \(0.392287\pi\)
\(450\) −2.08662 −0.0983642
\(451\) −9.50528 −0.447586
\(452\) −11.3017 −0.531589
\(453\) −10.4598 −0.491444
\(454\) −27.0598 −1.26998
\(455\) 9.90390 0.464302
\(456\) −2.74404 −0.128501
\(457\) 2.31968 0.108510 0.0542550 0.998527i \(-0.482722\pi\)
0.0542550 + 0.998527i \(0.482722\pi\)
\(458\) −13.4293 −0.627508
\(459\) 26.6703 1.24486
\(460\) −14.9925 −0.699028
\(461\) −5.12438 −0.238666 −0.119333 0.992854i \(-0.538076\pi\)
−0.119333 + 0.992854i \(0.538076\pi\)
\(462\) 5.38477 0.250522
\(463\) 14.2523 0.662360 0.331180 0.943568i \(-0.392553\pi\)
0.331180 + 0.943568i \(0.392553\pi\)
\(464\) −3.04955 −0.141572
\(465\) −1.93949 −0.0899417
\(466\) 25.4347 1.17824
\(467\) 13.4011 0.620128 0.310064 0.950716i \(-0.399650\pi\)
0.310064 + 0.950716i \(0.399650\pi\)
\(468\) 4.19103 0.193730
\(469\) −0.501849 −0.0231733
\(470\) 21.5217 0.992724
\(471\) −22.3786 −1.03115
\(472\) 0.529488 0.0243717
\(473\) 34.5962 1.59074
\(474\) 8.26767 0.379747
\(475\) 2.87523 0.131925
\(476\) 11.2236 0.514434
\(477\) 14.9881 0.686257
\(478\) −15.9974 −0.731702
\(479\) 34.5704 1.57956 0.789780 0.613390i \(-0.210195\pi\)
0.789780 + 0.613390i \(0.210195\pi\)
\(480\) 2.31551 0.105688
\(481\) −12.6619 −0.577335
\(482\) 29.8860 1.36127
\(483\) −11.7762 −0.535834
\(484\) −3.15565 −0.143439
\(485\) −3.31606 −0.150574
\(486\) −16.1405 −0.732150
\(487\) 21.3436 0.967170 0.483585 0.875297i \(-0.339334\pi\)
0.483585 + 0.875297i \(0.339334\pi\)
\(488\) −7.57201 −0.342769
\(489\) −1.40911 −0.0637223
\(490\) 7.02379 0.317303
\(491\) 38.9925 1.75971 0.879854 0.475245i \(-0.157640\pi\)
0.879854 + 0.475245i \(0.157640\pi\)
\(492\) −3.21053 −0.144742
\(493\) −16.8411 −0.758484
\(494\) −5.77498 −0.259828
\(495\) −14.4313 −0.648641
\(496\) −0.837606 −0.0376096
\(497\) −2.58766 −0.116072
\(498\) 14.2650 0.639232
\(499\) −34.5883 −1.54838 −0.774191 0.632952i \(-0.781843\pi\)
−0.774191 + 0.632952i \(0.781843\pi\)
\(500\) 9.81227 0.438818
\(501\) −9.56385 −0.427281
\(502\) 22.8719 1.02082
\(503\) 0.0152657 0.000680664 0 0.000340332 1.00000i \(-0.499892\pi\)
0.000340332 1.00000i \(0.499892\pi\)
\(504\) −4.27828 −0.190570
\(505\) 6.52870 0.290523
\(506\) −17.1551 −0.762639
\(507\) 8.54832 0.379644
\(508\) −1.86707 −0.0828380
\(509\) 33.0886 1.46663 0.733313 0.679891i \(-0.237973\pi\)
0.733313 + 0.679891i \(0.237973\pi\)
\(510\) 12.7874 0.566235
\(511\) −14.3963 −0.636854
\(512\) 1.00000 0.0441942
\(513\) 14.0086 0.618493
\(514\) 21.6713 0.955879
\(515\) 37.4847 1.65177
\(516\) 11.6853 0.514417
\(517\) 24.6262 1.08306
\(518\) 12.9256 0.567916
