Properties

Label 847.2.b.f.846.12
Level $847$
Weight $2$
Character 847.846
Analytic conductor $6.763$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,2,Mod(846,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.846");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 20x^{14} + 260x^{12} + 2030x^{10} + 11605x^{8} + 42100x^{6} + 106925x^{4} + 113575x^{2} + 87025 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 846.12
Root \(-0.551501 - 0.955228i\) of defining polynomial
Character \(\chi\) \(=\) 847.846
Dual form 847.2.b.f.846.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.672816i q^{2} +2.65257i q^{3} +1.54732 q^{4} +3.54984i q^{5} -1.78470 q^{6} +(1.10300 - 2.40487i) q^{7} +2.38669i q^{8} -4.03615 q^{9} +O(q^{10})\) \(q+0.672816i q^{2} +2.65257i q^{3} +1.54732 q^{4} +3.54984i q^{5} -1.78470 q^{6} +(1.10300 - 2.40487i) q^{7} +2.38669i q^{8} -4.03615 q^{9} -2.38839 q^{10} +4.10438i q^{12} +1.10300 q^{13} +(1.61803 + 0.742118i) q^{14} -9.41620 q^{15} +1.48883 q^{16} -4.17308 q^{17} -2.71559i q^{18} -1.24551 q^{19} +5.49273i q^{20} +(6.37909 + 2.92579i) q^{21} +2.85410 q^{23} -6.33088 q^{24} -7.60134 q^{25} +0.742118i q^{26} -2.74846i q^{27} +(1.70670 - 3.72109i) q^{28} +2.04277i q^{29} -6.33538i q^{30} -2.99530i q^{31} +5.77510i q^{32} -2.80772i q^{34} +(8.53689 + 3.91548i) q^{35} -6.24520 q^{36} +2.76202 q^{37} -0.838003i q^{38} +2.92579i q^{39} -8.47237 q^{40} +5.49660 q^{41} +(-1.96852 + 4.29195i) q^{42} -1.73205i q^{43} -14.3277i q^{45} +1.92029i q^{46} -6.82860i q^{47} +3.94923i q^{48} +(-4.56677 - 5.30515i) q^{49} -5.11431i q^{50} -11.0694i q^{51} +1.70670 q^{52} +1.07985 q^{53} +1.84921 q^{54} +(5.73968 + 2.63253i) q^{56} -3.30382i q^{57} -1.37441 q^{58} -2.28980i q^{59} -14.5699 q^{60} +13.3518 q^{61} +2.01529 q^{62} +(-4.45188 + 9.70640i) q^{63} -0.907920 q^{64} +3.91548i q^{65} +0.489806 q^{67} -6.45709 q^{68} +7.57072i q^{69} +(-2.63440 + 5.74376i) q^{70} +10.2062 q^{71} -9.63305i q^{72} -12.5276 q^{73} +1.85833i q^{74} -20.1631i q^{75} -1.92721 q^{76} -1.96852 q^{78} -12.4332i q^{79} +5.28510i q^{80} -4.81795 q^{81} +3.69820i q^{82} -1.61862 q^{83} +(9.87048 + 4.52714i) q^{84} -14.8138i q^{85} +1.16535 q^{86} -5.41860 q^{87} +2.30985i q^{89} +9.63989 q^{90} +(1.21661 - 2.65257i) q^{91} +4.41620 q^{92} +7.94525 q^{93} +4.59439 q^{94} -4.42137i q^{95} -15.3189 q^{96} +12.6682i q^{97} +(3.56939 - 3.07260i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 32 q^{9} + 8 q^{14} - 20 q^{15} + 16 q^{16} - 8 q^{23} - 40 q^{25} - 60 q^{36} - 36 q^{37} - 20 q^{42} + 48 q^{49} + 20 q^{53} - 4 q^{56} + 28 q^{58} - 140 q^{60} + 12 q^{64} - 4 q^{67} + 100 q^{70} + 44 q^{71} - 20 q^{78} - 56 q^{81} - 24 q^{86} + 80 q^{91} - 60 q^{92} - 20 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.672816i 0.475753i 0.971295 + 0.237877i \(0.0764514\pi\)
−0.971295 + 0.237877i \(0.923549\pi\)
\(3\) 2.65257i 1.53146i 0.643160 + 0.765732i \(0.277623\pi\)
−0.643160 + 0.765732i \(0.722377\pi\)
\(4\) 1.54732 0.773659
\(5\) 3.54984i 1.58754i 0.608221 + 0.793768i \(0.291883\pi\)
−0.608221 + 0.793768i \(0.708117\pi\)
\(6\) −1.78470 −0.728599
\(7\) 1.10300 2.40487i 0.416896 0.908954i
\(8\) 2.38669i 0.843824i
\(9\) −4.03615 −1.34538
\(10\) −2.38839 −0.755275
\(11\) 0 0
\(12\) 4.10438i 1.18483i
\(13\) 1.10300 0.305918 0.152959 0.988233i \(-0.451120\pi\)
0.152959 + 0.988233i \(0.451120\pi\)
\(14\) 1.61803 + 0.742118i 0.432438 + 0.198339i
\(15\) −9.41620 −2.43125
\(16\) 1.48883 0.372207
\(17\) −4.17308 −1.01212 −0.506061 0.862498i \(-0.668899\pi\)
−0.506061 + 0.862498i \(0.668899\pi\)
\(18\) 2.71559i 0.640070i
\(19\) −1.24551 −0.285741 −0.142870 0.989741i \(-0.545633\pi\)
−0.142870 + 0.989741i \(0.545633\pi\)
\(20\) 5.49273i 1.22821i
\(21\) 6.37909 + 2.92579i 1.39203 + 0.638461i
\(22\) 0 0
\(23\) 2.85410 0.595121 0.297561 0.954703i \(-0.403827\pi\)
0.297561 + 0.954703i \(0.403827\pi\)
\(24\) −6.33088 −1.29229
\(25\) −7.60134 −1.52027
\(26\) 0.742118i 0.145541i
\(27\) 2.74846i 0.528941i
\(28\) 1.70670 3.72109i 0.322535 0.703221i
\(29\) 2.04277i 0.379333i 0.981849 + 0.189666i \(0.0607407\pi\)
−0.981849 + 0.189666i \(0.939259\pi\)
\(30\) 6.33538i 1.15668i
\(31\) 2.99530i 0.537971i −0.963144 0.268986i \(-0.913312\pi\)
0.963144 0.268986i \(-0.0866884\pi\)
\(32\) 5.77510i 1.02090i
\(33\) 0 0
\(34\) 2.80772i 0.481520i
\(35\) 8.53689 + 3.91548i 1.44300 + 0.661837i
\(36\) −6.24520 −1.04087
\(37\) 2.76202 0.454074 0.227037 0.973886i \(-0.427096\pi\)
0.227037 + 0.973886i \(0.427096\pi\)
\(38\) 0.838003i 0.135942i
\(39\) 2.92579i 0.468502i
\(40\) −8.47237 −1.33960
\(41\) 5.49660 0.858424 0.429212 0.903204i \(-0.358791\pi\)
0.429212 + 0.903204i \(0.358791\pi\)
\(42\) −1.96852 + 4.29195i −0.303750 + 0.662263i
\(43\) 1.73205i 0.264135i −0.991241 0.132068i \(-0.957838\pi\)
0.991241 0.132068i \(-0.0421616\pi\)
\(44\) 0 0
\(45\) 14.3277i 2.13584i
\(46\) 1.92029i 0.283131i
\(47\) 6.82860i 0.996053i −0.867162 0.498027i \(-0.834058\pi\)
0.867162 0.498027i \(-0.165942\pi\)
\(48\) 3.94923i 0.570022i
\(49\) −4.56677 5.30515i −0.652396 0.757878i
\(50\) 5.11431i 0.723272i
\(51\) 11.0694i 1.55003i
\(52\) 1.70670 0.236676
\(53\) 1.07985 0.148329 0.0741646 0.997246i \(-0.476371\pi\)
0.0741646 + 0.997246i \(0.476371\pi\)
\(54\) 1.84921 0.251645
\(55\) 0 0
\(56\) 5.73968 + 2.63253i 0.766997 + 0.351786i
\(57\) 3.30382i 0.437602i
\(58\) −1.37441 −0.180469
\(59\) 2.28980i 0.298107i −0.988829 0.149054i \(-0.952377\pi\)
0.988829 0.149054i \(-0.0476227\pi\)
\(60\) −14.5699 −1.88096
\(61\) 13.3518 1.70952 0.854761 0.519022i \(-0.173704\pi\)
0.854761 + 0.519022i \(0.173704\pi\)
\(62\) 2.01529 0.255941
\(63\) −4.45188 + 9.70640i −0.560884 + 1.22289i
