Properties

Label 8032.2.a.j.1.16
Level $8032$
Weight $2$
Character 8032.1
Self dual yes
Analytic conductor $64.136$
Analytic rank $0$
Dimension $30$
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] = [8032,2,Mod(1,8032)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8032, 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("8032.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8032 = 2^{5} \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8032.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: \(64.1358429035\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 8032.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.692263 q^{3} +3.18782 q^{5} -3.79509 q^{7} -2.52077 q^{9} +O(q^{10})\) \(q+0.692263 q^{3} +3.18782 q^{5} -3.79509 q^{7} -2.52077 q^{9} +2.76100 q^{11} +2.89831 q^{13} +2.20681 q^{15} -7.05358 q^{17} +5.44520 q^{19} -2.62720 q^{21} +5.85093 q^{23} +5.16220 q^{25} -3.82182 q^{27} -0.0264724 q^{29} +1.32998 q^{31} +1.91134 q^{33} -12.0981 q^{35} +9.73112 q^{37} +2.00639 q^{39} +1.29149 q^{41} -8.70603 q^{43} -8.03577 q^{45} +8.73457 q^{47} +7.40273 q^{49} -4.88293 q^{51} -6.78784 q^{53} +8.80157 q^{55} +3.76951 q^{57} +2.43996 q^{59} -10.8180 q^{61} +9.56656 q^{63} +9.23928 q^{65} +8.31102 q^{67} +4.05038 q^{69} +3.40977 q^{71} -1.12050 q^{73} +3.57360 q^{75} -10.4782 q^{77} +1.98388 q^{79} +4.91661 q^{81} +7.57987 q^{83} -22.4855 q^{85} -0.0183258 q^{87} -3.29651 q^{89} -10.9993 q^{91} +0.920692 q^{93} +17.3583 q^{95} +18.3429 q^{97} -6.95985 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 9 q^{3} + 5 q^{7} + 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 9 q^{3} + 5 q^{7} + 35 q^{9} + 31 q^{11} + 5 q^{13} + 8 q^{15} - q^{17} + 29 q^{19} + 6 q^{21} + 27 q^{23} + 34 q^{25} + 36 q^{27} + q^{29} - 9 q^{31} - 8 q^{33} + 51 q^{35} + 5 q^{37} - 8 q^{39} - 3 q^{41} + 43 q^{43} + 42 q^{47} + 41 q^{49} + 54 q^{51} - 11 q^{53} - 10 q^{55} + 2 q^{57} + 49 q^{59} + 21 q^{61} + 15 q^{63} - 14 q^{65} + 68 q^{67} - 10 q^{69} + 44 q^{71} + 25 q^{73} + 51 q^{75} - 20 q^{77} - 49 q^{79} + 6 q^{81} + 88 q^{83} - 5 q^{85} + 16 q^{87} - 16 q^{89} + 46 q^{91} - 4 q^{93} + 28 q^{95} - 4 q^{97} + 71 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.692263 0.399678 0.199839 0.979829i \(-0.435958\pi\)
0.199839 + 0.979829i \(0.435958\pi\)
\(4\) 0 0
\(5\) 3.18782 1.42564 0.712818 0.701349i \(-0.247418\pi\)
0.712818 + 0.701349i \(0.247418\pi\)
\(6\) 0 0
\(7\) −3.79509 −1.43441 −0.717205 0.696862i \(-0.754579\pi\)
−0.717205 + 0.696862i \(0.754579\pi\)
\(8\) 0 0
\(9\) −2.52077 −0.840257
\(10\) 0 0
\(11\) 2.76100 0.832473 0.416236 0.909256i \(-0.363349\pi\)
0.416236 + 0.909256i \(0.363349\pi\)
\(12\) 0 0
\(13\) 2.89831 0.803846 0.401923 0.915674i \(-0.368342\pi\)
0.401923 + 0.915674i \(0.368342\pi\)
\(14\) 0 0
\(15\) 2.20681 0.569796
\(16\) 0 0
\(17\) −7.05358 −1.71074 −0.855372 0.518014i \(-0.826672\pi\)
−0.855372 + 0.518014i \(0.826672\pi\)
\(18\) 0 0
\(19\) 5.44520 1.24921 0.624607 0.780939i \(-0.285259\pi\)
0.624607 + 0.780939i \(0.285259\pi\)
\(20\) 0 0
\(21\) −2.62720 −0.573302
\(22\) 0 0
\(23\) 5.85093 1.22000 0.610001 0.792401i \(-0.291169\pi\)
0.610001 + 0.792401i \(0.291169\pi\)
\(24\) 0 0
\(25\) 5.16220 1.03244
\(26\) 0 0
\(27\) −3.82182 −0.735511
\(28\) 0 0
\(29\) −0.0264724 −0.00491579 −0.00245790 0.999997i \(-0.500782\pi\)
−0.00245790 + 0.999997i \(0.500782\pi\)
\(30\) 0 0
\(31\) 1.32998 0.238871 0.119435 0.992842i \(-0.461892\pi\)
0.119435 + 0.992842i \(0.461892\pi\)
\(32\) 0 0
\(33\) 1.91134 0.332721
\(34\) 0 0
\(35\) −12.0981 −2.04495
\(36\) 0 0
\(37\) 9.73112 1.59979 0.799894 0.600142i \(-0.204889\pi\)
0.799894 + 0.600142i \(0.204889\pi\)
\(38\) 0 0
\(39\) 2.00639 0.321279
\(40\) 0 0
\(41\) 1.29149 0.201696 0.100848 0.994902i \(-0.467844\pi\)
0.100848 + 0.994902i \(0.467844\pi\)
\(42\) 0 0
\(43\) −8.70603 −1.32766 −0.663829 0.747885i \(-0.731070\pi\)
−0.663829 + 0.747885i \(0.731070\pi\)
\(44\) 0 0
\(45\) −8.03577 −1.19790
\(46\) 0 0
\(47\) 8.73457 1.27407 0.637034 0.770836i \(-0.280161\pi\)
0.637034 + 0.770836i \(0.280161\pi\)
\(48\) 0 0
\(49\) 7.40273 1.05753
\(50\) 0 0
\(51\) −4.88293 −0.683747
\(52\) 0 0
\(53\) −6.78784 −0.932381 −0.466190 0.884684i \(-0.654374\pi\)
