Properties

Label 4001.2.a.b.1.18
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $0$
Dimension $184$
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] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, 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("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.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: \(31.9481458487\)
Analytic rank: \(0\)
Dimension: \(184\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.40164 q^{2} -1.91938 q^{3} +3.76787 q^{4} -2.41584 q^{5} +4.60966 q^{6} -1.95333 q^{7} -4.24578 q^{8} +0.684021 q^{9} +O(q^{10})\) \(q-2.40164 q^{2} -1.91938 q^{3} +3.76787 q^{4} -2.41584 q^{5} +4.60966 q^{6} -1.95333 q^{7} -4.24578 q^{8} +0.684021 q^{9} +5.80197 q^{10} -0.661784 q^{11} -7.23197 q^{12} +3.28103 q^{13} +4.69118 q^{14} +4.63691 q^{15} +2.66109 q^{16} -6.82644 q^{17} -1.64277 q^{18} +3.26699 q^{19} -9.10256 q^{20} +3.74918 q^{21} +1.58937 q^{22} -6.36815 q^{23} +8.14927 q^{24} +0.836275 q^{25} -7.87984 q^{26} +4.44525 q^{27} -7.35988 q^{28} -1.41430 q^{29} -11.1362 q^{30} -3.18044 q^{31} +2.10057 q^{32} +1.27022 q^{33} +16.3946 q^{34} +4.71892 q^{35} +2.57730 q^{36} +5.91293 q^{37} -7.84612 q^{38} -6.29753 q^{39} +10.2571 q^{40} +0.877003 q^{41} -9.00417 q^{42} +4.37063 q^{43} -2.49351 q^{44} -1.65248 q^{45} +15.2940 q^{46} -10.3864 q^{47} -5.10765 q^{48} -3.18452 q^{49} -2.00843 q^{50} +13.1025 q^{51} +12.3625 q^{52} -6.93570 q^{53} -10.6759 q^{54} +1.59876 q^{55} +8.29340 q^{56} -6.27059 q^{57} +3.39664 q^{58} -7.14427 q^{59} +17.4713 q^{60} +2.14088 q^{61} +7.63827 q^{62} -1.33612 q^{63} -10.3670 q^{64} -7.92643 q^{65} -3.05060 q^{66} -11.2787 q^{67} -25.7211 q^{68} +12.2229 q^{69} -11.3331 q^{70} +7.19157 q^{71} -2.90420 q^{72} -9.65095 q^{73} -14.2007 q^{74} -1.60513 q^{75} +12.3096 q^{76} +1.29268 q^{77} +15.1244 q^{78} -0.353871 q^{79} -6.42877 q^{80} -10.5842 q^{81} -2.10624 q^{82} +0.410926 q^{83} +14.1264 q^{84} +16.4916 q^{85} -10.4967 q^{86} +2.71458 q^{87} +2.80979 q^{88} +1.94551 q^{89} +3.96867 q^{90} -6.40891 q^{91} -23.9943 q^{92} +6.10448 q^{93} +24.9444 q^{94} -7.89251 q^{95} -4.03180 q^{96} -12.5183 q^{97} +7.64806 q^{98} -0.452674 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40164 −1.69821 −0.849107 0.528220i \(-0.822860\pi\)
−0.849107 + 0.528220i \(0.822860\pi\)
\(3\) −1.91938 −1.10815 −0.554077 0.832465i \(-0.686929\pi\)
−0.554077 + 0.832465i \(0.686929\pi\)
\(4\) 3.76787 1.88393
\(5\) −2.41584 −1.08040 −0.540198 0.841538i \(-0.681651\pi\)
−0.540198 + 0.841538i \(0.681651\pi\)
\(6\) 4.60966 1.88188
\(7\) −1.95333 −0.738288 −0.369144 0.929372i \(-0.620349\pi\)
−0.369144 + 0.929372i \(0.620349\pi\)
\(8\) −4.24578 −1.50111
\(9\) 0.684021 0.228007
\(10\) 5.80197 1.83474
\(11\) −0.661784 −0.199535 −0.0997677 0.995011i \(-0.531810\pi\)
−0.0997677 + 0.995011i \(0.531810\pi\)
\(12\) −7.23197 −2.08769
\(13\) 3.28103 0.909993 0.454996 0.890493i \(-0.349641\pi\)
0.454996 + 0.890493i \(0.349641\pi\)
\(14\) 4.69118 1.25377
\(15\) 4.63691 1.19725
\(16\) 2.66109 0.665274
\(17\) −6.82644 −1.65565 −0.827827 0.560984i \(-0.810423\pi\)
−0.827827 + 0.560984i \(0.810423\pi\)
\(18\) −1.64277 −0.387205
\(19\) 3.26699 0.749498 0.374749 0.927126i \(-0.377729\pi\)
0.374749 + 0.927126i \(0.377729\pi\)
\(20\) −9.10256 −2.03539
\(21\) 3.74918 0.818137
\(22\) 1.58937 0.338854
\(23\) −6.36815 −1.32785 −0.663925 0.747799i \(-0.731111\pi\)
−0.663925 + 0.747799i \(0.731111\pi\)
\(24\) 8.14927 1.66346
\(25\) 0.836275 0.167255
\(26\) −7.87984 −1.54536
\(27\) 4.44525 0.855488
\(28\) −7.35988 −1.39089
\(29\) −1.41430 −0.262629 −0.131315 0.991341i \(-0.541920\pi\)
−0.131315 + 0.991341i \(0.541920\pi\)
\(30\) −11.1362 −2.03318
\(31\) −3.18044 −0.571224 −0.285612 0.958345i \(-0.592197\pi\)
−0.285612 + 0.958345i \(0.592197\pi\)
\(32\) 2.10057 0.371333
\(33\) 1.27022 0.221116
\(34\) 16.3946 2.81166
\(35\) 4.71892 0.797643
\(36\) 2.57730 0.429550
\(37\) 5.91293 0.972080 0.486040 0.873937i \(-0.338441\pi\)
0.486040 + 0.873937i \(0.338441\pi\)
\(38\) −7.84612 −1.27281
\(39\) −6.29753 −1.00841
\(40\) 10.2571 1.62179
\(41\) 0.877003 0.136965 0.0684824 0.997652i \(-0.478184\pi\)
0.0684824 + 0.997652i \(0.478184\pi\)
\(42\) −9.00417 −1.38937
\(43\) 4.37063 0.666515 0.333258 0.942836i \(-0.391852\pi\)
0.333258 + 0.942836i \(0.391852\pi\)
\(44\) −2.49351 −0.375912
\(45\) −1.65248 −0.246338
\(46\) 15.2940 2.25498
\(47\) −10.3864 −1.51501 −0.757505 0.652829i \(-0.773582\pi\)
−0.757505 + 0.652829i \(0.773582\pi\)
\(48\) −5.10765 −0.737226
\(49\) −3.18452 −0.454931
\(50\) −2.00843 −0.284035
\(51\) 13.1025 1.83472
\(52\) 12.3625 1.71437
\(53\) −6.93570 −0.952691 −0.476346 0.879258i \(-0.658039\pi\)
−0.476346 + 0.879258i \(0.658039\pi\)
\(54\) −10.6759 −1.45280
\(55\) 1.59876 0.215577
\(56\) 8.29340 1.10825
\(57\) −6.27059 −0.830560
\(58\) 3.39664 0.446001
\(59\) −7.14427 −0.930104 −0.465052 0.885283i \(-0.653964\pi\)
−0.465052 + 0.885283i \(0.653964\pi\)
\(60\) 17.4713 2.25553
\(61\) 2.14088 0.274112 0.137056 0.990563i \(-0.456236\pi\)
0.137056 + 0.990563i \(0.456236\pi\)
\(62\) 7.63827 0.970062
