Properties

Label 1470.2.g.h.589.3
Level $1470$
Weight $2$
Character 1470.589
Analytic conductor $11.738$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(589,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.589");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.g (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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.29160000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 20x^{3} + 125 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.3
Root \(-1.40280 + 1.74131i\) of defining polynomial
Character \(\chi\) \(=\) 1470.589
Dual form 1470.2.g.h.589.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.40280 + 1.74131i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(1.40280 + 1.74131i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(1.74131 - 1.40280i) q^{10} +1.67701 q^{11} +1.00000i q^{12} -4.48261i q^{13} +(1.74131 - 1.40280i) q^{15} +1.00000 q^{16} +7.61121i q^{17} +1.00000i q^{18} +4.48261 q^{19} +(-1.40280 - 1.74131i) q^{20} -1.67701i q^{22} -0.482613i q^{23} +1.00000 q^{24} +(-1.06430 + 4.88541i) q^{25} -4.48261 q^{26} +1.00000i q^{27} -1.19440 q^{29} +(-1.40280 - 1.74131i) q^{30} +3.48261 q^{31} -1.00000i q^{32} -1.67701i q^{33} +7.61121 q^{34} +1.00000 q^{36} +0.482613i q^{37} -4.48261i q^{38} -4.48261 q^{39} +(-1.74131 + 1.40280i) q^{40} +12.0938 q^{41} -2.00000i q^{43} -1.67701 q^{44} +(-1.40280 - 1.74131i) q^{45} -0.482613 q^{46} -11.4478i q^{47} -1.00000i q^{48} +(4.88541 + 1.06430i) q^{50} +7.61121 q^{51} +4.48261i q^{52} +9.57643i q^{53} +1.00000 q^{54} +(2.35251 + 2.92019i) q^{55} -4.48261i q^{57} +1.19440i q^{58} +5.77083 q^{59} +(-1.74131 + 1.40280i) q^{60} +10.5764 q^{61} -3.48261i q^{62} -1.00000 q^{64} +(7.80560 - 6.28822i) q^{65} -1.67701 q^{66} +3.35402i q^{67} -7.61121i q^{68} -0.482613 q^{69} +6.00000 q^{71} -1.00000i q^{72} -4.00000i q^{73} +0.482613 q^{74} +(4.88541 + 1.06430i) q^{75} -4.48261 q^{76} +4.48261i q^{78} -4.51739 q^{79} +(1.40280 + 1.74131i) q^{80} +1.00000 q^{81} -12.0938i q^{82} -1.87141i q^{83} +(-13.2534 + 10.6770i) q^{85} -2.00000 q^{86} +1.19440i q^{87} +1.67701i q^{88} -3.35402 q^{89} +(-1.74131 + 1.40280i) q^{90} +0.482613i q^{92} -3.48261i q^{93} -11.4478 q^{94} +(6.28822 + 7.80560i) q^{95} -1.00000 q^{96} -17.7708i q^{97} -1.67701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 6 q^{11} + 6 q^{16} + 6 q^{19} + 6 q^{24} - 6 q^{26} - 24 q^{29} + 12 q^{34} + 6 q^{36} - 6 q^{39} + 18 q^{41} - 6 q^{44} + 18 q^{46} + 12 q^{51} + 6 q^{54} - 30 q^{55} - 24 q^{59} - 12 q^{61} - 6 q^{64} + 30 q^{65} - 6 q^{66} + 18 q^{69} + 36 q^{71} - 18 q^{74} - 6 q^{76} - 48 q^{79} + 6 q^{81} - 12 q^{86} - 12 q^{89} - 6 q^{94} - 6 q^{96} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 1.40280 + 1.74131i 0.627352 + 0.778736i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 1.74131 1.40280i 0.550649 0.443605i
\(11\) 1.67701 0.505638 0.252819 0.967514i \(-0.418642\pi\)
0.252819 + 0.967514i \(0.418642\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 4.48261i 1.24325i −0.783314 0.621627i \(-0.786472\pi\)
0.783314 0.621627i \(-0.213528\pi\)
\(14\) 0 0
\(15\) 1.74131 1.40280i 0.449603 0.362202i
\(16\) 1.00000 0.250000
\(17\) 7.61121i 1.84599i 0.384814 + 0.922994i \(0.374266\pi\)
−0.384814 + 0.922994i \(0.625734\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.48261 1.02838 0.514191 0.857676i \(-0.328092\pi\)
0.514191 + 0.857676i \(0.328092\pi\)
\(20\) −1.40280 1.74131i −0.313676 0.389368i
\(21\) 0 0
\(22\) 1.67701i 0.357540i
\(23\) 0.482613i 0.100632i −0.998733 0.0503159i \(-0.983977\pi\)
0.998733 0.0503159i \(-0.0160228\pi\)
\(24\) 1.00000 0.204124
\(25\) −1.06430 + 4.88541i −0.212859 + 0.977083i
\(26\) −4.48261 −0.879113
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −1.19440 −0.221794 −0.110897 0.993832i \(-0.535372\pi\)
−0.110897 + 0.993832i \(0.535372\pi\)
\(30\) −1.40280 1.74131i −0.256115 0.317918i
\(31\) 3.48261 0.625496 0.312748 0.949836i \(-0.398751\pi\)
0.312748 + 0.949836i \(0.398751\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.67701i 0.291930i
\(34\) 7.61121 1.30531
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 0.482613i 0.0793411i 0.999213 + 0.0396705i \(0.0126308\pi\)
−0.999213 + 0.0396705i \(0.987369\pi\)
\(38\) 4.48261i 0.727176i
\(39\) −4.48261 −0.717793
\(40\) −1.74131 + 1.40280i −0.275325 + 0.221802i
\(41\) 12.0938 1.88874 0.944369 0.328889i \(-0.106674\pi\)
0.944369 + 0.328889i \(0.106674\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) −1.67701 −0.252819
\(45\) −1.40280 1.74131i −0.209117 0.259579i
\(46\) −0.482613 −0.0711574
\(47\) 11.4478i 1.66984i −0.550372 0.834919i \(-0.685514\pi\)
0.550372 0.834919i \(-0.314486\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.88541 + 1.06430i 0.690902 + 0.150514i
\(51\) 7.61121 1.06578
\(52\) 4.48261i 0.621627i
\(53\) 9.57643i 1.31542i 0.753269 + 0.657712i \(0.228476\pi\)
−0.753269 + 0.657712i \(0.771524\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.35251 + 2.92019i 0.317213 + 0.393758i
\(56\) 0 0
\(57\) 4.48261i 0.593737i
\(58\) 1.19440i 0.156832i
\(59\) 5.77083 0.751298 0.375649 0.926762i \(-0.377420\pi\)
0.375649 + 0.926762i \(0.377420\pi\)
\(60\) −1.74131 + 1.40280i −0.224802 + 0.181101i
\(61\) 10.5764 1.35417 0.677087 0.735903i \(-0.263242\pi\)
0.677087 + 0.735903i \(0.263242\pi\)
\(62\) 3.48261i 0.442292i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 7.80560 6.28822i 0.968166 0.779957i
\(66\) −1.67701 −0.206426
\(67\) 3.35402i 0.409759i 0.978787 + 0.204879i \(0.0656802\pi\)
−0.978787 + 0.204879i \(0.934320\pi\)
\(68\) 7.61121i 0.922994i
