Properties

Label 8003.2.a.d.1.8
Level $8003$
Weight $2$
Character 8003.1
Self dual yes
Analytic conductor $63.904$
Analytic rank $0$
Dimension $179$
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] = [8003,2,Mod(1,8003)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8003, 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("8003.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.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: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(179\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8003.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.63717 q^{2} +2.57307 q^{3} +4.95467 q^{4} -2.90004 q^{5} -6.78562 q^{6} +1.48673 q^{7} -7.79198 q^{8} +3.62067 q^{9} +O(q^{10})\) \(q-2.63717 q^{2} +2.57307 q^{3} +4.95467 q^{4} -2.90004 q^{5} -6.78562 q^{6} +1.48673 q^{7} -7.79198 q^{8} +3.62067 q^{9} +7.64791 q^{10} -3.69629 q^{11} +12.7487 q^{12} -4.29547 q^{13} -3.92076 q^{14} -7.46201 q^{15} +10.6394 q^{16} -6.37694 q^{17} -9.54833 q^{18} -4.90196 q^{19} -14.3688 q^{20} +3.82545 q^{21} +9.74774 q^{22} -4.46996 q^{23} -20.0493 q^{24} +3.41026 q^{25} +11.3279 q^{26} +1.59703 q^{27} +7.36625 q^{28} -3.41264 q^{29} +19.6786 q^{30} +6.91544 q^{31} -12.4740 q^{32} -9.51079 q^{33} +16.8171 q^{34} -4.31158 q^{35} +17.9392 q^{36} +5.19098 q^{37} +12.9273 q^{38} -11.0525 q^{39} +22.5971 q^{40} +3.22172 q^{41} -10.0884 q^{42} -0.0314304 q^{43} -18.3139 q^{44} -10.5001 q^{45} +11.7880 q^{46} -8.50271 q^{47} +27.3760 q^{48} -4.78964 q^{49} -8.99343 q^{50} -16.4083 q^{51} -21.2826 q^{52} +1.00000 q^{53} -4.21165 q^{54} +10.7194 q^{55} -11.5846 q^{56} -12.6131 q^{57} +8.99971 q^{58} -0.680943 q^{59} -36.9718 q^{60} +2.90398 q^{61} -18.2372 q^{62} +5.38296 q^{63} +11.6173 q^{64} +12.4570 q^{65} +25.0816 q^{66} +8.26279 q^{67} -31.5957 q^{68} -11.5015 q^{69} +11.3704 q^{70} -5.76751 q^{71} -28.2122 q^{72} +4.37688 q^{73} -13.6895 q^{74} +8.77482 q^{75} -24.2876 q^{76} -5.49537 q^{77} +29.1474 q^{78} -9.74121 q^{79} -30.8548 q^{80} -6.75275 q^{81} -8.49624 q^{82} +4.69891 q^{83} +18.9539 q^{84} +18.4934 q^{85} +0.0828874 q^{86} -8.78095 q^{87} +28.8014 q^{88} +13.2060 q^{89} +27.6906 q^{90} -6.38619 q^{91} -22.1472 q^{92} +17.7939 q^{93} +22.4231 q^{94} +14.2159 q^{95} -32.0965 q^{96} +8.75996 q^{97} +12.6311 q^{98} -13.3830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63717 −1.86476 −0.932381 0.361478i \(-0.882272\pi\)
−0.932381 + 0.361478i \(0.882272\pi\)
\(3\) 2.57307 1.48556 0.742780 0.669535i \(-0.233507\pi\)
0.742780 + 0.669535i \(0.233507\pi\)
\(4\) 4.95467 2.47734
\(5\) −2.90004 −1.29694 −0.648470 0.761240i \(-0.724591\pi\)
−0.648470 + 0.761240i \(0.724591\pi\)
\(6\) −6.78562 −2.77022
\(7\) 1.48673 0.561931 0.280965 0.959718i \(-0.409345\pi\)
0.280965 + 0.959718i \(0.409345\pi\)
\(8\) −7.79198 −2.75488
\(9\) 3.62067 1.20689
\(10\) 7.64791 2.41848
\(11\) −3.69629 −1.11447 −0.557236 0.830354i \(-0.688138\pi\)
−0.557236 + 0.830354i \(0.688138\pi\)
\(12\) 12.7487 3.68023
\(13\) −4.29547 −1.19135 −0.595674 0.803226i \(-0.703115\pi\)
−0.595674 + 0.803226i \(0.703115\pi\)
\(14\) −3.92076 −1.04787
\(15\) −7.46201 −1.92668
\(16\) 10.6394 2.65986
\(17\) −6.37694 −1.54664 −0.773318 0.634019i \(-0.781404\pi\)
−0.773318 + 0.634019i \(0.781404\pi\)
\(18\) −9.54833 −2.25056
\(19\) −4.90196 −1.12459 −0.562293 0.826938i \(-0.690081\pi\)
−0.562293 + 0.826938i \(0.690081\pi\)
\(20\) −14.3688 −3.21295
\(21\) 3.82545 0.834782
\(22\) 9.74774 2.07822
\(23\) −4.46996 −0.932051 −0.466025 0.884771i \(-0.654314\pi\)
−0.466025 + 0.884771i \(0.654314\pi\)
\(24\) −20.0493 −4.09254
\(25\) 3.41026 0.682052
\(26\) 11.3279 2.22158
\(27\) 1.59703 0.307349
\(28\) 7.36625 1.39209
\(29\) −3.41264 −0.633711 −0.316856 0.948474i \(-0.602627\pi\)
−0.316856 + 0.948474i \(0.602627\pi\)
\(30\) 19.6786 3.59280
\(31\) 6.91544 1.24205 0.621025 0.783791i \(-0.286717\pi\)
0.621025 + 0.783791i \(0.286717\pi\)
\(32\) −12.4740 −2.20512
\(33\) −9.51079 −1.65562
\(34\) 16.8171 2.88411
\(35\) −4.31158 −0.728790
\(36\) 17.9392 2.98987
\(37\) 5.19098 0.853392 0.426696 0.904395i \(-0.359677\pi\)
0.426696 + 0.904395i \(0.359677\pi\)
\(38\) 12.9273 2.09709
\(39\) −11.0525 −1.76982
\(40\) 22.5971 3.57291
\(41\) 3.22172 0.503149 0.251574 0.967838i \(-0.419052\pi\)
0.251574 + 0.967838i \(0.419052\pi\)
\(42\) −10.0884 −1.55667
\(43\) −0.0314304 −0.00479310 −0.00239655 0.999997i \(-0.500763\pi\)
−0.00239655 + 0.999997i \(0.500763\pi\)
\(44\) −18.3139 −2.76092
\(45\) −10.5001 −1.56526
\(46\) 11.7880 1.73805
\(47\) −8.50271 −1.24025 −0.620124 0.784504i \(-0.712918\pi\)
−0.620124 + 0.784504i \(0.712918\pi\)
\(48\) 27.3760 3.95138
\(49\) −4.78964 −0.684234
\(50\) −8.99343 −1.27186
\(51\) −16.4083 −2.29762
\(52\) −21.2826 −2.95137
\(53\) 1.00000 0.137361
\(54\) −4.21165 −0.573133
\(55\) 10.7194 1.44540
\(56\) −11.5846 −1.54805
\(57\) −12.6131 −1.67064
\(58\) 8.99971 1.18172
\(59\) −0.680943 −0.0886512 −0.0443256 0.999017i \(-0.514114\pi\)
−0.0443256 + 0.999017i \(0.514114\pi\)
\(60\) −36.9718 −4.77304