\(63\) −1.33612 −0.168335
\(64\) −10.3670 −1.29588
\(65\) −7.92643 −0.983152
\(66\) −3.05060 −0.375503
\(67\) −11.2787 −1.37791 −0.688956 0.724803i \(-0.741931\pi\)
−0.688956 + 0.724803i \(0.741931\pi\)
\(68\) −25.7211 −3.11914
\(69\) 12.2229 1.47146
\(70\) −11.3331 −1.35457
\(71\) 7.19157 0.853482 0.426741 0.904374i \(-0.359662\pi\)
0.426741 + 0.904374i \(0.359662\pi\)
\(72\) −2.90420 −0.342263
\(73\) −9.65095 −1.12956 −0.564779 0.825242i \(-0.691039\pi\)
−0.564779 + 0.825242i \(0.691039\pi\)
\(74\) −14.2007 −1.65080
\(75\) −1.60513 −0.185344
\(76\) 12.3096 1.41201
\(77\) 1.29268 0.147315
\(78\) 15.1244 1.71250
\(79\) −0.353871 −0.0398136 −0.0199068 0.999802i \(-0.506337\pi\)
−0.0199068 + 0.999802i \(0.506337\pi\)
\(80\) −6.42877 −0.718759
\(81\) −10.5842 −1.17602
\(82\) −2.10624 −0.232596
\(83\) 0.410926 0.0451050 0.0225525 0.999746i \(-0.492821\pi\)
0.0225525 + 0.999746i \(0.492821\pi\)
\(84\) 14.1264 1.54132
\(85\) 16.4916 1.78876
\(86\) −10.4967 −1.13189
\(87\) 2.71458 0.291034
\(88\) 2.80979 0.299525
\(89\) 1.94551 0.206223 0.103112 0.994670i \(-0.467120\pi\)
0.103112 + 0.994670i \(0.467120\pi\)
\(90\) 3.96867 0.418334
\(91\) −6.40891 −0.671837
\(92\) −23.9943 −2.50158
\(93\) 6.10448 0.633005
\(94\) 24.9444 2.57281
\(95\) −7.89251 −0.809755
\(96\) −4.03180 −0.411494
\(97\) −12.5183 −1.27104 −0.635519 0.772085i \(-0.719214\pi\)
−0.635519 + 0.772085i \(0.719214\pi\)
\(98\) 7.64806 0.772570
\(99\) −0.452674 −0.0454954
\(100\) 3.15097 0.315097
\(101\) 3.68698 0.366868 0.183434 0.983032i \(-0.441279\pi\)
0.183434 + 0.983032i \(0.441279\pi\)
\(102\) −31.4675 −3.11575
\(103\) −9.34932 −0.921216 −0.460608 0.887604i \(-0.652369\pi\)
−0.460608 + 0.887604i \(0.652369\pi\)
\(104\) −13.9305 −1.36600
\(105\) −9.05740 −0.883912
\(106\) 16.6570 1.61787
\(107\) 1.71192 0.165498 0.0827489 0.996570i \(-0.473630\pi\)
0.0827489 + 0.996570i \(0.473630\pi\)
\(108\) 16.7491 1.61168
\(109\) −7.64974 −0.732712 −0.366356 0.930475i \(-0.619395\pi\)
−0.366356 + 0.930475i \(0.619395\pi\)
\(110\) −3.83965 −0.366096
\(111\) −11.3492 −1.07722
\(112\) −5.19799 −0.491164
\(113\) −15.0525 −1.41602 −0.708011 0.706201i \(-0.750407\pi\)
−0.708011 + 0.706201i \(0.750407\pi\)
\(114\) 15.0597 1.41047
\(115\) 15.3844 1.43460
\(116\) −5.32890 −0.494776
\(117\) 2.24429 0.207485
\(118\) 17.1580 1.57952
\(119\) 13.3343 1.22235
\(120\) −19.6873 −1.79720
\(121\) −10.5620 −0.960186
\(122\) −5.14162 −0.465501
\(123\) −1.68330 −0.151778
\(124\) −11.9835 −1.07615
\(125\) 10.0589 0.899694
\(126\) 3.20887 0.285869
\(127\) −11.8598 −1.05239 −0.526193 0.850365i \(-0.676381\pi\)
−0.526193 + 0.850365i \(0.676381\pi\)
\(128\) 20.6967 1.82934
\(129\) −8.38890 −0.738602
\(130\) 19.0364 1.66960
\(131\) −6.50084 −0.567981 −0.283991 0.958827i \(-0.591658\pi\)
−0.283991 + 0.958827i \(0.591658\pi\)
\(132\) 4.78600 0.416568
\(133\) −6.38149 −0.553346
\(134\) 27.0873 2.33999
\(135\) −10.7390 −0.924265
\(136\) 28.9835 2.48532
\(137\) −1.46698 −0.125333 −0.0626663 0.998035i \(-0.519960\pi\)
−0.0626663 + 0.998035i \(0.519960\pi\)
\(138\) −29.3550 −2.49886
\(139\) 15.2297 1.29177 0.645885 0.763435i \(-0.276489\pi\)
0.645885 + 0.763435i \(0.276489\pi\)
\(140\) 17.7803 1.50271
\(141\) 19.9354 1.67887
\(142\) −17.2715 −1.44940
\(143\) −2.17133 −0.181576
\(144\) 1.82024 0.151687
\(145\) 3.41673 0.283744
\(146\) 23.1781 1.91823
\(147\) 6.11230 0.504134
\(148\) 22.2791 1.83133
\(149\) 5.26037 0.430946 0.215473 0.976510i \(-0.430871\pi\)
0.215473 + 0.976510i \(0.430871\pi\)
\(150\) 3.85494 0.314755
\(151\) −2.08132 −0.169376 −0.0846879 0.996408i \(-0.526989\pi\)
−0.0846879 + 0.996408i \(0.526989\pi\)
\(152\) −13.8709 −1.12508
\(153\) −4.66942 −0.377500
\(154\) −3.10455 −0.250172
\(155\) 7.68343 0.617148
\(156\) −23.7283 −1.89978
\(157\) −0.112095 −0.00894618 −0.00447309 0.999990i \(-0.501424\pi\)
−0.00447309 + 0.999990i \(0.501424\pi\)
\(158\) 0.849871 0.0676121
\(159\) 13.3122 1.05573
\(160\) −5.07465 −0.401186
\(161\) 12.4391 0.980336
\(162\) 25.4194 1.99713
\(163\) −12.9707 −1.01594 −0.507970 0.861375i \(-0.669604\pi\)
−0.507970 + 0.861375i \(0.669604\pi\)
\(164\) 3.30443 0.258033
\(165\) −3.06863 −0.238893
\(166\) −0.986897 −0.0765981
\(167\) −20.1266 −1.55745 −0.778723 0.627367i \(-0.784132\pi\)
−0.778723 + 0.627367i \(0.784132\pi\)
\(168\) −15.9182 −1.22811
\(169\) −2.23487 −0.171913
\(170\) −39.6068 −3.03770
\(171\) 2.23469 0.170891
\(172\) 16.4680 1.25567
\(173\) −8.09988 −0.615822 −0.307911 0.951415i \(-0.599630\pi\)
−0.307911 + 0.951415i \(0.599630\pi\)
\(174\) −6.51945 −0.494238
\(175\) −1.63352 −0.123482
\(176\) −1.76107 −0.132746
\(177\) 13.7126 1.03070
\(178\) −4.67240 −0.350211
\(179\) −3.91190 −0.292389 −0.146194 0.989256i \(-0.546703\pi\)
−0.146194 + 0.989256i \(0.546703\pi\)
\(180\) −6.22634 −0.464084
\(181\) −19.4450 −1.44533 −0.722666 0.691197i \(-0.757084\pi\)
−0.722666 + 0.691197i \(0.757084\pi\)
\(182\) 15.3919 1.14092
\(183\) −4.10916 −0.303758
\(184\) 27.0378 1.99325
\(185\) −14.2847 −1.05023
\(186\) −14.6607 −1.07498
\(187\) 4.51763 0.330361
\(188\) −39.1346 −2.85418
\(189\) −8.68302 −0.631596