\(69\) −0.482613 −0.0580998
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 0.482613 0.0561026
\(75\) 4.88541 + 1.06430i 0.564119 + 0.122894i
\(76\) −4.48261 −0.514191
\(77\) 0 0
\(78\) 4.48261i 0.507556i
\(79\) −4.51739 −0.508246 −0.254123 0.967172i \(-0.581787\pi\)
−0.254123 + 0.967172i \(0.581787\pi\)
\(80\) 1.40280 + 1.74131i 0.156838 + 0.194684i
\(81\) 1.00000 0.111111
\(82\) 12.0938i 1.33554i
\(83\) 1.87141i 0.205414i −0.994712 0.102707i \(-0.967250\pi\)
0.994712 0.102707i \(-0.0327503\pi\)
\(84\) 0 0
\(85\) −13.2534 + 10.6770i −1.43754 + 1.15808i
\(86\) −2.00000 −0.215666
\(87\) 1.19440i 0.128053i
\(88\) 1.67701i 0.178770i
\(89\) −3.35402 −0.355525 −0.177763 0.984073i \(-0.556886\pi\)
−0.177763 + 0.984073i \(0.556886\pi\)
\(90\) −1.74131 + 1.40280i −0.183550 + 0.147868i
\(91\) 0 0
\(92\) 0.482613i 0.0503159i
\(93\) 3.48261i 0.361130i
\(94\) −11.4478 −1.18075
\(95\) 6.28822 + 7.80560i 0.645157 + 0.800838i
\(96\) −1.00000 −0.102062
\(97\) 17.7708i 1.80435i −0.431366 0.902177i \(-0.641968\pi\)
0.431366 0.902177i \(-0.358032\pi\)
\(98\) 0 0
\(99\) −1.67701 −0.168546
\(100\) 1.06430 4.88541i 0.106430 0.488541i
\(101\) 8.00000 0.796030 0.398015 0.917379i \(-0.369699\pi\)
0.398015 + 0.917379i \(0.369699\pi\)
\(102\) 7.61121i 0.753622i
\(103\) 13.6112i 1.34115i 0.741841 + 0.670576i \(0.233953\pi\)
−0.741841 + 0.670576i \(0.766047\pi\)
\(104\) 4.48261 0.439556
\(105\) 0 0
\(106\) 9.57643 0.930145
\(107\) 3.87141i 0.374263i −0.982335 0.187132i \(-0.940081\pi\)
0.982335 0.187132i \(-0.0599191\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −17.2224 −1.64961 −0.824804 0.565419i \(-0.808715\pi\)
−0.824804 + 0.565419i \(0.808715\pi\)
\(110\) 2.92019 2.35251i 0.278429 0.224303i
\(111\) 0.482613 0.0458076
\(112\) 0 0
\(113\) 8.96523i 0.843378i −0.906741 0.421689i \(-0.861437\pi\)
0.906741 0.421689i \(-0.138563\pi\)
\(114\) −4.48261 −0.419835
\(115\) 0.840377 0.677010i 0.0783656 0.0631315i
\(116\) 1.19440 0.110897
\(117\) 4.48261i 0.414418i
\(118\) 5.77083i 0.531248i
\(119\) 0 0
\(120\) 1.40280 + 1.74131i 0.128058 + 0.158959i
\(121\) −8.18764 −0.744331
\(122\) 10.5764i 0.957545i
\(123\) 12.0938i 1.09046i
\(124\) −3.48261 −0.312748
\(125\) −10.0000 + 5.00000i −0.894427 + 0.447214i
\(126\) 0 0
\(127\) 13.9342i 1.23646i −0.785997 0.618230i \(-0.787850\pi\)
0.785997 0.618230i \(-0.212150\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −2.00000 −0.176090
\(130\) −6.28822 7.80560i −0.551513 0.684597i
\(131\) −3.28822 −0.287293 −0.143646 0.989629i \(-0.545883\pi\)
−0.143646 + 0.989629i \(0.545883\pi\)
\(132\) 1.67701i 0.145965i
\(133\) 0 0
\(134\) 3.35402 0.289743
\(135\) −1.74131 + 1.40280i −0.149868 + 0.120734i
\(136\) −7.61121 −0.652656
\(137\) 4.25719i 0.363716i 0.983325 + 0.181858i \(0.0582111\pi\)
−0.983325 + 0.181858i \(0.941789\pi\)
\(138\) 0.482613i 0.0410827i
\(139\) 18.9652 1.60861 0.804305 0.594217i \(-0.202538\pi\)
0.804305 + 0.594217i \(0.202538\pi\)
\(140\) 0 0
\(141\) −11.4478 −0.964082
\(142\) 6.00000i 0.503509i
\(143\) 7.51739i 0.628635i
\(144\) −1.00000 −0.0833333
\(145\) −1.67550 2.07981i −0.139143 0.172719i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 0.482613i 0.0396705i
\(149\) −7.03477 −0.576311 −0.288156 0.957584i \(-0.593042\pi\)
−0.288156 + 0.957584i \(0.593042\pi\)
\(150\) 1.06430 4.88541i 0.0868994 0.398892i
\(151\) −6.44784 −0.524718 −0.262359 0.964970i \(-0.584500\pi\)
−0.262359 + 0.964970i \(0.584500\pi\)
\(152\) 4.48261i 0.363588i
\(153\) 7.61121i 0.615330i
\(154\) 0 0
\(155\) 4.88541 + 6.06430i 0.392406 + 0.487096i
\(156\) 4.48261 0.358896
\(157\) 0.0938186i 0.00748754i −0.999993 0.00374377i \(-0.998808\pi\)
0.999993 0.00374377i \(-0.00119168\pi\)
\(158\) 4.51739i 0.359384i
\(159\) 9.57643 0.759460
\(160\) 1.74131 1.40280i 0.137662 0.110901i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 20.5764i 1.61167i 0.592140 + 0.805835i \(0.298283\pi\)
−0.592140 + 0.805835i \(0.701717\pi\)
\(164\) −12.0938 −0.944369
\(165\) 2.92019 2.35251i 0.227336 0.183143i
\(166\) −1.87141 −0.145249
\(167\) 14.0938i 1.09061i 0.838237 + 0.545306i \(0.183587\pi\)
−0.838237 + 0.545306i \(0.816413\pi\)
\(168\) 0 0
\(169\) −7.09382 −0.545678
\(170\) 10.6770 + 13.2534i 0.818889 + 1.01649i
\(171\) −4.48261 −0.342794
\(172\) 2.00000i 0.152499i
\(173\) 1.12859i 0.0858053i −0.999079 0.0429027i \(-0.986339\pi\)
0.999079 0.0429027i \(-0.0136605\pi\)
\(174\) 1.19440 0.0905470
\(175\) 0 0
\(176\) 1.67701 0.126409
\(177\) 5.77083i 0.433762i
\(178\) 3.35402i 0.251394i
\(179\) 3.44784 0.257704 0.128852 0.991664i \(-0.458871\pi\)
0.128852 + 0.991664i \(0.458871\pi\)
\(180\) 1.40280 + 1.74131i 0.104559 + 0.129789i
\(181\) −22.8957 −1.70182 −0.850911 0.525310i \(-0.823950\pi\)
−0.850911 + 0.525310i \(0.823950\pi\)
\(182\) 0 0
\(183\) 10.5764i 0.781832i
\(184\) 0.482613 0.0355787
\(185\) −0.840377 + 0.677010i −0.0617857 + 0.0497748i
\(186\) −3.48261 −0.255358
\(187\) 12.7641i 0.933401i
\(188\) 11.4478i 0.834919i
\(189\) 0 0
\(190\) 7.80560 6.28822i 0.566278 0.456195i
\(191\) 25.1529 1.82000 0.909999 0.414611i \(-0.136082\pi\)
0.909999 + 0.414611i \(0.136082\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 12.8056i 0.921767i −0.887461 0.460884i \(-0.847533\pi\)
0.887461 0.460884i \(-0.152467\pi\)
\(194\) −17.7708 −1.27587
\(195\) −6.28822 7.80560i −0.450308 0.558971i
\(196\) 0 0
\(197\) 2.87141i 0.204579i −0.994755 0.102290i \(-0.967383\pi\)
0.994755 0.102290i \(-0.0326169\pi\)
\(198\) 1.67701i 0.119180i
\(199\) −3.03477 −0.215129 −0.107565 0.994198i \(-0.534305\pi\)
−0.107565 + 0.994198i \(0.534305\pi\)
\(200\) −4.88541 1.06430i −0.345451 0.0752571i