\(519\) 6.73209 0.295506
\(520\) 4.87312 0.213701
\(521\) 2.38215 0.104364 0.0521820 0.998638i \(-0.483382\pi\)
0.0521820 + 0.998638i \(0.483382\pi\)
\(522\) 6.41958 0.280977
\(523\) −2.31364 −0.101169 −0.0505843 0.998720i \(-0.516108\pi\)
−0.0505843 + 0.998720i \(0.516108\pi\)
\(524\) −4.97772 −0.217453
\(525\) −1.90573 −0.0831728
\(526\) −1.96752 −0.0857880
\(527\) −4.62567 −0.201497
\(528\) 2.64953 0.115306
\(529\) 14.5173 0.631187
\(530\) 17.4274 0.756999
\(531\) −1.11462 −0.0483704
\(532\) 5.89521 0.255590
\(533\) −6.75672 −0.292666
\(534\) −9.80071 −0.424118
\(535\) −35.2940 −1.52589
\(536\) −0.246931 −0.0106658
\(537\) 22.7379 0.981212
\(538\) −7.94985 −0.342742
\(539\) 8.03697 0.346177
\(540\) −11.8209 −0.508691
\(541\) 34.4381 1.48061 0.740306 0.672270i \(-0.234681\pi\)
0.740306 + 0.672270i \(0.234681\pi\)
\(542\) −23.2965 −1.00067
\(543\) 10.1835 0.437016
\(544\) 5.52248 0.236774
\(545\) 6.41524 0.274799
\(546\) 3.82770 0.163810
\(547\) 40.0425 1.71209 0.856046 0.516900i \(-0.172914\pi\)
0.856046 + 0.516900i \(0.172914\pi\)
\(548\) −16.0530 −0.685751
\(549\) 15.9398 0.680292
\(550\) −2.77620 −0.118378
\(551\) −8.84578 −0.376843
\(552\) −5.79436 −0.246624
\(553\) −17.7620 −0.755317
\(554\) −27.0992 −1.15133
\(555\) 14.7265 0.625103
\(556\) −16.7441 −0.710110
\(557\) −24.8877 −1.05453 −0.527263 0.849702i \(-0.676782\pi\)
−0.527263 + 0.849702i \(0.676782\pi\)
\(558\) 1.76324 0.0746438
\(559\) 24.5923 1.04014
\(560\) −4.97458 −0.210214
\(561\) 14.6320 0.617762
\(562\) −10.1699 −0.428992
\(563\) −5.50949 −0.232197 −0.116099 0.993238i \(-0.537039\pi\)
−0.116099 + 0.993238i \(0.537039\pi\)
\(564\) 8.31781 0.350243
\(565\) 27.6632 1.16380
\(566\) −19.4096 −0.815845
\(567\) 3.54985 0.149080
\(568\) −1.27323 −0.0534237
\(569\) 32.9404 1.38093 0.690467 0.723364i \(-0.257405\pi\)
0.690467 + 0.723364i \(0.257405\pi\)
\(570\) 6.71658 0.281326
\(571\) 42.1235 1.76281 0.881407 0.472358i \(-0.156597\pi\)
0.881407 + 0.472358i \(0.156597\pi\)
\(572\) 5.57607 0.233147
\(573\) −19.9779 −0.834590
\(574\) 6.89739 0.287892
\(575\) 6.07139 0.253195
\(576\) −2.10509 −0.0877121
\(577\) −24.5786 −1.02322 −0.511611 0.859217i \(-0.670951\pi\)
−0.511611 + 0.859217i \(0.670951\pi\)
\(578\) 13.4978 0.561435
\(579\) −15.6857 −0.651876
\(580\) 7.46438 0.309941
\(581\) −30.6466 −1.27143
\(582\) −1.28160 −0.0531242
\(583\) 19.9413 0.825885
\(584\) −7.08356 −0.293120
\(585\) −10.2584 −0.424131
\(586\) −4.93456 −0.203845
\(587\) 25.2733 1.04314 0.521570 0.853209i \(-0.325347\pi\)
0.521570 + 0.853209i \(0.325347\pi\)
\(588\) 2.71459 0.111948
