Properties

Label 483.3.g.a.139.4
Level $483$
Weight $3$
Character 483.139
Analytic conductor $13.161$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,3,Mod(139,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.139");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.g (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.4
Character \(\chi\) \(=\) 483.139
Dual form 483.3.g.a.139.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.48909 q^{2} -1.73205i q^{3} +8.17374 q^{4} +1.46096i q^{5} +6.04328i q^{6} +(6.91536 + 1.08528i) q^{7} -14.5626 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-3.48909 q^{2} -1.73205i q^{3} +8.17374 q^{4} +1.46096i q^{5} +6.04328i q^{6} +(6.91536 + 1.08528i) q^{7} -14.5626 q^{8} -3.00000 q^{9} -5.09743i q^{10} -8.08381 q^{11} -14.1573i q^{12} -10.0187i q^{13} +(-24.1283 - 3.78664i) q^{14} +2.53046 q^{15} +18.1151 q^{16} -14.6817i q^{17} +10.4673 q^{18} +9.90546i q^{19} +11.9415i q^{20} +(1.87976 - 11.9778i) q^{21} +28.2051 q^{22} -4.79583 q^{23} +25.2231i q^{24} +22.8656 q^{25} +34.9562i q^{26} +5.19615i q^{27} +(56.5243 + 8.87081i) q^{28} -0.216442 q^{29} -8.82900 q^{30} -27.4353i q^{31} -4.95494 q^{32} +14.0016i q^{33} +51.2259i q^{34} +(-1.58555 + 10.1031i) q^{35} -24.5212 q^{36} -12.4301 q^{37} -34.5610i q^{38} -17.3529 q^{39} -21.2753i q^{40} +29.2097i q^{41} +(-6.55866 + 41.7914i) q^{42} +16.6889 q^{43} -66.0750 q^{44} -4.38289i q^{45} +16.7331 q^{46} -2.99973i q^{47} -31.3763i q^{48} +(46.6443 + 15.0102i) q^{49} -79.7801 q^{50} -25.4295 q^{51} -81.8904i q^{52} +18.5951 q^{53} -18.1298i q^{54} -11.8101i q^{55} +(-100.705 - 15.8045i) q^{56} +17.1568 q^{57} +0.755185 q^{58} -106.226i q^{59} +20.6833 q^{60} -100.179i q^{61} +95.7243i q^{62} +(-20.7461 - 3.25584i) q^{63} -55.1722 q^{64} +14.6370 q^{65} -48.8527i q^{66} -27.9224 q^{67} -120.005i q^{68} +8.30662i q^{69} +(5.53214 - 35.2505i) q^{70} -14.0375 q^{71} +43.6877 q^{72} -99.0175i q^{73} +43.3698 q^{74} -39.6044i q^{75} +80.9647i q^{76} +(-55.9024 - 8.77321i) q^{77} +60.5459 q^{78} -1.25724 q^{79} +26.4655i q^{80} +9.00000 q^{81} -101.915i q^{82} -50.4640i q^{83} +(15.3647 - 97.9030i) q^{84} +21.4495 q^{85} -58.2290 q^{86} +0.374888i q^{87} +117.721 q^{88} -121.967i q^{89} +15.2923i q^{90} +(10.8731 - 69.2830i) q^{91} -39.1999 q^{92} -47.5194 q^{93} +10.4663i q^{94} -14.4715 q^{95} +8.58220i q^{96} +111.721i q^{97} +(-162.746 - 52.3720i) q^{98} +24.2514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.48909 −1.74454 −0.872272 0.489021i \(-0.837354\pi\)
−0.872272 + 0.489021i \(0.837354\pi\)
\(3\) 1.73205i 0.577350i
\(4\) 8.17374 2.04344
\(5\) 1.46096i 0.292192i 0.989270 + 0.146096i \(0.0466709\pi\)
−0.989270 + 0.146096i \(0.953329\pi\)
\(6\) 6.04328i 1.00721i
\(7\) 6.91536 + 1.08528i 0.987908 + 0.155040i
\(8\) −14.5626 −1.82032
\(9\) −3.00000 −0.333333
\(10\) 5.09743i 0.509743i
\(11\) −8.08381 −0.734892 −0.367446 0.930045i \(-0.619768\pi\)
−0.367446 + 0.930045i \(0.619768\pi\)
\(12\) 14.1573i 1.17978i
\(13\) 10.0187i 0.770671i −0.922777 0.385335i \(-0.874086\pi\)
0.922777 0.385335i \(-0.125914\pi\)
\(14\) −24.1283 3.78664i −1.72345 0.270474i
\(15\) 2.53046 0.168697
\(16\) 18.1151 1.13219
\(17\) 14.6817i 0.863632i −0.901962 0.431816i \(-0.857873\pi\)
0.901962 0.431816i \(-0.142127\pi\)
\(18\) 10.4673 0.581515
\(19\) 9.90546i 0.521340i 0.965428 + 0.260670i \(0.0839435\pi\)
−0.965428 + 0.260670i \(0.916057\pi\)
\(20\) 11.9415i 0.597076i
\(21\) 1.87976 11.9778i 0.0895125 0.570369i
\(22\) 28.2051 1.28205
\(23\) −4.79583 −0.208514
\(24\) 25.2231i 1.05096i
\(25\) 22.8656 0.914624
\(26\) 34.9562i 1.34447i
\(27\) 5.19615i 0.192450i
\(28\) 56.5243 + 8.87081i 2.01873 + 0.316815i
\(29\) −0.216442 −0.00746351 −0.00373175 0.999993i \(-0.501188\pi\)
−0.00373175 + 0.999993i \(0.501188\pi\)
\(30\) −8.82900 −0.294300
\(31\) 27.4353i 0.885010i −0.896766 0.442505i \(-0.854090\pi\)
0.896766 0.442505i \(-0.145910\pi\)
\(32\) −4.95494 −0.154842
\(33\) 14.0016i 0.424290i
\(34\) 51.2259i 1.50664i
\(35\) −1.58555 + 10.1031i −0.0453016 + 0.288659i
\(36\) −24.5212 −0.681145
\(37\) −12.4301 −0.335949 −0.167975 0.985791i \(-0.553723\pi\)
−0.167975 + 0.985791i \(0.553723\pi\)
\(38\) 34.5610i 0.909501i
\(39\) −17.3529 −0.444947
\(40\) 21.2753i 0.531884i
\(41\) 29.2097i 0.712431i 0.934404 + 0.356215i \(0.115933\pi\)
−0.934404 + 0.356215i \(0.884067\pi\)
\(42\) −6.55866 + 41.7914i −0.156158 + 0.995034i
\(43\) 16.6889 0.388113 0.194057 0.980990i \(-0.437835\pi\)
0.194057 + 0.980990i \(0.437835\pi\)
\(44\) −66.0750 −1.50170
\(45\) 4.38289i 0.0973975i
\(46\) 16.7331 0.363763
\(47\) 2.99973i 0.0638241i −0.999491 0.0319120i \(-0.989840\pi\)
0.999491 0.0319120i \(-0.0101596\pi\)
\(48\) 31.3763i 0.653672i
\(49\) 46.6443 + 15.0102i 0.951925 + 0.306331i
\(50\) −79.7801 −1.59560
\(51\) −25.4295 −0.498618
\(52\) 81.8904i 1.57482i
\(53\) 18.5951 0.350851 0.175425 0.984493i \(-0.443870\pi\)
0.175425 + 0.984493i \(0.443870\pi\)
\(54\) 18.1298i 0.335738i
\(55\) 11.8101i 0.214730i
\(56\) −100.705 15.8045i −1.79831 0.282223i
\(57\) 17.1568 0.300996
\(58\) 0.755185 0.0130204
\(59\) 106.226i 1.80044i −0.435434 0.900221i \(-0.643405\pi\)
0.435434 0.900221i \(-0.356595\pi\)
\(60\) 20.6833 0.344722
\(61\) 100.179i 1.64228i −0.570725 0.821142i \(-0.693338\pi\)
0.570725 0.821142i \(-0.306662\pi\)
\(62\) 95.7243i 1.54394i
\(63\) −20.7461 3.25584i −0.329303 0.0516800i
\(64\) −55.1722 −0.862065
\(65\) 14.6370 0.225184
\(66\) 48.8527i 0.740193i
\(67\) −27.9224 −0.416752 −0.208376 0.978049i \(-0.566818\pi\)
−0.208376 + 0.978049i \(0.566818\pi\)
\(68\) 120.005i 1.76478i
