Properties

Label 6019.2.a.b.1.12
Level $6019$
Weight $2$
Character 6019.1
Self dual yes
Analytic conductor $48.062$
Analytic rank $1$
Dimension $101$
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] = [6019,2,Mod(1,6019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6019, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6019 = 13 \cdot 463 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6019.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: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(101\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 6019.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.32242 q^{2} +2.86947 q^{3} +3.39365 q^{4} +0.571930 q^{5} -6.66413 q^{6} -0.979167 q^{7} -3.23665 q^{8} +5.23387 q^{9} +O(q^{10})\) \(q-2.32242 q^{2} +2.86947 q^{3} +3.39365 q^{4} +0.571930 q^{5} -6.66413 q^{6} -0.979167 q^{7} -3.23665 q^{8} +5.23387 q^{9} -1.32826 q^{10} +2.35621 q^{11} +9.73799 q^{12} +1.00000 q^{13} +2.27404 q^{14} +1.64114 q^{15} +0.729563 q^{16} -4.66455 q^{17} -12.1553 q^{18} -4.95588 q^{19} +1.94093 q^{20} -2.80969 q^{21} -5.47212 q^{22} -3.34642 q^{23} -9.28747 q^{24} -4.67290 q^{25} -2.32242 q^{26} +6.41003 q^{27} -3.32295 q^{28} -3.01230 q^{29} -3.81142 q^{30} -3.57054 q^{31} +4.77894 q^{32} +6.76108 q^{33} +10.8331 q^{34} -0.560015 q^{35} +17.7619 q^{36} +7.40235 q^{37} +11.5097 q^{38} +2.86947 q^{39} -1.85114 q^{40} +10.6844 q^{41} +6.52529 q^{42} -4.49197 q^{43} +7.99615 q^{44} +2.99341 q^{45} +7.77181 q^{46} -8.78651 q^{47} +2.09346 q^{48} -6.04123 q^{49} +10.8524 q^{50} -13.3848 q^{51} +3.39365 q^{52} -0.840938 q^{53} -14.8868 q^{54} +1.34759 q^{55} +3.16922 q^{56} -14.2208 q^{57} +6.99584 q^{58} -12.4051 q^{59} +5.56945 q^{60} -3.72827 q^{61} +8.29230 q^{62} -5.12483 q^{63} -12.5578 q^{64} +0.571930 q^{65} -15.7021 q^{66} +0.970763 q^{67} -15.8299 q^{68} -9.60247 q^{69} +1.30059 q^{70} -7.34122 q^{71} -16.9402 q^{72} -6.41439 q^{73} -17.1914 q^{74} -13.4087 q^{75} -16.8185 q^{76} -2.30712 q^{77} -6.66413 q^{78} +13.2468 q^{79} +0.417259 q^{80} +2.69180 q^{81} -24.8136 q^{82} +2.87692 q^{83} -9.53511 q^{84} -2.66780 q^{85} +10.4323 q^{86} -8.64372 q^{87} -7.62622 q^{88} +1.52562 q^{89} -6.95197 q^{90} -0.979167 q^{91} -11.3566 q^{92} -10.2456 q^{93} +20.4060 q^{94} -2.83442 q^{95} +13.7130 q^{96} +0.356445 q^{97} +14.0303 q^{98} +12.3321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32242 −1.64220 −0.821101 0.570783i \(-0.806640\pi\)
−0.821101 + 0.570783i \(0.806640\pi\)
\(3\) 2.86947 1.65669 0.828345 0.560218i \(-0.189283\pi\)
0.828345 + 0.560218i \(0.189283\pi\)
\(4\) 3.39365 1.69683
\(5\) 0.571930 0.255775 0.127888 0.991789i \(-0.459180\pi\)
0.127888 + 0.991789i \(0.459180\pi\)
\(6\) −6.66413 −2.72062
\(7\) −0.979167 −0.370090 −0.185045 0.982730i \(-0.559243\pi\)
−0.185045 + 0.982730i \(0.559243\pi\)
\(8\) −3.23665 −1.14433
\(9\) 5.23387 1.74462
\(10\) −1.32826 −0.420034
\(11\) 2.35621 0.710424 0.355212 0.934786i \(-0.384409\pi\)
0.355212 + 0.934786i \(0.384409\pi\)
\(12\) 9.73799 2.81111
\(13\) 1.00000 0.277350
\(14\) 2.27404 0.607763
\(15\) 1.64114 0.423740
\(16\) 0.729563 0.182391
\(17\) −4.66455 −1.13132 −0.565660 0.824639i \(-0.691378\pi\)
−0.565660 + 0.824639i \(0.691378\pi\)
\(18\) −12.1553 −2.86502
\(19\) −4.95588 −1.13696 −0.568479 0.822698i \(-0.692468\pi\)
−0.568479 + 0.822698i \(0.692468\pi\)
\(20\) 1.94093 0.434006
\(21\) −2.80969 −0.613125
\(22\) −5.47212 −1.16666
\(23\) −3.34642 −0.697778 −0.348889 0.937164i \(-0.613441\pi\)
−0.348889 + 0.937164i \(0.613441\pi\)
\(24\) −9.28747 −1.89580
\(25\) −4.67290 −0.934579
\(26\) −2.32242 −0.455465
\(27\) 6.41003 1.23361
\(28\) −3.32295 −0.627978
\(29\) −3.01230 −0.559371 −0.279685 0.960092i \(-0.590230\pi\)
−0.279685 + 0.960092i \(0.590230\pi\)
\(30\) −3.81142 −0.695867
\(31\) −3.57054 −0.641288 −0.320644 0.947200i \(-0.603899\pi\)
−0.320644 + 0.947200i \(0.603899\pi\)
\(32\) 4.77894 0.844805
\(33\) 6.76108 1.17695
\(34\) 10.8331 1.85785
\(35\) −0.560015 −0.0946598
\(36\) 17.7619 2.96032
\(37\) 7.40235 1.21694 0.608470 0.793577i \(-0.291784\pi\)
0.608470 + 0.793577i \(0.291784\pi\)
\(38\) 11.5097 1.86711
\(39\) 2.86947 0.459483
\(40\) −1.85114 −0.292690
\(41\) 10.6844 1.66862 0.834308 0.551299i \(-0.185868\pi\)
0.834308 + 0.551299i \(0.185868\pi\)
\(42\) 6.52529 1.00687
\(43\) −4.49197 −0.685019 −0.342510 0.939514i \(-0.611277\pi\)
−0.342510 + 0.939514i \(0.611277\pi\)
\(44\) 7.99615 1.20547
\(45\) 2.99341 0.446231
\(46\) 7.77181 1.14589
\(47\) −8.78651 −1.28164 −0.640822 0.767690i \(-0.721406\pi\)
−0.640822 + 0.767690i \(0.721406\pi\)
\(48\) 2.09346 0.302165
\(49\) −6.04123 −0.863033
\(50\) 10.8524 1.53477
\(51\) −13.3848 −1.87425
\(52\) 3.39365 0.470615
\(53\) −0.840938 −0.115512 −0.0577558 0.998331i \(-0.518394\pi\)
−0.0577558 + 0.998331i \(0.518394\pi\)
\(54\) −14.8868 −2.02584
\(55\) 1.34759 0.181709
\(56\) 3.16922 0.423504
\(57\) −14.2208 −1.88359
\(58\) 6.99584 0.918599
\(59\) −12.4051 −1.61501 −0.807503 0.589863i \(-0.799182\pi\)
−0.807503 + 0.589863i \(0.799182\pi\)
\(60\) 5.56945 0.719013
\(61\) −3.72827 −0.477356 −0.238678 0.971099i \(-0.576714\pi\)
