Properties

Label 6003.2.a.u.1.3
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $22$
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] = [6003,2,Mod(1,6003)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6003, 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("6003.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.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: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 6003.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.08661 q^{2} +2.35393 q^{4} -1.43041 q^{5} -0.274571 q^{7} -0.738503 q^{8} +O(q^{10})\) \(q-2.08661 q^{2} +2.35393 q^{4} -1.43041 q^{5} -0.274571 q^{7} -0.738503 q^{8} +2.98470 q^{10} +6.10520 q^{11} +0.188265 q^{13} +0.572921 q^{14} -3.16689 q^{16} +2.24526 q^{17} +3.65245 q^{19} -3.36708 q^{20} -12.7391 q^{22} -1.00000 q^{23} -2.95393 q^{25} -0.392834 q^{26} -0.646319 q^{28} -1.00000 q^{29} -4.05707 q^{31} +8.08505 q^{32} -4.68496 q^{34} +0.392749 q^{35} -4.16777 q^{37} -7.62122 q^{38} +1.05636 q^{40} +3.24174 q^{41} -4.69667 q^{43} +14.3712 q^{44} +2.08661 q^{46} -6.10569 q^{47} -6.92461 q^{49} +6.16369 q^{50} +0.443161 q^{52} -3.87730 q^{53} -8.73294 q^{55} +0.202771 q^{56} +2.08661 q^{58} -2.91676 q^{59} -2.77700 q^{61} +8.46551 q^{62} -10.5365 q^{64} -0.269296 q^{65} +7.02715 q^{67} +5.28516 q^{68} -0.819512 q^{70} +3.49275 q^{71} -12.1979 q^{73} +8.69650 q^{74} +8.59759 q^{76} -1.67631 q^{77} -8.81856 q^{79} +4.52994 q^{80} -6.76424 q^{82} +2.42899 q^{83} -3.21163 q^{85} +9.80011 q^{86} -4.50871 q^{88} +1.75647 q^{89} -0.0516920 q^{91} -2.35393 q^{92} +12.7402 q^{94} -5.22450 q^{95} -5.73211 q^{97} +14.4489 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 3 q^{2} + 17 q^{4} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 3 q^{2} + 17 q^{4} - 6 q^{7} + 6 q^{8} - 12 q^{10} - 28 q^{13} + q^{14} + 3 q^{16} + 10 q^{17} - 8 q^{19} - 11 q^{22} - 22 q^{23} - 11 q^{26} - 21 q^{28} - 22 q^{29} - 18 q^{31} - 5 q^{32} - 33 q^{34} - 2 q^{35} - 28 q^{37} - 14 q^{38} - 30 q^{40} + 10 q^{41} - 14 q^{43} - 37 q^{44} - 3 q^{46} + 18 q^{47} + 2 q^{49} - 7 q^{50} - 57 q^{52} - 20 q^{53} - 42 q^{55} + 2 q^{56} - 3 q^{58} + 20 q^{59} - 38 q^{61} - 4 q^{62} - 24 q^{64} - 12 q^{65} - 50 q^{67} - 11 q^{68} - 48 q^{70} - 12 q^{71} - 46 q^{73} + 6 q^{74} - 16 q^{76} + 14 q^{77} - 20 q^{79} + 58 q^{80} - 42 q^{82} - 22 q^{83} - 66 q^{85} - 22 q^{86} - 68 q^{88} + 14 q^{89} - 16 q^{91} - 17 q^{92} - 27 q^{94} + 20 q^{95} - 48 q^{97} + 28 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08661 −1.47545 −0.737727 0.675099i \(-0.764101\pi\)
−0.737727 + 0.675099i \(0.764101\pi\)
\(3\) 0 0
\(4\) 2.35393 1.17696
\(5\) −1.43041 −0.639698 −0.319849 0.947468i \(-0.603632\pi\)
−0.319849 + 0.947468i \(0.603632\pi\)
\(6\) 0 0
\(7\) −0.274571 −0.103778 −0.0518890 0.998653i \(-0.516524\pi\)
−0.0518890 + 0.998653i \(0.516524\pi\)
\(8\) −0.738503 −0.261100
\(9\) 0 0
\(10\) 2.98470 0.943845
\(11\) 6.10520 1.84079 0.920394 0.390993i \(-0.127868\pi\)
0.920394 + 0.390993i \(0.127868\pi\)
\(12\) 0 0
\(13\) 0.188265 0.0522152 0.0261076 0.999659i \(-0.491689\pi\)
0.0261076 + 0.999659i \(0.491689\pi\)
\(14\) 0.572921 0.153120
\(15\) 0 0
\(16\) −3.16689 −0.791721
\(17\) 2.24526 0.544554 0.272277 0.962219i \(-0.412223\pi\)
0.272277 + 0.962219i \(0.412223\pi\)
\(18\) 0 0
\(19\) 3.65245 0.837929 0.418965 0.908003i \(-0.362393\pi\)
0.418965 + 0.908003i \(0.362393\pi\)
\(20\) −3.36708 −0.752901
\(21\) 0 0
\(22\) −12.7391 −2.71600
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −2.95393 −0.590786
\(26\) −0.392834 −0.0770412
\(27\) 0 0
\(28\) −0.646319 −0.122143
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −4.05707 −0.728671 −0.364336 0.931268i \(-0.618704\pi\)
−0.364336 + 0.931268i \(0.618704\pi\)
\(32\) 8.08505 1.42925
\(33\) 0 0
\(34\) −4.68496 −0.803465
\(35\) 0.392749 0.0663866
\(36\) 0 0
\(37\) −4.16777 −0.685178 −0.342589 0.939485i \(-0.611304\pi\)
−0.342589 + 0.939485i \(0.611304\pi\)
\(38\) −7.62122 −1.23633
\(39\) 0 0
\(40\) 1.05636 0.167025
\(41\) 3.24174 0.506275 0.253138 0.967430i \(-0.418537\pi\)
0.253138 + 0.967430i \(0.418537\pi\)
\(42\) 0 0
\(43\) −4.69667 −0.716236 −0.358118 0.933676i \(-0.616581\pi\)
−0.358118 + 0.933676i \(0.616581\pi\)
\(44\) 14.3712 2.16654
\(45\) 0 0
\(46\) 2.08661 0.307653
\(47\) −6.10569 −0.890606 −0.445303 0.895380i \(-0.646904\pi\)
−0.445303 + 0.895380i \(0.646904\pi\)
\(48\) 0 0
\(49\) −6.92461 −0.989230
\(50\) 6.16369 0.871677
\(51\) 0 0
\(52\) 0.443161 0.0614554
\(53\) −3.87730 −0.532588 −0.266294 0.963892i \(-0.585799\pi\)