\(589\) −2.42963 −0.100111
\(590\) −1.29603 −0.0533566
\(591\) −16.8789 −0.694307
\(592\) 6.35990 0.261390
\(593\) 10.3757 0.426079 0.213040 0.977044i \(-0.431664\pi\)
0.213040 + 0.977044i \(0.431664\pi\)
\(594\) −13.5261 −0.554981
\(595\) −27.4720 −1.12624
\(596\) −9.63045 −0.394479
\(597\) 2.21393 0.0906102
\(598\) −12.1945 −0.498672
\(599\) 14.9728 0.611771 0.305885 0.952068i \(-0.401048\pi\)
0.305885 + 0.952068i \(0.401048\pi\)
\(600\) −0.937697 −0.0382813
\(601\) 25.0716 1.02269 0.511347 0.859375i \(-0.329147\pi\)
0.511347 + 0.859375i \(0.329147\pi\)
\(602\) −25.1043 −1.02318
\(603\) 0.519811 0.0211683
\(604\) 11.0569 0.449899
\(605\) 7.72408 0.314029
\(606\) 2.52324 0.102500
\(607\) 5.27851 0.214248 0.107124 0.994246i \(-0.465836\pi\)
0.107124 + 0.994246i \(0.465836\pi\)
\(608\) 2.90068 0.117638
\(609\) 5.86306 0.237583
\(610\) 18.5340 0.750419
\(611\) 17.5053 0.708188
\(612\) −11.6253 −0.469926
\(613\) 35.5060 1.43407 0.717037 0.697036i \(-0.245498\pi\)
0.717037 + 0.697036i \(0.245498\pi\)
\(614\) −15.2499 −0.615438
\(615\) 7.85840 0.316881
\(616\) −5.69216 −0.229344
\(617\) −16.3935 −0.659976 −0.329988 0.943985i \(-0.607045\pi\)
−0.329988 + 0.943985i \(0.607045\pi\)
\(618\) 14.4873 0.582763
\(619\) −35.3362 −1.42028 −0.710141 0.704059i \(-0.751369\pi\)
−0.710141 + 0.704059i \(0.751369\pi\)
\(620\) 2.05021 0.0823383
\(621\) 29.5807 1.18703
\(622\) 21.6782 0.869218
\(623\) 21.0556 0.843573
\(624\) 1.88339 0.0753958
\(625\) −28.9736 −1.15894
\(626\) −15.4715 −0.618364
\(627\) 7.68544 0.306927
\(628\) 23.6561 0.943982
\(629\) 35.1225 1.40042
\(630\) 10.4719 0.417212
\(631\) 8.66161 0.344813 0.172407 0.985026i \(-0.444846\pi\)
0.172407 + 0.985026i \(0.444846\pi\)
\(632\) −8.73964 −0.347644
\(633\) −16.8706 −0.670547
\(634\) −1.67493 −0.0665199
\(635\) 4.57003 0.181356
\(636\) 6.73542 0.267077
\(637\) 5.71299 0.226357
\(638\) 8.54111 0.338146
\(639\) 2.68027 0.106030
\(640\) −2.44770 −0.0967538
\(641\) 29.1668 1.15202 0.576010 0.817442i \(-0.304609\pi\)
0.576010 + 0.817442i \(0.304609\pi\)
\(642\) −13.6406 −0.538350
\(643\) −26.7037 −1.05309 −0.526546 0.850146i \(-0.676513\pi\)
−0.526546 + 0.850146i \(0.676513\pi\)
\(644\) 12.4484 0.490537
\(645\) −28.6021 −1.12621
\(646\) 16.0190 0.630258
\(647\) 29.4245 1.15680 0.578398 0.815755i \(-0.303678\pi\)
0.578398 + 0.815755i \(0.303678\pi\)
\(648\) 1.74667 0.0686157
\(649\) −1.48298 −0.0582120
\(650\) −1.97343 −0.0774044
\(651\) 1.61038 0.0631158
\(652\) 1.48955 0.0583354
\(653\) −12.0244 −0.470552 −0.235276 0.971929i \(-0.575599\pi\)
−0.235276 + 0.971929i \(0.575599\pi\)
