Properties

Label 720.2.q.k.241.3
Level $720$
Weight $2$
Character 720.241
Analytic conductor $5.749$
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] = [720,2,Mod(241,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.241");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.q (of order \(3\), degree \(2\), not 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: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 180)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 241.3
Root \(1.71903 + 0.211943i\) of defining polynomial
Character \(\chi\) \(=\) 720.241
Dual form 720.2.q.k.481.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.71903 - 0.211943i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.36710 - 2.36788i) q^{7} +(2.91016 - 0.728674i) q^{9} +O(q^{10})\) \(q+(1.71903 - 0.211943i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.36710 - 2.36788i) q^{7} +(2.91016 - 0.728674i) q^{9} +(2.76210 - 4.78410i) q^{11} +(1.76210 + 3.05205i) q^{13} +(1.04307 + 1.38276i) q^{15} -5.52420 q^{17} -7.52420 q^{19} +(1.84823 - 4.36021i) q^{21} +(0.367095 + 0.635828i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.84823 - 1.86940i) q^{27} +(2.23419 - 3.86973i) q^{29} +(3.76210 + 6.51615i) q^{31} +(3.73419 - 8.80944i) q^{33} +2.73419 q^{35} +6.05582 q^{37} +(3.67597 + 4.87311i) q^{39} +(0.527909 + 0.914365i) q^{41} +(-1.76210 + 3.05205i) q^{43} +(2.08613 + 2.15594i) q^{45} +(0.604996 - 1.04788i) q^{47} +(-0.237900 - 0.412055i) q^{49} +(-9.49629 + 1.17081i) q^{51} +1.46838 q^{53} +5.52420 q^{55} +(-12.9344 + 1.59470i) q^{57} +(-0.734191 - 1.27166i) q^{59} +(-4.52791 + 7.84257i) q^{61} +(2.25306 - 7.88707i) q^{63} +(-1.76210 + 3.05205i) q^{65} +(-2.12920 - 3.68787i) q^{67} +(0.765809 + 1.01521i) q^{69} -10.0558 q^{71} +8.00000 q^{73} +(-0.675970 + 1.59470i) q^{75} +(-7.55211 - 13.0806i) q^{77} +(1.00000 - 1.73205i) q^{79} +(7.93807 - 4.24111i) q^{81} +(-2.63290 + 4.56032i) q^{83} +(-2.76210 - 4.78410i) q^{85} +(3.02049 - 7.12572i) q^{87} -3.00000 q^{89} +9.63583 q^{91} +(7.84823 + 10.4041i) q^{93} +(-3.76210 - 6.51615i) q^{95} +(-4.73419 + 8.19986i) q^{97} +(4.55211 - 15.9352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 3 q^{5} + 3 q^{7} + 5 q^{9} - 6 q^{13} - q^{15} - 12 q^{19} - 20 q^{21} - 3 q^{23} - 3 q^{25} - 2 q^{27} + 3 q^{29} + 6 q^{31} + 12 q^{33} + 6 q^{35} + 24 q^{37} + 20 q^{39} - 3 q^{41} + 6 q^{43} - 2 q^{45} + 15 q^{47} - 18 q^{49} - 30 q^{51} - 12 q^{53} - 32 q^{57} + 6 q^{59} - 21 q^{61} + 29 q^{63} + 6 q^{65} + 9 q^{67} + 15 q^{69} - 48 q^{71} + 48 q^{73} - 2 q^{75} - 6 q^{77} + 6 q^{79} + 29 q^{81} - 21 q^{83} - 42 q^{87} - 18 q^{89} + 16 q^{93} - 6 q^{95} - 18 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.71903 0.211943i 0.992485 0.122365i
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 1.36710 2.36788i 0.516714 0.894974i −0.483098 0.875566i \(-0.660489\pi\)
0.999812 0.0194079i \(-0.00617810\pi\)
\(8\) 0 0
\(9\) 2.91016 0.728674i 0.970054 0.242891i
\(10\) 0 0
\(11\) 2.76210 4.78410i 0.832804 1.44246i −0.0630012 0.998013i \(-0.520067\pi\)
0.895806 0.444446i \(-0.146599\pi\)
\(12\) 0 0
\(13\) 1.76210 + 3.05205i 0.488719 + 0.846485i 0.999916 0.0129781i \(-0.00413116\pi\)
−0.511197 + 0.859463i \(0.670798\pi\)
\(14\) 0 0
\(15\) 1.04307 + 1.38276i 0.269318 + 0.357026i
\(16\) 0 0
\(17\) −5.52420 −1.33982 −0.669908 0.742444i \(-0.733666\pi\)
−0.669908 + 0.742444i \(0.733666\pi\)
\(18\) 0 0
\(19\) −7.52420 −1.72617 −0.863085 0.505059i \(-0.831471\pi\)
−0.863085 + 0.505059i \(0.831471\pi\)
\(20\) 0 0
\(21\) 1.84823 4.36021i 0.403317 0.951476i
\(22\) 0 0
\(23\) 0.367095 + 0.635828i 0.0765447 + 0.132579i 0.901757 0.432243i \(-0.142278\pi\)
−0.825212 + 0.564823i \(0.808945\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 4.84823 1.86940i 0.933042 0.359767i
\(28\) 0 0
\(29\) 2.23419 3.86973i 0.414879 0.718591i −0.580537 0.814234i \(-0.697157\pi\)
0.995416 + 0.0956427i \(0.0304906\pi\)
\(30\) 0 0
\(31\) 3.76210 + 6.51615i 0.675693 + 1.17033i 0.976266 + 0.216576i \(0.0694889\pi\)
−0.300573 + 0.953759i \(0.597178\pi\)
\(32\) 0 0
\(33\) 3.73419 8.80944i 0.650039 1.53353i
\(34\) 0 0
\(35\) 2.73419 0.462163
\(36\) 0 0
\(37\) 6.05582 0.995570 0.497785 0.867300i \(-0.334147\pi\)
0.497785 + 0.867300i \(0.334147\pi\)
\(38\) 0 0
\(39\) 3.67597 + 4.87311i 0.588626 + 0.780322i
\(40\) 0 0
\(41\) 0.527909 + 0.914365i 0.0824455 + 0.142800i 0.904300 0.426898i \(-0.140394\pi\)
−0.821854 + 0.569698i \(0.807060\pi\)
\(42\) 0 0
\(43\) −1.76210 + 3.05205i −0.268718 + 0.465433i −0.968531 0.248893i \(-0.919933\pi\)
0.699813 + 0.714326i \(0.253267\pi\)
\(44\) 0 0
\(45\) 2.08613 + 2.15594i 0.310982 + 0.321388i
\(46\) 0 0
\(47\) 0.604996 1.04788i 0.0882477 0.152849i −0.818523 0.574474i \(-0.805207\pi\)
0.906771 + 0.421625i \(0.138540\pi\)
\(48\) 0 0
\(49\) −0.237900 0.412055i −0.0339857 0.0588650i
\(50\) 0 0
\(51\) −9.49629 + 1.17081i −1.32975 + 0.163947i
\(52\) 0 0
\(53\) 1.46838 0.201698 0.100849 0.994902i \(-0.467844\pi\)
0.100849 + 0.994902i \(0.467844\pi\)
\(54\) 0 0
\(55\) 5.52420 0.744883
\(56\) 0 0
\(57\) −12.9344 + 1.59470i −1.71320 + 0.211223i
\(58\) 0 0
\(59\) −0.734191 1.27166i −0.0955835 0.165556i 0.814268 0.580488i \(-0.197138\pi\)
−0.909852 + 0.414933i \(0.863805\pi\)
\(60\) 0 0
\(61\) −4.52791 + 7.84257i −0.579739 + 1.00414i 0.415770 + 0.909470i \(0.363512\pi\)
−0.995509 + 0.0946680i \(0.969821\pi\)
\(62\) 0 0
\(63\) 2.25306 7.88707i 0.283858 0.993678i
\(64\) 0 0
\(65\) −1.76210 + 3.05205i −0.218562 + 0.378560i
\(66\) 0 0
