Properties

Label 1815.2.c.e.364.6
Level $1815$
Weight $2$
Character 1815.364
Analytic conductor $14.493$
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] = [1815,2,Mod(364,1815)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1815, 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("1815.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.c (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: \(14.4928479669\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.6
Root \(-0.854638 + 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 1815.364
Dual form 1815.2.c.e.364.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.17009i q^{2} +1.00000i q^{3} -2.70928 q^{4} +(2.17009 + 0.539189i) q^{5} -2.17009 q^{6} +3.70928i q^{7} -1.53919i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+2.17009i q^{2} +1.00000i q^{3} -2.70928 q^{4} +(2.17009 + 0.539189i) q^{5} -2.17009 q^{6} +3.70928i q^{7} -1.53919i q^{8} -1.00000 q^{9} +(-1.17009 + 4.70928i) q^{10} -2.70928i q^{12} +1.70928i q^{13} -8.04945 q^{14} +(-0.539189 + 2.17009i) q^{15} -2.07838 q^{16} -6.04945i q^{17} -2.17009i q^{18} -3.07838 q^{19} +(-5.87936 - 1.46081i) q^{20} -3.70928 q^{21} +4.00000i q^{23} +1.53919 q^{24} +(4.41855 + 2.34017i) q^{25} -3.70928 q^{26} -1.00000i q^{27} -10.0494i q^{28} +5.26180 q^{29} +(-4.70928 - 1.17009i) q^{30} -6.34017 q^{31} -7.58864i q^{32} +13.1278 q^{34} +(-2.00000 + 8.04945i) q^{35} +2.70928 q^{36} +3.41855i q^{37} -6.68035i q^{38} -1.70928 q^{39} +(0.829914 - 3.34017i) q^{40} -9.57531 q^{41} -8.04945i q^{42} +3.12783i q^{43} +(-2.17009 - 0.539189i) q^{45} -8.68035 q^{46} -2.73820i q^{47} -2.07838i q^{48} -6.75872 q^{49} +(-5.07838 + 9.58864i) q^{50} +6.04945 q^{51} -4.63090i q^{52} +13.7587i q^{53} +2.17009 q^{54} +5.70928 q^{56} -3.07838i q^{57} +11.4186i q^{58} +3.60197 q^{59} +(1.46081 - 5.87936i) q^{60} +14.6803 q^{61} -13.7587i q^{62} -3.70928i q^{63} +12.3112 q^{64} +(-0.921622 + 3.70928i) q^{65} -1.84324i q^{67} +16.3896i q^{68} -4.00000 q^{69} +(-17.4680 - 4.34017i) q^{70} -7.23513 q^{71} +1.53919i q^{72} -6.38962i q^{73} -7.41855 q^{74} +(-2.34017 + 4.41855i) q^{75} +8.34017 q^{76} -3.70928i q^{78} -7.44521 q^{79} +(-4.51026 - 1.12064i) q^{80} +1.00000 q^{81} -20.7792i q^{82} +7.86603i q^{83} +10.0494 q^{84} +(3.26180 - 13.1278i) q^{85} -6.78765 q^{86} +5.26180i q^{87} +5.02052 q^{89} +(1.17009 - 4.70928i) q^{90} -6.34017 q^{91} -10.8371i q^{92} -6.34017i q^{93} +5.94214 q^{94} +(-6.68035 - 1.65983i) q^{95} +7.58864 q^{96} -16.9939i q^{97} -14.6670i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{4} + 2 q^{5} - 2 q^{6} - 6 q^{9} + 4 q^{10} - 12 q^{14} - 6 q^{16} - 12 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{24} - 2 q^{25} - 8 q^{26} + 16 q^{29} - 14 q^{30} - 16 q^{31} + 36 q^{34} - 12 q^{35} + 2 q^{36} + 4 q^{39} + 16 q^{40} - 16 q^{41} - 2 q^{45} - 8 q^{46} + 10 q^{49} - 24 q^{50} + 2 q^{54} + 20 q^{56} - 16 q^{59} + 12 q^{60} + 44 q^{61} + 22 q^{64} - 12 q^{65} - 24 q^{69} - 40 q^{70} - 24 q^{71} - 16 q^{74} + 8 q^{75} + 28 q^{76} - 20 q^{79} + 6 q^{80} + 6 q^{81} + 24 q^{84} + 4 q^{85} - 20 q^{86} - 36 q^{89} - 4 q^{90} - 16 q^{91} - 24 q^{94} + 4 q^{95} + 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(1211\) \(1696\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.17009i 1.53448i 0.641358 + 0.767241i \(0.278371\pi\)
−0.641358 + 0.767241i \(0.721629\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −2.70928 −1.35464
\(5\) 2.17009 + 0.539189i 0.970492 + 0.241133i
\(6\) −2.17009 −0.885934
\(7\) 3.70928i 1.40197i 0.713174 + 0.700987i \(0.247257\pi\)
−0.713174 + 0.700987i \(0.752743\pi\)
\(8\) 1.53919i 0.544185i
\(9\) −1.00000 −0.333333
\(10\) −1.17009 + 4.70928i −0.370014 + 1.48920i
\(11\) 0 0
\(12\) 2.70928i 0.782100i
\(13\) 1.70928i 0.474068i 0.971501 + 0.237034i \(0.0761752\pi\)
−0.971501 + 0.237034i \(0.923825\pi\)
\(14\) −8.04945 −2.15131
\(15\) −0.539189 + 2.17009i −0.139218 + 0.560314i
\(16\) −2.07838 −0.519594
\(17\) 6.04945i 1.46721i −0.679578 0.733603i \(-0.737837\pi\)
0.679578 0.733603i \(-0.262163\pi\)
\(18\) 2.17009i 0.511494i
\(19\) −3.07838 −0.706228 −0.353114 0.935580i \(-0.614877\pi\)
−0.353114 + 0.935580i \(0.614877\pi\)
\(20\) −5.87936 1.46081i −1.31467 0.326647i
\(21\) −3.70928 −0.809430
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 1.53919 0.314186
\(25\) 4.41855 + 2.34017i 0.883710 + 0.468035i
\(26\) −3.70928 −0.727449
\(27\) 1.00000i 0.192450i
\(28\) 10.0494i 1.89917i
\(29\) 5.26180 0.977091 0.488545 0.872538i \(-0.337528\pi\)
0.488545 + 0.872538i \(0.337528\pi\)
\(30\) −4.70928 1.17009i −0.859792 0.213628i
\(31\) −6.34017 −1.13873 −0.569364 0.822085i \(-0.692811\pi\)
−0.569364 + 0.822085i \(0.692811\pi\)
\(32\) 7.58864i 1.34149i
\(33\) 0 0
\(34\) 13.1278 2.25140
\(35\) −2.00000 + 8.04945i −0.338062 + 1.36061i
\(36\) 2.70928 0.451546
\(37\) 3.41855i 0.562006i 0.959707 + 0.281003i \(0.0906671\pi\)
−0.959707 + 0.281003i \(0.909333\pi\)
\(38\) 6.68035i 1.08370i
\(39\) −1.70928 −0.273703
\(40\) 0.829914 3.34017i 0.131221 0.528128i
\(41\) −9.57531 −1.49541 −0.747706 0.664030i \(-0.768845\pi\)
−0.747706 + 0.664030i \(0.768845\pi\)
\(42\) 8.04945i 1.24206i
\(43\) 3.12783i 0.476989i 0.971144 + 0.238495i \(0.0766539\pi\)
−0.971144 + 0.238495i \(0.923346\pi\)
\(44\) 0 0
\(45\) −2.17009 0.539189i −0.323497 0.0803775i
\(46\) −8.68035 −1.27985
\(47\) 2.73820i 0.399408i −0.979856 0.199704i \(-0.936002\pi\)
0.979856 0.199704i \(-0.0639981\pi\)
\(48\) 2.07838i 0.299988i
\(49\) −6.75872 −0.965532
\(50\) −5.07838 + 9.58864i −0.718191 + 1.35604i
\(51\) 6.04945 0.847092
\(52\) 4.63090i 0.642190i
\(53\) 13.7587i 1.88991i 0.327206 + 0.944953i \(0.393893\pi\)
