Properties

Label 6044.2.a.b.1.10
Level $6044$
Weight $2$
Character 6044.1
Self dual yes
Analytic conductor $48.262$
Analytic rank $0$
Dimension $63$
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] = [6044,2,Mod(1,6044)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6044.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6044 = 2^{2} \cdot 1511 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6044.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: \(48.2615829817\)
Analytic rank: \(0\)
Dimension: \(63\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6044.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.38781 q^{3} +2.32923 q^{5} +0.907839 q^{7} +2.70165 q^{9} +O(q^{10})\) \(q-2.38781 q^{3} +2.32923 q^{5} +0.907839 q^{7} +2.70165 q^{9} -1.04154 q^{11} +4.23918 q^{13} -5.56176 q^{15} -6.62050 q^{17} +1.90051 q^{19} -2.16775 q^{21} +2.80035 q^{23} +0.425308 q^{25} +0.712408 q^{27} +2.30952 q^{29} +6.25461 q^{31} +2.48700 q^{33} +2.11456 q^{35} -10.0624 q^{37} -10.1224 q^{39} +3.97060 q^{41} -5.68322 q^{43} +6.29276 q^{45} +7.35422 q^{47} -6.17583 q^{49} +15.8085 q^{51} -4.38380 q^{53} -2.42598 q^{55} -4.53807 q^{57} +11.1332 q^{59} +8.35639 q^{61} +2.45266 q^{63} +9.87401 q^{65} +12.6964 q^{67} -6.68670 q^{69} +11.0778 q^{71} -0.989184 q^{73} -1.01556 q^{75} -0.945549 q^{77} +9.07763 q^{79} -9.80604 q^{81} -16.8401 q^{83} -15.4207 q^{85} -5.51470 q^{87} -2.38252 q^{89} +3.84849 q^{91} -14.9348 q^{93} +4.42673 q^{95} +4.71850 q^{97} -2.81387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 63 q + 5 q^{3} + 5 q^{5} + 22 q^{7} + 62 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 63 q + 5 q^{3} + 5 q^{5} + 22 q^{7} + 62 q^{9} + 21 q^{11} + 17 q^{13} + 26 q^{15} - 5 q^{17} + 57 q^{19} + 18 q^{21} + 16 q^{23} + 60 q^{25} + 14 q^{27} + 22 q^{29} + 36 q^{31} - q^{33} + 28 q^{35} + 21 q^{37} + 69 q^{39} - 3 q^{41} + 86 q^{43} + 39 q^{45} + 23 q^{47} + 63 q^{49} + 67 q^{51} + 18 q^{53} + 67 q^{55} + 27 q^{59} + 62 q^{61} + 58 q^{63} - 13 q^{65} + 62 q^{67} + 45 q^{69} + 29 q^{71} - q^{73} + 39 q^{75} + 19 q^{77} + 132 q^{79} + 51 q^{81} + 35 q^{83} + 60 q^{85} + 55 q^{87} - 2 q^{89} + 84 q^{91} + 29 q^{93} + 53 q^{95} - 10 q^{97} + 95 q^{99}+O(q^{100}) \) 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
\(3\) −2.38781 −1.37860 −0.689302 0.724474i \(-0.742083\pi\)
−0.689302 + 0.724474i \(0.742083\pi\)
\(4\) 0 0
\(5\) 2.32923 1.04166 0.520831 0.853660i \(-0.325622\pi\)
0.520831 + 0.853660i \(0.325622\pi\)
\(6\) 0 0
\(7\) 0.907839 0.343131 0.171565 0.985173i \(-0.445118\pi\)
0.171565 + 0.985173i \(0.445118\pi\)
\(8\) 0 0
\(9\) 2.70165 0.900549
\(10\) 0 0
\(11\) −1.04154 −0.314036 −0.157018 0.987596i \(-0.550188\pi\)
−0.157018 + 0.987596i \(0.550188\pi\)
\(12\) 0 0
\(13\) 4.23918 1.17574 0.587868 0.808957i \(-0.299967\pi\)
0.587868 + 0.808957i \(0.299967\pi\)
\(14\) 0 0
\(15\) −5.56176 −1.43604
\(16\) 0 0
\(17\) −6.62050 −1.60571 −0.802853 0.596177i \(-0.796686\pi\)
−0.802853 + 0.596177i \(0.796686\pi\)
\(18\) 0 0
\(19\) 1.90051 0.436008 0.218004 0.975948i \(-0.430045\pi\)
0.218004 + 0.975948i \(0.430045\pi\)
\(20\) 0 0
\(21\) −2.16775 −0.473042
\(22\) 0 0
\(23\) 2.80035 0.583913 0.291956 0.956432i \(-0.405694\pi\)
0.291956 + 0.956432i \(0.405694\pi\)
\(24\) 0 0
\(25\) 0.425308 0.0850617
\(26\) 0 0
\(27\) 0.712408 0.137103
\(28\) 0 0
\(29\) 2.30952 0.428867 0.214433 0.976739i \(-0.431210\pi\)
0.214433 + 0.976739i \(0.431210\pi\)
\(30\) 0 0
\(31\) 6.25461 1.12336 0.561680 0.827354i \(-0.310155\pi\)
0.561680 + 0.827354i \(0.310155\pi\)
\(32\) 0 0
\(33\) 2.48700 0.432931
\(34\) 0 0
\(35\) 2.11456 0.357427
\(36\) 0 0
\(37\) −10.0624 −1.65425 −0.827125 0.562018i \(-0.810025\pi\)
−0.827125 + 0.562018i \(0.810025\pi\)
\(38\) 0 0
\(39\) −10.1224 −1.62087
\(40\) 0 0
\(41\) 3.97060 0.620103 0.310052 0.950720i \(-0.399654\pi\)
0.310052 + 0.950720i \(0.399654\pi\)
\(42\) 0 0
\(43\) −5.68322 −0.866684 −0.433342 0.901230i \(-0.642666\pi\)
−0.433342 + 0.901230i \(0.642666\pi\)
\(44\) 0 0
\(45\) 6.29276 0.938069
\(46\) 0 0
\(47\) 7.35422 1.07272 0.536362 0.843988i \(-0.319798\pi\)
0.536362 + 0.843988i \(0.319798\pi\)
\(48\) 0 0
\(49\) −6.17583 −0.882261
\(50\) 0 0
\(51\) 15.8085 2.21363
\(52\) 0 0