−0.238678 + 0.971099i \(0.576714\pi\)
\(62\) 8.29230 1.05312
\(63\) −5.12483 −0.645668
\(64\) −12.5578 −1.56973
\(65\) 0.571930 0.0709392
\(66\) −15.7021 −1.93279
\(67\) 0.970763 0.118598 0.0592988 0.998240i \(-0.481114\pi\)
0.0592988 + 0.998240i \(0.481114\pi\)
\(68\) −15.8299 −1.91965
\(69\) −9.60247 −1.15600
\(70\) 1.30059 0.155450
\(71\) −7.34122 −0.871243 −0.435621 0.900130i \(-0.643471\pi\)
−0.435621 + 0.900130i \(0.643471\pi\)
\(72\) −16.9402 −1.99642
\(73\) −6.41439 −0.750748 −0.375374 0.926873i \(-0.622486\pi\)
−0.375374 + 0.926873i \(0.622486\pi\)
\(74\) −17.1914 −1.99846
\(75\) −13.4087 −1.54831
\(76\) −16.8185 −1.92922
\(77\) −2.30712 −0.262921
\(78\) −6.66413 −0.754564
\(79\) 13.2468 1.49038 0.745192 0.666850i \(-0.232358\pi\)
0.745192 + 0.666850i \(0.232358\pi\)
\(80\) 0.417259 0.0466510
\(81\) 2.69180 0.299089
\(82\) −24.8136 −2.74020
\(83\) 2.87692 0.315783 0.157892 0.987456i \(-0.449530\pi\)
0.157892 + 0.987456i \(0.449530\pi\)
\(84\) −9.53511 −1.04037
\(85\) −2.66780 −0.289363
\(86\) 10.4323 1.12494
\(87\) −8.64372 −0.926704
\(88\) −7.62622 −0.812958
\(89\) 1.52562 0.161716 0.0808579 0.996726i \(-0.474234\pi\)
0.0808579 + 0.996726i \(0.474234\pi\)
\(90\) −6.95197 −0.732802
\(91\) −0.979167 −0.102645
\(92\) −11.3566 −1.18401
\(93\) −10.2456 −1.06242
\(94\) 20.4060 2.10472
\(95\) −2.83442 −0.290805
\(96\) 13.7130 1.39958
\(97\) 0.356445 0.0361915 0.0180957 0.999836i \(-0.494240\pi\)
0.0180957 + 0.999836i \(0.494240\pi\)
\(98\) 14.0303 1.41727
\(99\) 12.3321 1.23942
\(100\) −15.8582 −1.58582
\(101\) −12.1221 −1.20619 −0.603096 0.797668i \(-0.706067\pi\)
−0.603096 + 0.797668i \(0.706067\pi\)
\(102\) 31.0852 3.07789
\(103\) −5.21941 −0.514283 −0.257142 0.966374i \(-0.582781\pi\)
−0.257142 + 0.966374i \(0.582781\pi\)
\(104\) −3.23665 −0.317379
\(105\) −1.60695 −0.156822
\(106\) 1.95301 0.189693
\(107\) 4.63827 0.448399 0.224199 0.974543i \(-0.428023\pi\)
0.224199 + 0.974543i \(0.428023\pi\)
\(108\) 21.7534 2.09322
\(109\) 8.74712 0.837822 0.418911 0.908027i \(-0.362412\pi\)
0.418911 + 0.908027i \(0.362412\pi\)
\(110\) −3.12967 −0.298402
\(111\) 21.2408 2.01609
\(112\) −0.714363 −0.0675010
\(113\) −9.23182 −0.868456 −0.434228 0.900803i \(-0.642979\pi\)
−0.434228 + 0.900803i \(0.642979\pi\)
\(114\) 33.0267 3.09323
\(115\) −1.91392 −0.178474
\(116\) −10.2227 −0.949154
\(117\) 5.23387 0.483872
\(118\) 28.8099 2.65217
\(119\) 4.56737 0.418690
\(120\) −5.31179 −0.484897
\(121\) −5.44828 −0.495298
\(122\) 8.65862 0.783914
\(123\) 30.6585 2.76438
\(124\) −12.1172 −1.08815
\(125\) −5.53222 −0.494817
\(126\) 11.9020 1.06032
\(127\) −8.11639 −0.720213 −0.360106 0.932911i \(-0.617260\pi\)
−0.360106 + 0.932911i \(0.617260\pi\)
\(128\) 19.6068 1.73301
\(129\) −12.8896 −1.13486
\(130\) −1.32826 −0.116497
\(131\) 3.87412 0.338483 0.169242 0.985575i \(-0.445868\pi\)
0.169242 + 0.985575i \(0.445868\pi\)
\(132\) 22.9447 1.99708
\(133\) 4.85264 0.420777
\(134\) −2.25452 −0.194761
\(135\) 3.66609 0.315527
\(136\) 15.0975 1.29460
\(137\) 1.71028 0.146119 0.0730594 0.997328i \(-0.476724\pi\)
0.0730594 + 0.997328i \(0.476724\pi\)
\(138\) 22.3010 1.89839
\(139\) 8.30153 0.704127 0.352063 0.935976i \(-0.385480\pi\)
0.352063 + 0.935976i \(0.385480\pi\)
\(140\) −1.90050 −0.160621
\(141\) −25.2126 −2.12329
\(142\) 17.0494 1.43076
\(143\) 2.35621 0.197036
\(144\) 3.81844 0.318203
\(145\) −1.72283 −0.143073
\(146\) 14.8969 1.23288
\(147\) −17.3352 −1.42978
\(148\) 25.1210 2.06493
\(149\) −5.26818 −0.431586 −0.215793 0.976439i \(-0.569234\pi\)
−0.215793 + 0.976439i \(0.569234\pi\)
\(150\) 31.1408 2.54263
\(151\) −1.61261 −0.131233 −0.0656163 0.997845i \(-0.520901\pi\)
−0.0656163 + 0.997845i \(0.520901\pi\)
\(152\) 16.0404 1.30105
\(153\) −24.4137 −1.97373
\(154\) 5.35811 0.431769
\(155\) −2.04210 −0.164025
\(156\) 9.73799 0.779663
\(157\) −12.4824 −0.996201 −0.498101 0.867119i \(-0.665969\pi\)
−0.498101 + 0.867119i \(0.665969\pi\)
\(158\) −30.7647 −2.44751
\(159\) −2.41305 −0.191367
\(160\) 2.73322 0.216080
\(161\) 3.27671 0.258241
\(162\) −6.25149 −0.491164
\(163\) 14.9418 1.17033 0.585166 0.810914i \(-0.301029\pi\)
0.585166 + 0.810914i \(0.301029\pi\)
\(164\) 36.2590 2.83135
\(165\) 3.86687 0.301035
\(166\) −6.68143 −0.518580
\(167\) −5.22044 −0.403970 −0.201985 0.979389i \(-0.564739\pi\)
−0.201985 + 0.979389i \(0.564739\pi\)
\(168\) 9.09398 0.701616
\(169\) 1.00000 0.0769231
\(170\) 6.19576 0.475193
\(171\) −25.9385 −1.98356
\(172\) −15.2442 −1.16236
\(173\) −17.5933 −1.33759 −0.668796 0.743446i \(-0.733190\pi\)
−0.668796 + 0.743446i \(0.733190\pi\)
\(174\) 20.0744 1.52184
\(175\) 4.57554 0.345879
\(176\) 1.71900 0.129575
\(177\) −35.5961 −2.67557
\(178\) −3.54315 −0.265570
\(179\) −6.04528 −0.451845 −0.225923 0.974145i \(-0.572540\pi\)
−0.225923 + 0.974145i \(0.572540\pi\)
\(180\) 10.1586 0.757176
\(181\) −15.4866 −1.15111 −0.575555 0.817763i \(-0.695214\pi\)
−0.575555 + 0.817763i \(0.695214\pi\)
\(182\) 2.27404 0.168563
\(183\) −10.6982 −0.790831
\(184\) 10.8312 0.798486
\(185\) 4.23363 0.311263
\(186\) 23.7945 1.74470
\(187\) −10.9907 −0.803717
\(188\) −29.8183 −2.17473