\(201\) 3.35402 0.236574
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) −7.61121 −0.532891
\(205\) 16.9652 + 21.0590i 1.18490 + 1.47083i
\(206\) 13.6112 0.948338
\(207\) 0.482613i 0.0335439i
\(208\) 4.48261i 0.310813i
\(209\) 7.51739 0.519989
\(210\) 0 0
\(211\) −10.4826 −0.721653 −0.360826 0.932633i \(-0.617505\pi\)
−0.360826 + 0.932633i \(0.617505\pi\)
\(212\) 9.57643i 0.657712i
\(213\) 6.00000i 0.411113i
\(214\) −3.87141 −0.264644
\(215\) 3.48261 2.80560i 0.237512 0.191341i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 17.2224i 1.16645i
\(219\) −4.00000 −0.270295
\(220\) −2.35251 2.92019i −0.158606 0.196879i
\(221\) 34.1181 2.29503
\(222\) 0.482613i 0.0323909i
\(223\) 15.1248i 1.01283i 0.862288 + 0.506417i \(0.169030\pi\)
−0.862288 + 0.506417i \(0.830970\pi\)
\(224\) 0 0
\(225\) 1.06430 4.88541i 0.0709531 0.325694i
\(226\) −8.96523 −0.596358
\(227\) 21.0938i 1.40005i 0.714120 + 0.700023i \(0.246827\pi\)
−0.714120 + 0.700023i \(0.753173\pi\)
\(228\) 4.48261i 0.296868i
\(229\) −23.2224 −1.53458 −0.767290 0.641300i \(-0.778395\pi\)
−0.767290 + 0.641300i \(0.778395\pi\)
\(230\) −0.677010 0.840377i −0.0446407 0.0554128i
\(231\) 0 0
\(232\) 1.19440i 0.0784160i
\(233\) 8.57643i 0.561861i 0.959728 + 0.280930i \(0.0906430\pi\)
−0.959728 + 0.280930i \(0.909357\pi\)
\(234\) 4.48261 0.293038
\(235\) 19.9342 16.0590i 1.30036 1.04758i
\(236\) −5.77083 −0.375649
\(237\) 4.51739i 0.293436i
\(238\) 0 0
\(239\) 4.57643 0.296025 0.148012 0.988986i \(-0.452712\pi\)
0.148012 + 0.988986i \(0.452712\pi\)
\(240\) 1.74131 1.40280i 0.112401 0.0905504i
\(241\) −9.96523 −0.641917 −0.320958 0.947093i \(-0.604005\pi\)
−0.320958 + 0.947093i \(0.604005\pi\)
\(242\) 8.18764i 0.526321i
\(243\) 1.00000i 0.0641500i
\(244\) −10.5764 −0.677087
\(245\) 0 0
\(246\) −12.0938 −0.771074
\(247\) 20.0938i 1.27854i
\(248\) 3.48261i 0.221146i
\(249\) −1.87141 −0.118596
\(250\) 5.00000 + 10.0000i 0.316228 + 0.632456i
\(251\) 4.38505 0.276782 0.138391 0.990378i \(-0.455807\pi\)
0.138391 + 0.990378i \(0.455807\pi\)
\(252\) 0 0
\(253\) 0.809347i 0.0508832i
\(254\) −13.9342 −0.874309
\(255\) 10.6770 + 13.2534i 0.668620 + 0.829963i
\(256\) 1.00000 0.0625000
\(257\) 4.70804i 0.293679i 0.989160 + 0.146840i \(0.0469102\pi\)
−0.989160 + 0.146840i \(0.953090\pi\)
\(258\) 2.00000i 0.124515i
\(259\) 0 0
\(260\) −7.80560 + 6.28822i −0.484083 + 0.389979i
\(261\) 1.19440 0.0739313
\(262\) 3.28822i 0.203147i
\(263\) 16.3192i 1.00629i −0.864203 0.503144i \(-0.832177\pi\)
0.864203 0.503144i \(-0.167823\pi\)
\(264\) 1.67701 0.103213
\(265\) −16.6755 + 13.4338i −1.02437 + 0.825234i
\(266\) 0 0
\(267\) 3.35402i 0.205263i
\(268\) 3.35402i 0.204879i
\(269\) −19.7708 −1.20545 −0.602724 0.797949i \(-0.705918\pi\)
−0.602724 + 0.797949i \(0.705918\pi\)
\(270\) 1.40280 + 1.74131i 0.0853718 + 0.105973i
\(271\) 2.26020 0.137297 0.0686487 0.997641i \(-0.478131\pi\)
0.0686487 + 0.997641i \(0.478131\pi\)
\(272\) 7.61121i 0.461497i
\(273\) 0 0
\(274\) 4.25719 0.257186
\(275\) −1.78484 + 8.19289i −0.107630 + 0.494050i
\(276\) 0.482613 0.0290499
\(277\) 18.2572i 1.09697i 0.836161 + 0.548484i \(0.184795\pi\)
−0.836161 + 0.548484i \(0.815205\pi\)
\(278\) 18.9652i 1.13746i
\(279\) −3.48261 −0.208499
\(280\) 0 0
\(281\) 10.4826 0.625340 0.312670 0.949862i \(-0.398777\pi\)
0.312670 + 0.949862i \(0.398777\pi\)
\(282\) 11.4478i 0.681709i
\(283\) 0.708040i 0.0420886i −0.999779 0.0210443i \(-0.993301\pi\)
0.999779 0.0210443i \(-0.00669911\pi\)
\(284\) −6.00000 −0.356034
\(285\) 7.80560 6.28822i 0.462364 0.372482i
\(286\) −7.51739 −0.444512
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −40.9305 −2.40767
\(290\) −2.07981 + 1.67550i −0.122131 + 0.0983889i
\(291\) −17.7708 −1.04174
\(292\) 4.00000i 0.234082i
\(293\) 12.6112i 0.736755i −0.929676 0.368377i \(-0.879913\pi\)
0.929676 0.368377i \(-0.120087\pi\)
\(294\) 0 0
\(295\) 8.09533 + 10.0488i 0.471328 + 0.585063i
\(296\) −0.482613 −0.0280513
\(297\) 1.67701i 0.0973100i
\(298\) 7.03477i 0.407514i
\(299\) −2.16337 −0.125111
\(300\) −4.88541 1.06430i −0.282060 0.0614472i
\(301\) 0 0
\(302\) 6.44784i 0.371031i
\(303\) 8.00000i 0.459588i
\(304\) 4.48261 0.257095
\(305\) 14.8366 + 18.4168i 0.849543 + 1.05454i
\(306\) −7.61121 −0.435104
\(307\) 9.54166i 0.544571i 0.962216 + 0.272286i \(0.0877795\pi\)
−0.962216 + 0.272286i \(0.912220\pi\)
\(308\) 0 0
\(309\) 13.6112 0.774314
\(310\) 6.06430 4.88541i 0.344429 0.277473i
\(311\) 20.9652 1.18883 0.594414 0.804159i \(-0.297384\pi\)
0.594414 + 0.804159i \(0.297384\pi\)
\(312\) 4.48261i 0.253778i
\(313\) 15.1944i 0.858838i 0.903105 + 0.429419i \(0.141282\pi\)
−0.903105 + 0.429419i \(0.858718\pi\)
\(314\) −0.0938186 −0.00529449
\(315\) 0 0
\(316\) 4.51739 0.254123
\(317\) 18.4478i 1.03613i 0.855340 + 0.518067i \(0.173348\pi\)
−0.855340 + 0.518067i \(0.826652\pi\)
\(318\) 9.57643i 0.537020i
\(319\) −2.00302 −0.112147
\(320\) −1.40280 1.74131i −0.0784190 0.0973420i
\(321\) −3.87141 −0.216081
\(322\) 0 0
\(323\) 34.1181i 1.89838i
\(324\) −1.00000 −0.0555556
\(325\) 21.8994 + 4.77083i 1.21476 + 0.264638i
\(326\) 20.5764 1.13962
\(327\) 17.2224i 0.952402i
\(328\) 12.0938i 0.667769i
\(329\) 0 0
\(330\) −2.35251 2.92019i −0.129502 0.160751i
\(331\) 22.8019 1.25330 0.626652 0.779299i \(-0.284425\pi\)
0.626652 + 0.779299i \(0.284425\pi\)
\(332\) 1.87141i 0.102707i
\(333\) 0.482613i 0.0264470i
\(334\) 14.0938 0.771179
\(335\) −5.84038 + 4.70502i −0.319094 + 0.257063i
\(336\) 0 0
\(337\) 9.12485i 0.497062i 0.968624 + 0.248531i \(0.0799478\pi\)
−0.968624 + 0.248531i \(0.920052\pi\)
\(338\) 7.09382i 0.385853i
\(339\) −8.96523 −0.486924
\(340\) 13.2534 10.6770i 0.718769 0.579042i
