Properties

Label 4029.2.a.k.1.26
Level $4029$
Weight $2$
Character 4029.1
Self dual yes
Analytic conductor $32.172$
Analytic rank $0$
Dimension $31$
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] = [4029,2,Mod(1,4029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4029, 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("4029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4029.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.26
Character \(\chi\) \(=\) 4029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.24319 q^{2} +1.00000 q^{3} +3.03191 q^{4} -4.27976 q^{5} +2.24319 q^{6} -0.0653339 q^{7} +2.31477 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.24319 q^{2} +1.00000 q^{3} +3.03191 q^{4} -4.27976 q^{5} +2.24319 q^{6} -0.0653339 q^{7} +2.31477 q^{8} +1.00000 q^{9} -9.60033 q^{10} +3.23018 q^{11} +3.03191 q^{12} -2.88004 q^{13} -0.146556 q^{14} -4.27976 q^{15} -0.871339 q^{16} +1.00000 q^{17} +2.24319 q^{18} +7.45327 q^{19} -12.9759 q^{20} -0.0653339 q^{21} +7.24592 q^{22} -1.14406 q^{23} +2.31477 q^{24} +13.3164 q^{25} -6.46048 q^{26} +1.00000 q^{27} -0.198086 q^{28} +7.28872 q^{29} -9.60033 q^{30} +3.60094 q^{31} -6.58413 q^{32} +3.23018 q^{33} +2.24319 q^{34} +0.279613 q^{35} +3.03191 q^{36} -2.70010 q^{37} +16.7191 q^{38} -2.88004 q^{39} -9.90668 q^{40} +12.7049 q^{41} -0.146556 q^{42} +2.63923 q^{43} +9.79362 q^{44} -4.27976 q^{45} -2.56634 q^{46} +5.16451 q^{47} -0.871339 q^{48} -6.99573 q^{49} +29.8712 q^{50} +1.00000 q^{51} -8.73202 q^{52} -8.09202 q^{53} +2.24319 q^{54} -13.8244 q^{55} -0.151233 q^{56} +7.45327 q^{57} +16.3500 q^{58} +12.2898 q^{59} -12.9759 q^{60} +4.85946 q^{61} +8.07759 q^{62} -0.0653339 q^{63} -13.0268 q^{64} +12.3259 q^{65} +7.24592 q^{66} -7.91890 q^{67} +3.03191 q^{68} -1.14406 q^{69} +0.627227 q^{70} +1.84117 q^{71} +2.31477 q^{72} -2.31371 q^{73} -6.05684 q^{74} +13.3164 q^{75} +22.5976 q^{76} -0.211040 q^{77} -6.46048 q^{78} +1.00000 q^{79} +3.72913 q^{80} +1.00000 q^{81} +28.4996 q^{82} +11.4658 q^{83} -0.198086 q^{84} -4.27976 q^{85} +5.92030 q^{86} +7.28872 q^{87} +7.47714 q^{88} -6.86540 q^{89} -9.60033 q^{90} +0.188164 q^{91} -3.46868 q^{92} +3.60094 q^{93} +11.5850 q^{94} -31.8982 q^{95} -6.58413 q^{96} +8.64709 q^{97} -15.6928 q^{98} +3.23018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24319 1.58618 0.793088 0.609107i \(-0.208472\pi\)
0.793088 + 0.609107i \(0.208472\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.03191 1.51596
\(5\) −4.27976 −1.91397 −0.956984 0.290140i \(-0.906298\pi\)
−0.956984 + 0.290140i \(0.906298\pi\)
\(6\) 2.24319 0.915779
\(7\) −0.0653339 −0.0246939 −0.0123469 0.999924i \(-0.503930\pi\)
−0.0123469 + 0.999924i \(0.503930\pi\)
\(8\) 2.31477 0.818396
\(9\) 1.00000 0.333333
\(10\) −9.60033 −3.03589
\(11\) 3.23018 0.973936 0.486968 0.873420i \(-0.338103\pi\)
0.486968 + 0.873420i \(0.338103\pi\)
\(12\) 3.03191 0.875237
\(13\) −2.88004 −0.798779 −0.399389 0.916781i \(-0.630778\pi\)
−0.399389 + 0.916781i \(0.630778\pi\)
\(14\) −0.146556 −0.0391688
\(15\) −4.27976 −1.10503
\(16\) −0.871339 −0.217835
\(17\) 1.00000 0.242536
\(18\) 2.24319 0.528725
\(19\) 7.45327 1.70990 0.854948 0.518713i \(-0.173589\pi\)
0.854948 + 0.518713i \(0.173589\pi\)
\(20\) −12.9759 −2.90149
\(21\) −0.0653339 −0.0142570
\(22\) 7.24592 1.54483
\(23\) −1.14406 −0.238552 −0.119276 0.992861i \(-0.538057\pi\)
−0.119276 + 0.992861i \(0.538057\pi\)
\(24\) 2.31477 0.472501
\(25\) 13.3164 2.66328
\(26\) −6.46048 −1.26700
\(27\) 1.00000 0.192450
\(28\) −0.198086 −0.0374348
\(29\) 7.28872 1.35348 0.676740 0.736222i \(-0.263392\pi\)
0.676740 + 0.736222i \(0.263392\pi\)
\(30\) −9.60033 −1.75277
\(31\) 3.60094 0.646747 0.323374 0.946271i \(-0.395183\pi\)
0.323374 + 0.946271i \(0.395183\pi\)
\(32\) −6.58413 −1.16392
\(33\) 3.23018 0.562302
\(34\) 2.24319 0.384704
\(35\) 0.279613 0.0472633
\(36\) 3.03191 0.505318
\(37\) −2.70010 −0.443893 −0.221947 0.975059i \(-0.571241\pi\)
−0.221947 + 0.975059i \(0.571241\pi\)
\(38\) 16.7191 2.71220
\(39\) −2.88004 −0.461175
\(40\) −9.90668 −1.56638
\(41\) 12.7049 1.98418 0.992089 0.125533i \(-0.0400641\pi\)
0.992089 + 0.125533i \(0.0400641\pi\)
\(42\) −0.146556 −0.0226141
\(43\) 2.63923 0.402479 0.201239 0.979542i \(-0.435503\pi\)
0.201239 + 0.979542i \(0.435503\pi\)
\(44\) 9.79362 1.47644
\(45\) −4.27976 −0.637990
\(46\) −2.56634 −0.378386
\(47\) 5.16451 0.753321 0.376661 0.926351i \(-0.377072\pi\)
0.376661 + 0.926351i \(0.377072\pi\)
\(48\) −0.871339 −0.125767
\(49\) −6.99573 −0.999390
\(50\) 29.8712 4.22442
\(51\) 1.00000 0.140028
\(52\) −8.73202 −1.21091
\(53\) −8.09202 −1.11152 −0.555762 0.831341i \(-0.687573\pi\)
−0.555762 + 0.831341i \(0.687573\pi\)
\(54\) 2.24319 0.305260
\(55\) −13.8244 −1.86408
\(56\) −0.151233 −0.0202094
\(57\) 7.45327 0.987209
\(58\) 16.3500 2.14686
\(59\) 12.2898 1.60000 0.800001 0.599999i \(-0.204832\pi\)
0.800001 + 0.599999i \(0.204832\pi\)
\(60\) −12.9759 −1.67518
\(61\) 4.85946 0.622190 0.311095 0.950379i \(-0.399304\pi\)
0.311095 + 0.950379i \(0.399304\pi\)
\(62\) 8.07759 1.02585
\(63\) −0.0653339 −0.00823129
\(64\) −13.0268 −1.62835
