Properties

Label 5225.2.a.bb.1.15
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $22$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.28593 q^{2} +0.496540 q^{3} -0.346393 q^{4} +0.638514 q^{6} +3.51780 q^{7} -3.01729 q^{8} -2.75345 q^{9} +O(q^{10})\) \(q+1.28593 q^{2} +0.496540 q^{3} -0.346393 q^{4} +0.638514 q^{6} +3.51780 q^{7} -3.01729 q^{8} -2.75345 q^{9} -1.00000 q^{11} -0.171998 q^{12} -2.55471 q^{13} +4.52364 q^{14} -3.18722 q^{16} +3.96000 q^{17} -3.54073 q^{18} -1.00000 q^{19} +1.74673 q^{21} -1.28593 q^{22} +7.91604 q^{23} -1.49821 q^{24} -3.28517 q^{26} -2.85682 q^{27} -1.21854 q^{28} -3.06230 q^{29} +1.12535 q^{31} +1.93604 q^{32} -0.496540 q^{33} +5.09227 q^{34} +0.953776 q^{36} +6.39797 q^{37} -1.28593 q^{38} -1.26852 q^{39} +1.65223 q^{41} +2.24617 q^{42} -8.34172 q^{43} +0.346393 q^{44} +10.1794 q^{46} +13.0685 q^{47} -1.58259 q^{48} +5.37494 q^{49} +1.96630 q^{51} +0.884934 q^{52} +7.33721 q^{53} -3.67366 q^{54} -10.6142 q^{56} -0.496540 q^{57} -3.93789 q^{58} -1.66706 q^{59} -3.64946 q^{61} +1.44712 q^{62} -9.68609 q^{63} +8.86406 q^{64} -0.638514 q^{66} +10.5579 q^{67} -1.37172 q^{68} +3.93064 q^{69} +13.9374 q^{71} +8.30795 q^{72} +9.76005 q^{73} +8.22731 q^{74} +0.346393 q^{76} -3.51780 q^{77} -1.63122 q^{78} -5.30165 q^{79} +6.84182 q^{81} +2.12465 q^{82} +3.85256 q^{83} -0.605056 q^{84} -10.7268 q^{86} -1.52056 q^{87} +3.01729 q^{88} -8.82721 q^{89} -8.98696 q^{91} -2.74207 q^{92} +0.558784 q^{93} +16.8051 q^{94} +0.961323 q^{96} +1.91792 q^{97} +6.91177 q^{98} +2.75345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 32 q^{4} - 12 q^{6} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 32 q^{4} - 12 q^{6} + 34 q^{9} - 22 q^{11} - 8 q^{14} + 40 q^{16} - 22 q^{19} - 22 q^{21} - 22 q^{24} + 16 q^{26} - 10 q^{29} + 76 q^{31} + 56 q^{34} + 104 q^{36} - 8 q^{39} + 6 q^{41} - 32 q^{44} + 88 q^{46} + 28 q^{49} + 8 q^{51} + 38 q^{54} + 44 q^{56} + 40 q^{59} - 6 q^{61} + 140 q^{64} + 12 q^{66} + 74 q^{69} + 62 q^{71} - 26 q^{74} - 32 q^{76} + 102 q^{79} + 94 q^{81} - 38 q^{84} + 28 q^{86} + 54 q^{89} + 88 q^{91} + 36 q^{94} + 2 q^{96} - 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28593 0.909287 0.454644 0.890673i \(-0.349767\pi\)
0.454644 + 0.890673i \(0.349767\pi\)
\(3\) 0.496540 0.286678 0.143339 0.989674i \(-0.454216\pi\)
0.143339 + 0.989674i \(0.454216\pi\)
\(4\) −0.346393 −0.173197
\(5\) 0 0
\(6\) 0.638514 0.260672
\(7\) 3.51780 1.32960 0.664802 0.747019i \(-0.268516\pi\)
0.664802 + 0.747019i \(0.268516\pi\)
\(8\) −3.01729 −1.06677
\(9\) −2.75345 −0.917816
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) −0.171998 −0.0496516
\(13\) −2.55471 −0.708548 −0.354274 0.935142i \(-0.615272\pi\)
−0.354274 + 0.935142i \(0.615272\pi\)
\(14\) 4.52364 1.20899
\(15\) 0 0
\(16\) −3.18722 −0.796806
\(17\) 3.96000 0.960440 0.480220 0.877148i \(-0.340557\pi\)
0.480220 + 0.877148i \(0.340557\pi\)
\(18\) −3.54073 −0.834558
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 1.74673 0.381168
\(22\) −1.28593 −0.274160
\(23\) 7.91604 1.65061 0.825305 0.564688i \(-0.191003\pi\)
0.825305 + 0.564688i \(0.191003\pi\)
\(24\) −1.49821 −0.305820
\(25\) 0 0
\(26\) −3.28517 −0.644274
\(27\) −2.85682 −0.549795
\(28\) −1.21854 −0.230283
\(29\) −3.06230 −0.568655 −0.284328 0.958727i \(-0.591770\pi\)
−0.284328 + 0.958727i \(0.591770\pi\)
\(30\) 0 0
\(31\) 1.12535 0.202120 0.101060 0.994880i \(-0.467777\pi\)
0.101060 + 0.994880i \(0.467777\pi\)
\(32\) 1.93604 0.342247
\(33\) −0.496540 −0.0864366
\(34\) 5.09227 0.873316
\(35\) 0 0
\(36\) 0.953776 0.158963
\(37\) 6.39797 1.05182 0.525910 0.850540i \(-0.323725\pi\)
0.525910 + 0.850540i \(0.323725\pi\)
\(38\) −1.28593 −0.208605
\(39\) −1.26852 −0.203125
\(40\) 0 0
\(41\) 1.65223 0.258036 0.129018 0.991642i \(-0.458818\pi\)
0.129018 + 0.991642i \(0.458818\pi\)
\(42\) 2.24617 0.346591
\(43\) −8.34172 −1.27210 −0.636050 0.771647i \(-0.719433\pi\)
−0.636050 + 0.771647i \(0.719433\pi\)
\(44\) 0.346393 0.0522208
\(45\) 0 0
\(46\) 10.1794 1.50088
\(47\) 13.0685 1.90623 0.953117 0.302601i \(-0.0978550\pi\)
0.953117 + 0.302601i \(0.0978550\pi\)
\(48\) −1.58259 −0.228427
\(49\) 5.37494 0.767848
\(50\) 0 0
\(51\) 1.96630 0.275337
\(52\) 0.884934 0.122718
\(53\) 7.33721 1.00784 0.503922 0.863749i \(-0.331890\pi\)
0.503922 + 0.863749i \(0.331890\pi\)
\(54\) −3.67366 −0.499922
\(55\) 0 0
\(56\) −10.6142 −1.41839
\(57\) −0.496540 −0.0657684
\(58\) −3.93789 −0.517071
\(59\) −1.66706 −0.217032 −0.108516 0.994095i \(-0.534610\pi\)
−0.108516 + 0.994095i \(0.534610\pi\)
\(60\) 0 0
\(61\) −3.64946 −0.467266 −0.233633 0.972325i \(-0.575061\pi\)
−0.233633 + 0.972325i \(0.575061\pi\)
\(62\) 1.44712 0.183785
\(63\) −9.68609 −1.22033
\(64\) 8.86406 1.10801
\(65\) 0 0
\(66\) −0.638514 −0.0785957