−0.466190 + 0.884684i \(0.654374\pi\)
\(54\) 0 0
\(55\) 8.80157 1.18680
\(56\) 0 0
\(57\) 3.76951 0.499283
\(58\) 0 0
\(59\) 2.43996 0.317656 0.158828 0.987306i \(-0.449228\pi\)
0.158828 + 0.987306i \(0.449228\pi\)
\(60\) 0 0
\(61\) −10.8180 −1.38511 −0.692553 0.721367i \(-0.743514\pi\)
−0.692553 + 0.721367i \(0.743514\pi\)
\(62\) 0 0
\(63\) 9.56656 1.20527
\(64\) 0 0
\(65\) 9.23928 1.14599
\(66\) 0 0
\(67\) 8.31102 1.01535 0.507676 0.861548i \(-0.330505\pi\)
0.507676 + 0.861548i \(0.330505\pi\)
\(68\) 0 0
\(69\) 4.05038 0.487608
\(70\) 0 0
\(71\) 3.40977 0.404665 0.202332 0.979317i \(-0.435148\pi\)
0.202332 + 0.979317i \(0.435148\pi\)
\(72\) 0 0
\(73\) −1.12050 −0.131145 −0.0655723 0.997848i \(-0.520887\pi\)
−0.0655723 + 0.997848i \(0.520887\pi\)
\(74\) 0 0
\(75\) 3.57360 0.412644
\(76\) 0 0
\(77\) −10.4782 −1.19411
\(78\) 0 0
\(79\) 1.98388 0.223204 0.111602 0.993753i \(-0.464402\pi\)
0.111602 + 0.993753i \(0.464402\pi\)
\(80\) 0 0
\(81\) 4.91661 0.546290
\(82\) 0 0
\(83\) 7.57987 0.831999 0.415999 0.909365i \(-0.363432\pi\)
0.415999 + 0.909365i \(0.363432\pi\)
\(84\) 0 0
\(85\) −22.4855 −2.43890
\(86\) 0 0
\(87\) −0.0183258 −0.00196474
\(88\) 0 0
\(89\) −3.29651 −0.349429 −0.174715 0.984619i \(-0.555900\pi\)
−0.174715 + 0.984619i \(0.555900\pi\)
\(90\) 0 0
\(91\) −10.9993 −1.15304
\(92\) 0 0
\(93\) 0.920692 0.0954714
\(94\) 0 0
\(95\) 17.3583 1.78092
\(96\) 0 0
\(97\) 18.3429 1.86244 0.931221 0.364454i \(-0.118745\pi\)
0.931221 + 0.364454i \(0.118745\pi\)
\(98\) 0 0
\(99\) −6.95985 −0.699491
\(100\) 0 0
\(101\) −2.41903 −0.240702 −0.120351 0.992731i \(-0.538402\pi\)
−0.120351 + 0.992731i \(0.538402\pi\)
\(102\) 0 0
\(103\) −12.9147 −1.27252 −0.636261 0.771474i \(-0.719520\pi\)
−0.636261 + 0.771474i \(0.719520\pi\)
\(104\) 0 0
\(105\) −8.37505 −0.817321
\(106\) 0 0
\(107\) 15.1989 1.46934 0.734669 0.678426i \(-0.237338\pi\)
0.734669 + 0.678426i \(0.237338\pi\)
\(108\) 0 0
\(109\) −11.8621 −1.13618 −0.568090 0.822966i \(-0.692318\pi\)
−0.568090 + 0.822966i \(0.692318\pi\)
\(110\) 0 0
\(111\) 6.73650 0.639400
\(112\) 0 0
\(113\) −9.17337 −0.862958 −0.431479 0.902123i \(-0.642008\pi\)
−0.431479 + 0.902123i \(0.642008\pi\)
\(114\) 0 0
\(115\) 18.6517 1.73928
\(116\) 0 0
\(117\) −7.30597 −0.675437
\(118\) 0 0
\(119\) 26.7690 2.45391
\(120\) 0 0
\(121\) −3.37688 −0.306989
\(122\) 0 0
\(123\) 0.894048 0.0806136
\(124\) 0 0
\(125\) 0.517064 0.0462476
\(126\) 0 0
\(127\) −7.59719 −0.674141 −0.337071 0.941479i \(-0.609436\pi\)
−0.337071 + 0.941479i \(0.609436\pi\)
\(128\) 0 0
\(129\) −6.02686 −0.530636
\(130\) 0 0
\(131\) 11.2028 0.978795 0.489397 0.872061i \(-0.337217\pi\)
0.489397 + 0.872061i \(0.337217\pi\)
\(132\) 0 0
\(133\) −20.6650 −1.79189
\(134\) 0 0
\(135\) −12.1833 −1.04857
\(136\) 0 0
\(137\) 5.23911 0.447608 0.223804 0.974634i \(-0.428152\pi\)
0.223804 + 0.974634i \(0.428152\pi\)
\(138\) 0 0
\(139\) 5.98594 0.507720 0.253860 0.967241i \(-0.418300\pi\)
0.253860 + 0.967241i \(0.418300\pi\)
\(140\) 0 0
\(141\) 6.04661 0.509217
\(142\) 0 0
\(143\) 8.00222 0.669179
\(144\) 0 0
\(145\) −0.0843891 −0.00700814
\(146\) 0 0
\(147\) 5.12463 0.422673
\(148\) 0 0
\(149\) 10.2512 0.839809 0.419905 0.907568i \(-0.362064\pi\)
0.419905 + 0.907568i \(0.362064\pi\)
\(150\) 0 0
\(151\) 10.7923 0.878268 0.439134 0.898422i \(-0.355285\pi\)
0.439134 + 0.898422i \(0.355285\pi\)
\(152\) 0 0
\(153\) 17.7805 1.43747
\(154\) 0 0
\(155\) 4.23972 0.340543
\(156\) 0 0
\(157\) −3.40554 −0.271792 −0.135896 0.990723i \(-0.543391\pi\)
−0.135896 + 0.990723i \(0.543391\pi\)
\(158\) 0 0
\(159\) −4.69897 −0.372652
\(160\) 0 0
\(161\) −22.2048 −1.74998
\(162\) 0 0
\(163\) −0.986389 −0.0772600 −0.0386300 0.999254i \(-0.512299\pi\)
−0.0386300 + 0.999254i \(0.512299\pi\)
\(164\) 0 0
\(165\) 6.09300 0.474339
\(166\) 0 0
\(167\) 15.0960 1.16816 0.584081 0.811695i \(-0.301455\pi\)
0.584081 + 0.811695i \(0.301455\pi\)
\(168\) 0 0
\(169\) −4.59982 −0.353832
\(170\) 0 0
\(171\) −13.7261 −1.04966
\(172\) 0 0
\(173\) 15.6440 1.18939 0.594694 0.803952i \(-0.297273\pi\)
0.594694 + 0.803952i \(0.297273\pi\)
\(174\) 0 0
\(175\) −19.5910 −1.48094
\(176\) 0 0
\(177\) 1.68910 0.126960
\(178\) 0 0
\(179\) 11.3507 0.848393 0.424196 0.905570i \(-0.360557\pi\)