\(67\) −2.12920 3.68787i −0.260123 0.450546i 0.706152 0.708061i \(-0.250430\pi\)
−0.966274 + 0.257515i \(0.917096\pi\)
\(68\) 0 0
\(69\) 0.765809 + 1.01521i 0.0921926 + 0.122217i
\(70\) 0 0
\(71\) −10.0558 −1.19341 −0.596703 0.802462i \(-0.703523\pi\)
−0.596703 + 0.802462i \(0.703523\pi\)
\(72\) 0 0
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) 0 0
\(75\) −0.675970 + 1.59470i −0.0780542 + 0.184140i
\(76\) 0 0
\(77\) −7.55211 13.0806i −0.860643 1.49068i
\(78\) 0 0
\(79\) 1.00000 1.73205i 0.112509 0.194871i −0.804272 0.594261i \(-0.797445\pi\)
0.916781 + 0.399390i \(0.130778\pi\)
\(80\) 0 0
\(81\) 7.93807 4.24111i 0.882008 0.471235i
\(82\) 0 0
\(83\) −2.63290 + 4.56032i −0.288999 + 0.500561i −0.973571 0.228384i \(-0.926656\pi\)
0.684572 + 0.728945i \(0.259989\pi\)
\(84\) 0 0
\(85\) −2.76210 4.78410i −0.299592 0.518908i
\(86\) 0 0
\(87\) 3.02049 7.12572i 0.323831 0.763958i
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 9.63583 1.01011
\(92\) 0 0
\(93\) 7.84823 + 10.4041i 0.813824 + 1.07886i
\(94\) 0 0
\(95\) −3.76210 6.51615i −0.385983 0.668543i
\(96\) 0 0
\(97\) −4.73419 + 8.19986i −0.480684 + 0.832570i −0.999754 0.0221621i \(-0.992945\pi\)
0.519070 + 0.854732i \(0.326278\pi\)
\(98\) 0 0
\(99\) 4.55211 15.9352i 0.457504 1.60154i
\(100\) 0 0
\(101\) −6.73419 + 11.6640i −0.670077 + 1.16061i 0.307805 + 0.951450i \(0.400406\pi\)
−0.977882 + 0.209158i \(0.932928\pi\)
\(102\) 0 0
\(103\) 9.28630 + 16.0843i 0.915006 + 1.58484i 0.806892 + 0.590699i \(0.201148\pi\)
0.108114 + 0.994138i \(0.465519\pi\)
\(104\) 0 0
\(105\) 4.70017 0.579492i 0.458690 0.0565526i
\(106\) 0 0
\(107\) −19.2510 −1.86106 −0.930531 0.366213i \(-0.880654\pi\)
−0.930531 + 0.366213i \(0.880654\pi\)
\(108\) 0 0
\(109\) −0.524200 −0.0502092 −0.0251046 0.999685i \(-0.507992\pi\)
−0.0251046 + 0.999685i \(0.507992\pi\)
\(110\) 0 0
\(111\) 10.4102 1.28349i 0.988089 0.121823i
\(112\) 0 0
\(113\) 3.73419 + 6.46781i 0.351283 + 0.608440i 0.986475 0.163915i \(-0.0524121\pi\)
−0.635191 + 0.772355i \(0.719079\pi\)
\(114\) 0 0
\(115\) −0.367095 + 0.635828i −0.0342318 + 0.0592913i
\(116\) 0 0
\(117\) 7.35194 + 7.59795i 0.679687 + 0.702431i
\(118\) 0 0
\(119\) −7.55211 + 13.0806i −0.692301 + 1.19910i
\(120\) 0 0
\(121\) −9.75839 16.9020i −0.887126 1.53655i
\(122\) 0 0
\(123\) 1.10129 + 1.45994i 0.0992997 + 0.131638i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −8.25839 −0.732814 −0.366407 0.930455i \(-0.619412\pi\)
−0.366407 + 0.930455i \(0.619412\pi\)
\(128\) 0 0
\(129\) −2.38225 + 5.62004i −0.209746 + 0.494817i
\(130\) 0 0
\(131\) −8.04840 13.9402i −0.703192 1.21796i −0.967340 0.253482i \(-0.918424\pi\)
0.264148 0.964482i \(-0.414909\pi\)
\(132\) 0 0
\(133\) −10.2863 + 17.8164i −0.891935 + 1.54488i
\(134\) 0 0
\(135\) 4.04307 + 3.26399i 0.347972 + 0.280919i
\(136\) 0 0
\(137\) 9.25839 16.0360i 0.790998 1.37005i −0.134352 0.990934i \(-0.542895\pi\)
0.925350 0.379115i \(-0.123771\pi\)
\(138\) 0 0
\(139\) −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i \(-0.220926\pi\)
−0.938293 + 0.345843i \(0.887593\pi\)
\(140\) 0 0
\(141\) 0.817917 1.92957i 0.0688811 0.162499i
\(142\) 0 0
\(143\) 19.4684 1.62803
\(144\) 0 0
\(145\) 4.46838 0.371079
\(146\) 0 0
\(147\) −0.496291 0.657916i −0.0409334 0.0542640i
\(148\) 0 0
\(149\) −6.78630 11.7542i −0.555955 0.962943i −0.997829 0.0658653i \(-0.979019\pi\)
0.441873 0.897078i \(-0.354314\pi\)
\(150\) 0 0
\(151\) −6.23048 + 10.7915i −0.507029 + 0.878201i 0.492937 + 0.870065i \(0.335923\pi\)
−0.999967 + 0.00813598i \(0.997410\pi\)
\(152\) 0 0
\(153\) −16.0763 + 4.02534i −1.29969 + 0.325429i
\(154\) 0 0
\(155\) −3.76210 + 6.51615i −0.302179 + 0.523390i
\(156\) 0 0
\(157\) 0.790009 + 1.36834i 0.0630496 + 0.109205i 0.895827 0.444403i \(-0.146584\pi\)
−0.832778 + 0.553608i \(0.813251\pi\)
\(158\) 0 0
\(159\) 2.52420 0.311213i 0.200182 0.0246808i
\(160\) 0 0
\(161\) 2.00742 0.158207
\(162\) 0 0
\(163\) 4.47580 0.350572 0.175286 0.984518i \(-0.443915\pi\)
0.175286 + 0.984518i \(0.443915\pi\)
\(164\) 0 0
\(165\) 9.49629 1.17081i 0.739285 0.0911477i
\(166\) 0 0
\(167\) 8.39500 + 14.5406i 0.649625 + 1.12518i 0.983212 + 0.182464i \(0.0584074\pi\)
−0.333588 + 0.942719i \(0.608259\pi\)
\(168\) 0 0
\(169\) 0.290009 0.502310i 0.0223084 0.0386392i
\(170\) 0 0
\(171\) −21.8966 + 5.48269i −1.67448 + 0.419271i
\(172\) 0 0
\(173\) 11.5242 19.9605i 0.876169 1.51757i 0.0206561 0.999787i \(-0.493424\pi\)
0.855513 0.517782i \(-0.173242\pi\)
\(174\) 0 0
\(175\) 1.36710 + 2.36788i 0.103343 + 0.178995i
\(176\) 0 0
\(177\) −1.53162 2.03041i −0.115123 0.152615i
\(178\) 0 0
\(179\) −12.9926 −0.971111 −0.485556 0.874206i \(-0.661383\pi\)
−0.485556 + 0.874206i \(0.661383\pi\)
\(180\) 0 0
\(181\) −24.5652 −1.82592 −0.912958 0.408054i \(-0.866207\pi\)
−0.912958 + 0.408054i \(0.866207\pi\)
\(182\) 0 0
\(183\) −6.12146 + 14.4413i −0.452511 + 1.06753i
\(184\) 0 0
\(185\) 3.02791 + 5.24449i 0.222616 + 0.385583i
\(186\) 0 0
\(187\) −15.2584 + 26.4283i −1.11580 + 1.93263i
\(188\) 0 0
\(189\) 2.20147 14.0357i 0.160134 1.02094i
\(190\) 0 0
\(191\) 7.55211 13.0806i 0.546451 0.946482i −0.452063 0.891986i \(-0.649312\pi\)
0.998514 0.0544954i \(-0.0173550\pi\)
\(192\) 0 0
\(193\) 7.28630 + 12.6202i 0.524479 + 0.908425i 0.999594 + 0.0285008i \(0.00907332\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(194\) 0 0
\(195\) −2.38225 + 5.62004i −0.170597 + 0.402459i
\(196\) 0 0
\(197\) −4.53162 −0.322864 −0.161432 0.986884i \(-0.551611\pi\)
−0.161432 + 0.986884i \(0.551611\pi\)
\(198\) 0 0
\(199\) 7.41256 0.525463 0.262731 0.964869i \(-0.415377\pi\)