\(67\) 10.5579 1.28985 0.644927 0.764244i \(-0.276888\pi\)
0.644927 + 0.764244i \(0.276888\pi\)
\(68\) −1.37172 −0.166345
\(69\) 3.93064 0.473193
\(70\) 0 0
\(71\) 13.9374 1.65407 0.827034 0.562152i \(-0.190026\pi\)
0.827034 + 0.562152i \(0.190026\pi\)
\(72\) 8.30795 0.979101
\(73\) 9.76005 1.14233 0.571164 0.820836i \(-0.306492\pi\)
0.571164 + 0.820836i \(0.306492\pi\)
\(74\) 8.22731 0.956406
\(75\) 0 0
\(76\) 0.346393 0.0397340
\(77\) −3.51780 −0.400891
\(78\) −1.63122 −0.184699
\(79\) −5.30165 −0.596482 −0.298241 0.954491i \(-0.596400\pi\)
−0.298241 + 0.954491i \(0.596400\pi\)
\(80\) 0 0
\(81\) 6.84182 0.760202
\(82\) 2.12465 0.234629
\(83\) 3.85256 0.422874 0.211437 0.977392i \(-0.432186\pi\)
0.211437 + 0.977392i \(0.432186\pi\)
\(84\) −0.605056 −0.0660170
\(85\) 0 0
\(86\) −10.7268 −1.15671
\(87\) −1.52056 −0.163021
\(88\) 3.01729 0.321644
\(89\) −8.82721 −0.935682 −0.467841 0.883813i \(-0.654968\pi\)
−0.467841 + 0.883813i \(0.654968\pi\)
\(90\) 0 0
\(91\) −8.98696 −0.942089
\(92\) −2.74207 −0.285880
\(93\) 0.558784 0.0579432
\(94\) 16.8051 1.73331
\(95\) 0 0
\(96\) 0.961323 0.0981146
\(97\) 1.91792 0.194736 0.0973678 0.995248i \(-0.468958\pi\)
0.0973678 + 0.995248i \(0.468958\pi\)
\(98\) 6.91177 0.698194
\(99\) 2.75345 0.276732
\(100\) 0 0
\(101\) −2.98725 −0.297243 −0.148621 0.988894i \(-0.547484\pi\)
−0.148621 + 0.988894i \(0.547484\pi\)
\(102\) 2.52852 0.250360
\(103\) 8.85180 0.872194 0.436097 0.899900i \(-0.356360\pi\)
0.436097 + 0.899900i \(0.356360\pi\)
\(104\) 7.70829 0.755860
\(105\) 0 0
\(106\) 9.43511 0.916419
\(107\) −4.84194 −0.468088 −0.234044 0.972226i \(-0.575196\pi\)
−0.234044 + 0.972226i \(0.575196\pi\)
\(108\) 0.989583 0.0952227
\(109\) −4.68491 −0.448733 −0.224366 0.974505i \(-0.572031\pi\)
−0.224366 + 0.974505i \(0.572031\pi\)
\(110\) 0 0
\(111\) 3.17685 0.301533
\(112\) −11.2120 −1.05944
\(113\) 18.8998 1.77794 0.888971 0.457963i \(-0.151421\pi\)
0.888971 + 0.457963i \(0.151421\pi\)
\(114\) −0.638514 −0.0598024
\(115\) 0 0
\(116\) 1.06076 0.0984892
\(117\) 7.03425 0.650317
\(118\) −2.14371 −0.197345
\(119\) 13.9305 1.27701
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −4.69294 −0.424879
\(123\) 0.820401 0.0739731
\(124\) −0.389815 −0.0350065
\(125\) 0 0
\(126\) −12.4556 −1.10963
\(127\) −13.2632 −1.17692 −0.588458 0.808528i \(-0.700265\pi\)
−0.588458 + 0.808528i \(0.700265\pi\)
\(128\) 7.52644 0.665250
\(129\) −4.14200 −0.364683
\(130\) 0 0
\(131\) −17.6530 −1.54235 −0.771176 0.636622i \(-0.780331\pi\)
−0.771176 + 0.636622i \(0.780331\pi\)
\(132\) 0.171998 0.0149705
\(133\) −3.51780 −0.305032
\(134\) 13.5767 1.17285
\(135\) 0 0
\(136\) −11.9485 −1.02457
\(137\) −4.42479 −0.378035 −0.189018 0.981974i \(-0.560530\pi\)
−0.189018 + 0.981974i \(0.560530\pi\)
\(138\) 5.05451 0.430268
\(139\) 12.4255 1.05392 0.526958 0.849892i \(-0.323333\pi\)
0.526958 + 0.849892i \(0.323333\pi\)
\(140\) 0 0
\(141\) 6.48903 0.546475
\(142\) 17.9225 1.50402
\(143\) 2.55471 0.213635
\(144\) 8.77586 0.731321
\(145\) 0 0
\(146\) 12.5507 1.03870
\(147\) 2.66887 0.220125
\(148\) −2.21621 −0.182172
\(149\) 10.0735 0.825251 0.412625 0.910901i \(-0.364612\pi\)
0.412625 + 0.910901i \(0.364612\pi\)
\(150\) 0 0
\(151\) −20.0465 −1.63136 −0.815680 0.578503i \(-0.803637\pi\)
−0.815680 + 0.578503i \(0.803637\pi\)
\(152\) 3.01729 0.244734
\(153\) −10.9036 −0.881507
\(154\) −4.52364 −0.364525
\(155\) 0 0
\(156\) 0.439405 0.0351806
\(157\) −13.2078 −1.05410 −0.527048 0.849836i \(-0.676701\pi\)
−0.527048 + 0.849836i \(0.676701\pi\)
\(158\) −6.81753 −0.542374
\(159\) 3.64322 0.288926
\(160\) 0 0
\(161\) 27.8471 2.19466
\(162\) 8.79807 0.691242
\(163\) 14.4001 1.12790 0.563951 0.825808i \(-0.309281\pi\)
0.563951 + 0.825808i \(0.309281\pi\)
\(164\) −0.572323 −0.0446909
\(165\) 0 0
\(166\) 4.95411 0.384513
\(167\) 20.5870 1.59307 0.796534 0.604593i \(-0.206664\pi\)
0.796534 + 0.604593i \(0.206664\pi\)
\(168\) −5.27039 −0.406620
\(169\) −6.47347 −0.497959
\(170\) 0 0
\(171\) 2.75345 0.210561
\(172\) 2.88952 0.220324
\(173\) 3.10430 0.236016 0.118008 0.993013i \(-0.462349\pi\)
0.118008 + 0.993013i \(0.462349\pi\)
\(174\) −1.95532 −0.148233
\(175\) 0 0
\(176\) 3.18722 0.240246
\(177\) −0.827761 −0.0622183
\(178\) −11.3511 −0.850804
\(179\) 13.5070 1.00956 0.504782 0.863247i \(-0.331573\pi\)
0.504782 + 0.863247i \(0.331573\pi\)
\(180\) 0 0
\(181\) 11.0629 0.822300 0.411150 0.911568i \(-0.365127\pi\)
0.411150 + 0.911568i \(0.365127\pi\)
\(182\) −11.5566 −0.856630
\(183\) −1.81210 −0.133955
\(184\) −23.8850 −1.76082
\(185\) 0 0
\(186\) 0.718555 0.0526870
\(187\) −3.96000 −0.289584
\(188\) −4.52684 −0.330154
\(189\) −10.0497 −0.731010
\(190\) 0 0
\(191\) 19.8472 1.43610 0.718048 0.695994i \(-0.245036\pi\)
0.718048 + 0.695994i \(0.245036\pi\)
\(192\) 4.40136 0.317641