\(64\) −0.907920 −0.113490
\(65\) 3.91548i 0.485655i
\(66\) 0 0
\(67\) 0.489806 0.0598393 0.0299197 0.999552i \(-0.490475\pi\)
0.0299197 + 0.999552i \(0.490475\pi\)
\(68\) −6.45709 −0.783037
\(69\) 7.57072i 0.911407i
\(70\) −2.63440 + 5.74376i −0.314871 + 0.686510i
\(71\) 10.2062 1.21125 0.605625 0.795750i \(-0.292923\pi\)
0.605625 + 0.795750i \(0.292923\pi\)
\(72\) 9.63305i 1.13527i
\(73\) −12.5276 −1.46624 −0.733121 0.680098i \(-0.761937\pi\)
−0.733121 + 0.680098i \(0.761937\pi\)
\(74\) 1.85833i 0.216027i
\(75\) 20.1631i 2.32824i
\(76\) −1.92721 −0.221066
\(77\) 0 0
\(78\) −1.96852 −0.222891
\(79\) 12.4332i 1.39885i −0.714708 0.699423i \(-0.753440\pi\)
0.714708 0.699423i \(-0.246560\pi\)
\(80\) 5.28510i 0.590892i
\(81\) −4.81795 −0.535328
\(82\) 3.69820i 0.408398i
\(83\) −1.61862 −0.177666 −0.0888332 0.996047i \(-0.528314\pi\)
−0.0888332 + 0.996047i \(0.528314\pi\)
\(84\) 9.87048 + 4.52714i 1.07696 + 0.493951i
\(85\) 14.8138i 1.60678i
\(86\) 1.16535 0.125663
\(87\) −5.41860 −0.580935
\(88\) 0 0
\(89\) 2.30985i 0.244844i 0.992478 + 0.122422i \(0.0390661\pi\)
−0.992478 + 0.122422i \(0.960934\pi\)
\(90\) 9.63989 1.01613
\(91\) 1.21661 2.65257i 0.127536 0.278065i
\(92\) 4.41620 0.460421
\(93\) 7.94525 0.823884
\(94\) 4.59439 0.473875
\(95\) 4.42137i 0.453623i
\(96\) −15.3189 −1.56348
\(97\) 12.6682i 1.28626i 0.765755 + 0.643132i \(0.222366\pi\)
−0.765755 + 0.643132i \(0.777634\pi\)
\(98\) 3.56939 3.07260i 0.360563 0.310379i
\(99\) 0 0
\(100\) −11.7617 −1.17617
\(101\) −3.16649 −0.315078 −0.157539 0.987513i \(-0.550356\pi\)
−0.157539 + 0.987513i \(0.550356\pi\)
\(102\) 7.44768 0.737430
\(103\) 9.73220i 0.958942i 0.877558 + 0.479471i \(0.159171\pi\)
−0.877558 + 0.479471i \(0.840829\pi\)
\(104\) 2.63253i 0.258141i
\(105\) −10.3861 + 22.6447i −1.01358 + 2.20990i
\(106\) 0.726543i 0.0705680i
\(107\) 10.5567i 1.02056i 0.860010 + 0.510278i \(0.170457\pi\)
−0.860010 + 0.510278i \(0.829543\pi\)
\(108\) 4.25274i 0.409220i
\(109\) 3.04683i 0.291833i −0.989297 0.145917i \(-0.953387\pi\)
0.989297 0.145917i \(-0.0466131\pi\)
\(110\) 0 0
\(111\) 7.32647i 0.695397i
\(112\) 1.64218 3.58044i 0.155172 0.338320i
\(113\) 7.25710 0.682691 0.341345 0.939938i \(-0.389117\pi\)
0.341345 + 0.939938i \(0.389117\pi\)
\(114\) 2.22286 0.208190
\(115\) 10.1316i 0.944776i
\(116\) 3.16082i 0.293474i
\(117\) −4.45188 −0.411576
\(118\) 1.54062 0.141825
\(119\) −4.60292 + 10.0357i −0.421949 + 0.919972i
\(120\) 22.4736i 2.05155i
\(121\) 0 0
\(122\) 8.98330i 0.813310i
\(123\) 14.5801i 1.31465i
\(124\) 4.63468i 0.416206i
\(125\) 9.23433i 0.825944i
\(126\) −6.53062 2.99530i −0.581794 0.266842i
\(127\) 6.12976i 0.543928i −0.962307 0.271964i \(-0.912327\pi\)
0.962307 0.271964i \(-0.0876732\pi\)
\(128\) 10.9393i 0.966909i
\(129\) 4.59439 0.404514
\(130\) −2.63440 −0.231052
\(131\) −18.8287 −1.64507 −0.822534 0.568715i \(-0.807441\pi\)
−0.822534 + 0.568715i \(0.807441\pi\)
\(132\) 0 0
\(133\) −1.37381 + 2.99530i −0.119124 + 0.259725i
\(134\) 0.329550i 0.0284687i
\(135\) 9.75658 0.839713
\(136\) 9.95987i 0.854052i
\(137\) −2.95939 −0.252837 −0.126419 0.991977i \(-0.540348\pi\)
−0.126419 + 0.991977i \(0.540348\pi\)
\(138\) −5.09370 −0.433605
\(139\) 14.7735 1.25307 0.626534 0.779394i \(-0.284473\pi\)
0.626534 + 0.779394i \(0.284473\pi\)
\(140\) 13.2093 + 6.05849i 1.11639 + 0.512036i
\(141\) 18.1134 1.52542
\(142\) 6.86688i 0.576256i
\(143\) 0 0
\(144\) −6.00914 −0.500761
\(145\) −7.25150 −0.602204
\(146\) 8.42876i 0.697569i
\(147\) 14.0723 12.1137i 1.16066 0.999121i
\(148\) 4.27373 0.351298
\(149\) 7.51223i 0.615426i 0.951479 + 0.307713i \(0.0995637\pi\)
−0.951479 + 0.307713i \(0.900436\pi\)
\(150\) 13.5661 1.10767
\(151\) 12.7284i 1.03582i −0.855434 0.517912i \(-0.826710\pi\)
0.855434 0.517912i \(-0.173290\pi\)
\(152\) 2.97266i 0.241115i
\(153\) 16.8432 1.36169
\(154\) 0 0
\(155\) 10.6328 0.854048
\(156\) 4.52714i 0.362461i
\(157\) 15.2616i 1.21800i −0.793168 0.609002i \(-0.791570\pi\)
0.793168 0.609002i \(-0.208430\pi\)
\(158\) 8.36527 0.665505
\(159\) 2.86439i 0.227161i
\(160\) −20.5006 −1.62072
\(161\) 3.14808 6.86374i 0.248104 0.540938i
\(162\) 3.24160i 0.254684i
\(163\) 21.0339 1.64750 0.823751 0.566951i \(-0.191877\pi\)
0.823751 + 0.566951i \(0.191877\pi\)
\(164\) 8.50499 0.664128
\(165\) 0 0
\(166\) 1.08903i 0.0845253i
\(167\) −8.34102 −0.645447 −0.322724 0.946493i \(-0.604598\pi\)
−0.322724 + 0.946493i \(0.604598\pi\)
\(168\) −6.98298 + 15.2249i −0.538748 + 1.17463i
\(169\) −11.7834 −0.906414
\(170\) 9.96694 0.764430
\(171\) 5.02708 0.384431
\(172\) 2.68003i 0.204351i
\(173\) 16.0588 1.22093 0.610466 0.792043i \(-0.290982\pi\)
0.610466 + 0.792043i \(0.290982\pi\)
\(174\) 3.64572i 0.276381i
\(175\) −8.38430 + 18.2802i −0.633793 + 1.38185i
\(176\) 0 0
\(177\) 6.07388 0.456540
\(178\) −1.55410 −0.116485
\(179\) 7.36816 0.550722 0.275361 0.961341i \(-0.411203\pi\)
0.275361 + 0.961341i \(0.411203\pi\)
\(180\) 22.1695i 1.65241i
\(181\) 14.4786i 1.07619i −0.842885 0.538094i \(-0.819145\pi\)
0.842885 0.538094i \(-0.180855\pi\)
\(182\) 1.78470 + 0.818558i 0.132290 + 0.0606755i
\(183\) 35.4166i 2.61807i
\(184\) 6.81187i 0.502178i
\(185\) 9.80473i 0.720858i
\(186\) 5.34569i 0.391965i
\(187\) 0 0
\(188\) 10.5660i 0.770606i
\(189\) −6.60968 3.03156i −0.480783 0.220513i
\(190\) 2.97477 0.215813
\(191\) 1.58944 0.115008 0.0575040 0.998345i \(-0.481686\pi\)
0.0575040 + 0.998345i \(0.481686\pi\)
\(192\) 2.40832i 0.173806i
\(193\) 11.2031i 0.806419i 0.915108 + 0.403209i \(0.132105\pi\)
−0.915108 + 0.403209i \(0.867895\pi\)
\(194\) −8.52340 −0.611944
\(195\) −10.3861 −0.743764
\(196\) −7.06625 8.20875i −0.504732 0.586339i