\(189\) −6.27649 −0.456547
\(190\) 6.58272 0.477561
\(191\) −12.8714 −0.931343 −0.465671 0.884958i \(-0.654187\pi\)
−0.465671 + 0.884958i \(0.654187\pi\)
\(192\) −36.0344 −2.60056
\(193\) −0.860241 −0.0619215 −0.0309607 0.999521i \(-0.509857\pi\)
−0.0309607 + 0.999521i \(0.509857\pi\)
\(194\) −0.827815 −0.0594337
\(195\) 1.64114 0.117524
\(196\) −20.5018 −1.46442
\(197\) 21.4849 1.53074 0.765369 0.643591i \(-0.222556\pi\)
0.765369 + 0.643591i \(0.222556\pi\)
\(198\) −28.6404 −2.03538
\(199\) 13.4535 0.953695 0.476847 0.878986i \(-0.341779\pi\)
0.476847 + 0.878986i \(0.341779\pi\)
\(200\) 15.1245 1.06946
\(201\) 2.78558 0.196479
\(202\) 28.1526 1.98081
\(203\) 2.94955 0.207018
\(204\) −45.4233 −3.18027
\(205\) 6.11071 0.426790
\(206\) 12.1217 0.844557
\(207\) −17.5148 −1.21736
\(208\) 0.729563 0.0505861
\(209\) −11.6771 −0.807722
\(210\) 3.73201 0.257533
\(211\) 27.8756 1.91903 0.959517 0.281652i \(-0.0908823\pi\)
0.959517 + 0.281652i \(0.0908823\pi\)
\(212\) −2.85385 −0.196003
\(213\) −21.0654 −1.44338
\(214\) −10.7720 −0.736361
\(215\) −2.56909 −0.175211
\(216\) −20.7470 −1.41166
\(217\) 3.49615 0.237334
\(218\) −20.3145 −1.37587
\(219\) −18.4059 −1.24376
\(220\) 4.57324 0.308328
\(221\) −4.66455 −0.313772
\(222\) −49.3302 −3.31083
\(223\) 5.50400 0.368575 0.184287 0.982872i \(-0.441002\pi\)
0.184287 + 0.982872i \(0.441002\pi\)
\(224\) −4.67938 −0.312654
\(225\) −24.4573 −1.63049
\(226\) 21.4402 1.42618
\(227\) 25.2791 1.67783 0.838916 0.544260i \(-0.183190\pi\)
0.838916 + 0.544260i \(0.183190\pi\)
\(228\) −48.2603 −3.19612
\(229\) 14.9970 0.991031 0.495515 0.868599i \(-0.334979\pi\)
0.495515 + 0.868599i \(0.334979\pi\)
\(230\) 4.44494 0.293090
\(231\) −6.62022 −0.435579
\(232\) 9.74976 0.640103
\(233\) −11.4853 −0.752426 −0.376213 0.926533i \(-0.622774\pi\)
−0.376213 + 0.926533i \(0.622774\pi\)
\(234\) −12.1553 −0.794615
\(235\) −5.02527 −0.327813
\(236\) −42.0986 −2.74038
\(237\) 38.0114 2.46911
\(238\) −10.6074 −0.687574
\(239\) 2.97256 0.192279 0.0961394 0.995368i \(-0.469351\pi\)
0.0961394 + 0.995368i \(0.469351\pi\)
\(240\) 1.19731 0.0772862
\(241\) 16.6307 1.07128 0.535639 0.844447i \(-0.320071\pi\)
0.535639 + 0.844447i \(0.320071\pi\)
\(242\) 12.6532 0.813379
\(243\) −11.5061 −0.738114
\(244\) −12.6524 −0.809989
\(245\) −3.45516 −0.220742
\(246\) −71.2019 −4.53967
\(247\) −4.95588 −0.315335
\(248\) 11.5566 0.733843
\(249\) 8.25525 0.523155
\(250\) 12.8482 0.812589
\(251\) −8.49727 −0.536343 −0.268172 0.963371i \(-0.586419\pi\)
−0.268172 + 0.963371i \(0.586419\pi\)
\(252\) −17.3919 −1.09559
\(253\) −7.88488 −0.495718
\(254\) 18.8497 1.18273
\(255\) −7.65517 −0.479386
\(256\) −20.4195 −1.27622
\(257\) 22.0383 1.37471 0.687357 0.726320i \(-0.258771\pi\)
0.687357 + 0.726320i \(0.258771\pi\)
\(258\) 29.9351 1.86368
\(259\) −7.24813 −0.450377
\(260\) 1.94093 0.120371
\(261\) −15.7660 −0.975892
\(262\) −8.99734 −0.555858
\(263\) 11.2609 0.694375 0.347188 0.937796i \(-0.387137\pi\)
0.347188 + 0.937796i \(0.387137\pi\)
\(264\) −21.8832 −1.34682
\(265\) −0.480958 −0.0295450
\(266\) −11.2699 −0.691000
\(267\) 4.37774 0.267913
\(268\) 3.29443 0.201239
\(269\) −10.4366 −0.636330 −0.318165 0.948035i \(-0.603067\pi\)
−0.318165 + 0.948035i \(0.603067\pi\)
\(270\) −8.51422 −0.518159
\(271\) −17.3213 −1.05219 −0.526097 0.850425i \(-0.676345\pi\)
−0.526097 + 0.850425i \(0.676345\pi\)
\(272\) −3.40308 −0.206342
\(273\) −2.80969 −0.170050
\(274\) −3.97199 −0.239957
\(275\) −11.0103 −0.663947
\(276\) −32.5874 −1.96153
\(277\) 8.67340 0.521134 0.260567 0.965456i \(-0.416090\pi\)
0.260567 + 0.965456i \(0.416090\pi\)
\(278\) −19.2797 −1.15632
\(279\) −18.6877 −1.11881
\(280\) 1.81257 0.108322
\(281\) −28.4321 −1.69612 −0.848058 0.529904i \(-0.822228\pi\)
−0.848058 + 0.529904i \(0.822228\pi\)
\(282\) 58.5544 3.48687
\(283\) 20.2386 1.20306 0.601531 0.798850i \(-0.294558\pi\)
0.601531 + 0.798850i \(0.294558\pi\)
\(284\) −24.9135 −1.47835
\(285\) −8.13329 −0.481775
\(286\) −5.47212 −0.323573
\(287\) −10.4618 −0.617538
\(288\) 25.0124 1.47387
\(289\) 4.75803 0.279884
\(290\) 4.00114 0.234955
\(291\) 1.02281 0.0599581
\(292\) −21.7682 −1.27389
\(293\) 4.22798 0.247001 0.123501 0.992344i \(-0.460588\pi\)
0.123501 + 0.992344i \(0.460588\pi\)
\(294\) 40.2596 2.34799
\(295\) −7.09486 −0.413078
\(296\) −23.9588 −1.39258
\(297\) 15.1034 0.876387
\(298\) 12.2349 0.708751
\(299\) −3.34642 −0.193529
\(300\) −45.5046 −2.62721
\(301\) 4.39839 0.253519
\(302\) 3.74517 0.215510
\(303\) −34.7840 −1.99829
\(304\) −3.61563 −0.207370
\(305\) −2.13231 −0.122096
\(306\) 56.6989 3.24126
\(307\) −26.0448 −1.48646 −0.743229 0.669038i \(-0.766707\pi\)
−0.743229 + 0.669038i \(0.766707\pi\)
\(308\) −7.82956 −0.446131
\(309\) −14.9769 −0.852009
\(310\) 4.74262 0.269363
\(311\) −1.84577 −0.104664 −0.0523320 0.998630i \(-0.516665\pi\)
−0.0523320 + 0.998630i \(0.516665\pi\)
\(312\) −9.28747 −0.525799
\(313\) 14.3900 0.813369 0.406685 0.913569i \(-0.366685\pi\)
0.406685 + 0.913569i \(0.366685\pi\)
\(314\) 28.9893 1.63596
\(315\) −2.93105 −0.165146
\(316\) 44.9551 2.52892
\(317\) −15.0050 −0.842766 −0.421383 0.906883i \(-0.638455\pi\)