\(193\) 17.1693 1.23587 0.617936 0.786228i \(-0.287969\pi\)
0.617936 + 0.786228i \(0.287969\pi\)
\(194\) 2.46631 0.177071
\(195\) 0 0
\(196\) −1.86184 −0.132989
\(197\) −7.76076 −0.552931 −0.276466 0.961024i \(-0.589163\pi\)
−0.276466 + 0.961024i \(0.589163\pi\)
\(198\) 3.54073 0.251629
\(199\) 13.9454 0.988560 0.494280 0.869303i \(-0.335432\pi\)
0.494280 + 0.869303i \(0.335432\pi\)
\(200\) 0 0
\(201\) 5.24243 0.369773
\(202\) −3.84139 −0.270279
\(203\) −10.7726 −0.756086
\(204\) −0.681113 −0.0476874
\(205\) 0 0
\(206\) 11.3828 0.793075
\(207\) −21.7964 −1.51496
\(208\) 8.14243 0.564576
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) 6.11231 0.420789 0.210394 0.977617i \(-0.432525\pi\)
0.210394 + 0.977617i \(0.432525\pi\)
\(212\) −2.54156 −0.174555
\(213\) 6.92049 0.474184
\(214\) −6.22637 −0.425626
\(215\) 0 0
\(216\) 8.61985 0.586506
\(217\) 3.95878 0.268739
\(218\) −6.02445 −0.408027
\(219\) 4.84626 0.327480
\(220\) 0 0
\(221\) −10.1166 −0.680519
\(222\) 4.08519 0.274180
\(223\) −15.2282 −1.01975 −0.509877 0.860247i \(-0.670309\pi\)
−0.509877 + 0.860247i \(0.670309\pi\)
\(224\) 6.81061 0.455053
\(225\) 0 0
\(226\) 24.3037 1.61666
\(227\) −23.3830 −1.55199 −0.775993 0.630741i \(-0.782751\pi\)
−0.775993 + 0.630741i \(0.782751\pi\)
\(228\) 0.171998 0.0113909
\(229\) −0.0884448 −0.00584460 −0.00292230 0.999996i \(-0.500930\pi\)
−0.00292230 + 0.999996i \(0.500930\pi\)
\(230\) 0 0
\(231\) −1.74673 −0.114926
\(232\) 9.23985 0.606626
\(233\) 13.5633 0.888562 0.444281 0.895888i \(-0.353459\pi\)
0.444281 + 0.895888i \(0.353459\pi\)
\(234\) 9.04553 0.591325
\(235\) 0 0
\(236\) 0.577458 0.0375893
\(237\) −2.63248 −0.170998
\(238\) 17.9136 1.16117
\(239\) −14.8357 −0.959642 −0.479821 0.877366i \(-0.659298\pi\)
−0.479821 + 0.877366i \(0.659298\pi\)
\(240\) 0 0
\(241\) −0.466928 −0.0300775 −0.0150388 0.999887i \(-0.504787\pi\)
−0.0150388 + 0.999887i \(0.504787\pi\)
\(242\) 1.28593 0.0826625
\(243\) 11.9677 0.767728
\(244\) 1.26415 0.0809289
\(245\) 0 0
\(246\) 1.05498 0.0672628
\(247\) 2.55471 0.162552
\(248\) −3.39552 −0.215616
\(249\) 1.91295 0.121228
\(250\) 0 0
\(251\) 1.71829 0.108458 0.0542288 0.998529i \(-0.482730\pi\)
0.0542288 + 0.998529i \(0.482730\pi\)
\(252\) 3.35520 0.211357
\(253\) −7.91604 −0.497677
\(254\) −17.0555 −1.07015
\(255\) 0 0
\(256\) −8.04967 −0.503104
\(257\) −0.514845 −0.0321151 −0.0160576 0.999871i \(-0.505111\pi\)
−0.0160576 + 0.999871i \(0.505111\pi\)
\(258\) −5.32631 −0.331602
\(259\) 22.5068 1.39850
\(260\) 0 0
\(261\) 8.43189 0.521921
\(262\) −22.7005 −1.40244
\(263\) −25.7582 −1.58832 −0.794158 0.607711i \(-0.792088\pi\)
−0.794158 + 0.607711i \(0.792088\pi\)
\(264\) 1.49821 0.0922082
\(265\) 0 0
\(266\) −4.52364 −0.277362
\(267\) −4.38307 −0.268239
\(268\) −3.65719 −0.223399
\(269\) −12.5554 −0.765513 −0.382757 0.923849i \(-0.625025\pi\)
−0.382757 + 0.923849i \(0.625025\pi\)
\(270\) 0 0
\(271\) −10.0377 −0.609745 −0.304873 0.952393i \(-0.598614\pi\)
−0.304873 + 0.952393i \(0.598614\pi\)
\(272\) −12.6214 −0.765285
\(273\) −4.46239 −0.270076
\(274\) −5.68996 −0.343743
\(275\) 0 0
\(276\) −1.36155 −0.0819555
\(277\) 1.86246 0.111904 0.0559522 0.998433i \(-0.482181\pi\)
0.0559522 + 0.998433i \(0.482181\pi\)
\(278\) 15.9782 0.958312
\(279\) −3.09861 −0.185509
\(280\) 0 0
\(281\) 13.0311 0.777372 0.388686 0.921370i \(-0.372929\pi\)
0.388686 + 0.921370i \(0.372929\pi\)
\(282\) 8.34442 0.496903
\(283\) −22.4810 −1.33636 −0.668179 0.744001i \(-0.732926\pi\)
−0.668179 + 0.744001i \(0.732926\pi\)
\(284\) −4.82783 −0.286479
\(285\) 0 0
\(286\) 3.28517 0.194256
\(287\) 5.81224 0.343085
\(288\) −5.33079 −0.314120
\(289\) −1.31842 −0.0775541
\(290\) 0 0
\(291\) 0.952327 0.0558264
\(292\) −3.38082 −0.197847
\(293\) 24.4894 1.43069 0.715343 0.698774i \(-0.246271\pi\)
0.715343 + 0.698774i \(0.246271\pi\)
\(294\) 3.43197 0.200157
\(295\) 0 0
\(296\) −19.3045 −1.12205
\(297\) 2.85682 0.165769
\(298\) 12.9537 0.750390
\(299\) −20.2232 −1.16954
\(300\) 0 0
\(301\) −29.3445 −1.69139
\(302\) −25.7783 −1.48338
\(303\) −1.48329 −0.0852129
\(304\) 3.18722 0.182800
\(305\) 0 0
\(306\) −14.0213 −0.801544
\(307\) 7.93720 0.453000 0.226500 0.974011i \(-0.427272\pi\)
0.226500 + 0.974011i \(0.427272\pi\)
\(308\) 1.21854 0.0694330
\(309\) 4.39528 0.250039
\(310\) 0 0
\(311\) −24.3499 −1.38075 −0.690377 0.723450i \(-0.742555\pi\)
−0.690377 + 0.723450i \(0.742555\pi\)
\(312\) 3.82748 0.216688
\(313\) 24.7333 1.39801 0.699005 0.715116i \(-0.253626\pi\)
0.699005 + 0.715116i \(0.253626\pi\)
\(314\) −16.9842 −0.958475
\(315\) 0 0
\(316\) 1.83646 0.103309
\(317\) −31.8563 −1.78923 −0.894615 0.446838i \(-0.852550\pi\)
−0.894615 + 0.446838i \(0.852550\pi\)
\(318\) 4.68492 0.262717
\(319\) 3.06230 0.171456
\(320\) 0 0
\(321\) −2.40422 −0.134190
\(322\) 35.8093 1.99557
\(323\) −3.96000 −0.220340