\(53\) −4.38380 −0.602162 −0.301081 0.953599i \(-0.597347\pi\)
−0.301081 + 0.953599i \(0.597347\pi\)
\(54\) 0 0
\(55\) −2.42598 −0.327119
\(56\) 0 0
\(57\) −4.53807 −0.601082
\(58\) 0 0
\(59\) 11.1332 1.44942 0.724710 0.689054i \(-0.241974\pi\)
0.724710 + 0.689054i \(0.241974\pi\)
\(60\) 0 0
\(61\) 8.35639 1.06993 0.534963 0.844875i \(-0.320325\pi\)
0.534963 + 0.844875i \(0.320325\pi\)
\(62\) 0 0
\(63\) 2.45266 0.309006
\(64\) 0 0
\(65\) 9.87401 1.22472
\(66\) 0 0
\(67\) 12.6964 1.55111 0.775557 0.631277i \(-0.217469\pi\)
0.775557 + 0.631277i \(0.217469\pi\)
\(68\) 0 0
\(69\) −6.68670 −0.804985
\(70\) 0 0
\(71\) 11.0778 1.31469 0.657345 0.753590i \(-0.271680\pi\)
0.657345 + 0.753590i \(0.271680\pi\)
\(72\) 0 0
\(73\) −0.989184 −0.115775 −0.0578876 0.998323i \(-0.518437\pi\)
−0.0578876 + 0.998323i \(0.518437\pi\)
\(74\) 0 0
\(75\) −1.01556 −0.117266
\(76\) 0 0
\(77\) −0.945549 −0.107755
\(78\) 0 0
\(79\) 9.07763 1.02131 0.510656 0.859785i \(-0.329402\pi\)
0.510656 + 0.859785i \(0.329402\pi\)
\(80\) 0 0
\(81\) −9.80604 −1.08956
\(82\) 0 0
\(83\) −16.8401 −1.84844 −0.924219 0.381863i \(-0.875283\pi\)
−0.924219 + 0.381863i \(0.875283\pi\)
\(84\) 0 0
\(85\) −15.4207 −1.67261
\(86\) 0 0
\(87\) −5.51470 −0.591238
\(88\) 0 0
\(89\) −2.38252 −0.252547 −0.126273 0.991995i \(-0.540302\pi\)
−0.126273 + 0.991995i \(0.540302\pi\)
\(90\) 0 0
\(91\) 3.84849 0.403431
\(92\) 0 0
\(93\) −14.9348 −1.54867
\(94\) 0 0
\(95\) 4.42673 0.454173
\(96\) 0 0
\(97\) 4.71850 0.479091 0.239545 0.970885i \(-0.423002\pi\)
0.239545 + 0.970885i \(0.423002\pi\)
\(98\) 0 0
\(99\) −2.81387 −0.282805
\(100\) 0 0
\(101\) −5.75643 −0.572786 −0.286393 0.958112i \(-0.592456\pi\)
−0.286393 + 0.958112i \(0.592456\pi\)
\(102\) 0 0
\(103\) −0.952242 −0.0938272 −0.0469136 0.998899i \(-0.514939\pi\)
−0.0469136 + 0.998899i \(0.514939\pi\)
\(104\) 0 0
\(105\) −5.04918 −0.492750
\(106\) 0 0
\(107\) −6.85561 −0.662757 −0.331378 0.943498i \(-0.607514\pi\)
−0.331378 + 0.943498i \(0.607514\pi\)
\(108\) 0 0
\(109\) 3.85367 0.369114 0.184557 0.982822i \(-0.440915\pi\)
0.184557 + 0.982822i \(0.440915\pi\)
\(110\) 0 0
\(111\) 24.0272 2.28056
\(112\) 0 0
\(113\) 8.79313 0.827188 0.413594 0.910461i \(-0.364273\pi\)
0.413594 + 0.910461i \(0.364273\pi\)
\(114\) 0 0
\(115\) 6.52265 0.608240
\(116\) 0 0
\(117\) 11.4528 1.05881
\(118\) 0 0
\(119\) −6.01035 −0.550967
\(120\) 0 0
\(121\) −9.91520 −0.901382
\(122\) 0 0
\(123\) −9.48105 −0.854877
\(124\) 0 0
\(125\) −10.6555 −0.953057
\(126\) 0 0
\(127\) 13.2679 1.17734 0.588668 0.808375i \(-0.299652\pi\)
0.588668 + 0.808375i \(0.299652\pi\)
\(128\) 0 0
\(129\) 13.5705 1.19481
\(130\) 0 0
\(131\) 11.2514 0.983042 0.491521 0.870866i \(-0.336441\pi\)
0.491521 + 0.870866i \(0.336441\pi\)
\(132\) 0 0
\(133\) 1.72536 0.149608
\(134\) 0 0
\(135\) 1.65936 0.142815
\(136\) 0 0
\(137\) −19.5519 −1.67043 −0.835214 0.549925i \(-0.814656\pi\)
−0.835214 + 0.549925i \(0.814656\pi\)
\(138\) 0 0
\(139\) −8.88490 −0.753608 −0.376804 0.926293i \(-0.622977\pi\)
−0.376804 + 0.926293i \(0.622977\pi\)
\(140\) 0 0
\(141\) −17.5605 −1.47886
\(142\) 0 0
\(143\) −4.41527 −0.369223
\(144\) 0 0
\(145\) 5.37940 0.446735
\(146\) 0 0
\(147\) 14.7467 1.21629
\(148\) 0 0
\(149\) 7.71713 0.632212 0.316106 0.948724i \(-0.397624\pi\)
0.316106 + 0.948724i \(0.397624\pi\)
\(150\) 0 0
\(151\) −0.262069 −0.0213269 −0.0106635 0.999943i \(-0.503394\pi\)
−0.0106635 + 0.999943i \(0.503394\pi\)
\(152\) 0 0
\(153\) −17.8863 −1.44602
\(154\) 0 0
\(155\) 14.5684 1.17016
\(156\) 0 0
\(157\) 20.4092 1.62883 0.814417 0.580279i \(-0.197057\pi\)
0.814417 + 0.580279i \(0.197057\pi\)
\(158\) 0 0
\(159\) 10.4677 0.830143
\(160\) 0 0
\(161\) 2.54226 0.200358
\(162\) 0 0
\(163\) −4.68148 −0.366682 −0.183341 0.983049i \(-0.558691\pi\)
−0.183341 + 0.983049i \(0.558691\pi\)
\(164\) 0 0
\(165\) 5.79279 0.450968
\(166\) 0 0
\(167\) −2.37414 −0.183716 −0.0918581 0.995772i \(-0.529281\pi\)
−0.0918581 + 0.995772i \(0.529281\pi\)
\(168\) 0 0
\(169\) 4.97062 0.382356
\(170\) 0 0
\(171\) 5.13452 0.392646
\(172\) 0 0
\(173\) 10.2464 0.779019 0.389509 0.921022i \(-0.372645\pi\)
0.389509 + 0.921022i \(0.372645\pi\)
\(174\) 0 0
\(175\) 0.386112 0.0291873
\(176\) 0 0
\(177\) −26.5840 −1.99818
\(178\) 0 0