\(197\) 15.0339i 1.07112i −0.844496 0.535561i \(-0.820100\pi\)
0.844496 0.535561i \(-0.179900\pi\)
\(198\) 0 0
\(199\) 21.9453i 1.55566i 0.628476 + 0.777829i \(0.283679\pi\)
−0.628476 + 0.777829i \(0.716321\pi\)
\(200\) 18.1421i 1.28284i
\(201\) 1.29925i 0.0916418i
\(202\) 2.13047i 0.149899i
\(203\) 4.91259 + 2.25318i 0.344796 + 0.158142i
\(204\) 17.1279i 1.19919i
\(205\) 19.5120i 1.36278i
\(206\) −6.54798 −0.456220
\(207\) −11.5196 −0.800666
\(208\) 1.64218 0.113865
\(209\) 0 0
\(210\) −15.2357 6.98793i −1.05137 0.482213i
\(211\) 14.3700i 0.989271i 0.869101 + 0.494635i \(0.164698\pi\)
−0.869101 + 0.494635i \(0.835302\pi\)
\(212\) 1.67088 0.114756
\(213\) 27.0726i 1.85499i
\(214\) −7.10273 −0.485532
\(215\) 6.14850 0.419324
\(216\) 6.55973 0.446333
\(217\) −7.20329 3.30382i −0.488991 0.224278i
\(218\) 2.04996 0.138840
\(219\) 33.2303i 2.24550i
\(220\) 0 0
\(221\) −4.60292 −0.309626
\(222\) −4.92937 −0.330837
\(223\) 17.7224i 1.18678i 0.804916 + 0.593388i \(0.202210\pi\)
−0.804916 + 0.593388i \(0.797790\pi\)
\(224\) 13.8883 + 6.36994i 0.927954 + 0.425610i
\(225\) 30.6801 2.04534
\(226\) 4.88270i 0.324792i
\(227\) 4.10131 0.272214 0.136107 0.990694i \(-0.456541\pi\)
0.136107 + 0.990694i \(0.456541\pi\)
\(228\) 5.11206i 0.338554i
\(229\) 9.80126i 0.647686i 0.946111 + 0.323843i \(0.104975\pi\)
−0.946111 + 0.323843i \(0.895025\pi\)
\(230\) −6.81670 −0.449480
\(231\) 0 0
\(232\) −4.87547 −0.320090
\(233\) 0.101962i 0.00667974i 0.999994 + 0.00333987i \(0.00106312\pi\)
−0.999994 + 0.00333987i \(0.998937\pi\)
\(234\) 2.99530i 0.195809i
\(235\) 24.2404 1.58127
\(236\) 3.54306i 0.230633i
\(237\) 32.9800 2.14228
\(238\) −6.75219 3.09692i −0.437680 0.200744i
\(239\) 6.13574i 0.396888i 0.980112 + 0.198444i \(0.0635888\pi\)
−0.980112 + 0.198444i \(0.936411\pi\)
\(240\) −14.0191 −0.904931
\(241\) −4.31560 −0.277992 −0.138996 0.990293i \(-0.544388\pi\)
−0.138996 + 0.990293i \(0.544388\pi\)
\(242\) 0 0
\(243\) 21.0254i 1.34878i
\(244\) 20.6595 1.32259
\(245\) 18.8324 16.2113i 1.20316 1.03570i
\(246\) −9.80975 −0.625447
\(247\) −1.37381 −0.0874132
\(248\) 7.14886 0.453953
\(249\) 4.29350i 0.272090i
\(250\) 6.21301 0.392945
\(251\) 30.6941i 1.93739i −0.248245 0.968697i \(-0.579854\pi\)
0.248245 0.968697i \(-0.420146\pi\)
\(252\) −6.88847 + 15.0189i −0.433933 + 0.946101i
\(253\) 0 0
\(254\) 4.12420 0.258776
\(255\) 39.2946 2.46072
\(256\) −9.17600 −0.573500
\(257\) 6.73271i 0.419975i 0.977704 + 0.209988i \(0.0673424\pi\)
−0.977704 + 0.209988i \(0.932658\pi\)
\(258\) 3.09118i 0.192449i
\(259\) 3.04652 6.64230i 0.189301 0.412732i
\(260\) 6.05849i 0.375732i
\(261\) 8.24492i 0.510348i
\(262\) 12.6682i 0.782646i
\(263\) 24.4460i 1.50741i 0.657215 + 0.753703i \(0.271734\pi\)
−0.657215 + 0.753703i \(0.728266\pi\)
\(264\) 0 0
\(265\) 3.83330i 0.235478i
\(266\) −2.01529 0.924319i −0.123565 0.0566736i
\(267\) −6.12705 −0.374969
\(268\) 0.757886 0.0462952
\(269\) 25.3199i 1.54378i −0.635755 0.771891i \(-0.719311\pi\)
0.635755 0.771891i \(-0.280689\pi\)
\(270\) 6.56439i 0.399496i
\(271\) 27.3409 1.66084 0.830421 0.557136i \(-0.188100\pi\)
0.830421 + 0.557136i \(0.188100\pi\)
\(272\) −6.21301 −0.376719
\(273\) 7.03615 + 3.22716i 0.425847 + 0.195316i
\(274\) 1.99112i 0.120288i
\(275\) 0 0
\(276\) 11.7143i 0.705118i
\(277\) 22.4190i 1.34703i 0.739175 + 0.673513i \(0.235216\pi\)
−0.739175 + 0.673513i \(0.764784\pi\)
\(278\) 9.93983i 0.596151i
\(279\) 12.0895i 0.723777i
\(280\) −9.34505 + 20.3749i −0.558473 + 1.21764i
\(281\) 21.5172i 1.28361i −0.766868 0.641805i \(-0.778186\pi\)
0.766868 0.641805i \(-0.221814\pi\)
\(282\) 12.1870i 0.725723i
\(283\) −30.9433 −1.83939 −0.919694 0.392637i \(-0.871563\pi\)
−0.919694 + 0.392637i \(0.871563\pi\)
\(284\) 15.7922 0.937094
\(285\) 11.7280 0.694708
\(286\) 0 0
\(287\) 6.06276 13.2186i 0.357873 0.780269i
\(288\) 23.3091i 1.37350i
\(289\) 0.414624 0.0243896
\(290\) 4.87893i 0.286500i
\(291\) −33.6034 −1.96987
\(292\) −19.3842 −1.13437
\(293\) −24.8510 −1.45181 −0.725904 0.687796i \(-0.758579\pi\)
−0.725904 + 0.687796i \(0.758579\pi\)
\(294\) 8.15030 + 9.46807i 0.475335 + 0.552189i
\(295\) 8.12843 0.473256
\(296\) 6.59210i 0.383158i
\(297\) 0 0
\(298\) −5.05435 −0.292791
\(299\) 3.14808 0.182058
\(300\) 31.1988i 1.80126i
\(301\) −4.16535 1.91046i −0.240087 0.110117i
\(302\) 8.56389 0.492796
\(303\) 8.39936i 0.482531i
\(304\) −1.85436 −0.106355
\(305\) 47.3967i 2.71393i
\(306\) 11.3324i 0.647828i
\(307\) 10.0029 0.570896 0.285448 0.958394i \(-0.407858\pi\)
0.285448 + 0.958394i \(0.407858\pi\)
\(308\) 0 0
\(309\) −25.8154 −1.46859
\(310\) 7.15393i 0.406316i
\(311\) 18.7190i 1.06146i −0.847542 0.530728i \(-0.821919\pi\)
0.847542 0.530728i \(-0.178081\pi\)
\(312\) −6.98298 −0.395333
\(313\) 5.28598i 0.298781i −0.988778 0.149391i \(-0.952269\pi\)
0.988778 0.149391i \(-0.0477312\pi\)
\(314\) 10.2682 0.579469
\(315\) −34.4561 15.8034i −1.94138 0.890423i
\(316\) 19.2381i 1.08223i
\(317\) −28.7541 −1.61499 −0.807497 0.589872i \(-0.799178\pi\)
−0.807497 + 0.589872i \(0.799178\pi\)
\(318\) −1.92721 −0.108072
\(319\) 0 0
\(320\) 3.22297i 0.180169i
\(321\) −28.0025 −1.56294
\(322\) 4.61803 + 2.11808i 0.257353 + 0.118036i
\(323\) 5.19764 0.289204
\(324\) −7.45491 −0.414162
\(325\) −8.38430 −0.465077
\(326\) 14.1520i 0.783804i
\(327\) 8.08193 0.446932
\(328\) 13.1187i 0.724359i
\(329\) −16.4219 7.53196i −0.905367 0.415250i
\(330\) 0 0
\(331\) 12.2266 0.672035 0.336017 0.941856i \(-0.390920\pi\)
0.336017 + 0.941856i \(0.390920\pi\)
\(332\) −2.50452 −0.137453
\(333\) −11.1479 −0.610903
\(334\) 5.61197i 0.307073i
\(335\) 1.73873i 0.0949971i
\(336\) 9.49738 + 4.35601i 0.518124 + 0.237640i
\(337\) 36.0841i 1.96563i −0.184603 0.982813i \(-0.559100\pi\)