\(65\) 12.3259 1.52884
\(66\) 7.24592 0.891911
\(67\) −7.91890 −0.967448 −0.483724 0.875221i \(-0.660716\pi\)
−0.483724 + 0.875221i \(0.660716\pi\)
\(68\) 3.03191 0.367673
\(69\) −1.14406 −0.137728
\(70\) 0.627227 0.0749679
\(71\) 1.84117 0.218507 0.109253 0.994014i \(-0.465154\pi\)
0.109253 + 0.994014i \(0.465154\pi\)
\(72\) 2.31477 0.272799
\(73\) −2.31371 −0.270799 −0.135400 0.990791i \(-0.543232\pi\)
−0.135400 + 0.990791i \(0.543232\pi\)
\(74\) −6.05684 −0.704093
\(75\) 13.3164 1.53764
\(76\) 22.5976 2.59213
\(77\) −0.211040 −0.0240503
\(78\) −6.46048 −0.731505
\(79\) 1.00000 0.112509
\(80\) 3.72913 0.416929
\(81\) 1.00000 0.111111
\(82\) 28.4996 3.14726
\(83\) 11.4658 1.25853 0.629265 0.777191i \(-0.283356\pi\)
0.629265 + 0.777191i \(0.283356\pi\)
\(84\) −0.198086 −0.0216130
\(85\) −4.27976 −0.464206
\(86\) 5.92030 0.638402
\(87\) 7.28872 0.781432
\(88\) 7.47714 0.797066
\(89\) −6.86540 −0.727731 −0.363866 0.931451i \(-0.618543\pi\)
−0.363866 + 0.931451i \(0.618543\pi\)
\(90\) −9.60033 −1.01196
\(91\) 0.188164 0.0197249
\(92\) −3.46868 −0.361635
\(93\) 3.60094 0.373400
\(94\) 11.5850 1.19490
\(95\) −31.8982 −3.27269
\(96\) −6.58413 −0.671990
\(97\) 8.64709 0.877979 0.438990 0.898492i \(-0.355337\pi\)
0.438990 + 0.898492i \(0.355337\pi\)
\(98\) −15.6928 −1.58521
\(99\) 3.23018 0.324645
\(100\) 40.3741 4.03741
\(101\) −13.6386 −1.35710 −0.678548 0.734556i \(-0.737390\pi\)
−0.678548 + 0.734556i \(0.737390\pi\)
\(102\) 2.24319 0.222109
\(103\) 7.16588 0.706075 0.353038 0.935609i \(-0.385149\pi\)
0.353038 + 0.935609i \(0.385149\pi\)
\(104\) −6.66663 −0.653717
\(105\) 0.279613 0.0272875
\(106\) −18.1520 −1.76307
\(107\) 9.38280 0.907070 0.453535 0.891238i \(-0.350163\pi\)
0.453535 + 0.891238i \(0.350163\pi\)
\(108\) 3.03191 0.291746
\(109\) 8.45836 0.810164 0.405082 0.914280i \(-0.367243\pi\)
0.405082 + 0.914280i \(0.367243\pi\)
\(110\) −31.0108 −2.95676
\(111\) −2.70010 −0.256282
\(112\) 0.0569280 0.00537919
\(113\) −3.94608 −0.371216 −0.185608 0.982624i \(-0.559425\pi\)
−0.185608 + 0.982624i \(0.559425\pi\)
\(114\) 16.7191 1.56589
\(115\) 4.89629 0.456582
\(116\) 22.0987 2.05182
\(117\) −2.88004 −0.266260
\(118\) 27.5685 2.53789
\(119\) −0.0653339 −0.00598914
\(120\) −9.90668 −0.904352
\(121\) −0.565931 −0.0514483
\(122\) 10.9007 0.986902
\(123\) 12.7049 1.14557
\(124\) 10.9177 0.980440
\(125\) −35.5921 −3.18346
\(126\) −0.146556 −0.0130563
\(127\) −17.7999 −1.57948 −0.789741 0.613440i \(-0.789785\pi\)
−0.789741 + 0.613440i \(0.789785\pi\)
\(128\) −16.0533 −1.41893
\(129\) 2.63923 0.232371
\(130\) 27.6493 2.42501
\(131\) 15.1266 1.32162 0.660809 0.750554i \(-0.270213\pi\)
0.660809 + 0.750554i \(0.270213\pi\)
\(132\) 9.79362 0.852425
\(133\) −0.486951 −0.0422240
\(134\) −17.7636 −1.53454
\(135\) −4.27976 −0.368343
\(136\) 2.31477 0.198490
\(137\) 10.9459 0.935168 0.467584 0.883949i \(-0.345125\pi\)
0.467584 + 0.883949i \(0.345125\pi\)
\(138\) −2.56634 −0.218461
\(139\) −5.85835 −0.496898 −0.248449 0.968645i \(-0.579921\pi\)
−0.248449 + 0.968645i \(0.579921\pi\)
\(140\) 0.847763 0.0716491
\(141\) 5.16451 0.434930
\(142\) 4.13010 0.346590
\(143\) −9.30304 −0.777959
\(144\) −0.871339 −0.0726116
\(145\) −31.1940 −2.59052
\(146\) −5.19010 −0.429536
\(147\) −6.99573 −0.576998
\(148\) −8.18645 −0.672922
\(149\) 22.3310 1.82943 0.914714 0.404103i \(-0.132416\pi\)
0.914714 + 0.404103i \(0.132416\pi\)
\(150\) 29.8712 2.43897
\(151\) −5.35488 −0.435774 −0.217887 0.975974i \(-0.569916\pi\)
−0.217887 + 0.975974i \(0.569916\pi\)
\(152\) 17.2526 1.39937
\(153\) 1.00000 0.0808452
\(154\) −0.473404 −0.0381480
\(155\) −15.4112 −1.23785
\(156\) −8.73202 −0.699121
\(157\) −17.8963 −1.42828 −0.714141 0.700002i \(-0.753183\pi\)
−0.714141 + 0.700002i \(0.753183\pi\)
\(158\) 2.24319 0.178459
\(159\) −8.09202 −0.641739
\(160\) 28.1785 2.22771
\(161\) 0.0747457 0.00589078
\(162\) 2.24319 0.176242
\(163\) 11.0501 0.865511 0.432756 0.901511i \(-0.357541\pi\)
0.432756 + 0.901511i \(0.357541\pi\)
\(164\) 38.5203 3.00793
\(165\) −13.8244 −1.07623
\(166\) 25.7199 1.99625
\(167\) −11.6924 −0.904789 −0.452394 0.891818i \(-0.649430\pi\)
−0.452394 + 0.891818i \(0.649430\pi\)
\(168\) −0.151233 −0.0116679
\(169\) −4.70538 −0.361953
\(170\) −9.60033 −0.736312
\(171\) 7.45327 0.569966
\(172\) 8.00191 0.610140
\(173\) −10.3964 −0.790424 −0.395212 0.918590i \(-0.629329\pi\)
−0.395212 + 0.918590i \(0.629329\pi\)
\(174\) 16.3500 1.23949
\(175\) −0.870010 −0.0657666
\(176\) −2.81458 −0.212157
\(177\) 12.2898 0.923762
\(178\) −15.4004 −1.15431
\(179\) −26.6599 −1.99265 −0.996326 0.0856454i \(-0.972705\pi\)
−0.996326 + 0.0856454i \(0.972705\pi\)
\(180\) −12.9759 −0.967164
\(181\) −14.5419 −1.08089 −0.540446 0.841379i \(-0.681744\pi\)
−0.540446 + 0.841379i \(0.681744\pi\)
\(182\) 0.422088 0.0312872
\(183\) 4.85946 0.359221
\(184\) −2.64823 −0.195230
\(185\) 11.5558 0.849598
\(186\) 8.07759 0.592278
\(187\) 3.23018 0.236214
\(188\) 15.6583 1.14200
\(189\) −0.0653339 −0.00475234
\(190\) −71.5538 −5.19106
\(191\) 10.3079 0.745853 0.372927 0.927861i \(-0.378354\pi\)
0.372927 + 0.927861i \(0.378354\pi\)
\(192\) −13.0268 −0.940127