\(179\) −1.70716 −0.127599 −0.0637996 0.997963i \(-0.520322\pi\)
−0.0637996 + 0.997963i \(0.520322\pi\)
\(180\) 0 0
\(181\) 0.414455 0.0308062 0.0154031 0.999881i \(-0.495097\pi\)
0.0154031 + 0.999881i \(0.495097\pi\)
\(182\) 0 0
\(183\) −19.9535 −1.47501
\(184\) 0 0
\(185\) −23.4377 −1.72317
\(186\) 0 0
\(187\) 6.89550 0.504249
\(188\) 0 0
\(189\) 0.646752 0.0470443
\(190\) 0 0
\(191\) 3.36045 0.243154 0.121577 0.992582i \(-0.461205\pi\)
0.121577 + 0.992582i \(0.461205\pi\)
\(192\) 0 0
\(193\) 5.99526 0.431548 0.215774 0.976443i \(-0.430773\pi\)
0.215774 + 0.976443i \(0.430773\pi\)
\(194\) 0 0
\(195\) −23.5773 −1.68841
\(196\) 0 0
\(197\) −4.26356 −0.303766 −0.151883 0.988398i \(-0.548534\pi\)
−0.151883 + 0.988398i \(0.548534\pi\)
\(198\) 0 0
\(199\) 4.91534 0.348439 0.174220 0.984707i \(-0.444260\pi\)
0.174220 + 0.984707i \(0.444260\pi\)
\(200\) 0 0
\(201\) −30.3167 −2.13837
\(202\) 0 0
\(203\) 2.09667 0.147157
\(204\) 0 0
\(205\) 9.24844 0.645939
\(206\) 0 0
\(207\) 7.56555 0.525842
\(208\) 0 0
\(209\) −1.97946 −0.136922
\(210\) 0 0
\(211\) −14.8714 −1.02379 −0.511893 0.859049i \(-0.671056\pi\)
−0.511893 + 0.859049i \(0.671056\pi\)
\(212\) 0 0
\(213\) −26.4516 −1.81244
\(214\) 0 0
\(215\) −13.2375 −0.902792
\(216\) 0 0
\(217\) 5.67817 0.385460
\(218\) 0 0
\(219\) 2.36199 0.159608
\(220\) 0 0
\(221\) −28.0655 −1.88789
\(222\) 0 0
\(223\) −1.91359 −0.128143 −0.0640717 0.997945i \(-0.520409\pi\)
−0.0640717 + 0.997945i \(0.520409\pi\)
\(224\) 0 0
\(225\) 1.14903 0.0766023
\(226\) 0 0
\(227\) −6.00054 −0.398270 −0.199135 0.979972i \(-0.563813\pi\)
−0.199135 + 0.979972i \(0.563813\pi\)
\(228\) 0 0
\(229\) −14.8457 −0.981033 −0.490516 0.871432i \(-0.663192\pi\)
−0.490516 + 0.871432i \(0.663192\pi\)
\(230\) 0 0
\(231\) 2.25779 0.148552
\(232\) 0 0
\(233\) −6.11518 −0.400618 −0.200309 0.979733i \(-0.564195\pi\)
−0.200309 + 0.979733i \(0.564195\pi\)
\(234\) 0 0
\(235\) 17.1297 1.11742
\(236\) 0 0
\(237\) −21.6757 −1.40799
\(238\) 0 0
\(239\) −26.0980 −1.68814 −0.844070 0.536233i \(-0.819847\pi\)
−0.844070 + 0.536233i \(0.819847\pi\)
\(240\) 0 0
\(241\) 28.4414 1.83207 0.916037 0.401094i \(-0.131370\pi\)
0.916037 + 0.401094i \(0.131370\pi\)
\(242\) 0 0
\(243\) 21.2778 1.36497
\(244\) 0 0
\(245\) −14.3849 −0.919019
\(246\) 0 0
\(247\) 8.05661 0.512630
\(248\) 0 0
\(249\) 40.2109 2.54826
\(250\) 0 0
\(251\) 14.2672 0.900540 0.450270 0.892893i \(-0.351328\pi\)
0.450270 + 0.892893i \(0.351328\pi\)
\(252\) 0 0
\(253\) −2.91667 −0.183369
\(254\) 0 0
\(255\) 36.8216 2.30586
\(256\) 0 0
\(257\) 21.5326 1.34317 0.671583 0.740930i \(-0.265615\pi\)
0.671583 + 0.740930i \(0.265615\pi\)
\(258\) 0 0
\(259\) −9.13505 −0.567624
\(260\) 0 0
\(261\) 6.23951 0.386216
\(262\) 0 0
\(263\) 16.7282 1.03151 0.515753 0.856737i \(-0.327512\pi\)
0.515753 + 0.856737i \(0.327512\pi\)
\(264\) 0 0
\(265\) −10.2109 −0.627250
\(266\) 0 0
\(267\) 5.68901 0.348162
\(268\) 0 0
\(269\) 18.3618 1.11954 0.559770 0.828648i \(-0.310890\pi\)
0.559770 + 0.828648i \(0.310890\pi\)
\(270\) 0 0
\(271\) 0.817864 0.0496817 0.0248409 0.999691i \(-0.492092\pi\)
0.0248409 + 0.999691i \(0.492092\pi\)
\(272\) 0 0
\(273\) −9.18947 −0.556172
\(274\) 0 0
\(275\) −0.442975 −0.0267124
\(276\) 0 0
\(277\) 3.48038 0.209116 0.104558 0.994519i \(-0.466657\pi\)
0.104558 + 0.994519i \(0.466657\pi\)
\(278\) 0 0
\(279\) 16.8977 1.01164
\(280\) 0 0
\(281\) 0.227107 0.0135481 0.00677405 0.999977i \(-0.497844\pi\)
0.00677405 + 0.999977i \(0.497844\pi\)
\(282\) 0 0
\(283\) 17.0300 1.01233 0.506164 0.862437i \(-0.331063\pi\)
0.506164 + 0.862437i \(0.331063\pi\)
\(284\) 0 0
\(285\) −10.5702 −0.626125
\(286\) 0 0
\(287\) 3.60466 0.212777
\(288\) 0 0
\(289\) 26.8310 1.57829
\(290\) 0 0
\(291\) −11.2669 −0.660477
\(292\) 0 0
\(293\) −7.04606 −0.411635 −0.205818 0.978590i \(-0.565985\pi\)
−0.205818 + 0.978590i \(0.565985\pi\)
\(294\) 0 0
\(295\) 25.9318 1.50981
\(296\) 0 0
\(297\) −0.742001 −0.0430553
\(298\) 0 0
\(299\) 11.8712 0.686527
\(300\) 0 0
\(301\) −5.15945 −0.297386
\(302\) 0 0
\(303\) 13.7453 0.789646
\(304\) 0 0
\(305\) 19.4640 1.11450
\(306\) 0 0
\(307\) 22.6994 1.29552 0.647761 0.761844i \(-0.275706\pi\)
0.647761 + 0.761844i \(0.275706\pi\)
\(308\) 0 0
\(309\) 2.27378 0.129351
\(310\) 0 0
