Properties

Label 6008.2.a.c.1.9
Level $6008$
Weight $2$
Character 6008.1
Self dual yes
Analytic conductor $47.974$
Analytic rank $1$
Dimension $44$
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] = [6008,2,Mod(1,6008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6008, 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("6008.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6008.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: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 6008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.15961 q^{3} +0.185718 q^{5} +3.00693 q^{7} +1.66392 q^{9} +O(q^{10})\) \(q-2.15961 q^{3} +0.185718 q^{5} +3.00693 q^{7} +1.66392 q^{9} +0.123870 q^{11} +1.56775 q^{13} -0.401078 q^{15} +0.758557 q^{17} -3.18817 q^{19} -6.49381 q^{21} -2.97273 q^{23} -4.96551 q^{25} +2.88541 q^{27} +3.26058 q^{29} +5.87406 q^{31} -0.267511 q^{33} +0.558440 q^{35} -9.61053 q^{37} -3.38573 q^{39} +5.98093 q^{41} -0.323388 q^{43} +0.309020 q^{45} -7.79465 q^{47} +2.04165 q^{49} -1.63819 q^{51} -13.4601 q^{53} +0.0230049 q^{55} +6.88521 q^{57} +1.94483 q^{59} -12.9913 q^{61} +5.00331 q^{63} +0.291159 q^{65} +8.01188 q^{67} +6.41995 q^{69} -2.36443 q^{71} +0.457187 q^{73} +10.7236 q^{75} +0.372469 q^{77} -2.18145 q^{79} -11.2231 q^{81} +0.917360 q^{83} +0.140877 q^{85} -7.04159 q^{87} +8.20797 q^{89} +4.71412 q^{91} -12.6857 q^{93} -0.592099 q^{95} -8.84686 q^{97} +0.206110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 4 q^{3} - 21 q^{5} - 10 q^{7} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 4 q^{3} - 21 q^{5} - 10 q^{7} + 38 q^{9} + 11 q^{11} - 36 q^{13} - 5 q^{15} - 10 q^{17} - 7 q^{19} - 42 q^{21} - 5 q^{23} + 29 q^{25} - 16 q^{27} - 57 q^{29} - 21 q^{31} - 32 q^{33} + 17 q^{35} - 52 q^{37} + 8 q^{39} - 16 q^{41} - 9 q^{43} - 84 q^{45} - q^{47} + 28 q^{49} - q^{51} - 52 q^{53} - 39 q^{55} - 15 q^{57} + 7 q^{59} - 85 q^{61} - 25 q^{63} - 9 q^{65} - 36 q^{67} - 72 q^{69} + 12 q^{71} - 60 q^{73} - 5 q^{75} - 81 q^{77} - 13 q^{79} + 20 q^{81} + 5 q^{83} - 72 q^{85} + 9 q^{87} - 37 q^{89} - 23 q^{91} - 60 q^{93} + 24 q^{95} - 79 q^{97} + 42 q^{99}+O(q^{100}) \) 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
\(3\) −2.15961 −1.24685 −0.623426 0.781882i \(-0.714260\pi\)
−0.623426 + 0.781882i \(0.714260\pi\)
\(4\) 0 0
\(5\) 0.185718 0.0830554 0.0415277 0.999137i \(-0.486778\pi\)
0.0415277 + 0.999137i \(0.486778\pi\)
\(6\) 0 0
\(7\) 3.00693 1.13651 0.568257 0.822851i \(-0.307618\pi\)
0.568257 + 0.822851i \(0.307618\pi\)
\(8\) 0 0
\(9\) 1.66392 0.554641
\(10\) 0 0
\(11\) 0.123870 0.0373483 0.0186741 0.999826i \(-0.494055\pi\)
0.0186741 + 0.999826i \(0.494055\pi\)
\(12\) 0 0
\(13\) 1.56775 0.434816 0.217408 0.976081i \(-0.430240\pi\)
0.217408 + 0.976081i \(0.430240\pi\)
\(14\) 0 0
\(15\) −0.401078 −0.103558
\(16\) 0 0
\(17\) 0.758557 0.183977 0.0919885 0.995760i \(-0.470678\pi\)
0.0919885 + 0.995760i \(0.470678\pi\)
\(18\) 0 0
\(19\) −3.18817 −0.731417 −0.365708 0.930730i \(-0.619173\pi\)
−0.365708 + 0.930730i \(0.619173\pi\)
\(20\) 0 0
\(21\) −6.49381 −1.41707
\(22\) 0 0
\(23\) −2.97273 −0.619858 −0.309929 0.950760i \(-0.600305\pi\)
−0.309929 + 0.950760i \(0.600305\pi\)
\(24\) 0 0
\(25\) −4.96551 −0.993102
\(26\) 0 0
\(27\) 2.88541 0.555297
\(28\) 0 0
\(29\) 3.26058 0.605475 0.302737 0.953074i \(-0.402099\pi\)
0.302737 + 0.953074i \(0.402099\pi\)
\(30\) 0 0
\(31\) 5.87406 1.05501 0.527506 0.849551i \(-0.323127\pi\)
0.527506 + 0.849551i \(0.323127\pi\)
\(32\) 0 0
\(33\) −0.267511 −0.0465678
\(34\) 0 0
\(35\) 0.558440 0.0943937
\(36\) 0 0
\(37\) −9.61053 −1.57996 −0.789981 0.613132i \(-0.789909\pi\)
−0.789981 + 0.613132i \(0.789909\pi\)
\(38\) 0 0
\(39\) −3.38573 −0.542151
\(40\) 0 0
\(41\) 5.98093 0.934065 0.467032 0.884240i \(-0.345323\pi\)
0.467032 + 0.884240i \(0.345323\pi\)
\(42\) 0 0
\(43\) −0.323388 −0.0493162 −0.0246581 0.999696i \(-0.507850\pi\)
−0.0246581 + 0.999696i \(0.507850\pi\)
\(44\) 0 0
\(45\) 0.309020 0.0460660
\(46\) 0 0
\(47\) −7.79465 −1.13697 −0.568483 0.822695i \(-0.692470\pi\)
−0.568483 + 0.822695i \(0.692470\pi\)
\(48\) 0 0
\(49\) 2.04165 0.291664
\(50\) 0 0
\(51\) −1.63819 −0.229392
\(52\) 0 0
\(53\) −13.4601 −1.84889 −0.924445 0.381316i \(-0.875471\pi\)