\(193\) 1.90532 0.137148 0.0685741 0.997646i \(-0.478155\pi\)
0.0685741 + 0.997646i \(0.478155\pi\)
\(194\) 19.3971 1.39263
\(195\) 12.3259 0.882675
\(196\) −21.2104 −1.51503
\(197\) 5.83384 0.415644 0.207822 0.978167i \(-0.433363\pi\)
0.207822 + 0.978167i \(0.433363\pi\)
\(198\) 7.24592 0.514945
\(199\) 5.83516 0.413643 0.206822 0.978379i \(-0.433688\pi\)
0.206822 + 0.978379i \(0.433688\pi\)
\(200\) 30.8244 2.17961
\(201\) −7.91890 −0.558556
\(202\) −30.5941 −2.15259
\(203\) −0.476200 −0.0334227
\(204\) 3.03191 0.212276
\(205\) −54.3742 −3.79766
\(206\) 16.0744 1.11996
\(207\) −1.14406 −0.0795175
\(208\) 2.50949 0.174002
\(209\) 24.0754 1.66533
\(210\) 0.627227 0.0432828
\(211\) −7.24857 −0.499012 −0.249506 0.968373i \(-0.580268\pi\)
−0.249506 + 0.968373i \(0.580268\pi\)
\(212\) −24.5343 −1.68502
\(213\) 1.84117 0.126155
\(214\) 21.0474 1.43877
\(215\) −11.2953 −0.770331
\(216\) 2.31477 0.157500
\(217\) −0.235263 −0.0159707
\(218\) 18.9737 1.28506
\(219\) −2.31371 −0.156346
\(220\) −41.9144 −2.82587
\(221\) −2.88004 −0.193732
\(222\) −6.05684 −0.406508
\(223\) −15.7699 −1.05603 −0.528014 0.849235i \(-0.677063\pi\)
−0.528014 + 0.849235i \(0.677063\pi\)
\(224\) 0.430167 0.0287417
\(225\) 13.3164 0.887759
\(226\) −8.85181 −0.588813
\(227\) −11.1561 −0.740457 −0.370228 0.928941i \(-0.620721\pi\)
−0.370228 + 0.928941i \(0.620721\pi\)
\(228\) 22.5976 1.49657
\(229\) −2.46171 −0.162674 −0.0813370 0.996687i \(-0.525919\pi\)
−0.0813370 + 0.996687i \(0.525919\pi\)
\(230\) 10.9833 0.724219
\(231\) −0.211040 −0.0138854
\(232\) 16.8717 1.10768
\(233\) 6.94093 0.454716 0.227358 0.973811i \(-0.426991\pi\)
0.227358 + 0.973811i \(0.426991\pi\)
\(234\) −6.46048 −0.422335
\(235\) −22.1029 −1.44183
\(236\) 37.2617 2.42553
\(237\) 1.00000 0.0649570
\(238\) −0.146556 −0.00949984
\(239\) 10.5045 0.679479 0.339739 0.940520i \(-0.389661\pi\)
0.339739 + 0.940520i \(0.389661\pi\)
\(240\) 3.72913 0.240714
\(241\) 25.0266 1.61210 0.806052 0.591844i \(-0.201600\pi\)
0.806052 + 0.591844i \(0.201600\pi\)
\(242\) −1.26949 −0.0816061
\(243\) 1.00000 0.0641500
\(244\) 14.7334 0.943212
\(245\) 29.9401 1.91280
\(246\) 28.4996 1.81707
\(247\) −21.4657 −1.36583
\(248\) 8.33535 0.529295
\(249\) 11.4658 0.726612
\(250\) −79.8400 −5.04952
\(251\) −17.4686 −1.10261 −0.551303 0.834305i \(-0.685869\pi\)
−0.551303 + 0.834305i \(0.685869\pi\)
\(252\) −0.198086 −0.0124783
\(253\) −3.69551 −0.232335
\(254\) −39.9285 −2.50534
\(255\) −4.27976 −0.268009
\(256\) −9.95712 −0.622320
\(257\) 16.5472 1.03219 0.516094 0.856532i \(-0.327386\pi\)
0.516094 + 0.856532i \(0.327386\pi\)
\(258\) 5.92030 0.368582
\(259\) 0.176408 0.0109614
\(260\) 37.3710 2.31765
\(261\) 7.28872 0.451160
\(262\) 33.9319 2.09632
\(263\) 1.84760 0.113928 0.0569640 0.998376i \(-0.481858\pi\)
0.0569640 + 0.998376i \(0.481858\pi\)
\(264\) 7.47714 0.460186
\(265\) 34.6319 2.12742
\(266\) −1.09232 −0.0669747
\(267\) −6.86540 −0.420156
\(268\) −24.0094 −1.46661
\(269\) 25.0351 1.52642 0.763209 0.646152i \(-0.223623\pi\)
0.763209 + 0.646152i \(0.223623\pi\)
\(270\) −9.60033 −0.584258
\(271\) −0.0889911 −0.00540583 −0.00270291 0.999996i \(-0.500860\pi\)
−0.00270291 + 0.999996i \(0.500860\pi\)
\(272\) −0.871339 −0.0528327
\(273\) 0.188164 0.0113882
\(274\) 24.5537 1.48334
\(275\) 43.0143 2.59386
\(276\) −3.46868 −0.208790
\(277\) 3.46495 0.208189 0.104094 0.994567i \(-0.466806\pi\)
0.104094 + 0.994567i \(0.466806\pi\)
\(278\) −13.1414 −0.788168
\(279\) 3.60094 0.215582
\(280\) 0.647242 0.0386801
\(281\) −20.4218 −1.21826 −0.609131 0.793070i \(-0.708482\pi\)
−0.609131 + 0.793070i \(0.708482\pi\)
\(282\) 11.5850 0.689876
\(283\) 10.7287 0.637755 0.318878 0.947796i \(-0.396694\pi\)
0.318878 + 0.947796i \(0.396694\pi\)
\(284\) 5.58227 0.331247
\(285\) −31.8982 −1.88949
\(286\) −20.8685 −1.23398
\(287\) −0.830063 −0.0489971
\(288\) −6.58413 −0.387974
\(289\) 1.00000 0.0588235
\(290\) −69.9741 −4.10902
\(291\) 8.64709 0.506901
\(292\) −7.01497 −0.410520
\(293\) 31.7647 1.85571 0.927857 0.372937i \(-0.121649\pi\)
0.927857 + 0.372937i \(0.121649\pi\)
\(294\) −15.6928 −0.915221
\(295\) −52.5977 −3.06235
\(296\) −6.25011 −0.363281
\(297\) 3.23018 0.187434
\(298\) 50.0927 2.90179
\(299\) 3.29493 0.190551
\(300\) 40.3741 2.33100
\(301\) −0.172431 −0.00993876
\(302\) −12.0120 −0.691214
\(303\) −13.6386 −0.783520
\(304\) −6.49432 −0.372475
\(305\) −20.7973 −1.19085
\(306\) 2.24319 0.128235
\(307\) −24.8838 −1.42019 −0.710097 0.704104i \(-0.751349\pi\)
−0.710097 + 0.704104i \(0.751349\pi\)
\(308\) −0.639855 −0.0364591
\(309\) 7.16588 0.407653
\(310\) −34.5702 −1.96345
\(311\) 1.31464 0.0745465 0.0372732 0.999305i \(-0.488133\pi\)
0.0372732 + 0.999305i \(0.488133\pi\)
\(312\) −6.66663 −0.377424
\(313\) −25.5573 −1.44459 −0.722293 0.691588i \(-0.756912\pi\)
−0.722293 + 0.691588i \(0.756912\pi\)
\(314\) −40.1449 −2.26551
\(315\) 0.279613 0.0157544
\(316\) 3.03191 0.170558
\(317\) −15.9302 −0.894730 −0.447365 0.894351i \(-0.647638\pi\)
−0.447365 + 0.894351i \(0.647638\pi\)
\(318\) −18.1520 −1.01791
\(319\) 23.5439 1.31820
\(320\) 55.7516 3.11661
\(321\) 9.38280 0.523697