\(69\) 8.30662i 0.120386i
\(70\) 5.53214 35.2505i 0.0790306 0.503579i
\(71\) −14.0375 −0.197711 −0.0988556 0.995102i \(-0.531518\pi\)
−0.0988556 + 0.995102i \(0.531518\pi\)
\(72\) 43.6877 0.606773
\(73\) 99.0175i 1.35640i −0.734876 0.678202i \(-0.762759\pi\)
0.734876 0.678202i \(-0.237241\pi\)
\(74\) 43.3698 0.586078
\(75\) 39.6044i 0.528058i
\(76\) 80.9647i 1.06532i
\(77\) −55.9024 8.77321i −0.726006 0.113938i
\(78\) 60.5459 0.776230
\(79\) −1.25724 −0.0159144 −0.00795721 0.999968i \(-0.502533\pi\)
−0.00795721 + 0.999968i \(0.502533\pi\)
\(80\) 26.4655i 0.330818i
\(81\) 9.00000 0.111111
\(82\) 101.915i 1.24287i
\(83\) 50.4640i 0.608000i −0.952672 0.304000i \(-0.901678\pi\)
0.952672 0.304000i \(-0.0983224\pi\)
\(84\) 15.3647 97.9030i 0.182913 1.16551i
\(85\) 21.4495 0.252347
\(86\) −58.2290 −0.677081
\(87\) 0.374888i 0.00430906i
\(88\) 117.721 1.33774
\(89\) 121.967i 1.37041i −0.728349 0.685207i \(-0.759712\pi\)
0.728349 0.685207i \(-0.240288\pi\)
\(90\) 15.2923i 0.169914i
\(91\) 10.8731 69.2830i 0.119485 0.761352i
\(92\) −39.1999 −0.426086
\(93\) −47.5194 −0.510961
\(94\) 10.4663i 0.111344i
\(95\) −14.4715 −0.152332
\(96\) 8.58220i 0.0893979i
\(97\) 111.721i 1.15176i 0.817533 + 0.575882i \(0.195341\pi\)
−0.817533 + 0.575882i \(0.804659\pi\)
\(98\) −162.746 52.3720i −1.66068 0.534408i
\(99\) 24.2514 0.244964
\(100\) 186.897 1.86897
\(101\) 114.914i 1.13777i −0.822418 0.568884i \(-0.807375\pi\)
0.822418 0.568884i \(-0.192625\pi\)
\(102\) 88.7259 0.869862
\(103\) 52.0049i 0.504902i −0.967610 0.252451i \(-0.918763\pi\)
0.967610 0.252451i \(-0.0812367\pi\)
\(104\) 145.898i 1.40287i
\(105\) 17.4990 + 2.74626i 0.166658 + 0.0261549i
\(106\) −64.8800 −0.612075
\(107\) 109.825 1.02640 0.513202 0.858268i \(-0.328459\pi\)
0.513202 + 0.858268i \(0.328459\pi\)
\(108\) 42.4720i 0.393259i
\(109\) −88.6154 −0.812985 −0.406493 0.913654i \(-0.633248\pi\)
−0.406493 + 0.913654i \(0.633248\pi\)
\(110\) 41.2066i 0.374606i
\(111\) 21.5296i 0.193960i
\(112\) 125.272 + 19.6600i 1.11850 + 0.175535i
\(113\) −90.3619 −0.799663 −0.399831 0.916589i \(-0.630931\pi\)
−0.399831 + 0.916589i \(0.630931\pi\)
\(114\) −59.8615 −0.525101
\(115\) 7.00653i 0.0609263i
\(116\) −1.76914 −0.0152512
\(117\) 30.0562i 0.256890i
\(118\) 370.632i 3.14095i
\(119\) 15.9338 101.530i 0.133898 0.853189i
\(120\) −36.8500 −0.307083
\(121\) −55.6520 −0.459934
\(122\) 349.534i 2.86504i
\(123\) 50.5926 0.411322
\(124\) 224.249i 1.80846i
\(125\) 69.9298i 0.559438i
\(126\) 72.3849 + 11.3599i 0.574483 + 0.0901581i
\(127\) 93.8066 0.738635 0.369318 0.929303i \(-0.379591\pi\)
0.369318 + 0.929303i \(0.379591\pi\)
\(128\) 212.320 1.65875
\(129\) 28.9060i 0.224077i
\(130\) −51.0697 −0.392844
\(131\) 16.6618i 0.127189i 0.997976 + 0.0635946i \(0.0202564\pi\)
−0.997976 + 0.0635946i \(0.979744\pi\)
\(132\) 114.445i 0.867009i
\(133\) −10.7502 + 68.4998i −0.0808286 + 0.515036i
\(134\) 97.4237 0.727042
\(135\) −7.59138 −0.0562325
\(136\) 213.804i 1.57209i
\(137\) −38.0207 −0.277524 −0.138762 0.990326i \(-0.544312\pi\)
−0.138762 + 0.990326i \(0.544312\pi\)
\(138\) 28.9826i 0.210018i
\(139\) 87.3612i 0.628498i −0.949341 0.314249i \(-0.898247\pi\)
0.949341 0.314249i \(-0.101753\pi\)
\(140\) −12.9599 + 82.5799i −0.0925708 + 0.589857i
\(141\) −5.19569 −0.0368488
\(142\) 48.9781 0.344916
\(143\) 80.9894i 0.566360i
\(144\) −54.3453 −0.377398
\(145\) 0.316213i 0.00218078i
\(146\) 345.481i 2.36631i
\(147\) 25.9984 80.7904i 0.176860 0.549594i
\(148\) −101.601 −0.686491
\(149\) −142.960 −0.959460 −0.479730 0.877416i \(-0.659265\pi\)
−0.479730 + 0.877416i \(0.659265\pi\)
\(150\) 138.183i 0.921221i
\(151\) −172.567 −1.14282 −0.571412 0.820663i \(-0.693604\pi\)
−0.571412 + 0.820663i \(0.693604\pi\)
\(152\) 144.249i 0.949006i
\(153\) 44.0452i 0.287877i
\(154\) 195.049 + 30.6105i 1.26655 + 0.198769i
\(155\) 40.0820 0.258593
\(156\) −141.838 −0.909220
\(157\) 81.7870i 0.520936i 0.965482 + 0.260468i \(0.0838769\pi\)
−0.965482 + 0.260468i \(0.916123\pi\)
\(158\) 4.38662 0.0277634
\(159\) 32.2077i 0.202564i
\(160\) 7.23897i 0.0452436i
\(161\) −33.1649 5.20482i −0.205993 0.0323281i
\(162\) −31.4018 −0.193838
\(163\) −22.4356 −0.137642 −0.0688208 0.997629i \(-0.521924\pi\)
−0.0688208 + 0.997629i \(0.521924\pi\)
\(164\) 238.752i 1.45581i
\(165\) −20.4558 −0.123974
\(166\) 176.074i 1.06068i
\(167\) 104.195i 0.623920i 0.950095 + 0.311960i \(0.100985\pi\)
−0.950095 + 0.311960i \(0.899015\pi\)
\(168\) −27.3741 + 174.427i −0.162941 + 1.03825i
\(169\) 68.6253 0.406067
\(170\) −74.8391 −0.440230
\(171\) 29.7164i 0.173780i
\(172\) 136.411 0.793085
\(173\) 61.2668i 0.354144i 0.984198 + 0.177072i \(0.0566625\pi\)
−0.984198 + 0.177072i \(0.943338\pi\)
\(174\) 1.30802i 0.00751735i
\(175\) 158.124 + 24.8156i 0.903564 + 0.141803i
\(176\) −146.439 −0.832040
\(177\) −183.989 −1.03949
\(178\) 425.553i 2.39075i
\(179\) 321.989 1.79882 0.899409 0.437107i \(-0.143997\pi\)
0.899409 + 0.437107i \(0.143997\pi\)
\(180\) 35.8246i 0.199025i
\(181\) 273.755i 1.51246i −0.654306 0.756230i \(-0.727039\pi\)
0.654306 0.756230i \(-0.272961\pi\)
\(182\) −37.9373 + 241.735i −0.208447 + 1.32821i
\(183\) −173.516 −0.948173
\(184\) 69.8396 0.379563
\(185\) 18.1599i 0.0981618i
\(186\) 165.799 0.891394
\(187\) 118.684i 0.634676i
\(188\) 24.5190i 0.130420i
\(189\) −5.63929 + 35.9333i −0.0298375 + 0.190123i
\(190\) 50.4924 0.265749
\(191\) 140.743 0.736876 0.368438 0.929652i \(-0.379893\pi\)
0.368438 + 0.929652i \(0.379893\pi\)
\(192\) 95.5610i 0.497713i
\(193\) −252.426 −1.30791 −0.653953 0.756535i \(-0.726891\pi\)
−0.653953 + 0.756535i \(0.726891\pi\)
\(194\) 389.805i 2.00930i