\(654\) 2.47939 0.0969518
\(655\) 12.1839 0.476066
\(656\) 3.39380 0.132506
\(657\) 14.9115 0.581754
\(658\) −17.8697 −0.696635
\(659\) 47.0705 1.83361 0.916803 0.399340i \(-0.130761\pi\)
0.916803 + 0.399340i \(0.130761\pi\)
\(660\) −6.48524 −0.252438
\(661\) −13.1809 −0.512677 −0.256338 0.966587i \(-0.582516\pi\)
−0.256338 + 0.966587i \(0.582516\pi\)
\(662\) 15.1393 0.588406
\(663\) 10.4010 0.403940
\(664\) −15.0794 −0.585193
\(665\) −14.4297 −0.559559
\(666\) −13.3882 −0.518781
\(667\) −18.6789 −0.723250
\(668\) 10.1098 0.391160
\(669\) 3.52763 0.136386
\(670\) 0.604411 0.0233504
\(671\) 21.2075 0.818706
\(672\) −1.92260 −0.0741658
\(673\) −21.3885 −0.824465 −0.412232 0.911079i \(-0.635251\pi\)
−0.412232 + 0.911079i \(0.635251\pi\)
\(674\) −14.3131 −0.551322
\(675\) 4.78703 0.184253
\(676\) −9.03631 −0.347551
\(677\) 4.15572 0.159717 0.0798587 0.996806i \(-0.474553\pi\)
0.0798587 + 0.996806i \(0.474553\pi\)
\(678\) 10.6914 0.410601
\(679\) 2.75336 0.105664
\(680\) −13.5174 −0.518367
\(681\) 25.5985 0.980935
\(682\) 2.34595 0.0898310
\(683\) −24.6042 −0.941452 −0.470726 0.882279i \(-0.656008\pi\)
−0.470726 + 0.882279i \(0.656008\pi\)
\(684\) −6.10620 −0.233476
\(685\) 39.2930 1.50131
\(686\) −20.0584 −0.765833
\(687\) 12.7040 0.484689
\(688\) −12.3524 −0.470929
\(689\) 14.1751 0.540027
\(690\) 14.1828 0.539932
\(691\) −34.8010 −1.32389 −0.661947 0.749551i \(-0.730270\pi\)
−0.661947 + 0.749551i \(0.730270\pi\)
\(692\) −7.11640 −0.270525
\(693\) 11.9825 0.455178
\(694\) −29.7433 −1.12904
\(695\) 40.9846 1.55463
\(696\) 2.88487 0.109351
\(697\) 18.7422 0.709912
\(698\) −18.8272 −0.712619
\(699\) −24.0612 −0.910078
\(700\) 2.01452 0.0761416
\(701\) 33.1897 1.25356 0.626778 0.779198i \(-0.284373\pi\)
0.626778 + 0.779198i \(0.284373\pi\)
\(702\) −9.61486 −0.362889
\(703\) 18.4481 0.695782
\(704\) −2.80078 −0.105558
\(705\) −20.3595 −0.766783
\(706\) −14.7578 −0.555416
\(707\) −5.42085 −0.203872
\(708\) −0.500894 −0.0188247
\(709\) −33.6642 −1.26429 −0.632143 0.774852i \(-0.717825\pi\)
−0.632143 + 0.774852i \(0.717825\pi\)
\(710\) 3.11649 0.116960
\(711\) 18.3977 0.689968
\(712\) 10.3602 0.388265
\(713\) −5.13045 −0.192137
\(714\) −10.6175 −0.397350
\(715\) −13.6485 −0.510426
\(716\) −24.0359 −0.898263
\(717\) 15.1335 0.565169
\(718\) 22.4878 0.839238
\(719\) −35.4095 −1.32055 −0.660276 0.751023i \(-0.729561\pi\)
−0.660276 + 0.751023i \(0.729561\pi\)
\(720\) 5.15262 0.192027
\(721\) −31.1240 −1.15912
\(722\) −10.5860 −0.393971
\(723\) −28.2720 −1.05145
\(724\) −10.7648 −0.400072
\(725\) −3.02279 −0.112264
\(726\) 2.98524 0.110793