\(322\) 0.167669 0.00934382
\(323\) 7.45327 0.414711
\(324\) 3.03191 0.168439
\(325\) −38.3517 −2.12737
\(326\) 24.7875 1.37285
\(327\) 8.45836 0.467748
\(328\) 29.4091 1.62384
\(329\) −0.337417 −0.0186024
\(330\) −31.0108 −1.70709
\(331\) 14.8737 0.817534 0.408767 0.912639i \(-0.365959\pi\)
0.408767 + 0.912639i \(0.365959\pi\)
\(332\) 34.7631 1.90787
\(333\) −2.70010 −0.147964
\(334\) −26.2284 −1.43515
\(335\) 33.8910 1.85166
\(336\) 0.0569280 0.00310567
\(337\) −1.91722 −0.104437 −0.0522187 0.998636i \(-0.516629\pi\)
−0.0522187 + 0.998636i \(0.516629\pi\)
\(338\) −10.5551 −0.574121
\(339\) −3.94608 −0.214321
\(340\) −12.9759 −0.703715
\(341\) 11.6317 0.629890
\(342\) 16.7191 0.904066
\(343\) 0.914395 0.0493727
\(344\) 6.10922 0.329387
\(345\) 4.89629 0.263608
\(346\) −23.3211 −1.25375
\(347\) −23.3849 −1.25537 −0.627685 0.778468i \(-0.715997\pi\)
−0.627685 + 0.778468i \(0.715997\pi\)
\(348\) 22.0987 1.18462
\(349\) 24.9527 1.33569 0.667844 0.744301i \(-0.267217\pi\)
0.667844 + 0.744301i \(0.267217\pi\)
\(350\) −1.95160 −0.104317
\(351\) −2.88004 −0.153725
\(352\) −21.2679 −1.13358
\(353\) 13.0410 0.694102 0.347051 0.937846i \(-0.387183\pi\)
0.347051 + 0.937846i \(0.387183\pi\)
\(354\) 27.5685 1.46525
\(355\) −7.87978 −0.418215
\(356\) −20.8153 −1.10321
\(357\) −0.0653339 −0.00345783
\(358\) −59.8032 −3.16070
\(359\) −21.4840 −1.13388 −0.566941 0.823758i \(-0.691873\pi\)
−0.566941 + 0.823758i \(0.691873\pi\)
\(360\) −9.90668 −0.522128
\(361\) 36.5512 1.92375
\(362\) −32.6203 −1.71449
\(363\) −0.565931 −0.0297037
\(364\) 0.570496 0.0299021
\(365\) 9.90214 0.518302
\(366\) 10.9007 0.569788
\(367\) −10.7360 −0.560415 −0.280208 0.959939i \(-0.590403\pi\)
−0.280208 + 0.959939i \(0.590403\pi\)
\(368\) 0.996862 0.0519650
\(369\) 12.7049 0.661393
\(370\) 25.9218 1.34761
\(371\) 0.528683 0.0274478
\(372\) 10.9177 0.566057
\(373\) −19.7906 −1.02472 −0.512359 0.858772i \(-0.671228\pi\)
−0.512359 + 0.858772i \(0.671228\pi\)
\(374\) 7.24592 0.374677
\(375\) −35.5921 −1.83797
\(376\) 11.9547 0.616515
\(377\) −20.9918 −1.08113
\(378\) −0.146556 −0.00753805
\(379\) 3.13241 0.160901 0.0804505 0.996759i \(-0.474364\pi\)
0.0804505 + 0.996759i \(0.474364\pi\)
\(380\) −96.7125 −4.96125
\(381\) −17.7999 −0.911915
\(382\) 23.1226 1.18305
\(383\) 22.7645 1.16321 0.581606 0.813471i \(-0.302425\pi\)
0.581606 + 0.813471i \(0.302425\pi\)
\(384\) −16.0533 −0.819218
\(385\) 0.903202 0.0460314
\(386\) 4.27401 0.217541
\(387\) 2.63923 0.134160
\(388\) 26.2172 1.33098
\(389\) 28.5165 1.44584 0.722921 0.690931i \(-0.242799\pi\)
0.722921 + 0.690931i \(0.242799\pi\)
\(390\) 27.6493 1.40008
\(391\) −1.14406 −0.0578575
\(392\) −16.1935 −0.817897
\(393\) 15.1266 0.763037
\(394\) 13.0864 0.659285
\(395\) −4.27976 −0.215338
\(396\) 9.79362 0.492148
\(397\) 36.9626 1.85510 0.927550 0.373699i \(-0.121911\pi\)
0.927550 + 0.373699i \(0.121911\pi\)
\(398\) 13.0894 0.656111
\(399\) −0.486951 −0.0243780
\(400\) −11.6031 −0.580154
\(401\) −14.5668 −0.727430 −0.363715 0.931510i \(-0.618492\pi\)
−0.363715 + 0.931510i \(0.618492\pi\)
\(402\) −17.7636 −0.885969
\(403\) −10.3708 −0.516608
\(404\) −41.3512 −2.05730
\(405\) −4.27976 −0.212663
\(406\) −1.06821 −0.0530143
\(407\) −8.72180 −0.432324
\(408\) 2.31477 0.114598
\(409\) −37.0354 −1.83128 −0.915640 0.401998i \(-0.868316\pi\)
−0.915640 + 0.401998i \(0.868316\pi\)
\(410\) −121.972 −6.02375
\(411\) 10.9459 0.539919
\(412\) 21.7263 1.07038
\(413\) −0.802943 −0.0395103
\(414\) −2.56634 −0.126129
\(415\) −49.0707 −2.40879
\(416\) 18.9625 0.929715
\(417\) −5.85835 −0.286884
\(418\) 54.0057 2.64151
\(419\) 38.5543 1.88350 0.941751 0.336311i \(-0.109179\pi\)
0.941751 + 0.336311i \(0.109179\pi\)
\(420\) 0.847763 0.0413666
\(421\) 11.8642 0.578223 0.289112 0.957295i \(-0.406640\pi\)
0.289112 + 0.957295i \(0.406640\pi\)
\(422\) −16.2599 −0.791522
\(423\) 5.16451 0.251107
\(424\) −18.7312 −0.909667
\(425\) 13.3164 0.645939
\(426\) 4.13010 0.200104
\(427\) −0.317487 −0.0153643
\(428\) 28.4478 1.37508
\(429\) −9.30304 −0.449155
\(430\) −25.3375 −1.22188
\(431\) −36.6782 −1.76672 −0.883362 0.468691i \(-0.844726\pi\)
−0.883362 + 0.468691i \(0.844726\pi\)
\(432\) −0.871339 −0.0419223
\(433\) 5.95020 0.285948 0.142974 0.989726i \(-0.454333\pi\)
0.142974 + 0.989726i \(0.454333\pi\)
\(434\) −0.527740 −0.0253323
\(435\) −31.1940 −1.49564
\(436\) 25.6450 1.22817
\(437\) −8.52696 −0.407900
\(438\) −5.19010 −0.247993
\(439\) 8.10451 0.386807 0.193404 0.981119i \(-0.438047\pi\)
0.193404 + 0.981119i \(0.438047\pi\)
\(440\) −32.0004 −1.52556
\(441\) −6.99573 −0.333130
\(442\) −6.46048 −0.307294
\(443\) −7.36079 −0.349722 −0.174861 0.984593i \(-0.555948\pi\)
−0.174861 + 0.984593i \(0.555948\pi\)
\(444\) −8.18645 −0.388512
\(445\) 29.3823 1.39285
\(446\) −35.3749 −1.67505
\(447\) 22.3310 1.05622
\(448\) 0.851090 0.0402102
\(449\) 7.87811 0.371791 0.185895 0.982570i \(-0.440481\pi\)
0.185895 + 0.982570i \(0.440481\pi\)
\(450\) 29.8712 1.40814
\(451\) 41.0393 1.93246
\(452\) −11.9642 −0.562746
\(453\) −5.35488 −0.251594
\(454\) −25.0253 −1.17450
\(455\) −0.805297 −0.0377529
\(456\) 17.2526 0.807928