\(195\) 25.3520i 0.130010i
\(196\) 381.259 + 122.690i 1.94520 + 0.625967i
\(197\) 308.146 1.56419 0.782097 0.623156i \(-0.214150\pi\)
0.782097 + 0.623156i \(0.214150\pi\)
\(198\) −84.6154 −0.427351
\(199\) 46.9336i 0.235847i 0.993023 + 0.117924i \(0.0376238\pi\)
−0.993023 + 0.117924i \(0.962376\pi\)
\(200\) −332.981 −1.66491
\(201\) 48.3630i 0.240612i
\(202\) 400.947i 1.98489i
\(203\) −1.49677 0.234900i −0.00737326 0.00115714i
\(204\) −207.854 −1.01889
\(205\) −42.6742 −0.208167
\(206\) 181.450i 0.880824i
\(207\) 14.3875 0.0695048
\(208\) 181.490i 0.872548i
\(209\) 80.0739i 0.383129i
\(210\) −61.0557 9.58195i −0.290741 0.0456283i
\(211\) −157.520 −0.746542 −0.373271 0.927722i \(-0.621764\pi\)
−0.373271 + 0.927722i \(0.621764\pi\)
\(212\) 151.992 0.716941
\(213\) 24.3137i 0.114149i
\(214\) −383.190 −1.79061
\(215\) 24.3818i 0.113404i
\(216\) 75.6693i 0.350321i
\(217\) 29.7750 189.725i 0.137212 0.874309i
\(218\) 309.187 1.41829
\(219\) −171.503 −0.783120
\(220\) 96.5330i 0.438787i
\(221\) −147.092 −0.665576
\(222\) 75.1187i 0.338372i
\(223\) 10.4417i 0.0468236i −0.999726 0.0234118i \(-0.992547\pi\)
0.999726 0.0234118i \(-0.00745290\pi\)
\(224\) −34.2652 5.37750i −0.152969 0.0240067i
\(225\) −68.5968 −0.304875
\(226\) 315.281 1.39505
\(227\) 393.299i 1.73259i −0.499529 0.866297i \(-0.666494\pi\)
0.499529 0.866297i \(-0.333506\pi\)
\(228\) 140.235 0.615066
\(229\) 414.362i 1.80944i −0.426008 0.904720i \(-0.640080\pi\)
0.426008 0.904720i \(-0.359920\pi\)
\(230\) 24.4464i 0.106289i
\(231\) −15.1956 + 96.8259i −0.0657820 + 0.419160i
\(232\) 3.15195 0.0135860
\(233\) 316.762 1.35950 0.679748 0.733446i \(-0.262089\pi\)
0.679748 + 0.733446i \(0.262089\pi\)
\(234\) 104.869i 0.448156i
\(235\) 4.38249 0.0186489
\(236\) 868.264i 3.67909i
\(237\) 2.17760i 0.00918819i
\(238\) −55.5945 + 354.246i −0.233590 + 1.48843i
\(239\) 347.307 1.45317 0.726583 0.687078i \(-0.241107\pi\)
0.726583 + 0.687078i \(0.241107\pi\)
\(240\) 45.8395 0.190998
\(241\) 61.3638i 0.254622i −0.991863 0.127311i \(-0.959365\pi\)
0.991863 0.127311i \(-0.0406346\pi\)
\(242\) 194.175 0.802375
\(243\) 15.5885i 0.0641500i
\(244\) 818.840i 3.35590i
\(245\) −21.9293 + 68.1456i −0.0895075 + 0.278145i
\(246\) −176.522 −0.717570
\(247\) 99.2400 0.401781
\(248\) 399.528i 1.61100i
\(249\) −87.4063 −0.351029
\(250\) 243.991i 0.975965i
\(251\) 177.416i 0.706838i −0.935465 0.353419i \(-0.885019\pi\)
0.935465 0.353419i \(-0.114981\pi\)
\(252\) −169.573 26.6124i −0.672909 0.105605i
\(253\) 38.7686 0.153236
\(254\) −327.300 −1.28858
\(255\) 37.1516i 0.145692i
\(256\) −520.116 −2.03170
\(257\) 276.116i 1.07438i −0.843461 0.537190i \(-0.819486\pi\)
0.843461 0.537190i \(-0.180514\pi\)
\(258\) 100.856i 0.390913i
\(259\) −85.9587 13.4902i −0.331887 0.0520856i
\(260\) 119.639 0.460149
\(261\) 0.649325 0.00248784
\(262\) 58.1344i 0.221887i
\(263\) 78.9193 0.300074 0.150037 0.988680i \(-0.452061\pi\)
0.150037 + 0.988680i \(0.452061\pi\)
\(264\) 203.899i 0.772344i
\(265\) 27.1667i 0.102516i
\(266\) 37.5084 239.002i 0.141009 0.898503i
\(267\) −211.253 −0.791209
\(268\) −228.230 −0.851606
\(269\) 233.553i 0.868227i −0.900858 0.434113i \(-0.857062\pi\)
0.900858 0.434113i \(-0.142938\pi\)
\(270\) 26.4870 0.0981000
\(271\) 480.406i 1.77272i 0.463000 + 0.886358i \(0.346773\pi\)
−0.463000 + 0.886358i \(0.653227\pi\)
\(272\) 265.961i 0.977798i
\(273\) −120.002 18.8328i −0.439567 0.0689846i
\(274\) 132.658 0.484152
\(275\) −184.841 −0.672150
\(276\) 67.8962i 0.246001i
\(277\) −5.33677 −0.0192663 −0.00963316 0.999954i \(-0.503066\pi\)
−0.00963316 + 0.999954i \(0.503066\pi\)
\(278\) 304.811i 1.09644i
\(279\) 82.3060i 0.295003i
\(280\) 23.0897 147.127i 0.0824633 0.525452i
\(281\) −247.522 −0.880860 −0.440430 0.897787i \(-0.645174\pi\)
−0.440430 + 0.897787i \(0.645174\pi\)
\(282\) 18.1282 0.0642845
\(283\) 428.419i 1.51385i 0.653502 + 0.756924i \(0.273299\pi\)
−0.653502 + 0.756924i \(0.726701\pi\)
\(284\) −114.739 −0.404010
\(285\) 25.0654i 0.0879487i
\(286\) 282.579i 0.988040i
\(287\) −31.7007 + 201.995i −0.110455 + 0.703816i
\(288\) 14.8648 0.0516139
\(289\) 73.4464 0.254140
\(290\) 1.10330i 0.00380447i
\(291\) 193.507 0.664972
\(292\) 809.343i 2.77172i
\(293\) 433.835i 1.48067i 0.672240 + 0.740333i \(0.265332\pi\)
−0.672240 + 0.740333i \(0.734668\pi\)
\(294\) −90.7109 + 281.885i −0.308540 + 0.958792i
\(295\) 155.192 0.526075
\(296\) 181.014 0.611535
\(297\) 42.0047i 0.141430i
\(298\) 498.799 1.67382
\(299\) 48.0481i 0.160696i
\(300\) 323.716i 1.07905i
\(301\) 115.410 + 18.1121i 0.383420 + 0.0601732i
\(302\) 602.100 1.99371
\(303\) −199.038 −0.656890
\(304\) 179.438i 0.590258i
\(305\) 146.358 0.479863
\(306\) 153.678i 0.502215i
\(307\) 257.477i 0.838687i 0.907828 + 0.419344i \(0.137740\pi\)
−0.907828 + 0.419344i \(0.862260\pi\)
\(308\) −456.932 71.7099i −1.48355 0.232824i
\(309\) −90.0752 −0.291505
\(310\) −139.850 −0.451128
\(311\) 258.171i 0.830130i 0.909792 + 0.415065i \(0.136241\pi\)
−0.909792 + 0.415065i \(0.863759\pi\)
\(312\) 252.703 0.809946
\(313\) 273.326i 0.873246i 0.899645 + 0.436623i \(0.143826\pi\)
−0.899645 + 0.436623i \(0.856174\pi\)
\(314\) 285.362i 0.908796i
\(315\) 4.75666 30.3092i 0.0151005 0.0962198i
\(316\) −10.2763 −0.0325201
\(317\) 143.102 0.451426 0.225713 0.974194i \(-0.427529\pi\)
0.225713 + 0.974194i \(0.427529\pi\)
\(318\) 112.375i 0.353382i
\(319\) 1.74967 0.00548487
\(320\) 80.6044i 0.251889i
\(321\) 190.223i 0.592594i
\(322\) 115.715 + 18.1601i 0.359364 + 0.0563978i
\(323\) 145.429 0.450246
\(324\) 73.5637 0.227048
\(325\) 229.084i 0.704874i
\(326\) 78.2797 0.240122