−0.924445 + 0.381316i \(0.875471\pi\)
\(54\) 0 0
\(55\) 0.0230049 0.00310198
\(56\) 0 0
\(57\) 6.88521 0.911969
\(58\) 0 0
\(59\) 1.94483 0.253196 0.126598 0.991954i \(-0.459594\pi\)
0.126598 + 0.991954i \(0.459594\pi\)
\(60\) 0 0
\(61\) −12.9913 −1.66337 −0.831684 0.555250i \(-0.812623\pi\)
−0.831684 + 0.555250i \(0.812623\pi\)
\(62\) 0 0
\(63\) 5.00331 0.630357
\(64\) 0 0
\(65\) 0.291159 0.0361138
\(66\) 0 0
\(67\) 8.01188 0.978807 0.489404 0.872057i \(-0.337215\pi\)
0.489404 + 0.872057i \(0.337215\pi\)
\(68\) 0 0
\(69\) 6.41995 0.772872
\(70\) 0 0
\(71\) −2.36443 −0.280606 −0.140303 0.990109i \(-0.544808\pi\)
−0.140303 + 0.990109i \(0.544808\pi\)
\(72\) 0 0
\(73\) 0.457187 0.0535096 0.0267548 0.999642i \(-0.491483\pi\)
0.0267548 + 0.999642i \(0.491483\pi\)
\(74\) 0 0
\(75\) 10.7236 1.23825
\(76\) 0 0
\(77\) 0.372469 0.0424468
\(78\) 0 0
\(79\) −2.18145 −0.245433 −0.122716 0.992442i \(-0.539161\pi\)
−0.122716 + 0.992442i \(0.539161\pi\)
\(80\) 0 0
\(81\) −11.2231 −1.24701
\(82\) 0 0
\(83\) 0.917360 0.100693 0.0503466 0.998732i \(-0.483967\pi\)
0.0503466 + 0.998732i \(0.483967\pi\)
\(84\) 0 0
\(85\) 0.140877 0.0152803
\(86\) 0 0
\(87\) −7.04159 −0.754938
\(88\) 0 0
\(89\) 8.20797 0.870043 0.435022 0.900420i \(-0.356741\pi\)
0.435022 + 0.900420i \(0.356741\pi\)
\(90\) 0 0
\(91\) 4.71412 0.494174
\(92\) 0 0
\(93\) −12.6857 −1.31544
\(94\) 0 0
\(95\) −0.592099 −0.0607481
\(96\) 0 0
\(97\) −8.84686 −0.898263 −0.449131 0.893466i \(-0.648266\pi\)
−0.449131 + 0.893466i \(0.648266\pi\)
\(98\) 0 0
\(99\) 0.206110 0.0207149
\(100\) 0 0
\(101\) 4.07703 0.405680 0.202840 0.979212i \(-0.434983\pi\)
0.202840 + 0.979212i \(0.434983\pi\)
\(102\) 0 0
\(103\) 1.80357 0.177711 0.0888553 0.996045i \(-0.471679\pi\)
0.0888553 + 0.996045i \(0.471679\pi\)
\(104\) 0 0
\(105\) −1.20601 −0.117695
\(106\) 0 0
\(107\) −8.35849 −0.808046 −0.404023 0.914749i \(-0.632388\pi\)
−0.404023 + 0.914749i \(0.632388\pi\)
\(108\) 0 0
\(109\) 10.1134 0.968692 0.484346 0.874876i \(-0.339058\pi\)
0.484346 + 0.874876i \(0.339058\pi\)
\(110\) 0 0
\(111\) 20.7550 1.96998
\(112\) 0 0
\(113\) 15.3774 1.44658 0.723290 0.690545i \(-0.242629\pi\)
0.723290 + 0.690545i \(0.242629\pi\)
\(114\) 0 0
\(115\) −0.552089 −0.0514826
\(116\) 0 0
\(117\) 2.60862 0.241167
\(118\) 0 0
\(119\) 2.28093 0.209092
\(120\) 0 0
\(121\) −10.9847 −0.998605
\(122\) 0 0
\(123\) −12.9165 −1.16464
\(124\) 0 0
\(125\) −1.85077 −0.165538
\(126\) 0 0
\(127\) 14.9686 1.32825 0.664125 0.747622i \(-0.268804\pi\)
0.664125 + 0.747622i \(0.268804\pi\)
\(128\) 0 0
\(129\) 0.698393 0.0614901
\(130\) 0 0
\(131\) −13.7545 −1.20173 −0.600867 0.799349i \(-0.705178\pi\)
−0.600867 + 0.799349i \(0.705178\pi\)
\(132\) 0 0
\(133\) −9.58662 −0.831265
\(134\) 0 0
\(135\) 0.535871 0.0461204
\(136\) 0 0
\(137\) −8.70396 −0.743629 −0.371815 0.928307i \(-0.621264\pi\)
−0.371815 + 0.928307i \(0.621264\pi\)
\(138\) 0 0
\(139\) 16.3690 1.38840 0.694200 0.719782i \(-0.255758\pi\)
0.694200 + 0.719782i \(0.255758\pi\)
\(140\) 0 0
\(141\) 16.8334 1.41763
\(142\) 0 0
\(143\) 0.194197 0.0162396
\(144\) 0 0
\(145\) 0.605548 0.0502880
\(146\) 0 0
\(147\) −4.40917 −0.363662
\(148\) 0 0
\(149\) −4.29603 −0.351945 −0.175972 0.984395i \(-0.556307\pi\)
−0.175972 + 0.984395i \(0.556307\pi\)
\(150\) 0 0
\(151\) 17.9440 1.46026 0.730132 0.683306i \(-0.239459\pi\)
0.730132 + 0.683306i \(0.239459\pi\)
\(152\) 0 0
\(153\) 1.26218 0.102041
\(154\) 0 0
\(155\) 1.09092 0.0876244
\(156\) 0 0
\(157\) −18.0006 −1.43660 −0.718301 0.695733i \(-0.755080\pi\)
−0.718301 + 0.695733i \(0.755080\pi\)
\(158\) 0 0
\(159\) 29.0686 2.30529
\(160\) 0 0
\(161\) −8.93882 −0.704477
\(162\) 0 0
\(163\) −10.8287 −0.848172 −0.424086 0.905622i \(-0.639405\pi\)
−0.424086 + 0.905622i \(0.639405\pi\)
\(164\) 0 0
\(165\) −0.0496816 −0.00386771
\(166\) 0 0
\(167\) 18.5314 1.43401 0.717003 0.697070i \(-0.245513\pi\)
0.717003 + 0.697070i \(0.245513\pi\)
\(168\) 0 0
\(169\) −10.5422 −0.810935
\(170\) 0 0
\(171\) −5.30487 −0.405674
\(172\) 0 0
\(173\) 23.4296 1.78132 0.890662 0.454667i \(-0.150242\pi\)
0.890662 + 0.454667i \(0.150242\pi\)
\(174\) 0 0
\(175\) −14.9310 −1.12867
\(176\) 0 0
\(177\) −4.20009 −0.315698
\(178\) 0 0
\(179\) −8.85816 −0.662090 −0.331045 0.943615i \(-0.607401\pi\)