0.424196 + 0.905570i \(0.360557\pi\)
\(180\) 0 0
\(181\) 9.10012 0.676407 0.338203 0.941073i \(-0.390181\pi\)
0.338203 + 0.941073i \(0.390181\pi\)
\(182\) 0 0
\(183\) −7.48892 −0.553597
\(184\) 0 0
\(185\) 31.0211 2.28072
\(186\) 0 0
\(187\) −19.4749 −1.42415
\(188\) 0 0
\(189\) 14.5042 1.05502
\(190\) 0 0
\(191\) 10.3414 0.748280 0.374140 0.927372i \(-0.377938\pi\)
0.374140 + 0.927372i \(0.377938\pi\)
\(192\) 0 0
\(193\) 21.2006 1.52605 0.763026 0.646367i \(-0.223713\pi\)
0.763026 + 0.646367i \(0.223713\pi\)
\(194\) 0 0
\(195\) 6.39601 0.458028
\(196\) 0 0
\(197\) 22.7730 1.62251 0.811254 0.584693i \(-0.198785\pi\)
0.811254 + 0.584693i \(0.198785\pi\)
\(198\) 0 0
\(199\) 23.6343 1.67539 0.837695 0.546138i \(-0.183903\pi\)
0.837695 + 0.546138i \(0.183903\pi\)
\(200\) 0 0
\(201\) 5.75341 0.405814
\(202\) 0 0
\(203\) 0.100465 0.00705127
\(204\) 0 0
\(205\) 4.11703 0.287546
\(206\) 0 0
\(207\) −14.7489 −1.02512
\(208\) 0 0
\(209\) 15.0342 1.03994
\(210\) 0 0
\(211\) 18.0811 1.24476 0.622379 0.782716i \(-0.286166\pi\)
0.622379 + 0.782716i \(0.286166\pi\)
\(212\) 0 0
\(213\) 2.36045 0.161736
\(214\) 0 0
\(215\) −27.7533 −1.89276
\(216\) 0 0
\(217\) −5.04738 −0.342639
\(218\) 0 0
\(219\) −0.775681 −0.0524156
\(220\) 0 0
\(221\) −20.4434 −1.37517
\(222\) 0 0
\(223\) 13.4484 0.900574 0.450287 0.892884i \(-0.351322\pi\)
0.450287 + 0.892884i \(0.351322\pi\)
\(224\) 0 0
\(225\) −13.0127 −0.867515
\(226\) 0 0
\(227\) −17.7353 −1.17713 −0.588566 0.808449i \(-0.700307\pi\)
−0.588566 + 0.808449i \(0.700307\pi\)
\(228\) 0 0
\(229\) 23.5514 1.55632 0.778160 0.628067i \(-0.216153\pi\)
0.778160 + 0.628067i \(0.216153\pi\)
\(230\) 0 0
\(231\) −7.25370 −0.477259
\(232\) 0 0
\(233\) −16.0903 −1.05411 −0.527054 0.849832i \(-0.676703\pi\)
−0.527054 + 0.849832i \(0.676703\pi\)
\(234\) 0 0
\(235\) 27.8442 1.81636
\(236\) 0 0
\(237\) 1.37336 0.0892096
\(238\) 0 0
\(239\) −22.6115 −1.46262 −0.731309 0.682046i \(-0.761090\pi\)
−0.731309 + 0.682046i \(0.761090\pi\)
\(240\) 0 0
\(241\) 11.3471 0.730934 0.365467 0.930824i \(-0.380909\pi\)
0.365467 + 0.930824i \(0.380909\pi\)
\(242\) 0 0
\(243\) 14.8691 0.953851
\(244\) 0 0
\(245\) 23.5986 1.50766
\(246\) 0 0
\(247\) 15.7818 1.00417
\(248\) 0 0
\(249\) 5.24726 0.332532
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) 16.1544 1.01562
\(254\) 0 0
\(255\) −15.5659 −0.974775
\(256\) 0 0
\(257\) −1.53878 −0.0959864 −0.0479932 0.998848i \(-0.515283\pi\)
−0.0479932 + 0.998848i \(0.515283\pi\)
\(258\) 0 0
\(259\) −36.9305 −2.29475
\(260\) 0 0
\(261\) 0.0667308 0.00413053
\(262\) 0 0
\(263\) 7.64663 0.471511 0.235756 0.971812i \(-0.424244\pi\)
0.235756 + 0.971812i \(0.424244\pi\)
\(264\) 0 0
\(265\) −21.6384 −1.32924
\(266\) 0 0
\(267\) −2.28205 −0.139659
\(268\) 0 0
\(269\) −23.9400 −1.45965 −0.729823 0.683636i \(-0.760398\pi\)
−0.729823 + 0.683636i \(0.760398\pi\)
\(270\) 0 0
\(271\) −12.8113 −0.778230 −0.389115 0.921189i \(-0.627219\pi\)
−0.389115 + 0.921189i \(0.627219\pi\)
\(272\) 0 0
\(273\) −7.61443 −0.460847
\(274\) 0 0
\(275\) 14.2528 0.859478
\(276\) 0 0
\(277\) 7.62818 0.458333 0.229167 0.973387i \(-0.426400\pi\)
0.229167 + 0.973387i \(0.426400\pi\)
\(278\) 0 0
\(279\) −3.35257 −0.200713
\(280\) 0 0
\(281\) −1.84530 −0.110082 −0.0550408 0.998484i \(-0.517529\pi\)
−0.0550408 + 0.998484i \(0.517529\pi\)
\(282\) 0 0
\(283\) −0.859606 −0.0510983 −0.0255491 0.999674i \(-0.508133\pi\)
−0.0255491 + 0.999674i \(0.508133\pi\)
\(284\) 0 0
\(285\) 12.0165 0.711797
\(286\) 0 0
\(287\) −4.90131 −0.289315
\(288\) 0 0
\(289\) 32.7530 1.92665
\(290\) 0 0
\(291\) 12.6981 0.744377
\(292\) 0 0
\(293\) −24.7664 −1.44687 −0.723433 0.690394i \(-0.757437\pi\)
−0.723433 + 0.690394i \(0.757437\pi\)
\(294\) 0 0
\(295\) 7.77816 0.452862
\(296\) 0 0
\(297\) −10.5521 −0.612292
\(298\) 0 0
\(299\) 16.9578 0.980693
\(300\) 0 0
\(301\) 33.0402 1.90441
\(302\) 0 0
\(303\) −1.67460 −0.0962035
\(304\) 0 0
\(305\) −34.4859 −1.97466
\(306\) 0 0
\(307\) −0.284741 −0.0162510 −0.00812552 0.999967i \(-0.502586\pi\)
−0.00812552 + 0.999967i \(0.502586\pi\)
\(308\) 0 0
\(309\) −8.94036 −0.508599
\(310\) 0 0
\(311\) −7.91584 −0.448866 −0.224433 0.974490i \(-0.572053\pi\)
−0.224433 + 0.974490i \(0.572053\pi\)
\(312\) 0 0