\(727\) −47.5717 −1.76434 −0.882168 0.470934i \(-0.843917\pi\)
−0.882168 + 0.470934i \(0.843917\pi\)
\(728\) −4.04621 −0.149962
\(729\) 10.0289 0.371440
\(730\) 17.3384 0.641724
\(731\) −68.2157 −2.52305
\(732\) 7.16310 0.264756
\(733\) −6.24495 −0.230662 −0.115331 0.993327i \(-0.536793\pi\)
−0.115331 + 0.993327i \(0.536793\pi\)
\(734\) 37.2009 1.37311
\(735\) −6.64449 −0.245086
\(736\) 6.12514 0.225776
\(737\) 0.691597 0.0254753
\(738\) −7.14426 −0.262984
\(739\) −21.8883 −0.805174 −0.402587 0.915382i \(-0.631889\pi\)
−0.402587 + 0.915382i \(0.631889\pi\)
\(740\) −15.5671 −0.572259
\(741\) 5.46311 0.200692
\(742\) −14.4702 −0.531217
\(743\) 41.8899 1.53679 0.768396 0.639974i \(-0.221055\pi\)
0.768396 + 0.639974i \(0.221055\pi\)
\(744\) 0.792373 0.0290498
\(745\) 23.5724 0.863627
\(746\) −23.6565 −0.866126
\(747\) 31.7434 1.16143
\(748\) −15.4672 −0.565538
\(749\) 29.3050 1.07078
\(750\) −9.28238 −0.338944
\(751\) 14.7118 0.536843 0.268421 0.963302i \(-0.413498\pi\)
0.268421 + 0.963302i \(0.413498\pi\)
\(752\) −8.79264 −0.320635
\(753\) −21.6367 −0.788487
\(754\) 6.07135 0.221106
\(755\) −27.0639 −0.984958
\(756\) 9.81503 0.356969
\(757\) −43.7693 −1.59082 −0.795411 0.606070i \(-0.792745\pi\)
−0.795411 + 0.606070i \(0.792745\pi\)
\(758\) 11.7923 0.428317
\(759\) 16.2287 0.589065
\(760\) −7.10000 −0.257544
\(761\) −33.5741 −1.21706 −0.608531 0.793530i \(-0.708241\pi\)
−0.608531 + 0.793530i \(0.708241\pi\)
\(762\) 1.76625 0.0639843
\(763\) −5.32665 −0.192838
\(764\) 21.1184 0.764037
\(765\) 28.4553 1.02880
\(766\) −36.7542 −1.32798
\(767\) −1.05416 −0.0380634
\(768\) −0.945997 −0.0341357
\(769\) 47.2920 1.70539 0.852697 0.522406i \(-0.174966\pi\)
0.852697 + 0.522406i \(0.174966\pi\)
\(770\) 13.9327 0.502099
\(771\) −20.5010 −0.738324
\(772\) 16.5811 0.596768
\(773\) 15.0744 0.542190 0.271095 0.962553i \(-0.412614\pi\)
0.271095 + 0.962553i \(0.412614\pi\)
\(774\) 26.0028 0.934653
\(775\) −0.830257 −0.0298237
\(776\) 1.35477 0.0486332
\(777\) −12.2275 −0.438660
\(778\) 28.9807 1.03901
\(779\) 9.84435 0.352710
\(780\) −4.60996 −0.165063
\(781\) 3.56604 0.127603
\(782\) 33.8260 1.20961
\(783\) −14.7275 −0.526318
\(784\) −2.86955 −0.102484
\(785\) −57.9030 −2.06665
\(786\) 4.70891 0.167961
\(787\) −28.4058 −1.01256 −0.506279 0.862370i \(-0.668979\pi\)
−0.506279 + 0.862370i \(0.668979\pi\)
\(788\) 17.8425 0.635612
\(789\) 1.86127 0.0662629
\(790\) 21.3920 0.761093
\(791\) −22.9691 −0.816686
\(792\) 5.89589 0.209501
\(793\) 15.0751 0.535333
\(794\) −34.8860 −1.23806
\(795\) −16.4863 −0.584708
\(796\) −2.34031 −0.0829503