\(327\) 153.486i 0.469377i
\(328\) 425.367i 1.29685i
\(329\) 3.25555 20.7442i 0.00989529 0.0630523i
\(330\) 71.3720 0.216279
\(331\) −349.567 −1.05609 −0.528047 0.849215i \(-0.677076\pi\)
−0.528047 + 0.849215i \(0.677076\pi\)
\(332\) 412.480i 1.24241i
\(333\) 37.2904 0.111983
\(334\) 363.544i 1.08846i
\(335\) 40.7935i 0.121772i
\(336\) 34.0521 216.978i 0.101345 0.645768i
\(337\) −77.8771 −0.231089 −0.115545 0.993302i \(-0.536861\pi\)
−0.115545 + 0.993302i \(0.536861\pi\)
\(338\) −239.440 −0.708401
\(339\) 156.511i 0.461685i
\(340\) 175.322 0.515654
\(341\) 221.782i 0.650387i
\(342\) 103.683i 0.303167i
\(343\) 306.272 + 154.423i 0.892921 + 0.450213i
\(344\) −243.033 −0.706491
\(345\) −12.1357 −0.0351758
\(346\) 213.765i 0.617819i
\(347\) −447.244 −1.28889 −0.644444 0.764651i \(-0.722911\pi\)
−0.644444 + 0.764651i \(0.722911\pi\)
\(348\) 3.06424i 0.00880528i
\(349\) 383.728i 1.09951i 0.835326 + 0.549754i \(0.185279\pi\)
−0.835326 + 0.549754i \(0.814721\pi\)
\(350\) −551.708 86.5838i −1.57631 0.247382i
\(351\) 52.0588 0.148316
\(352\) 40.0548 0.113792
\(353\) 550.197i 1.55863i 0.626631 + 0.779316i \(0.284433\pi\)
−0.626631 + 0.779316i \(0.715567\pi\)
\(354\) 641.954 1.81343
\(355\) 20.5083i 0.0577697i
\(356\) 996.925i 2.80035i
\(357\) −175.854 27.5982i −0.492589 0.0773058i
\(358\) −1123.45 −3.13812
\(359\) 322.417 0.898098 0.449049 0.893507i \(-0.351763\pi\)
0.449049 + 0.893507i \(0.351763\pi\)
\(360\) 63.8260i 0.177295i
\(361\) 262.882 0.728205
\(362\) 955.157i 2.63855i
\(363\) 96.3921i 0.265543i
\(364\) 88.8741 566.302i 0.244160 1.55577i
\(365\) 144.661 0.396331
\(366\) 605.411 1.65413
\(367\) 54.1731i 0.147611i −0.997273 0.0738053i \(-0.976486\pi\)
0.997273 0.0738053i \(-0.0235143\pi\)
\(368\) −86.8769 −0.236079
\(369\) 87.6290i 0.237477i
\(370\) 63.3616i 0.171248i
\(371\) 128.592 + 20.1809i 0.346609 + 0.0543960i
\(372\) −388.411 −1.04412
\(373\) 495.211 1.32764 0.663822 0.747890i \(-0.268933\pi\)
0.663822 + 0.747890i \(0.268933\pi\)
\(374\) 414.101i 1.10722i
\(375\) 121.122 0.322992
\(376\) 43.6838i 0.116180i
\(377\) 2.16847i 0.00575191i
\(378\) 19.6760 125.374i 0.0520528 0.331678i
\(379\) −305.273 −0.805470 −0.402735 0.915317i \(-0.631940\pi\)
−0.402735 + 0.915317i \(0.631940\pi\)
\(380\) −118.286 −0.311280
\(381\) 162.478i 0.426451i
\(382\) −491.066 −1.28551
\(383\) 400.831i 1.04656i 0.852162 + 0.523279i \(0.175291\pi\)
−0.852162 + 0.523279i \(0.824709\pi\)
\(384\) 367.750i 0.957681i
\(385\) 12.8173 81.6713i 0.0332917 0.212133i
\(386\) 880.736 2.28170
\(387\) −50.0666 −0.129371
\(388\) 913.180i 2.35356i
\(389\) −364.606 −0.937291 −0.468646 0.883386i \(-0.655258\pi\)
−0.468646 + 0.883386i \(0.655258\pi\)
\(390\) 88.4553i 0.226808i
\(391\) 70.4112i 0.180080i
\(392\) −679.261 218.587i −1.73281 0.557620i
\(393\) 28.8590 0.0734327
\(394\) −1075.15 −2.72881
\(395\) 1.83678i 0.00465007i
\(396\) 198.225 0.500568
\(397\) 43.3239i 0.109128i −0.998510 0.0545641i \(-0.982623\pi\)
0.998510 0.0545641i \(-0.0173769\pi\)
\(398\) 163.755i 0.411446i
\(399\) 118.645 + 18.6199i 0.297356 + 0.0466664i
\(400\) 414.212 1.03553
\(401\) −401.189 −1.00047 −0.500235 0.865890i \(-0.666753\pi\)
−0.500235 + 0.865890i \(0.666753\pi\)
\(402\) 168.743i 0.419758i
\(403\) −274.867 −0.682052
\(404\) 939.281i 2.32495i
\(405\) 13.1487i 0.0324658i
\(406\) 5.22237 + 0.819587i 0.0128630 + 0.00201869i
\(407\) 100.483 0.246886
\(408\) 370.319 0.907645
\(409\) 138.402i 0.338392i −0.985582 0.169196i \(-0.945883\pi\)
0.985582 0.169196i \(-0.0541171\pi\)
\(410\) 148.894 0.363156
\(411\) 65.8539i 0.160228i
\(412\) 425.075i 1.03174i
\(413\) 115.285 734.591i 0.279141 1.77867i
\(414\) −50.1992 −0.121254
\(415\) 73.7260 0.177653
\(416\) 49.6421i 0.119332i
\(417\) −151.314 −0.362863
\(418\) 279.385i 0.668385i
\(419\) 423.644i 1.01108i 0.862802 + 0.505542i \(0.168707\pi\)
−0.862802 + 0.505542i \(0.831293\pi\)
\(420\) 143.033 + 22.4472i 0.340554 + 0.0534458i
\(421\) −719.394 −1.70877 −0.854387 0.519637i \(-0.826067\pi\)
−0.854387 + 0.519637i \(0.826067\pi\)
\(422\) 549.602 1.30238
\(423\) 8.99919i 0.0212747i
\(424\) −270.792 −0.638661
\(425\) 335.707i 0.789898i
\(426\) 84.8325i 0.199137i
\(427\) 108.723 692.775i 0.254620 1.62242i
\(428\) 897.683 2.09739
\(429\) 140.278 0.326988
\(430\) 85.0703i 0.197838i
\(431\) −227.377 −0.527557 −0.263778 0.964583i \(-0.584969\pi\)
−0.263778 + 0.964583i \(0.584969\pi\)
\(432\) 94.1288i 0.217891i
\(433\) 175.458i 0.405214i −0.979260 0.202607i \(-0.935059\pi\)
0.979260 0.202607i \(-0.0649414\pi\)
\(434\) −103.888 + 661.968i −0.239373 + 1.52527i
\(435\) −0.547697 −0.00125907
\(436\) −724.319 −1.66128
\(437\) 47.5049i 0.108707i
\(438\) 598.390 1.36619
\(439\) 348.758i 0.794437i 0.917724 + 0.397219i \(0.130025\pi\)
−0.917724 + 0.397219i \(0.869975\pi\)
\(440\) 171.986i 0.390877i
\(441\) −139.933 45.0306i −0.317308 0.102110i
\(442\) 513.218 1.16113
\(443\) 350.502 0.791201 0.395601 0.918423i \(-0.370536\pi\)
0.395601 + 0.918423i \(0.370536\pi\)
\(444\) 175.977i 0.396345i
\(445\) 178.189 0.400424
\(446\) 36.4319i 0.0816859i
\(447\) 247.613i 0.553945i
\(448\) −381.535 59.8773i −0.851641 0.133655i
\(449\) 568.236 1.26556 0.632779 0.774332i \(-0.281914\pi\)
0.632779 + 0.774332i \(0.281914\pi\)
\(450\) 239.340 0.531867
\(451\) 236.125i 0.523560i
\(452\) −738.595 −1.63406
\(453\) 298.894i 0.659810i
\(454\) 1372.25i 3.02259i
\(455\) 101.220 + 15.8852i 0.222461 + 0.0349126i
\(456\) −249.846 −0.547909
\(457\) 234.695 0.513555 0.256778 0.966470i \(-0.417339\pi\)
0.256778 + 0.966470i \(0.417339\pi\)
\(458\) 1445.74i 3.15665i
\(459\) 76.2886 0.166206
\(460\) 57.2696i 0.124499i