\(311\) −0.954336 −0.0541154 −0.0270577 0.999634i \(-0.508614\pi\)
−0.0270577 + 0.999634i \(0.508614\pi\)
\(312\) 0 0
\(313\) 22.0245 1.24490 0.622448 0.782661i \(-0.286138\pi\)
0.622448 + 0.782661i \(0.286138\pi\)
\(314\) 0 0
\(315\) 5.71281 0.321880
\(316\) 0 0
\(317\) −17.3676 −0.975460 −0.487730 0.872995i \(-0.662175\pi\)
−0.487730 + 0.872995i \(0.662175\pi\)
\(318\) 0 0
\(319\) −2.40545 −0.134680
\(320\) 0 0
\(321\) 16.3699 0.913679
\(322\) 0 0
\(323\) −12.5823 −0.700100
\(324\) 0 0
\(325\) 1.80296 0.100010
\(326\) 0 0
\(327\) −9.20183 −0.508862
\(328\) 0 0
\(329\) 6.67645 0.368085
\(330\) 0 0
\(331\) 12.0016 0.659668 0.329834 0.944039i \(-0.393007\pi\)
0.329834 + 0.944039i \(0.393007\pi\)
\(332\) 0 0
\(333\) −27.1851 −1.48973
\(334\) 0 0
\(335\) 29.5729 1.61574
\(336\) 0 0
\(337\) −8.88456 −0.483973 −0.241987 0.970280i \(-0.577799\pi\)
−0.241987 + 0.970280i \(0.577799\pi\)
\(338\) 0 0
\(339\) −20.9963 −1.14036
\(340\) 0 0
\(341\) −6.51441 −0.352775
\(342\) 0 0
\(343\) −11.9615 −0.645862
\(344\) 0 0
\(345\) −15.5749 −0.838523
\(346\) 0 0
\(347\) 20.2220 1.08558 0.542788 0.839870i \(-0.317369\pi\)
0.542788 + 0.839870i \(0.317369\pi\)
\(348\) 0 0
\(349\) 25.4699 1.36337 0.681687 0.731644i \(-0.261247\pi\)
0.681687 + 0.731644i \(0.261247\pi\)
\(350\) 0 0
\(351\) 3.02003 0.161197
\(352\) 0 0
\(353\) −1.90681 −0.101489 −0.0507446 0.998712i \(-0.516159\pi\)
−0.0507446 + 0.998712i \(0.516159\pi\)
\(354\) 0 0
\(355\) 25.8027 1.36946
\(356\) 0 0
\(357\) 14.3516 0.759566
\(358\) 0 0
\(359\) −11.7172 −0.618409 −0.309205 0.950996i \(-0.600063\pi\)
−0.309205 + 0.950996i \(0.600063\pi\)
\(360\) 0 0
\(361\) −15.3881 −0.809897
\(362\) 0 0
\(363\) 23.6756 1.24265
\(364\) 0 0
\(365\) −2.30404 −0.120599
\(366\) 0 0
\(367\) 19.0286 0.993284 0.496642 0.867955i \(-0.334566\pi\)
0.496642 + 0.867955i \(0.334566\pi\)
\(368\) 0 0
\(369\) 10.7272 0.558434
\(370\) 0 0
\(371\) −3.97979 −0.206620
\(372\) 0 0
\(373\) 29.4686 1.52583 0.762914 0.646500i \(-0.223768\pi\)
0.762914 + 0.646500i \(0.223768\pi\)
\(374\) 0 0
\(375\) 25.4433 1.31389
\(376\) 0 0
\(377\) 9.79046 0.504234
\(378\) 0 0
\(379\) 19.1939 0.985924 0.492962 0.870051i \(-0.335914\pi\)
0.492962 + 0.870051i \(0.335914\pi\)
\(380\) 0 0
\(381\) −31.6813 −1.62308
\(382\) 0 0
\(383\) −14.5482 −0.743379 −0.371690 0.928357i \(-0.621221\pi\)
−0.371690 + 0.928357i \(0.621221\pi\)
\(384\) 0 0
\(385\) −2.20240 −0.112245
\(386\) 0 0
\(387\) −15.3541 −0.780491
\(388\) 0 0
\(389\) 34.1354 1.73073 0.865367 0.501139i \(-0.167085\pi\)
0.865367 + 0.501139i \(0.167085\pi\)
\(390\) 0 0
\(391\) −18.5397 −0.937593
\(392\) 0 0
\(393\) −26.8663 −1.35523
\(394\) 0 0
\(395\) 21.1439 1.06386
\(396\) 0 0
\(397\) −16.4105 −0.823618 −0.411809 0.911270i \(-0.635103\pi\)
−0.411809 + 0.911270i \(0.635103\pi\)
\(398\) 0 0
\(399\) −4.11983 −0.206250
\(400\) 0 0
\(401\) 34.8862 1.74213 0.871066 0.491167i \(-0.163429\pi\)
0.871066 + 0.491167i \(0.163429\pi\)
\(402\) 0 0
\(403\) 26.5144 1.32078
\(404\) 0 0
\(405\) −22.8405 −1.13495
\(406\) 0 0
\(407\) 10.4804 0.519494
\(408\) 0 0
\(409\) 27.9642 1.38274 0.691369 0.722502i \(-0.257008\pi\)
0.691369 + 0.722502i \(0.257008\pi\)
\(410\) 0 0
\(411\) 46.6862 2.30286
\(412\) 0 0
\(413\) 10.1072 0.497341
\(414\) 0 0
\(415\) −39.2244 −1.92545
\(416\) 0 0
\(417\) 21.2155 1.03893
\(418\) 0 0
\(419\) −12.1868 −0.595363 −0.297682 0.954665i \(-0.596213\pi\)
−0.297682 + 0.954665i \(0.596213\pi\)
\(420\) 0 0
\(421\) −17.0228 −0.829639 −0.414820 0.909904i \(-0.636155\pi\)
−0.414820 + 0.909904i \(0.636155\pi\)
\(422\) 0 0
\(423\) 19.8685 0.966041
\(424\) 0 0
\(425\) −2.81575 −0.136584
\(426\) 0 0
\(427\) 7.58626 0.367125
\(428\) 0 0
\(429\) 10.5428 0.509013
\(430\) 0 0
\(431\) −0.216822 −0.0104439 −0.00522196 0.999986i \(-0.501662\pi\)
−0.00522196 + 0.999986i \(0.501662\pi\)
\(432\) 0 0
\(433\) 32.3426 1.55429 0.777144 0.629323i \(-0.216668\pi\)
0.777144 + 0.629323i \(0.216668\pi\)
\(434\) 0 0
\(435\) −12.8450 −0.615870
\(436\) 0 0
\(437\) 5.32210 0.254590
\(438\) 0 0
\(439\) 29.7034 1.41767 0.708833 0.705377i \(-0.249222\pi\)
0.708833 + 0.705377i \(0.249222\pi\)
\(440\) 0 0
\(441\) −16.6849 −0.794520
\(442\) 0 0
\(443\) 31.2347 1.48401 0.742003 0.670397i \(-0.233876\pi\)
0.742003 + 0.670397i \(0.233876\pi\)