−0.331045 + 0.943615i \(0.607401\pi\)
\(180\) 0 0
\(181\) 7.58982 0.564147 0.282073 0.959393i \(-0.408978\pi\)
0.282073 + 0.959393i \(0.408978\pi\)
\(182\) 0 0
\(183\) 28.0562 2.07397
\(184\) 0 0
\(185\) −1.78484 −0.131224
\(186\) 0 0
\(187\) 0.0939625 0.00687122
\(188\) 0 0
\(189\) 8.67623 0.631103
\(190\) 0 0
\(191\) 15.4585 1.11854 0.559269 0.828986i \(-0.311082\pi\)
0.559269 + 0.828986i \(0.311082\pi\)
\(192\) 0 0
\(193\) 23.7730 1.71122 0.855611 0.517620i \(-0.173182\pi\)
0.855611 + 0.517620i \(0.173182\pi\)
\(194\) 0 0
\(195\) −0.628790 −0.0450286
\(196\) 0 0
\(197\) −22.5479 −1.60647 −0.803237 0.595660i \(-0.796891\pi\)
−0.803237 + 0.595660i \(0.796891\pi\)
\(198\) 0 0
\(199\) −5.63389 −0.399376 −0.199688 0.979860i \(-0.563993\pi\)
−0.199688 + 0.979860i \(0.563993\pi\)
\(200\) 0 0
\(201\) −17.3026 −1.22043
\(202\) 0 0
\(203\) 9.80436 0.688131
\(204\) 0 0
\(205\) 1.11076 0.0775792
\(206\) 0 0
\(207\) −4.94640 −0.343799
\(208\) 0 0
\(209\) −0.394919 −0.0273171
\(210\) 0 0
\(211\) −22.8158 −1.57071 −0.785354 0.619048i \(-0.787519\pi\)
−0.785354 + 0.619048i \(0.787519\pi\)
\(212\) 0 0
\(213\) 5.10625 0.349874
\(214\) 0 0
\(215\) −0.0600589 −0.00409598
\(216\) 0 0
\(217\) 17.6629 1.19904
\(218\) 0 0
\(219\) −0.987346 −0.0667186
\(220\) 0 0
\(221\) 1.18923 0.0799961
\(222\) 0 0
\(223\) −16.7482 −1.12154 −0.560770 0.827972i \(-0.689495\pi\)
−0.560770 + 0.827972i \(0.689495\pi\)
\(224\) 0 0
\(225\) −8.26223 −0.550815
\(226\) 0 0
\(227\) −5.46239 −0.362552 −0.181276 0.983432i \(-0.558023\pi\)
−0.181276 + 0.983432i \(0.558023\pi\)
\(228\) 0 0
\(229\) −8.83811 −0.584039 −0.292019 0.956412i \(-0.594327\pi\)
−0.292019 + 0.956412i \(0.594327\pi\)
\(230\) 0 0
\(231\) −0.804389 −0.0529249
\(232\) 0 0
\(233\) 2.54676 0.166844 0.0834220 0.996514i \(-0.473415\pi\)
0.0834220 + 0.996514i \(0.473415\pi\)
\(234\) 0 0
\(235\) −1.44760 −0.0944313
\(236\) 0 0
\(237\) 4.71109 0.306018
\(238\) 0 0
\(239\) 7.96480 0.515200 0.257600 0.966252i \(-0.417068\pi\)
0.257600 + 0.966252i \(0.417068\pi\)
\(240\) 0 0
\(241\) −21.9559 −1.41430 −0.707151 0.707063i \(-0.750020\pi\)
−0.707151 + 0.707063i \(0.750020\pi\)
\(242\) 0 0
\(243\) 15.5814 0.999546
\(244\) 0 0
\(245\) 0.379170 0.0242243
\(246\) 0 0
\(247\) −4.99825 −0.318031
\(248\) 0 0
\(249\) −1.98114 −0.125550
\(250\) 0 0
\(251\) −1.05711 −0.0667243 −0.0333622 0.999443i \(-0.510621\pi\)
−0.0333622 + 0.999443i \(0.510621\pi\)
\(252\) 0 0
\(253\) −0.368233 −0.0231506
\(254\) 0 0
\(255\) −0.304240 −0.0190523
\(256\) 0 0
\(257\) −15.0351 −0.937863 −0.468931 0.883235i \(-0.655361\pi\)
−0.468931 + 0.883235i \(0.655361\pi\)
\(258\) 0 0
\(259\) −28.8982 −1.79565
\(260\) 0 0
\(261\) 5.42536 0.335821
\(262\) 0 0
\(263\) −31.6009 −1.94860 −0.974299 0.225261i \(-0.927677\pi\)
−0.974299 + 0.225261i \(0.927677\pi\)
\(264\) 0 0
\(265\) −2.49978 −0.153560
\(266\) 0 0
\(267\) −17.7260 −1.08482
\(268\) 0 0
\(269\) −25.5039 −1.55500 −0.777501 0.628882i \(-0.783513\pi\)
−0.777501 + 0.628882i \(0.783513\pi\)
\(270\) 0 0
\(271\) −30.5125 −1.85350 −0.926752 0.375674i \(-0.877411\pi\)
−0.926752 + 0.375674i \(0.877411\pi\)
\(272\) 0 0
\(273\) −10.1807 −0.616162
\(274\) 0 0
\(275\) −0.615078 −0.0370906
\(276\) 0 0
\(277\) −31.8739 −1.91511 −0.957557 0.288243i \(-0.906929\pi\)
−0.957557 + 0.288243i \(0.906929\pi\)
\(278\) 0 0
\(279\) 9.77398 0.585153
\(280\) 0 0
\(281\) −24.5286 −1.46325 −0.731627 0.681705i \(-0.761239\pi\)
−0.731627 + 0.681705i \(0.761239\pi\)
\(282\) 0 0
\(283\) −15.0966 −0.897401 −0.448701 0.893682i \(-0.648113\pi\)
−0.448701 + 0.893682i \(0.648113\pi\)
\(284\) 0 0
\(285\) 1.27870 0.0757439
\(286\) 0 0
\(287\) 17.9843 1.06158
\(288\) 0 0
\(289\) −16.4246 −0.966152
\(290\) 0 0
\(291\) 19.1058 1.12000
\(292\) 0 0
\(293\) 8.51542 0.497476 0.248738 0.968571i \(-0.419984\pi\)
0.248738 + 0.968571i \(0.419984\pi\)
\(294\) 0 0
\(295\) 0.361190 0.0210293
\(296\) 0 0
\(297\) 0.357416 0.0207394
\(298\) 0 0
\(299\) −4.66050 −0.269524
\(300\) 0 0
\(301\) −0.972407 −0.0560486
\(302\) 0 0
\(303\) −8.80480 −0.505823
\(304\) 0 0
\(305\) −2.41272 −0.138152
\(306\) 0 0
\(307\) 33.0858 1.88831 0.944155 0.329503i \(-0.106881\pi\)
0.944155 + 0.329503i \(0.106881\pi\)
\(308\) 0 0
\(309\) −3.89500 −0.221579
\(310\) 0 0