−0.421383 + 0.906883i \(0.638455\pi\)
\(318\) 5.60412 0.314263
\(319\) −7.09762 −0.397390
\(320\) −7.18221 −0.401498
\(321\) 13.3094 0.742858
\(322\) −7.60990 −0.424083
\(323\) 23.1170 1.28626
\(324\) 9.13502 0.507501
\(325\) −4.67290 −0.259206
\(326\) −34.7012 −1.92192
\(327\) 25.0996 1.38801
\(328\) −34.5815 −1.90944
\(329\) 8.60345 0.474324
\(330\) −8.98050 −0.494360
\(331\) 5.14142 0.282598 0.141299 0.989967i \(-0.454872\pi\)
0.141299 + 0.989967i \(0.454872\pi\)
\(332\) 9.76327 0.535829
\(333\) 38.7430 2.12310
\(334\) 12.1241 0.663400
\(335\) 0.555209 0.0303343
\(336\) −2.04985 −0.111828
\(337\) 16.4429 0.895700 0.447850 0.894109i \(-0.352190\pi\)
0.447850 + 0.894109i \(0.352190\pi\)
\(338\) −2.32242 −0.126323
\(339\) −26.4904 −1.43876
\(340\) −9.05357 −0.490999
\(341\) −8.41294 −0.455586
\(342\) 60.2401 3.25741
\(343\) 12.7695 0.689490
\(344\) 14.5389 0.783886
\(345\) −5.49194 −0.295676
\(346\) 40.8590 2.19660
\(347\) −32.8934 −1.76581 −0.882905 0.469551i \(-0.844416\pi\)
−0.882905 + 0.469551i \(0.844416\pi\)
\(348\) −29.3338 −1.57246
\(349\) −16.7956 −0.899046 −0.449523 0.893269i \(-0.648406\pi\)
−0.449523 + 0.893269i \(0.648406\pi\)
\(350\) −10.6263 −0.568002
\(351\) 6.41003 0.342142
\(352\) 11.2602 0.600170
\(353\) −24.4411 −1.30087 −0.650435 0.759562i \(-0.725413\pi\)
−0.650435 + 0.759562i \(0.725413\pi\)
\(354\) 82.6692 4.39382
\(355\) −4.19867 −0.222842
\(356\) 5.17744 0.274404
\(357\) 13.1059 0.693640
\(358\) 14.0397 0.742021
\(359\) 34.3641 1.81367 0.906833 0.421490i \(-0.138493\pi\)
0.906833 + 0.421490i \(0.138493\pi\)
\(360\) −9.68861 −0.510635
\(361\) 5.56078 0.292673
\(362\) 35.9664 1.89035
\(363\) −15.6337 −0.820555
\(364\) −3.32295 −0.174170
\(365\) −3.66859 −0.192023
\(366\) 24.8457 1.29870
\(367\) 28.9391 1.51061 0.755305 0.655373i \(-0.227489\pi\)
0.755305 + 0.655373i \(0.227489\pi\)
\(368\) −2.44143 −0.127268
\(369\) 55.9205 2.91111
\(370\) −9.83228 −0.511156
\(371\) 0.823418 0.0427497
\(372\) −34.7699 −1.80273
\(373\) −6.61730 −0.342631 −0.171315 0.985216i \(-0.554802\pi\)
−0.171315 + 0.985216i \(0.554802\pi\)
\(374\) 25.5250 1.31986
\(375\) −15.8746 −0.819759
\(376\) 28.4388 1.46662
\(377\) −3.01230 −0.155142
\(378\) 14.5767 0.749743
\(379\) 2.43718 0.125190 0.0625948 0.998039i \(-0.480062\pi\)
0.0625948 + 0.998039i \(0.480062\pi\)
\(380\) −9.61903 −0.493446
\(381\) −23.2897 −1.19317
\(382\) 29.8929 1.52945
\(383\) 3.34133 0.170734 0.0853671 0.996350i \(-0.472794\pi\)
0.0853671 + 0.996350i \(0.472794\pi\)
\(384\) 56.2610 2.87106
\(385\) −1.31951 −0.0672486
\(386\) 1.99784 0.101688
\(387\) −23.5104 −1.19510
\(388\) 1.20965 0.0614106
\(389\) 28.4636 1.44316 0.721580 0.692331i \(-0.243416\pi\)
0.721580 + 0.692331i \(0.243416\pi\)
\(390\) −3.81142 −0.192999
\(391\) 15.6096 0.789409
\(392\) 19.5533 0.987593
\(393\) 11.1167 0.560762
\(394\) −49.8971 −2.51378
\(395\) 7.57626 0.381203
\(396\) 41.8508 2.10308
\(397\) 26.5099 1.33049 0.665246 0.746624i \(-0.268327\pi\)
0.665246 + 0.746624i \(0.268327\pi\)
\(398\) −31.2448 −1.56616
\(399\) 13.9245 0.697097
\(400\) −3.40917 −0.170459
\(401\) 2.59226 0.129451 0.0647256 0.997903i \(-0.479383\pi\)
0.0647256 + 0.997903i \(0.479383\pi\)
\(402\) −6.46929 −0.322659
\(403\) −3.57054 −0.177861
\(404\) −41.1381 −2.04670
\(405\) 1.53952 0.0764994
\(406\) −6.85010 −0.339965
\(407\) 17.4415 0.864543
\(408\) 43.3219 2.14475
\(409\) 27.2328 1.34658 0.673288 0.739381i \(-0.264882\pi\)
0.673288 + 0.739381i \(0.264882\pi\)
\(410\) −14.1916 −0.700875
\(411\) 4.90759 0.242074
\(412\) −17.7128 −0.872649
\(413\) 12.1467 0.597698
\(414\) 40.6767 1.99915
\(415\) 1.64540 0.0807695
\(416\) 4.77894 0.234307
\(417\) 23.8210 1.16652
\(418\) 27.1192 1.32644
\(419\) −17.1980 −0.840177 −0.420089 0.907483i \(-0.638001\pi\)
−0.420089 + 0.907483i \(0.638001\pi\)
\(420\) −5.45342 −0.266100
\(421\) −6.94089 −0.338278 −0.169139 0.985592i \(-0.554099\pi\)
−0.169139 + 0.985592i \(0.554099\pi\)
\(422\) −64.7389 −3.15144
\(423\) −45.9875 −2.23599
\(424\) 2.72182 0.132183
\(425\) 21.7970 1.05731
\(426\) 48.9228 2.37032
\(427\) 3.65059 0.176665
\(428\) 15.7407 0.760854
\(429\) 6.76108 0.326428
\(430\) 5.96653 0.287731
\(431\) −37.5906 −1.81068 −0.905338 0.424692i \(-0.860383\pi\)
−0.905338 + 0.424692i \(0.860383\pi\)
\(432\) 4.67652 0.224999
\(433\) −27.5733 −1.32509 −0.662545 0.749022i \(-0.730524\pi\)
−0.662545 + 0.749022i \(0.730524\pi\)
\(434\) −8.11954 −0.389751
\(435\) −4.94361 −0.237028
\(436\) 29.6847 1.42164
\(437\) 16.5845 0.793344
\(438\) 42.7463 2.04250
\(439\) 7.25912 0.346459 0.173229 0.984882i \(-0.444580\pi\)
0.173229 + 0.984882i \(0.444580\pi\)
\(440\) −4.36167 −0.207934
\(441\) −31.6190 −1.50567
\(442\) 10.8331 0.515276
\(443\) −16.1892 −0.769173 −0.384586 0.923089i \(-0.625656\pi\)
−0.384586 + 0.923089i \(0.625656\pi\)
\(444\) 72.0840 3.42095
\(445\) 0.872551 0.0413629
\(446\) −12.7826 −0.605274
\(447\) −15.1169 −0.715004
\(448\) 12.2962 0.580942
\(449\) −8.45649 −0.399087 −0.199543 0.979889i \(-0.563946\pi\)
−0.199543 + 0.979889i \(0.563946\pi\)
\(450\) 56.8003 2.67759
\(451\) 25.1746 1.18542