\(341\) 5.84038 0.316274
\(342\) 4.48261i 0.242392i
\(343\) 0 0
\(344\) 2.00000 0.107833
\(345\) −0.677010 0.840377i −0.0364490 0.0452444i
\(346\) −1.12859 −0.0606735
\(347\) 19.2224i 1.03191i −0.856615 0.515957i \(-0.827437\pi\)
0.856615 0.515957i \(-0.172563\pi\)
\(348\) 1.19440i 0.0640264i
\(349\) −6.18764 −0.331217 −0.165608 0.986192i \(-0.552959\pi\)
−0.165608 + 0.986192i \(0.552959\pi\)
\(350\) 0 0
\(351\) 4.48261 0.239264
\(352\) 1.67701i 0.0893849i
\(353\) 11.2224i 0.597309i 0.954361 + 0.298654i \(0.0965378\pi\)
−0.954361 + 0.298654i \(0.903462\pi\)
\(354\) −5.77083 −0.306716
\(355\) 8.41681 + 10.4478i 0.446718 + 0.554514i
\(356\) 3.35402 0.177763
\(357\) 0 0
\(358\) 3.44784i 0.182224i
\(359\) −9.61121 −0.507260 −0.253630 0.967301i \(-0.581625\pi\)
−0.253630 + 0.967301i \(0.581625\pi\)
\(360\) 1.74131 1.40280i 0.0917749 0.0739341i
\(361\) 1.09382 0.0575694
\(362\) 22.8957i 1.20337i
\(363\) 8.18764i 0.429740i
\(364\) 0 0
\(365\) 6.96523 5.61121i 0.364577 0.293704i
\(366\) −10.5764 −0.552839
\(367\) 26.2534i 1.37042i −0.728346 0.685209i \(-0.759711\pi\)
0.728346 0.685209i \(-0.240289\pi\)
\(368\) 0.482613i 0.0251579i
\(369\) −12.0938 −0.629579
\(370\) 0.677010 + 0.840377i 0.0351961 + 0.0436891i
\(371\) 0 0
\(372\) 3.48261i 0.180565i
\(373\) 17.4796i 0.905059i −0.891749 0.452530i \(-0.850522\pi\)
0.891749 0.452530i \(-0.149478\pi\)
\(374\) 12.7641 0.660014
\(375\) 5.00000 + 10.0000i 0.258199 + 0.516398i
\(376\) 11.4478 0.590377
\(377\) 5.35402i 0.275746i
\(378\) 0 0
\(379\) −32.2815 −1.65819 −0.829094 0.559110i \(-0.811143\pi\)
−0.829094 + 0.559110i \(0.811143\pi\)
\(380\) −6.28822 7.80560i −0.322579 0.400419i
\(381\) −13.9342 −0.713870
\(382\) 25.1529i 1.28693i
\(383\) 18.0938i 0.924551i 0.886736 + 0.462275i \(0.152967\pi\)
−0.886736 + 0.462275i \(0.847033\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −12.8056 −0.651788
\(387\) 2.00000i 0.101666i
\(388\) 17.7708i 0.902177i
\(389\) 8.18764 0.415130 0.207565 0.978221i \(-0.433446\pi\)
0.207565 + 0.978221i \(0.433446\pi\)
\(390\) −7.80560 + 6.28822i −0.395252 + 0.318416i
\(391\) 3.67327 0.185765
\(392\) 0 0
\(393\) 3.28822i 0.165869i
\(394\) −2.87141 −0.144659
\(395\) −6.33700 7.86616i −0.318849 0.395789i
\(396\) 1.67701 0.0842729
\(397\) 36.1876i 1.81621i −0.418747 0.908103i \(-0.637531\pi\)
0.418747 0.908103i \(-0.362469\pi\)
\(398\) 3.03477i 0.152119i
\(399\) 0 0
\(400\) −1.06430 + 4.88541i −0.0532148 + 0.244271i
\(401\) −30.9895 −1.54754 −0.773771 0.633466i \(-0.781632\pi\)
−0.773771 + 0.633466i \(0.781632\pi\)
\(402\) 3.35402i 0.167283i
\(403\) 15.6112i 0.777650i
\(404\) −8.00000 −0.398015
\(405\) 1.40280 + 1.74131i 0.0697058 + 0.0865262i
\(406\) 0 0
\(407\) 0.809347i 0.0401178i
\(408\) 7.61121i 0.376811i
\(409\) 13.0938 0.647448 0.323724 0.946152i \(-0.395065\pi\)
0.323724 + 0.946152i \(0.395065\pi\)
\(410\) 21.0590 16.9652i 1.04003 0.837853i
\(411\) 4.25719 0.209991
\(412\) 13.6112i 0.670576i
\(413\) 0 0
\(414\) 0.482613 0.0237191
\(415\) 3.25869 2.62521i 0.159963 0.128867i
\(416\) −4.48261 −0.219778
\(417\) 18.9652i 0.928731i
\(418\) 7.51739i 0.367687i
\(419\) 33.3783 1.63064 0.815318 0.579013i \(-0.196562\pi\)
0.815318 + 0.579013i \(0.196562\pi\)
\(420\) 0 0
\(421\) −6.90317 −0.336440 −0.168220 0.985750i \(-0.553802\pi\)
−0.168220 + 0.985750i \(0.553802\pi\)
\(422\) 10.4826i 0.510286i
\(423\) 11.4478i 0.556613i
\(424\) −9.57643 −0.465073
\(425\) −37.1839 8.10058i −1.80368 0.392936i
\(426\) −6.00000 −0.290701
\(427\) 0 0
\(428\) 3.87141i 0.187132i
\(429\) −7.51739 −0.362943
\(430\) −2.80560 3.48261i −0.135298 0.167947i
\(431\) −26.1181 −1.25806 −0.629032 0.777379i \(-0.716549\pi\)
−0.629032 + 0.777379i \(0.716549\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 25.9305i 1.24614i 0.782167 + 0.623069i \(0.214114\pi\)
−0.782167 + 0.623069i \(0.785886\pi\)
\(434\) 0 0
\(435\) −2.07981 + 1.67550i −0.0997193 + 0.0803342i
\(436\) 17.2224 0.824804
\(437\) 2.16337i 0.103488i
\(438\) 4.00000i 0.191127i
\(439\) −7.55216 −0.360445 −0.180222 0.983626i \(-0.557682\pi\)
−0.180222 + 0.983626i \(0.557682\pi\)
\(440\) −2.92019 + 2.35251i −0.139215 + 0.112152i
\(441\) 0 0
\(442\) 34.1181i 1.62283i
\(443\) 24.3162i 1.15530i −0.816285 0.577649i \(-0.803970\pi\)
0.816285 0.577649i \(-0.196030\pi\)
\(444\) −0.482613 −0.0229038
\(445\) −4.70502 5.84038i −0.223040 0.276860i
\(446\) 15.1248 0.716182
\(447\) 7.03477i 0.332733i
\(448\) 0 0
\(449\) −14.7398 −0.695614 −0.347807 0.937566i \(-0.613074\pi\)
−0.347807 + 0.937566i \(0.613074\pi\)
\(450\) −4.88541 1.06430i −0.230301 0.0501714i
\(451\) 20.2815 0.955016
\(452\) 8.96523i 0.421689i
\(453\) 6.44784i 0.302946i
\(454\) 21.0938 0.989982
\(455\) 0 0
\(456\) 4.48261 0.209918
\(457\) 0.805603i 0.0376845i 0.999822 + 0.0188423i \(0.00599803\pi\)
−0.999822 + 0.0188423i \(0.994002\pi\)
\(458\) 23.2224i 1.08511i
\(459\) −7.61121 −0.355261
\(460\) −0.840377 + 0.677010i −0.0391828 + 0.0315658i
\(461\) −23.8609 −1.11131 −0.555657 0.831412i \(-0.687533\pi\)
−0.555657 + 0.831412i \(0.687533\pi\)
\(462\) 0 0
\(463\) 9.19065i 0.427126i −0.976929 0.213563i \(-0.931493\pi\)
0.976929 0.213563i \(-0.0685068\pi\)
\(464\) −1.19440 −0.0554485
\(465\) 6.06430 4.88541i 0.281225 0.226556i
\(466\) 8.57643 0.397296
\(467\) 22.1181i 1.02350i −0.859133 0.511752i \(-0.828997\pi\)
0.859133 0.511752i \(-0.171003\pi\)
\(468\) 4.48261i 0.207209i
\(469\) 0 0
\(470\) −16.0590 19.9342i −0.740748 0.919496i
\(471\) −0.0938186 −0.00432293
\(472\) 5.77083i 0.265624i
\(473\) 3.35402i 0.154218i
\(474\) 4.51739 0.207490
\(475\) −4.77083 + 21.8994i −0.218901 + 1.00481i
\(476\) 0 0
\(477\) 9.57643i 0.438475i