\(313\) 20.2409 1.14408 0.572042 0.820224i \(-0.306151\pi\)
0.572042 + 0.820224i \(0.306151\pi\)
\(314\) 0 0
\(315\) 30.4965 1.71828
\(316\) 0 0
\(317\) −16.6944 −0.937652 −0.468826 0.883291i \(-0.655323\pi\)
−0.468826 + 0.883291i \(0.655323\pi\)
\(318\) 0 0
\(319\) −0.0730902 −0.00409226
\(320\) 0 0
\(321\) 10.5217 0.587262
\(322\) 0 0
\(323\) −38.4081 −2.13709
\(324\) 0 0
\(325\) 14.9616 0.829922
\(326\) 0 0
\(327\) −8.21167 −0.454107
\(328\) 0 0
\(329\) −33.1485 −1.82754
\(330\) 0 0
\(331\) 19.3193 1.06189 0.530943 0.847407i \(-0.321838\pi\)
0.530943 + 0.847407i \(0.321838\pi\)
\(332\) 0 0
\(333\) −24.5299 −1.34423
\(334\) 0 0
\(335\) 26.4940 1.44752
\(336\) 0 0
\(337\) 18.9173 1.03049 0.515246 0.857042i \(-0.327701\pi\)
0.515246 + 0.857042i \(0.327701\pi\)
\(338\) 0 0
\(339\) −6.35038 −0.344906
\(340\) 0 0
\(341\) 3.67206 0.198853
\(342\) 0 0
\(343\) −1.52840 −0.0825257
\(344\) 0 0
\(345\) 12.9119 0.695152
\(346\) 0 0
\(347\) 31.4847 1.69019 0.845094 0.534618i \(-0.179544\pi\)
0.845094 + 0.534618i \(0.179544\pi\)
\(348\) 0 0
\(349\) −10.0100 −0.535822 −0.267911 0.963444i \(-0.586333\pi\)
−0.267911 + 0.963444i \(0.586333\pi\)
\(350\) 0 0
\(351\) −11.0768 −0.591237
\(352\) 0 0
\(353\) 16.2836 0.866688 0.433344 0.901229i \(-0.357334\pi\)
0.433344 + 0.901229i \(0.357334\pi\)
\(354\) 0 0
\(355\) 10.8697 0.576905
\(356\) 0 0
\(357\) 18.5312 0.980774
\(358\) 0 0
\(359\) −35.5621 −1.87690 −0.938449 0.345418i \(-0.887737\pi\)
−0.938449 + 0.345418i \(0.887737\pi\)
\(360\) 0 0
\(361\) 10.6502 0.560535
\(362\) 0 0
\(363\) −2.33769 −0.122697
\(364\) 0 0
\(365\) −3.57195 −0.186965
\(366\) 0 0
\(367\) 1.72195 0.0898849 0.0449424 0.998990i \(-0.485690\pi\)
0.0449424 + 0.998990i \(0.485690\pi\)
\(368\) 0 0
\(369\) −3.25554 −0.169477
\(370\) 0 0
\(371\) 25.7605 1.33742
\(372\) 0 0
\(373\) −29.4746 −1.52614 −0.763068 0.646318i \(-0.776308\pi\)
−0.763068 + 0.646318i \(0.776308\pi\)
\(374\) 0 0
\(375\) 0.357944 0.0184841
\(376\) 0 0
\(377\) −0.0767250 −0.00395154
\(378\) 0 0
\(379\) −7.18299 −0.368965 −0.184483 0.982836i \(-0.559061\pi\)
−0.184483 + 0.982836i \(0.559061\pi\)
\(380\) 0 0
\(381\) −5.25925 −0.269440
\(382\) 0 0
\(383\) 24.1908 1.23609 0.618046 0.786142i \(-0.287924\pi\)
0.618046 + 0.786142i \(0.287924\pi\)
\(384\) 0 0
\(385\) −33.4028 −1.70236
\(386\) 0 0
\(387\) 21.9459 1.11557
\(388\) 0 0
\(389\) −6.43968 −0.326505 −0.163252 0.986584i \(-0.552198\pi\)
−0.163252 + 0.986584i \(0.552198\pi\)
\(390\) 0 0
\(391\) −41.2700 −2.08711
\(392\) 0 0
\(393\) 7.75529 0.391203
\(394\) 0 0
\(395\) 6.32425 0.318207
\(396\) 0 0
\(397\) 8.39591 0.421379 0.210689 0.977553i \(-0.432429\pi\)
0.210689 + 0.977553i \(0.432429\pi\)
\(398\) 0 0
\(399\) −14.3056 −0.716177
\(400\) 0 0
\(401\) 36.8030 1.83786 0.918928 0.394425i \(-0.129056\pi\)
0.918928 + 0.394425i \(0.129056\pi\)
\(402\) 0 0
\(403\) 3.85468 0.192015
\(404\) 0 0
\(405\) 15.6733 0.778811
\(406\) 0 0
\(407\) 26.8676 1.33178
\(408\) 0 0
\(409\) −27.3352 −1.35164 −0.675819 0.737068i \(-0.736210\pi\)
−0.675819 + 0.737068i \(0.736210\pi\)
\(410\) 0 0
\(411\) 3.62684 0.178899
\(412\) 0 0
\(413\) −9.25988 −0.455649
\(414\) 0 0
\(415\) 24.1633 1.18613
\(416\) 0 0
\(417\) 4.14384 0.202925
\(418\) 0 0
\(419\) 13.3918 0.654231 0.327116 0.944984i \(-0.393923\pi\)
0.327116 + 0.944984i \(0.393923\pi\)
\(420\) 0 0
\(421\) −14.9695 −0.729569 −0.364784 0.931092i \(-0.618857\pi\)
−0.364784 + 0.931092i \(0.618857\pi\)
\(422\) 0 0
\(423\) −22.0179 −1.07054
\(424\) 0 0
\(425\) −36.4120 −1.76624
\(426\) 0 0
\(427\) 41.0554 1.98681
\(428\) 0 0
\(429\) 5.53964 0.267456
\(430\) 0 0
\(431\) 33.3376 1.60582 0.802909 0.596102i \(-0.203285\pi\)
0.802909 + 0.596102i \(0.203285\pi\)
\(432\) 0 0
\(433\) 4.23369 0.203458 0.101729 0.994812i \(-0.467563\pi\)
0.101729 + 0.994812i \(0.467563\pi\)
\(434\) 0 0
\(435\) −0.0584195 −0.00280100
\(436\) 0 0
\(437\) 31.8594 1.52404
\(438\) 0 0
\(439\) −20.7546 −0.990564 −0.495282 0.868732i \(-0.664935\pi\)
−0.495282 + 0.868732i \(0.664935\pi\)
\(440\) 0 0
\(441\) −18.6606 −0.888600
\(442\) 0 0
\(443\) −24.1315 −1.14652 −0.573261 0.819373i \(-0.694322\pi\)
−0.573261 + 0.819373i \(0.694322\pi\)
\(444\) 0 0
\(445\) −10.5087 −0.498159
\(446\) 0 0
\(447\) 7.09651 0.335653
\(448\) 0 0