\(190\) 18.9550 1.37514
\(191\) −6.89866 −0.499169 −0.249585 0.968353i \(-0.580294\pi\)
−0.249585 + 0.968353i \(0.580294\pi\)
\(192\) 19.8982 1.43603
\(193\) −5.56850 −0.400829 −0.200415 0.979711i \(-0.564229\pi\)
−0.200415 + 0.979711i \(0.564229\pi\)
\(194\) 30.0644 2.15850
\(195\) 15.2138 1.08948
\(196\) −11.9988 −0.857060
\(197\) −11.2946 −0.804707 −0.402354 0.915484i \(-0.631808\pi\)
−0.402354 + 0.915484i \(0.631808\pi\)
\(198\) 1.08716 0.0772610
\(199\) −23.3799 −1.65736 −0.828679 0.559724i \(-0.810907\pi\)
−0.828679 + 0.559724i \(0.810907\pi\)
\(200\) −3.55064 −0.251068
\(201\) 21.6481 1.52694
\(202\) −8.85478 −0.623020
\(203\) 2.76259 0.193896
\(204\) 49.3686 3.45649
\(205\) −2.11870 −0.147976
\(206\) 22.4537 1.56442
\(207\) −4.35594 −0.302759
\(208\) 8.73112 0.605394
\(209\) −2.16204 −0.149551
\(210\) 21.7526 1.50107
\(211\) 17.2283 1.18605 0.593023 0.805185i \(-0.297934\pi\)
0.593023 + 0.805185i \(0.297934\pi\)
\(212\) −26.1328 −1.79481
\(213\) −13.8034 −0.945790
\(214\) −4.11142 −0.281051
\(215\) −10.5587 −0.720100
\(216\) −18.8735 −1.28418
\(217\) 6.21244 0.421728
\(218\) 18.3719 1.24430
\(219\) 18.5238 1.25173
\(220\) 6.02393 0.406133
\(221\) −22.3977 −1.50663
\(222\) 27.2566 1.82934
\(223\) −10.6011 −0.709903 −0.354951 0.934885i \(-0.615503\pi\)
−0.354951 + 0.934885i \(0.615503\pi\)
\(224\) −4.10311 −0.274150
\(225\) 0.572029 0.0381353
\(226\) 36.1507 2.40471
\(227\) 9.03942 0.599968 0.299984 0.953944i \(-0.403019\pi\)
0.299984 + 0.953944i \(0.403019\pi\)
\(228\) −23.6268 −1.56472
\(229\) 0.468543 0.0309622 0.0154811 0.999880i \(-0.495072\pi\)
0.0154811 + 0.999880i \(0.495072\pi\)
\(230\) −36.9478 −2.43627
\(231\) −2.48114 −0.163247
\(232\) 6.00482 0.394236
\(233\) −8.82531 −0.578165 −0.289082 0.957304i \(-0.593350\pi\)
−0.289082 + 0.957304i \(0.593350\pi\)
\(234\) −5.38997 −0.352353
\(235\) 25.0918 1.63681
\(236\) −26.9187 −1.75226
\(237\) 0.679213 0.0441197
\(238\) −32.0241 −2.07581
\(239\) −16.2907 −1.05376 −0.526878 0.849941i \(-0.676638\pi\)
−0.526878 + 0.849941i \(0.676638\pi\)
\(240\) 12.3393 0.796496
\(241\) 2.78334 0.179291 0.0896454 0.995974i \(-0.471427\pi\)
0.0896454 + 0.995974i \(0.471427\pi\)
\(242\) 25.3662 1.63060
\(243\) 6.97933 0.447724
\(244\) 8.06656 0.516408
\(245\) 7.69327 0.491505
\(246\) 4.04268 0.257752
\(247\) 10.7191 0.682038
\(248\) 13.5035 0.857470
\(249\) −0.788724 −0.0499834
\(250\) −24.1578 −1.52787
\(251\) 1.46310 0.0923501 0.0461750 0.998933i \(-0.485297\pi\)
0.0461750 + 0.998933i \(0.485297\pi\)
\(252\) −5.03431 −0.317132
\(253\) 4.21434 0.264953
\(254\) 28.4829 1.78718
\(255\) −31.6536 −1.98222
\(256\) −28.9719 −1.81074
\(257\) −9.95063 −0.620703 −0.310352 0.950622i \(-0.600447\pi\)
−0.310352 + 0.950622i \(0.600447\pi\)
\(258\) 20.1471 1.25430
\(259\) −11.5499 −0.717675
\(260\) −29.8657 −1.85219
\(261\) −0.967412 −0.0598813
\(262\) 15.6127 0.964554
\(263\) −14.9582 −0.922359 −0.461180 0.887307i \(-0.652574\pi\)
−0.461180 + 0.887307i \(0.652574\pi\)
\(264\) −5.39305 −0.331920
\(265\) 16.7555 1.02928
\(266\) 15.3260 0.939700
\(267\) −3.73416 −0.228527
\(268\) −42.4966 −2.59590
\(269\) −5.04541 −0.307624 −0.153812 0.988100i \(-0.549155\pi\)
−0.153812 + 0.988100i \(0.549155\pi\)
\(270\) 25.7912 1.56960
\(271\) 28.3487 1.72206 0.861030 0.508555i \(-0.169820\pi\)
0.861030 + 0.508555i \(0.169820\pi\)
\(272\) −18.1658 −1.10146
\(273\) 12.3011 0.744499
\(274\) 3.52316 0.212842
\(275\) −0.553433 −0.0333733
\(276\) 46.0543 2.77214
\(277\) 23.1036 1.38816 0.694080 0.719898i \(-0.255811\pi\)
0.694080 + 0.719898i \(0.255811\pi\)
\(278\) −36.5763 −2.19370
\(279\) −2.17549 −0.130243
\(280\) −20.0355 −1.19735
\(281\) 6.86479 0.409519 0.204760 0.978812i \(-0.434359\pi\)
0.204760 + 0.978812i \(0.434359\pi\)
\(282\) −47.8777 −2.85108
\(283\) 1.80221 0.107130 0.0535651 0.998564i \(-0.482942\pi\)
0.0535651 + 0.998564i \(0.482942\pi\)
\(284\) 27.0969 1.60790
\(285\) 15.1487 0.897333
\(286\) 5.21475 0.308355
\(287\) −1.71307 −0.101119
\(288\) 1.43684 0.0846664
\(289\) 29.6002 1.74119
\(290\) −8.20574 −0.481858
\(291\) 24.0273 1.40851
\(292\) −36.3635 −2.12801
\(293\) 7.23580 0.422720 0.211360 0.977408i \(-0.432211\pi\)
0.211360 + 0.977408i \(0.432211\pi\)
\(294\) −14.6795 −0.856127
\(295\) 17.2594 1.00488
\(296\) −25.1050 −1.45920
\(297\) −2.94179 −0.170700
\(298\) −12.6335 −0.731839
\(299\) −20.8941 −1.20833
\(300\) −6.04791 −0.349177
\(301\) −8.53727 −0.492080
\(302\) 4.99859 0.287637
\(303\) −7.07671 −0.406546
\(304\) 8.69376 0.498621
\(305\) −5.17202 −0.296149
\(306\) 11.2143 0.641077
\(307\) 24.1293 1.37713 0.688565 0.725174i \(-0.258241\pi\)
0.688565 + 0.725174i \(0.258241\pi\)
\(308\) 4.87065 0.277531
\(309\) 17.9449 1.02085
\(310\) −18.4528 −1.04805
\(311\) 2.09617 0.118863 0.0594314 0.998232i \(-0.481071\pi\)
0.0594314 + 0.998232i \(0.481071\pi\)
\(312\) 26.7380 1.51374
\(313\) 9.93427 0.561518 0.280759 0.959778i \(-0.409414\pi\)
0.280759 + 0.959778i \(0.409414\pi\)
\(314\) 0.269212 0.0151925
\(315\) 3.22784 0.181868
\(316\) −1.33334 −0.0750062
\(317\) 5.38850 0.302648 0.151324 0.988484i \(-0.451646\pi\)
0.151324 + 0.988484i \(0.451646\pi\)