−0.327206 + 0.944953i \(0.606107\pi\)
\(54\) 2.17009 0.295311
\(55\) 0 0
\(56\) 5.70928 0.762934
\(57\) 3.07838i 0.407741i
\(58\) 11.4186i 1.49933i
\(59\) 3.60197 0.468936 0.234468 0.972124i \(-0.424665\pi\)
0.234468 + 0.972124i \(0.424665\pi\)
\(60\) 1.46081 5.87936i 0.188590 0.759022i
\(61\) 14.6803 1.87963 0.939813 0.341690i \(-0.110999\pi\)
0.939813 + 0.341690i \(0.110999\pi\)
\(62\) 13.7587i 1.74736i
\(63\) 3.70928i 0.467325i
\(64\) 12.3112 1.53891
\(65\) −0.921622 + 3.70928i −0.114313 + 0.460079i
\(66\) 0 0
\(67\) 1.84324i 0.225188i −0.993641 0.112594i \(-0.964084\pi\)
0.993641 0.112594i \(-0.0359160\pi\)
\(68\) 16.3896i 1.98753i
\(69\) −4.00000 −0.481543
\(70\) −17.4680 4.34017i −2.08783 0.518750i
\(71\) −7.23513 −0.858652 −0.429326 0.903150i \(-0.641249\pi\)
−0.429326 + 0.903150i \(0.641249\pi\)
\(72\) 1.53919i 0.181395i
\(73\) 6.38962i 0.747849i −0.927459 0.373924i \(-0.878012\pi\)
0.927459 0.373924i \(-0.121988\pi\)
\(74\) −7.41855 −0.862389
\(75\) −2.34017 + 4.41855i −0.270220 + 0.510210i
\(76\) 8.34017 0.956683
\(77\) 0 0
\(78\) 3.70928i 0.419993i
\(79\) −7.44521 −0.837652 −0.418826 0.908067i \(-0.637558\pi\)
−0.418826 + 0.908067i \(0.637558\pi\)
\(80\) −4.51026 1.12064i −0.504262 0.125291i
\(81\) 1.00000 0.111111
\(82\) 20.7792i 2.29468i
\(83\) 7.86603i 0.863409i 0.902015 + 0.431705i \(0.142088\pi\)
−0.902015 + 0.431705i \(0.857912\pi\)
\(84\) 10.0494 1.09648
\(85\) 3.26180 13.1278i 0.353791 1.42391i
\(86\) −6.78765 −0.731931
\(87\) 5.26180i 0.564124i
\(88\) 0 0
\(89\) 5.02052 0.532174 0.266087 0.963949i \(-0.414269\pi\)
0.266087 + 0.963949i \(0.414269\pi\)
\(90\) 1.17009 4.70928i 0.123338 0.496401i
\(91\) −6.34017 −0.664631
\(92\) 10.8371i 1.12985i
\(93\) 6.34017i 0.657445i
\(94\) 5.94214 0.612885
\(95\) −6.68035 1.65983i −0.685389 0.170295i
\(96\) 7.58864 0.774512
\(97\) 16.9939i 1.72546i −0.505661 0.862732i \(-0.668751\pi\)
0.505661 0.862732i \(-0.331249\pi\)
\(98\) 14.6670i 1.48159i
\(99\) 0 0
\(100\) −11.9711 6.34017i −1.19711 0.634017i
\(101\) 18.9360 1.88420 0.942101 0.335329i \(-0.108847\pi\)
0.942101 + 0.335329i \(0.108847\pi\)
\(102\) 13.1278i 1.29985i
\(103\) 11.7854i 1.16125i −0.814172 0.580624i \(-0.802809\pi\)
0.814172 0.580624i \(-0.197191\pi\)
\(104\) 2.63090 0.257981
\(105\) −8.04945 2.00000i −0.785546 0.195180i
\(106\) −29.8576 −2.90003
\(107\) 11.2846i 1.09092i 0.838136 + 0.545461i \(0.183645\pi\)
−0.838136 + 0.545461i \(0.816355\pi\)
\(108\) 2.70928i 0.260700i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) −3.41855 −0.324474
\(112\) 7.70928i 0.728458i
\(113\) 0.496928i 0.0467471i −0.999727 0.0233735i \(-0.992559\pi\)
0.999727 0.0233735i \(-0.00744071\pi\)
\(114\) 6.68035 0.625672
\(115\) −2.15676 + 8.68035i −0.201118 + 0.809446i
\(116\) −14.2557 −1.32360
\(117\) 1.70928i 0.158023i
\(118\) 7.81658i 0.719575i
\(119\) 22.4391 2.05699
\(120\) 3.34017 + 0.829914i 0.304915 + 0.0757604i
\(121\) 0 0
\(122\) 31.8576i 2.88425i
\(123\) 9.57531i 0.863376i
\(124\) 17.1773 1.54256
\(125\) 8.32684 + 7.46081i 0.744775 + 0.667315i
\(126\) 8.04945 0.717102
\(127\) 2.81432i 0.249730i 0.992174 + 0.124865i \(0.0398498\pi\)
−0.992174 + 0.124865i \(0.960150\pi\)
\(128\) 11.5392i 1.01993i
\(129\) −3.12783 −0.275390
\(130\) −8.04945 2.00000i −0.705983 0.175412i
\(131\) −8.68035 −0.758405 −0.379203 0.925314i \(-0.623802\pi\)
−0.379203 + 0.925314i \(0.623802\pi\)
\(132\) 0 0
\(133\) 11.4186i 0.990114i
\(134\) 4.00000 0.345547
\(135\) 0.539189 2.17009i 0.0464060 0.186771i
\(136\) −9.31124 −0.798433
\(137\) 1.07838i 0.0921320i −0.998938 0.0460660i \(-0.985332\pi\)
0.998938 0.0460660i \(-0.0146685\pi\)
\(138\) 8.68035i 0.738920i
\(139\) 10.2823 0.872135 0.436067 0.899914i \(-0.356371\pi\)
0.436067 + 0.899914i \(0.356371\pi\)
\(140\) 5.41855 21.8082i 0.457951 1.84313i
\(141\) 2.73820 0.230598
\(142\) 15.7009i 1.31759i
\(143\) 0 0
\(144\) 2.07838 0.173198
\(145\) 11.4186 + 2.83710i 0.948259 + 0.235608i
\(146\) 13.8660 1.14756
\(147\) 6.75872i 0.557450i
\(148\) 9.26180i 0.761315i
\(149\) 11.4186 0.935444 0.467722 0.883876i \(-0.345075\pi\)
0.467722 + 0.883876i \(0.345075\pi\)
\(150\) −9.58864 5.07838i −0.782909 0.414648i
\(151\) 4.92162 0.400516 0.200258 0.979743i \(-0.435822\pi\)
0.200258 + 0.979743i \(0.435822\pi\)
\(152\) 4.73820i 0.384319i
\(153\) 6.04945i 0.489069i
\(154\) 0 0
\(155\) −13.7587 3.41855i −1.10513 0.274585i
\(156\) 4.63090 0.370769
\(157\) 3.41855i 0.272830i 0.990652 + 0.136415i \(0.0435581\pi\)
−0.990652 + 0.136415i \(0.956442\pi\)
\(158\) 16.1568i 1.28536i
\(159\) −13.7587 −1.09114
\(160\) 4.09171 16.4680i 0.323478 1.30191i
\(161\) −14.8371 −1.16933
\(162\) 2.17009i 0.170498i
\(163\) 9.26180i 0.725440i 0.931898 + 0.362720i \(0.118152\pi\)
−0.931898 + 0.362720i \(0.881848\pi\)
\(164\) 25.9421 2.02574
\(165\) 0 0
\(166\) −17.0700 −1.32489
\(167\) 7.55252i 0.584432i 0.956352 + 0.292216i \(0.0943925\pi\)
−0.956352 + 0.292216i \(0.905607\pi\)
\(168\) 5.70928i 0.440480i
\(169\) 10.0784 0.775260
\(170\) 28.4885 + 7.07838i 2.18497 + 0.542887i
\(171\) 3.07838 0.235409
\(172\) 8.47414i 0.646147i
\(173\) 6.14834i 0.467450i −0.972303 0.233725i \(-0.924908\pi\)
0.972303 0.233725i \(-0.0750915\pi\)
\(174\) −11.4186 −0.865638
\(175\) −8.68035 + 16.3896i −0.656172 + 1.23894i
\(176\) 0 0
\(177\) 3.60197i 0.270741i
\(178\) 10.8950i 0.816612i
\(179\) 6.15676 0.460178 0.230089 0.973170i \(-0.426098\pi\)
0.230089 + 0.973170i \(0.426098\pi\)
\(180\) 5.87936 + 1.46081i 0.438222 + 0.108882i
\(181\) 14.5958 1.08490 0.542450 0.840088i \(-0.317497\pi\)
0.542450 + 0.840088i \(0.317497\pi\)
\(182\) 13.7587i 1.01986i
\(183\) 14.6803i 1.08520i
\(184\) 6.15676 0.453882
\(185\) −1.84324 + 7.41855i −0.135518 + 0.545423i