\(61\) 2.90398 0.371816 0.185908 0.982567i \(-0.440477\pi\)
0.185908 + 0.982567i \(0.440477\pi\)
\(62\) −18.2372 −2.31613
\(63\) 5.38296 0.678189
\(64\) 11.6173 1.45217
\(65\) 12.4570 1.54511
\(66\) 25.0816 3.08733
\(67\) 8.26279 1.00946 0.504730 0.863277i \(-0.331592\pi\)
0.504730 + 0.863277i \(0.331592\pi\)
\(68\) −31.5957 −3.83154
\(69\) −11.5015 −1.38462
\(70\) 11.3704 1.35902
\(71\) −5.76751 −0.684478 −0.342239 0.939613i \(-0.611185\pi\)
−0.342239 + 0.939613i \(0.611185\pi\)
\(72\) −28.2122 −3.32484
\(73\) 4.37688 0.512275 0.256138 0.966640i \(-0.417550\pi\)
0.256138 + 0.966640i \(0.417550\pi\)
\(74\) −13.6895 −1.59137
\(75\) 8.77482 1.01323
\(76\) −24.2876 −2.78598
\(77\) −5.49537 −0.626256
\(78\) 29.1474 3.30029
\(79\) −9.74121 −1.09597 −0.547986 0.836488i \(-0.684605\pi\)
−0.547986 + 0.836488i \(0.684605\pi\)
\(80\) −30.8548 −3.44967
\(81\) −6.75275 −0.750305
\(82\) −8.49624 −0.938253
\(83\) 4.69891 0.515772 0.257886 0.966175i \(-0.416974\pi\)
0.257886 + 0.966175i \(0.416974\pi\)
\(84\) 18.9539 2.06804
\(85\) 18.4934 2.00589
\(86\) 0.0828874 0.00893798
\(87\) −8.78095 −0.941417
\(88\) 28.8014 3.07024
\(89\) 13.2060 1.39984 0.699918 0.714223i \(-0.253220\pi\)
0.699918 + 0.714223i \(0.253220\pi\)
\(90\) 27.6906 2.91884
\(91\) −6.38619 −0.669455
\(92\) −22.1472 −2.30900
\(93\) 17.7939 1.84514
\(94\) 22.4231 2.31277
\(95\) 14.2159 1.45852
\(96\) −32.0965 −3.27584
\(97\) 8.75996 0.889439 0.444720 0.895670i \(-0.353303\pi\)
0.444720 + 0.895670i \(0.353303\pi\)
\(98\) 12.6311 1.27593
\(99\) −13.3830 −1.34505
\(100\) 16.8967 1.68967
\(101\) 9.15275 0.910733 0.455367 0.890304i \(-0.349508\pi\)
0.455367 + 0.890304i \(0.349508\pi\)
\(102\) 43.2715 4.28452
\(103\) −5.15534 −0.507971 −0.253985 0.967208i \(-0.581741\pi\)
−0.253985 + 0.967208i \(0.581741\pi\)
\(104\) 33.4702 3.28202
\(105\) −11.0940 −1.08266
\(106\) −2.63717 −0.256145
\(107\) −9.54415 −0.922668 −0.461334 0.887227i \(-0.652629\pi\)
−0.461334 + 0.887227i \(0.652629\pi\)
\(108\) 7.91277 0.761407
\(109\) −6.27584 −0.601117 −0.300558 0.953763i \(-0.597173\pi\)
−0.300558 + 0.953763i \(0.597173\pi\)
\(110\) −28.2689 −2.69533
\(111\) 13.3567 1.26777
\(112\) 15.8179 1.49465
\(113\) 15.1481 1.42501 0.712507 0.701665i \(-0.247560\pi\)
0.712507 + 0.701665i \(0.247560\pi\)
\(114\) 33.2628 3.11535
\(115\) 12.9631 1.20881
\(116\) −16.9085 −1.56992
\(117\) −15.5525 −1.43783
\(118\) 1.79576 0.165313
\(119\) −9.48078 −0.869102
\(120\) 58.1438 5.30778
\(121\) 2.66253 0.242048
\(122\) −7.65829 −0.693349
\(123\) 8.28971 0.747458
\(124\) 34.2637 3.07697
\(125\) 4.61032 0.412360
\(126\) −14.1958 −1.26466
\(127\) 10.6958 0.949100 0.474550 0.880228i \(-0.342611\pi\)
0.474550 + 0.880228i \(0.342611\pi\)
\(128\) −5.68881 −0.502824
\(129\) −0.0808726 −0.00712043
\(130\) −32.8513 −2.88125
\(131\) 10.2277 0.893600 0.446800 0.894634i \(-0.352563\pi\)
0.446800 + 0.894634i \(0.352563\pi\)
\(132\) −47.1228 −4.10152
\(133\) −7.28788 −0.631939
\(134\) −21.7904 −1.88240
\(135\) −4.63147 −0.398613
\(136\) 49.6890 4.26079
\(137\) 9.60311 0.820449 0.410225 0.911985i \(-0.365450\pi\)
0.410225 + 0.911985i \(0.365450\pi\)
\(138\) 30.3314 2.58198
\(139\) −10.7069 −0.908149 −0.454074 0.890964i \(-0.650030\pi\)
−0.454074 + 0.890964i \(0.650030\pi\)
\(140\) −21.3625 −1.80546
\(141\) −21.8780 −1.84246
\(142\) 15.2099 1.27639
\(143\) 15.8773 1.32772
\(144\) 38.5219 3.21016
\(145\) 9.89681 0.821885
\(146\) −11.5426 −0.955271
\(147\) −12.3241 −1.01647
\(148\) 25.7196 2.11414
\(149\) 0.971180 0.0795622 0.0397811 0.999208i \(-0.487334\pi\)
0.0397811 + 0.999208i \(0.487334\pi\)
\(150\) −23.1407 −1.88943
\(151\) −1.00000 −0.0813788
\(152\) 38.1959 3.09810
\(153\) −23.0888 −1.86662
\(154\) 14.4922 1.16782
\(155\) −20.0551 −1.61086
\(156\) −54.7616 −4.38444
\(157\) 1.07348 0.0856731 0.0428365 0.999082i \(-0.486361\pi\)
0.0428365 + 0.999082i \(0.486361\pi\)
\(158\) 25.6892 2.04373
\(159\) 2.57307 0.204057
\(160\) 36.1753 2.85991
\(161\) −6.64561 −0.523748
\(162\) 17.8082 1.39914
\(163\) 1.68888 0.132283 0.0661415 0.997810i \(-0.478931\pi\)
0.0661415 + 0.997810i \(0.478931\pi\)
\(164\) 15.9626 1.24647
\(165\) 27.5817 2.14723
\(166\) −12.3918 −0.961793
\(167\) −18.9897 −1.46947 −0.734733 0.678356i \(-0.762693\pi\)
−0.734733 + 0.678356i \(0.762693\pi\)
\(168\) −29.8078 −2.29972
\(169\) 5.45102 0.419309
\(170\) −48.7703 −3.74051
\(171\) −17.7484 −1.35725
\(172\) −0.155727 −0.0118741
\(173\) 20.7337 1.57635 0.788175 0.615451i \(-0.211026\pi\)
0.788175 + 0.615451i \(0.211026\pi\)
\(174\) 23.1569 1.75552
\(175\) 5.07013 0.383266
\(176\) −39.3264 −2.96434
\(177\) −1.75211 −0.131697
\(178\) −34.8265 −2.61036
\(179\) −7.01718 −0.524489 −0.262244 0.965002i \(-0.584463\pi\)
−0.262244 + 0.965002i \(0.584463\pi\)
\(180\) −52.0246 −3.87769
\(181\) 3.04172 0.226089 0.113045 0.993590i \(-0.463940\pi\)
0.113045 + 0.993590i \(0.463940\pi\)
\(182\) 16.8415 1.24837
\(183\) 7.47213 0.552356
\(184\) 34.8298 2.56769
\(185\) −15.0541 −1.10680
\(186\) −46.9255 −3.44075
\(187\) 23.5710 1.72368
\(188\) −42.1281 −3.07251
\(189\) 2.37435 0.172709
\(190\) −37.4898 −2.71979
