Properties

Label 1815.2.c.k.364.1
Level $1815$
Weight $2$
Character 1815.364
Analytic conductor $14.493$
Analytic rank $0$
Dimension $24$
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: \(24\)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.1
Character \(\chi\) \(=\) 1815.364
Dual form 1815.2.c.k.364.24

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.72592i q^{2} +1.00000i q^{3} -5.43063 q^{4} +(1.85250 - 1.25229i) q^{5} +2.72592 q^{6} -0.486331i q^{7} +9.35163i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.72592i q^{2} +1.00000i q^{3} -5.43063 q^{4} +(1.85250 - 1.25229i) q^{5} +2.72592 q^{6} -0.486331i q^{7} +9.35163i q^{8} -1.00000 q^{9} +(-3.41365 - 5.04977i) q^{10} -5.43063i q^{12} +3.61034i q^{13} -1.32570 q^{14} +(1.25229 + 1.85250i) q^{15} +14.6305 q^{16} +3.64283i q^{17} +2.72592i q^{18} -1.63130 q^{19} +(-10.0603 + 6.80074i) q^{20} +0.486331 q^{21} +3.54253i q^{23} -9.35163 q^{24} +(1.86353 - 4.63975i) q^{25} +9.84148 q^{26} -1.00000i q^{27} +2.64109i q^{28} +1.05606 q^{29} +(5.04977 - 3.41365i) q^{30} +6.10088 q^{31} -21.1784i q^{32} +9.93007 q^{34} +(-0.609029 - 0.900930i) q^{35} +5.43063 q^{36} +8.59108i q^{37} +4.44679i q^{38} -3.61034 q^{39} +(11.7110 + 17.3239i) q^{40} -10.9830 q^{41} -1.32570i q^{42} +7.41765i q^{43} +(-1.85250 + 1.25229i) q^{45} +9.65665 q^{46} +5.21295i q^{47} +14.6305i q^{48} +6.76348 q^{49} +(-12.6476 - 5.07983i) q^{50} -3.64283 q^{51} -19.6064i q^{52} +1.49020i q^{53} -2.72592 q^{54} +4.54799 q^{56} -1.63130i q^{57} -2.87874i q^{58} +7.97599 q^{59} +(-6.80074 - 10.0603i) q^{60} +10.8638 q^{61} -16.6305i q^{62} +0.486331i q^{63} -28.4694 q^{64} +(4.52120 + 6.68815i) q^{65} -0.432515i q^{67} -19.7829i q^{68} -3.54253 q^{69} +(-2.45586 + 1.66016i) q^{70} +6.01324 q^{71} -9.35163i q^{72} -1.16412i q^{73} +23.4186 q^{74} +(4.63975 + 1.86353i) q^{75} +8.85898 q^{76} +9.84148i q^{78} -4.42494 q^{79} +(27.1031 - 18.3217i) q^{80} +1.00000 q^{81} +29.9386i q^{82} +3.17731i q^{83} -2.64109 q^{84} +(4.56189 + 6.74836i) q^{85} +20.2199 q^{86} +1.05606i q^{87} -1.38354 q^{89} +(3.41365 + 5.04977i) q^{90} +1.75582 q^{91} -19.2382i q^{92} +6.10088i q^{93} +14.2101 q^{94} +(-3.02198 + 2.04286i) q^{95} +21.1784 q^{96} -1.39973i q^{97} -18.4367i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.72592i 1.92752i −0.266778 0.963758i \(-0.585959\pi\)
0.266778 0.963758i \(-0.414041\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −5.43063 −2.71532
\(5\) 1.85250 1.25229i 0.828464 0.560042i
\(6\) 2.72592 1.11285
\(7\) 0.486331i 0.183816i −0.995768 0.0919080i \(-0.970703\pi\)
0.995768 0.0919080i \(-0.0292966\pi\)
\(8\) 9.35163i 3.30630i
\(9\) −1.00000 −0.333333
\(10\) −3.41365 5.04977i −1.07949 1.59688i
\(11\) 0 0
\(12\) 5.43063i 1.56769i
\(13\) 3.61034i 1.00133i 0.865642 + 0.500663i \(0.166911\pi\)
−0.865642 + 0.500663i \(0.833089\pi\)
\(14\) −1.32570 −0.354308
\(15\) 1.25229 + 1.85250i 0.323340 + 0.478314i
\(16\) 14.6305 3.65763
\(17\) 3.64283i 0.883517i 0.897134 + 0.441758i \(0.145645\pi\)
−0.897134 + 0.441758i \(0.854355\pi\)
\(18\) 2.72592i 0.642505i
\(19\) −1.63130 −0.374245 −0.187123 0.982337i \(-0.559916\pi\)
−0.187123 + 0.982337i \(0.559916\pi\)
\(20\) −10.0603 + 6.80074i −2.24954 + 1.52069i
\(21\) 0.486331 0.106126
\(22\) 0 0
\(23\) 3.54253i 0.738668i 0.929297 + 0.369334i \(0.120414\pi\)
−0.929297 + 0.369334i \(0.879586\pi\)
\(24\) −9.35163 −1.90889
\(25\) 1.86353 4.63975i 0.372706 0.927950i
\(26\) 9.84148 1.93007
\(27\) 1.00000i 0.192450i
\(28\) 2.64109i 0.499119i
\(29\) 1.05606 0.196106 0.0980530 0.995181i \(-0.468739\pi\)
0.0980530 + 0.995181i \(0.468739\pi\)
\(30\) 5.04977 3.41365i 0.921958 0.623244i
\(31\) 6.10088 1.09575 0.547876 0.836560i \(-0.315437\pi\)
0.547876 + 0.836560i \(0.315437\pi\)
\(32\) 21.1784i 3.74384i
\(33\) 0 0
\(34\) 9.93007 1.70299
\(35\) −0.609029 0.900930i −0.102945 0.152285i
\(36\) 5.43063 0.905106
\(37\) 8.59108i 1.41236i 0.708030 + 0.706182i \(0.249584\pi\)
−0.708030 + 0.706182i \(0.750416\pi\)
\(38\) 4.44679i 0.721364i
\(39\) −3.61034 −0.578116
\(40\) 11.7110 + 17.3239i 1.85167 + 2.73915i
\(41\) −10.9830 −1.71525 −0.857624 0.514276i \(-0.828061\pi\)
−0.857624 + 0.514276i \(0.828061\pi\)
\(42\) 1.32570i 0.204560i
\(43\) 7.41765i 1.13118i 0.824686 + 0.565591i \(0.191352\pi\)
−0.824686 + 0.565591i \(0.808648\pi\)
\(44\) 0 0
\(45\) −1.85250 + 1.25229i −0.276155 + 0.186681i
\(46\) 9.65665 1.42379
\(47\) 5.21295i 0.760386i 0.924907 + 0.380193i \(0.124142\pi\)
−0.924907 + 0.380193i \(0.875858\pi\)
\(48\) 14.6305i 2.11173i
\(49\) 6.76348 0.966212
\(50\) −12.6476 5.07983i −1.78864 0.718396i
\(51\) −3.64283 −0.510099
\(52\) 19.6064i 2.71892i
\(53\) 1.49020i 0.204694i 0.994749 + 0.102347i \(0.0326353\pi\)
−0.994749 + 0.102347i \(0.967365\pi\)
\(54\) −2.72592 −0.370951
\(55\) 0 0
\(56\) 4.54799 0.607751
\(57\) 1.63130i 0.216071i
\(58\) 2.87874i 0.377998i
\(59\) 7.97599 1.03839 0.519193 0.854657i \(-0.326233\pi\)
0.519193 + 0.854657i \(0.326233\pi\)
\(60\) −6.80074 10.0603i −0.877972 1.29877i
\(61\) 10.8638 1.39097 0.695484 0.718542i \(-0.255190\pi\)
0.695484 + 0.718542i \(0.255190\pi\)
\(62\) 16.6305i 2.11208i
\(63\) 0.486331i 0.0612720i
\(64\) −28.4694 −3.55868
\(65\) 4.52120 + 6.68815i 0.560785 + 0.829563i
\(66\) 0 0
\(67\) 0.432515i 0.0528401i −0.999651 0.0264201i \(-0.991589\pi\)
0.999651 0.0264201i \(-0.00841075\pi\)
\(68\) 19.7829i 2.39903i
\(69\) −3.54253 −0.426470
\(70\) −2.45586 + 1.66016i −0.293532 + 0.198427i
\(71\) 6.01324 0.713640 0.356820 0.934173i \(-0.383861\pi\)
0.356820 + 0.934173i \(0.383861\pi\)
\(72\) 9.35163i 1.10210i
\(73\) 1.16412i 0.136250i −0.997677 0.0681252i \(-0.978298\pi\)