\(186\) 13.7587 1.00884
\(187\) 0 0
\(188\) 7.41855i 0.541053i
\(189\) 3.70928 0.269810
\(190\) 3.60197 14.4969i 0.261314 1.05172i
\(191\) 5.84324 0.422802 0.211401 0.977399i \(-0.432197\pi\)
0.211401 + 0.977399i \(0.432197\pi\)
\(192\) 12.3112i 0.888487i
\(193\) 2.02279i 0.145603i −0.997346 0.0728017i \(-0.976806\pi\)
0.997346 0.0728017i \(-0.0231940\pi\)
\(194\) 36.8781 2.64770
\(195\) −3.70928 0.921622i −0.265627 0.0659987i
\(196\) 18.3112 1.30795
\(197\) 17.8348i 1.27068i 0.772233 + 0.635340i \(0.219140\pi\)
−0.772233 + 0.635340i \(0.780860\pi\)
\(198\) 0 0
\(199\) −25.6742 −1.82000 −0.909998 0.414613i \(-0.863917\pi\)
−0.909998 + 0.414613i \(0.863917\pi\)
\(200\) 3.60197 6.80098i 0.254698 0.480902i
\(201\) 1.84324 0.130012
\(202\) 41.0928i 2.89128i
\(203\) 19.5174i 1.36986i
\(204\) −16.3896 −1.14750
\(205\) −20.7792 5.16290i −1.45129 0.360592i
\(206\) 25.5753 1.78192
\(207\) 4.00000i 0.278019i
\(208\) 3.55252i 0.246323i
\(209\) 0 0
\(210\) 4.34017 17.4680i 0.299500 1.20541i
\(211\) −8.43907 −0.580970 −0.290485 0.956880i \(-0.593817\pi\)
−0.290485 + 0.956880i \(0.593817\pi\)
\(212\) 37.2762i 2.56014i
\(213\) 7.23513i 0.495743i
\(214\) −24.4885 −1.67400
\(215\) −1.68649 + 6.78765i −0.115018 + 0.462914i
\(216\) −1.53919 −0.104729
\(217\) 23.5174i 1.59647i
\(218\) 21.7009i 1.46977i
\(219\) 6.38962 0.431771
\(220\) 0 0
\(221\) 10.3402 0.695555
\(222\) 7.41855i 0.497901i
\(223\) 12.5814i 0.842516i 0.906941 + 0.421258i \(0.138411\pi\)
−0.906941 + 0.421258i \(0.861589\pi\)
\(224\) 28.1483 1.88074
\(225\) −4.41855 2.34017i −0.294570 0.156012i
\(226\) 1.07838 0.0717326
\(227\) 4.23287i 0.280945i 0.990085 + 0.140473i \(0.0448622\pi\)
−0.990085 + 0.140473i \(0.955138\pi\)
\(228\) 8.34017i 0.552341i
\(229\) 26.1978 1.73120 0.865599 0.500737i \(-0.166938\pi\)
0.865599 + 0.500737i \(0.166938\pi\)
\(230\) −18.8371 4.68035i −1.24208 0.308613i
\(231\) 0 0
\(232\) 8.09890i 0.531719i
\(233\) 18.6309i 1.22055i 0.792189 + 0.610275i \(0.208941\pi\)
−0.792189 + 0.610275i \(0.791059\pi\)
\(234\) 3.70928 0.242483
\(235\) 1.47641 5.94214i 0.0963103 0.387623i
\(236\) −9.75872 −0.635239
\(237\) 7.44521i 0.483619i
\(238\) 48.6947i 3.15641i
\(239\) 22.3545 1.44600 0.722998 0.690850i \(-0.242764\pi\)
0.722998 + 0.690850i \(0.242764\pi\)
\(240\) 1.12064 4.51026i 0.0723369 0.291136i
\(241\) −9.20394 −0.592878 −0.296439 0.955052i \(-0.595799\pi\)
−0.296439 + 0.955052i \(0.595799\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) −39.7731 −2.54621
\(245\) −14.6670 3.64423i −0.937041 0.232821i
\(246\) 20.7792 1.32484
\(247\) 5.26180i 0.334800i
\(248\) 9.75872i 0.619680i
\(249\) −7.86603 −0.498489
\(250\) −16.1906 + 18.0700i −1.02398 + 1.14285i
\(251\) −22.1256 −1.39655 −0.698276 0.715828i \(-0.746049\pi\)
−0.698276 + 0.715828i \(0.746049\pi\)
\(252\) 10.0494i 0.633056i
\(253\) 0 0
\(254\) −6.10731 −0.383207
\(255\) 13.1278 + 3.26180i 0.822096 + 0.204262i
\(256\) −0.418551 −0.0261594
\(257\) 3.02052i 0.188415i −0.995553 0.0942074i \(-0.969968\pi\)
0.995553 0.0942074i \(-0.0300317\pi\)
\(258\) 6.78765i 0.422581i
\(259\) −12.6803 −0.787918
\(260\) 2.49693 10.0494i 0.154853 0.623240i
\(261\) −5.26180 −0.325697
\(262\) 18.8371i 1.16376i
\(263\) 18.2907i 1.12785i −0.825825 0.563927i \(-0.809290\pi\)
0.825825 0.563927i \(-0.190710\pi\)
\(264\) 0 0
\(265\) −7.41855 + 29.8576i −0.455718 + 1.83414i
\(266\) 24.7792 1.51931
\(267\) 5.02052i 0.307251i
\(268\) 4.99386i 0.305048i
\(269\) −30.5646 −1.86356 −0.931779 0.363026i \(-0.881744\pi\)
−0.931779 + 0.363026i \(0.881744\pi\)
\(270\) 4.70928 + 1.17009i 0.286597 + 0.0712092i
\(271\) 20.0722 1.21930 0.609651 0.792670i \(-0.291310\pi\)
0.609651 + 0.792670i \(0.291310\pi\)
\(272\) 12.5730i 0.762352i
\(273\) 6.34017i 0.383725i
\(274\) 2.34017 0.141375
\(275\) 0 0
\(276\) 10.8371 0.652317
\(277\) 0.760991i 0.0457235i 0.999739 + 0.0228618i \(0.00727776\pi\)
−0.999739 + 0.0228618i \(0.992722\pi\)
\(278\) 22.3135i 1.33828i
\(279\) 6.34017 0.379576
\(280\) 12.3896 + 3.07838i 0.740421 + 0.183968i
\(281\) −0.581449 −0.0346864 −0.0173432 0.999850i \(-0.505521\pi\)
−0.0173432 + 0.999850i \(0.505521\pi\)
\(282\) 5.94214i 0.353849i
\(283\) 10.8143i 0.642844i 0.946936 + 0.321422i \(0.104161\pi\)
−0.946936 + 0.321422i \(0.895839\pi\)
\(284\) 19.6020 1.16316
\(285\) 1.65983 6.68035i 0.0983197 0.395710i
\(286\) 0 0
\(287\) 35.5174i 2.09653i
\(288\) 7.58864i 0.447165i
\(289\) −19.5958 −1.15270
\(290\) −6.15676 + 24.7792i −0.361537 + 1.45509i
\(291\) 16.9939 0.996198
\(292\) 17.3112i 1.01306i
\(293\) 7.04331i 0.411474i −0.978607 0.205737i \(-0.934041\pi\)
0.978607 0.205737i \(-0.0659592\pi\)
\(294\) 14.6670 0.855398
\(295\) 7.81658 + 1.94214i 0.455099 + 0.113076i
\(296\) 5.26180 0.305836
\(297\) 0 0
\(298\) 24.7792i 1.43542i
\(299\) −6.83710 −0.395400
\(300\) 6.34017 11.9711i 0.366050 0.691150i
\(301\) −11.6020 −0.668726
\(302\) 10.6803i 0.614585i
\(303\) 18.9360i 1.08784i
\(304\) 6.39803 0.366952
\(305\) 31.8576 + 7.91548i 1.82416 + 0.453239i
\(306\) −13.1278 −0.750468
\(307\) 20.1750i 1.15145i −0.817644 0.575724i \(-0.804720\pi\)
0.817644 0.575724i \(-0.195280\pi\)
\(308\) 0 0
\(309\) 11.7854 0.670447
\(310\) 7.41855 29.8576i 0.421345 1.69580i
\(311\) 21.2762 1.20646 0.603230 0.797567i \(-0.293880\pi\)
0.603230 + 0.797567i \(0.293880\pi\)
\(312\) 2.63090i 0.148945i
\(313\) 16.4657i 0.930698i 0.885127 + 0.465349i \(0.154071\pi\)
−0.885127 + 0.465349i \(0.845929\pi\)
\(314\) −7.41855 −0.418653
\(315\) 2.00000 8.04945i 0.112687 0.453535i
\(316\) 20.1711 1.13471
\(317\) 22.1711i 1.24525i 0.782518 + 0.622627i \(0.213935\pi\)
−0.782518 + 0.622627i \(0.786065\pi\)
\(318\) 29.8576i 1.67433i
\(319\) 0 0
\(320\) 26.7165 + 6.63809i 1.49350 + 0.371080i