\(452\) −31.3296 −1.47362
\(453\) −4.62735 −0.217412
\(454\) −58.7088 −2.75534
\(455\) −0.560015 −0.0262539
\(456\) 46.0276 2.15544
\(457\) −4.60629 −0.215473 −0.107737 0.994179i \(-0.534360\pi\)
−0.107737 + 0.994179i \(0.534360\pi\)
\(458\) −34.8294 −1.62747
\(459\) −29.8999 −1.39561
\(460\) −6.49518 −0.302839
\(461\) −14.6700 −0.683250 −0.341625 0.939836i \(-0.610977\pi\)
−0.341625 + 0.939836i \(0.610977\pi\)
\(462\) 15.3750 0.715308
\(463\) 1.00000 0.0464739
\(464\) −2.19766 −0.102024
\(465\) −5.85975 −0.271739
\(466\) 26.6737 1.23564
\(467\) 26.9256 1.24597 0.622983 0.782235i \(-0.285920\pi\)
0.622983 + 0.782235i \(0.285920\pi\)
\(468\) 17.7619 0.821046
\(469\) −0.950538 −0.0438918
\(470\) 11.6708 0.538334
\(471\) −35.8178 −1.65040
\(472\) 40.1509 1.84810
\(473\) −10.5840 −0.486654
\(474\) −88.2786 −4.05477
\(475\) 23.1583 1.06258
\(476\) 15.5001 0.710444
\(477\) −4.40136 −0.201524
\(478\) −6.90354 −0.315761
\(479\) 14.9843 0.684649 0.342325 0.939582i \(-0.388786\pi\)
0.342325 + 0.939582i \(0.388786\pi\)
\(480\) 7.84290 0.357978
\(481\) 7.40235 0.337518
\(482\) −38.6236 −1.75926
\(483\) 9.40242 0.427825
\(484\) −18.4895 −0.840434
\(485\) 0.203862 0.00925688
\(486\) 26.7219 1.21213
\(487\) −12.6809 −0.574624 −0.287312 0.957837i \(-0.592762\pi\)
−0.287312 + 0.957837i \(0.592762\pi\)
\(488\) 12.0671 0.546251
\(489\) 42.8751 1.93888
\(490\) 8.02436 0.362503
\(491\) −29.5808 −1.33496 −0.667481 0.744627i \(-0.732627\pi\)
−0.667481 + 0.744627i \(0.732627\pi\)
\(492\) 104.044 4.69067
\(493\) 14.0510 0.632827
\(494\) 11.5097 0.517844
\(495\) 7.05310 0.317013
\(496\) −2.60493 −0.116965
\(497\) 7.18828 0.322438
\(498\) −19.1722 −0.859126
\(499\) −13.2261 −0.592082 −0.296041 0.955175i \(-0.595666\pi\)
−0.296041 + 0.955175i \(0.595666\pi\)
\(500\) −18.7744 −0.839618
\(501\) −14.9799 −0.669254
\(502\) 19.7343 0.880783
\(503\) −2.93051 −0.130665 −0.0653324 0.997864i \(-0.520811\pi\)
−0.0653324 + 0.997864i \(0.520811\pi\)
\(504\) 16.5873 0.738856
\(505\) −6.93299 −0.308514
\(506\) 18.3120 0.814069
\(507\) 2.86947 0.127438
\(508\) −27.5442 −1.22208
\(509\) 32.9616 1.46100 0.730498 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(510\) 17.7786 0.787248
\(511\) 6.28076 0.277844
\(512\) 8.20921 0.362799
\(513\) −31.7674 −1.40256
\(514\) −51.1824 −2.25756
\(515\) −2.98514 −0.131541
\(516\) −43.7428 −1.92567
\(517\) −20.7029 −0.910511
\(518\) 16.8332 0.739610
\(519\) −50.4834 −2.21598
\(520\) −1.85114 −0.0811777
\(521\) −16.0345 −0.702486 −0.351243 0.936284i \(-0.614241\pi\)
−0.351243 + 0.936284i \(0.614241\pi\)
\(522\) 36.6154 1.60261
\(523\) 17.3235 0.757505 0.378753 0.925498i \(-0.376353\pi\)
0.378753 + 0.925498i \(0.376353\pi\)
\(524\) 13.1474 0.574347
\(525\) 13.1294 0.573014
\(526\) −26.1525 −1.14030
\(527\) 16.6550 0.725501
\(528\) 4.93263 0.214665
\(529\) −11.8014 −0.513106
\(530\) 1.11699 0.0485188
\(531\) −64.9267 −2.81758
\(532\) 16.4681 0.713985
\(533\) 10.6844 0.462791
\(534\) −10.1670 −0.439967
\(535\) 2.65277 0.114689
\(536\) −3.14202 −0.135714
\(537\) −17.3468 −0.748568
\(538\) 24.2382 1.04498
\(539\) −14.2344 −0.613120
\(540\) 12.4414 0.535394
\(541\) 4.91193 0.211180 0.105590 0.994410i \(-0.466327\pi\)
0.105590 + 0.994410i \(0.466327\pi\)
\(542\) 40.2274 1.72791
\(543\) −44.4384 −1.90703
\(544\) −22.2916 −0.955745
\(545\) 5.00274 0.214294
\(546\) 6.52529 0.279257
\(547\) −0.290860 −0.0124363 −0.00621814 0.999981i \(-0.501979\pi\)
−0.00621814 + 0.999981i \(0.501979\pi\)
\(548\) 5.80408 0.247938
\(549\) −19.5133 −0.832806
\(550\) 25.5706 1.09034
\(551\) 14.9286 0.635981
\(552\) 31.0798 1.32284
\(553\) −12.9709 −0.551577
\(554\) −20.1433 −0.855807
\(555\) 12.1483 0.515666
\(556\) 28.1725 1.19478
\(557\) −1.49971 −0.0635449 −0.0317724 0.999495i \(-0.510115\pi\)
−0.0317724 + 0.999495i \(0.510115\pi\)
\(558\) 43.4008 1.83730
\(559\) −4.49197 −0.189990
\(560\) −0.408566 −0.0172651
\(561\) −31.5374 −1.33151
\(562\) 66.0313 2.78536
\(563\) 23.2439 0.979612 0.489806 0.871831i \(-0.337068\pi\)
0.489806 + 0.871831i \(0.337068\pi\)
\(564\) −85.5629 −3.60285
\(565\) −5.27996 −0.222129
\(566\) −47.0027 −1.97567
\(567\) −2.63572 −0.110690
\(568\) 23.7609 0.996987
\(569\) −24.4067 −1.02318 −0.511590 0.859230i \(-0.670943\pi\)
−0.511590 + 0.859230i \(0.670943\pi\)
\(570\) 18.8889 0.791171
\(571\) 32.4328 1.35727 0.678636 0.734475i \(-0.262572\pi\)
0.678636 + 0.734475i \(0.262572\pi\)
\(572\) 7.99615 0.334336
\(573\) −36.9342 −1.54295
\(574\) 24.2966 1.01412
\(575\) 15.6375 0.652128
\(576\) −65.7262 −2.73859
\(577\) 23.1097 0.962068 0.481034 0.876702i \(-0.340261\pi\)
0.481034 + 0.876702i \(0.340261\pi\)
\(578\) −11.0502 −0.459626
\(579\) −2.46844 −0.102585
\(580\) −5.84668 −0.242770
\(581\) −2.81699 −0.116868
\(582\) −2.37539 −0.0984632
\(583\) −1.98143 −0.0820623
\(584\) 20.7611 0.859101
\(585\) 2.99341 0.123762
\(586\) −9.81917 −0.405626
\(587\) 15.2383 0.628951 0.314476 0.949266i \(-0.398171\pi\)
0.314476 + 0.949266i \(0.398171\pi\)
\(588\) −58.8294 −2.42609
\(589\) 17.6952 0.729117
\(590\) 16.4773 0.678358
\(591\) 61.6505 2.53596
\(592\) 5.40048 0.221958
\(593\) −6.77311 −0.278138 −0.139069 0.990283i \(-0.544411\pi\)