\(457\) −29.7161 −1.39006 −0.695030 0.718981i \(-0.744609\pi\)
−0.695030 + 0.718981i \(0.744609\pi\)
\(458\) −5.52208 −0.258030
\(459\) 1.00000 0.0466760
\(460\) 14.8451 0.692158
\(461\) 29.8469 1.39011 0.695053 0.718958i \(-0.255381\pi\)
0.695053 + 0.718958i \(0.255381\pi\)
\(462\) −0.473404 −0.0220247
\(463\) −21.1974 −0.985126 −0.492563 0.870277i \(-0.663940\pi\)
−0.492563 + 0.870277i \(0.663940\pi\)
\(464\) −6.35095 −0.294835
\(465\) −15.4112 −0.714675
\(466\) 15.5698 0.721259
\(467\) −35.0045 −1.61982 −0.809908 0.586557i \(-0.800483\pi\)
−0.809908 + 0.586557i \(0.800483\pi\)
\(468\) −8.73202 −0.403638
\(469\) 0.517372 0.0238900
\(470\) −49.5810 −2.28700
\(471\) −17.8963 −0.824619
\(472\) 28.4482 1.30944
\(473\) 8.52519 0.391988
\(474\) 2.24319 0.103033
\(475\) 99.2505 4.55393
\(476\) −0.198086 −0.00907928
\(477\) −8.09202 −0.370508
\(478\) 23.5636 1.07777
\(479\) −9.11379 −0.416419 −0.208210 0.978084i \(-0.566764\pi\)
−0.208210 + 0.978084i \(0.566764\pi\)
\(480\) 28.1785 1.28617
\(481\) 7.77638 0.354572
\(482\) 56.1395 2.55708
\(483\) 0.0747457 0.00340105
\(484\) −1.71585 −0.0779933
\(485\) −37.0075 −1.68042
\(486\) 2.24319 0.101753
\(487\) 8.56392 0.388068 0.194034 0.980995i \(-0.437843\pi\)
0.194034 + 0.980995i \(0.437843\pi\)
\(488\) 11.2485 0.509197
\(489\) 11.0501 0.499703
\(490\) 67.1613 3.03404
\(491\) −13.8472 −0.624917 −0.312458 0.949931i \(-0.601152\pi\)
−0.312458 + 0.949931i \(0.601152\pi\)
\(492\) 38.5203 1.73663
\(493\) 7.28872 0.328267
\(494\) −48.1517 −2.16645
\(495\) −13.8244 −0.621361
\(496\) −3.13764 −0.140884
\(497\) −0.120291 −0.00539578
\(498\) 25.7199 1.15254
\(499\) −41.5122 −1.85834 −0.929171 0.369650i \(-0.879478\pi\)
−0.929171 + 0.369650i \(0.879478\pi\)
\(500\) −107.912 −4.82598
\(501\) −11.6924 −0.522380
\(502\) −39.1853 −1.74893
\(503\) 17.2207 0.767833 0.383917 0.923368i \(-0.374575\pi\)
0.383917 + 0.923368i \(0.374575\pi\)
\(504\) −0.151233 −0.00673646
\(505\) 58.3702 2.59744
\(506\) −8.28974 −0.368524
\(507\) −4.70538 −0.208973
\(508\) −53.9676 −2.39442
\(509\) −33.8186 −1.49898 −0.749491 0.662014i \(-0.769702\pi\)
−0.749491 + 0.662014i \(0.769702\pi\)
\(510\) −9.60033 −0.425110
\(511\) 0.151164 0.00668709
\(512\) 9.77092 0.431818
\(513\) 7.45327 0.329070
\(514\) 37.1186 1.63723
\(515\) −30.6683 −1.35141
\(516\) 8.00191 0.352264
\(517\) 16.6823 0.733687
\(518\) 0.395717 0.0173868
\(519\) −10.3964 −0.456351
\(520\) 28.5316 1.25119
\(521\) 1.22209 0.0535409 0.0267705 0.999642i \(-0.491478\pi\)
0.0267705 + 0.999642i \(0.491478\pi\)
\(522\) 16.3500 0.715620
\(523\) −16.2375 −0.710017 −0.355009 0.934863i \(-0.615522\pi\)
−0.355009 + 0.934863i \(0.615522\pi\)
\(524\) 45.8626 2.00351
\(525\) −0.870010 −0.0379704
\(526\) 4.14453 0.180710
\(527\) 3.60094 0.156859
\(528\) −2.81458 −0.122489
\(529\) −21.6911 −0.943093
\(530\) 77.6861 3.37447
\(531\) 12.2898 0.533334
\(532\) −1.47639 −0.0640097
\(533\) −36.5907 −1.58492
\(534\) −15.4004 −0.666441
\(535\) −40.1562 −1.73610
\(536\) −18.3305 −0.791755
\(537\) −26.6599 −1.15046
\(538\) 56.1586 2.42117
\(539\) −22.5975 −0.973342
\(540\) −12.9759 −0.558392
\(541\) −31.0112 −1.33328 −0.666638 0.745382i \(-0.732267\pi\)
−0.666638 + 0.745382i \(0.732267\pi\)
\(542\) −0.199624 −0.00857459
\(543\) −14.5419 −0.624053
\(544\) −6.58413 −0.282292
\(545\) −36.1998 −1.55063
\(546\) 0.422088 0.0180637
\(547\) −7.23456 −0.309328 −0.154664 0.987967i \(-0.549429\pi\)
−0.154664 + 0.987967i \(0.549429\pi\)
\(548\) 33.1869 1.41767
\(549\) 4.85946 0.207397
\(550\) 96.4894 4.11432
\(551\) 54.3247 2.31431
\(552\) −2.64823 −0.112716
\(553\) −0.0653339 −0.00277828
\(554\) 7.77255 0.330224
\(555\) 11.5558 0.490516
\(556\) −17.7620 −0.753276
\(557\) 16.7212 0.708501 0.354250 0.935151i \(-0.384736\pi\)
0.354250 + 0.935151i \(0.384736\pi\)
\(558\) 8.07759 0.341952
\(559\) −7.60108 −0.321491
\(560\) −0.243638 −0.0102956
\(561\) 3.23018 0.136378
\(562\) −45.8100 −1.93238
\(563\) 8.37738 0.353064 0.176532 0.984295i \(-0.443512\pi\)
0.176532 + 0.984295i \(0.443512\pi\)
\(564\) 15.6583 0.659335
\(565\) 16.8883 0.710495
\(566\) 24.0665 1.01159
\(567\) −0.0653339 −0.00274376
\(568\) 4.26189 0.178825
\(569\) −6.47451 −0.271426 −0.135713 0.990748i \(-0.543332\pi\)
−0.135713 + 0.990748i \(0.543332\pi\)
\(570\) −71.5538 −2.99706
\(571\) −5.08808 −0.212930 −0.106465 0.994316i \(-0.533953\pi\)
−0.106465 + 0.994316i \(0.533953\pi\)
\(572\) −28.2060 −1.17935
\(573\) 10.3079 0.430619
\(574\) −1.86199 −0.0777180
\(575\) −15.2347 −0.635331
\(576\) −13.0268 −0.542783
\(577\) 26.9593 1.12233 0.561166 0.827703i \(-0.310353\pi\)
0.561166 + 0.827703i \(0.310353\pi\)
\(578\) 2.24319 0.0933045
\(579\) 1.90532 0.0791825
\(580\) −94.5774 −3.92711
\(581\) −0.749102 −0.0310780
\(582\) 19.3971 0.804035
\(583\) −26.1387 −1.08255
\(584\) −5.35572 −0.221621
\(585\) 12.3259 0.509612
\(586\) 71.2543 2.94349
\(587\) −7.56818 −0.312372 −0.156186 0.987728i \(-0.549920\pi\)
−0.156186 + 0.987728i \(0.549920\pi\)
\(588\) −21.2104 −0.874703
\(589\) 26.8387 1.10587
\(590\) −117.987 −4.85743
\(591\) 5.83384 0.239972
\(592\) 2.35270 0.0966954
\(593\) 33.8791 1.39125 0.695624 0.718406i \(-0.255128\pi\)