\(311\) 13.4761 0.764162 0.382081 0.924129i \(-0.375207\pi\)
0.382081 + 0.924129i \(0.375207\pi\)
\(312\) 0 0
\(313\) 7.22129 0.408171 0.204086 0.978953i \(-0.434578\pi\)
0.204086 + 0.978953i \(0.434578\pi\)
\(314\) 0 0
\(315\) 0.929202 0.0523546
\(316\) 0 0
\(317\) −3.30500 −0.185628 −0.0928138 0.995683i \(-0.529586\pi\)
−0.0928138 + 0.995683i \(0.529586\pi\)
\(318\) 0 0
\(319\) 0.403889 0.0226134
\(320\) 0 0
\(321\) 18.0511 1.00751
\(322\) 0 0
\(323\) −2.41841 −0.134564
\(324\) 0 0
\(325\) −7.78468 −0.431816
\(326\) 0 0
\(327\) −21.8411 −1.20782
\(328\) 0 0
\(329\) −23.4380 −1.29218
\(330\) 0 0
\(331\) 25.8668 1.42177 0.710884 0.703309i \(-0.248295\pi\)
0.710884 + 0.703309i \(0.248295\pi\)
\(332\) 0 0
\(333\) −15.9912 −0.876311
\(334\) 0 0
\(335\) 1.48795 0.0812952
\(336\) 0 0
\(337\) −11.2463 −0.612627 −0.306313 0.951931i \(-0.599096\pi\)
−0.306313 + 0.951931i \(0.599096\pi\)
\(338\) 0 0
\(339\) −33.2091 −1.80367
\(340\) 0 0
\(341\) 0.727620 0.0394028
\(342\) 0 0
\(343\) −14.9094 −0.805033
\(344\) 0 0
\(345\) 1.19230 0.0641912
\(346\) 0 0
\(347\) 14.9008 0.799914 0.399957 0.916534i \(-0.369025\pi\)
0.399957 + 0.916534i \(0.369025\pi\)
\(348\) 0 0
\(349\) −27.9580 −1.49656 −0.748278 0.663385i \(-0.769119\pi\)
−0.748278 + 0.663385i \(0.769119\pi\)
\(350\) 0 0
\(351\) 4.52360 0.241452
\(352\) 0 0
\(353\) 3.05626 0.162668 0.0813341 0.996687i \(-0.474082\pi\)
0.0813341 + 0.996687i \(0.474082\pi\)
\(354\) 0 0
\(355\) −0.439116 −0.0233059
\(356\) 0 0
\(357\) −4.92592 −0.260707
\(358\) 0 0
\(359\) −0.670710 −0.0353987 −0.0176994 0.999843i \(-0.505634\pi\)
−0.0176994 + 0.999843i \(0.505634\pi\)
\(360\) 0 0
\(361\) −8.83556 −0.465030
\(362\) 0 0
\(363\) 23.7226 1.24511
\(364\) 0 0
\(365\) 0.0849076 0.00444427
\(366\) 0 0
\(367\) 34.0680 1.77833 0.889167 0.457584i \(-0.151285\pi\)
0.889167 + 0.457584i \(0.151285\pi\)
\(368\) 0 0
\(369\) 9.95181 0.518071
\(370\) 0 0
\(371\) −40.4737 −2.10129
\(372\) 0 0
\(373\) −3.42167 −0.177167 −0.0885837 0.996069i \(-0.528234\pi\)
−0.0885837 + 0.996069i \(0.528234\pi\)
\(374\) 0 0
\(375\) 3.99695 0.206401
\(376\) 0 0
\(377\) 5.11178 0.263270
\(378\) 0 0
\(379\) −9.74129 −0.500376 −0.250188 0.968197i \(-0.580492\pi\)
−0.250188 + 0.968197i \(0.580492\pi\)
\(380\) 0 0
\(381\) −32.3264 −1.65613
\(382\) 0 0
\(383\) 29.4963 1.50719 0.753595 0.657339i \(-0.228318\pi\)
0.753595 + 0.657339i \(0.228318\pi\)
\(384\) 0 0
\(385\) 0.0691741 0.00352544
\(386\) 0 0
\(387\) −0.538093 −0.0273528
\(388\) 0 0
\(389\) −8.93654 −0.453101 −0.226550 0.973999i \(-0.572745\pi\)
−0.226550 + 0.973999i \(0.572745\pi\)
\(390\) 0 0
\(391\) −2.25499 −0.114040
\(392\) 0 0
\(393\) 29.7043 1.49838
\(394\) 0 0
\(395\) −0.405134 −0.0203845
\(396\) 0 0
\(397\) −23.4543 −1.17714 −0.588569 0.808447i \(-0.700308\pi\)
−0.588569 + 0.808447i \(0.700308\pi\)
\(398\) 0 0
\(399\) 20.7034 1.03647
\(400\) 0 0
\(401\) −8.22726 −0.410850 −0.205425 0.978673i \(-0.565858\pi\)
−0.205425 + 0.978673i \(0.565858\pi\)
\(402\) 0 0
\(403\) 9.20905 0.458735
\(404\) 0 0
\(405\) −2.08433 −0.103571
\(406\) 0 0
\(407\) −1.19046 −0.0590088
\(408\) 0 0
\(409\) 0.542389 0.0268194 0.0134097 0.999910i \(-0.495731\pi\)
0.0134097 + 0.999910i \(0.495731\pi\)
\(410\) 0 0
\(411\) 18.7972 0.927196
\(412\) 0 0
\(413\) 5.84799 0.287761
\(414\) 0 0
\(415\) 0.170370 0.00836312
\(416\) 0 0
\(417\) −35.3507 −1.73113
\(418\) 0 0
\(419\) 11.7197 0.572544 0.286272 0.958148i \(-0.407584\pi\)
0.286272 + 0.958148i \(0.407584\pi\)
\(420\) 0 0
\(421\) −27.4556 −1.33811 −0.669053 0.743215i \(-0.733300\pi\)
−0.669053 + 0.743215i \(0.733300\pi\)
\(422\) 0 0
\(423\) −12.9697 −0.630608
\(424\) 0 0
\(425\) −3.76662 −0.182708
\(426\) 0 0
\(427\) −39.0640 −1.89044
\(428\) 0 0
\(429\) −0.419391 −0.0202484
\(430\) 0 0
\(431\) −7.44537 −0.358631 −0.179316 0.983792i \(-0.557388\pi\)
−0.179316 + 0.983792i \(0.557388\pi\)
\(432\) 0 0
\(433\) −22.8573 −1.09845 −0.549225 0.835674i \(-0.685077\pi\)
−0.549225 + 0.835674i \(0.685077\pi\)
\(434\) 0 0
\(435\) −1.30775 −0.0627017
\(436\) 0 0
\(437\) 9.47759 0.453375
\(438\) 0 0
\(439\) −17.9643 −0.857391 −0.428696 0.903449i \(-0.641027\pi\)
−0.428696 + 0.903449i \(0.641027\pi\)
\(440\) 0 0
\(441\) 3.39715 0.161769
\(442\) 0 0