\(797\) 10.1299 0.358819 0.179409 0.983775i \(-0.442581\pi\)
0.179409 + 0.983775i \(0.442581\pi\)
\(798\) −5.57685 −0.197418
\(799\) −48.5572 −1.71783
\(800\) 0.991226 0.0350451
\(801\) −21.8091 −0.770588
\(802\) 0.263485 0.00930398
\(803\) 19.8395 0.700120
\(804\) 0.233596 0.00823828
\(805\) −30.4700 −1.07393
\(806\) 1.66759 0.0587384
\(807\) 7.52053 0.264735
\(808\) −2.66728 −0.0938346
\(809\) −19.6349 −0.690327 −0.345164 0.938543i \(-0.612177\pi\)
−0.345164 + 0.938543i \(0.612177\pi\)
\(810\) −4.27533 −0.150220
\(811\) 32.6240 1.14558 0.572791 0.819701i \(-0.305861\pi\)
0.572791 + 0.819701i \(0.305861\pi\)
\(812\) −6.19775 −0.217499
\(813\) 22.0385 0.772922
\(814\) −17.8127 −0.624334
\(815\) −3.64598 −0.127713
\(816\) −5.22425 −0.182885
\(817\) −35.8303 −1.25354
\(818\) −6.03471 −0.210999
\(819\) 8.51763 0.297630
\(820\) −8.30700 −0.290093
\(821\) −50.2708 −1.75446 −0.877232 0.480066i \(-0.840613\pi\)
−0.877232 + 0.480066i \(0.840613\pi\)
\(822\) 15.1861 0.529677
\(823\) 24.3559 0.848992 0.424496 0.905430i \(-0.360451\pi\)
0.424496 + 0.905430i \(0.360451\pi\)
\(824\) −15.3143 −0.533498
\(825\) 2.62628 0.0914353
\(826\) 1.07611 0.0374425
\(827\) −36.9365 −1.28441 −0.642204 0.766533i \(-0.721980\pi\)
−0.642204 + 0.766533i \(0.721980\pi\)
\(828\) −12.8940 −0.448096
\(829\) −35.1963 −1.22242 −0.611209 0.791470i \(-0.709316\pi\)
−0.611209 + 0.791470i \(0.709316\pi\)
\(830\) 36.9097 1.28116
\(831\) 25.6358 0.889294
\(832\) −1.99090 −0.0690221
\(833\) −15.8470 −0.549068
\(834\) 15.8399 0.548491
\(835\) −24.7458 −0.856362
\(836\) −8.12417 −0.280980
\(837\) −4.04514 −0.139820
\(838\) 17.2897 0.597263
\(839\) −45.7810 −1.58053 −0.790267 0.612762i \(-0.790058\pi\)
−0.790267 + 0.612762i \(0.790058\pi\)
\(840\) 4.70594 0.162370
\(841\) −19.7002 −0.679319
\(842\) −21.0468 −0.725320
\(843\) 9.62072 0.331355
\(844\) 17.8337 0.613861
\(845\) 22.1182 0.760888
\(846\) 18.5093 0.636363
\(847\) −6.41339 −0.220367
\(848\) −7.11992 −0.244499
\(849\) 18.3614 0.630162
\(850\) 5.47403 0.187758
\(851\) 38.9553 1.33537
\(852\) 1.20448 0.0412647
\(853\) 16.9231 0.579435 0.289718 0.957112i \(-0.406439\pi\)
0.289718 + 0.957112i \(0.406439\pi\)
\(854\) −15.3890 −0.526600
\(855\) 14.9461 0.511147
\(856\) 14.4192 0.492840
\(857\) −1.71618 −0.0586234 −0.0293117 0.999570i \(-0.509332\pi\)
−0.0293117 + 0.999570i \(0.509332\pi\)
\(858\) −5.27494 −0.180084
\(859\) −49.5674 −1.69122 −0.845609 0.533803i \(-0.820762\pi\)
−0.845609 + 0.533803i \(0.820762\pi\)
\(860\) 30.2349 1.03100
\(861\) −6.52491 −0.222368
\(862\) −37.9200 −1.29156