0.695624 + 0.718406i \(0.255128\pi\)
\(594\) 7.24592 0.297304
\(595\) 0.279613 0.0114630
\(596\) 67.7056 2.77333
\(597\) 5.83516 0.238817
\(598\) 7.39115 0.302247
\(599\) −30.1074 −1.23015 −0.615077 0.788467i \(-0.710875\pi\)
−0.615077 + 0.788467i \(0.710875\pi\)
\(600\) 30.8244 1.25840
\(601\) −5.03682 −0.205456 −0.102728 0.994709i \(-0.532757\pi\)
−0.102728 + 0.994709i \(0.532757\pi\)
\(602\) −0.386796 −0.0157646
\(603\) −7.91890 −0.322483
\(604\) −16.2355 −0.660614
\(605\) 2.42205 0.0984705
\(606\) −30.5941 −1.24280
\(607\) −10.2109 −0.414448 −0.207224 0.978294i \(-0.566443\pi\)
−0.207224 + 0.978294i \(0.566443\pi\)
\(608\) −49.0733 −1.99018
\(609\) −0.476200 −0.0192966
\(610\) −46.6524 −1.88890
\(611\) −14.8740 −0.601737
\(612\) 3.03191 0.122558
\(613\) 5.75216 0.232328 0.116164 0.993230i \(-0.462940\pi\)
0.116164 + 0.993230i \(0.462940\pi\)
\(614\) −55.8192 −2.25268
\(615\) −54.3742 −2.19258
\(616\) −0.488510 −0.0196826
\(617\) −40.0191 −1.61111 −0.805555 0.592521i \(-0.798133\pi\)
−0.805555 + 0.592521i \(0.798133\pi\)
\(618\) 16.0744 0.646609
\(619\) 6.83554 0.274744 0.137372 0.990520i \(-0.456134\pi\)
0.137372 + 0.990520i \(0.456134\pi\)
\(620\) −46.7252 −1.87653
\(621\) −1.14406 −0.0459094
\(622\) 2.94899 0.118244
\(623\) 0.448543 0.0179705
\(624\) 2.50949 0.100460
\(625\) 85.7440 3.42976
\(626\) −57.3300 −2.29137
\(627\) 24.0754 0.961479
\(628\) −54.2601 −2.16521
\(629\) −2.70010 −0.107660
\(630\) 0.627227 0.0249893
\(631\) 11.9665 0.476378 0.238189 0.971219i \(-0.423446\pi\)
0.238189 + 0.971219i \(0.423446\pi\)
\(632\) 2.31477 0.0920767
\(633\) −7.24857 −0.288105
\(634\) −35.7345 −1.41920
\(635\) 76.1792 3.02308
\(636\) −24.5343 −0.972847
\(637\) 20.1480 0.798292
\(638\) 52.8134 2.09090
\(639\) 1.84117 0.0728356
\(640\) 68.7044 2.71578
\(641\) 20.3054 0.802017 0.401008 0.916074i \(-0.368660\pi\)
0.401008 + 0.916074i \(0.368660\pi\)
\(642\) 21.0474 0.830676
\(643\) −6.76980 −0.266975 −0.133487 0.991051i \(-0.542618\pi\)
−0.133487 + 0.991051i \(0.542618\pi\)
\(644\) 0.226622 0.00893016
\(645\) −11.2953 −0.444751
\(646\) 16.7191 0.657804
\(647\) −10.7095 −0.421034 −0.210517 0.977590i \(-0.567515\pi\)
−0.210517 + 0.977590i \(0.567515\pi\)
\(648\) 2.31477 0.0909329
\(649\) 39.6984 1.55830
\(650\) −86.0302 −3.37438
\(651\) −0.235263 −0.00922068
\(652\) 33.5029 1.31208
\(653\) 32.8301 1.28474 0.642371 0.766393i \(-0.277951\pi\)
0.642371 + 0.766393i \(0.277951\pi\)
\(654\) 18.9737 0.741932
\(655\) −64.7383 −2.52954
\(656\) −11.0703 −0.432223
\(657\) −2.31371 −0.0902665
\(658\) −0.756892 −0.0295067
\(659\) 27.9870 1.09022 0.545110 0.838365i \(-0.316488\pi\)
0.545110 + 0.838365i \(0.316488\pi\)
\(660\) −41.9144 −1.63151
\(661\) 3.39998 0.132244 0.0661219 0.997812i \(-0.478937\pi\)
0.0661219 + 0.997812i \(0.478937\pi\)
\(662\) 33.3646 1.29675
\(663\) −2.88004 −0.111851
\(664\) 26.5406 1.02998
\(665\) 2.08403 0.0808154
\(666\) −6.05684 −0.234698
\(667\) −8.33871 −0.322876
\(668\) −35.4504 −1.37162
\(669\) −15.7699 −0.609699
\(670\) 76.0241 2.93707
\(671\) 15.6969 0.605973
\(672\) 0.430167 0.0165940
\(673\) −34.9002 −1.34530 −0.672651 0.739960i \(-0.734845\pi\)
−0.672651 + 0.739960i \(0.734845\pi\)
\(674\) −4.30069 −0.165656
\(675\) 13.3164 0.512548
\(676\) −14.2663 −0.548704
\(677\) 44.6542 1.71620 0.858100 0.513482i \(-0.171645\pi\)
0.858100 + 0.513482i \(0.171645\pi\)
\(678\) −8.85181 −0.339952
\(679\) −0.564948 −0.0216807
\(680\) −9.90668 −0.379904
\(681\) −11.1561 −0.427503
\(682\) 26.0921 0.999117
\(683\) 0.715961 0.0273955 0.0136978 0.999906i \(-0.495640\pi\)
0.0136978 + 0.999906i \(0.495640\pi\)
\(684\) 22.5976 0.864042
\(685\) −46.8457 −1.78988
\(686\) 2.05116 0.0783138
\(687\) −2.46171 −0.0939199
\(688\) −2.29966 −0.0876739
\(689\) 23.3053 0.887862
\(690\) 10.9833 0.418128
\(691\) 11.3132 0.430375 0.215187 0.976573i \(-0.430964\pi\)
0.215187 + 0.976573i \(0.430964\pi\)
\(692\) −31.5210 −1.19825
\(693\) −0.211040 −0.00801675
\(694\) −52.4569 −1.99124
\(695\) 25.0723 0.951048
\(696\) 16.8717 0.639521
\(697\) 12.7049 0.481234
\(698\) 55.9737 2.11864
\(699\) 6.94093 0.262530
\(700\) −2.63779 −0.0996992
\(701\) 39.4997 1.49188 0.745942 0.666011i \(-0.231999\pi\)
0.745942 + 0.666011i \(0.231999\pi\)
\(702\) −6.46048 −0.243835
\(703\) −20.1245 −0.759012
\(704\) −42.0789 −1.58591
\(705\) −22.1029 −0.832443
\(706\) 29.2535 1.10097
\(707\) 0.891065 0.0335120
\(708\) 37.2617 1.40038
\(709\) 7.83441 0.294227 0.147114 0.989120i \(-0.453002\pi\)
0.147114 + 0.989120i \(0.453002\pi\)
\(710\) −17.6759 −0.663363
\(711\) 1.00000 0.0375029
\(712\) −15.8919 −0.595572
\(713\) −4.11968 −0.154283
\(714\) −0.146556 −0.00548473
\(715\) 39.8148 1.48899
\(716\) −80.8303 −3.02077
\(717\) 10.5045 0.392297
\(718\) −48.1928 −1.79854
\(719\) 0.919912 0.0343069 0.0171535 0.999853i \(-0.494540\pi\)
0.0171535 + 0.999853i \(0.494540\pi\)
\(720\) 3.72913 0.138976
\(721\) −0.468175 −0.0174357
\(722\) 81.9913 3.05140
\(723\) 25.0266 0.930749
\(724\) −44.0898 −1.63858
\(725\) 97.0593 3.60469
\(726\) −1.26949 −0.0471153
\(727\) 18.6452 0.691511 0.345756 0.938325i \(-0.387623\pi\)