\(443\) −23.1568 −1.10021 −0.550106 0.835095i \(-0.685413\pi\)
−0.550106 + 0.835095i \(0.685413\pi\)
\(444\) 0 0
\(445\) 1.52436 0.0722618
\(446\) 0 0
\(447\) 9.27777 0.438823
\(448\) 0 0
\(449\) 20.5958 0.971974 0.485987 0.873966i \(-0.338460\pi\)
0.485987 + 0.873966i \(0.338460\pi\)
\(450\) 0 0
\(451\) 0.740859 0.0348857
\(452\) 0 0
\(453\) −38.7521 −1.82073
\(454\) 0 0
\(455\) 0.875495 0.0410438
\(456\) 0 0
\(457\) 5.35187 0.250350 0.125175 0.992135i \(-0.460051\pi\)
0.125175 + 0.992135i \(0.460051\pi\)
\(458\) 0 0
\(459\) 2.18874 0.102162
\(460\) 0 0
\(461\) −7.14059 −0.332570 −0.166285 0.986078i \(-0.553177\pi\)
−0.166285 + 0.986078i \(0.553177\pi\)
\(462\) 0 0
\(463\) −5.45647 −0.253584 −0.126792 0.991929i \(-0.540468\pi\)
−0.126792 + 0.991929i \(0.540468\pi\)
\(464\) 0 0
\(465\) −2.35595 −0.109255
\(466\) 0 0
\(467\) −24.0783 −1.11421 −0.557105 0.830442i \(-0.688088\pi\)
−0.557105 + 0.830442i \(0.688088\pi\)
\(468\) 0 0
\(469\) 24.0912 1.11243
\(470\) 0 0
\(471\) 38.8742 1.79123
\(472\) 0 0
\(473\) −0.0400581 −0.00184188
\(474\) 0 0
\(475\) 15.8309 0.726371
\(476\) 0 0
\(477\) −22.3966 −1.02547
\(478\) 0 0
\(479\) 32.4939 1.48468 0.742342 0.670021i \(-0.233715\pi\)
0.742342 + 0.670021i \(0.233715\pi\)
\(480\) 0 0
\(481\) −15.0669 −0.686992
\(482\) 0 0
\(483\) 19.3044 0.878379
\(484\) 0 0
\(485\) −1.64302 −0.0746056
\(486\) 0 0
\(487\) 26.4002 1.19631 0.598154 0.801381i \(-0.295901\pi\)
0.598154 + 0.801381i \(0.295901\pi\)
\(488\) 0 0
\(489\) 23.3859 1.05755
\(490\) 0 0
\(491\) 19.8605 0.896291 0.448145 0.893961i \(-0.352085\pi\)
0.448145 + 0.893961i \(0.352085\pi\)
\(492\) 0 0
\(493\) 2.47334 0.111393
\(494\) 0 0
\(495\) 0.0382783 0.00172048
\(496\) 0 0
\(497\) −7.10968 −0.318913
\(498\) 0 0
\(499\) 11.8942 0.532458 0.266229 0.963910i \(-0.414222\pi\)
0.266229 + 0.963910i \(0.414222\pi\)
\(500\) 0 0
\(501\) −40.0207 −1.78799
\(502\) 0 0
\(503\) 9.15677 0.408280 0.204140 0.978942i \(-0.434560\pi\)
0.204140 + 0.978942i \(0.434560\pi\)
\(504\) 0 0
\(505\) 0.757176 0.0336939
\(506\) 0 0
\(507\) 22.7670 1.01112
\(508\) 0 0
\(509\) 17.7270 0.785737 0.392868 0.919595i \(-0.371483\pi\)
0.392868 + 0.919595i \(0.371483\pi\)
\(510\) 0 0
\(511\) 1.37473 0.0608145
\(512\) 0 0
\(513\) −9.19917 −0.406153
\(514\) 0 0
\(515\) 0.334954 0.0147598
\(516\) 0 0
\(517\) −0.965525 −0.0424637
\(518\) 0 0
\(519\) −50.5989 −2.22105
\(520\) 0 0
\(521\) 14.4733 0.634089 0.317044 0.948411i \(-0.397310\pi\)
0.317044 + 0.948411i \(0.397310\pi\)
\(522\) 0 0
\(523\) −41.8021 −1.82788 −0.913938 0.405854i \(-0.866974\pi\)
−0.913938 + 0.405854i \(0.866974\pi\)
\(524\) 0 0
\(525\) 32.2451 1.40729
\(526\) 0 0
\(527\) 4.45580 0.194098
\(528\) 0 0
\(529\) −14.1628 −0.615776
\(530\) 0 0
\(531\) 3.23606 0.140433
\(532\) 0 0
\(533\) 9.37661 0.406146
\(534\) 0 0
\(535\) −1.55232 −0.0671126
\(536\) 0 0
\(537\) 19.1302 0.825529
\(538\) 0 0
\(539\) 0.252900 0.0108932
\(540\) 0 0
\(541\) −17.0011 −0.730934 −0.365467 0.930824i \(-0.619091\pi\)
−0.365467 + 0.930824i \(0.619091\pi\)
\(542\) 0 0
\(543\) −16.3911 −0.703408
\(544\) 0 0
\(545\) 1.87824 0.0804552
\(546\) 0 0
\(547\) −36.1741 −1.54669 −0.773347 0.633984i \(-0.781419\pi\)
−0.773347 + 0.633984i \(0.781419\pi\)
\(548\) 0 0
\(549\) −21.6165 −0.922572
\(550\) 0 0
\(551\) −10.3953 −0.442854
\(552\) 0 0
\(553\) −6.55948 −0.278938
\(554\) 0 0
\(555\) 3.85457 0.163617
\(556\) 0 0
\(557\) 7.86711 0.333340 0.166670 0.986013i \(-0.446699\pi\)
0.166670 + 0.986013i \(0.446699\pi\)
\(558\) 0 0
\(559\) −0.506992 −0.0214435
\(560\) 0 0
\(561\) −0.202923 −0.00856740
\(562\) 0 0
\(563\) −40.7498 −1.71740 −0.858701 0.512477i \(-0.828728\pi\)
−0.858701 + 0.512477i \(0.828728\pi\)
\(564\) 0 0
\(565\) 2.85585 0.120146
\(566\) 0 0
\(567\) −33.7472 −1.41725
\(568\) 0 0
\(569\) −8.02204 −0.336302 −0.168151 0.985761i \(-0.553780\pi\)
−0.168151 + 0.985761i \(0.553780\pi\)
\(570\) 0 0
\(571\) 8.97557 0.375616 0.187808 0.982206i \(-0.439862\pi\)
0.187808 + 0.982206i \(0.439862\pi\)
\(572\) 0 0
\(573\) −33.3844 −1.39465
\(574\) 0 0
\(575\) 14.7611 0.615582
\(576\) 0 0
\(577\) −16.9508 −0.705670 −0.352835 0.935686i \(-0.614782\pi\)
−0.352835 + 0.935686i \(0.614782\pi\)
\(578\) 0 0
\(579\) −51.3405 −2.13364
\(580\) 0 0
\(581\) 2.75844 0.114439
\(582\) 0 0