\(449\) −37.4130 −1.76563 −0.882815 0.469720i \(-0.844355\pi\)
−0.882815 + 0.469720i \(0.844355\pi\)
\(450\) 0 0
\(451\) 3.56579 0.167907
\(452\) 0 0
\(453\) 7.47113 0.351024
\(454\) 0 0
\(455\) −35.0639 −1.64382
\(456\) 0 0
\(457\) 15.1698 0.709612 0.354806 0.934940i \(-0.384547\pi\)
0.354806 + 0.934940i \(0.384547\pi\)
\(458\) 0 0
\(459\) 26.9575 1.25827
\(460\) 0 0
\(461\) −32.4457 −1.51115 −0.755573 0.655064i \(-0.772642\pi\)
−0.755573 + 0.655064i \(0.772642\pi\)
\(462\) 0 0
\(463\) 12.9901 0.603703 0.301851 0.953355i \(-0.402395\pi\)
0.301851 + 0.953355i \(0.402395\pi\)
\(464\) 0 0
\(465\) 2.93500 0.136107
\(466\) 0 0
\(467\) −15.9067 −0.736074 −0.368037 0.929811i \(-0.619970\pi\)
−0.368037 + 0.929811i \(0.619970\pi\)
\(468\) 0 0
\(469\) −31.5411 −1.45643
\(470\) 0 0
\(471\) −2.35753 −0.108629
\(472\) 0 0
\(473\) −24.0373 −1.10524
\(474\) 0 0
\(475\) 28.1092 1.28974
\(476\) 0 0
\(477\) 17.1106 0.783440
\(478\) 0 0
\(479\) 1.78977 0.0817768 0.0408884 0.999164i \(-0.486981\pi\)
0.0408884 + 0.999164i \(0.486981\pi\)
\(480\) 0 0
\(481\) 28.2038 1.28598
\(482\) 0 0
\(483\) −15.3716 −0.699430
\(484\) 0 0
\(485\) 58.4740 2.65517
\(486\) 0 0
\(487\) −33.9530 −1.53856 −0.769279 0.638913i \(-0.779384\pi\)
−0.769279 + 0.638913i \(0.779384\pi\)
\(488\) 0 0
\(489\) −0.682840 −0.0308791
\(490\) 0 0
\(491\) −38.1809 −1.72308 −0.861540 0.507690i \(-0.830500\pi\)
−0.861540 + 0.507690i \(0.830500\pi\)
\(492\) 0 0
\(493\) 0.186725 0.00840967
\(494\) 0 0
\(495\) −22.1868 −0.997221
\(496\) 0 0
\(497\) −12.9404 −0.580456
\(498\) 0 0
\(499\) 21.1759 0.947963 0.473982 0.880535i \(-0.342816\pi\)
0.473982 + 0.880535i \(0.342816\pi\)
\(500\) 0 0
\(501\) 10.4504 0.466889
\(502\) 0 0
\(503\) −39.2551 −1.75030 −0.875149 0.483854i \(-0.839236\pi\)
−0.875149 + 0.483854i \(0.839236\pi\)
\(504\) 0 0
\(505\) −7.71143 −0.343154
\(506\) 0 0
\(507\) −3.18428 −0.141419
\(508\) 0 0
\(509\) −29.7738 −1.31970 −0.659850 0.751397i \(-0.729380\pi\)
−0.659850 + 0.751397i \(0.729380\pi\)
\(510\) 0 0
\(511\) 4.25240 0.188115
\(512\) 0 0
\(513\) −20.8106 −0.918810
\(514\) 0 0
\(515\) −41.1697 −1.81416
\(516\) 0 0
\(517\) 24.1161 1.06063
\(518\) 0 0
\(519\) 10.8297 0.475372
\(520\) 0 0
\(521\) 21.5279 0.943156 0.471578 0.881824i \(-0.343684\pi\)
0.471578 + 0.881824i \(0.343684\pi\)
\(522\) 0 0
\(523\) −23.6347 −1.03347 −0.516737 0.856144i \(-0.672854\pi\)
−0.516737 + 0.856144i \(0.672854\pi\)
\(524\) 0 0
\(525\) −13.5621 −0.591900
\(526\) 0 0
\(527\) −9.38109 −0.408647
\(528\) 0 0
\(529\) 11.2333 0.488406
\(530\) 0 0
\(531\) −6.15059 −0.266913
\(532\) 0 0
\(533\) 3.74312 0.162133
\(534\) 0 0
\(535\) 48.4515 2.09474
\(536\) 0 0
\(537\) 7.85768 0.339084
\(538\) 0 0
\(539\) 20.4389 0.880367
\(540\) 0 0
\(541\) −17.1463 −0.737178 −0.368589 0.929592i \(-0.620159\pi\)
−0.368589 + 0.929592i \(0.620159\pi\)
\(542\) 0 0
\(543\) 6.29968 0.270345
\(544\) 0 0
\(545\) −37.8142 −1.61978
\(546\) 0 0
\(547\) 27.4058 1.17179 0.585893 0.810389i \(-0.300744\pi\)
0.585893 + 0.810389i \(0.300744\pi\)
\(548\) 0 0
\(549\) 27.2698 1.16385
\(550\) 0 0
\(551\) −0.144147 −0.00614088
\(552\) 0 0
\(553\) −7.52900 −0.320166
\(554\) 0 0
\(555\) 21.4747 0.911552
\(556\) 0 0
\(557\) 31.6536 1.34121 0.670603 0.741817i \(-0.266035\pi\)
0.670603 + 0.741817i \(0.266035\pi\)
\(558\) 0 0
\(559\) −25.2327 −1.06723
\(560\) 0 0
\(561\) −13.4818 −0.569201
\(562\) 0 0
\(563\) −6.64185 −0.279921 −0.139960 0.990157i \(-0.544697\pi\)
−0.139960 + 0.990157i \(0.544697\pi\)
\(564\) 0 0
\(565\) −29.2431 −1.23027
\(566\) 0 0
\(567\) −18.6590 −0.783604
\(568\) 0 0
\(569\) 13.8101 0.578948 0.289474 0.957186i \(-0.406520\pi\)
0.289474 + 0.957186i \(0.406520\pi\)
\(570\) 0 0
\(571\) 28.9911 1.21324 0.606619 0.794992i \(-0.292525\pi\)
0.606619 + 0.794992i \(0.292525\pi\)
\(572\) 0 0
\(573\) 7.15899 0.299071
\(574\) 0 0
\(575\) 30.2036 1.25958
\(576\) 0 0
\(577\) 32.0491 1.33422 0.667110 0.744959i \(-0.267531\pi\)
0.667110 + 0.744959i \(0.267531\pi\)
\(578\) 0 0
\(579\) 14.6764 0.609930
\(580\) 0 0
\(581\) −28.7663 −1.19343
\(582\) 0 0
\(583\) −18.7412 −0.776182
\(584\) 0 0
\(585\) −23.2901 −0.962928
\(586\) 0 0
\(587\) −22.7229 −0.937876 −0.468938 0.883231i \(-0.655363\pi\)
−0.468938 + 0.883231i \(0.655363\pi\)