\(478\) 4.57643i 0.209321i
\(479\) −33.4100 −1.52654 −0.763272 0.646077i \(-0.776408\pi\)
−0.763272 + 0.646077i \(0.776408\pi\)
\(480\) −1.40280 1.74131i −0.0640288 0.0794794i
\(481\) 2.16337 0.0986410
\(482\) 9.96523i 0.453904i
\(483\) 0 0
\(484\) 8.18764 0.372165
\(485\) 30.9445 24.9289i 1.40512 1.13197i
\(486\) −1.00000 −0.0453609
\(487\) 2.34726i 0.106365i −0.998585 0.0531823i \(-0.983064\pi\)
0.998585 0.0531823i \(-0.0169364\pi\)
\(488\) 10.5764i 0.478773i
\(489\) 20.5764 0.930498
\(490\) 0 0
\(491\) 23.3820 1.05522 0.527608 0.849488i \(-0.323089\pi\)
0.527608 + 0.849488i \(0.323089\pi\)
\(492\) 12.0938i 0.545231i
\(493\) 9.09080i 0.409429i
\(494\) −20.0938 −0.904064
\(495\) −2.35251 2.92019i −0.105738 0.131253i
\(496\) 3.48261 0.156374
\(497\) 0 0
\(498\) 1.87141i 0.0838598i
\(499\) −14.9652 −0.669936 −0.334968 0.942230i \(-0.608725\pi\)
−0.334968 + 0.942230i \(0.608725\pi\)
\(500\) 10.0000 5.00000i 0.447214 0.223607i
\(501\) 14.0938 0.629665
\(502\) 4.38505i 0.195714i
\(503\) 5.35402i 0.238724i −0.992851 0.119362i \(-0.961915\pi\)
0.992851 0.119362i \(-0.0380849\pi\)
\(504\) 0 0
\(505\) 11.2224 + 13.9305i 0.499391 + 0.619897i
\(506\) −0.809347 −0.0359799
\(507\) 7.09382i 0.315048i
\(508\) 13.9342i 0.618230i
\(509\) −20.9237 −0.927426 −0.463713 0.885985i \(-0.653483\pi\)
−0.463713 + 0.885985i \(0.653483\pi\)
\(510\) 13.2534 10.6770i 0.586872 0.472786i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 4.48261i 0.197912i
\(514\) 4.70804 0.207663
\(515\) −23.7013 + 19.0938i −1.04440 + 0.841374i
\(516\) 2.00000 0.0880451
\(517\) 19.1981i 0.844333i
\(518\) 0 0
\(519\) −1.12859 −0.0495397
\(520\) 6.28822 + 7.80560i 0.275757 + 0.342298i
\(521\) −4.35100 −0.190621 −0.0953105 0.995448i \(-0.530384\pi\)
−0.0953105 + 0.995448i \(0.530384\pi\)
\(522\) 1.19440i 0.0522773i
\(523\) 39.2845i 1.71779i 0.512152 + 0.858895i \(0.328849\pi\)
−0.512152 + 0.858895i \(0.671151\pi\)
\(524\) 3.28822 0.143646
\(525\) 0 0
\(526\) −16.3192 −0.711553
\(527\) 26.5069i 1.15466i
\(528\) 1.67701i 0.0729825i
\(529\) 22.7671 0.989873
\(530\) 13.4338 + 16.6755i 0.583528 + 0.724338i
\(531\) −5.77083 −0.250433
\(532\) 0 0
\(533\) 54.2119i 2.34818i
\(534\) 3.35402 0.145143
\(535\) 6.74131 5.43082i 0.291452 0.234795i
\(536\) −3.35402 −0.144872
\(537\) 3.44784i 0.148785i
\(538\) 19.7708i 0.852381i
\(539\) 0 0
\(540\) 1.74131 1.40280i 0.0749339 0.0603670i
\(541\) 14.9032 0.640737 0.320369 0.947293i \(-0.396193\pi\)
0.320369 + 0.947293i \(0.396193\pi\)
\(542\) 2.26020i 0.0970840i
\(543\) 22.8957i 0.982548i
\(544\) 7.61121 0.326328
\(545\) −24.1596 29.9895i −1.03488 1.28461i
\(546\) 0 0
\(547\) 43.9865i 1.88073i 0.340173 + 0.940363i \(0.389515\pi\)
−0.340173 + 0.940363i \(0.610485\pi\)
\(548\) 4.25719i 0.181858i
\(549\) −10.5764 −0.451391
\(550\) 8.19289 + 1.78484i 0.349346 + 0.0761057i
\(551\) −5.35402 −0.228089
\(552\) 0.482613i 0.0205414i
\(553\) 0 0
\(554\) 18.2572 0.775673
\(555\) 0.677010 + 0.840377i 0.0287375 + 0.0356720i
\(556\) −18.9652 −0.804305
\(557\) 4.86839i 0.206280i −0.994667 0.103140i \(-0.967111\pi\)
0.994667 0.103140i \(-0.0328890\pi\)
\(558\) 3.48261i 0.147431i
\(559\) −8.96523 −0.379189
\(560\) 0 0
\(561\) 12.7641 0.538899
\(562\) 10.4826i 0.442182i
\(563\) 5.35100i 0.225518i −0.993622 0.112759i \(-0.964031\pi\)
0.993622 0.112759i \(-0.0359688\pi\)
\(564\) 11.4478 0.482041
\(565\) 15.6112 12.5764i 0.656768 0.529094i
\(566\) −0.708040 −0.0297612
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) −8.15588 −0.341912 −0.170956 0.985279i \(-0.554686\pi\)
−0.170956 + 0.985279i \(0.554686\pi\)
\(570\) −6.28822 7.80560i −0.263384 0.326941i
\(571\) −5.61121 −0.234822 −0.117411 0.993083i \(-0.537459\pi\)
−0.117411 + 0.993083i \(0.537459\pi\)
\(572\) 7.51739i 0.314318i
\(573\) 25.1529i 1.05078i
\(574\) 0 0
\(575\) 2.35776 + 0.513643i 0.0983256 + 0.0214204i
\(576\) 1.00000 0.0416667
\(577\) 4.67399i 0.194581i 0.995256 + 0.0972905i \(0.0310176\pi\)
−0.995256 + 0.0972905i \(0.968982\pi\)
\(578\) 40.9305i 1.70248i
\(579\) −12.8056 −0.532183
\(580\) 1.67550 + 2.07981i 0.0695714 + 0.0863595i
\(581\) 0 0
\(582\) 17.7708i 0.736625i
\(583\) 16.0598i 0.665128i
\(584\) 4.00000 0.165521
\(585\) −7.80560 + 6.28822i −0.322722 + 0.259986i
\(586\) −12.6112 −0.520964
\(587\) 18.9062i 0.780342i 0.920742 + 0.390171i \(0.127584\pi\)
−0.920742 + 0.390171i \(0.872416\pi\)
\(588\) 0 0
\(589\) 15.6112 0.643249
\(590\) 10.0488 8.09533i 0.413702 0.333279i
\(591\) −2.87141 −0.118114
\(592\) 0.482613i 0.0198353i
\(593\) 21.5417i 0.884610i −0.896865 0.442305i \(-0.854161\pi\)
0.896865 0.442305i \(-0.145839\pi\)
\(594\) 1.67701 0.0688086
\(595\) 0 0
\(596\) 7.03477 0.288156
\(597\) 3.03477i 0.124205i
\(598\) 2.16337i 0.0884667i
\(599\) −34.7641 −1.42042 −0.710211 0.703989i \(-0.751400\pi\)
−0.710211 + 0.703989i \(0.751400\pi\)
\(600\) −1.06430 + 4.88541i −0.0434497 + 0.199446i
\(601\) −4.19814 −0.171246 −0.0856229 0.996328i \(-0.527288\pi\)
−0.0856229 + 0.996328i \(0.527288\pi\)
\(602\) 0 0
\(603\) 3.35402i 0.136586i
\(604\) 6.44784 0.262359
\(605\) −11.4856 14.2572i −0.466957 0.579637i
\(606\) −8.00000 −0.324978
\(607\) 42.1218i 1.70967i −0.518898 0.854836i \(-0.673658\pi\)
0.518898 0.854836i \(-0.326342\pi\)
\(608\) 4.48261i 0.181794i
\(609\) 0 0
\(610\) 18.4168 14.8366i 0.745675 0.600718i
\(611\) −51.3162 −2.07603
\(612\) 7.61121i 0.307665i
\(613\) 18.5522i 0.749315i −0.927163 0.374657i \(-0.877760\pi\)
0.927163 0.374657i \(-0.122240\pi\)
\(614\) 9.54166 0.385070
\(615\) 21.0590 16.9652i 0.849183 0.684104i
\(616\) 0 0
\(617\) 13.4236i 0.540413i 0.962802 + 0.270206i \(0.0870919\pi\)
−0.962802 + 0.270206i \(0.912908\pi\)