0.262731 + 0.964869i \(0.415377\pi\)
\(200\) 0 0
\(201\) −4.44178 5.88832i −0.313299 0.415330i
\(202\) 0 0
\(203\) −6.10870 10.5806i −0.428747 0.742612i
\(204\) 0 0
\(205\) −0.527909 + 0.914365i −0.0368708 + 0.0638620i
\(206\) 0 0
\(207\) 1.53162 + 1.58287i 0.106455 + 0.110017i
\(208\) 0 0
\(209\) −20.7826 + 35.9965i −1.43756 + 2.48993i
\(210\) 0 0
\(211\) −6.70628 11.6156i −0.461680 0.799652i 0.537365 0.843350i \(-0.319420\pi\)
−0.999045 + 0.0436972i \(0.986086\pi\)
\(212\) 0 0
\(213\) −17.2863 + 2.13126i −1.18444 + 0.146031i
\(214\) 0 0
\(215\) −3.52420 −0.240348
\(216\) 0 0
\(217\) 20.5726 1.39656
\(218\) 0 0
\(219\) 13.7523 1.69554i 0.929293 0.114574i
\(220\) 0 0
\(221\) −9.73419 16.8601i −0.654793 1.13413i
\(222\) 0 0
\(223\) −4.39500 + 7.61237i −0.294311 + 0.509762i −0.974824 0.222974i \(-0.928424\pi\)
0.680513 + 0.732736i \(0.261757\pi\)
\(224\) 0 0
\(225\) −0.824030 + 2.88461i −0.0549354 + 0.192307i
\(226\) 0 0
\(227\) 2.02791 3.51244i 0.134597 0.233129i −0.790846 0.612015i \(-0.790359\pi\)
0.925443 + 0.378886i \(0.123693\pi\)
\(228\) 0 0
\(229\) −1.29001 2.23436i −0.0852462 0.147651i 0.820250 0.572005i \(-0.193834\pi\)
−0.905496 + 0.424355i \(0.860501\pi\)
\(230\) 0 0
\(231\) −15.7547 20.8855i −1.03658 1.37416i
\(232\) 0 0
\(233\) −1.94418 −0.127368 −0.0636838 0.997970i \(-0.520285\pi\)
−0.0636838 + 0.997970i \(0.520285\pi\)
\(234\) 0 0
\(235\) 1.20999 0.0789311
\(236\) 0 0
\(237\) 1.35194 3.18940i 0.0878179 0.207174i
\(238\) 0 0
\(239\) 3.73419 + 6.46781i 0.241545 + 0.418368i 0.961154 0.276011i \(-0.0890126\pi\)
−0.719610 + 0.694379i \(0.755679\pi\)
\(240\) 0 0
\(241\) −1.20628 + 2.08934i −0.0777035 + 0.134586i −0.902259 0.431195i \(-0.858092\pi\)
0.824555 + 0.565781i \(0.191425\pi\)
\(242\) 0 0
\(243\) 12.7469 8.97304i 0.817717 0.575621i
\(244\) 0 0
\(245\) 0.237900 0.412055i 0.0151989 0.0263252i
\(246\) 0 0
\(247\) −13.2584 22.9642i −0.843611 1.46118i
\(248\) 0 0
\(249\) −3.55953 + 8.39738i −0.225576 + 0.532162i
\(250\) 0 0
\(251\) 6.99258 0.441368 0.220684 0.975345i \(-0.429171\pi\)
0.220684 + 0.975345i \(0.429171\pi\)
\(252\) 0 0
\(253\) 4.05582 0.254987
\(254\) 0 0
\(255\) −5.76210 7.63862i −0.360837 0.478349i
\(256\) 0 0
\(257\) 14.0484 + 24.3325i 0.876315 + 1.51782i 0.855355 + 0.518042i \(0.173339\pi\)
0.0209598 + 0.999780i \(0.493328\pi\)
\(258\) 0 0
\(259\) 8.27888 14.3394i 0.514425 0.891010i
\(260\) 0 0
\(261\) 3.68208 12.8895i 0.227915 0.797842i
\(262\) 0 0
\(263\) 3.81792 6.61283i 0.235423 0.407764i −0.723973 0.689829i \(-0.757686\pi\)
0.959395 + 0.282064i \(0.0910192\pi\)
\(264\) 0 0
\(265\) 0.734191 + 1.27166i 0.0451010 + 0.0781172i
\(266\) 0 0
\(267\) −5.15710 + 0.635828i −0.315610 + 0.0389120i
\(268\) 0 0
\(269\) −18.6210 −1.13534 −0.567671 0.823255i \(-0.692155\pi\)
−0.567671 + 0.823255i \(0.692155\pi\)
\(270\) 0 0
\(271\) −6.57260 −0.399257 −0.199628 0.979872i \(-0.563974\pi\)
−0.199628 + 0.979872i \(0.563974\pi\)
\(272\) 0 0
\(273\) 16.5643 2.04224i 1.00252 0.123602i
\(274\) 0 0
\(275\) 2.76210 + 4.78410i 0.166561 + 0.288492i
\(276\) 0 0
\(277\) −0.762100 + 1.32000i −0.0457901 + 0.0793108i −0.888012 0.459820i \(-0.847914\pi\)
0.842222 + 0.539131i \(0.181247\pi\)
\(278\) 0 0
\(279\) 15.6965 + 16.2217i 0.939722 + 0.971167i
\(280\) 0 0
\(281\) −7.26210 + 12.5783i −0.433221 + 0.750360i −0.997149 0.0754640i \(-0.975956\pi\)
0.563928 + 0.825824i \(0.309290\pi\)
\(282\) 0 0
\(283\) −8.36710 14.4922i −0.497372 0.861474i 0.502623 0.864506i \(-0.332368\pi\)
−0.999995 + 0.00303167i \(0.999035\pi\)
\(284\) 0 0
\(285\) −7.84823 10.4041i −0.464889 0.616288i
\(286\) 0 0
\(287\) 2.88681 0.170403
\(288\) 0 0
\(289\) 13.5168 0.795105
\(290\) 0 0
\(291\) −6.40034 + 15.0992i −0.375194 + 0.885132i
\(292\) 0 0
\(293\) 10.2305 + 17.7197i 0.597671 + 1.03520i 0.993164 + 0.116728i \(0.0372405\pi\)
−0.395493 + 0.918469i \(0.629426\pi\)
\(294\) 0 0
\(295\) 0.734191 1.27166i 0.0427463 0.0740387i
\(296\) 0 0
\(297\) 4.44789 28.3579i 0.258093 1.64549i
\(298\) 0 0
\(299\) −1.29372 + 2.24078i −0.0748176 + 0.129588i
\(300\) 0 0
\(301\) 4.81792 + 8.34488i 0.277700 + 0.480991i
\(302\) 0 0
\(303\) −9.10422 + 21.4780i −0.523024 + 1.23388i
\(304\) 0 0
\(305\) −9.05582 −0.518535
\(306\) 0 0
\(307\) 18.2026 1.03888 0.519438 0.854508i \(-0.326141\pi\)
0.519438 + 0.854508i \(0.326141\pi\)
\(308\) 0 0
\(309\) 19.3724 + 25.6814i 1.10206 + 1.46096i
\(310\) 0 0
\(311\) 1.55211 + 2.68833i 0.0880120 + 0.152441i 0.906671 0.421839i \(-0.138615\pi\)
−0.818659 + 0.574280i \(0.805282\pi\)
\(312\) 0 0
\(313\) 9.55211 16.5447i 0.539917 0.935164i −0.458991 0.888441i \(-0.651789\pi\)
0.998908 0.0467228i \(-0.0148777\pi\)
\(314\) 0 0
\(315\) 7.95693 1.99233i 0.448322 0.112255i
\(316\) 0 0
\(317\) −2.50371 + 4.33655i −0.140622 + 0.243565i −0.927731 0.373249i \(-0.878244\pi\)
0.787109 + 0.616814i \(0.211577\pi\)
\(318\) 0 0
\(319\) −12.3421 21.3772i −0.691026 1.19689i
\(320\) 0 0
\(321\) −33.0931 + 4.08010i −1.84708 + 0.227729i
\(322\) 0 0
\(323\) 41.5652 2.31275
\(324\) 0 0
\(325\) −3.52420 −0.195487
\(326\) 0 0
\(327\) −0.901117 + 0.111100i −0.0498319 + 0.00614386i
\(328\) 0 0
\(329\) −1.65417 2.86511i −0.0911976 0.157959i
\(330\) 0 0
\(331\) −1.74161 + 3.01656i −0.0957275 + 0.165805i −0.909912 0.414801i \(-0.863851\pi\)
0.814184 + 0.580606i \(0.197184\pi\)
\(332\) 0 0
\(333\) 17.6234 4.41271i 0.965756 0.241815i
\(334\) 0 0
\(335\) 2.12920 3.68787i 0.116330 0.201490i
\(336\) 0 0
\(337\) −5.79001 10.0286i −0.315402 0.546292i 0.664121 0.747625i \(-0.268806\pi\)
−0.979523 + 0.201333i \(0.935473\pi\)