−0.266294 + 0.963892i \(0.585799\pi\)
\(54\) 0 0
\(55\) −8.73294 −1.17755
\(56\) 0.202771 0.0270965
\(57\) 0 0
\(58\) 2.08661 0.273985
\(59\) −2.91676 −0.379730 −0.189865 0.981810i \(-0.560805\pi\)
−0.189865 + 0.981810i \(0.560805\pi\)
\(60\) 0 0
\(61\) −2.77700 −0.355559 −0.177779 0.984070i \(-0.556891\pi\)
−0.177779 + 0.984070i \(0.556891\pi\)
\(62\) 8.46551 1.07512
\(63\) 0 0
\(64\) −10.5365 −1.31707
\(65\) −0.269296 −0.0334020
\(66\) 0 0
\(67\) 7.02715 0.858502 0.429251 0.903185i \(-0.358778\pi\)
0.429251 + 0.903185i \(0.358778\pi\)
\(68\) 5.28516 0.640920
\(69\) 0 0
\(70\) −0.819512 −0.0979504
\(71\) 3.49275 0.414514 0.207257 0.978287i \(-0.433546\pi\)
0.207257 + 0.978287i \(0.433546\pi\)
\(72\) 0 0
\(73\) −12.1979 −1.42766 −0.713830 0.700319i \(-0.753041\pi\)
−0.713830 + 0.700319i \(0.753041\pi\)
\(74\) 8.69650 1.01095
\(75\) 0 0
\(76\) 8.59759 0.986211
\(77\) −1.67631 −0.191033
\(78\) 0 0
\(79\) −8.81856 −0.992165 −0.496083 0.868275i \(-0.665229\pi\)
−0.496083 + 0.868275i \(0.665229\pi\)
\(80\) 4.52994 0.506463
\(81\) 0 0
\(82\) −6.76424 −0.746986
\(83\) 2.42899 0.266616 0.133308 0.991075i \(-0.457440\pi\)
0.133308 + 0.991075i \(0.457440\pi\)
\(84\) 0 0
\(85\) −3.21163 −0.348351
\(86\) 9.80011 1.05677
\(87\) 0 0
\(88\) −4.50871 −0.480630
\(89\) 1.75647 0.186185 0.0930926 0.995657i \(-0.470325\pi\)
0.0930926 + 0.995657i \(0.470325\pi\)
\(90\) 0 0
\(91\) −0.0516920 −0.00541879
\(92\) −2.35393 −0.245414
\(93\) 0 0
\(94\) 12.7402 1.31405
\(95\) −5.22450 −0.536022
\(96\) 0 0
\(97\) −5.73211 −0.582008 −0.291004 0.956722i \(-0.593989\pi\)
−0.291004 + 0.956722i \(0.593989\pi\)
\(98\) 14.4489 1.45956
\(99\) 0 0
\(100\) −6.95333 −0.695333
\(101\) −9.23902 −0.919317 −0.459659 0.888096i \(-0.652028\pi\)
−0.459659 + 0.888096i \(0.652028\pi\)
\(102\) 0 0
\(103\) −7.23178 −0.712568 −0.356284 0.934378i \(-0.615957\pi\)
−0.356284 + 0.934378i \(0.615957\pi\)
\(104\) −0.139034 −0.0136334
\(105\) 0 0
\(106\) 8.09040 0.785809
\(107\) 3.16077 0.305563 0.152781 0.988260i \(-0.451177\pi\)
0.152781 + 0.988260i \(0.451177\pi\)
\(108\) 0 0
\(109\) 9.56401 0.916066 0.458033 0.888935i \(-0.348554\pi\)
0.458033 + 0.888935i \(0.348554\pi\)
\(110\) 18.2222 1.73742
\(111\) 0 0
\(112\) 0.869534 0.0821633
\(113\) 19.3625 1.82147 0.910734 0.412994i \(-0.135517\pi\)
0.910734 + 0.412994i \(0.135517\pi\)
\(114\) 0 0
\(115\) 1.43041 0.133386
\(116\) −2.35393 −0.218556
\(117\) 0 0
\(118\) 6.08613 0.560274
\(119\) −0.616482 −0.0565128
\(120\) 0 0
\(121\) 26.2735 2.38850
\(122\) 5.79451 0.524610
\(123\) 0 0
\(124\) −9.55004 −0.857619
\(125\) 11.3774 1.01762
\(126\) 0 0
\(127\) −12.6479 −1.12232 −0.561161 0.827706i \(-0.689645\pi\)
−0.561161 + 0.827706i \(0.689645\pi\)
\(128\) 5.81552 0.514024
\(129\) 0 0
\(130\) 0.561914 0.0492831
\(131\) −7.81787 −0.683050 −0.341525 0.939873i \(-0.610943\pi\)
−0.341525 + 0.939873i \(0.610943\pi\)
\(132\) 0 0
\(133\) −1.00286 −0.0869586
\(134\) −14.6629 −1.26668
\(135\) 0 0
\(136\) −1.65813 −0.142183
\(137\) 2.22227 0.189861 0.0949305 0.995484i \(-0.469737\pi\)
0.0949305 + 0.995484i \(0.469737\pi\)
\(138\) 0 0
\(139\) 13.7510 1.16635 0.583174 0.812347i \(-0.301811\pi\)
0.583174 + 0.812347i \(0.301811\pi\)
\(140\) 0.924501 0.0781346
\(141\) 0 0
\(142\) −7.28800 −0.611595
\(143\) 1.14939 0.0961171
\(144\) 0 0
\(145\) 1.43041 0.118789
\(146\) 25.4523 2.10645
\(147\) 0 0
\(148\) −9.81063 −0.806428
\(149\) −6.77408 −0.554954 −0.277477 0.960732i \(-0.589498\pi\)
−0.277477 + 0.960732i \(0.589498\pi\)
\(150\) 0 0
\(151\) −10.6096 −0.863395 −0.431698 0.902018i \(-0.642085\pi\)
−0.431698 + 0.902018i \(0.642085\pi\)
\(152\) −2.69734 −0.218784
\(153\) 0 0
\(154\) 3.49780 0.281861
\(155\) 5.80327 0.466130
\(156\) 0 0
\(157\) 17.0603 1.36156 0.680778 0.732489i \(-0.261642\pi\)
0.680778 + 0.732489i \(0.261642\pi\)
\(158\) 18.4009 1.46389
\(159\) 0 0
\(160\) −11.5649 −0.914288
\(161\) 0.274571 0.0216392
\(162\) 0 0
\(163\) −24.0671 −1.88508 −0.942539 0.334096i \(-0.891569\pi\)
−0.942539 + 0.334096i \(0.891569\pi\)
\(164\) 7.63082 0.595867
\(165\) 0 0
\(166\) −5.06835 −0.393380
\(167\) −4.02327 −0.311330 −0.155665 0.987810i \(-0.549752\pi\)
−0.155665 + 0.987810i \(0.549752\pi\)
\(168\) 0 0
\(169\) −12.9646 −0.997274
\(170\) 6.70141 0.513975
\(171\) 0 0
\(172\) −11.0556 −0.842983
\(173\) 0.0249861 0.00189966 0.000949830 1.00000i \(-0.499698\pi\)
0.000949830 1.00000i \(0.499698\pi\)
\(174\) 0 0
\(175\) 0.811063 0.0613106
\(176\) −19.3345 −1.45739
\(177\) 0 0
\(178\) −3.66506 −0.274707
\(179\) 1.00959 0.0754606 0.0377303 0.999288i \(-0.487987\pi\)
0.0377303 + 0.999288i \(0.487987\pi\)