\(618\) 13.6112i 0.547523i
\(619\) −31.1211 −1.25086 −0.625431 0.780279i \(-0.715077\pi\)
−0.625431 + 0.780279i \(0.715077\pi\)
\(620\) −4.88541 6.06430i −0.196203 0.243548i
\(621\) 0.482613 0.0193666
\(622\) 20.9652i 0.840629i
\(623\) 0 0
\(624\) −4.48261 −0.179448
\(625\) −22.7345 10.3991i −0.909382 0.415962i
\(626\) 15.1944 0.607290
\(627\) 7.51739i 0.300216i
\(628\) 0.0938186i 0.00374377i
\(629\) −3.67327 −0.146463
\(630\) 0 0
\(631\) −1.15588 −0.0460148 −0.0230074 0.999735i \(-0.507324\pi\)
−0.0230074 + 0.999735i \(0.507324\pi\)
\(632\) 4.51739i 0.179692i
\(633\) 10.4826i 0.416646i
\(634\) 18.4478 0.732657
\(635\) 24.2637 19.5469i 0.962876 0.775695i
\(636\) −9.57643 −0.379730
\(637\) 0 0
\(638\) 2.00302i 0.0793002i
\(639\) −6.00000 −0.237356
\(640\) −1.74131 + 1.40280i −0.0688312 + 0.0554506i
\(641\) −15.0590 −0.594796 −0.297398 0.954754i \(-0.596119\pi\)
−0.297398 + 0.954754i \(0.596119\pi\)
\(642\) 3.87141i 0.152792i
\(643\) 35.2149i 1.38874i −0.719618 0.694371i \(-0.755683\pi\)
0.719618 0.694371i \(-0.244317\pi\)
\(644\) 0 0
\(645\) −2.80560 3.48261i −0.110471 0.137128i
\(646\) 34.1181 1.34236
\(647\) 4.41306i 0.173495i 0.996230 + 0.0867477i \(0.0276474\pi\)
−0.996230 + 0.0867477i \(0.972353\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 9.67774 0.379884
\(650\) 4.77083 21.8994i 0.187127 0.858966i
\(651\) 0 0
\(652\) 20.5764i 0.805835i
\(653\) 18.0968i 0.708184i −0.935211 0.354092i \(-0.884790\pi\)
0.935211 0.354092i \(-0.115210\pi\)
\(654\) 17.2224 0.673450
\(655\) −4.61271 5.72579i −0.180234 0.223725i
\(656\) 12.0938 0.472184
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) −25.6112 −0.997671 −0.498835 0.866697i \(-0.666239\pi\)
−0.498835 + 0.866697i \(0.666239\pi\)
\(660\) −2.92019 + 2.35251i −0.113668 + 0.0915714i
\(661\) −22.2497 −0.865413 −0.432706 0.901535i \(-0.642441\pi\)
−0.432706 + 0.901535i \(0.642441\pi\)
\(662\) 22.8019i 0.886219i
\(663\) 34.1181i 1.32504i
\(664\) 1.87141 0.0726247
\(665\) 0 0
\(666\) −0.482613 −0.0187009
\(667\) 0.576432i 0.0223195i
\(668\) 14.0938i 0.545306i
\(669\) 15.1248 0.584760
\(670\) 4.70502 + 5.84038i 0.181771 + 0.225633i
\(671\) 17.7368 0.684721
\(672\) 0 0
\(673\) 36.5349i 1.40832i 0.710043 + 0.704158i \(0.248676\pi\)
−0.710043 + 0.704158i \(0.751324\pi\)
\(674\) 9.12485 0.351476
\(675\) −4.88541 1.06430i −0.188040 0.0409648i
\(676\) 7.09382 0.272839
\(677\) 28.6112i 1.09962i 0.835290 + 0.549809i \(0.185299\pi\)
−0.835290 + 0.549809i \(0.814701\pi\)
\(678\) 8.96523i 0.344307i
\(679\) 0 0
\(680\) −10.6770 13.2534i −0.409445 0.508246i
\(681\) 21.0938 0.808317
\(682\) 5.84038i 0.223640i
\(683\) 12.5099i 0.478678i 0.970936 + 0.239339i \(0.0769307\pi\)
−0.970936 + 0.239339i \(0.923069\pi\)
\(684\) 4.48261 0.171397
\(685\) −7.41306 + 5.97199i −0.283239 + 0.228178i
\(686\) 0 0
\(687\) 23.2224i 0.885990i
\(688\) 2.00000i 0.0762493i
\(689\) 42.9274 1.63541
\(690\) −0.840377 + 0.677010i −0.0319926 + 0.0257733i
\(691\) −18.4448 −0.701674 −0.350837 0.936437i \(-0.614103\pi\)
−0.350837 + 0.936437i \(0.614103\pi\)
\(692\) 1.12859i 0.0429027i
\(693\) 0 0
\(694\) −19.2224 −0.729673
\(695\) 26.6044 + 33.0243i 1.00916 + 1.25268i
\(696\) −1.19440 −0.0452735
\(697\) 92.0485i 3.48659i
\(698\) 6.18764i 0.234206i
\(699\) 8.57643 0.324390
\(700\) 0 0
\(701\) −2.15962 −0.0815678 −0.0407839 0.999168i \(-0.512986\pi\)
−0.0407839 + 0.999168i \(0.512986\pi\)
\(702\) 4.48261i 0.169185i
\(703\) 2.16337i 0.0815929i
\(704\) −1.67701 −0.0632047
\(705\) −16.0590 19.9342i −0.604819 0.750765i
\(706\) 11.2224 0.422361
\(707\) 0 0
\(708\) 5.77083i 0.216881i
\(709\) 19.6037 0.736233 0.368117 0.929780i \(-0.380003\pi\)
0.368117 + 0.929780i \(0.380003\pi\)
\(710\) 10.4478 8.41681i 0.392100 0.315877i
\(711\) 4.51739 0.169415
\(712\) 3.35402i 0.125697i
\(713\) 1.68075i 0.0629447i
\(714\) 0 0
\(715\) 13.0901 10.5454i 0.489541 0.394376i
\(716\) −3.44784 −0.128852
\(717\) 4.57643i 0.170910i
\(718\) 9.61121i 0.358687i
\(719\) 53.0213 1.97736 0.988680 0.150042i \(-0.0479410\pi\)
0.988680 + 0.150042i \(0.0479410\pi\)
\(720\) −1.40280 1.74131i −0.0522793 0.0648947i
\(721\) 0 0
\(722\) 1.09382i 0.0407077i
\(723\) 9.96523i 0.370611i
\(724\) 22.8957 0.850911
\(725\) 1.27119 5.83513i 0.0472109 0.216711i
\(726\) 8.18764 0.303872
\(727\) 28.3155i 1.05016i −0.851052 0.525082i \(-0.824035\pi\)
0.851052 0.525082i \(-0.175965\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −5.61121 6.96523i −0.207680 0.257795i
\(731\) 15.2224 0.563021
\(732\) 10.5764i 0.390916i
\(733\) 24.9895i 0.923008i −0.887138 0.461504i \(-0.847310\pi\)
0.887138 0.461504i \(-0.152690\pi\)
\(734\) −26.2534 −0.969032
\(735\) 0 0
\(736\) −0.482613 −0.0177893
\(737\) 5.62473i 0.207189i
\(738\) 12.0938i 0.445180i
\(739\) −43.2467 −1.59085 −0.795427 0.606049i \(-0.792754\pi\)
−0.795427 + 0.606049i \(0.792754\pi\)
\(740\) 0.840377 0.677010i 0.0308929 0.0248874i
\(741\) −20.0938 −0.738165
\(742\) 0 0
\(743\) 21.9062i 0.803660i −0.915714 0.401830i \(-0.868374\pi\)
0.915714 0.401830i \(-0.131626\pi\)
\(744\) 3.48261 0.127679
\(745\) −9.86839 12.2497i −0.361550 0.448794i
\(746\) −17.4796 −0.639974
\(747\) 1.87141i 0.0684712i
\(748\) 12.7641i 0.466701i
\(749\) 0 0
\(750\) 10.0000 5.00000i 0.365148 0.182574i
\(751\) 26.8927 0.981327 0.490664 0.871349i \(-0.336754\pi\)
0.490664 + 0.871349i \(0.336754\pi\)
\(752\) 11.4478i 0.417460i
\(753\) 4.38505i 0.159800i
\(754\) 5.35402 0.194982
\(755\) −9.04504 11.2277i −0.329183 0.408617i
\(756\) 0 0
\(757\) 11.1529i 0.405358i −0.979245 0.202679i \(-0.935035\pi\)
0.979245 0.202679i \(-0.0649647\pi\)
\(758\) 32.2815i 1.17252i
\(759\) −0.809347 −0.0293774
\(760\) −7.80560 + 6.28822i −0.283139 + 0.228098i