\(324\) −2.36996 −0.131664
\(325\) 0 0
\(326\) 18.5175 1.02559
\(327\) −2.32625 −0.128642
\(328\) −4.98527 −0.275265
\(329\) 45.9724 2.53454
\(330\) 0 0
\(331\) −0.532253 −0.0292552 −0.0146276 0.999893i \(-0.504656\pi\)
−0.0146276 + 0.999893i \(0.504656\pi\)
\(332\) −1.33450 −0.0732403
\(333\) −17.6165 −0.965376
\(334\) 26.4733 1.44856
\(335\) 0 0
\(336\) −5.56723 −0.303717
\(337\) 21.0568 1.14704 0.573519 0.819192i \(-0.305578\pi\)
0.573519 + 0.819192i \(0.305578\pi\)
\(338\) −8.32441 −0.452788
\(339\) 9.38451 0.509696
\(340\) 0 0
\(341\) −1.12535 −0.0609414
\(342\) 3.54073 0.191461
\(343\) −5.71665 −0.308670
\(344\) 25.1694 1.35704
\(345\) 0 0
\(346\) 3.99190 0.214606
\(347\) −29.1458 −1.56463 −0.782316 0.622882i \(-0.785962\pi\)
−0.782316 + 0.622882i \(0.785962\pi\)
\(348\) 0.526711 0.0282347
\(349\) 22.4161 1.19991 0.599953 0.800035i \(-0.295186\pi\)
0.599953 + 0.800035i \(0.295186\pi\)
\(350\) 0 0
\(351\) 7.29834 0.389556
\(352\) −1.93604 −0.103191
\(353\) 16.4937 0.877869 0.438935 0.898519i \(-0.355356\pi\)
0.438935 + 0.898519i \(0.355356\pi\)
\(354\) −1.06444 −0.0565743
\(355\) 0 0
\(356\) 3.05769 0.162057
\(357\) 6.91705 0.366089
\(358\) 17.3691 0.917983
\(359\) 11.3098 0.596910 0.298455 0.954424i \(-0.403529\pi\)
0.298455 + 0.954424i \(0.403529\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 14.2261 0.747707
\(363\) 0.496540 0.0260616
\(364\) 3.11302 0.163167
\(365\) 0 0
\(366\) −2.33023 −0.121803
\(367\) 4.45032 0.232305 0.116152 0.993231i \(-0.462944\pi\)
0.116152 + 0.993231i \(0.462944\pi\)
\(368\) −25.2302 −1.31522
\(369\) −4.54934 −0.236829
\(370\) 0 0
\(371\) 25.8109 1.34003
\(372\) −0.193559 −0.0100356
\(373\) 4.45578 0.230712 0.115356 0.993324i \(-0.463199\pi\)
0.115356 + 0.993324i \(0.463199\pi\)
\(374\) −5.09227 −0.263315
\(375\) 0 0
\(376\) −39.4314 −2.03352
\(377\) 7.82328 0.402920
\(378\) −12.9232 −0.664698
\(379\) 15.8233 0.812787 0.406393 0.913698i \(-0.366786\pi\)
0.406393 + 0.913698i \(0.366786\pi\)
\(380\) 0 0
\(381\) −6.58570 −0.337396
\(382\) 25.5221 1.30582
\(383\) 1.83670 0.0938509 0.0469255 0.998898i \(-0.485058\pi\)
0.0469255 + 0.998898i \(0.485058\pi\)
\(384\) 3.73718 0.190712
\(385\) 0 0
\(386\) 22.0784 1.12376
\(387\) 22.9685 1.16755
\(388\) −0.664356 −0.0337276
\(389\) −17.5818 −0.891433 −0.445717 0.895174i \(-0.647051\pi\)
−0.445717 + 0.895174i \(0.647051\pi\)
\(390\) 0 0
\(391\) 31.3475 1.58531
\(392\) −16.2177 −0.819119
\(393\) −8.76544 −0.442158
\(394\) −9.97977 −0.502774
\(395\) 0 0
\(396\) −0.953776 −0.0479291
\(397\) −8.70488 −0.436885 −0.218443 0.975850i \(-0.570098\pi\)
−0.218443 + 0.975850i \(0.570098\pi\)
\(398\) 17.9327 0.898885
\(399\) −1.74673 −0.0874459
\(400\) 0 0
\(401\) 28.1153 1.40401 0.702006 0.712171i \(-0.252288\pi\)
0.702006 + 0.712171i \(0.252288\pi\)
\(402\) 6.74138 0.336230
\(403\) −2.87495 −0.143212
\(404\) 1.03476 0.0514815
\(405\) 0 0
\(406\) −13.8527 −0.687500
\(407\) −6.39797 −0.317135
\(408\) −5.93289 −0.293722
\(409\) −11.2277 −0.555172 −0.277586 0.960701i \(-0.589534\pi\)
−0.277586 + 0.960701i \(0.589534\pi\)
\(410\) 0 0
\(411\) −2.19709 −0.108374
\(412\) −3.06621 −0.151061
\(413\) −5.86438 −0.288567
\(414\) −28.0286 −1.37753
\(415\) 0 0
\(416\) −4.94602 −0.242499
\(417\) 6.16975 0.302134
\(418\) 1.28593 0.0628967
\(419\) −10.3008 −0.503228 −0.251614 0.967828i \(-0.580961\pi\)
−0.251614 + 0.967828i \(0.580961\pi\)
\(420\) 0 0
\(421\) 16.7955 0.818564 0.409282 0.912408i \(-0.365779\pi\)
0.409282 + 0.912408i \(0.365779\pi\)
\(422\) 7.85998 0.382618
\(423\) −35.9834 −1.74957
\(424\) −22.1385 −1.07514
\(425\) 0 0
\(426\) 8.89925 0.431170
\(427\) −12.8381 −0.621278
\(428\) 1.67721 0.0810712
\(429\) 1.26852 0.0612445
\(430\) 0 0
\(431\) 14.2315 0.685506 0.342753 0.939425i \(-0.388641\pi\)
0.342753 + 0.939425i \(0.388641\pi\)
\(432\) 9.10533 0.438080
\(433\) −28.8922 −1.38847 −0.694236 0.719747i \(-0.744258\pi\)
−0.694236 + 0.719747i \(0.744258\pi\)
\(434\) 5.09069 0.244361
\(435\) 0 0
\(436\) 1.62282 0.0777190
\(437\) −7.91604 −0.378676
\(438\) 6.23193 0.297773
\(439\) 28.1483 1.34344 0.671722 0.740803i \(-0.265555\pi\)
0.671722 + 0.740803i \(0.265555\pi\)
\(440\) 0 0
\(441\) −14.7996 −0.704743
\(442\) −13.0092 −0.618787
\(443\) −19.5365 −0.928205 −0.464102 0.885782i \(-0.653623\pi\)
−0.464102 + 0.885782i \(0.653623\pi\)
\(444\) −1.10044 −0.0522245
\(445\) 0 0
\(446\) −19.5823 −0.927249
\(447\) 5.00189 0.236581
\(448\) 31.1820 1.47321
\(449\) −20.5402 −0.969351 −0.484675 0.874694i \(-0.661062\pi\)
−0.484675 + 0.874694i \(0.661062\pi\)
\(450\) 0 0
\(451\) −1.65223 −0.0778007
\(452\) −6.54676 −0.307934
\(453\) −9.95389 −0.467675
\(454\) −30.0689 −1.41120
\(455\) 0 0
\(456\) 1.49821 0.0701599
\(457\) −12.1384 −0.567812 −0.283906 0.958852i \(-0.591630\pi\)
−0.283906 + 0.958852i \(0.591630\pi\)