0.997677 0.0681252i \(-0.0217017\pi\)
\(74\) 23.4186 2.72236
\(75\) 4.63975 + 1.86353i 0.535752 + 0.215182i
\(76\) 8.85898 1.01619
\(77\) 0 0
\(78\) 9.84148i 1.11433i
\(79\) −4.42494 −0.497845 −0.248922 0.968523i \(-0.580076\pi\)
−0.248922 + 0.968523i \(0.580076\pi\)
\(80\) 27.1031 18.3217i 3.03022 2.04843i
\(81\) 1.00000 0.111111
\(82\) 29.9386i 3.30617i
\(83\) 3.17731i 0.348755i 0.984679 + 0.174377i \(0.0557912\pi\)
−0.984679 + 0.174377i \(0.944209\pi\)
\(84\) −2.64109 −0.288166
\(85\) 4.56189 + 6.74836i 0.494807 + 0.731962i
\(86\) 20.2199 2.18037
\(87\) 1.05606i 0.113222i
\(88\) 0 0
\(89\) −1.38354 −0.146655 −0.0733274 0.997308i \(-0.523362\pi\)
−0.0733274 + 0.997308i \(0.523362\pi\)
\(90\) 3.41365 + 5.04977i 0.359830 + 0.532293i
\(91\) 1.75582 0.184060
\(92\) 19.2382i 2.00572i
\(93\) 6.10088i 0.632632i
\(94\) 14.2101 1.46566
\(95\) −3.02198 + 2.04286i −0.310049 + 0.209593i
\(96\) 21.1784 2.16151
\(97\) 1.39973i 0.142121i −0.997472 0.0710605i \(-0.977362\pi\)
0.997472 0.0710605i \(-0.0226383\pi\)
\(98\) 18.4367i 1.86239i
\(99\) 0 0
\(100\) −10.1201 + 25.1968i −1.01201 + 2.51968i
\(101\) 0.113225 0.0112663 0.00563315 0.999984i \(-0.498207\pi\)
0.00563315 + 0.999984i \(0.498207\pi\)
\(102\) 9.93007i 0.983223i
\(103\) 7.24830i 0.714197i −0.934067 0.357098i \(-0.883766\pi\)
0.934067 0.357098i \(-0.116234\pi\)
\(104\) −33.7625 −3.31069
\(105\) 0.900930 0.609029i 0.0879217 0.0594351i
\(106\) 4.06216 0.394551
\(107\) 8.65879i 0.837077i −0.908199 0.418539i \(-0.862542\pi\)
0.908199 0.418539i \(-0.137458\pi\)
\(108\) 5.43063i 0.522563i
\(109\) 4.41573 0.422951 0.211475 0.977383i \(-0.432173\pi\)
0.211475 + 0.977383i \(0.432173\pi\)
\(110\) 0 0
\(111\) −8.59108 −0.815429
\(112\) 7.11528i 0.672331i
\(113\) 18.3647i 1.72761i −0.503829 0.863803i \(-0.668076\pi\)
0.503829 0.863803i \(-0.331924\pi\)
\(114\) −4.44679 −0.416480
\(115\) 4.43628 + 6.56254i 0.413685 + 0.611960i
\(116\) −5.73509 −0.532490
\(117\) 3.61034i 0.333776i
\(118\) 21.7419i 2.00150i
\(119\) 1.77162 0.162405
\(120\) −17.3239 + 11.7110i −1.58145 + 1.06906i
\(121\) 0 0
\(122\) 29.6139i 2.68111i
\(123\) 10.9830i 0.990299i
\(124\) −33.1317 −2.97531
\(125\) −2.35813 10.9288i −0.210918 0.977504i
\(126\) 1.32570 0.118103
\(127\) 10.6069i 0.941211i 0.882344 + 0.470605i \(0.155964\pi\)
−0.882344 + 0.470605i \(0.844036\pi\)
\(128\) 35.2487i 3.11557i
\(129\) −7.41765 −0.653088
\(130\) 18.2314 12.3244i 1.59900 1.08092i
\(131\) −16.5042 −1.44198 −0.720989 0.692946i \(-0.756312\pi\)
−0.720989 + 0.692946i \(0.756312\pi\)
\(132\) 0 0
\(133\) 0.793351i 0.0687923i
\(134\) −1.17900 −0.101850
\(135\) −1.25229 1.85250i −0.107780 0.159438i
\(136\) −34.0664 −2.92117
\(137\) 6.08516i 0.519890i −0.965623 0.259945i \(-0.916296\pi\)
0.965623 0.259945i \(-0.0837045\pi\)
\(138\) 9.65665i 0.822028i
\(139\) −17.3522 −1.47179 −0.735897 0.677093i \(-0.763239\pi\)
−0.735897 + 0.677093i \(0.763239\pi\)
\(140\) 3.30741 + 4.89262i 0.279527 + 0.413502i
\(141\) −5.21295 −0.439009
\(142\) 16.3916i 1.37555i
\(143\) 0 0
\(144\) −14.6305 −1.21921
\(145\) 1.95636 1.32250i 0.162467 0.109828i
\(146\) −3.17331 −0.262625
\(147\) 6.76348i 0.557843i
\(148\) 46.6550i 3.83502i
\(149\) 19.8854 1.62907 0.814537 0.580112i \(-0.196991\pi\)
0.814537 + 0.580112i \(0.196991\pi\)
\(150\) 5.07983 12.6476i 0.414766 1.03267i
\(151\) 0.0635504 0.00517166 0.00258583 0.999997i \(-0.499177\pi\)
0.00258583 + 0.999997i \(0.499177\pi\)
\(152\) 15.2553i 1.23737i
\(153\) 3.64283i 0.294506i
\(154\) 0 0
\(155\) 11.3019 7.64009i 0.907790 0.613667i
\(156\) 19.6064 1.56977
\(157\) 0.974621i 0.0777832i 0.999243 + 0.0388916i \(0.0123827\pi\)
−0.999243 + 0.0388916i \(0.987617\pi\)
\(158\) 12.0620i 0.959604i
\(159\) −1.49020 −0.118180
\(160\) −26.5215 39.2329i −2.09671 3.10164i
\(161\) 1.72284 0.135779
\(162\) 2.72592i 0.214168i
\(163\) 17.7133i 1.38741i 0.720259 + 0.693706i \(0.244023\pi\)
−0.720259 + 0.693706i \(0.755977\pi\)
\(164\) 59.6444 4.65744
\(165\) 0 0
\(166\) 8.66108 0.672230
\(167\) 9.77201i 0.756181i 0.925769 + 0.378091i \(0.123419\pi\)
−0.925769 + 0.378091i \(0.876581\pi\)
\(168\) 4.54799i 0.350885i
\(169\) −0.0345228 −0.00265560
\(170\) 18.3955 12.4353i 1.41087 0.953748i
\(171\) 1.63130 0.124748
\(172\) 40.2826i 3.07152i
\(173\) 8.18166i 0.622040i 0.950403 + 0.311020i \(0.100671\pi\)
−0.950403 + 0.311020i \(0.899329\pi\)
\(174\) 2.87874 0.218237
\(175\) −2.25645 0.906292i −0.170572 0.0685092i
\(176\) 0 0
\(177\) 7.97599i 0.599512i
\(178\) 3.77141i 0.282679i
\(179\) −0.535958 −0.0400593 −0.0200297 0.999799i \(-0.506376\pi\)
−0.0200297 + 0.999799i \(0.506376\pi\)
\(180\) 10.0603 6.80074i 0.749848 0.506897i
\(181\) −5.09381 −0.378620 −0.189310 0.981917i \(-0.560625\pi\)
−0.189310 + 0.981917i \(0.560625\pi\)
\(182\) 4.78622i 0.354778i
\(183\) 10.8638i 0.803076i
\(184\) −33.1284 −2.44226
\(185\) 10.7585 + 15.9150i 0.790984 + 1.17009i
\(186\) 16.6305 1.21941
\(187\) 0 0
\(188\) 28.3096i 2.06469i
\(189\) −0.486331 −0.0353754
\(190\) 5.56867 + 8.23768i 0.403994 + 0.597624i
\(191\) 12.1508 0.879204 0.439602 0.898193i \(-0.355120\pi\)
0.439602 + 0.898193i \(0.355120\pi\)
\(192\) 28.4694i 2.05460i
\(193\) 9.45132i 0.680321i −0.940367 0.340161i \(-0.889519\pi\)
0.940367 0.340161i \(-0.110481\pi\)
\(194\) −3.81555 −0.273941
\(195\) −6.68815 + 4.52120i −0.478949 + 0.323770i
\(196\) −36.7300 −2.62357
\(197\) 7.89908i 0.562786i 0.959593 + 0.281393i \(0.0907965\pi\)
−0.959593 + 0.281393i \(0.909203\pi\)
\(198\) 0 0
\(199\) −2.60454 −0.184631 −0.0923155 0.995730i \(-0.529427\pi\)
−0.0923155 + 0.995730i \(0.529427\pi\)
\(200\) 43.3892 + 17.4270i 3.06808 + 1.23228i
\(201\) 0.432515 0.0305073