−0.139069 + 0.990283i \(0.544411\pi\)
\(594\) −35.0765 −1.43920
\(595\) 2.61222 0.107091
\(596\) −17.8783 −0.732326
\(597\) 38.6045 1.57998
\(598\) 7.77181 0.317813
\(599\) −34.8707 −1.42478 −0.712390 0.701784i \(-0.752387\pi\)
−0.712390 + 0.701784i \(0.752387\pi\)
\(600\) 43.3994 1.77177
\(601\) −6.82519 −0.278405 −0.139203 0.990264i \(-0.544454\pi\)
−0.139203 + 0.990264i \(0.544454\pi\)
\(602\) −10.2149 −0.416329
\(603\) 5.08085 0.206908
\(604\) −5.47265 −0.222679
\(605\) −3.11603 −0.126685
\(606\) 80.7832 3.28159
\(607\) 38.1504 1.54848 0.774238 0.632895i \(-0.218134\pi\)
0.774238 + 0.632895i \(0.218134\pi\)
\(608\) −23.6839 −0.960508
\(609\) 8.46364 0.342964
\(610\) 4.95213 0.200506
\(611\) −8.78651 −0.355464
\(612\) −82.8514 −3.34907
\(613\) 4.58957 0.185371 0.0926856 0.995695i \(-0.470455\pi\)
0.0926856 + 0.995695i \(0.470455\pi\)
\(614\) 60.4871 2.44106
\(615\) 17.5345 0.707059
\(616\) 7.46734 0.300868
\(617\) 14.7453 0.593623 0.296812 0.954936i \(-0.404077\pi\)
0.296812 + 0.954936i \(0.404077\pi\)
\(618\) 34.7828 1.39917
\(619\) −28.3322 −1.13877 −0.569384 0.822072i \(-0.692818\pi\)
−0.569384 + 0.822072i \(0.692818\pi\)
\(620\) −6.93017 −0.278322
\(621\) −21.4507 −0.860786
\(622\) 4.28666 0.171879
\(623\) −1.49384 −0.0598495
\(624\) 2.09346 0.0838055
\(625\) 20.2004 0.808017
\(626\) −33.4196 −1.33572
\(627\) −33.5071 −1.33815
\(628\) −42.3608 −1.69038
\(629\) −34.5286 −1.37675
\(630\) 6.80713 0.271203
\(631\) 25.7618 1.02556 0.512780 0.858520i \(-0.328616\pi\)
0.512780 + 0.858520i \(0.328616\pi\)
\(632\) −42.8753 −1.70549
\(633\) 79.9882 3.17924
\(634\) 34.8480 1.38399
\(635\) −4.64201 −0.184212
\(636\) −8.18904 −0.324717
\(637\) −6.04123 −0.239362
\(638\) 16.4837 0.652595
\(639\) −38.4230 −1.51999
\(640\) 11.2137 0.443260
\(641\) −10.9491 −0.432462 −0.216231 0.976342i \(-0.569376\pi\)
−0.216231 + 0.976342i \(0.569376\pi\)
\(642\) −30.9100 −1.21992
\(643\) 26.4676 1.04378 0.521890 0.853013i \(-0.325227\pi\)
0.521890 + 0.853013i \(0.325227\pi\)
\(644\) 11.1200 0.438189
\(645\) −7.37195 −0.290270
\(646\) −53.6874 −2.11230
\(647\) −17.7380 −0.697351 −0.348676 0.937243i \(-0.613369\pi\)
−0.348676 + 0.937243i \(0.613369\pi\)
\(648\) −8.71240 −0.342255
\(649\) −29.2290 −1.14734
\(650\) 10.8524 0.425668
\(651\) 10.0321 0.393189
\(652\) 50.7072 1.98585
\(653\) 13.2646 0.519083 0.259541 0.965732i \(-0.416429\pi\)
0.259541 + 0.965732i \(0.416429\pi\)
\(654\) −58.2919 −2.27939
\(655\) 2.21573 0.0865756
\(656\) 7.79491 0.304340
\(657\) −33.5721 −1.30977
\(658\) −19.9809 −0.778935
\(659\) 1.22113 0.0475686 0.0237843 0.999717i \(-0.492429\pi\)
0.0237843 + 0.999717i \(0.492429\pi\)
\(660\) 13.1228 0.510804
\(661\) −0.861660 −0.0335147 −0.0167574 0.999860i \(-0.505334\pi\)
−0.0167574 + 0.999860i \(0.505334\pi\)
\(662\) −11.9406 −0.464083
\(663\) −13.3848 −0.519822
\(664\) −9.31158 −0.361359
\(665\) 2.77537 0.107624
\(666\) −89.9775 −3.48656
\(667\) 10.0804 0.390316
\(668\) −17.7164 −0.685467
\(669\) 15.7936 0.610615
\(670\) −1.28943 −0.0498150
\(671\) −8.78458 −0.339125
\(672\) −13.4273 −0.517971
\(673\) 6.65418 0.256500 0.128250 0.991742i \(-0.459064\pi\)
0.128250 + 0.991742i \(0.459064\pi\)
\(674\) −38.1873 −1.47092
\(675\) −29.9534 −1.15291
\(676\) 3.39365 0.130525
\(677\) −37.9495 −1.45852 −0.729258 0.684238i \(-0.760135\pi\)
−0.729258 + 0.684238i \(0.760135\pi\)
\(678\) 61.5220 2.36274
\(679\) −0.349019 −0.0133941
\(680\) 8.63472 0.331126
\(681\) 72.5377 2.77965
\(682\) 19.5384 0.748164
\(683\) 18.2028 0.696511 0.348256 0.937400i \(-0.386774\pi\)
0.348256 + 0.937400i \(0.386774\pi\)
\(684\) −88.0261 −3.36576
\(685\) 0.978160 0.0373736
\(686\) −29.6563 −1.13228
\(687\) 43.0335 1.64183
\(688\) −3.27717 −0.124941
\(689\) −0.840938 −0.0320372
\(690\) 12.7546 0.485560
\(691\) −14.4140 −0.548335 −0.274168 0.961682i \(-0.588402\pi\)
−0.274168 + 0.961682i \(0.588402\pi\)
\(692\) −59.7054 −2.26966
\(693\) −12.0752 −0.458698
\(694\) 76.3924 2.89982
\(695\) 4.74790 0.180098
\(696\) 27.9767 1.06045
\(697\) −49.8377 −1.88774
\(698\) 39.0064 1.47641
\(699\) −32.9567 −1.24654
\(700\) 15.5278 0.586895
\(701\) 8.09220 0.305638 0.152819 0.988254i \(-0.451165\pi\)
0.152819 + 0.988254i \(0.451165\pi\)
\(702\) −14.8868 −0.561866
\(703\) −36.6852 −1.38361
\(704\) −29.5889 −1.11517
\(705\) −14.4199 −0.543084
\(706\) 56.7626 2.13629
\(707\) 11.8695 0.446400
\(708\) −120.801 −4.53997
\(709\) −13.8050 −0.518459 −0.259230 0.965816i \(-0.583469\pi\)
−0.259230 + 0.965816i \(0.583469\pi\)
\(710\) 9.75108 0.365952
\(711\) 69.3322 2.60016
\(712\) −4.93791 −0.185056
\(713\) 11.9485 0.447476
\(714\) −30.4376 −1.13910
\(715\) 1.34759 0.0503969
\(716\) −20.5156 −0.766703
\(717\) 8.52967 0.318546
\(718\) −79.8079 −2.97840
\(719\) 0.573972 0.0214056 0.0107028 0.999943i \(-0.496593\pi\)
0.0107028 + 0.999943i \(0.496593\pi\)
\(720\) 2.18388 0.0813884
\(721\) 5.11067 0.190331
\(722\) −12.9145 −0.480627
\(723\) 47.7214 1.77478
\(724\) −52.5561 −1.95323
\(725\) 14.0762 0.522776
\(726\) 36.3080 1.34752
\(727\) −7.89664 −0.292870 −0.146435 0.989220i \(-0.546780\pi\)