\(458\) −0.113733 −0.00531442
\(459\) −11.3130 −0.528045
\(460\) 0 0
\(461\) −29.3582 −1.36735 −0.683673 0.729788i \(-0.739619\pi\)
−0.683673 + 0.729788i \(0.739619\pi\)
\(462\) −2.24617 −0.104501
\(463\) −0.547114 −0.0254265 −0.0127133 0.999919i \(-0.504047\pi\)
−0.0127133 + 0.999919i \(0.504047\pi\)
\(464\) 9.76024 0.453108
\(465\) 0 0
\(466\) 17.4414 0.807958
\(467\) 3.82267 0.176892 0.0884460 0.996081i \(-0.471810\pi\)
0.0884460 + 0.996081i \(0.471810\pi\)
\(468\) −2.43662 −0.112633
\(469\) 37.1407 1.71500
\(470\) 0 0
\(471\) −6.55819 −0.302186
\(472\) 5.02999 0.231524
\(473\) 8.34172 0.383553
\(474\) −3.38518 −0.155486
\(475\) 0 0
\(476\) −4.82543 −0.221173
\(477\) −20.2026 −0.925015
\(478\) −19.0776 −0.872590
\(479\) −0.914772 −0.0417970 −0.0208985 0.999782i \(-0.506653\pi\)
−0.0208985 + 0.999782i \(0.506653\pi\)
\(480\) 0 0
\(481\) −16.3449 −0.745265
\(482\) −0.600436 −0.0273491
\(483\) 13.8272 0.629159
\(484\) −0.346393 −0.0157452
\(485\) 0 0
\(486\) 15.3896 0.698085
\(487\) 36.8291 1.66888 0.834442 0.551095i \(-0.185790\pi\)
0.834442 + 0.551095i \(0.185790\pi\)
\(488\) 11.0115 0.498466
\(489\) 7.15023 0.323345
\(490\) 0 0
\(491\) −20.3717 −0.919360 −0.459680 0.888085i \(-0.652036\pi\)
−0.459680 + 0.888085i \(0.652036\pi\)
\(492\) −0.284182 −0.0128119
\(493\) −12.1267 −0.546159
\(494\) 3.28517 0.147807
\(495\) 0 0
\(496\) −3.58676 −0.161050
\(497\) 49.0291 2.19926
\(498\) 2.45992 0.110231
\(499\) 9.18801 0.411312 0.205656 0.978624i \(-0.434067\pi\)
0.205656 + 0.978624i \(0.434067\pi\)
\(500\) 0 0
\(501\) 10.2223 0.456697
\(502\) 2.20960 0.0986192
\(503\) −40.2078 −1.79278 −0.896390 0.443267i \(-0.853819\pi\)
−0.896390 + 0.443267i \(0.853819\pi\)
\(504\) 29.2257 1.30182
\(505\) 0 0
\(506\) −10.1794 −0.452532
\(507\) −3.21434 −0.142754
\(508\) 4.59427 0.203838
\(509\) 43.0322 1.90737 0.953684 0.300811i \(-0.0972575\pi\)
0.953684 + 0.300811i \(0.0972575\pi\)
\(510\) 0 0
\(511\) 34.3339 1.51884
\(512\) −25.4042 −1.12272
\(513\) 2.85682 0.126132
\(514\) −0.662052 −0.0292019
\(515\) 0 0
\(516\) 1.43476 0.0631619
\(517\) −13.0685 −0.574751
\(518\) 28.9421 1.27164
\(519\) 1.54141 0.0676604
\(520\) 0 0
\(521\) 34.9660 1.53189 0.765944 0.642908i \(-0.222272\pi\)
0.765944 + 0.642908i \(0.222272\pi\)
\(522\) 10.8428 0.474576
\(523\) −17.5898 −0.769147 −0.384574 0.923094i \(-0.625652\pi\)
−0.384574 + 0.923094i \(0.625652\pi\)
\(524\) 6.11489 0.267130
\(525\) 0 0
\(526\) −33.1231 −1.44424
\(527\) 4.45640 0.194124
\(528\) 1.58259 0.0688732
\(529\) 39.6637 1.72451
\(530\) 0 0
\(531\) 4.59015 0.199196
\(532\) 1.21854 0.0528306
\(533\) −4.22098 −0.182831
\(534\) −5.63630 −0.243907
\(535\) 0 0
\(536\) −31.8563 −1.37598
\(537\) 6.70679 0.289419
\(538\) −16.1453 −0.696071
\(539\) −5.37494 −0.231515
\(540\) 0 0
\(541\) 24.1969 1.04030 0.520152 0.854074i \(-0.325875\pi\)
0.520152 + 0.854074i \(0.325875\pi\)
\(542\) −12.9077 −0.554434
\(543\) 5.49319 0.235735
\(544\) 7.66672 0.328708
\(545\) 0 0
\(546\) −5.73830 −0.245577
\(547\) −11.6589 −0.498498 −0.249249 0.968439i \(-0.580184\pi\)
−0.249249 + 0.968439i \(0.580184\pi\)
\(548\) 1.53272 0.0654745
\(549\) 10.0486 0.428864
\(550\) 0 0
\(551\) 3.06230 0.130458
\(552\) −11.8599 −0.504789
\(553\) −18.6502 −0.793085
\(554\) 2.39499 0.101753
\(555\) 0 0
\(556\) −4.30410 −0.182535
\(557\) −0.691233 −0.0292885 −0.0146442 0.999893i \(-0.504662\pi\)
−0.0146442 + 0.999893i \(0.504662\pi\)
\(558\) −3.98458 −0.168681
\(559\) 21.3107 0.901345
\(560\) 0 0
\(561\) −1.96630 −0.0830172
\(562\) 16.7571 0.706854
\(563\) 46.5572 1.96215 0.981075 0.193627i \(-0.0620251\pi\)
0.981075 + 0.193627i \(0.0620251\pi\)
\(564\) −2.24776 −0.0946477
\(565\) 0 0
\(566\) −28.9089 −1.21513
\(567\) 24.0682 1.01077
\(568\) −42.0532 −1.76451
\(569\) −17.3675 −0.728083 −0.364041 0.931383i \(-0.618603\pi\)
−0.364041 + 0.931383i \(0.618603\pi\)
\(570\) 0 0
\(571\) 30.8085 1.28930 0.644649 0.764479i \(-0.277004\pi\)
0.644649 + 0.764479i \(0.277004\pi\)
\(572\) −0.884934 −0.0370009
\(573\) 9.85496 0.411697
\(574\) 7.47411 0.311963
\(575\) 0 0
\(576\) −24.4067 −1.01695
\(577\) −9.11130 −0.379308 −0.189654 0.981851i \(-0.560737\pi\)
−0.189654 + 0.981851i \(0.560737\pi\)
\(578\) −1.69539 −0.0705190
\(579\) 8.52525 0.354297
\(580\) 0 0
\(581\) 13.5525 0.562254
\(582\) 1.22462 0.0507622
\(583\) −7.33721 −0.303876
\(584\) −29.4489 −1.21860
\(585\) 0 0
\(586\) 31.4916 1.30090
\(587\) −26.4096 −1.09004 −0.545021 0.838422i \(-0.683478\pi\)
−0.545021 + 0.838422i \(0.683478\pi\)
\(588\) −0.924480 −0.0381249
\(589\) −1.12535 −0.0463694
\(590\) 0 0
\(591\) −3.85353 −0.158513
\(592\) −20.3918 −0.838096
\(593\) 37.1161 1.52417 0.762087 0.647475i \(-0.224175\pi\)
0.762087 + 0.647475i \(0.224175\pi\)
\(594\) 3.67366 0.150732
\(595\) 0 0
\(596\) −3.48938 −0.142931
\(597\) 6.92443 0.283398