\(202\) 0.308642i 0.0217160i
\(203\) 0.513597i 0.0360474i
\(204\) 19.7829 1.38508
\(205\) −20.3459 + 13.7539i −1.42102 + 0.960612i
\(206\) −19.7583 −1.37663
\(207\) 3.54253i 0.246223i
\(208\) 52.8211i 3.66248i
\(209\) 0 0
\(210\) −1.66016 2.45586i −0.114562 0.169471i
\(211\) 10.3434 0.712070 0.356035 0.934473i \(-0.384128\pi\)
0.356035 + 0.934473i \(0.384128\pi\)
\(212\) 8.09271i 0.555810i
\(213\) 6.01324i 0.412020i
\(214\) −23.6032 −1.61348
\(215\) 9.28907 + 13.7412i 0.633509 + 0.937143i
\(216\) 9.35163 0.636298
\(217\) 2.96705i 0.201417i
\(218\) 12.0369i 0.815244i
\(219\) 1.16412 0.0786642
\(220\) 0 0
\(221\) −13.1519 −0.884689
\(222\) 23.4186i 1.57175i
\(223\) 14.3880i 0.963495i 0.876310 + 0.481747i \(0.159998\pi\)
−0.876310 + 0.481747i \(0.840002\pi\)
\(224\) −10.2997 −0.688177
\(225\) −1.86353 + 4.63975i −0.124235 + 0.309317i
\(226\) −50.0607 −3.32999
\(227\) 1.42444i 0.0945433i −0.998882 0.0472716i \(-0.984947\pi\)
0.998882 0.0472716i \(-0.0150526\pi\)
\(228\) 8.85898i 0.586700i
\(229\) 5.05918 0.334320 0.167160 0.985930i \(-0.446540\pi\)
0.167160 + 0.985930i \(0.446540\pi\)
\(230\) 17.8890 12.0929i 1.17956 0.797385i
\(231\) 0 0
\(232\) 9.87592i 0.648386i
\(233\) 20.9099i 1.36985i 0.728613 + 0.684925i \(0.240165\pi\)
−0.728613 + 0.684925i \(0.759835\pi\)
\(234\) −9.84148 −0.643358
\(235\) 6.52813 + 9.65699i 0.425848 + 0.629953i
\(236\) −43.3147 −2.81955
\(237\) 4.42494i 0.287431i
\(238\) 4.82930i 0.313037i
\(239\) −18.5389 −1.19918 −0.599590 0.800307i \(-0.704670\pi\)
−0.599590 + 0.800307i \(0.704670\pi\)
\(240\) 18.3217 + 27.1031i 1.18266 + 1.74950i
\(241\) 21.5816 1.39019 0.695095 0.718918i \(-0.255362\pi\)
0.695095 + 0.718918i \(0.255362\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) −58.9974 −3.77692
\(245\) 12.5294 8.46986i 0.800472 0.541119i
\(246\) −29.9386 −1.90882
\(247\) 5.88953i 0.374742i
\(248\) 57.0532i 3.62288i
\(249\) −3.17731 −0.201354
\(250\) −29.7911 + 6.42807i −1.88415 + 0.406547i
\(251\) 0.628046 0.0396419 0.0198209 0.999804i \(-0.493690\pi\)
0.0198209 + 0.999804i \(0.493690\pi\)
\(252\) 2.64109i 0.166373i
\(253\) 0 0
\(254\) 28.9136 1.81420
\(255\) −6.74836 + 4.56189i −0.422599 + 0.285677i
\(256\) 39.1461 2.44663
\(257\) 3.40943i 0.212674i −0.994330 0.106337i \(-0.966088\pi\)
0.994330 0.106337i \(-0.0339123\pi\)
\(258\) 20.2199i 1.25884i
\(259\) 4.17811 0.259615
\(260\) −24.5530 36.3209i −1.52271 2.25253i
\(261\) −1.05606 −0.0653687
\(262\) 44.9891i 2.77944i
\(263\) 14.4795i 0.892843i 0.894823 + 0.446422i \(0.147302\pi\)
−0.894823 + 0.446422i \(0.852698\pi\)
\(264\) 0 0
\(265\) 1.86616 + 2.76059i 0.114637 + 0.169582i
\(266\) 2.16261 0.132598
\(267\) 1.38354i 0.0846711i
\(268\) 2.34883i 0.143478i
\(269\) 29.8686 1.82112 0.910562 0.413373i \(-0.135650\pi\)
0.910562 + 0.413373i \(0.135650\pi\)
\(270\) −5.04977 + 3.41365i −0.307319 + 0.207748i
\(271\) 1.50128 0.0911961 0.0455981 0.998960i \(-0.485481\pi\)
0.0455981 + 0.998960i \(0.485481\pi\)
\(272\) 53.2966i 3.23158i
\(273\) 1.75582i 0.106267i
\(274\) −16.5876 −1.00210
\(275\) 0 0
\(276\) 19.2382 1.15800
\(277\) 6.32633i 0.380112i −0.981773 0.190056i \(-0.939133\pi\)
0.981773 0.190056i \(-0.0608670\pi\)
\(278\) 47.3007i 2.83691i
\(279\) −6.10088 −0.365250
\(280\) 8.42516 5.69541i 0.503500 0.340366i
\(281\) −13.1632 −0.785251 −0.392626 0.919698i \(-0.628433\pi\)
−0.392626 + 0.919698i \(0.628433\pi\)
\(282\) 14.2101i 0.846197i
\(283\) 8.68234i 0.516112i 0.966130 + 0.258056i \(0.0830819\pi\)
−0.966130 + 0.258056i \(0.916918\pi\)
\(284\) −32.6557 −1.93776
\(285\) −2.04286 3.02198i −0.121009 0.179007i
\(286\) 0 0
\(287\) 5.34135i 0.315290i
\(288\) 21.1784i 1.24795i
\(289\) 3.72976 0.219398
\(290\) −3.60503 5.33288i −0.211695 0.313157i
\(291\) 1.39973 0.0820536
\(292\) 6.32193i 0.369963i
\(293\) 19.7389i 1.15316i −0.817041 0.576580i \(-0.804387\pi\)
0.817041 0.576580i \(-0.195613\pi\)
\(294\) 18.4367 1.07525
\(295\) 14.7755 9.98827i 0.860265 0.581540i
\(296\) −80.3406 −4.66970
\(297\) 0 0
\(298\) 54.2059i 3.14007i
\(299\) −12.7897 −0.739648
\(300\) −25.1968 10.1201i −1.45474 0.584287i
\(301\) 3.60744 0.207929
\(302\) 0.173233i 0.00996845i
\(303\) 0.113225i 0.00650461i
\(304\) −23.8667 −1.36885
\(305\) 20.1252 13.6047i 1.15237 0.779001i
\(306\) −9.93007 −0.567664
\(307\) 12.9484i 0.739003i 0.929230 + 0.369501i \(0.120471\pi\)
−0.929230 + 0.369501i \(0.879529\pi\)
\(308\) 0 0
\(309\) 7.24830 0.412342
\(310\) −20.8263 30.8081i −1.18285 1.74978i
\(311\) −28.4988 −1.61602 −0.808009 0.589171i \(-0.799455\pi\)
−0.808009 + 0.589171i \(0.799455\pi\)
\(312\) 33.7625i 1.91143i
\(313\) 6.79055i 0.383825i 0.981412 + 0.191912i \(0.0614689\pi\)
−0.981412 + 0.191912i \(0.938531\pi\)
\(314\) 2.65674 0.149928
\(315\) 0.609029 + 0.900930i 0.0343149 + 0.0507616i
\(316\) 24.0302 1.35181
\(317\) 30.6235i 1.71999i 0.510306 + 0.859993i \(0.329532\pi\)
−0.510306 + 0.859993i \(0.670468\pi\)
\(318\) 4.06216i 0.227794i
\(319\) 0 0
\(320\) −52.7397 + 35.6520i −2.94824 + 1.99301i
\(321\) 8.65879 0.483287
\(322\) 4.69633i 0.261716i
\(323\) 5.94255i 0.330652i
\(324\) −5.43063 −0.301702
\(325\) 16.7510 + 6.72796i 0.929181 + 0.373200i
\(326\) 48.2850 2.67426
\(327\) 4.41573i 0.244191i
\(328\) 102.709i 5.67113i
\(329\) 2.53522 0.139771
\(330\) 0 0
\(331\) −34.9532 −1.92120 −0.960601 0.277932i \(-0.910351\pi\)
−0.960601 + 0.277932i \(0.910351\pi\)
\(332\) 17.2548i 0.946979i
\(333\) 8.59108i 0.470788i
\(334\) 26.6377 1.45755
\(335\) −0.541635 0.801235i −0.0295927 0.0437761i
\(336\) 7.11528 0.388170
\(337\) 5.81556i 0.316794i 0.987376 + 0.158397i \(0.0506325\pi\)
−0.987376 + 0.158397i \(0.949367\pi\)
\(338\) 0.0941064i 0.00511872i