\(588\) 0 0
\(589\) 7.24198 0.298401
\(590\) 0 0
\(591\) 15.7649 0.648481
\(592\) 0 0
\(593\) 2.81024 0.115403 0.0577014 0.998334i \(-0.481623\pi\)
0.0577014 + 0.998334i \(0.481623\pi\)
\(594\) 0 0
\(595\) 85.3347 3.49838
\(596\) 0 0
\(597\) 16.3611 0.669617
\(598\) 0 0
\(599\) 0.412660 0.0168608 0.00843041 0.999964i \(-0.497316\pi\)
0.00843041 + 0.999964i \(0.497316\pi\)
\(600\) 0 0
\(601\) −20.3952 −0.831938 −0.415969 0.909379i \(-0.636558\pi\)
−0.415969 + 0.909379i \(0.636558\pi\)
\(602\) 0 0
\(603\) −20.9502 −0.853157
\(604\) 0 0
\(605\) −10.7649 −0.437655
\(606\) 0 0
\(607\) 3.01905 0.122539 0.0612697 0.998121i \(-0.480485\pi\)
0.0612697 + 0.998121i \(0.480485\pi\)
\(608\) 0 0
\(609\) 0.0695482 0.00281824
\(610\) 0 0
\(611\) 25.3154 1.02415
\(612\) 0 0
\(613\) −23.9897 −0.968933 −0.484467 0.874810i \(-0.660986\pi\)
−0.484467 + 0.874810i \(0.660986\pi\)
\(614\) 0 0
\(615\) 2.85007 0.114926
\(616\) 0 0
\(617\) 4.03444 0.162420 0.0812102 0.996697i \(-0.474121\pi\)
0.0812102 + 0.996697i \(0.474121\pi\)
\(618\) 0 0
\(619\) 7.05253 0.283465 0.141732 0.989905i \(-0.454733\pi\)
0.141732 + 0.989905i \(0.454733\pi\)
\(620\) 0 0
\(621\) −22.3612 −0.897325
\(622\) 0 0
\(623\) 12.5106 0.501225
\(624\) 0 0
\(625\) −24.1627 −0.966508
\(626\) 0 0
\(627\) 10.4076 0.415640
\(628\) 0 0
\(629\) −68.6393 −2.73683
\(630\) 0 0
\(631\) 1.46677 0.0583912 0.0291956 0.999574i \(-0.490705\pi\)
0.0291956 + 0.999574i \(0.490705\pi\)
\(632\) 0 0
\(633\) 12.5169 0.497502
\(634\) 0 0
\(635\) −24.2185 −0.961081
\(636\) 0 0
\(637\) 21.4554 0.850093
\(638\) 0 0
\(639\) −8.59525 −0.340023
\(640\) 0 0
\(641\) 0.390772 0.0154346 0.00771728 0.999970i \(-0.497543\pi\)
0.00771728 + 0.999970i \(0.497543\pi\)
\(642\) 0 0
\(643\) −15.1837 −0.598788 −0.299394 0.954130i \(-0.596785\pi\)
−0.299394 + 0.954130i \(0.596785\pi\)
\(644\) 0 0
\(645\) −19.2126 −0.756494
\(646\) 0 0
\(647\) 24.8127 0.975486 0.487743 0.872987i \(-0.337820\pi\)
0.487743 + 0.872987i \(0.337820\pi\)
\(648\) 0 0
\(649\) 6.73674 0.264440
\(650\) 0 0
\(651\) −3.49411 −0.136945
\(652\) 0 0
\(653\) 41.4722 1.62293 0.811465 0.584401i \(-0.198670\pi\)
0.811465 + 0.584401i \(0.198670\pi\)
\(654\) 0 0
\(655\) 35.7126 1.39541
\(656\) 0 0
\(657\) 2.82453 0.110195
\(658\) 0 0
\(659\) −33.5869 −1.30836 −0.654180 0.756339i \(-0.726986\pi\)
−0.654180 + 0.756339i \(0.726986\pi\)
\(660\) 0 0
\(661\) −40.8961 −1.59068 −0.795338 0.606167i \(-0.792706\pi\)
−0.795338 + 0.606167i \(0.792706\pi\)
\(662\) 0 0
\(663\) −14.1522 −0.549627
\(664\) 0 0
\(665\) −65.8764 −2.55458
\(666\) 0 0
\(667\) −0.154888 −0.00599728
\(668\) 0 0
\(669\) 9.30985 0.359940
\(670\) 0 0
\(671\) −29.8686 −1.15306
\(672\) 0 0
\(673\) −3.82118 −0.147295 −0.0736477 0.997284i \(-0.523464\pi\)
−0.0736477 + 0.997284i \(0.523464\pi\)
\(674\) 0 0
\(675\) −19.7290 −0.759370
\(676\) 0 0
\(677\) 36.9609 1.42052 0.710261 0.703938i \(-0.248577\pi\)
0.710261 + 0.703938i \(0.248577\pi\)
\(678\) 0 0
\(679\) −69.6131 −2.67151
\(680\) 0 0
\(681\) −12.2775 −0.470474
\(682\) 0 0
\(683\) −39.8824 −1.52606 −0.763029 0.646364i \(-0.776289\pi\)
−0.763029 + 0.646364i \(0.776289\pi\)
\(684\) 0 0
\(685\) 16.7014 0.638126
\(686\) 0 0
\(687\) 16.3037 0.622027
\(688\) 0 0
\(689\) −19.6732 −0.749490
\(690\) 0 0
\(691\) −30.9976 −1.17920 −0.589602 0.807694i \(-0.700715\pi\)
−0.589602 + 0.807694i \(0.700715\pi\)
\(692\) 0 0
\(693\) 26.4133 1.00336
\(694\) 0 0
\(695\) 19.0821 0.723825
\(696\) 0 0
\(697\) −9.10961 −0.345051
\(698\) 0 0
\(699\) −11.1387 −0.421304
\(700\) 0 0
\(701\) −37.5425 −1.41796 −0.708981 0.705228i \(-0.750845\pi\)
−0.708981 + 0.705228i \(0.750845\pi\)
\(702\) 0 0
\(703\) 52.9879 1.99848
\(704\) 0 0
\(705\) 19.2755 0.725958
\(706\) 0 0
\(707\) 9.18044 0.345266
\(708\) 0 0
\(709\) −5.66690 −0.212825 −0.106412 0.994322i \(-0.533936\pi\)
−0.106412 + 0.994322i \(0.533936\pi\)
\(710\) 0 0
\(711\) −5.00091 −0.187549
\(712\) 0 0
\(713\) 7.78159 0.291423
\(714\) 0 0
\(715\) 25.5096 0.954007
\(716\) 0 0
\(717\) −15.6531 −0.584576
\(718\) 0 0
\(719\) 8.62894 0.321805 0.160903 0.986970i \(-0.448560\pi\)
0.160903 + 0.986970i \(0.448560\pi\)
\(720\) 0 0
\(721\) 49.0125 1.82532
\(722\) 0 0
\(723\) 7.85520 0.292138
\(724\) 0 0
\(725\) −0.136656 −0.00507526