\(321\) −11.2846 −0.629844
\(322\) 32.1978i 1.79431i
\(323\) 18.6225i 1.03618i
\(324\) −2.70928 −0.150515
\(325\) −4.00000 + 7.55252i −0.221880 + 0.418938i
\(326\) −20.0989 −1.11317
\(327\) 10.0000i 0.553001i
\(328\) 14.7382i 0.813781i
\(329\) 10.1568 0.559960
\(330\) 0 0
\(331\) −6.34017 −0.348487 −0.174244 0.984703i \(-0.555748\pi\)
−0.174244 + 0.984703i \(0.555748\pi\)
\(332\) 21.3112i 1.16961i
\(333\) 3.41855i 0.187335i
\(334\) −16.3896 −0.896800
\(335\) 0.993857 4.00000i 0.0543002 0.218543i
\(336\) 7.70928 0.420575
\(337\) 3.18568i 0.173535i 0.996229 + 0.0867677i \(0.0276538\pi\)
−0.996229 + 0.0867677i \(0.972346\pi\)
\(338\) 21.8710i 1.18962i
\(339\) 0.496928 0.0269894
\(340\) −8.83710 + 35.5669i −0.479259 + 1.92889i
\(341\) 0 0
\(342\) 6.68035i 0.361232i
\(343\) 0.894960i 0.0483233i
\(344\) 4.81432 0.259570
\(345\) −8.68035 2.15676i −0.467334 0.116116i
\(346\) 13.3424 0.717294
\(347\) 5.39576i 0.289660i −0.989457 0.144830i \(-0.953737\pi\)
0.989457 0.144830i \(-0.0462635\pi\)
\(348\) 14.2557i 0.764183i
\(349\) −15.6742 −0.839021 −0.419510 0.907751i \(-0.637798\pi\)
−0.419510 + 0.907751i \(0.637798\pi\)
\(350\) −35.5669 18.8371i −1.90113 1.00689i
\(351\) 1.70928 0.0912344
\(352\) 0 0
\(353\) 5.75872i 0.306506i −0.988187 0.153253i \(-0.951025\pi\)
0.988187 0.153253i \(-0.0489749\pi\)
\(354\) −7.81658 −0.415447
\(355\) −15.7009 3.90110i −0.833315 0.207049i
\(356\) −13.6020 −0.720903
\(357\) 22.4391i 1.18760i
\(358\) 13.3607i 0.706135i
\(359\) −10.5236 −0.555414 −0.277707 0.960666i \(-0.589574\pi\)
−0.277707 + 0.960666i \(0.589574\pi\)
\(360\) −0.829914 + 3.34017i −0.0437403 + 0.176043i
\(361\) −9.52359 −0.501242
\(362\) 31.6742i 1.66476i
\(363\) 0 0
\(364\) 17.1773 0.900334
\(365\) 3.44521 13.8660i 0.180331 0.725781i
\(366\) −31.8576 −1.66522
\(367\) 8.89496i 0.464313i −0.972678 0.232157i \(-0.925422\pi\)
0.972678 0.232157i \(-0.0745782\pi\)
\(368\) 8.31351i 0.433372i
\(369\) 9.57531 0.498471
\(370\) −16.0989 4.00000i −0.836942 0.207950i
\(371\) −51.0349 −2.64960
\(372\) 17.1773i 0.890600i
\(373\) 23.1689i 1.19964i 0.800136 + 0.599819i \(0.204761\pi\)
−0.800136 + 0.599819i \(0.795239\pi\)
\(374\) 0 0
\(375\) −7.46081 + 8.32684i −0.385275 + 0.429996i
\(376\) −4.21461 −0.217352
\(377\) 8.99386i 0.463207i
\(378\) 8.04945i 0.414019i
\(379\) 11.8310 0.607716 0.303858 0.952717i \(-0.401725\pi\)
0.303858 + 0.952717i \(0.401725\pi\)
\(380\) 18.0989 + 4.49693i 0.928454 + 0.230688i
\(381\) −2.81432 −0.144182
\(382\) 12.6803i 0.648783i
\(383\) 25.9421i 1.32558i 0.748805 + 0.662791i \(0.230628\pi\)
−0.748805 + 0.662791i \(0.769372\pi\)
\(384\) −11.5392 −0.588857
\(385\) 0 0
\(386\) 4.38962 0.223426
\(387\) 3.12783i 0.158996i
\(388\) 46.0410i 2.33738i
\(389\) −1.00614 −0.0510135 −0.0255067 0.999675i \(-0.508120\pi\)
−0.0255067 + 0.999675i \(0.508120\pi\)
\(390\) 2.00000 8.04945i 0.101274 0.407600i
\(391\) 24.1978 1.22374
\(392\) 10.4030i 0.525428i
\(393\) 8.68035i 0.437866i
\(394\) −38.7031 −1.94984
\(395\) −16.1568 4.01438i −0.812935 0.201985i
\(396\) 0 0
\(397\) 34.7214i 1.74262i −0.490736 0.871308i \(-0.663272\pi\)
0.490736 0.871308i \(-0.336728\pi\)
\(398\) 55.7152i 2.79275i
\(399\) 11.4186 0.571643
\(400\) −9.18342 4.86376i −0.459171 0.243188i
\(401\) −13.0205 −0.650214 −0.325107 0.945677i \(-0.605400\pi\)
−0.325107 + 0.945677i \(0.605400\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 10.8371i 0.539834i
\(404\) −51.3028 −2.55241
\(405\) 2.17009 + 0.539189i 0.107832 + 0.0267925i
\(406\) −42.3545 −2.10202
\(407\) 0 0
\(408\) 9.31124i 0.460975i
\(409\) −29.5174 −1.45954 −0.729772 0.683691i \(-0.760374\pi\)
−0.729772 + 0.683691i \(0.760374\pi\)
\(410\) 11.2039 45.0928i 0.553323 2.22697i
\(411\) 1.07838 0.0531925
\(412\) 31.9299i 1.57307i
\(413\) 13.3607i 0.657437i
\(414\) 8.68035 0.426616
\(415\) −4.24128 + 17.0700i −0.208196 + 0.837932i
\(416\) 12.9711 0.635959
\(417\) 10.2823i 0.503527i
\(418\) 0 0
\(419\) 6.15676 0.300777 0.150389 0.988627i \(-0.451948\pi\)
0.150389 + 0.988627i \(0.451948\pi\)
\(420\) 21.8082 + 5.41855i 1.06413 + 0.264398i
\(421\) 9.96880 0.485850 0.242925 0.970045i \(-0.421893\pi\)
0.242925 + 0.970045i \(0.421893\pi\)
\(422\) 18.3135i 0.891488i
\(423\) 2.73820i 0.133136i
\(424\) 21.1773 1.02846
\(425\) 14.1568 26.7298i 0.686704 1.29659i
\(426\) 15.7009 0.760709
\(427\) 54.4534i 2.63519i
\(428\) 30.5730i 1.47780i
\(429\) 0 0
\(430\) −14.7298 3.65983i −0.710334 0.176493i
\(431\) −8.68035 −0.418118 −0.209059 0.977903i \(-0.567040\pi\)
−0.209059 + 0.977903i \(0.567040\pi\)
\(432\) 2.07838i 0.0999960i
\(433\) 16.0000i 0.768911i −0.923144 0.384455i \(-0.874389\pi\)
0.923144 0.384455i \(-0.125611\pi\)
\(434\) 51.0349 2.44975
\(435\) −2.83710 + 11.4186i −0.136029 + 0.547478i
\(436\) 27.0928 1.29751
\(437\) 12.3135i 0.589035i
\(438\) 13.8660i 0.662545i
\(439\) 3.07838 0.146923 0.0734615 0.997298i \(-0.476595\pi\)
0.0734615 + 0.997298i \(0.476595\pi\)
\(440\) 0 0
\(441\) 6.75872 0.321844
\(442\) 22.4391i 1.06732i
\(443\) 29.2618i 1.39027i 0.718879 + 0.695135i \(0.244655\pi\)
−0.718879 + 0.695135i \(0.755345\pi\)
\(444\) 9.26180 0.439545
\(445\) 10.8950 + 2.70701i 0.516471 + 0.128324i
\(446\) −27.3028 −1.29283
\(447\) 11.4186i 0.540079i
\(448\) 45.6658i 2.15751i
\(449\) −10.6947 −0.504715 −0.252358 0.967634i \(-0.581206\pi\)
−0.252358 + 0.967634i \(0.581206\pi\)
\(450\) 5.07838 9.58864i 0.239397 0.452013i
\(451\) 0 0
\(452\) 1.34632i 0.0633254i
\(453\) 4.92162i 0.231238i
\(454\) −9.18568 −0.431106
\(455\) −13.7587 3.41855i −0.645019 0.160264i
\(456\) −4.73820 −0.221887
\(457\) 22.8554i 1.06913i 0.845128 + 0.534564i \(0.179524\pi\)
−0.845128 + 0.534564i \(0.820476\pi\)
\(458\) 56.8515i 2.65650i