\(444\) 0 0
\(445\) −5.54944 −0.263069
\(446\) 0 0
\(447\) −18.4271 −0.871571
\(448\) 0 0
\(449\) −35.4936 −1.67505 −0.837523 0.546402i \(-0.815997\pi\)
−0.837523 + 0.546402i \(0.815997\pi\)
\(450\) 0 0
\(451\) −4.13553 −0.194735
\(452\) 0 0
\(453\) 0.625773 0.0294014
\(454\) 0 0
\(455\) 8.96401 0.420239
\(456\) 0 0
\(457\) 14.7043 0.687836 0.343918 0.939000i \(-0.388246\pi\)
0.343918 + 0.939000i \(0.388246\pi\)
\(458\) 0 0
\(459\) −4.71650 −0.220147
\(460\) 0 0
\(461\) 29.6079 1.37898 0.689488 0.724297i \(-0.257836\pi\)
0.689488 + 0.724297i \(0.257836\pi\)
\(462\) 0 0
\(463\) −27.6639 −1.28565 −0.642825 0.766013i \(-0.722238\pi\)
−0.642825 + 0.766013i \(0.722238\pi\)
\(464\) 0 0
\(465\) −34.7866 −1.61319
\(466\) 0 0
\(467\) −12.9157 −0.597670 −0.298835 0.954305i \(-0.596598\pi\)
−0.298835 + 0.954305i \(0.596598\pi\)
\(468\) 0 0
\(469\) 11.5263 0.532235
\(470\) 0 0
\(471\) −48.7334 −2.24552
\(472\) 0 0
\(473\) 5.91930 0.272170
\(474\) 0 0
\(475\) 0.808304 0.0370875
\(476\) 0 0
\(477\) −11.8435 −0.542277
\(478\) 0 0
\(479\) 23.0944 1.05521 0.527606 0.849489i \(-0.323090\pi\)
0.527606 + 0.849489i \(0.323090\pi\)
\(480\) 0 0
\(481\) −42.6563 −1.94496
\(482\) 0 0
\(483\) −6.07045 −0.276215
\(484\) 0 0
\(485\) 10.9905 0.499051
\(486\) 0 0
\(487\) 10.2435 0.464178 0.232089 0.972695i \(-0.425444\pi\)
0.232089 + 0.972695i \(0.425444\pi\)
\(488\) 0 0
\(489\) 11.1785 0.505509
\(490\) 0 0
\(491\) −23.2520 −1.04935 −0.524675 0.851303i \(-0.675813\pi\)
−0.524675 + 0.851303i \(0.675813\pi\)
\(492\) 0 0
\(493\) −15.2902 −0.688634
\(494\) 0 0
\(495\) −6.55415 −0.294587
\(496\) 0 0
\(497\) 10.0568 0.451110
\(498\) 0 0
\(499\) −0.835053 −0.0373821 −0.0186910 0.999825i \(-0.505950\pi\)
−0.0186910 + 0.999825i \(0.505950\pi\)
\(500\) 0 0
\(501\) 5.66900 0.253272
\(502\) 0 0
\(503\) 20.9918 0.935979 0.467990 0.883734i \(-0.344978\pi\)
0.467990 + 0.883734i \(0.344978\pi\)
\(504\) 0 0
\(505\) −13.4080 −0.596650
\(506\) 0 0
\(507\) −11.8689 −0.527117
\(508\) 0 0
\(509\) 12.6336 0.559975 0.279988 0.960004i \(-0.409670\pi\)
0.279988 + 0.960004i \(0.409670\pi\)
\(510\) 0 0
\(511\) −0.898020 −0.0397261
\(512\) 0 0
\(513\) 1.35394 0.0597780
\(514\) 0 0
\(515\) −2.21799 −0.0977364
\(516\) 0 0
\(517\) −7.65971 −0.336874
\(518\) 0 0
\(519\) −24.4665 −1.07396
\(520\) 0 0
\(521\) 17.1830 0.752802 0.376401 0.926457i \(-0.377162\pi\)
0.376401 + 0.926457i \(0.377162\pi\)
\(522\) 0 0
\(523\) 26.2317 1.14703 0.573515 0.819195i \(-0.305579\pi\)
0.573515 + 0.819195i \(0.305579\pi\)
\(524\) 0 0
\(525\) −0.921962 −0.0402377
\(526\) 0 0
\(527\) −41.4086 −1.80379
\(528\) 0 0
\(529\) −15.1581 −0.659046
\(530\) 0 0
\(531\) 30.0780 1.30527
\(532\) 0 0
\(533\) 16.8321 0.729078
\(534\) 0 0
\(535\) −15.9683 −0.690369
\(536\) 0 0
\(537\) 4.07638 0.175909
\(538\) 0 0
\(539\) 6.43236 0.277062
\(540\) 0 0
\(541\) 29.3807 1.26318 0.631588 0.775304i \(-0.282403\pi\)
0.631588 + 0.775304i \(0.282403\pi\)
\(542\) 0 0
\(543\) −0.989641 −0.0424695
\(544\) 0 0
\(545\) 8.97607 0.384493
\(546\) 0 0
\(547\) −1.55830 −0.0666282 −0.0333141 0.999445i \(-0.510606\pi\)
−0.0333141 + 0.999445i \(0.510606\pi\)
\(548\) 0 0
\(549\) 22.5760 0.963522
\(550\) 0 0
\(551\) 4.38927 0.186989
\(552\) 0 0
\(553\) 8.24102 0.350444
\(554\) 0 0
\(555\) 55.9647 2.37557
\(556\) 0 0
\(557\) 31.2761 1.32521 0.662606 0.748968i \(-0.269450\pi\)
0.662606 + 0.748968i \(0.269450\pi\)
\(558\) 0 0
\(559\) −24.0922 −1.01899
\(560\) 0 0
\(561\) −16.4652 −0.695160
\(562\) 0 0
\(563\) 20.4821 0.863216 0.431608 0.902061i \(-0.357946\pi\)
0.431608 + 0.902061i \(0.357946\pi\)
\(564\) 0 0
\(565\) 20.4812 0.861651
\(566\) 0 0
\(567\) −8.90231 −0.373862
\(568\) 0 0
\(569\) −11.2733 −0.472601 −0.236301 0.971680i \(-0.575935\pi\)
−0.236301 + 0.971680i \(0.575935\pi\)
\(570\) 0 0
\(571\) −30.8440 −1.29078 −0.645390 0.763853i \(-0.723305\pi\)
−0.645390 + 0.763853i \(0.723305\pi\)
\(572\) 0 0
\(573\) −8.02413 −0.335213
\(574\) 0 0
\(575\) 1.19101 0.0496686
\(576\) 0 0
\(577\) −26.2626 −1.09333 −0.546663 0.837353i \(-0.684102\pi\)
−0.546663 + 0.837353i \(0.684102\pi\)
\(578\) 0 0
\(579\) −14.3155 −0.594934
\(580\) 0 0
\(581\) −15.2881 −0.634256
\(582\) 0 0
\(583\) 4.56590 0.189100
\(584\) 0 0
\(585\) 26.6761 1.10292
\(586\) 0 0