\(318\) −31.9712 −1.79286
\(319\) 0.935963 0.0524038
\(320\) 25.0450 1.40006
\(321\) −3.28583 −0.183397
\(322\) −29.8742 −1.66482
\(323\) −22.3019 −1.24091
\(324\) −39.8798 −2.21554
\(325\) 2.74384 0.152201
\(326\) 31.1508 1.72529
\(327\) 14.6828 0.811958
\(328\) −3.72356 −0.205599
\(329\) 20.2880 1.11851
\(330\) 7.36975 0.405691
\(331\) 16.5480 0.909559 0.454779 0.890604i \(-0.349718\pi\)
0.454779 + 0.890604i \(0.349718\pi\)
\(332\) 1.54832 0.0849749
\(333\) 4.04457 0.221641
\(334\) 48.3369 2.64488
\(335\) 27.2475 1.48869
\(336\) 9.97691 0.544285
\(337\) 15.5503 0.847079 0.423539 0.905878i \(-0.360788\pi\)
0.423539 + 0.905878i \(0.360788\pi\)
\(338\) 5.36736 0.291946
\(339\) 28.8915 1.56917
\(340\) 62.1380 3.36991
\(341\) 2.10477 0.113979
\(342\) −5.36691 −0.290209
\(343\) 19.8937 1.07416
\(344\) −18.5567 −1.00051
\(345\) −29.5285 −1.58976
\(346\) 19.4530 1.04580
\(347\) 0.237153 0.0127310 0.00636551 0.999980i \(-0.497974\pi\)
0.00636551 + 0.999980i \(0.497974\pi\)
\(348\) 10.2282 0.548289
\(349\) −12.1902 −0.652525 −0.326263 0.945279i \(-0.605789\pi\)
−0.326263 + 0.945279i \(0.605789\pi\)
\(350\) 3.92312 0.209700
\(351\) 14.5850 0.778488
\(352\) −1.39013 −0.0740940
\(353\) −14.5713 −0.775551 −0.387775 0.921754i \(-0.626756\pi\)
−0.387775 + 0.921754i \(0.626756\pi\)
\(354\) −32.9326 −1.75035
\(355\) −17.3737 −0.922098
\(356\) 7.33041 0.388511
\(357\) −25.5935 −1.35455
\(358\) 9.39497 0.496539
\(359\) 19.9049 1.05054 0.525270 0.850936i \(-0.323964\pi\)
0.525270 + 0.850936i \(0.323964\pi\)
\(360\) 7.01608 0.369780
\(361\) −8.32680 −0.438252
\(362\) 46.6998 2.45449
\(363\) 20.2726 1.06403
\(364\) −24.1479 −1.26570
\(365\) 23.3151 1.22037
\(366\) 9.86873 0.515847
\(367\) 10.6854 0.557775 0.278887 0.960324i \(-0.410034\pi\)
0.278887 + 0.960324i \(0.410034\pi\)
\(368\) −16.9462 −0.883384
\(369\) 0.599888 0.0312289
\(370\) 34.3067 1.78352
\(371\) 13.5477 0.703360
\(372\) 23.0009 1.19254
\(373\) −11.8408 −0.613092 −0.306546 0.951856i \(-0.599173\pi\)
−0.306546 + 0.951856i \(0.599173\pi\)
\(374\) −10.8497 −0.561025
\(375\) −19.3068 −0.997000
\(376\) 44.0983 2.27420
\(377\) −4.64036 −0.238991
\(378\) 20.8535 1.07259
\(379\) −1.89434 −0.0973059 −0.0486530 0.998816i \(-0.515493\pi\)
−0.0486530 + 0.998816i \(0.515493\pi\)
\(380\) −29.7379 −1.52552
\(381\) 22.7635 1.16621
\(382\) 16.5681 0.847697
\(383\) 12.8909 0.658696 0.329348 0.944209i \(-0.393171\pi\)
0.329348 + 0.944209i \(0.393171\pi\)
\(384\) −39.7248 −2.02720
\(385\) −3.12291 −0.159158
\(386\) 13.3735 0.680694
\(387\) 2.98960 0.151970
\(388\) −47.1672 −2.39455
\(389\) −14.7884 −0.749800 −0.374900 0.927065i \(-0.622323\pi\)
−0.374900 + 0.927065i \(0.622323\pi\)
\(390\) −36.5381 −1.85018
\(391\) 43.4718 2.19846
\(392\) 13.5208 0.682901
\(393\) 12.4776 0.629411
\(394\) 27.1256 1.36657
\(395\) 0.854896 0.0430145
\(396\) −1.70562 −0.0857104
\(397\) −3.24499 −0.162861 −0.0814306 0.996679i \(-0.525949\pi\)
−0.0814306 + 0.996679i \(0.525949\pi\)
\(398\) 56.1501 2.81455
\(399\) 12.2485 0.613193
\(400\) 2.22541 0.111270
\(401\) 24.0365 1.20032 0.600162 0.799878i \(-0.295103\pi\)
0.600162 + 0.799878i \(0.295103\pi\)
\(402\) −51.9909 −2.59307
\(403\) −10.4351 −0.519810
\(404\) 13.8920 0.691155
\(405\) 25.5697 1.27057
\(406\) −6.63475 −0.329277
\(407\) −3.91308 −0.193964
\(408\) −55.6304 −2.75412
\(409\) −0.423743 −0.0209527 −0.0104764 0.999945i \(-0.503335\pi\)
−0.0104764 + 0.999945i \(0.503335\pi\)
\(410\) 5.08834 0.251295
\(411\) 2.81569 0.138888
\(412\) −35.2270 −1.73551
\(413\) 13.9551 0.686685
\(414\) 10.4614 0.514150
\(415\) −0.992732 −0.0487313
\(416\) 6.89204 0.337910
\(417\) −29.2317 −1.43148
\(418\) 5.19244 0.253970
\(419\) −10.3485 −0.505556 −0.252778 0.967524i \(-0.581344\pi\)
−0.252778 + 0.967524i \(0.581344\pi\)
\(420\) −34.1271 −1.66523
\(421\) −19.2110 −0.936288 −0.468144 0.883652i \(-0.655077\pi\)
−0.468144 + 0.883652i \(0.655077\pi\)
\(422\) −41.3762 −2.01416
\(423\) −7.10451 −0.345433
\(424\) 29.4474 1.43009
\(425\) −5.70877 −0.276916
\(426\) 33.1507 1.60616
\(427\) −4.18184 −0.202373
\(428\) 6.45030 0.311787
\(429\) 4.16761 0.201214
\(430\) 25.3583 1.22288
\(431\) −5.96194 −0.287177 −0.143588 0.989637i \(-0.545864\pi\)
−0.143588 + 0.989637i \(0.545864\pi\)
\(432\) 11.8292 0.569134
\(433\) −12.7289 −0.611713 −0.305857 0.952078i \(-0.598943\pi\)
−0.305857 + 0.952078i \(0.598943\pi\)
\(434\) −14.9200 −0.716185
\(435\) −6.55800 −0.314432
\(436\) −28.8232 −1.38038
\(437\) −20.8047 −0.995222
\(438\) −44.4876 −2.12570
\(439\) 35.8163 1.70942 0.854709 0.519108i \(-0.173736\pi\)
0.854709 + 0.519108i \(0.173736\pi\)
\(440\) −6.78800 −0.323605
\(441\) −2.17827 −0.103727
\(442\) 53.7912 2.55859
\(443\) 4.99409 0.237276 0.118638 0.992938i \(-0.462147\pi\)
0.118638 + 0.992938i \(0.462147\pi\)
\(444\) −42.7622 −2.02940
\(445\) −4.70003 −0.222803
\(446\) 25.4600 1.20557
\(447\) −10.0966 −0.477555
\(448\) 20.2502 0.956730
\(449\) 16.8464 0.795031 0.397515 0.917595i \(-0.369873\pi\)
0.397515 + 0.917595i \(0.369873\pi\)
\(450\) −1.37381 −0.0647619
\(451\) −0.580386 −0.0273293
\(452\) −56.7159 −2.66769