\(459\) −6.04945 −0.282364
\(460\) 5.84324 23.5174i 0.272443 1.09651i
\(461\) 21.7731 1.01407 0.507037 0.861924i \(-0.330741\pi\)
0.507037 + 0.861924i \(0.330741\pi\)
\(462\) 0 0
\(463\) 24.8950i 1.15697i 0.815694 + 0.578483i \(0.196355\pi\)
−0.815694 + 0.578483i \(0.803645\pi\)
\(464\) −10.9360 −0.507691
\(465\) 3.41855 13.7587i 0.158531 0.638046i
\(466\) −40.4307 −1.87291
\(467\) 19.2039i 0.888652i 0.895865 + 0.444326i \(0.146557\pi\)
−0.895865 + 0.444326i \(0.853443\pi\)
\(468\) 4.63090i 0.214063i
\(469\) 6.83710 0.315708
\(470\) 12.8950 + 3.20394i 0.594800 + 0.147787i
\(471\) −3.41855 −0.157519
\(472\) 5.54411i 0.255188i
\(473\) 0 0
\(474\) 16.1568 0.742104
\(475\) −13.6020 7.20394i −0.624101 0.330539i
\(476\) −60.7936 −2.78647
\(477\) 13.7587i 0.629969i
\(478\) 48.5113i 2.21886i
\(479\) 9.47641 0.432988 0.216494 0.976284i \(-0.430538\pi\)
0.216494 + 0.976284i \(0.430538\pi\)
\(480\) 16.4680 + 4.09171i 0.751658 + 0.186760i
\(481\) −5.84324 −0.266429
\(482\) 19.9733i 0.909761i
\(483\) 14.8371i 0.675111i
\(484\) 0 0
\(485\) 9.16290 36.8781i 0.416066 1.67455i
\(486\) −2.17009 −0.0984371
\(487\) 35.2039i 1.59524i −0.603159 0.797621i \(-0.706091\pi\)
0.603159 0.797621i \(-0.293909\pi\)
\(488\) 22.5958i 1.02286i
\(489\) −9.26180 −0.418833
\(490\) 7.90829 31.8287i 0.357260 1.43787i
\(491\) 8.00000 0.361035 0.180517 0.983572i \(-0.442223\pi\)
0.180517 + 0.983572i \(0.442223\pi\)
\(492\) 25.9421i 1.16956i
\(493\) 31.8310i 1.43359i
\(494\) 11.4186 0.513745
\(495\) 0 0
\(496\) 13.1773 0.591677
\(497\) 26.8371i 1.20381i
\(498\) 17.0700i 0.764924i
\(499\) −26.1568 −1.17094 −0.585469 0.810695i \(-0.699089\pi\)
−0.585469 + 0.810695i \(0.699089\pi\)
\(500\) −22.5597 20.2134i −1.00890 0.903970i
\(501\) −7.55252 −0.337422
\(502\) 48.0144i 2.14299i
\(503\) 28.2784i 1.26087i 0.776241 + 0.630437i \(0.217124\pi\)
−0.776241 + 0.630437i \(0.782876\pi\)
\(504\) −5.70928 −0.254311
\(505\) 41.0928 + 10.2101i 1.82860 + 0.454343i
\(506\) 0 0
\(507\) 10.0784i 0.447596i
\(508\) 7.62475i 0.338294i
\(509\) −8.47027 −0.375438 −0.187719 0.982223i \(-0.560109\pi\)
−0.187719 + 0.982223i \(0.560109\pi\)
\(510\) −7.07838 + 28.4885i −0.313436 + 1.26149i
\(511\) 23.7009 1.04846
\(512\) 22.1701i 0.979789i
\(513\) 3.07838i 0.135914i
\(514\) 6.55479 0.289119
\(515\) 6.35455 25.5753i 0.280015 1.12698i
\(516\) 8.47414 0.373053
\(517\) 0 0
\(518\) 27.5174i 1.20905i
\(519\) 6.14834 0.269882
\(520\) 5.70928 + 1.41855i 0.250368 + 0.0622076i
\(521\) 13.7009 0.600246 0.300123 0.953901i \(-0.402972\pi\)
0.300123 + 0.953901i \(0.402972\pi\)
\(522\) 11.4186i 0.499776i
\(523\) 24.4885i 1.07081i −0.844596 0.535404i \(-0.820159\pi\)
0.844596 0.535404i \(-0.179841\pi\)
\(524\) 23.5174 1.02736
\(525\) −16.3896 8.68035i −0.715302 0.378841i
\(526\) 39.6925 1.73067
\(527\) 38.3545i 1.67075i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) −64.7936 16.0989i −2.81445 0.699291i
\(531\) −3.60197 −0.156312
\(532\) 30.9360i 1.34125i
\(533\) 16.3668i 0.708926i
\(534\) −10.8950 −0.471471
\(535\) −6.08452 + 24.4885i −0.263057 + 1.05873i
\(536\) −2.83710 −0.122544
\(537\) 6.15676i 0.265684i
\(538\) 66.3279i 2.85960i
\(539\) 0 0
\(540\) −1.46081 + 5.87936i −0.0628633 + 0.253007i
\(541\) −4.83710 −0.207963 −0.103982 0.994579i \(-0.533158\pi\)
−0.103982 + 0.994579i \(0.533158\pi\)
\(542\) 43.5585i 1.87100i
\(543\) 14.5958i 0.626367i
\(544\) −45.9071 −1.96825
\(545\) −21.7009 5.39189i −0.929563 0.230963i
\(546\) 13.7587 0.588819
\(547\) 30.5464i 1.30607i −0.757328 0.653034i \(-0.773496\pi\)
0.757328 0.653034i \(-0.226504\pi\)
\(548\) 2.92162i 0.124806i
\(549\) −14.6803 −0.626542
\(550\) 0 0
\(551\) −16.1978 −0.690049
\(552\) 6.15676i 0.262049i
\(553\) 27.6163i 1.17437i
\(554\) −1.65142 −0.0701620
\(555\) −7.41855 1.84324i −0.314900 0.0782414i
\(556\) −27.8576 −1.18143
\(557\) 7.57918i 0.321140i −0.987024 0.160570i \(-0.948667\pi\)
0.987024 0.160570i \(-0.0513333\pi\)
\(558\) 13.7587i 0.582453i
\(559\) −5.34632 −0.226125
\(560\) 4.15676 16.7298i 0.175655 0.706963i
\(561\) 0 0
\(562\) 1.26180i 0.0532256i
\(563\) 14.1750i 0.597405i 0.954346 + 0.298703i \(0.0965539\pi\)
−0.954346 + 0.298703i \(0.903446\pi\)
\(564\) −7.41855 −0.312377
\(565\) 0.267938 1.07838i 0.0112722 0.0453677i
\(566\) −23.4680 −0.986434
\(567\) 3.70928i 0.155775i
\(568\) 11.1362i 0.467266i
\(569\) −14.7382 −0.617858 −0.308929 0.951085i \(-0.599970\pi\)
−0.308929 + 0.951085i \(0.599970\pi\)
\(570\) 14.4969 + 3.60197i 0.607210 + 0.150870i
\(571\) −1.23513 −0.0516887 −0.0258444 0.999666i \(-0.508227\pi\)
−0.0258444 + 0.999666i \(0.508227\pi\)
\(572\) 0 0
\(573\) 5.84324i 0.244105i
\(574\) 77.0759 3.21709
\(575\) −9.36069 + 17.6742i −0.390368 + 0.737065i
\(576\) −12.3112 −0.512968
\(577\) 28.9770i 1.20633i −0.797617 0.603165i \(-0.793906\pi\)
0.797617 0.603165i \(-0.206094\pi\)
\(578\) 42.5246i 1.76879i
\(579\) 2.02279 0.0840641
\(580\) −30.9360 7.68649i −1.28455 0.319164i
\(581\) −29.1773 −1.21048
\(582\) 36.8781i 1.52865i
\(583\) 0 0
\(584\) −9.83483 −0.406968
\(585\) 0.921622 3.70928i 0.0381044 0.153360i
\(586\) 15.2846 0.631400
\(587\) 20.9939i 0.866509i 0.901272 + 0.433255i \(0.142635\pi\)
−0.901272 + 0.433255i \(0.857365\pi\)
\(588\) 18.3112i 0.755143i
\(589\) 19.5174 0.804202
\(590\) −4.21461 + 16.9627i −0.173513 + 0.698342i
\(591\) −17.8348 −0.733627
\(592\) 7.10504i 0.292015i
\(593\) 23.8927i 0.981155i 0.871397 + 0.490578i \(0.163214\pi\)
−0.871397 + 0.490578i \(0.836786\pi\)
\(594\) 0 0
\(595\) 48.6947 + 12.0989i 1.99629 + 0.496006i
\(596\) −30.9360 −1.26719
\(597\) 25.6742i 1.05078i
\(598\) 14.8371i 0.606734i
\(599\) 45.6742 1.86620 0.933099 0.359620i \(-0.117094\pi\)
0.933099 + 0.359620i \(0.117094\pi\)