\(461\) 460.577i 0.999082i −0.866290 0.499541i \(-0.833502\pi\)
0.866290 0.499541i \(-0.166498\pi\)
\(462\) 53.0189 337.834i 0.114760 0.731243i
\(463\) −29.1279 −0.0629112 −0.0314556 0.999505i \(-0.510014\pi\)
−0.0314556 + 0.999505i \(0.510014\pi\)
\(464\) −3.92086 −0.00845013
\(465\) 69.4240i 0.149299i
\(466\) −1105.21 −2.37170
\(467\) 38.6664i 0.0827973i 0.999143 + 0.0413987i \(0.0131814\pi\)
−0.999143 + 0.0413987i \(0.986819\pi\)
\(468\) 245.671i 0.524939i
\(469\) −193.093 30.3036i −0.411713 0.0646133i
\(470\) −15.2909 −0.0325339
\(471\) 141.659 0.300763
\(472\) 1546.92i 3.27738i
\(473\) −134.910 −0.285221
\(474\) 7.59785i 0.0160292i
\(475\) 226.494i 0.476830i
\(476\) 130.239 829.876i 0.273611 1.74344i
\(477\) −55.7853 −0.116950
\(478\) −1211.78 −2.53511
\(479\) 579.411i 1.20963i 0.796368 + 0.604813i \(0.206752\pi\)
−0.796368 + 0.604813i \(0.793248\pi\)
\(480\) −12.5383 −0.0261214
\(481\) 124.534i 0.258906i
\(482\) 214.104i 0.444199i
\(483\) −9.01502 + 57.4433i −0.0186646 + 0.118930i
\(484\) −454.885 −0.939845
\(485\) −163.220 −0.336537
\(486\) 54.3895i 0.111913i
\(487\) 753.901 1.54805 0.774026 0.633154i \(-0.218240\pi\)
0.774026 + 0.633154i \(0.218240\pi\)
\(488\) 1458.87i 2.98948i
\(489\) 38.8595i 0.0794674i
\(490\) 76.5135 237.766i 0.156150 0.485237i
\(491\) −277.996 −0.566183 −0.283091 0.959093i \(-0.591360\pi\)
−0.283091 + 0.959093i \(0.591360\pi\)
\(492\) 413.531 0.840510
\(493\) 3.17774i 0.00644573i
\(494\) −346.257 −0.700926
\(495\) 35.4304i 0.0715766i
\(496\) 496.993i 1.00200i
\(497\) −97.0743 15.2346i −0.195321 0.0306532i
\(498\) 304.968 0.612386
\(499\) 760.839 1.52473 0.762364 0.647149i \(-0.224039\pi\)
0.762364 + 0.647149i \(0.224039\pi\)
\(500\) 571.588i 1.14318i
\(501\) 180.470 0.360220
\(502\) 619.021i 1.23311i
\(503\) 815.950i 1.62217i 0.584931 + 0.811083i \(0.301122\pi\)
−0.584931 + 0.811083i \(0.698878\pi\)
\(504\) 302.116 + 47.4134i 0.599436 + 0.0940742i
\(505\) 167.886 0.332447
\(506\) −135.267 −0.267326
\(507\) 118.862i 0.234443i
\(508\) 766.751 1.50935
\(509\) 63.1818i 0.124129i 0.998072 + 0.0620647i \(0.0197685\pi\)
−0.998072 + 0.0620647i \(0.980231\pi\)
\(510\) 129.625i 0.254167i
\(511\) 107.462 684.741i 0.210297 1.34000i
\(512\) 965.449 1.88564
\(513\) −51.4703 −0.100332
\(514\) 963.393i 1.87431i
\(515\) 75.9772 0.147529
\(516\) 236.270i 0.457888i
\(517\) 24.2493i 0.0469038i
\(518\) 299.918 + 47.0684i 0.578992 + 0.0908657i
\(519\) 106.117 0.204465
\(520\) −213.152 −0.409907
\(521\) 113.598i 0.218038i 0.994040 + 0.109019i \(0.0347710\pi\)
−0.994040 + 0.109019i \(0.965229\pi\)
\(522\) −2.26555 −0.00434014
\(523\) 839.032i 1.60427i 0.597144 + 0.802134i \(0.296302\pi\)
−0.597144 + 0.802134i \(0.703698\pi\)
\(524\) 136.189i 0.259903i
\(525\) 42.9819 273.878i 0.0818702 0.521673i
\(526\) −275.357 −0.523492
\(527\) −402.798 −0.764323
\(528\) 253.640i 0.480378i
\(529\) 23.0000 0.0434783
\(530\) 94.7872i 0.178844i
\(531\) 318.678i 0.600147i
\(532\) −87.8694 + 559.900i −0.165168 + 1.05244i
\(533\) 292.643 0.549049
\(534\) 737.079 1.38030
\(535\) 160.450i 0.299907i
\(536\) 406.621 0.758622
\(537\) 557.701i 1.03855i
\(538\) 814.887i 1.51466i
\(539\) −377.064 121.340i −0.699562 0.225120i
\(540\) −62.0500 −0.114907
\(541\) −111.214 −0.205571 −0.102785 0.994704i \(-0.532775\pi\)
−0.102785 + 0.994704i \(0.532775\pi\)
\(542\) 1676.18i 3.09258i
\(543\) −474.158 −0.873220
\(544\) 72.7471i 0.133726i
\(545\) 129.464i 0.237548i
\(546\) 418.697 + 65.7093i 0.766844 + 0.120347i
\(547\) 29.0925 0.0531856 0.0265928 0.999646i \(-0.491534\pi\)
0.0265928 + 0.999646i \(0.491534\pi\)
\(548\) −310.772 −0.567102
\(549\) 300.538i 0.547428i
\(550\) 644.927 1.17259
\(551\) 2.14396i 0.00389103i
\(552\) 120.966i 0.219141i
\(553\) −8.69426 1.36446i −0.0157220 0.00246737i
\(554\) 18.6205 0.0336110
\(555\) −31.4539 −0.0566737
\(556\) 714.068i 1.28429i
\(557\) −932.764 −1.67462 −0.837310 0.546728i \(-0.815873\pi\)
−0.837310 + 0.546728i \(0.815873\pi\)
\(558\) 287.173i 0.514647i
\(559\) 167.201i 0.299108i
\(560\) −28.7225 + 183.018i −0.0512901 + 0.326818i
\(561\) 205.568 0.366430
\(562\) 863.625 1.53670
\(563\) 549.628i 0.976249i −0.872774 0.488124i \(-0.837681\pi\)
0.872774 0.488124i \(-0.162319\pi\)
\(564\) −42.4682 −0.0752982
\(565\) 132.015i 0.233655i
\(566\) 1494.79i 2.64098i
\(567\) 62.2382 + 9.76753i 0.109768 + 0.0172267i
\(568\) 204.422 0.359898
\(569\) 223.921 0.393534 0.196767 0.980450i \(-0.436956\pi\)
0.196767 + 0.980450i \(0.436956\pi\)
\(570\) 87.4553i 0.153430i
\(571\) 650.294 1.13887 0.569435 0.822037i \(-0.307162\pi\)
0.569435 + 0.822037i \(0.307162\pi\)
\(572\) 661.987i 1.15732i
\(573\) 243.774i 0.425435i
\(574\) 110.607 704.779i 0.192694 1.22784i
\(575\) −109.660 −0.190712
\(576\) 165.516 0.287355
\(577\) 1120.34i 1.94166i −0.239772 0.970829i \(-0.577073\pi\)
0.239772 0.970829i \(-0.422927\pi\)
\(578\) −256.261 −0.443358
\(579\) 437.214i 0.755120i
\(580\) 2.58465i 0.00445628i
\(581\) 54.7677 348.977i 0.0942645 0.600649i
\(582\) −675.162 −1.16007
\(583\) −150.319 −0.257838
\(584\) 1441.95i 2.46909i
\(585\) −43.9109 −0.0750614
\(586\) 1513.69i 2.58309i
\(587\) 519.842i 0.885592i 0.896622 + 0.442796i \(0.146013\pi\)
−0.896622 + 0.442796i \(0.853987\pi\)
\(588\) 212.505 660.359i 0.361402 1.12306i
\(589\) 271.760 0.461391
\(590\) −541.479 −0.917762
\(591\) 533.725i 0.903088i
\(592\) −225.173 −0.380359
\(593\) 289.795i 0.488692i 0.969688 + 0.244346i \(0.0785733\pi\)
−0.969688 + 0.244346i \(0.921427\pi\)
\(594\) 146.558i 0.246731i
\(595\) 148.331 + 23.2787i 0.249295 + 0.0391239i
\(596\) −1168.51 −1.96059
\(597\) 81.2913 0.136166