\(180\) 0 0
\(181\) 22.8161 1.69591 0.847955 0.530069i \(-0.177834\pi\)
0.847955 + 0.530069i \(0.177834\pi\)
\(182\) 0.107861 0.00799518
\(183\) 0 0
\(184\) 0.738503 0.0544432
\(185\) 5.96162 0.438307
\(186\) 0 0
\(187\) 13.7077 1.00241
\(188\) −14.3723 −1.04821
\(189\) 0 0
\(190\) 10.9015 0.790875
\(191\) −2.91312 −0.210786 −0.105393 0.994431i \(-0.533610\pi\)
−0.105393 + 0.994431i \(0.533610\pi\)
\(192\) 0 0
\(193\) −3.51894 −0.253299 −0.126650 0.991948i \(-0.540422\pi\)
−0.126650 + 0.991948i \(0.540422\pi\)
\(194\) 11.9607 0.858725
\(195\) 0 0
\(196\) −16.3000 −1.16429
\(197\) −14.7731 −1.05254 −0.526272 0.850317i \(-0.676410\pi\)
−0.526272 + 0.850317i \(0.676410\pi\)
\(198\) 0 0
\(199\) 23.7774 1.68553 0.842767 0.538278i \(-0.180925\pi\)
0.842767 + 0.538278i \(0.180925\pi\)
\(200\) 2.18149 0.154254
\(201\) 0 0
\(202\) 19.2782 1.35641
\(203\) 0.274571 0.0192711
\(204\) 0 0
\(205\) −4.63702 −0.323864
\(206\) 15.0899 1.05136
\(207\) 0 0
\(208\) −0.596213 −0.0413399
\(209\) 22.2989 1.54245
\(210\) 0 0
\(211\) 0.588832 0.0405369 0.0202684 0.999795i \(-0.493548\pi\)
0.0202684 + 0.999795i \(0.493548\pi\)
\(212\) −9.12688 −0.626837
\(213\) 0 0
\(214\) −6.59527 −0.450844
\(215\) 6.71817 0.458175
\(216\) 0 0
\(217\) 1.11395 0.0756201
\(218\) −19.9563 −1.35161
\(219\) 0 0
\(220\) −20.5567 −1.38593
\(221\) 0.422702 0.0284340
\(222\) 0 0
\(223\) −17.5937 −1.17816 −0.589079 0.808075i \(-0.700509\pi\)
−0.589079 + 0.808075i \(0.700509\pi\)
\(224\) −2.21992 −0.148325
\(225\) 0 0
\(226\) −40.4018 −2.68749
\(227\) −27.3659 −1.81634 −0.908169 0.418603i \(-0.862520\pi\)
−0.908169 + 0.418603i \(0.862520\pi\)
\(228\) 0 0
\(229\) −20.2749 −1.33980 −0.669900 0.742451i \(-0.733663\pi\)
−0.669900 + 0.742451i \(0.733663\pi\)
\(230\) −2.98470 −0.196805
\(231\) 0 0
\(232\) 0.738503 0.0484851
\(233\) 3.03886 0.199082 0.0995412 0.995033i \(-0.468263\pi\)
0.0995412 + 0.995033i \(0.468263\pi\)
\(234\) 0 0
\(235\) 8.73363 0.569719
\(236\) −6.86584 −0.446928
\(237\) 0 0
\(238\) 1.28635 0.0833820
\(239\) 1.74365 0.112787 0.0563936 0.998409i \(-0.482040\pi\)
0.0563936 + 0.998409i \(0.482040\pi\)
\(240\) 0 0
\(241\) 3.99474 0.257324 0.128662 0.991689i \(-0.458932\pi\)
0.128662 + 0.991689i \(0.458932\pi\)
\(242\) −54.8224 −3.52412
\(243\) 0 0
\(244\) −6.53685 −0.418479
\(245\) 9.90503 0.632809
\(246\) 0 0
\(247\) 0.687627 0.0437527
\(248\) 2.99616 0.190256
\(249\) 0 0
\(250\) −23.7401 −1.50146
\(251\) 7.41675 0.468141 0.234070 0.972220i \(-0.424795\pi\)
0.234070 + 0.972220i \(0.424795\pi\)
\(252\) 0 0
\(253\) −6.10520 −0.383831
\(254\) 26.3913 1.65594
\(255\) 0 0
\(256\) 8.93839 0.558649
\(257\) −19.0615 −1.18902 −0.594512 0.804087i \(-0.702655\pi\)
−0.594512 + 0.804087i \(0.702655\pi\)
\(258\) 0 0
\(259\) 1.14435 0.0711064
\(260\) −0.633902 −0.0393129
\(261\) 0 0
\(262\) 16.3128 1.00781
\(263\) −2.53582 −0.156365 −0.0781827 0.996939i \(-0.524912\pi\)
−0.0781827 + 0.996939i \(0.524912\pi\)
\(264\) 0 0
\(265\) 5.54613 0.340696
\(266\) 2.09257 0.128303
\(267\) 0 0
\(268\) 16.5414 1.01043
\(269\) 4.13080 0.251859 0.125930 0.992039i \(-0.459809\pi\)
0.125930 + 0.992039i \(0.459809\pi\)
\(270\) 0 0
\(271\) −4.10014 −0.249066 −0.124533 0.992215i \(-0.539743\pi\)
−0.124533 + 0.992215i \(0.539743\pi\)
\(272\) −7.11047 −0.431135
\(273\) 0 0
\(274\) −4.63700 −0.280131
\(275\) −18.0343 −1.08751
\(276\) 0 0
\(277\) 7.14419 0.429253 0.214626 0.976696i \(-0.431147\pi\)
0.214626 + 0.976696i \(0.431147\pi\)
\(278\) −28.6930 −1.72089
\(279\) 0 0
\(280\) −0.290046 −0.0173336
\(281\) 15.6506 0.933635 0.466817 0.884354i \(-0.345401\pi\)
0.466817 + 0.884354i \(0.345401\pi\)
\(282\) 0 0
\(283\) 8.24117 0.489887 0.244943 0.969537i \(-0.421231\pi\)
0.244943 + 0.969537i \(0.421231\pi\)
\(284\) 8.22168 0.487867
\(285\) 0 0
\(286\) −2.39833 −0.141816
\(287\) −0.890088 −0.0525403
\(288\) 0 0
\(289\) −11.9588 −0.703461
\(290\) −2.98470 −0.175268
\(291\) 0 0
\(292\) −28.7130 −1.68030
\(293\) −20.9302 −1.22275 −0.611377 0.791340i \(-0.709384\pi\)
−0.611377 + 0.791340i \(0.709384\pi\)
\(294\) 0 0
\(295\) 4.17216 0.242913
\(296\) 3.07791 0.178900
\(297\) 0 0
\(298\) 14.1348 0.818809
\(299\) −0.188265 −0.0108876
\(300\) 0 0
\(301\) 1.28957 0.0743296
\(302\) 22.1380 1.27390
\(303\) 0 0
\(304\) −11.5669 −0.663406
\(305\) 3.97225 0.227450
\(306\) 0 0
\(307\) 19.1315 1.09189 0.545947 0.837819i \(-0.316170\pi\)
0.545947 + 0.837819i \(0.316170\pi\)
\(308\) −3.94591 −0.224839
\(309\) 0 0
\(310\) −12.1091 −0.687753
\(311\) −30.8388 −1.74871 −0.874353 0.485291i \(-0.838714\pi\)
−0.874353 + 0.485291i \(0.838714\pi\)
\(312\) 0 0