\(191\) 5.31681 0.384711 0.192355 0.981325i \(-0.438387\pi\)
0.192355 + 0.981325i \(0.438387\pi\)
\(192\) 29.8922 2.15728
\(193\) −25.0274 −1.80152 −0.900758 0.434322i \(-0.856988\pi\)
−0.900758 + 0.434322i \(0.856988\pi\)
\(194\) −23.1015 −1.65859
\(195\) 32.0528 2.29535
\(196\) −23.7311 −1.69508
\(197\) 13.0527 0.929967 0.464984 0.885319i \(-0.346060\pi\)
0.464984 + 0.885319i \(0.346060\pi\)
\(198\) 35.2934 2.50819
\(199\) 14.9935 1.06286 0.531430 0.847102i \(-0.321655\pi\)
0.531430 + 0.847102i \(0.321655\pi\)
\(200\) −26.5726 −1.87897
\(201\) 21.2607 1.49962
\(202\) −24.1374 −1.69830
\(203\) −5.07367 −0.356102
\(204\) −81.2977 −5.69198
\(205\) −9.34314 −0.652553
\(206\) 13.5955 0.947244
\(207\) −16.1843 −1.12488
\(208\) −45.7013 −3.16881
\(209\) 18.1190 1.25332
\(210\) 29.2567 2.01891
\(211\) 2.74882 0.189237 0.0946185 0.995514i \(-0.469837\pi\)
0.0946185 + 0.995514i \(0.469837\pi\)
\(212\) 4.95467 0.340288
\(213\) −14.8402 −1.01683
\(214\) 25.1696 1.72056
\(215\) 0.0911496 0.00621635
\(216\) −12.4440 −0.846709
\(217\) 10.2814 0.697946
\(218\) 16.5505 1.12094
\(219\) 11.2620 0.761016
\(220\) 53.1111 3.58075
\(221\) 27.3919 1.84258
\(222\) −35.2240 −2.36408
\(223\) −18.1285 −1.21397 −0.606986 0.794712i \(-0.707622\pi\)
−0.606986 + 0.794712i \(0.707622\pi\)
\(224\) −18.5455 −1.23912
\(225\) 12.3474 0.823162
\(226\) −39.9482 −2.65731
\(227\) 9.58649 0.636278 0.318139 0.948044i \(-0.396942\pi\)
0.318139 + 0.948044i \(0.396942\pi\)
\(228\) −62.4936 −4.13874
\(229\) 21.2902 1.40689 0.703447 0.710748i \(-0.251643\pi\)
0.703447 + 0.710748i \(0.251643\pi\)
\(230\) −34.1858 −2.25415
\(231\) −14.1400 −0.930341
\(232\) 26.5912 1.74580
\(233\) 13.8308 0.906086 0.453043 0.891489i \(-0.350338\pi\)
0.453043 + 0.891489i \(0.350338\pi\)
\(234\) 41.0145 2.68120
\(235\) 24.6582 1.60853
\(236\) −3.37385 −0.219619
\(237\) −25.0648 −1.62813
\(238\) 25.0024 1.62067
\(239\) 22.8217 1.47621 0.738107 0.674684i \(-0.235720\pi\)
0.738107 + 0.674684i \(0.235720\pi\)
\(240\) −79.3915 −5.12470
\(241\) 1.00428 0.0646911 0.0323456 0.999477i \(-0.489702\pi\)
0.0323456 + 0.999477i \(0.489702\pi\)
\(242\) −7.02154 −0.451361
\(243\) −22.1664 −1.42197
\(244\) 14.3883 0.921114
\(245\) 13.8902 0.887410
\(246\) −21.8614 −1.39383
\(247\) 21.0562 1.33977
\(248\) −53.8849 −3.42170
\(249\) 12.0906 0.766211
\(250\) −12.1582 −0.768953
\(251\) −7.75507 −0.489496 −0.244748 0.969587i \(-0.578705\pi\)
−0.244748 + 0.969587i \(0.578705\pi\)
\(252\) 26.6708 1.68010
\(253\) 16.5222 1.03874
\(254\) −28.2067 −1.76985
\(255\) 47.5848 2.97988
\(256\) −8.23231 −0.514519
\(257\) 3.31503 0.206786 0.103393 0.994641i \(-0.467030\pi\)
0.103393 + 0.994641i \(0.467030\pi\)
\(258\) 0.213275 0.0132779
\(259\) 7.71758 0.479547
\(260\) 61.7205 3.82775
\(261\) −12.3561 −0.764820
\(262\) −26.9723 −1.66635
\(263\) 16.4652 1.01529 0.507644 0.861567i \(-0.330516\pi\)
0.507644 + 0.861567i \(0.330516\pi\)
\(264\) 74.1078 4.56102
\(265\) −2.90004 −0.178148
\(266\) 19.2194 1.17842
\(267\) 33.9800 2.07954
\(268\) 40.9394 2.50077
\(269\) 3.91928 0.238962 0.119481 0.992836i \(-0.461877\pi\)
0.119481 + 0.992836i \(0.461877\pi\)
\(270\) 12.2140 0.743318
\(271\) −16.2709 −0.988386 −0.494193 0.869352i \(-0.664536\pi\)
−0.494193 + 0.869352i \(0.664536\pi\)
\(272\) −67.8470 −4.11383
\(273\) −16.4321 −0.994516
\(274\) −25.3250 −1.52994
\(275\) −12.6053 −0.760127
\(276\) −56.9862 −3.43016
\(277\) −24.9225 −1.49745 −0.748724 0.662882i \(-0.769333\pi\)
−0.748724 + 0.662882i \(0.769333\pi\)
\(278\) 28.2360 1.69348
\(279\) 25.0385 1.49902
\(280\) 33.5957 2.00773
\(281\) −30.9217 −1.84463 −0.922317 0.386435i \(-0.873706\pi\)
−0.922317 + 0.386435i \(0.873706\pi\)
\(282\) 57.6961 3.43576
\(283\) −13.0306 −0.774587 −0.387293 0.921957i \(-0.626590\pi\)
−0.387293 + 0.921957i \(0.626590\pi\)
\(284\) −28.5761 −1.69568
\(285\) 36.5785 2.16672
\(286\) −41.8711 −2.47589
\(287\) 4.78983 0.282735
\(288\) −45.1644 −2.66134
\(289\) 23.6654 1.39208
\(290\) −26.0996 −1.53262
\(291\) 22.5400 1.32132
\(292\) 21.6860 1.26908
\(293\) 8.72238 0.509567 0.254784 0.966998i \(-0.417996\pi\)
0.254784 + 0.966998i \(0.417996\pi\)
\(294\) 32.5007 1.89548
\(295\) 1.97476 0.114975
\(296\) −40.4480 −2.35099
\(297\) −5.90309 −0.342532
\(298\) −2.56117 −0.148365
\(299\) 19.2005 1.11040
\(300\) 43.4764 2.51011
\(301\) −0.0467285 −0.00269339
\(302\) 2.63717 0.151752
\(303\) 23.5506 1.35295
\(304\) −52.1540 −2.99124
\(305\) −8.42166 −0.482223
\(306\) 60.8892 3.48080
\(307\) 33.6079 1.91810 0.959051 0.283233i \(-0.0914071\pi\)
0.959051 + 0.283233i \(0.0914071\pi\)
\(308\) −27.2278 −1.55145
\(309\) −13.2650 −0.754621
\(310\) 52.8887 3.00388
\(311\) −24.9450 −1.41450 −0.707251 0.706962i \(-0.750065\pi\)
−0.707251 + 0.706962i \(0.750065\pi\)
\(312\) 86.1210 4.87564
\(313\) 22.5492 1.27456 0.637279 0.770633i \(-0.280060\pi\)
0.637279 + 0.770633i \(0.280060\pi\)
\(314\) −2.83095 −0.159760
\(315\) −15.6108 −0.879570
\(316\) −48.2645 −2.71509
\(317\) 28.2208 1.58504 0.792519 0.609848i \(-0.208769\pi\)
0.792519 + 0.609848i \(0.208769\pi\)
\(318\) −6.78562 −0.380519