\(761\) −1.58694 −0.0575264 −0.0287632 0.999586i \(-0.509157\pi\)
−0.0287632 + 0.999586i \(0.509157\pi\)
\(762\) 13.9342i 0.504783i
\(763\) 0 0
\(764\) −25.1529 −0.909999
\(765\) 13.2534 10.6770i 0.479179 0.386028i
\(766\) 18.0938 0.653756
\(767\) 25.8684i 0.934053i
\(768\) 1.00000i 0.0360844i
\(769\) 19.2572 0.694432 0.347216 0.937785i \(-0.387127\pi\)
0.347216 + 0.937785i \(0.387127\pi\)
\(770\) 0 0
\(771\) 4.70804 0.169556
\(772\) 12.8056i 0.460884i
\(773\) 30.2815i 1.08915i −0.838713 0.544574i \(-0.816691\pi\)
0.838713 0.544574i \(-0.183309\pi\)
\(774\) 2.00000 0.0718885
\(775\) −3.70653 + 17.0140i −0.133143 + 0.611161i
\(776\) 17.7708 0.637936
\(777\) 0 0
\(778\) 8.18764i 0.293541i
\(779\) 54.2119 1.94234
\(780\) 6.28822 + 7.80560i 0.225154 + 0.279485i
\(781\) 10.0621 0.360049
\(782\) 3.67327i 0.131356i
\(783\) 1.19440i 0.0426843i
\(784\) 0 0
\(785\) 0.163367 0.131609i 0.00583081 0.00469732i
\(786\) 3.28822 0.117287
\(787\) 33.2224i 1.18425i −0.805846 0.592126i \(-0.798289\pi\)
0.805846 0.592126i \(-0.201711\pi\)
\(788\) 2.87141i 0.102290i
\(789\) −16.3192 −0.580981
\(790\) −7.86616 + 6.33700i −0.279865 + 0.225460i
\(791\) 0 0
\(792\) 1.67701i 0.0595900i
\(793\) 47.4100i 1.68358i
\(794\) −36.1876 −1.28425
\(795\) 13.4338 + 16.6755i 0.476449 + 0.591419i
\(796\) 3.03477 0.107565
\(797\) 41.7883i 1.48022i −0.672486 0.740109i \(-0.734774\pi\)
0.672486 0.740109i \(-0.265226\pi\)
\(798\) 0 0
\(799\) 87.1319 3.08250
\(800\) 4.88541 + 1.06430i 0.172725 + 0.0376286i
\(801\) 3.35402 0.118508
\(802\) 30.9895i 1.09428i
\(803\) 6.70804i 0.236722i
\(804\) −3.35402 −0.118287
\(805\) 0 0
\(806\) −15.6112 −0.549881
\(807\) 19.7708i 0.695966i
\(808\) 8.00000i 0.281439i
\(809\) −5.05904 −0.177867 −0.0889333 0.996038i \(-0.528346\pi\)
−0.0889333 + 0.996038i \(0.528346\pi\)
\(810\) 1.74131 1.40280i 0.0611833 0.0492894i
\(811\) 33.5039 1.17648 0.588240 0.808686i \(-0.299821\pi\)
0.588240 + 0.808686i \(0.299821\pi\)
\(812\) 0 0
\(813\) 2.26020i 0.0792687i
\(814\) 0.809347 0.0283676
\(815\) −35.8299 + 28.8646i −1.25507 + 1.01108i
\(816\) 7.61121 0.266445
\(817\) 8.96523i 0.313654i
\(818\) 13.0938i 0.457815i
\(819\) 0 0
\(820\) −16.9652 21.0590i −0.592451 0.735414i
\(821\) 29.7013 1.03658 0.518291 0.855204i \(-0.326568\pi\)
0.518291 + 0.855204i \(0.326568\pi\)
\(822\) 4.25719i 0.148486i
\(823\) 38.2497i 1.33330i −0.745371 0.666650i \(-0.767727\pi\)
0.745371 0.666650i \(-0.232273\pi\)
\(824\) −13.6112 −0.474169
\(825\) 8.19289 + 1.78484i 0.285240 + 0.0621400i
\(826\) 0 0
\(827\) 13.3510i 0.464260i −0.972685 0.232130i \(-0.925431\pi\)
0.972685 0.232130i \(-0.0745695\pi\)
\(828\) 0.482613i 0.0167720i
\(829\) −3.61121 −0.125422 −0.0627112 0.998032i \(-0.519975\pi\)
−0.0627112 + 0.998032i \(0.519975\pi\)
\(830\) −2.62521 3.25869i −0.0911225 0.113111i
\(831\) 18.2572 0.633335
\(832\) 4.48261i 0.155407i
\(833\) 0 0
\(834\) −18.9652 −0.656712
\(835\) −24.5417 + 19.7708i −0.849299 + 0.684198i
\(836\) −7.51739 −0.259994
\(837\) 3.48261i 0.120377i
\(838\) 33.3783i 1.15303i
\(839\) 1.68075 0.0580261 0.0290130 0.999579i \(-0.490764\pi\)
0.0290130 + 0.999579i \(0.490764\pi\)
\(840\) 0 0
\(841\) −27.5734 −0.950807
\(842\) 6.90317i 0.237899i
\(843\) 10.4826i 0.361040i
\(844\) 10.4826 0.360826
\(845\) −9.95122 12.3525i −0.342332 0.424939i
\(846\) 11.4478 0.393585
\(847\) 0 0
\(848\) 9.57643i 0.328856i
\(849\) −0.708040 −0.0242999
\(850\) −8.10058 + 37.1839i −0.277848 + 1.27540i
\(851\) 0.232915 0.00798423
\(852\) 6.00000i 0.205557i
\(853\) 1.70502i 0.0583789i −0.999574 0.0291895i \(-0.990707\pi\)
0.999574 0.0291895i \(-0.00929261\pi\)
\(854\) 0 0
\(855\) −6.28822 7.80560i −0.215052 0.266946i
\(856\) 3.87141 0.132322
\(857\) 28.6945i 0.980186i −0.871670 0.490093i \(-0.836963\pi\)
0.871670 0.490093i \(-0.163037\pi\)
\(858\) 7.51739i 0.256639i
\(859\) −26.7641 −0.913178 −0.456589 0.889678i \(-0.650929\pi\)
−0.456589 + 0.889678i \(0.650929\pi\)
\(860\) −3.48261 + 2.80560i −0.118756 + 0.0956703i
\(861\) 0 0
\(862\) 26.1181i 0.889586i
\(863\) 32.0243i 1.09012i −0.838397 0.545059i \(-0.816507\pi\)
0.838397 0.545059i \(-0.183493\pi\)
\(864\) 1.00000 0.0340207
\(865\) 1.96523 1.58319i 0.0668197 0.0538301i
\(866\) 25.9305 0.881153
\(867\) 40.9305i 1.39007i
\(868\) 0 0
\(869\) −7.57570 −0.256988
\(870\) 1.67550 + 2.07981i 0.0568048 + 0.0705122i
\(871\) 15.0348 0.509434
\(872\) 17.2224i 0.583224i
\(873\) 17.7708i 0.601451i
\(874\) −2.16337 −0.0731770
\(875\) 0 0
\(876\) 4.00000 0.135147
\(877\) 18.1634i 0.613333i 0.951817 + 0.306667i \(0.0992137\pi\)
−0.951817 + 0.306667i \(0.900786\pi\)
\(878\) 7.55216i 0.254873i
\(879\) −12.6112 −0.425365
\(880\) 2.35251 + 2.92019i 0.0793032 + 0.0984395i
\(881\) 24.2254 0.816175 0.408088 0.912943i \(-0.366196\pi\)
0.408088 + 0.912943i \(0.366196\pi\)
\(882\) 0 0
\(883\) 32.3753i 1.08951i −0.838594 0.544757i \(-0.816622\pi\)
0.838594 0.544757i \(-0.183378\pi\)
\(884\) −34.1181 −1.14752
\(885\) 10.0488 8.09533i 0.337786 0.272121i
\(886\) −24.3162 −0.816920
\(887\) 32.9517i 1.10641i 0.833045 + 0.553205i \(0.186595\pi\)
−0.833045 + 0.553205i \(0.813405\pi\)
\(888\) 0.482613i 0.0161954i
\(889\) 0 0
\(890\) −5.84038 + 4.70502i −0.195770 + 0.157713i
\(891\) 1.67701 0.0561820
\(892\) 15.1248i 0.506417i
\(893\) 51.3162i 1.71723i
\(894\) 7.03477 0.235278
\(895\) 4.83663 + 6.00374i 0.161671 + 0.200683i
\(896\) 0 0
\(897\) 2.16337i 0.0722327i
\(898\) 14.7398i 0.491873i
\(899\) −4.15962 −0.138731
\(900\) −1.06430 + 4.88541i −0.0354765 + 0.162847i
\(901\) −72.8882 −2.42826
\(902\) 20.2815i 0.675299i
\(903\) 0 0
\(904\) 8.96523 0.298179
\(905\) −32.1181 39.8684i −1.06764 1.32527i