\(598\) −26.0055 −1.06344
\(599\) −44.1959 −1.80580 −0.902899 0.429853i \(-0.858565\pi\)
−0.902899 + 0.429853i \(0.858565\pi\)
\(600\) 0 0
\(601\) 26.0883 1.06416 0.532081 0.846693i \(-0.321410\pi\)
0.532081 + 0.846693i \(0.321410\pi\)
\(602\) −37.7349 −1.53796
\(603\) −29.0707 −1.18385
\(604\) 6.94397 0.282546
\(605\) 0 0
\(606\) −1.90740 −0.0774830
\(607\) 17.9808 0.729819 0.364910 0.931043i \(-0.381100\pi\)
0.364910 + 0.931043i \(0.381100\pi\)
\(608\) −1.93604 −0.0785169
\(609\) −5.34902 −0.216753
\(610\) 0 0
\(611\) −33.3862 −1.35066
\(612\) 3.77695 0.152674
\(613\) −7.45345 −0.301042 −0.150521 0.988607i \(-0.548095\pi\)
−0.150521 + 0.988607i \(0.548095\pi\)
\(614\) 10.2067 0.411907
\(615\) 0 0
\(616\) 10.6142 0.427659
\(617\) 22.5986 0.909785 0.454892 0.890546i \(-0.349678\pi\)
0.454892 + 0.890546i \(0.349678\pi\)
\(618\) 5.65200 0.227357
\(619\) 34.2496 1.37661 0.688303 0.725423i \(-0.258356\pi\)
0.688303 + 0.725423i \(0.258356\pi\)
\(620\) 0 0
\(621\) −22.6147 −0.907497
\(622\) −31.3121 −1.25550
\(623\) −31.0524 −1.24409
\(624\) 4.04304 0.161851
\(625\) 0 0
\(626\) 31.8052 1.27119
\(627\) 0.496540 0.0198299
\(628\) 4.57509 0.182566
\(629\) 25.3359 1.01021
\(630\) 0 0
\(631\) −20.4459 −0.813940 −0.406970 0.913442i \(-0.633415\pi\)
−0.406970 + 0.913442i \(0.633415\pi\)
\(632\) 15.9966 0.636311
\(633\) 3.03501 0.120631
\(634\) −40.9649 −1.62692
\(635\) 0 0
\(636\) −1.26199 −0.0500411
\(637\) −13.7314 −0.544057
\(638\) 3.93789 0.155903
\(639\) −38.3760 −1.51813
\(640\) 0 0
\(641\) −32.1759 −1.27087 −0.635436 0.772154i \(-0.719180\pi\)
−0.635436 + 0.772154i \(0.719180\pi\)
\(642\) −3.09165 −0.122018
\(643\) −6.17037 −0.243336 −0.121668 0.992571i \(-0.538824\pi\)
−0.121668 + 0.992571i \(0.538824\pi\)
\(644\) −9.64604 −0.380107
\(645\) 0 0
\(646\) −5.09227 −0.200352
\(647\) −20.2691 −0.796861 −0.398430 0.917199i \(-0.630445\pi\)
−0.398430 + 0.917199i \(0.630445\pi\)
\(648\) −20.6437 −0.810963
\(649\) 1.66706 0.0654377
\(650\) 0 0
\(651\) 1.96569 0.0770415
\(652\) −4.98810 −0.195349
\(653\) −49.9790 −1.95583 −0.977916 0.209000i \(-0.932979\pi\)
−0.977916 + 0.209000i \(0.932979\pi\)
\(654\) −2.99138 −0.116972
\(655\) 0 0
\(656\) −5.26604 −0.205604
\(657\) −26.8738 −1.04845
\(658\) 59.1171 2.30462
\(659\) −39.7429 −1.54816 −0.774082 0.633085i \(-0.781788\pi\)
−0.774082 + 0.633085i \(0.781788\pi\)
\(660\) 0 0
\(661\) −1.09749 −0.0426876 −0.0213438 0.999772i \(-0.506794\pi\)
−0.0213438 + 0.999772i \(0.506794\pi\)
\(662\) −0.684438 −0.0266014
\(663\) −5.02332 −0.195090
\(664\) −11.6243 −0.451110
\(665\) 0 0
\(666\) −22.6535 −0.877804
\(667\) −24.2413 −0.938627
\(668\) −7.13120 −0.275914
\(669\) −7.56140 −0.292341
\(670\) 0 0
\(671\) 3.64946 0.140886
\(672\) 3.38174 0.130454
\(673\) 14.4864 0.558410 0.279205 0.960231i \(-0.409929\pi\)
0.279205 + 0.960231i \(0.409929\pi\)
\(674\) 27.0775 1.04299
\(675\) 0 0
\(676\) 2.24237 0.0862449
\(677\) −21.4670 −0.825045 −0.412522 0.910947i \(-0.635352\pi\)
−0.412522 + 0.910947i \(0.635352\pi\)
\(678\) 12.0678 0.463460
\(679\) 6.74688 0.258921
\(680\) 0 0
\(681\) −11.6106 −0.444920
\(682\) −1.44712 −0.0554132
\(683\) 13.1753 0.504140 0.252070 0.967709i \(-0.418889\pi\)
0.252070 + 0.967709i \(0.418889\pi\)
\(684\) −0.953776 −0.0364685
\(685\) 0 0
\(686\) −7.35120 −0.280670
\(687\) −0.0439164 −0.00167552
\(688\) 26.5869 1.01362
\(689\) −18.7444 −0.714106
\(690\) 0 0
\(691\) 44.3448 1.68695 0.843477 0.537165i \(-0.180505\pi\)
0.843477 + 0.537165i \(0.180505\pi\)
\(692\) −1.07531 −0.0408771
\(693\) 9.68609 0.367944
\(694\) −37.4794 −1.42270
\(695\) 0 0
\(696\) 4.58796 0.173906
\(697\) 6.54284 0.247828
\(698\) 28.8255 1.09106
\(699\) 6.73473 0.254731
\(700\) 0 0
\(701\) −25.5155 −0.963707 −0.481853 0.876252i \(-0.660036\pi\)
−0.481853 + 0.876252i \(0.660036\pi\)
\(702\) 9.38512 0.354219
\(703\) −6.39797 −0.241304
\(704\) −8.86406 −0.334077
\(705\) 0 0
\(706\) 21.2096 0.798235
\(707\) −10.5086 −0.395215
\(708\) 0.286731 0.0107760
\(709\) −7.94123 −0.298239 −0.149120 0.988819i \(-0.547644\pi\)
−0.149120 + 0.988819i \(0.547644\pi\)
\(710\) 0 0
\(711\) 14.5978 0.547461
\(712\) 26.6342 0.998161
\(713\) 8.90836 0.333621
\(714\) 8.89482 0.332880
\(715\) 0 0
\(716\) −4.67875 −0.174853
\(717\) −7.36653 −0.275108
\(718\) 14.5436 0.542762
\(719\) 18.7440 0.699035 0.349517 0.936930i \(-0.386346\pi\)
0.349517 + 0.936930i \(0.386346\pi\)
\(720\) 0 0
\(721\) 31.1389 1.15967
\(722\) 1.28593 0.0478572
\(723\) −0.231849 −0.00862255
\(724\) −3.83212 −0.142420
\(725\) 0 0
\(726\) 0.638514 0.0236975
\(727\) −40.5490 −1.50388 −0.751940 0.659232i \(-0.770881\pi\)
−0.751940 + 0.659232i \(0.770881\pi\)
\(728\) 27.1162 1.00499
\(729\) −14.5830 −0.540111
\(730\) 0 0
\(731\) −33.0332 −1.22178
\(732\) 0.627701 0.0232005