\(319\) 12.6141 0.706253
\(320\) −33.6908 −1.88337
\(321\) −24.5577 −1.37068
\(322\) 17.5256 0.976665
\(323\) 31.2595 1.73933
\(324\) −33.4576 −1.85876
\(325\) −14.6486 −0.812561
\(326\) −4.45386 −0.246676
\(327\) −16.1482 −0.892995
\(328\) −25.1036 −1.38611
\(329\) −12.6412 −0.696933
\(330\) −72.7377 −4.00408
\(331\) −0.799618 −0.0439510 −0.0219755 0.999759i \(-0.506996\pi\)
−0.0219755 + 0.999759i \(0.506996\pi\)
\(332\) 23.2816 1.27774
\(333\) 18.7949 1.02995
\(334\) 50.0791 2.74020
\(335\) −23.9625 −1.30921
\(336\) 40.7006 2.22040
\(337\) −9.58027 −0.521870 −0.260935 0.965356i \(-0.584031\pi\)
−0.260935 + 0.965356i \(0.584031\pi\)
\(338\) −14.3753 −0.781912
\(339\) 38.9771 2.11695
\(340\) 91.6288 4.96927
\(341\) −25.5614 −1.38423
\(342\) 46.8055 2.53095
\(343\) −17.5280 −0.946423
\(344\) 0.244905 0.0132044
\(345\) 33.3549 1.79577
\(346\) −54.6782 −2.93952
\(347\) −16.1218 −0.865462 −0.432731 0.901523i \(-0.642450\pi\)
−0.432731 + 0.901523i \(0.642450\pi\)
\(348\) −43.5067 −2.33221
\(349\) −25.1886 −1.34831 −0.674157 0.738588i \(-0.735493\pi\)
−0.674157 + 0.738588i \(0.735493\pi\)
\(350\) −13.3708 −0.714699
\(351\) −6.86000 −0.366160
\(352\) 46.1076 2.45754
\(353\) 27.6568 1.47202 0.736011 0.676969i \(-0.236707\pi\)
0.736011 + 0.676969i \(0.236707\pi\)
\(354\) 4.62062 0.245583
\(355\) 16.7260 0.887727
\(356\) 65.4315 3.46786
\(357\) −24.3947 −1.29110
\(358\) 18.5055 0.978046
\(359\) −18.3900 −0.970585 −0.485292 0.874352i \(-0.661287\pi\)
−0.485292 + 0.874352i \(0.661287\pi\)
\(360\) 81.8166 4.31211
\(361\) 5.02919 0.264694
\(362\) −8.02154 −0.421603
\(363\) 6.85086 0.359577
\(364\) −31.6415 −1.65846
\(365\) −12.6931 −0.664390
\(366\) −19.7053 −1.03001
\(367\) −21.3033 −1.11203 −0.556013 0.831174i \(-0.687669\pi\)
−0.556013 + 0.831174i \(0.687669\pi\)
\(368\) −47.5578 −2.47912
\(369\) 11.6648 0.607246
\(370\) 39.7002 2.06391
\(371\) 1.48673 0.0771871
\(372\) 88.1629 4.57103
\(373\) 26.5523 1.37482 0.687412 0.726268i \(-0.258747\pi\)
0.687412 + 0.726268i \(0.258747\pi\)
\(374\) −62.1608 −3.21426
\(375\) 11.8627 0.612585
\(376\) 66.2529 3.41673
\(377\) 14.6589 0.754970
\(378\) −6.26158 −0.322061
\(379\) 1.33021 0.0683284 0.0341642 0.999416i \(-0.489123\pi\)
0.0341642 + 0.999416i \(0.489123\pi\)
\(380\) 70.4351 3.61324
\(381\) 27.5211 1.40995
\(382\) −14.0213 −0.717394
\(383\) 5.59909 0.286100 0.143050 0.989715i \(-0.454309\pi\)
0.143050 + 0.989715i \(0.454309\pi\)
\(384\) −14.6377 −0.746976
\(385\) 15.9368 0.812216
\(386\) 66.0017 3.35940
\(387\) −0.113799 −0.00578474
\(388\) 43.4027 2.20344
\(389\) −24.1642 −1.22518 −0.612588 0.790402i \(-0.709872\pi\)
−0.612588 + 0.790402i \(0.709872\pi\)
\(390\) −84.5287 −4.28028
\(391\) 28.5047 1.44154
\(392\) 37.3207 1.88498
\(393\) 26.3166 1.32750
\(394\) −34.4222 −1.73417
\(395\) 28.2499 1.42141
\(396\) −66.3086 −3.33213
\(397\) 29.4144 1.47627 0.738134 0.674654i \(-0.235707\pi\)
0.738134 + 0.674654i \(0.235707\pi\)
\(398\) −39.5404 −1.98198
\(399\) −18.7522 −0.938784
\(400\) 36.2832 1.81416
\(401\) 28.2144 1.40896 0.704480 0.709724i \(-0.251180\pi\)
0.704480 + 0.709724i \(0.251180\pi\)
\(402\) −56.0681 −2.79642
\(403\) −29.7050 −1.47971
\(404\) 45.3489 2.25619
\(405\) 19.5833 0.973100
\(406\) 13.3801 0.664045
\(407\) −19.1874 −0.951082
\(408\) 127.853 6.32967
\(409\) 27.7090 1.37012 0.685060 0.728486i \(-0.259776\pi\)
0.685060 + 0.728486i \(0.259776\pi\)
\(410\) 24.6395 1.21686
\(411\) 24.7094 1.21883
\(412\) −25.5430 −1.25841
\(413\) −1.01238 −0.0498158
\(414\) 42.6806 2.09764
\(415\) −13.6271 −0.668926
\(416\) 53.5818 2.62707
\(417\) −27.5496 −1.34911
\(418\) −47.7830 −2.33714
\(419\) −34.3433 −1.67778 −0.838889 0.544303i \(-0.816794\pi\)
−0.838889 + 0.544303i \(0.816794\pi\)
\(420\) −54.9670 −2.68212
\(421\) −12.9770 −0.632459 −0.316230 0.948683i \(-0.602417\pi\)
−0.316230 + 0.948683i \(0.602417\pi\)
\(422\) −7.24912 −0.352882
\(423\) −30.7855 −1.49684
\(424\) −7.79198 −0.378412
\(425\) −21.7470 −1.05489
\(426\) 39.1361 1.89615
\(427\) 4.31743 0.208935
\(428\) −47.2881 −2.28576
\(429\) 40.8533 1.97241
\(430\) −0.240377 −0.0115920
\(431\) −8.34407 −0.401920 −0.200960 0.979599i \(-0.564406\pi\)
−0.200960 + 0.979599i \(0.564406\pi\)
\(432\) 16.9915 0.817505
\(433\) 1.28569 0.0617865 0.0308932 0.999523i \(-0.490165\pi\)
0.0308932 + 0.999523i \(0.490165\pi\)
\(434\) −27.1138 −1.30150
\(435\) 25.4651 1.22096
\(436\) −31.0947 −1.48917
\(437\) 21.9115 1.04817
\(438\) −29.6998 −1.41911
\(439\) −7.87133 −0.375678 −0.187839 0.982200i \(-0.560148\pi\)
−0.187839 + 0.982200i \(0.560148\pi\)
\(440\) −83.5252 −3.98191
\(441\) −17.3417 −0.825796
\(442\) −72.2372 −3.43597
\(443\) 6.94662 0.330044 0.165022 0.986290i \(-0.447231\pi\)
0.165022 + 0.986290i \(0.447231\pi\)
\(444\) 66.1783 3.14068
\(445\) −38.2981 −1.81550
\(446\) 47.8079 2.26377
\(447\) 2.49891 0.118194
\(448\) 17.2718 0.816017
\(449\) −9.40260 −0.443736 −0.221868 0.975077i \(-0.571215\pi\)
−0.221868 + 0.975077i \(0.571215\pi\)
\(450\) −32.5623 −1.53500
\(451\) −11.9084 −0.560745
\(452\) 75.0539 3.53024
\(453\) −2.57307 −0.120893