\(453\) 3.99485 0.187695
\(454\) −21.7094 −1.01887
\(455\) 15.4829 0.725849
\(456\) 26.6236 1.24676
\(457\) 34.6162 1.61928 0.809639 0.586928i \(-0.199663\pi\)
0.809639 + 0.586928i \(0.199663\pi\)
\(458\) −1.12527 −0.0525804
\(459\) −30.3452 −1.41639
\(460\) 57.9665 2.70270
\(461\) 17.6626 0.822630 0.411315 0.911493i \(-0.365070\pi\)
0.411315 + 0.911493i \(0.365070\pi\)
\(462\) 5.95881 0.277229
\(463\) 19.9329 0.926361 0.463181 0.886264i \(-0.346708\pi\)
0.463181 + 0.886264i \(0.346708\pi\)
\(464\) −3.76359 −0.174720
\(465\) −14.7474 −0.683896
\(466\) 21.1952 0.981848
\(467\) 4.76380 0.220442 0.110221 0.993907i \(-0.464844\pi\)
0.110221 + 0.993907i \(0.464844\pi\)
\(468\) 8.45618 0.390887
\(469\) 22.0310 1.01730
\(470\) −60.2615 −2.77966
\(471\) 0.215153 0.00991375
\(472\) 30.3330 1.39619
\(473\) −2.89241 −0.132993
\(474\) −1.63123 −0.0749247
\(475\) 2.73210 0.125357
\(476\) 50.2417 2.30283
\(477\) −4.74416 −0.217220
\(478\) 39.1243 1.78951
\(479\) 26.7735 1.22331 0.611657 0.791123i \(-0.290503\pi\)
0.611657 + 0.791123i \(0.290503\pi\)
\(480\) 9.74018 0.444576
\(481\) 19.4005 0.884586
\(482\) −6.68458 −0.304474
\(483\) −23.8753 −1.08636
\(484\) −39.7964 −1.80893
\(485\) 30.2421 1.37323
\(486\) −16.7618 −0.760332
\(487\) −22.1954 −1.00577 −0.502884 0.864354i \(-0.667728\pi\)
−0.502884 + 0.864354i \(0.667728\pi\)
\(488\) −9.08971 −0.411472
\(489\) 24.8956 1.12582
\(490\) −18.4765 −0.834682
\(491\) 22.1242 0.998452 0.499226 0.866472i \(-0.333618\pi\)
0.499226 + 0.866472i \(0.333618\pi\)
\(492\) −6.34246 −0.285940
\(493\) 9.65464 0.434823
\(494\) −25.7433 −1.15825
\(495\) 1.09359 0.0491531
\(496\) −8.46346 −0.380020
\(497\) −14.0475 −0.630116
\(498\) 1.89423 0.0848825
\(499\) −40.8792 −1.83000 −0.915001 0.403450i \(-0.867811\pi\)
−0.915001 + 0.403450i \(0.867811\pi\)
\(500\) 37.9006 1.69496
\(501\) 38.6307 1.72589
\(502\) −3.51384 −0.156830
\(503\) −21.5219 −0.959613 −0.479807 0.877374i \(-0.659293\pi\)
−0.479807 + 0.877374i \(0.659293\pi\)
\(504\) 5.67285 0.252689
\(505\) −8.90714 −0.396362
\(506\) −10.1213 −0.449948
\(507\) 4.28957 0.190507
\(508\) −44.6862 −1.98263
\(509\) −13.5703 −0.601494 −0.300747 0.953704i \(-0.597236\pi\)
−0.300747 + 0.953704i \(0.597236\pi\)
\(510\) 76.0205 3.36624
\(511\) 18.8515 0.833939
\(512\) 28.1867 1.24569
\(513\) 14.5226 0.641187
\(514\) 23.8978 1.05409
\(515\) 22.5864 0.995278
\(516\) −31.6083 −1.39148
\(517\) 6.87355 0.302298
\(518\) 27.7387 1.21877
\(519\) 15.5467 0.682426
\(520\) 33.6539 1.47582
\(521\) 17.3415 0.759744 0.379872 0.925039i \(-0.375968\pi\)
0.379872 + 0.925039i \(0.375968\pi\)
\(522\) 2.32337 0.101691
\(523\) 13.1524 0.575115 0.287558 0.957763i \(-0.407157\pi\)
0.287558 + 0.957763i \(0.407157\pi\)
\(524\) −24.4943 −1.07004
\(525\) 3.13534 0.136838
\(526\) 35.9241 1.56636
\(527\) 21.7111 0.945750
\(528\) 3.38016 0.147103
\(529\) 17.5533 0.763188
\(530\) −40.2407 −1.74794
\(531\) −4.88683 −0.212070
\(532\) −24.0446 −1.04247
\(533\) 2.87747 0.124637
\(534\) 8.96811 0.388088
\(535\) −4.13573 −0.178803
\(536\) 47.8869 2.06840
\(537\) 7.50842 0.324012
\(538\) 12.1172 0.522411
\(539\) 2.10746 0.0907748
\(540\) −40.4631 −1.74126
\(541\) 34.9176 1.50122 0.750612 0.660743i \(-0.229759\pi\)
0.750612 + 0.660743i \(0.229759\pi\)
\(542\) −68.0833 −2.92443
\(543\) 37.3223 1.60165
\(544\) −14.3394 −0.614798
\(545\) 18.4805 0.791619
\(546\) −29.5429 −1.26432
\(547\) 37.3153 1.59549 0.797744 0.602996i \(-0.206027\pi\)
0.797744 + 0.602996i \(0.206027\pi\)
\(548\) −5.52739 −0.236118
\(549\) 1.46441 0.0624994
\(550\) 1.32915 0.0566750
\(551\) −4.62051 −0.196840
\(552\) −51.8958 −2.20883
\(553\) 0.691226 0.0293939
\(554\) −55.4865 −2.35739
\(555\) 27.4177 1.16382
\(556\) 57.3837 2.43361
\(557\) −39.1178 −1.65748 −0.828738 0.559637i \(-0.810941\pi\)
−0.828738 + 0.559637i \(0.810941\pi\)
\(558\) 5.22474 0.221181
\(559\) 14.3402 0.606524
\(560\) 12.5575 0.530651
\(561\) −8.67104 −0.366092
\(562\) −16.4868 −0.695452
\(563\) −41.5306 −1.75031 −0.875153 0.483846i \(-0.839240\pi\)
−0.875153 + 0.483846i \(0.839240\pi\)
\(564\) 75.1141 3.16287
\(565\) 36.3645 1.52986
\(566\) −4.32825 −0.181930
\(567\) 20.6744 0.868241
\(568\) −30.5338 −1.28117
\(569\) −9.13224 −0.382844 −0.191422 0.981508i \(-0.561310\pi\)
−0.191422 + 0.981508i \(0.561310\pi\)
\(570\) −36.3818 −1.52387
\(571\) −7.11507 −0.297756 −0.148878 0.988856i \(-0.547566\pi\)
−0.148878 + 0.988856i \(0.547566\pi\)
\(572\) −8.18128 −0.342077
\(573\) 13.2411 0.553157
\(574\) 4.11418 0.171723
\(575\) −5.32552 −0.222090
\(576\) −7.09125 −0.295469
\(577\) −44.1924 −1.83975 −0.919877 0.392207i \(-0.871712\pi\)
−0.919877 + 0.392207i \(0.871712\pi\)
\(578\) −71.0890 −2.95691
\(579\) 10.6881 0.444181
\(580\) 12.8738 0.534554
\(581\) −0.802674 −0.0333005
\(582\) −57.7050 −2.39195
\(583\) 4.58993 0.190096
\(584\) 40.9758 1.69559
\(585\) −5.42184 −0.224165
\(586\) −17.3778 −0.717869
\(587\) 30.8270 1.27237 0.636183 0.771538i \(-0.280512\pi\)
0.636183 + 0.771538i \(0.280512\pi\)
\(588\) 23.0303 0.949755
\(589\) −10.3905 −0.428132
\(590\) −41.4508 −1.70650
\(591\) 21.6786 0.891740
\(592\) 15.7349 0.646699