−0.146435 + 0.989220i \(0.546780\pi\)
\(728\) 3.16922 0.117459
\(729\) −41.0917 −1.52192
\(730\) 8.52001 0.315340
\(731\) 20.9530 0.774976
\(732\) −36.3058 −1.34190
\(733\) −52.5363 −1.94047 −0.970236 0.242161i \(-0.922144\pi\)
−0.970236 + 0.242161i \(0.922144\pi\)
\(734\) −67.2089 −2.48073
\(735\) −9.91450 −0.365702
\(736\) −15.9924 −0.589486
\(737\) 2.28732 0.0842545
\(738\) −129.871 −4.78062
\(739\) 24.8907 0.915621 0.457810 0.889050i \(-0.348634\pi\)
0.457810 + 0.889050i \(0.348634\pi\)
\(740\) 14.3675 0.528158
\(741\) −14.2208 −0.522413
\(742\) −1.91233 −0.0702037
\(743\) −45.6196 −1.67362 −0.836810 0.547494i \(-0.815582\pi\)
−0.836810 + 0.547494i \(0.815582\pi\)
\(744\) 33.1613 1.21575
\(745\) −3.01303 −0.110389
\(746\) 15.3682 0.562669
\(747\) 15.0574 0.550923
\(748\) −37.2985 −1.36377
\(749\) −4.54164 −0.165948
\(750\) 36.8675 1.34621
\(751\) −36.8924 −1.34622 −0.673112 0.739541i \(-0.735043\pi\)
−0.673112 + 0.739541i \(0.735043\pi\)
\(752\) −6.41031 −0.233760
\(753\) −24.3827 −0.888555
\(754\) 6.99584 0.254774
\(755\) −0.922303 −0.0335660
\(756\) −21.3002 −0.774681
\(757\) 8.30946 0.302012 0.151006 0.988533i \(-0.451749\pi\)
0.151006 + 0.988533i \(0.451749\pi\)
\(758\) −5.66017 −0.205587
\(759\) −22.6254 −0.821251
\(760\) 9.17402 0.332777
\(761\) 17.9599 0.651045 0.325523 0.945534i \(-0.394460\pi\)
0.325523 + 0.945534i \(0.394460\pi\)
\(762\) 54.0886 1.95942
\(763\) −8.56488 −0.310070
\(764\) −43.6811 −1.58033
\(765\) −13.9629 −0.504830
\(766\) −7.75999 −0.280380
\(767\) −12.4051 −0.447922
\(768\) −58.5932 −2.11430
\(769\) 19.4730 0.702216 0.351108 0.936335i \(-0.385805\pi\)
0.351108 + 0.936335i \(0.385805\pi\)
\(770\) 3.06447 0.110436
\(771\) 63.2384 2.27748
\(772\) −2.91936 −0.105070
\(773\) −54.8489 −1.97278 −0.986390 0.164424i \(-0.947423\pi\)
−0.986390 + 0.164424i \(0.947423\pi\)
\(774\) 54.6011 1.96260
\(775\) 16.6848 0.599334
\(776\) −1.15369 −0.0414149
\(777\) −20.7983 −0.746136
\(778\) −66.1044 −2.36996
\(779\) −52.9504 −1.89715
\(780\) 5.56945 0.199418
\(781\) −17.2975 −0.618952
\(782\) −36.2520 −1.29637
\(783\) −19.3090 −0.690046
\(784\) −4.40746 −0.157409
\(785\) −7.13904 −0.254803
\(786\) −25.8176 −0.920884
\(787\) 9.50916 0.338965 0.169482 0.985533i \(-0.445790\pi\)
0.169482 + 0.985533i \(0.445790\pi\)
\(788\) 72.9124 2.59740
\(789\) 32.3128 1.15036
\(790\) −17.5953 −0.626012
\(791\) 9.03949 0.321407
\(792\) −39.9146 −1.41831
\(793\) −3.72827 −0.132395
\(794\) −61.5671 −2.18494
\(795\) −1.38009 −0.0489469
\(796\) 45.6565 1.61825
\(797\) −32.0224 −1.13429 −0.567146 0.823618i \(-0.691952\pi\)
−0.567146 + 0.823618i \(0.691952\pi\)
\(798\) −32.3386 −1.14477
\(799\) 40.9851 1.44995
\(800\) −22.3315 −0.789537
\(801\) 7.98492 0.282133
\(802\) −6.02032 −0.212585
\(803\) −15.1137 −0.533349
\(804\) 9.45327 0.333391
\(805\) 1.87405 0.0660515
\(806\) 8.29230 0.292084
\(807\) −29.9475 −1.05420
\(808\) 39.2349 1.38028
\(809\) −3.65769 −0.128598 −0.0642988 0.997931i \(-0.520481\pi\)
−0.0642988 + 0.997931i \(0.520481\pi\)
\(810\) −3.57542 −0.125627
\(811\) −45.3660 −1.59302 −0.796508 0.604628i \(-0.793322\pi\)
−0.796508 + 0.604628i \(0.793322\pi\)
\(812\) 10.0097 0.351273
\(813\) −49.7030 −1.74316
\(814\) −40.5065 −1.41975
\(815\) 8.54567 0.299342
\(816\) −9.76505 −0.341845
\(817\) 22.2617 0.778838
\(818\) −63.2461 −2.21135
\(819\) −5.12483 −0.179076
\(820\) 20.7376 0.724188
\(821\) 35.6698 1.24489 0.622443 0.782665i \(-0.286140\pi\)
0.622443 + 0.782665i \(0.286140\pi\)
\(822\) −11.3975 −0.397534
\(823\) −43.4128 −1.51327 −0.756637 0.653835i \(-0.773159\pi\)
−0.756637 + 0.653835i \(0.773159\pi\)
\(824\) 16.8934 0.588509
\(825\) −31.5938 −1.09996
\(826\) −28.2097 −0.981541
\(827\) 26.5291 0.922508 0.461254 0.887268i \(-0.347400\pi\)
0.461254 + 0.887268i \(0.347400\pi\)
\(828\) −59.4389 −2.06565
\(829\) −50.6791 −1.76016 −0.880078 0.474828i \(-0.842510\pi\)
−0.880078 + 0.474828i \(0.842510\pi\)
\(830\) −3.82131 −0.132640
\(831\) 24.8881 0.863358
\(832\) −12.5578 −0.435365
\(833\) 28.1796 0.976366
\(834\) −55.3225 −1.91566
\(835\) −2.98573 −0.103325
\(836\) −39.6280 −1.37056
\(837\) −22.8873 −0.791100
\(838\) 39.9410 1.37974
\(839\) 11.1416 0.384650 0.192325 0.981331i \(-0.438397\pi\)
0.192325 + 0.981331i \(0.438397\pi\)
\(840\) 5.20112 0.179456
\(841\) −19.9260 −0.687104
\(842\) 16.1197 0.555521
\(843\) −81.5850 −2.80994
\(844\) 94.5999 3.25626
\(845\) 0.571930 0.0196750
\(846\) 106.802 3.67194
\(847\) 5.33477 0.183305
\(848\) −0.613517 −0.0210682
\(849\) 58.0742 1.99310
\(850\) −50.6218 −1.73631
\(851\) −24.7714 −0.849153
\(852\) −71.4887 −2.44916
\(853\) −11.8635 −0.406197 −0.203099 0.979158i \(-0.565101\pi\)
−0.203099 + 0.979158i \(0.565101\pi\)
\(854\) −8.47823 −0.290119
\(855\) −14.8350 −0.507346
\(856\) −15.0124 −0.513115
\(857\) 17.2528 0.589344 0.294672 0.955599i \(-0.404790\pi\)
0.294672 + 0.955599i \(0.404790\pi\)
\(858\) −15.7021 −0.536060
\(859\) 30.2049 1.03058 0.515288 0.857017i \(-0.327685\pi\)
0.515288 + 0.857017i \(0.327685\pi\)
\(860\) −8.71861 −0.297302
\(861\) −30.0197 −1.02307
\(862\) 87.3013 2.97349
\(863\) −12.4538 −0.423933 −0.211967 0.977277i \(-0.567987\pi\)