\(339\) 18.3647 0.997434
\(340\) −24.7740 36.6479i −1.34356 1.98751i
\(341\) 0 0
\(342\) 4.44679i 0.240455i
\(343\) 6.69361i 0.361421i
\(344\) −69.3671 −3.74003
\(345\) −6.56254 + 4.43628i −0.353315 + 0.238841i
\(346\) 22.3026 1.19899
\(347\) 27.6122i 1.48230i −0.671340 0.741150i \(-0.734281\pi\)
0.671340 0.741150i \(-0.265719\pi\)
\(348\) 5.73509i 0.307433i
\(349\) 12.9167 0.691417 0.345708 0.938342i \(-0.387639\pi\)
0.345708 + 0.938342i \(0.387639\pi\)
\(350\) −2.47048 + 6.15091i −0.132053 + 0.328780i
\(351\) 3.61034 0.192705
\(352\) 0 0
\(353\) 10.6615i 0.567454i 0.958905 + 0.283727i \(0.0915710\pi\)
−0.958905 + 0.283727i \(0.908429\pi\)
\(354\) 21.7419 1.15557
\(355\) 11.1395 7.53033i 0.591225 0.399669i
\(356\) 7.51349 0.398214
\(357\) 1.77162i 0.0937643i
\(358\) 1.46098i 0.0772150i
\(359\) −12.9369 −0.682785 −0.341392 0.939921i \(-0.610899\pi\)
−0.341392 + 0.939921i \(0.610899\pi\)
\(360\) −11.7110 17.3239i −0.617223 0.913051i
\(361\) −16.3389 −0.859940
\(362\) 13.8853i 0.729795i
\(363\) 0 0
\(364\) −9.53521 −0.499781
\(365\) −1.45782 2.15654i −0.0763060 0.112879i
\(366\) 29.6139 1.54794
\(367\) 36.3258i 1.89619i 0.317987 + 0.948095i \(0.396993\pi\)
−0.317987 + 0.948095i \(0.603007\pi\)
\(368\) 51.8290i 2.70178i
\(369\) 10.9830 0.571750
\(370\) 43.3830 29.3269i 2.25537 1.52463i
\(371\) 0.724729 0.0376261
\(372\) 33.1317i 1.71780i
\(373\) 18.8902i 0.978099i −0.872256 0.489050i \(-0.837344\pi\)
0.872256 0.489050i \(-0.162656\pi\)
\(374\) 0 0
\(375\) 10.9288 2.35813i 0.564362 0.121773i
\(376\) −48.7495 −2.51407
\(377\) 3.81274i 0.196366i
\(378\) 1.32570i 0.0681866i
\(379\) −27.2095 −1.39766 −0.698830 0.715288i \(-0.746296\pi\)
−0.698830 + 0.715288i \(0.746296\pi\)
\(380\) 16.4113 11.0940i 0.841881 0.569112i
\(381\) −10.6069 −0.543408
\(382\) 33.1222i 1.69468i
\(383\) 10.9174i 0.557854i −0.960312 0.278927i \(-0.910021\pi\)
0.960312 0.278927i \(-0.0899788\pi\)
\(384\) −35.2487 −1.79878
\(385\) 0 0
\(386\) −25.7635 −1.31133
\(387\) 7.41765i 0.377060i
\(388\) 7.60142i 0.385904i
\(389\) −13.1738 −0.667938 −0.333969 0.942584i \(-0.608388\pi\)
−0.333969 + 0.942584i \(0.608388\pi\)
\(390\) 12.3244 + 18.2314i 0.624071 + 0.923181i
\(391\) −12.9048 −0.652626
\(392\) 63.2496i 3.19459i
\(393\) 16.5042i 0.832527i
\(394\) 21.5323 1.08478
\(395\) −8.19721 + 5.54132i −0.412446 + 0.278814i
\(396\) 0 0
\(397\) 35.1144i 1.76234i 0.472800 + 0.881170i \(0.343243\pi\)
−0.472800 + 0.881170i \(0.656757\pi\)
\(398\) 7.09977i 0.355879i
\(399\) −0.793351 −0.0397172
\(400\) 27.2644 67.8819i 1.36322 3.39410i
\(401\) 18.5113 0.924410 0.462205 0.886773i \(-0.347058\pi\)
0.462205 + 0.886773i \(0.347058\pi\)
\(402\) 1.17900i 0.0588032i
\(403\) 22.0262i 1.09721i
\(404\) −0.614884 −0.0305916
\(405\) 1.85250 1.25229i 0.0920516 0.0622269i
\(406\) −1.40002 −0.0694820
\(407\) 0 0
\(408\) 34.0664i 1.68654i
\(409\) 10.9713 0.542497 0.271249 0.962509i \(-0.412563\pi\)
0.271249 + 0.962509i \(0.412563\pi\)
\(410\) 37.4919 + 55.4614i 1.85159 + 2.73904i
\(411\) 6.08516 0.300159
\(412\) 39.3629i 1.93927i
\(413\) 3.87897i 0.190872i
\(414\) −9.65665 −0.474598
\(415\) 3.97891 + 5.88596i 0.195317 + 0.288931i
\(416\) 76.4610 3.74881
\(417\) 17.3522i 0.849741i
\(418\) 0 0
\(419\) 22.8017 1.11394 0.556969 0.830533i \(-0.311964\pi\)
0.556969 + 0.830533i \(0.311964\pi\)
\(420\) −4.89262 + 3.30741i −0.238735 + 0.161385i
\(421\) 9.62286 0.468989 0.234495 0.972117i \(-0.424656\pi\)
0.234495 + 0.972117i \(0.424656\pi\)
\(422\) 28.1953i 1.37253i
\(423\) 5.21295i 0.253462i
\(424\) −13.9358 −0.676781
\(425\) 16.9018 + 6.78852i 0.819859 + 0.329292i
\(426\) 16.3916 0.794176
\(427\) 5.28341i 0.255682i
\(428\) 47.0227i 2.27293i
\(429\) 0 0
\(430\) 37.4574 25.3212i 1.80636 1.22110i
\(431\) 3.56888 0.171907 0.0859535 0.996299i \(-0.472606\pi\)
0.0859535 + 0.996299i \(0.472606\pi\)
\(432\) 14.6305i 0.703911i
\(433\) 5.87835i 0.282496i −0.989974 0.141248i \(-0.954889\pi\)
0.989974 0.141248i \(-0.0451114\pi\)
\(434\) −8.08794 −0.388234
\(435\) 1.32250 + 1.95636i 0.0634090 + 0.0938003i
\(436\) −23.9802 −1.14844
\(437\) 5.77892i 0.276443i
\(438\) 3.17331i 0.151627i
\(439\) 2.88592 0.137737 0.0688686 0.997626i \(-0.478061\pi\)
0.0688686 + 0.997626i \(0.478061\pi\)
\(440\) 0 0
\(441\) −6.76348 −0.322071
\(442\) 35.8509i 1.70525i
\(443\) 27.9155i 1.32631i −0.748484 0.663153i \(-0.769218\pi\)
0.748484 0.663153i \(-0.230782\pi\)
\(444\) 46.6550 2.21415
\(445\) −2.56301 + 1.73259i −0.121498 + 0.0821328i
\(446\) 39.2206 1.85715
\(447\) 19.8854i 0.940546i
\(448\) 13.8456i 0.654142i
\(449\) −19.0508 −0.899065 −0.449532 0.893264i \(-0.648409\pi\)
−0.449532 + 0.893264i \(0.648409\pi\)
\(450\) 12.6476 + 5.07983i 0.596213 + 0.239465i
\(451\) 0 0
\(452\) 99.7320i 4.69100i
\(453\) 0.0635504i 0.00298586i
\(454\) −3.88290 −0.182234
\(455\) 3.25266 2.19880i 0.152487 0.103081i
\(456\) 15.2553 0.714395
\(457\) 21.2244i 0.992834i −0.868084 0.496417i \(-0.834649\pi\)
0.868084 0.496417i \(-0.165351\pi\)
\(458\) 13.7909i 0.644407i
\(459\) 3.64283 0.170033
\(460\) −24.0918 35.6388i −1.12329 1.66167i
\(461\) −20.7585 −0.966818 −0.483409 0.875395i \(-0.660602\pi\)
−0.483409 + 0.875395i \(0.660602\pi\)
\(462\) 0 0
\(463\) 13.4393i 0.624575i 0.949988 + 0.312288i \(0.101095\pi\)
−0.949988 + 0.312288i \(0.898905\pi\)
\(464\) 15.4508 0.717283
\(465\) 7.64009 + 11.3019i 0.354301 + 0.524113i
\(466\) 56.9986 2.64041
\(467\) 34.9512i 1.61735i −0.588257 0.808674i \(-0.700186\pi\)
0.588257 0.808674i \(-0.299814\pi\)
\(468\) 19.6064i 0.906307i
\(469\) −0.210346 −0.00971286
\(470\) 26.3242 17.7952i 1.21424 0.820829i
\(471\) −0.974621 −0.0449082
\(472\) 74.5885i 3.43322i
\(473\) 0 0