\(454\) −25.2812 −1.18651
\(455\) 18.5202 0.868242
\(456\) 98.2807 4.60242
\(457\) 24.8208 1.16107 0.580533 0.814236i \(-0.302844\pi\)
0.580533 + 0.814236i \(0.302844\pi\)
\(458\) −56.1458 −2.62352
\(459\) −10.1842 −0.475357
\(460\) 64.2278 2.99464
\(461\) 17.1494 0.798725 0.399363 0.916793i \(-0.369231\pi\)
0.399363 + 0.916793i \(0.369231\pi\)
\(462\) 37.2895 1.73486
\(463\) 9.77502 0.454284 0.227142 0.973862i \(-0.427062\pi\)
0.227142 + 0.973862i \(0.427062\pi\)
\(464\) −36.3085 −1.68558
\(465\) −51.6031 −2.39304
\(466\) −36.4742 −1.68964
\(467\) −22.2334 −1.02884 −0.514419 0.857539i \(-0.671992\pi\)
−0.514419 + 0.857539i \(0.671992\pi\)
\(468\) −77.0574 −3.56198
\(469\) 12.2845 0.567247
\(470\) −65.0280 −2.99952
\(471\) 2.76214 0.127273
\(472\) 5.30589 0.244223
\(473\) 0.116176 0.00534177
\(474\) 66.1001 3.03608
\(475\) −16.7169 −0.767026
\(476\) −46.9742 −2.15306
\(477\) 3.62067 0.165779
\(478\) −60.1847 −2.75279
\(479\) −36.5836 −1.67155 −0.835775 0.549072i \(-0.814981\pi\)
−0.835775 + 0.549072i \(0.814981\pi\)
\(480\) 93.0814 4.24857
\(481\) −22.2977 −1.01669
\(482\) −2.64845 −0.120634
\(483\) −17.0996 −0.778059
\(484\) 13.1919 0.599634
\(485\) −25.4043 −1.15355
\(486\) 58.4565 2.65164
\(487\) −20.8560 −0.945076 −0.472538 0.881310i \(-0.656662\pi\)
−0.472538 + 0.881310i \(0.656662\pi\)
\(488\) −22.6277 −1.02431
\(489\) 4.34559 0.196515
\(490\) −36.6307 −1.65481
\(491\) −7.18588 −0.324294 −0.162147 0.986767i \(-0.551842\pi\)
−0.162147 + 0.986767i \(0.551842\pi\)
\(492\) 41.0728 1.85170
\(493\) 21.7622 0.980120
\(494\) −55.5288 −2.49836
\(495\) 38.8114 1.74444
\(496\) 73.5763 3.30368
\(497\) −8.57473 −0.384629
\(498\) −31.8850 −1.42880
\(499\) −32.7283 −1.46512 −0.732561 0.680702i \(-0.761675\pi\)
−0.732561 + 0.680702i \(0.761675\pi\)
\(500\) 22.8426 1.02155
\(501\) −48.8617 −2.18298
\(502\) 20.4515 0.912793
\(503\) −27.1250 −1.20944 −0.604722 0.796437i \(-0.706716\pi\)
−0.604722 + 0.796437i \(0.706716\pi\)
\(504\) −41.9439 −1.86833
\(505\) −26.5434 −1.18117
\(506\) −43.5720 −1.93701
\(507\) 14.0258 0.622909
\(508\) 52.9943 2.35124
\(509\) −13.3052 −0.589742 −0.294871 0.955537i \(-0.595277\pi\)
−0.294871 + 0.955537i \(0.595277\pi\)
\(510\) −125.489 −5.55676
\(511\) 6.50723 0.287863
\(512\) 33.0876 1.46228
\(513\) −7.82859 −0.345641
\(514\) −8.74230 −0.385606
\(515\) 14.9507 0.658807
\(516\) −0.400697 −0.0176397
\(517\) 31.4284 1.38222
\(518\) −20.3526 −0.894241
\(519\) 53.3491 2.34176
\(520\) −97.0649 −4.25658
\(521\) 4.51369 0.197749 0.0988743 0.995100i \(-0.468476\pi\)
0.0988743 + 0.995100i \(0.468476\pi\)
\(522\) 32.5850 1.42621
\(523\) −10.4701 −0.457826 −0.228913 0.973447i \(-0.573517\pi\)
−0.228913 + 0.973447i \(0.573517\pi\)
\(524\) 50.6750 2.21375
\(525\) 13.0458 0.569364
\(526\) −43.4216 −1.89327
\(527\) −44.0994 −1.92100
\(528\) −101.189 −4.40370
\(529\) −3.01948 −0.131282
\(530\) 7.64791 0.332204
\(531\) −2.46547 −0.106992
\(532\) −36.1091 −1.56553
\(533\) −13.8388 −0.599425
\(534\) −89.6110 −3.87785
\(535\) 27.6785 1.19664
\(536\) −64.3835 −2.78094
\(537\) −18.0557 −0.779160
\(538\) −10.3358 −0.445608
\(539\) 17.7039 0.762560
\(540\) −22.9474 −0.987498
\(541\) 2.83582 0.121922 0.0609608 0.998140i \(-0.480584\pi\)
0.0609608 + 0.998140i \(0.480584\pi\)
\(542\) 42.9091 1.84310
\(543\) 7.82656 0.335870
\(544\) 79.5463 3.41052
\(545\) 18.2002 0.779612
\(546\) 43.3342 1.85453
\(547\) 15.0891 0.645163 0.322582 0.946542i \(-0.395449\pi\)
0.322582 + 0.946542i \(0.395449\pi\)
\(548\) 47.5803 2.03253
\(549\) 10.5144 0.448742
\(550\) 33.2423 1.41746
\(551\) 16.7286 0.712663
\(552\) 89.6194 3.81445
\(553\) −14.4825 −0.615860
\(554\) 65.7249 2.79238
\(555\) −38.7352 −1.64422
\(556\) −53.0493 −2.24979
\(557\) 13.5015 0.572078 0.286039 0.958218i \(-0.407661\pi\)
0.286039 + 0.958218i \(0.407661\pi\)
\(558\) −66.0309 −2.79531
\(559\) 0.135008 0.00571024
\(560\) −45.8727 −1.93848
\(561\) 60.6498 2.56063
\(562\) 81.5458 3.43980
\(563\) −41.1858 −1.73577 −0.867887 0.496761i \(-0.834523\pi\)
−0.867887 + 0.496761i \(0.834523\pi\)
\(564\) −108.399 −4.56440
\(565\) −43.9302 −1.84816
\(566\) 34.3638 1.44442
\(567\) −10.0395 −0.421619
\(568\) 44.9403 1.88565
\(569\) 1.46558 0.0614401 0.0307201 0.999528i \(-0.490220\pi\)
0.0307201 + 0.999528i \(0.490220\pi\)
\(570\) −96.4636 −4.04042
\(571\) 10.3343 0.432478 0.216239 0.976340i \(-0.430621\pi\)
0.216239 + 0.976340i \(0.430621\pi\)
\(572\) 78.6666 3.28922
\(573\) 13.6805 0.571511
\(574\) −12.6316 −0.527233
\(575\) −15.2437 −0.635707
\(576\) 42.0626 1.75261
\(577\) −17.8421 −0.742777 −0.371388 0.928478i \(-0.621118\pi\)
−0.371388 + 0.928478i \(0.621118\pi\)
\(578\) −62.4097 −2.59590
\(579\) −64.3973 −2.67626
\(580\) 49.0354 2.03609
\(581\) 6.98600 0.289828
\(582\) −59.4417 −2.46394
\(583\) −3.69629 −0.153084
\(584\) −34.1045 −1.41126
\(585\) 45.1029 1.86477
\(586\) −23.0024 −0.950221
\(587\) 15.7618 0.650560 0.325280 0.945618i \(-0.394541\pi\)
0.325280 + 0.945618i \(0.394541\pi\)
\(588\) −61.0617 −2.51814
\(589\) −33.8992 −1.39679
\(590\) −5.20779 −0.214401
\(591\) 33.5855 1.38152