0.184603 0.982813i \(-0.440900\pi\)
\(338\) 7.92806i 0.431229i
\(339\) 19.2500i 1.04552i
\(340\) 22.9216i 1.24310i
\(341\) 0 0
\(342\) 3.38230i 0.182894i
\(343\) −17.7953 + 5.13089i −0.960858 + 0.277042i
\(344\) 4.13387 0.222884
\(345\) −26.8748 −1.44689
\(346\) 10.8047i 0.580862i
\(347\) 27.5091i 1.47677i 0.674380 + 0.738384i \(0.264411\pi\)
−0.674380 + 0.738384i \(0.735589\pi\)
\(348\) −8.38430 −0.449445
\(349\) 14.1265 0.756174 0.378087 0.925770i \(-0.376582\pi\)
0.378087 + 0.925770i \(0.376582\pi\)
\(350\) −12.2992 5.64109i −0.657421 0.301529i
\(351\) 3.03156i 0.161812i
\(352\) 0 0
\(353\) 8.23958i 0.438549i −0.975663 0.219274i \(-0.929631\pi\)
0.975663 0.219274i \(-0.0703690\pi\)
\(354\) 4.08660i 0.217200i
\(355\) 36.2302i 1.92290i
\(356\) 3.57407i 0.189425i
\(357\) −26.6205 12.2096i −1.40890 0.646200i
\(358\) 4.95742i 0.262008i
\(359\) 29.9242i 1.57934i −0.613533 0.789669i \(-0.710252\pi\)
0.613533 0.789669i \(-0.289748\pi\)
\(360\) 34.1957 1.80227
\(361\) −17.4487 −0.918352
\(362\) 9.74145 0.511999
\(363\) 0 0
\(364\) 1.88249 4.10438i 0.0986692 0.215128i
\(365\) 44.4709i 2.32771i
\(366\) −23.8289 −1.24556
\(367\) 4.63468i 0.241928i −0.992657 0.120964i \(-0.961401\pi\)
0.992657 0.120964i \(-0.0385986\pi\)
\(368\) 4.24927 0.221509
\(369\) −22.1851 −1.15491
\(370\) −6.59678 −0.342950
\(371\) 1.19108 2.59690i 0.0618378 0.134824i
\(372\) 12.2938 0.637405
\(373\) 15.2702i 0.790662i −0.918539 0.395331i \(-0.870630\pi\)
0.918539 0.395331i \(-0.129370\pi\)
\(374\) 0 0
\(375\) 24.4947 1.26490
\(376\) 16.2978 0.840493
\(377\) 2.25318i 0.116045i
\(378\) 2.03968 4.44710i 0.104910 0.228734i
\(379\) 22.7591 1.16906 0.584529 0.811373i \(-0.301279\pi\)
0.584529 + 0.811373i \(0.301279\pi\)
\(380\) 6.84127i 0.350950i
\(381\) 16.2596 0.833007
\(382\) 1.06940i 0.0547154i
\(383\) 28.9146i 1.47746i 0.673999 + 0.738732i \(0.264575\pi\)
−0.673999 + 0.738732i \(0.735425\pi\)
\(384\) −29.0174 −1.48079
\(385\) 0 0
\(386\) −7.53765 −0.383656
\(387\) 6.99081i 0.355363i
\(388\) 19.6018i 0.995130i
\(389\) −21.9665 −1.11375 −0.556873 0.830598i \(-0.687999\pi\)
−0.556873 + 0.830598i \(0.687999\pi\)
\(390\) 6.98793i 0.353848i
\(391\) −11.9104 −0.602335
\(392\) 12.6618 10.8995i 0.639516 0.550507i
\(393\) 49.9444i 2.51936i
\(394\) 10.1151 0.509590
\(395\) 44.1359 2.22072
\(396\) 0 0
\(397\) 3.02008i 0.151573i 0.997124 + 0.0757866i \(0.0241468\pi\)
−0.997124 + 0.0757866i \(0.975853\pi\)
\(398\) −14.7651 −0.740109
\(399\) −7.94525 3.64412i −0.397760 0.182434i
\(400\) −11.3171 −0.565855
\(401\) 7.88407 0.393712 0.196856 0.980432i \(-0.436927\pi\)
0.196856 + 0.980432i \(0.436927\pi\)
\(402\) −0.874155 −0.0435989
\(403\) 3.30382i 0.164575i
\(404\) −4.89957 −0.243763
\(405\) 17.1030i 0.849852i
\(406\) −1.51598 + 3.30527i −0.0752366 + 0.164038i
\(407\) 0 0
\(408\) 26.4193 1.30795
\(409\) −26.5465 −1.31264 −0.656320 0.754483i \(-0.727888\pi\)
−0.656320 + 0.754483i \(0.727888\pi\)
\(410\) −13.1280 −0.648346
\(411\) 7.84999i 0.387211i
\(412\) 15.0588i 0.741894i
\(413\) −5.50668 2.52566i −0.270966 0.124280i
\(414\) 7.75056i 0.380919i
\(415\) 5.74583i 0.282052i
\(416\) 6.36994i 0.312312i
\(417\) 39.1877i 1.91903i
\(418\) 0 0
\(419\) 7.28466i 0.355879i 0.984041 + 0.177940i \(0.0569431\pi\)
−0.984041 + 0.177940i \(0.943057\pi\)
\(420\) −16.0706 + 35.0386i −0.784165 + 1.70971i
\(421\) −23.8041 −1.16014 −0.580070 0.814567i \(-0.696975\pi\)
−0.580070 + 0.814567i \(0.696975\pi\)
\(422\) −9.66836 −0.470648
\(423\) 27.5612i 1.34007i
\(424\) 2.57728i 0.125164i
\(425\) 31.7210 1.53870
\(426\) −18.2149 −0.882515
\(427\) 14.7271 32.1093i 0.712692 1.55388i
\(428\) 16.3346i 0.789562i
\(429\) 0 0
\(430\) 4.13681i 0.199495i
\(431\) 0.640406i 0.0308473i 0.999881 + 0.0154236i \(0.00490969\pi\)
−0.999881 + 0.0154236i \(0.995090\pi\)
\(432\) 4.09199i 0.196876i
\(433\) 17.2215i 0.827611i −0.910365 0.413806i \(-0.864199\pi\)
0.910365 0.413806i \(-0.135801\pi\)
\(434\) 2.22286 4.84649i 0.106701 0.232639i
\(435\) 19.2351i 0.922254i
\(436\) 4.71441i 0.225779i
\(437\) −3.55483 −0.170050
\(438\) 22.3579 1.06830
\(439\) −0.0381286 −0.00181978 −0.000909889 1.00000i \(-0.500290\pi\)
−0.000909889 1.00000i \(0.500290\pi\)
\(440\) 0 0
\(441\) 18.4322 + 21.4124i 0.877722 + 1.01964i
\(442\) 3.09692i 0.147305i
\(443\) 30.6420 1.45585 0.727923 0.685658i \(-0.240486\pi\)
0.727923 + 0.685658i \(0.240486\pi\)
\(444\) 11.3364i 0.538001i
\(445\) −8.19959 −0.388698
\(446\) −11.9239 −0.564613
\(447\) −19.9267 −0.942503
\(448\) −1.00144 + 2.18343i −0.0473135 + 0.103157i
\(449\) −29.5218 −1.39322 −0.696609 0.717451i \(-0.745309\pi\)
−0.696609 + 0.717451i \(0.745309\pi\)
\(450\) 20.6421i 0.973078i
\(451\) 0 0
\(452\) 11.2290 0.528170
\(453\) 33.7631 1.58633
\(454\) 2.75943i 0.129506i
\(455\) 9.41620 + 4.31878i 0.441438 + 0.202468i
\(456\) 7.88521 0.369259
\(457\) 4.24787i 0.198707i −0.995052 0.0993534i \(-0.968323\pi\)
0.995052 0.0993534i \(-0.0316774\pi\)
\(458\) −6.59445 −0.308138
\(459\) 11.4695i 0.535353i
\(460\) 15.6768i 0.730935i
\(461\) −11.8930 −0.553913 −0.276957 0.960882i \(-0.589326\pi\)
−0.276957 + 0.960882i \(0.589326\pi\)
\(462\) 0 0
\(463\) 29.5007 1.37102 0.685508 0.728066i \(-0.259580\pi\)
0.685508 + 0.728066i \(0.259580\pi\)
\(464\) 3.04134i 0.141191i
\(465\) 28.2043i 1.30794i
\(466\) −0.0686016 −0.00317791
\(467\) 11.1490i 0.515913i −0.966156 0.257957i \(-0.916951\pi\)
0.966156 0.257957i \(-0.0830492\pi\)
\(468\) −6.88847 −0.318420
\(469\) 0.540257 1.17792i 0.0249468 0.0543912i
\(470\) 16.3093i 0.752294i
\(471\) 40.4824 1.86533
\(472\) 5.46506 0.251550
\(473\) 0 0
\(474\) 22.1895i 1.01920i
\(475\) 9.46758 0.434402
\(476\) −7.12218 + 15.5284i −0.326445 + 0.711745i