\(598\) 167.644i 0.280341i
\(599\) −591.525 −0.987521 −0.493761 0.869598i \(-0.664378\pi\)
−0.493761 + 0.869598i \(0.664378\pi\)
\(600\) 576.741i 0.961235i
\(601\) 125.235i 0.208377i 0.994558 + 0.104188i \(0.0332245\pi\)
−0.994558 + 0.104188i \(0.966775\pi\)
\(602\) −402.674 63.1948i −0.668894 0.104975i
\(603\) 83.7671 0.138917
\(604\) −1410.51 −2.33529
\(605\) 81.3055i 0.134389i
\(606\) 694.460 1.14597
\(607\) 96.8852i 0.159613i 0.996810 + 0.0798066i \(0.0254303\pi\)
−0.996810 + 0.0798066i \(0.974570\pi\)
\(608\) 49.0809i 0.0807252i
\(609\) −0.406859 + 2.59249i −0.000668077 + 0.00425695i
\(610\) −510.656 −0.837142
\(611\) −30.0535 −0.0491873
\(612\) 360.014i 0.588259i
\(613\) 557.666 0.909732 0.454866 0.890560i \(-0.349687\pi\)
0.454866 + 0.890560i \(0.349687\pi\)
\(614\) 898.360i 1.46313i
\(615\) 73.9139i 0.120185i
\(616\) 814.083 + 127.760i 1.32156 + 0.207403i
\(617\) −6.30866 −0.0102247 −0.00511237 0.999987i \(-0.501627\pi\)
−0.00511237 + 0.999987i \(0.501627\pi\)
\(618\) 314.280 0.508544
\(619\) 355.187i 0.573808i 0.957959 + 0.286904i \(0.0926260\pi\)
−0.957959 + 0.286904i \(0.907374\pi\)
\(620\) 327.620 0.528419
\(621\) 24.9199i 0.0401286i
\(622\) 900.780i 1.44820i
\(623\) 132.368 843.444i 0.212469 1.35384i
\(624\) −314.350 −0.503766
\(625\) 469.475 0.751160
\(626\) 953.658i 1.52342i
\(627\) −138.692 −0.221199
\(628\) 668.506i 1.06450i
\(629\) 182.496i 0.290137i
\(630\) −16.5964 + 105.752i −0.0263435 + 0.167860i
\(631\) 711.988 1.12835 0.564175 0.825656i \(-0.309194\pi\)
0.564175 + 0.825656i \(0.309194\pi\)
\(632\) 18.3086 0.0289693
\(633\) 272.833i 0.431016i
\(634\) −499.296 −0.787533
\(635\) 137.048i 0.215824i
\(636\) 263.257i 0.413926i
\(637\) 150.383 467.316i 0.236080 0.733621i
\(638\) −6.10477 −0.00956860
\(639\) 42.1125 0.0659037
\(640\) 310.192i 0.484675i
\(641\) −341.832 −0.533279 −0.266639 0.963796i \(-0.585913\pi\)
−0.266639 + 0.963796i \(0.585913\pi\)
\(642\) 663.704i 1.03381i
\(643\) 331.892i 0.516162i −0.966123 0.258081i \(-0.916910\pi\)
0.966123 0.258081i \(-0.0830902\pi\)
\(644\) −271.081 42.5429i −0.420934 0.0660604i
\(645\) 42.2305 0.0654737
\(646\) −507.416 −0.785474
\(647\) 663.004i 1.02474i −0.858766 0.512368i \(-0.828768\pi\)
0.858766 0.512368i \(-0.171232\pi\)
\(648\) −131.063 −0.202258
\(649\) 858.711i 1.32313i
\(650\) 799.294i 1.22968i
\(651\) −328.613 51.5719i −0.504783 0.0792195i
\(652\) −183.383 −0.281262
\(653\) 784.805 1.20184 0.600922 0.799307i \(-0.294800\pi\)
0.600922 + 0.799307i \(0.294800\pi\)
\(654\) 535.528i 0.818850i
\(655\) −24.3422 −0.0371637
\(656\) 529.136i 0.806609i
\(657\) 297.052i 0.452135i
\(658\) −11.3589 + 72.3784i −0.0172628 + 0.109998i
\(659\) −1308.17 −1.98509 −0.992543 0.121898i \(-0.961102\pi\)
−0.992543 + 0.121898i \(0.961102\pi\)
\(660\) −167.200 −0.253334
\(661\) 1061.20i 1.60545i −0.596349 0.802725i \(-0.703382\pi\)
0.596349 0.802725i \(-0.296618\pi\)
\(662\) 1219.67 1.84240
\(663\) 254.771i 0.384270i
\(664\) 734.885i 1.10676i
\(665\) −100.076 15.7056i −0.150490 0.0236175i
\(666\) −130.109 −0.195359
\(667\) 1.03802 0.00155625
\(668\) 851.660i 1.27494i
\(669\) −18.0855 −0.0270336
\(670\) 142.332i 0.212436i
\(671\) 809.830i 1.20690i
\(672\) −9.31410 + 59.3490i −0.0138603 + 0.0883169i
\(673\) −482.238 −0.716549 −0.358275 0.933616i \(-0.616635\pi\)
−0.358275 + 0.933616i \(0.616635\pi\)
\(674\) 271.720 0.403146
\(675\) 118.813i 0.176019i
\(676\) 560.925 0.829771
\(677\) 5.11810i 0.00755997i 0.999993 + 0.00377998i \(0.00120321\pi\)
−0.999993 + 0.00377998i \(0.998797\pi\)
\(678\) 546.082i 0.805431i
\(679\) −121.249 + 772.592i −0.178570 + 1.13784i
\(680\) −312.359 −0.459352
\(681\) −681.214 −1.00031
\(682\) 773.817i 1.13463i
\(683\) −601.461 −0.880616 −0.440308 0.897847i \(-0.645131\pi\)
−0.440308 + 0.897847i \(0.645131\pi\)
\(684\) 242.894i 0.355108i
\(685\) 55.5469i 0.0810903i
\(686\) −1068.61 538.796i −1.55774 0.785417i
\(687\) −717.695 −1.04468
\(688\) 302.321 0.439419
\(689\) 186.299i 0.270391i
\(690\) 42.3424 0.0613658
\(691\) 575.488i 0.832834i 0.909174 + 0.416417i \(0.136714\pi\)
−0.909174 + 0.416417i \(0.863286\pi\)
\(692\) 500.779i 0.723670i
\(693\) 167.707 + 26.3196i 0.242002 + 0.0379792i
\(694\) 1560.47 2.24852
\(695\) 127.631 0.183642
\(696\) 5.45933i 0.00784386i
\(697\) 428.849 0.615278
\(698\) 1338.86i 1.91814i
\(699\) 548.649i 0.784905i
\(700\) 1292.46 + 202.836i 1.84638 + 0.289766i
\(701\) −328.856 −0.469124 −0.234562 0.972101i \(-0.575366\pi\)
−0.234562 + 0.972101i \(0.575366\pi\)
\(702\) −181.638 −0.258743
\(703\) 123.126i 0.175144i
\(704\) 446.001 0.633525
\(705\) 7.59070i 0.0107670i
\(706\) 1919.69i 2.71910i
\(707\) 124.715 794.675i 0.176400 1.12401i
\(708\) −1503.88 −2.12412
\(709\) −1214.87 −1.71349 −0.856746 0.515738i \(-0.827518\pi\)
−0.856746 + 0.515738i \(0.827518\pi\)
\(710\) 71.5551i 0.100782i
\(711\) 3.77172 0.00530481
\(712\) 1776.15i 2.49459i
\(713\) 131.575i 0.184537i
\(714\) 613.571 + 96.2925i 0.859343 + 0.134863i
\(715\) −118.322 −0.165486
\(716\) 2631.85 3.67577
\(717\) 601.553i 0.838986i
\(718\) −1124.94 −1.56677
\(719\) 1056.98i 1.47008i 0.678026 + 0.735038i \(0.262836\pi\)
−0.678026 + 0.735038i \(0.737164\pi\)
\(720\) 79.3964i 0.110273i
\(721\) 56.4400 359.633i 0.0782801 0.498797i
\(722\) −917.218 −1.27039
\(723\) −106.285 −0.147006
\(724\) 2237.61i 3.09062i
\(725\) −4.94907 −0.00682630
\(726\) 336.321i 0.463251i
\(727\) 1130.45i 1.55495i −0.628911 0.777477i \(-0.716499\pi\)
0.628911 0.777477i \(-0.283501\pi\)
\(728\) −158.341 + 1008.94i −0.217501 + 1.38590i
\(729\) −27.0000 −0.0370370
\(730\) −504.734 −0.691417
\(731\) 245.022i 0.335187i