\(313\) 0.287106 0.0162282 0.00811409 0.999967i \(-0.497417\pi\)
0.00811409 + 0.999967i \(0.497417\pi\)
\(314\) −35.5980 −2.00891
\(315\) 0 0
\(316\) −20.7582 −1.16774
\(317\) −4.79550 −0.269342 −0.134671 0.990890i \(-0.542998\pi\)
−0.134671 + 0.990890i \(0.542998\pi\)
\(318\) 0 0
\(319\) −6.10520 −0.341826
\(320\) 15.0716 0.842526
\(321\) 0 0
\(322\) −0.572921 −0.0319276
\(323\) 8.20068 0.456298
\(324\) 0 0
\(325\) −0.556121 −0.0308480
\(326\) 50.2185 2.78134
\(327\) 0 0
\(328\) −2.39404 −0.132189
\(329\) 1.67644 0.0924253
\(330\) 0 0
\(331\) −7.68460 −0.422384 −0.211192 0.977445i \(-0.567735\pi\)
−0.211192 + 0.977445i \(0.567735\pi\)
\(332\) 5.71766 0.313798
\(333\) 0 0
\(334\) 8.39498 0.459353
\(335\) −10.0517 −0.549183
\(336\) 0 0
\(337\) 0.712372 0.0388054 0.0194027 0.999812i \(-0.493824\pi\)
0.0194027 + 0.999812i \(0.493824\pi\)
\(338\) 27.0519 1.47143
\(339\) 0 0
\(340\) −7.55995 −0.409996
\(341\) −24.7692 −1.34133
\(342\) 0 0
\(343\) 3.82329 0.206438
\(344\) 3.46851 0.187009
\(345\) 0 0
\(346\) −0.0521362 −0.00280286
\(347\) 20.4402 1.09729 0.548645 0.836056i \(-0.315144\pi\)
0.548645 + 0.836056i \(0.315144\pi\)
\(348\) 0 0
\(349\) 3.84665 0.205907 0.102953 0.994686i \(-0.467171\pi\)
0.102953 + 0.994686i \(0.467171\pi\)
\(350\) −1.69237 −0.0904609
\(351\) 0 0
\(352\) 49.3608 2.63094
\(353\) −6.68615 −0.355868 −0.177934 0.984042i \(-0.556941\pi\)
−0.177934 + 0.984042i \(0.556941\pi\)
\(354\) 0 0
\(355\) −4.99607 −0.265164
\(356\) 4.13459 0.219133
\(357\) 0 0
\(358\) −2.10662 −0.111339
\(359\) 25.6460 1.35355 0.676773 0.736191i \(-0.263378\pi\)
0.676773 + 0.736191i \(0.263378\pi\)
\(360\) 0 0
\(361\) −5.65962 −0.297875
\(362\) −47.6083 −2.50223
\(363\) 0 0
\(364\) −0.121679 −0.00637772
\(365\) 17.4480 0.913272
\(366\) 0 0
\(367\) 12.3016 0.642141 0.321070 0.947055i \(-0.395957\pi\)
0.321070 + 0.947055i \(0.395957\pi\)
\(368\) 3.16689 0.165085
\(369\) 0 0
\(370\) −12.4396 −0.646702
\(371\) 1.06459 0.0552710
\(372\) 0 0
\(373\) −22.4264 −1.16120 −0.580598 0.814190i \(-0.697181\pi\)
−0.580598 + 0.814190i \(0.697181\pi\)
\(374\) −28.6026 −1.47901
\(375\) 0 0
\(376\) 4.50907 0.232537
\(377\) −0.188265 −0.00969613
\(378\) 0 0
\(379\) 33.7025 1.73118 0.865590 0.500754i \(-0.166944\pi\)
0.865590 + 0.500754i \(0.166944\pi\)
\(380\) −12.2981 −0.630878
\(381\) 0 0
\(382\) 6.07853 0.311004
\(383\) −21.0513 −1.07567 −0.537836 0.843050i \(-0.680758\pi\)
−0.537836 + 0.843050i \(0.680758\pi\)
\(384\) 0 0
\(385\) 2.39781 0.122204
\(386\) 7.34265 0.373731
\(387\) 0 0
\(388\) −13.4930 −0.685001
\(389\) 34.5723 1.75288 0.876442 0.481507i \(-0.159910\pi\)
0.876442 + 0.481507i \(0.159910\pi\)
\(390\) 0 0
\(391\) −2.24526 −0.113547
\(392\) 5.11385 0.258288
\(393\) 0 0
\(394\) 30.8257 1.55298
\(395\) 12.6141 0.634686
\(396\) 0 0
\(397\) 12.2736 0.615995 0.307997 0.951387i \(-0.400341\pi\)
0.307997 + 0.951387i \(0.400341\pi\)
\(398\) −49.6140 −2.48693
\(399\) 0 0
\(400\) 9.35476 0.467738
\(401\) 9.95916 0.497337 0.248668 0.968589i \(-0.420007\pi\)
0.248668 + 0.968589i \(0.420007\pi\)
\(402\) 0 0
\(403\) −0.763803 −0.0380478
\(404\) −21.7480 −1.08200
\(405\) 0 0
\(406\) −0.572921 −0.0284336
\(407\) −25.4451 −1.26127
\(408\) 0 0
\(409\) −28.5666 −1.41253 −0.706264 0.707949i \(-0.749621\pi\)
−0.706264 + 0.707949i \(0.749621\pi\)
\(410\) 9.67564 0.477846
\(411\) 0 0
\(412\) −17.0231 −0.838666
\(413\) 0.800858 0.0394076
\(414\) 0 0
\(415\) −3.47445 −0.170554
\(416\) 1.52213 0.0746285
\(417\) 0 0
\(418\) −46.5291 −2.27581
\(419\) −7.55392 −0.369033 −0.184517 0.982829i \(-0.559072\pi\)
−0.184517 + 0.982829i \(0.559072\pi\)
\(420\) 0 0
\(421\) −7.74446 −0.377442 −0.188721 0.982031i \(-0.560434\pi\)
−0.188721 + 0.982031i \(0.560434\pi\)
\(422\) −1.22866 −0.0598103
\(423\) 0 0
\(424\) 2.86340 0.139059
\(425\) −6.63233 −0.321715
\(426\) 0 0
\(427\) 0.762484 0.0368992
\(428\) 7.44021 0.359636
\(429\) 0 0
\(430\) −14.0182 −0.676016
\(431\) −38.6217 −1.86034 −0.930172 0.367124i \(-0.880342\pi\)
−0.930172 + 0.367124i \(0.880342\pi\)
\(432\) 0 0
\(433\) −5.41271 −0.260118 −0.130059 0.991506i \(-0.541517\pi\)
−0.130059 + 0.991506i \(0.541517\pi\)
\(434\) −2.32438 −0.111574
\(435\) 0 0
\(436\) 22.5130 1.07818
\(437\) −3.65245 −0.174720
\(438\) 0 0
\(439\) −12.2447 −0.584407 −0.292203 0.956356i \(-0.594388\pi\)
−0.292203 + 0.956356i \(0.594388\pi\)
\(440\) 6.44930 0.307458
\(441\) 0 0
\(442\) −0.882013 −0.0419531
\(443\) 11.2775 0.535808 0.267904 0.963446i \(-0.413669\pi\)
0.267904 + 0.963446i \(0.413669\pi\)
\(444\) 0 0
\(445\) −2.51247 −0.119102
\(446\) 36.7110 1.73832
\(447\) 0 0