\(593\) −26.1364 −1.07329 −0.536646 0.843807i \(-0.680309\pi\)
−0.536646 + 0.843807i \(0.680309\pi\)
\(594\) 7.06512 0.289885
\(595\) −32.2134 −1.32062
\(596\) 19.8204 0.811874
\(597\) 44.8749 1.83661
\(598\) 50.1800 2.05201
\(599\) −42.9686 −1.75565 −0.877824 0.478983i \(-0.841005\pi\)
−0.877824 + 0.478983i \(0.841005\pi\)
\(600\) 6.81503 0.278222
\(601\) −12.3714 −0.504638 −0.252319 0.967644i \(-0.581193\pi\)
−0.252319 + 0.967644i \(0.581193\pi\)
\(602\) 20.5034 0.835658
\(603\) −7.71486 −0.314173
\(604\) −7.84216 −0.319093
\(605\) 25.5162 1.03738
\(606\) 16.9957 0.690403
\(607\) −17.9270 −0.727635 −0.363817 0.931470i \(-0.618527\pi\)
−0.363817 + 0.931470i \(0.618527\pi\)
\(608\) 6.86255 0.278313
\(609\) −5.30247 −0.214867
\(610\) 12.4213 0.502925
\(611\) −34.0780 −1.37865
\(612\) −17.5938 −0.711186
\(613\) −9.50776 −0.384015 −0.192007 0.981393i \(-0.561500\pi\)
−0.192007 + 0.981393i \(0.561500\pi\)
\(614\) −57.9498 −2.33866
\(615\) 4.06658 0.163981
\(616\) −5.48844 −0.221135
\(617\) −38.4300 −1.54713 −0.773566 0.633715i \(-0.781529\pi\)
−0.773566 + 0.633715i \(0.781529\pi\)
\(618\) −43.0972 −1.73362
\(619\) 15.3425 0.616669 0.308334 0.951278i \(-0.400228\pi\)
0.308334 + 0.951278i \(0.400228\pi\)
\(620\) 28.9502 1.16267
\(621\) −28.3080 −1.13596
\(622\) −5.03424 −0.201855
\(623\) −3.80021 −0.152252
\(624\) −16.7583 −0.670870
\(625\) −28.4820 −1.13928
\(626\) −23.8585 −0.953578
\(627\) 4.14978 0.165726
\(628\) −0.422360 −0.0168540
\(629\) −40.3642 −1.60943
\(630\) −7.75210 −0.308851
\(631\) 2.60971 0.103891 0.0519455 0.998650i \(-0.483458\pi\)
0.0519455 + 0.998650i \(0.483458\pi\)
\(632\) 1.50246 0.0597646
\(633\) −33.0677 −1.31432
\(634\) −12.9412 −0.513962
\(635\) 28.6514 1.13699
\(636\) 50.1588 1.98892
\(637\) −10.4485 −0.413984
\(638\) −2.24784 −0.0889930
\(639\) 4.91918 0.194600
\(640\) −49.9998 −1.97642
\(641\) 25.5763 1.01020 0.505101 0.863060i \(-0.331455\pi\)
0.505101 + 0.863060i \(0.331455\pi\)
\(642\) 7.89138 0.311448
\(643\) 28.9415 1.14134 0.570671 0.821179i \(-0.306683\pi\)
0.570671 + 0.821179i \(0.306683\pi\)
\(644\) 46.8688 1.84689
\(645\) 20.2662 0.797982
\(646\) 53.5610 2.10733
\(647\) 47.9062 1.88339 0.941694 0.336470i \(-0.109233\pi\)
0.941694 + 0.336470i \(0.109233\pi\)
\(648\) 44.9381 1.76534
\(649\) 4.72796 0.185589
\(650\) −6.58971 −0.258470
\(651\) −11.9240 −0.467340
\(652\) −48.8717 −1.91396
\(653\) 23.3821 0.915013 0.457507 0.889206i \(-0.348743\pi\)
0.457507 + 0.889206i \(0.348743\pi\)
\(654\) −35.2627 −1.37888
\(655\) 15.7050 0.613644
\(656\) 2.33379 0.0911191
\(657\) −6.60145 −0.257547
\(658\) −48.7245 −1.89948
\(659\) 6.71032 0.261397 0.130699 0.991422i \(-0.458278\pi\)
0.130699 + 0.991422i \(0.458278\pi\)
\(660\) −11.5622 −0.450058
\(661\) 9.78504 0.380594 0.190297 0.981727i \(-0.439055\pi\)
0.190297 + 0.981727i \(0.439055\pi\)
\(662\) −39.7422 −1.54463
\(663\) 42.9897 1.66958
\(664\) −1.74470 −0.0677076
\(665\) 15.4167 0.597832
\(666\) −9.71359 −0.376394
\(667\) 9.00649 0.348733
\(668\) −75.8346 −2.93413
\(669\) 20.3476 0.786682
\(670\) −65.4387 −2.52812
\(671\) −1.41680 −0.0546950
\(672\) 7.87542 0.303801
\(673\) −45.2457 −1.74409 −0.872047 0.489421i \(-0.837208\pi\)
−0.872047 + 0.489421i \(0.837208\pi\)
\(674\) −37.3462 −1.43852
\(675\) 3.71745 0.143085
\(676\) −8.42071 −0.323874
\(677\) −0.600190 −0.0230672 −0.0115336 0.999933i \(-0.503671\pi\)
−0.0115336 + 0.999933i \(0.503671\pi\)
\(678\) −69.3870 −2.66479
\(679\) 24.4523 0.938393
\(680\) −70.0196 −2.68513
\(681\) −17.3501 −0.664857
\(682\) −5.05489 −0.193562
\(683\) −16.1530 −0.618079 −0.309039 0.951049i \(-0.600007\pi\)
−0.309039 + 0.951049i \(0.600007\pi\)
\(684\) 8.42000 0.321947
\(685\) 3.54399 0.135409
\(686\) −47.7774 −1.82415
\(687\) −0.899312 −0.0343109
\(688\) 11.6307 0.443415
\(689\) −22.7562 −0.866942
\(690\) 70.9169 2.69976
\(691\) −45.3242 −1.72421 −0.862106 0.506727i \(-0.830855\pi\)
−0.862106 + 0.506727i \(0.830855\pi\)
\(692\) −30.5193 −1.16017
\(693\) 0.884220 0.0335887
\(694\) −0.569555 −0.0216200
\(695\) −36.7926 −1.39562
\(696\) −11.5255 −0.436874
\(697\) −5.98680 −0.226766
\(698\) 29.2764 1.10813
\(699\) 16.9391 0.640696
\(700\) −6.15488 −0.232633
\(701\) 25.1855 0.951243 0.475621 0.879650i \(-0.342223\pi\)
0.475621 + 0.879650i \(0.342223\pi\)
\(702\) −35.0278 −1.32204
\(703\) 19.3175 0.728572
\(704\) 6.86072 0.258573
\(705\) −48.1608 −1.81384
\(706\) 34.9949 1.31705
\(707\) −7.20187 −0.270854
\(708\) 51.6671 1.94177
\(709\) −31.2398 −1.17323 −0.586617 0.809864i \(-0.699541\pi\)
−0.586617 + 0.809864i \(0.699541\pi\)
\(710\) 41.7253 1.56592
\(711\) −0.242055 −0.00907778
\(712\) −8.26019 −0.309564
\(713\) 20.2535 0.758501
\(714\) 61.4664 2.30032
\(715\) 5.24558 0.196174
\(716\) −14.7395 −0.550842
\(717\) 31.2680 1.16773
\(718\) −47.8043 −1.78404
\(719\) 35.8470 1.33687 0.668434 0.743771i \(-0.266965\pi\)
0.668434 + 0.743771i \(0.266965\pi\)
\(720\) −4.39741 −0.163882
\(721\) 18.2623 0.680123
\(722\) 19.9980 0.744247
\(723\) −5.34229 −0.198682
\(724\) −73.2660 −2.72291
\(725\) −1.18275 −0.0439261
\(726\) −48.6874 −1.80696
\(727\) 29.3426 1.08826 0.544129 0.839002i \(-0.316860\pi\)