\(338\) 0 0
\(339\) 7.79001 + 10.3270i 0.423095 + 0.560883i
\(340\) 0 0
\(341\) 41.5652 2.25088
\(342\) 0 0
\(343\) 17.8384 0.963183
\(344\) 0 0
\(345\) −0.496291 + 1.17081i −0.0267194 + 0.0630345i
\(346\) 0 0
\(347\) 13.2305 + 22.9159i 0.710249 + 1.23019i 0.964763 + 0.263119i \(0.0847512\pi\)
−0.254514 + 0.967069i \(0.581915\pi\)
\(348\) 0 0
\(349\) 13.0168 22.5457i 0.696772 1.20685i −0.272807 0.962069i \(-0.587952\pi\)
0.969580 0.244776i \(-0.0787145\pi\)
\(350\) 0 0
\(351\) 14.2486 + 11.5029i 0.760532 + 0.613982i
\(352\) 0 0
\(353\) 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 0 0
\(355\) −5.02791 8.70859i −0.266854 0.462204i
\(356\) 0 0
\(357\) −10.2100 + 24.0867i −0.540370 + 1.27480i
\(358\) 0 0
\(359\) −6.04098 −0.318831 −0.159415 0.987212i \(-0.550961\pi\)
−0.159415 + 0.987212i \(0.550961\pi\)
\(360\) 0 0
\(361\) 37.6136 1.97966
\(362\) 0 0
\(363\) −20.3573 26.9870i −1.06848 1.41645i
\(364\) 0 0
\(365\) 4.00000 + 6.92820i 0.209370 + 0.362639i
\(366\) 0 0
\(367\) 11.2305 19.4518i 0.586226 1.01537i −0.408495 0.912761i \(-0.633946\pi\)
0.994721 0.102613i \(-0.0327204\pi\)
\(368\) 0 0
\(369\) 2.20257 + 2.27628i 0.114661 + 0.118498i
\(370\) 0 0
\(371\) 2.00742 3.47695i 0.104220 0.180514i
\(372\) 0 0
\(373\) 1.26581 + 2.19245i 0.0655411 + 0.113521i 0.896934 0.442165i \(-0.145789\pi\)
−0.831393 + 0.555685i \(0.812456\pi\)
\(374\) 0 0
\(375\) −1.71903 + 0.211943i −0.0887706 + 0.0109447i
\(376\) 0 0
\(377\) 15.7475 0.811036
\(378\) 0 0
\(379\) 21.0484 1.08118 0.540592 0.841285i \(-0.318200\pi\)
0.540592 + 0.841285i \(0.318200\pi\)
\(380\) 0 0
\(381\) −14.1965 + 1.75031i −0.727307 + 0.0896709i
\(382\) 0 0
\(383\) −3.81792 6.61283i −0.195086 0.337900i 0.751842 0.659343i \(-0.229165\pi\)
−0.946929 + 0.321443i \(0.895832\pi\)
\(384\) 0 0
\(385\) 7.55211 13.0806i 0.384891 0.666651i
\(386\) 0 0
\(387\) −2.90405 + 10.1659i −0.147621 + 0.516764i
\(388\) 0 0
\(389\) 9.46467 16.3933i 0.479878 0.831173i −0.519856 0.854254i \(-0.674014\pi\)
0.999734 + 0.0230811i \(0.00734760\pi\)
\(390\) 0 0
\(391\) −2.02791 3.51244i −0.102556 0.177632i
\(392\) 0 0
\(393\) −16.7900 22.2580i −0.846944 1.12277i
\(394\) 0 0
\(395\) 2.00000 0.100631
\(396\) 0 0
\(397\) −29.1600 −1.46350 −0.731750 0.681573i \(-0.761296\pi\)
−0.731750 + 0.681573i \(0.761296\pi\)
\(398\) 0 0
\(399\) −13.9065 + 32.8071i −0.696193 + 1.64241i
\(400\) 0 0
\(401\) −16.3142 28.2570i −0.814693 1.41109i −0.909548 0.415598i \(-0.863572\pi\)
0.0948557 0.995491i \(-0.469761\pi\)
\(402\) 0 0
\(403\) −13.2584 + 22.9642i −0.660447 + 1.14393i
\(404\) 0 0
\(405\) 7.64195 + 4.75401i 0.379731 + 0.236229i
\(406\) 0 0
\(407\) 16.7268 28.9716i 0.829115 1.43607i
\(408\) 0 0
\(409\) −16.1042 27.8933i −0.796302 1.37924i −0.922009 0.387169i \(-0.873453\pi\)
0.125707 0.992067i \(-0.459880\pi\)
\(410\) 0 0
\(411\) 12.5168 29.5287i 0.617407 1.45654i
\(412\) 0 0
\(413\) −4.01484 −0.197557
\(414\) 0 0
\(415\) −5.26581 −0.258488
\(416\) 0 0
\(417\) −4.17226 5.53103i −0.204316 0.270855i
\(418\) 0 0
\(419\) −10.7063 18.5438i −0.523036 0.905925i −0.999641 0.0268073i \(-0.991466\pi\)
0.476605 0.879118i \(-0.341867\pi\)
\(420\) 0 0
\(421\) 0.944182 1.63537i 0.0460166 0.0797031i −0.842100 0.539322i \(-0.818681\pi\)
0.888116 + 0.459619i \(0.152014\pi\)
\(422\) 0 0
\(423\) 0.997070 3.49035i 0.0484792 0.169707i
\(424\) 0 0
\(425\) 2.76210 4.78410i 0.133982 0.232063i
\(426\) 0 0
\(427\) 12.3802 + 21.4431i 0.599118 + 1.03770i
\(428\) 0 0
\(429\) 33.4668 4.12618i 1.61579 0.199214i
\(430\) 0 0
\(431\) 2.11164 0.101714 0.0508569 0.998706i \(-0.483805\pi\)
0.0508569 + 0.998706i \(0.483805\pi\)
\(432\) 0 0
\(433\) −9.52420 −0.457704 −0.228852 0.973461i \(-0.573497\pi\)
−0.228852 + 0.973461i \(0.573497\pi\)
\(434\) 0 0
\(435\) 7.68130 0.947041i 0.368290 0.0454071i
\(436\) 0 0
\(437\) −2.76210 4.78410i −0.132129 0.228854i
\(438\) 0 0
\(439\) −7.20257 + 12.4752i −0.343760 + 0.595410i −0.985128 0.171824i \(-0.945034\pi\)
0.641368 + 0.767234i \(0.278367\pi\)
\(440\) 0 0
\(441\) −0.992582 1.02580i −0.0472658 0.0488474i
\(442\) 0 0
\(443\) −9.60500 + 16.6363i −0.456347 + 0.790416i −0.998765 0.0496927i \(-0.984176\pi\)
0.542417 + 0.840109i \(0.317509\pi\)
\(444\) 0 0
\(445\) −1.50000 2.59808i −0.0711068 0.123161i
\(446\) 0 0
\(447\) −14.1571 18.7676i −0.669608 0.887677i
\(448\) 0 0
\(449\) 33.5800 1.58474 0.792369 0.610041i \(-0.208847\pi\)
0.792369 + 0.610041i \(0.208847\pi\)
\(450\) 0 0
\(451\) 5.83255 0.274644
\(452\) 0 0
\(453\) −8.42323 + 19.8715i −0.395758 + 0.933644i
\(454\) 0 0
\(455\) 4.81792 + 8.34488i 0.225867 + 0.391214i
\(456\) 0 0
\(457\) −1.08373 + 1.87707i −0.0506946 + 0.0878056i −0.890259 0.455454i \(-0.849477\pi\)
0.839565 + 0.543260i \(0.182810\pi\)
\(458\) 0 0
\(459\) −26.7826 + 10.3270i −1.25010 + 0.482021i
\(460\) 0 0
\(461\) 12.8700 22.2915i 0.599417 1.03822i −0.393490 0.919329i \(-0.628733\pi\)
0.992907 0.118892i \(-0.0379341\pi\)
\(462\) 0 0
\(463\) 6.02791 + 10.4406i 0.280141 + 0.485218i 0.971419 0.237371i \(-0.0762855\pi\)
−0.691279 + 0.722588i \(0.742952\pi\)
\(464\) 0 0
\(465\) −5.08613 + 11.9988i −0.235864 + 0.556433i
\(466\) 0 0
\(467\) 14.4610 0.669174 0.334587 0.942365i \(-0.391403\pi\)
0.334587 + 0.942365i \(0.391403\pi\)
\(468\) 0 0
\(469\) −11.6433 −0.537635
\(470\) 0 0
\(471\) 1.64806 + 2.18478i 0.0759386 + 0.100669i
\(472\) 0 0
\(473\) 9.73419 + 16.8601i 0.447579 + 0.775229i
\(474\) 0 0
\(475\) 3.76210 6.51615i 0.172617 0.298981i
\(476\) 0 0
\(477\) 4.27323 1.06997i 0.195658 0.0489906i
\(478\) 0 0