0.345756 + 0.938325i \(0.387623\pi\)
\(728\) 0.435557 0.0161428
\(729\) 1.00000 0.0370370
\(730\) 22.2124 0.822118
\(731\) 2.63923 0.0976154
\(732\) 14.7334 0.544563
\(733\) −42.2388 −1.56013 −0.780064 0.625700i \(-0.784813\pi\)
−0.780064 + 0.625700i \(0.784813\pi\)
\(734\) −24.0829 −0.888917
\(735\) 29.9401 1.10436
\(736\) 7.53262 0.277656
\(737\) −25.5795 −0.942232
\(738\) 28.4996 1.04909
\(739\) −42.2571 −1.55445 −0.777227 0.629221i \(-0.783374\pi\)
−0.777227 + 0.629221i \(0.783374\pi\)
\(740\) 35.0361 1.28795
\(741\) −21.4657 −0.788562
\(742\) 1.18594 0.0435371
\(743\) 2.82361 0.103588 0.0517941 0.998658i \(-0.483506\pi\)
0.0517941 + 0.998658i \(0.483506\pi\)
\(744\) 8.33535 0.305589
\(745\) −95.5714 −3.50147
\(746\) −44.3941 −1.62538
\(747\) 11.4658 0.419510
\(748\) 9.79362 0.358090
\(749\) −0.613015 −0.0223991
\(750\) −79.8400 −2.91534
\(751\) 40.7594 1.48733 0.743665 0.668552i \(-0.233086\pi\)
0.743665 + 0.668552i \(0.233086\pi\)
\(752\) −4.50004 −0.164100
\(753\) −17.4686 −0.636590
\(754\) −47.0886 −1.71487
\(755\) 22.9176 0.834058
\(756\) −0.198086 −0.00720433
\(757\) 16.7162 0.607560 0.303780 0.952742i \(-0.401751\pi\)
0.303780 + 0.952742i \(0.401751\pi\)
\(758\) 7.02660 0.255217
\(759\) −3.69551 −0.134139
\(760\) −73.8372 −2.67836
\(761\) −31.3212 −1.13539 −0.567696 0.823238i \(-0.692165\pi\)
−0.567696 + 0.823238i \(0.692165\pi\)
\(762\) −39.9285 −1.44646
\(763\) −0.552617 −0.0200061
\(764\) 31.2526 1.13068
\(765\) −4.27976 −0.154735
\(766\) 51.0651 1.84506
\(767\) −35.3952 −1.27805
\(768\) −9.95712 −0.359297
\(769\) 55.1421 1.98848 0.994238 0.107199i \(-0.0341883\pi\)
0.994238 + 0.107199i \(0.0341883\pi\)
\(770\) 2.02606 0.0730140
\(771\) 16.5472 0.595934
\(772\) 5.77677 0.207910
\(773\) −20.2070 −0.726795 −0.363397 0.931634i \(-0.618383\pi\)
−0.363397 + 0.931634i \(0.618383\pi\)
\(774\) 5.92030 0.212801
\(775\) 47.9514 1.72247
\(776\) 20.0161 0.718535
\(777\) 0.176408 0.00632859
\(778\) 63.9679 2.29336
\(779\) 94.6933 3.39274
\(780\) 37.3710 1.33810
\(781\) 5.94732 0.212812
\(782\) −2.56634 −0.0917721
\(783\) 7.28872 0.260477
\(784\) 6.09566 0.217702
\(785\) 76.5920 2.73369
\(786\) 33.9319 1.21031
\(787\) −20.9602 −0.747151 −0.373576 0.927600i \(-0.621868\pi\)
−0.373576 + 0.927600i \(0.621868\pi\)
\(788\) 17.6877 0.630098
\(789\) 1.84760 0.0657764
\(790\) −9.60033 −0.341564
\(791\) 0.257812 0.00916675
\(792\) 7.47714 0.265689
\(793\) −13.9954 −0.496992
\(794\) 82.9142 2.94252
\(795\) 34.6319 1.22827
\(796\) 17.6917 0.627065
\(797\) −16.4859 −0.583962 −0.291981 0.956424i \(-0.594314\pi\)
−0.291981 + 0.956424i \(0.594314\pi\)
\(798\) −1.09232 −0.0386678
\(799\) 5.16451 0.182707
\(800\) −87.6768 −3.09984
\(801\) −6.86540 −0.242577
\(802\) −32.6761 −1.15383
\(803\) −7.47371 −0.263741
\(804\) −24.0094 −0.846746
\(805\) −0.319894 −0.0112748
\(806\) −23.2638 −0.819431
\(807\) 25.0351 0.881278
\(808\) −31.5704 −1.11064
\(809\) 3.19727 0.112410 0.0562050 0.998419i \(-0.482100\pi\)
0.0562050 + 0.998419i \(0.482100\pi\)
\(810\) −9.60033 −0.337321
\(811\) 52.9353 1.85881 0.929404 0.369064i \(-0.120322\pi\)
0.929404 + 0.369064i \(0.120322\pi\)
\(812\) −1.44380 −0.0506673
\(813\) −0.0889911 −0.00312106
\(814\) −19.5647 −0.685742
\(815\) −47.2919 −1.65656
\(816\) −0.871339 −0.0305030
\(817\) 19.6709 0.688197
\(818\) −83.0774 −2.90473
\(819\) 0.188164 0.00657498
\(820\) −164.858 −5.75708
\(821\) −10.3302 −0.360528 −0.180264 0.983618i \(-0.557695\pi\)
−0.180264 + 0.983618i \(0.557695\pi\)
\(822\) 24.5537 0.856407
\(823\) −20.5023 −0.714665 −0.357333 0.933977i \(-0.616314\pi\)
−0.357333 + 0.933977i \(0.616314\pi\)
\(824\) 16.5874 0.577849
\(825\) 43.0143 1.49757
\(826\) −1.80116 −0.0626702
\(827\) 16.2558 0.565271 0.282636 0.959227i \(-0.408791\pi\)
0.282636 + 0.959227i \(0.408791\pi\)
\(828\) −3.46868 −0.120545
\(829\) 44.2832 1.53802 0.769010 0.639237i \(-0.220750\pi\)
0.769010 + 0.639237i \(0.220750\pi\)
\(830\) −110.075 −3.82076
\(831\) 3.46495 0.120198
\(832\) 37.5176 1.30069
\(833\) −6.99573 −0.242388
\(834\) −13.1414 −0.455049
\(835\) 50.0409 1.73174
\(836\) 72.9945 2.52457
\(837\) 3.60094 0.124467
\(838\) 86.4847 2.98757
\(839\) −3.09167 −0.106736 −0.0533681 0.998575i \(-0.516996\pi\)
−0.0533681 + 0.998575i \(0.516996\pi\)
\(840\) 0.647242 0.0223320
\(841\) 24.1254 0.831910
\(842\) 26.6136 0.917164
\(843\) −20.4218 −0.703364
\(844\) −21.9770 −0.756480
\(845\) 20.1379 0.692766
\(846\) 11.5850 0.398300
\(847\) 0.0369745 0.00127046
\(848\) 7.05089 0.242129
\(849\) 10.7287 0.368208
\(850\) 29.8712 1.02457
\(851\) 3.08907 0.105892
\(852\) 5.58227 0.191245
\(853\) −54.8783 −1.87900 −0.939499 0.342551i \(-0.888709\pi\)
−0.939499 + 0.342551i \(0.888709\pi\)
\(854\) −0.712184 −0.0243704
\(855\) −31.8982 −1.09090
\(856\) 21.7191 0.742343
\(857\) 1.62498 0.0555083 0.0277541 0.999615i \(-0.491164\pi\)
0.0277541 + 0.999615i \(0.491164\pi\)
\(858\) −20.8685 −0.712439
\(859\) −8.63692 −0.294688 −0.147344 0.989085i \(-0.547072\pi\)
−0.147344 + 0.989085i \(0.547072\pi\)
\(860\) −34.2463 −1.16779
\(861\) −0.830063 −0.0282885
\(862\) −82.2761 −2.80234
\(863\) −37.1114 −1.26329 −0.631643 0.775259i \(-0.717619\pi\)