\(474\) −12.0620 −0.554027
\(475\) −3.03997 + 7.56881i −0.139483 + 0.347281i
\(476\) −9.62104 −0.440980
\(477\) 1.49020i 0.0682314i
\(478\) 50.5355i 2.31144i
\(479\) −19.9477 −0.911434 −0.455717 0.890125i \(-0.650617\pi\)
−0.455717 + 0.890125i \(0.650617\pi\)
\(480\) 39.2329 26.5215i 1.79073 1.21053i
\(481\) −31.0167 −1.41424
\(482\) 58.8296i 2.67961i
\(483\) 1.72284i 0.0783921i
\(484\) 0 0
\(485\) −1.75287 2.59300i −0.0795938 0.117742i
\(486\) 2.72592 0.123650
\(487\) 6.76135i 0.306386i −0.988196 0.153193i \(-0.951044\pi\)
0.988196 0.153193i \(-0.0489556\pi\)
\(488\) 101.594i 4.59896i
\(489\) −17.7133 −0.801022
\(490\) −23.0881 34.1540i −1.04302 1.54292i
\(491\) 3.36903 0.152042 0.0760210 0.997106i \(-0.475778\pi\)
0.0760210 + 0.997106i \(0.475778\pi\)
\(492\) 59.6444i 2.68898i
\(493\) 3.84706i 0.173263i
\(494\) −16.0544 −0.722321
\(495\) 0 0
\(496\) 89.2591 4.00785
\(497\) 2.92443i 0.131178i
\(498\) 8.66108i 0.388112i
\(499\) −17.5815 −0.787057 −0.393528 0.919312i \(-0.628746\pi\)
−0.393528 + 0.919312i \(0.628746\pi\)
\(500\) 12.8061 + 59.3505i 0.572708 + 2.65423i
\(501\) −9.77201 −0.436581
\(502\) 1.71200i 0.0764104i
\(503\) 33.1092i 1.47626i −0.674656 0.738132i \(-0.735708\pi\)
0.674656 0.738132i \(-0.264292\pi\)
\(504\) −4.54799 −0.202584
\(505\) 0.209750 0.141791i 0.00933373 0.00630961i
\(506\) 0 0
\(507\) 0.0345228i 0.00153321i
\(508\) 57.6022i 2.55569i
\(509\) 29.7124 1.31698 0.658489 0.752590i \(-0.271196\pi\)
0.658489 + 0.752590i \(0.271196\pi\)
\(510\) 12.4353 + 18.3955i 0.550647 + 0.814565i
\(511\) −0.566150 −0.0250450
\(512\) 36.2118i 1.60035i
\(513\) 1.63130i 0.0720235i
\(514\) −9.29382 −0.409933
\(515\) −9.07699 13.4275i −0.399980 0.591686i
\(516\) 40.2826 1.77334
\(517\) 0 0
\(518\) 11.3892i 0.500412i
\(519\) −8.18166 −0.359135
\(520\) −62.5452 + 42.2806i −2.74279 + 1.85412i
\(521\) 33.3727 1.46209 0.731043 0.682331i \(-0.239034\pi\)
0.731043 + 0.682331i \(0.239034\pi\)
\(522\) 2.87874i 0.125999i
\(523\) 1.69075i 0.0739313i −0.999317 0.0369657i \(-0.988231\pi\)
0.999317 0.0369657i \(-0.0117692\pi\)
\(524\) 89.6283 3.91543
\(525\) 0.906292 2.25645i 0.0395538 0.0984798i
\(526\) 39.4699 1.72097
\(527\) 22.2245i 0.968115i
\(528\) 0 0
\(529\) 10.4505 0.454369
\(530\) 7.52515 5.08701i 0.326872 0.220965i
\(531\) −7.97599 −0.346129
\(532\) 4.30840i 0.186793i
\(533\) 39.6521i 1.71752i
\(534\) −3.77141 −0.163205
\(535\) −10.8433 16.0404i −0.468799 0.693489i
\(536\) 4.04472 0.174705
\(537\) 0.535958i 0.0231283i
\(538\) 81.4195i 3.51024i
\(539\) 0 0
\(540\) 6.80074 + 10.0603i 0.292657 + 0.432925i
\(541\) 44.3013 1.90466 0.952330 0.305070i \(-0.0986799\pi\)
0.952330 + 0.305070i \(0.0986799\pi\)
\(542\) 4.09236i 0.175782i
\(543\) 5.09381i 0.218596i
\(544\) 77.1492 3.30775
\(545\) 8.18016 5.52979i 0.350399 0.236870i
\(546\) 4.78622 0.204831
\(547\) 37.4177i 1.59987i 0.600089 + 0.799933i \(0.295132\pi\)
−0.600089 + 0.799933i \(0.704868\pi\)
\(548\) 33.0463i 1.41167i
\(549\) −10.8638 −0.463656
\(550\) 0 0
\(551\) −1.72275 −0.0733918
\(552\) 33.1284i 1.41004i
\(553\) 2.15199i 0.0915118i
\(554\) −17.2451 −0.732673
\(555\) −15.9150 + 10.7585i −0.675554 + 0.456675i
\(556\) 94.2335 3.99639
\(557\) 6.04930i 0.256317i 0.991754 + 0.128159i \(0.0409067\pi\)
−0.991754 + 0.128159i \(0.959093\pi\)
\(558\) 16.6305i 0.704026i
\(559\) −26.7802 −1.13268
\(560\) −8.91041 13.1811i −0.376534 0.557002i
\(561\) 0 0
\(562\) 35.8818i 1.51358i
\(563\) 10.6819i 0.450188i −0.974337 0.225094i \(-0.927731\pi\)
0.974337 0.225094i \(-0.0722689\pi\)
\(564\) 28.3096 1.19205
\(565\) −22.9980 34.0207i −0.967533 1.43126i
\(566\) 23.6674 0.994814
\(567\) 0.486331i 0.0204240i
\(568\) 56.2336i 2.35951i
\(569\) 26.8071 1.12381 0.561906 0.827201i \(-0.310068\pi\)
0.561906 + 0.827201i \(0.310068\pi\)
\(570\) −8.23768 + 5.56867i −0.345038 + 0.233246i
\(571\) −9.73293 −0.407310 −0.203655 0.979043i \(-0.565282\pi\)
−0.203655 + 0.979043i \(0.565282\pi\)
\(572\) 0 0
\(573\) 12.1508i 0.507608i
\(574\) 14.5601 0.607727
\(575\) 16.4364 + 6.60160i 0.685447 + 0.275306i
\(576\) 28.4694 1.18623
\(577\) 1.27249i 0.0529746i 0.999649 + 0.0264873i \(0.00843216\pi\)
−0.999649 + 0.0264873i \(0.991568\pi\)
\(578\) 10.1670i 0.422893i
\(579\) 9.45132 0.392784
\(580\) −10.6243 + 7.18201i −0.441149 + 0.298217i
\(581\) 1.54522 0.0641066
\(582\) 3.81555i 0.158160i
\(583\) 0 0
\(584\) 10.8865 0.450485
\(585\) −4.52120 6.68815i −0.186928 0.276521i
\(586\) −53.8067 −2.22273
\(587\) 15.0272i 0.620238i 0.950698 + 0.310119i \(0.100369\pi\)
−0.950698 + 0.310119i \(0.899631\pi\)
\(588\) 36.7300i 1.51472i
\(589\) −9.95236 −0.410080
\(590\) −27.2272 40.2769i −1.12093 1.65817i
\(591\) −7.89908 −0.324925
\(592\) 125.692i 5.16591i
\(593\) 11.4115i 0.468615i −0.972163 0.234307i \(-0.924718\pi\)
0.972163 0.234307i \(-0.0752822\pi\)
\(594\) 0 0
\(595\) 3.28194 2.21859i 0.134546 0.0909534i
\(596\) −107.990 −4.42345
\(597\) 2.60454i 0.106597i
\(598\) 34.8637i 1.42568i
\(599\) 13.3076 0.543734 0.271867 0.962335i \(-0.412359\pi\)
0.271867 + 0.962335i \(0.412359\pi\)
\(600\) −17.4270 + 43.3892i −0.711455 + 1.77136i
\(601\) 35.6473 1.45409 0.727043 0.686592i \(-0.240894\pi\)
0.727043 + 0.686592i \(0.240894\pi\)
\(602\) 9.83358i 0.400787i
\(603\) 0.432515i 0.0176134i
\(604\) −0.345119 −0.0140427
\(605\) 0 0
\(606\) 0.308642 0.0125377
\(607\) 30.0322i 1.21897i −0.792798 0.609485i \(-0.791376\pi\)
0.792798 0.609485i \(-0.208624\pi\)
\(608\) 34.5482i 1.40111i
\(609\) 0.513597 0.0208120
\(610\) −37.0852 54.8597i −1.50154 2.22121i
\(611\) −18.8205 −0.761395
\(612\) 19.7829i 0.799676i
\(613\) 40.7593i 1.64625i 0.567859 + 0.823126i \(0.307772\pi\)
−0.567859 + 0.823126i \(0.692228\pi\)