\(592\) 55.2291 2.26990
\(593\) −35.8669 −1.47288 −0.736439 0.676504i \(-0.763494\pi\)
−0.736439 + 0.676504i \(0.763494\pi\)
\(594\) 15.5675 0.638740
\(595\) 27.4947 1.12717
\(596\) 4.81188 0.197102
\(597\) 38.5792 1.57894
\(598\) −50.6351 −2.07062
\(599\) 42.9173 1.75355 0.876776 0.480899i \(-0.159690\pi\)
0.876776 + 0.480899i \(0.159690\pi\)
\(600\) −68.3732 −2.79132
\(601\) −14.4177 −0.588109 −0.294055 0.955789i \(-0.595005\pi\)
−0.294055 + 0.955789i \(0.595005\pi\)
\(602\) 0.123231 0.00502252
\(603\) 29.9169 1.21831
\(604\) −4.95467 −0.201603
\(605\) −7.72144 −0.313921
\(606\) −62.1071 −2.52293
\(607\) −16.0990 −0.653439 −0.326720 0.945121i \(-0.605943\pi\)
−0.326720 + 0.945121i \(0.605943\pi\)
\(608\) 61.1472 2.47985
\(609\) −13.0549 −0.529011
\(610\) 22.2094 0.899231
\(611\) 36.5231 1.47757
\(612\) −114.398 −4.62425
\(613\) −26.5491 −1.07231 −0.536154 0.844120i \(-0.680123\pi\)
−0.536154 + 0.844120i \(0.680123\pi\)
\(614\) −88.6297 −3.57680
\(615\) −24.0405 −0.969408
\(616\) 42.8198 1.72526
\(617\) −6.10564 −0.245804 −0.122902 0.992419i \(-0.539220\pi\)
−0.122902 + 0.992419i \(0.539220\pi\)
\(618\) 34.9822 1.40719
\(619\) 19.4193 0.780527 0.390263 0.920703i \(-0.372384\pi\)
0.390263 + 0.920703i \(0.372384\pi\)
\(620\) −99.3664 −3.99065
\(621\) −7.13867 −0.286465
\(622\) 65.7843 2.63771
\(623\) 19.6338 0.786610
\(624\) −117.592 −4.70747
\(625\) −30.4214 −1.21686
\(626\) −59.4662 −2.37675
\(627\) 46.6215 1.86188
\(628\) 5.31874 0.212241
\(629\) −33.1026 −1.31989
\(630\) 41.1684 1.64019
\(631\) 34.0860 1.35694 0.678471 0.734627i \(-0.262643\pi\)
0.678471 + 0.734627i \(0.262643\pi\)
\(632\) 75.9033 3.01927
\(633\) 7.07291 0.281123
\(634\) −74.4230 −2.95572
\(635\) −31.0184 −1.23093
\(636\) 12.7487 0.505519
\(637\) 20.5737 0.815161
\(638\) −33.2655 −1.31699
\(639\) −20.8823 −0.826090
\(640\) 16.4978 0.652132
\(641\) 8.33126 0.329065 0.164533 0.986372i \(-0.447388\pi\)
0.164533 + 0.986372i \(0.447388\pi\)
\(642\) 64.7630 2.55599
\(643\) −22.7920 −0.898827 −0.449414 0.893324i \(-0.648367\pi\)
−0.449414 + 0.893324i \(0.648367\pi\)
\(644\) −32.9268 −1.29750
\(645\) 0.234534 0.00923477
\(646\) −82.4367 −3.24343
\(647\) −49.5113 −1.94649 −0.973245 0.229771i \(-0.926202\pi\)
−0.973245 + 0.229771i \(0.926202\pi\)
\(648\) 52.6172 2.06700
\(649\) 2.51696 0.0987993
\(650\) 38.6310 1.51523
\(651\) 26.4547 1.03684
\(652\) 8.36783 0.327710
\(653\) 38.6818 1.51374 0.756868 0.653568i \(-0.226729\pi\)
0.756868 + 0.653568i \(0.226729\pi\)
\(654\) 42.5855 1.66522
\(655\) −29.6609 −1.15895
\(656\) 34.2773 1.33830
\(657\) 15.8473 0.618260
\(658\) 33.3371 1.29961
\(659\) −44.5685 −1.73614 −0.868071 0.496441i \(-0.834640\pi\)
−0.868071 + 0.496441i \(0.834640\pi\)
\(660\) 136.658 5.31942
\(661\) 26.2480 1.02093 0.510465 0.859898i \(-0.329473\pi\)
0.510465 + 0.859898i \(0.329473\pi\)
\(662\) 2.10873 0.0819581
\(663\) 70.4813 2.73727
\(664\) −36.6138 −1.42089
\(665\) 21.1352 0.819587
\(666\) −49.5652 −1.92061
\(667\) 15.2544 0.590651
\(668\) −94.0877 −3.64036
\(669\) −46.6458 −1.80343
\(670\) 63.1931 2.44136
\(671\) −10.7339 −0.414379
\(672\) −47.7189 −1.84079
\(673\) 9.36570 0.361021 0.180511 0.983573i \(-0.442225\pi\)
0.180511 + 0.983573i \(0.442225\pi\)
\(674\) 25.2648 0.973164
\(675\) 5.44629 0.209628
\(676\) 27.0080 1.03877
\(677\) −28.1827 −1.08315 −0.541575 0.840652i \(-0.682172\pi\)
−0.541575 + 0.840652i \(0.682172\pi\)
\(678\) −102.789 −3.94760
\(679\) 13.0237 0.499803
\(680\) −144.100 −5.52599
\(681\) 24.6667 0.945229
\(682\) 67.4099 2.58126
\(683\) −34.7040 −1.32791 −0.663956 0.747772i \(-0.731124\pi\)
−0.663956 + 0.747772i \(0.731124\pi\)
\(684\) −87.9374 −3.36237
\(685\) −27.8494 −1.06407
\(686\) 46.2243 1.76485
\(687\) 54.7810 2.09003
\(688\) −0.334402 −0.0127489
\(689\) −4.29547 −0.163644
\(690\) −87.9625 −3.34867
\(691\) −32.7369 −1.24537 −0.622686 0.782472i \(-0.713959\pi\)
−0.622686 + 0.782472i \(0.713959\pi\)
\(692\) 102.728 3.90515
\(693\) −19.8969 −0.755822
\(694\) 42.5159 1.61388
\(695\) 31.0505 1.17781
\(696\) 68.4209 2.59349
\(697\) −20.5447 −0.778188
\(698\) 66.4266 2.51428
\(699\) 35.5876 1.34605
\(700\) 25.1208 0.949478
\(701\) 5.40409 0.204110 0.102055 0.994779i \(-0.467458\pi\)
0.102055 + 0.994779i \(0.467458\pi\)
\(702\) 18.0910 0.682800
\(703\) −25.4460 −0.959713
\(704\) −42.9410 −1.61840
\(705\) 63.4473 2.38956
\(706\) −72.9357 −2.74497
\(707\) 13.6077 0.511769
\(708\) −8.68114 −0.326257
\(709\) 42.2359 1.58620 0.793101 0.609090i \(-0.208465\pi\)
0.793101 + 0.609090i \(0.208465\pi\)
\(710\) −44.1095 −1.65540
\(711\) −35.2697 −1.32272
\(712\) −102.901 −3.85638
\(713\) −30.9117 −1.15765
\(714\) 64.3330 2.40760
\(715\) −46.0448 −1.72198
\(716\) −34.7678 −1.29933
\(717\) 58.7218 2.19300
\(718\) 48.4975 1.80991
\(719\) 16.6282 0.620127 0.310063 0.950716i \(-0.399650\pi\)
0.310063 + 0.950716i \(0.399650\pi\)
\(720\) −111.715 −4.16338
\(721\) −7.66459 −0.285444
\(722\) −13.2628 −0.493592
\(723\) 2.58407 0.0961026
\(724\) 15.0707 0.560100
\(725\) −11.6380 −0.432224
\(726\) −18.0669 −0.670525