\(587\) −25.1067 −1.03627 −0.518133 0.855300i \(-0.673373\pi\)
−0.518133 + 0.855300i \(0.673373\pi\)
\(588\) 0 0
\(589\) 11.8870 0.489794
\(590\) 0 0
\(591\) 10.1806 0.418774
\(592\) 0 0
\(593\) −46.4128 −1.90594 −0.952972 0.303059i \(-0.901992\pi\)
−0.952972 + 0.303059i \(0.901992\pi\)
\(594\) 0 0
\(595\) −13.9995 −0.573922
\(596\) 0 0
\(597\) −11.7369 −0.480360
\(598\) 0 0
\(599\) −7.61988 −0.311340 −0.155670 0.987809i \(-0.549754\pi\)
−0.155670 + 0.987809i \(0.549754\pi\)
\(600\) 0 0
\(601\) −14.8210 −0.604561 −0.302280 0.953219i \(-0.597748\pi\)
−0.302280 + 0.953219i \(0.597748\pi\)
\(602\) 0 0
\(603\) 34.3013 1.39686
\(604\) 0 0
\(605\) −23.0948 −0.938936
\(606\) 0 0
\(607\) −9.02153 −0.366173 −0.183086 0.983097i \(-0.558609\pi\)
−0.183086 + 0.983097i \(0.558609\pi\)
\(608\) 0 0
\(609\) −5.00646 −0.202872
\(610\) 0 0
\(611\) 31.1759 1.26124
\(612\) 0 0
\(613\) −18.9957 −0.767229 −0.383615 0.923493i \(-0.625321\pi\)
−0.383615 + 0.923493i \(0.625321\pi\)
\(614\) 0 0
\(615\) −22.0835 −0.890494
\(616\) 0 0
\(617\) 42.6433 1.71675 0.858377 0.513020i \(-0.171473\pi\)
0.858377 + 0.513020i \(0.171473\pi\)
\(618\) 0 0
\(619\) −12.1388 −0.487900 −0.243950 0.969788i \(-0.578443\pi\)
−0.243950 + 0.969788i \(0.578443\pi\)
\(620\) 0 0
\(621\) 1.99499 0.0800562
\(622\) 0 0
\(623\) −2.16295 −0.0866566
\(624\) 0 0
\(625\) −26.9457 −1.07783
\(626\) 0 0
\(627\) 4.72657 0.188761
\(628\) 0 0
\(629\) 66.6182 2.65624
\(630\) 0 0
\(631\) −6.63292 −0.264052 −0.132026 0.991246i \(-0.542148\pi\)
−0.132026 + 0.991246i \(0.542148\pi\)
\(632\) 0 0
\(633\) 35.5100 1.41140
\(634\) 0 0
\(635\) 30.9040 1.22639
\(636\) 0 0
\(637\) −26.1804 −1.03731
\(638\) 0 0
\(639\) 29.9282 1.18394
\(640\) 0 0
\(641\) 40.9095 1.61583 0.807914 0.589301i \(-0.200597\pi\)
0.807914 + 0.589301i \(0.200597\pi\)
\(642\) 0 0
\(643\) 3.35908 0.132469 0.0662346 0.997804i \(-0.478901\pi\)
0.0662346 + 0.997804i \(0.478901\pi\)
\(644\) 0 0
\(645\) 31.6087 1.24459
\(646\) 0 0
\(647\) −22.2191 −0.873522 −0.436761 0.899577i \(-0.643875\pi\)
−0.436761 + 0.899577i \(0.643875\pi\)
\(648\) 0 0
\(649\) −11.5957 −0.455170
\(650\) 0 0
\(651\) −13.5584 −0.531396
\(652\) 0 0
\(653\) 36.9752 1.44695 0.723477 0.690349i \(-0.242543\pi\)
0.723477 + 0.690349i \(0.242543\pi\)
\(654\) 0 0
\(655\) 26.2072 1.02400
\(656\) 0 0
\(657\) −2.67243 −0.104261
\(658\) 0 0
\(659\) 25.7712 1.00390 0.501952 0.864896i \(-0.332616\pi\)
0.501952 + 0.864896i \(0.332616\pi\)
\(660\) 0 0
\(661\) −1.19415 −0.0464469 −0.0232235 0.999730i \(-0.507393\pi\)
−0.0232235 + 0.999730i \(0.507393\pi\)
\(662\) 0 0
\(663\) 67.0151 2.60265
\(664\) 0 0
\(665\) 4.01876 0.155841
\(666\) 0 0
\(667\) 6.46745 0.250421
\(668\) 0 0
\(669\) 4.56929 0.176659
\(670\) 0 0
\(671\) −8.70351 −0.335995
\(672\) 0 0
\(673\) 13.1419 0.506585 0.253292 0.967390i \(-0.418487\pi\)
0.253292 + 0.967390i \(0.418487\pi\)
\(674\) 0 0
\(675\) 0.302993 0.0116622
\(676\) 0 0
\(677\) −34.1967 −1.31428 −0.657142 0.753766i \(-0.728235\pi\)
−0.657142 + 0.753766i \(0.728235\pi\)
\(678\) 0 0
\(679\) 4.28364 0.164391
\(680\) 0 0
\(681\) 14.3282 0.549057
\(682\) 0 0
\(683\) −31.9776 −1.22359 −0.611794 0.791017i \(-0.709552\pi\)
−0.611794 + 0.791017i \(0.709552\pi\)
\(684\) 0 0
\(685\) −45.5408 −1.74002
\(686\) 0 0
\(687\) 35.4488 1.35246
\(688\) 0 0
\(689\) −18.5837 −0.707984
\(690\) 0 0
\(691\) 16.4414 0.625461 0.312730 0.949842i \(-0.398756\pi\)
0.312730 + 0.949842i \(0.398756\pi\)
\(692\) 0 0
\(693\) −2.55454 −0.0970390
\(694\) 0 0
\(695\) −20.6950 −0.785005
\(696\) 0 0
\(697\) −26.2873 −0.995704
\(698\) 0 0
\(699\) 14.6019 0.552294
\(700\) 0 0
\(701\) −4.74986 −0.179400 −0.0896998 0.995969i \(-0.528591\pi\)
−0.0896998 + 0.995969i \(0.528591\pi\)
\(702\) 0 0
\(703\) −19.1237 −0.721266
\(704\) 0 0
\(705\) −40.9025 −1.54048
\(706\) 0 0
\(707\) −5.22591 −0.196541
\(708\) 0 0
\(709\) 1.65939 0.0623197 0.0311599 0.999514i \(-0.490080\pi\)
0.0311599 + 0.999514i \(0.490080\pi\)
\(710\) 0 0
\(711\) 24.5246 0.919742
\(712\) 0 0
\(713\) 17.5151 0.655944
\(714\) 0 0
\(715\) −10.2842 −0.384606
\(716\) 0 0
\(717\) 62.3171 2.32728
\(718\) 0 0
\(719\) −47.6457 −1.77689 −0.888443 0.458987i \(-0.848213\pi\)
−0.888443 + 0.458987i \(0.848213\pi\)
\(720\) 0 0
\(721\) −0.864483 −0.0321950