\(906\) 6.44784 0.214215
\(907\) 7.93794i 0.263575i 0.991278 + 0.131787i \(0.0420716\pi\)
−0.991278 + 0.131787i \(0.957928\pi\)
\(908\) 21.0938i 0.700023i
\(909\) −8.00000 −0.265343
\(910\) 0 0
\(911\) −6.00000 −0.198789 −0.0993944 0.995048i \(-0.531691\pi\)
−0.0993944 + 0.995048i \(0.531691\pi\)
\(912\) 4.48261i 0.148434i
\(913\) 3.13837i 0.103865i
\(914\) 0.805603 0.0266470
\(915\) 18.4168 14.8366i 0.608841 0.490484i
\(916\) 23.2224 0.767290
\(917\) 0 0
\(918\) 7.61121i 0.251207i
\(919\) −1.15286 −0.0380294 −0.0190147 0.999819i \(-0.506053\pi\)
−0.0190147 + 0.999819i \(0.506053\pi\)
\(920\) 0.677010 + 0.840377i 0.0223204 + 0.0277064i
\(921\) 9.54166 0.314408
\(922\) 23.8609i 0.785817i
\(923\) 26.8957i 0.885282i
\(924\) 0 0
\(925\) −2.35776 0.513643i −0.0775228 0.0168885i
\(926\) −9.19065 −0.302024
\(927\) 13.6112i 0.447051i
\(928\) 1.19440i 0.0392080i
\(929\) 58.9199 1.93310 0.966550 0.256477i \(-0.0825617\pi\)
0.966550 + 0.256477i \(0.0825617\pi\)
\(930\) −4.88541 6.06430i −0.160199 0.198856i
\(931\) 0 0
\(932\) 8.57643i 0.280930i
\(933\) 20.9652i 0.686371i
\(934\) −22.1181 −0.723726
\(935\) −22.2262 + 17.9055i −0.726873 + 0.585571i
\(936\) −4.48261 −0.146519
\(937\) 42.4168i 1.38570i −0.721083 0.692848i \(-0.756356\pi\)
0.721083 0.692848i \(-0.243644\pi\)
\(938\) 0 0
\(939\) 15.1944 0.495850
\(940\) −19.9342 + 16.0590i −0.650182 + 0.523788i
\(941\) −42.6665 −1.39089 −0.695444 0.718580i \(-0.744792\pi\)
−0.695444 + 0.718580i \(0.744792\pi\)
\(942\) 0.0938186i 0.00305677i
\(943\) 5.83663i 0.190067i
\(944\) 5.77083 0.187824
\(945\) 0 0
\(946\) −3.35402 −0.109049
\(947\) 53.7914i 1.74798i −0.485940 0.873992i \(-0.661523\pi\)
0.485940 0.873992i \(-0.338477\pi\)
\(948\) 4.51739i 0.146718i
\(949\) −17.9305 −0.582047
\(950\) 21.8994 + 4.77083i 0.710511 + 0.154786i
\(951\) 18.4478 0.598212
\(952\) 0 0
\(953\) 6.24970i 0.202448i −0.994864 0.101224i \(-0.967724\pi\)
0.994864 0.101224i \(-0.0322758\pi\)
\(954\) −9.57643 −0.310048
\(955\) 35.2845 + 43.7988i 1.14178 + 1.41730i
\(956\) −4.57643 −0.148012
\(957\) 2.00302i 0.0647483i
\(958\) 33.4100i 1.07943i
\(959\) 0 0
\(960\) −1.74131 + 1.40280i −0.0562004 + 0.0452752i
\(961\) −18.8714 −0.608755
\(962\) 2.16337i 0.0697497i
\(963\) 3.87141i 0.124754i
\(964\) 9.96523 0.320958
\(965\) 22.2985 17.9637i 0.717813 0.578273i
\(966\) 0 0
\(967\) 31.9585i 1.02771i −0.857876 0.513857i \(-0.828216\pi\)
0.857876 0.513857i \(-0.171784\pi\)
\(968\) 8.18764i 0.263161i
\(969\) 34.1181 1.09603
\(970\) −24.9289 30.9445i −0.800420 0.993567i
\(971\) 23.0175 0.738667 0.369334 0.929297i \(-0.379586\pi\)
0.369334 + 0.929297i \(0.379586\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 0 0
\(974\) −2.34726 −0.0752111
\(975\) 4.77083 21.8994i 0.152789 0.701343i
\(976\) 10.5764 0.338543
\(977\) 7.86839i 0.251732i 0.992047 + 0.125866i \(0.0401710\pi\)
−0.992047 + 0.125866i \(0.959829\pi\)
\(978\) 20.5764i 0.657962i
\(979\) −5.62473 −0.179767
\(980\) 0 0
\(981\) 17.2224 0.549869
\(982\) 23.3820i 0.746151i
\(983\) 12.0938i 0.385733i 0.981225 + 0.192866i \(0.0617784\pi\)
−0.981225 + 0.192866i \(0.938222\pi\)
\(984\) 12.0938 0.385537
\(985\) 5.00000 4.02801i 0.159313 0.128343i
\(986\) −9.09080 −0.289510
\(987\) 0 0
\(988\) 20.0938i 0.639270i
\(989\) −0.965226 −0.0306924
\(990\) −2.92019 + 2.35251i −0.0928097 + 0.0747677i
\(991\) 26.3783 0.837934 0.418967 0.908001i \(-0.362392\pi\)
0.418967 + 0.908001i \(0.362392\pi\)
\(992\) 3.48261i 0.110573i
\(993\) 22.8019i 0.723595i
\(994\) 0 0
\(995\) −4.25719 5.28447i −0.134962 0.167529i
\(996\) 1.87141 0.0592978
\(997\) 15.0908i 0.477931i −0.971028 0.238965i \(-0.923192\pi\)
0.971028 0.238965i \(-0.0768082\pi\)
\(998\) 14.9652i 0.473716i
\(999\) −0.482613 −0.0152692
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 1470.2.g.h.589.3 6
5.2 odd 4 7350.2.a.dp.1.2 3
5.3 odd 4 7350.2.a.do.1.2 3
5.4 even 2 inner 1470.2.g.h.589.6 6
7.2 even 3 1470.2.n.j.949.2 12
7.3 odd 6 210.2.n.b.79.6 yes 12
7.4 even 3 1470.2.n.j.79.4 12
7.5 odd 6 210.2.n.b.109.2 yes 12
7.6 odd 2 1470.2.g.i.589.1 6
21.5 even 6 630.2.u.f.109.5 12
21.17 even 6 630.2.u.f.289.1 12
28.3 even 6 1680.2.di.c.289.3 12
28.19 even 6 1680.2.di.c.529.5 12
35.3 even 12 1050.2.i.v.751.1 6
35.4 even 6 1470.2.n.j.79.2 12
35.9 even 6 1470.2.n.j.949.4 12
35.12 even 12 1050.2.i.u.151.3 6
35.13 even 4 7350.2.a.dn.1.2 3
35.17 even 12 1050.2.i.u.751.3 6
35.19 odd 6 210.2.n.b.109.6 yes 12
35.24 odd 6 210.2.n.b.79.2 12
35.27 even 4 7350.2.a.dq.1.2 3
35.33 even 12 1050.2.i.v.151.1 6
35.34 odd 2 1470.2.g.i.589.4 6
105.59 even 6 630.2.u.f.289.5 12
105.89 even 6 630.2.u.f.109.1 12
140.19 even 6 1680.2.di.c.529.3 12
140.59 even 6 1680.2.di.c.289.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.n.b.79.2 12 35.24 odd 6
210.2.n.b.79.6 yes 12 7.3 odd 6
210.2.n.b.109.2 yes 12 7.5 odd 6
210.2.n.b.109.6 yes 12 35.19 odd 6
630.2.u.f.109.1 12 105.89 even 6
630.2.u.f.109.5 12 21.5 even 6
630.2.u.f.289.1 12 21.17 even 6
630.2.u.f.289.5 12 105.59 even 6
1050.2.i.u.151.3 6 35.12 even 12
1050.2.i.u.751.3 6 35.17 even 12
1050.2.i.v.151.1 6 35.33 even 12
1050.2.i.v.751.1 6 35.3 even 12
1470.2.g.h.589.3 6 1.1 even 1 trivial
1470.2.g.h.589.6 6 5.4 even 2 inner
1470.2.g.i.589.1 6 7.6 odd 2
1470.2.g.i.589.4 6 35.34 odd 2
1470.2.n.j.79.2 12 35.4 even 6
1470.2.n.j.79.4 12 7.4 even 3
1470.2.n.j.949.2 12 7.2 even 3
1470.2.n.j.949.4 12 35.9 even 6
1680.2.di.c.289.3 12 28.3 even 6
1680.2.di.c.289.5 12 140.59 even 6
1680.2.di.c.529.3 12 140.19 even 6
1680.2.di.c.529.5 12 28.19 even 6
7350.2.a.dn.1.2 3 35.13 even 4
7350.2.a.do.1.2 3 5.3 odd 4
7350.2.a.dp.1.2 3 5.2 odd 4
7350.2.a.dq.1.2 3 35.27 even 4