\(863\) 5.09731 0.173514 0.0867572 0.996229i \(-0.472350\pi\)
0.0867572 + 0.996229i \(0.472350\pi\)
\(864\) 4.82940 0.164300
\(865\) 17.4188 0.592257
\(866\) −31.0593 −1.05544
\(867\) −12.7689 −0.433654
\(868\) −1.70231 −0.0577802
\(869\) 24.4778 0.830351
\(870\) −7.06128 −0.239400
\(871\) 0.491614 0.0166577
\(872\) −2.62093 −0.0887558
\(873\) −2.85190 −0.0965223
\(874\) 17.7671 0.600981
\(875\) 19.9420 0.674162
\(876\) 6.70103 0.226407
\(877\) 37.3296 1.26053 0.630265 0.776380i \(-0.282946\pi\)
0.630265 + 0.776380i \(0.282946\pi\)
\(878\) 14.5169 0.489922
\(879\) 4.66808 0.157450
\(880\) 6.85545 0.231097
\(881\) −29.5385 −0.995179 −0.497589 0.867413i \(-0.665781\pi\)
−0.497589 + 0.867413i \(0.665781\pi\)
\(882\) 6.04066 0.203400
\(883\) −5.47182 −0.184141 −0.0920707 0.995752i \(-0.529349\pi\)
−0.0920707 + 0.995752i \(0.529349\pi\)
\(884\) −10.9947 −0.369792
\(885\) 1.22604 0.0412128
\(886\) 2.05491 0.0690359
\(887\) −1.83418 −0.0615859 −0.0307929 0.999526i \(-0.509803\pi\)
−0.0307929 + 0.999526i \(0.509803\pi\)
\(888\) −6.01645 −0.201899
\(889\) −3.79455 −0.127265
\(890\) −25.3586 −0.850023
\(891\) −4.89204 −0.163889
\(892\) −3.72901 −0.124856
\(893\) −25.5047 −0.853482
\(894\) 9.11038 0.304697
\(895\) 58.8326 1.96656
\(896\) 2.03235 0.0678961
\(897\) 11.5360 0.385176
\(898\) 14.0686 0.469475
\(899\) 2.55432 0.0851914
\(900\) −2.08662 −0.0695540
\(901\) −39.3196 −1.30993
\(902\) −9.50528 −0.316491
\(903\) 23.7486 0.790305
\(904\) −11.3017 −0.375890
\(905\) 26.3491 0.875874
\(906\) −10.4598 −0.347503
\(907\) 49.8121 1.65398 0.826991 0.562215i \(-0.190050\pi\)
0.826991 + 0.562215i \(0.190050\pi\)
\(908\) −27.0598 −0.898010
\(909\) 5.61486 0.186233
\(910\) 9.90390 0.328311
\(911\) 44.7340 1.48210 0.741052 0.671448i \(-0.234327\pi\)
0.741052 + 0.671448i \(0.234327\pi\)
\(912\) −2.74404 −0.0908642
\(913\) 42.2339 1.39774
\(914\) 2.31968 0.0767282
\(915\) −17.5331 −0.579626
\(916\) −13.4293 −0.443715
\(917\) −10.1165 −0.334075
\(918\) 26.6703 0.880250
\(919\) −12.9339 −0.426650 −0.213325 0.976981i \(-0.568429\pi\)
−0.213325 + 0.976981i \(0.568429\pi\)
\(920\) −14.9925 −0.494288
\(921\) 14.4264 0.475366
\(922\) −5.12438 −0.168762
\(923\) 2.53488 0.0834367
\(924\) 5.38477 0.177146
\(925\) 6.30410 0.207278
\(926\) 14.2523 0.468359
\(927\) 32.2379 1.05883
\(928\) −3.04955 −0.100106
\(929\) 22.8592 0.749987 0.374994 0.927027i \(-0.377645\pi\)
0.374994 + 0.927027i \(0.377645\pi\)
\(930\) −1.93949 −0.0635984
\(931\) −8.32366 −0.272797
\(932\) 25.4347 0.833143
\(933\) −20.5076 −0.671387
\(934\) 13.4011 0.438496
\(935\) 37.8591 1.23813