\(583\) −1.66731 −0.0690528
\(584\) 0 0
\(585\) 0.484466 0.0200302
\(586\) 0 0
\(587\) −45.0833 −1.86079 −0.930394 0.366562i \(-0.880535\pi\)
−0.930394 + 0.366562i \(0.880535\pi\)
\(588\) 0 0
\(589\) −18.7275 −0.771653
\(590\) 0 0
\(591\) 48.6948 2.00304
\(592\) 0 0
\(593\) 34.3125 1.40904 0.704522 0.709682i \(-0.251161\pi\)
0.704522 + 0.709682i \(0.251161\pi\)
\(594\) 0 0
\(595\) 0.423609 0.0173663
\(596\) 0 0
\(597\) 12.1670 0.497962
\(598\) 0 0
\(599\) 36.5543 1.49357 0.746783 0.665068i \(-0.231597\pi\)
0.746783 + 0.665068i \(0.231597\pi\)
\(600\) 0 0
\(601\) 4.28152 0.174647 0.0873235 0.996180i \(-0.472169\pi\)
0.0873235 + 0.996180i \(0.472169\pi\)
\(602\) 0 0
\(603\) 13.3312 0.542887
\(604\) 0 0
\(605\) −2.04004 −0.0829396
\(606\) 0 0
\(607\) −1.35162 −0.0548606 −0.0274303 0.999624i \(-0.508732\pi\)
−0.0274303 + 0.999624i \(0.508732\pi\)
\(608\) 0 0
\(609\) −21.1736 −0.857998
\(610\) 0 0
\(611\) −12.2201 −0.494371
\(612\) 0 0
\(613\) −25.0267 −1.01082 −0.505410 0.862879i \(-0.668659\pi\)
−0.505410 + 0.862879i \(0.668659\pi\)
\(614\) 0 0
\(615\) −2.39882 −0.0967298
\(616\) 0 0
\(617\) 23.2952 0.937830 0.468915 0.883243i \(-0.344645\pi\)
0.468915 + 0.883243i \(0.344645\pi\)
\(618\) 0 0
\(619\) −6.05784 −0.243485 −0.121743 0.992562i \(-0.538848\pi\)
−0.121743 + 0.992562i \(0.538848\pi\)
\(620\) 0 0
\(621\) −8.57755 −0.344205
\(622\) 0 0
\(623\) 24.6808 0.988817
\(624\) 0 0
\(625\) 24.4838 0.979353
\(626\) 0 0
\(627\) 0.852872 0.0340604
\(628\) 0 0
\(629\) −7.29013 −0.290676
\(630\) 0 0
\(631\) −35.6830 −1.42052 −0.710259 0.703940i \(-0.751422\pi\)
−0.710259 + 0.703940i \(0.751422\pi\)
\(632\) 0 0
\(633\) 49.2734 1.95844
\(634\) 0 0
\(635\) 2.77994 0.110318
\(636\) 0 0
\(637\) 3.20080 0.126820
\(638\) 0 0
\(639\) −3.93423 −0.155636
\(640\) 0 0
\(641\) −26.9261 −1.06352 −0.531759 0.846896i \(-0.678469\pi\)
−0.531759 + 0.846896i \(0.678469\pi\)
\(642\) 0 0
\(643\) 16.5169 0.651363 0.325682 0.945480i \(-0.394406\pi\)
0.325682 + 0.945480i \(0.394406\pi\)
\(644\) 0 0
\(645\) 0.129704 0.00510709
\(646\) 0 0
\(647\) −7.67446 −0.301714 −0.150857 0.988556i \(-0.548203\pi\)
−0.150857 + 0.988556i \(0.548203\pi\)
\(648\) 0 0
\(649\) 0.240907 0.00945643
\(650\) 0 0
\(651\) −38.1450 −1.49502
\(652\) 0 0
\(653\) −28.7242 −1.12406 −0.562032 0.827115i \(-0.689980\pi\)
−0.562032 + 0.827115i \(0.689980\pi\)
\(654\) 0 0
\(655\) −2.55445 −0.0998105
\(656\) 0 0
\(657\) 0.760723 0.0296786
\(658\) 0 0
\(659\) 32.3867 1.26161 0.630804 0.775943i \(-0.282725\pi\)
0.630804 + 0.775943i \(0.282725\pi\)
\(660\) 0 0
\(661\) 27.1627 1.05651 0.528254 0.849086i \(-0.322847\pi\)
0.528254 + 0.849086i \(0.322847\pi\)
\(662\) 0 0
\(663\) −2.56827 −0.0997433
\(664\) 0 0
\(665\) −1.78040 −0.0690411
\(666\) 0 0
\(667\) −9.69285 −0.375309
\(668\) 0 0
\(669\) 36.1695 1.39839
\(670\) 0 0
\(671\) −1.60924 −0.0621239
\(672\) 0 0
\(673\) 3.38022 0.130298 0.0651489 0.997876i \(-0.479248\pi\)
0.0651489 + 0.997876i \(0.479248\pi\)
\(674\) 0 0
\(675\) −14.3275 −0.551466
\(676\) 0 0
\(677\) −27.2040 −1.04554 −0.522768 0.852475i \(-0.675101\pi\)
−0.522768 + 0.852475i \(0.675101\pi\)
\(678\) 0 0
\(679\) −26.6019 −1.02089
\(680\) 0 0
\(681\) 11.7966 0.452048
\(682\) 0 0
\(683\) 22.0966 0.845503 0.422751 0.906246i \(-0.361064\pi\)
0.422751 + 0.906246i \(0.361064\pi\)
\(684\) 0 0
\(685\) −1.61648 −0.0617625
\(686\) 0 0
\(687\) 19.0869 0.728210
\(688\) 0 0
\(689\) −21.1021 −0.803926
\(690\) 0 0
\(691\) −26.9351 −1.02466 −0.512330 0.858788i \(-0.671218\pi\)
−0.512330 + 0.858788i \(0.671218\pi\)
\(692\) 0 0
\(693\) 0.619760 0.0235427
\(694\) 0 0
\(695\) 3.04001 0.115314
\(696\) 0 0
\(697\) 4.53688 0.171846
\(698\) 0 0
\(699\) −5.50002 −0.208030
\(700\) 0 0
\(701\) 26.3883 0.996673 0.498337 0.866984i \(-0.333944\pi\)
0.498337 + 0.866984i \(0.333944\pi\)
\(702\) 0 0
\(703\) 30.6400 1.15561
\(704\) 0 0
\(705\) 3.12626 0.117742
\(706\) 0 0
\(707\) 12.2594 0.461061
\(708\) 0 0
\(709\) 42.3313 1.58979 0.794893 0.606750i \(-0.207527\pi\)
0.794893 + 0.606750i \(0.207527\pi\)
\(710\) 0 0
\(711\) −3.62977 −0.136127
\(712\) 0 0
\(713\) −17.4620 −0.653957
\(714\) 0 0
\(715\) 0.0360659 0.00134879
\(716\) 0 0
\(717\) −17.2009 −0.642378
\(718\) 0 0
\(719\) 10.7951 0.402589 0.201295 0.979531i \(-0.435485\pi\)