\(732\) −1418.27 −1.93753
\(733\) 630.457i 0.860105i 0.902804 + 0.430052i \(0.141505\pi\)
−0.902804 + 0.430052i \(0.858495\pi\)
\(734\) 189.015i 0.257513i
\(735\) 118.032 + 37.9827i 0.160587 + 0.0516772i
\(736\) 23.7630 0.0322867
\(737\) 225.719 0.306268
\(738\) 305.745i 0.414289i
\(739\) 1068.43 1.44578 0.722890 0.690963i \(-0.242813\pi\)
0.722890 + 0.690963i \(0.242813\pi\)
\(740\) 148.435i 0.200587i
\(741\) 171.889i 0.231969i
\(742\) −448.668 70.4130i −0.604674 0.0948962i
\(743\) 823.811 1.10876 0.554382 0.832263i \(-0.312955\pi\)
0.554382 + 0.832263i \(0.312955\pi\)
\(744\) 692.004 0.930112
\(745\) 208.858i 0.280347i
\(746\) −1727.84 −2.31613
\(747\) 151.392i 0.202667i
\(748\) 970.096i 1.29692i
\(749\) 759.481 + 119.191i 1.01399 + 0.159134i
\(750\) −422.605 −0.563474
\(751\) 1167.64 1.55477 0.777387 0.629022i \(-0.216545\pi\)
0.777387 + 0.629022i \(0.216545\pi\)
\(752\) 54.3404i 0.0722612i
\(753\) −307.294 −0.408093
\(754\) 7.56598i 0.0100345i
\(755\) 252.113i 0.333925i
\(756\) −46.0941 + 293.709i −0.0609710 + 0.388504i
\(757\) 564.937 0.746283 0.373142 0.927774i \(-0.378281\pi\)
0.373142 + 0.927774i \(0.378281\pi\)
\(758\) 1065.12 1.40518
\(759\) 67.1492i 0.0884706i
\(760\) 210.742 0.277292
\(761\) 1346.43i 1.76929i 0.466264 + 0.884646i \(0.345600\pi\)
−0.466264 + 0.884646i \(0.654400\pi\)
\(762\) 566.900i 0.743963i
\(763\) −612.807 96.1726i −0.803155 0.126045i
\(764\) 1150.40 1.50576
\(765\) −64.3484 −0.0841156
\(766\) 1398.54i 1.82577i
\(767\) −1064.25 −1.38755
\(768\) 900.867i 1.17300i
\(769\) 854.281i 1.11090i 0.831550 + 0.555450i \(0.187454\pi\)
−0.831550 + 0.555450i \(0.812546\pi\)
\(770\) −44.7208 + 284.959i −0.0580789 + 0.370076i
\(771\) −478.247 −0.620294
\(772\) −2063.26 −2.67262
\(773\) 532.431i 0.688785i −0.938826 0.344392i \(-0.888085\pi\)
0.938826 0.344392i \(-0.111915\pi\)
\(774\) 174.687 0.225694
\(775\) 627.325i 0.809451i
\(776\) 1626.95i 2.09658i
\(777\) −23.3657 + 148.885i −0.0300716 + 0.191615i
\(778\) 1272.14 1.63515
\(779\) −289.335 −0.371419
\(780\) 207.220i 0.265667i
\(781\) 113.476 0.145296
\(782\) 245.671i 0.314157i
\(783\) 1.12466i 0.00143635i
\(784\) 844.966 + 271.911i 1.07776 + 0.346826i
\(785\) −119.488 −0.152214
\(786\) −100.692 −0.128107
\(787\) 5.75166i 0.00730833i −0.999993 0.00365417i \(-0.998837\pi\)
0.999993 0.00365417i \(-0.00116316\pi\)
\(788\) 2518.71 3.19633
\(789\) 136.692i 0.173248i
\(790\) 6.40868i 0.00811226i
\(791\) −624.885 98.0680i −0.789993 0.123980i
\(792\) −353.163 −0.445913
\(793\) −1003.67 −1.26566
\(794\) 151.161i 0.190379i
\(795\) 47.0542 0.0591876
\(796\) 383.623i 0.481938i
\(797\) 1260.72i 1.58183i −0.611924 0.790917i \(-0.709604\pi\)
0.611924 0.790917i \(-0.290396\pi\)
\(798\) −413.963 64.9665i −0.518751 0.0814117i
\(799\) −44.0413 −0.0551205
\(800\) −113.298 −0.141622
\(801\) 365.900i 0.456804i
\(802\) 1399.78 1.74537
\(803\) 800.439i 0.996810i
\(804\) 395.306i 0.491675i
\(805\) 7.60405 48.4526i 0.00944603 0.0601896i
\(806\) 959.035 1.18987
\(807\) −404.526 −0.501271
\(808\) 1673.45i 2.07110i
\(809\) −105.646 −0.130589 −0.0652943 0.997866i \(-0.520799\pi\)
−0.0652943 + 0.997866i \(0.520799\pi\)
\(810\) 45.8768i 0.0566381i
\(811\) 1181.24i 1.45652i 0.685299 + 0.728262i \(0.259672\pi\)
−0.685299 + 0.728262i \(0.740328\pi\)
\(812\) −12.2342 1.92001i −0.0150668 0.00236455i
\(813\) 832.088 1.02348
\(814\) −350.593 −0.430704
\(815\) 32.7775i 0.0402178i
\(816\) −460.658 −0.564532
\(817\) 165.311i 0.202339i
\(818\) 482.898i 0.590340i
\(819\) −32.6194 + 207.849i −0.0398283 + 0.253784i
\(820\) −348.808 −0.425375
\(821\) 479.585 0.584147 0.292073 0.956396i \(-0.405655\pi\)
0.292073 + 0.956396i \(0.405655\pi\)
\(822\) 229.770i 0.279526i
\(823\) −525.864 −0.638960 −0.319480 0.947593i \(-0.603508\pi\)
−0.319480 + 0.947593i \(0.603508\pi\)
\(824\) 757.325i 0.919083i
\(825\) 320.154i 0.388066i
\(826\) −402.240 + 2563.05i −0.486973 + 3.10297i
\(827\) −451.526 −0.545980 −0.272990 0.962017i \(-0.588013\pi\)
−0.272990 + 0.962017i \(0.588013\pi\)
\(828\) 117.600 0.142029
\(829\) 1247.66i 1.50502i 0.658580 + 0.752511i \(0.271157\pi\)
−0.658580 + 0.752511i \(0.728843\pi\)
\(830\) −257.237 −0.309924
\(831\) 9.24356i 0.0111234i
\(832\) 552.754i 0.664368i
\(833\) 220.376 684.820i 0.264557 0.822113i
\(834\) 527.948 0.633031
\(835\) −152.224 −0.182305
\(836\) 654.503i 0.782899i
\(837\) 142.558 0.170320
\(838\) 1478.13i 1.76388i
\(839\) 118.810i 0.141609i −0.997490 0.0708047i \(-0.977443\pi\)
0.997490 0.0708047i \(-0.0225567\pi\)
\(840\) −254.831 39.9926i −0.303370 0.0476102i
\(841\) −840.953 −0.999944
\(842\) 2510.03 2.98103
\(843\) 428.720i 0.508565i
\(844\) −1287.53 −1.52551
\(845\) 100.259i 0.118650i
\(846\) 31.3990i 0.0371146i
\(847\) −384.853 60.3981i −0.454372 0.0713082i
\(848\) 336.852 0.397231
\(849\) 742.044 0.874021
\(850\) 1171.31i 1.37801i
\(851\) 59.6128 0.0700503
\(852\) 198.734i 0.233255i
\(853\) 445.451i 0.522217i 0.965309 + 0.261109i \(0.0840881\pi\)
−0.965309 + 0.261109i \(0.915912\pi\)
\(854\) −379.343 + 2417.16i −0.444196 + 2.83039i
\(855\) 43.4145 0.0507772
\(856\) −1599.34 −1.86838
\(857\) 778.359i 0.908236i 0.890941 + 0.454118i \(0.150046\pi\)
−0.890941 + 0.454118i \(0.849954\pi\)
\(858\) −489.442 −0.570445
\(859\) 1143.51i 1.33121i −0.746305 0.665604i \(-0.768174\pi\)
0.746305 0.665604i \(-0.231826\pi\)
\(860\) 199.291i 0.231733i
\(861\) 349.866 + 54.9072i 0.406348 + 0.0637714i
\(862\) 793.339 0.920347
\(863\) 1298.91 1.50511 0.752554 0.658531i \(-0.228822\pi\)
0.752554 + 0.658531i \(0.228822\pi\)
\(864\) 25.7466i 0.0297993i
\(865\) −89.5085 −0.103478