\(479\) −9.99258 + 17.3077i −0.456573 + 0.790807i −0.998777 0.0494395i \(-0.984257\pi\)
0.542204 + 0.840247i \(0.317590\pi\)
\(480\) 0 0
\(481\) 10.6710 + 18.4826i 0.486554 + 0.842736i
\(482\) 0 0
\(483\) 3.45082 0.425458i 0.157018 0.0193590i
\(484\) 0 0
\(485\) −9.46838 −0.429937
\(486\) 0 0
\(487\) 18.1526 0.822574 0.411287 0.911506i \(-0.365079\pi\)
0.411287 + 0.911506i \(0.365079\pi\)
\(488\) 0 0
\(489\) 7.69406 0.948613i 0.347937 0.0428978i
\(490\) 0 0
\(491\) 19.7900 + 34.2773i 0.893111 + 1.54691i 0.836126 + 0.548538i \(0.184815\pi\)
0.0569849 + 0.998375i \(0.481851\pi\)
\(492\) 0 0
\(493\) −12.3421 + 21.3772i −0.555861 + 0.962779i
\(494\) 0 0
\(495\) 16.0763 4.02534i 0.722576 0.180926i
\(496\) 0 0
\(497\) −13.7473 + 23.8110i −0.616649 + 1.06807i
\(498\) 0 0
\(499\) −21.3142 36.9173i −0.954155 1.65264i −0.736290 0.676666i \(-0.763424\pi\)
−0.217865 0.975979i \(-0.569909\pi\)
\(500\) 0 0
\(501\) 17.5131 + 23.2165i 0.782426 + 1.03724i
\(502\) 0 0
\(503\) −21.1952 −0.945045 −0.472523 0.881319i \(-0.656657\pi\)
−0.472523 + 0.881319i \(0.656657\pi\)
\(504\) 0 0
\(505\) −13.4684 −0.599335
\(506\) 0 0
\(507\) 0.392074 0.924953i 0.0174126 0.0410786i
\(508\) 0 0
\(509\) 11.0168 + 19.0816i 0.488310 + 0.845778i 0.999910 0.0134460i \(-0.00428012\pi\)
−0.511599 + 0.859224i \(0.670947\pi\)
\(510\) 0 0
\(511\) 10.9368 18.9430i 0.483814 0.837990i
\(512\) 0 0
\(513\) −36.4791 + 14.0658i −1.61059 + 0.621018i
\(514\) 0 0
\(515\) −9.28630 + 16.0843i −0.409203 + 0.708761i
\(516\) 0 0
\(517\) −3.34212 5.78872i −0.146986 0.254587i
\(518\) 0 0
\(519\) 15.5800 36.7553i 0.683887 1.61338i
\(520\) 0 0
\(521\) 1.40515 0.0615606 0.0307803 0.999526i \(-0.490201\pi\)
0.0307803 + 0.999526i \(0.490201\pi\)
\(522\) 0 0
\(523\) 11.8532 0.518306 0.259153 0.965836i \(-0.416557\pi\)
0.259153 + 0.965836i \(0.416557\pi\)
\(524\) 0 0
\(525\) 2.85194 + 3.78072i 0.124469 + 0.165004i
\(526\) 0 0
\(527\) −20.7826 35.9965i −0.905304 1.56803i
\(528\) 0 0
\(529\) 11.2305 19.4518i 0.488282 0.845729i
\(530\) 0 0
\(531\) −3.06324 3.16574i −0.132933 0.137381i
\(532\) 0 0
\(533\) −1.86046 + 3.22240i −0.0805853 + 0.139578i
\(534\) 0 0
\(535\) −9.62549 16.6718i −0.416146 0.720786i
\(536\) 0 0
\(537\) −22.3347 + 2.75368i −0.963813 + 0.118830i
\(538\) 0 0
\(539\) −2.62842 −0.113214
\(540\) 0 0
\(541\) −8.98516 −0.386302 −0.193151 0.981169i \(-0.561871\pi\)
−0.193151 + 0.981169i \(0.561871\pi\)
\(542\) 0 0
\(543\) −42.2284 + 5.20641i −1.81219 + 0.223428i
\(544\) 0 0
\(545\) −0.262100 0.453970i −0.0112271 0.0194459i
\(546\) 0 0
\(547\) −3.10129 + 5.37159i −0.132601 + 0.229672i −0.924679 0.380749i \(-0.875666\pi\)
0.792077 + 0.610421i \(0.209000\pi\)
\(548\) 0 0
\(549\) −7.46227 + 26.1225i −0.318482 + 1.11488i
\(550\) 0 0
\(551\) −16.8105 + 29.1166i −0.716151 + 1.24041i
\(552\) 0 0
\(553\) −2.73419 4.73576i −0.116270 0.201385i
\(554\) 0 0
\(555\) 6.31661 + 8.37372i 0.268125 + 0.355445i
\(556\) 0 0
\(557\) 6.00000 0.254228 0.127114 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) 0 0
\(559\) −12.4200 −0.525309
\(560\) 0 0
\(561\) −20.6284 + 48.6651i −0.870932 + 2.05464i
\(562\) 0 0
\(563\) −2.13661 3.70072i −0.0900475 0.155967i 0.817483 0.575952i \(-0.195369\pi\)
−0.907531 + 0.419985i \(0.862035\pi\)
\(564\) 0 0
\(565\) −3.73419 + 6.46781i −0.157099 + 0.272103i
\(566\) 0 0
\(567\) 0.809653 24.5944i 0.0340022 1.03287i
\(568\) 0 0
\(569\) −8.04840 + 13.9402i −0.337406 + 0.584405i −0.983944 0.178477i \(-0.942883\pi\)
0.646538 + 0.762882i \(0.276216\pi\)
\(570\) 0 0
\(571\) 5.46838 + 9.47152i 0.228845 + 0.396371i 0.957466 0.288546i \(-0.0931719\pi\)
−0.728621 + 0.684917i \(0.759839\pi\)
\(572\) 0 0
\(573\) 10.2100 24.0867i 0.426529 1.00624i
\(574\) 0 0
\(575\) −0.734191 −0.0306179
\(576\) 0 0
\(577\) −37.6620 −1.56789 −0.783944 0.620831i \(-0.786795\pi\)
−0.783944 + 0.620831i \(0.786795\pi\)
\(578\) 0 0
\(579\) 15.2002 + 20.1504i 0.631697 + 0.837420i
\(580\) 0 0
\(581\) 7.19886 + 12.4688i 0.298659 + 0.517293i
\(582\) 0 0
\(583\) 4.05582 7.02488i 0.167975 0.290941i
\(584\) 0 0
\(585\) −2.90405 + 10.1659i −0.120068 + 0.420310i
\(586\) 0 0
\(587\) 10.8987 18.8771i 0.449838 0.779142i −0.548537 0.836126i \(-0.684815\pi\)
0.998375 + 0.0569839i \(0.0181484\pi\)
\(588\) 0 0
\(589\) −28.3068 49.0288i −1.16636 2.02020i
\(590\) 0 0
\(591\) −7.79001 + 0.960443i −0.320438 + 0.0395074i
\(592\) 0 0
\(593\) 28.2643 1.16067 0.580337 0.814377i \(-0.302921\pi\)
0.580337 + 0.814377i \(0.302921\pi\)
\(594\) 0 0
\(595\) −15.1042 −0.619213
\(596\) 0 0
\(597\) 12.7425 1.57104i 0.521514 0.0642983i
\(598\) 0 0
\(599\) 7.05582 + 12.2210i 0.288293 + 0.499338i 0.973402 0.229102i \(-0.0735790\pi\)
−0.685109 + 0.728440i \(0.740246\pi\)
\(600\) 0 0
\(601\) 14.1042 24.4292i 0.575323 0.996489i −0.420683 0.907207i \(-0.638210\pi\)
0.996006 0.0892812i \(-0.0284570\pi\)
\(602\) 0 0
\(603\) −8.88356 9.18082i −0.361766 0.373872i
\(604\) 0 0
\(605\) 9.75839 16.9020i 0.396735 0.687165i
\(606\) 0 0
\(607\) 14.1850 + 24.5692i 0.575752 + 0.997232i 0.995959 + 0.0898036i \(0.0286239\pi\)
−0.420208 + 0.907428i \(0.638043\pi\)
\(608\) 0 0
\(609\) −12.7436 16.8937i −0.516395 0.684567i
\(610\) 0 0
\(611\) 4.26425 0.172513
\(612\) 0 0
\(613\) 24.5726 0.992478 0.496239 0.868186i \(-0.334714\pi\)
0.496239 + 0.868186i \(0.334714\pi\)
\(614\) 0 0
\(615\) −0.713701 + 1.68371i −0.0287792 + 0.0678938i
\(616\) 0 0
\(617\) 13.3142 + 23.0609i 0.536010 + 0.928396i 0.999114 + 0.0420923i \(0.0134023\pi\)
−0.463104 + 0.886304i \(0.653264\pi\)
\(618\) 0 0
\(619\) 15.2863 26.4766i 0.614408 1.06419i −0.376080 0.926587i \(-0.622728\pi\)