0.201295 + 0.979531i \(0.435485\pi\)
\(720\) 0 0
\(721\) 5.42320 0.201971
\(722\) 0 0
\(723\) 47.4162 1.76343
\(724\) 0 0
\(725\) −16.1905 −0.601298
\(726\) 0 0
\(727\) −48.6662 −1.80493 −0.902466 0.430762i \(-0.858245\pi\)
−0.902466 + 0.430762i \(0.858245\pi\)
\(728\) 0 0
\(729\) 0.0196552 0.000727972 0
\(730\) 0 0
\(731\) −0.245308 −0.00907305
\(732\) 0 0
\(733\) 41.4139 1.52966 0.764829 0.644233i \(-0.222823\pi\)
0.764829 + 0.644233i \(0.222823\pi\)
\(734\) 0 0
\(735\) −0.818861 −0.0302041
\(736\) 0 0
\(737\) 0.992433 0.0365567
\(738\) 0 0
\(739\) 22.2022 0.816723 0.408361 0.912820i \(-0.366100\pi\)
0.408361 + 0.912820i \(0.366100\pi\)
\(740\) 0 0
\(741\) 10.7943 0.396538
\(742\) 0 0
\(743\) 25.7936 0.946276 0.473138 0.880988i \(-0.343121\pi\)
0.473138 + 0.880988i \(0.343121\pi\)
\(744\) 0 0
\(745\) −0.797849 −0.0292309
\(746\) 0 0
\(747\) 1.52642 0.0558486
\(748\) 0 0
\(749\) −25.1334 −0.918355
\(750\) 0 0
\(751\) 1.00000 0.0364905
\(752\) 0 0
\(753\) 2.28295 0.0831954
\(754\) 0 0
\(755\) 3.33252 0.121283
\(756\) 0 0
\(757\) −39.0976 −1.42103 −0.710513 0.703684i \(-0.751537\pi\)
−0.710513 + 0.703684i \(0.751537\pi\)
\(758\) 0 0
\(759\) 0.795241 0.0288654
\(760\) 0 0
\(761\) −0.291090 −0.0105520 −0.00527601 0.999986i \(-0.501679\pi\)
−0.00527601 + 0.999986i \(0.501679\pi\)
\(762\) 0 0
\(763\) 30.4105 1.10093
\(764\) 0 0
\(765\) 0.234409 0.00847507
\(766\) 0 0
\(767\) 3.04901 0.110094
\(768\) 0 0
\(769\) 0.941041 0.0339348 0.0169674 0.999856i \(-0.494599\pi\)
0.0169674 + 0.999856i \(0.494599\pi\)
\(770\) 0 0
\(771\) 32.4700 1.16938
\(772\) 0 0
\(773\) −21.7263 −0.781440 −0.390720 0.920510i \(-0.627774\pi\)
−0.390720 + 0.920510i \(0.627774\pi\)
\(774\) 0 0
\(775\) −29.1677 −1.04773
\(776\) 0 0
\(777\) 62.4089 2.23891
\(778\) 0 0
\(779\) −19.0682 −0.683191
\(780\) 0 0
\(781\) −0.292882 −0.0104801
\(782\) 0 0
\(783\) 9.40811 0.336218
\(784\) 0 0
\(785\) −3.34302 −0.119318
\(786\) 0 0
\(787\) −18.0634 −0.643890 −0.321945 0.946758i \(-0.604337\pi\)
−0.321945 + 0.946758i \(0.604337\pi\)
\(788\) 0 0
\(789\) 68.2457 2.42961
\(790\) 0 0
\(791\) 46.2387 1.64406
\(792\) 0 0
\(793\) −20.3671 −0.723258
\(794\) 0 0
\(795\) 5.39856 0.191467
\(796\) 0 0
\(797\) 5.92165 0.209756 0.104878 0.994485i \(-0.466555\pi\)
0.104878 + 0.994485i \(0.466555\pi\)
\(798\) 0 0
\(799\) −5.91268 −0.209176
\(800\) 0 0
\(801\) 13.6574 0.482562
\(802\) 0 0
\(803\) 0.0566318 0.00199849
\(804\) 0 0
\(805\) −1.66010 −0.0585107
\(806\) 0 0
\(807\) 55.0786 1.93886
\(808\) 0 0
\(809\) 31.3365 1.10173 0.550866 0.834594i \(-0.314298\pi\)
0.550866 + 0.834594i \(0.314298\pi\)
\(810\) 0 0
\(811\) −16.5095 −0.579729 −0.289864 0.957068i \(-0.593610\pi\)
−0.289864 + 0.957068i \(0.593610\pi\)
\(812\) 0 0
\(813\) 65.8952 2.31105
\(814\) 0 0
\(815\) −2.01109 −0.0704453
\(816\) 0 0
\(817\) 1.03102 0.0360707
\(818\) 0 0
\(819\) 7.84393 0.274089
\(820\) 0 0
\(821\) 15.3100 0.534324 0.267162 0.963652i \(-0.413914\pi\)
0.267162 + 0.963652i \(0.413914\pi\)
\(822\) 0 0
\(823\) 24.7942 0.864273 0.432137 0.901808i \(-0.357760\pi\)
0.432137 + 0.901808i \(0.357760\pi\)
\(824\) 0 0
\(825\) 1.32833 0.0462465
\(826\) 0 0
\(827\) −50.8640 −1.76872 −0.884358 0.466810i \(-0.845403\pi\)
−0.884358 + 0.466810i \(0.845403\pi\)
\(828\) 0 0
\(829\) 37.7297 1.31041 0.655204 0.755452i \(-0.272583\pi\)
0.655204 + 0.755452i \(0.272583\pi\)
\(830\) 0 0
\(831\) 68.8352 2.38787
\(832\) 0 0
\(833\) 1.54871 0.0536595
\(834\) 0 0
\(835\) 3.44161 0.119102
\(836\) 0 0
\(837\) 16.9490 0.585845
\(838\) 0 0
\(839\) 35.6616 1.23117 0.615587 0.788069i \(-0.288919\pi\)
0.615587 + 0.788069i \(0.288919\pi\)
\(840\) 0 0
\(841\) −18.3686 −0.633400
\(842\) 0 0
\(843\) 52.9722 1.82446
\(844\) 0 0
\(845\) −1.95786 −0.0673526
\(846\) 0 0
\(847\) −33.0301 −1.13493
\(848\) 0 0
\(849\) 32.6029 1.11893
\(850\) 0 0
\(851\) 28.5696 0.979352
\(852\) 0 0
\(853\) 25.0875 0.858979 0.429490 0.903072i \(-0.358693\pi\)
0.429490 + 0.903072i \(0.358693\pi\)
\(854\) 0 0
\(855\) −0.985208 −0.0336934
\(856\) 0 0
\(857\) −43.0907 −1.47195 −0.735975 0.677008i \(-0.763276\pi\)
−0.735975 + 0.677008i \(0.763276\pi\)
\(858\) 0 0
\(859\) −31.5470 −1.07637 −0.538184 0.842827i \(-0.680890\pi\)
−0.538184 + 0.842827i \(0.680890\pi\)
\(860\) 0 0