\(600\) 6.80098 + 3.60197i 0.277649 + 0.147050i
\(601\) 16.2101 0.661223 0.330611 0.943767i \(-0.392745\pi\)
0.330611 + 0.943767i \(0.392745\pi\)
\(602\) 25.1773i 1.02615i
\(603\) 1.84324i 0.0750627i
\(604\) −13.3340 −0.542554
\(605\) 0 0
\(606\) −41.0928 −1.66928
\(607\) 20.8020i 0.844328i 0.906519 + 0.422164i \(0.138729\pi\)
−0.906519 + 0.422164i \(0.861271\pi\)
\(608\) 23.3607i 0.947401i
\(609\) −19.5174 −0.790887
\(610\) −17.1773 + 69.1338i −0.695488 + 2.79915i
\(611\) 4.68035 0.189347
\(612\) 16.3896i 0.662511i
\(613\) 15.3835i 0.621333i −0.950519 0.310666i \(-0.899448\pi\)
0.950519 0.310666i \(-0.100552\pi\)
\(614\) 43.7815 1.76688
\(615\) 5.16290 20.7792i 0.208188 0.837900i
\(616\) 0 0
\(617\) 21.9733i 0.884613i −0.896864 0.442307i \(-0.854160\pi\)
0.896864 0.442307i \(-0.145840\pi\)
\(618\) 25.5753i 1.02879i
\(619\) −10.3935 −0.417750 −0.208875 0.977942i \(-0.566980\pi\)
−0.208875 + 0.977942i \(0.566980\pi\)
\(620\) 37.2762 + 9.26180i 1.49705 + 0.371963i
\(621\) 4.00000 0.160514
\(622\) 46.1711i 1.85129i
\(623\) 18.6225i 0.746094i
\(624\) 3.55252 0.142215
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) −35.7321 −1.42814
\(627\) 0 0
\(628\) 9.26180i 0.369586i
\(629\) 20.6803 0.824579
\(630\) 17.4680 + 4.34017i 0.695942 + 0.172917i
\(631\) 38.7214 1.54147 0.770737 0.637153i \(-0.219888\pi\)
0.770737 + 0.637153i \(0.219888\pi\)
\(632\) 11.4596i 0.455838i
\(633\) 8.43907i 0.335423i
\(634\) −48.1133 −1.91082
\(635\) −1.51745 + 6.10731i −0.0602181 + 0.242361i
\(636\) 37.2762 1.47810
\(637\) 11.5525i 0.457728i
\(638\) 0 0
\(639\) 7.23513 0.286217
\(640\) −6.22180 + 25.0410i −0.245938 + 0.989834i
\(641\) 24.2245 0.956808 0.478404 0.878140i \(-0.341215\pi\)
0.478404 + 0.878140i \(0.341215\pi\)
\(642\) 24.4885i 0.966485i
\(643\) 25.8888i 1.02096i −0.859891 0.510478i \(-0.829469\pi\)
0.859891 0.510478i \(-0.170531\pi\)
\(644\) 40.1978 1.58401
\(645\) −6.78765 1.68649i −0.267264 0.0664054i
\(646\) −40.4124 −1.59000
\(647\) 0.581449i 0.0228591i 0.999935 + 0.0114296i \(0.00363822\pi\)
−0.999935 + 0.0114296i \(0.996362\pi\)
\(648\) 1.53919i 0.0604650i
\(649\) 0 0
\(650\) −16.3896 8.68035i −0.642854 0.340471i
\(651\) 23.5174 0.921721
\(652\) 25.0928i 0.982708i
\(653\) 37.0082i 1.44824i 0.689672 + 0.724122i \(0.257755\pi\)
−0.689672 + 0.724122i \(0.742245\pi\)
\(654\) 21.7009 0.848571
\(655\) −18.8371 4.68035i −0.736026 0.182876i
\(656\) 19.9011 0.777008
\(657\) 6.38962i 0.249283i
\(658\) 22.0410i 0.859249i
\(659\) 30.5236 1.18903 0.594515 0.804084i \(-0.297344\pi\)
0.594515 + 0.804084i \(0.297344\pi\)
\(660\) 0 0
\(661\) 5.88428 0.228872 0.114436 0.993431i \(-0.463494\pi\)
0.114436 + 0.993431i \(0.463494\pi\)
\(662\) 13.7587i 0.534748i
\(663\) 10.3402i 0.401579i
\(664\) 12.1073 0.469855
\(665\) 6.15676 24.7792i 0.238749 0.960898i
\(666\) 7.41855 0.287463
\(667\) 21.0472i 0.814950i
\(668\) 20.4619i 0.791693i
\(669\) −12.5814 −0.486427
\(670\) 8.68035 + 2.15676i 0.335351 + 0.0833227i
\(671\) 0 0
\(672\) 28.1483i 1.08585i
\(673\) 26.9711i 1.03966i 0.854270 + 0.519829i \(0.174004\pi\)
−0.854270 + 0.519829i \(0.825996\pi\)
\(674\) −6.91321 −0.266287
\(675\) 2.34017 4.41855i 0.0900733 0.170070i
\(676\) −27.3051 −1.05020
\(677\) 17.9506i 0.689896i −0.938622 0.344948i \(-0.887897\pi\)
0.938622 0.344948i \(-0.112103\pi\)
\(678\) 1.07838i 0.0414148i
\(679\) 63.0349 2.41906
\(680\) −20.2062 5.02052i −0.774873 0.192528i
\(681\) −4.23287 −0.162204
\(682\) 0 0
\(683\) 8.77924i 0.335928i 0.985793 + 0.167964i \(0.0537193\pi\)
−0.985793 + 0.167964i \(0.946281\pi\)
\(684\) −8.34017 −0.318894
\(685\) 0.581449 2.34017i 0.0222160 0.0894134i
\(686\) −1.94214 −0.0741513
\(687\) 26.1978i 0.999508i
\(688\) 6.50080i 0.247841i
\(689\) −23.5174 −0.895943
\(690\) 4.68035 18.8371i 0.178178 0.717116i
\(691\) −14.7214 −0.560028 −0.280014 0.959996i \(-0.590339\pi\)
−0.280014 + 0.959996i \(0.590339\pi\)
\(692\) 16.6576i 0.633225i
\(693\) 0 0
\(694\) 11.7093 0.444478
\(695\) 22.3135 + 5.54411i 0.846400 + 0.210300i
\(696\) 8.09890 0.306988
\(697\) 57.9253i 2.19408i
\(698\) 34.0144i 1.28746i
\(699\) −18.6309 −0.704685
\(700\) 23.5174 44.4040i 0.888876 1.67831i
\(701\) 7.10504 0.268354 0.134177 0.990957i \(-0.457161\pi\)
0.134177 + 0.990957i \(0.457161\pi\)
\(702\) 3.70928i 0.139998i
\(703\) 10.5236i 0.396905i
\(704\) 0 0
\(705\) 5.94214 + 1.47641i 0.223794 + 0.0556048i
\(706\) 12.4969 0.470328
\(707\) 70.2388i 2.64160i
\(708\) 9.75872i 0.366755i
\(709\) 34.1666 1.28315 0.641577 0.767059i \(-0.278281\pi\)
0.641577 + 0.767059i \(0.278281\pi\)
\(710\) 8.46573 34.0722i 0.317713 1.27871i
\(711\) 7.44521 0.279217
\(712\) 7.72753i 0.289601i
\(713\) 25.3607i 0.949765i
\(714\) −48.6947 −1.82235
\(715\) 0 0
\(716\) −16.6803 −0.623374
\(717\) 22.3545i 0.834846i
\(718\) 22.8371i 0.852273i
\(719\) −31.8310 −1.18709 −0.593547 0.804799i \(-0.702273\pi\)
−0.593547 + 0.804799i \(0.702273\pi\)
\(720\) 4.51026 + 1.12064i 0.168087 + 0.0417637i
\(721\) 43.7152 1.62804
\(722\) 20.6670i 0.769147i
\(723\) 9.20394i 0.342298i
\(724\) −39.5441 −1.46965
\(725\) 23.2495 + 12.3135i 0.863465 + 0.457312i
\(726\) 0 0
\(727\) 5.16290i 0.191481i −0.995406 0.0957407i \(-0.969478\pi\)
0.995406 0.0957407i \(-0.0305219\pi\)
\(728\) 9.75872i 0.361682i
\(729\) −1.00000 −0.0370370
\(730\) 30.0905 + 7.47641i 1.11370 + 0.276714i
\(731\) 18.9216 0.699841
\(732\) 39.7731i 1.47006i
\(733\) 36.4475i 1.34622i 0.739543 + 0.673109i \(0.235042\pi\)
−0.739543 + 0.673109i \(0.764958\pi\)
\(734\) 19.3028 0.712481
\(735\) 3.64423 14.6670i 0.134419 0.541001i
\(736\) 30.3545 1.11888
\(737\) 0 0
\(738\) 20.7792i 0.764894i
\(739\) 25.4329 0.935565 0.467783 0.883844i \(-0.345053\pi\)