\(727\) 50.0953 1.85793 0.928966 0.370164i \(-0.120699\pi\)
0.928966 + 0.370164i \(0.120699\pi\)
\(728\) 49.7610 1.84427
\(729\) −36.7773 −1.36212
\(730\) 33.4740 1.23893
\(731\) 0.200430 0.00741317
\(732\) 37.0219 1.36837
\(733\) 36.2651 1.33948 0.669741 0.742595i \(-0.266405\pi\)
0.669741 + 0.742595i \(0.266405\pi\)
\(734\) 56.1806 2.07366
\(735\) 35.7403 1.31830
\(736\) 55.7584 2.05528
\(737\) −30.5416 −1.12502
\(738\) −30.7621 −1.13237
\(739\) 1.94419 0.0715180 0.0357590 0.999360i \(-0.488615\pi\)
0.0357590 + 0.999360i \(0.488615\pi\)
\(740\) −74.5880 −2.74191
\(741\) 54.1790 1.99031
\(742\) −3.92076 −0.143936
\(743\) 9.92315 0.364045 0.182022 0.983294i \(-0.441736\pi\)
0.182022 + 0.983294i \(0.441736\pi\)
\(744\) −138.650 −5.08314
\(745\) −2.81647 −0.103187
\(746\) −70.0229 −2.56372
\(747\) 17.0132 0.622481
\(748\) 116.787 4.27014
\(749\) −14.1896 −0.518475
\(750\) −31.2839 −1.14233
\(751\) 40.3651 1.47294 0.736472 0.676468i \(-0.236490\pi\)
0.736472 + 0.676468i \(0.236490\pi\)
\(752\) −90.4640 −3.29888
\(753\) −19.9543 −0.727176
\(754\) −38.6580 −1.40784
\(755\) 2.90004 0.105543
\(756\) 11.7641 0.427858
\(757\) −10.1163 −0.367684 −0.183842 0.982956i \(-0.558853\pi\)
−0.183842 + 0.982956i \(0.558853\pi\)
\(758\) −3.50800 −0.127416
\(759\) 42.5128 1.54312
\(760\) −110.770 −4.01805
\(761\) 18.6996 0.677860 0.338930 0.940812i \(-0.389935\pi\)
0.338930 + 0.940812i \(0.389935\pi\)
\(762\) −72.5777 −2.62921
\(763\) −9.33047 −0.337786
\(764\) 26.3431 0.953058
\(765\) 66.9586 2.42089
\(766\) −14.7658 −0.533508
\(767\) 2.92497 0.105614
\(768\) −21.1823 −0.764350
\(769\) −28.9857 −1.04525 −0.522625 0.852563i \(-0.675047\pi\)
−0.522625 + 0.852563i \(0.675047\pi\)
\(770\) −42.0281 −1.51459
\(771\) 8.52979 0.307193
\(772\) −124.003 −4.46296
\(773\) −21.9410 −0.789164 −0.394582 0.918861i \(-0.629111\pi\)
−0.394582 + 0.918861i \(0.629111\pi\)
\(774\) 0.300108 0.0107872
\(775\) 23.5834 0.847142
\(776\) −68.2574 −2.45030
\(777\) 19.8579 0.712397
\(778\) 63.7253 2.28466
\(779\) −15.7928 −0.565834
\(780\) 158.811 5.68635
\(781\) 21.3184 0.762832
\(782\) −75.1717 −2.68813
\(783\) −5.45010 −0.194771
\(784\) −50.9590 −1.81996
\(785\) −3.11314 −0.111113
\(786\) −69.4014 −2.47547
\(787\) −19.3800 −0.690821 −0.345411 0.938452i \(-0.612260\pi\)
−0.345411 + 0.938452i \(0.612260\pi\)
\(788\) 64.6719 2.30384
\(789\) 42.3661 1.50827
\(790\) −74.4999 −2.65059
\(791\) 22.5211 0.800759
\(792\) 104.280 3.70544
\(793\) −12.4739 −0.442962
\(794\) −77.5709 −2.75289
\(795\) −7.46201 −0.264650
\(796\) 74.2878 2.63306
\(797\) −25.8944 −0.917228 −0.458614 0.888635i \(-0.651654\pi\)
−0.458614 + 0.888635i \(0.651654\pi\)
\(798\) 49.4528 1.75061
\(799\) 54.2213 1.91821
\(800\) −42.5397 −1.50401
\(801\) 47.8147 1.68945
\(802\) −74.4062 −2.62737
\(803\) −16.1782 −0.570916
\(804\) 105.340 3.71505
\(805\) 19.2726 0.679269
\(806\) 78.3373 2.75931
\(807\) 10.0846 0.354993
\(808\) −71.3180 −2.50896
\(809\) −36.2889 −1.27585 −0.637926 0.770098i \(-0.720207\pi\)
−0.637926 + 0.770098i \(0.720207\pi\)
\(810\) −51.6444 −1.81460
\(811\) 40.6657 1.42796 0.713982 0.700164i \(-0.246890\pi\)
0.713982 + 0.700164i \(0.246890\pi\)
\(812\) −25.1384 −0.882183
\(813\) −41.8661 −1.46831
\(814\) 50.6003 1.77354
\(815\) −4.89782 −0.171563
\(816\) −174.575 −6.11134
\(817\) 0.154071 0.00539025
\(818\) −73.0733 −2.55495
\(819\) −23.1223 −0.807959
\(820\) −46.2922 −1.61659
\(821\) 24.5384 0.856397 0.428198 0.903685i \(-0.359148\pi\)
0.428198 + 0.903685i \(0.359148\pi\)
\(822\) −65.1630 −2.27282
\(823\) 22.1881 0.773430 0.386715 0.922199i \(-0.373610\pi\)
0.386715 + 0.922199i \(0.373610\pi\)
\(824\) 40.1703 1.39940
\(825\) −32.4342 −1.12922
\(826\) 2.66981 0.0928946
\(827\) 28.2855 0.983584 0.491792 0.870713i \(-0.336342\pi\)
0.491792 + 0.870713i \(0.336342\pi\)
\(828\) −80.1877 −2.78671
\(829\) 44.9937 1.56270 0.781348 0.624096i \(-0.214532\pi\)
0.781348 + 0.624096i \(0.214532\pi\)
\(830\) 35.9369 1.24739
\(831\) −64.1273 −2.22455
\(832\) −49.9018 −1.73004
\(833\) 30.5432 1.05826
\(834\) 72.6530 2.51577
\(835\) 55.0709 1.90581
\(836\) 89.7739 3.10489
\(837\) 11.0442 0.381743
\(838\) 90.5691 3.12866
\(839\) 44.5379 1.53762 0.768810 0.639477i \(-0.220849\pi\)
0.768810 + 0.639477i \(0.220849\pi\)
\(840\) 86.4440 2.98260
\(841\) −17.3539 −0.598410
\(842\) 34.2225 1.17939
\(843\) −79.5636 −2.74031
\(844\) 13.6195 0.468803
\(845\) −15.8082 −0.543819
\(846\) 81.1867 2.79126
\(847\) 3.95845 0.136014
\(848\) 10.6394 0.365359
\(849\) −33.5285 −1.15070
\(850\) 57.3506 1.96711
\(851\) −23.2035 −0.795405
\(852\) −73.5283 −2.51904
\(853\) −5.89725 −0.201918 −0.100959 0.994891i \(-0.532191\pi\)
−0.100959 + 0.994891i \(0.532191\pi\)
\(854\) −11.3858 −0.389614
\(855\) 51.4711 1.76027
\(856\) 74.3678 2.54184
\(857\) −21.4682 −0.733339 −0.366669 0.930351i \(-0.619502\pi\)
−0.366669 + 0.930351i \(0.619502\pi\)
\(858\) −107.737 −3.67808
\(859\) 7.81771 0.266737 0.133368 0.991067i \(-0.457421\pi\)
0.133368 + 0.991067i \(0.457421\pi\)
\(860\) 0.451617 0.0154000
\(861\) 12.3245 0.420020
\(862\) 22.0047 0.749485