\(726\) 0 0
\(727\) −30.7941 −1.14209 −0.571046 0.820918i \(-0.693462\pi\)
−0.571046 + 0.820918i \(0.693462\pi\)
\(728\) 0 0
\(729\) −4.45653 −0.165057
\(730\) 0 0
\(731\) 61.4087 2.27128
\(732\) 0 0
\(733\) −10.6430 −0.393107 −0.196554 0.980493i \(-0.562975\pi\)
−0.196554 + 0.980493i \(0.562975\pi\)
\(734\) 0 0
\(735\) 16.3364 0.602578
\(736\) 0 0
\(737\) 22.9467 0.845253
\(738\) 0 0
\(739\) −19.0597 −0.701124 −0.350562 0.936539i \(-0.614009\pi\)
−0.350562 + 0.936539i \(0.614009\pi\)
\(740\) 0 0
\(741\) 10.9252 0.401347
\(742\) 0 0
\(743\) −12.7132 −0.466402 −0.233201 0.972429i \(-0.574920\pi\)
−0.233201 + 0.972429i \(0.574920\pi\)
\(744\) 0 0
\(745\) 32.6789 1.19726
\(746\) 0 0
\(747\) −19.1071 −0.699093
\(748\) 0 0
\(749\) −57.6814 −2.10763
\(750\) 0 0
\(751\) 26.8832 0.980982 0.490491 0.871446i \(-0.336817\pi\)
0.490491 + 0.871446i \(0.336817\pi\)
\(752\) 0 0
\(753\) −0.692263 −0.0252275
\(754\) 0 0
\(755\) 34.4040 1.25209
\(756\) 0 0
\(757\) 4.85548 0.176475 0.0882377 0.996099i \(-0.471876\pi\)
0.0882377 + 0.996099i \(0.471876\pi\)
\(758\) 0 0
\(759\) 11.1831 0.405920
\(760\) 0 0
\(761\) 43.4115 1.57366 0.786832 0.617167i \(-0.211720\pi\)
0.786832 + 0.617167i \(0.211720\pi\)
\(762\) 0 0
\(763\) 45.0177 1.62975
\(764\) 0 0
\(765\) 56.6809 2.04930
\(766\) 0 0
\(767\) 7.07176 0.255346
\(768\) 0 0
\(769\) −22.8291 −0.823239 −0.411619 0.911356i \(-0.635037\pi\)
−0.411619 + 0.911356i \(0.635037\pi\)
\(770\) 0 0
\(771\) −1.06524 −0.0383636
\(772\) 0 0
\(773\) 8.96647 0.322501 0.161251 0.986913i \(-0.448447\pi\)
0.161251 + 0.986913i \(0.448447\pi\)
\(774\) 0 0
\(775\) 6.86560 0.246620
\(776\) 0 0
\(777\) −25.5656 −0.917162
\(778\) 0 0
\(779\) 7.03240 0.251962
\(780\) 0 0
\(781\) 9.41437 0.336872
\(782\) 0 0
\(783\) 0.101173 0.00361562
\(784\) 0 0
\(785\) −10.8562 −0.387476
\(786\) 0 0
\(787\) −20.6377 −0.735655 −0.367828 0.929894i \(-0.619898\pi\)
−0.367828 + 0.929894i \(0.619898\pi\)
\(788\) 0 0
\(789\) 5.29347 0.188453
\(790\) 0 0
\(791\) 34.8138 1.23784
\(792\) 0 0
\(793\) −31.3540 −1.11341
\(794\) 0 0
\(795\) −14.9795 −0.531267
\(796\) 0 0
\(797\) −9.94902 −0.352413 −0.176206 0.984353i \(-0.556383\pi\)
−0.176206 + 0.984353i \(0.556383\pi\)
\(798\) 0 0
\(799\) −61.6100 −2.17960
\(800\) 0 0
\(801\) 8.30975 0.293611
\(802\) 0 0
\(803\) −3.09370 −0.109174
\(804\) 0 0
\(805\) −70.7849 −2.49484
\(806\) 0 0
\(807\) −16.5728 −0.583389
\(808\) 0 0
\(809\) −20.2389 −0.711562 −0.355781 0.934569i \(-0.615785\pi\)
−0.355781 + 0.934569i \(0.615785\pi\)
\(810\) 0 0
\(811\) 37.9341 1.33205 0.666024 0.745930i \(-0.267995\pi\)
0.666024 + 0.745930i \(0.267995\pi\)
\(812\) 0 0
\(813\) −8.86878 −0.311042
\(814\) 0 0
\(815\) −3.14443 −0.110145
\(816\) 0 0
\(817\) −47.4061 −1.65853
\(818\) 0 0
\(819\) 27.7268 0.968854
\(820\) 0 0
\(821\) 20.5637 0.717677 0.358839 0.933400i \(-0.383173\pi\)
0.358839 + 0.933400i \(0.383173\pi\)
\(822\) 0 0
\(823\) −50.4042 −1.75698 −0.878489 0.477762i \(-0.841448\pi\)
−0.878489 + 0.477762i \(0.841448\pi\)
\(824\) 0 0
\(825\) 9.86670 0.343515
\(826\) 0 0
\(827\) −5.89613 −0.205028 −0.102514 0.994732i \(-0.532689\pi\)
−0.102514 + 0.994732i \(0.532689\pi\)
\(828\) 0 0
\(829\) −1.16574 −0.0404880 −0.0202440 0.999795i \(-0.506444\pi\)
−0.0202440 + 0.999795i \(0.506444\pi\)
\(830\) 0 0
\(831\) 5.28071 0.183186
\(832\) 0 0
\(833\) −52.2157 −1.80917
\(834\) 0 0
\(835\) 48.1233 1.66537
\(836\) 0 0
\(837\) −5.08293 −0.175692
\(838\) 0 0
\(839\) −48.8260 −1.68566 −0.842831 0.538179i \(-0.819112\pi\)
−0.842831 + 0.538179i \(0.819112\pi\)
\(840\) 0 0
\(841\) −28.9993 −0.999976
\(842\) 0 0
\(843\) −1.27743 −0.0439972
\(844\) 0 0
\(845\) −14.6634 −0.504436
\(846\) 0 0
\(847\) 12.8156 0.440349
\(848\) 0 0
\(849\) −0.595073 −0.0204229
\(850\) 0 0
\(851\) 56.9361 1.95174
\(852\) 0 0
\(853\) 24.7449 0.847248 0.423624 0.905838i \(-0.360758\pi\)
0.423624 + 0.905838i \(0.360758\pi\)
\(854\) 0 0
\(855\) −43.7563 −1.49644
\(856\) 0 0
\(857\) 25.8182 0.881932 0.440966 0.897524i \(-0.354636\pi\)
0.440966 + 0.897524i \(0.354636\pi\)
\(858\) 0 0
\(859\) 34.9861 1.19371 0.596855 0.802349i \(-0.296417\pi\)
0.596855 + 0.802349i \(0.296417\pi\)
\(860\) 0 0
\(861\) −3.39300 −0.115633
\(862\) 0 0
\(863\) 37.1255 1.26377 0.631884 0.775063i \(-0.282282\pi\)