0.990488 0.137599i \(-0.0439385\pi\)
\(620\) 0 0
\(621\) 2.96838 + 2.39639i 0.119117 + 0.0961639i
\(622\) 0 0
\(623\) −4.10129 + 7.10364i −0.164315 + 0.284601i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −28.0968 + 66.2840i −1.12208 + 2.64713i
\(628\) 0 0
\(629\) −33.4535 −1.33388
\(630\) 0 0
\(631\) −27.4684 −1.09350 −0.546750 0.837296i \(-0.684135\pi\)
−0.546750 + 0.837296i \(0.684135\pi\)
\(632\) 0 0
\(633\) −13.9902 18.5463i −0.556060 0.737150i
\(634\) 0 0
\(635\) −4.12920 7.15198i −0.163862 0.283818i
\(636\) 0 0
\(637\) 0.838408 1.45216i 0.0332189 0.0575369i
\(638\) 0 0
\(639\) −29.2640 + 7.32741i −1.15767 + 0.289868i
\(640\) 0 0
\(641\) −6.26952 + 10.8591i −0.247631 + 0.428910i −0.962868 0.269972i \(-0.912985\pi\)
0.715237 + 0.698882i \(0.246319\pi\)
\(642\) 0 0
\(643\) −5.12920 8.88403i −0.202276 0.350352i 0.746986 0.664840i \(-0.231500\pi\)
−0.949261 + 0.314488i \(0.898167\pi\)
\(644\) 0 0
\(645\) −6.05822 + 0.746928i −0.238542 + 0.0294103i
\(646\) 0 0
\(647\) −16.7900 −0.660083 −0.330042 0.943966i \(-0.607063\pi\)
−0.330042 + 0.943966i \(0.607063\pi\)
\(648\) 0 0
\(649\) −8.11164 −0.318410
\(650\) 0 0
\(651\) 35.3650 4.36021i 1.38606 0.170890i
\(652\) 0 0
\(653\) −25.0131 43.3239i −0.978837 1.69540i −0.666643 0.745377i \(-0.732269\pi\)
−0.312194 0.950018i \(-0.601064\pi\)
\(654\) 0 0
\(655\) 8.04840 13.9402i 0.314477 0.544690i
\(656\) 0 0
\(657\) 23.2813 5.82939i 0.908289 0.227426i
\(658\) 0 0
\(659\) 2.78259 4.81959i 0.108394 0.187744i −0.806726 0.590926i \(-0.798762\pi\)
0.915120 + 0.403182i \(0.132096\pi\)
\(660\) 0 0
\(661\) 19.6284 + 33.9974i 0.763457 + 1.32235i 0.941059 + 0.338244i \(0.109833\pi\)
−0.177602 + 0.984102i \(0.556834\pi\)
\(662\) 0 0
\(663\) −20.3068 26.9200i −0.788650 1.04549i
\(664\) 0 0
\(665\) −20.5726 −0.797771
\(666\) 0 0
\(667\) 3.28065 0.127027
\(668\) 0 0
\(669\) −5.94178 + 14.0174i −0.229722 + 0.541945i
\(670\) 0 0
\(671\) 25.0131 + 43.3239i 0.965619 + 1.67250i
\(672\) 0 0
\(673\) −7.97209 + 13.8081i −0.307302 + 0.532262i −0.977771 0.209675i \(-0.932759\pi\)
0.670470 + 0.741937i \(0.266093\pi\)
\(674\) 0 0
\(675\) −0.805165 + 5.13339i −0.0309908 + 0.197584i
\(676\) 0 0
\(677\) 10.4479 18.0963i 0.401545 0.695497i −0.592368 0.805668i \(-0.701807\pi\)
0.993913 + 0.110171i \(0.0351400\pi\)
\(678\) 0 0
\(679\) 12.9442 + 22.4200i 0.496752 + 0.860400i
\(680\) 0 0
\(681\) 2.74161 6.46781i 0.105059 0.247847i
\(682\) 0 0
\(683\) 19.6358 0.751344 0.375672 0.926753i \(-0.377412\pi\)
0.375672 + 0.926753i \(0.377412\pi\)
\(684\) 0 0
\(685\) 18.5168 0.707490
\(686\) 0 0
\(687\) −2.69113 3.56754i −0.102673 0.136110i
\(688\) 0 0
\(689\) 2.58744 + 4.48157i 0.0985734 + 0.170734i
\(690\) 0 0
\(691\) −21.5726 + 37.3648i −0.820660 + 1.42143i 0.0845309 + 0.996421i \(0.473061\pi\)
−0.905191 + 0.425005i \(0.860272\pi\)
\(692\) 0 0
\(693\) −31.5094 32.5637i −1.19694 1.23699i
\(694\) 0 0
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) 0 0
\(697\) −2.91627 5.05113i −0.110462 0.191325i
\(698\) 0 0
\(699\) −3.34212 + 0.412055i −0.126410 + 0.0155854i
\(700\) 0 0
\(701\) 27.0410 1.02132 0.510662 0.859782i \(-0.329400\pi\)
0.510662 + 0.859782i \(0.329400\pi\)
\(702\) 0 0
\(703\) −45.5652 −1.71852
\(704\) 0 0
\(705\) 2.08002 0.256449i 0.0783380 0.00965842i
\(706\) 0 0
\(707\) 18.4126 + 31.8915i 0.692476 + 1.19940i
\(708\) 0 0
\(709\) −21.7510 + 37.6738i −0.816875 + 1.41487i 0.0910989 + 0.995842i \(0.470962\pi\)
−0.907974 + 0.419027i \(0.862371\pi\)
\(710\) 0 0
\(711\) 1.64806 5.76922i 0.0618071 0.216363i
\(712\) 0 0
\(713\) −2.76210 + 4.78410i −0.103441 + 0.179166i
\(714\) 0 0
\(715\) 9.73419 + 16.8601i 0.364038 + 0.630532i
\(716\) 0 0
\(717\) 7.79001 + 10.3270i 0.290923 + 0.385667i
\(718\) 0 0
\(719\) 4.40515 0.164284 0.0821421 0.996621i \(-0.473824\pi\)
0.0821421 + 0.996621i \(0.473824\pi\)
\(720\) 0 0
\(721\) 50.7810 1.89118
\(722\) 0 0
\(723\) −1.63082 + 3.84731i −0.0606509 + 0.143083i
\(724\) 0 0
\(725\) 2.23419 + 3.86973i 0.0829758 + 0.143718i
\(726\) 0 0
\(727\) 6.24083 10.8094i 0.231460 0.400900i −0.726778 0.686872i \(-0.758983\pi\)
0.958238 + 0.285972i \(0.0923166\pi\)
\(728\) 0 0
\(729\) 20.0107 18.1266i 0.741136 0.671355i
\(730\) 0 0
\(731\) 9.73419 16.8601i 0.360032 0.623594i
\(732\) 0 0
\(733\) −19.5168 33.8041i −0.720869 1.24858i −0.960652 0.277755i \(-0.910410\pi\)
0.239783 0.970826i \(-0.422924\pi\)
\(734\) 0 0
\(735\) 0.321627 0.758758i 0.0118634 0.0279872i
\(736\) 0 0
\(737\) −23.5242 −0.866525
\(738\) 0 0
\(739\) 12.2935 0.452224 0.226112 0.974101i \(-0.427398\pi\)
0.226112 + 0.974101i \(0.427398\pi\)
\(740\) 0 0
\(741\) −27.6587 36.6662i −1.01607 1.34697i
\(742\) 0 0
\(743\) −20.4155 35.3607i −0.748972 1.29726i −0.948316 0.317328i \(-0.897214\pi\)
0.199344 0.979930i \(-0.436119\pi\)
\(744\) 0 0
\(745\) 6.78630 11.7542i 0.248631 0.430641i
\(746\) 0 0
\(747\) −4.33919 + 15.1898i −0.158763 + 0.555766i
\(748\) 0 0
\(749\) −26.3179 + 45.5840i −0.961636 + 1.66560i
\(750\) 0 0
\(751\) −7.54469 13.0678i −0.275310 0.476850i 0.694904 0.719103i \(-0.255447\pi\)
−0.970213 + 0.242253i \(0.922114\pi\)
\(752\) 0 0
\(753\) 12.0205 1.48203i 0.438051 0.0540080i
\(754\) 0 0
\(755\) −12.4610 −0.453501
\(756\) 0 0
\(757\) 34.4610 1.25251 0.626253 0.779620i \(-0.284588\pi\)
0.626253 + 0.779620i \(0.284588\pi\)
\(758\) 0 0
\(759\) 6.97209 0.859601i 0.253071 0.0312015i
\(760\) 0 0
\(761\) 4.17837 + 7.23716i 0.151466 + 0.262347i 0.931767 0.363058i \(-0.118267\pi\)
−0.780301 + 0.625405i \(0.784934\pi\)
\(762\) 0 0
\(763\) −0.716631 + 1.24124i −0.0259438 + 0.0449359i