\(448\) 2.89303 0.136683
\(449\) 20.3814 0.961858 0.480929 0.876760i \(-0.340300\pi\)
0.480929 + 0.876760i \(0.340300\pi\)
\(450\) 0 0
\(451\) 19.7915 0.931945
\(452\) 45.5778 2.14380
\(453\) 0 0
\(454\) 57.1019 2.67992
\(455\) 0.0739407 0.00346639
\(456\) 0 0
\(457\) −14.2683 −0.667442 −0.333721 0.942672i \(-0.608304\pi\)
−0.333721 + 0.942672i \(0.608304\pi\)
\(458\) 42.3057 1.97681
\(459\) 0 0
\(460\) 3.36708 0.156991
\(461\) 28.9224 1.34705 0.673525 0.739164i \(-0.264779\pi\)
0.673525 + 0.739164i \(0.264779\pi\)
\(462\) 0 0
\(463\) −10.8540 −0.504429 −0.252215 0.967671i \(-0.581159\pi\)
−0.252215 + 0.967671i \(0.581159\pi\)
\(464\) 3.16689 0.147019
\(465\) 0 0
\(466\) −6.34090 −0.293737
\(467\) 18.3096 0.847267 0.423633 0.905834i \(-0.360755\pi\)
0.423633 + 0.905834i \(0.360755\pi\)
\(468\) 0 0
\(469\) −1.92945 −0.0890937
\(470\) −18.2236 −0.840594
\(471\) 0 0
\(472\) 2.15404 0.0991476
\(473\) −28.6741 −1.31844
\(474\) 0 0
\(475\) −10.7891 −0.495037
\(476\) −1.45115 −0.0665134
\(477\) 0 0
\(478\) −3.63831 −0.166412
\(479\) −29.2790 −1.33779 −0.668896 0.743356i \(-0.733233\pi\)
−0.668896 + 0.743356i \(0.733233\pi\)
\(480\) 0 0
\(481\) −0.784645 −0.0357767
\(482\) −8.33544 −0.379669
\(483\) 0 0
\(484\) 61.8458 2.81117
\(485\) 8.19926 0.372309
\(486\) 0 0
\(487\) 2.51914 0.114153 0.0570766 0.998370i \(-0.481822\pi\)
0.0570766 + 0.998370i \(0.481822\pi\)
\(488\) 2.05082 0.0928365
\(489\) 0 0
\(490\) −20.6679 −0.933680
\(491\) 18.0791 0.815896 0.407948 0.913005i \(-0.366244\pi\)
0.407948 + 0.913005i \(0.366244\pi\)
\(492\) 0 0
\(493\) −2.24526 −0.101121
\(494\) −1.43481 −0.0645550
\(495\) 0 0
\(496\) 12.8483 0.576905
\(497\) −0.959008 −0.0430174
\(498\) 0 0
\(499\) 19.8082 0.886736 0.443368 0.896340i \(-0.353784\pi\)
0.443368 + 0.896340i \(0.353784\pi\)
\(500\) 26.7815 1.19770
\(501\) 0 0
\(502\) −15.4758 −0.690720
\(503\) −12.8927 −0.574855 −0.287428 0.957802i \(-0.592800\pi\)
−0.287428 + 0.957802i \(0.592800\pi\)
\(504\) 0 0
\(505\) 13.2156 0.588086
\(506\) 12.7391 0.566324
\(507\) 0 0
\(508\) −29.7723 −1.32093
\(509\) −8.87677 −0.393456 −0.196728 0.980458i \(-0.563032\pi\)
−0.196728 + 0.980458i \(0.563032\pi\)
\(510\) 0 0
\(511\) 3.34920 0.148160
\(512\) −30.2819 −1.33829
\(513\) 0 0
\(514\) 39.7739 1.75435
\(515\) 10.3444 0.455829
\(516\) 0 0
\(517\) −37.2764 −1.63942
\(518\) −2.38780 −0.104914
\(519\) 0 0
\(520\) 0.198876 0.00872127
\(521\) −4.07848 −0.178681 −0.0893407 0.996001i \(-0.528476\pi\)
−0.0893407 + 0.996001i \(0.528476\pi\)
\(522\) 0 0
\(523\) −41.7215 −1.82436 −0.912178 0.409795i \(-0.865600\pi\)
−0.912178 + 0.409795i \(0.865600\pi\)
\(524\) −18.4027 −0.803925
\(525\) 0 0
\(526\) 5.29126 0.230710
\(527\) −9.10916 −0.396801
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −11.5726 −0.502681
\(531\) 0 0
\(532\) −2.36065 −0.102347
\(533\) 0.610306 0.0264353
\(534\) 0 0
\(535\) −4.52119 −0.195468
\(536\) −5.18957 −0.224155
\(537\) 0 0
\(538\) −8.61935 −0.371607
\(539\) −42.2761 −1.82096
\(540\) 0 0
\(541\) −20.0737 −0.863038 −0.431519 0.902104i \(-0.642022\pi\)
−0.431519 + 0.902104i \(0.642022\pi\)
\(542\) 8.55538 0.367485
\(543\) 0 0
\(544\) 18.1530 0.778303
\(545\) −13.6804 −0.586006
\(546\) 0 0
\(547\) −13.2512 −0.566583 −0.283291 0.959034i \(-0.591426\pi\)
−0.283291 + 0.959034i \(0.591426\pi\)
\(548\) 5.23105 0.223459
\(549\) 0 0
\(550\) 37.6305 1.60457
\(551\) −3.65245 −0.155600
\(552\) 0 0
\(553\) 2.42132 0.102965
\(554\) −14.9071 −0.633342
\(555\) 0 0
\(556\) 32.3689 1.37275
\(557\) 29.8454 1.26459 0.632295 0.774727i \(-0.282113\pi\)
0.632295 + 0.774727i \(0.282113\pi\)
\(558\) 0 0
\(559\) −0.884218 −0.0373984
\(560\) −1.24379 −0.0525597
\(561\) 0 0
\(562\) −32.6566 −1.37753
\(563\) 6.32526 0.266578 0.133289 0.991077i \(-0.457446\pi\)
0.133289 + 0.991077i \(0.457446\pi\)
\(564\) 0 0
\(565\) −27.6962 −1.16519
\(566\) −17.1961 −0.722805
\(567\) 0 0
\(568\) −2.57941 −0.108230
\(569\) 13.4246 0.562788 0.281394 0.959592i \(-0.409203\pi\)
0.281394 + 0.959592i \(0.409203\pi\)
\(570\) 0 0
\(571\) −31.9335 −1.33638 −0.668188 0.743992i \(-0.732930\pi\)
−0.668188 + 0.743992i \(0.732930\pi\)
\(572\) 2.70559 0.113126
\(573\) 0 0
\(574\) 1.85726 0.0775207
\(575\) 2.95393 0.123187
\(576\) 0 0
\(577\) 12.4350 0.517677 0.258838 0.965921i \(-0.416660\pi\)
0.258838 + 0.965921i \(0.416660\pi\)
\(578\) 24.9534 1.03792
\(579\) 0 0
\(580\) 3.36708 0.139810
\(581\) −0.666930 −0.0276689
\(582\) 0 0
\(583\) −23.6717 −0.980382
\(584\) 9.00821 0.372762
\(585\) 0 0
\(586\) 43.6730 1.80412
\(587\) −24.0000 −0.990586 −0.495293 0.868726i \(-0.664939\pi\)