\(722\) 0 0
\(723\) −67.9128 −2.52571
\(724\) 0 0
\(725\) 0.982258 0.0364801
\(726\) 0 0
\(727\) −23.4611 −0.870125 −0.435063 0.900400i \(-0.643274\pi\)
−0.435063 + 0.900400i \(0.643274\pi\)
\(728\) 0 0
\(729\) −21.3892 −0.792192
\(730\) 0 0
\(731\) 37.6258 1.39164
\(732\) 0 0
\(733\) 25.8143 0.953471 0.476736 0.879047i \(-0.341820\pi\)
0.476736 + 0.879047i \(0.341820\pi\)
\(734\) 0 0
\(735\) 34.3485 1.26696
\(736\) 0 0
\(737\) −13.2238 −0.487105
\(738\) 0 0
\(739\) 19.5668 0.719778 0.359889 0.932995i \(-0.382815\pi\)
0.359889 + 0.932995i \(0.382815\pi\)
\(740\) 0 0
\(741\) −19.2377 −0.706714
\(742\) 0 0
\(743\) −40.4757 −1.48491 −0.742455 0.669896i \(-0.766339\pi\)
−0.742455 + 0.669896i \(0.766339\pi\)
\(744\) 0 0
\(745\) 17.9750 0.658552
\(746\) 0 0
\(747\) −45.4960 −1.66461
\(748\) 0 0
\(749\) −6.22379 −0.227412
\(750\) 0 0
\(751\) 30.4753 1.11206 0.556030 0.831162i \(-0.312324\pi\)
0.556030 + 0.831162i \(0.312324\pi\)
\(752\) 0 0
\(753\) −34.0675 −1.24149
\(754\) 0 0
\(755\) −0.610420 −0.0222154
\(756\) 0 0
\(757\) −36.6072 −1.33051 −0.665256 0.746616i \(-0.731678\pi\)
−0.665256 + 0.746616i \(0.731678\pi\)
\(758\) 0 0
\(759\) 6.96446 0.252794
\(760\) 0 0
\(761\) −30.7453 −1.11452 −0.557258 0.830339i \(-0.688147\pi\)
−0.557258 + 0.830339i \(0.688147\pi\)
\(762\) 0 0
\(763\) 3.49851 0.126654
\(764\) 0 0
\(765\) −41.6612 −1.50626
\(766\) 0 0
\(767\) 47.1956 1.70414
\(768\) 0 0
\(769\) 30.9218 1.11507 0.557534 0.830154i \(-0.311748\pi\)
0.557534 + 0.830154i \(0.311748\pi\)
\(770\) 0 0
\(771\) −51.4157 −1.85169
\(772\) 0 0
\(773\) −37.4626 −1.34744 −0.673719 0.738988i \(-0.735304\pi\)
−0.673719 + 0.738988i \(0.735304\pi\)
\(774\) 0 0
\(775\) 2.66014 0.0955549
\(776\) 0 0
\(777\) 21.8128 0.782529
\(778\) 0 0
\(779\) 7.54617 0.270370
\(780\) 0 0
\(781\) −11.5379 −0.412859
\(782\) 0 0
\(783\) 1.64532 0.0587990
\(784\) 0 0
\(785\) 47.5378 1.69670
\(786\) 0 0
\(787\) −4.62500 −0.164863 −0.0824317 0.996597i \(-0.526269\pi\)
−0.0824317 + 0.996597i \(0.526269\pi\)
\(788\) 0 0
\(789\) −39.9439 −1.42204
\(790\) 0 0
\(791\) 7.98274 0.283834
\(792\) 0 0
\(793\) 35.4242 1.25795
\(794\) 0 0
\(795\) 24.3817 0.864729
\(796\) 0 0
\(797\) −40.6947 −1.44148 −0.720739 0.693206i \(-0.756198\pi\)
−0.720739 + 0.693206i \(0.756198\pi\)
\(798\) 0 0
\(799\) −48.6886 −1.72248
\(800\) 0 0
\(801\) −6.43673 −0.227431
\(802\) 0 0
\(803\) 1.03027 0.0363576
\(804\) 0 0
\(805\) 5.92152 0.208706
\(806\) 0 0
\(807\) −43.8446 −1.54340
\(808\) 0 0
\(809\) −3.45930 −0.121622 −0.0608112 0.998149i \(-0.519369\pi\)
−0.0608112 + 0.998149i \(0.519369\pi\)
\(810\) 0 0
\(811\) 4.91960 0.172750 0.0863752 0.996263i \(-0.472472\pi\)
0.0863752 + 0.996263i \(0.472472\pi\)
\(812\) 0 0
\(813\) −1.95291 −0.0684914
\(814\) 0 0
\(815\) −10.9042 −0.381959
\(816\) 0 0
\(817\) −10.8010 −0.377881
\(818\) 0 0
\(819\) 10.3973 0.363310
\(820\) 0 0
\(821\) 2.42588 0.0846637 0.0423319 0.999104i \(-0.486521\pi\)
0.0423319 + 0.999104i \(0.486521\pi\)
\(822\) 0 0
\(823\) 5.29374 0.184528 0.0922642 0.995735i \(-0.470590\pi\)
0.0922642 + 0.995735i \(0.470590\pi\)
\(824\) 0 0
\(825\) 1.05774 0.0368258
\(826\) 0 0
\(827\) 33.4382 1.16276 0.581381 0.813632i \(-0.302513\pi\)
0.581381 + 0.813632i \(0.302513\pi\)
\(828\) 0 0
\(829\) −38.4602 −1.33578 −0.667889 0.744260i \(-0.732802\pi\)
−0.667889 + 0.744260i \(0.732802\pi\)
\(830\) 0 0
\(831\) −8.31050 −0.288288
\(832\) 0 0
\(833\) 40.8871 1.41665
\(834\) 0 0
\(835\) −5.52991 −0.191370
\(836\) 0 0
\(837\) 4.45583 0.154016
\(838\) 0 0
\(839\) 2.88565 0.0996236 0.0498118 0.998759i \(-0.484138\pi\)
0.0498118 + 0.998759i \(0.484138\pi\)
\(840\) 0 0
\(841\) −23.6661 −0.816073
\(842\) 0 0
\(843\) −0.542290 −0.0186775
\(844\) 0 0
\(845\) 11.5777 0.398286
\(846\) 0 0
\(847\) −9.00140 −0.309292
\(848\) 0 0
\(849\) −40.6645 −1.39560
\(850\) 0 0
\(851\) −28.1782 −0.965938
\(852\) 0 0
\(853\) −30.8701 −1.05697 −0.528486 0.848942i \(-0.677240\pi\)
−0.528486 + 0.848942i \(0.677240\pi\)
\(854\) 0 0
\(855\) 11.9595 0.409005
\(856\) 0 0
\(857\) 1.29361 0.0441888 0.0220944 0.999756i \(-0.492967\pi\)
0.0220944 + 0.999756i \(0.492967\pi\)
\(858\) 0 0
\(859\) 56.8946 1.94122 0.970610 0.240660i \(-0.0773637\pi\)
0.970610 + 0.240660i \(0.0773637\pi\)
\(860\) 0 0