−0.631643 + 0.775259i \(0.717619\pi\)
\(864\) −6.58413 −0.223997
\(865\) 44.4941 1.51285
\(866\) 13.3474 0.453565
\(867\) 1.00000 0.0339618
\(868\) −0.713296 −0.0242109
\(869\) 3.23018 0.109576
\(870\) −69.9741 −2.37234
\(871\) 22.8067 0.772777
\(872\) 19.5792 0.663035
\(873\) 8.64709 0.292660
\(874\) −19.1276 −0.647001
\(875\) 2.32537 0.0786119
\(876\) −7.01497 −0.237014
\(877\) 9.62427 0.324989 0.162494 0.986709i \(-0.448046\pi\)
0.162494 + 0.986709i \(0.448046\pi\)
\(878\) 18.1800 0.613544
\(879\) 31.7647 1.07140
\(880\) 12.0458 0.406062
\(881\) 16.4726 0.554977 0.277489 0.960729i \(-0.410498\pi\)
0.277489 + 0.960729i \(0.410498\pi\)
\(882\) −15.6928 −0.528403
\(883\) 23.4669 0.789724 0.394862 0.918741i \(-0.370792\pi\)
0.394862 + 0.918741i \(0.370792\pi\)
\(884\) −8.73202 −0.293689
\(885\) −52.5977 −1.76805
\(886\) −16.5117 −0.554720
\(887\) 46.3409 1.55598 0.777988 0.628279i \(-0.216240\pi\)
0.777988 + 0.628279i \(0.216240\pi\)
\(888\) −6.25011 −0.209740
\(889\) 1.16293 0.0390035
\(890\) 65.9101 2.20931
\(891\) 3.23018 0.108215
\(892\) −47.8129 −1.60089
\(893\) 38.4925 1.28810
\(894\) 50.0927 1.67535
\(895\) 114.098 3.81387
\(896\) 1.04883 0.0350388
\(897\) 3.29493 0.110014
\(898\) 17.6721 0.589726
\(899\) 26.2462 0.875360
\(900\) 40.3741 1.34580
\(901\) −8.09202 −0.269584
\(902\) 92.0590 3.06523
\(903\) −0.172431 −0.00573814
\(904\) −9.13427 −0.303801
\(905\) 62.2360 2.06879
\(906\) −12.0120 −0.399073
\(907\) 18.7815 0.623631 0.311815 0.950143i \(-0.399063\pi\)
0.311815 + 0.950143i \(0.399063\pi\)
\(908\) −33.8243 −1.12250
\(909\) −13.6386 −0.452365
\(910\) −1.80644 −0.0598828
\(911\) 10.9307 0.362152 0.181076 0.983469i \(-0.442042\pi\)
0.181076 + 0.983469i \(0.442042\pi\)
\(912\) −6.49432 −0.215049
\(913\) 37.0365 1.22573
\(914\) −66.6589 −2.20488
\(915\) −20.7973 −0.687538
\(916\) −7.46367 −0.246607
\(917\) −0.988280 −0.0326359
\(918\) 2.24319 0.0740364
\(919\) 18.8356 0.621330 0.310665 0.950519i \(-0.399448\pi\)
0.310665 + 0.950519i \(0.399448\pi\)
\(920\) 11.3338 0.373665
\(921\) −24.8838 −0.819949
\(922\) 66.9522 2.20495
\(923\) −5.30264 −0.174539
\(924\) −0.639855 −0.0210497
\(925\) −35.9555 −1.18221
\(926\) −47.5498 −1.56258
\(927\) 7.16588 0.235358
\(928\) −47.9899 −1.57534
\(929\) 13.5613 0.444933 0.222466 0.974940i \(-0.428589\pi\)
0.222466 + 0.974940i \(0.428589\pi\)
\(930\) −34.5702 −1.13360
\(931\) −52.1410 −1.70885
\(932\) 21.0443 0.689328
\(933\) 1.31464 0.0430394
\(934\) −78.5218 −2.56931
\(935\) −13.8244 −0.452107
\(936\) −6.66663 −0.217906
\(937\) −37.2320 −1.21632 −0.608158 0.793816i \(-0.708091\pi\)
−0.608158 + 0.793816i \(0.708091\pi\)
\(938\) 1.16057 0.0378938
\(939\) −25.5573 −0.834032
\(940\) −67.0140 −2.18575
\(941\) 52.2433 1.70308 0.851542 0.524287i \(-0.175668\pi\)
0.851542 + 0.524287i \(0.175668\pi\)
\(942\) −40.1449 −1.30799
\(943\) −14.5352 −0.473331
\(944\) −10.7086 −0.348536
\(945\) 0.279613 0.00909583
\(946\) 19.1236 0.621763
\(947\) −23.1081 −0.750912 −0.375456 0.926840i \(-0.622514\pi\)
−0.375456 + 0.926840i \(0.622514\pi\)
\(948\) 3.03191 0.0984719
\(949\) 6.66357 0.216309
\(950\) 222.638 7.22333
\(951\) −15.9302 −0.516573
\(952\) −0.151233 −0.00490149
\(953\) −30.5266 −0.988855 −0.494427 0.869219i \(-0.664622\pi\)
−0.494427 + 0.869219i \(0.664622\pi\)
\(954\) −18.1520 −0.587691
\(955\) −44.1154 −1.42754
\(956\) 31.8487 1.03006
\(957\) 23.5439 0.761065
\(958\) −20.4440 −0.660515
\(959\) −0.715135 −0.0230929
\(960\) 55.7516 1.79937
\(961\) −18.0333 −0.581718
\(962\) 17.4439 0.562414
\(963\) 9.38280 0.302357
\(964\) 75.8784 2.44388
\(965\) −8.15433 −0.262497
\(966\) 0.167669 0.00539466
\(967\) −28.5510 −0.918137 −0.459069 0.888401i \(-0.651817\pi\)
−0.459069 + 0.888401i \(0.651817\pi\)
\(968\) −1.31000 −0.0421051
\(969\) 7.45327 0.239433
\(970\) −83.0150 −2.66545
\(971\) −57.0453 −1.83067 −0.915336 0.402691i \(-0.868075\pi\)
−0.915336 + 0.402691i \(0.868075\pi\)
\(972\) 3.03191 0.0972486
\(973\) 0.382748 0.0122703
\(974\) 19.2105 0.615545
\(975\) −38.3517 −1.22824
\(976\) −4.23424 −0.135535
\(977\) 13.8746 0.443889 0.221945 0.975059i \(-0.428760\pi\)
0.221945 + 0.975059i \(0.428760\pi\)
\(978\) 24.7875 0.792617
\(979\) −22.1765 −0.708764
\(980\) 90.7756 2.89972
\(981\) 8.45836 0.270055
\(982\) −31.0620 −0.991228
\(983\) −24.8229 −0.791728 −0.395864 0.918309i \(-0.629555\pi\)
−0.395864 + 0.918309i \(0.629555\pi\)
\(984\) 29.4091 0.937527
\(985\) −24.9675 −0.795530
\(986\) 16.3500 0.520690
\(987\) −0.337417 −0.0107401
\(988\) −65.0820 −2.07054
\(989\) −3.01943 −0.0960122
\(990\) −31.0108 −0.985588
\(991\) 38.1462 1.21175 0.605877 0.795558i \(-0.292822\pi\)
0.605877 + 0.795558i \(0.292822\pi\)
\(992\) −23.7090 −0.752762
\(993\) 14.8737 0.472003
\(994\) −0.269835 −0.00855866
\(995\) −24.9731 −0.791701
\(996\) 34.7631 1.10151
\(997\) −7.97553 −0.252588 −0.126294 0.991993i \(-0.540308\pi\)
−0.126294 + 0.991993i \(0.540308\pi\)
\(998\) −93.1199 −2.94766
\(999\) −2.70010 −0.0854273
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 4029.2.a.k.1.26 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.26 31 1.1 even 1 trivial