\(733\) 25.5111 0.942274 0.471137 0.882060i \(-0.343844\pi\)
0.471137 + 0.882060i \(0.343844\pi\)
\(734\) 5.72278 0.211232
\(735\) 0 0
\(736\) 15.3258 0.564916
\(737\) −10.5579 −0.388906
\(738\) −5.85012 −0.215346
\(739\) −39.4859 −1.45251 −0.726256 0.687424i \(-0.758741\pi\)
−0.726256 + 0.687424i \(0.758741\pi\)
\(740\) 0 0
\(741\) 1.26852 0.0466001
\(742\) 33.1909 1.21848
\(743\) −3.90702 −0.143335 −0.0716674 0.997429i \(-0.522832\pi\)
−0.0716674 + 0.997429i \(0.522832\pi\)
\(744\) −1.68601 −0.0618122
\(745\) 0 0
\(746\) 5.72980 0.209783
\(747\) −10.6078 −0.388120
\(748\) 1.37172 0.0501549
\(749\) −17.0330 −0.622371
\(750\) 0 0
\(751\) 17.1331 0.625194 0.312597 0.949886i \(-0.398801\pi\)
0.312597 + 0.949886i \(0.398801\pi\)
\(752\) −41.6522 −1.51890
\(753\) 0.853202 0.0310924
\(754\) 10.0602 0.366370
\(755\) 0 0
\(756\) 3.48116 0.126609
\(757\) 23.8080 0.865315 0.432657 0.901558i \(-0.357576\pi\)
0.432657 + 0.901558i \(0.357576\pi\)
\(758\) 20.3476 0.739057
\(759\) −3.93064 −0.142673
\(760\) 0 0
\(761\) −21.3690 −0.774627 −0.387313 0.921948i \(-0.626597\pi\)
−0.387313 + 0.921948i \(0.626597\pi\)
\(762\) −8.46872 −0.306789
\(763\) −16.4806 −0.596637
\(764\) −6.87495 −0.248727
\(765\) 0 0
\(766\) 2.36186 0.0853374
\(767\) 4.25884 0.153778
\(768\) −3.99698 −0.144229
\(769\) −34.2173 −1.23391 −0.616954 0.786999i \(-0.711634\pi\)
−0.616954 + 0.786999i \(0.711634\pi\)
\(770\) 0 0
\(771\) −0.255641 −0.00920669
\(772\) −5.94733 −0.214049
\(773\) −48.0641 −1.72874 −0.864372 0.502852i \(-0.832284\pi\)
−0.864372 + 0.502852i \(0.832284\pi\)
\(774\) 29.5358 1.06164
\(775\) 0 0
\(776\) −5.78693 −0.207739
\(777\) 11.1755 0.400920
\(778\) −22.6089 −0.810569
\(779\) −1.65223 −0.0591974
\(780\) 0 0
\(781\) −13.9374 −0.498720
\(782\) 40.3106 1.44150
\(783\) 8.74844 0.312644
\(784\) −17.1311 −0.611826
\(785\) 0 0
\(786\) −11.2717 −0.402049
\(787\) −42.8263 −1.52659 −0.763296 0.646049i \(-0.776420\pi\)
−0.763296 + 0.646049i \(0.776420\pi\)
\(788\) 2.68828 0.0957659
\(789\) −12.7900 −0.455335
\(790\) 0 0
\(791\) 66.4857 2.36396
\(792\) −8.30795 −0.295210
\(793\) 9.32330 0.331080
\(794\) −11.1938 −0.397254
\(795\) 0 0
\(796\) −4.83058 −0.171215
\(797\) 39.4762 1.39832 0.699160 0.714965i \(-0.253557\pi\)
0.699160 + 0.714965i \(0.253557\pi\)
\(798\) −2.24617 −0.0795135
\(799\) 51.7512 1.83082
\(800\) 0 0
\(801\) 24.3053 0.858784
\(802\) 36.1542 1.27665
\(803\) −9.76005 −0.344425
\(804\) −1.81594 −0.0640434
\(805\) 0 0
\(806\) −3.69698 −0.130220
\(807\) −6.23424 −0.219456
\(808\) 9.01341 0.317091
\(809\) −25.3312 −0.890596 −0.445298 0.895382i \(-0.646902\pi\)
−0.445298 + 0.895382i \(0.646902\pi\)
\(810\) 0 0
\(811\) 0.958500 0.0336575 0.0168287 0.999858i \(-0.494643\pi\)
0.0168287 + 0.999858i \(0.494643\pi\)
\(812\) 3.73155 0.130952
\(813\) −4.98411 −0.174800
\(814\) −8.22731 −0.288367
\(815\) 0 0
\(816\) −6.26704 −0.219390
\(817\) 8.34172 0.291840
\(818\) −14.4379 −0.504810
\(819\) 24.7451 0.864664
\(820\) 0 0
\(821\) −1.74252 −0.0608144 −0.0304072 0.999538i \(-0.509680\pi\)
−0.0304072 + 0.999538i \(0.509680\pi\)
\(822\) −2.82529 −0.0985434
\(823\) −24.2792 −0.846320 −0.423160 0.906055i \(-0.639079\pi\)
−0.423160 + 0.906055i \(0.639079\pi\)
\(824\) −26.7084 −0.930433
\(825\) 0 0
\(826\) −7.54116 −0.262390
\(827\) 24.7673 0.861242 0.430621 0.902533i \(-0.358295\pi\)
0.430621 + 0.902533i \(0.358295\pi\)
\(828\) 7.55013 0.262385
\(829\) 28.8962 1.00361 0.501803 0.864982i \(-0.332670\pi\)
0.501803 + 0.864982i \(0.332670\pi\)
\(830\) 0 0
\(831\) 0.924786 0.0320805
\(832\) −22.6451 −0.785077
\(833\) 21.2847 0.737472
\(834\) 7.93385 0.274727
\(835\) 0 0
\(836\) −0.346393 −0.0119803
\(837\) −3.21493 −0.111124
\(838\) −13.2461 −0.457579
\(839\) −27.4268 −0.946878 −0.473439 0.880827i \(-0.656988\pi\)
−0.473439 + 0.880827i \(0.656988\pi\)
\(840\) 0 0
\(841\) −19.6223 −0.676631
\(842\) 21.5978 0.744310
\(843\) 6.47048 0.222855
\(844\) −2.11726 −0.0728792
\(845\) 0 0
\(846\) −46.2720 −1.59086
\(847\) 3.51780 0.120873
\(848\) −23.3853 −0.803056
\(849\) −11.1627 −0.383104
\(850\) 0 0
\(851\) 50.6466 1.73614
\(852\) −2.39721 −0.0821272
\(853\) −0.802929 −0.0274918 −0.0137459 0.999906i \(-0.504376\pi\)
−0.0137459 + 0.999906i \(0.504376\pi\)
\(854\) −16.5088 −0.564920
\(855\) 0 0
\(856\) 14.6095 0.499343
\(857\) −14.5854 −0.498228 −0.249114 0.968474i \(-0.580139\pi\)
−0.249114 + 0.968474i \(0.580139\pi\)
\(858\) 1.63122 0.0556888
\(859\) −26.3712 −0.899775 −0.449888 0.893085i \(-0.648536\pi\)
−0.449888 + 0.893085i \(0.648536\pi\)
\(860\) 0 0
\(861\) 2.88601 0.0983549
\(862\) 18.3006 0.623322
\(863\) 9.36128 0.318662 0.159331 0.987225i \(-0.449066\pi\)
0.159331 + 0.987225i \(0.449066\pi\)
\(864\) −5.53092 −0.188166
\(865\) 0 0
\(866\) −37.1533 −1.26252
\(867\) −0.654649 −0.0222330
\(868\) −1.37129 −0.0465447
\(869\) 5.30165 0.179846