\(614\) 35.2962 1.42444
\(615\) −13.7539 20.3459i −0.554609 0.820428i
\(616\) 0 0
\(617\) 38.2194i 1.53865i −0.638855 0.769327i \(-0.720592\pi\)
0.638855 0.769327i \(-0.279408\pi\)
\(618\) 19.7583i 0.794795i
\(619\) 13.2105 0.530976 0.265488 0.964114i \(-0.414467\pi\)
0.265488 + 0.964114i \(0.414467\pi\)
\(620\) −61.3765 + 41.4905i −2.46494 + 1.66630i
\(621\) 3.54253 0.142157
\(622\) 77.6853i 3.11490i
\(623\) 0.672858i 0.0269575i
\(624\) −52.8211 −2.11454
\(625\) −18.0545 17.2926i −0.722181 0.691704i
\(626\) 18.5105 0.739828
\(627\) 0 0
\(628\) 5.29281i 0.211206i
\(629\) −31.2959 −1.24785
\(630\) 2.45586 1.66016i 0.0978439 0.0661425i
\(631\) −41.5894 −1.65565 −0.827824 0.560987i \(-0.810422\pi\)
−0.827824 + 0.560987i \(0.810422\pi\)
\(632\) 41.3804i 1.64602i
\(633\) 10.3434i 0.411114i
\(634\) 83.4771 3.31530
\(635\) 13.2830 + 19.6493i 0.527118 + 0.779760i
\(636\) 8.09271 0.320897
\(637\) 24.4184i 0.967494i
\(638\) 0 0
\(639\) −6.01324 −0.237880
\(640\) 44.1416 + 65.2982i 1.74485 + 2.58114i
\(641\) −34.2525 −1.35289 −0.676447 0.736491i \(-0.736481\pi\)
−0.676447 + 0.736491i \(0.736481\pi\)
\(642\) 23.6032i 0.931543i
\(643\) 39.3183i 1.55056i 0.631616 + 0.775281i \(0.282392\pi\)
−0.631616 + 0.775281i \(0.717608\pi\)
\(644\) −9.35613 −0.368683
\(645\) −13.7412 + 9.28907i −0.541060 + 0.365757i
\(646\) −16.1989 −0.637337
\(647\) 14.6461i 0.575796i −0.957661 0.287898i \(-0.907044\pi\)
0.957661 0.287898i \(-0.0929564\pi\)
\(648\) 9.35163i 0.367367i
\(649\) 0 0
\(650\) 18.3399 45.6620i 0.719349 1.79101i
\(651\) 2.96705 0.116288
\(652\) 96.1943i 3.76726i
\(653\) 35.4313i 1.38653i −0.720682 0.693266i \(-0.756171\pi\)
0.720682 0.693266i \(-0.243829\pi\)
\(654\) 12.0369 0.470681
\(655\) −30.5741 + 20.6681i −1.19463 + 0.807569i
\(656\) −160.686 −6.27375
\(657\) 1.16412i 0.0454168i
\(658\) 6.91080i 0.269411i
\(659\) −39.2826 −1.53023 −0.765116 0.643893i \(-0.777318\pi\)
−0.765116 + 0.643893i \(0.777318\pi\)
\(660\) 0 0
\(661\) −29.7431 −1.15687 −0.578436 0.815728i \(-0.696337\pi\)
−0.578436 + 0.815728i \(0.696337\pi\)
\(662\) 95.2796i 3.70315i
\(663\) 13.1519i 0.510776i
\(664\) −29.7130 −1.15309
\(665\) 0.993507 + 1.46968i 0.0385266 + 0.0569919i
\(666\) −23.4186 −0.907452
\(667\) 3.74114i 0.144857i
\(668\) 53.0682i 2.05327i
\(669\) −14.3880 −0.556274
\(670\) −2.18410 + 1.47645i −0.0843792 + 0.0570404i
\(671\) 0 0
\(672\) 10.2997i 0.397319i
\(673\) 44.6403i 1.72076i 0.509655 + 0.860379i \(0.329773\pi\)
−0.509655 + 0.860379i \(0.670227\pi\)
\(674\) 15.8527 0.610625
\(675\) −4.63975 1.86353i −0.178584 0.0717272i
\(676\) 0.187481 0.00721080
\(677\) 25.8595i 0.993860i −0.867791 0.496930i \(-0.834461\pi\)
0.867791 0.496930i \(-0.165539\pi\)
\(678\) 50.0607i 1.92257i
\(679\) −0.680732 −0.0261241
\(680\) −63.1081 + 42.6611i −2.42009 + 1.63598i
\(681\) 1.42444 0.0545846
\(682\) 0 0
\(683\) 36.8419i 1.40972i −0.709348 0.704858i \(-0.751011\pi\)
0.709348 0.704858i \(-0.248989\pi\)
\(684\) −8.85898 −0.338732
\(685\) −7.62040 11.2728i −0.291160 0.430710i
\(686\) −18.2462 −0.696645
\(687\) 5.05918i 0.193020i
\(688\) 108.524i 4.13744i
\(689\) −5.38011 −0.204966
\(690\) 12.0929 + 17.8890i 0.460371 + 0.681021i
\(691\) −39.6288 −1.50755 −0.753775 0.657133i \(-0.771769\pi\)
−0.753775 + 0.657133i \(0.771769\pi\)
\(692\) 44.4316i 1.68904i
\(693\) 0 0
\(694\) −75.2686 −2.85716
\(695\) −32.1450 + 21.7300i −1.21933 + 0.824267i
\(696\) −9.87592 −0.374346
\(697\) 40.0091i 1.51545i
\(698\) 35.2100i 1.33272i
\(699\) −20.9099 −0.790884
\(700\) 12.2540 + 4.92174i 0.463157 + 0.186024i
\(701\) −21.7728 −0.822347 −0.411174 0.911557i \(-0.634881\pi\)
−0.411174 + 0.911557i \(0.634881\pi\)
\(702\) 9.84148i 0.371443i
\(703\) 14.0146i 0.528571i
\(704\) 0 0
\(705\) −9.65699 + 6.52813i −0.363703 + 0.245864i
\(706\) 29.0624 1.09378
\(707\) 0.0550649i 0.00207093i
\(708\) 43.3147i 1.62787i
\(709\) 37.4566 1.40671 0.703356 0.710838i \(-0.251684\pi\)
0.703356 + 0.710838i \(0.251684\pi\)
\(710\) −20.5271 30.3655i −0.770367 1.13960i
\(711\) 4.42494 0.165948
\(712\) 12.9383i 0.484885i
\(713\) 21.6126i 0.809397i
\(714\) 4.82930 0.180732
\(715\) 0 0
\(716\) 2.91059 0.108774
\(717\) 18.5389i 0.692347i
\(718\) 35.2650i 1.31608i
\(719\) −13.0332 −0.486057 −0.243029 0.970019i \(-0.578141\pi\)
−0.243029 + 0.970019i \(0.578141\pi\)
\(720\) −27.1031 + 18.3217i −1.01007 + 0.682809i
\(721\) −3.52508 −0.131281
\(722\) 44.5384i 1.65755i
\(723\) 21.5816i 0.802627i
\(724\) 27.6626 1.02807
\(725\) 1.96800 4.89987i 0.0730898 0.181977i
\(726\) 0 0
\(727\) 50.8515i 1.88598i −0.332824 0.942989i \(-0.608002\pi\)
0.332824 0.942989i \(-0.391998\pi\)
\(728\) 16.4198i 0.608557i
\(729\) −1.00000 −0.0370370
\(730\) −5.87856 + 3.97391i −0.217575 + 0.147081i
\(731\) −27.0213 −0.999418
\(732\) 58.9974i 2.18061i
\(733\) 14.7956i 0.546488i 0.961945 + 0.273244i \(0.0880966\pi\)
−0.961945 + 0.273244i \(0.911903\pi\)
\(734\) 99.0211 3.65494
\(735\) 8.46986 + 12.5294i 0.312415 + 0.462153i
\(736\) 75.0249 2.76546
\(737\) 0 0
\(738\) 29.9386i 1.10206i
\(739\) −3.10843 −0.114345 −0.0571727 0.998364i \(-0.518209\pi\)
−0.0571727 + 0.998364i \(0.518209\pi\)
\(740\) −58.4257 86.4285i −2.14777 3.17718i
\(741\) 5.88953 0.216357
\(742\) 1.97555i 0.0725249i
\(743\) 5.87175i 0.215414i 0.994183 + 0.107707i \(0.0343508\pi\)
−0.994183 + 0.107707i \(0.965649\pi\)
\(744\) −57.0532 −2.09167
\(745\) 36.8377 24.9023i 1.34963 0.912350i
\(746\) −51.4932 −1.88530
\(747\) 3.17731i 0.116252i
\(748\) 0 0
\(749\) −4.21104 −0.153868
\(750\) −6.42807 29.7911i −0.234720 1.08782i
\(751\) 17.5613 0.640821 0.320411 0.947279i \(-0.396179\pi\)
0.320411 + 0.947279i \(0.396179\pi\)