−0.495293 + 0.868726i \(0.664939\pi\)
\(588\) 0 0
\(589\) −14.8182 −0.610575
\(590\) −8.70566 −0.358406
\(591\) 0 0
\(592\) 13.1989 0.542470
\(593\) 19.4433 0.798441 0.399221 0.916855i \(-0.369281\pi\)
0.399221 + 0.916855i \(0.369281\pi\)
\(594\) 0 0
\(595\) 0.881821 0.0361511
\(596\) −15.9457 −0.653161
\(597\) 0 0
\(598\) 0.392834 0.0160642
\(599\) −13.7703 −0.562640 −0.281320 0.959614i \(-0.590772\pi\)
−0.281320 + 0.959614i \(0.590772\pi\)
\(600\) 0 0
\(601\) −1.23499 −0.0503764 −0.0251882 0.999683i \(-0.508018\pi\)
−0.0251882 + 0.999683i \(0.508018\pi\)
\(602\) −2.69082 −0.109670
\(603\) 0 0
\(604\) −24.9742 −1.01618
\(605\) −37.5818 −1.52792
\(606\) 0 0
\(607\) −29.5165 −1.19804 −0.599019 0.800735i \(-0.704443\pi\)
−0.599019 + 0.800735i \(0.704443\pi\)
\(608\) 29.5302 1.19761
\(609\) 0 0
\(610\) −8.28852 −0.335592
\(611\) −1.14949 −0.0465032
\(612\) 0 0
\(613\) 11.7152 0.473172 0.236586 0.971611i \(-0.423972\pi\)
0.236586 + 0.971611i \(0.423972\pi\)
\(614\) −39.9200 −1.61104
\(615\) 0 0
\(616\) 1.23796 0.0498788
\(617\) −29.9849 −1.20715 −0.603573 0.797308i \(-0.706257\pi\)
−0.603573 + 0.797308i \(0.706257\pi\)
\(618\) 0 0
\(619\) 7.17569 0.288415 0.144208 0.989547i \(-0.453937\pi\)
0.144208 + 0.989547i \(0.453937\pi\)
\(620\) 13.6605 0.548618
\(621\) 0 0
\(622\) 64.3484 2.58013
\(623\) −0.482275 −0.0193219
\(624\) 0 0
\(625\) −1.50465 −0.0601861
\(626\) −0.599077 −0.0239439
\(627\) 0 0
\(628\) 40.1586 1.60250
\(629\) −9.35771 −0.373116
\(630\) 0 0
\(631\) −22.8076 −0.907955 −0.453977 0.891013i \(-0.649995\pi\)
−0.453977 + 0.891013i \(0.649995\pi\)
\(632\) 6.51253 0.259055
\(633\) 0 0
\(634\) 10.0063 0.397402
\(635\) 18.0917 0.717948
\(636\) 0 0
\(637\) −1.30366 −0.0516529
\(638\) 12.7391 0.504348
\(639\) 0 0
\(640\) −8.31857 −0.328820
\(641\) −2.68538 −0.106066 −0.0530331 0.998593i \(-0.516889\pi\)
−0.0530331 + 0.998593i \(0.516889\pi\)
\(642\) 0 0
\(643\) 8.39727 0.331156 0.165578 0.986197i \(-0.447051\pi\)
0.165578 + 0.986197i \(0.447051\pi\)
\(644\) 0.646319 0.0254685
\(645\) 0 0
\(646\) −17.1116 −0.673246
\(647\) 13.2389 0.520476 0.260238 0.965545i \(-0.416199\pi\)
0.260238 + 0.965545i \(0.416199\pi\)
\(648\) 0 0
\(649\) −17.8074 −0.699002
\(650\) 1.16040 0.0455148
\(651\) 0 0
\(652\) −56.6521 −2.21867
\(653\) −30.6244 −1.19842 −0.599212 0.800591i \(-0.704519\pi\)
−0.599212 + 0.800591i \(0.704519\pi\)
\(654\) 0 0
\(655\) 11.1827 0.436946
\(656\) −10.2662 −0.400829
\(657\) 0 0
\(658\) −3.49808 −0.136369
\(659\) −33.9602 −1.32290 −0.661450 0.749989i \(-0.730059\pi\)
−0.661450 + 0.749989i \(0.730059\pi\)
\(660\) 0 0
\(661\) 16.1979 0.630027 0.315013 0.949087i \(-0.397991\pi\)
0.315013 + 0.949087i \(0.397991\pi\)
\(662\) 16.0347 0.623208
\(663\) 0 0
\(664\) −1.79382 −0.0696136
\(665\) 1.43449 0.0556273
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −9.47047 −0.366424
\(669\) 0 0
\(670\) 20.9739 0.810293
\(671\) −16.9542 −0.654508
\(672\) 0 0
\(673\) −38.7576 −1.49400 −0.746998 0.664827i \(-0.768505\pi\)
−0.746998 + 0.664827i \(0.768505\pi\)
\(674\) −1.48644 −0.0572555
\(675\) 0 0
\(676\) −30.5176 −1.17375
\(677\) −34.2894 −1.31785 −0.658925 0.752208i \(-0.728989\pi\)
−0.658925 + 0.752208i \(0.728989\pi\)
\(678\) 0 0
\(679\) 1.57387 0.0603996
\(680\) 2.37180 0.0909544
\(681\) 0 0
\(682\) 51.6836 1.97907
\(683\) −7.15688 −0.273851 −0.136925 0.990581i \(-0.543722\pi\)
−0.136925 + 0.990581i \(0.543722\pi\)
\(684\) 0 0
\(685\) −3.17875 −0.121454
\(686\) −7.97770 −0.304590
\(687\) 0 0
\(688\) 14.8738 0.567060
\(689\) −0.729959 −0.0278092
\(690\) 0 0
\(691\) −27.4957 −1.04599 −0.522993 0.852337i \(-0.675184\pi\)
−0.522993 + 0.852337i \(0.675184\pi\)
\(692\) 0.0588155 0.00223583
\(693\) 0 0
\(694\) −42.6507 −1.61900
\(695\) −19.6696 −0.746111
\(696\) 0 0
\(697\) 7.27854 0.275694
\(698\) −8.02645 −0.303806
\(699\) 0 0
\(700\) 1.90918 0.0721603
\(701\) 13.8109 0.521630 0.260815 0.965389i \(-0.416009\pi\)
0.260815 + 0.965389i \(0.416009\pi\)
\(702\) 0 0
\(703\) −15.2226 −0.574130
\(704\) −64.3277 −2.42444
\(705\) 0 0
\(706\) 13.9514 0.525067
\(707\) 2.53677 0.0954049
\(708\) 0 0
\(709\) −0.924764 −0.0347303 −0.0173651 0.999849i \(-0.505528\pi\)
−0.0173651 + 0.999849i \(0.505528\pi\)
\(710\) 10.4248 0.391237
\(711\) 0 0
\(712\) −1.29716 −0.0486130
\(713\) 4.05707 0.151938
\(714\) 0 0
\(715\) −1.64410 −0.0614860
\(716\) 2.37651 0.0888143
\(717\) 0 0
\(718\) −53.5132 −1.99709
\(719\) −20.1522 −0.751552 −0.375776 0.926711i \(-0.622624\pi\)
−0.375776 + 0.926711i \(0.622624\pi\)
\(720\) 0 0
\(721\) 1.98564 0.0739489
\(722\) 11.8094 0.439500
\(723\) 0 0