0.467783 + 0.883844i \(0.345053\pi\)
\(740\) 4.99386 20.0989i 0.183578 0.738850i
\(741\) 5.26180 0.193297
\(742\) 110.750i 4.06577i
\(743\) 10.1217i 0.371329i −0.982613 0.185664i \(-0.940556\pi\)
0.982613 0.185664i \(-0.0594437\pi\)
\(744\) −9.75872 −0.357772
\(745\) 24.7792 + 6.15676i 0.907841 + 0.225566i
\(746\) −50.2784 −1.84082
\(747\) 7.86603i 0.287803i
\(748\) 0 0
\(749\) −41.8576 −1.52944
\(750\) −18.0700 16.1906i −0.659822 0.591197i
\(751\) 10.4703 0.382065 0.191033 0.981584i \(-0.438816\pi\)
0.191033 + 0.981584i \(0.438816\pi\)
\(752\) 5.69102i 0.207530i
\(753\) 22.1256i 0.806300i
\(754\) −19.5174 −0.710784
\(755\) 10.6803 + 2.65368i 0.388698 + 0.0965774i
\(756\) −10.0494 −0.365495
\(757\) 6.73820i 0.244904i 0.992474 + 0.122452i \(0.0390758\pi\)
−0.992474 + 0.122452i \(0.960924\pi\)
\(758\) 25.6742i 0.932529i
\(759\) 0 0
\(760\) −2.55479 + 10.2823i −0.0926719 + 0.372979i
\(761\) 5.57531 0.202105 0.101052 0.994881i \(-0.467779\pi\)
0.101052 + 0.994881i \(0.467779\pi\)
\(762\) 6.10731i 0.221244i
\(763\) 37.0928i 1.34285i
\(764\) −15.8310 −0.572744
\(765\) −3.26180 + 13.1278i −0.117930 + 0.474638i
\(766\) −56.2967 −2.03408
\(767\) 6.15676i 0.222308i
\(768\) 0.418551i 0.0151031i
\(769\) −11.5297 −0.415773 −0.207886 0.978153i \(-0.566658\pi\)
−0.207886 + 0.978153i \(0.566658\pi\)
\(770\) 0 0
\(771\) 3.02052 0.108781
\(772\) 5.48029i 0.197240i
\(773\) 28.7480i 1.03400i −0.855987 0.516998i \(-0.827050\pi\)
0.855987 0.516998i \(-0.172950\pi\)
\(774\) 6.78765 0.243977
\(775\) −28.0144 14.8371i −1.00631 0.532964i
\(776\) −26.1568 −0.938973
\(777\) 12.6803i 0.454905i
\(778\) 2.18342i 0.0782793i
\(779\) 29.4764 1.05610
\(780\) 10.0494 + 2.49693i 0.359828 + 0.0894044i
\(781\) 0 0
\(782\) 52.5113i 1.87780i
\(783\) 5.26180i 0.188041i
\(784\) 14.0472 0.501685
\(785\) −1.84324 + 7.41855i −0.0657882 + 0.264779i
\(786\) 18.8371 0.671897
\(787\) 13.4536i 0.479570i −0.970826 0.239785i \(-0.922923\pi\)
0.970826 0.239785i \(-0.0770769\pi\)
\(788\) 48.3195i 1.72131i
\(789\) 18.2907 0.651167
\(790\) 8.71154 35.0616i 0.309943 1.24743i
\(791\) 1.84324 0.0655382
\(792\) 0 0
\(793\) 25.0928i 0.891070i
\(794\) 75.3484 2.67401
\(795\) −29.8576 7.41855i −1.05894 0.263109i
\(796\) 69.5585 2.46544
\(797\) 48.3279i 1.71186i 0.517090 + 0.855931i \(0.327015\pi\)
−0.517090 + 0.855931i \(0.672985\pi\)
\(798\) 24.7792i 0.877176i
\(799\) −16.5646 −0.586014
\(800\) 17.7587 33.5308i 0.627866 1.18549i
\(801\) −5.02052 −0.177391
\(802\) 28.2557i 0.997742i
\(803\) 0 0
\(804\) −4.99386 −0.176120
\(805\) −32.1978 8.00000i −1.13482 0.281963i
\(806\) 23.5174 0.828367
\(807\) 30.5646i 1.07593i
\(808\) 29.1461i 1.02536i
\(809\) −43.8141 −1.54042 −0.770212 0.637789i \(-0.779849\pi\)
−0.770212 + 0.637789i \(0.779849\pi\)
\(810\) −1.17009 + 4.70928i −0.0411126 + 0.165467i
\(811\) 47.2762 1.66009 0.830045 0.557696i \(-0.188314\pi\)
0.830045 + 0.557696i \(0.188314\pi\)
\(812\) 52.8781i 1.85566i
\(813\) 20.0722i 0.703964i
\(814\) 0 0
\(815\) −4.99386 + 20.0989i −0.174927 + 0.704034i
\(816\) −12.5730 −0.440144
\(817\) 9.62863i 0.336863i
\(818\) 64.0554i 2.23965i
\(819\) 6.34017 0.221544
\(820\) 56.2967 + 13.9877i 1.96597 + 0.488472i
\(821\) 3.30283 0.115270 0.0576348 0.998338i \(-0.481644\pi\)
0.0576348 + 0.998338i \(0.481644\pi\)
\(822\) 2.34017i 0.0816229i
\(823\) 11.0517i 0.385239i 0.981274 + 0.192619i \(0.0616982\pi\)
−0.981274 + 0.192619i \(0.938302\pi\)
\(824\) −18.1399 −0.631935
\(825\) 0 0
\(826\) −28.9939 −1.00883
\(827\) 5.12783i 0.178312i 0.996018 + 0.0891560i \(0.0284170\pi\)
−0.996018 + 0.0891560i \(0.971583\pi\)
\(828\) 10.8371i 0.376615i
\(829\) 6.39803 0.222213 0.111106 0.993809i \(-0.464561\pi\)
0.111106 + 0.993809i \(0.464561\pi\)
\(830\) −37.0433 9.20394i −1.28579 0.319473i
\(831\) −0.760991 −0.0263985
\(832\) 21.0433i 0.729545i
\(833\) 40.8865i 1.41663i
\(834\) −22.3135 −0.772654
\(835\) −4.07223 + 16.3896i −0.140925 + 0.567186i
\(836\) 0 0
\(837\) 6.34017i 0.219148i
\(838\) 13.3607i 0.461537i
\(839\) 22.0722 0.762018 0.381009 0.924571i \(-0.375577\pi\)
0.381009 + 0.924571i \(0.375577\pi\)
\(840\) −3.07838 + 12.3896i −0.106214 + 0.427483i
\(841\) −1.31351 −0.0452935
\(842\) 21.6332i 0.745528i
\(843\) 0.581449i 0.0200262i
\(844\) 22.8638 0.787003
\(845\) 21.8710 + 5.43415i 0.752384 + 0.186940i
\(846\) −5.94214 −0.204295
\(847\) 0 0
\(848\) 28.5958i 0.981985i
\(849\) −10.8143 −0.371146
\(850\) 58.0060 + 30.7214i 1.98959 + 1.05373i
\(851\) −13.6742 −0.468746
\(852\) 19.6020i 0.671552i
\(853\) 8.76099i 0.299971i 0.988688 + 0.149985i \(0.0479226\pi\)
−0.988688 + 0.149985i \(0.952077\pi\)
\(854\) −118.169 −4.04365
\(855\) 6.68035 + 1.65983i 0.228463 + 0.0567649i
\(856\) 17.3691 0.593664
\(857\) 36.5730i 1.24931i −0.780900 0.624656i \(-0.785239\pi\)
0.780900 0.624656i \(-0.214761\pi\)
\(858\) 0 0
\(859\) 49.6886 1.69535 0.847676 0.530514i \(-0.178001\pi\)
0.847676 + 0.530514i \(0.178001\pi\)
\(860\) 4.56916 18.3896i 0.155807 0.627081i
\(861\) 35.5174 1.21043
\(862\) 18.8371i 0.641594i
\(863\) 34.1399i 1.16214i −0.813855 0.581068i \(-0.802635\pi\)
0.813855 0.581068i \(-0.197365\pi\)
\(864\) −7.58864 −0.258171
\(865\) 3.31512 13.3424i 0.112717 0.453657i
\(866\) 34.7214 1.17988
\(867\) 19.5958i 0.665509i
\(868\) 63.7152i 2.16264i
\(869\) 0 0
\(870\) −24.7792 6.15676i −0.840095 0.208734i
\(871\) 3.15061 0.106754
\(872\) 15.3919i 0.521235i
\(873\) 16.9939i 0.575155i
\(874\) 26.7214 0.903864
\(875\) −27.6742 + 30.8865i −0.935559 + 1.04416i
\(876\) −17.3112 −0.584893
\(877\) 43.5357i 1.47010i −0.678015 0.735048i \(-0.737160\pi\)
0.678015 0.735048i \(-0.262840\pi\)
\(878\) 6.68035i 0.225451i
\(879\) 7.04331 0.237565
\(880\) 0 0
\(881\) −8.52359 −0.287167 −0.143584 0.989638i \(-0.545863\pi\)