0.544129 + 0.839002i \(0.316860\pi\)
\(728\) 27.2108 1.00850
\(729\) 18.3566 0.679872
\(730\) −55.9945 −2.07245
\(731\) −29.8358 −1.10352
\(732\) −15.4828 −0.572260
\(733\) 5.96577 0.220351 0.110175 0.993912i \(-0.464859\pi\)
0.110175 + 0.993912i \(0.464859\pi\)
\(734\) −25.6625 −0.947221
\(735\) −14.7663 −0.544664
\(736\) −13.3768 −0.493074
\(737\) 7.46406 0.274942
\(738\) −1.44071 −0.0530334
\(739\) 14.3069 0.526287 0.263144 0.964757i \(-0.415241\pi\)
0.263144 + 0.964757i \(0.415241\pi\)
\(740\) −53.8228 −1.97857
\(741\) −20.5740 −0.755803
\(742\) −32.5366 −1.19446
\(743\) 3.57676 0.131219 0.0656093 0.997845i \(-0.479101\pi\)
0.0656093 + 0.997845i \(0.479101\pi\)
\(744\) −25.9183 −0.950210
\(745\) −12.7082 −0.465592
\(746\) 28.4373 1.04116
\(747\) 0.281082 0.0102843
\(748\) 17.0218 0.622379
\(749\) −3.34394 −0.122185
\(750\) 46.3680 1.69312
\(751\) 17.9465 0.654878 0.327439 0.944872i \(-0.393814\pi\)
0.327439 + 0.944872i \(0.393814\pi\)
\(752\) −27.6392 −1.00790
\(753\) −2.80825 −0.102338
\(754\) 11.1445 0.405858
\(755\) 5.02814 0.182993
\(756\) −32.7165 −1.18989
\(757\) 17.9786 0.653442 0.326721 0.945121i \(-0.394056\pi\)
0.326721 + 0.945121i \(0.394056\pi\)
\(758\) 4.54953 0.165246
\(759\) −8.08892 −0.293609
\(760\) 33.5099 1.21553
\(761\) 2.63730 0.0956020 0.0478010 0.998857i \(-0.484779\pi\)
0.0478010 + 0.998857i \(0.484779\pi\)
\(762\) −54.6696 −1.98047
\(763\) 14.9424 0.540952
\(764\) −25.9932 −0.940402
\(765\) 11.2806 0.407850
\(766\) −30.9594 −1.11861
\(767\) −23.4405 −0.846388
\(768\) 55.6081 2.00658
\(769\) −44.4599 −1.60326 −0.801632 0.597817i \(-0.796035\pi\)
−0.801632 + 0.597817i \(0.796035\pi\)
\(770\) 7.50009 0.270285
\(771\) 19.0990 0.687835
\(772\) −20.9814 −0.755136
\(773\) 27.6340 0.993927 0.496964 0.867771i \(-0.334448\pi\)
0.496964 + 0.867771i \(0.334448\pi\)
\(774\) −7.17994 −0.258078
\(775\) −2.65972 −0.0955401
\(776\) 53.1499 1.90797
\(777\) 22.1686 0.795295
\(778\) 35.5163 1.27332
\(779\) 2.86516 0.102655
\(780\) 57.3237 2.05252
\(781\) −4.75926 −0.170300
\(782\) −104.403 −3.73346
\(783\) −6.28692 −0.224676
\(784\) −8.47430 −0.302653
\(785\) 0.270804 0.00966541
\(786\) −29.9667 −1.06888
\(787\) 33.5212 1.19490 0.597451 0.801905i \(-0.296180\pi\)
0.597451 + 0.801905i \(0.296180\pi\)
\(788\) −42.5566 −1.51602
\(789\) 28.7104 1.02212
\(790\) −2.05315 −0.0730478
\(791\) 29.4025 1.04543
\(792\) 1.92195 0.0682937
\(793\) 7.02428 0.249440
\(794\) 7.79328 0.276573
\(795\) −32.1602 −1.14061
\(796\) −88.0924 −3.12235
\(797\) 13.9337 0.493556 0.246778 0.969072i \(-0.420628\pi\)
0.246778 + 0.969072i \(0.420628\pi\)
\(798\) −29.4165 −1.04133
\(799\) 70.9020 2.50833
\(800\) 1.75666 0.0621072
\(801\) 1.33077 0.0470203
\(802\) −57.7269 −2.03841
\(803\) 6.38684 0.225387
\(804\) 81.5672 2.87665
\(805\) −30.0508 −1.05915
\(806\) 25.0614 0.882749
\(807\) 9.68405 0.340895
\(808\) −15.6541 −0.550709
\(809\) 36.6018 1.28685 0.643425 0.765509i \(-0.277513\pi\)
0.643425 + 0.765509i \(0.277513\pi\)
\(810\) −61.4091 −2.15770
\(811\) −41.5592 −1.45934 −0.729671 0.683798i \(-0.760327\pi\)
−0.729671 + 0.683798i \(0.760327\pi\)
\(812\) 10.4091 0.365287
\(813\) −54.4119 −1.90831
\(814\) 9.39781 0.329393
\(815\) 31.3350 1.09762
\(816\) 34.8671 1.22059
\(817\) 14.2788 0.499552
\(818\) 1.01768 0.0355822
\(819\) −4.38383 −0.153183
\(820\) −7.98297 −0.278777
\(821\) −10.9706 −0.382876 −0.191438 0.981505i \(-0.561315\pi\)
−0.191438 + 0.981505i \(0.561315\pi\)
\(822\) −6.76228 −0.235861
\(823\) −28.1758 −0.982146 −0.491073 0.871118i \(-0.663395\pi\)
−0.491073 + 0.871118i \(0.663395\pi\)
\(824\) 39.6952 1.38285
\(825\) 1.06225 0.0369828
\(826\) −33.5151 −1.16614
\(827\) −53.1178 −1.84709 −0.923544 0.383493i \(-0.874721\pi\)
−0.923544 + 0.383493i \(0.874721\pi\)
\(828\) −16.4126 −0.570378
\(829\) −42.9561 −1.49193 −0.745964 0.665986i \(-0.768011\pi\)
−0.745964 + 0.665986i \(0.768011\pi\)
\(830\) 2.38418 0.0827562
\(831\) −44.3446 −1.53830
\(832\) −34.0144 −1.17924
\(833\) 21.7389 0.753208
\(834\) 70.2039 2.43096
\(835\) 48.6227 1.68266
\(836\) −8.14628 −0.281745
\(837\) −14.1378 −0.488675
\(838\) 24.8533 0.858542
\(839\) 33.6731 1.16252 0.581262 0.813717i \(-0.302559\pi\)
0.581262 + 0.813717i \(0.302559\pi\)
\(840\) 38.4558 1.32685
\(841\) −26.9997 −0.931026
\(842\) 46.1379 1.59002
\(843\) −13.1762 −0.453811
\(844\) 64.9141 2.23443
\(845\) 5.39910 0.185735
\(846\) 17.0625 0.586619
\(847\) 20.6311 0.708894
\(848\) −18.4565 −0.633800
\(849\) −3.45912 −0.118717
\(850\) 13.7104 0.470263
\(851\) −37.6544 −1.29078
\(852\) −52.0092 −1.78181
\(853\) 17.2295 0.589928 0.294964 0.955508i \(-0.404692\pi\)
0.294964 + 0.955508i \(0.404692\pi\)
\(854\) 10.0433 0.343674
\(855\) −5.39864 −0.184630
\(856\) −7.26845 −0.248430
\(857\) 22.5237 0.769394 0.384697 0.923043i \(-0.374306\pi\)
0.384697 + 0.923043i \(0.374306\pi\)
\(858\) −10.0091 −0.341705
\(859\) −35.6082 −1.21494 −0.607468 0.794344i \(-0.707815\pi\)
−0.607468 + 0.794344i \(0.707815\pi\)
\(860\) −39.7839 −1.35662
\(861\) 3.28804 0.112056
\(862\) 14.3184 0.487688
\(863\) −53.5774 −1.82379 −0.911897 0.410418i \(-0.865383\pi\)