\(724\) 53.7075 1.99602
\(725\) 2.95393 0.109706
\(726\) 0 0
\(727\) 2.08270 0.0772429 0.0386215 0.999254i \(-0.487703\pi\)
0.0386215 + 0.999254i \(0.487703\pi\)
\(728\) 0.0381747 0.00141485
\(729\) 0 0
\(730\) −36.4072 −1.34749
\(731\) −10.5452 −0.390030
\(732\) 0 0
\(733\) 8.15634 0.301261 0.150631 0.988590i \(-0.451870\pi\)
0.150631 + 0.988590i \(0.451870\pi\)
\(734\) −25.6687 −0.947449
\(735\) 0 0
\(736\) −8.08505 −0.298019
\(737\) 42.9021 1.58032
\(738\) 0 0
\(739\) −25.8699 −0.951638 −0.475819 0.879543i \(-0.657848\pi\)
−0.475819 + 0.879543i \(0.657848\pi\)
\(740\) 14.0332 0.515871
\(741\) 0 0
\(742\) −2.22139 −0.0815497
\(743\) −34.9391 −1.28179 −0.640896 0.767628i \(-0.721437\pi\)
−0.640896 + 0.767628i \(0.721437\pi\)
\(744\) 0 0
\(745\) 9.68971 0.355003
\(746\) 46.7951 1.71329
\(747\) 0 0
\(748\) 32.2670 1.17980
\(749\) −0.867854 −0.0317107
\(750\) 0 0
\(751\) 10.4297 0.380585 0.190293 0.981727i \(-0.439056\pi\)
0.190293 + 0.981727i \(0.439056\pi\)
\(752\) 19.3360 0.705112
\(753\) 0 0
\(754\) 0.392834 0.0143062
\(755\) 15.1760 0.552313
\(756\) 0 0
\(757\) 46.0068 1.67215 0.836073 0.548619i \(-0.184846\pi\)
0.836073 + 0.548619i \(0.184846\pi\)
\(758\) −70.3238 −2.55428
\(759\) 0 0
\(760\) 3.85831 0.139956
\(761\) 33.1684 1.20235 0.601177 0.799116i \(-0.294699\pi\)
0.601177 + 0.799116i \(0.294699\pi\)
\(762\) 0 0
\(763\) −2.62600 −0.0950675
\(764\) −6.85726 −0.248087
\(765\) 0 0
\(766\) 43.9258 1.58710
\(767\) −0.549123 −0.0198277
\(768\) 0 0
\(769\) −23.9544 −0.863816 −0.431908 0.901918i \(-0.642159\pi\)
−0.431908 + 0.901918i \(0.642159\pi\)
\(770\) −5.00328 −0.180306
\(771\) 0 0
\(772\) −8.28333 −0.298124
\(773\) 37.4046 1.34535 0.672674 0.739939i \(-0.265146\pi\)
0.672674 + 0.739939i \(0.265146\pi\)
\(774\) 0 0
\(775\) 11.9843 0.430489
\(776\) 4.23318 0.151962
\(777\) 0 0
\(778\) −72.1387 −2.58630
\(779\) 11.8403 0.424223
\(780\) 0 0
\(781\) 21.3240 0.763031
\(782\) 4.68496 0.167534
\(783\) 0 0
\(784\) 21.9295 0.783195
\(785\) −24.4032 −0.870986
\(786\) 0 0
\(787\) 4.05977 0.144715 0.0723576 0.997379i \(-0.476948\pi\)
0.0723576 + 0.997379i \(0.476948\pi\)
\(788\) −34.7749 −1.23880
\(789\) 0 0
\(790\) −26.3208 −0.936450
\(791\) −5.31637 −0.189028
\(792\) 0 0
\(793\) −0.522811 −0.0185656
\(794\) −25.6102 −0.908871
\(795\) 0 0
\(796\) 55.9702 1.98381
\(797\) 1.56174 0.0553196 0.0276598 0.999617i \(-0.491194\pi\)
0.0276598 + 0.999617i \(0.491194\pi\)
\(798\) 0 0
\(799\) −13.7088 −0.484983
\(800\) −23.8827 −0.844380
\(801\) 0 0
\(802\) −20.7808 −0.733797
\(803\) −74.4708 −2.62802
\(804\) 0 0
\(805\) −0.392749 −0.0138426
\(806\) 1.59376 0.0561377
\(807\) 0 0
\(808\) 6.82305 0.240034
\(809\) 9.09173 0.319648 0.159824 0.987146i \(-0.448907\pi\)
0.159824 + 0.987146i \(0.448907\pi\)
\(810\) 0 0
\(811\) 6.07851 0.213445 0.106723 0.994289i \(-0.465964\pi\)
0.106723 + 0.994289i \(0.465964\pi\)
\(812\) 0.646319 0.0226814
\(813\) 0 0
\(814\) 53.0939 1.86094
\(815\) 34.4257 1.20588
\(816\) 0 0
\(817\) −17.1544 −0.600155
\(818\) 59.6073 2.08412
\(819\) 0 0
\(820\) −10.9152 −0.381175
\(821\) −29.7440 −1.03807 −0.519036 0.854752i \(-0.673709\pi\)
−0.519036 + 0.854752i \(0.673709\pi\)
\(822\) 0 0
\(823\) 12.8740 0.448758 0.224379 0.974502i \(-0.427965\pi\)
0.224379 + 0.974502i \(0.427965\pi\)
\(824\) 5.34069 0.186052
\(825\) 0 0
\(826\) −1.67107 −0.0581441
\(827\) −36.2049 −1.25897 −0.629484 0.777014i \(-0.716734\pi\)
−0.629484 + 0.777014i \(0.716734\pi\)
\(828\) 0 0
\(829\) −31.7283 −1.10197 −0.550985 0.834515i \(-0.685748\pi\)
−0.550985 + 0.834515i \(0.685748\pi\)
\(830\) 7.24981 0.251645
\(831\) 0 0
\(832\) −1.98366 −0.0687710
\(833\) −15.5475 −0.538690
\(834\) 0 0
\(835\) 5.75492 0.199157
\(836\) 52.4900 1.81541
\(837\) 0 0
\(838\) 15.7621 0.544491
\(839\) 29.9699 1.03468 0.517338 0.855781i \(-0.326923\pi\)
0.517338 + 0.855781i \(0.326923\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 16.1596 0.556898
\(843\) 0 0
\(844\) 1.38607 0.0477104
\(845\) 18.5446 0.637954
\(846\) 0 0
\(847\) −7.21393 −0.247874
\(848\) 12.2790 0.421662
\(849\) 0 0
\(850\) 13.8391 0.474676
\(851\) 4.16777 0.142869
\(852\) 0 0
\(853\) −43.0788 −1.47499 −0.737495 0.675352i \(-0.763992\pi\)
−0.737495 + 0.675352i \(0.763992\pi\)
\(854\) −1.59100 −0.0544430
\(855\) 0 0
\(856\) −2.33424 −0.0797825
\(857\) 56.4937 1.92979 0.964895 0.262637i \(-0.0845921\pi\)
0.964895 + 0.262637i \(0.0845921\pi\)
\(858\) 0 0
\(859\) 13.8657 0.473093 0.236547 0.971620i \(-0.423984\pi\)
0.236547 + 0.971620i \(0.423984\pi\)
\(860\) 15.8141 0.539255
\(861\) 0 0
\(862\) 80.5884 2.74485