−0.143584 + 0.989638i \(0.545863\pi\)
\(882\) 14.6670i 0.493864i
\(883\) 43.0349i 1.44824i 0.689674 + 0.724120i \(0.257754\pi\)
−0.689674 + 0.724120i \(0.742246\pi\)
\(884\) −28.0144 −0.942225
\(885\) −1.94214 + 7.81658i −0.0652844 + 0.262752i
\(886\) −63.5006 −2.13335
\(887\) 17.0289i 0.571775i 0.958263 + 0.285888i \(0.0922884\pi\)
−0.958263 + 0.285888i \(0.907712\pi\)
\(888\) 5.26180i 0.176574i
\(889\) −10.4391 −0.350115
\(890\) −5.87444 + 23.6430i −0.196912 + 0.792515i
\(891\) 0 0
\(892\) 34.0866i 1.14130i
\(893\) 8.42923i 0.282073i
\(894\) −24.7792 −0.828742
\(895\) 13.3607 + 3.31965i 0.446599 + 0.110964i
\(896\) −42.8020 −1.42992
\(897\) 6.83710i 0.228284i
\(898\) 23.2085i 0.774477i
\(899\) −33.3607 −1.11264
\(900\) 11.9711 + 6.34017i 0.399036 + 0.211339i
\(901\) 83.2327 2.77288
\(902\) 0 0
\(903\) 11.6020i 0.386089i
\(904\) −0.764867 −0.0254391
\(905\) 31.6742 + 7.86991i 1.05289 + 0.261605i
\(906\) −10.6803 −0.354831
\(907\) 6.13993i 0.203873i −0.994791 0.101937i \(-0.967496\pi\)
0.994791 0.101937i \(-0.0325039\pi\)
\(908\) 11.4680i 0.380579i
\(909\) −18.9360 −0.628067
\(910\) 7.41855 29.8576i 0.245923 0.989770i
\(911\) 53.8720 1.78486 0.892429 0.451187i \(-0.148999\pi\)
0.892429 + 0.451187i \(0.148999\pi\)
\(912\) 6.39803i 0.211860i
\(913\) 0 0
\(914\) −49.5981 −1.64056
\(915\) −7.91548 + 31.8576i −0.261678 + 1.05318i
\(916\) −70.9770 −2.34515
\(917\) 32.1978i 1.06326i
\(918\) 13.1278i 0.433283i
\(919\) −48.2700 −1.59228 −0.796141 0.605112i \(-0.793128\pi\)
−0.796141 + 0.605112i \(0.793128\pi\)
\(920\) 13.3607 + 3.31965i 0.440489 + 0.109446i
\(921\) 20.1750 0.664789
\(922\) 47.2495i 1.55608i
\(923\) 12.3668i 0.407059i
\(924\) 0 0
\(925\) −8.00000 + 15.1050i −0.263038 + 0.496651i
\(926\) −54.0242 −1.77535
\(927\) 11.7854i 0.387083i
\(928\) 39.9299i 1.31076i
\(929\) −4.10343 −0.134629 −0.0673146 0.997732i \(-0.521443\pi\)
−0.0673146 + 0.997732i \(0.521443\pi\)
\(930\) 29.8576 + 7.41855i 0.979070 + 0.243264i
\(931\) 20.8059 0.681886
\(932\) 50.4762i 1.65340i
\(933\) 21.2762i 0.696551i
\(934\) −41.6742 −1.36362
\(935\) 0 0
\(936\) −2.63090 −0.0859936
\(937\) 38.5341i 1.25885i −0.777060 0.629427i \(-0.783290\pi\)
0.777060 0.629427i \(-0.216710\pi\)
\(938\) 14.8371i 0.484449i
\(939\) −16.4657 −0.537339
\(940\) −4.00000 + 16.0989i −0.130466 + 0.525088i
\(941\) −14.6849 −0.478713 −0.239357 0.970932i \(-0.576937\pi\)
−0.239357 + 0.970932i \(0.576937\pi\)
\(942\) 7.41855i 0.241709i
\(943\) 38.3012i 1.24726i
\(944\) −7.48625 −0.243657
\(945\) 8.04945 + 2.00000i 0.261849 + 0.0650600i
\(946\) 0 0
\(947\) 6.05786i 0.196854i −0.995144 0.0984270i \(-0.968619\pi\)
0.995144 0.0984270i \(-0.0313811\pi\)
\(948\) 20.1711i 0.655128i
\(949\) 10.9216 0.354531
\(950\) 15.6332 29.5174i 0.507207 0.957672i
\(951\) −22.1711 −0.718948
\(952\) 34.5380i 1.11938i
\(953\) 40.1438i 1.30039i −0.759769 0.650193i \(-0.774688\pi\)
0.759769 0.650193i \(-0.225312\pi\)
\(954\) 29.8576 0.966676
\(955\) 12.6803 + 3.15061i 0.410326 + 0.101951i
\(956\) −60.5646 −1.95880
\(957\) 0 0
\(958\) 20.5646i 0.664413i
\(959\) 4.00000 0.129167
\(960\) −6.63809 + 26.7165i −0.214243 + 0.862270i
\(961\) 9.19779 0.296703
\(962\) 12.6803i 0.408831i
\(963\) 11.2846i 0.363641i
\(964\) 24.9360 0.803134
\(965\) 1.09066 4.38962i 0.0351097 0.141307i
\(966\) 32.1978 1.03595
\(967\) 50.6285i 1.62810i −0.580794 0.814051i \(-0.697258\pi\)
0.580794 0.814051i \(-0.302742\pi\)
\(968\) 0 0
\(969\) −18.6225 −0.598240
\(970\) 80.0288 + 19.8843i 2.56957 + 0.638446i
\(971\) −6.69263 −0.214777 −0.107388 0.994217i \(-0.534249\pi\)
−0.107388 + 0.994217i \(0.534249\pi\)
\(972\) 2.70928i 0.0869000i
\(973\) 38.1399i 1.22271i
\(974\) 76.3956 2.44787
\(975\) −7.55252 4.00000i −0.241874 0.128103i
\(976\) −30.5113 −0.976643
\(977\) 38.5835i 1.23440i −0.786808 0.617198i \(-0.788268\pi\)
0.786808 0.617198i \(-0.211732\pi\)
\(978\) 20.0989i 0.642692i
\(979\) 0 0
\(980\) 39.7370 + 9.87322i 1.26935 + 0.315388i
\(981\) 10.0000 0.319275
\(982\) 17.3607i 0.554002i
\(983\) 28.4657i 0.907916i −0.891023 0.453958i \(-0.850012\pi\)
0.891023 0.453958i \(-0.149988\pi\)
\(984\) −14.7382 −0.469837
\(985\) −9.61634 + 38.7031i −0.306402 + 1.23318i
\(986\) 69.0759 2.19983
\(987\) 10.1568i 0.323293i
\(988\) 14.2557i 0.453533i
\(989\) −12.5113 −0.397836
\(990\) 0 0
\(991\) 2.65368 0.0842970 0.0421485 0.999111i \(-0.486580\pi\)
0.0421485 + 0.999111i \(0.486580\pi\)
\(992\) 48.1133i 1.52760i
\(993\) 6.34017i 0.201199i
\(994\) 58.2388 1.84722
\(995\) −55.7152 13.8432i −1.76629 0.438860i
\(996\) 21.3112 0.675273
\(997\) 8.08065i 0.255917i −0.991780 0.127958i \(-0.959158\pi\)
0.991780 0.127958i \(-0.0408424\pi\)
\(998\) 56.7624i 1.79678i
\(999\) 3.41855 0.108158
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 1815.2.c.e.364.6 6
5.2 odd 4 9075.2.a.cg.1.1 3
5.3 odd 4 9075.2.a.ch.1.3 3
5.4 even 2 inner 1815.2.c.e.364.1 6
11.10 odd 2 165.2.c.b.34.1 6
33.32 even 2 495.2.c.e.199.6 6
44.43 even 2 2640.2.d.h.529.3 6
55.32 even 4 825.2.a.l.1.3 3
55.43 even 4 825.2.a.j.1.1 3
55.54 odd 2 165.2.c.b.34.6 yes 6
165.32 odd 4 2475.2.a.ba.1.1 3
165.98 odd 4 2475.2.a.bc.1.3 3
165.164 even 2 495.2.c.e.199.1 6
220.219 even 2 2640.2.d.h.529.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.c.b.34.1 6 11.10 odd 2
165.2.c.b.34.6 yes 6 55.54 odd 2
495.2.c.e.199.1 6 165.164 even 2
495.2.c.e.199.6 6 33.32 even 2
825.2.a.j.1.1 3 55.43 even 4
825.2.a.l.1.3 3 55.32 even 4
1815.2.c.e.364.1 6 5.4 even 2 inner
1815.2.c.e.364.6 6 1.1 even 1 trivial
2475.2.a.ba.1.1 3 165.32 odd 4
2475.2.a.bc.1.3 3 165.98 odd 4
2640.2.d.h.529.3 6 44.43 even 2
2640.2.d.h.529.6 6 220.219 even 2
9075.2.a.cg.1.1 3 5.2 odd 4
9075.2.a.ch.1.3 3 5.3 odd 4