\(477\) −4.35844 −0.199559
\(478\) −4.12823 −0.188821
\(479\) −11.3316 −0.517753 −0.258877 0.965910i \(-0.583352\pi\)
−0.258877 + 0.965910i \(0.583352\pi\)
\(480\) 54.3795i 2.48207i
\(481\) 3.04652 0.138909
\(482\) 2.90360i 0.132256i
\(483\) 18.2066 + 8.35052i 0.828427 + 0.379962i
\(484\) 0 0
\(485\) −44.9702 −2.04199
\(486\) 14.1462 0.641685
\(487\) 15.5058 0.702637 0.351318 0.936256i \(-0.385733\pi\)
0.351318 + 0.936256i \(0.385733\pi\)
\(488\) 31.8666i 1.44253i
\(489\) 55.7940i 2.52309i
\(490\) 10.9072 + 12.6708i 0.492738 + 0.572406i
\(491\) 10.4088i 0.469742i 0.972027 + 0.234871i \(0.0754668\pi\)
−0.972027 + 0.234871i \(0.924533\pi\)
\(492\) 22.5601i 1.01709i
\(493\) 8.52465i 0.383931i
\(494\) 0.924319i 0.0415871i
\(495\) 0 0
\(496\) 4.45949i 0.200237i
\(497\) 11.2574 24.5445i 0.504965 1.10097i
\(498\) 2.88874 0.129447
\(499\) −23.2190 −1.03942 −0.519712 0.854342i \(-0.673961\pi\)
−0.519712 + 0.854342i \(0.673961\pi\)
\(500\) 14.2885i 0.638999i
\(501\) 22.1252i 0.988479i
\(502\) 20.6515 0.921721
\(503\) 1.15636 0.0515596 0.0257798 0.999668i \(-0.491793\pi\)
0.0257798 + 0.999668i \(0.491793\pi\)
\(504\) −23.1662 10.6253i −1.03190 0.473287i
\(505\) 11.2405i 0.500197i
\(506\) 0 0
\(507\) 31.2563i 1.38814i
\(508\) 9.48469i 0.420815i
\(509\) 17.8327i 0.790420i −0.918591 0.395210i \(-0.870672\pi\)
0.918591 0.395210i \(-0.129328\pi\)
\(510\) 26.4381i 1.17070i
\(511\) −13.8180 + 30.1272i −0.611270 + 1.33275i
\(512\) 15.7049i 0.694065i
\(513\) 3.42325i 0.151140i
\(514\) −4.52988 −0.199804
\(515\) −34.5477 −1.52235
\(516\) 7.10899 0.312956
\(517\) 0 0
\(518\) 4.46905 + 2.04975i 0.196359 + 0.0900607i
\(519\) 42.5973i 1.86981i
\(520\) −9.34505 −0.409807
\(521\) 35.9158i 1.57350i −0.617273 0.786749i \(-0.711763\pi\)
0.617273 0.786749i \(-0.288237\pi\)
\(522\) 5.54732 0.242800
\(523\) −9.86251 −0.431257 −0.215629 0.976475i \(-0.569180\pi\)
−0.215629 + 0.976475i \(0.569180\pi\)
\(524\) −29.1339 −1.27272
\(525\) −48.4896 22.2400i −2.11626 0.970632i
\(526\) −16.4477 −0.717153
\(527\) 12.4996i 0.544492i
\(528\) 0 0
\(529\) −14.8541 −0.645831
\(530\) −2.57911 −0.112029
\(531\) 9.24199i 0.401068i
\(532\) −2.12571 + 4.63468i −0.0921614 + 0.200939i
\(533\) 6.06276 0.262607
\(534\) 4.12238i 0.178393i
\(535\) −37.4746 −1.62017
\(536\) 1.16902i 0.0504938i
\(537\) 19.5446i 0.843411i
\(538\) 17.0356 0.734459
\(539\) 0 0
\(540\) 15.0965 0.649651
\(541\) 20.6287i 0.886897i −0.896300 0.443449i \(-0.853755\pi\)
0.896300 0.443449i \(-0.146245\pi\)
\(542\) 18.3954i 0.790151i
\(543\) 38.4056 1.64814
\(544\) 24.1000i 1.03328i
\(545\) 10.8157 0.463295
\(546\) −2.17128 + 4.73404i −0.0929224 + 0.202598i
\(547\) 28.8672i 1.23427i 0.786856 + 0.617136i \(0.211707\pi\)
−0.786856 + 0.617136i \(0.788293\pi\)
\(548\) −4.57911 −0.195610
\(549\) −53.8898 −2.29996
\(550\) 0 0
\(551\) 2.54430i 0.108391i
\(552\) −18.0690 −0.769067
\(553\) −29.9002 13.7139i −1.27149 0.583173i
\(554\) −15.0839 −0.640852
\(555\) −26.0078 −1.10397
\(556\) 22.8592 0.969448
\(557\) 14.5467i 0.616365i 0.951327 + 0.308183i \(0.0997208\pi\)
−0.951327 + 0.308183i \(0.900279\pi\)
\(558\) −8.13399 −0.344339
\(559\) 1.91046i 0.0808037i
\(560\) 12.7100 + 5.82948i 0.537094 + 0.246340i
\(561\) 0 0
\(562\) 14.4771 0.610681
\(563\) 6.04411 0.254729 0.127365 0.991856i \(-0.459348\pi\)
0.127365 + 0.991856i \(0.459348\pi\)
\(564\) 28.0271 1.18016
\(565\) 25.7615i 1.08380i
\(566\) 20.8191i 0.875094i
\(567\) −5.31421 + 11.5865i −0.223176 + 0.486589i
\(568\) 24.3590i 1.02208i
\(569\) 13.1065i 0.549455i −0.961522 0.274727i \(-0.911412\pi\)
0.961522 0.274727i \(-0.0885876\pi\)
\(570\) 7.89080i 0.330509i
\(571\) 14.5264i 0.607910i 0.952686 + 0.303955i \(0.0983073\pi\)
−0.952686 + 0.303955i \(0.901693\pi\)
\(572\) 0 0
\(573\) 4.21612i 0.176131i
\(574\) 8.89368 + 4.07912i 0.371215 + 0.170259i
\(575\) −21.6950 −0.904744
\(576\) 3.66450 0.152687
\(577\) 27.4793i 1.14398i −0.820261 0.571990i \(-0.806172\pi\)
0.820261 0.571990i \(-0.193828\pi\)
\(578\) 0.278966i 0.0116034i
\(579\) −29.7171 −1.23500
\(580\) −11.2204 −0.465901
\(581\) −1.78534 + 3.89256i −0.0740683 + 0.161491i
\(582\) 22.6089i 0.937171i
\(583\) 0 0
\(584\) 29.8995i 1.23725i
\(585\) 15.8034i 0.653392i
\(586\) 16.7201i 0.690702i
\(587\) 14.3085i 0.590575i −0.955408 0.295287i \(-0.904585\pi\)
0.955408 0.295287i \(-0.0954154\pi\)
\(588\) 21.7743 18.7437i 0.897958 0.772979i
\(589\) 3.73069i 0.153720i
\(590\) 5.46894i 0.225153i
\(591\) 39.8786 1.64039
\(592\) 4.11218 0.169010
\(593\) 31.8607 1.30836 0.654181 0.756338i \(-0.273013\pi\)
0.654181 + 0.756338i \(0.273013\pi\)
\(594\) 0 0
\(595\) −35.6251 16.3396i −1.46049 0.669859i
\(596\) 11.6238i 0.476130i
\(597\) −58.2114 −2.38243
\(598\) 2.11808i 0.0866147i
\(599\) 22.5485 0.921307 0.460653 0.887580i \(-0.347615\pi\)
0.460653 + 0.887580i \(0.347615\pi\)
\(600\) 48.1232 1.96462
\(601\) 28.9546 1.18108 0.590542 0.807007i \(-0.298914\pi\)
0.590542 + 0.807007i \(0.298914\pi\)
\(602\) 1.28539 2.80252i 0.0523884 0.114222i
\(603\) −1.97693 −0.0805068
\(604\) 19.6949i 0.801374i
\(605\) 0 0
\(606\) 5.65123 0.229565
\(607\) 28.4019 1.15280 0.576400 0.817168i \(-0.304457\pi\)
0.576400 + 0.817168i \(0.304457\pi\)
\(608\) 7.19297i 0.291713i
\(609\) −5.97673 + 13.0310i −0.242189 + 0.528043i
\(610\) −31.8893 −1.29116
\(611\) 7.53196i 0.304710i
\(612\) 26.0618 1.05348
\(613\) 17.0228i 0.687545i −0.939053 0.343773i \(-0.888295\pi\)
0.939053 0.343773i \(-0.111705\pi\)
\(614\) 6.73012i 0.271606i
\(615\) −51.7571 −2.08705
\(616\) 0 0
\(617\) 19.0794 0.768109 0.384055 0.923310i \(-0.374527\pi\)
0.384055 + 0.923310i \(0.374527\pi\)
\(618\) 17.3690i 0.698684i
\(619\) 22.6115i 0.908834i −0.890789 0.454417i \(-0.849848\pi\)