\(752\) 76.2681i 2.78121i
\(753\) 0.628046i 0.0228873i
\(754\) 10.3932 0.378499
\(755\) 0.117727 0.0795836i 0.00428453 0.00289635i
\(756\) 2.64109 0.0960554
\(757\) 11.9599i 0.434689i −0.976095 0.217344i \(-0.930261\pi\)
0.976095 0.217344i \(-0.0697395\pi\)
\(758\) 74.1710i 2.69401i
\(759\) 0 0
\(760\) −19.1041 28.2605i −0.692978 1.02511i
\(761\) 15.8337 0.573970 0.286985 0.957935i \(-0.407347\pi\)
0.286985 + 0.957935i \(0.407347\pi\)
\(762\) 28.9136i 1.04743i
\(763\) 2.14751i 0.0777451i
\(764\) −65.9867 −2.38732
\(765\) −4.56189 6.74836i −0.164936 0.243987i
\(766\) −29.7600 −1.07527
\(767\) 28.7960i 1.03976i
\(768\) 39.1461i 1.41256i
\(769\) 36.6876 1.32299 0.661494 0.749950i \(-0.269923\pi\)
0.661494 + 0.749950i \(0.269923\pi\)
\(770\) 0 0
\(771\) 3.40943 0.122787
\(772\) 51.3267i 1.84729i
\(773\) 1.66936i 0.0600427i 0.999549 + 0.0300214i \(0.00955753\pi\)
−0.999549 + 0.0300214i \(0.990442\pi\)
\(774\) −20.2199 −0.726790
\(775\) 11.3692 28.3066i 0.408393 1.01680i
\(776\) 13.0898 0.469895
\(777\) 4.17811i 0.149889i
\(778\) 35.9107i 1.28746i
\(779\) 17.9165 0.641924
\(780\) 36.3209 24.5530i 1.30050 0.879137i
\(781\) 0 0
\(782\) 35.1776i 1.25795i
\(783\) 1.05606i 0.0377406i
\(784\) 98.9533 3.53405
\(785\) 1.22051 + 1.80549i 0.0435619 + 0.0644406i
\(786\) −44.9891 −1.60471
\(787\) 34.7442i 1.23850i 0.785195 + 0.619249i \(0.212563\pi\)
−0.785195 + 0.619249i \(0.787437\pi\)
\(788\) 42.8970i 1.52814i
\(789\) −14.4795 −0.515483
\(790\) 15.1052 + 22.3449i 0.537418 + 0.794997i
\(791\) −8.93133 −0.317562
\(792\) 0 0
\(793\) 39.2220i 1.39281i
\(794\) 95.7189 3.39694
\(795\) −2.76059 + 1.86616i −0.0979081 + 0.0661859i
\(796\) 14.1443 0.501332
\(797\) 30.3361i 1.07456i −0.843404 0.537280i \(-0.819452\pi\)
0.843404 0.537280i \(-0.180548\pi\)
\(798\) 2.16261i 0.0765556i
\(799\) −18.9899 −0.671814
\(800\) −98.2622 39.4665i −3.47409 1.39535i
\(801\) 1.38354 0.0488849
\(802\) 50.4603i 1.78181i
\(803\) 0 0
\(804\) −2.34883 −0.0828369
\(805\) 3.19157 2.15750i 0.112488 0.0760420i
\(806\) 60.0417 2.11488
\(807\) 29.8686i 1.05143i
\(808\) 1.05884i 0.0372498i
\(809\) −5.49659 −0.193250 −0.0966250 0.995321i \(-0.530805\pi\)
−0.0966250 + 0.995321i \(0.530805\pi\)
\(810\) −3.41365 5.04977i −0.119943 0.177431i
\(811\) −16.4998 −0.579385 −0.289692 0.957120i \(-0.593553\pi\)
−0.289692 + 0.957120i \(0.593553\pi\)
\(812\) 2.78916i 0.0978802i
\(813\) 1.50128i 0.0526521i
\(814\) 0 0
\(815\) 22.1822 + 32.8139i 0.777009 + 1.14942i
\(816\) −53.2966 −1.86575
\(817\) 12.1004i 0.423339i
\(818\) 29.9069i 1.04567i
\(819\) −1.75582 −0.0613533
\(820\) 110.491 74.6922i 3.85853 2.60837i
\(821\) 47.4838 1.65720 0.828598 0.559844i \(-0.189139\pi\)
0.828598 + 0.559844i \(0.189139\pi\)
\(822\) 16.5876i 0.578561i
\(823\) 27.5803i 0.961389i −0.876888 0.480695i \(-0.840385\pi\)
0.876888 0.480695i \(-0.159615\pi\)
\(824\) 67.7835 2.36135
\(825\) 0 0
\(826\) −10.5738 −0.367908
\(827\) 28.8948i 1.00477i −0.864644 0.502385i \(-0.832456\pi\)
0.864644 0.502385i \(-0.167544\pi\)
\(828\) 19.2382i 0.668573i
\(829\) 3.29357 0.114390 0.0571951 0.998363i \(-0.481784\pi\)
0.0571951 + 0.998363i \(0.481784\pi\)
\(830\) 16.0447 10.8462i 0.556918 0.376477i
\(831\) 6.32633 0.219458
\(832\) 102.784i 3.56340i
\(833\) 24.6382i 0.853664i
\(834\) −47.3007 −1.63789
\(835\) 12.2374 + 18.1027i 0.423493 + 0.626469i
\(836\) 0 0
\(837\) 6.10088i 0.210877i
\(838\) 62.1557i 2.14713i
\(839\) 6.47781 0.223639 0.111819 0.993729i \(-0.464332\pi\)
0.111819 + 0.993729i \(0.464332\pi\)
\(840\) 5.69541 + 8.42516i 0.196510 + 0.290696i
\(841\) −27.8847 −0.961542
\(842\) 26.2311i 0.903985i
\(843\) 13.1632i 0.453365i
\(844\) −56.1713 −1.93349
\(845\) −0.0639536 + 0.0432327i −0.00220007 + 0.00148725i
\(846\) −14.2101 −0.488552
\(847\) 0 0
\(848\) 21.8024i 0.748696i
\(849\) −8.68234 −0.297977
\(850\) 18.5050 46.0730i 0.634715 1.58029i
\(851\) −30.4342 −1.04327
\(852\) 32.6557i 1.11877i
\(853\) 44.1409i 1.51136i −0.654943 0.755678i \(-0.727307\pi\)
0.654943 0.755678i \(-0.272693\pi\)
\(854\) −14.4021 −0.492831
\(855\) 3.02198 2.04286i 0.103350 0.0698644i
\(856\) 80.9739 2.76763
\(857\) 16.2984i 0.556744i −0.960473 0.278372i \(-0.910205\pi\)
0.960473 0.278372i \(-0.0897948\pi\)
\(858\) 0 0
\(859\) 41.9250 1.43046 0.715231 0.698888i \(-0.246321\pi\)
0.715231 + 0.698888i \(0.246321\pi\)
\(860\) −50.4455 74.6235i −1.72018 2.54464i
\(861\) −5.34135 −0.182033
\(862\) 9.72848i 0.331353i
\(863\) 27.1455i 0.924044i −0.886869 0.462022i \(-0.847124\pi\)
0.886869 0.462022i \(-0.152876\pi\)
\(864\) −21.1784 −0.720502
\(865\) 10.2458 + 15.1565i 0.348369 + 0.515338i
\(866\) −16.0239 −0.544515
\(867\) 3.72976i 0.126669i
\(868\) 16.1130i 0.546910i
\(869\) 0 0
\(870\) 5.33288 3.60503i 0.180802 0.122222i
\(871\) 1.56152 0.0529102
\(872\) 41.2943i 1.39840i
\(873\) 1.39973i 0.0473737i
\(874\) −15.7529 −0.532849
\(875\) −5.31503 + 1.14683i −0.179681 + 0.0387700i
\(876\) −6.32193 −0.213598
\(877\) 24.6151i 0.831193i −0.909549 0.415597i \(-0.863573\pi\)
0.909549 0.415597i \(-0.136427\pi\)
\(878\) 7.86677i 0.265491i
\(879\) 19.7389 0.665777
\(880\) 0 0
\(881\) −27.3598 −0.921777 −0.460888 0.887458i \(-0.652469\pi\)
−0.460888 + 0.887458i \(0.652469\pi\)
\(882\) 18.4367i 0.620796i
\(883\) 59.1173i 1.98946i 0.102546 + 0.994728i \(0.467301\pi\)
−0.102546 + 0.994728i \(0.532699\pi\)
\(884\) 71.4229 2.40221
\(885\) 9.98827 + 14.7755i 0.335752 + 0.496674i
\(886\) −76.0954 −2.55648
\(887\) 6.13583i 0.206021i −0.994680 0.103010i \(-0.967152\pi\)
0.994680 0.103010i \(-0.0328475\pi\)
\(888\) 80.3406i 2.69605i
\(889\) 5.15847 0.173010
\(890\) 4.72291 + 6.98655i 0.158312 + 0.234190i
\(891\) 0 0
\(892\) 78.1362i 2.61619i