\(764\) 0 0
\(765\) −11.5242 11.9098i −0.416658 0.430601i
\(766\) 0 0
\(767\) 2.58744 4.48157i 0.0934269 0.161820i
\(768\) 0 0
\(769\) 9.17837 + 15.8974i 0.330981 + 0.573275i 0.982704 0.185181i \(-0.0592872\pi\)
−0.651724 + 0.758456i \(0.725954\pi\)
\(770\) 0 0
\(771\) 29.3068 + 38.8510i 1.05546 + 1.39919i
\(772\) 0 0
\(773\) −10.0968 −0.363157 −0.181578 0.983376i \(-0.558121\pi\)
−0.181578 + 0.983376i \(0.558121\pi\)
\(774\) 0 0
\(775\) −7.52420 −0.270277
\(776\) 0 0
\(777\) 11.1925 26.4046i 0.401530 0.947261i
\(778\) 0 0
\(779\) −3.97209 6.87986i −0.142315 0.246497i
\(780\) 0 0
\(781\) −27.7752 + 48.1080i −0.993874 + 1.72144i
\(782\) 0 0
\(783\) 3.59778 22.9380i 0.128574 0.819736i
\(784\) 0 0
\(785\) −0.790009 + 1.36834i −0.0281966 + 0.0488380i
\(786\) 0 0
\(787\) −7.28630 12.6202i −0.259729 0.449863i 0.706441 0.707772i \(-0.250300\pi\)
−0.966169 + 0.257909i \(0.916966\pi\)
\(788\) 0 0
\(789\) 5.16159 12.1769i 0.183758 0.433508i
\(790\) 0 0
\(791\) 20.4200 0.726051
\(792\) 0 0
\(793\) −31.9145 −1.13332
\(794\) 0 0
\(795\) 1.53162 + 2.03041i 0.0543209 + 0.0720114i
\(796\) 0 0
\(797\) 1.03533 + 1.79324i 0.0366732 + 0.0635198i 0.883779 0.467904i \(-0.154991\pi\)
−0.847106 + 0.531424i \(0.821657\pi\)
\(798\) 0 0
\(799\) −3.34212 + 5.78872i −0.118236 + 0.204790i
\(800\) 0 0
\(801\) −8.73048 + 2.18602i −0.308476 + 0.0772393i
\(802\) 0 0
\(803\) 22.0968 38.2728i 0.779779 1.35062i
\(804\) 0 0
\(805\) 1.00371 + 1.73848i 0.0353761 + 0.0612732i
\(806\) 0 0
\(807\) −32.0101 + 3.94658i −1.12681 + 0.138926i
\(808\) 0 0
\(809\) 3.37158 0.118539 0.0592693 0.998242i \(-0.481123\pi\)
0.0592693 + 0.998242i \(0.481123\pi\)
\(810\) 0 0
\(811\) 12.9368 0.454271 0.227136 0.973863i \(-0.427064\pi\)
0.227136 + 0.973863i \(0.427064\pi\)
\(812\) 0 0
\(813\) −11.2985 + 1.39301i −0.396257 + 0.0488551i
\(814\) 0 0
\(815\) 2.23790 + 3.87616i 0.0783902 + 0.135776i
\(816\) 0 0
\(817\) 13.2584 22.9642i 0.463852 0.803416i
\(818\) 0 0
\(819\) 28.0418 7.02138i 0.979861 0.245347i
\(820\) 0 0
\(821\) 10.9963 19.0461i 0.383773 0.664715i −0.607825 0.794071i \(-0.707958\pi\)
0.991598 + 0.129356i \(0.0412911\pi\)
\(822\) 0 0
\(823\) 7.45082 + 12.9052i 0.259719 + 0.449847i 0.966167 0.257919i \(-0.0830366\pi\)
−0.706447 + 0.707766i \(0.749703\pi\)
\(824\) 0 0
\(825\) 5.76210 + 7.63862i 0.200611 + 0.265943i
\(826\) 0 0
\(827\) −56.5785 −1.96743 −0.983713 0.179747i \(-0.942472\pi\)
−0.983713 + 0.179747i \(0.942472\pi\)
\(828\) 0 0
\(829\) 27.0558 0.939687 0.469844 0.882750i \(-0.344310\pi\)
0.469844 + 0.882750i \(0.344310\pi\)
\(830\) 0 0
\(831\) −1.03031 + 2.43064i −0.0357411 + 0.0843180i
\(832\) 0 0
\(833\) 1.31421 + 2.27628i 0.0455346 + 0.0788683i
\(834\) 0 0
\(835\) −8.39500 + 14.5406i −0.290521 + 0.503197i
\(836\) 0 0
\(837\) 30.4208 + 24.5589i 1.05150 + 0.848880i
\(838\) 0 0
\(839\) −17.2863 + 29.9407i −0.596789 + 1.03367i 0.396502 + 0.918034i \(0.370224\pi\)
−0.993292 + 0.115636i \(0.963109\pi\)
\(840\) 0 0
\(841\) 4.51678 + 7.82329i 0.155751 + 0.269769i
\(842\) 0 0
\(843\) −9.81792 + 23.1617i −0.338147 + 0.797732i
\(844\) 0 0
\(845\) 0.580017 0.0199532
\(846\) 0 0
\(847\) −53.3626 −1.83356
\(848\) 0 0
\(849\) −17.4549 23.1393i −0.599049 0.794139i
\(850\) 0 0
\(851\) 2.22306 + 3.85046i 0.0762056 + 0.131992i
\(852\) 0 0
\(853\) −8.48887 + 14.7032i −0.290653 + 0.503427i −0.973964 0.226701i \(-0.927206\pi\)
0.683311 + 0.730127i \(0.260539\pi\)
\(854\) 0 0
\(855\) −15.6965 16.2217i −0.536808 0.554770i
\(856\) 0 0
\(857\) −1.70628 + 2.95537i −0.0582855 + 0.100953i −0.893696 0.448673i \(-0.851897\pi\)
0.835410 + 0.549627i \(0.185230\pi\)
\(858\) 0 0
\(859\) −4.91627 8.51524i −0.167741 0.290536i 0.769884 0.638184i \(-0.220314\pi\)
−0.937625 + 0.347647i \(0.886981\pi\)
\(860\) 0 0
\(861\) 4.96252 0.611838i 0.169122 0.0208514i
\(862\) 0 0
\(863\) 48.9836 1.66742 0.833711 0.552202i \(-0.186212\pi\)
0.833711 + 0.552202i \(0.186212\pi\)
\(864\) 0 0
\(865\) 23.0484 0.783669
\(866\) 0 0
\(867\) 23.2358 2.86478i 0.789130 0.0972931i
\(868\) 0 0
\(869\) −5.52420 9.56819i −0.187396 0.324579i
\(870\) 0 0
\(871\) 7.50371 12.9968i 0.254253 0.440380i
\(872\) 0 0
\(873\) −7.80223 + 27.3126i −0.264066 + 0.924391i
\(874\) 0 0
\(875\) −1.36710 + 2.36788i −0.0462163 + 0.0800489i
\(876\) 0 0
\(877\) 6.33470 + 10.9720i 0.213908 + 0.370499i 0.952934 0.303178i \(-0.0980475\pi\)
−0.739027 + 0.673676i \(0.764714\pi\)
\(878\) 0 0
\(879\) 21.3421 + 28.2925i 0.719852 + 0.954283i
\(880\) 0 0
\(881\) −26.0894 −0.878974 −0.439487 0.898249i \(-0.644840\pi\)
−0.439487 + 0.898249i \(0.644840\pi\)
\(882\) 0 0
\(883\) −2.69321 −0.0906337 −0.0453169 0.998973i \(-0.514430\pi\)
−0.0453169 + 0.998973i \(0.514430\pi\)
\(884\) 0 0
\(885\) 0.992582 2.34163i 0.0333653 0.0787129i
\(886\) 0 0
\(887\) −12.2789 21.2676i −0.412284 0.714098i 0.582855 0.812576i \(-0.301936\pi\)
−0.995139 + 0.0984788i \(0.968602\pi\)
\(888\) 0 0
\(889\) −11.2900 + 19.5549i −0.378655 + 0.655849i
\(890\) 0 0
\(891\) 1.63583 49.6909i 0.0548025 1.66471i
\(892\) 0 0
\(893\) −4.55211 + 7.88448i −0.152330 + 0.263844i
\(894\) 0 0
\(895\) −6.49629 11.2519i −0.217147 0.376110i
\(896\) 0 0
\(897\) −1.74903 + 4.12618i −0.0583983 + 0.137769i
\(898\) 0 0
\(899\) 33.6210 1.12132
\(900\) 0 0
\(901\) −8.11164 −0.270238
\(902\) 0 0
\(903\) 10.0508 + 13.3240i 0.334470 + 0.443395i
\(904\) 0 0
\(905\) −12.2826 21.2741i −0.408287 0.707174i
\(906\) 0 0
\(907\) 17.1850 29.7653i 0.570619 0.988341i −0.425884 0.904778i \(-0.640037\pi\)
0.996502 0.0835631i \(-0.0266300\pi\)
\(908\) 0 0