\(861\) −8.60726 −0.293335
\(862\) 0 0
\(863\) 18.5502 0.631457 0.315729 0.948849i \(-0.397751\pi\)
0.315729 + 0.948849i \(0.397751\pi\)
\(864\) 0 0
\(865\) 23.8662 0.811475
\(866\) 0 0
\(867\) −64.0674 −2.17584
\(868\) 0 0
\(869\) −9.45470 −0.320729
\(870\) 0 0
\(871\) 53.8224 1.82370
\(872\) 0 0
\(873\) 12.7477 0.431445
\(874\) 0 0
\(875\) −9.67348 −0.327023
\(876\) 0 0
\(877\) 27.3743 0.924363 0.462181 0.886785i \(-0.347067\pi\)
0.462181 + 0.886785i \(0.347067\pi\)
\(878\) 0 0
\(879\) 16.8247 0.567482
\(880\) 0 0
\(881\) 30.5996 1.03093 0.515464 0.856911i \(-0.327620\pi\)
0.515464 + 0.856911i \(0.327620\pi\)
\(882\) 0 0
\(883\) −41.5888 −1.39958 −0.699788 0.714351i \(-0.746722\pi\)
−0.699788 + 0.714351i \(0.746722\pi\)
\(884\) 0 0
\(885\) −61.9202 −2.08143
\(886\) 0 0
\(887\) −40.7938 −1.36972 −0.684861 0.728674i \(-0.740137\pi\)
−0.684861 + 0.728674i \(0.740137\pi\)
\(888\) 0 0
\(889\) 12.0451 0.403980
\(890\) 0 0
\(891\) 10.2134 0.342161
\(892\) 0 0
\(893\) 13.9768 0.467716
\(894\) 0 0
\(895\) −3.97637 −0.132915
\(896\) 0 0
\(897\) −28.3461 −0.946449
\(898\) 0 0
\(899\) 14.4451 0.481772
\(900\) 0 0
\(901\) 29.0230 0.966895
\(902\) 0 0
\(903\) 12.3198 0.409977
\(904\) 0 0
\(905\) 0.965360 0.0320897
\(906\) 0 0
\(907\) 34.3558 1.14076 0.570382 0.821380i \(-0.306795\pi\)
0.570382 + 0.821380i \(0.306795\pi\)
\(908\) 0 0
\(909\) −15.5519 −0.515822
\(910\) 0 0
\(911\) 1.79316 0.0594099 0.0297049 0.999559i \(-0.490543\pi\)
0.0297049 + 0.999559i \(0.490543\pi\)
\(912\) 0 0
\(913\) 17.5396 0.580476
\(914\) 0 0
\(915\) −46.4763 −1.53646
\(916\) 0 0
\(917\) 10.2145 0.337312
\(918\) 0 0
\(919\) 17.4890 0.576908 0.288454 0.957494i \(-0.406859\pi\)
0.288454 + 0.957494i \(0.406859\pi\)
\(920\) 0 0
\(921\) −54.2018 −1.78601
\(922\) 0 0
\(923\) 46.9606 1.54573
\(924\) 0 0
\(925\) −4.27963 −0.140713
\(926\) 0 0
\(927\) −2.57262 −0.0844961
\(928\) 0 0
\(929\) 14.7977 0.485498 0.242749 0.970089i \(-0.421951\pi\)
0.242749 + 0.970089i \(0.421951\pi\)
\(930\) 0 0
\(931\) −11.7372 −0.384673
\(932\) 0 0
\(933\) 2.27878 0.0746038
\(934\) 0 0
\(935\) 16.0612 0.525258
\(936\) 0 0
\(937\) −41.9510 −1.37048 −0.685239 0.728318i \(-0.740302\pi\)
−0.685239 + 0.728318i \(0.740302\pi\)
\(938\) 0 0
\(939\) −52.5903 −1.71622
\(940\) 0 0
\(941\) −22.5890 −0.736381 −0.368190 0.929750i \(-0.620022\pi\)
−0.368190 + 0.929750i \(0.620022\pi\)
\(942\) 0 0
\(943\) 11.1191 0.362086
\(944\) 0 0
\(945\) 1.50643 0.0490043
\(946\) 0 0
\(947\) 39.3420 1.27844 0.639222 0.769023i \(-0.279257\pi\)
0.639222 + 0.769023i \(0.279257\pi\)
\(948\) 0 0
\(949\) −4.19333 −0.136121
\(950\) 0 0
\(951\) 41.4705 1.34477
\(952\) 0 0
\(953\) −40.9239 −1.32565 −0.662827 0.748772i \(-0.730644\pi\)
−0.662827 + 0.748772i \(0.730644\pi\)
\(954\) 0 0
\(955\) 7.82727 0.253284
\(956\) 0 0
\(957\) 5.74377 0.185670
\(958\) 0 0
\(959\) −17.7499 −0.573175
\(960\) 0 0
\(961\) 8.12009 0.261938
\(962\) 0 0
\(963\) −18.5214 −0.596845
\(964\) 0 0
\(965\) 13.9643 0.449528
\(966\) 0 0
\(967\) −6.79331 −0.218458 −0.109229 0.994017i \(-0.534838\pi\)
−0.109229 + 0.994017i \(0.534838\pi\)
\(968\) 0 0
\(969\) 30.0443 0.965161
\(970\) 0 0
\(971\) 39.9929 1.28343 0.641717 0.766941i \(-0.278222\pi\)
0.641717 + 0.766941i \(0.278222\pi\)
\(972\) 0 0
\(973\) −8.06606 −0.258586
\(974\) 0 0
\(975\) −4.30513 −0.137874
\(976\) 0 0
\(977\) −12.9994 −0.415887 −0.207943 0.978141i \(-0.566677\pi\)
−0.207943 + 0.978141i \(0.566677\pi\)
\(978\) 0 0
\(979\) 2.48149 0.0793087
\(980\) 0 0
\(981\) 10.4112 0.332406
\(982\) 0 0
\(983\) 19.9226 0.635433 0.317716 0.948186i \(-0.397084\pi\)
0.317716 + 0.948186i \(0.397084\pi\)
\(984\) 0 0
\(985\) −9.93082 −0.316422
\(986\) 0 0
\(987\) −15.9421 −0.507443
\(988\) 0 0
\(989\) −15.9150 −0.506068
\(990\) 0 0
\(991\) −53.6986 −1.70579 −0.852896 0.522082i \(-0.825156\pi\)
−0.852896 + 0.522082i \(0.825156\pi\)
\(992\) 0 0
\(993\) −28.6576 −0.909421
\(994\) 0 0
\(995\) 11.4490 0.362956
\(996\) 0 0
\(997\) 32.0105 1.01378 0.506891 0.862010i \(-0.330795\pi\)
0.506891 + 0.862010i \(0.330795\pi\)
\(998\) 0 0
\(999\) −7.16855 −0.226803
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 6044.2.a.b.1.10 63
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6044.2.a.b.1.10 63 1.1 even 1 trivial