\(861\) −38.8390 −1.32363
\(862\) 0 0
\(863\) −43.2603 −1.47260 −0.736298 0.676657i \(-0.763428\pi\)
−0.736298 + 0.676657i \(0.763428\pi\)
\(864\) 0 0
\(865\) 4.35130 0.147949
\(866\) 0 0
\(867\) 35.4707 1.20465
\(868\) 0 0
\(869\) −0.270217 −0.00916648
\(870\) 0 0
\(871\) 12.5606 0.425601
\(872\) 0 0
\(873\) −14.7205 −0.498213
\(874\) 0 0
\(875\) −5.56514 −0.188136
\(876\) 0 0
\(877\) 32.6615 1.10290 0.551450 0.834208i \(-0.314075\pi\)
0.551450 + 0.834208i \(0.314075\pi\)
\(878\) 0 0
\(879\) −18.3900 −0.620279
\(880\) 0 0
\(881\) 27.1491 0.914677 0.457338 0.889293i \(-0.348803\pi\)
0.457338 + 0.889293i \(0.348803\pi\)
\(882\) 0 0
\(883\) 42.1691 1.41910 0.709552 0.704653i \(-0.248898\pi\)
0.709552 + 0.704653i \(0.248898\pi\)
\(884\) 0 0
\(885\) −0.780030 −0.0262204
\(886\) 0 0
\(887\) 13.6522 0.458397 0.229198 0.973380i \(-0.426390\pi\)
0.229198 + 0.973380i \(0.426390\pi\)
\(888\) 0 0
\(889\) 45.0096 1.50957
\(890\) 0 0
\(891\) −1.39021 −0.0465738
\(892\) 0 0
\(893\) 24.8507 0.831596
\(894\) 0 0
\(895\) −1.64512 −0.0549902
\(896\) 0 0
\(897\) 10.0649 0.336057
\(898\) 0 0
\(899\) 19.1528 0.638783
\(900\) 0 0
\(901\) −10.2103 −0.340153
\(902\) 0 0
\(903\) 2.10002 0.0698843
\(904\) 0 0
\(905\) 1.40956 0.0468555
\(906\) 0 0
\(907\) −36.0484 −1.19697 −0.598483 0.801135i \(-0.704230\pi\)
−0.598483 + 0.801135i \(0.704230\pi\)
\(908\) 0 0
\(909\) 6.78387 0.225007
\(910\) 0 0
\(911\) −46.3666 −1.53620 −0.768098 0.640333i \(-0.778796\pi\)
−0.768098 + 0.640333i \(0.778796\pi\)
\(912\) 0 0
\(913\) 0.113633 0.00376072
\(914\) 0 0
\(915\) 5.21053 0.172255
\(916\) 0 0
\(917\) −41.3588 −1.36579
\(918\) 0 0
\(919\) 21.2309 0.700344 0.350172 0.936685i \(-0.386123\pi\)
0.350172 + 0.936685i \(0.386123\pi\)
\(920\) 0 0
\(921\) −71.4526 −2.35444
\(922\) 0 0
\(923\) −3.70683 −0.122012
\(924\) 0 0
\(925\) 47.7212 1.56906
\(926\) 0 0
\(927\) 3.00099 0.0985656
\(928\) 0 0
\(929\) 24.2004 0.793989 0.396995 0.917821i \(-0.370053\pi\)
0.396995 + 0.917821i \(0.370053\pi\)
\(930\) 0 0
\(931\) −6.50913 −0.213328
\(932\) 0 0
\(933\) −29.1032 −0.952798
\(934\) 0 0
\(935\) 0.0174505 0.000570692 0
\(936\) 0 0
\(937\) 17.9568 0.586623 0.293311 0.956017i \(-0.405243\pi\)
0.293311 + 0.956017i \(0.405243\pi\)
\(938\) 0 0
\(939\) −15.5952 −0.508929
\(940\) 0 0
\(941\) 25.2375 0.822720 0.411360 0.911473i \(-0.365054\pi\)
0.411360 + 0.911473i \(0.365054\pi\)
\(942\) 0 0
\(943\) −17.7797 −0.578988
\(944\) 0 0
\(945\) 1.61133 0.0524165
\(946\) 0 0
\(947\) −37.2824 −1.21151 −0.605757 0.795650i \(-0.707130\pi\)
−0.605757 + 0.795650i \(0.707130\pi\)
\(948\) 0 0
\(949\) 0.716754 0.0232668
\(950\) 0 0
\(951\) 7.13753 0.231450
\(952\) 0 0
\(953\) 2.73424 0.0885706 0.0442853 0.999019i \(-0.485899\pi\)
0.0442853 + 0.999019i \(0.485899\pi\)
\(954\) 0 0
\(955\) 2.87092 0.0929007
\(956\) 0 0
\(957\) −0.872243 −0.0281956
\(958\) 0 0
\(959\) −26.1722 −0.845145
\(960\) 0 0
\(961\) 3.50453 0.113049
\(962\) 0 0
\(963\) −13.9079 −0.448175
\(964\) 0 0
\(965\) 4.41507 0.142126
\(966\) 0 0
\(967\) 7.31745 0.235313 0.117657 0.993054i \(-0.462462\pi\)
0.117657 + 0.993054i \(0.462462\pi\)
\(968\) 0 0
\(969\) 5.22282 0.167781
\(970\) 0 0
\(971\) −8.13022 −0.260911 −0.130456 0.991454i \(-0.541644\pi\)
−0.130456 + 0.991454i \(0.541644\pi\)
\(972\) 0 0
\(973\) 49.2205 1.57794
\(974\) 0 0
\(975\) 16.8119 0.538411
\(976\) 0 0
\(977\) 11.0026 0.352003 0.176002 0.984390i \(-0.443684\pi\)
0.176002 + 0.984390i \(0.443684\pi\)
\(978\) 0 0
\(979\) 1.01672 0.0324946
\(980\) 0 0
\(981\) 16.8280 0.537276
\(982\) 0 0
\(983\) −24.2979 −0.774982 −0.387491 0.921874i \(-0.626658\pi\)
−0.387491 + 0.921874i \(0.626658\pi\)
\(984\) 0 0
\(985\) −4.18755 −0.133426
\(986\) 0 0
\(987\) 50.6170 1.61116
\(988\) 0 0
\(989\) 0.961348 0.0305691
\(990\) 0 0
\(991\) −22.9229 −0.728170 −0.364085 0.931366i \(-0.618618\pi\)
−0.364085 + 0.931366i \(0.618618\pi\)
\(992\) 0 0
\(993\) −55.8623 −1.77274
\(994\) 0 0
\(995\) −1.04631 −0.0331703
\(996\) 0 0
\(997\) −37.3956 −1.18433 −0.592165 0.805817i \(-0.701726\pi\)
−0.592165 + 0.805817i \(0.701726\pi\)
\(998\) 0 0
\(999\) −27.7303 −0.877347
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 6008.2.a.c.1.9 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.c.1.9 44 1.1 even 1 trivial