0.890789 0.454417i \(-0.150152\pi\)
\(620\) 16.4524 0.660742
\(621\) 7.84438i 0.314784i
\(622\) 12.5944 0.504991
\(623\) 5.55488 + 2.54777i 0.222552 + 0.102074i
\(624\) 4.35601i 0.174380i
\(625\) −5.22633 −0.209053
\(626\) 3.55649 0.142146
\(627\) 0 0
\(628\) 23.6145i 0.942320i
\(629\) −11.5261 −0.459578
\(630\) 10.6328 23.1826i 0.423622 0.923619i
\(631\) −6.59183 −0.262417 −0.131208 0.991355i \(-0.541886\pi\)
−0.131208 + 0.991355i \(0.541886\pi\)
\(632\) 29.6743 1.18038
\(633\) −38.1174 −1.51503
\(634\) 19.3463i 0.768338i
\(635\) 21.7597 0.863505
\(636\) 4.43212i 0.175745i
\(637\) −5.03716 5.85159i −0.199580 0.231848i
\(638\) 0 0
\(639\) −41.1936 −1.62959
\(640\) −38.8328 −1.53500
\(641\) 10.3555 0.409017 0.204509 0.978865i \(-0.434440\pi\)
0.204509 + 0.978865i \(0.434440\pi\)
\(642\) 18.8405i 0.743576i
\(643\) 29.1774i 1.15065i −0.817926 0.575323i \(-0.804876\pi\)
0.817926 0.575323i \(-0.195124\pi\)
\(644\) 4.87108 10.6204i 0.191948 0.418502i
\(645\) 16.3093i 0.642180i
\(646\) 3.49706i 0.137590i
\(647\) 1.57539i 0.0619349i 0.999520 + 0.0309675i \(0.00985882\pi\)
−0.999520 + 0.0309675i \(0.990141\pi\)
\(648\) 11.4990i 0.451723i
\(649\) 0 0
\(650\) 5.64109i 0.221262i
\(651\) 8.76363 19.1073i 0.343474 0.748873i
\(652\) 32.5461 1.27461
\(653\) 14.5691 0.570134 0.285067 0.958508i \(-0.407984\pi\)
0.285067 + 0.958508i \(0.407984\pi\)
\(654\) 5.43766i 0.212629i
\(655\) 66.8387i 2.61160i
\(656\) 8.18350 0.319512
\(657\) 50.5632 1.97266
\(658\) 5.06763 11.0489i 0.197557 0.430731i
\(659\) 28.4616i 1.10871i −0.832281 0.554353i \(-0.812966\pi\)
0.832281 0.554353i \(-0.187034\pi\)
\(660\) 0 0
\(661\) 32.7887i 1.27533i −0.770313 0.637666i \(-0.779900\pi\)
0.770313 0.637666i \(-0.220100\pi\)
\(662\) 8.22626i 0.319723i
\(663\) 12.2096i 0.474181i
\(664\) 3.86314i 0.149919i
\(665\) −10.6328 4.87679i −0.412323 0.189114i
\(666\) 7.50051i 0.290639i
\(667\) 5.83027i 0.225749i
\(668\) −12.9062 −0.499356
\(669\) −47.0099 −1.81751
\(670\) −1.16985 −0.0451951
\(671\) 0 0
\(672\) −16.8967 + 36.8398i −0.651806 + 1.42113i
\(673\) 10.2694i 0.395858i 0.980216 + 0.197929i \(0.0634215\pi\)
−0.980216 + 0.197929i \(0.936579\pi\)
\(674\) 24.2780 0.935153
\(675\) 20.8920i 0.804132i
\(676\) −18.2326 −0.701256
\(677\) 35.0099 1.34554 0.672769 0.739852i \(-0.265105\pi\)
0.672769 + 0.739852i \(0.265105\pi\)
\(678\) −12.9517 −0.497408
\(679\) 30.4654 + 13.9731i 1.16916 + 0.536238i
\(680\) 35.3559 1.35584
\(681\) 10.8790i 0.416885i
\(682\) 0 0
\(683\) −18.0603 −0.691059 −0.345529 0.938408i \(-0.612301\pi\)
−0.345529 + 0.938408i \(0.612301\pi\)
\(684\) 7.77850 0.297418
\(685\) 10.5053i 0.401388i
\(686\) −3.45215 11.9730i −0.131804 0.457131i
\(687\) −25.9986 −0.991907
\(688\) 2.57873i 0.0983131i
\(689\) 1.19108 0.0453765
\(690\) 18.0818i 0.688363i
\(691\) 23.6161i 0.898398i −0.893432 0.449199i \(-0.851709\pi\)
0.893432 0.449199i \(-0.148291\pi\)
\(692\) 24.8481 0.944585
\(693\) 0 0
\(694\) −18.5086 −0.702577
\(695\) 52.4434i 1.98929i
\(696\) 12.9325i 0.490206i
\(697\) −22.9378 −0.868830
\(698\) 9.50453i 0.359752i
\(699\) −0.270461 −0.0102298
\(700\) −12.9732 + 28.2853i −0.490340 + 1.06908i
\(701\) 36.7279i 1.38719i 0.720363 + 0.693597i \(0.243975\pi\)
−0.720363 + 0.693597i \(0.756025\pi\)
\(702\) 2.03968 0.0769828
\(703\) −3.44014 −0.129747
\(704\) 0 0
\(705\) 64.2995i 2.42166i
\(706\) 5.54373 0.208641
\(707\) −3.49265 + 7.61500i −0.131355 + 0.286391i
\(708\) 9.39822 0.353207
\(709\) −25.4613 −0.956219 −0.478109 0.878300i \(-0.658678\pi\)
−0.478109 + 0.878300i \(0.658678\pi\)
\(710\) −24.3763 −0.914826
\(711\) 50.1823i 1.88198i
\(712\) −5.51290 −0.206605
\(713\) 8.54889i 0.320158i
\(714\) 8.21481 17.9107i 0.307431 0.670290i
\(715\) 0 0
\(716\) 11.4009 0.426071
\(717\) −16.2755 −0.607820
\(718\) 20.1335 0.751375
\(719\) 30.5473i 1.13922i −0.821914 0.569612i \(-0.807094\pi\)
0.821914 0.569612i \(-0.192906\pi\)
\(720\) 21.3315i 0.794976i
\(721\) 23.4047 + 10.7346i 0.871635 + 0.399779i
\(722\) 11.7398i 0.436909i
\(723\) 11.4474i 0.425735i
\(724\) 22.4030i 0.832602i
\(725\) 15.5278i 0.576688i
\(726\) 0 0
\(727\) 2.80772i 0.104133i −0.998644 0.0520663i \(-0.983419\pi\)
0.998644 0.0520663i \(-0.0165807\pi\)
\(728\) 6.33088 + 2.90368i 0.234638 + 0.107618i
\(729\) 41.3174 1.53028
\(730\) 29.9207 1.10742
\(731\) 7.22799i 0.267337i
\(732\) 54.8008i 2.02549i
\(733\) 6.75560 0.249524 0.124762 0.992187i \(-0.460183\pi\)
0.124762 + 0.992187i \(0.460183\pi\)
\(734\) 3.11829 0.115098
\(735\) 43.0017 + 49.9544i 1.58614 + 1.84259i
\(736\) 16.4827i 0.607561i
\(737\) 0 0
\(738\) 14.9265i 0.549452i
\(739\) 12.6084i 0.463809i −0.972739 0.231905i \(-0.925504\pi\)
0.972739 0.231905i \(-0.0744957\pi\)
\(740\) 15.1710i 0.557698i
\(741\) 3.64412i 0.133870i
\(742\) 1.74724 + 0.801378i 0.0641431 + 0.0294195i
\(743\) 7.01399i 0.257318i −0.991689 0.128659i \(-0.958933\pi\)
0.991689 0.128659i \(-0.0410673\pi\)
\(744\) 18.9629i 0.695213i
\(745\) −26.6672 −0.977010
\(746\) 10.2741 0.376160
\(747\) 6.53298 0.239029
\(748\) 0 0
\(749\) 25.3875 + 11.6441i 0.927639 + 0.425465i
\(750\) 16.4805i 0.601782i
\(751\) 8.92542 0.325693 0.162847 0.986651i \(-0.447932\pi\)
0.162847 + 0.986651i \(0.447932\pi\)
\(752\) 10.1666i 0.370738i
\(753\) 81.4184 2.96705
\(754\) −1.51598 −0.0552086
\(755\) 45.1838 1.64441
\(756\) −10.2273 4.69078i −0.371962 0.170602i
\(757\) 28.3234 1.02943 0.514716 0.857361i \(-0.327897\pi\)
0.514716 + 0.857361i \(0.327897\pi\)
\(758\) 15.3127i 0.556183i
\(759\) 0 0
\(760\) 10.5525 0.382778
\(761\) −7.02091 −0.254508 −0.127254 0.991870i \(-0.540616\pi\)
−0.127254 + 0.991870i \(0.540616\pi\)
\(762\) 10.9398i 0.396305i