\(909\) −11.0984 + 38.8510i −0.368109 + 1.28861i
\(910\) 0 0
\(911\) 18.7752 32.5196i 0.622049 1.07742i −0.367054 0.930199i \(-0.619634\pi\)
0.989104 0.147221i \(-0.0470330\pi\)
\(912\) 0 0
\(913\) 14.5447 + 25.1921i 0.481359 + 0.833738i
\(914\) 0 0
\(915\) −15.5673 + 1.91931i −0.514638 + 0.0634506i
\(916\) 0 0
\(917\) −44.0117 −1.45340
\(918\) 0 0
\(919\) −10.1116 −0.333552 −0.166776 0.985995i \(-0.553336\pi\)
−0.166776 + 0.985995i \(0.553336\pi\)
\(920\) 0 0
\(921\) 31.2909 3.85790i 1.03107 0.127122i
\(922\) 0 0
\(923\) −17.7194 30.6908i −0.583240 1.01020i
\(924\) 0 0
\(925\) −3.02791 + 5.24449i −0.0995570 + 0.172438i
\(926\) 0 0
\(927\) 38.7449 + 40.0413i 1.27255 + 1.31513i
\(928\) 0 0
\(929\) −12.4126 + 21.4992i −0.407243 + 0.705366i −0.994580 0.103977i \(-0.966843\pi\)
0.587337 + 0.809343i \(0.300176\pi\)
\(930\) 0 0
\(931\) 1.79001 + 3.10039i 0.0586652 + 0.101611i
\(932\) 0 0
\(933\) 3.23790 + 4.29238i 0.106004 + 0.140526i
\(934\) 0 0
\(935\) −30.5168 −0.998005
\(936\) 0 0
\(937\) 1.56518 0.0511322 0.0255661 0.999673i \(-0.491861\pi\)
0.0255661 + 0.999673i \(0.491861\pi\)
\(938\) 0 0
\(939\) 12.9139 30.4655i 0.421428 0.994203i
\(940\) 0 0
\(941\) 5.23419 + 9.06588i 0.170630 + 0.295539i 0.938640 0.344898i \(-0.112086\pi\)
−0.768010 + 0.640437i \(0.778753\pi\)
\(942\) 0 0
\(943\) −0.387586 + 0.671318i −0.0126215 + 0.0218611i
\(944\) 0 0
\(945\) 13.2560 5.11130i 0.431217 0.166271i
\(946\) 0 0
\(947\) −1.59758 + 2.76709i −0.0519143 + 0.0899182i −0.890815 0.454367i \(-0.849866\pi\)
0.838900 + 0.544285i \(0.183199\pi\)
\(948\) 0 0
\(949\) 14.0968 + 24.4164i 0.457601 + 0.792589i
\(950\) 0 0
\(951\) −3.38486 + 7.98533i −0.109762 + 0.258942i
\(952\) 0 0
\(953\) −33.9293 −1.09908 −0.549540 0.835468i \(-0.685197\pi\)
−0.549540 + 0.835468i \(0.685197\pi\)
\(954\) 0 0
\(955\) 15.1042 0.488761
\(956\) 0 0
\(957\) −25.7473 34.1323i −0.832291 1.10334i
\(958\) 0 0
\(959\) −25.3142 43.8455i −0.817438 1.41584i
\(960\) 0 0
\(961\) −12.8068 + 22.1820i −0.413122 + 0.715549i
\(962\) 0 0
\(963\) −56.0234 + 14.0277i −1.80533 + 0.452036i
\(964\) 0 0
\(965\) −7.28630 + 12.6202i −0.234554 + 0.406260i
\(966\) 0 0
\(967\) 19.2129 + 33.2778i 0.617846 + 1.07014i 0.989878 + 0.141921i \(0.0453278\pi\)
−0.372032 + 0.928220i \(0.621339\pi\)
\(968\) 0 0
\(969\) 71.4520 8.80944i 2.29537 0.283000i
\(970\) 0 0
\(971\) −29.7326 −0.954166 −0.477083 0.878858i \(-0.658306\pi\)
−0.477083 + 0.878858i \(0.658306\pi\)
\(972\) 0 0
\(973\) −10.9368 −0.350617
\(974\) 0 0
\(975\) −6.05822 + 0.746928i −0.194018 + 0.0239209i
\(976\) 0 0
\(977\) 16.4889 + 28.5596i 0.527526 + 0.913701i 0.999485 + 0.0320812i \(0.0102135\pi\)
−0.471960 + 0.881620i \(0.656453\pi\)
\(978\) 0 0
\(979\) −8.28630 + 14.3523i −0.264831 + 0.458701i
\(980\) 0 0
\(981\) −1.52551 + 0.381970i −0.0487056 + 0.0121954i
\(982\) 0 0
\(983\) −3.68872 + 6.38905i −0.117652 + 0.203779i −0.918837 0.394638i \(-0.870870\pi\)
0.801185 + 0.598417i \(0.204203\pi\)
\(984\) 0 0
\(985\) −2.26581 3.92450i −0.0721947 0.125045i
\(986\) 0 0
\(987\) −3.45082 4.57464i −0.109841 0.145612i
\(988\) 0 0
\(989\) −2.58744 −0.0822757
\(990\) 0 0
\(991\) 4.51678 0.143480 0.0717401 0.997423i \(-0.477145\pi\)
0.0717401 + 0.997423i \(0.477145\pi\)
\(992\) 0 0
\(993\) −2.35455 + 5.55469i −0.0747194 + 0.176273i
\(994\) 0 0
\(995\) 3.70628 + 6.41947i 0.117497 + 0.203511i
\(996\) 0 0
\(997\) 24.3142 42.1134i 0.770039 1.33375i −0.167502 0.985872i \(-0.553570\pi\)
0.937541 0.347874i \(-0.113096\pi\)
\(998\) 0 0
\(999\) 29.3600 11.3208i 0.928909 0.358173i
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 720.2.q.k.241.3 6
3.2 odd 2 2160.2.q.i.721.2 6
4.3 odd 2 180.2.i.b.61.1 6
9.2 odd 6 6480.2.a.bw.1.2 3
9.4 even 3 inner 720.2.q.k.481.3 6
9.5 odd 6 2160.2.q.i.1441.2 6
9.7 even 3 6480.2.a.bt.1.2 3
12.11 even 2 540.2.i.b.181.2 6
20.3 even 4 900.2.s.c.349.3 12
20.7 even 4 900.2.s.c.349.4 12
20.19 odd 2 900.2.i.c.601.3 6
36.7 odd 6 1620.2.a.i.1.2 3
36.11 even 6 1620.2.a.j.1.2 3
36.23 even 6 540.2.i.b.361.2 6
36.31 odd 6 180.2.i.b.121.1 yes 6
60.23 odd 4 2700.2.s.c.2449.4 12
60.47 odd 4 2700.2.s.c.2449.3 12
60.59 even 2 2700.2.i.c.1801.2 6
180.7 even 12 8100.2.d.p.649.4 6
180.23 odd 12 2700.2.s.c.1549.3 12
180.43 even 12 8100.2.d.p.649.3 6
180.47 odd 12 8100.2.d.o.649.4 6
180.59 even 6 2700.2.i.c.901.2 6
180.67 even 12 900.2.s.c.49.3 12
180.79 odd 6 8100.2.a.v.1.2 3
180.83 odd 12 8100.2.d.o.649.3 6
180.103 even 12 900.2.s.c.49.4 12
180.119 even 6 8100.2.a.u.1.2 3
180.139 odd 6 900.2.i.c.301.3 6
180.167 odd 12 2700.2.s.c.1549.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
180.2.i.b.61.1 6 4.3 odd 2
180.2.i.b.121.1 yes 6 36.31 odd 6
540.2.i.b.181.2 6 12.11 even 2
540.2.i.b.361.2 6 36.23 even 6
720.2.q.k.241.3 6 1.1 even 1 trivial
720.2.q.k.481.3 6 9.4 even 3 inner
900.2.i.c.301.3 6 180.139 odd 6
900.2.i.c.601.3 6 20.19 odd 2
900.2.s.c.49.3 12 180.67 even 12
900.2.s.c.49.4 12 180.103 even 12
900.2.s.c.349.3 12 20.3 even 4
900.2.s.c.349.4 12 20.7 even 4
1620.2.a.i.1.2 3 36.7 odd 6
1620.2.a.j.1.2 3 36.11 even 6
2160.2.q.i.721.2 6 3.2 odd 2
2160.2.q.i.1441.2 6 9.5 odd 6
2700.2.i.c.901.2 6 180.59 even 6
2700.2.i.c.1801.2 6 60.59 even 2
2700.2.s.c.1549.3 12 180.23 odd 12
2700.2.s.c.1549.4 12 180.167 odd 12
2700.2.s.c.2449.3 12 60.47 odd 4
2700.2.s.c.2449.4 12 60.23 odd 4
6480.2.a.bt.1.2 3 9.7 even 3
6480.2.a.bw.1.2 3 9.2 odd 6
8100.2.a.u.1.2 3 180.119 even 6
8100.2.a.v.1.2 3 180.79 odd 6
8100.2.d.o.649.3 6 180.83 odd 12
8100.2.d.o.649.4 6 180.47 odd 12
8100.2.d.p.649.3 6 180.43 even 12
8100.2.d.p.649.4 6 180.7 even 12