−0.211967 + 0.977277i \(0.567987\pi\)
\(864\) 30.6332 1.04216
\(865\) −10.0621 −0.342123
\(866\) 64.0370 2.17606
\(867\) 13.6530 0.463681
\(868\) 11.8647 0.402715
\(869\) 31.2123 1.05881
\(870\) 11.4811 0.389247
\(871\) 0.970763 0.0328930
\(872\) −28.3113 −0.958743
\(873\) 1.86559 0.0631405
\(874\) −38.5162 −1.30283
\(875\) 5.41697 0.183127
\(876\) −62.4633 −2.11044
\(877\) 53.5856 1.80946 0.904729 0.425987i \(-0.140073\pi\)
0.904729 + 0.425987i \(0.140073\pi\)
\(878\) −16.8587 −0.568955
\(879\) 12.1321 0.409205
\(880\) 0.983150 0.0331420
\(881\) 8.96305 0.301973 0.150986 0.988536i \(-0.451755\pi\)
0.150986 + 0.988536i \(0.451755\pi\)
\(882\) 73.4328 2.47261
\(883\) 11.7289 0.394710 0.197355 0.980332i \(-0.436765\pi\)
0.197355 + 0.980332i \(0.436765\pi\)
\(884\) −15.8299 −0.532416
\(885\) −20.3585 −0.684343
\(886\) 37.5982 1.26314
\(887\) −4.40709 −0.147975 −0.0739877 0.997259i \(-0.523573\pi\)
−0.0739877 + 0.997259i \(0.523573\pi\)
\(888\) −68.7491 −2.30707
\(889\) 7.94729 0.266544
\(890\) −2.02643 −0.0679262
\(891\) 6.34244 0.212480
\(892\) 18.6786 0.625407
\(893\) 43.5449 1.45717
\(894\) 35.1078 1.17418
\(895\) −3.45748 −0.115571
\(896\) −19.1983 −0.641370
\(897\) −9.60247 −0.320617
\(898\) 19.6396 0.655380
\(899\) 10.7555 0.358718
\(900\) −82.9997 −2.76666
\(901\) 3.92260 0.130681
\(902\) −58.4660 −1.94671
\(903\) 12.6211 0.420002
\(904\) 29.8801 0.993798
\(905\) −8.85726 −0.294425
\(906\) 10.7467 0.357034
\(907\) −36.9735 −1.22768 −0.613842 0.789429i \(-0.710377\pi\)
−0.613842 + 0.789429i \(0.710377\pi\)
\(908\) 85.7884 2.84699
\(909\) −63.4454 −2.10435
\(910\) 1.30059 0.0431142
\(911\) 8.83375 0.292675 0.146338 0.989235i \(-0.453251\pi\)
0.146338 + 0.989235i \(0.453251\pi\)
\(912\) −10.3749 −0.343549
\(913\) 6.77863 0.224340
\(914\) 10.6978 0.353850
\(915\) −6.11860 −0.202275
\(916\) 50.8946 1.68161
\(917\) −3.79341 −0.125269
\(918\) 69.4403 2.29187
\(919\) −1.21791 −0.0401750 −0.0200875 0.999798i \(-0.506394\pi\)
−0.0200875 + 0.999798i \(0.506394\pi\)
\(920\) 6.19469 0.204233
\(921\) −74.7349 −2.46260
\(922\) 34.0700 1.12203
\(923\) −7.34122 −0.241639
\(924\) −22.4667 −0.739101
\(925\) −34.5904 −1.13733
\(926\) −2.32242 −0.0763196
\(927\) −27.3177 −0.897231
\(928\) −14.3956 −0.472559
\(929\) −46.7273 −1.53307 −0.766536 0.642202i \(-0.778021\pi\)
−0.766536 + 0.642202i \(0.778021\pi\)
\(930\) 13.6088 0.446251
\(931\) 29.9396 0.981232
\(932\) −38.9771 −1.27674
\(933\) −5.29638 −0.173396
\(934\) −62.5326 −2.04613
\(935\) −6.28589 −0.205571
\(936\) −16.9402 −0.553708
\(937\) 39.7903 1.29989 0.649946 0.759980i \(-0.274791\pi\)
0.649946 + 0.759980i \(0.274791\pi\)
\(938\) 2.20755 0.0720791
\(939\) 41.2916 1.34750
\(940\) −17.0540 −0.556241
\(941\) −19.9305 −0.649717 −0.324859 0.945763i \(-0.605317\pi\)
−0.324859 + 0.945763i \(0.605317\pi\)
\(942\) 83.1841 2.71028
\(943\) −35.7544 −1.16432
\(944\) −9.05030 −0.294562
\(945\) −3.58972 −0.116773
\(946\) 24.5806 0.799184
\(947\) 32.2991 1.04958 0.524790 0.851232i \(-0.324144\pi\)
0.524790 + 0.851232i \(0.324144\pi\)
\(948\) 128.997 4.18964
\(949\) −6.41439 −0.208220
\(950\) −53.7834 −1.74497
\(951\) −43.0565 −1.39620
\(952\) −14.7830 −0.479119
\(953\) −26.7351 −0.866035 −0.433017 0.901386i \(-0.642551\pi\)
−0.433017 + 0.901386i \(0.642551\pi\)
\(954\) 10.2218 0.330944
\(955\) −7.36155 −0.238214
\(956\) 10.0878 0.326264
\(957\) −20.3664 −0.658353
\(958\) −34.7999 −1.12433
\(959\) −1.67465 −0.0540772
\(960\) −20.6092 −0.665158
\(961\) −18.2513 −0.588750
\(962\) −17.1914 −0.554273
\(963\) 24.2761 0.782287
\(964\) 56.4388 1.81777
\(965\) −0.491998 −0.0158380
\(966\) −21.8364 −0.702574
\(967\) 26.6867 0.858186 0.429093 0.903260i \(-0.358833\pi\)
0.429093 + 0.903260i \(0.358833\pi\)
\(968\) 17.6341 0.566783
\(969\) 66.3335 2.13094
\(970\) −0.473453 −0.0152017
\(971\) −17.5028 −0.561692 −0.280846 0.959753i \(-0.590615\pi\)
−0.280846 + 0.959753i \(0.590615\pi\)
\(972\) −39.0475 −1.25245
\(973\) −8.12858 −0.260590
\(974\) 29.4503 0.943649
\(975\) −13.4087 −0.429424
\(976\) −2.72001 −0.0870652
\(977\) −5.03697 −0.161147 −0.0805734 0.996749i \(-0.525675\pi\)
−0.0805734 + 0.996749i \(0.525675\pi\)
\(978\) −99.5741 −3.18403
\(979\) 3.59469 0.114887
\(980\) −11.7256 −0.374561
\(981\) 45.7813 1.46168
\(982\) 68.6991 2.19228
\(983\) 3.41467 0.108911 0.0544555 0.998516i \(-0.482658\pi\)
0.0544555 + 0.998516i \(0.482658\pi\)
\(984\) −99.2306 −3.16336
\(985\) 12.2879 0.391525
\(986\) −32.6325 −1.03923
\(987\) 24.6874 0.785808
\(988\) −16.8185 −0.535069
\(989\) 15.0320 0.477991
\(990\) −16.3803 −0.520600
\(991\) −28.2617 −0.897761 −0.448880 0.893592i \(-0.648177\pi\)
−0.448880 + 0.893592i \(0.648177\pi\)
\(992\) −17.0634 −0.541763
\(993\) 14.7532 0.468177
\(994\) −16.6942 −0.529509
\(995\) 7.69448 0.243931
\(996\) 28.0154 0.887703
\(997\) 21.7739 0.689587 0.344793 0.938679i \(-0.387949\pi\)
0.344793 + 0.938679i \(0.387949\pi\)
\(998\) 30.7166 0.972317
\(999\) 47.4493 1.50123
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 6019.2.a.b.1.12 101
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6019.2.a.b.1.12 101 1.1 even 1 trivial