−0.911897 + 0.410418i \(0.865383\pi\)
\(864\) 9.33757 0.317670
\(865\) 19.5680 0.665332
\(866\) 30.5703 1.03882
\(867\) −56.8141 −1.92951
\(868\) 23.4077 0.794508
\(869\) 0.234186 0.00794423
\(870\) 15.7499 0.533973
\(871\) −37.0057 −1.25389
\(872\) 32.4791 1.09988
\(873\) −8.56276 −0.289806
\(874\) 49.9653 1.69010
\(875\) −19.6483 −0.664233
\(876\) 69.7954 2.35817
\(877\) 0.600351 0.0202724 0.0101362 0.999949i \(-0.496773\pi\)
0.0101362 + 0.999949i \(0.496773\pi\)
\(878\) −86.0177 −2.90296
\(879\) −13.8883 −0.468439
\(880\) 4.25446 0.143418
\(881\) −19.2905 −0.649915 −0.324958 0.945729i \(-0.605350\pi\)
−0.324958 + 0.945729i \(0.605350\pi\)
\(882\) 5.23143 0.176151
\(883\) 9.00751 0.303127 0.151563 0.988448i \(-0.451569\pi\)
0.151563 + 0.988448i \(0.451569\pi\)
\(884\) −84.3916 −2.83840
\(885\) −33.1273 −1.11356
\(886\) −11.9940 −0.402946
\(887\) −2.58077 −0.0866539 −0.0433269 0.999061i \(-0.513796\pi\)
−0.0433269 + 0.999061i \(0.513796\pi\)
\(888\) 48.1861 1.61702
\(889\) 23.1661 0.776965
\(890\) 11.2878 0.378367
\(891\) 7.00444 0.234658
\(892\) −39.9436 −1.33741
\(893\) −33.9322 −1.13550
\(894\) 24.2485 0.810991
\(895\) 9.45051 0.315896
\(896\) −40.4273 −1.35058
\(897\) 40.1036 1.33902
\(898\) −40.4590 −1.35013
\(899\) 4.49811 0.150020
\(900\) 2.15533 0.0718443
\(901\) 47.3461 1.57733
\(902\) 1.39388 0.0464111
\(903\) 16.3863 0.545301
\(904\) 63.9097 2.12561
\(905\) 46.9759 1.56153
\(906\) −9.59419 −0.318746
\(907\) 6.34947 0.210831 0.105415 0.994428i \(-0.466383\pi\)
0.105415 + 0.994428i \(0.466383\pi\)
\(908\) 34.0594 1.13030
\(909\) 2.52197 0.0836484
\(910\) −37.1843 −1.23265
\(911\) 52.1970 1.72936 0.864682 0.502319i \(-0.167520\pi\)
0.864682 + 0.502319i \(0.167520\pi\)
\(912\) −16.6866 −0.552550
\(913\) −0.271945 −0.00900005
\(914\) −83.1356 −2.74988
\(915\) 9.92708 0.328179
\(916\) 1.76541 0.0583307
\(917\) 12.6983 0.419334
\(918\) 72.8782 2.40534
\(919\) 24.2446 0.799755 0.399877 0.916569i \(-0.369053\pi\)
0.399877 + 0.916569i \(0.369053\pi\)
\(920\) −65.3189 −2.15350
\(921\) −46.3133 −1.52607
\(922\) −42.4192 −1.39700
\(923\) 23.5957 0.776662
\(924\) −9.34863 −0.307547
\(925\) 4.94484 0.162585
\(926\) −47.8717 −1.57316
\(927\) −6.39513 −0.210044
\(928\) −2.97085 −0.0975228
\(929\) 9.67059 0.317282 0.158641 0.987336i \(-0.449289\pi\)
0.158641 + 0.987336i \(0.449289\pi\)
\(930\) 35.4180 1.16140
\(931\) −10.4038 −0.340970
\(932\) −33.2526 −1.08922
\(933\) −4.02334 −0.131718
\(934\) −11.4409 −0.374359
\(935\) −10.9139 −0.356921
\(936\) −9.52876 −0.311457
\(937\) −34.0517 −1.11242 −0.556210 0.831042i \(-0.687745\pi\)
−0.556210 + 0.831042i \(0.687745\pi\)
\(938\) −52.9104 −1.72759
\(939\) −19.0676 −0.622249
\(940\) 94.5428 3.08364
\(941\) 5.38602 0.175579 0.0877896 0.996139i \(-0.472020\pi\)
0.0877896 + 0.996139i \(0.472020\pi\)
\(942\) −0.516721 −0.0168357
\(943\) −5.58488 −0.181869
\(944\) −19.0116 −0.618774
\(945\) 20.9768 0.682374
\(946\) 6.94653 0.225851
\(947\) 51.0898 1.66020 0.830098 0.557617i \(-0.188284\pi\)
0.830098 + 0.557617i \(0.188284\pi\)
\(948\) 2.55919 0.0831185
\(949\) −31.6650 −1.02789
\(950\) −6.56151 −0.212884
\(951\) −10.3426 −0.335381
\(952\) −56.6143 −1.83488
\(953\) 1.43687 0.0465448 0.0232724 0.999729i \(-0.492591\pi\)
0.0232724 + 0.999729i \(0.492591\pi\)
\(954\) 11.3938 0.368886
\(955\) 16.6660 0.539301
\(956\) −61.3811 −1.98521
\(957\) −1.79647 −0.0580716
\(958\) −64.3004 −2.07745
\(959\) 2.86549 0.0925315
\(960\) −48.0709 −1.55148
\(961\) −20.8848 −0.673703
\(962\) −46.5929 −1.50222
\(963\) 1.17099 0.0377346
\(964\) 10.4873 0.337772
\(965\) 13.4526 0.433054
\(966\) 57.3399 1.84488
\(967\) −22.1536 −0.712411 −0.356205 0.934408i \(-0.615930\pi\)
−0.356205 + 0.934408i \(0.615930\pi\)
\(968\) 44.8441 1.44134
\(969\) 42.8058 1.37512
\(970\) −72.6307 −2.33203
\(971\) 0.788995 0.0253201 0.0126600 0.999920i \(-0.495970\pi\)
0.0126600 + 0.999920i \(0.495970\pi\)
\(972\) 26.2972 0.843482
\(973\) −29.7487 −0.953698
\(974\) 53.3052 1.70801
\(975\) −5.26647 −0.168662
\(976\) 5.69709 0.182359
\(977\) −42.9843 −1.37519 −0.687594 0.726095i \(-0.741333\pi\)
−0.687594 + 0.726095i \(0.741333\pi\)
\(978\) −59.7903 −1.91188
\(979\) −1.28750 −0.0411488
\(980\) 28.9872 0.925964
\(981\) −5.23258 −0.167063
\(982\) −53.1344 −1.69559
\(983\) 32.5447 1.03801 0.519007 0.854770i \(-0.326302\pi\)
0.519007 + 0.854770i \(0.326302\pi\)
\(984\) 7.14693 0.227836
\(985\) 27.2859 0.869402
\(986\) −23.1870 −0.738423
\(987\) −38.9404 −1.23949
\(988\) 40.3880 1.28491
\(989\) −27.8328 −0.885033
\(990\) −2.62640 −0.0834725
\(991\) −28.1564 −0.894418 −0.447209 0.894430i \(-0.647582\pi\)
−0.447209 + 0.894430i \(0.647582\pi\)
\(992\) −6.68075 −0.212114
\(993\) −31.7619 −1.00793
\(994\) 33.7370 1.07007
\(995\) 56.4821 1.79060
\(996\) −2.97181 −0.0941654
\(997\) −1.49681 −0.0474044 −0.0237022 0.999719i \(-0.507545\pi\)
−0.0237022 + 0.999719i \(0.507545\pi\)
\(998\) 98.1770 3.10774
\(999\) 26.2844 0.831603
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 4001.2.a.b.1.18 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.18 184 1.1 even 1 trivial