\(870\) 0 0
\(871\) −26.9724 −0.913925
\(872\) 14.1357 0.478696
\(873\) −5.28090 −0.178731
\(874\) −10.1794 −0.344325
\(875\) 0 0
\(876\) −1.67871 −0.0567184
\(877\) −41.8351 −1.41267 −0.706335 0.707878i \(-0.749653\pi\)
−0.706335 + 0.707878i \(0.749653\pi\)
\(878\) 36.1966 1.22158
\(879\) 12.1600 0.410146
\(880\) 0 0
\(881\) −42.1365 −1.41962 −0.709808 0.704396i \(-0.751218\pi\)
−0.709808 + 0.704396i \(0.751218\pi\)
\(882\) −19.0312 −0.640814
\(883\) −35.4866 −1.19422 −0.597109 0.802160i \(-0.703684\pi\)
−0.597109 + 0.802160i \(0.703684\pi\)
\(884\) 3.50434 0.117864
\(885\) 0 0
\(886\) −25.1224 −0.844005
\(887\) −9.49861 −0.318932 −0.159466 0.987203i \(-0.550977\pi\)
−0.159466 + 0.987203i \(0.550977\pi\)
\(888\) −9.58547 −0.321667
\(889\) −46.6572 −1.56483
\(890\) 0 0
\(891\) −6.84182 −0.229209
\(892\) 5.27494 0.176618
\(893\) −13.0685 −0.437320
\(894\) 6.43206 0.215120
\(895\) 0 0
\(896\) 26.4765 0.884519
\(897\) −10.0416 −0.335280
\(898\) −26.4132 −0.881418
\(899\) −3.44617 −0.114936
\(900\) 0 0
\(901\) 29.0553 0.967974
\(902\) −2.12465 −0.0707432
\(903\) −14.5707 −0.484884
\(904\) −57.0261 −1.89666
\(905\) 0 0
\(906\) −12.8000 −0.425251
\(907\) 23.5091 0.780608 0.390304 0.920686i \(-0.372370\pi\)
0.390304 + 0.920686i \(0.372370\pi\)
\(908\) 8.09973 0.268799
\(909\) 8.22524 0.272814
\(910\) 0 0
\(911\) −56.8014 −1.88192 −0.940958 0.338524i \(-0.890072\pi\)
−0.940958 + 0.338524i \(0.890072\pi\)
\(912\) 1.58259 0.0524047
\(913\) −3.85256 −0.127501
\(914\) −15.6091 −0.516304
\(915\) 0 0
\(916\) 0.0306367 0.00101226
\(917\) −62.0999 −2.05072
\(918\) −14.5477 −0.480145
\(919\) −28.7186 −0.947338 −0.473669 0.880703i \(-0.657071\pi\)
−0.473669 + 0.880703i \(0.657071\pi\)
\(920\) 0 0
\(921\) 3.94114 0.129865
\(922\) −37.7524 −1.24331
\(923\) −35.6060 −1.17199
\(924\) 0.605056 0.0199049
\(925\) 0 0
\(926\) −0.703548 −0.0231200
\(927\) −24.3730 −0.800513
\(928\) −5.92874 −0.194621
\(929\) 1.43519 0.0470871 0.0235436 0.999723i \(-0.492505\pi\)
0.0235436 + 0.999723i \(0.492505\pi\)
\(930\) 0 0
\(931\) −5.37494 −0.176156
\(932\) −4.69824 −0.153896
\(933\) −12.0907 −0.395831
\(934\) 4.91567 0.160846
\(935\) 0 0
\(936\) −21.2244 −0.693740
\(937\) 30.7588 1.00485 0.502423 0.864622i \(-0.332442\pi\)
0.502423 + 0.864622i \(0.332442\pi\)
\(938\) 47.7602 1.55942
\(939\) 12.2811 0.400779
\(940\) 0 0
\(941\) −29.2576 −0.953770 −0.476885 0.878966i \(-0.658234\pi\)
−0.476885 + 0.878966i \(0.658234\pi\)
\(942\) −8.43335 −0.274774
\(943\) 13.0792 0.425916
\(944\) 5.31329 0.172933
\(945\) 0 0
\(946\) 10.7268 0.348760
\(947\) −20.3395 −0.660945 −0.330472 0.943816i \(-0.607208\pi\)
−0.330472 + 0.943816i \(0.607208\pi\)
\(948\) 0.911875 0.0296163
\(949\) −24.9341 −0.809394
\(950\) 0 0
\(951\) −15.8180 −0.512932
\(952\) −42.0323 −1.36228
\(953\) 44.0412 1.42664 0.713318 0.700841i \(-0.247192\pi\)
0.713318 + 0.700841i \(0.247192\pi\)
\(954\) −25.9791 −0.841104
\(955\) 0 0
\(956\) 5.13899 0.166207
\(957\) 1.52056 0.0491526
\(958\) −1.17633 −0.0380055
\(959\) −15.5655 −0.502638
\(960\) 0 0
\(961\) −29.7336 −0.959148
\(962\) −21.0184 −0.677660
\(963\) 13.3320 0.429618
\(964\) 0.161741 0.00520932
\(965\) 0 0
\(966\) 17.7808 0.572087
\(967\) 37.4983 1.20586 0.602932 0.797793i \(-0.293999\pi\)
0.602932 + 0.797793i \(0.293999\pi\)
\(968\) −3.01729 −0.0969793
\(969\) −1.96630 −0.0631666
\(970\) 0 0
\(971\) −12.4049 −0.398094 −0.199047 0.979990i \(-0.563785\pi\)
−0.199047 + 0.979990i \(0.563785\pi\)
\(972\) −4.14553 −0.132968
\(973\) 43.7104 1.40129
\(974\) 47.3595 1.51750
\(975\) 0 0
\(976\) 11.6317 0.372320
\(977\) 51.5047 1.64778 0.823891 0.566748i \(-0.191799\pi\)
0.823891 + 0.566748i \(0.191799\pi\)
\(978\) 9.19467 0.294013
\(979\) 8.82721 0.282119
\(980\) 0 0
\(981\) 12.8996 0.411854
\(982\) −26.1965 −0.835963
\(983\) 18.7339 0.597518 0.298759 0.954329i \(-0.403427\pi\)
0.298759 + 0.954329i \(0.403427\pi\)
\(984\) −2.47539 −0.0789125
\(985\) 0 0
\(986\) −15.5940 −0.496616
\(987\) 22.8271 0.726596
\(988\) −0.884934 −0.0281535
\(989\) −66.0334 −2.09974
\(990\) 0 0
\(991\) −12.6275 −0.401125 −0.200563 0.979681i \(-0.564277\pi\)
−0.200563 + 0.979681i \(0.564277\pi\)
\(992\) 2.17873 0.0691749
\(993\) −0.264285 −0.00838683
\(994\) 63.0478 1.99976
\(995\) 0 0
\(996\) −0.662634 −0.0209964
\(997\) 37.1826 1.17758 0.588792 0.808284i \(-0.299604\pi\)
0.588792 + 0.808284i \(0.299604\pi\)
\(998\) 11.8151 0.374001
\(999\) −18.2778 −0.578285
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 5225.2.a.bb.1.15 22
5.2 odd 4 1045.2.b.d.419.15 yes 22
5.3 odd 4 1045.2.b.d.419.8 22
5.4 even 2 inner 5225.2.a.bb.1.8 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.b.d.419.8 22 5.3 odd 4
1045.2.b.d.419.15 yes 22 5.2 odd 4
5225.2.a.bb.1.8 22 5.4 even 2 inner
5225.2.a.bb.1.15 22 1.1 even 1 trivial