\(893\) 8.50387i 0.284571i
\(894\) 54.2059 1.81292
\(895\) −0.992862 + 0.671175i −0.0331877 + 0.0224349i
\(896\) 17.1425 0.572692
\(897\) 12.7897i 0.427036i
\(898\) 51.9310i 1.73296i
\(899\) 6.44292 0.214883
\(900\) 10.1201 25.1968i 0.337338 0.839893i
\(901\) −5.42854 −0.180851
\(902\) 0 0
\(903\) 3.60744i 0.120048i
\(904\) 171.740 5.71199
\(905\) −9.43629 + 6.37894i −0.313673 + 0.212043i
\(906\) 0.173233 0.00575529
\(907\) 0.00196868i 6.53690e-5i −1.00000 3.26845e-5i \(-0.999990\pi\)
1.00000 3.26845e-5i \(-1.04038e-5\pi\)
\(908\) 7.73560i 0.256715i
\(909\) −0.113225 −0.00375544
\(910\) −5.99375 8.86648i −0.198691 0.293921i
\(911\) −41.9211 −1.38891 −0.694454 0.719537i \(-0.744354\pi\)
−0.694454 + 0.719537i \(0.744354\pi\)
\(912\) 23.8667i 0.790307i
\(913\) 0 0
\(914\) −57.8559 −1.91370
\(915\) 13.6047 + 20.1252i 0.449756 + 0.665319i
\(916\) −27.4745 −0.907784
\(917\) 8.02651i 0.265059i
\(918\) 9.93007i 0.327741i
\(919\) −17.4839 −0.576740 −0.288370 0.957519i \(-0.593113\pi\)
−0.288370 + 0.957519i \(0.593113\pi\)
\(920\) −61.3705 + 41.4865i −2.02332 + 1.36777i
\(921\) −12.9484 −0.426663
\(922\) 56.5859i 1.86356i
\(923\) 21.7098i 0.714587i
\(924\) 0 0
\(925\) 39.8605 + 16.0097i 1.31060 + 0.526396i
\(926\) 36.6343 1.20388
\(927\) 7.24830i 0.238066i
\(928\) 22.3657i 0.734190i
\(929\) −44.0582 −1.44550 −0.722752 0.691108i \(-0.757123\pi\)
−0.722752 + 0.691108i \(0.757123\pi\)
\(930\) 30.8081 20.8263i 1.01024 0.682920i
\(931\) −11.0333 −0.361600
\(932\) 113.554i 3.71958i
\(933\) 28.4988i 0.933008i
\(934\) −95.2741 −3.11746
\(935\) 0 0
\(936\) 33.7625 1.10356
\(937\) 14.0261i 0.458212i −0.973401 0.229106i \(-0.926420\pi\)
0.973401 0.229106i \(-0.0735803\pi\)
\(938\) 0.573385i 0.0187217i
\(939\) −6.79055 −0.221601
\(940\) −35.4519 52.4436i −1.15631 1.71052i
\(941\) −0.891403 −0.0290589 −0.0145295 0.999894i \(-0.504625\pi\)
−0.0145295 + 0.999894i \(0.504625\pi\)
\(942\) 2.65674i 0.0865612i
\(943\) 38.9074i 1.26700i
\(944\) 116.693 3.79803
\(945\) −0.900930 + 0.609029i −0.0293072 + 0.0198117i
\(946\) 0 0
\(947\) 5.19472i 0.168806i 0.996432 + 0.0844029i \(0.0268983\pi\)
−0.996432 + 0.0844029i \(0.973102\pi\)
\(948\) 24.0302i 0.780466i
\(949\) 4.20288 0.136431
\(950\) 20.6320 + 8.28671i 0.669389 + 0.268856i
\(951\) −30.6235 −0.993035
\(952\) 16.5676i 0.536958i
\(953\) 22.0876i 0.715488i −0.933820 0.357744i \(-0.883546\pi\)
0.933820 0.357744i \(-0.116454\pi\)
\(954\) −4.06216 −0.131517
\(955\) 22.5094 15.2164i 0.728389 0.492391i
\(956\) 100.678 3.25615
\(957\) 0 0
\(958\) 54.3758i 1.75680i
\(959\) −2.95940 −0.0955641
\(960\) −35.6520 52.7397i −1.15066 1.70217i
\(961\) 6.22078 0.200670
\(962\) 84.5490i 2.72597i
\(963\) 8.65879i 0.279026i
\(964\) −117.202 −3.77481
\(965\) −11.8358 17.5086i −0.381008 0.563622i
\(966\) 4.69633 0.151102
\(967\) 3.71338i 0.119414i −0.998216 0.0597072i \(-0.980983\pi\)
0.998216 0.0597072i \(-0.0190167\pi\)
\(968\) 0 0
\(969\) 5.94255 0.190902
\(970\) −7.06832 + 4.77818i −0.226950 + 0.153418i
\(971\) 7.64022 0.245186 0.122593 0.992457i \(-0.460879\pi\)
0.122593 + 0.992457i \(0.460879\pi\)
\(972\) 5.43063i 0.174188i
\(973\) 8.43892i 0.270539i
\(974\) −18.4309 −0.590563
\(975\) −6.72796 + 16.7510i −0.215467 + 0.536463i
\(976\) 158.943 5.08765
\(977\) 29.0026i 0.927876i −0.885868 0.463938i \(-0.846436\pi\)
0.885868 0.463938i \(-0.153564\pi\)
\(978\) 48.2850i 1.54398i
\(979\) 0 0
\(980\) −68.0424 + 45.9967i −2.17353 + 1.46931i
\(981\) −4.41573 −0.140984
\(982\) 9.18369i 0.293063i
\(983\) 9.02079i 0.287718i −0.989598 0.143859i \(-0.954049\pi\)
0.989598 0.143859i \(-0.0459513\pi\)
\(984\) 102.709 3.27423
\(985\) 9.89196 + 14.6331i 0.315184 + 0.466248i
\(986\) 10.4868 0.333967
\(987\) 2.53522i 0.0806969i
\(988\) 31.9839i 1.01754i
\(989\) −26.2772 −0.835568
\(990\) 0 0
\(991\) −14.7651 −0.469028 −0.234514 0.972113i \(-0.575350\pi\)
−0.234514 + 0.972113i \(0.575350\pi\)
\(992\) 129.207i 4.10232i
\(993\) 34.9532i 1.10921i
\(994\) −7.97175 −0.252848
\(995\) −4.82492 + 3.26165i −0.152960 + 0.103401i
\(996\) 17.2548 0.546739
\(997\) 44.9321i 1.42301i −0.702679 0.711507i \(-0.748013\pi\)
0.702679 0.711507i \(-0.251987\pi\)
\(998\) 47.9258i 1.51706i
\(999\) 8.59108 0.271810
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.k.364.1 24
5.2 odd 4 9075.2.a.ea.1.12 12
5.3 odd 4 9075.2.a.dx.1.1 12
5.4 even 2 inner 1815.2.c.k.364.24 24
11.2 odd 10 165.2.s.a.4.12 yes 48
11.6 odd 10 165.2.s.a.124.1 yes 48
11.10 odd 2 1815.2.c.j.364.24 24
33.2 even 10 495.2.ba.c.334.1 48
33.17 even 10 495.2.ba.c.289.12 48
55.2 even 20 825.2.n.p.301.6 24
55.13 even 20 825.2.n.o.301.1 24
55.17 even 20 825.2.n.p.751.6 24
55.24 odd 10 165.2.s.a.4.1 48
55.28 even 20 825.2.n.o.751.1 24
55.32 even 4 9075.2.a.dy.1.1 12
55.39 odd 10 165.2.s.a.124.12 yes 48
55.43 even 4 9075.2.a.dz.1.12 12
55.54 odd 2 1815.2.c.j.364.1 24
165.134 even 10 495.2.ba.c.334.12 48
165.149 even 10 495.2.ba.c.289.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.s.a.4.1 48 55.24 odd 10
165.2.s.a.4.12 yes 48 11.2 odd 10
165.2.s.a.124.1 yes 48 11.6 odd 10
165.2.s.a.124.12 yes 48 55.39 odd 10
495.2.ba.c.289.1 48 165.149 even 10
495.2.ba.c.289.12 48 33.17 even 10
495.2.ba.c.334.1 48 33.2 even 10
495.2.ba.c.334.12 48 165.134 even 10
825.2.n.o.301.1 24 55.13 even 20
825.2.n.o.751.1 24 55.28 even 20
825.2.n.p.301.6 24 55.2 even 20
825.2.n.p.751.6 24 55.17 even 20
1815.2.c.j.364.1 24 55.54 odd 2
1815.2.c.j.364.24 24 11.10 odd 2
1815.2.c.k.364.1 24 1.1 even 1 trivial
1815.2.c.k.364.24 24 5.4 even 2 inner
9075.2.a.dx.1.1 12 5.3 odd 4
9075.2.a.dy.1.1 12 55.32 even 4
9075.2.a.dz.1.12 12 55.43 even 4
9075.2.a.ea.1.12 12 5.2 odd 4