\(763\) −7.32721 3.36066i −0.265263 0.121664i
\(764\) 2.45937 0.0889770
\(765\) 59.7905i 2.16173i
\(766\) −19.4542 −0.702908
\(767\) 2.52566i 0.0911963i
\(768\) 24.3400i 0.878295i
\(769\) 27.4453 0.989703 0.494851 0.868978i \(-0.335222\pi\)
0.494851 + 0.868978i \(0.335222\pi\)
\(770\) 0 0
\(771\) −17.8590 −0.643177
\(772\) 17.3348i 0.623893i
\(773\) 28.6264i 1.02962i 0.857305 + 0.514809i \(0.172137\pi\)
−0.857305 + 0.514809i \(0.827863\pi\)
\(774\) −4.70353 −0.169065
\(775\) 22.7683i 0.817861i
\(776\) −30.2352 −1.08538
\(777\) 17.6192 + 8.08111i 0.632085 + 0.289908i
\(778\) 14.7794i 0.529868i
\(779\) −6.84609 −0.245287
\(780\) −16.0706 −0.575419
\(781\) 0 0
\(782\) 8.01352i 0.286563i
\(783\) 5.61447 0.200645
\(784\) −6.79915 7.89846i −0.242827 0.282088i
\(785\) 54.1760 1.93363
\(786\) 33.6034 1.19860
\(787\) 7.62353 0.271749 0.135875 0.990726i \(-0.456616\pi\)
0.135875 + 0.990726i \(0.456616\pi\)
\(788\) 23.2623i 0.828684i
\(789\) −64.8449 −2.30854
\(790\) 29.6954i 1.05651i
\(791\) 8.00460 17.4524i 0.284611 0.620535i
\(792\) 0 0
\(793\) 14.7271 0.522973
\(794\) −2.03196 −0.0721114
\(795\) −10.1681 −0.360626
\(796\) 33.9563i 1.20355i
\(797\) 34.7434i 1.23067i 0.788264 + 0.615337i \(0.210980\pi\)
−0.788264 + 0.615337i \(0.789020\pi\)
\(798\) 2.45182 5.34569i 0.0867936 0.189235i
\(799\) 28.4963i 1.00813i
\(800\) 43.8985i 1.55205i
\(801\) 9.32290i 0.329408i
\(802\) 5.30453i 0.187309i
\(803\) 0 0
\(804\) 2.01035i 0.0708995i
\(805\) 24.3651 + 11.1752i 0.858758 + 0.393873i
\(806\) 2.22286 0.0782971
\(807\) 67.1629 2.36425
\(808\) 7.55745i 0.265870i
\(809\) 22.4247i 0.788412i 0.919022 + 0.394206i \(0.128980\pi\)
−0.919022 + 0.394206i \(0.871020\pi\)
\(810\) 11.5071 0.404320
\(811\) −19.5492 −0.686464 −0.343232 0.939251i \(-0.611522\pi\)
−0.343232 + 0.939251i \(0.611522\pi\)
\(812\) 7.60134 + 3.48639i 0.266755 + 0.122348i
\(813\) 72.5238i 2.54352i
\(814\) 0 0
\(815\) 74.6669i 2.61547i
\(816\) 16.4805i 0.576932i
\(817\) 2.15729i 0.0754742i
\(818\) 17.8609i 0.624493i
\(819\) −4.91043 + 10.7062i −0.171584 + 0.374104i
\(820\) 30.1913i 1.05433i
\(821\) 18.3901i 0.641818i −0.947110 0.320909i \(-0.896012\pi\)
0.947110 0.320909i \(-0.103988\pi\)
\(822\) 5.28160 0.184217
\(823\) 22.2604 0.775950 0.387975 0.921670i \(-0.373175\pi\)
0.387975 + 0.921670i \(0.373175\pi\)
\(824\) −23.2278 −0.809178
\(825\) 0 0
\(826\) 1.69931 3.70498i 0.0591264 0.128913i
\(827\) 46.5155i 1.61750i −0.588151 0.808751i \(-0.700144\pi\)
0.588151 0.808751i \(-0.299856\pi\)
\(828\) −17.8245 −0.619442
\(829\) 20.7816i 0.721776i −0.932609 0.360888i \(-0.882474\pi\)
0.932609 0.360888i \(-0.117526\pi\)
\(830\) 3.86589 0.134187
\(831\) −59.4680 −2.06292
\(832\) −1.00144 −0.0347186
\(833\) 19.0575 + 22.1388i 0.660304 + 0.767065i
\(834\) −26.3661 −0.912984
\(835\) 29.6092i 1.02467i
\(836\) 0 0
\(837\) −8.23245 −0.284555
\(838\) −4.90124 −0.169311
\(839\) 7.54175i 0.260370i −0.991490 0.130185i \(-0.958443\pi\)
0.991490 0.130185i \(-0.0415571\pi\)
\(840\) −54.0460 24.7884i −1.86476 0.855282i
\(841\) 24.8271 0.856107
\(842\) 16.0158i 0.551940i
\(843\) 57.0760 1.96580
\(844\) 22.2349i 0.765358i
\(845\) 41.8291i 1.43896i
\(846\) −18.5436 −0.637544
\(847\) 0 0
\(848\) 1.60772 0.0552092
\(849\) 82.0793i 2.81696i
\(850\) 21.3424i 0.732039i
\(851\) 7.88309 0.270229
\(852\) 41.8900i 1.43513i
\(853\) −1.58216 −0.0541720 −0.0270860 0.999633i \(-0.508623\pi\)
−0.0270860 + 0.999633i \(0.508623\pi\)
\(854\) 21.6037 + 9.90860i 0.739262 + 0.339065i
\(855\) 17.8453i 0.610297i
\(856\) −25.1956 −0.861169
\(857\) −52.3232 −1.78733 −0.893664 0.448737i \(-0.851874\pi\)
−0.893664 + 0.448737i \(0.851874\pi\)
\(858\) 0 0
\(859\) 7.18932i 0.245296i −0.992450 0.122648i \(-0.960861\pi\)
0.992450 0.122648i \(-0.0391387\pi\)
\(860\) 9.51368 0.324414
\(861\) 35.0633 + 16.0819i 1.19495 + 0.548070i
\(862\) −0.430876 −0.0146757
\(863\) −43.8560 −1.49288 −0.746438 0.665455i \(-0.768238\pi\)
−0.746438 + 0.665455i \(0.768238\pi\)
\(864\) 15.8726 0.539997
\(865\) 57.0063i 1.93827i
\(866\) 11.5869 0.393738
\(867\) 1.09982i 0.0373519i
\(868\) −11.1458 5.11206i −0.378313 0.173515i
\(869\) 0 0
\(870\) 12.9417 0.438765
\(871\) 0.540257 0.0183059
\(872\) 7.27184 0.246256
\(873\) 51.1309i 1.73052i
\(874\) 2.39175i 0.0809020i
\(875\) −22.2073 10.1855i −0.750745 0.344332i
\(876\) 51.4179i 1.73725i
\(877\) 14.3775i 0.485494i −0.970090 0.242747i \(-0.921952\pi\)
0.970090 0.242747i \(-0.0780484\pi\)
\(878\) 0.0256535i 0.000865765i
\(879\) 65.9190i 2.22339i
\(880\) 0 0
\(881\) 2.45261i 0.0826304i −0.999146 0.0413152i \(-0.986845\pi\)
0.999146 0.0413152i \(-0.0131548\pi\)
\(882\) −14.4066 + 12.4015i −0.485095 + 0.417579i
\(883\) 4.78704 0.161097 0.0805484 0.996751i \(-0.474333\pi\)
0.0805484 + 0.996751i \(0.474333\pi\)
\(884\) −7.12218 −0.239545
\(885\) 21.5613i 0.724774i
\(886\) 20.6165i 0.692624i
\(887\) −35.8413 −1.20343 −0.601717 0.798709i \(-0.705517\pi\)
−0.601717 + 0.798709i \(0.705517\pi\)
\(888\) −17.4860 −0.586793
\(889\) −14.7413 6.76114i −0.494406 0.226761i
\(890\) 5.51682i 0.184924i
\(891\) 0 0
\(892\) 27.4221i 0.918161i
\(893\) 8.50512i 0.284613i
\(894\) 13.4070i 0.448399i
\(895\) 26.1558i 0.874291i
\(896\) 26.3076 + 12.0661i 0.878876 + 0.403100i
\(897\) 8.35052i 0.278816i
\(898\) 19.8627i 0.662828i
\(899\) 6.11870 0.204070
\(900\) 47.4719 1.58240
\(901\) −4.50631 −0.150127
\(902\) 0 0
\(903\) 5.06763 11.0489i 0.168640 0.367685i
\(904\) 17.3205i 0.576071i
\(905\) 51.3967 1.70849
\(906\) 22.7163i 0.754700i
\(907\) 7.18813 0.238678 0.119339 0.992854i \(-0.461922\pi\)
0.119339 + 0.992854i \(0.461922\pi\)
\(908\) 6.34603 0.210601
\(909\) 12.7804 0.423900
\(910\) −2.90575 + 6.33538i −0.0963245 + 0.210016i