\(936\) 4.19103 0.136988
\(937\) 12.5428 0.409755 0.204877 0.978788i \(-0.434320\pi\)
0.204877 + 0.978788i \(0.434320\pi\)
\(938\) −0.501849 −0.0163860
\(939\) 14.6360 0.477626
\(940\) 21.5217 0.701962
\(941\) −45.9702 −1.49859 −0.749294 0.662238i \(-0.769607\pi\)
−0.749294 + 0.662238i \(0.769607\pi\)
\(942\) −22.3786 −0.729135
\(943\) 20.7875 0.676934
\(944\) 0.529488 0.0172334
\(945\) −24.0242 −0.781508
\(946\) 34.5962 1.12482
\(947\) −26.8961 −0.874006 −0.437003 0.899460i \(-0.643960\pi\)
−0.437003 + 0.899460i \(0.643960\pi\)
\(948\) 8.26767 0.268521
\(949\) 14.1027 0.457792
\(950\) 2.87523 0.0932849
\(951\) 1.58448 0.0513802
\(952\) 11.2236 0.363760
\(953\) 38.8508 1.25850 0.629250 0.777203i \(-0.283362\pi\)
0.629250 + 0.777203i \(0.283362\pi\)
\(954\) 14.9881 0.485257
\(955\) −51.6914 −1.67270
\(956\) −15.9974 −0.517391
\(957\) −8.07986 −0.261185
\(958\) 34.5704 1.11692
\(959\) −32.6254 −1.05353
\(960\) 2.31551 0.0747329
\(961\) −30.2984 −0.977368
\(962\) −12.6619 −0.408237
\(963\) −30.3538 −0.978138
\(964\) 29.8860 0.962562
\(965\) −40.5856 −1.30650
\(966\) −11.7762 −0.378892
\(967\) 7.68393 0.247098 0.123549 0.992338i \(-0.460572\pi\)
0.123549 + 0.992338i \(0.460572\pi\)
\(968\) −3.15565 −0.101427
\(969\) −15.1539 −0.486813
\(970\) −3.31606 −0.106472
\(971\) 61.5889 1.97648 0.988241 0.152901i \(-0.0488616\pi\)
0.988241 + 0.152901i \(0.0488616\pi\)
\(972\) −16.1405 −0.517708
\(973\) −34.0300 −1.09095
\(974\) 21.3436 0.683893
\(975\) 1.86686 0.0597874
\(976\) −7.57201 −0.242374
\(977\) 55.7670 1.78414 0.892072 0.451893i \(-0.149251\pi\)
0.892072 + 0.451893i \(0.149251\pi\)
\(978\) −1.40911 −0.0450585
\(979\) −29.0166 −0.927374
\(980\) 7.02379 0.224367
\(981\) 5.51729 0.176154
\(982\) 38.9925 1.24430
\(983\) 23.8112 0.759459 0.379730 0.925098i \(-0.376017\pi\)
0.379730 + 0.925098i \(0.376017\pi\)
\(984\) −3.21053 −0.102348
\(985\) −43.6730 −1.39154
\(986\) −16.8411 −0.536329
\(987\) 16.9047 0.538083
\(988\) −5.77498 −0.183726
\(989\) −75.6599 −2.40585
\(990\) −14.4313 −0.458658
\(991\) 23.4798 0.745862 0.372931 0.927859i \(-0.378353\pi\)
0.372931 + 0.927859i \(0.378353\pi\)
\(992\) −0.837606 −0.0265940
\(993\) −14.3217 −0.454486
\(994\) −2.58766 −0.0820755
\(995\) 5.72838 0.181602
\(996\) 14.2650 0.452005
\(997\) 54.6426 1.73055 0.865275 0.501298i \(-0.167144\pi\)
0.865275 + 0.501298i \(0.167144\pi\)
\(998\) −34.5883 −1.09487
\(999\) 30.7145 0.971764
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 4034.2.a.a.1.14 33
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.a.1.14 33 1.1 even 1 trivial