0.631884 + 0.775063i \(0.282282\pi\)
\(864\) 0 0
\(865\) 49.8701 1.69564
\(866\) 0 0
\(867\) 22.6737 0.770039
\(868\) 0 0
\(869\) 5.47749 0.185811
\(870\) 0 0
\(871\) 24.0879 0.816186
\(872\) 0 0
\(873\) −46.2384 −1.56493
\(874\) 0 0
\(875\) −1.96231 −0.0663380
\(876\) 0 0
\(877\) 9.08105 0.306645 0.153323 0.988176i \(-0.451003\pi\)
0.153323 + 0.988176i \(0.451003\pi\)
\(878\) 0 0
\(879\) −17.1448 −0.578281
\(880\) 0 0
\(881\) −18.1440 −0.611286 −0.305643 0.952146i \(-0.598871\pi\)
−0.305643 + 0.952146i \(0.598871\pi\)
\(882\) 0 0
\(883\) 58.4498 1.96699 0.983497 0.180925i \(-0.0579090\pi\)
0.983497 + 0.180925i \(0.0579090\pi\)
\(884\) 0 0
\(885\) 5.38453 0.180999
\(886\) 0 0
\(887\) −25.7133 −0.863369 −0.431685 0.902025i \(-0.642081\pi\)
−0.431685 + 0.902025i \(0.642081\pi\)
\(888\) 0 0
\(889\) 28.8320 0.966995
\(890\) 0 0
\(891\) 13.5748 0.454771
\(892\) 0 0
\(893\) 47.5614 1.59158
\(894\) 0 0
\(895\) 36.1841 1.20950
\(896\) 0 0
\(897\) 11.7392 0.391962
\(898\) 0 0
\(899\) −0.0352076 −0.00117424
\(900\) 0 0
\(901\) 47.8785 1.59507
\(902\) 0 0
\(903\) 22.8725 0.761149
\(904\) 0 0
\(905\) 29.0096 0.964310
\(906\) 0 0
\(907\) 50.2876 1.66977 0.834887 0.550422i \(-0.185533\pi\)
0.834887 + 0.550422i \(0.185533\pi\)
\(908\) 0 0
\(909\) 6.09782 0.202252
\(910\) 0 0
\(911\) 55.5893 1.84176 0.920878 0.389852i \(-0.127474\pi\)
0.920878 + 0.389852i \(0.127474\pi\)
\(912\) 0 0
\(913\) 20.9280 0.692616
\(914\) 0 0
\(915\) −23.8733 −0.789228
\(916\) 0 0
\(917\) −42.5157 −1.40399
\(918\) 0 0
\(919\) −24.3486 −0.803186 −0.401593 0.915818i \(-0.631543\pi\)
−0.401593 + 0.915818i \(0.631543\pi\)
\(920\) 0 0
\(921\) −0.197116 −0.00649518
\(922\) 0 0
\(923\) 9.88255 0.325288
\(924\) 0 0
\(925\) 50.2340 1.65168
\(926\) 0 0
\(927\) 32.5550 1.06925
\(928\) 0 0
\(929\) 44.1855 1.44968 0.724839 0.688918i \(-0.241914\pi\)
0.724839 + 0.688918i \(0.241914\pi\)
\(930\) 0 0
\(931\) 40.3093 1.32108
\(932\) 0 0
\(933\) −5.47984 −0.179402
\(934\) 0 0
\(935\) −62.0826 −2.03032
\(936\) 0 0
\(937\) −40.3389 −1.31781 −0.658907 0.752225i \(-0.728981\pi\)
−0.658907 + 0.752225i \(0.728981\pi\)
\(938\) 0 0
\(939\) 14.0120 0.457265
\(940\) 0 0
\(941\) −38.6135 −1.25876 −0.629382 0.777096i \(-0.716692\pi\)
−0.629382 + 0.777096i \(0.716692\pi\)
\(942\) 0 0
\(943\) 7.55639 0.246070
\(944\) 0 0
\(945\) 46.2367 1.50408
\(946\) 0 0
\(947\) −3.82218 −0.124204 −0.0621021 0.998070i \(-0.519780\pi\)
−0.0621021 + 0.998070i \(0.519780\pi\)
\(948\) 0 0
\(949\) −3.24755 −0.105420
\(950\) 0 0
\(951\) −11.5569 −0.374759
\(952\) 0 0
\(953\) 21.5098 0.696771 0.348385 0.937351i \(-0.386730\pi\)
0.348385 + 0.937351i \(0.386730\pi\)
\(954\) 0 0
\(955\) 32.9667 1.06678
\(956\) 0 0
\(957\) −0.0505976 −0.00163559
\(958\) 0 0
\(959\) −19.8829 −0.642053
\(960\) 0 0
\(961\) −29.2312 −0.942941
\(962\) 0 0
\(963\) −38.3131 −1.23462
\(964\) 0 0
\(965\) 67.5837 2.17560
\(966\) 0 0
\(967\) −6.97580 −0.224326 −0.112163 0.993690i \(-0.535778\pi\)
−0.112163 + 0.993690i \(0.535778\pi\)
\(968\) 0 0
\(969\) −26.5885 −0.854146
\(970\) 0 0
\(971\) −4.46260 −0.143212 −0.0716058 0.997433i \(-0.522812\pi\)
−0.0716058 + 0.997433i \(0.522812\pi\)
\(972\) 0 0
\(973\) −22.7172 −0.728279
\(974\) 0 0
\(975\) 10.3574 0.331702
\(976\) 0 0
\(977\) 43.4911 1.39140 0.695702 0.718330i \(-0.255093\pi\)
0.695702 + 0.718330i \(0.255093\pi\)
\(978\) 0 0
\(979\) −9.10166 −0.290890
\(980\) 0 0
\(981\) 29.9016 0.954685
\(982\) 0 0
\(983\) 26.7255 0.852411 0.426205 0.904626i \(-0.359850\pi\)
0.426205 + 0.904626i \(0.359850\pi\)
\(984\) 0 0
\(985\) 72.5962 2.31311
\(986\) 0 0
\(987\) −22.9475 −0.730426
\(988\) 0 0
\(989\) −50.9383 −1.61975
\(990\) 0 0
\(991\) −41.0783 −1.30490 −0.652448 0.757834i \(-0.726258\pi\)
−0.652448 + 0.757834i \(0.726258\pi\)
\(992\) 0 0
\(993\) 13.3741 0.424413
\(994\) 0 0
\(995\) 75.3419 2.38850
\(996\) 0 0
\(997\) −18.2506 −0.578001 −0.289001 0.957329i \(-0.593323\pi\)
−0.289001 + 0.957329i \(0.593323\pi\)
\(998\) 0 0
\(999\) −37.1907 −1.17666
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 8032.2.a.j.1.16 yes 30
4.3 odd 2 8032.2.a.g.1.15 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8032.2.a.g.1.15 30 4.3 odd 2
8032.2.a.j.1.16 yes 30 1.1 even 1 trivial