\(911\) 20.0130 0.663060 0.331530 0.943445i \(-0.392435\pi\)
0.331530 + 0.943445i \(0.392435\pi\)
\(912\) 4.91883i 0.162879i
\(913\) 0 0
\(914\) 2.85803 0.0945354
\(915\) −125.723 −4.15628
\(916\) 15.1657i 0.501088i
\(917\) −20.7681 + 45.2805i −0.685822 + 1.49529i
\(918\) −7.71690 −0.254696
\(919\) 3.54390i 0.116903i −0.998290 0.0584513i \(-0.981384\pi\)
0.998290 0.0584513i \(-0.0186162\pi\)
\(920\) −24.1810 −0.797224
\(921\) 26.5335i 0.874307i
\(922\) 8.00182i 0.263526i
\(923\) 11.2574 0.370543
\(924\) 0 0
\(925\) −20.9951 −0.690314
\(926\) 19.8486i 0.652265i
\(927\) 39.2806i 1.29014i
\(928\) −11.7972 −0.387262
\(929\) 27.2210i 0.893092i 0.894761 + 0.446546i \(0.147346\pi\)
−0.894761 + 0.446546i \(0.852654\pi\)
\(930\) −18.9763 −0.622259
\(931\) 5.68798 + 6.60764i 0.186416 + 0.216557i
\(932\) 0.157767i 0.00516784i
\(933\) 49.6535 1.62558
\(934\) 7.50122 0.245447
\(935\) 0 0
\(936\) 10.6253i 0.347298i
\(937\) 47.9616 1.56684 0.783418 0.621495i \(-0.213474\pi\)
0.783418 + 0.621495i \(0.213474\pi\)
\(938\) 0.792523 + 0.363494i 0.0258768 + 0.0118685i
\(939\) 14.0214 0.457573
\(940\) 37.5076 1.22336
\(941\) 10.4613 0.341028 0.170514 0.985355i \(-0.445457\pi\)
0.170514 + 0.985355i \(0.445457\pi\)
\(942\) 27.2372i 0.887437i
\(943\) 15.6879 0.510867
\(944\) 3.40913i 0.110958i
\(945\) 10.7615 23.4633i 0.350073 0.763260i
\(946\) 0 0
\(947\) −31.5419 −1.02497 −0.512487 0.858695i \(-0.671276\pi\)
−0.512487 + 0.858695i \(0.671276\pi\)
\(948\) 51.0306 1.65740
\(949\) −13.8180 −0.448550
\(950\) 6.36994i 0.206668i
\(951\) 76.2725i 2.47330i
\(952\) −23.9522 10.9858i −0.776294 0.356051i
\(953\) 3.69767i 0.119779i −0.998205 0.0598897i \(-0.980925\pi\)
0.998205 0.0598897i \(-0.0190749\pi\)
\(954\) 2.93243i 0.0949410i
\(955\) 5.64226i 0.182579i
\(956\) 9.49395i 0.307056i
\(957\) 0 0
\(958\) 7.62407i 0.246323i
\(959\) −3.26421 + 7.11693i −0.105407 + 0.229818i
\(960\) 8.54916 0.275923
\(961\) 22.0282 0.710587
\(962\) 2.04975i 0.0660865i
\(963\) 42.6084i 1.37304i
\(964\) −6.67760 −0.215071
\(965\) −39.7693 −1.28022
\(966\) −5.61836 + 12.2497i −0.180768 + 0.394127i
\(967\) 22.8572i 0.735038i 0.930016 + 0.367519i \(0.119793\pi\)
−0.930016 + 0.367519i \(0.880207\pi\)
\(968\) 0 0
\(969\) 13.7871i 0.442906i
\(970\) 30.2567i 0.971483i
\(971\) 1.02730i 0.0329675i −0.999864 0.0164837i \(-0.994753\pi\)
0.999864 0.0164837i \(-0.00524718\pi\)
\(972\) 32.5329i 1.04349i
\(973\) 16.2952 35.5282i 0.522399 1.13898i
\(974\) 10.4326i 0.334282i
\(975\) 22.2400i 0.712249i
\(976\) 19.8785 0.636297
\(977\) 20.2745 0.648638 0.324319 0.945948i \(-0.394865\pi\)
0.324319 + 0.945948i \(0.394865\pi\)
\(978\) −37.5391 −1.20037
\(979\) 0 0
\(980\) 29.1397 25.0840i 0.930834 0.801280i
\(981\) 12.2974i 0.392627i
\(982\) −7.00320 −0.223481
\(983\) 19.6549i 0.626894i −0.949606 0.313447i \(-0.898516\pi\)
0.949606 0.313447i \(-0.101484\pi\)
\(984\) −34.7983 −1.10933
\(985\) 53.3680 1.70044
\(986\) 5.73552 0.182656
\(987\) 19.9791 43.5602i 0.635941 1.38654i
\(988\) −2.12571 −0.0676280
\(989\) 4.94345i 0.157193i
\(990\) 0 0
\(991\) 12.4581 0.395744 0.197872 0.980228i \(-0.436597\pi\)
0.197872 + 0.980228i \(0.436597\pi\)
\(992\) 17.2981 0.549216
\(993\) 32.4320i 1.02920i
\(994\) 16.5139 + 7.57418i 0.523790 + 0.240238i
\(995\) −77.9021 −2.46966
\(996\) 6.64341i 0.210505i
\(997\) −20.0672 −0.635533 −0.317767 0.948169i \(-0.602933\pi\)
−0.317767 + 0.948169i \(0.602933\pi\)
\(998\) 15.6221i 0.494509i
\(999\) 7.59130i 0.240178i
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 847.2.b.f.846.12 16
7.6 odd 2 inner 847.2.b.f.846.11 16
11.2 odd 10 77.2.l.b.62.4 yes 16
11.3 even 5 847.2.l.j.475.1 16
11.4 even 5 847.2.l.e.699.4 16
11.5 even 5 77.2.l.b.41.3 16
11.6 odd 10 847.2.l.i.118.1 16
11.7 odd 10 847.2.l.j.699.2 16
11.8 odd 10 847.2.l.e.475.3 16
11.9 even 5 847.2.l.i.524.2 16
11.10 odd 2 inner 847.2.b.f.846.6 16
33.2 even 10 693.2.bu.d.370.2 16
33.5 odd 10 693.2.bu.d.118.1 16
77.2 odd 30 539.2.s.b.227.1 16
77.5 odd 30 539.2.s.c.129.1 16
77.6 even 10 847.2.l.i.118.2 16
77.13 even 10 77.2.l.b.62.3 yes 16
77.16 even 15 539.2.s.c.129.2 16
77.20 odd 10 847.2.l.i.524.1 16
77.24 even 30 539.2.s.c.117.2 16
77.27 odd 10 77.2.l.b.41.4 yes 16
77.38 odd 30 539.2.s.b.19.1 16
77.41 even 10 847.2.l.e.475.4 16
77.46 odd 30 539.2.s.c.117.1 16
77.48 odd 10 847.2.l.e.699.3 16
77.60 even 15 539.2.s.b.19.2 16
77.62 even 10 847.2.l.j.699.1 16
77.68 even 30 539.2.s.b.227.2 16
77.69 odd 10 847.2.l.j.475.2 16
77.76 even 2 inner 847.2.b.f.846.5 16
231.104 even 10 693.2.bu.d.118.2 16
231.167 odd 10 693.2.bu.d.370.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.l.b.41.3 16 11.5 even 5
77.2.l.b.41.4 yes 16 77.27 odd 10
77.2.l.b.62.3 yes 16 77.13 even 10
77.2.l.b.62.4 yes 16 11.2 odd 10
539.2.s.b.19.1 16 77.38 odd 30
539.2.s.b.19.2 16 77.60 even 15
539.2.s.b.227.1 16 77.2 odd 30
539.2.s.b.227.2 16 77.68 even 30
539.2.s.c.117.1 16 77.46 odd 30
539.2.s.c.117.2 16 77.24 even 30
539.2.s.c.129.1 16 77.5 odd 30
539.2.s.c.129.2 16 77.16 even 15
693.2.bu.d.118.1 16 33.5 odd 10
693.2.bu.d.118.2 16 231.104 even 10
693.2.bu.d.370.1 16 231.167 odd 10
693.2.bu.d.370.2 16 33.2 even 10
847.2.b.f.846.5 16 77.76 even 2 inner
847.2.b.f.846.6 16 11.10 odd 2 inner
847.2.b.f.846.11 16 7.6 odd 2 inner
847.2.b.f.846.12 16 1.1 even 1 trivial
847.2.l.e.475.3 16 11.8 odd 10
847.2.l.e.475.4 16 77.41 even 10
847.2.l.e.699.3 16 77.48 odd 10
847.2.l.e.699.4 16 11.4 even 5
847.2.l.i.118.1 16 11.6 odd 10
847.2.l.i.118.2 16 77.6 even 10
847.2.l.i.524.1 16 77.20 odd 10
847.2.l.i.524.2 16 11.9 even 5
847.2.l.j.475.1 16 11.3 even 5
847.2.l.j.475.2 16 77.69 odd 10
847.2.l.j.699.1 16 77.62 even 10
847.2.l.j.699.2 16 11.7 odd 10