\(866\) 612.187i 0.706913i
\(867\) 127.213i 0.146728i
\(868\) 243.373 1550.76i 0.280384 1.78659i
\(869\) 10.1633 0.0116954
\(870\) 1.91096 0.00219651
\(871\) 279.746i 0.321178i
\(872\) 1290.47 1.47989
\(873\) 335.164i 0.383922i
\(874\) 165.749i 0.189644i
\(875\) −75.8935 + 483.590i −0.0867354 + 0.552674i
\(876\) −1401.82 −1.60026
\(877\) −1381.00 −1.57469 −0.787346 0.616512i \(-0.788545\pi\)
−0.787346 + 0.616512i \(0.788545\pi\)
\(878\) 1216.85i 1.38593i
\(879\) 751.425 0.854863
\(880\) 213.942i 0.243116i
\(881\) 1468.58i 1.66695i −0.552558 0.833475i \(-0.686348\pi\)
0.552558 0.833475i \(-0.313652\pi\)
\(882\) 488.239 + 157.116i 0.553559 + 0.178136i
\(883\) 453.515 0.513607 0.256804 0.966464i \(-0.417331\pi\)
0.256804 + 0.966464i \(0.417331\pi\)
\(884\) −1202.29 −1.36006
\(885\) 268.801i 0.303730i
\(886\) −1222.93 −1.38029
\(887\) 748.985i 0.844403i 0.906502 + 0.422201i \(0.138742\pi\)
−0.906502 + 0.422201i \(0.861258\pi\)
\(888\) 313.526i 0.353070i
\(889\) 648.706 + 101.807i 0.729704 + 0.114518i
\(890\) −621.717 −0.698558
\(891\) −72.7543 −0.0816547
\(892\) 85.3475i 0.0956811i
\(893\) 29.7137 0.0332740
\(894\) 863.945i 0.966381i
\(895\) 470.413i 0.525601i
\(896\) 1468.27 + 230.427i 1.63869 + 0.257173i
\(897\) 83.2217 0.0927778
\(898\) −1982.63 −2.20782
\(899\) 5.93815i 0.00660528i
\(900\) −560.692 −0.622991
\(901\) 273.009i 0.303006i
\(902\) 823.862i 0.913373i
\(903\) 31.3711 199.895i 0.0347410 0.221368i
\(904\) 1315.90 1.45564
\(905\) 399.946 0.441930
\(906\) 1042.87i 1.15107i
\(907\) 1704.51 1.87928 0.939641 0.342163i \(-0.111159\pi\)
0.939641 + 0.342163i \(0.111159\pi\)
\(908\) 3214.72i 3.54044i
\(909\) 344.743i 0.379256i
\(910\) −353.165 55.4250i −0.388094 0.0609065i
\(911\) −668.129 −0.733402 −0.366701 0.930339i \(-0.619513\pi\)
−0.366701 + 0.930339i \(0.619513\pi\)
\(912\) 310.796 0.340785
\(913\) 407.942i 0.446815i
\(914\) −818.871 −0.895920
\(915\) 253.500i 0.277049i
\(916\) 3386.88i 3.69747i
\(917\) −18.0827 + 115.222i −0.0197194 + 0.125651i
\(918\) −266.178 −0.289954
\(919\) −867.877 −0.944371 −0.472185 0.881499i \(-0.656535\pi\)
−0.472185 + 0.881499i \(0.656535\pi\)
\(920\) 102.033i 0.110905i
\(921\) 445.963 0.484216
\(922\) 1606.99i 1.74294i
\(923\) 140.638i 0.152370i
\(924\) −124.205 + 791.430i −0.134421 + 0.856526i
\(925\) −284.222 −0.307267
\(926\) 101.630 0.109751
\(927\) 156.015i 0.168301i
\(928\) 1.07246 0.00115566
\(929\) 1209.41i 1.30184i −0.759147 0.650919i \(-0.774384\pi\)
0.759147 0.650919i \(-0.225616\pi\)
\(930\) 242.227i 0.260459i
\(931\) −148.683 + 462.034i −0.159703 + 0.496277i
\(932\) 2589.13 2.77804
\(933\) 447.164 0.479276
\(934\) 134.910i 0.144444i
\(935\) −173.393 −0.185448
\(936\) 437.695i 0.467622i
\(937\) 106.970i 0.114162i 0.998370 + 0.0570811i \(0.0181794\pi\)
−0.998370 + 0.0570811i \(0.981821\pi\)
\(938\) 673.719 + 105.732i 0.718251 + 0.112721i
\(939\) 473.414 0.504169
\(940\) 35.8214 0.0381078
\(941\) 930.978i 0.989350i 0.869078 + 0.494675i \(0.164713\pi\)
−0.869078 + 0.494675i \(0.835287\pi\)
\(942\) −494.261 −0.524694
\(943\) 140.085i 0.148552i
\(944\) 1924.29i 2.03845i
\(945\) −52.4971 8.23878i −0.0555525 0.00871829i
\(946\) 470.712 0.497581
\(947\) −594.943 −0.628239 −0.314120 0.949383i \(-0.601709\pi\)
−0.314120 + 0.949383i \(0.601709\pi\)
\(948\) 17.7992i 0.0187755i
\(949\) −992.028 −1.04534
\(950\) 790.258i 0.831851i
\(951\) 247.860i 0.260631i
\(952\) −232.037 + 1478.53i −0.243737 + 1.55308i
\(953\) −563.659 −0.591457 −0.295729 0.955272i \(-0.595562\pi\)
−0.295729 + 0.955272i \(0.595562\pi\)
\(954\) 194.640 0.204025
\(955\) 205.621i 0.215309i
\(956\) 2838.80 2.96945
\(957\) 3.03052i 0.00316669i
\(958\) 2021.62i 2.11025i
\(959\) −262.927 41.2632i −0.274168 0.0430273i
\(960\) −139.611 −0.145428
\(961\) 208.303 0.216757
\(962\) 434.510i 0.451673i
\(963\) −329.476 −0.342135
\(964\) 501.572i 0.520303i
\(965\) 368.785i 0.382160i
\(966\) 31.4542 200.425i 0.0325613 0.207479i
\(967\) −533.769 −0.551984 −0.275992 0.961160i \(-0.589006\pi\)
−0.275992 + 0.961160i \(0.589006\pi\)
\(968\) 810.435 0.837227
\(969\) 251.891i 0.259950i
\(970\) 569.490 0.587104
\(971\) 237.067i 0.244147i 0.992521 + 0.122073i \(0.0389543\pi\)
−0.992521 + 0.122073i \(0.961046\pi\)
\(972\) 127.416i 0.131086i
\(973\) 94.8114 604.134i 0.0974424 0.620898i
\(974\) −2630.43 −2.70064
\(975\) −396.785 −0.406959
\(976\) 1814.76i 1.85938i
\(977\) −317.705 −0.325185 −0.162592 0.986693i \(-0.551986\pi\)
−0.162592 + 0.986693i \(0.551986\pi\)
\(978\) 135.584i 0.138634i
\(979\) 985.957i 1.00711i
\(980\) −179.245 + 557.005i −0.182903 + 0.568372i
\(981\) 265.846 0.270995
\(982\) 969.952 0.987731
\(983\) 187.630i 0.190874i −0.995435 0.0954372i \(-0.969575\pi\)
0.995435 0.0954372i \(-0.0304249\pi\)
\(984\) −736.758 −0.748738
\(985\) 450.190i 0.457046i
\(986\) 11.0874i 0.0112449i
\(987\) −35.9300 5.63878i −0.0364033 0.00571305i
\(988\) 811.162 0.821015
\(989\) −80.0370 −0.0809272
\(990\) 123.620i 0.124869i
\(991\) 1895.27 1.91248 0.956241 0.292579i \(-0.0945135\pi\)
0.956241 + 0.292579i \(0.0945135\pi\)
\(992\) 135.940i 0.137037i
\(993\) 605.468i 0.609736i
\(994\) 338.701 + 53.1550i 0.340745 + 0.0534758i
\(995\) −68.5681 −0.0689127
\(996\) −714.436 −0.717306
\(997\) 828.968i 0.831462i −0.909488 0.415731i \(-0.863526\pi\)
0.909488 0.415731i \(-0.136474\pi\)
\(998\) −2654.63 −2.65995
\(999\) 64.5888i 0.0646535i
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 483.3.g.a.139.4 yes 60
7.6 odd 2 inner 483.3.g.a.139.3 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.3.g.a.139.3 60 7.6 odd 2 inner
483.3.g.a.139.4 yes 60 1.1 even 1 trivial