\(863\) 19.3770 0.659600 0.329800 0.944051i \(-0.393019\pi\)
0.329800 + 0.944051i \(0.393019\pi\)
\(864\) −19.9215 −0.677742
\(865\) −60.1285 −2.04443
\(866\) −3.39059 −0.115217
\(867\) 60.8926 2.06802
\(868\) 50.9409 1.72905
\(869\) 36.0063 1.22143
\(870\) −67.1559 −2.27680
\(871\) −35.4925 −1.20262
\(872\) 48.9012 1.65600
\(873\) 31.7170 1.07346
\(874\) −57.7845 −1.95459
\(875\) 6.85430 0.231718
\(876\) 55.7995 1.88529
\(877\) 40.9518 1.38285 0.691423 0.722450i \(-0.256984\pi\)
0.691423 + 0.722450i \(0.256984\pi\)
\(878\) 20.7580 0.700550
\(879\) 22.4433 0.756993
\(880\) 114.048 3.84456
\(881\) 8.97015 0.302212 0.151106 0.988518i \(-0.451717\pi\)
0.151106 + 0.988518i \(0.451717\pi\)
\(882\) 45.7331 1.53991
\(883\) 32.0250 1.07773 0.538864 0.842393i \(-0.318854\pi\)
0.538864 + 0.842393i \(0.318854\pi\)
\(884\) 135.718 4.56469
\(885\) 5.08120 0.170803
\(886\) −18.3194 −0.615453
\(887\) 3.53183 0.118587 0.0592936 0.998241i \(-0.481115\pi\)
0.0592936 + 0.998241i \(0.481115\pi\)
\(888\) −104.075 −3.49254
\(889\) 15.9018 0.533329
\(890\) 100.999 3.38548
\(891\) 24.9601 0.836194
\(892\) −89.8207 −3.00742
\(893\) 41.6799 1.39477
\(894\) −6.59006 −0.220405
\(895\) 20.3501 0.680230
\(896\) −8.45771 −0.282552
\(897\) 49.4043 1.64956
\(898\) 24.7963 0.827462
\(899\) −23.5999 −0.787101
\(900\) 61.1775 2.03925
\(901\) −6.37694 −0.212447
\(902\) 31.4045 1.04566
\(903\) −0.120236 −0.00400119
\(904\) −118.034 −3.92574
\(905\) −8.82113 −0.293224
\(906\) 6.78562 0.225437
\(907\) −56.2770 −1.86865 −0.934323 0.356427i \(-0.883995\pi\)
−0.934323 + 0.356427i \(0.883995\pi\)
\(908\) 47.4979 1.57627
\(909\) 33.1391 1.09916
\(910\) −48.8410 −1.61906
\(911\) 31.0489 1.02869 0.514347 0.857582i \(-0.328034\pi\)
0.514347 + 0.857582i \(0.328034\pi\)
\(912\) −134.196 −4.44367
\(913\) −17.3685 −0.574814
\(914\) −65.4566 −2.16511
\(915\) −21.6695 −0.716372
\(916\) 105.486 3.48535
\(917\) 15.2058 0.502141
\(918\) 26.8574 0.886427
\(919\) −41.8810 −1.38153 −0.690764 0.723081i \(-0.742725\pi\)
−0.690764 + 0.723081i \(0.742725\pi\)
\(920\) −101.008 −3.33013
\(921\) 86.4753 2.84946
\(922\) −45.2258 −1.48943
\(923\) 24.7742 0.815451
\(924\) −70.0589 −2.30477
\(925\) 17.7026 0.582058
\(926\) −25.7784 −0.847131
\(927\) −18.6658 −0.613065
\(928\) 42.5694 1.39741
\(929\) 8.89587 0.291864 0.145932 0.989295i \(-0.453382\pi\)
0.145932 + 0.989295i \(0.453382\pi\)
\(930\) 136.086 4.46244
\(931\) 23.4786 0.769480
\(932\) 68.5271 2.24468
\(933\) −64.1852 −2.10133
\(934\) 58.6332 1.91854
\(935\) −68.3569 −2.23551
\(936\) 121.184 3.96104
\(937\) 25.1324 0.821041 0.410520 0.911851i \(-0.365347\pi\)
0.410520 + 0.911851i \(0.365347\pi\)
\(938\) −32.3964 −1.05778
\(939\) 58.0207 1.89343
\(940\) 122.173 3.98486
\(941\) −23.2201 −0.756955 −0.378478 0.925610i \(-0.623552\pi\)
−0.378478 + 0.925610i \(0.623552\pi\)
\(942\) −7.28423 −0.237333
\(943\) −14.4010 −0.468960
\(944\) −7.24484 −0.235800
\(945\) −6.88573 −0.223993
\(946\) −0.306376 −0.00996113
\(947\) −3.51095 −0.114091 −0.0570453 0.998372i \(-0.518168\pi\)
−0.0570453 + 0.998372i \(0.518168\pi\)
\(948\) −124.188 −4.03343
\(949\) −18.8007 −0.610298
\(950\) 44.0854 1.43032
\(951\) 72.6140 2.35467
\(952\) 73.8740 2.39427
\(953\) 18.6789 0.605068 0.302534 0.953139i \(-0.402167\pi\)
0.302534 + 0.953139i \(0.402167\pi\)
\(954\) −9.54833 −0.309139
\(955\) −15.4190 −0.498947
\(956\) 113.074 3.65708
\(957\) 32.4569 1.04918
\(958\) 96.4773 3.11704
\(959\) 14.2772 0.461035
\(960\) −86.6886 −2.79786
\(961\) 16.8233 0.542688
\(962\) 58.8028 1.89588
\(963\) −34.5563 −1.11356
\(964\) 4.97586 0.160262
\(965\) 72.5807 2.33646
\(966\) 45.0946 1.45089
\(967\) 12.9642 0.416901 0.208451 0.978033i \(-0.433158\pi\)
0.208451 + 0.978033i \(0.433158\pi\)
\(968\) −20.7463 −0.666812
\(969\) 80.4328 2.58387
\(970\) 66.9954 2.15109
\(971\) 49.7705 1.59721 0.798605 0.601855i \(-0.205571\pi\)
0.798605 + 0.601855i \(0.205571\pi\)
\(972\) −109.827 −3.52270
\(973\) −15.9183 −0.510317
\(974\) 55.0009 1.76234
\(975\) −37.6919 −1.20711
\(976\) 30.8967 0.988978
\(977\) 29.0302 0.928758 0.464379 0.885637i \(-0.346278\pi\)
0.464379 + 0.885637i \(0.346278\pi\)
\(978\) −11.4601 −0.366453
\(979\) −48.8132 −1.56008
\(980\) 68.8212 2.19841
\(981\) −22.7228 −0.725482
\(982\) 18.9504 0.604732
\(983\) −30.5622 −0.974782 −0.487391 0.873184i \(-0.662051\pi\)
−0.487391 + 0.873184i \(0.662051\pi\)
\(984\) −64.5932 −2.05916
\(985\) −37.8534 −1.20611
\(986\) −57.3907 −1.82769
\(987\) −32.5267 −1.03534
\(988\) 104.327 3.31907
\(989\) 0.140493 0.00446741
\(990\) −102.352 −3.25297
\(991\) 11.8419 0.376169 0.188084 0.982153i \(-0.439772\pi\)
0.188084 + 0.982153i \(0.439772\pi\)
\(992\) −86.2635 −2.73887
\(993\) −2.05747 −0.0652918
\(994\) 22.6130 0.717242
\(995\) −43.4818 −1.37846
\(996\) 59.9050 1.89816
\(997\) 40.4466 1.28096 0.640478 0.767977i \(-0.278736\pi\)
0.640478 + 0.767977i \(0.278736\pi\)
\(998\) 86.3102 2.73210
\(999\) 8.29017 0.262289
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 8003.2.a.d.1.8 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.d.1.8 179 1.1 even 1 trivial