\(863\) −12.0348 −0.409669 −0.204835 0.978797i \(-0.565666\pi\)
−0.204835 + 0.978797i \(0.565666\pi\)
\(864\) 0 0
\(865\) −0.0357404 −0.00121521
\(866\) 11.2942 0.383792
\(867\) 0 0
\(868\) 2.62216 0.0890020
\(869\) −53.8391 −1.82636
\(870\) 0 0
\(871\) 1.32296 0.0448269
\(872\) −7.06305 −0.239185
\(873\) 0 0
\(874\) 7.62122 0.257792
\(875\) −3.12389 −0.105607
\(876\) 0 0
\(877\) −26.0150 −0.878463 −0.439232 0.898374i \(-0.644749\pi\)
−0.439232 + 0.898374i \(0.644749\pi\)
\(878\) 25.5498 0.862265
\(879\) 0 0
\(880\) 27.6562 0.932291
\(881\) −18.7821 −0.632785 −0.316392 0.948628i \(-0.602472\pi\)
−0.316392 + 0.948628i \(0.602472\pi\)
\(882\) 0 0
\(883\) −8.62443 −0.290235 −0.145118 0.989414i \(-0.546356\pi\)
−0.145118 + 0.989414i \(0.546356\pi\)
\(884\) 0.995010 0.0334658
\(885\) 0 0
\(886\) −23.5316 −0.790560
\(887\) −39.3782 −1.32219 −0.661095 0.750302i \(-0.729908\pi\)
−0.661095 + 0.750302i \(0.729908\pi\)
\(888\) 0 0
\(889\) 3.47275 0.116472
\(890\) 5.24253 0.175730
\(891\) 0 0
\(892\) −41.4142 −1.38665
\(893\) −22.3007 −0.746265
\(894\) 0 0
\(895\) −1.44413 −0.0482720
\(896\) −1.59677 −0.0533444
\(897\) 0 0
\(898\) −42.5280 −1.41918
\(899\) 4.05707 0.135311
\(900\) 0 0
\(901\) −8.70553 −0.290023
\(902\) −41.2971 −1.37504
\(903\) 0 0
\(904\) −14.2992 −0.475586
\(905\) −32.6364 −1.08487
\(906\) 0 0
\(907\) 8.33324 0.276701 0.138350 0.990383i \(-0.455820\pi\)
0.138350 + 0.990383i \(0.455820\pi\)
\(908\) −64.4173 −2.13776
\(909\) 0 0
\(910\) −0.154285 −0.00511450
\(911\) −40.2510 −1.33358 −0.666788 0.745247i \(-0.732331\pi\)
−0.666788 + 0.745247i \(0.732331\pi\)
\(912\) 0 0
\(913\) 14.8295 0.490784
\(914\) 29.7723 0.984780
\(915\) 0 0
\(916\) −47.7255 −1.57690
\(917\) 2.14656 0.0708856
\(918\) 0 0
\(919\) 34.7016 1.14470 0.572351 0.820009i \(-0.306032\pi\)
0.572351 + 0.820009i \(0.306032\pi\)
\(920\) −1.05636 −0.0348272
\(921\) 0 0
\(922\) −60.3497 −1.98751
\(923\) 0.657562 0.0216439
\(924\) 0 0
\(925\) 12.3113 0.404793
\(926\) 22.6481 0.744262
\(927\) 0 0
\(928\) −8.08505 −0.265405
\(929\) −25.0656 −0.822376 −0.411188 0.911551i \(-0.634886\pi\)
−0.411188 + 0.911551i \(0.634886\pi\)
\(930\) 0 0
\(931\) −25.2918 −0.828905
\(932\) 7.15325 0.234313
\(933\) 0 0
\(934\) −38.2049 −1.25010
\(935\) −19.6077 −0.641239
\(936\) 0 0
\(937\) −48.2923 −1.57764 −0.788821 0.614623i \(-0.789308\pi\)
−0.788821 + 0.614623i \(0.789308\pi\)
\(938\) 4.02600 0.131454
\(939\) 0 0
\(940\) 20.5583 0.670538
\(941\) −16.0613 −0.523582 −0.261791 0.965125i \(-0.584313\pi\)
−0.261791 + 0.965125i \(0.584313\pi\)
\(942\) 0 0
\(943\) −3.24174 −0.105566
\(944\) 9.23705 0.300640
\(945\) 0 0
\(946\) 59.8316 1.94529
\(947\) −36.9475 −1.20063 −0.600316 0.799763i \(-0.704959\pi\)
−0.600316 + 0.799763i \(0.704959\pi\)
\(948\) 0 0
\(949\) −2.29644 −0.0745456
\(950\) 22.5126 0.730404
\(951\) 0 0
\(952\) 0.455274 0.0147555
\(953\) −31.1650 −1.00953 −0.504766 0.863256i \(-0.668421\pi\)
−0.504766 + 0.863256i \(0.668421\pi\)
\(954\) 0 0
\(955\) 4.16695 0.134839
\(956\) 4.10442 0.132746
\(957\) 0 0
\(958\) 61.0938 1.97385
\(959\) −0.610170 −0.0197034
\(960\) 0 0
\(961\) −14.5402 −0.469038
\(962\) 1.63724 0.0527869
\(963\) 0 0
\(964\) 9.40331 0.302860
\(965\) 5.03353 0.162035
\(966\) 0 0
\(967\) 57.2912 1.84236 0.921181 0.389134i \(-0.127226\pi\)
0.921181 + 0.389134i \(0.127226\pi\)
\(968\) −19.4030 −0.623637
\(969\) 0 0
\(970\) −17.1086 −0.549325
\(971\) 36.2034 1.16182 0.580912 0.813966i \(-0.302696\pi\)
0.580912 + 0.813966i \(0.302696\pi\)
\(972\) 0 0
\(973\) −3.77563 −0.121041
\(974\) −5.25646 −0.168428
\(975\) 0 0
\(976\) 8.79445 0.281503
\(977\) 36.0090 1.15203 0.576015 0.817439i \(-0.304607\pi\)
0.576015 + 0.817439i \(0.304607\pi\)
\(978\) 0 0
\(979\) 10.7236 0.342727
\(980\) 23.3157 0.744793
\(981\) 0 0
\(982\) −37.7239 −1.20382
\(983\) −14.3777 −0.458576 −0.229288 0.973359i \(-0.573640\pi\)
−0.229288 + 0.973359i \(0.573640\pi\)
\(984\) 0 0
\(985\) 21.1316 0.673310
\(986\) 4.68496 0.149200
\(987\) 0 0
\(988\) 1.61862 0.0514953
\(989\) 4.69667 0.149346
\(990\) 0 0
\(991\) 5.18303 0.164644 0.0823221 0.996606i \(-0.473766\pi\)
0.0823221 + 0.996606i \(0.473766\pi\)
\(992\) −32.8016 −1.04145
\(993\) 0 0
\(994\) 2.00107 0.0634702
\(995\) −34.0114 −1.07823
\(996\) 0 0
\(997\) −50.0974 −1.58660 −0.793301 0.608830i \(-0.791639\pi\)
−0.793301 + 0.608830i \(0.791639\pi\)
\(998\) −41.3319 −1.30834
\(999\) 0 0
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 6003.2.a.u.1.3 yes 22
3.2 odd 2 6003.2.a.t.1.20 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6003.2.a.t.1.20 22 3.2 odd 2
6003.2.a.u.1.3 yes 22 1.1 even 1 trivial